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1 GAS ADSORPTION, DIFFUSION, AND EX CHANGE IN ONE-DIMENSIONAL NANOTUBE SYSTEMS BY HYPE RPOLARIZED XE-129 NMR By CHI-YUAN CHENG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008
2 2008 Chi-Yuan Cheng
3 To my family
4 ACKNOWLEDGMENTS Throughout the five years of my graduate career at the Univer sity of Florida, there have been many people who helped me. Fi rst of all, I would like to appreciate my research advisor: Prof. Russ Bowers. It is a great privilege for me to study physical chemistry and NMR with him. Russ not only gives me the opportunities to share the fun of science, but also reminds me the enjoyable parts of research whenever I encount er the frustrations. His knowledge, hard working and creativity in new ideas will always be an insp iration to me. I would also like to appreciate my supervisory committee, Prof. Angerhofer, Prof Brucat, Prof. Mareci, and Prof. Omenetto for their advice and the inspiration which I dr ew from their knowledge and experience. There are numerous people w ho contributed to the success of this dissertation. In particular, I would like to express my sincer e gratitude to Prof. Cynthia Jameson at the University of Illinois at Chicago who firs t suggested us to try the hyperpolarized 129Xe NMR experiments on AV dipeptide nanotubes. She gave us valuable suggesti ons on our preliminary results during her visit to our lab in 2005. She also encouraged me to participate in the conferences and to discuss the results with peop le. I benefit a lot in learning from her. I am grateful to Prof. Sergey Vasenkov for his insi ghtful consults on the single-file diffusion. I gratefully acknowledge Prof. George Christou a nd Dr. Theocharis Stamatatos for their kindly providing the molecular wheel samples. In a ddition, I appreciate Steve Miles in chemistry electronic shop for his huge assistance on the temperature controller and TTL device. Steve always does perfect works on the troubleshooting of our spectrometer. I thank Joe Shalosky and Todd Prox in chemistry machine shop for teaching me the basic skills of the machining. I also appreciate Marc Link in physics machine shop for generously repairing the broken sample holders as my requests. I am grateful to Joe Ca ruso in chemistry glass shop who constructed the optical pumping cell and numerous elegant glass components for our experiments. I am indebted
5 to Greg Labbe and John Graham in physics cr yogenic service for suppl ying us liquid nitrogen and helium, and always give me a hand promptly when I need help in the lab. I would also like to thank Yuying and her husband Liwen for their a ssistance in collecting the SEM images on the molecular wheels. I am grateful for collaborations, suggestions discussions, and contributions from the previous and current group members in the Bowers group: Bhavin Adhyaru, Joshua Caldwell, Jessica Pfeilsticker; Caroline Po inter-Keenan, Yuying Wei and Shea McKeon. Finally, I would like to apprec iate my grandparents, my pa rents and my wife for their understanding, support, and encour agement in my choosing the career of physical chemistry and NMR.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ................................................................................................................ ...........9LIST OF FIGURES ............................................................................................................... ........10LIST OF ABBREVIATIONS ........................................................................................................1 4ABSTRACT ...................................................................................................................... .............161. INTRODUCTION ............................................................................................................... ...182. BACKGROUND ................................................................................................................. ...212.1 Introduction ............................................................................................................ .........212.2 Introduction to NMR ..................................................................................................... .212.2.1 Spin Polarization ..................................................................................................222.2.2 Chemical Shift Anisotropy ...................................................................................252.2.3 Exchange NMR ....................................................................................................302.2.4 2D Exchange NMR Spectroscopy ........................................................................332.3 Introduction to 129Xe NMR .............................................................................................362.3.1 Physical Properties of Xe .....................................................................................362.3.2 One-dimensional van der Waals Guest/Host Systems in Xe NMR .....................382.3.3 Xe Chemical Shift ................................................................................................392.4 Introduction to Hyperpolarized 129Xe NMR ...................................................................402.4.1 Improvement of NMR Sensitivity ........................................................................412.4.2 Optical Pumping and Spin Exchange ...................................................................432.4.3 Continuous-flow Hyperpolarized 129Xe NMR .....................................................482.4.4 Development of Continuous-flow Hyperpolarized Xe Polarizer .........................493. INVESTIGATIONS OF THERMODYNAM IC PROPERTIES IN DIPEPTIDE NANOTUBES BY HYPERPOLARIZED XE-129 NMR .....................................................553.1 Introduction ............................................................................................................ .........553.1.1 Determination of Adsorption En thalpy from Xe Chemical Shift .........................563.1.2 Xe Anisotropic NMR Line-s hapes in 1D Nanotube Systems ..............................583.1.3 Dipeptide Nanotubes ............................................................................................603.2 Experimental ............................................................................................................ .......623.2.1 13C T1 Relaxation Experiment ..............................................................................623.2.2 Hyperpolarized 129Xe NMR Experiments ............................................................633.2.3 Scanning Electron Microscopy .............................................................................643.3 Results and Discussions .................................................................................................. .653.3.1 13C T1 Relaxation Measurements in AV ..............................................................653.3.2 Hyperpolarized 129Xe NMR Spectra in AV ..........................................................673.3.3 129Xe T2 Relaxation Measurements in AV ...........................................................68
7 3.3.4 Determination of Xe Occupancy in AV ...............................................................703.3.5 Isosteric Adsorption Enthalpy of Xe in AV .........................................................713.4 Conclusions ............................................................................................................. ........744. OBSERVATION OF SINGLE-FILE DIFFU SION IN DIPEPTIDE NANOTUBES BY HYPERPOLARIZED TRACER EXCHANGE XE-129 NMR .............................................764.1 Introduction ............................................................................................................ .........764.1.1 One-Dimensional Diffusion: Fickia n Diffusion and Single-file Diffusion ..........774.1.2 Tracer Exchange ...................................................................................................804.2 Experimental ............................................................................................................ .......834.3 Magnetization Exchange Model for Saturation-recovery in 1D Channel ......................864.4 Results and Discussions ................................................................................................. .904.5 Conclusions ............................................................................................................. ........945. INVESTIGATIONS OF CHANNEL DIAM ETER EFFECT ON GAS DIFFUSION IN GA WHEEL NANOTUBES BY HYPE RPOLARIZED XE-129 NMR ................................965.1 Introduction ............................................................................................................ .........965.2 Experimental ............................................................................................................ .......985.2.1 Hyperpolarized 129Xe NMR Experiment ..............................................................995.2.2 Scanning Electron Microscopy ...........................................................................1005.3 Results and Discussions ................................................................................................1 015.3.1 Temperature Dependent Study in Ga10 and Ga18 Nanotubes .............................1015.3.2 Temperature Dependent Study in Mn84 Nanotubes ............................................1045.3.3 Pressure Dependent Study in Ga10 and Ga18 Nanotubes ....................................1055.3.4 Saturation-recovery Hyperpolarized 129Xe NMR in Ga10 and Ga18 Nanotubes .1075.4 Conclusions ............................................................................................................. ......1126. DIRECT OBSERVATION OF ATOMS ENTERING AND EXIT ING SINGLE-FILE NANOTUBES BY A TWO-DIMENSIONA L HYPERPOLARIZED XE-129 NMR ........1146.1 Introduction ............................................................................................................ .......1146.1.1 Thermally-polarized Xe 2D Exchange NMR .....................................................1156.1.2 Hyperpolarized Xe 2D Exchange NMR .............................................................1176.2 Experimental ............................................................................................................ .....1186.3 Magnetization Exchange Model for C ontinuous-flow Hyperpolarized Xe 2DEXSY NMR ...................................................................................................................... 1206.4 Results and Discussions ................................................................................................1 236.5 Conclusions ............................................................................................................. ......1307. SIGNAL ENHANCEMENT OF HYPERPOL ARIZED XE-129 2D-NMR EXCHANGE CROSS PEAKs IN NANOTUBES BY IN TERRUPTION OF THE GAS FLOW .............1327.1 Introduction ............................................................................................................ .......1327.2 Experimental ............................................................................................................ .....1357.3 Results and Discussions ................................................................................................1 377.4 Conclusions ............................................................................................................. ......141
8 8. INVESTIGATIONS OF GAS EXCHANGE IN GA10 WHEEL NANOTUBES BY 2D EXCHANGE HYPERPOLARIZED XE-129 NMR ............................................................1438.1 Introduction ............................................................................................................ .......1438.2 Experimental ............................................................................................................ .....1458.3 Magnetization Exchange Model fo r 2D-EXSY under Flow Interruption ....................1468.4 Results and Discussions ................................................................................................1 508.5 Conclusions ............................................................................................................. ......1589. CONCLUSIONS AND OUTLOOK ....................................................................................161APPENDIX ..................................................................................................................... ............166A. DERIVATION OF AVERAGE ZEEM AN ORDER IN NANOTUBE PHASE BY GAMMA FUNCTION IDENTITIES ...................................................................................166B. MATRIX FORMULATION FOR TWO-SITE EXCHANGE SYSTEM ............................169LIST OF REFERENCES ............................................................................................................ .171BIOGRAPHICAL SKETCH .......................................................................................................185
9 LIST OF TABLES Table page 2-1 Comparison of NMR properties of 1H, 129Xe and 131Xe ....................................................373-1 Summary of axial sy mmetric CSA tensors ( =0) in 1D single-file channel .....................593-2 Summary of 13C T1 relaxation times in AV at 9.4 T and 25 oC .........................................674-1 Nonlinear regression analysis of saturation-recovery hyperpolarized 129Xe NMR of Xe in AV nanotubes at -10 oC. ...........................................................................................925-1 Summary of Xe NMR acquisition pa rameters of the molecular wheels .........................1006-1 Best-fit kinetic parameters for CF HP Xe 2D-EXSY spectra in AV at -10 oC .. ...............1268-1 Kinetic parameters of Ga10 nanotubes in CFHP and IFHP 2D-EXSY at 25 oC. .............158
10 LIST OF FIGURES Figure page 2-1 Temperature dependence of 129Xe spin polarization at va riable magnetic fields.. ............242-2 The energy levels of (a) thermal pol arization (hot-spin system) and (b) hyperpolarization (cold-spin sy stem) for spin-1/2 system. ............................................252-3 Chemical shift tensor in di fferent coordinate systems. ......................................................27 2-4 Simulated CSA powered spectra of (a) lo wer symmetry, (b) axial symmetry, (c) cubic symmetry ... .. 292-5 Simulated NMR spectra for two-site exchange. (a)(b) fast exchange; (c)(d) intermediate exchange; (e)(f ) slow exchange regime. .......................................................322-6 NMR pulse sequence of 2D exchange NMR.. ...................................................................332-7 Simulated 2D-EXSY spectra with (a) ch emical exchange, and (b) no exchange. .............362-8 Chemical shift range of 129Xe NMR with examples of specified materials. .....................402-9 The 87Rb energy levels with spin orbital interaction, hyperfin e interaction, and Zeeman splitting in the presence of a weak external magnetic field. ................................452-10 The 87Rb ( I =3/2) optical pumping for negative circularly polarized light in a weak external magnetic field.. ...........................................................................................462-11 Spin-exchange between Rb and Xe.. .................................................................................472-12 Continuous-flow hyperpolarized 129Xe apparatus. ............................................................512-13 (a) Optical transmission spectra of Rb va por in the pumping cell at four different cell temperatures (100, 125, 145, 165 oC ) at a total gas pressu re of 3000 torr (2 % Xe mixture) at 100 W laser power. (b) Flow-rate dependence of Xe spin polarization at different pumping cell temperatures. .................................................................................532-14 (a) Hyperpolarized 129Xe NMR spectrum. (b) Thermally-polarized 129Xe NMR spectrum. ..................................................................................................................... .......543-1 (a) Molecular structure of L-alanylL-valine. (b) Space-filling model of AV nanotube viewed along the channel axis. (c ) Stick packing arrangement of AV.. ............613-2 Carbon-13 inversion-recovery NMR pul se sequence with proton decoupling during signal acquisition. ........................................................................................................... ...633-3 (a) SEM Image of AV polycrystalline nanot ubes. (b) Distribution of channel lengths in AV nanotube samples. ...................................................................................................65
11 3-4 Inversion-recovery 13C NMR spectra recorded as a function of recovery time in AV nanotubes at room temperature... .......................................................................................663-5 Continuous-flow hyperpolarized 129Xe NMR spectra in AV at variable temperatures and 3300 mbar Xe partial pressure at a total gas pressure of 4600 mbar. .........................683-6 Hahn spin-echo Xe NMR spectra as a func tion of interpulse delay at Xe partial pressure of (a) 92 mbar and (b) 3300 mbar at -10 oC .......................................................693-7 (a) Experimental thermally-polarized 129Xe spectra at 20 oC at various Xe molar occupancies.21 (b) The corresponding CSA spectra were simulated to obtain the shielding components.........................................................................................................703-8 Correlation between Xe molar occupancy m and component in AV nanotubes. .......713-9 Variation of Xe fractional occupancy with temperature in AV at variable Xe density. ...................................................................................................................... .........723-10 (a) Variation of the Xe isosteric adso rption enthalpy with th e Xe occupancy in AV.(b) Temperature dependence of the Xe e quilibrium constant in AV nanotubes... ......744-1 The model of asymmetric simple exclusion process (ASEP) with symmetric open boundaries. ................................................................................................................... ......774-2 The waveforms of probability density f unction of (a) normal 1D Fickian diffusion and (b) single-file diffusion corresponding to successively in creasing observation time (123ttt ). ...............................................................................................................794-3 Molecular tracer exchange. ................................................................................................ 814-4 Hyperpolarized NMR tracer exchange.. ............................................................................824-5 NMR pulse sequence of selective co ntinuous-flow saturation-recovery (CFSR) hyperpolarized 129Xe NMR experiment. ............................................................................844-6 Selective continuous-flow satura tion-recovery (CFSR) hyperpolarized 129Xe NMR experiment in AV nanotubes. ............................................................................................854-7 Least-squares fits to the selective saturation-recovery NMR signal of 129Xe in AV at T= -10 oC to the expressions for single-file diffusion (SFD, Eq. (4-20)) and normal diffusion (ND, Eq. (4-22)). (a) Low occupancy: 56 Torr Xe,0.16 (c) High occupancy: 2650 Torr Xe, 0.66 Time-base expansions of (a) and (c) are presented in (b) and (d), respectively. ................................................................................914-8 (a) Fractional occupancy dependence of the T1c of 129Xe in the adsorbed Xe phase at T= -10, 10, 25, and 40 oC (b) Fractional occupancy dependence of FC ranged from =0.14 to 0.70 at -10 oC. ..........................................................................................93
12 5-1 Structures of molecular wheels, (a)(d) Ga10, (b)(e) Ga18, and (c)(f) Mn84 with internal diameter of 8.1 10.4 and 1.9 nm, respectively. (a )(b)(c) are the top view of molecular structures of Ga10, Ga18, and Mn84 wheels, respectively. (d)(e)(f) are the corresponding space filling representations of Ga10, Ga18, and Mn84 wheel compounds, respectively. ...................................................................................................975-2 SEM images of Ga10 nanotubes shown at length scales of (a) 10 m, (b) 100 m, and (c) 1mm. (d) Length distribution of the Ga10 crystals.. ....................................................1015-3 Temperature dependence of hyperpolarized 129Xe NMR Spectra of Xe adsorbed in (a) Ga10 and (b) Ga18 molecular wheels. ..........................................................................1025-4 Temperature dependence of chemical shift of adsorbed Xe peaks in Ga10 and Ga18 nanotubes. .................................................................................................................... ....1045-5 Temperature dependence of hyper polarized Xe NMR spectra of Mn84 nanotubes. ........1055-6 Pressure dependence of hyperpol arized Xe NMR Spectra in (a) Ga10 and (b) Ga18 nanotubes at 25 oC ..........................................................................................................1065-7 Hyperpolarized CFSR 129Xe NMR experiments in Ga10 nanotubes with variable Xe partial pressures at room temperature.. ............................................................................1085-8 Hyperpolarized CFSR 129Xe NMR experiments in Ga18 nanotubes in (a)16.7% and (b)100% Xe with total gas pressure of 4000 mbar. The corresponding time-axis expansions of (a) and (c) are presente d in (b) and (d), respectively.. ..............................1095-9 Xe pressure dependence of (a) T1c and (b) CF determined by least-squares fit of Eq. (4-20) in Ga10 nanotubes. Xe pressure dependence of (c) T1c and (d) CD determined by least-squares fit of Eq. (4-22) in Ga18 nanotubes. .......................................................1116-1 Simulated mixing-time dependence of (a) diagonal-peak and (b) cross-peak intensities in 2D-EXSY based on two-site exchange model. ..........................................1166-2 NMR pulse sequence of CFHP 2D-EXSY. ....................................................................1196-3 Steady-state conti nuous-flow hyperpolarized 129Xe NMR spectra in AV nanotubes, acquired at -10 oC at the following Xe partial pressu res: (a) 92 mbar (b) 1320 mbar (c) 3300 mbar.. ............................................................................................................... ..1236-4 Continuous-flow hyperpolarized 129Xe 2D-EXSY spectra in AV nanotubes at -10 oC acquired at the mixing times yielding maximu m cross-peak intensities: (a) 92 mbar, m =35 ms (b) 1320 mbar m =100 ms (c) 3300 mbar m =100 ms. .........................1256-5 Mixing-time dependence of crossand dia gonal-peak signal integr als in the CFHP 129Xe 2D-EXSY spectra in AV nanotubes at -10 oC (a) Channel-to-gas, (b) Gas-tochannel cross-peak integrals. (c) Gas-to -gas, (d) channel-to-channel diagonal peak mixing time dependences at 92, 1320 and 3300 mbar. ....................................................127
13 7-1 Simulated mixing-time dependence of crosspeak signals at vari able gas residence time R and constant desorption rate constant (13dks ).. ...........................................1347-2 Pulse sequence for (a) continuous-flo w (CF) and (b) interrupted-flow (IF) hyperpolarized 2D-EXSY. ...............................................................................................1367-3 HP 129Xe 2D-EXSY spectra of Xe in AV at -10 oC with mixing times of (a,b) 300 ms and (c,d) 1s. Spectra in (b) and (d) were acquired in continuous-flow (CF) mode. Spectra in (a) and (c) were acquire d in interrupted-flow (IF) mode ..............................1397-4 3D representation of HP 129Xe 2D-EXSY spectra of Xe in AV at -10 oC acquired in (a) IF mode and (b) CF mode, each with a mixing time of m=1s. ..................................1408-1 Simulated mixing-time dependences of norma lized cross-peak signa ls at (a) variable T1c ( kd = 2.5 s-1) and (b) variable kd ( T1c = 5 s). Y-axis expansions of (a) and (b) are presented in (c) and (d), respectively.. .............................................................................1498-2 Hyperpolarized 129Xe 2D-EXSY spectra in (a)(b) continuous-flow and (c)(d) interrupted-flow modes in Ga10 nanotubes at 25 oC at variable mixing times.................1518-3 3D representations of HP 2D-EXSY spectra of Xe in Ga10 nanotubes at 25 oC acquired in (a) IF mode and (b) CF mode. .......................................................................1528-4 Mixing-time dependences of (a) gas-toga s, (b) channel-to-channel diagonal-peak integra;. (c) gas-to-channel and (d) channelto-gas cross-peak integrals in CFHP Xe 2D-EXSY spectra of Ga10 nanotubes at 25 oC ................................................................1548-5 Mixing-time dependences of (a) gas-toga s, (b) channel-to-channel diagonal-peak integral; (c) gas-to-channel, and (d) channel-to-gas crosspeak integrals in IFHP Xe 2D-EXSY spectra of Ga10 nanotube at 25 oC .................................................................155
14 LIST OF ABBREVIATIONS 1D one dimensional 2D two dimensional 3D three dimensional ASEP asymmetric simple exclusion process AV L-alanyl-L-valine CF continuous flow CSA chemical shift anisotropy DNP dynamic nuclear polarization EXSY exchange spectroscopy FT Fourier transformation FWHM full width at half maximum HP hyperpolarized IF interrupted flow LAB laboratory axis system ND normal diffusion NOESY nuclear Overhauser enhancement spectroscopy OD outside diameter OP optical pumping PAS principal axis system PDF probability density function PEEK polyetheretherketone PFA perfluoroalkoxy PFG pulsed-field gradient PHIP para-hydrogen induced polarization
15 QENS quasi-elastic neutron scattering RF radio frequency SAT saturation pulse train SE spin exchange SEM scanning electron microscope SEOP spin-exchange optical-pumping SFD single-file diffusion SMM single molecular magnet SN solenoid valve SPINOE spin polarization induced nuclear Overhauser effect TMS tetramethylsilane TPP tris( o -phenylenedioxy) cyclotriphosphazene TTL transistor-to-tran sistor logic gate
16 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy GAS ADSORPTION, DIFFUSION, AND EX CHANGE IN ONE-DIMENSIONAL NANOTUBE SYSTEMS BY HYPE RPOLARIZED XE-129 NMR By Chi-Yuan Cheng August 2008 Chair: Clifford R. Bowers Major: Chemistry One-dimensional (1D) nanotube materials hold great promise for a vast range of practical applications. Understanding the fundamental adsorption and transport properties of guest molecules in 1D nanotubes is essential to optimi ze their performance in such applications. At thermal equilibrium, the symmetric simple exclusion model for 1D channels too narrow for particles to pass one-another predicts the emergence of anomalous diffusion properties. Depending on the density and time-s cale, single-file diffusion ( SFD) may be observed, where the mean-squared displacement increases as t1/2 rather than t as in normal Fickian diffusion (ND). While there are numerous theoretical works on SFD, it is noted that SFD has not been investigated experimentally in detailed. We have employed conti nuous-flow hyperpolarized 129Xe NMR to systematically investigate molecular adsorption, diffusion and ex change of Xe in two types of 1D nanotube systems: the self-assembled L-alanyl-L-valine (AV) dipeptide na notubes and gallium based wheel-shaped nanotubes (Ga10 and Ga18), which have the internal channel diameter of 5.13 8.1 and 10.4 respectively. The Xe spectral lineshape in AV exhibits an axially symmetric chemical shielding anisotropy, wh ereas Xe adsorbed peaks in Ga10 and Ga18 nanotubes demonstrate the isotropic NMR line-shapes, implyi ng that Xe in the gall ic-wheel nanotubes is
17 less restricted than Xe in AV na notubes. Xe occupancy at variable temperature and pressure can be determined from Xe chemical shift. The isos teric enthalpy of Xe adsorption in AV becomes increasing exothermic with increasing Xe occ upancy. Moreover, Xe chemical shifts in Ga10 and Ga18 nanotubes are almost independent of Xe occ upancy over a wide range of Xe pressures at room temperature, indicating Xe-wall interaction is dominated in gallic-w heel nanotube system. The selective saturation-recovery pulse seque nce has been utilized to explore the Xe diffusion in AV and gallic channels. The kinetic model assuming diffusion-limited Langmuir adsorption and the distribution of desorption rate has been proposed. The data clearly showed that the mean-squared displa cements of Xe in AV and Ga10 nanotubes are pr oportional to the square root of time, 21/2() ztt as in SFD. However, the mean-s quared displacement of Xe in Ga18 nanotubes was observed to be proportional to the diffusion time, 2() ztt revealing that the SFD and ND time-scaling of Xe in 1D nanotube systems with different internal diameters can be evidently distinguis hed by the saturation-r ecovery hyperpolarized 129Xe NMR. Xe exchange in the vicinity of the na notube openings has been investigated by hyperpolarized 129Xe 2D exchange NMR (2D-EXSY) in AV and Ga10 nanotubes. Kinetic analysis of cross and diagonalpeak signals as a function of exchange time yielded the mean desorption rate, which was observed to decrease with increased Xe occupancy in AV channels. Furthermore, our kinetic model indicates that cross-peak amplitudes in the 2D spectrum are strongly attenuated under flow c onditions. By incorporating a brie f interrupting of the gas flow during the exchange period, we demonstrated that the cross-peak signal s can be dramatically enhanced, thereby providing a way to probe sl ow exchange and diffusion processes in 1D nanotube systems. The results are relevant to po tential applications of nanotubes, including gas storage, gas separations, catalysis drug-delivery and nanofluidics.
18 CHAPTER 1 INTRODUCTION Recently, the physical and chemical propertie s of materials with one-dimensional (1D) atomic or molecular arrangements have been b ecome the subject of intense studies for the developments and applications of future mole cular-sized devices, such as gas storage, gas separation, nanofluid ics, and catalysts.1 The adsorption and kinetic pr ocesses play a key role in the functions and performances of nanoporous so lids. In channels with inner diameters too narrow for the confined particles to mutu al passage, normal 1D Fickian diffusion, 2 02 ztDt no longer be valid. Instead, the mean-s quared displacement of a particle at sufficiently long diffusion time follows 21/22 ztFt where F is the single file mobility. The single-file mobility can be affected by several factors, including channel internal structure, adsorbate occupancies, presence of other adso rbates, and guest-guest/ guest-host interactions. 129Xe NMR spectroscopy has evolved into a unique technique in nanoporous materials over the past three decades.2 Its large chemical sh ift range allows the p hysisorbed phase to be distinguished from the free gas, revealing the interactions with the surface and Xe atoms. For these reasons, 129Xe NMR has become one of the most powerful techniques available to investigate the local st ructure in nanoporous mate rials, such as zeolite3-12, polymer13-18, nanotube19-24, as well as protein25-31 and liquid crystal.32-34 Over the past few decades, hyperpolarized 129Xe has been extensively developed to improve the sensitivity of 129Xe NMR.16 Hyperpolarized 129Xe NMR signals can be enhanced up to four orders of magnitude or more compared to thermally-polarized Xe NMR.35 Therefore, hyperpolarized 129Xe NMR can provide exceptionally high sensitivity in th e applications of materials ch aracterization, thereby requiring relatively small sample quantities and short instrumentation time for the experiments. It should
19 be noted that most of the previous works on the nanoporous materials, particularly nanotubes, have focused on the guest-guest/guest-host inte ractions, pore-space conn ectivity and structure architectures.13-23 However, many significant aspects, such as gas adsorption/desorption, exchange, and transport behaviors in nanotubes, ar e still unclear and need to be investigated further. In this dissertation, the feasibil ity of applying continuous-flow hyperpolarized 129Xe NMR to explore Xe gas adsorption/desorption, di ffusion, and exchange in single-file nanotubes and other types of 1D nanotube systems will be demonstrated. This dissertation is organized as follows: In Chapter 2, the relevant portions of theoretical and experimental NMR, particular ly hyperpolarized NMR, and the physical properties of Xe gas are briefly reviewed. The development of conti nuous-flow hyperpolarized Xe polarizer will be presented. Chapter 3 concerns the use of hyperpolarized 129Xe NMR to explore the adsorption properties of Xe in 1D self-assembled L-alanyl L-valine (AV) dipeptide nanotubes. Chemical shift anisotropy (CSA ) powder patterns of Xe in AV nanotube s were recorded as a function of temperature and pressure. The sign inversio n of the anisotropy was achieved over the experimental temperature and pressure ranges. The Xe shielding component can be utilized to quantitatively determine Xe occupancy in 1D channels. The determinations of isosteric Xe adsorption enthalpy and equilibrium constant in the AV nanotubes according to the ClausiusClapeyron equation and Langmuir equation will be demonstrated. Chapter 4 describes how selective saturation-recovery hyperpolarized Xe NMR can be used to study the gas diffusion inside the AV channels. A theoretical formalis m for the quantitative analysis of saturationrecovery experiments in single-file diffusion a nd normal 1D Fickian diffusion will be presented. The data in AV nanotubes exhibits the clear si gnature of single-file diffusion over time scales ranging from 0.5-150 sec. It will be s hown that it is feas ible to measure F by saturation-recovery
20 hyperpolarized 129Xe NMR. Chapter 5 presents the saturation-recovery hyperpolarized 129Xe NMR experiments on the molecular wheels nanotubes, Ga10 and Ga18. The internal diameters of gallic-wheel nanotubes are relatively larger than that of AV nanotubes.36 ( i.e. 8.1 for Ga10; 10.4 for Ga18 ; 5.13 for AV) It will be shown that the cross-over of time-scaling of singlefile diffusion and normal 1D Fickian diffusion in gallic-wheel nanotubes can be distinguished by saturation-recovery hyperpolarized 129Xe experiments. In Chapter 6, it will be demonstrated that it is possible to directly observe Xe atoms ente ring and exiting the sing le-file nanotube, AV, by continuous-flow hyperpolarized 129Xe 2D exchange NMR (CFHP 2D-EXSY). The theoretical expressions will be presented to quantitatively extract the average desorption rates of Xe in AV nanotube systems. From the expressions, it become s evident that the cross-peak intensities of 2D-EXSY are strongly attenuated by the finite residence time of hyper polarized gas in the sample space. By briefly interrupting the gas fl ow during the exchange periods, the cross-peak intensities are dramatically enhanced. The significant cross-peak signal enhancements of 2DEXSY in AV nanotubes will be de monstrated in Chapter 7. The mixing-time dependences of 2DEXSY in Ga10 nanotubes under continuous-flow and interru pted-flow conditions associated with the corresponding theoretical analysis will be presented in Chapter 8. Chapter 9 summarizes the dissertation and provides some promising futu re directions of th is exciting area.
21 CHAPTER 2 BACKGROUND 2.1 Introduction A brief review of the essential aspects of NMR and hyperpolarized NMR that will be used in the following chapters is presented. Section 2.2 presents the basics of NMR, including spin polarization, chemical shift anisotropy, and exchange NMR, following the classic NMR texts of Spiess37, Ernst38, and Levitt39. The physical properties of 129Xe, Xe chemical shifts and potential applications will be discussed in Section 2.3. In NMR, the signal is typically weak under the ambient conditions. The technique of spin-exchange optical-pumping is a wa y to overcome this limitation. This aspect will be discussed in Section 2.4. 2.2 Introduction to NMR Magnetic resonance spectroscopy is one of the most powerful tools for studies of molecular structures and dynamics in both liquid a nd solid systems. It has been extensively used in numerous applications in physics, chemistr y and biology since its fi rst discovery by Bloch40 and Purcell41 in 1946. The NMR experiment involves a stu dy of interactions of nuclear spins. The bulk NMR sample consists of an ensemble sp in systems, which can be described by the total Hamiltonian composed of several spin interaction terms. In principle, the total Hamiltonian in the nuclear spin system is the summation of i ndividual Hamiltonians that describes particular spin interactions: interactions 1zJDCSQHHHHHHHH (2-1) where zH is the Zeeman interaction, which is much great er than any of the other interactions in a strong external magnetic field. J H is the scalar coupling, whic h is the inter action of two nuclear-spins through bonding electrons. It is also called the indirect dipolar or J coupling.
22 D H is the dipolar coupling, which is the magne tic interaction of two nuclear-spins through space. CSH corresponds to the chemical shift interacti on, which results from the shielding of the magnetic field due to the electron cloud surrounding the nuclear spin. QH represents the quadrupole interaction for 1/2 I nuclei, which is due to the coupling of the electric field gradient and nuclear quadrupole moment. 1 H is the time-dependent, applied radiofrequency (RF) field. It can be applied to manipulate the nucle ar spins into unique quantum mechanical spin states in such a way that the measured spin dynamics reports selective information about the chemical structures, molecular motions, spin interact ions, and the distribution of spin densities. 2.2.1 Spin Polarization When a static external magnetic field 0B is applied, it breaks th e degeneracy and causes each 21 I sublevel to have a slightly different energy. The interacti on between the magnetic dipole moment ( ) and the external magnetic field is known as the Zeeman interaction. The Hamiltonian for the Zeeman interaction is 0zzHBI (2-2) where is gyromagnetic ratio, and z I is angular momentum operator along 0B field (z-axis) with the eigenstate of m, following z I mmm According to Boltzmann distribution, the nuclear spin polarization is determined by the popul ation difference between m-states. For instance, the polarization of 12 I nuclei is 0 001exp 2 1expB BB kT z B kTNN PI NN (2-3)
23 where N and N are the populations of spin in (spin-up, 12 m ) and (spin-down, 12 m ) states, respectively, B k is the Boltzmann constant, and T is temperature. The observed NMR signal is proportional to the z-magnetization42, which is the product of the nuclei spin polarization 0P the fractional isotopic abundance f and the total number of detected nuclei in the RF coil region NMRn. 0 zNMRNMRsignalMPfn (2-4) Hence, NMR signal is proportional to the nuclear spin polarization. If and state are equally populated, 00P, leading to no NMR signal. This situa tion occurs at thermal equilibrium at sufficiently high temperature or can be reached by saturating the spin system by irradiation in a continuous-wave RF field or by application of a single /2 RF pulse followed by a delay longer than the 2T relaxation time but shorter than the 1T relaxation time. At thermal equilibrium, the population difference between the and states is very small, thereby yielding an extremely weak NMR signal. For 129Xe in the field of 9.4 T (400 MHz NMR) at 300 K, the polarization is only 6 0910P In Eq. (2-3), it is obvious that lower T and higher 0B can achieve higher 0P. For example, at a magnetic fi eld strength of 4.7 T (200 MHz NMR, 01 P can be achieved at ~310 K ( see Figure 2-1). The sensitivity improvement obtained using a cryogenic NMR probe43 has been demonstrated in a va riety of applications in solid44-46 and liquid47-49 systems. While it is feasible to enhance the NMR signal by cooling the sample to cryogenic temperatures, this approach is usually limited by the increasingly long 1T relaxation times which result from quenching of molecu lar motions and/or phonon modes upon lowering the temperature which prevents the nuclear spin system from reaching thermal equilibrium. On
24 the other hand, the polari zation can also be incr eased by increasing the magnetic field. In the high temperature regime, where 0 BBkT, the polarization increases in proportion to the magnetic field. Thus, for 129Xe spin at 298 K and 21 T (900 MH z NMR), which is the highest magnetic field of the commercial NMR spectrometer to date, the thermal equilibrium polarization is5 0210 P. Therefore, the sensitivity increa se that can be achieved by simply increasing the magnetic field is relatively modest. Figure 2-1. Temperat ure dependence of 129Xe spin polarization at variable magnetic fields, based on Eq. (2-3). In hyperpolarized NMR, the nuclear spin polarization is not limited by T and 0B. In Eq. (2-3), the spin polarization can be alternatively expr essed in terms of a spin temperature s T. At thermal equilibrium, the ensemble of spin systems has relatively lo w spin polarization, or 1.0 0.8 0.6 0.4 0.2 0.0129Xe Polarization, P0 10-4 10-3 10-2 10-1 100 101 102 Tem p erature ( K ) 900 MHz 400 MHz 200 MHz
25 equivalently, high spin temperature. High nucle ar spin polarization co rresponds to low spin temperature. The schematic diagram for the popul ation distribution among the energy levels for thermal polarization and hyperpolarization is illustrated in Figure 2-2. The aim of hyperpolarized NMR is to increase the popu lation difference between the spin states, i.e. to cool down the spins, leading to NMR signal e nhancement. The details of hyperpolarized NMR will be discussed in Section 2.4. Figure 2-2. The energy levels of (a) therma l polarization (hot-spin system) and (b) hyperpolarization (cold-spin system) for spin-1/2 system. 2.2.2 Chemical Shift Anisotropy In the presence of a static external magnetic field 0B, the motion of electron cloud around a nuclear spin can generate a localized anisotropi c magnetic field that interacts with the nuclear spin. This induced magnetic field is proportional to 0B, but opposite in di rection. At the i -th nucleus, a local magnetic field is induced by the surrounding electrons 0 ()()induced B iiB (2-5)
26 where ()i is the chemical shift tensor (or shielding tensor). The chemical shielding tensor can be expressed as a 33 matrix. The energy of chemical shift resulting from the induced field of each nucleus is 0 ()()()CSiinducediEiBiiB (2-6) Since the local environments of each nucleus ar e different, the shielding tensors of nuclei in a spin system are generally differe nt. Replacing the magnetic moment with its quantum equivalent and summing over all the spin s in the systems, the Hamiltonian of chemical shift in a spin system yields 0 ()()()spinsspins CSCSi iiHHiiiB (2-7) The Hamiltonian of individual spin can be described by the tensor in the laboratory frame (LAB) 0 ()()()LABLAB CSiHiiiB (2-8) Because the chemical shift interaction has a spec ifically spatial orientation with respect to 0B, any molecular motions in space must include the rotation of its three components in the chemical shift tensor. To simplify the problem, th e chemical shielding te nsor can be treated on its own principal axis system (PAS), yielding a diagonal tensor. The axes of PAS point in the same directions as the eigenve ctors of the shielding tensor, By convention, the z-axis of the PAS points along the largest eigenvect or of the chemical shielding te nsor and x-axis points along the smallest eigenvector.50,51 The eigenvalues, 11 22 and 33 are the principal components of the tensor 332211 The shielding tensor in PAS is 11 22 3300 00 00PAS (2-9)
27 Here the numerical subscripts are used in PAS, while the elements are denoted by x y, and z in LAB. The chemical shielding tensor can be transformed from PAS to LAB coordination system by operating with rotation matrices in terms of Euler angle transformation37,52 1 R,,R,,LABPAS (2-10) where and are the Euler angles.52 In Figure 2-3, the shape of three-dimensional ellipsoid is defined by the principal tensor components (11 ,22 ,33 ). Figure 2-3. Chemical shift tens or in different coordinate systems. In CSA tensor, the 33 points along the value of th e largest shielding. 22 and 11 are orthogonal to 33 Since the Hamiltonian of chem ical shift is a small perturbation of Zeeman Hamiltonian, the terms in Eq. (2-8) which do not commute with zI can be neglected. Therefore, in a high external magnetic field, only zz in the LAB is of interest and Eq. (2-8) can be rewritten as
28 0CSizzz H iIB (2-11) An expression of the experimental meas urable quantity of shielding tensor, zz in terms of the principal values of shielding tensor and the Euler angles of PAS to LAB can be obtained by applying the rotation operators to PAS.37 1 22222 112233 222 (,,)(,,) sincossinsincos 1 3cos1sinsin2 2PAS zz zz isoRR (2-12) where iso is isotropic chemical shift, 33iso is shielding anisotropy, 221133 iso is asymmetric parameter. The powder sample with randomly orientated crystallites has the characteristic spec tral line-shape. It is typically called powder pattern, in which is weighted according to the is otropic probability distribution.42 The CSA line-shapes are shown in Figure 2-4. Three ty pical CSA powder patterns are summarized as follows: (1) If three shielding components are not equal, 332211 it yields the asymmetric spectra (0 ), as shown in Figure 2-4a. (2) For a tensor with an axially symmetry, where the asymmetric parameter is 0 the line-shape can be simplified to Figure 2-4b. and can be referred to the shielding along and perpendicular to the principle z-axis, where 33 and 2211 The anisotropy of axially symmetry tensor is As shown in Figure 2-4b, the spectra line-shapes with opposite anisotropy signs are the mirro r images with respect to iso
29 (3) If three tensor components are equal, 332211 the spectrum collapses to an isotropic peak at iso frequency (Figure 2-4c). Figure 2-4. Simulated CSA powered spectra of (a) lower symmetry (332211 ), =0.7, =70 ppm, (b) axial symmetry (332211 ), =0.7, =70 ppm. (dash line, = -70 ppm), (c) cubic symmetry (332211 ), =0, =0 ppm. The spectral width =200 ppm, Gaussian broadening =0.3 kHz. Larmor frequency=100 MHz, 0iso ( is asymmetric parameter. is shielding anisotropy. is shielding anisotropy for axially symmetry tensor) If the molecules are randomly tumbling, the chem ical shift interaction is average to zero, allowing the observation of an isot ropic peak. The isotropic chemical shift value can be taken as average of the trace: 11223311 33isoTr (2-13) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 100 50 0 -50 -100ppm (a) (b) (c) 33 22 11 iso
30 For a single crystal sample, where discrete mo lecular orientations are present, the NMR spectrum consists of a sharp isotropic peak, if the chemical shift interaction is dominated. The frequencies of these peaks depend on the orientations of the crystal c -axis with respect to the external magnetic field. By meas uring these frequencies as a func tion of crystal orientation, the shielding tensor can be determined. However, for some materials, it is infeasible to grow a crystal to an appropriate size for NMR measurements. In addition, some solid samples, such as amorphous polymers, do not have regular crysta lline structures. Inst ead, they contain a distribution of orientations of the CSA tensor with respect to the external magnetic field. Therefore, the spectral line-shape from such s ubstances is broadened by the distribution of resonance frequencies. For solid samples, the magic-angle spinni ng (MAS) can be utilized to produce high resolution NMR spectrum by aver aging the chemical shift anisotropy to its isotropic value.42 2.2.3 Exchange NMR Another important feature of NMR is its sensit ivity to molecular dynamics in the presence of exchange processes. In the exchange system, the species ( e.g. nuclei, molecules, or particles) can generally exchange among one-another in two or multiple states. In most cases, the exchange rate of such process is within the range of NMR time-scale, which refers to the lifetimes of the order of 1 second to 10-6 second for each state.39 It allows NMR to be a un ique tool to extract the dynamic information in the exchange systems, the result which is not usually achievable by other spectroscopic techniques. Several NMR techniques have been developed for the studies of exchange processes, including line-shape analysis53,54, selective inversion55,56, and two-dimensional exchange NMR spectroscopy (2D-EXSY).57,58 For simplicity, considering exchange between two magnetically
31 inequivalent sites A and B with frequency A and B the twosite exchange processes can be easily analyzed by the NMR line-shapes, since the exchange processes can be evidently observed from the characteristic changes in the NMR spectral line-shapes. The details of NMR line-shapes in different exchange regimes are described as follows: Fast exchange In fast exchange regime, the exchange rate constant exk (assuming equally forward and reverse exchange rates, exABBAkkk) is greater than the chemical shift offset between two sites: 0 A B leading to the two signals complete ly collapse to a single sharp peak (Figure 2-5a and b). The resonance frequency 0 f ast can be expressed by the weighing average of two sites (1ABpp ), 0 fast A ABBpp (2-14) The peak can be characterized by an averaged transverse relaxation rate 2221AB fast ABpp TTT (2-15) where 2 f astTis the observed 2T relaxation time in the fast exchange limit ( i.e. 0 exk ). The full width at half maximum (FWHM) of Lorentzian peak is given by 1/221 f astT. Slow exchange If the exchange of observed nucleus between s ite A and B is in slow exchange regime, the individual frequencies for each site can be resolved with offset of 0 A B and the exchange rate constant must be less than 0 ( i.e. 0 exk ), as seen in Figure 2-5e and f. In this case, the adsorption Lorentzian peaks of both sites can be obtai ned by solving the Bloch equation on two exchange sites59, and the FWHM of A site is
32 1/2 211ex Ak T (2-16) Similar expression can be obtaine d for site B. On the contrary to the fast exchange, slow exchange results in two separated peaks with an excess line broadening factor, /exk (in Hz ), of the signal at each site. Intermediate exchange As the exchange time-scale between the abov e two regimes, a broader line-width is observed in an intermediate exchange spectrum. A decrease in sensitivity in the intermediate exchange regime is apparent in Figure 2-5c and d due to broader line-width and lower amplitude. Figure 2-5. Simulated NMR spect ra for two-site exchange. (a)(b) fast exchange; (c)(d) intermediate exchange; (e)(f) slow exchange regime. Chem ical shift offset between two sites: 041.310/secrad, populations: 0.5ABpp 111ABTTs 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 4 2 0 -2 -4 kHz (a) 20 kex (ms-1) (b) 13 (c) 5 (d) 3 (e) 1 (f) 0.5
33 2.2.4 2D Exchange NMR Spectroscopy 2D-EXSY experiment is a technique to explor e the frequency exchange in slow exchange limit (0 11/exTk ). 2D-EXSY is in principle iden tical to the Nuclear Overhauser Enhancement Spectroscopy (NOESY). However, th e mixing time of 2D-EXSY is usually shorter than that of NOESY, becau se the exchange rate is generally mu ch faster than the cross-relaxation rate.39 The use of 2D-EXSY NMR for the study of molecular exchange was first proposed by Jeener and co-workers.57 The pulse sequence of EXSY is shown in Figure 2-6. Figure 2-6. NMR pulse sequen ce of 2D exchange NMR. m is mixing time. The NMR signal of 2D-EXSY experiment can be calculated in terms of product operators.38,39,60 In the case of two-spin system (spinA and spin-B) without J-coupling and spin relaxations, the equilibrium magnetization prior to the first /2 pulse is (0) A B zzz M tII For simplicity, the magnetization from spin-A is first considered. The first /2 x pulse rotates the magnetization onto y /2/2AB xxII A A zy I I (2-17) Following the evolution during 1t
34 1111cossinAABB zztItI A AAAA yyx I tItI (2-18) The second arrows in Eq. (2-17) and Eq. (2-18) have no effect, since A I and B I are commute. The second /2 x pulse rotates first term of Eq. (2-18) onto z-axis and leaves the second term unaffected. /2/2 11 /2/2 11coscos sinsinAB xx AB xxII A AAA yz II AAAA xxtItI tItI (2-19) During the mixing time m only longitudinal magnetizations lead to cross-peaks by exchange; therefore, the A x I term in Eq. (2-19) can be ignored. In the EXSY experiment, it can be achieved by selecting an appropriate coherence transfer pathway by the phase cycling.39 In the beginning of mixing time m the magnitude of z-magnetization of spin-A depends on 1t and processing frequency A ( i.e. 1cos A A ztI ). This z-magnetization is called frequency labeled during 2D preparation time 1t. During m spin-A may undergo site exchange with spin-B. If so, for the spin-B after m it carries the information with the fre quency labeled of spin-A recorded during 1t. If a fraction ex f of spin-A is lost due to exchange w ith spin-B, the effect of mixing process can be written 111cos(1)coscosmix A AAAAB zexzexztIftIftI (2-20) The final /2 x rotates the z-magnetization back ont o y-axis for signal detection /2/2 11 /2/2 11(1)cos(1)cos coscosAB xx AB xxII A AAA exzexy II ABAA exzexy f tIftI ftIftI (2-21)
35 Although the magnetization started on spin-A, there is a magnetization presented on spin-B at the end of EXSY sequence. This process is also called longit udinal magnetization transfer. Finally, A y I and B y I evolve during detection period 2t 22 221 1212 1 1212(1)cos (1)coscos(1)cossin cos coscoscossinAABB zz AABB zztItI AA exy AAAAAA exyexx tItI AB y ABBABB exyexxftI f ttIfttI ftI fttIfttI (2-22) If assuming y-magnetization is detected during 2t, the NMR signal on time domain yields 1212(1)coscoscoscos A AAABB exyexy f ttIfttI (2-23) Similarly, repeat the same procedure on spin-B fr om the initial condition, ti me-domain signals is 1212(1)coscoscoscosBBBBAA exyexy f ttIfttI (2-24) By taking the Fourier transformation along 2t and 1t on Eq. (2-23) and Eq. (2-24), it results in four absorption line-shapes in 2D spectrum. The first terms of Eq. (2-23) and Eq. (2-24) form diagonal peaks, which are located at 12,(,) A Aff and 12,(,)BBff with amplitudes (1)ex f The second terms of Eq. (2-23) and Eq. (2 -24) form cross peaks which are located at 12,(,) A Bff and12,(,)BAff with amplitudes ex f (Figure 2-7a). Obviously, as shown in Figure 2-7b, if no exchange takes place between two sites (0)exf cross peaks are absent in 2D-EXSY spectrum.
36 Figure 2-7. Simulated 2D -EXSY spectra with (a) chemical exchange (150ABBAkkms 111ABTTs ), and (b) no exchange (0ABBAkk ). Larmor frequency=100MHz. In principle, the exchange rate constant can be determined by fit the cross and diagonalpeak signals of 2D EXSY spectra as a functi on of mixing time with the appropriate kinetic model. The thermodynamic parameters, such as activation energy and enthalpy, in the exchange process can be calculated by measuri ng exchange rates from a serial of m -dependence 2DEXSY experiments at variable temperatures.39 2.3 Introduction to 129Xe NMR Xenon was first experimentally brought in to NMR spotlight by Ito and Fraissard12, the pioneers of 129Xe NMR, for the study of porous solids. Their motivation was to utilize the sensitivity of 129Xe to (1) its local environment, (2) phys ical interactions w ith other chemical species, such as other nuclei, and (3) the na ture of adsorption sites in the materials. 2.3.1 Physical Properties of Xe The Xe atom has an atomic weight of 131.29 u. It possesses the electron configuration [Kr] 4d105s25d6 and has 54 electrons. Due to its small size and chemical inertness, Xe atom can serve f2, ppmf1, ppm(a) -15 -10 -5 0 5 10 15 20 -15 -10 -5 0 5 10 15 20 AA BB AB BA f2, ppmf1, ppm(b) -15 -10 -5 0 5 10 15 20 -15 -10 -5 0 5 10 15 20 AA BB
37 as an ideal atomic probe for char acterizations of materials on th e nanometer length scales. From 13 known isotopes of Xenon (9 stab le ones and 4 radioactive ones)61, only two of them are NMR observable: 129Xe with 1/2 I and 131Xe with 3/2 I Because of its fully occupied external electroni c orbital, Xe is chemically inert. However, this highly polarizable elec tron cloud makes Xe strongly hydrophobic, thereby leading to significant interactions between Xe and othe r hydrophobic molecules in solution or on solid surface. In ambient condition, gaseous Xe exists in nature, but liquid and solid phases can be easily obtained within an experi mental accessible range of temp eratures and pressures. The boiling and melting points of Xe at 1 ba r are 165.02 K and 161.38 K, respectively.2 It makes the separation of hyperpolarized Xe from gas mixture at temperatur e of liquid nitrogen (77 K) practical. The extremely lengthy 1T relaxation time of 129Xe is the key characteristic that makes Xe feasible to be optically polar ized prior to NMR experiments. The NMR properties of Xe isotopes a nd proton are listed in Table 2-1. Table 2-1. Comparison of NMR properties of 1H, 129Xe and 131Xe 1H 129Xe 131Xe Spin I 1/2 1/2 3/2 (108 s-1Tesla-1) 2.675 -0.74 0.22 Natural abundance (%) 99.99 26.44 21.18 : gyromagnetic ratio For 129Xe, the low gyromagnetic ratio combined with the low natura l isotopic abundance yields much lower NMR sensitivities in comparison to the 1H nuclei. Thus, for the thermallypolarized 129Xe, it is necessary to significantly increas e the number of scans and acquisition time to achieve acceptable signal-to-noise ratios in NMR measurements. This problem can be overcome by hyperpolarized NMR whic h makes the single shot of 129Xe NMR measurement feasible. It will be discussed in Section 2.4.
38 In addition to 129Xe, the quadrupole nuclei in the noble gases, such as 131Xe and 83Kr, have been optically polarized, and th e surface studies by hyperpolarized 83Kr NMR have been reported.62-65 These nuclei possess electric quad rupole moments which lead to quadruple relaxation and short 1T relaxation time, making the storag e of hyperpolariza tion infeasible. However, the quadruple moments of 131Xe and 83Kr can provide a wealth of information in the local structures directly through the observed quadrupolar splitting in the NMR spectrum. 2.3.2 One-dimensional van der Waals Guest/Host systems in Xe NMR The sizes of Xe atom and pore-spaces of materials strongly affect the 129Xe NMR spectral line-shape. Here the definitions of the Xe diamet er and the pore sizes of the host materials, 1D channel diameter in the present case, are discus sed. The van der Waals diameter of Xe atom is 4.4 which can be estimated from the b coeffi cient of the van der Waals equation by assuming Xe is a hard-sphere atom. While the Xe diameter can be measured from other methods, such as Stokes-Einstein equation66, the van der Waals diameter is mostly used to describe the size of Xe atom in 129Xe NMR studies in the literature.20-22,24,67-72 For 1D nanotubes, the channel diameter can be measured from the space group of the nanotubular structure assuming the channel is the van der Waals surface, where each atom on the cross section of channel is consid ered as the van der Waals atom.73 For example, the L-alanly-Lvaline (AV) dipeptide nanotubes ar e the polycrystalline materials in which the AV molecules can form a self-assembled host channel structur e. The crystal of AV is hexagonal with a P61 space group. Since the channel pore of AV is not a r ound shape and the atoms forming the channel interior are not uniformly distri buted, the average value of diamet er is used to express the van der Waals internal diameter of AV channel, which is 5.13 .74
39 2.3.3 Xe Chemical Shift The 129Xe chemical shift is well-known as its extremely high sensitivity to the interactions with the local environments. It is a mono-at omic gas with a very large and spherically symmetrical electron cloud. Any distortion of the el ectron cloud can be refl ected directly at the level of the nucleus and is conseque ntly expressed as a variation of 129Xe NMR chemical shifts. An overview over the accessible chemical shift range of 129Xe NMR is given in Figure 2-8. It shows that the range of Xe chem ical shift is up to 7500 ppm, extremely large compared with most other NMR sensitive nuclei. In Xe gas pha se, interatomic collisions can distort the Xe electron clouds so that the nucleus becomes deshielded and 129Xe resonance fre quency increases (or shifts to down-field) with increasing Xe ga s density. The natural reference of Xe chemical shift in the gas phase is typically extrapolated the chemical shift to zero pressure. Jameson and co-workers75,76 described the chemical shift of dilute Xe gas in terms of virial expansion 2 ,012,XegasXeXeXeTTT (2-25) where 0 is reference chemical shift, X e is Xe density, T is temperature, and i are the virial coefficients of the shielding. Likewise, the obser ved Xe chemical shift can be expressed by the weighted average of several interactions on the NMR time scale.77 ,0 XesSXeXeEM (2-26) where 0 is Xe reference shift, s reflects the interactions between Xe and solid surface, which does not contain any electrical charges. In such a case, s depends only on the dimensions and shapes of pores in solids, and does not depend on Xe density. X eXe arises from Xe-Xe interactions. It is expected to vary linearly w ith Xe density at low Xe pressure and to become predominant at high Xe density.78 E and M are due to the electrical and magnetic field caused
40 by cations in the porous materials, respectively. In general, the smaller pore dimensions and/or slower Xe diffusivity inside the pores, the larger the s chemical shift value.78 Figure 2-8. Chemical shift range of 129Xe NMR with examples of specified materials. The chemical shift is referenced to Xe gas extrapolated to zero Xe density.(Adapt from Ref 79 ) Currently, the studies of zeolites by thermally-polarized 129Xe NMR have already been highly successful.5,6,12,80-84 Several models have been proposed to quantify the relations of s chemical shift and porous geometry in nanoporous sy stems, especially in zeolites, under various experimental conditions.19,83,85-88 It has formed a standard technique for the characterizations of nanoporous materials.78 2.4 Introduction to Hyperpolarized 129Xe NMR In light of quantum physics pict ure, the nuclear spin polarizat ion can be artificially aligned along the quantization axis defined by a uniform magnetic field, yieldi ng hyperpolarization, which is far beyond the polarization in Boltzmann equilibrium. There are various techniques which can achieve the hyperpolarization. In this dissertatio n, the hyperpolarized 129Xe gas was generated from spin-exchange optical-pumping (SEOP), which will be discussed in Section
41 2.4.2. With four to five orders of magnitude of the signal enhancement over Boltzmann polarization, hyperpolarized 129Xe NMR can greatly facilitate th e studies of surfaces, nanotubes, and biological applications. 2.4.1 Improvement of NMR Sensitivity In addition to achieve high 0B and low T, there are a variety of techniques developed to improve NMR sensitivities. For example, transferring polarization from highnucleus to lownucleus in solid is used routinely and is well-known as cross-polarization (CP).89,90 More recently, NMR remote detection technique has b een successfully developed, and allowed to separately optimizing the en coding and detection for NM R and imaging experiments.91-98 It has demonstrated a significant amplifi cation of signals on NMR and MRI. Besides NMR sensitivity enhanced techniques me ntioned above, in the past two decades, it has witnessed the developments of several met hods to enhance polariza tion of nuclear spins, including dynamic nuclear polarization (DNP), para -hydrogen induced polarization (PHIP), and optical-pumping NMR. Dynamic Nuclear Polarization (DNP) In DNP, the large spin polarizati on of electrons can be transfe rred to nuclei, leading to an enhancement of nuclear spin polarization, which is maximally /en ( e.g. ~600 for 1H). The polarization transfer relies on th e electron-nuclear mutual spin-flip which was first predicted by Overhauser99 and was demonstrated experimentally by Slichter et al .100 DNP has been integrated with high resolution solid-stat e NMR experiments in polymers101,102 and biological solids.103-105 More recently, with the developments of solubl e polarized agents, DNP has been employed in the aqueous systems to investigate metabolism106, proteins dynamics,107 and paramagnetic ligand
42 systems.108 Additionally, DNP has been used to e nhance the contrast of NMR imaging by polarizing the protons in water molecules.109-111 Para-Hydrogen Induced Polarization (PHIP) Twenty years ago, Bowers and Weitekamp112,113 discovered that the catalyzed hydrogenation of small organic molecules with para -hydrogen ( p -H2) can produce a highly ordered spin state, leading to intense and antiphase NMR signa ls for the corresponding protons. This phenomenon arises from the quantum sta tistical mechanical properties of dihydrogen. The equilibrium ortho/para ratio is about 3:1 at room temperatur e, whereas at liquid nitrogen temperature (~77 K) the rati o shift toward almost pure p -H2. However, to detect the enhanced NMR signal, the equivalence of two hydrogen atoms has to be broken. The symmetry of p -H2 can be eventually broken by appropriate hydr ogenation reactions, where two protons of p -H2 attach at the magnetically inequivalent sites on the substrate molecules. The p -H2 has a long lifetime at room temperature, and transfer of the polarization from p -H2 to interesting nuclei has been demonstrated.114-116 The induced polarization of p -H2 in the heterogeneous hydrogenation reaction has recently been reported.117 This technique allows a direct visualization of mechanism of heterogeneous hydrogenation reactions118, and has been used to study the micro-fluidic device.119 Optical Pumping NMR Optical pumping NMR (OPNMR) experiments transfer polarization from photons of circularly polarized light to electron spins and/or nuclear spins. Applications of OPNMR have been involved in the studies of semiconductors120-123 ( e.g. GaAs quantum wells, and InP semiconductors) and in the productions of hyperp olarized noble gases through optically pumped rubidium vapors.2 Four to five order of magnitude of sensitivity enhancement has been achieved
43 by OPNMR. Moreover, hyperpolarized 129Xe can further tran sfer the polariza tion to neighboring nuclei, especially to the surface nuclei, t hough SPINOE (Spin Polarization Induced nuclear Overhauser Effect) 124-126, Cross-Polarization127-129 and thermal mixing130,131 mechanism. Recently, a biosensor containing hyperpolarized 129Xe has been developed and several applications in aqueous systems have been reported.26,132-135 2.4.2 Optical Pumping and Spin Exchange Spin-exchange optical-pumping (SEOP) is th e technique commonly applied for producing hyperpolarized noble gases. The utilization of SE OP for the polarization of noble gases was first demonstrated by Happer and co-workers.136,137 SEOP involves two proce sses: Firstly, in optical pumping, angular momentum is transferred from phot ons of a circularly pol arized laser beam to alkali metal electrons. Secondly, the angular momentum is transf erred from polarized electron spins of alkali metal to unpolari zed nuclear spins of noble gas th rough spin-exchange collisions. Optical Pumping The large population difference between sublev els of ground state in an atom can be obtained by polarized light, which was first discovered by A. Kastler.138 This idea was named optical pumping. Rubidium metal is the mo st common alkali metal in optical pumping experiments because it has an appropriate vapor density ( i.e.12153610~10cm) at moderate temperatures (100-200 oC ).139 Another advantage is the D1 tr ansition line (794.7 nm) for Rb is available for high power tunabl e commercial diode lasers. Rubidium has two stable isotopes: 85Rb (5/2 I ) with 72.2% and 87Rb (3/2 I ) with 27.2% natural abundance. The electron total angular momentum is JSL where electron spin is 1/2 S L is the orbital angular momentum, with 0 L for s state and 1 L for p
44 states. The atomic total angul ar momentum is defined as FJI When an external magnetic field 0Bis applied, the Hamiltonian of Rb is137,140 0ISI RbsBzz H AgSIB I (2-27) where the first term is hyperfine interaction between nuclear spin I and electron spin Sof Rb, and A is the hyperfine coupling constant. The last two terms represent the magnetic-dipole couplings of electron and nuclear spins to the magnetic field, in which 2.00232sg is g value of electron, I is nuclear spin quantum number; B and I are Bohn magneton and nuclear magnetic moment, respectively. A weak magnetic field, such as 10-20 gauss, is typically used in the optical-pumping experiment, such that th e hyperfine interaction is dominant and the eigenstates of the Hamiltonian in Eq. (2-27) ar e also eigenstates of total angular momentum Fand its projection along magnetic field z F Figure 2-9 is displayed the schematic diagram of 87Rb energy levels as various interactions applied to the Bohr model. A si milar diagram can be obtained for 85Rb isotope with additional total angular momentum values of F =2 and 3 for 5S1/2 and 5P1/2. In the presence of a weak external magnetic field, the Zeeman splitting of atomic energy levels can be neglected. The electron in the ground state can tr ansit to higher energy states by the absorption of photons with matching D1 transition wavelengths.
45 Figure 2-9. The 87Rb energy levels with spin orbital interaction, hyperfin e interaction, and Zeeman splitting in the presence of a weak external magnetic field. (The splitting of energy levels is not shown on the same scale) The selection rules for the allowed tr ansition correspond to the incident photon polarization with respect to the ma gnetic field. By irradiating with a circularly polarized light to Rb atoms, the allowed transiti on of electric dipole radiation is 1Fm If negative helicity of light ( ) with respect to the magnetic field directi on is applied, the transition of electron is restricted to 1Fm The lifetime of excited state is about 10-8-10-9 sec. and electrons relax back into ground states following the selection rule of 0,1Fm .137 If the pumping light is continuously irradiated, it causes strong depopulation of high Fm ground state towards lower Fm ground state. The net result is that the populat ion will be eventually accumulated on the lowest Fm ground state. For example, for pumping light, the electr ons will be ultimately
46 populated onto 2Fm state for 87Rb, as shown in Figure 2-10. It results in the highly polarized electron spins of 87Rb. If the positive helicity of polarized light ( ) is applied with respect to the magnetic field direction, transition pr ocess is reversed, yielding the highest Fm ground state being polarized. Figure 2-10. The 87Rb ( I =3/2) optical pumping for negative circularly polarized light in a weak external magnetic field. According to selection rule, allowed transition is 1Fm for light. The values on each transition lines are represented the relative transition intensity 2 tE I E The emissive transitions from the excited states, which follow the 1,0Fm and non-radiative decay processes, which lead to the accumulation of atoms in the polarized state are not shown Spin Exchange In the spin-exchange collision, the Rb electron is flipped by coupling w ith the nuclear spin of colliding Xe atom. A spin exchange can be described schematically in Figure 2-11. The Fermi-contact hyperfine interac tion between electron spins ( S ) and nuclear spins of noble gas ( I ) is given by SI 2zzSISISI (2-28)
47 where is the coupling constant, which is depended upon the relative distan ce between electron and nucleus. The flip-flop term in the bracket of Eq. (2-28) is responsible to the spin exchange. This process is critical because the spin temperature of Xe nuclear spin is reduced through the collisions with Rb spin by forming van der Waals complexes.137 Figure 2-11. Spin-exchange between Rb and Xe. Blue color represents cold spin with higher polarization, and red color represents hot spin w ith lower polarization. The polarization is transferred fr om highly polarized electron sp in of Rb to unpolarized nuclear spin of Xe through collisions. Buffer gases, usually nitrogen and helium ga ses, are mixed with Rb vapor in order to increase the optical-pumping effi ciency. There are several reasons for the presence of buffer gases in the optical-pumping gas mixtures: (1) que nching the fluorescence of the excited state, (2) collision mixing of excited state, and (3) pr essure broadening of D1 adsorption line. Nitrogen gas is commonly used in the gas mixture to quench the Rb excited state energy into its vibrational level.136 Collisions of Rb atoms with buffer ga ses, especially helium, result in a mixing of atomic sublevels. It has been reporte d the optical-pumping efficiency can be increased
48 1/3 to 1/2 by the collision mixing of Rb excited states.137 Another advantage of using large quantities of buffer gases in optical pumping is the pressure broadening of Rb spectral lines, which is a consequence of interactions betw een Rb electronic cloud a nd buffer gases through collisions. The Rb adsorption profile is charac terized by the Doppler br oadening with the value 1GHz.35 The spectral width of commercially availa ble high-power laser diode array (LDA) is typically 760-1500 GHz, which is much greater than Rb adsorption line.35 The pressure broadening by buffer gases can increase the Rb D1 absorption line-width up to ~20 GHz/bar in order to improve the adsorption efficiency of LDA.141 2.4.3 Continuous-flow Hyperpolarized 129Xe NMR In the case of thermally-polarized 129Xe NMR, numerous studies have demonstrated that it is an extremely sensitive probe for chemical and physical environments. However, due to the typically long 129Xe 1T relaxation time and low spin pol arization, thermally-polarized 129Xe NMR usually requires long recycl e delay and numerous signal av eraging, resultin g in lengthy acquisition time. As mentioned pr eviously, the development of SEOP has led to the use of hyperpolarized (HP) 129Xe for NMR sensitivity enhancement. The batch method of hyperpolarized 129Xe NMR was first developed by Al ex Pines group at Berkeley.16 An isolated pumping cell with valves is regular ly filled with Rb metal and fresh Xe gas mixtures. After Xe is optically polarized, the gas mixture is transf erred to NMR probe by gas expansion. Several surface studies have been successful ly investigated by hyperpolarized 129Xe NMR batch method. 16,142,143 The continuous-flow hyperpolarized (CFHP) 129Xe NMR method was developed in Happers group at Princeton.144 The gas flow rate, typically 2 to 20 sccma for 129Xe, allowed for a sccm: standard cubic centimeters per minute
49 129Xe gas to be polarized to hyperpolarization steady state dur ing few minutes and to pass through the pumping cell.35 After leaving the pumping cell, th e gas mixture containing polarized Xe flowed through NMR sample and 129Xe NMR signal was acquired. It takes advantage of retaining high Xe spin polarization during the en tire course of NMR experiments. For CFHP 129Xe NMR, Xe spin polarization can be replenished on a time-scal e determined by the gas flow rate, not by the 129Xe longitudinal relaxation time. As a co nsequence, the NMR recycle delay is not limited by the long 129Xe 1T relaxation time, permitting phas e cycling, signal averaging, and a variety of multi-dimensional NMR experiments. In particular, the sensit ivity of hyperpolarized 129Xe NMR is 4 to 5 orders of magnit ude greater than thermally-polarized 129Xe NMR, thereby making the applications of 129Xe NMR or MRI more practical. In addition, a variety of systems that deliver polarized 129Xe gas to NMR sample have been designed.35,145-148 All of these developments aim to achieve maximum 129Xe polarization that can be delivered to NMR samples. Moreover, a nu mber of experimental variables, including gas pressure, flow rate, laser power, and gas compos ition, have been carefully examined in an attempt to optimize the 129Xe polarization.35,145 A polarization of 2-20 % is currently a standard degree for 129Xe continuously-flow optical polarizer with an output to 1 L/hour of hyperpolarized Xe.2 For large quantities, a much higher degree of polarization of approximately 70% has been reported.145 To extend the application of 129Xe NMR to a wide range of systems, it would be significant to develop an apparatus whic h can efficiently perform hyperpolarized 129Xe NMR experiments, especially in the continuous-flow operation mode. 2.4.4 Development of Continuous-flow Hyperpolarized Xe Polarizer The NHMFL-UF 129Xe polarizer was designed by Anthony Zook, a former Ph.D. student in our group.35 By using a 150 Watt fiber-optic coupled laser diode array (LDA) and after
50 systematic optimization of the pumping ga s composition and operating conditions, the UF polarizer achieved a record of 68 % Xe spin polarization.35 When our lab moved from Leigh Hall to the New Physics Building in November 2005, we took the opportunity to redesign and reassemble the gas handling system to improve the efficiency and flexibility for various types of experiments. The schematic design is presente d in Figure 2-12. The optical pumping systems, including optical polarizer, pumping cell, and Helmholtz pairs, were installed on the laser table. The gas handling system was mounted on a home-built aluminum table which was built on the top of optical pumping system. The entire gas handli ng system was located in the fringe field of 20 gauss Helmholtz pairs to retain the Xe polari zation during gas recirc ulation. In addition, the gas handling system is about 2 ft. closed to 9.4 T NMR magnet to prevent the depolarization of hyperpolarized 129Xe gas during the transportation to NMR samples. Approximately 0.2 g of Rubidium metalb was filled into the optical pumping cell. The procedure of filling the Ru metal was performed in a dry N2 glove box to prevent Rb from oxidation and contaminations. The oxygen trapc was installed outside the gas re-circulating loop in order to remove the oxygen in gas cylinders before entering the gas handling system. To extend the lifetime of pumping cell, the gas purifi cation device, such as a rubidium reservoir or titanium getter, can be installed in the inlet of the pumping cell.147 Such device can help pick up the impurities before entering the pumping cell and reacting with rubidium. For experiments which required the accumulation of hyperpolarized Xe gas, 1 Liter of ballast tank can be used to increase the volume of Xe gas. Two 3-way valvesd were installed in the inlet and outlet of NMR sample holder. It allows the ga s handling system to be isolated while changing the NMR samples. The total volume of the gas re-c irculating system (without 1L ba llast tank) is approximately b part no.: 44214; Alfa-Aesar, Ward Hill, WA. c part no.: Model-4002; Alltech Associates Inc., Deerfield, IL. d part no.: B-42XS4; Swagelok, Solon, OH.
51 350 mL The details of spin-exchange optical-pumping apparatus were described in our previous work.35 Figure 2-12. Continuous-flow hyperpolarized 129Xe apparatus.
52 We have completed the modification of th e Bruker wideline probe for continuous-flow hyperpolarized 129Xe NMR experiments on solid samples. The NMR sample holder was constructed using 1/4 O.D. ( outside diameter) PEEK (polyeth eretherketone) tube with two vacuum-tight fittingse on both ends. The inside diameter of sample holder is 1/16 and the length of sample holder in the detection coil region is 0.3. The volume of sample holder within RF coil region is only 15 L, and it is particularly well adapted to the experiments with relatively small amounts of sample ( i.e. 10-20 mg). The 1/8 PFA (perfluoroa lkoxy) tubings were connected to the inlet and outlet of the sample holder ( see Figure 2-12). This assembly allows polarized Xe gas flow through the entire samp le in order to retain the maximum Xe polarization during experiments. A 9-turn detection coil for 129Xe resonance frequency (=110.7 MHz at 9.4 Tesla magnet) was wound directly around the sample holder. The /2 pulse width is typically 4 s. The Rb absorption has been optimized as a function of the optical pumping cell temperature, as shown in Figure 2-13a. Fi gure 2-13b presents the flow-rate dependence of 129Xe spin polarization at fo ur different pumping cell temperatur es. The temperatures of optical pumping cell were read directly from the therma l couple located outside the inlet of the pumping cell. The measured temperature in Figure 2-13 ma y not reflect the actual temperature of Rb in the pumping cell, since it was found the temperat ure in the pumping cell was not uniformly distributed during the optical pumpi ng process in th e current setup.35 The maximum 129Xe polarization obtained by the current polarizer is about 20 % at a flow rate of 150 mL/min and at pumping cell temperature of 125 oC with 100 W LDA laser pow er. The Xe polarization measurements were conducted by using 2% Xe /2% N2 /96% He gas mixture.f The typical hyperpolarized and thermally-polarized 129Xe NMR spectra in the gas phase were shown in e Nuts, part no.: AT37075; Ferrules, part no.: AT201271; Alltech Associates Inc., Deerfield, IL.. f part no.: ISO-XHN-C; Spectra Gases Inc., West Branchburg, NJ.
53 Figure 2-13. The application of CFHP 129Xe apparatus affords enormous NMR sensitivity, allowing numerous experiments to be rapidly and systematically performed under varying conditions ( i.e. variable temperatures a nd Xe partial pressures). (a) (b) Figure 2-13. (a) Optical transmission spectra of Rb vapor in the pumping cell at four different cell temperatures (100, 125, 145, 165 oC ) at a total gas pressu re of 3000 torr (2 % Xe mixture) at 100 W laser power. (b) Flow-rate dependence of Xe spin polarization at different pumping cell temperatures. 1200 1000 800 600 400 200Transmitted Intensity (a.u.) 798 796 794 792 790Wavelen g th ( nm ) 100oC 125oC 145oC 165oC Top 20 15 10 5Xe Polarization (%) 200 150 100 50 0 Flow rate ( mL/min ) 100oC 165oC 145oC 125oC Top
54 Figure 2-14. (a) Hyperpolarized 129Xe NMR spectrum (single scan). 2% Xe mixture with total gas pressure of 2327 torr under flow rate of 100 mL/min. Pumping cell temperature is 145 oC with 100 W laser power. The Xe polari zation is about 27 %. (b) Thermallypolarized 129Xe NMR spectrum (16 scans). Xe pressu re is 1557 torr in the presence of 635 torr O2 to reduce the Xe 1T Both spectra were acqui red by the modified Bruker wideline probe with empty sample holder at room temperature. 1.0 0.8 0.6 0.4 0.2 0.0x106 -15 -10 -5 0 5 10 15 (pp m ) 15 Hz (a) (b) x20
55 CHAPTER 3 INVESTIGATIONS OF THERMODYNAMIC PR OPERTIES IN DIPEPTIDE NANOTUBES BY HYPERPOLARIZED XE-129 NMR 3.1 Introduction Xenon-129 NMR has been extensively used in th e structural characterizations of porous materials. As mentioned previously, the major advantage of 129Xe NMR is the extremely high sensitivity of the Xe chemical shift to the local environment of Xe atoms. Although in many cases the 129Xe chemical shifts of the adsorbed sites and free Xe ga ses can be clearly distinguished, the main obstacle to using 129Xe NMR for structural characterizations is that as the Xe atoms are in fast exchange among the multiple -adsorbed sites, an observed chemical shift represents a dynamical average of Xe on each adsorbed site ; therefore, it cannot be attribut ed to a specific location. Analysis of all th e contributions of Xe to the obs erved chemical shift is usually very complicated. In recent decades, numerous em pirical relations between the Xe chemical shift and pore geometry have been successfu lly developed to solve this problem.3,9,149-151 However, the extraction of the structural information, such as porosity and pore dimensions, still requires the combination of 129Xe NMR and other methods, such as adsorption isotherm. The adsorption property of porous materials ha s been emerging as an attractive issue of recent researches boosted by promising industrial and environmental applications, such as gas storage.69,72,152,153 The key issues of the development of novel porous materials for the gas storage are to understand (1) how the adsorbates in teract with the frameworks, (2) which specific regions adsorbates are located, and (3) how long adsorbates reside in the specific regions. Hyperpolarized 129Xe NMR is particularly suitab le to answer these questions. More recently, the organic-based framewor ks, such as self-assembled dipeptide nanochannels, have attracted consider able attention in the basis of gas storage. Unlike artificially
56 created nanotubular materials, dipeptide nanotubes can be constr ucted naturally by self-assembly of dipeptide molecules. Recent adsorption studies of dipeptide nanotubes have revealed that the peptide-based adsorbents have large gas storage capacities to particular guest molecules (He and Xe).68,74 In addition, the adsorption be haviors of dipeptide nanotubes with small sizes of cavities match the zeolite-mimics, and have been recognized as biozeolite.68 Therefore, it is of great interest to use the dipeptide nanotubes as simple models to investigate the molecular architectures and adsorption properties by hyperpolarized 129Xe NMR. In this chapter, the co ntinuous-flow hyperpolarized 129Xe NMR has been utilized to explore the adsorption properties of Xe in the 1D self-assembled AV dipeptide nanotubes. The anisotropic Xe line-shapes arising from confin ement of Xe atoms in the AV channels were observed. Additionally, the Xe adsorption propertie s in AV and the quantitative measurements of thermodynamic parameters will be described. 3.1.1 Determination of Adsorption Enthalpy from Xe Chemical Shift Xenon has a van der Waals diameter of 4.4 co mparable in the size to that of methane (4.3 ). The small atomic diameter of Xe enable s it to penetrate almost any sizes of porous materials through exchange and diffusion, conseque ntly adsorbing onto the specific locations. The observed chemical shift of the adsorbed Xe varies by over 300 ppm for most materials, and it is extremely sensitive to the local environment of Xe.2 In most of the continuous-flow hyperpolarized 129Xe NMR studies, a gas mixture containing a low density ( c.a. 20-200 mbar) of 129Xe is optically polarized and tr ansported to the NMR sample space35, and thus the dilute adsorption regime (Henrys law) can be appli cable. The isotropic spectral line-shape in the adsorbed Xe phase, which is typically observed in the hyperpolarized 129Xe NMR spectrum, can be interpreted as a result of a fast exchange between adsorbed Xe and free Xe atoms located in
57 the interporous spaces of the materials. In such a case, the temperature dependence of observed Xe chemical shift can be expressed by th e equation based on the fast-exchange model154 1 01 exp(/)obss aV SKRTHRT (3-1) where s is the characteristic chemical shift, repr esenting the chemical shift arising from Xesurface interactions, V and S is the free volume inside the adsorbent and specific surface area of the materials, respectively. 0 K is Henrys law constant, a H is the adsorption enthalpy, R is the gas constant, and T is the temperature. This equation e xhibits that the observed chemical shift must be Xe pressure independent, since Xe-X e interactions in the dilute Xe system can be neglected. The values of V and S can be obtained from a volumetric N2 adsorption isotherm, and other parameters, s 0 K and a H can be determined by the non-linear least-squares fits of the observed Xe chemical shifts (obs ) as a function of temperatur e according to Eq. (3-1). Since hyperpolarized 129Xe NMR only requires a low Xe density to achieve high NMR sensitivity and gas mixtures of low Xe com positions are commercially available, the Xe adsorption enthalpy in porous materials determined by Eq. (3-1) has recen tly become a standard technique for hyperpolarized 129Xe NMR. The adsorption enthalpies of several materials, such as silica155-157, Vycor Glass158 and zeolite159,160, have been measured acco rding to this technique. However, for some unique systems, such as 1D nanotubes with narrow pores, much higher Xe pressures are required to force Xe atoms adsorb into the pores.161-165 In this case, the chemical shift arising from Xe-Xe inte ractions becomes more pronounced, and Henrys law is no longer valid. Therefore, in such systems, alternative ap proaches to measure the Xe adsorption enthalpy are needed.
58 3.1.2 Xe Anisotropic NMR Line-s hapes in 1D Nanotube Systems In most cases, Xe exhibits a symmetric NMR li ne-shape; however, when Xe is confined in a small void space where the size is on the same or der as the Xe atom, the chemical shift depends on the geometry of the pore space and its orientati on with respect to the external magnetic field, resulting in an anisotropic chemical shift po wder pattern in polycrystalline samples. The information on the symmetry of the pore spaces can be extracted by the chemical shift tensor, thereby providing a useful tool for the characterizations of the porous structure.19 The Xe anisotropic NMR line-shape has been discovered previously in various materials, including clathrates166, aluminophosphate (AlPO4)167, tris(ethylenediamine) cobalt (III) chloride (()-[Co(en)3]Cl3)165, tris( o -phenylenedioxy) cyclotriphosphazene (TPP) 20,24, and dipeptide nanotubes.21,68,74 Although the components of the chemical shift tensor can be characterized by the orientations of the tensor with respect to the external magnetic field, in a 1D cylindrical channel its orientation is identical to the orient ation with respect to the principle channel frame system. In the axially symmetric chemical shift tensor, and are assigned to be parallel and perpendicular to the channel axis respectively. The anis otropy of the axially symmetric shielding tensor is given by An inversion in the sign of the CSA has been discovered pr eviously by increasing the Xe density at constant temperature in several ma terials with 1D pore structure, such as TPP20 and dipeptide nanotubes.21 This CSA sign inversion is the resu lt of a competition between the Xe-Xe and Xe-wall interactions which have differe nt contributions to the shielding tensor.19,20 The Xe occupancy dependence of the axially symmetric CSA line-shape, and the corresponding tensors and interactions are summarized in Table 3-1.
59 Table 3-1. Summary of axial symmetric CSA tensors ( =0) in 1D single-file channel The intermolecular Xe shielding of Xe conf ined in 1D nanochannels has been studied theoretically by Jameson.19 In 1D channel, two t ypes of interactions need to be considered: Xewall and Xe-Xe interactions. In the case where the confined Xe cannot transverse ly pass oneanother inside the channel, is mainly attributed to the Xe-wall interaction, while is mainly influenced by the Xe-Xe interaction. The shieldin g tensor in 1D channels can be described by an ellipsoidal, as shown in Table 3-1. At low Xe density, the Xe becomes prolate where includes the interaction with the atoms forming the interior s of channel wall. On the basis of this fact, must be the smaller shielded component, f ree where f ree represents the chemical shift of free Xe. Such order is valid when Xe-Xe interaction is relatively small in the channel. When a sufficient amount of Xe atoms are adsorbed into the channel such that Xe-Xe interactions become significant, a change in the component can result. The Xe-Xe interactions will give rise to an observable contribution to leading to less shielded
60 component, f ree This effect will be more pronounced as the Xe occupancy progressively increases. A mu ch larger deshielding on than is expected by increasing the number of adsorbed Xe atoms in the channels. Therefore, the Xe occupancy of the 1D channel can be inferred from the component. 3.1.3 Dipeptide Nanotubes Recently, various inorganic and carbon-based nano-materials, such as nanocavities and nanotubes, have been used as building blocks to assemble the nanometer-scale supramolecular structures. In particular, the class of self-asse mbled dipeptide nanotubes has been proven to be practical in the design of solid-state porous materials168-170, soluble cylindrical supramolecular structures171, and biologically relevant ion chan nels and transmembrane pore assemblies.172,173 While the concept of applying biological nano-ma terials, such as dipeptide nanotubes, as building blocks is relatively new, the self-assembly of peptides has been investigated extensively for decades.174-177 Since the dipeptide molecules can effi ciently form into exact 1D crystal structures with certain hydrophobi cities by the self-assembly, they can serve as an ideal model system for the advanced studies.178 L-alanylL-valine (AV) is one of the dipeptide compounds which can form essentially defect-free 1D cylindri cal structure through self-assembly. C onfinement of Xe atoms into such structures results in an effectively 1D Xe nanot ube phase. The chemical structure of AV and its self-assembled 1D channel are illustrated in Figu re 3-1a and b, respectively. The inner diameter of the AV nanotube is 5.13 which is slightly larger than the 4.4 van der Waals diameter of Xe atom.74 Furthermore, AV is thermally stable and does not decompose or have any phase transitions up to the melting point of 238 oC .74 As shown in Figure 3-1c, the hydrophobic channels of AV are lined with -CH3 groups,74,179 providing a favorable Xe adsorption
61 environment with extremely high Xe storage capacity ( 60 mL/g).74 In addition, the polycrystalline sample of AV is commercially available and inexpensive (~$35 USD for 250 mg of AV samples). Hence, AV represents an ideal single-file model system in the present study. Figure 3-1. (a) mol ecular structure of L-alanylL-valine. (b) Space-filling model of AV nanotube viewed along the channel axis.74 (H: yellow, C:green, O: red, N:blue )(c) Stick packing arrangement of AV.178 The channel walls are lined with -CH3 groups, providing the hydrophobic inte rior of AV nanotubes. It has been reported recently that the 129Xe NMR line-shapes in AV nanotubes strongly depend on Xe-Xe and Xe-wall interactions. Ripmeester et al. studied the Xe occupancy dependence of 129Xe NMR chemical shifts in AV nanot ubes and found that the adsorption properties of AV are very similar to TPP.21,68,74 A sign inversion of the Xe shielding anisotropy in AV as varying the Xe density has been observed by the thermally-polarized 129Xe NMR at room temperature.21 Moreover, as Xe atoms adsorbed in to the AV nanotubes, they come into close proximity to the protons and carbons of th e methyl groups on the interior channel walls, and the 129Xe-1H and 129Xe-13C dipolar interactions can become significant. In principle, such dipolar couplings and the associ ated dipole-dipole induced nucle ar spin cross-relaxation could facilitate polarization tran sfer from hyperpolarized 129Xe to the nuclei of AV, such as in the
62 SPINOE. However, the efficiency of polariz ation transfer depends strongly on the 1T relaxation time of the contacted nuclei. While the 129Xe 1T relaxation time in AV nanotube is on the order of 50-150 sec in 9.4 T, depending on the Xe density180, the 13C 1T relaxation times on the various carbon atoms of AV can be expected to vary with the local environment. For example, the methyl group 13C 1T can be expected to be very short ( c.a. several 100 ms, see Table 3-2) due to the methyl rotation which provides an effici ent leakage mechanism for any non-equilibrium nuclear spin polarization that might be bui lt-up by the SPINOE. Thus, it is essential to understand the 1T relaxation times of 13C in AV nanotubes when contem plating spin polarization transfer experiments. 3.2 Experimental 3.2.1 13C T1 Relaxation Experiment All 13C magic-angle spinning NMR spectra we re acquired on a Bruker Avance 400 MHz spectrometer operating at a 13C frequency of 100.62 MHz and at r oom temperature using a triple resonance probe with a 4.0 mm ro tor. Approximate 100 mg of AVa sample was packed into a 4 mm Zirconia rotor with a Kel-F cap. For this amount of material, 32 transients were required to obtain 13C spectra with an acceptable signal-to-noise ratio. 13C chemical shifts were referenced to tetramethylsilane (TMS), and NMR parameters were optimized on a sample of adamantane. Typical experimental parameters were as follows: 13C 2 pulse width, 2 s; recycle delay, 100 s; spectral width, 40 kHz; sample spinning rate, 6 kHz. The time-domain signals were apodized using a line broadening of 50 Hz prio r to the Fourier transformation. High-power proton decoupling ( see Figure 3-2) was utilized in the 13C 1T inversion-recovery measurements. a part no.: 0210032883; MP Biochemicals, Santa Ana, CA
63 The 1T values were obtained by the least-squares fits of a mono-exponential function to the dependent inversion-rec overy signals of the 13C nuclei in AV. Figure 3-2. Carbon-13 inversio n-recovery NMR pulse sequence with proton decoupling during signal acquisition. 3.2.2 Hyperpolarized 129Xe NMR Experiments Continuous-flow hyperpolarized 129Xe NMR experiments were performed on a 15 mg sample of AV in a magnetic fi eld of 9.4 T field using a modified variable temperature wideline probe. The polycrystalline AV samp le was loosely packed into th e sample holder and evacuated at 100 oC for 2-3 hours prior to NMR measurements Details of the Rb-Xe spin-exchange optical-pumping system were described in Section 2.4.4. The ultra-pure (99.999%) 4He gasb was used as a buffer gas to adjust th e concentration of nature abundance 129Xec at a total pressure of 4600 mbar Xe/He gas mixture. The gas was con tinuously re-circulated between the optical pumping cell and the NMR sample space at a flow rate of 100 mL/min Hyperpolarized 129Xe NMR spectra were acquire d on the Bruker Avance 400 NMR spectrometer using a one-pulse sequence with a /2 pulse width of 4 s and a recycle delay of b part no.: UN1046; Praxair, Danbury, CT c part no.: XE5.0RS-D8; Praxair, Danbury, CT
64 200 s. With the hyperpolarization signal enhancem ent, only a single scan was necessary to obtain the sufficient signal-to-noise ra tio. Variable temperature experi ments were carr ied out over a temperature range of 100 to -70 oC The 129Xe chemical shift was referenced to dilute Xe gas as 0 ppm. The CSA spectral line-shapes were fit by a Matlab programd to obtain the components of chemical shift tensor, and Hyperpolarized Xe 2T measurements were performed at two Xe partial pressures (92 mbar and 3300 mbar) at -10 oC using the Hahn spin-echo pulse sequence, /2.echoecho x xx A cq. 3.2.3 Scanning Electron Microscopy The scanning electron microscopes (SEM) im age of the polycrystalline AV sample is shown in Figure 3-3a. It was recorded usin g a JEOL 6400 at the UF Major Analytical Instrumentation Center. The nanotube lengths of AV were measured in the SEM images taken from four different areas of the polycrystalli ne AV sample. The length distribution of the AV crystallites is presented in Figure 3-3b. The aver age crystallite length in the AV sample was found to be 29.42.1 m. Assuming no internal defects th at might block the channels, the distribution of crystallit e lengths should be equivalent to the distribution of channel lengths. d The Mathworks Inc., Natick, MA.
65 (a) (b) Figure 3-3. (a) SEM Image of AV polycrystalline nanotubes. (b) Di stribution of ch annel lengths in AV nanotube samples. The av erage channel length is 29.42.1 m (n=38). 3.3 Results and Discussions 3.3.1 13C T1 Relaxation Measurements in AV Inversion-recovery 13C NMR spectra acquired as a function of recovery time in AV nanotubes at 25 oC are shown in Figure 3-4, and the assignment of the 13C NMR peaks is listed in Table 3-2. In most solid samples, molecula r motions are generally in the slow motion regime, where the correlation time of the motion is gr eater than the inverse Larmor frequency (1 co ), leading to an increase in 1T as molecular motions are reduced (corresponding to an increase in the correlation time of the motion). Therefore, in the solid state of AV nanotubes, the rigid carbonyl groups (carbon f and g) have longer 13C 1T relaxation times, while the mobile -CH3 side chain (carbon a) on the interior wall of AV nanotube has shorter 1T. Because the 13C 1T of the methyl group (carbon a), whic h is anticipated to be in direct dipolar contact with Xe in AV nanotubes, is extrem ely short (366 76 ms), it is likely infeasible to perform the 129Xe 13C polarization transfer experiment s. However, as the Xe atoms accumulate into the AV channels, the motion of me thyl groups may be sterically hindered by the 12 10 8 6 4 2 0number of channels 45 40 35 30 25 20channel length ( m)
66 confined Xe, leading to an increase in 13C 1T of the methyl group. In addition, the cross polarization transfer efficiency may be increa sed at low temperatures via the anticipated reduction in the correlation time for the 13C-129Xe dipolar coupling. Therefore, it may still be practical to transfer the pol arization of hyperpolarized 129Xe to 13C nuclei on methyl groups in AV. Furthermore, it was found that 13C spectra in AV powder samples were not resolved under the static condition (non-s pinning) due to strong 13C dipolar interactions. For the 129Xe 13C polarization transfer experi ments, the combination of continuous-flow hyperpolarize 129Xe NMR and magic-angle spinning may be required.126 Figure 3-4. Inversion-recovery 13C NMR spectra recorded as a function of recovery time in AV nanotubes at room temperature. The labe ls above the spectra correspond to the carbon atoms in AV shown in Table 3-2. Chemic al shifts were referenced to TMS. 3 2 1 0x106 200 150 100 50 0 ppm 1 ms 50 ms 100 ms 200 ms 1 s 3 s 4 s 5 s 10 s 15 s 20 s 30 s 100 s a b c d e f g
67 Table 3-2. Summary of 13C 1Trelaxation times in AV at 9.4 T and 25 oC Structure of AV carbon 1T a 366 76ms b 173 29ms c 342 50ms d 14 1.8s e 5 0.3s f 18 2.5s g 18 1.8s 3.3.2 Hyperpolarized 129Xe NMR Spectra in AV In the sample space of the CFHP 129Xe NMR probe, the Xe density is increased as the temperature is reduced. Therefore, two factors will be changed simultaneously in the sample space in variable-temperature CFHP 129Xe NMR experiments: Xe density and temperature. Hyperpolarized 129Xe NMR spectra in AV nanotube phase at variable temperatures are presented in Figure 3-5. When 129Xe atoms adsorb into AV, the 129Xe NMR line-shape exhibits an axially symmetric CSA powder patter n, as in TPP nanotubes.20 The isotropic chemical shielding value (iso ) of Xe in AV increases as the temperature is lowered or as the Xe density is increased. The chemical shift anisotropy is strongly depended on the Xe density and temp erature. As illustrated in Figure 3-5, the sign of the anisotropy of the shielding tensor changes from positive 0, at high temperature (or low Xe density), to negative 0, at low temperature (or high Xe density). Since the Xe spectral line-shape arises from an axially symmetric shielding tensor, two unique principle tensor components, and can be measured, as described previously. The former is collinear with the chan nel axis, while the latter point s towards the channel walls. The chemical shielding of is absent in the limit of infinite ly dilute Xe, and increases with increasing Xe density inside the channels, whereas is almost independent of Xe density.19
68 Therefore, the component can be used to quantitativel y determine the Xe density inside the channels. Figure 3-5. Continuous -flow hyperpolarized 129Xe NMR spectra in AV at variable temperatures and 3300 mbar Xe partial pressure at a total gas pressure of 4600 mbar. 3.3.3 129Xe T2 Relaxation Measurements in AV In addition to the orientation dependence of th e chemical shielding of Xe in AV nanotubes, it was found that the transverse 2T relaxation of Xe in AV is also orientation dependent. The transverse relaxation times at two Xe gas pressu res (92 mbar and 3300 mbar) with different signs of the anisotropy in AV were studied at -10 oC by typical Hahn spin-echo experiments, and the hyperpolarized 129Xe NMR spectra are pres ented in Figure 3-6. The 2T values were determined 200 180 160 140 120 100 80 ppm 100 80 60 40 20 0 -20 T/oC 90 70 50 30 10 -10 -30
69 by the least-squares fits to the mono-exponential decay of the signal integrations over the powder peaks as a function of inter-pulse delay, echo The Xe 2T relaxation times at 92 mbar and 3300 mbar Xe pressures in AV at -10 oC are about 10.1 ms and 7.1 ms respectively. As more Xe atoms adsorbed into the channels, the Xe-Xe inte raction dominates over th e Xe-wall interaction, which appears to accelerate the 2T relaxation, lead ing to shorter 2T relaxation time at higher Xe density. Moreover, the 2T relaxations of two shielding components, and are qualitatively compared in Figure 3-6a and b. Interestingly, Xe 2T relaxation of decays more rapidly than that of in both Xe densities. As mentioned previously, is mainly attributed to the Xe-Xe interactions. The observed rapid 2T decay rate in the component which results from the pronounced Xe-Xe interaction is in good ag reement with the results of shorter 2T at higher Xe density. Figure 3-6. Hahn spin-echo Xe NM R spectra as a function of inte r-pulse delay at Xe partial pressure of (a) 92 mbar and (b) 3300 mbar at -10 oC 500 400 300 200 100 0x106 160 140 120 100 80 60ppm (a) echo 10 s 1 ms 2 ms 3 ms 5 ms 10 ms 30 ms 80 60 40 20 0x106 200 180 160 140 120 100 ppm (b) echo 10 s 1 ms 2 ms 3 ms 5 ms 10 ms 20 ms
70 3.3.4 Determination of Xe Occupancy in AV Ripmeester and co-worker have acquired thermally-polarized 129Xe NMR spectra in AV as a function of Xe molar occupancy at 20 oC .21 The experimental and simulated spectra in AV are presented in Figure 3-7. By performing leastsquares fits of the CSA tensor to the 129Xe spectral line-shapes, the two shielding components, and in the axially symmetric CSA tensor can be determined. Since is less sensitive to temperature and most sensitive to Xe density, it can be used to determine the Xe occupancies at variable experimental conditions. Figure 3-8 demonstrates the correlation between and Xe molar occupancy, m The empirical relationship between m and is 0.005360.51964m (3-2) Figure 3-7. (a) Experiment al thermally-polarized 129Xe spectra at 20 oC at various Xe molar occupancies.21 (b) The corresponding CSA spectra were simulated to obtain the shielding components.
71 Figure 3-8. Correlation betw een Xe molar occupancy m and component in AV nanotubes. The solid line is the linear regulation of th e data points. The correlation equation is 0.005360.51964m ( r2 =0.9780) at 20 oC The maximum Xe molar occupancy in AV nanotubes is about 0.525 mol Xe/mol AV, where the AV nanotube is fully occupied by Xe atoms.21 In such a case, the Xe fractional occupancy is 1 The Xe fractional occupancy can be expressed as /0.525m Therefore, the fraction occupancy at arbitrary Xe pressure and temper ature can be determined from the shielding component. The determination of from the Xe chemical shift is extremely convenient and useful for th e systematic hyperpolarized 129Xe kinetic studies in 1D nanotube systems as a function of this key variable. 3.3.5 Isosteric Adsorption Enthalpy of Xe in AV Figure 3-9 demonstrates the temperature de pendences of Xe fractional occupancies at variable Xe densities. The plot is equivalent to a Xe adsorption isobar. Thus, it can be anticipated 0.3 0.2 0.1 0.0molar occupancy, m 160 140 120 100 (ppm)
72 that the Xe isobar curves in Figure 3-9 can provide the information of the adsorption thermodynamics of Xe in AV nanotubes. Figure 3-9. Variation of Xe fractional occupancy with temperature in AV at variable Xe density. (Total gas pressure is 4300 mbar) To analyze the plot of Xe adsorption isobar in Figure 3-9, the Clau sius-Clapeyron equation at a given Xe occupancy was applied ,ln (1/)a XeH dp dTR (3-3) where a H is the isosteric enthalpy of adsorption, R is the ideal gas constant, X ep is the Xe partial pressure, and T is temperature. A se ries of hyperpolarized 129Xe spectra were acquired at variable Xe pressures and temperatures, and the corresponding Xe fractional occupancies were 0.8 0.6 0.4 0.2 0.0Xe fractional occupancy, 100 50 0 -50Temerature (oC ) 100 % Xe 43% Xe 23% Xe 8% Xe 2% Xe
73 measured. The slope of each ln X ep vs.1/T plot gives the isosteric adsorption enthalpy, aH at a given based on Eq. (3-3). As seen in Figure 3-10a, it clearly shows that a H increases with increasing suggesting the importance of Xe-Xe inte ractions in the adsorption enthalpy at high Xe density. The negative sign of the ad sorption enthalpy indicates Xe adsorption is exothermic. The enthalpy can be further extr apolated to zero Xe occupancy, yielding1 ,(0)~10a H kJmol, which is primarily dependent on the nature of the interior AV channel structure and is typical for a process of physisorption. The enthalpy of vaporization at the boiling point of Xe is 12.6 1kJmol Therefore, the estimated value of Xe adsorption enthalpy at zero occupanc y implies the stabilization energy due to the Xe-wall interaction in AV is about 22.6 1kJmol. It can be considered that the Xe-wall interaction results in an effective stabilization of Xe inside the hydrophobic AV channels. It has been proven by using a standard vol umetric Xe adsorption isotherm that Xe adsorption in AV nanotubes follows the Langmuir equation74 1xe x eKp Kp (3-4) where /ad K kk is the equilibrium constant, which is temperature dependent. The equilibrium constant at a given temperatur e can be consequently determined from Figure 3-9 based on Eq. (3-4). As shown in Figure 3-10b, the therm odynamic equilibrium constant increases as the temperature decreases. Furthermore, the equilibrium constant in AV at 20 oC is about 0.1950.114 bar-1, which is consistent with th e literature value of 0.12 bar-1.74 As the temperature is reduced at o10 TC ak gradually increases to the values greater than dk, implying Xe adsorption in AV is more favorab le at reduced temperatures.
74 Figure 3-10. (a) Variation of the Xe isosteri c adsorption enthalpy with the Xe occupancy in AV.(b) Temperature dependence of the Xe equilibrium constant in AV nanotubes. Error bars indicate 95% confidence intervals. 3.4 Conclusions Continuous-flow hyperpolarized 129Xe NMR experiments have been carried out to examine the thermodynamic properties of Xe in AV nanotubes. The 129Xe spectral line-shape exhibited a typical powder pattern broadened by th e anisotropy of an axially symmetric chemical shift tensor. The temperature dependence of th e CSA in AV showed a sign inversion, which is known as a result of the competition between Xe-w all and XeXe interactions in the nanotubes. The Xe fractional occupancy in AV nanotubes ha s been quantitatively determined from the shielding component. Moreover, th e Xe isosteric adsorption enth alpy in AV has been estimated according to the Clausius-Clapeyron equation. The approach is based on the extraction of Xe adsorption isobar under the stea dy-state condition imposed by co ntinuous-flow hyperpolarized 129Xe NMR. The Xe adsorption enthalpy extr apolated to zero occupancy is about 110 kJmol The increase of the adsorption enthalpy at high Xe occupancy suggests that Xe-Xe interaction assists the Xe adsorption in AV nanotubes. The e quilibrium constant of Xe in AV, estimated -25 -20 -15 -10 Xe Adsorption enthalpy (kJ/mol) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 (a) 12 10 8 6 4 2 0 80 40 0 -40 Temperature ( oC ) K=ka/kd (bar1 ) (b)
75 from Langmuir equation, increases at lower temper ature, implying Xe is more favorable to enter AV channels at low temperature. The technique de monstrated in the present work may become a useful tool for the evaluation of fundament al thermodynamic prope rties and quantitative understanding of the adsorption of guest molecule s in the 1D host nanotubes in a wide range of nanoporous materials. It was found that large uncertainties of ad sorption enthalpy and equilibrium constant appear at high Xe occupancy and low temperatur e regions in Figure 3-10. It may be due to the experimental errors of Xe pressu res, resulting from the difficulty in accurately measuring the Xe partial pressures under continuous-flow and op tical-pumping conditions. As pressurizing the polarizer, Xe/He mixture was mixed manually and ga s pressures were directly recorded from the pressure gauge. The recorded values of the Xe pressures may be overestimated due to the heating of the optical pumping cell which causes an expansi on of the gas mixture. In addition, the Xe gas may not be distributed uniformly throughout the continuous-flow spin-exchange opticalpumping setup. An easy way to improve the accuracy of the Xe partial pre ssures would be to use pre-mixed pumping gas mixtures with accura tely known gas compositions in continuous-flow hyperpolarized 129Xe NMR experiments.
76 CHAPTER 4 OBSERVATION OF SINGLE-FILE DIFFUSI ON IN DIPEPTIDE NANOTUBES BY HYPERPOLARIZED TRACER EXCHANGE XE-129 NMR 4.1 Introduction Nanotube systems are currently of great interest s in a variety of fiel ds, including biosensor, catalysis, molecular confinement, and selective adsorption.1 Compared to the molecular motions in free-space, dynamic properties of confined particles in the nanotubes are extremely different. The restricted diffusion of guest particles in 1D channels, where the individual pores are too narrow for particles to pass one-another, is known as single-file diffusion (SFD).1,181,182 The concept of SFD was originally introduced in biophysics about 30 years ago to account for the transport of water and ions through channel proteins in the membranes.183 Since then, in addition to biological systems, SFD has been explored in the context of transpor t of adsorbates through 1D zeolites184-186 and diffusion of colloidal particles in narrow tubes.187-190 SFD has shown particularly interesting characteristics with extreme difference from normal Fickian diffusion. The important distinguishing feature of SFD is that the mean-squared displacement is proportional to the square root of the observation time. This correlation is reflected in the longtime behavior of the mean-squared di splacement in a single-file system.191 The study of SFD is motivated not only by its ubiquity indicated a bove, but it has shown that 1D driven diffusion systems with non-e quilibrium steady state exhibit a remarkably interesting phenomena. Most of these phenomena have been noticeable in the past decade. Asymmetric simple exclusion process (ASEP), a discrete non-equilibrium model that usually describes the stochastic dynamics of mu lti-particle transport along 1D lattices192, has been successfully modeled the macro/mi croscopic 1D systems with the universal phenomena. The examples of the 1D systems are listed as follows:
77 The reptation of entangled polymers wher e the motions of polymer chains are restricted by the surrounding chains.193-195 The motion of ribosome along mRNA during protein synthesis.196-199 Molecular motors along micr otubuli or actin filaments.200,201 Boundary-induced phase transition.202-204 Vehicular traffic problems on road networks. 205,206 In principle, ASEP lattice model with symm etric open boundaries illustrated in Figure 4-1 can be used to model the single-file process, a nd exact analytical solutions have been obtained.207 The rules of ASEP with sy mmetric boundaries are: Each site along 1D lattice can be either empty or occ upied by a single particle. If neighboring site of the particle is em pty, the particle can move onto it with a hopping rate of 1/a Particles interact only through ha rd-sphere exclusion potential. Particles cannot pass one-another in 1D lattice (SFD behavior). Figure 4-1. The model of asymmetric simple exclusion process (ASEP) with symmetric open boundaries. is the probability of moving a particle from the reservoir to the last site of lattice. is a reverse process of A particle is moved to the next unoccupied site in the lattice with the rate 1/a 4.1.1 One-Dimensional Diffusion: Fickian Diffusion and Single-file Diffusion In a normal 1D system with infinite length, the probability density function (PDF), or commonly named diffusion propagator of tagged particles at position z, initially starting at
78 0z, approaches the Gaussian at long diffusion tim e, and it can be expressed based on the Ficks law: 2 0 0 0 0() 1 (,)exp 4 4NDzz Pzzt Dt Dt (4-1) where the mean-squared displacement increasing as diffusion time ( i.e. 2 0()2 ztDt ), as in normal (random-walk) diffusion, and 0 D is the diffusion coefficient. For a single-file system, where the tagged particles are too large to pass on e-another inside the channels, the displacement of particles are upon collisions. The restricted motion of particles in SFD systems makes the diffusion of individual tagged part icles anomalously slow. The pr opagator of SFD particles is also Gaussian, but with mean-squared displ acement increasing as square root of time181,184 ( i.e. 2()2 ztFt ) 2 0 0 0.5 0.5() 1 (,)exp 4 4SFDzz Pzzt Ft Ft (4-2) where Fis single-file mobility. In SFD system, anomalous diffusion properties may also depend on the density of confined particles and the observation NMR time-scale NMRt. At sufficiently low or short NMRt, particles in the channels are essentially isol ated from one another, leading to normal 1D diffusion (Figure 4-2a). However, at higher or longer NMRt, the net displacement over longer length scales requires correlated movement of particle s in the channel, le ading to single-file diffusion (Figure 4-2b). For an idealized single-file system of hard-sphere particles with density and diameter d, single-file mobility is given by208-210
79 0011 DD d Fd (4-3) As 1 the channels become fully occupi ed and the particles immobilized (0 F ). According to the Ansatz of Lin et al.189 2111 2 () 2oDt zt F t (4-4) The mean-squared displacement in Eq. (4-4) leads to 2 1/222 () 1(/) 1(/)oo x oDtDt zt tt DFt (4-5) It follows that a cross-over between the two di ffusion regimes occurs at a characteristic time, 2/xotFD A third regime, referred to as center-of-mass diffusion, emerges at still longer observations times, where SFD in finite systems with rapid exchange at the channel boundaries involves the correlated motion of all particles in th e channel, resulti ng in normal Fickian diffusion once again (as in the short observati on time regime) but with greatly reduced diffusivity.211 Figure 4-2. The waveforms of probability densit y function of (a) normal 1D Fickian diffusion (Eq. (4-1)) and (b) single-file diffusion (Eq. (4-2)) corresponding to successively increasing observation time (123ttt ). is the length of each lattice.
80 While theoretical considerations make defini te predictions about the cross-over between the different regimes, validation of theory in nanoporous systems has been severely hampered by the limitations of the available experimental methods and the lack of sufficie ntly ideal si ngle file host-guest systems. In r eal nanotube materials, () F can be expected to deviate from the simple hard-spheres model due to particle -particle and particle-channel in teractions, the presence of an exchange barrier at the si ngle-file boundaries, and non-cy lindrical channel topology. Experimental investigations of anomalous diffu sion in single-file systems have been limited mostly to macroscopic channels, where it is possible to use direct video analysis of the statistics of the trajectories of micromete r-size colloidal particles in circul ar channels or channels created by optical tweezers.187,190 Proton pulsed-field gradient (P FG) NMR, the standard method for measuring the molecular diffusivity in porous solids, is generally restricted to relatively short time scales due to the typically short proton transverse relaxati on time in heterogeneous media. For measuring molecular displacem ent in nanometer length scales, it requires extremely strong pulse-gradient strength for PFG NMR. For example, Krger et al.212 have measured the singlefile mobility of methane in AlPO4-5 zeolites by using PFG NM R with maximum gradient strength of 24 T/m 4.1.2 Tracer Exchange Alternatively, the tracer exchange method can be experimentally and theoretically employed to study diffusion at arbitrarily long time-scales by observing the time-dependence of the accumulation of labeled molecules, initiall y located outside the ch annels, under steady-state adsorption conditions. The schematic diagram of molecular tracer exchange is shown in Figure 4-3. In tracer exchange expe riments, the molecular tracer can generally be radioactive or isotopic labeled. The quasi-elastic neutron sca ttering (QENS) can also be utilized to trace
81 molecular displacements in nanometer length scales.213,214 In principle, the tracer exchange curve () t can be defined as number of labeled particle at number of labeled particle at t t t (4-6) Figure 4-3. Molecular tracer exchange. Red ball s represent unlabeled molecules. Blue balls represent labeled molecules. The system reaches to steady-state adsorption at t In the NMR tracer exchange method, the nuclear spin serves as the particle label, while spin interactions ( e.g. chemical shift) report on the particle location. There are several approaches to label the spins by NMR. For instance, in nanotube systems, if the spins located inside and outside channels are in the slow exchange regime where the chemical shifts can be distinguished, the frequency sele ctive pulse can be applied to invert the spins outside the channels, and the spins inside the channels rema in at thermal equilibrium. By monitoring the decay and growth of NMR signals inside and outs ide the channels, the information of molecular diffusion in the nanotubes can be obtained. More over, hyperpolarized NMR can also be used on the tracer exchange experime nts. The schematic diagram of hyperpolarized NMR tracer exchange is illustrated in Figur e 4-4. The polarized spins or cold spins can be used as the
82 tracers, since unpolarized spins or hot spins are not NMR obs ervable. At sufficient long diffusion time, the signals inside the channel will eventually decay due to the relaxation. Figure 4-4. Hyperpolarized NMR tracer ex change. Red balls represent hot spins (unpolarized). Blue balls represent cold sp ins (polarized). The arrows indicate spin with different polarizations. At t the spins are depolarized due to the relaxation. Note that only polarized spin s give rise to obs ervable NMR signals. As first demonstrated by Meersmann et al.215, Xe diffusion inside the TPP nanochannels has be monitored over a three orders of magn itude range of time-scales due to the long 1T in this material as a function of temperature a nd occupancy by continuous-flow hyperpolarized 129Xe saturation-recovery NMR. In th eir experiments, the non-selectiv e saturation RF pulse train was first employed to destroy all the Xe magnetizations in the sample space, and the recovery of Xe signals inside the channels was monitored as a function of diffusion time under the continuousflow condition. Although the SFD behavior of Xe in TPP has been confirmed in their work, the experiments were noted to have a few problems: Firstly, the recovery of Xe adsorbed-phase magnetization can interfere with the recovery of Xe gas magnetization at very short diffusion time, where the exchange occu rs near the channe l openings. Secondly, when the CFHP 129Xe
83 saturation-recovery NMR experime nts carried out at variable te mperatures, the Xe occupancies were also varied with the temp eratures. It is not appropriate to discuss the results with two dependent variables in the experiment. Finally, they did not provide the quantitative expression for the single-file mobility. In this chapter, we report the re sults of continuous-flow hyperpolarized 129Xe selective saturation-recovery (CFSR) NMR experiments perf ormed over a wide range of Xe occupancies and observation times in the dipeptide nanotubes, AV. It will be shown that the hyperpolarized 129Xe tracer exchange signals can be analyzed in terms of a magnetization exchange model to obtain the theoretical dependence on the single-file mobility. The derived -dependence of the nanotube/gas phase signal ratio, assuming the idealized hard-spheres expression for F is compared to the experimental data. Finally, the -dependence of the nuclear longitudinal relaxation time (1cT) of 129Xe inside the channels will be presented. 4.2 Experimental Hyperpolarized 129Xe NMR experiments were performed on a 15 mg sample of AVa at a magnetic field of 9.4 T field (110.7 MHz 129Xe resonance frequency ) us ing a modified variable temperature wideline probe. Details of the Rb -Xe spin-exchange optical-pumping system and NMR sample preparations were described in Section 2.4.4. The sample was immersed in a flowing mixture of hyperpolarized 129Xe in 4He carrier gasb at a total pressure of 3500 torr. As indicated previously, in th e optical-pumping process, N2 gas is usually added to the Xe/4He gas mixture to reduce radiation trapping in order to enhance the efficiency of laser polarization. However, it was removed in the experiments to avoid interference with Xe gas diffusion, since N2 molecule, with the van der Waals diameter of 3.64 may affect the motion of Xe inside the a part no.: 0210032883; MP Biochemicals, Santa Ana, CA b part no.: UN1046; Praxair, Danbury, CT.
84 channel. 4He gas is much smaller compared with 129Xe, and it is assumed not to alter SFD behavior of Xe. The gas mixtur e was continuously re -circulated between the optical pumping cell and the sample space at a flow rate of 100 mL/min The NMR pulse sequence of selective saturati on-recovery experiment is illustrated in Figure 4-5. As shown in Figure 4-6, after re aching a hyperpolarization steady state, the 129Xe magnetization in the nanotubes was destroyed by a frequency-selective saturation pulse train with Gaussian-shaped pulses, which left th e magnetization in the gas phase unaffected. Following a delay to allow the accumulati on of hyperpolarized Xe in the channel, the longitudinal magnetization was converted into an observable NMR signal by a 4 s nonselective /2 pulse. Figure 4-5. NMR pulse sequen ce of selective continuous-flo w saturation-recovery (CFSR) hyperpolarized 129Xe NMR experiment. It should be noted that only the hyperpolarized 129Xe contributes to NMR signal, since the thermally-polarized 129Xe signal cannot be detected wit hout signal averaging. The molar occupancies m were inferred using the correla tion between Xe molar occupancy m and as determined from Figure 3-8 in Chapter 3: =0.00536-0.51964m (at 20oTC ). The molar
85 occupancies m were converted to volume tric fractional occupancies using the published value for the Xe gas adsorption capacity of AV.74 Figure 4-6. Selective con tinuous-flow saturation-recove ry (CFSR) hyperpolarized 129Xe NMR experiment in AV nanotubes. Blue balls re present cold polarized Xe, and red balls represent hot unpolarized Xe.
86 4.3 Magnetization Exchange Model fo r Saturation-recovery in 1D Channel To extract quantitative information from se lective continuous-flow saturation recovery (CFSR) experiments, the derivation of an analy tical expression is required. Since the selective CFSR experiment does not affect Xe magnetiza tion in the gas phase, only time-dependence of nanotube phase signal is considered. Base on diffusion-limited Langmuir adsorption, the magnetization in nanotube phase is: cazc M NfI (4-7) where f is fractional isotopic abundance of 129Xe, is the monolayer coverage (01 ), aN is number of adsorbed sites, and zcI is the average longitudinal nuc lear spin angular momenta ( i.e. Zeeman orders) inside the cha nnels. In the case of nanotubes, is equivalent to a filling factor. In the CFSR expe riment, time-dependence of c M was not affected by the gas flow rate. Therefore, the rate of magne tization in nanotube phase is 1 1(1)c aXeazdazcccdM kpNfIkNfIMT dt (4-8) where X ep is the vapor pressure, ak and dk are the adsorption and desorption rate constants, 1 1cT is the longitudinal relaxation ra te of adsorbed phases, and zI is the average Zeeman order in the gas phase. In the steady-state condition, is time-independent; therefore, Eq. (4-7) yields czc adMdI Nf dtdt (4-9) Combined Eq. (4-8) and Eq. (4-9) 1 11zc aXezdzczccdI kpIkIIT dt (4-10)
87 Based on the assumption of steadystate Langmuir adsorption, where (1)daaXeakNkpN Eq. (4-10) can be rewritten in terms of dk: 1 1 zc dzdzczccdI kIkIIT dt (4-11) Under the conditions where the surface has negligible depolarizing effect on the gas phase, 0zdIdt and zzi I I where zi I is the Zeeman order induced by optical-pumping spinexchange. Thus, for a homogeneous surface comprised of identical adsorption sites, the solution to Eq. (4-11) is 1 1 1 1()1exp()d zczidc dck I tIkTt kT (4-12) Clearly, this expression goes to the appropriate limits as 0,dk or 10,cT However, the molecular adsorption sites in a nanotube while exhibiting Langmuir adsorption74, are not uniformly accessible to the gas phase. The deso rption of a Xe atom with a displacement z from the channel opening can be consider ed as a two-step seque ntial process: the atom must first make its way to the channel opening, and then it must overcome a potential energy barrier to enter the gas phase. The equilibrium is preserved by the reve rse process. In the case where the barrier does not affect the overall rate of desorption and desorption is diffusion-limited the nanotube may be modeled as a surface with a di stribution of desorption rates 1 ddk where d is the diffusion time from a site with a mean displacement 0(,)ddzzPzdz (4-13)
88 where d P is the diffusion propagator. Thus, 2 1 0 d D z and 4 2 1 dFz are for normal and single file diffusion, respectively. The average Zeeman order of a nanotube of average length L is calculated from the distribut ion of rates, or displacements z: 1 1 1 1 0()1expL zid zcdc dcIk I kTdz LkT (4-14) It can be shown that in the long channel limit, where 1/4 22 1 cFTL, Eq. (4-14) can be rewritten using the identities for the incomplete function. 13/4 3/2 0() 21/4ctT zcziF I Itedt L (4-15) The deviation from Eq. (4-14) to Eq. (4-15) wi ll be demonstrated in Appendix A. The analogous result for normal diffusion is 10 1/2 0() 4ctT zcziD I Itedt L (4-16) The observed NMR signal of the adsorbed phase is proportional to th e total longitudinal magnetization of 129Xe inside the channels, c M which is obtained by multiplying zc I by cN, the number of channels in the sample, and f Ld, the number of 129Xe atoms per channel. Hence, the total NMR signal in the nanot ube phase for SFD systems is 13/4 0() 4ctT SFD cccziF SMNfItedt d (4-17) The corresponding expression for normal diffusion is: 10 1/2 0() 4ctT ND cccziD SMN f Itedt d (4-18)
89 Notably, the ()SFD cSF dependence also emerge s in the derivation of ()SFD cS from the standard tracer exchange curve211 28() () 14 () ()SFD c SFD cz S F SLL (4-19) which gives the fraction of labelled mo lecules in the channels at time Eq. (4-17) can also be validated on the ba sis of simple consid erations: the signal contribution due to atoms reaching the channel segment zzdz is exponentially damped due to longitudinal relaxation: 1/()ctT cSzedz, where 1/23/4(2) dzFtdt. Integration up to the observation time yields Eq. (4-17) The analogous e xpression for normal diffusion (Eq. (4-18)) can be obtained similarly. In principle, the -dependence of the steady-state 129Xe signal expressed in Eq. (4-17) could form the basis for experimental determination of () F except for a technical complication: ziI varies with the optical pumping gas composition,35 and even at a fixed composition, zi I may drift during the course of an experi ment due to factors that are hard to control. Therefore, to compare the signal intensiti es obtained at different Xe pressures, it is necessary to standardize the signals to an in tensity reference. As suggested by Meersmann et al. 215, it is convenient to take the ratio of the nanotube and gas phase signals, ()cgasSS which eliminates the variation of ziI due to optical pumping with diffe rent Xe pressures in the gas mixture. Since magnetization in gas phase is g gaszi M nfI 1/ 3/4 0() (,)cSFD tT c F gasS CTtedt S (4-20)
90 where 1/2 3/2(,) 21/4c F g asN F CT dn (4-21) The corresponding expression for 1D normal diffusion is 1/ 1/2 0() (,)cND tT c D gasS CTtedt S (4-22) where 1/2 0(,) 4c D g asD N CT dn (4-23) Eq. (4-20) and Eq. (4-22) have comparable expressions as Eq. (3) and Eq. (4) of Ref. 215, but advantageously, our derivation yields an explicit expression for the coefficient ()FC revealing its proportionality to (1) ratio of the numb er of channels (cN) to the number of gas phase atoms ( g asn) and (2) the square root of th e single file mobility. However, g asn is infeasible to determine from gas peak integral since the peak area in gas phase is relative to hyperpolarized Xe gas in the sample space, not the total number of Xe gas molecules. In principle, if /cgasNn is known, a quantitative estimation of F can be obtained from measurement of ()FC and Eq. (4-21). 4.4 Results and Discussions Representative selective saturationrecovery signals acquired at -10 oC for two Xe partial pressures, 2650 torr and 56 torr, co rresponding to occupancies of 0.66 and 0.16, respectively, are presented in Figure 4-7, along with the non-lin ear least-squares fits to Eq. (4-20) and (4-22). The NMR signals were integrated over the powd er pattern and divided by the integrated gas signals. Th e two variable parameters in the fits were the longitudinal relaxation time 1 cT in nanotube phase and F C. Results of the regression analysis are summarized in Table 4-1.
91 Figure 4-7. Least-squares fits to the selective saturation-recovery NMR signal (normalized to the steady-state gas phase signal) of 129Xe inside 15mg AV, obtained at T= -10 oC to the expressions for single-file diffusion (SFD, Eq. (4-20)) and normal diffusion (ND, Eq. (4-22)). (a) Low occupancy: 56 Torr Xe,0.16 (c) High occupancy: 2650 Torr Xe, 0.66 Error bars indicate 90% confidence intervals. Time-base expansions of (a) and (c) are presented in (b) and (d), re spectively. Values for fitted parameters are given in Table 4-1. 1.5 1.0 0.5 0.0Sc( )/Sgas 300 250 200 150 100 50 0 (s) SFD ND 56 torr, =0.16 (a) 0.25 0.20 0.15 0.10 0.05Sc( )/Sgas 300 250 200 150 100 50 0 (s) SFD ND 2650 torr, =0.66 (c) 1.2 1.0 0.8 0.6 0.4 0.2Sc( )/Sgas 20 15 10 5 0 (s) SFD ND 56 torr, =0.16 (b) 0.25 0.20 0.15 0.10 0.05 0.00Sc( )/Sgas 20 15 10 5 0 ( s ) SFD ND 2650 torr, =0.66 (d)
92 Table 4-1. Nonlinear regression analysis of saturation-recovery hyperpolarized 129Xe NMR of Xe in AV nanotubes at -10 oC. pXe /torr ptotal/torr DIFFUSION MODEL Single-File; Eq.(4-20) Normal; Eq.(4-22) T1c 95 (s) C F 95 r2 T1c 95 (s) r2 56 3500 0.16 217 90 0.125 0.0060.974 305 0.973 2560 3500 0.66 35 6 0.029 0.0010.981 8.51.3 0.969 Although the SFD model yielded supe rior agreement to the data at both low and high occupancy for all the most decisive comparison was obtained for the 0.66 run, which unequivocally confirmed single-file diffusion of Xe in AV nanotubes. The tabul ated results also reveal a substantial decrease in 1cT with increasing Xe occupancy. Figure 4-8a presents the dependence at T = -10, +10, +25 and +40 oC all of which show a monotonic decrease in 1 cT The measured 1cT did not change after re-p acking the sample, and was not affected by changing the gas flow rate. Spin relaxation inside the channels of AV can occur via several possible mechanisms, including the dipolar (129Xe-129Xe and 129Xe-1H) and chemical shift mechanisms, and spin-rotation relaxation in tr ansient Xe-Xe complexes. Rotati onal modes are expected to be suppressed due to the spatial confinement of the channels. The spectral density due to fluctuations of the 129Xe-1H dipolar interaction with the methyl groups of the channel could vary with The chemical shift interaction, which incr eases in proportion to occupancy, could also account for the spin relaxation inside the cha nnels. Variable magnetic field studies would identify the dominant relaxation mechanism, but are beyond the scope of the present work.
93 Figure 4-8. (a) Fractional occupancy dependence of the T1c of 129Xe in the adsorbed Xe phase. The T1c values were extracted from non-linear least-squares fitting of Eq. (4-20) to the measured saturation-recovery data at T= -10, 10, 25, and 40 oC (b) The experimental values of FC ranged from =0.14 to 0.70 at -10 oC were also extracted in the non-linear least squares fi tting. The dashed line is the theoretical function3/2 1/21/FC scaled vertically to overlap with the experimental data points to aid qualitative comp arison to the th eoretical trend. Figure 4-8b presents plots of FC extracted from the non-linear least-squares fits for the data acquired in a second series of experiment s, performed after re-p acking the sample, at 10oTC with varying Xe pressure at a fixe d total pressure of 3500 torr, spanning a occupancy range of 14-70 %. The theoretical dependence 3/2 1/21/FC which follows from Eq. (4-3) when Langmuir adsorption and the hard-spheres expression for F are assumed, is consistent with the experi mentally observed monotonic decrease in FC with increasing Therefore, we can conclude that the single-file diffusion in AV nanotubes is attenuated as the Xe occupancy increased. 200 150 100 50T1c (s) 0.8 0.6 0.4 0.2 0.0 -10 oC +10 oC +25 oC +40 oC (a) 50 40 30 20 10 0 CF( x10-3 1.0 0.8 0.6 0.4 0.2 0.0 ~ (1(b)
94 4.5 Conclusions Hyperpolarized (saturation-r ecovery) NMR tracer exchange method has proven to be an effective method for characteri zing diffusion in self-assemble d nanotube systems. The NMR signal enhancement afforded by spin-exchange op tical-pumping facilitate d studies on milligramscale quantities of material at occupancies down to 10%. Expressions for the NMR saturationrecovery signals for normal diffusion and SFD ha ve been derived from the magnetization rate equations, assuming a distribution of desorption rate s. The nonlinear regression analysis is clear indicative of SFD for Xe in AV, especially at high occupancy. The theoretical occupancy dependence of the channel-to-gas signal ratio ag rees qualitatively with the data, although the deviation between experiment and theory app ears to be greater at low occupancy, which suggesting that the mobility of the Xe is proba bly more restricted at low occupancy than is predicted by the simple hard-spheres mobili ty in ideal linear channels. The helium gas background, particularly at low Xe partial pressu re, will also have an effect on the single-file mobility. In the gas phase, the diffusivity of Xe in He has been found to decrease with increasing Xe/He mole ratio.216 The helical topology of the channels of AV will reduc e the mobility in comparison to that of idea l, cylindrical nanotubes. The observation of single-file Xe diff usion in AV is consistent with a x t that is shorter than the minimum observation time that can be probed under our experimental conditions, which is limited to 500 ms by the signal-to-noise. Unfortunately, neither F nor 0 D has been measured in this system, so it is impossible to estimate x t with any certainty. Although the magnetization exchange kinetic anal ysis might not be re alistic in describing the actual physical process of incorporation of the tracer into the single-file channels, it does yield the same analytical form of the saturation -recovery signal (Eq. (4-17 )) as is obtained from
95 the standard diffusion propagator de scription in the limit of long ch annels. Both models yield the same Fdependence on the single-file mobility.211 This leads us to conclude that the statistic for hyperpolarized atom accumulation in an ensemble of channels is the same in each model. The advantage of our magnetization ex change model is that it is easily adapted to samples with distributions of channel lengths. Moreover, in samples for which the long channel approximation does not apply, or under condition for which the pol arization of the gas phase is significantly affected by exchange with unpolarized gas inside the channels, it will still be possible to obtain the theoretical saturation-recovery curve by numerical integration of the rate equations.
96 CHAPTER 5 INVESTIGATIONS OF CHANNEL DIAMET ER EFFECT ON GAS DIFFUSION IN GA WHEEL NANOTUBES BY HYPERPOLARIZED XE-129 NMR 5.1 Introduction In recent years, rapid developments of nanotubul ar frameworks with their intrinsic beauty and potential applications have been witnesse d. In particular, inorga nic nanotubes constructed from the molecular wheels have recently been the subject of intense res earches because of the fundamental interests in the magnetic propertie s, such as single molecular magnets (SMM)217-219 and their quantum phenomena.220-223 In addition, theoretical works have proposed that the spin states of the transition-metal clusters can be the basis for the quantum computation.224-226 Following the pioneering works of Dr. George Christou (UF Chemistry) in synthesizing transition-metal molecular cluste rs, a variety of novel supramol ecular channels with highly symmetric building blocks have been constructed. One of the characteristic molecular clusters, the gallic wheel, has been successfully synthesized by nontemplate methods.36 As shown in Figure 5-1a and b, the Ga10 and Ga18 wheel structures consist of 10 and 18 Ga(III) atoms bridged by the ligands in nearly octahedral geometr y. Moreover, the molecular wheels stack along the crystal c -axis to form the elegant nanotubular stru ctures. The crystal structures of the Ga10 and Ga18 wheels viewed along their crystal c -axis are illustrated in Figure 5-1 d and e, respectively. The inner diameters of the Ga10 and Ga18 channels are 8.1 and 10.4 respectively.36 In 2004, Christou et al. reported a giant molecular wheel com pound composed of 84 manganese atoms (Figure 5-1c). The Mn84 structure is in a hexagonal symmetry space group.227 The tubular structure of the Mn84 wheel has a cylindrical 1D channel w ith an internal diameter of 1.9 nm (Figure 5-1f).
97 Figure 5-1. Structures of molecular wheels, (a)(d) Ga10, (b)(e) Ga18, and (c)(f) Mn84 with inner diameter of 8.1 10.4 and 1.9 nm, resp ectively. (a)(b)(c) are the top view of molecular structures of Ga10, Ga18, and Mn84 wheels, respectively. (d)(e)(f) are the corresponding space filling representations of Ga10, Ga18, and Mn84 wheel compounds, respectively. The structures are not represented on the same scale. (Ga: yellow; O: red; C:gray; H: white; N: bl ue in (b); Mn: blue in (c)) (Adapt from Ref 36 and 227)
98 The kinetics of gas diffusion in 1D nanotube systems has been investigated by saturationrecovery hyperpolarized 129Xe NMR, and the results of Xe diffusion in the model single-file system, dipeptide nanotube AV, have been pres ented in Chapter 4. The diffusion properties of Xe may be expected to drastically depend on the di ameter of the channel re lative to the size of Xe atom. In our previous studies of Xe diffu sion in AV nanotubes, where Xe diameter exceeds the radius of channel but is smaller than chan nel diameter, compliance with SFD behavior has been observed.180 The normal 1D diffusion of Xe should emerge in the cha nnel with an inner diameter 2 times the Xe diameter ( i.e. 8.8 ), because the confined Xe can transversely pass one-another in the channel. Henc e, it would be interesting if the CFSR technique developed herein could be applied to nanot ubes with larger pores in order to verify this prediction. However, the inside diameters of self-assemb led dipeptide nanotubes with hydrophobic interiors are limited to ~5 .178 Thus, the molecular wheel nanochannels with controllable channel sizes are excellent candidates to study the channel-si ze dependence of molecular diffusion in 1D nanotube systems. Additionally, in the paper of Christou, it has been pointed out that the supramolecular architecture of the molecular wh eel nanotubes may be suitable for a variety of applications, such as the insertion of guest molecules.227 These considerations motivated us to explore the kinetics of gas diffusion in the mol ecular wheel nanotubes. Here we present the gas diffusion studies of Xe in gallic-wheel nanotubes (Ga10 and Ga18) using selective continuousflow saturation-recovery (CFSR) hyperpolarized 129Xe NMR. 5.2 Experimental The molecular wheels, Ga10, Ga18, and Mn84, were synthesized by Dr. Theocharis Stamatatos in Prof. George Christous group. Th e detailed procedures of the molecular wheels synthesis associated with their crystal structure identifications can be found in the literature.36 227 It is noted that the samples of molecular wheel nanotubes are not stable in air or elevated
99 temperatures. Additionally, the samples readily ad sorb moisture, which causes the collapse of the nanotubular structures. For example, the nanotubular st ructures of Ga18 samples were found to be completely collapsed by SEM after their exposure to air for 1-2 weeks. Therefore, after the molecular wheel samples were synthesized, NMR measurements were performed promptly and completed within 2-3 days to ensure the nano tubular structures were not collapsed in the samples. The stock molecular wheel samples were stored in a dry N2 glove box for further studies. Approximately 40-50 mg of the polycrystalline samples were loosely packed into the NMR sample holder and evacuated to ~10-5 torr at room temperature overnight prior to NMR measurements. It is crucial to remove the solven t in the samples because an additional Xe solvent peak at ~100 ppm can be observed in hyperpolarized 129Xe NMR spectra when the evacuation of solvent was not complete. On the other hand, the extremely high sensitivity of hyperpolarized Xe NMR allows the small amount of solvent in the samples to be detected. 5.2.1 Hyperpolarized 129Xe NMR Experiment Hyperpolarized Xe gas was generated by c ontinuous-flow Rb-Xe spin-exchange opticalpumping polarizer described in Section 2.4.4. Th e gas mixture was re-circulated through the sample space during the experiments at a flow rate of 100 mL/min The total gas pressure was 4000 mbar in all the experiments. The 2%/2%/96% nature isotopic abundance Xe/N2/He gas mixturea was used for the variable temperature experiments. The natural isotopic abundance 129Xe gasb and 4He gasc were used to adjust the Xe gas composition for the continuous-flow selective saturation-recove ry (CFSR) hyperpolarized 129Xe NMR experiments at room temperature. The pulse sequence of selective CFSR hyperpolarized 129Xe NMR is shown in Figure 4-5. The principles of CFSR 129Xe NMR were discussed in Chapter 4. a part no.: ISO-XHN-C; Spectra Gases Inc., West Branchburg, NJ. b part no.: XE5.0RS-D8; Praxair, Danbury, CT. c part no.: UN1046; Praxair, Danbury, CT.
100 All the NMR measurements were carried out on a 9.4 T Bruker Avance NMR spectrometer operating on a 129Xe Larmor frequency of 110.7 MHz. The 2 pulse width was about 4.5 s. The single-pulse sequence was applied to acquire variable-temperature 129Xe NMR spectra in Ga10 and Ga18 nanotubes. For Mn84 nanotubes, the typical Hahn spin-echo pulse sequence was used in order to refocus the signal dephasing due to the field inhomogeneity. The inter-pulse delay of Hahn spin-echo was optimized to 50 s. The 129Xe NMR acquisition parameters are listed in Table 5-1. For Ga18 nanotubes, 128 transients were av eraged in CFSR experiments in order to obtain the sufficient signal-to-noise ra tio on the adsorbed peaks for the quantitative measurements. A Gaussian line-broadening factor was applied to the free induction decay prior to the Fourier transformation. Since the structures of molecular wheels are not stable at high temperature, all the NMR measurements were conducted at or belo w room temperature. Table 5-1. Summary of Xe NMR acquisiti on parameters of the molecular wheels polycrystalline samples recycle delay transients spectral width (kHz) line broadening (Hz) Ga10 1 sec 16 60 300 Ga18 1 sec 32 55 300 Mn84 1 sec 128 250 500 5.2.2 Scanning Electron Microscopy The scanning electron microscopy (SEM ) was performed using JOEL 6400 with acceleration voltage as low as 5 kV in order to get sufficient resolution to study the morphology of nanotubes. The SEM images of Ga10 nanotubes with variable magnifications are presented in Figure 5-2a-c. The additional substances around the nanotubular structures in Figure 5-2c may be the collapsed nanotubes since Ga10 nanotubes can be colla psed in the exposure to air or moisture. The channel lengths were measured manually in the SEM images taken from six different areas of polycrystalline sample. Th e length distribution of Ga10 channels is presented in Figure 5-2d. The average length of Ga10 channel is 606.549.3 m.
101 (a) (b) (c) (d) Figure 5-2. SEM images of Ga10 nanotubes shown at length scales of (a) 10 m, (b) 100 m, and (c) 1mm. (d) Length distribution of the Ga10 crystals. The average length is 606.549.3 m. (n=83) 5.3 Results and Discussions 5.3.1 Temperature Dependent Study in Ga10 and Ga18 Nanotubes The temperature dependences of 129Xe NMR spectra of Xe adsorbed in the Ga10 and Ga18 wheel nanotubes are presented in Fi gure 5-3. The morphology of the Ga10 and Ga18 wheel polycrystalline samples is expected to be ve ry similar. From the X-ray crystal structure analysis36, the inner diameters of Ga10 (8.1 ) and Ga18 (10.4 ) are relatively larger than that of AV or TPP channel ( i.e. ~5 ). Therefore, the motions of Xe atoms in Ga10 and Ga18 nanotubes are less restricted than in AV or TPP, leadi ng to the isotropic NMR line-shapes of Xe in Ga10 and Ga18 nanotube phases over the range of experimental temperatures (Figure 5-3). Such isotropic 16 14 12 10 8 6 4 2number of channels 1000 800 600 400 200 channel length ( m)
102 129Xe NMR spectral line-shapes are completely di fferent from the CSA pow der pattern of AV or TPP.20,21,180 Figure 5-3. Temperature de pendence of hyperpolarized 129Xe NMR Spectra of Xe adsorbed in (a) Ga10 and (b) Ga18 molecular wheels. In Figure 5-3, the adsorbed Xe peaks in both nanotubes become broader as the temperature is reduced. At low temperature, more Xe atom s accumulate into the channels and the Xe-Xe interaction is dominant, resulting in a deshielding of Xe chemical shift in Ga10 and Ga18 nanotubes. As more Xe atoms adsorb into the ch annels at low temperature, the confinement of Xe may break the symmetry of shielding tensor leading to an observed anisotropic NMR lineshape. However, due to low signal-to-noise ratio of Xe in gallic nanotubes in Figure 5-3, more signal averaging may be required in order to identify the spectral line-shapes at low temperature. Moreover, two distinctions were found in the temperature-dependent 129Xe NMR spectra of Ga10 and Ga18 wheel nanotubes: (1) The intensit y of the adsorbed Xe peak in Ga18 nanotubes is much 1.4 1.2 1.0 0.8 0.6 0.4 0.2 280 260 240 220 200 180 160 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 T/ oC ppm (a) 100 80 60 40 20 0x10-3 280 260 240 220 200 180 160ppm 25 20 10 0 -10 -20 -30 -40 -50 -60 -70 -80 T/ oC (b)
103 weaker than its gas peak intensity, implying Xe 1cT relaxation time in Ga18 nanotubes may be relatively shorter or the density of unobstructed channels may be lower. (2) The si gnal intensity of the adsorbed Xe peak in Ga18 nanotubes increases when the temperature is lowered. Conversely, in Ga10 nanotubes, the intensity of Xe adso rbed peak decreases and broadens upon lowering the temperature, and eventually disappears at -40 oC It can be interpreted by a reduction of Xe motion inside the Ga10 nanotubes upon cooling the syst em. As the temperature is lowered, more Xe atoms adsorb into the Ga10 channels and the Xe diffusivity is reduced, consequently reducing the 2T relaxation time. Therefore, the adsorbed Xe peak in Ga10 nanotubes becomes broadened and weaker at lower temperature. Since the Ga18 nanotube has a large inner diameter than Ga10 nanotube, Xe motion in Ga18 nanotubes should be more mobile than in Ga10 nanotubes. Thus, Xe 2T in Ga18 nanotubes does not exhibit such a drastic change upon lowering the temperature. The temperature dependences of the chemical shifts of the adsorbed 129Xe peaks in Ga10 and Ga18 nanotubes are summarized in Figure 5-4. Becau se Xe is more tightly confined in Ga10 nanotubes than in Ga18 nanotubes, the chemical shift of Xe in Ga10 nanotubes is more deshielded than that in Ga18 nanotubes over the range of experimental temperatures.
104 Figure 5-4. Temperature dependence of ch emical shift of adsorbed Xe in Ga10 and Ga18 nanotubes. 5.3.2 Temperature Dependent Study in Mn84 Nanotubes The hyperpolarized 129Xe spin-echo NMR spectra in Mn84 nanotubes at variable temperatures are presented in Figure 5-5. Extreme broadening of the adsorbed 129Xe peaks occurs. The chemical shifts of Xe adsorbed peak s up to 400 ppm were obse rved in the variabletemperature hyperpolarized 129Xe NMR spectra. The line-shape a ppears to consist of more than one peak or perhaps even a conti nuous distribution of ad sorbed Xe peaks. As the temperature is reduced, the line-shape of Xe adsorbed into Mn84 nanotubes becomes incr easingly broadened. The Xe 1T relaxation time in the adsorbed phase of Mn84 nanotubes was approximately 10 ms at room temperature, as measured by the time-de pendence of the peak amplitude in the nonselective saturation-re covery hyperpolarized 129Xe NMR signal. The manganese atom is paramagnetic and can induce fast nuclear spin relaxation on 129Xe in the Mn84 channels. It might be the reason for the weak and strongly broadened Xe signals in this nanotube system. This type 230 225 220 215 210 205 200Xe chemical shift (ppm) -80 -60 -40 -20 0 20Tem p erature ( oC ) Ga10 Ga18
105 of spectral line-broadening is typically seen in the 129Xe NMR spectra of car bon nanotubes in the presence of metallic partcles.228-230 In addition, since the Mn84 wheel is known as a single molecular magnet227, the difference of magnetic susceptibility distribution in Mn84 sample may present a spatial dependence of the magnetic environments seen by the 129Xe nuclear spin, leading to a dispersion of the Xe resonance frequency that conse quently yields the drastic linebroadening. Figure 5-5. Temperature de pendence of hyperpolarized Xe NMR spectra of Mn84 nanotubes. 5.3.3 Pressure Dependent Study in Ga10 and Ga18 Nanotubes The pressure dependences of the hyperpolarized 129Xe NMR spectra of Xe adsorbed in Ga10 and Ga18 nanotubes are presented in Figure 5-6. Inte restingly, the Xe chemical shifts in the Ga10 and Ga18 nanotubes were almost indepe ndent of Xe pressure at 25 oC over a wide range of Xe partial pressures. The chemical shift of adso rbed Xe can be expressed by the contributions of 1.5 1.0 0.5 0.0 600 400 200 0 -200ppm 25 20 10 0 -10 -20 -30 -40 -50 T/oC
106 several interactions, as shown in Eq. (2-26). Among the interactions in Eq. (2-26), only the s term arises from Xe-surface interactions, or in the present case Xe-wall interactions, and this term does not depend on the Xe pressure. Hence, the results indicate that the chemical shift of Xe inside the Ga10 and Ga18 nanotube is governed by Xe-wall inte ractions over a wide range of Xe densities. Such pressure-independent behavior has been observed previously in the system of Xe gas adsorbed in the nanoporous materials.14,155,231,232 For example, Nagasaka et al.232 have recently reported chemical shifts of adsorbed Xe in two polymer systems, bisphenol-A polycarbonate (PC) and polytetra fluoroethylene (PTFE), with pore size of 4.7 and 7.9 respectively, were not affected by a drastic variation of the Xe density, and suggested the Xe chemical shifts in these systems are dominated by the Xe-wall interactions. Figure 5-6. Pressure dependence of hype rpolarized Xe NMR Spectra in (a) Ga10 and (b) Ga18 nanotubes at 25 oC The total pressure of Xe/H e gas mixture is 4000 mbar. The chemical shifts are reference to the dilute Xe gas (0 ppm). Since Xe gas peak is much larger than Xe adsorbed peak in Ga18 sample, the gas peaks of Ga18 nanotubes were neglected for easily visualized the Xe adsorbed peaks in Ga18 samples. At 25 oC and 80 mbar of Xe partial pressu re, the Xe chemical shifts of Ga10 and Ga18 nanotubes are about 198 ppm which are mainly governed by th e Xe-wall interac tions. As noted 2.0 1.5 1.0 0.5 0.0ppm 250 200 150 100 50 0ppm 100% 2% 66.7% 16.7% 50% Xe (a) 15 10 5 0x10-3 280 260 240 220 200 180 160 140 120ppm 100% 2% Xe 16.7% 50% (b)
107 above, Xe-wall interactions can be reflected in in 1D nanotube systems with an axial symmetry, such as AV or TPP.19 Under the same experimental condition as present studies, =121 ppm was reported in the Xe/AV system, a value which is substantially smaller than that observed in the gallic wheel nanotubes. It appear s that Xe-wall interactions in gallic nanotubes are stronger than those in AV nanotubes at 25 oC However, since the channel walls in both systems are completely different, the Xe-wall interactions may influence the Xe shielding tensor differently in both nanotube systems. 5.3.4 Saturation-recovery Hyperpolarized 129Xe NMR in Ga10 and Ga18 Nanotubes The continuous-flow selective satura tion-recovery (CFSR) hyperpolarized 129Xe NMR experiments were carried out in Ga10 and Ga18 nanotubes in order to compare the effect of channel diameters on the Xe diffusion. The inner diameters of Ga10 and Ga18 nanotube are 8.1 and 10.4 respectively.36 Thus, it is possible for two Xe atoms to fit side-by-side in the channels of Ga18, but not in Ga10. The rigid nanotubular structure formed by stacking of gallic wheels has a uniform internal diameter. As show n in Figure 5-3, the adsorbed peaks of Xe in Ga10 and Ga18 nanotubes can be distingui shed from the gas peaks. Such features make Ga10 and Ga18 wheel compounds unique model systems to probe the different diffusion time-scaling of Xe inside the channels. Since the Xe adsorb ed peak cannot be resolved and the Xe 1cT is too short in Mn84 nanotube, it is infeasible to co nduct the Xe CFSR experiments on Mn84 nanotubes. The selective saturation-recovery hyperpolarized 129Xe NMR experiments in Ga10 nanotubes acquired at four diffe rent Xe compositions, 16.7%, 33.3%, 66.7% and 100%, as well as least-squares fits of normal Fickian diffusi on (Eq. (4-22)) and single-fi le diffusion (Eq. (4-20)) are presented in Figure 5-7. In Ga10 nanotubes at 25 oC it is apparent that the expression for single-file diffusion has the best fit to the satu ration-recovery curves over four different Xe
108 densities. Therefore, it can be conclude d that the diffusion of Xe inside the Ga10 channels is still single-file over a wide ra nge of Xe pressures at 25 oC The inner diameter of the Ga10 nanotubes is slightly smaller than two times the Xe va n der Waals diameter, and therefore the mutual passage of confined Xe atoms insi de the channel is still forbidden. Figure 5-7. Hyperpolarized CFSR 129Xe NMR experiments in Ga10 nanotubes with variable Xe partial pressures at room temperature. Leastsquares fits of Eq. (4-20) and Eq. (4-22) are represented as solid line and dash line, respectively. Total pressure of Xe/He gas mixture is 4000 mbar. 0.35 0.30 0.25 0.20 0.15 0.10 0.05Sc( )/Sgas 6 5 4 3 2 1 0 (s) PXe=667 mbar (16.7% Xe) SFD ND (a) 0.35 0.30 0.25 0.20 0.15 0.10 0.05Sc( )/Sgas 5 4 3 2 1 0 (s) PXe=1333 mbar (33.3% Xe) SFD ND (b) 0.3 0.2 0.1Sc( )/Sgas 5 4 3 2 1 0 (s) PXe=2667 mbar (66.7% Xe) SFD ND (c) 0.3 0.2 0.1Sc( )/Sgas 5 4 3 2 1 0 (s) PXe=4000 mbar (100% Xe) SFD ND (d)
109 Figure 5-8. Hyperpolarized CFSR 129Xe NMR experiments in Ga18 nanotubes in (a)16.7% and (b)100% Xe with total gas pressure of 4000 mbar. The corresponding time-axis expansions of (a) and (c) are presented in (b ) and (d), respectively. Least-squares fits of Eq. (4-22) and Eq. (4-20) are represente d as solid line and dash line, respectively. 30x10-3 25 20 15 10 5 0Sc( )/Sgas 2.0 1.5 1.0 0.5 0.0 (s) PXe=667 mbar(16.7% Xe) ND SFD (a) 35x10-3 30 25 20 15 10 5 0Sc( )/Sgas 2.0 1.5 1.0 0.5 0.0 (s) PXe=4000 mbar(100% Xe) ND SFD (c) 30x10-3 25 20 15 10 5 0Sc( )/Sgas 0.25 0.20 0.15 0.10 0.05 0.00 (s) PXe=667 mbar(16.7% Xe) ND SFD (b) 35x10-3 30 25 20 15 10 5 0Sc( )/Sgas 0.25 0.20 0.15 0.10 0.05 0.00 (s) (d) PXe=4000 mbar(100% Xe) ND SFD
110 Selective CFSR hyperpolarized 129Xe NMR experiments were also performed in Ga18 nanotubes at 25 oC where the inner diameter is a bout 22% larger than that of Ga10 nanotubes. The representative selective saturation-recovery curves, along with the least-squares fits to Eq. (4-22) and Eq. (4-20), are shown in Figure 5-8a and c. The fitting curves for SFD and ND in Ga18 nanotubes are very similar. However, with the expansion of time-axis at short recoverytime in 16.7% and 100% Xe gas mixture (Figure 5-8b and d), the normal 1D diffusion function (Eq. (4-22)) evidently yields the best fit, revealing that Xe in the Ga18 system obeys normal 1D Fickian diffusion time-scaling. The results sugges t that CFSR technique has the capability to distinguish between normal 1D Fickian diffusion a nd single-file diffusion of the confined atoms inside the nanotube systems with different internal diameters. The 1cT and pre-factor terms of Eq. (4-20) and Eq. (4-22) ( i.e. CF and CD) in Ga10 and Ga18 nanotubes extracted from CFSR hyperpolarized 129Xe NMR experiments are summarized in Figure 5-9. Both Xe 1cT relaxation times in gallic wheel nanotubes are much shorter than Xe 1cTin AV.180 From SEM analysis of Ga10 nanotubes, the average length of the nanotube crystals is longer by a factor of ~30 than that of AV nanotube crystals, suggesting that the fast 129Xe NMR signal recovery observed in the gallic nanotube s is not due to short channel length. While 1cTrelaxation time of Xe in Ga18 was found to be shorter than that in Ga10 nanotubes, the 1cTvalues in either gallic nanotube syst em are roughly the same, within th e experimental uncertainties, at variable Xe pressures (Fi gure 5-9a and c). The rapid 1cT relaxation of Xe in Ga18 nanotubes may result from the presence of paramagnetic im purities. The relaxation mechanisms in Xe/Ga10 and Xe/Ga18 systems appear to be dominated by the Xe-wall interactions, because the spin relaxation time does not depend on the density of Xe atoms inside the channels. This is in good agreement with the pressure independence of the Xe ch emical shift of the adsorbed phase in Ga10 and Ga18
111 nanotubes. The pre-factor terms, CF and CD, of Eq. (4-20) and Eq. (4-22) in Ga10 and Ga18 nanotubes are on the same order of magnitude as CF in AV nanotubes.180 As shown in Figure 5-9b and d, CF and CD in Ga10 and Ga18 nanotubes are nearly pressure independent. However, due to lack of the information about the Xe adsorption capacity of Ga10 and Ga18 nanotubes, a quantitative interpretation has not been yet possible. If Xe adsorption into the channels is favorable, the channels might be readily saturated (1 ) at very low Xe density, resulting in a lack of pr essure dependence of the CF or CD over the pressure range studied. To clarify it, the measurements of Xe adsorption isotherm and Xe fractional occupancy in Ga10 and Ga18 nanotubes are needed. Figure 5-9. Xe pressu re dependence of (a) T1c and (b) CF determined by least-squares fit of Eq. (4-20) in Ga10 nanotubes. Xe pressure dependence of (c) T1c and (d) CD determined by least-squares fit of Eq. (4-22) in Ga18 nanotubes. Error bars indicate 95% confidence intervals. Total pressure of Xe/He gas mixture is 4000 mbar. 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5T1c (sec) 100 80 60 40 20 % of Xe in Ga10 ( a) 86x10-3 84 82 80 78 76CF( ) 100 80 60 40 20 % of Xe in Ga10 (b) 110 100 90 80 70 60T1c(ms) 100 80 60 40 20 % of Xe in Ga18 (c) 75x10-3 70 65 60 CD( ) 100 80 60 40 20 % of Xe in Ga18 (d)
112 5.4 Conclusions In addition to the dipeptide nanotube system, the diffusion properties of Xe in two gallic molecular wheel nanotube systems with different channel diameters have been investigated. The isotropic spectral line-shapes of Xe inside the Ga10 and Ga18 nanotubes were observed, indicating the motion of Xe atoms in Ga10 and Ga18 is less restricted than in AV nanotubes. The observed Xe chemical shifts in the nanotube phase of Ga10 and Ga18 nanotubes do not depend on Xe pressure at room temperature. The results sugges t that the Xe-wall interaction dominates over the Xe-Xe interaction in the ga llic-wheel nanotubes at 25 oC The kinetic analysis of the selective CFSR hyperpolarized 129Xe NMR based on the magnetizati on exchange model successfully distinguished between drastica lly different diffusion time-sca ling behaviors in the gallic nanotubes. Single-file diffusion and normal 1D Fickian diffusion have been observed in the Ga10 and Ga18 nanotubes, respectively. These results are cons istent with expectations in the basis of different inner diameters relative to the size of Xe atom. The 1cT relaxation time of Xe in Ga18 was found to be shorter than that in Ga10 nanotubes. The relative shor t relaxation time is likely due to paramagnetic impurities in the sample. Furthermore, Xe 1cT relaxation times in Ga10 and Ga18 nanotubes were found to be almost independent of Xe pressure, a result which is consistent with a spin-lattice relaxation mechanism dominated by Xe-wall interactions in these gallic nanotube systems at 25 oC Moreover, the observed pressure independence of CD and CF over the 667 4000 mbar pressure range may be attributed to the full occupation of channels at low Xe pressure. While the 1cT relaxation time and CF or CD value can be quantita tively obtained from CFSR technique, the information of channel lengths and adsorption properties must be determined from other types of characteriza tion techniques, such as SEM and adsorption isotherm studies.
113 Although the 1cT relaxation time in the gallic nanotubes was observed to be relatively short, the Xe diffusion inside the channels, as investigated by CFSR experiments, was not limited by such short 1cT relaxation time. As noted previously, in the steady-state continuousflow hyperpolarization condi tion, fresh hyperpolarized 129Xe gas in the sample space can be replenished on the time-scale of the gas residence time, not the 1T relaxation time, as in thermally polarized NMR experiments. Ther efore, the complete diffusion route of hyperpolarized gas in the channels can be traced by CFSR even under conditions where 1T relaxation is rapid. In summar y, single-file diffusion and normal -diffusion nanotube systems can be explicitly distinguished by the CFSR tec hnique presented herein, suggesting that this approach can be potentially applicable to dive rse 1D nanotube systems with different channel dimensions and chemical compositions.
114 CHAPTER 6 DIRECT OBSERVATION OF ATOMS ENTERING AND EXIT ING SINGLE-FILE NANOTUBES BY A TWO-DIMENSIO NAL HYPERPOLARIZED XE-129 NMR 6.1 Introduction In single-file systems, the rates of adsorption and desorption are expected to be determined by the rate at which molecules en ter or escape at the channel openi ngs, rather than the internal displacement.1 However, such effects of the molecular exchange and diffusion localized in the vicinity of channel openings ha ve not been investig ated experimentally in detail. We have demonstrated the gas adsorption and diffusi on in AV and gallic wheel nanotubes by CFHP 129Xe NMR. The locations of Xe in the channels an d gas phases can be explicitly reported by the chemical shifts at variable experimental conditions It is therefore of great interests to study the microscopic molecular exchange in the single-file nanotubes by 129Xe NMR. Two-dimensional exchange 129Xe NMR spectroscopy (2D-EXSY ) has been utilized to investigate the slow exchange processes among th e multiple adsorbed sites in diverse systems, including liquid crystals,33,233 zeolites,5,234,235 polymers,13,236,237 aerogels,238,239 and carbon nanotubes.229,230 The presence of molecular exchange within a time scale on the order of longitudinal 1T relaxation time gives rise to cross p eaks in the 2D-EXSY spectrum between the frequencies of exchange sites.38 Numerous thermally-polarized 129Xe NMR studies in the basis of quantitative kinetic analysis of gas exchange in the nanoporous materials have been reported in few decades. With the advent of continuous-flow hyperpolarized 129Xe NMR, it is now feasible to overcome conventional sensitivity limitations.35,144,240 While CFHP 129Xe 2D-EXSY is well-suited for the kinetic studies of gas ex change in nanoporous materials, the information obtained by most of the previous CFHP 129Xe 2D-EXSY NMR works ha s been of a qualitative nature, such as the determina tion of pore-space interconnectivity238,239,241, pore geometry153, and
115 exchange pathways.147,238,242 It would appear that extraction of quantitative exchange rates has been hampered by the lack of an appropriate kinetic formalism to the analysis of 2D-EXSY spectra acquired under CFHP condition. The quantita tive kinetic studies of thermally-polarized and hyperpolarized Xe 2D-EXSY in the litera ture are briefly summarized as follows. 6.1.1 Thermally-polarized Xe 2D Exchange NMR For quantitative interpretation of the thermally-polarized 129Xe 2D-EXSY experiments, the time evolution of integrated diag onal and cross-peak signals ca n be substantially fit to an appropriate kinetic model, which is fundamentally based on Ernst et al .38 In the case of two-site exchange, a simple exchange model w ith first-order exchange process is AB BAk kAB (6-1) where A and B represent the exchange sites; ABk and BAk are the exchange rate constants. The time evolutions of z magnetizations, ()A z M t and ()B z M t, are given by the following master equation: ()(0)()(0) ()(0)()(0)AAAA zzzz BBBB zzzzMtMMtM d dt MtMMtM (6-2) where is the kinetic matrix. If cross relaxation is absent in the system, it is a sum of exchange and relaxation matrices. 1 1 1 1 ABABA ABBABkTk kkT (6-3) 1AT and 1 B T are longitudinal relaxation times in the two exchange sites. The analytical solutions of Eq. (6-2) provides time-dependence of diagona l and cross-peak intensities, which can be found in Ref 38. An example of matrix representati on for the two-site exchange will be given in Appendix B. The advantage of using matrix repr esentation to deal with the site exchange
116 problem is the multi-site exchange is non-trivia l, and exchange rates corresponding to multi-site exchange can be solved easily. The typical gra phs of time-dependent diagonal and cross-peak peak integrals are shown in Figure 6-1. In the simplest case of th e two-site exchange with equal exchange rates (ABABkk) and relaxation time (11ABTT ), the diagonalpeak intensity monotonically decays as increasing the mixing time (Figure 6-1a), whereas the cross-peak intensity initially raises to its maximum and decays gradually with the mixing time due to the 1T relaxation (Figure 6-1b). Figure 6-1. Simulated mixing-time dependence of (a) diagonal-peak and (b) cross-peak intensities in 2D-EXSY based on two-site exchange model. (150ABABkkms ;112ABTTs ) It was noted that almost all the previous quantitative works of thermally-polarized 129Xe 2D-EXSY NMR were analyzed according to the matrix representation. Ripmeester et al.5 have first investigated the intraand inter-particle exchanges of Xe in zeolites by thermally-polarized 129Xe 2D-EXSY NMR associated with matrix representation analysis. Since then, several reports were following this approach to determine Xe exchange rates in various porous materials. Jokisaari et al.33,243 performed a series of kinetic studies on liquid-crystalline systems confined in 14x103 12 10 8 6 4 2 0Diagonal-peak intensity (a.u.) 20 15 10 5 0mixing time (sec.) (a) MAA=MBB 400 300 200 100 0Cross-peak intensity (a.u.) 20 15 10 5 0mixing time (sec.) (b) MAB=MBA
117 controlled glass. Brotin et al.244 investigated the gas dynamics in the Xe/cryptophane complex in the aqueous systems. The kinetic paramete rs, including Xe exchange rate constant, 1T relaxation time, diffusion coefficient, and activation energy of diffusion, as well as adsorption enthalpy and free energy of Xe on the adsorbed site can be determined accordingly. These parameters significantly depend on the particle size, pore geometry, and Xe 1T relaxation times on the exchange sites.5 To quantitativel y extract such information, a seri es of 2D-EXSY spectra must be acquired as a function of mixing time. However, as noted above, total ex perimental time per 2DEXSY spectrum may take seve ral hours due to lengthy 1T relaxation time and inherently low sensitivity of thermally-polarized 129Xe NMR. Therefore, although the kinetic model is available to apply on thermally-polarized 129Xe 2D-EXSY NMR, mixingtime dependent study is generally impractical. 6.1.2 Hyperpolarized Xe 2D Exchange NMR The analytical expressions for the mixing-time dependences of the cr oss and diagonal-peak signals found in the literature5,58 are validated only in the case of (1) thermally-polarized spins in the absence of flow ( e.g. in a sealed NMR tube) and (2) equa l cross-peak signals represent the forward and reverse exchange processes. Howe ver, the conventional matrix formalism was applied without modification to estim ate exchange rates in recent CFHP 129Xe 2D-EXSY study of gas exchange in porous silicon.242 The low integrated intensities of the exchange cross-peaks and correspondingly low exchange rates in their studies may not reflect the true intrinsic exchange rates under CFHP condition. As the ki netic model presented below reveals, flow effects must be considered when the gas residence time in the sample space is shorter than exchange time: 1 Rdk. In this regime, flow attenuates the exchange cross-peaks involving the gas phase, leading to a possible underestimation of the exchange rates. Moreover, the cross-
118 peaks representing the forward and re verse exchange processes in CFHP 129Xe 2D-EXSY spectra are generally asymmetric with respect to the spec trum diagonal, as discussed in qualitative terms by Anala et al. in a study of the combustion process.245 Here we demonstrate how CFHP 129Xe 2D-EXSY can be used to detect Xe atoms entering and exiting the channel openings in AV. The mi xing-time dependence of the diagonal and crosspeak signal integrals will be fit to analytical expressions assuming slow exchange between the gas phase and a surface exhibiting Langmuir ad sorption. The mean desorption rate was determined at low, moderate and high Xe fractional occupancies in AV, yielding semiquantitative information about mo lecular exchange in the vicin ity of the channel openings. 6.2 Experimental 15 mg sample of polycrystalline AVa was packed loosely into NMR sample holder and evacuated to about 10-5 mbar at 100 oC for 2-3 hours prior to NMR measurements. Spectra were acquired at a field of 9.4 T (110.7 MHz 129Xe resonance frequency) with a Bruker Avance spectrometer. The Rapid accumulation of spectra was achieved by pre-pending the standard 2DEXSY pulse sequence with a satu rating RF pulse train (SAT) follo wed by a fixed re-polarization delay 1 The modification serves to (1) circumvent the lengthy acquisiti on recycle delay that would be required using thermally-polarized 129Xe NMR due to lengthy 1T relaxation time and (2) produce a reproducible polarization distribu tion as a function of displacement from the channel openings. Prior to each repetition of the 2D-EXSY pulse program, the 129Xe magnetization in the sample space is initially destroyed by the application of a non-selective /2 pulse train followed by a re-polarization delay of 1 =4s to allow the build-up of hyperpolarized Xe inside the channels. The comp lete CFHP 2D-EXSY pulse sequence is shown a part no.: 0210032883; MP Biochemicals, Santa Ana, CA
119 in Figure 6-2, where m is the mixing time. An 8-step phase-cycle was employed for coherence transfer pathway selection.38 It should be noted that under the present experimental conditions only hyperpolarized 129Xe gives rise to observable NMR signal, since thermally-polarized 129Xe signal cannot be detected w ithout signal averaging. Figure 6-2. NMR pulse sequence of CFHP 2D-EXSY. (SAT is the non-selective saturation RF pulse train.) A series of ten CFHP 2D-EXSY spectra we re acquired with mixing times ranging from m 10 to 600 ms at Xe partial pressu res of 92, 1320, and 3300 mbar at -10 oC Typically, 64 and 1024 points were collected in the t1 and t2 dimensions. A line-broa dening of 300 Hz was applied in both time dimensions prior to Fourier transformation. Chemical shifts were referenced to dilute Xe gas (0 ppm). Hyperpolarized 129Xe gas was generated by the home-built continuous-flow Rb-Xe spinexchange optical-pumping system described in Section 2.4.4. The Xe gas mixture was recirculated through the sample space at a flow rate of 100 ml/min as measured on a calibrated flow meter. The experiments at 92 mbar were carried out using a 2%/2 %/96% natural isotopic
120 abundance 129Xe/N2/He gas mixture.b At this pressure, the 129Xe spin polarization reached levels as high as about 20 %. The total gas pressure was 4600 mbar in all experiments. A mixture of natural abundance 129Xe gasc and heliumd was used for the experiments at 1320 mbar and 3300 mbar Xe partial pressure. The fractional occupa ncies of Xe in AV were estimated from the perpendicular component of the cylindrical ly symmetric chemical shielding tensor, of NMR spectra, as described in Section 3.3.4. Although the experiments presented herein were performed at -10 oC the temperature dependence of (at constant m ) is assumed to be only weak since depends primarily on Xe-Xe interactions.19,22 6.3 Magnetization Exchange Model for Continuous-flow Hyperpolarized Xe 2D-EXSY NMR A kinetic model is postulated on the basi s of the master equations describing the continuous-flow hyperpolarized 129Xe 2D exchange NMR. In the assumption of steady-state adsorption on a Langmuir surfac e, the rate equations of gaseous and nanotube phase magnetizations, g M and c M can be described as 1 g gig c dgdc ggRdMMMM n kMkM dtnT (6-4) 1 ccc dgdc g cdMnM kMkM dtnT (6-5) where /cgnn ratio of total adsorption sites to gas atoms, dk desorption rate constant, and i M is the magnetization of freshly hyperpolarized gas entering the sample space. R is the gas residence time in the sample space, which is inversely proportional to the gas flow rate. The b part no.: ISO-XHN-C; Spectra Gases Inc., West Branchburg, NJ. c part no.: XE5.0RS-D8; Praxair, Danbury, CT d part no.: UN1046; Praxair, Danbury, CT
121 longitudinal relaxation times of Xe inside th e channels and in the gas phase are given by 1cT and 1 g T, respectively. For 129Xe in AV at 9.4 T, 150150cTs depending on ,180 and 1 g T>600 s Since the re-polarization delay of 14 s during which the hyperpolarized atoms enter and diffuse into the channels, is much shorter th an either longitudinal relaxation time, the longitudinal relaxation terms can be neglected in Eq. (6-4) and E q. (6-5). Assuming an excess of Xe gas ( i.e. /1cgnn ), the re-polarization of the gas during 1 will be dominated by the influx of freshly hyperpolarized gas into the sample space. This assumption is validated by the observation that selective satu ration of the nanotube phase 129Xe transition did not significantly affect the gas phase signal.180 During pre-polarization delay 1 Eq. (6-4) and Eq. (6-5) can be solved by the steady-state approximation, where 0gcdMdtdMdt Hence, the initial magnetizations in the gas and channels at the beginning of the mixing delay 0m are as follows: 111Ro ggiMMMe (6-6) 1 1/ 1 1 111d Rk Rd o c cci gRdeek n MMM nk (6-7) Longitudinal magnetizations (stored from tr ansverse magnetization which evolves during t1) that do not exchange during m yield the diagonal peaks in the 2D-EXSY spectrum. The gas and channel diagonal-peaks are expected to decay mono-exponentially: 11 ,expo c ggmgmd Rgn MMk n (6-8) 1,dmk o ccmcMMe (6-9)
122 The mixing-time dependences of the longitudina l magnetizations representing Xe entering and exiting the channels during the mixing time (assuming excess gas) are / 1 1,k dc dmmR gcmg g Rdkn MMee n k (6-10) / 1 1,k d dmmR cgmc Rdk MMee k (6-11) The expressions reveal that the cross-peaks will generally have unequal amplitudes, vanish in the limit 0R or 0dk and are significantly affected by the flow when 1 Rdk. However, the time dependence of the two cross-peaks will be a pproximately the same in this model, and each is predicted to pass through a maximum at max1ln/mdRdRkk Eq. (6-10) and Eq. (6-11) pertain to a homogeneous surface consisting of cn adsorption sites. It is important to note th at the average channel length in our AV sample is roughly five orders of magnitude greater than the diameter of Xe atom. For an atom to escape from the channel, it must first diffuse to the opening an d sequentially overcome a potential energy barrier. In Chapter 4, we have postulated that the diffu sion-limited exchange kinetics in 1D channel can be modeled by taking a distribut ion of desorption rates: 2 14//ddkFz for single-file diffusion or 12 0//ddkDz for normal 1D diffusion. In the present work, the distribution dkz will be replaced by a single mean value, dk. This should yield semiquantitative results at sufficiently short mixing times.
123 6.4 Results and Discussions Xe adsorption in AV nanotubes is known to obey the Langmuir equation74 where the steady-state fractional occupancy is given by = occupied sites/total sites = /(1)XeXe K pKp ad K kk is the equilibrium constant, and X ep is Xe partial pressure. By varying X epat constant T the effect of occupancy on the exchange rate can be explor ed under steady-state adsorption condition. Figure 6-3 presents the 1D CFHP 129Xe spectra in AV acquired at Xe partial pressures of 92, 1 320 and 3300 mbar at -10 oC The contribution of Xe -Xe interactions to the isotropic chemical shift becomes significant as the Xe occupancy increases. The chemical shielding anisotropy exhib its a sign inversion at 0.4 due to the relative contributions of Xe Xe and Xewall interactions to the perpendicu lar and parallel components of the shielding tensor.19,179 At 92 mbar, the anisotropy is dominated by the Xe-wall interactions (Figure 6-3a), while at 3300 mbar (Figure 6-3c ), Xe-Xe interactions dominate. Validating the assumption of steady-state Langmuir adsorption, the estimated e quilibrium constants reported in Table 6-1 are within experimental error the sa me at all three pressures. Figure 6-3. Steady-state c ontinuous-flow hyperpolarized 129Xe NMR spectra in AV nanotubes, acquired at -10 oC at the following Xe partial pressu res: (a) 92 mbar (b) 1320 mbar (c) 3300 mbar. The chemical shift scale is referenced to dilute Xe gas (0 ppm). 14012010080 160140120100 180160140120 (ppm)(a) 92 mbar(b) 1320 mbar(c) 3300 mbar || 14012010080 160140120100 180160140120 (ppm)(a) 92 mbar(b) 1320 mbar(c) 3300 mbar ||
124 The 129Xe 2D-EXSY spectra at 92, 1320 and 3300 mb ar are presented in Figure 6-4. The gas channel and channel gas cross-peaks are strongly attenua ted by the gas flow rate which limits the residence time R of gas atoms in the sample sp ace. The observation of gas atoms entering (upper left cross-peak) and exiting (low er right cross-peak) the single-file nanotubes is evidenced by the appearance of cross-peaks. El ongated diagonal-peaks due to Xe which did not exchange during m are observed at 92 mbar (Figure 6-4a ) and 3300 mbar (Figure 6-4c), while the contours of the diagonal peak at 1320 mbar exhi bit a roughly circular shape (Figure 6-4b). As in the 1D spectra presented in Figure 6-3, the sh ape of the adsorbed-phase diagonal peaks in the 2D-EXSY spectrum reflects the orientation of AV cr ystallites with different orientations with respect to the magnetic field. Cross-peaks co rresponding to exchange between different individual channel orientations are not observed, indicating that multiple Xe exchange events between different channels canno t be detected under the pres ent experimental conditions.
125 Figure 6-4. Continuous -flow hyperpolarized 129Xe 2D-EXSY spectra in AV nanotubes at -10 oC acquired at the mixing times yielding maximum cross-peak intensities: (a) 92 mbar, m =35 ms (b) 1320 mbar m =100 ms (c) 3300 mbar m =100 ms. The spectra were recorded with 641024 data points with 8 scans per spectrum. A Gaussian li ne-broadening of 300 Hz was applied in both time dimensions. The tota l experiment time per 2D spectrum with 14 s was about 30 min. (a) (b) (c) f2, ppm f2, ppm f2, ppm f1, ppm f1, ppm f1, ppm f2, ppm f2, ppm f2, ppm f1, ppm f 1, pp m f1, ppm 125 0 50 100 150 0 50 100 150 0 50 100 150 0 50 100 150 gas channel Xe Entering Xe Exiting 0 50 100 150 0 50 100 150
126 Figure 6-5 presents the m -dependence of the crossand diagonal-peak integrals along with the non-linear least squares fits to Eq. (6-8) (6-11). Note that each data point in Figure 6-5 represents a full 2D spectrum, but due to hyperp olarized Xe signal enhancement, the acquisition time of each point requires only 30 minutes. The fitted values for dk and R at each pressure are reported in Table 6-1. Although a mono-exponen tial decay of gas-phase diagonal peak is expected in Eq. (6-8), a bi-expone ntial function yielded better f its. However, the pre-exponential factors obtained from least-squares fits show th at the more rapidly decaying exponential term of the two accounts for about 90% of the initial gas signal at 92 and 3300 mbar. Although the 2DEXSY spectra were acquired at a nominal flow rate of 100 mL/min at all three pressures (as indicated by the gas flow meter), no correctio n was made for gas composition. The actual residence times at 1320 and 3300 mbar appear to have been substantially longer than in the experiments at 92 mbar. The gas phase diagonal-peak at 1320 mbar yielded 68R ms. Table 6-1. Best-fit kinetic parameters fo r CFHP Xe 2D-EXSY sp ectra in AV at -10 oC (Uncertainties represent 95% confidence intervals.) tube-tube gasgas gaschannel Eq.(6-10) channel gas Eq.(6-11) Xe p /mbar K /1bar dk/s-1 R /ms dk/s-1 R /ms dk/s-1 R /ms 92 0.047 0.520.03 2.51 19 3 6.1 2 19(fixed) 3.21 19 (fixed) 4.2 2 11 5 2.21.4 13.4 5 1320 0.39 0.480.15 1.50.6 68 35 68(fixed) 68(fixed) 2.3 0.5 35 3 2.70.5 43 3 3300 0.64 0.540.08 n/a 28 5 1.9 0.8 28(fixed) < 2.2 28 (fixed)
127 Figure 6-5. Mixing-time dependence of crossand diagonal-peak si gnal integrals in the CFHP 129Xe 2D-EXSY spectra in AV nanotubes at -10 oC (a) Channel-to-gas cross-peak signal integrals at three different Xe partia l pressures. (b) Gas-to-channel cross-peak integrals (c) Gas-to-gas diagonal-peak mi xing time dependences at 92 and 3300 mbar. The solid and dashed lines represent the leas t-squares fits to the decay functions given in the legend. (d) Channel-to-channel di agonal peak mixing time dependences at 92, 1320 and 3300 mbar. The dash lines represents the least squares fits to a single exponential decay function. 1000 800 600 400 200 0Channel-to-Gas Cross Peak Integral 600 400 200 0m(ms) 92 mbar 1320 mbar 3300 mbar Equation (6-11) 2 param fit w/ R fixed 3 param fit w/ R free (a) 1500 1000 500 0Gas-to-Channel Cross Peak Integral 600 400 200 0m (ms) 92 mbar 1320 mbar 3300 mbar Equation (6-10) 2 param fit w/ R fixed 3 param fit w/ R free (b) 101 102 103 104 Gas Diagonal Peak Integral 500 400 300 200 100 0m (ms) 92 mbar 3300 mbar a exp(-b m) aexp(-c m)+bexp(-d m) (c) 4 3 2 1 0 Channel Diagonal Peak Integral /104 600 400 200 0m(ms) 92 mbar 1320 mbar 3300 mbar (d)
128 To assess the validity of our simple kinetic mode l, fits to each of the cross-peak mixing time dependences at each pressure were performed in two different ways: by either fixing R to the value established from the ga s diagonal-peak in the same spec trum, or by allowing all three parameters ( dk, R and the pre-exponential fact or) to vary freely. The pa rameters resulting from the 2 and 3 parameter least-squa res fits are reported in Tabl e 6-1 as the upper and lower row entries for dk and R at each of the three pressures studi ed. Where no table entries are reported, the fits did not exhibit good qualitative agreement with the experimental data. Despite the large relative errors, the cross-peak fits reveal a clear decrease in the rate constant dk upon increasing the occupancy from 0.047 (92 mbar) to 0.39 (1320 mbar). The trend is more pronounced for the gas ( g )channel ( c ) process. At 92 mbar (low occupancy), reasonable self-consistency of the model was obta ined. The residence time extracted from the decay of g gM is within the 95% confidence interval of the values obtained from the fits to both cross-peaks. However, the best-fit desorption rate for the g c (Xe entering) process was about a factor of 2 higher than that for the cg (Xe exiting) process. This asymmetry might be attributed to one or more of the following factors which are not accounted for by our simplified model: re-adsorption, presence of a desorption barrier, cha nnel boundary effects, or onedimensional diffusion effects. At 3300 mbar, where the occupancy is relativ ely high, the fixed value for the residence time of 28 ms (obtained from the diagonal-peak decay) yielded good qualitative fits to the crosspeaks, and close agreement between the dk values obtained from the cg and gc crosspeaks was obtained. Allowing R to vary yielded poor agreement to the data at this pressure due to low signal-to-noise of the cr oss-peaks. At 1320 mbar, holding 68R ms constant yielded
129 unacceptable two-parameter fits of the cross-peaks (not shown). We do not have an explanation for this irregularity. However, the three-parameter cross-peak fits allowing R vary freely gave self-consistent results, and dk obtained from the entering and exit ing processes are in agreement. Several factors could account for the observed decrease in dk. A decrease in the rate with occupancy might be explained by the -7.4 kJ/mol increase in the enthal py of desorption upon increasing the pressure from 92 mbar to 1320 mbar at -10 oC a change which would be expected to reduce dk by a factor of about 100. However, the actua l reduction in only by a factor of about 3, implying diffusion-limited rather than ther modynamic-limited desorption. For SFD, which has been confirmed in AV for time-scales longer th an about 0.5 s, the mean-squared displacement increases according to 22 zFt where F is the single-file mobility. For hard-spheres particles in cylindrical channels, 1 F .184 Thus, the observed reduction in desorption rate upon increasing the occupancy is consistent with a decrease in th e diffusivity in the channels. As shown in Figure 6-5d, the diagonal-peak re presenting Xe which remains in the channels throughout the exchange delay also exhibited a decrease in diag dk with increasing occupancy, but the values are slightly lower than those extrac ted from the cross-peaks. This result can be explained qualitatively in terms of diffusion-limited gas exchange. The cross-peak signals arise from atoms close enough to the channel openings to escape during the finite residence time. In contrast, the diagonal peak includes signal contri butions from all Xe atoms which have diffused into the channels during the l onger re-polarization delay of 14 s. For this larger ensemble of Xe atoms, the mean diffusion time to return to the channel opening is longer, consistent with an apparent reduction in the desorption rate.
130 While the single file mobility of Xe in AV nanotubes is unknown, a rough estimate of the mean displacement can be made from previously measured single-file m obility in zeolites with 1D channels. For example, a PFG NMR study212 of CF4 (4.7 ) in AlPO4-5 zeolite (8.2 cylindrical channels) at m oderate occupancy yielded 1221/2110ms F, while a quasi-elastic neutron diffraction study214 of CH4 (3.8 ) in zeolite-48 (5.35.6 ) yielded 1221/2210ms F. Assuming a similar single-file mobili ty for Xe in AV, the atoms would reach a depth of ~2 m during the pre-polarization delay 14 s The residence time of Xe atoms in the sample space limits the cross-peak inte nsities. At the flow rate used in the present study, the maximum cross-peak in tensities were observed at 50 ms, where the exchange is limited to polarized gas atoms within ~0.7 m of the channel opening. Interrupting the gas flow momentarily during the exchange delay is envisaged as a means to increase cross-peak intensities. By increasing the residence time, it should be possi ble to probe the kinetics of desorption over a much wider range of length scales or inter-crystalline exchange between nanotubes with different orientations. The interrupted-flow experiments will be presented in the following chapters. 6.5 Conclusions Direct observation of Xe entering and exiting self-assembled L-alanyl-L-valine nanotubes has been facilitated by c ontinuous-flow hyperpolarized 129Xe two-dimensional exchange NMR spectroscopy. Analytical expressi ons for the mixing-time dependence of the diagonal and crosspeak signals have been derived under conditions of excess Xe gas, revealing that the flow effect needs to be considered when 1Rdk as is the case for Xe in AV under our experimental condition. Nonlinear least-squares fitting to these expressions yi elded the mean rate of Xe escaped from the AV channels. Although the assu mption of a single mean desorption rate (as
131 opposed to a distribution of rates) probably contributes to the rela tively large uncertainties in the fitted values of the desorption rate, a reduction in mean desorption rate constant with increased Xe density has been clearly observed. This findi ng is consistent with a decrease in the Xe mobility of the channels in the diffusion-limited exchange regime. While single-file diffusion of Xe in AV has been confirmed at longer time-scales,180 the semi-quantitative analysis of the present work precludes any definite conclusions to be made concerning the relative importance of normal one-dimensional diffusion versus singl e file diffusion to the exchange process. Nonetheless, this study ha s shown how hyperpolarized 129Xe NMR can be applied to the investigation of gas exchange dynamics in nanotubes, and the kinetic model developed herein should serve as a starting point for future hype rpolarized NMR studies of adsorption, diffusion and exchange processes in such materials.
132 CHAPTER 7 SIGNAL ENHANCEMENT OF HYPERPOLARI ZED XE-129 2D-NMR EXCHANGE CROSS PEAKS IN NANOTUBES BY INTERRUPTION OF THE GAS FLOW 7.1 Introduction It has been noted that previous qu antitative kinetic studies employing 129Xe 2D-EXSY have been mostly limited to thermally-polari zed conditions, for which multi-site exchange models have been established.5,33,38,58,235,244 The thermally-polarized 129Xe experiments generally suffer from inherently low sensitivity or una cceptably long acquisition times for mixing-time dependence studies, ranging from hours to days per 2D spectrum. As noted previously, only a few quantitative applications of CFHP 129Xe 2D-EXSY have been reported,242 and the potential complications and limitations due to gas flow effects have not been discussed in the literature. In this chapter, the issue of flow effects in CFHP 129Xe 2D-EXSY will be investigated. In Chapter 6, we proposed a kinetic model to describe the magnetization exchange between the flowing gas phase and a Langmuir adsorption surface.246 Under the flow condition, the gas residence time R in the sample space is determined by the gas flow rate ( i.e. 1RG ). In the diamagnetic solids, the Xe longitu dinal relaxation time in the gas phase is generally much longer than any of the other relevant experiment al time-scales. The spectra acquired under the continuous-flow condition will be affected by gas flow if the gas residenc e time is much shorter than the longitudinal relaxation time of the Xe gas ( i.e. 1RgT ). In such a case, the gas diagonal-peak and all cross-peak signals repres enting exchange with the gas phase in 2D-EXSY spectrum will strongly depend on the residence time and exchange rates. According to Eq. (6-10) and Eq. (6 -11), a simple comparison of the m -dependences of the cross-peak intensities with variable R and constant dk can be made and illustrated in Figure 7-1.
133 As 50Rms where it is on the same time-scale of residence time in Xe/AV system under the flow rate of 100 mL/min and Xe partial pressu re of 1320 mbar at -10 oC246, the cross-peaks are strongly attenuated. Nevertheless, as R gradually increases, th e cross-peak signal is significantly enhanced and the location of its maximum is shifted to longer m In the limit of R where gas flow is absent in the sample space, the cross-peak intensity exponentially grows to its maximum and eventually reaches a pl ateau. This comparison indicates that the finite residence time of Xe gas in the sample space strongly suppresses the cross-peak intensities associated with the exchange betw een surface and gas phase. While R can be increased by simply reducing the gas flow rate hyperpolarized gases will be de polarized due to the relaxation during gas transport from pu mping cell to sample space.35 It is not usually favorable for retaining high Xe polarization in the gas handling system. As will be shown below, interrupting the gas flow briefly during the mixing time can be an alternative and simple approach to extend gas residence time and consequently enhance the crosspeak intensities. By increasing the cross-peak intensities, it will be possible to explore the coupling of the gas exchange and diffusion processes over a longer range of exchange times and diffusion length scales by hyperpolarized 129Xe 2DEXSY NMR.
134 Figure 7-1. Simulated mixing-tim e dependence of the cross-peak signals at variable gas residence time R and constant desorption rate constant (13dks) based on Eq. (6-11). It will be shown how the standard CFHP 129Xe 2D-EXSY experiment can be easily modified to achieve dramatic cross-peak signal enhancement. The technique is demonstrated for Xe in the dipeptide nanotube L-alanyl-L-valine (AV),170,247 where Xe interactions,19,74 single-file diffusion180, and gas-channel exchange246 have been characterized previously. 1.0 0.8 0.6 0.4 0.2 0.0Cross-peak Intensity (a.u.) 10 8 6 4 2 0mixing time, m (sec) R= 50 ms R= 1 s R= 5 s R
135 7.2 Experimental Polycrystalline AV was studied without further purification. A 15 mg AV samplea was evacuated to ~10-5 torr at 100C in situ for 2-3 hours to remove moisture prior to NMR measurements. The gas mixtureb consisted of 2% natural abundance 129Xe, 2% N2 and 96% He at a total pressure of 4600 mbar was used in all the Xe NMR experiments. The 129Xe spin polarization is estimated to be ~20 %. Under certain c onditions, only hyperpolarized 129Xe yields observable NMR signal, since thermally-polarized 129Xe cannot be detected at this density without signal averaging. Fract ional channel occupancy of 0.047 for Xe in AV was inferred from the Xe chemical shift tensor, as describe d in Section 3.3.4. Spectra were acquired at -10 Cin a magnetic field of 9.4 T (110.7 MHz 129Xe Larmor frequency). The /2 RF pulse width was 4s Chemical shifts were referen ced to diluted Xe gas as 0 ppm. The isotropic chemical shift difference between the gaseous and adsorbed phases of 129Xe under the experimental conditions is about 110 ppm. The layout of the hyperpolarized 129Xe gas generator35 is shown in Figure 2-12. To control the flow of hyperpolarized gas, the outlet of the sample space was connected by 1/8 O.D. PFA tubing to a two-way solenoid valve.c An auxiliary transistor-to-transistor logic (TTL) gate on the Bruker Avance NMR spectrometer was used to c ontrol the solenoid valve from the pulse sequence. a part no.: 0210032883; MP Biochemicals, Santa Ana, CA b part no.: ISO-XHN-C; Spectra Gases Inc., West Branchburg, NJ. c part no.: 1327BV122T; Jefferson Solenoid Valves, Miami, FL.
136 Figure 7-2. Pulse sequence for (a) continuous -flow (CF) and (b) interrupted-flow (IF) hyperpolarized 2D-EXSY. The solenoid valve stops the flow near the end of the repolarization delay 1 =4s. The system was allowed to settle for 2 =1s prior to application of the EXSY pulse sequence. (SAT is the non-selective saturation RF pulse train.) To create a reproducible, well-defined initial po larization condition prio r to each repetition of the 2D-EXSY pulse program, the 129Xe polarization was initially saturated by a non-selective 2 pulse train, as shown in Figure 7-2. Follo wing the saturation, freshly hyperpolarized 129Xe enters the sample space where it accumulates inside the nanot ubes during the re-polarization delay, 1 2D-EXSY spectra were acquired in either of two different modes, referred to as CF and IF, as illustrated in Figure 72. In CF mode (Figure 7-2a), the hyperpolarized gas mixture is continuously re-circulated through the sample space at a steady flow rate of 100 mL/min recorded from a calibrated flow meter, during th e entire experiment. In IF mode (Figure 7-2b), the re-circulation at a flow rate of 100 mL/min is briefly paused during the 2D-EXSY pulse
137 sequence. The normally closed solenoid valve is closed at the end of the re-polarization delay, 1 A settling time of 2 =1s following switching of the valve was allowed prior to application of the /2 EXSY preparation pulse. 2D Spectra were collected with 100 and 1024 points in the t1 and t2 dimensions with a spectral width of 26 kHz. At each t1 point, 8 transients were signal averaged. A line-broadening of 300 Hz was applied with respect to both time dimensions prior to Fourier transformation. The total experimental time for each 2D spectrum was ~65 min. The 2D spectral processing was pe rformed using of MATLABd and matNMRe. 7.3 Results and Discussions We have suggested that a momentary interrup tion of the gas flow, as shown in the pulse sequence in Figure 7-2b, should produce increased cross-peak signals and allow much longer exchange time-scales to be probed. We now demonstrate the direct comparison of the hyperpolarized 129Xe 2D-EXSY spectra acquired on Xe in AV in the interrupted-flow (IF) and continuous-flow (CF) modes. The conti nuous and interrupted-flow hyperpolarized 129Xe 2DEXSY spectra acquired at two different mixing ti mes are presented in Figure 7-3. The 1D spectra at f1=0 ppm are presented on the top of each 2D spectrum. The gaseous diagonal peak in IF mode decays very slowly from 300mms (Figure 7-3a) to 1ms (Figure 7-3c), probably dominated by gas diffusion or drift out of th e RF detection coil. In contrast, the Xe diagonal peak in gas phase obtained by the same EXSY pulse sequence but at an uninterrupted flow rate of 100 mL/min decays much more rapidly, indicating th at the gas peak in the CFHP 2D-EXSY spectrum is strongly affected by the gas flow. The decay of the adsorbed phase diagonal-peak is much less sensitive to the effects of flow than in the gas peak. d The Mathworks Inc., Natick, MA e http://www.nmr.ethz.ch/matnmr; written by J. van Beek
138 The differences of cross peaks in IF and CF modes can be summarized as follows. Firstly, the cross-peak integrals for the gas channel and channel gas processes are not equal in both modes, which is in agreement with our kinetic m odels. This may be traced to a difference in the spin polarization in the gaseous and nanotube pha ses. Secondly, the signal-to-noise of the gas phase diagonal and exchange cross-peaks is much higher in IF than in CF mode. As the mixing time increased to 1ms CFHP 2D-EXSY barely yielded any cross peaks (Figure 7-3d). However, in the IF mode, both the gas and cros s-peak signals are still clearly visible at 1ms (Figure 7-3c). The dramatic differences in th e spectra obtained under CF and IF conditions are especially evident in the 3D representations sh own in Figure 7-4. While the gas and cross-peak signals nearly vanish under CF conditions (F igure 7-4b), these peaks are observed with extremely high signal-to-noise ratio under IF conditions (Figure 7-4a). Thus, by simply interrupting the gas flow during the exchange pe riod in the 2D-EXSY pulse sequence, the crosspeak signals were enhanced by a factor of ~60. We refer to this experimental method as IFHPEXSY. Interrupting the gas flow during the mixing ti me allows gas atoms desorbing from the surface, or nanotubes as in the present case, to accumulate in the sample space for detection. For the reverse processes, a longer residence time in creases the probability that gas atoms tagged by the preparation pulse will be adsorbed by the nano tubes during the mixing time. In principle, the mixing-time dependences of the cr oss-peak and diagonal-peak si gnal integrals in thermallypolarized and IFHP 129Xe 2D-EXSY spectra should be essentially the same.
139 Figure 7-3. HP 129Xe 2D-EXSY spectra of Xe in AV at -10 oC with mixing times of (a,b) 300 ms and (c,d) 1s. Spectra in (b) and (d) we re acquired in contin uous-flow (CF) mode. Spectra in (a) and (c) were acquired in interrupted-flow (IF) m ode (see text). 1D spectral slices at f1=0 ppm are also presented at the top of each 2D spectrum. f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 x30 (a) IF, m=300ms(b) CF, m=300ms f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 x100 (c) IF, m=1s(d) CF, m=1s f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 x30 (a) IF, m=300ms(b) CF, m=300ms f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 f2 (ppm) f 1 (ppm) 0 50 100 0 50 100 x100 (c) IF, m=1s(d) CF, m=1s
140 Figure 7-4. 3D repr esentation of HP 129Xe 2D-EXSY spectra of Xe in AV at -10 oC acquired in (a) IF mode and (b) CF mode, each with a mixing time of m=1s. The gas peak in (a) was truncated to facilitate comparison of the cross-peaks in each spectrum. f2(pp m ) f2(p p m )f1( p p m ) f1( p p m )(a) interrupted flow, m=1s (b) continuous flow m=1s f2(pp m ) f2(p p m )f1( p p m ) f1( p p m )(a) interrupted flow, m=1s (b) continuous flow m=1s
141 7.4 Conclusions To summarize, a simple but highly eff ective modification of the CFHP 2D-EXSY experiment has been demonstrated in AV, a polycrystalline nanotube material. We have demonstrated that by interrupting the flow during the mixing time, cross-peak intensities in the Xe/AV system can be increased by a factor of ~60. The interrupted fl ow 2D-EXSY experiment can overcome the effects of gas flow which strongly affects the peak intensi ties and sets an upper limit on the maximum exchange time that will yield observable crosspeak signals. IFHP 129Xe 2D-EXSY is particularly well-suited for studies of diffusion-limited gas exchange kinetics in nanotube systems which, under continuous flow c onditions, yield cross-peaks with substantially lower signal-to-noise ratio. The experimental uncer tainty in kinetic parameters extracted from 2D-EXSY spectra are highly sensitiv e to the signal-to-noise ratio.38 The IFHP 2D-EXSY method can be expected to provide significantly greater accuracy in determination of multi-site exchange rates and facilitate the measurement of smaller exchange rates. In addition to the 2D-EXSY experiments, th e interrupted-flow experiment may also be applicable in the 129Xe polarization transf er techniques, such as cross-polarization127-129 or SPINOE.124-126 Since the cross-polarization and Overha user effect involve the polarization transfer, which is similar to the mechanism of magnetization exchange presented above, the efficiency of polarization transfer is expect ed to be enhanced by incorporating gas flow interruption. Moreover, IFHP-EXSY may be appl ied to other hyperpolarized species, such as 1H or 13C generated from parahydrogen112,113 or DNP.101-105 In principle, mixing times in IFHPEXSY are limited only by intrinsic longitudinal relaxation time 1cT and desorption rate. The ability to probe longer mixing times will facilit ate extension of hyperpolarized 2D-EXSY to
142 slower exchange processes or longer diffusion time/length scales for characterization of porespace architecture, exchange and transport proce ss in nanotubes or other nanoporous materials.
143 CHAPTER 8 INVESTIGATIONS OF GAS EXCHANGE IN GA10 WHEEL NANOTUBES BY 2D EXCHANGE HYPERPOLARIZED XE-129 NMR 8.1 Introduction The interrupted-flow hyperpolarized 2D-EXS Y technique has successfully overcome the suppressions of cross-peak intensities due to finite residence time in CFHP 129Xe 2D-EXSY, and the dramatic enhancement of cross-peak signals in IFHP-EXSY has been demonstrated in AV nanotubes.248 While the magnetization exchange model has been developed to quantitatively measure the mean desorption rates of guest mo lecules in the 1D nanotube system by CFHP 129Xe 2D-EXSY246, it is exclusively valid in the system where the 129Xe longitudinal relaxation time (1cT) inside the channels is relatively longer than the gas residence time in the sample space ( i.e. 1cRT ). In the kinetic model of CFHP 2D -EXSY presented in Section 6.3, under the interrupted-flow (IF) condition, where R Eq. (6-10) and (6-11) can be rewritten as 1,,1dmk o c gcmRg gn MMe n (8-1) 1,,1dmk o cgmRcMMe (8-2) where /cgnn ratio of total adsorption sites to gas atoms, dkis the desorption rate constant, and g M and c M are the magnetizations in the gas and chan nels at the beginning of the mixing delay which have been labeled according to their chemical shift during the 2D evolution (1t) period. Although Eq. (8-1) and Eq. (8-2) clearly exhibit th e exponential growth tre nds as a function of mixing time m as predicted in Figure 7-1, the equations are only valid in the systems, such as 129Xe in AV or TPP nanotubes, in which Xe 1cT on the diamagnetic solid surface or in the
144 nanotubes is much longer than the mixing time or any of the other relevant time-scales. The kinetic model needs to be modified in order to describe the detailed exch ange kinetic processes in 1D nanotube systems spanning from 1cmT to 1cmT regimes. In practice, the mixing time in IFHP-EXSY experiments can be extended up to the timescale of longitudinal relaxation time of Xe in th e sample. However, Xe/AV is not an appropriate system to test the validity of the 1cT-dependence of the theoretical IFHP-EXSY signal expressions. In our previous studies, Xe 1cT in AV nanotubes was determined to range from 50150 sec, depending on Xe density in the channels, at 9.4 T .180 Assuming the experimental parameters of IFHP-EXSY are set to pre-polarization delay 14 s mixing time 50ms 8 scans per t1 increment, and 64 increments on t1 domain, it would take ~8 hours to acquire a single 2D spectrum in the case of AV. Obviously, it would be impractical to acquire a series of IFHP 2D-EXSY spectra as a functio n of mixing time in AV nanotubes. One possibility to demonstrate the complete m -dependence of IFHP-EXSY is to find a system with a relatively short 1cT relaxation time. In Chapter 5, we have utilized the selective CFSR hyperpolarized 129Xe NMR experiments to inve stigate Xe diffusion in Ga10 and Ga18 nanotubes, revealing dramatically different diffusion behaviors in both nanotube systems. The Xe diffusion in Ga10 nanotubes exhibits a clea r SFD behavior, and the Xe 1cTin Ga10 is about 2.5 sec at room temperature. Therefore, Ga10 wheel nanotubes can serve as an excellent candidate of single-file nanotube system in m -dependence of IFHP Xe 2D-EXSY studies in the 1mcT limit. The Xe 1cT relaxation time in Ga18 nanotubes is ~80 ms, which is too short to conduct the IFHP-EXSY experiments since expe rimental mixing time is mostly limited by 1cT relaxation time.
145 Here, the experimental mixing-time dependence of IFHP 2D-EXSY in Ga10 nanotubes along with the modified kinetic model incorporating 1cTrelaxation time under the interruptedflow condition will be presented. The results will be compared with the 2D-EXSY results obtained in Ga10 nanotubes under the continuous-flow condi tion. It will be shown that the IFHP 2D-EXSY experiment can indeed explore th e slower exchange process in nanotubes. 8.2 Experimental Ga10 wheel nanotubes were synthe sized by Dr. Theocharis Stamatatos in Prof. George Christous laboratory (UF Chemistr y Department). The detailed procedures of the molecular wheels synthesis along with their crystal structur e identifications can be found in the literature.36 A 40 mg polycrystalline sample of Ga10 nanotubes was loosely packed into NMR sample holder and evacuated at 10-5 torr and room temperature overn ight prior to NMR measurements. The hyperpolarized Xe gas was generated by continuous-flow Rb-Xe optical-pumping spin-exchange, as described in Section 2.4.4. The gas mixture was re-circulated through the sample space during the experiments at a flow rate of 100 mL/min The 2%/2%/96% nature isotopic abundance 129Xe/N2/He gas mixturea with a total gas pressure of 4000 mbar was used for all the 2D experiments. The 2D EXSY experiments were carried out on a 9.4 T Bruker Avance NMR spectrometer operating at a 129Xe Larmor frequency of 110.7 MHz and at room temperature. The 2D-EXSY NMR spectra were acquired using the pulse sequences of CFHPEXSY and IFHP-EXSY describe d in Figure 7-2. A typical /2 pulse duration was about 4.5 s. During the re-polarization delay of 12 s the polarized Xe was allowed to flow into the sample space and to diffuse and accumulate in the chan nels. Each 2D spectrum consisted of 64 and 1024 points in t1 and t2 dimensions, respectively. The free i nduction decay was accumulated in 8 scans a part no.: ISO-XHN-C; Spectra Gases Inc., West Branchburg, NJ.
146 for each t1 increment. The spectral width is 38 kHz in both the t1 and t2 dimensions. For IFHPEXSY, a gas flow settling time 21 s was allowed following closing of the solenoid valve. The total acquisition time for each 2D spectrum is a bout 25 min. The spectra were processed with 300 Hz of Gaussian line-broa dening applied to both dimens ions prior to the Fourier transformation. The mixing time was varied from 10 ms to 1s. The reported Xe NMR chemical shifts were referenced to the dilute Xe gas as 0 ppm. 8.3 Magnetization Exchange Model for 2D-EXSY under Flow Interruption Here we propose a modified magnetization exchange model to describe the 2D-EXSY signals under the condition of fl ow interruption. As i ndicated in the IFHP-EXSY pulse sequence presented in Figure 7-2b, Xe gas remains in CF mode during the pre-polarization delay, 1 The hyperpolarized gas flow is halted prior to the first /2 pulse of EXSY sequence. During the 2D preparation delay, 1t, the Xe flow is interrupted. Since 11 g T the initial magnetizations in the gas and channels, g M and c M at the beginning of mixing time are given by Eq. (6-6) and Eq. (6-7). Under IF condition, the rate equatio ns describing the magnetization dynamics in the gas and nanotube phases during the mixing time are 1 g g c dgdc g gdMM n kMkM dtnT (8-3) 1 ccc dgdc g cdMnM kMkM dtnT (8-4) where 1 g Tand 1cTare the longitudinal relaxation time s in the gas and nanotube phases, respectively. As noted previousl y, since gaseous Xe relaxation time 1 g T is much longer than any other relevant experimental timescales in most diamagnetic surf aces, it can be safely ignored from Eq. (8-3). Additionally, under the condition where the excess of Xe gas is in the sample
147 space, 1cgnn can be safely assumed.246 Thus, the mixing-time dependences of diagonalpeak intensities in gas and nanotube phases are 1 100 1(,)c c dgm dm g gn n kT k n n ggmggMMeMe (8-5) 1 10 1(,)dcmkT ccmcMMe (8-6) Both diagonal-peak intensities mono-exponentially decay with mixing time; however, because of the assumption of excess Xe gases, 1cgnn the m -dependence of the gas diagonal-peak signal in Eq. (8-5) is anticipated to decay very slowly. The mixing-time dependence of the crosspeak signals for the gas channel and channel gas processes can be solved and expressed by the following equations, assuming excess of Xe gas in exchange with a Langmuir adsorption surface: 11 1111 1 0 1 22 11(,) 2dcmdcmkTkT dc gcmgkT MMee (8-7) 11 1111 1 0 1 22 11(,) 2dcmdcmkTkT dc cgmckT MMee (8-8) where 2 11 114cgdcdcnnkTkT. The detailed deviations of Eq. (8-7) and Eq. (8-8) can be found in Appendix B. The expression s clearly shown that the trends in the m dependence of Eq. (8-7) and Eq. (8-8) are essen tially the same but with unequal amplitudes, as was also the case for Eq. (6-10) and Eq. (6-11) under the CFHP condition. In the limit of 1 10cT, the equations are comparable to Eq. (8-1) and Eq. (8-2). Hence, the modified kinetic model presented above should be valid to describe the exchange process in the 1cmT regime under the IF condition.
148 To understand how the exchange process is affected by longitu dinal relaxation and desorption in the modified exchange kinetic model, a further comparison can be made. The simulations were performed based on Eq. (8-7 ) and normalized to its initial magnetization, o g M The simulated results and their corresponding y-axis expansion plot s are presented in Figure 8-1. As the simulations of Figure 8-1a show, by varying 1cT at constant de sorption rate (12.5dks ), the cross-peak signal reaches a maximal steadystate value at a mixing time which depends on 1cT. The difference of 1cT-dependence of cross-peak signals is more apparent if the y-axis of Figure 8-1a is expanded (F igure 8-1c). At short 1cT, the cross-peak signal r ecovers at a relatively short mixing time. At sufficiently long mi xing times, the cross-peak signal at short 1cT decays due to relaxation. In Figure 8-1b, cross-p eak intensity recovers rapidly at large dkand constant 1cT. However, in the y-axis expansion plot of Figure 8-1b, all three curves decay uniformly at longer mixing time due to constant 1cT relaxation time in the simulated conditions (Figure 8-1d). The features theoretically indicate that th e IFHP-EXSY with the approximation of long 1 g T and excess Xe gas ( i.e. 1cgnn ) can yield intense cross-peak intensities, thereby efficiently improving the cross-peak si gnals in CFHP 2D-EXSY.
149 (a) (b) (c) (d) Figure 8-1. Simulated mixing-time de pendences of normalized cross-p eak signals at (a) variable 1cT ( kd = 2.5 s-1) and (b) variable kd (1cT = 5 s) based on Eq. (8-7). Y-axis expansions of (a) and (b) are presented in (c) and (d), respectively. 410cgnn 1.0 0.8 0.6 0.4 0.2 0.0Mgc( m)/Mg0 10 8 6 4 2 0Mixing time, m(sec.) T1c=100 ms, (kd=2.5 s-1) T1c=1 s, (kd=2.5 s-1) T1c=100 s, (kd=2.5 s-1) 1.0 0.8 0.6 0.4 0.2 0.0Mgc( m)/Mg0 10 8 6 4 2 0Mixing time, m(sec.) kd=1 s-1, (T1c=5 s) kd=2.5 s-1, (T1c=5 s) kd=10 s-1, (T1c=5 s) 1.00 0.99 0.98 0.97 0.96Mgc( m)/Mg0 10 8 6 4 2 0Mixing time, m(sec.) T1c=100 ms, (kd=2.5 s-1) T1c=1 s, (kd=2.5 s-1) T1c=100 s, (kd=2.5 s-1) 1.00 0.99 0.98 0.97 0.96Mgc( m)/Mg0 10 8 6 4 2 0Mixing time, m(sec.) kd=1 s-1, (T1c=5 s) kd=2.5 s-1, (T1c=5 s) kd=10 s-1, (T1c=5 s)
150 8.4 Results and Discussions Hyperpolarized 129Xe 2D-EXSY experiments were performed under continuous-flow and interrupted-flow conditions in Ga10 nanotubes at 80 mbar Xe partial pressure and 25 oC Representative CFHP and IFHP 2D-EXSY spectra of Ga10 nanotubes are demonstrated in Figure 8-2. For CFHP 2D-EXSY, the cross peaks are clearly visible at 12mms (Figure 8-2a), revealing that Xe atoms entered or exited the Ga10 nanotubes during the 12 ms mixing time. As the mixing time increases to 250 ms (Figure 8-2b), the single-to-noi se ratios of the cross-peak and gas diagonal-peak signals are extremely weak due to the finite residence time, as discussed previously. In the interr upted-flow experiment, the cross-peak signals at 1mms (Figure 8-2c) are approximately the same as those at 12mms in the CFHP 2D-EXSY spectrum (Figure 8-2a). Furthermore, drasti cally stronger cross-peak signals are apparent at the relatively long mixing time of 1ms in IFHP-EXSY spectrum (Figure 82d) in comparison to the crosspeaks observed by CFHP 2D-EXSY (Figure 8-2b) The corresponding 3D representations of IFHP and CFHP 2D-EXSY spectra in Ga10 nanotube are illustrated in Figure 8-3. In Figure 8-3b, the cross peaks and gas diagona l peak are barely seen at 250mms in CFHP-EXSY in Ga10 nanotubes due to the finite residence time. Neve rtheless, the intense gas diagonal and exchange cross-peaks are still clearly observable in IF HP-EXSY spectrum demonstrated in Figure 8-3a. The dramatic cross-peak signal e nhancement of IFHP 2D-EXSY in Ga10 nanotubes is in good qualitative agreement with the 2D sp ectra of AV presented in Chapter 7.248
151 Figure 8-2. Hyperpolarized 129Xe 2D-EXSY spectra in (a)(b) continuous-flow and (c)(d) interrupted-flow modes in Ga10 nanotubes at 25 oC at different mixing times.
152 Figure 8-3. 3D representations of HP 2D-EXSY spectra of Xe in Ga10 nanotubes at 25 oC acquired in (a) IF mode and (b) CF mode. The mixing times are indicated. The gas peak in (a) was truncated to facilitate comp arison of the cross-peak s in each spectrum.
153 The mixing-time dependences of the diagonaland cross-peak signals of CFHP 2D-EXSY in Ga10 nanotubes at 25 oC, along with the least-squares fits of Eq. (6-8) (6-11), are presented in Figure 8-4. For the diagonal peaks in Figure 8-4a and b, a bi-exponential f unction yielded better fits than a mono-exponential decay, which was also the case for the least-squares fits to the diagonal-peak m -dependence in the CFHP 2D-EXSY experiment in AV.246 To compare the exchange kinetic models of 2D-EXSY in CF and IF modes, the mean desorption rate dk in Ga10 nanotubes was determined by non-linear regression analysis of the cross peaks in CFHP and IFHP 2D-EXSY. The results are summarized in Table 8-1. The dk in Ga10 nanotubes at 25 oC determined by gas channel and channel gas cross-peak signals of CFHP 2D-EXSY are 10.260.51 s-1 and 14.761.40 s-1, respectively. From the Xe isotropic spectral line-shapes reported in Chapter 5, Xe in Ga10 nanotubes is more mobile th an in AV nanotubes. A possible explanation for the higher exchange rate is the larger inner diameter of Ga10 nanotube in comparison to that of AV. More specifically, the estimated dk of Xe in Ga10 nanotubes is about a factor of 2 to 5 greater than that in AV246, implying that Xe gas is more favorable to escape from Ga10 than from AV channels. However, CFHP 2D-EXSY experiments in Ga10 nanotubes were conducted in the temperature of 35 oC higher than in AV nanotubes. The higher Xe desorption rate in Ga10 nanotubes may be due to the combin ations of higher temperature and larger inner diameter in Ga10 nanotubes.
154 (a) (b) (c) (d) Figure 8-4. Mixing-time dependences of (a) gasto-gas, (b) channel-to -channel diagonal-peak integral (c) gas-to-channel and (d) channelto-gas cross-peak integrals in CFHP Xe 2D-EXSY spectra of Ga10 nanotubes at 25 oC The solid and dashed curves represent the least-squares fits to the functions given in the legend. 16x103 14 12 10 8 6 4 2 0Gas-to-Gas Diagonal Peak Integral 250 200 150 100 50 0 m (ms) Eq. (6-8) aexp(-c m)+bexp(-d m) 3000 2500 2000 1500 1000 500 0Channel-to-Channel Diagonal Peak Integral 250 200 150 100 50 0 m (ms) Eq. (6-9) aexp(-c m)+bexp(-d m) 500 400 300 200 100 0Gas-to-Channel Cross Peak Integral 250 200 150 100 50 0 m (ms) Eq. (6-10) 400 300 200 100 0Channel-to-Gas Cross Peak Integral 250 200 150 100 50 0 m (ms) Eq. (6-11)
155 (a) (b) (c) (d) Figure 8-5. Mixing-time dependences of (a) ga s-to-gas, (b) channel-to -channel diagonal-peak integral, (c) gas-to-channel, and (d) channel-to-gas cross-peak integrals in IFHP Xe 2D-EXSY spectra of Ga10 nanotube at 25 oC The solid and dashed curves represent the least-squares fits to the functions given in the legend. 2500 2000 1500 1000 500Gas-to-Gas Diagonal Peak Integral 1000 800 600 400 200 0 m (ms) Eq. (8-5) aexp(-c m)+bexp(-d m) 700 600 500 400 300 200 100Channel-to-Channel Diagonal Peak Integral 1000 800 600 400 200 0 m (ms) Eq. (8-6) aexp(-c m)+bexp(-d m) 500 400 300 200 100 0Gas-to-Channel Cross Peak Integral 1000 800 600 400 200 0 m (ms) Eq. (8-7) 300 250 200 150 100 50 0Channel-to-Gas Cross Peak Integral 1000 800 600 400 200 0 m (ms) Eq. (8-8)
156 Figure 8-5 presents the m -dependence of the diagonalan d cross-peak signals of IFHP 2D-EXSY in Ga10 nanotubes at 25oC associated with the least-squa res fits of Eq. (8-5) (8-8). As seen in Figure 8-5a, the ga s diagonal-peak signal in the IF HP-EXSY spectrum drops rapidly between 0100mms followed by a slow decay as 100mms Eq. (8-5) predicted the m dependence of the gas diagonal-p eak signal to decay ve ry slowly under the conditions of excess Xe gas and long Xe gaseous 1 g T relaxation time. Such a slow decay of Eq. (8-5) was indeed observed for 100mms in the gas-phase diagonal peak, as shown in Figure 8-5a. In addition, in Figure 8-5b, the m -dependence of the diagonal-peak signals in Ga10 nanotube phase exhibits a poor agreement to the mono-e xponential function, Eq. (8-6). Once again, a rapid decay of diagonal-peak IFHP-EXSY signal of the nanot ube phase appears at short mixing time, 0100mms (Figure 8-5b). The observed rapid decays in the gas and nanotube-phase diagonal peaks at short mixing time in the IFHP -EXSY experiment may be due to the following reasons: (1) longitudinal relaxation of Xe on the surface of the cr ystallites, where the Xe atoms are in fast exchange with Xe in gas and/or in nanotube phase. (2) Hyperpolarized Xe gas may drift or diffuse out of the de tection region during the course of Xe exchange, since the hyperpolarized gas cannot be trapped completely within the sample sp ace in the current setup. (3) Diffusion effects (single-file or normal) are not included in the simple two-site exchange model. The desorption rates of IFHP 2D-EXSY were measured by the least-squares fits of gas channel and channel gas cross-peak intensities based on Eq. (8-7) and Eq. (8-8), respectively. In the least-squares fits of IFHP-EXSY, 1cT and cgnn are the fixed parameters, and two fit parameters (p re-exponential factor, and dk) were varied freely. The determinations
157 of 1cT and cgnn are as follows: (1) 1cT relaxation time is determined from CFSR experiments discussed in Chapter 4 and 5. For Xe in Ga10 nanotubes at 80 mbar Xe pressure and 25 oC in 9.4T, 1cTis about 2.831.02 sec. (2) In the assumption of excess Xe gases in the sample space, 1cgnn The value of cgnn was varied from 0.01 to 0.0001 as a fixed input parameter in the fit, but less than a 0.05% differe nce was found on the fitted values of dk. Therefore, a fixed value of 0.001cgnn was used in all subsequent fits. The mean Xe desorption rate constants in Ga10 nanotube at 25 oC estimated from leastsquares fits to m -dependence of cross-peak integrals in CFHP and IFHP 2D-EXSY are summarized in Table 8-1. In compari ng the CFHP and IFHP 2D-EXSY in Ga10 nanotubes, the desorption rates measured by IFHP-EXSY are about a factor of 2 to 7 higher than in CFHP EXSY. Since the exchange time in IF mode was monitored over a range which was about an order of magnitude longer than in CF mode, the desorption ra tes determined by IFHP 2D-EXSY should be expected to be more accurate. However, it should be noted that diffusion effects, readsorption effects and the drift of gas out of th e detected volume are not considered by either model and will in general limit the accuracy of rate constant determination by either technique. One or more of these effects may also explain the observed asymmetry of the desorption rates for the gas-to-channel and channel-to -gas exchange processes.
158 Table 8-1. Kinetic parameters of Ga10 nanotubes in CFHP and IFHP 2D-EXSY at 25 oC. Uncertainties represent 95% confidence intervals. EXSY gas-to-channel channel-to-gas dk (s-1) R (ms) dk (s-1) R (ms) CFHP 10.260.51 3.060.49 14.761.40 2.040.60 IFHP* 26.1312.03 --71.1741.40 --* cgnn =0.001 and T1c=2.83 s were used in the fits of IFHP 2D-EXSY 8.5 Conclusions The gas exchange kinetics in Ga10 wheel nanotubes have been investigated by CFHP and IFHP 2D-EXSY. The mean Xe desorption rate dk of Ga10 nanotubes at 25 oC estimated from non-linear least-squares fits of CFHP 2D-EXSY are relatively larger than dk of AV at -10 oC The increase of dk in Ga10 nanotubes may result from the larger channel diameter and/or higher temperature. As noted previously, the adsorption rate in the diffusion-lim ited regime depends on the occupancy of Xe atoms in the channels. Since the Xe occupancy in Ga10 nanotubes is unknown, the temperature effect on the gas desorpti on cannot be excluded. If Xe desorption in Ga10 nanotubes is diffusion-limited, the effect of the channel diameter on the gas desorption should be more pronounced than th e effect of temperature. IFHP 2D-EXSY has yielded dramatic cross-peak signal enhancement in Ga10 nanotubes. The quantitative expressions of mixing-time dependences of IFHP 2D-EXSY with finite 1cT relaxation time have been derived, assuming La ngmuir adsorption and excess Xe gas in sample space. The estimated mean desorption rates in CFHP and IFHP 2D-EXSY should be selfconsistent. However, the desorpti on rates of IFHP 2D-EXSY in Ga10 nanotubes were found to have large uncertainties, which are mostly due to the large fluctuations of the cross-peak intensities at long mixing times. The differences in the extracted rates may be due to one or more of the following effects which are not considered in the present exchange kinetic model: gas
159 diffusion, re-adsorption, and Xe ga s drift out of detec tion region during gas interruption. Further improvement in the experimental technique coul d be achieved by replacing the single solenoid valve in our current setup with two non-magnetic p itch valves located close to the inlet and outlet of the sample holder. By closing both pitch valv es simultaneously, the hyperpolarized gas will be trapped more completely within the sample space, thereby mitigating the loss of signal due to diffusion or drift out of the detection region. While the mixing-time dependence of IFHP-EXSY in the 1mcT regime has been demonstrated in Ga10 nanotubes, such a study would be impractical in a system with a long 1cTrelaxation time, such as in AV. Recently, severa l works regarding accelerating the acquisition of multi-dimensional NMR have been reported.249-252 For example, Frydman et al. have demonstrated the possibility to combine the single-scan 2D NMR method with DNP, and the acquisition time of DNP-enhanced 2D NMR spectru m in liquid sample within ~0.1 sec has been presented.253 Therefore, it would also be feasible to incorporate the fast acquisition NMR technique to IFHP-EXSY in or der to reduce the instrumentat ion time required to obtain the kinetic information. The present study provides an example of how CFSR and 2D-E XSY hyperpolarized 129Xe NMR can be employed to explore the transport eff ects in 1D nanotube systems. In Chapter 5, the single-file diffusion behavior of Xe in Ga10 nanotubes has been observe d, and the corresponding 1cT relaxation time was obtained by CFSR. In this ch apter, the average rate of Xe escape from Ga10 nanotubes was quantitatively determined and the exchange process was traced in Ga10 nanotubes by IFHP-EXSY. However, the investig ation of the exchange process in nanotube systems using IFHP-EXSY demonstrated that the ki netic behaviors of Xe inside and outside the channels can be drastically different. For descri bing the completely exch ange process during the
160 long exchange time in IFHP 2D-E XSY, the diffusion and gas re-ads orption effects may need to be incorporated into the kinetic models. In add ition to 1D nanotube systems, this technique is potentially applicable to the quantita tively exchange kinetic studies on the nm-m length scales, such as inter-crystall ine or inter-partic le exchange, in nanoporous materials by hyperpolarized 129Xe NMR.
161 CHAPTER 9 CONCLUSIONS AND OUTLOOK This dissertation has demonstrated the capabil ity of exploring the adsorption and transport behaviors of adsorbates in the one-dimensional na notube systems with different internal channel diameters by hyperpolarized 129Xe NMR. In addition to hyperpolarized 129Xe NMR chemical shifts and spectral line-shape analysis, selective saturation-recovery and 2D exchange NMR experiments were subjected to magnetization ex change kinetic analysis to investigate the dynamic processes of guest molecules in 1D nanotube host systems. The Xe atom has a van der Waals diameter of 4.4 and Xe chemical shift is well-known to be extremely sensitive to its local environment, resu lting in a unique atomic probe in the nanoporous materials. The spin polarization of 129Xe gas can be enhanced to up to ~70 % by spin-exchange optical-pumping (SEOP), dramatically increasing NMR sensitivity. SEOP prepared 129Xe offers an approximate 10,000-70,000 fold sensitivity enhancement in comparison to thermally-polarized 129Xe NMR, providing a wide range of applica tions in nanoporous materials. In this dissertation, two types of 1D nanotube systems, L-alanyl-L-valine dipeptide nanot ube (AV) and Ga-based wheel nanotubes (Ga10 and Ga18), with different channel diameters were utilized as model 1D systems. The inner diameters of AV, Ga10, and Ga18 nanotubes are 5.13 8.1 and 10.4 respectively. Adsorption The Xe chemical shift anisotropy (CSA) sp ectral line-shape has been observed in AV nanotubes, whereas isotropic line-sha pes have been exhibited in the Ga10 and Ga18 nanotubes. Anisotropic Xe NMR line-shapes in AV nanotubes can be characterized by an axially symmetric chemical shielding tensor, implying that the inner diameter of AV is on the same order of the van der Waals diameter of Xe atom. The sign invers ion of the chemical shielding anisotropy with
162 increasing Xe occupancy in AV is well understood in terms of the competition between Xe-wall and Xe-Xe interactions which have opposite contributions to the shielding anisotropy. The isotropic Xe chemical shift is increased upon reducing the temperature in all three nanotube systems, which is the result of increasing the cont ribution of Xe-Xe interactions to the chemical shift tensor. Since the perpe ndicular component of the Xe chemical shielding tensor, in AV nanotubes is most sensitive to Xe density and almost independent of temperature, it can be used to determine the Xe fractional occupancy in AV nanotubes. The Xe chemical shifts were found to be almost independe nt of Xe pressures in Ga10 and Ga18 nanotubes at 25 oC indicating that the Xe-wall interactions dominate the shielding in the gallic nanotubes. Since the channel diameters of Ga10 and Ga18 nanotubes are larger than that in AV nanotubes, and isotropic lineshapes, rather than an anisotropic chemical shif t powder pattern, as in AV, have been observed in gallic nanotubes, it can be concluded that Xe is less motionally restricted in the gallic wheel nanotubes. The Xe isosteric adsorption enthalpies (,a H ) in AV have been calculated at various Xe occupancies according to Clausius-Clapeyron equation. The increase in ,a H with Xe occupancy is mainly attributed to the Xe-Xe in teraction. The isosteric ad sorption enthalpy of Xe in AV extracted to zero occupa ncy was determin ed to be -10 kJ/mol which is consistent with the typical physiosorption process. Furthe rmore, the exchange constant ( ad K kk ) of Xe in AV increased upon reducing the temperature, qualitati vely implying the proce ss of Xe adsorption in AV is more favorable at low temperature. Ho wever, the quantitative measurements of Xe adsorption enthalpy and exchange constant in AV were found to have large uncertainties, especially at high Xe occupancy. This could be due to the experimental errors of the Xe gas pressures in the gas handling sy stem. The accuracy of the adsorption enthalpy and exchange
163 constant can be improved by using the pre-mixe d Xe gas mixtures with accurately known Xe compositions. In addition, the 13C 1T relaxation times in AV nanotubes have been determined by solidstate inversion-recovery NMR experi ments. The results show that the 13C of methyl groups on the channel interior, which is anticipated to be in direct dipolar contact with Xe in AV nanotubes, has short 1T relaxation time (366 76 ms). The methyl group 13C 1T is expected to be increased when Xe atoms accumulate into the channels. This information can be a resource for the future hyperpolarized 129Xe 13C polarization transfer studies. Diffusion The selective continuous-flow satura tion-recovery (CFSR) hyperpolarized 129Xe NMR experiments have been carried out to explore th e tracer exchange of hype rpolarized gas in 1D nanotube systems. The magnetization kinetic mode ls of single-file diffusion (SFD) and normal 1D Fickian diffusion (ND) based on diffusi on-limited Langmuir adsorption have been developed, and the quantitative ex pressions of magnetization rec overy curves of SFD and ND have been presented. From the kinetic analysis of CFSR, Xe motion insi de AV nanotubes clearly exhibited single-file diffusion beha vior, especially at high Xe occ upancy. The pre-factor terms of the saturation-recovery equations for SFD and ND FC and D C have been derived, and were found to be depended mainly on temperature, diffusivity, and Xe occupancy. The -dependence of the experimentally measured coefficient CF in AV is in good qualitatively agreement with the theoretical expression. Th e techniques have been further app lied to the gallic-wheel nanotube systems, Ga10 and Ga18 nanotubes, with internal diameters greater than AV nanotubes. As in the Xe/AV systems, Xe in 8.1 Ga10 nanotubes exhibited single-fil e diffusion behavior, whereas normal 1D diffusion of Xe in 10.4 Ga18 nanotubes was explicitly observed. The cross-over of
164 the time-scaling from SFD to ND by varying th e channel inner diameters in 1D nanotube systems has been apparently observed by CFSR hyperpolarized 129Xe NMR. Recently, Takamizawa et al. have demonstrated the possibility to investigate the adsorptions of various guest adso rbates, such as water, Xe, CH4 and CCl4, in the tris(ethylenediamine) cobalt (III) chloride ([CoIII(en)3] Cl3) channels with inner diameter of 5.7 by single-crystal Xe-ray diffraction analysis.254 The channel architectures in the presence of gas adsorbates and the determinati on of positions of adsorbates in side the channels have been presented. The combination of CFSR and X-ray cr ystallography in the presence of gas molecules in nanotubes can provide a dis tinct understanding of dynamic processes in guest/host nanotube systems with variable size distributions. Exchange In order to understand the complete transport process of adsorbates in the nanotubes, gas exchange in the vicinity of ch annel openings has been systematically investigated by CFHP 2DEXSY. The exchange kinetic model based on diffusion-limited Langmuir adsorption has been proposed. The quantitative expressions for the mixing-time dependence of crossand diagonalpeak integrals have been derived, assuming excess Xe gas and long 129Xe 1T relaxation time in the sample space. From the least-squares fits of the expressions to the CFHP 2D-EXSY datasets, the mean desorption rates of Xe ( dk) in AV nanotubes was quanti tatively determined. The dkwas shown to decrease with increasing Xe o ccupancy, which is in good agreement with the approximation of diffusion-limited Langmuir adsorption. The cross-peak intensities in 2D-EXSY were found to be strongly attenuated by the finite gas residence time in the sample space under th e continuous-flow condition. The issue of how hyperpolarized NMR signal is affected by the gas flow rate has not been noticed until recently,
165 by us. We demonstrated that it is feasible to significantly enhance the cross-peak intensities represented gas exchange between adsorbed si tes and gas phase in 2D-EXSY by momentarily interrupted the gas flow during the exchange time of 2D-EXSY pulse sequence. In AV nanotubes, a factor of ~60 signal enhancement of cross-peak intensities in IFHP-EXSY has be achieved, providing a greatly promising techni que to probe slow exchange process by hyperpolarized 129Xe 2D-EXSY NMR. Furthermore, th e mixing-time dependence of IFHPEXSY has been demonstrated in Ga10 nanotubes at room temperature. The corresponding magnetization exchange kinetic analysis of IFHP-EXSY in the 1mcT regime has been presented. However, the mean desorption rate in Ga10 nanotubes measured from 2D-EXSY in IF mode is about a factor of 2 to 7 greater than dk in CF mode. It can be due to the factors such as diffusion, gas re-adsorption, or gas drift out of detection region wh ich are not considered in the simplified kinetic model during th e relatively longer exchange time in IFHP-EXSY. Further improvement can be made by refining the expe riments in the aspect of preventing the hyperpolarized Xe gas drift out of the detect ion coil region during th e duration of the gas interruption. In this dissertation, the funda mental aspects as well as th e potential applications of hyperpolarized 129Xe NMR have been presented. This wo rk gives access to a wide range of future utilizations in divers e fields of materials and biol ogical sciences. The advantages presented herein, such as NMR sensitivity enhancement, the sensitivity to the local environment, capability to probe slow exchange process, and the possibility of time-resolved quantitatively kinetic measurements in 1D nanotube systems fulfill the requirements of investigations of the thermodynamics, chemical exchange and diffusions of guest/host chemistry.
166 APPENDIX A DERIVATION OF AVERAGE ZEEMAN ORDE R IN NANOTUBE PHASE BY GAMMA FUNCTION IDENTITIES We start from the Eq. (4-14) in Chapter 4 1 1 1 1 0()1expL zid zcdc dcIk I kTdz LkT (A-1) For simpfication, let 2 2 24//dkFzar, where 2/aF and 1 1 cbT, and assume the long channel limit, where 1/4abL. Therefore, Eq. (A-1 ) can be rewritten 4 4 4 0/ ()1exp/ /zi zcI ar I arbdr Larb (A-2) Evaluate the integration in Eq. (A-2) 4 4 4 0 1/4 1/4 1/4() / 1exp/ / 111 42, 1644 1111 42, 16444 1111 421, 16444zc ziI ar arbdr ILarb a b b a Qb b a Pb b 1/41 111 4 421 1 1644 4 b a b (A-3) where the regulatized gamma functions are defined as ,, Pcxcxc (A-4) ,, Qcxcxc (A-5) (,)(,)1 PcxQcx (A-6)
167 From the identity for the gamma function, 11 44(1/4)sin(/4) (A-7) Thus, Eq. (A-2) yields 1/4 1/4 1/4 11 () 1 4 421 1 161/4sin/4 4 1 1 4 42421 1 16 4 211 444 2 4zc zib I a ILb b a b a b b a b 1/4 13/4 01 4bed (A-8) where the incomplete gamma funciton is 1 0,x ctcxtedt. To substitude the variable from to uin Eq. (A-8), we assume ub ; thus, dbdu 1/4 13/4 0 1/4 13/4 0() 21 () 44 21 44b bu zc zi b buIt a bbuedu ILb auedu (A-9) Plugging 2/ aF and 1 1cbT into Eq. (A-9) yields 1 11/2 / 13/4 0 / 13/4 3/2 0() 21 44 1 24c cuT zc zi uTIt F uedu IL F uedu (A-10)
168 Finally, Eq. (4-15) is obtained 13/4 3/2 0() 21/4ctT zcziF I Itedt L (A-11)
169 APPENDIX B MATRIX FORMULATION FOR TW O-SITE EXCHANGE SYSTEM As discussed in Section 6.1, the m dependence of diagonala nd cross-peak intensities can be solved by the matrix representation. Here we take an example of time dependences of cross-peak intensities in the limit of 1 mcT (Section 8.3). The rate equations of magentizations in gas and nanotube phase under interrupted-flow condition are g c dgdc gdM n kMkM dtn (B-1) 1 ccc dgdc g cdMnM kMkM dtnT (B-2) The identical matrix representation of the rate equations is gmgm cmcmMM d MM dt (B-3) where 1 1 c dd g c ddc gn kk n n kkT n (B-4) Eq. (B-3) can be rewritten as exp0mm (B-5) is a matrix which contains information of di agonal and cross-peak intensities in 2D-EXSY. The solution to Eq. (B-5) can be performed according the eigenvalue-eigenvector method.58 1exp0mmXDX (B-6) where () g ggc m cgccMM MM (B-7)
170 where Dis a diagonal matrix with eigenvalues of The X and its inverse 1 X are eigenvectors of Solving Eq. (B-6), the integrated inte nsities of cross peak s can be obtained: 11 1111 1 11 22 0 1(1) 2cc dcmdcm ccnn kTkT nn ccdc gcgnnkT MMee (B-8) 11 1111 1 11 22 0 1(1) 2cc dcmdcm ccnn kTkT nn ccdc cgcnnkT MMee (B-9) where 2 11 1141cc dcdc ggnn kTkT nn In the assumption of excess gases in the sample space, 1c gn n Eq. (B-8) and Eq. (B-9) yield 11 1111 1 0 1 222dcmdcmkTkT dc gcgkT MMee (B-10) 11 1111 1 0 1 222dcmdcmkTkT dc cgckT MMee (B-11) where 2 11 114c dcdc gn kTkT n
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185 BIOGRAPHICAL SKETCH Chi-Yuan Cheng was born in Taipei, Taiwan in 1976. He received his B.S. degree in pharmacy from Taipei Medical University, Taipei Taiwan, in 1998, and M.S. degree in physical chemistry from National Taiwan University, Taipei, Taiwan, in 2000. He joined Dr. Russ Bowers research group at the University of Florida in 2003 to pursu e his Ph.D. degree in physical chemistry, and since then he has worked as a full-time graduate student and teaching assistant. Since he entered the field of magne tic resonance in 1998, he has been involved in various projects, including pul sed-filed gradient NMR, 2H double-quantum filtered NMR in mesoporous materials; magic-angle spinning NMR in solid materials; 2H solid-echo NMR in predeuterated polymers, and hyperpolarized 129Xe NMR in nanotubes and other nanoporous materials. His current research interests including so lid-state NMR applications, dynamic nuclear polarization, para-hyd rogen enhanced NMR, and hyperpol arized noble gas NMR. After graduation in 2008, he plans to extend his rese arch area to ESR and DNP-NMR, and holds a postdoctoral position in the research group of Dr. Song-I Han at the University of California, Santa Barbara.