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NMR Determination Of Channel Lengths  In One-Dimensional Crystalline Dipeptide Nanotubes

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Title:
NMR Determination Of Channel Lengths In One-Dimensional Crystalline Dipeptide Nanotubes
Creator:
Mirnazari, Navid
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Language:
English

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Continuous production ( jstor )
Diameters ( jstor )
Nuclear magnetic resonance ( jstor )
Oxygen ( jstor )
Particle diffusion ( jstor )
Physics ( jstor )
Rubidium ( jstor )
Signals ( jstor )
Tracer bullets ( jstor )
Xenon ( jstor )
Diffusion
Nanotubes
Nuclear magnetic resonance
Polycrystals
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Undergraduate Honors Thesis

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Abstract:
Nanoscale materials present a vast range of potential applications. In particular interest are one-dimensional nanochannels for their possible applications in drug delivery, gas storage, gas separations, and catalysis. Anomalous diffusion arises in confined spaces within a 1D channel in which molecules cannot pass one another. In these situations, Single-File Diffusion can occur where the mean squared displacement (MSD) varies with t^0.5 instead of t, as seen in normal Fickian Diffusion. A point of interest in 1D channels is the open persistence length (i.e. the length from a channel opening to the first obstruction) and a methodology to derive this length, utilizing hyperpolarized xenon-129 NMR, is presented in this dissertation. This approach was applied to two different self-assembled polycrystalline dipeptide nanotubes: L-alanyl-L-valine (AV) and its retro-analog L-valyl-L-alanine (VA). Average channel lengths were calculated for samples of AV and VA, as received, as well as a sample of AV pulverized in a mortar and pestle (p-AV). AV and VA samples yielded channel lengths of approximately 50 and 20 μm, respectively, while p-AV was reduced to 6.6 μm. These results are consistent with images taken using a scanning electron microscope (SEM), leading to the conclusion that the channels are virtually defect free. ( en )
General Note:
Awarded Bachelor of Science in Chemical Engineering; Graduated May 6, 2014 magna cum laude. Major: Chemical Engineering
General Note:
Advisor: Russ Bowers
General Note:
College of Engineering

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University of Florida
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University of Florida
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Copyright Navid Mirnazari. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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NMR DETERMINATION OF CHANNEL LENGTHS IN ONE DIMENSIONAL CRYSTALLINE DIPEPTIDE NANOTUBES BY: NAVID M. MIRNAZARI UNDERGRADUATE THESIS PRESENTED TO THE UNIVERSITY OF FLORIDA DEPARTMENT OF CHEMICAL ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR A BACHELOR OF SCIENCE DEGREE WITH HIGH HONORS. UNIVERSITY OF FLORIDA SPRING 2014

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Page | 2 ACKNOWLEDGMENTS I would like to take the opportunity to thank Dr. Russ Bowers for mentoring my research activities and giving me the opportunity to work on some very interesting research topics related to diffusion and catalysis. He was always available to provide insight and guidance and never f ailed to make research fun and rewarding None of my work would have been possible without Ryan Wood whom I thank for approaching me and introducing me to the Bowers group. Special thanks to my thesis committee an d valued research collaborators, Dr. S erge y Vasenkov and Dr. Helena Hagelin Weaver. Thanks to the entire Bowers research group, especially Hrishi Bhase, Ronghui Zhou, and Dr. Muslim Dvoyashkin for their assistance when joining the research group and during experimentation Thanks to the National High Magnetic Field Lab for funding through their REU program and also thank the Center for Condensed Matter Sciences at the University of Florida for awarding me with an undergraduate research fellowship award. Finally, I would like to express my gratitude to my family and friends for their continued support of my education and all their encouragement during my studies and research while at the University of Florida. This material is based upon work supported by the National Science Foundation und er Grant No. CHE 0957641. Any expressed in this material are those of the author(s) and do Foundation

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Page | 3 Table of Contents Acknowledgments ................................ ................................ ................................ ............................ 2 List o f Tables ................................ ................................ ................................ ................................ .. 4 List of Figures ................................ ................................ ................................ ................................ .. 4 Abstract ................................ ................................ ................................ ................................ ............ 7 Introduction and Background ................................ ................................ ................................ .......... 8 I. Nuclear Magnetic Resonance and Hyperpolarization ................................ .................. 8 II. Xenon, Ideal Chemical Probe For Studying Diffusion Dynamics ................................ 9 III. Spin Exchange Optical Pumping ................................ ................................ ............... 10 IV. Single File Diffusion ................................ ................................ ................................ .. 1 1 Experimental Design and Methods ................................ ................................ ................................ 1 4 I. Use of AV and VA nanotubes ................................ ................................ .................... 1 4 II. Design of 129 Xe Polarizer and Continuous Flow Experimental Setup ......................... 1 5 III. Hyperpolarized Tracer Exchange NMR ................................ ................................ ..... 1 7 IV. Derivation of Open Persistence Channel Length Appendix ................................ ...... 1 8 V. Experimental Conditions ................................ ................................ ............................ 20 Results and Discussion ................................ ................................ ................................ .................. 2 1 Conclusion and Future Work ................................ ................................ ................................ ......... 25 Appendix ................................ ................................ ................................ ................................ ........ 26 A. Abbreviations ................................ ................................ ................................ ............. 26 References ................................ ................................ ................................ ................................ ...... 27

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Page | 4 List of Tables Table 1: C F value calculated using the three methods described previously. All three methods yield very similar results ................................ ................................ ........ 24 List of Figures Figure 1 : Population distribution for a system in (a) thermal polarization and (b) hyperpolarization. ................................ ................................ ................................ .... 9 Figure 2: Rb Xe spin exchange. N 2 and He represent the presence of buffer gases. Blue the unpolarized Xe results in polarization trans fer. ................................ .............. 1 0 Figure 3: Schematic representation of ND and SFD. Small particles (red) can diffuse freely through a 1D channel in which the pore size is significantly large, whereas larger particles (blue) cannot when the particle diameter approaches the pore di ameter. In this instance diffusion deviates from a ND regime to a SFD regime. ................... 1 1 Figure 4: or the reverse process (particles exiting the channel). Particles can only diffuse if the next site is empty and this diffusion occurs with a rate of 1 / j .............................. 1 2

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Page | 5 Figure 5: (A) Space Filling Model of AV, (B) Chemical Structure of AV [19] (C) Chemical Structure of VA [19] ................................ ................................ ................................ 1 4 Figure 6: Experimental Setup: (left) Bruker superconducting magnet operating at 9.4 T; (center) CF HP 129 Xe setup; (right) Image of the wideline probe, detection region, and direction of flow ................................ ................................ .............................. 1 5 Figure 7: Reconstructed portable SEOP system, gas delivery system, and 9.4 T Bruker superconducting magnet ................................ ................................ ........................ 1 6 Figure 8: Schematic representation of the continuous HSTE NMR setup. Selective saturation of the xenon confined in nanochannels causes complete silencing if the NMR signal. Following saturation, CF HP 129 Xe can exchange into the channel and the growing signal intens ity can be measured over times until steady state (~200 seconds) ................................ ................................ ................................ .................. 1 7 Figure 9: SEM images of three different samples: [25] (a) VA, as received, from Bachem Americas, LLC (b) AV, as received, from Bachem Americas, LLC (c) AV pulverized using a mortar and pestle ................................ ........................... 2 1 Figure 10: Mixture of 3 bar xenon and 0.2 bar oxygen at ambient temperature. Spectra taken using a 3.5 s pulse in a 9.4 T field. Oxygen was used to lower the relaxation time and a long recycle delay was used to assure full relaxation. Signals were taken averaging 32 scans ................................ ................................ ................................ 22

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Page | 6 Figure 11: HSTE NMR Data for all three samples. Blue circles represent the normalized gas phase signal integral and solid dots represent normalized adsorbed phase signal integrals. Dashed lines represent SFD regime, whereas, solid lines represent ND regime. AV and p AV show nearly perfect SFD adherence, however, VA deviates from the SFD regime at short times. Plot insets show the same data on a log log scale. ................................ ................................ ................................ ....................... 23

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Page | 7 Committee Chair: Dr. Sergey Vasenkov, Dept. of Chemical Engineering Committee Members: Dr. Helena Hagelin Weaver, Dept. of Chemical Engineering Dr. Clifford Russ ell Bowers, Dept. of Chemistry A BS T RACT Nanoscale materials present a vast range of potential applications. In particular interest are one dimensional nanochannels for their possible applications in drug delivery gas storage, gas separations, and catalysis Anomalous diffusion arises i n confined spaces within a 1D channel in which molecules cannot pass one another. In these situations S ingle File Diffusion can occur where the mean squared displacement (MSD) varies with t 1/2 instead of t as s een in normal Fickian Diffusion. A point of interest in 1D channels is the open persistence length (i.e. the length from a channel opening to the fi rst obstr uction ) and a methodology to derive this length utilizing hyperpolarized xenon 129 NMR is presented in this dissertation. This approach was applied to two different self assembled polycrystalline dipeptide nanotubes: L alanyl L valine (AV) and i ts retro analog L valyl L alanine (VA). Average channel lengths were calculated for s amples of AV and VA as received as well as a sample of AV pulverized in a mortar and p estle (p AV). A V and VA samples yielded channel lengths of approximately 50 and 20 while p AV w as consistent with images taken using a sca nning electron microscope (SEM), le ading to the conclusion that the channels are virtually defect free.

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Page | 8 INTRODUCTION AND BACKGROUND I. Nuclear Magnetic Resonance and H yperpolarization: Nuclear Magnetic Resonance (NMR) is a very powerful tool that can be implemented in the study of molecular dynamics on the nanoscale. An NMR signal is proportional to the nuclear spin polarization. For a spin nuclei, such as xenon 129, the polarization can be described by: (1) where is the angular momentum along the magnetic field ( ), and are the populations occupying the spin u p ( m = +1/2) or spin down ( m= 1/2) state, is the gyromagnetic ratio, is the Boltzmann constant, and is the temperature. The NMR signal is proportional to the spin polarization. Hence if the spin up and spin down states are equally populated, s pin polarization will approach zero and no NMR signal will be observed. This is the situation at thermal equilibrium for a system with high temperature. At ambient temperatures the polariza tion is very small and yields extremely low signals. From Equation 1, it is evident that two ways of improving the NMR signal are raising the magnetic field strength and/or lowering the temperature of the NMR detection probe cryogenically. These sensitivity i ssues can be overcome through hyperpolarization methods. Using hyperpolarized NMR overcomes the limitations of T and B 0 Below, in Figure 1, a diagram of the

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Page | 9 population of spin states can be seen for a system at thermal polarization and hyperpolarization. Hyperpolarization can be used for a nuclei such as xenon 129 in order to achieve polarization enhancement of 10 4 10 5 [1, 2, 3] II. Xenon Ideal C hemical P robe F or S tudy ing D iffusion D ynamics The first reported use of xen on NMR was by Ito and Fraissard [4 ] in their study of porous solids. Xenon is an ideal system to be used in the study of physical interactions between various species as well multitude of systems, including those that may be highly chemically active. It has many stable isotopes, but only two of them are NMR observable ( 129 Xe and 131 Xe) due to their non zero nuclear spin Between these two choices 129 Xe is th e best due to its long T 1 relaxation time. This allows adequate time for optical hyper polarization of xenon prior to any experiments of interest Figure 1: P opulation distribution for a system in (a) thermal polarization and (b) hyperpolarization.

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Page | 10 III. Spin E xchange O ptical P umping A common method used to produce hyperpolarized noble gases is spin exchange optical pumping (SEOP). The first reported use of SEOP was shown by Happer et al [ 5, 6 ] SEOP is based on a two step process. In the first step, an alkali metal is polarized through the transfer of angular momentum from the photons of a circularly polarized laser. Then the polarization of the alkali metal is transferred to the noble gas through collisions. This polarization transfer is shown below In this situation the alkali metal used for SEOP is rubidium. Buffer gases such as heli u m or nitrogen are typically used in these systems in order to increase SEOP efficiency Figure 2: Rb Xe spin exchange. N 2 and He represent the presence of buffer gases. Blue represents higher polarization while red represents lower polarization Molecular collisions between the polarized Rb vapor and the unpolarized Xe results in polarization transfer.

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Page | 11 IV. Single File Diffusion Single file diffusion is a class of anomolous diffusion in which particles in a one dimensional ( 1D ) channel are confined to narrow pores inhibiting particles from pass ing one another [ 7, 8, 9 ] SFD was first introduced many years ago in order to describe transport of water and ions through cell membrane proteins [ 10 ] S chematic s of ND and SFD are depicted in Figure 3. The small red molecules exhibit Fickian diffusion since the pores are large enough to allow Brownian motion to occur, resulting in mean squared displacement to scale with time. However, when larger molecules, depicted in blue, are us ed, anomalous SFD occurs where the mean squared displacement results in t 1/2 time scaling. Under the SFD regime the standard diffusion model for a 1D system (2) is no longer valid. Instead the SFD can be modeled by the following formulation at sufficiently long diffusion times: (3) Figure 3: Schematic representation of ND and SFD. Small particles (red) can diffuse freely through a 1D channel in which the pore size is significantly lar ge, whereas larger particles (blue) cannot when the particle diameter approaches the pore diameter. In this instance diffusion deviates from a ND regime to a SFD regime.

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Page | 12 where F is the single file mobility. [ 11 ] This single file mobility can be affected by various factors such as channel structure and molecule molecule/molecule channel wall interactions. One stochastic model to describe diffusion in finite 1D systems is called the simple exclusion process ( SEP). This process has been used to model SFD, resulting in analytical solutions [ 12 ] A schematic of a finite 1D channel with in SEP lattice is shown in Figure 4. The SEP SFD model is based on a series of conditions: Each site along the lattice must either be empty or occupied by a single particle If a neighboring site is empty, the particle can move to that site with a jump rate of 1/ j If a neighboring site is occupied, the particle cannot move to that site or pass the other particle. If diffusion is modeled in a system with a particle size approaching the pore size in a 1D channel, pr oportion of occupied channel sites). At very low loadings, particles do not feel the effects of other particles in the channel and 1D ND is expected to occur. However as loading is increased, 1/ j 1/ j Figure 4 : represent the probability for the reverse process (particles exiting the channel). Particles can only diffuse if the next site is empty and this diffusion occurs with a rate of 1 / j

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Page | 13 particle particle interactions increase and a transition is mad e to a SFD regime. For an ideal 1D single file system the single file mobility ha s the following analytical representation: [ 13, 14, 15 ] (4) where is the density of confined particles d is the particle diameter, and D 0 is the diffusion coefficient. Applying limiting cases to this formulation gives some insight into expected mobility. 0, F which is consistent with expectations as mobility is not hindered due to any particle pa 1, F 0, also as expected since there can be no particle movement as all sites are occupied. Finally of (COM) diffusion is possible. This regime can take over whe n a very fast exchange rate at channel boundaries leads to a correlated movement of all particles in the channel. This diffusion regime results in ND time scaling, but the diffusion rate is significantly reduced. However, COM diffusion has not been observed experimentally.

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Page | 14 EXPERIMENTAL DESIGN AND METHODS I. Use of AV and VA nanotubes L alanyl L valine (AV), and its retro analog L valyl L alanine (VA), are self assembling poly crystalline nanochannels. They provide an ideal system to study SFD of xenon due to their channel properties The average channel diameter for AV and VA are 5.1 and 4.9 respectively [ 16, 17, 18 ] These systems satisfy the SFD criteria for xenon which has an atomic diameter of 4.36 Below is the space filling representations of AV and VA. Diffusion of xenon within these nanochannels has been determined to exhibit SFD. [ 1, 20 ] Previous work has also derived the single file mobility for these nanochannels through the use of pulsed field gradient (PFG) NMR. [20 ] A B C Figure 5 : (A) Space Filling Model of AV, [18] (B) Chemical Structure of AV [19] (A) Space Filling Model of VA, [18] (D) Chemical Structure of VA [19] D

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Page | 15 II. Design of 129 Xe Polarizer and Continuous Flow Experimental Setup The original xenon hyperpolarize r was desig ned by Anthony Zook, a previous group member of the Bowers research group. [21] When the group was moved from Leigh Hall to the Physics Building, some new improvements on the gas delivery system were implemented. The SEOP system fun c tions optimally at approximately 140 C, where the highest xenon polarization is seen. The optical pu mping cell contains a small amount of rubidium (< 0.5 g). The optical setup uses a 100 W laser diode array (LDA) in order polarize the rubidium vapor. Once the xenon 129 has been hyperpolarized, it continuously flows through the sample holder, within th e NMR detection region. The sample holder is manufactured out of polyether ether ketone (PE s the lifetime of the rubidium i n the pumping cell by removing impurities that may react with the rubidium. The Getter is a reinforced glass vessel that is also loaded with a small amount of rubidium that acts to protect the pumping cell efficiency. Figure 6 : Experimental Setu p: (left) Bruker superconducting magnet operating at 9.4 T ; (center) CF HP 129 Xe setup; (right) Image of the wideline probe, detection region, and direction of flow.

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Page | 16 Recently, upon the acquisition of a new laser, and in the interest of making the xenon polarizer accessible to multiple NMR magnets, the polarizer was rebuilt onto a portable unit. A few months were spent to disassemble all the components rearrange them o nto a newly designed portable cart and reestablish xenon polarization. An image o f the new setup are shown below. Figure 7: Reconstructed portable SEOP system, gas delivery system, and 9.4 T Bruker superconducting magnet.

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Page | 17 III. Hyperpolarized Tracer Exchange NMR The xenon chemical shift deviates significantly in the adsorbed state compared to the bulk phase gas. By applying a saturation recovery pulse sequence, the exchange between the adsorbed and bulk phases can be studied. [1, 2] Hyperpolariz ed tracer exchange (HSTE) NMR can be applied for this use. Tracer exchange methodology essentially uses the exchange between labelled and unlabeled particles to ascertain particle displacements. The tracer exchange curve can be represented by the foll owing expression : (5) [22, 23, 24] Illustrated below is the representation of HSTE NMR. Optical Pumping Cell Unpolarized xenon Polarized xenon Selective Saturation Steady State Figure 8 : Schematic representation of the continuous HSTE NMR setup. Selective saturation of the xenon confined in nanochan nels causes complete silencing o f the NMR signal. Following saturation, CF HP 129 Xe can exchange into the channel and the growing signal intensity can be measured ove r times until stead y state (~200 seconds).

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Page | 18 Xenon polarization occurs through the use of the SEOP cell described previously Using selective radio frequency (RF) pulses, xenon confined in the channels can be saturated. Then, under a continuous flow (CF) system, hyperpolarized xenon can be pumped and multiple NMR spectra can be acquired over time, measuring the increase in NMR s ignal. Since only the polarized xenon 129 produces an NMR spectra, the signal intensity will increase with time. IV. Derivation o f Open Persistence Channel Length For sufficiently long channels, the NMR signal arising from hyperpolarized adsorbed particles can be derived for SFD and ND regimes: [1] SFD (6) ND (7) Where is the average number of channel openings for the entire sample (ranging from 0 to 2), and is the average persistence channel length and represents the gamma function However, these are for the limiting cases of SFD and ND. During transition from N D to SFD, when MSD time scaling will be in between 1 and 0.5 n either of these formulations will be valid. Hence a more general form is needed : (8) can be measured through thermally polarized spectra, and as such is the only unknown parameter. Hence, can be fitted for any set of data. For SFD and for ND The pre integral terms in Equations 6 and 7 can be solved for by utilizing the ratio of the adsorbed phase and bulk gas NMR signals for the cases of SFD and ND:

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Page | 19 ( 9 ) SFD ( 10 ) ND (11 ) Equations 10 and 11 were first reported by Meersmann et. al. [2] but did not provide explicit expressions for the pre integral factors. Those expressions were published in Ref. [1]: SFD (1 2 ) ND (1 3 ) where refers to the ratio of the number of confined particles to the number of bulk particles. Rearranging Equations 1 2 and 1 3 yields expressions for the average persistence channel length for the ensemble: [2 5 ] SFD (1 4 ) ND (1 5 ) As can be seen from Equation s 14 and 1 5 in order to calculate channel length a few different factors are needed. can be found by equating the ratio of adsorbed phase signal to the bulk phase signal in a thermally polarized experiment F or D can be found through PFG NMR and has been

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Page | 20 found for this experimental system. [20] C F can be found by the following three methods through the continuous flow HSTE NMR experiment: [25] 1) Nonli near least squares fitting of data to Equation 10 utilizing C F as the unknown parameter 2) Use of the steady state signal ratio where: 3) Linear least squares fitting of the log of Equation 10. In this situation the plot intercept provides log( C F ) V. Experimental Conditions (a) Thermally Polarized Experiment In order to determine the ratio of adsorbed phase to bulk phase signal, thermally polarized experiments were conducted with a mixture of 3 bar xenon and 0.2 bar oxygen at ambient temperature. Spectra were taken using a 3.5 s pulse in a 9.4 T field. Oxygen was used to lower the relaxation time and a long recycle delay was used to assure full relaxation. Signals were taken averaging 32 scans. [25 ] (b) C ontinuous Flow HSTE Experiment Single scan NMR signals were acquired under 3 bar xenon continuous flow (~100 mL/min) between 10 ms to 300 s. Spectra were taken using 9.4 T field at ambient temperature. [25 ]

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Page | 21 RESULTS AND DISCUSSION Samples of AV, VA, and p AV were imaged with an SEM in order to obtain a basis to compare NMR results with. SEM images were collected using the Major Analytical & Particle Analysis Instrumentation Centers (MAIC) at the University of Florida. The i mages are shown below. whereas, the p AV sample seems to have a much more uniform size distribution well below 20 m. Figure 9 : SEM images of three different samples: [25 ] (a) VA, as received, from Bachem Americas, LLC (b) AV, as received, from Bachem Americas, LLC (c) AV pulverized using a mortar and pestle

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Page | 22 Thermally polarized data acquired using the experimental conditions listed previously are shown belo w. [25 ] The peak at 0 ppm represents the bulk phase xenon signal while the other peaks represent the adsorbed phase signal. This signal occurs at 120 and 15 0 ppm for AV and VA samples, respectively. The p AV adsorbed phase line attributed to t he increased rate of exchange in much smaller channels. B ased on these spectra, n c /n g is determined to be 2.7 0.1 for VA, 1.43 0.07 for AV, and 1.4 0.1 for p AV. [2 5 ] Figure 10 : M ixture of 3 bar xenon and 0.2 bar oxygen at ambient temperature. Spectra taken using a 3.5 s pulse in a 9.4 T field. Oxygen was used to lower the relaxation time and a long recycle delay was used to assure full relaxation. Signals were taken averaging 32 scans.

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Page | 23 Continuous flow HSTE NMR data taken for all three samples are shown below in figure 1 1 [25 ] Figure 11 : HSTE NMR Data for all three samples. Blue circles represent the normalized gas phase signal integral and solid dots represent normalized adsorbed phase signal integrals. Dashed lines represent SFD regime, whereas, solid lines represent ND regime. AV and p AV show nearly perfect SFD adherence, however, VA deviates from the SFD regime at sho rt times. Plot insets show the same data on a log log scale.

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Page | 24 Results shown in Figure 1 1 can be fit ted to Equation 8 to confirm SFD For AV and p AV samples the calculated a value was 0.25 0.01 and 0.24 0.01 respectively This result shows almost perfect adherence to the SFD model. However, for VA the data deviates slightly from SFD at short times, as can be seen in Figure 1 1 (a). This deviation leads to an increase in the fitting parameter a yielding 0.3 0.1 Utilizing the HSTE data the C F values for all three methods are shown in the table b elow. [25] Sample C F Method 1 Method 2 Method 3 VA 0.054 0.040 AV 0.0099 0.0097 0.0095 p AV 0.071 0.072 0.072 Utilizing the values calculat ed for data plotted in Figures 10 and 1 1 along with the single file mobility factors, it is possible to calculate mean persistence channel lengths for all three samples. Channels with single openings were considered for this calculation and, as such, true channel lengths may be greater (up to d ouble for doubly open ended channels). Single file mobilities of 4.4 0.2 X 10 13 and 6 0.7 X 10 13 have been reported for VA and AV, respectively. [20] With these values mean channel persistence lengths were found to be 20 2 m, 50 10 m, and 6.6 0.3 m for VA, AV, and p AV, respectively. [25] This result is consistent with the SEM images in Figure 9 Table 1 : C F value calculated using the three methods described previously. All three methods yield very similar results.

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Page | 25 CONCLUS ION AND FUTURE WORK In concl usion, PFG NMR can be combined with HSTE NMR in order to derive open persistence channel lengths within nanochannel systems. This methodology was applied to samples of VA, AV, and p AV. Calculated channel lengths are consistent with SEM images and accurately describe the significant decrease in channel length between AV and p AV. Since channel lengths are co nsistent with SEM images, it can be postulated that these channels are virtually free of defects. With VA and AV samples, where there is a wide range of channels lengths seen in SEM images, it is difficult to comment on the channel boundary conditions. How ever, for p AV, where most channels are under 5 m, channels seem to be singly open ended. This may be due to damage through the mechanical processing used to reduce the channel dimensions. Samples of AV and p AV clearly adhere to the SFD regime. VA deviat es from the SFD regime at short times. However, there is no apparent transition from SFD to COM diffusion at long diffusion times for any of the samples Further work must be done in order to elucidate whether COM can occur in these systems.

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Page | 26 APPENDIX A. A bbreviations AV L Alanyl L Valine CF continuous flow COM center of mass diffusion HP h yperpolarized HSTE h yperpolarized spin tracer exchange LDA laser diode array ND n ormal Fickian diffusion p AV L Alanyl L Valine pulverized in mortar and pestle PEEK polyetheretherketone PFG pulsed field gradient MAIC Major Analytical & Particle Analysis Instrumentation Centers at the Univ. of Florida RF radio frequency SEM scanning electron microscope SEOP s pin exchange optical pumping SEP simple exclusion process SFD s ingle file diffusion VA L Valyl L Alanine

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