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Single-File Diffusion in Dipeptide Nanotubes

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Title:
Single-File Diffusion in Dipeptide Nanotubes Experimental Study by Xe-129 PFG NMR
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1 online resource (33 p.)
Language:
english
Creator:
Wang, Aiping
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
Vasenkov, Sergey
Committee Members:
Myers, Michele V
Jiang, Peng

Subjects

Subjects / Keywords:
diffusion -- pfgnmr
Chemical Engineering -- Dissertations, Academic -- UF
Genre:
Chemical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In this thesis, pulsed field gradient nuclear magnetic resonance (PFG NMR) has been exploited to investigate transport properties of xenon atoms diffusing in dipeptide nanotubes under single-file conditions, i.e. when guest molecules cannot pass one another in one-dimensional channels. Two types of nanotubes have been used:L-alanyl-L-valine (AV) and L-val-L-ala (VA).  This work is divided into two parts.  The first introductory part discusses thefollowing items: the concept of transport diffusion and self-diffusion, two distinct forms of self-diffusion, detailed description of single-file diffusion, and basics of NMR. The second part presents results of PFG NMR diffusion studies of xenon in sigle-file nanotubes systems. The measured data is consistent with the expectation that this diffusion process obeys the mechanismof single-file diffusion. This work is significant because there are only a few reports in the literature on the experimental observation of molecular single-file diffusion.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Aiping Wang.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Vasenkov, Sergey.

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Source Institution:
UFRGP
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Applicable rights reserved.
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lcc - LD1780 2013
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UFE0046007:00001

MISSING IMAGE

Material Information

Title:
Single-File Diffusion in Dipeptide Nanotubes Experimental Study by Xe-129 PFG NMR
Physical Description:
1 online resource (33 p.)
Language:
english
Creator:
Wang, Aiping
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
Vasenkov, Sergey
Committee Members:
Myers, Michele V
Jiang, Peng

Subjects

Subjects / Keywords:
diffusion -- pfgnmr
Chemical Engineering -- Dissertations, Academic -- UF
Genre:
Chemical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In this thesis, pulsed field gradient nuclear magnetic resonance (PFG NMR) has been exploited to investigate transport properties of xenon atoms diffusing in dipeptide nanotubes under single-file conditions, i.e. when guest molecules cannot pass one another in one-dimensional channels. Two types of nanotubes have been used:L-alanyl-L-valine (AV) and L-val-L-ala (VA).  This work is divided into two parts.  The first introductory part discusses thefollowing items: the concept of transport diffusion and self-diffusion, two distinct forms of self-diffusion, detailed description of single-file diffusion, and basics of NMR. The second part presents results of PFG NMR diffusion studies of xenon in sigle-file nanotubes systems. The measured data is consistent with the expectation that this diffusion process obeys the mechanismof single-file diffusion. This work is significant because there are only a few reports in the literature on the experimental observation of molecular single-file diffusion.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Aiping Wang.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Vasenkov, Sergey.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0046007:00001


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1 SINGLEFILE DIFFUSION IN DIPEPTIDE NANOTUBES: EXPERIMENTAL STUDY BY XE129 PFG NMR By AIPING 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 Aiping Wang

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3 To my mother, my father and my grandmother

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4 ACKNOWLEDGMENTS I am so grateful to these 2 years I spent here at University of Florida, and so proud to be a gator. I have a l ot of people to thank for their significant positive influence on me not only in these years, but also in my entire life time. First of all, I want to thank my advisor Prof. Dr. Sergey Vasenkov f or his constant support and patient guidance. Throughout my entire research here, he inspired me by his true enthusiasm towards science, and provided me with lot of the encouragement and sound advice. He explained things clearly and patiently, and as a mentor he was always considerate to me, making me encouraged all the time during the work. I would like to thank my colleague Dr. Muslim Dvoyashkin for his dedicated guidance. H e was so devoted to science, and did experiments so precisely that his attitude wo uld have a long effect on me in my future study. I want to thank Eric Hazelbaker and Robert Muller for being friends with me and supporting me during the work. I am also grateful to the stuff working at the Advanced Magnetic Resonance Imaging and Spectrosc opy (AMRIS), especially Dr. Daniel Plant for all the necessary technical support with all conducted experiments. I would like to thank all my friends who accompanied me for 26 years, and who are the most valuable treasures in my life. I also wish to thank my best friend Zhe Liu for accompanying me from my college until now, helping me get through all my tough times, and providing me with emotional support and care. Last and most importantly, I want to thank my family, especially my mother Mrs. Lei Weng, my father Professor Yue Wang, and my grandmother Naifeng Zhao. They raised me up like the apple of their eye, taught me the truth of life, to live a righteous life. I would like to contribute all my success to them, and always indebted to them for their pure love and selfless sacrifices.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF FIGURES .......................................................................................................... 6 LIST OF ABBREVIATIONS ............................................................................................. 7 ABSTRACT ..................................................................................................................... 9 CHAPTER 1 INTRODUCTION .................................................................................................... 10 Transport and Self Diffusion of Molecules .............................................................. 10 Single file and Fickian Diffusion Modes .................................................................. 11 Basics of NMR ........................................................................................................ 12 Spin Precession ............................................................................................... 12 Longitudinal Magnetization and SpinLattice Relaxation .................................. 13 Transverse Magnetization and SpinSpin Relaxation ....................................... 14 Signal Detection ............................................................................................... 15 Pulsed Field Gradient (PFG) NMR ......................................................................... 16 PFG NMR Stimulated Echo Pulse Sequence ................................................... 16 PFG NMR Stimulated Echo Longitudinal EncodeDecode Pulse Sequence .... 18 Attenuation Equation Applied in PFG NMR ...................................................... 18 2 SINGLEFILE DIFFUSION OF 129XE IN AV AND VA NANOTUBES ...................... 21 PFG NMR Experiment Details ................................................................................ 21 Sample Preparation .......................................................................................... 21 PFG NMR Diffusion Studies ............................................................................. 23 Experimental Results and Their Analysis ................................................................ 24 Summary ................................................................................................................ 30 LIST OF REFERENCES ............................................................................................... 31 BIOGRAPHICAL SKETCH ............................................................................................ 33

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6 LIST OF FIGURES Figure page 1 1 Schematic motion of spin precession in external magnetic field. .................... 13 1 2 Schematic of standard PFG NMR echo pulse sequence, consisting three / 2 r.f. pulses in the sequence.. ................................................................................ 16 1 3 Schematic of the PFG NMR Stimulated echo longitudinal encode decode pulse sequence, which consist five /2 r.f. pulses. ............................................ 18 2 1 Schematic presentation of singlefile diffusion of Xenon in AV or VA nano channels .. 21 2 2 SEM micrograph of the samples of AV dipeptide nanotubes ... .. 22 2 3 129Xe PFG NMR attenuations curves for Xenon in AV nanotubes obtained for diffusion times of 40ms, 0.3s, 2s, 3s,12s at 298K . ......................................... 24 2 4 129Xe PFG NMR attenuations curves for Xenon in AV nanotubes obtained for diffusion times of 40ms, 0.3s, 2s, 3s,12s at 298K ... 25 2 5 129Xe PFG NMR attenuation curves for Xenon in AV nanotubes obtained for a broader range of diffusion times that includes 15ms, 40ms, 110ms, 300ms, 1s, 2s, 3s,12s at 298K.. ...................................................................................... 26 2 6 129Xe PFG NMR attenuations curve for Xenon in VA nanotubes obtained for diffusion times of 40ms,110ms,300ms,1s,2s,3s,6s,12s at 298K.. ...................... 27 2 7 Mean square displacements (MSD) of 129Xe in AV and VA nanotubes plotted as a function of diffusion time at 298K.. .............................................................. 28

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7 LIST OF ABBREVIATIONS L alanyl L valine Fr ee Induction Decay MeanSquare Displacement Nuclear Magnetic Resonance Pulsed Field Gradient Nuclear Magnetic Resonance PFG NMR Stimulated echo pulse sequence PFG NMR Stimulated echo longitudinal encode decode pulse sequence . Radio Frequency Pulse Scanning Electron Microscope Single File Diffusion L val L Ala Xenon Amplitude of the External Static Magnetic Field Amplitude of the Oscillating Microscope Magnetic Field due to r.f. P ulse Concentration of Molecules Concentration of Labeled Molecules Diffusion Coefficient Single File Mobility Factor Amplitude of the Magnetic Field Gradient Flux of Molecules Flux of Labeled Molecules The Total Number of Diffusing Molecules Net Total Longitudinal Magnetization

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8 Net Total Longitudinal Magnetization at Equilibrium State Distribution of Spin Phase Mean Square Displacement Time 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 Larmor Frequency Position of Molecule or Spin i s at z Coordinate Gyro magnetic Ratio Duration of the Magnetic Field Gradient Pulse Diffusion Time Magnetic Moment of Nuclear Spin 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 Attenuation of the Amplitude of Signal in PFG NMR Experiment

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9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science SINGLEFILE DIFFUSION IN DIPEPTIDE NANOTUBES: EXPERIMENTAL STUDY BY XE129 PFG NMR By Aiping Wang August 2013 Chair: Sergey Vasenkov Major: Chemical Engineering In this thesis, pulsed field gradient nuclear magnetic resonance (PFG NMR) has been exploited to investigate transport properties of xenon atoms diffusing in dipeptide nanotubes under singlefile conditions i.e. when guest molecules cannot pass one another in onedimensional channels Two types of nanotubes have been used: L alanyl L valine (AV) and L val L ala (VA) T his work is divided into two parts. The first i ntroductory part discusses the following items: the c o ncept of transport diffusion and self diffusion, two distinct forms of self diffusion, detailed description of singlefile diffusion, and basics of NMR. The second part presents results of PFG NMR diffusion studies of xenon in si n gle file nanotubes systems. The measured data is consistent with the expectation that this diffusion process obeys the mechanism of single file diffusion. This work is significant because there are only a few reports in the literature on the experimental observation of molec ular single file diffusion.

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10 CHAPTER 1 INTRODUCTION Transport and Self Diffusion of Molecules Diffusion is a process which occurs at temperatures above zero Kelvin This process renders the tendency of the mater to migrate in a way to eliminate spat ial gradients in chemical potential towards maximum entropy. During the period 18501855, Thomas Graham and Adolf Fick initiated the study of diffusion, which has resulted in establishing the interrelation between the flux of matter J, and gradient of concentration c, also known as Ficks First Law of Diffusion1, = (1.1) where D is the diffusion coefficient or diffusivity In the late 1820s, the Scottish botanist Robert Brown observed the phenomenon that through the microscope that particles found in pollen grains mov ed through the water, which was referred to as Brownian M otion3. Einstein7 elaborated the close relationship between Brownian Motion and diffusion for the first time. In Brownian M otion, the labeled diffusants were initially located wit hin a given limit of space and the experimental accessible quantity that describes this movement is the time dependence of the concentration distribution of the labeled particles. With the total concentration being constant, the self diffusivity or self di ffusion coefficient is performed as, = (1.2) It is easy to differentiate that J is the flux of the labeled molecules; and c is the concentration of the labeled molecules; c = const means the total concentration of labeled and unlabeled molecules stays constant. For a constant diffusivity system,

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11 assuming a parallel walled container with unite cross sectional area, the total num ber of molecules (M) that diffuses is presented by4. = (1.3) Where = / (1.4) The probability of finding the molecule at radius r after time t, which is initially located at the origin, is rendered as4: = / ( ) / (1.5) During which, r refers as the term propagator12 and derived and integrated from E quation 1.5, we get the mean square displacement of the diffusing molecules in onedimensional space: ( ) = / ( ) / = 2 (1.6) Equation is wellknown as Einsteins relations7. Singlefile and Fickian Diffusion M odes Within recent years, research involving gaseous sorbates in onedimensional nanotube systems are of high interest, because of its high relevance of a number of application s, such as separation of gaseous mixtures20 and catalysis13. T he two wellknown modes of diffusion in infinite onedimensional channels are normal diffus ion and singlefile diffusion. N ormal diffusion takes place when confinement is large enough to allow mutual pass ages of the molecules, and the mean square displacement (MSD) increases with time t according to7: [ ( ) (0 ) ] = 2 (1. 7 )

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12 I n case of singlefile regime, mutual passages are prohibited, and MSD increases as the square root of diffusion time8, 14, 17: [ ( ) (0 ) ] = 2 / (1. 8 ) w here F is the singlefile mobility factor. Basics of NMR Among all the important properties of the atomic nuclei19, the less t angible property of nuclei is nuclear spin, which is highly abstract, but of significant importance for e xploring and providing information of the microscopic and internal structures of objects without disturbing them. Spin (if not indicated specifically in the following text, it is referred as spin of the nucleus) of the nucleus is called spin angular momentum, not produced by rotation of the particle, but is an intrinsic property of the particle itself. The spin and magnetism is proportional to each other: = ( 1. 9 ) Where is the magnetic moment representing the interaction between the magnetic substance and magnetic field, and s is the spin of nucleus we talked above, is gyro magnetic ratio, determining whether the magnetic moment will be aligned or opposite in the direction parallel to the spin. Spin Precession Under no external magnetic field the angular momentum of the nuclei with spin point at all possible directions, resulting in a isotropic distribution of the magnetic moments, and the net nuclear magnetization is zero. Since the angular momentum of a rotating nuclei with a spin is a vector, the direction of the spin angular momentum is

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13 called the spin polarization axis19. However, when a magnetic field is applied, it exerts a torque on the magnetic moment of the nuclei, causing the spin polarization a xis moving a round the field at the constant angle between spin magnetic moment and the field. This process is called precession, and the angle is fixed between the field and the direction of the spin when there was no external filed (Figure 1 1). Larmor fr equency16 is dependent on the external magnetic filed : = (1.10) Figure 11 Schematic motion of spin precession in external magnetic field. (A ) Schematic motion of spin precession in external magnetic fiel d B (B ) The angle of the precession depends on initial spin polarization axis. Longitudinal Magnetization and SpinLattice Relaxation T he spin polarizations are pointing at all possible direction in the absence of an external magnetic field. In the presence of external magnetic field all the spins start to precess and all the spin polarization still remain isotropic at the very beginning However, if we take a closer look microscopically, each nuclear spin is surrounded by

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14 local magnetic field resulting from rapid fluctuati on of other nuclear spins. Although these variations are comparably small to the external field, these tiny fluctuations gradually develop a break down of constant angle with which the spins conduct precession, resulting in anisotropy distribution of all the spins polarization. The resulting steadystate distribution of spin polarization point slightly towards the lower energy orientation in which all the spin point long the direction of the applied magnetic field. Assuming the external magnetic field and resulting spin magnetization in the +z dire ction (or longitudinal direction), this is defined as longitudinal magnetization. Since these local fields try to reorient the spin polarization to reach the direction of the field favorable as low energy, it is aimed at restoring the magnetization along the z axis to a stable and equilibrium state, during which the rate of restoring can be defined as the longitudinal relaxation time T1, during which spinlattice relaxation or T1 relaxation occurred. = (1 ) (1.11) Where is the net total longitudinal magnetization at t, and is the net total longitudinal magnetization at equilibrium state. Transverse Magnetization and SpinSpin Relaxation The longitudinal nuclear spin magnetization is small compared to magnetization resulting from other entities such as typical diamagnetism associated with electrons. Thus in NMR, transverse magnetization is detected instead. This is achieved by applying an ort hogonal radiofrequency pulse, which is an oscillating magnetic field. The spin polarization is suddenly tilted to x y plane from +z direction, thus this net magnetic

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15 moment along with x y plane perpendicular to the main magnetic field is referred transvers e magnetization. After the orthogonal field is turned off, the spins gradually assume precession, resulting in the bulk magnetic moment conducting precession too. A new feature occurred, where the transverse magnetizations begin to decay until the transverse magnetism is gone, because of the T2 relaxation which is called spinspin relaxation, resulting from the impossibility to maintain exact synchronic precession between different nuclear magnets. The reason in this relaxation i s similar to that for the T1 relaxation, and both because the local microscopic magnetic fields are different, so they eventually get out of phase with each other. This decay process is known as T2 relaxation, and the rate that characterizes this transvers e relaxation is defined as T2, which is defined in Equation 1.12 : = ( 0 ) ( ) ( 1.1 2) Signal Detection Even though the transverse magnetization after an application of the orthogonal radio f requency is not large, its detectable as it oscillates at a well defined frequency. The detection is achieved by arranging a winding axis of coil perpendicular to the main magnetic field, and receiving the electric current in the coil resulting from the continuously precessing transverse magnetization according to the Maxwells law. The oscillating cur rent in the coil is called NMR signal or freeinduction decay (FID). When we process the data, we usually operate Fourier transformation to transform FID into frequency domain data which we see as NMR spectra.

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16 Pulsed Field Gradient (PFG) NMR In PFG NMR, th e Larmor frequency of the nuclear spins in the transverse plane is dependent on the z coordinate. This is achieved by an application of a gradient of magnetic field along the z direction when magnetization is in the transverse plane: = (+ ) ( 1.1 3 ) In here, is the larmor frequency, g is the linear gradi ent of magnetic field applied along z direction, and represents the constant e xternal magnetic field. The work in this thesis focuses on singlefile self diffusion studies, so we applied 129Xe pulsed field gradient (PFG) NMR. The studies have benefited from a combination of advantage of high ( 30T/m) magnetic field gradients and high (17.6T) magnetic field. T he application of strong gradients was needed to record slow transport in nanotubes. The standard PFG NMR stimulated echo pulse sequence with eddy current delay (PGSTE LED) was used in this work, and this is explained in detail in next section. PFG NMR Sti mulated Echo Pulse Sequence Figure 12 Schematic of standard PFG NMR echo pulse sequence, consisting three /2 r.f. pulses in the sequence. This sequence benefit s the systems where T2 relaxation is shorter than T1 relaxation time. gradient gradien t

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17 Figure 12 is th e schematic process of the PFG NMR stimulated echo pulse sequence. After the first r.f pulse is applied the net magnetization is tilted to the x y plane from the +z direction, and in the meantime, the gradient is applied which labels the spins at different position along the +z directio n by a different Larmor frequency The second r.f pulse tilt s the magnetization to the z direction, and subsequently the third r. f. pulse tilt s the magnetization to x y plane. And then the gradient with the same amplitude, duration and direction is applied to the transverse magnetization. The latter process can be referred to as rephrasing. Due to diffusion between the two gradients the rephrasing is not complete and the final intensity is less than the maximum intensity. The decrease in the intensity of the acquired signal contains information about the rate of diffusion of molecules and also about the mean square displacement of the diffusants. The time period between the first and second r.f. pulse is called dephasing interval, and the time period between the third r.f. pulse and the beginning of the acquisition is called rephrasing interval. During the period, the T2 relaxation happens, and during the period, T1 relaxation happens. This sequence benefits the diffusion study for the systems in which spins have slower T1 relaxation than T2 relaxation.

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18 PFG NMR Stimulated E cho L ongitudinal E ncodeD ecode P ulse S equence Figure 13 Schematic of the PFG NMR Stimulated echo longitudinal encode decode pulse sequence, which consist five /2 r.f. pulses. This PFG NMR stimulated echo longitudinal encodedecode (PGSTE LED)9 is modified from the PFG NMR Stimulated echo pulse sequence to decrease an influence of eddy currents resulting from the constantly turning on and off the gradient pulses. E ddy currents may lead to inhomogeneity in the magnetic field which presents a problem for the measurements T he additional two /2 r.f. pulses and the time delay between them helps to reduce the eddy currents by tilting the transverse magnetization to z direction and after the LED delay tilting the magneti zation to x y plane again. This sequence benefit s the system with the combination of short T2 relaxation and the need for large magnetic gradient field, which may result in large eddy currents. Attenuation Equation A pplied in PFG NMR Since magnetic field gradient labels the spin locations along z direction by the Larmor frequency of spin precession it is possible to detect the displacement of the spin along +z direction. The sum of the magnetization phase angle of every nuclear spin under the gradient pulse is presented as gradient gradie nt

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19 ( ) = ( + ) (1.14) T wo gradient pulses are applied i n the stimulated echo sequence along z direction to depha se and rephrase the spins to achieve the information of the displacement of the diffusing sorbates. T he difference in phase accumulation between the first two gradient pulses can be written as = ( + ) ( + ) = ( 1.15) and represent the position of the spins when the first and second gradient are applied. If they change position during the process, then = is nonzero, and causes the attenuation of the intensity of the NMR signal Thus, the attenuation for all spins beginning at position z1 is = ( ) (1.16) Where ( ) is the distribution of the spin phase beginning at So E quation 1.16 can be rewritten as = / (1.17) Where renders the average of the over the displacement which means the average value of the change of phase accumulation between the first and second gradients pulses It can be rewritten in terms of mean square displacement = ( ) (1.18) Equation 1.18 is applicable for spins with any initial position, and consequentl y the attenuation curve equation for all spins due to the applied gradient pulses can be presented

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20 = ( ( ) ) (1.19) In a typical PGSTELED experime nt t means effective diffusion time given by = /3 (1.20) T he attenuation of the signal is usually measured when one parameter is fixed, such as g or and plot t ed as the function of the other parameter, to find the experimental diffusion coefficients.

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21 CHAPTER 2 SINGLEFILE DIFFUSION OF 129XE IN AV AND VA NANOTUBES The studies on diffusion in systems of onedimensional nanochannels are of strong interest and have significant practical value in a lot of applications such as molecular separation, nanofluids, and catalysts. Confining in onedimensional channel can lead to anomalous diffusions, and among them single file diffusion is the most fascinating one. Although a number of computational simulations and theoretical studies were published over the past decade8, 14, only a few publications of the experimental observation of single file diffusion are available11, 18. In the following section, a detailed experiment report of the microscopic studies of self diffusion of 129Xe in AV and VA dipeptide nanotubes by 129Xe pulsed field gradient unclear magnetic resonance (PFG NMR) is presented. PFG NMR Experiment Details Sample P reparation In this work 129Xe is chosen as sorbate, and self assembled Lalanyl L valine (AV) and nanotubes L val L Ala (VA) nanotubes 10, 24 are chosen as sorbents X e atoms are spherical with the diameter around 0.47nm, while the radius of AV and VA is about 0.25nm. U nder these conditions single diffusi on is expected (see Figure 21 ). Figure 21 S chematic presentation of singlefile diffusion of Xe non in AV or VA nano channel s. The nanochannel diameter is too narrow for mutual passage of the molecules

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22 T2 NMR relaxation time of 129Xe is expected to be longer than that of protons under conditions of extreme confinement in nanotubes6. S ince chemical shift of 129Xe is sensitive to the size of confining pores orientation and geometry2123, 25, the absorbed peak of 129Xe is wellresolved from the gas peak Self assembled Lalanyl L valine was bought from Bachem company and was use d as received. AV can form hydrophobic dipeptide crystalline channels with the inner diameter of 0.51nm10, 24, the average length of which are around 5 0 m determined from the micrographs by JEOL 6400 scanning electron microscope(SEM) located at the UF major analytical instrumentation center. Figure 22 shows the recorded micrographs of the AV nanotubes : Figure 2 2 SEM micrograph of the samples of AV dipeptide nanotubes. Adapted from M. Dvo yashkin, and A. Wang. 2013. 'Signatures of Normal and Anomalous Diffusion in Nanotube Systems by Nmr',(Page 2,Figure 1)Microporous and Mesoporous Materials.

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23 Because AV and VA materials are similar only the preparation of AV samples is discussed below In this work, 65mg of AV nanotubes with 3bar of Xe was prepared for experimental study. 1) 65mg of AV nanotubes was placed into a 5mm medium wall tip off sample tube.( NE HP5 M TTO) 2) The tube was hooked up to high vacuum(104Mbar) system to evacuate mois ture and air in the sample tubes, and this process was kept with the tube in the furnace at the constant temperature of 120 degree Celsius for 24 hours. 3) A fixed mass of 129Xe was transferred cryogenically into the NMR tube containing the AV nanotubes. 4) The tube was then flame sealed and ready to use after the equilibration at room temperature. PFG NMR D iffusion S tudies PFG NMR is used as powerful tool for studying diffusive molecules15. PFG NMR diffusion measurement s in this work were performed on a 17.6T Bruker BioSpin NMR spectrometer at the resonance frequencies of 208.6 MHz for 129Xe. Diff60 diffusion probe (up to 30T/m, Bruker BioSpin ) and Great60 gradient amplifier (Bruker BioSpin) were used. In this work, the combination of strong gradients and high fi e l d is needed to record slow transport in nanotubes and to obtain sufficiently strong signals from Xe nuclei having a low gyromagneti c ratio. The pulse sequence used in this work is standard PFG NMR stimulated echo pulse sequence with eddy current delay (PGSTE LED)9. Xenon129 PFG NMR attenuation curves were measured under a broad range of diffusion times for studying the diffusion mobility inside the nanotubes. For each diffusion time the signal attenuation is plotted as a function of the magnetic field gradient Detailed results are presented in the following section.

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24 Experimental Results and Their A nalysis In this work, single file diffusion exper imental observation is expected. In random ly oriented and defect free nanochannels PFG NMR a ttenuation curve s are expected to obey the E quation 2.111, 18: = ( ) / ( 2.1) Figure 23 129Xe PFG NMR attenuations curves for Xenon in AV nanotubes obtained for diffusi on times of 40ms, 0.3s, 2s, 3s,12s at 298K. The attenuation is plotted as a function of qt, The loading of xenon in AV nanotubes corresponds to sorption equilibrium with xenon in the gas phase at the pressure of 3bar. The black dashed lines show the results of the best fit by E quation 2. 1. Adapted from M. Dvoyashkin, and A. Wang. 2013. 'Signatures of Normal and Anomalous Diffusi on in Nanotube Systems by Nmr',(Page 3, Figure 4) Microporous and Mesoporous Materials.

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25 Figure 24 129Xe PFG NMR attenuations curves for Xenon in AV nanotubes obtained for diffusion times of 40ms, 0.3s, 2s, 3s,12s at 298K. The attenuation is plotted as a function of qt / The loading of xenon in AV nanotubes corresponds to sorption equilibrium with xenon in the gas phase at the pressure of 3bar. The black dashed lines show the results of the best fit by Equation 2. 1. Adapted from M. Dvoyashkin, and A. Wang. 2013. 'Signatures of Normal and Anomalous Diffusi on i n Nanotube Systems by Nmr',(Page 3, Figure 4) Microporous and Mesoporous Materials. F igure 23 and Figure 2 4 show the 129Xe PFG NMR attenuation curves for Xenon diffusion inside AV nanotubes for the range of diffusion times from 40ms to 12s. T hese two figures present the same PFG NMR diffusion data in two different ways. In F igure 23 the attenuation curve is plotted in coordinates qt. If this is normal diffusion process, t he attenuation curves measured for different diffusion times are expected to collapse i nto a single curve when plot ted this way. I n F igure 24 the attenuation curves are plotted in coordinates vs qt / For the case of singlefile

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26 diffusion all the attenuations curves measured for different effective diffusion times are ex pected to collapse i nto a single curve in the presentation of Figure 25 The results in F igure 23 and 24 clearly show that the diffusion process of Xenon in AV nanotubes obeys the time scaling of singlefile diffusion. Figure 25 129Xe PFG NMR attenuation curves for Xe non in AV nanotubes obtained for a broader range of diffusion times that includes 15ms, 40ms, 110ms, 300ms, 1s, 2s, 3s,12s at 298K. The attenuation is plotted as a function of qt / The loading of xenon in AV nanotubes corresponds to sorption equilibrium with xenon in the gas phase at the pressure of 3bar. The black dashed lines show the results of the best fit by Equation 2. 1.

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27 Figure 26 129Xe PFG NMR attenuations curve for Xenon in VA nanotubes obtained for diff usion times of 40ms,110ms,300ms,1s,2s,3s,6s,12s at 298K. The attenuation is plotted as a function of qt / The loading of xenon in VA nanotubes corresponds to sorption equilibrium with xenon in the gas phase at the pressure of 3bar. T he black dashed lines show the results of the best fit by Equation 2. 1. Figure 25 present s the PFG N MR diffusion data for 129Xe in AV in a broader range of diffusion times. Figure 2 6 shows the corresponding data for 129Xe in VA. In both figures t he attenuation are plotted as the function of / according to E quation 2.1. It is seen that the results in both figures obey the time scaling of singlefile diffusion. The PFG NMR data in these figures do not show any evidence of the existence of longrange diffusion, i.e. diffusion under conditions of fast exchange

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28 between the nanotubes and the surrounding gas phase6. This is in agreement with the observation that the maximum root MSDs of x e non in AV and VA nanotubes was one order of magnitude smaller than the average lengths of AV and VA nanotubes ( around 5 0 m ) Figure 27 Mean square displacement s (MSD) of 129Xe in AV and VA nanotubes plotted as a function of diffusion time at 298K The solid and dashed line show the dependence of MSD for the case when MSD is proportional to the square root of diffusion time. T he grey line shows the dependence of MSD for the case when MSD is proportional to diffusion time

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29 Figure 27 shows the time dependences of MSD of Xenon in AV and VA dipeptide nanotubes at 298K. It can be seen that MS D scales with the square root of the diffusion time, which is in di rect agreem ent with Equation 1.8. T his observation agrees with the expectation that Xenon atoms are too large to pass one another in the channels of AV and VA natotubes.

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30 Summa ry 129Xe PFG NMR measurements were performed to study the diffusion of xenon in AV and VA nanotubes. The experimental data in F igure 23 2 4 2 5 and 26 demonstrate that in all cases the diffusion of Xenon obey s the time scaling of singlefile diffusion. This observation is consistent with the expectation that Xenon atoms are too large to pas s one another in the channels of AV and VA nanotubes Figure 27 presents the distinct signature of singlefile diffusion of Xenon atoms in AV and VA nanotubes by showing that PFG NMR mean square displacement of Xenon atoms scales with the square root of diffusion time in the studied range of diffusion times. The data in this figure rule out the existence of longrange diffusion of Xenon under our measurement conditions by presenting that even for the largest diffusion time 12s, the root MSDs of Xenon atoms inside nanotubes channels are at least one order of magnitude smaller than the average length of the nanotubes of AV and VA(around 50 m).

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31 LIST OF REFERENCES 1 A. Fick T he london, Edinburgh, and Philosophical Magazine and Journal of Science X (1855) 3039. 2 C. R. Bowers, C.Y. Cheng, T. C. Stamatatos, G. Christou, AIP Conf. Proc. 1300 (2011) 4346. 3 R Brown, Phil. Mag. 4 (1828) 16173. 4 J. Crank The Mathematics of Diffusion, Second ed., Oxford University Press USA, 1975. 5 M. Dvoyashkin, A. Wang, A. Katihar, J. Zang, G. I. Yucelen, S. Nair, D. S. Sholl, C. R. Bowers, S. Vasenkov, Microporous and Mesoporous Mater 178 (2013) 119122 6 M. Dvoyashkin, J. Zang, G. I. Yucelen, A Katihar, S Nair, D S. Sholl, C. R. Bowers, S Vasenkov, J. Phys Chem C 116 (2012) 2135021355. 7 A. Einstein, Annalen der Physik. 17 (1905) 349. 8 P. A. Fedders, Phys. Rev B 17 (1978) 4046. 9 S J. Gibbs, C S. Johnson, J. Magn. Reson. 93(1991) 395402. 10 C. H Grbitz, Chem. Eur J. 7 (2001) 51535159. 11 K. Hahn, J. Krger, V. Kukla, Phys. Rev Lett. 76 (1996) 27622765. 12 K Jrg, V Sergey, M. A Scott, H andbook of Zeolite Science and Technology CRC Press, USA, 2003. 13 J. Krger, S. Vasenkov, Microporous and M esoporous M ater 85 (2005) 195206. 14 J. Krger, Phys Rev A 45 (1992) 41734174. 15 J. Krger, D. M. Ruthven, Diffusion in Zeolites and Other Microporous Solids John Wiley, New York, 1992. 16 J. Keeler, Understanding N MR Spectroscopy, Second ed. John Wiley and Sons, Chichester, 2010. 17 M Kollmann, Phys Rev Lett 90 (2003) 180602.

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32 18 V Kukla, J Kornatowski, D Demuth, I Girnus, H Pfeifer, L V. C. Rees, S. Schunk, K K. Unger, J Krger, Science 272 (1996) 7027 04. 19 M H. Levitt, Spin Dynamics : Basic s of Nuclear Magnetic Resonance, Second ed,. John Wiley and Sons, Chichester, 2001. 20 A. A. Marchione, E. F. McCord, J Magn. Reson. 201 (2009) 343 8. 21 I. L. Moudrakovski, C. I. Ratcliffe, J. A. Ripmeester, Studies i n Surface Science and Catalysis 97 (1995) 243250. 22 I. Moudrakovski, D. V. Soldatov, J. A. Ripmeester, D. N. Sears, C. J. Jameson, P roc Natl. Acad Sci. USA 101 (2004) 1792417929. 23 D. V. Soldatov, I. L. Moudrakovski, E. V. Grachev, J. A. Ripmeester, J. Am Chem Soc. 128 (2006) 67376744. 24 D V. Soldatov, I L. Moudrakovski, E V. Grachev, J. Ripmeester, J. Am Chem Soc. 128 (2006) 67376744. 25 D V. Soldatov, I L. Moudrakovski, J. A. Ripmeester, Angewandt e Chemie International Edition 43 (2004) 63086311.

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33 BIOGRAPHICAL SKETCH Aiping Wang was born in 1987 at Fushun, China to Yue Wang and Lei Weng. She grew up with her parents went to her primary school, middle school, and high school in her hometown. She was versatile and diligent in her early school years, and rewarded with high recommendation from school teachers and exceptional grades. She got first prize in National Piano Championship at the end of 2006. Aiping went to Dalian University of Technology in China for her undergraduate study, and earned doublemajor which was Bachelor of Chemical Engineering and Bachelor of English in 2011. After that, she came to United States, and attended University of Florida (UF), and earned a Master of Science in Chemical Engineering in August 2013.