NMR Study of Diffusion in Mixtures of Carbon Dioxide and Functionalized Ionic Liquid

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NMR Study of Diffusion in Mixtures of Carbon Dioxide and Functionalized Ionic Liquid
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english
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Wang, Han
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University of Florida
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Master's ( M.S.)
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University of Florida
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Chemical Engineering
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VASENKOV,SERGEY
Committee Co-Chair:
JIANG,PENG

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diffusion -- nmr -- pfg
Chemical Engineering -- Dissertations, Academic -- UF
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Chemical Engineering thesis, M.S.
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Abstract:
This thesis focuses on pulsed-field gradient nuclear magnetic resonance (PFG NMR) study of self-diffusion in mixtures of CO2 and a task-specific ionic liquid. Complementary chemical exchange experiments performed for CO2 provided additional information that allowed understanding and quantifying the self-diffusion data. The thesis discusses basic background knowledge of self-diffusion and PFG NMR. Furthermore, a brief discussion of the task-specific ionic liquid will also be given. The measured PFG NMR and NMR chemical exchange data are presented and discussed. The data interpretation is provided at the end of the thesis.
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by Han Wang.
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Thesis (M.S.)--University of Florida, 2013.
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Adviser: VASENKOV,SERGEY.
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Co-adviser: JIANG,PENG.

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1 NMR STUDY OF DIFFUSION IN MIXTURES OF CARBON DIOXIDE AND FUNCTIONALIZED IONIC LIQUID By HAN WANG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Han Wang

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3 To my Mom, my Dad and my Grandparents

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4 ACKNOWLEDGMENTS I am surrounded by people who have encouraged me during my studies at the University of Florida First, I would like to thank Dr. Sergey Vasenkov who has provided me the opportunity to do research with his group for 2 years. It has given me a great background in research. I also want to appreciate Eric Hazalbaker who is the PhD student in Dr.Vasenkov s group that brings me great assistants no matter during measurement time or a t the results discussions. I also want to thank Robert Mueller who is the other PhD student in group that are always willing to clarify my doubts during research. Leaving motherland and perusing a degree in a foreign country is not an easy task for me Thanks to all my family members who give me economic and spiritual support all the time especially when I was feeling frustrated by some difficulties Than ks to Ellen who is always a good companion in my life. It is my honor to be a gator here and lets go gators!

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 6 LIST OF FIGURES .......................................................................................................... 7 LIST OF ABBREVIATIONS ............................................................................................. 8 ABSTRACT ................................................................................................................... 10 CHAPTER 1 INTRODUCTION .................................................................................................... 11 Transport and Diffusion........................................................................................... 11 Diffusion Measurements by Using PFG NMR ......................................................... 13 Basics of NMR ........................................................................................................ 13 Longitudinal and Transverse Magnetization ........................................................... 14 NMR Relaxation ...................................................................................................... 16 Signal Detecti on ...................................................................................................... 17 PFG NMR Stimulated Echo Pulse Sequence ......................................................... 18 PFG NMR Stimulated Echo Longitudinal Encodedecode Pulse Sequence ........... 19 PFG NMR Stimulated Echo with Bipolar Gradients Pulse Sequence ..................... 20 PFG NMR Attenuation ............................................................................................ 21 2 SELF DIFFUSION OF 13CO2 IN TASK SPECIFIC IONIC LIQUID .......................... 22 Introduction about Ionic Liquid ................................................................................ 22 Results and Discussion ........................................................................................... 22 Conclusion .............................................................................................................. 31 LIST OF REFERENCES ............................................................................................... 32 BIOGRAPHICAL SKETCH ............................................................................................ 34

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6 LIST OF TABLES Table page 1 1 Attenuation parameters in different types of pulse sequences Equations .......... 21 2 1 Updated diffusion data acquired using 1 value, 10.004845s ........................ 29

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7 LIST OF FIGURES Figure page 1 1 Spin Figure ................... 14 1 2 Magnezation Figure ............................................................................................ 15 1 3 R elaxation Figure ............................................................................................... 16 1 4 PFG NMR Stimulated Echo Pulse Sequence. .................................................... 18 1 5 PFG NMR Stimulated Echo Longitudinal Encode Decode Pulse Sequence ...... 19 1 6 PFG NMR Stimulated Echo Pulse Sequence with Bipolar Gradients ................ 20 2 1 NMR Spectrum ................................................................................................... 23 2 2 Exchange Experiment Data. ............................................................................... 26 2 3 Attenuation Curve Data. ..................................................................................... 30 2 4 Self Diffusivity Data ........................................................................................... 30

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8 LIST OF ABBREVIATIONS FID Free Induction Delay MSD Mean Square Displacement NMR Nuclear Magnetic Resonance PFG NMR Pulsed Field Gradient Nuclear Magnetic Resonance PGSTE PFG NMR Stimulated echo pulse sequence PGSTE LED PFG NMR Stimulated echo longitudinal encode decode pulse sequence r.f. Pulse Radio Frequency Pulse 0B Amplitude of the External Static Magnetic Field 1B Amplitude of the Oscillating Microscope Magnetic Field due to r.f. Pulse c Concentration of Molecules *c Concentration of Labeled Molecules D Diffusion Coefficient g Amplitude of the Magnetic Field Gradient J Flux of Molecules *J Flux of Labeled Molecules M The Total Number of Diffusing Molecules Net Total Longitudinal Magnetization Net Total Longitudinal Magnetization at Equilibrium State Distribution of Spin Phase 2r Mean Square Displacement Gyro magnetic Ratio Time

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9 Duration between the First and Second r.f. pulses in PFG NMR Echo Longitudinal Encode Decode Pulse Sequence Duration between the Second and Third r.f. pulses in PFG NMR Echo Longitudinal Encode Decode Pulse Sequence Diffusion Time Duration of the Magnetic Field Gradient Pulse Spin Lattice NMR Relaxation Time Spin Spin NMR Relaxation Time Duration between the Fourth and Fifth r.f. pulses in PFG NMR Echo Longitudinal Encode Decode Pulse Sequence for Dissipating the Eddy Current Magnetic Moment of Nuclear Spin Larmor Frequency Attenuation of the Amplitude of Signal in PFG NMR Experiment z Position of Molecule or Spin is at z Coordinate

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10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree o f Master of Science NMR STUDY OF DIFFUSION IN MIXTURES OF CARBON DIOXIDE AND FUNCTIONALIZED IONIC LIQUID By Han Wang December 2013 Chair: Sergey Vasenkov Major: Chemical Engineering This thesis focus es on pulsedfield gradient nuclear magnetic resonance (PFG NMR) study of self diffusion in mixtures of CO2 and a taskspecific ionic liquid. Complementary chemical exchange experiments performed for CO2 provided additional information that allowed understanding and quantifying the self diffusion data T he thesis discusses bas ic background knowledge of self diffusion and PFG NMR. Furthermore, a brief discussion of the task specific ionic liquid will also be given. The measured PFG NMR and NMR chemical exchange data are presented and discussed. The data interpretation is provided at the end of the thesis.

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11 CHAPTER 1 INTRODUCTION Transport and Diffusion One dimensional diffusion can be described by Fick s First Law[1]: cJDz (1 1) w here J is the flux of diffusing molecules/ions along the z direction, c(z) is concentration and D is the corresponding diffusion coefficient known as transport diffusion coefficient. It relates flux of molecules and concentration/chemical potential gradient under non equilibrium conditions. Assume D is independent of concentration. Then combined with mass balance we could conver t Equation 1 1 to below, which is Fick s second Law of diffusion [()] c Dc c z tz (1 2) As mentioned above that D is independent of concentration, then the Equation 1 2 could be simplified to 22ccDtz (1 3) In addition to transport diffusion briefly discussed above we can also consider self diffusion, viz. diffusion process that exists due to thermal motion of molecules e ven when there are no macrosc opic concentration gradients and gradients of chemical potentials. It is important to note that the coefficients of transport and self diffusion are not always the same under the same conditions Based on Equation 1 1, self diffusion coefficient could be expressed under the circumstance that all the tagged molecules in system are confined to a certain region of

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12 space at time zero when overall molecular concentration is the same. Then the Equation could be rearranged as shown below: **selfcconstcJDz (1 4) w here, *c is the concentration of the tagged molecules. For the case of onedimensional diffusion with a constant diffusivity and the initial concentration of tagged molecules, the solution could be described as following: 2exp() 4 Az c Dt t (1 5) where A is the normalized constant. Fickian flux Equation for the case of threedimens ional diffusion can be presented as i ij jc JD j (1 6) W here ijD is the diffusion coefficient in i direction due to concentration gradient in the j direction. As at close system situation the total mass of diffusing species remains unchanged. Then total mass M of diffusants could be gained from corresponding concentration profiles. In a case of isotropic diffusion starting at r=0, the distribution Equation of co ncentration could be written 2 3 2exp() 4 (4) r c Dt M Dt (1 7)

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13 W here c/M is equivalent to the diffusion progagator[2] or a probability density function P (r2,r1,t). Then the mean square displacement of the molecules could be gained from the variance of the Gaussian as 22232exp()4() 6(4)rDtrtrdrDtDt (1 8) Diffusion studies can be achieved on many experimental techniques. However, length scale around 1 nm or similar would be too small in comparison to displacements. Pulsed field gradient NMR (PFG NMR) becomes the most capable method of collecting self diffus ion data especially coefficient Diffusion Measurements by U sing PFG NMR NMR stands for nuclear magnetic resonance which is a spectroscopy technique for utilizing nuclear magnetism. I ts function is usually associated with atomic nuclei. Application of NM R requires knowledge of NMR background which is briefly outlined below. Basics of NMR Spin is a property that many atomic nuclei possess. It is also named as spin angular momentum but does not have similar characteristic like angular momentum in cla ssical mechanics which arises from some rotational motion. Instead, it is an intrinsic property of protons and neutrons that nuclei are composed of Its magnetic sensitivity makes it relate to the magnetic moment as the Equation shown below S (1 9) w here is the magnetic moment and S is the spin angular momentum. is the gyromagnetic ratio which could be either negative or positive. The sign of determines

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14 the magnetic moment being parallel or counter parallel to the direction of spin polarization. Figure 1 1 A) Schematic representation of spin precession on the presence of a n external magnetic field B0; B ): Angle of precession cone depends on initial spin polarization. In the case of no external magnetic field, spin polarization turns to isotropic and net nuclear magnetization becomes zero. But as long as there is an external magnetic field being applied, it exerts a torque which forces the spin polarization to move on a cone always keeping the same angle between the directions of magnetic moment and the field ( Fi g 1 1 A ). This motion is known as precession ( Fig 1 1 B ). T he frequency of precession is known as as Larmor frequency It depends on the amplitude of the magnetic field B0 [ 3][4] 00B (1 10) w here 0 is the Larmor frequency. Longitudinal and Transverse M agnetization As mentioned above, in the absence of the external field, the spin polarization is isotropic, which indicates that all the nuclei spins are pointing at random directions. I n this case the net magnetization equals to zero As long as the external magnetic field is

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15 turned on, all the spins begin to process around the field. And eventually the spin polarization would be directed along the magnetic field direction resulting in longitudinal magnet ization. Figure 1 2 A ) No magnetization in abs ence of external magnetic field; B ) Schematic representation of longitudinal net magnetization when external magnetic field B0 is switched on. The longitudinal magnetization M0 is the vector sum of the individual magnetic moments mi [4] Compared with other magnetization mechanisms such as electronic magnetization, bulk magnetization, the value of nuclear magnetization b ecomes quite small, which causes detecting the magnetization along z direction unreasonable. Another oscillating magnetic field B1 need to be applied to make the detection more reliable. B1 field frequency is typically in the range of radio waves Application of this filed is referred to as a n r.f. pulse. This r.f. pulse will make all the spin flip to transverse direction and makes the magnetization measurement detectable ( Fig 1 3) ( A ) 0im ( B ) Net M agnetic Moment 0imM 0B

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16 Figure 1 3 Rotation of net initial magnetization M0 oriented along +z direction, into the transverse plane by 90 r.f. pulse. T he transverse magnetization Mx y precesses in the transverse plane with Larmor frequency 0 [5] NMR Relaxation T he pr ocess of the returning of the net nuclear magnetization to its equilibrium state is NMR relaxation. There are two types of NMR relaxation: (1) Spinlattice/Longitudinal relaxation, also named as T1 relaxation; ( 2 ) Spin spin/transverse relaxation, also name d as T2 relaxation.[3][4][6] T1 relaxation is the process that deals with the gradual growt h of the net nuclear magnetization back to its equilibrium value along +z direction in the presence of a B0 field. Non secular part of transverse relaxation would be caused along the transverse plane during the T1 relaxation. The rate of the growth of the net magnetization along the z direction due the T1 relaxation can be generated by the longitudinal relaxat ion time(T1) 01()(1exp())ZtMtMT ( 1 11 ) W here ()ZMt is the net longitudinal magnetization at time t, 0M is the net equilibrium magnetization, which points along +z direction. The Equation 1 11 holds for the cases y z M 0 Initial Magnetization y z Transverse Magnetization 90 R.F.Pulse M x y

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17 when the net longitudinal magnetization is equal to zero at t=0, in presence of an external magnetic field. As mentioned above T2 relaxation is at when all the spins are flipped to the transverse plan e, furthermore, all the spins remain in a phase coherence situation It is caused by disturbances in local magnetic field by neighboring magnetic entities that when time goes on, various spins would dephase and makes the net transverse magnetization gradually decay to zero. Also, the presence of fluctuation microscopic magnetic field is another reason of T2 relaxation. The net rate of T2 relaxation can be generated by a time constant T2 2()(0)exp()XYXYtMtMT (1 1 2) where ()XYMt is the net transverse magnetization at time t Signal Detection The signal detection is completed along the transverse plane. Due the rephasing, the net magnetization would gradually decay to zero which would become an echo received by the particular coil installed in the spectrometer. The decay is known as free induction decay(FID). With the application of Fourier transformation, FID data would be collected as NMR spectra. Though in an external magnetic field B0, all the atomic nuclei of a certain type should be the same and equal to Larmor frequency. In facts, some deviations would occur due to chemical shift. It is a consequence of slight variations in the effective field experienced by a nucleus because of the local atomic environment. Chemical shift in ppm units could be calculated as

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18 01 ref SF (1 13) where is the chemical shift in ppm, is the measured frequency, ref is the reference frequency and 01 SF is Carrier Frequency known as the operating frequency of the magnet. T h e use of ppm scale greatly simplifies the comparis on of data acquired at different amplitudes of the constant magnetic field. PFG NMR Stimulated Echo Pulse Sequence PFG NMR makes use of the dependence of Larmor frequency on the applied constant magnetic field. In PFG NMR a gradient of magnetic field along the z direction is applied that labels the nuclear spins based on their spatial positions along the z direction 0() Bgz (1 14) W here is the Larmor frequency, is the gyromagnetic ratio, 0B is the external magnetic field, g is the linear gradient of the magnetic field applied on transverse field. Figure 1 4 Schematic of PFG NMR simulated echo pulse sequence. T h is sequence is of great advantage for systems in which the T2 NMR relaxation time is much shorter than T1 NMR relaxation time.

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19 Fig 1 4 indicates the schematic of PFG NMR simulated echo pulse sequence. It is made of three 2 pulses and two field gradient of identical amplitude g and duration The first r.f. pulse is the one that flipped the spins and make longitudinal magnetization to the transverse plane and the first gradient is to tag the spins precessing with different Larmor frequency and dephasing. The time interval 1 is the dephasing interval. Then the second r.f. pulse is to tilted the spins to the z direction and the third one is to flipped the spins back to the transverse plane. And the time interval refers to the measuring diffusion time. If diffusion happens during the time interval, then the dephasing will not be completed and there would a decrease of the intensity amplitude. This pulse sequence is very useful for the situation when the product s T1 value is larger than its T2 value. PFG NMR Stimulated Echo Longitudinal Encode decode Pulse Sequence Figure 1 5 Schematic of the PFG NMR stimulated echo longitudinal encode decode pulse sequence. PFG NMR stimulated echo longitudinal encode decode pulse sequence is basically applied when eddy current, which in the coil that causes inhomogeneity in the

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20 magnetic field, needs to be avoided to get clear data. This method is also known as longitudinal eddy current delay pulse sequence (PGSTE LED)[7]. There are two more r.f. pulses compared with simulated echo pulse sequence. And the extra two r.f. pulses could be seen that are applied at the very end of the sequence which is to eliminate the eddy current. This sequence could be applied when T2 is very small so increasing the time interval would affect the signal produced by T2. During TLED time only T1 affect the signal reception so which could easily help to divide the affection of both T1 and T2. PFG NMR Stimulated Echo with Bipolar Gradients Pulse Sequence This pulse sequence is also known as the 13interval sequence.[8] [11]The advantage of this pulse sequence is that it could eliminate the background gradients produced by some heterogeneous media. Figure 1 6 Schematic of the PFG NMR stimulated echo pulse sequence with bipolar gradients. Bipolar Gradients are used to suppress internal gradients. This stimulated echo pulse sequence with bipolar gradients introduces two negative r.f. pulses right after another pulse which is to help get rid of the background gradients.

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21 PFG NMR Attenuation Dependence of the attenuation of the PFG NMR signal on the amplitude g of the applied field gradient allows obtaini ng molecular diffusivities. T he general form of attenuation Equation for normal isotropic diffusion is 2(.)exp(())eff effgtkDt (1 15) The table 11 below gives the parameter expression at each different types of pulse sequences. Table 1 1 Attenuation parameters in different types of pulse sequences Equations Sequence Type PGSTE/PGSTE LED efft 13 interval sequence k g 2g efft 3 26 In case when several molecular ensembles with different diffusivities contribute to th e measured PFG NMR signal Eq. 115 needs to be modified as follows 2 22() (.)exp(())exp(() 6nn ieff eff i ieff i iirt gtpkDtpk (1 16) w here ip refers to the fraction of molecules diffusing with the Diffusivity constant iD

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22 CHAPTER 2 SELF DIFFUSION OF 13CO2 IN TASK SPECIFIC IONIC LIQUID Introduction about Ionic Liquid It is essential to find applicable liquid adsorbent for CO2 capture. Ionic liquids, molten salts that are liquid at temperatures around room temperature, show many useful properties including negligible vapor pressure and high thermal stability which make these liquids promising sorbents for CO2 capture .[ 1 2 ] C hemical modification of an ionic liquid consisted of an attachment of an amine group to the cation has been determined to result in highly selective and reversible capture of CO2.[ 1316] T h is task specific ionic liquids (TSIL) used as CO2 absorbents has an disadvantage of high viscosity [ 13] which can lead to transport limitations in the process of CO2 absorption. The main focus of this thesis is to fin d out the relationship between CO2 diffusion and the process of CO2 exchange between the chemically bound, viz. chemisorbed, and physisorbed states in the mixture of CO2 and the TSIL. The TSIL chosen for these studies is composed of (CH3)3N(CH2)2NH2 + cation and (CF3SO2)2Nanion. The expected stoichiometric reaction of CO2 with this TSIL is given by the following Equation 2(CH3)3N(CH2)2NH2 + + 2(CF3SO2)2N+ CO2 (CH3)3N(CH2)2NH3 2+ + CH3)3N(CH2)2NHCOO + 2(CF3SO2)2N-, ( 2 1 ) where the first and second species on the right hand part are dication and zwitterion. Results and D iscussion Figure 2 1 shows examples of the 13C NMR spectra obtained by a one pulse sequence for pure TSIL of [(CH3)3N(CH2)2NH2]+ and [CF3SO2)2N]and a mixture of TSIL [(CH3)3N(CH2)2NH2]+[CF3SO2)2N]and CO2. In the [(CH3)3N(CH2)2NH2]+[CF3SO2)2N]-

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23 spectrum (Fig. 2 1A ) the quartet centered at around 120 ppm originate from the anion, with the rest of the lines originating from the cation. Compared with the pure TSIL spectrum, there are two more additional lines at around 161 and 125 ppm appeared in the mixture sample which refers to the CO2 peaks The chemical shift of the former line corresponds to the known chemical shift of the carbonate group (HN13C(O)O-) [ 17,18]. Hence, this line can be assigned to chemisorbed CO2. The line at around 125 ppm originates from physisorbed CO2. T he lines at around 161 and 125 ppm were used to study diffusion and chemical exchange of CO2. The strongest anion lines at 119 and 120 ppm were used for determining the anion diffusivity. The cation diffusivity was obtained using the strongest overlapping cation lines at around 53 ppm. The diffusivities is g ained from 35 repeating steps of the average attenuation curve measurement. Figure 2 1 A) NMR spectrum pure TSIL; B) NMR spectrum of t hat containing 0.06 13CO2 molecules per anioncation pair The spectra were recorded by a 13C NMR one pulse seq uence. The chemical shifts are referenced to a doped dioxane in benzene standard.[ 19] 180 120 60 0 ppm ppmA B 180 120 60 0

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24 The exchange of CO2 between the chemisorbed and physisorbed states is performed by applying a sequence of 13C NMR exchange experiments (EXSY) One dimensional (1D) EXSY sequence (selective /2 ) /2 mix /2 Acquisition[ 20,21] with a selective excitation pulse being used because of being compared with 2D it is more efficient and simpler [ 202 3 ]. 1D EXSY measurements result can be viewed as relaxationtype experiments where the selective /2 pulse was applied for the onresonance spins of physisorbed carbon dioxide and the NMR signals of both chemisorbed and physisorbed CO2 were monitored as a function of the mixing time mix To separate the effects of longitudinal T1 r elaxation from the effects of chemical exchange during mixing time the standard inversion recovery (IR) measurements were also performed. Fig. 22 shows the results of 1D EXSY and inversion recovery measurements. The data in Fig.22 indicate that while the normalized signals measured by the 1D EXSY sequence experience an order of magnitude change when the mixing time is increased from around 0 to 0.03 s, the corresponding normalized signals measured by the IR sequence remains essentially fixed for the same mixing time range. Hence, it can be concluded that the chemical exchange revealed by the 1D EXSY experiment occurs on a much shorter time scale than the T1 relaxation. S implifying analysis of the exchange data could be achieved from the results In particu lar, the mean residence time of CO2 in the physisorbed state can be estimated from the initial slope of the decay of the signal at 125 ppm shown in Fig. 22 B using [ 24] ()(0)exp(/)physmixphys mixphysIIt (2 2 ) where physI is the intensity of the normalized signal at 125 ppm and physt is the mean residence time in the physisorbed state. This Equation is expected to hold for

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25 sufficiently small values of the mixing time corresponding to ()0.4(0)physmixphysII when it can be assumed that the contribution to physI of the CO2 molecules that experienced the transition from the physisorbed to chemisorbed state, and then back to the physisorbed state is negligibly small [ 24]. This assumption is justified by the observation that the equilibr ium population of the chemisorbed state is around 8.7 times larger than that of the physisorbed state, as revealed by the ratio of the CO2 line intensities at 125 and 156 ppm in Fig. 11 B. Hence, for the considered range of small mixing times corresponding to () 0.4 (0)physmix physI I a vast majority of the molecules in the chemisorbed state are expected to be those that also were there at 0mix Obviously, these molecules make great contributions to the transition from chemisorbed to physisorbed Best fit of the initial portion of the 1D EXSY decay curve in Fig. 22 B to Eq. 2 2 yields 8.8phystms The mean residence time in the chemisorbed state ( chemt ) can be estimated by taking into account that for a twostate exchange the ratio of the equilibrium populations of molecules in the two states is equal to the corresponding ratio of the mean residence times. T hen it could be easily determined that the mean residence time of chemis orbed by multiple the value of physisorbed mean residence time of 7.6 times as mentioned above. 76chemtms

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26 Figure 22 A) Results of 13C NMR selective 1D EXSY experiments where the selective /2 pulse was applied for the onresonance spins of the physisorbed carbon dioxide at 125 ppm. Also shown for comparison are the corresponding data obtained by a standard inversion recovery (IR) pulse sequence. B) The same data for the line of the physisorbed carbon dioxide at 125 ppm but zoom in at smaller time scale. Solid line shows the best fit of the exchange data at small mixing times of Eq. 2 2 13 C PFG NMR diffusion measurements for the ions and CO 2 were performed using the standar d stimulated echo PFG NMR sequence /2 1 /2 2 /2 1 Acquisition as mentioned in Chapter 1. The measurements were carried out for the effective diffusion times comparable with and much larger than the values of the mean residence times of CO2 molecules in the physisorbed and chemisorbed states ( physt and chemt ). It was not technically possible to perform 13C PFG NMR studies for diffusion times smaller than physt Due to the signal to noise limitations in the PFG NMR measurements the maximum signal attenuation by diffusion did not accede 6570% of the total signal at zero or small gradient strength. It was observed that the measured attenuation curves in all cases did not show any significant deviations from the monoexponential behavior expected for normal diffusion with a single diffusivi ty. Fig.2 3 shows examples of the measured attenuation curves for the ion lines discussed above as well as for CO2 lines at 156 and 125 ppm. When

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27 performing diffusion measurements under the conditions of chemical exchange special care must be taken when choosing the duration of the time interval 1 of the stimulated echo PFG NMR sequence to make the mean residence time of exc hange negligible. The choice of this time interval is important because the contribution of CO2 molecules that were in different states during the first and second time interval 1 of the sequence to the measured signal is expected to be proportional to cos( 1 ), where is the difference between the precession frequencies in the chemisorbed and physisorbed states [ 25]. Under experimental conditions the existence of such dependence was confirmed by performing measurements with the PFG NMR stimulated echo sequence at a fixed, small gradient strength. The measurements were carried out with different values of 1 chosen such that the probed range of the values of 1 covered around 3 for each diffusion time used. The PFG NMR diffusion data reported were obtained under conditions when cos( 1 ) = 1. This corresponds to the situation when the spins that were in different chemical environments during the first and second time interval 1 of the sequence fully contribute to the measured signal. An analytical solution for this case is presented in Refs. [ 26, 27 ] With Equation s below 000 000 000 000()() [ ]exp[()][ ]exp[()] 22 22 ()() [ ]exp[()][ ]exp[()] 22 22AABB AABB A BBAA BBAA BMMkM MMkM MTT MMkM MMkM MTT (2 3 A,B ) where AM is the species physisorbed CO2 onresonance nuclear magnetization and Bk is the rate constant of species chemisorbed CO2, with

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28 222221[]21[]2ABABABABABkkDKDKkkDKDKkk A nd AD is the diffusion constant of species physisorbed CO2. It is important to note that this solution was developed for the measurement conditions when NMR relaxation effects can be neglected. It was observed that in agreement with this solution the effective diffusivities given by the initial slopes of the measured attenuation curves for the CO2 lines at 125 and 156 ppm are different at short diffusion times and approach the same diffusivity with increasing diffusion time (Fig. 2 4). For the largest diffusion time of 1.2 s both diffusivities are the same within the experimental uncertainty indicating that the condition of fast exchange of CO2 molecules between the chemisorbed and physisorbed states is reached for this diffusion time. Fitting the initial parts of the carbon dioxide PFG NMR attenuation curves to Eqs. 2 3A and 23B for the effective diffusion times between 0.03 s and 1.2 s allowed estimating the diffusivities of the chemisorbed and physisorbed carbon dioxide. For these times only the initial parts of the attenuation curves ( which can change the shape of the measured PFG NMR curves, but is not taken into account in the derivation of Eqs. 2 3A and 23B For the largest diffusion time of 1.2 s the attenuation curves predicted by Eqs. 2 3A and 2 3B are monoexponential in agreement with the experimental obs ervation. In this case the fitting was performed for the whole measured attenuation curves. The resulting CO2 diffusivities in the physisorbed and chemisorbed states are shown in Table 2 1 together with the ranges of diffusion times used to obtain the diff usion data.

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29 Table 2 1 Updated diffusion data acquired using 1 value, 10.004845 s Diffusion Time s Physisorbed CO 2 Diffusivity x 10 12 m 2 s 1 Chemisorbed CO 2 Diffusivity x 10 12 m 2 s 1 0.03 16.1 3.2 2.7 0.5 0.04 13.6 2.7 3.7 0.7 0.16 11.4 2.3 4.4 0.9 0.64 8.8 1.8 4.8 1.0 1.2 4.7 0.9 4.2 0.8 Fig. 2 4 and Table 2 1 show the cation and anion diffusivities obtained from fitting the measured PFG NMR attenuation curves by Eq. 22 It is seen that within the experimental uncertainty the ion diffusivities in the samples with and without CO2 are the same (Table 2 1) and do not depend on diffusion time (Fig. 2 4). These results can be understood by noting that in the sample with CO2 the number of CO2 molecules is several times smaller than the number of the anioncation pairs. Hence, the measured ion diffusivities, which were obtained from a relatively small PFG NMR attenuation range reflecting the diffusion behavior of the majority of ions in the sample, are not expected to be very different in the samples with and without CO2 or to show any dependence on diffusion time.

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30 Figure 2 3 13C PFG NMR attenuation curves obtained by the 13C PFG NMR STE sequence for the mixture of [(CH3)3N(CH2)2NH2]+[CF3SO2)2N]with CO2 for efft averaging the attenuation curves measured for the NMR lines of the anion at 122 ppm and 120 ppm The attenuation curve for the cation corresponds to the cation line at 54 ppm. The attenuation curve for chemisorbed CO2 corresponds to the line at 161 ppm. The attenuation curve for physisorbed CO2 corresponds to the line at 125 ppm. Figure 2 4 D ependence of the self diffusivity of the cation, anion, chemisorbed CO 2 and physisorbed CO2 to the diffusion time at 297 K. The data were obtained by 13C PFG NMR. 0.0 0.4 0.8 1.2 1 10 CO2 (P-P) CO2 (C-C) Cation AnionD x10-12 m2s-1teff s

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31 Conclusion This is the first time observation of chemical exchange in real 13C system in the mixtures of carbon dioxide and task specific ionic liquid. T h e PFG NMR measurement on diffusion of chemical exchange of CO2 in this 13C system shows the evidence and species diffusivities The analytical solution applied with Equation 2 3A, B also corresp ond well to the initial slope of the experimental attenuation data. It shows that chemical exchange phenomenon can affect the diffusivity of the species of physisorbed and chemisorbed CO2 in certain effective diffusion time range which needs to be taken in to account for further diffusion study.

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34 BIOGRAPHICAL SKETCH Han Wang was born in 1989 at Ruian, China to Lingli Zhang and Beijiao Wang. He grew up with his parents. All his early schooling was done in Ruian itself. A n d after junior high school he moved to Shanghai Fuxing senior high school. He finished up his bachelor degree in South China University of Technology in Guangzhou, China. He attended the University of Florida and obtained his Master of Science in chemical engineering.