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Diffusion of Light Gases in Nanostructured Sorbents

Permanent Link: http://ufdc.ufl.edu/UFE0043836/00001

Material Information

Title: Diffusion of Light Gases in Nanostructured Sorbents
Physical Description: 1 online resource (56 p.)
Language: english
Creator: Katihar, Aakanksha
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: aluminosilicate -- diffusion -- nanostructured -- nanotubes -- nmr -- pfg -- rtils -- tetrafluoromethane
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 work the potential of pulsed field gradient nuclear magnetic resonance (PFG NMR) at high magnetic field and high magnetic field gradients for uncovering the relationship between the structural and transport properties of nanostructured sorbents is explored and demonstrated. The systems under study can be divided into two types: (i) organized soft matter systems (room temperature ionic liquids): and, (ii) porous solids (aluminosilicate nanotubes). In the first part of the work, the reported diffusion studies are focused on room temperature ionic liquids and their mixtures with carbon dioxide. The effect of absorption of CO2 in RTILs on diffusion properties is investigated and discussed. The results also help to estimate the diffusion coefficients of all the three species i.e., the cation, anion and CO2. In the later part of the work, diffusion of a light gas tetrafluoromethane in a new type of inorganic nanotubes (aluminosilicate nanotubes) is discussed. The measured data show that there are two ensembles of gas molecules. The first ensemble consists of molecules undergoing intra-channel diffusion, while the other represents molecules undergoing long-range diffusion. The results allow the estimation of the diffusivity of tetrafluoromethane inside the nanotubes as well as the diffusivity for these molecules undergoing fast exchange between many nanotubes. The results were found to support the assumption about the one-dimensional nature of the tetrafluoromethane diffusion inside nanotubes.
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 Aakanksha Katihar.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Vasenkov, Sergey.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043836:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043836/00001

Material Information

Title: Diffusion of Light Gases in Nanostructured Sorbents
Physical Description: 1 online resource (56 p.)
Language: english
Creator: Katihar, Aakanksha
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: aluminosilicate -- diffusion -- nanostructured -- nanotubes -- nmr -- pfg -- rtils -- tetrafluoromethane
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 work the potential of pulsed field gradient nuclear magnetic resonance (PFG NMR) at high magnetic field and high magnetic field gradients for uncovering the relationship between the structural and transport properties of nanostructured sorbents is explored and demonstrated. The systems under study can be divided into two types: (i) organized soft matter systems (room temperature ionic liquids): and, (ii) porous solids (aluminosilicate nanotubes). In the first part of the work, the reported diffusion studies are focused on room temperature ionic liquids and their mixtures with carbon dioxide. The effect of absorption of CO2 in RTILs on diffusion properties is investigated and discussed. The results also help to estimate the diffusion coefficients of all the three species i.e., the cation, anion and CO2. In the later part of the work, diffusion of a light gas tetrafluoromethane in a new type of inorganic nanotubes (aluminosilicate nanotubes) is discussed. The measured data show that there are two ensembles of gas molecules. The first ensemble consists of molecules undergoing intra-channel diffusion, while the other represents molecules undergoing long-range diffusion. The results allow the estimation of the diffusivity of tetrafluoromethane inside the nanotubes as well as the diffusivity for these molecules undergoing fast exchange between many nanotubes. The results were found to support the assumption about the one-dimensional nature of the tetrafluoromethane diffusion inside nanotubes.
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 Aakanksha Katihar.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Vasenkov, Sergey.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043836:00001


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1 DIFFUSION OF LIGHT GASES IN NANOSTRUCTURED SORBENTS By AAKANKSHA KATIHAR A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DE GREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011

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2 2011 Aakanksha Katihar

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3 To my Mom, Dad and Brother

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4 ACKNOWLEDGMENTS I have a lot of people to thank for the support they extended to me for completion of this thesis. First of all, I would like to thank my advisor Dr Sergey Vasenk ov for his guidance and support. Working on the experiments was fu n because of his enthusiasm, inspiration, and his great efforts to explain things clearly and simply Throughout my thesis writing period, he provid ed encouragement, sound advice and lots of good ideas I would also like to thank my colleagues Dr Muslim D voyashkin, Eric Hazelbaker and Robert Mueller for their support, company and all the help they provided during this work. I am also indebted to the staff at the Advanced Magnetic Resonance Imaging and Spectroscopy (AMRIS) facility They were very supportive and friendly and always provided the necessary help during the experiments. I would take the pleasure to especially thank Dr. Daniel Plant for his advice and technical support. My brother has always been a source of inspiration to me. I wish to thank him for his love and support throughout my life. I also wish to thank my best friend Rohit Kanungo for helping me get through the difficult times and f or all the emotional support he provided to me. Lastly, and most importantly, I wish to thank my parents Mrs Meena Katihar and Dr Govind Singh Katihar. They taught me the importance of education, patience and hard work. I will always be indebted to them for their love, care, support and the sacrifices they made for me.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ............................. 9 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 Molecular Transport and Diffusion ................................ ................................ .......... 14 Experimental Study of Diffusion at Micrometer Length Scale ................................ 17 Diffusion Measurements using Pulsed Field Gradient N uclear M agnetic R esonance (P FG NMR) ................................ ................................ ....................... 17 Basics of NMR ................................ ................................ ................................ .. 18 Longitudinal and transverse magnetization ................................ ................ 19 Relaxation: spin lattice and transverse ................................ ...................... 21 Signal detection ................................ ................................ ......................... 23 Pulsed Field Gradie nt NMR ................................ ................................ .............. 24 PFG NMR stim ulated echo pulse sequence ................................ .............. 25 PFG NMR stimulated echo longitudinal encode decode pulse sequence .. 26 PFG NMR stimulated echo with bipolar gradients pulse sequence ............ 27 Generalized Attenuation Equation ................................ ................................ .... 28 2 ROOM TEMPERATURE IONIC LIQUIDS ................................ .............................. 32 Motivation ................................ ................................ ................................ ............... 32 PFG NMR Experiment Details ................................ ................................ ................ 33 Sample P reparations ................................ ................................ ........................ 33 Pulsed Field Gradient NMR Studies ................................ ................................ 34 Results and Discussion ................................ ................................ ........................... 36 Conclusions ................................ ................................ ................................ ............ 42 3 ALUMINOSILICATE NA NOTUBES ................................ ................................ ........ 43 Motivation ................................ ................................ ................................ ............... 43 PFG NMR Experiment Details ................................ ................................ ................ 44 Sample Preparations ................................ ................................ ........................ 44 PFG NMR Measurements ................................ ................................ ................ 45 Experimental Results and their D iscussion ................................ ............................. 46

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6 Conclusions ................................ ................................ ................................ ............ 51 LIST OF REFERENCES ................................ ................................ ............................... 52 BIOGRAPHICAL S KETCH ................................ ................................ ............................ 56

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7 LIST OF TABLES Table page 2 1 Self diffusivities of the cation, anion and CO 2 by 13 C PFG NMR in the sample of [bmim][Tf2N] with different 13 CO 2 loadings and at different temperatures ...... 37 2 2 Activation energy of self diffusion for the cation, anion, and CO 2 for different CO 2 loadings ................................ ................................ ................................ ...... 41

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8 LIST OF FIGURES Figure page 1 1 Schematic representation of s pin precession in presence of an external magnetic field ................................ ................................ ................................ ..... 19 1 2 Sche matic representation of longitudinal net magnetization in presence of external magnetic field ................................ ................................ ........................ 20 1 3 Schematic of P ulsed F ield G radient N uclear M agnetic R esonance (PFG NMR) stimulated ec ho pulse sequence ................................ .............................. 25 1 4 Schematic of the PFG NMR stimulated echo longitudin al encode decode pulse sequence ................................ ................................ ................................ .. 26 1 5 Schematic of the PFG NMR stimulated echo pulse sequence with bipolar grad ients ................................ ................................ ................................ ............. 28 2 1 Comparison between the attenuation curves obtained from proton and carbon 13 (C 13) PFG NMR experiments ................................ .......................... 36 2 2 Proton and C 13 NMR spectra of [bmim][Tf 2 N] with a 13 CO 2 loading of 0.011 carbon dioxide molecules per anion cation pai r ................................ .................. 38 2 3 C 13 PFG NMR attenu ation curve measured for the sample of [bmim][Tf2N] with a 13 CO 2 loading of 0.15 13 CO 2 mole cules per anion cation pair ................... 40 2 4 The dependence of the self d iffusion coefficient for the cation anion and 13 CO 2 on the concentration of 13 CO 2 inside the ionic liquid ................................ 41 2 5 Temperature dependence of the se lf diffusivity for the sample of [bmim][Tf 2 N] with the 13 CO 2 loading of 0.063 CO 2 molecules per cati on anion pair ................................ ................................ ................................ ..................... 42 3 1 S canning E lectron M icroscope (SEM) images of aluminosilicate s ingle walled nanotubes (SWNTs) bundl es ................................ ................................ .............. 45 3 2 Attenuation curves for diffusion measurements of tetrafluoromethane in aluminosilicate nanotubes obtained for different effective diffusion times .......... 49 3 3 PFG NMR attenuation curves for tetrafluoromethane in aluminosilicate nanotubes at effective diffusion time of 4 ms extended to larger gradients ........ 50

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9 LIST OF ABBREVIATION S FID Free Induction Decay IL Ionic Liquid 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 RTIL Room Temperature Ionic Liquid SEM Scanning Electron Microscop e SWNT Single walled nanotube Amplitude of PFG NMR signal as a function of magnetic field gradient The amplitude of the applied external static magnetic fie ld The amplitude of the oscillating applied magnetic field due to a radio frequency pulse The amplitude of net effective magnetic field Concentration of molecules or ions A constant in the Stokes Einstein equation Diffusion coefficient Activation energy for diffusion Amplitude of the magnetic field gradient Flux of molecules or ions

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10 Boltzmann constant Amplitude of net transverse magnetization Amplitude of net magnetization along z axis Equilibrium value of net magnetization along z axis Probability density Mean square displacement Gas constant Spin angular momentum Time Duration between the first and the second r.f. pulse in 2D NMR exchange spectroscopy pulse sequence The duration of signal acquisition in 2D NMR exchange spectroscopy pulse sequence Effective diffusion time Absolute temperature Longitudinal (Spin Lattice) NMR relaxation time Transverse (Spin Spin) NMR relaxation time Duration between the fourth and fifth r.f. pulse in PGSTE LED pulse sequence for eddy current dissipation Velocity as a function of time z coordinate of position of molecule/ion/ nuclear spin Gyromagnetic ratio Duration of magnetic field gradient pulse Diffusion time

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11 Magnetic moment of a nuclear spin Duration between and r.f. pulse in PFG NMR spin echo pulse sequence Duration between the first and second r.f. pulse in PFG NMR stimulated echo pulse sequence Duration between the second and third r.f. pulse in PFG NMR stimulated echo pulse sequence Duration of the r.f. pulse The phase angle of individual spin magnetization vectors Flip angle of a r.f. pulse Amplitude of signal attenuation in PFG NMR experiment Larmor frequency Larmor frequency of referenc e nuclei Operating frequency of NMR spectrometer

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12 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for th e Degree of Master of Science DIFFUSION OF LIGHT GASES IN NANOSTRUCTURED SORBENTS By Aakanksha Katihar December 2011 Chair: Sergey Vasenkov Major: Chemical Engineering In this work the potential of pulsed field gradient nuclear magnetic resonance (PFG NMR) at high magnetic field and high magnetic field gradients for uncovering the relationship between the structural and transport properties of nanostructured sorbents is explored and demonstrated The systems under study can be divided into two types: (i) organi zed soft matter systems (room temperature ionic l iqu ids): and, (ii) porous solids (a luminosilicate nanotubes) In the first part of the work, t he reported diffusion studies are focused on room temperature ionic liquids and their mixtur es with carbon dioxide. The effect of absorption of CO 2 in RTILs on diffusion properties is investigated and discussed The results also help to estimate the diffus ion coefficients of all the three species i.e ., the cation, anion and CO 2 In the later part of the work, d iffusion of a light gas tetrafluoromethane in a new type of inorganic nanotubes (a luminosilicate nanotubes) is discussed. The measured data show that there are two ensembles of gas molecu les. Th e first ensemble consists of molecules undergoing intra chann e l diffusion, while the other represents molecules undergoing long range diffusion. The results allow the estimation of the diffusivity of

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13 tetrafluoromethane inside the nanotubes as well as the d iffusivity for these molecules undergoing fast exchange between many nanotubes. The results were found to support the assumption about the one dimensional nature of the tetrafluoromethane diffusion inside nanotubes.

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14 CHAPTER 1 INTRODUCTION Molecular Transport and Diffusion Since a long time, d iffusion has been defined as tendency of matter (molecules, ions etc. ), at temperatures above absolute zero, to migrate randomly in such a way as to eliminate s patial variations in concentration or densities. However it is now known that the real driving force for diffusion is a gradient of chemical potential. Diffusion can be differentiated in two different processes : Transport d iffusion (which involves movement of molecules in order to reduce gradients of che mical potential) and Self diffusion ( random motion of matter that takes place even when there is no chemical potential or concentration gradients and is driven by thermal energy ). The study of diffusion dates back to 18 50s when Adolf Fick started his exper imental studies and came up with 1 2 for one dimensional diffusion (1.1) where is the flux of the diff using molecules/ions along the direction, is their concentration and is t he corresponding diffusion coefficient known as t ransport diffusion coefficient It relates flux of molecules and concentration/ chemical potential gradient under non equilibrium conditions. If, however, a fraction of mole cules in a sample is tagged or labeled, similar equ ation can be developed for self diffusion as well. Here an assumption needs to be made that there is an uneven distribution of the labeled and unlabeled molecules while overall molecular concentration rema ins the same at any point in the system. Thus self diffusivity or self diffusion coefficient (for one dimensional diffusion) can be defined as

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15 (1.2) w here is concentration of labeled molecules w hile the total concentration remains constant and is the flux of the labeled molecules For three dimension al diffusion (transport or self) E quation 1.2 becomes (1.3) where will be the diffusion coefficient (can be transport or self) in direction due to concentration gradient in direction. Equation 1. 1 along with the principle of s second law for one dimension, which is written as (1.4) W hen is independent of concentration E quation 1.4 takes the following form (1.5) Again f or the case of three dimensional diffusion with concentration independent diffusivity (self or transport), (1.6) For the case of closed system (where the total mass of diffusing species remains constant) and isot ropic diffusion (where the self diffusion coefficient is equal in all directions) the concentration distribution is given by 3 (1.7)

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16 where is the total mass of the diffusing species and is a probability function or D iffusion Propagator 4 and gives probability o f finding a molec ule/ion at a certain position at time This is a Gaussian function, variance of which gives the mean square displacement (1.8) Using E quation 1.8 we get the following expressions for mean square displacements of molecules/ions for 1, 2 and 3 dime nsional isotropic diffusion (1.9) (1.10) (1.11) Equations 1.9 to 1.11 are called Einstein Relations. 4 Studying molecular transport on small length scales is important as it not only helps to understand various system properties but also controls them on macroscopic length scales. The primary mechanism of molecular transport is related to self diffusion and thus investigation of self diffusion under the conditions of in terest becomes indispensible in orde r to study molecular transport at small length scales This work reports self diffusion of light gases in complex nanostructured materials which ar e h eterogeneous on length scales from nanometer to several micrometers. Due to their heterogeneity on such l ength scales, these materials ex hibit a lot of unique and interesting properties important for industrial applications. The systems selected for this work are of two types: 1) organized soft matter systems ( room t emperature i onic l iquid s ) and 2) porous solids ( a l uminosilicate n anotubes ).

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17 Experimental Study of Diffusion at Micrometer Length Scale To study diffu sion on different length scales, different techniques can be used. The main experimental technique used in this work is high field (17.6 T) and high gradient ( up to 30 T/m) p ulsed field gradient nuclear magnetic resonance (PFG NMR ) PFG NMR technique has proven to be a powerful tool for the study of diffusive 5 6 7 molecular motions. High field and high gradient PFG NMR is a non invasive technique that combines the advantages of high field and high magneti c field gradients for diffusion studies High magnetic field helps to achieve high sensitivity, while application of high gradients allows for diffusion studies on small length scales using nuclei with small gyromagnetic ratios ( such as C 13) The next section discusses the theory of PFG NMR in detail. Diffusion Measurements using Pulsed Field Gradient N uclear M agnetic R esonance (PFG NMR) All substances have the capability of interacting with magnets. The microscopic sources of this magnetism are: 1) circulation of electric currents (due to the electrons), 2) the magnetic moments of the electrons and 3) the magnetic moments of the nuclei. N uclear magnetic resonance (NMR) spectroscopy uses the nuclear magnetism ( due to their magnetic moment or spin) associated with some nuclei This i ntrinsic nuclear magnetism can be exploited in the presence of an external magnetic field (B 0 ) by applying electromagnetic radio frequency (r.f.) pulses. When these r.f pulses are applied under the conditions of resonance, the nuclei absorb energy which is radiated back and is received as the signal by a coil. The signal contains a lot of information about the structure and dynamics of the molecules containing the nuclei.

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18 Basics of NMR Spin angular momentum or just spin is an intrinsic quantum mechanical property of atomic nuclei. This is related to the magnetic moment as shown below (1.12) where is the magnetic moment and is the spin angular momentum. The direction of the spin angular momentum is also called the spin polarization axis. E quation 1.12 suggests that n uclei which have a non zero value of spin exhibit magnetism as they ha ve a non zero magnetic moment. which is called the gyromagnetic or magnetogyric ratio is a property of the nuclei and can be positive or negative. T he sign determines whether magnetic moment will be aligned in the direction or opposite to the direction of the spin or the direction of spin polarization. When there is no external field, these magnetic moments are randomly aligned and there is no net nu clear magnetization As soon as a magnetic field is switched on it exerts a torque on the magne tic moment which in turn forces the spin polarization to start mo vi ng around the field on a cone at a constant angle (the constant angle depends on angle between initial spin polarization vector and the field) between direction of spin polarization and the field (Figure 1 1) This is called precession and is a result of intrinsic spin angular momentum of the nuclei. The external magnetic field B 0 determines the frequency of precession (also called the Larmo r frequency 8 9 ) as given by the Equation 1.13 (1.13)

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19 Figure 1 1 (a ): Schematic representation of s pin precession in presence of an external magnetic field B 0 (b): The a ngle of the precession cone depends on initial spin polarization. Longitudinal and transverse magnetization In the absence of an external magnetic field, t he distribution of the spin polarizations is isotropic and thus there is no net magnetization in the sample (Fig ure 1 2a). As soon as an external field is switched on all the spins start executing precession around the field. But the distribution of spin polarizations still remains isotropic and consequently the total mag netic moment of the material does not change. However microscopically, e ach nuclear spin is surrounded by other magnetic entities, (i.e., other nuclear spins and electron clouds ) and switching on the field leads to formation of local, microscopic magnetic fields around each nucleus which fluctuate rapidly in both magnitude and direction because of the thermal agitation of the environment. The se microscopic fluctuating fields result in a gradual breakdown of constant angle spin precession of the nuclear spi ns and the magnetic moments of the nuclear spins wander between different precession angles eventually sampling all possible orientations. This process brings about an isotropy in distribution o f spin polarization directions and t he resulting steady state distribution of spin polarizations is slightly biased towards an

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20 orientation with lower energy where spin orient ations have corresponding magnetic moments along the direction of the applied magnetic field (Fig ure 1 2b) This is referred to as longitudinal mag netization as t he direction of the external magnetic field and resulting nuclear magnetization is assumed to be in the +z direction (or longitudinal direction) of the s tatic coordinate system. Figure 1 2 (a) No magnetization in absence of external magnetic field. (b) Schematic representation of longitudinal net magnetization when external magnetic field B 0 is switched on The longitudinal magnetization is the vector sum o f individual magnetic moments 8 Nuclear magnetization is very small as compared to magnetization produced by other mechanisms (electronic magnetization, bulk magnetization etc) Thus, d etection of longitudinal magnetization becomes extremely difficult. Thus in NMR, magnetization in a transverse plane is detected. This is done by applying a n orthog onal oscillating magnetic field (which has a frequency close to Larmor frequency and magnitude smaller than ) by passing an alternating current th rough a coil Application of the field is called application of r.f. pulses as the Larmor frequencies are typically in the range of radio waves Once the magnetization is tilted in the transverse (X Y) plane, it

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21 starts precessing and when the r.f. pulse is turned off it gradually returns to the eq uilibrium direction of the static external magnetic field This process of relaxat ion is discussed in the next section. Thus the basic idea of NMR is to apply a torque that is orthogonal to the torque exerted by the static magnetic field on the spins and that varies with time in exact frequency match with the natural precession frequency of the nuclear spins. This is achieved by applying a magnetic field that is orthogonal to the main magnetic field and oscillating in time in exact synchrony with the precession frequency of the atomic nuclei. Relaxation: spin lattice and t ransverse In the pre sence of static magnetic field the net magnetization is in the longitudinal direction. This is the equilibrium condition and when an r.f. pulse is applied, it tilts the magnetization in transv erse plane and results in a non equilibrium condition. As time passes, the net magne tization returns back to its equilibrium state -a process known as NMR relaxation. This is of two types: 1) Spin S pin/Transverse, or relaxation (which is the gradual decay of transverse magnetization to zero) and 2) Spin Lattice/ Longitudinal, or relaxation (which is the gradual growth of net nuclear magnetization to its equilibrium value in the +z direction) 8 10 Just after the r.f. pulse is applied and net magnetization is turned to transverse plane, all the spins remain in phase coherence. It is due to disturbances in local magnetic field by neighboring ma gnetic entities (like other nuclear spins and electronic clouds ) that a s time progresses, various sp ins in the sample de phase (called the secular contribution to T 2 relaxation) As a result, the net transverse magnetization gradually decays to zero

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22 Anoth er reason of transverse relaxation is the presence of fluctuating, microscopic magnetic field s. T hese fields might exhibit frequencies in the range of Larmor frequency, thereby act ing as tiny r.f. pulses gradually turning the magnetic moments away from the X Y plane (called the non secular contribution to T 2 relaxation) T he net rate of transverse relaxation can be characterized by a time constant as shown in Equation 1.14 (1.14) where is the net transverse magnetization at time and is the spin spin/ t ransverse NMR relaxation time constant Immediately after the application of r.f. pulse, the longitudinal magnetization is zero. Disturbances that cause the non secular part of NMR relaxation can also cause the NMR relaxation process. In addition, the nuclear spins experience perturbati ons in the local magnetic field d ue to rapid molecular tumbling These local fields try to reorient individual nuclear spin magnets and orientation s with the magnetic moment along the direction of the field are favored as they have lower energy This is also responsible for re growth of the magnetization along the z axis to the equilibrium value, t he rate of which can be characterized by the longitudinal relaxation time (1.15) where is the net longitudinal magnetizatio n at time is the net equilibrium magnetization, which points along +z direction and is longitudinal relaxation time constant

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23 Signal detection The signal is detected by a coil placed near the sample. The continuously changing magnetic field (changing because of the precession of spins in the transverse plane) induces an electric current in the coil detected as a signal gradually decaying w ith time and is referred to as free Induction decay (FID). Fourier transformation of the FID gives frequency domain data known as NMR spectra. Again due to variations in the local magnetic field experienced by individual spins the resonance frequencies of a ll nuclei show small deviations from the Larmor frequency. This effect is known as chemical shift. Thus the resonance frequencies and in turn the chemical shifts of same element in different chemical environments are different i.e., 1 H in a CH 3 group will have a different chemical shift than that of 1 H in CH 2 or 1 H in water. Thus k nowing the c hemical shift data allow s identifying different atomic environments and helps in investigating the properties of the system under consideration. Resonance frequencies are magnetic field dependent and thus they can vary from one experimental setup to another To overcome this problem and to simplify comparison of data measured at different amplitudes chemical shifts are calculated in parts per million (ppm) units instead of frequency units using the E quation 1.16 (1.16) where is the chemical shift in ppm, the measured frequency, is the reference frequency and the magnet

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24 Thus some ideas worth noting about NMR are : 1) t he strength of the magnetic field determines the amount of magne tization in the atomic nuclei at thermal eq uilibrium and the precession frequency of the nuclei. 2) The coil is used to produce an oscillating magnetic field that is in resonance with nuclei and causes the torque that tips the magnetization out of equilibrium in the transverse plane. 3) The same co il is not only used to transmit to the nuclei b ut also used to receive the signal i.e, to pick up the E lectro M otive F orce (EMF) at oscillating voltage as the nuclear magnetization precesses around the coil with signal gradually decaying with time as the spins come back to their equilibrium value. Pulsed Field Gradient (PFG) NMR PFG NMR makes use of the fact that the Larmor frequency of the precession of the n uclear spins is field dependent. In PFG NMR, when magnetization is in the transverse plane, a gradient of magnetic f ield is applied along the z direction. Application of magnetic field gradients makes the Larmor frequency position dependent (according to Equation 1.18) and thus helps in labeling the nuclear spins based on their spatial c oordinate along the z direction (1.17) where is the Larmor frequency, is the gyromagnetic ratio, denotes static external magnetic field; is the linear gradient of the magnetic field superimposed on the field and is the coordinate along the z axis The pul se sequences used in this work are explained in detail in the next few section s

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25 PFG NMR stimulated echo pulse sequence Fig ure 1 3 Schematic of PFG NMR stimulated echo pulse sequence. This sequence is of great advantage for systems in which the NMR relaxation time is much shorter than NMR relaxation time. Figure 1 3 shows the s chematic of the standard PFG NMR stimulated echo pulse sequence which consists of three pulses and two field gradient s of identical amplitude and duration The first r .f. pulse bring s the longitudinal magnetization to the transverse plane and the first field gradient pulse labels the spins according to their spatial coordinate in th e z direction In the process of such labeling the spins precess with differe nt Larmor frequencies given by E quation 1.1 8 and consequently de phase. H ence the time interval between the two pulses is called the de phasing interval. The time i nterval is approximately equal to the effective diffusion time used to measure diffusivity Following the dephasing t he net magnetization is tilted to z direction by the second r .f pulse and again to the transverse plane by the third one. Again a field gradient of the same duration and amplitude is applied. D uring this ( second ) gradient pulse the individual spin magnetization vectors experience rephrasing. Hence the time

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26 interval b etween the third r.f. pulse and the beginning of acquisition is called the rephasing interval. If molecules diffuse during the time between gradient pulses, the refocusing of the magnetization is not complete and final intensity is lesser than the maxi mum intensity. This decrease in amplitude of the intensity contains information about diffusion of the molecules. This pulse sequence is particularly advantageous for diffusion studies of systems which experience slower decay of ma gnetization due to longit udinal relaxation (i.e, relaxation during the time interval of duration ) than that due to transverse (i.e, relaxation during the two time intervals of duration ). Another advantage of using this pulse sequence is that the diffusion time can be incr eased in this pulse sequence by increasing the time interval PFG NMR stimulated echo longitudinal encode decode pulse sequence Figure 1 4 Schematic of the PFG NMR stimulated echo longitudinal encode decode pulse sequence. In a PFG NMR experiment, the gradient pulses are repeatedly switched on and off T his generates eddy currents in the coil and in turn inhomogeneities in the magnetic field. These undesirable inhomogeneities can be avoided by using PFG NMR stimulated

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27 echo longitudinal encode decode or longitudinal eddy current delay pulse sequence (PGSTE LED) 11 which is a modified form of the PFG NMR stimulated echo pulse sequence ( F igure 1 4 ). T he difference being that there are two additional r.f pulses separated by the time at the end of this sequence. Using these r.f. pulses, the direction of the net magnetization is changed to longitudinal plane ( z direction) from the transverse plane for the time and then brought back to th e transverse plane This time delay between the end of second field gradient pulse and the beginning of acquisition helps to dissipate the eddy currents. In the stimulated pulse sequence to introduce a delay between the end of the second gradient pulse a nd the beginning of acquisition, same delay has to be introduced between the end of the first gradient pulse and the next r.f. pulse thereby increasing the time for which the net magnetizatio n is in the transverse plane a nd reducing the signal by T 2 relaxation This problem is not encountered in PGSTE LED sequence as the net magnetization is taken from the transverse plane to the longitudinal direction ( z) axis, which is followed by the LED delay During the LED delay, s ignal is reduced only due to NMR relaxation This is an advantage over the other sequences for the measurement conditions which are likely to introduce disturbing eddy currents. PFG NMR stimulated echo wi th bipolar gradients pulse sequence The puls e sequences discussed above use unipolar gradients. Figure 1 5 shows a schematic for the PFG NMR stimulated echo pulse sequence with bi polar gradients 12 15 also called the 13 interval sequence

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28 Figure 1 5. Schematic of the PFG NMR stimulated echo pulse sequence with bipolar gradi ents. B ipolar gradients are used to suppress internal gradients. I n a heterogeneous media the magnetic susceptibility variations cause some background magnetic field gradients. This may lead to signal attenuation and may even introduce artifacts in the measurements of self diffusion. Th ese proble m s are reduced by using PFG NMR stimulated echo pulse sequence with b ipolar gradients (Figure 1 5) Each of the two positive field gradient pulses of duration and amplitude in the PFG NMR stimulated echo pulse sequence is replaced by a pair of gradient pulses, each of duration and amplitude with opposite polarity separated by a r.f. pulse. This sequence elimina tes influence of the background gr adients (those that have the same polarity and amplitude over the duration of the sequence) on the measured signal. Generalized Attenuation Equation The signal attenuation can be related to the molecular diffusion by deter mining the net phase accumulated by the spins ( Equation 1.19) and calculating the vector sum of individual magnetic moments by the end of the pulse sequence.

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29 (1.18) where for the cases where there is no field gradient and in the presence of field gradient pulses. The duration of field gradient is taken to be much smaller than diffusion interval. Thus for a spin diffusing from position to the net phase accumulated will be given as (1.19) T he net transverse magnetization at any time will be proportional to cosine of the net phase as projection of magnetization vectors in the direction of transverse magnetization ( immediately after first r.f. pulse is applied ) is proportional to it. Using this and the conditional probability ( probability of finding a molecule at any position between and ) with the corresponding one dimensional diffusio n propagator the net transverse magnetization at the end of the spin echo pulse sequence 10 16 can be written as (1.20) Now, the signal attenuation is given by the ratio of attenuated signal (in presence of field gradients) to the signal recorded in the abs ence of any field gradients i.e (1.21) where is the signal intensity at the gradient g and is the sign al intensity at zero gradient. E quation 1.21 can be written in terms of signal attenuation as

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30 (1.22) For a homogenous medium and for normal (i.e., Fickian diffusion) 17 and is given by E quation 1.23 (1.23) By combining these equations signal attenuation ca n be simplified to the E quation 1.24 (1.24) where is the gradient duration, denotes th e effective diffusion time and denotes the self diffusion coefficient or self diffusivity. The general form of attenuation equation for normal isotropic diffusion used for all the pulse sequences discussed above can be simplified to the following form (1.25) where for PGSTE/ PGSTE LED pulse sequences and for the 13 interval pulse sequence. The effective diffusion time for both PGSTE and PGSTE LED is given by Equation 1.26 and for the 13 interval sequenc e, it is given by Equation 1.27 (1.26) (1.27) Substituting Einstein relation into E quation 1.26 gives Equation 1.28 for isotropic one dimensional diffusion in the direction of field gradients and E q uation 1.29 for isotropic three dimensional diffusion

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31 (1.28) (1.29) where is the mean square displacement in the direction of the field gradients and In PFG NMR experiments signal attenuation is determined as a function of square of the amplitude i.e., keeping all other parameters of the pulse sequence constant. These are the so called PFG NMR attenuation curves that are used to determine mean square displacements and the corresponding diffusivities using above mentioned equations. As attenuation is the ratio of signal at a particular gradient to the signal at zero gradient, contribution of NMR relaxation remains the same for both and thus does not make any contribution to the PFG NMR attenuation

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32 CHAPTER 2 ROOM TEMPERATURE ION IC LIQUIDS R oom t emperature i onic l iquids (or RTILs) are molten salts that are liquid around room temperature Generally, they are composed of a large asymmetric organic cation and either an organic or inorganic anion 18 It is believed that the low melting point of i onic liquids is a result of the asymmetry of the cation and the nature of the anion is considered to be responsible for a lot of their interesting phys ical properties such as miscibility with conventional solvents, hygroscopicity etc 19 The most commonly studied RTIL s are imidazolium based salt s which are not only easy to synthesize but also have interesting physical properties that make them highly useful for many chemical processes. A go od thing about ionic liquids is that t he ir physical properties can be made by judicious ly selecting cation, anion, and their substituents 20 Some of these tailor made or have proven very useful in both synthetic and separations applications 21 23 Motivation Ionic liquids are getting a lot of scientific attention because of their unique and interesting propert ies. These liquids have high solubility for polar as well as non polar compounds and they can simultaneously dissolve organic and inorganic substances they have negligible vapor press ure, a stable liquid range of up to 400 K, excellent ionic conductivit y, thermal stability and their density is greater than water. Due to these properties, RTILs are used as m edia for gas and liquid separations 24 26 solvents for homogeneous catalysis for a variety of organic reactions 24 27 29 electrolytes for batt eries and fuel cells 30 31 heat transfer /storage fluids and lubricants 20 24 32 33 and are also being

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33 because they are nonvolatile, nonflammable, and thermally stable 34 By far one of t he most attractive approach es for the separation of a compound from a mixture of gases is absorption into a liquid. Ionic liquids because of their properties like negligible vapor pressure and thermal stability h ave been proposed as solve nt reagents for gas separations 35 Howe ver, f undamental understanding of transport properties of mixtures of RTILs with carbon dioxide is essential for potential applications of RTILs for CO 2 separations. Such applications are feasible in view of the recent results indicating that the absorptio n capabilities of RTILs for CO 2 can be quite high 36 40 D iffusion studies of CO 2 in RTILs have been reported in the literature but these studies until now, measurements of gas fluxes through macroscopic IL samples 41 43 This work focuses on studies of the influence of absorption of carbon dioxide into an imidazolium based RTIL on the diffusion properties of ions. In addition, the diffusion of CO 2 in mixtures of the ionic liquid with carbon dioxide was also studied. Both 13 C and proton pulsed field gradient nuclear magnetic resonance ( PFG NMR ) w ere used to study self diffusion in the mixtures. PFG NMR Experiment Details Sample P reparations The RTIL chosen for the study was 1 Butyl 3 methylimidazolium bis( trifluoromethylsulfonyl )imide ([bmim][Tf2N]) and was purchased from Ionic Liquid Technologies (99% purity). The samples of RTIL mixtures with carbon 13 labeled CO 2 wer e prepared by the following procedure. Five 5 mm NMR tubes were filled with the

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34 chosen RTIL. In all cases the sample height in a vertically oriented tube was kept around 12 mm or smaller to make sure that there are no effects of convection on the data measured at elevated temperatures. These samples were then evacuated under hi gh vacu um at around 100 degree Celsius for 24 hours to remove any moisture present. The loading of CO 2 was then performed either by exposing the dry liquid to CO 2 gas at a fixed pressure for at least 4 hours or by cryogenically transferring the required amount of CO 2 from the calibrated volume of th e vacuum system into the NMR tube using liquid nitrogen. After this, the tubes were flame sealed. The 13 CO 2 loading or the amount of carbon dioxide in the mixtures of RTIL and CO 2 is expressed as number of carbon dioxid e molecules per anion cation pair. This 13 CO 2 loading constants reported in 43 for carbon dioxide absorption into [bmim][Tf2N], (ii) known mass of CO 2 introduced into the tubes with the IL before they were sealed, and (iii) known volumes of the IL and the gas phase in the sealed NMR tubes. One of the tubes contained pur e IL with no carbon dioxide whi le the others had increasing carbon dioxide loadings of 0.033 0.063, 0.15 and 0.35 carbon dioxide molecules per anion cation pair. Pulsed Field Gradient (PFG) NMR Studies 1 H and 13 C PFG NMR diffusion studies were carried out usin g a wide bore 17.6 T Bruker Biospin spectrometer. Magnetic field gradients were generated using diff60 diffusion probe (Bruker Biospin) and Great60 gradient amplifier (Bruker Biospin). The diffusion experiments were done over a broad range of temperatures from 297 to 351 K. and were repeated under the same conditions to make sure the reproducibility of data In most cases diffusion studies were performed by using the standard PFG NMR stimulated echo pulse sequence. T he absence of susceptibility effects and

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35 measu rement artifacts was confirmed : ( i) by verifying that the diffusion data obtained under same conditions but at different magnetic field amplitudes were the same within the limits of e xperimental uncertainty, and (i i) by the fact that 1 H and 13 C PFG NMR diffusion data measured for the same diffusing species in the same samples and under the same conditions were found to coincide within the limits of experimental error (Figure 2 1) Also in each cas e the self diffusivity was calculated for two diffusion times (8.6 ms and 38.6 ms) to ensure that the convection effects do not affect the data under the measurement conditions. The signal intensity was determined by integrating the area under selected lin e(s) of the spectra rec orded by the PFG NMR pulse sequence or by using the amplitudes of these line(s). Figure 2 2 shows an example of the proton and 13 C NMR spectra for a mixture of [bmim][Tf2N] and carbon dioxide Different lines in such spectra can corr espond to different species Hence, for data processing, it becomes essential to select appropriate line (or lines) for each type of species. For the l ines in the NMR spectra that originate from the diffusing species in the same ty pes of local environments and that exhibit no significant overlap with the lines of other types of ions/ molecules in a sample Equation 1.25 wa s used to determine the diffusivity However when the selected line has contributions either from species in different types of domains or from different types of molecules and/or ions having different diffusivities the attenuation curves are described as a sum of two or three weighted exponent ial terms of the type shown in E q uation 2. 1 (2.1)

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36 where and respectively represent the fraction and diffusivity of ensemble Figure 2 1. Comparison between the attenuation curves obtained from 1 H ( ) and 13 C ( ) nuclear magnetic resonance ( NMR ) experiments. The 1 H NMR experiment was done using a 13 interval pulse sequence and the 13 C NMR experiments were done using a stimulated echo pulse sequence Results and Discussion Table 2 1 shows the self diffusion coefficients for each species at all temperatures and CO 2 loadings. Fig ure 2 3 shows an example of the results of self diffusion measurements for a mixture of ([bmim][Tf2N]) and 13 CO 2 (A loading of 0.15 CO 2 per anion cation pair). All attenuation curves in Figure 2 3 are monoexponential in ag reement with Equation 1.25 As expected of all the three species, CO 2 has the fastest diffusivity (the slope of the attenuation curve is the largest). However the cation diffuses faster than the anion in spite of being larger in size than the anion. Such b ehaviour is attributed to the existence of well defined local structures in the pure

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37 Table 2 1 Self diffusivities of [bmim]+, [Tf2N] and CO 2 recorded by 13 C PFG NMR in the samples of [bmim][Tf2N] with different 13 CO 2 loadings and at different temperatures. Diffusivity 10 10 (m 2 s 1 ) 297 K 315 K 333 K 351 K [bmim][tf2n] with no CO 2 [bmim] + 0.288 0.023 0.62 0.012 1.06 0.053 1.71 0.068 [Tf2N] 0.213 0.019 0.45 0.023 0.815 0.041 1.41 0.01 CO 2 N/A N/A N/A N/A [ bmim][tf2n] with 0.033 13 CO 2 molecules per anion cation pair [bmim] + 0.298 0.014 0.596 0.072 1.04 0.01 1.53 0.061 [Tf2N] 0.227 0.0045 0.473 0.014 0.839 0.034 1.26 0.16 CO 2 3.70 0.22 6.15 0.062 8.58 0.60 11.6 0.35 [bmim][tf2n] with 0.063 13 CO 2 molecules per anion cation pair [bmim] + 0.308 0.0092 0.671 0.013 1.10 0.011 1.75 0.07 [Tf2N] 0.243 0.036 0.510 0.015 0.830 0.0083 1.31 0.039 CO 2 4.07 0.16 6.96 0.21 9.83 0.39 13.2 1.5 [bmim][tf2n] with 0.15 13 CO 2 molecules per anion cation pair [bmim] + 0.393 0.039 0.733 0.073 1.13 0.045 1.86 0.074 [Tf2N] 0.308 0.018 0.611 0.055 0.860 0.095 1.67 0.017 CO 2 5.00 0.20 7.73 0.31 10.8 0.043 15.6 0.4 [bmim ][tf2n] with 0.35 13 CO 2 molecules per anion cation pair [bmim] + ( 13 C) 0.441 0.031 0.681 0.027 1.07 0.032 1.87 0.22 [Tf2N] 0.334 0.023 0.525 0.053 0.887 0.063 1.58 0.22 CO 2 5.52 0.22 7.74 0.31 11.1 0.44 16.0 0.64 The experimental uncertainty reflects deviations between the diffusivities measured at the same conditions but for different diffusion times and different delays between the first and the second r.f. pulses of the PFG NMR stimulated echo sequence. It al so reflects deviations between the corresponding data obtained using different NMR lines of the same type of species under the same measurement conditions.

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38 Figure 2 2 N M R spectra of [bmim][Tf2N] containing 0.011 carbon dioxide molecules per anion cation pair: (A) 1 H NMR spectrum recorded by one pulse sequence, (B) 13 C NMR spectrum recorded by one pulse sequence. The 1 H and 13 C chemical shifts were referenced internally to HDO, viz. D 2 O in H 2 O mixt ure. In the proton spectrum all lines originate from the [bmim] cation because the other two species i.e, anion and CO 2 do not contain any protons. In the carbon carb 2 13 spectrum originate from the catio n

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39 RTIL resulti ng in an appearance of anisotropy for the cation diffusion. At the same time, these structures do not lead to significant diffusion anisot ropy for the anion. This is the reason the cation has a higher diffusion coefficient than the anion. Another observation is that the a bsorption of carbon dioxide into the studied RTIL did not result in any significant changes in the relationship between the diffusivities of the cation and anion (Figure.2 3 ). An important point to be noted here is that the CO 2 diffusivity reported for a m ixture of [bmim][Tf2N] and CO 2 is much lower than that of CO 2 dissolved in traditional organic solvents. This observation can be explained by a relatively low mobility of ions that surround CO 2 molecules in the RTIL. Figure 2 4 shows the dependencies of th e diffusivities of all three species in the mixtures of the RTIL and carbon dioxide on the concentrations of carbon dioxide. It is seen that the absorption of carbon dioxide into the RTIL increases the diffusivities of both the cation as well as the anion. T he diffusivity of CO 2 in the RTIL also increases with increasing CO 2 loading This behavior can be explained by the fact that the system is a mixture and as the fraction of smaller molecules is increased all diffusivities are expected to increase. The di ffusion measurements were done over a wide range of temperatures to understand the temperature dependence of diffusivities of all the species present in the mixture. Figure 2 5 gives an example of this temperature dependence for one of the CO 2 loadings (0. 063 13 CO 2 molecules per anion cation pair). As it is suggested by the figure, the temperature dependence of the cation, anion, and carbon dioxide diffusivities in each studied sample can be satisfactorily described by the Arrhenius equation as given in Equ ation 2.2

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40 (2.2) where E a is the activation energy of diffusion, R is the gas constant, and D 0 is a pre exponential factor. Figure 2 3 13 C PFG NMR attenuation curves measured for the sample of [bmim][Tf2N] loaded with 13 C labelled CO 2 ( 0.15 13 CO 2 molecules per anion cation pair ) The attenuation curves were measured for effective diffusion time of 8.6 ms at T = 297 K. The data are shown for the average of the [bmim] lines at 129.4, 42.3, 24.3, and 11.7 ppm ( ), the average of the [Tf 2N] lines at 113.6 and 111.9 ppm ( ), and the ca rbon dioxide line at 117.6 ppm ( ). Solid curves s how the best fit results using E q uation 1.25 The calculated values of the activation energy of self diffusion for the cation, anion, and CO 2 are shown in Table 2 1. The values were obtained by calculating the slope from the best fit line to the Arrhenius plot data.

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41 F igure 2 4 The dependence of the self diffusion coefficient for the ( ) cation [bmim] + ( ) anion [tf2n] and ( ) 13 CO 2 on t he concentration of 13 CO 2 inside the ionic liquid. The error bars represent the difference between the diffusion coefficients calculated from the 10 ms and 40 ms experiments. Where error bars cannot be seen the error can be interpreted as the size of the data point Table 2 2 Activation energy of self diffusion for the cation, anion, and CO 2 The values were obtained from a best fit line to the Arrhenius plot data and using the slope of the line to calculate the activation energy. n CO2 / n cation a nion pa ir E a (cation), KJ/mol E a (anion), KJ/mol E a (CO 2 ), KJ/mol 0 28.46 2.10 30.51 1.83 0.033 26.87 1.34 27.62 2.17 18.22 1.59 0.0626 27.76 1.33 26.84 3.28 18.79 2.43 0.149 24.57 2.70 25.86 2.43 18.05 1.18 0.348 22.87 3.30 24.86 3.35 17.06 1.30

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42 Figure 2 5. Temperature dependence of the self diffusivity of the cation ( ), the anion ( ), and carbon dioxide ( ) for the CO 2 loading of 0.063 carbon dioxide molecules per cation anion pair. The best fit for the curve is obtaine d by using Arrhenius equation (E quation 2 .2 ). Conclusion s The results reported above demonstrate that comb ined application of proton and c arbon 13 PFG NMR at high magnetic field and high gradients allow s obtaining detailed information on self diffusion in mixtures of an RTIL and CO 2 It was observed that under our experimental conditions the addition of CO 2 into the RTIL does not change the anomalous relationship between the size and diffusivity of the ions. Addition of CO 2 was found to increase the ion diffu sivities.

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43 CHAPTER 3 ALUMINOSILICATE NANO TUBES Recent discoveries of n ovel synthesis routes have led to an impressively large spectrum of nanoporous materials which vary in composition, pore architecture, and shape. For their use in technical applications appropriate fluid transport properties are essenti al 44 45 Thus s tudying the t ransport of fluids in materials with micro or meso pores is highly important for using these materials successfully in applications like catalysis and separation of gases. One such system of potentially high industrial relevance is a luminosilicate nanotube s (NTs) Results presented in this chapter contribute to the understanding of molecular transport of a light gas carbon tetrafluoride in aluminosilicate nanotubes by 13 C pulsed field gradient nuclear magnetic resonance (PFG NMR ) Motivation Nanotubes have a lot of interesting properties due to which they are being investigated as strong candidates for use in a lot of potential technological applications. Some of their interesting properties are their nanoscale dimensions, hollow cylindrical s hape, structure, composition, and porosity Other interesting properties of s ingle walled metal oxide NTs are that they have a well defined solid state structure In contrast to single walled carbon nanotubes (SWCNTs) these have precisely tunable diameter and length 46 and have a hydrophilic and funct ionalizable interior which is useful for tuning transport and adsorption selectivity 47 Also unlike SWCNTs b oth t he diameters and lengths of s ynthetic aluminosilicate NTs are monodisperse 48 49 Thus due to all the above mentioned points, i nformation about diffusion of confined molecular species inside nanotube channels has high relevance and understanding

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44 transport phenomena of fluids through NTs is very important in order to be able to use these for potential applications such as catalysis, separations molecular sensors and encapsulation media for molecule storage etc. Studies of transport in one dimensional channels are also of high interest because of the possibility of an observation of the 50 In th is work, the potential of 13 C pulsed field gradient (PFG) NMR at high magnetic field and high magnetic field gradients for investigations of transport of adsorbed gas molecules in novel aluminosilicate nanotubes is discussed P FG NMR Experiment Details Sample P reparations The aluminosilicate nanotubes used in this work have an outer diameter of around 2.2 nm and inner diameter of around 1.0 nm. As shown in the s canning e lectron m icroscope (SEM) images of the studied aluminosilicate nanotubes (Figure 3 1) these are packed into bundles forming sandwich like structures. The size ranges from half a micrometer to few tens of micrometers Single walled aluminosilicate nanotubes were synthesized according to the protocol given in references 51 52 To prepare the samples a round 150 mg of the nanotubes was placed into a 5 mm medium walled NMR t ube. The sample was evacuated to remove any moisture present by keeping it under high vacuum (10 4 mbar) at 453 K for 24 hours Following the sample activation, a fixed amount of 13 C labelled CF 4 was cryogenically transferred into the NMR tube containing the sample. T he tube was then flame sealed and separated from the vacuum system. After equilibrium at 298 K t he resulting gas pressure inside the tube for the sample studied was estimated to be around 8 bar s.

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45 Fig ure 3 1. SEM images of aluminosilicate SWNT bundles. The white scale bars represent 10 m (left) and 1 m (right). PFG NM R M easurements D iffusion measurements were performed using the 17.6 T Bruker BioSpin NMR spectrometer equipped with the Diff60 probe and Great 60 gradi ent amplifier (Bruker BioSpin). The measurements were performed at a 13 C resonance frequency of 188.6 MHz The pulse sequence used for the d iffusion studies w as the stimulated echo pulse sequence with the longitudinal eddy current delay (PGSTE LED) 53 Attenuation curves were plotted to study the dependence of the PFG NMR signal intensity (obtained by integrating the area under the single line of the 13 C NMR spectrum of tetrafluoromethane ) on the amplitude of the magnetic field gradient For molecules confined in nanopores, the proton T 2 NMR relaxation times are generally very short. This is because intra molecular and inter molecular dipole dipole interactions are not completely averaged out by molecular motion and magnetic susceptibility. Thus for this work, 13 C PFG NMR was employed instead of 1 H PFG NMR

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46 to take advantage of the longer 13 C T 2 relaxation times that are typically observed for guest molecules confined in nanopores Experimental Results and their Discussion Figure 3 2 shows t he 13 C PFG NMR attenuation curves for diffusion of CF 4 in the studied nanotube sample at 298 K The attenuation curves are plotted for three different effective diffusion times ( ) i.e., 4, 8 and 16 ms. PFG NMR measurements for effective diffusion times greater than 16 ms could not be don e because of considerable decrease in the CF 4 signal due to T 1 NMR relaxation for high diffusion times. In the curves shown, the contribution from the CF 4 diffusion in the gas phase (above the bed of nanotube bundles) is subtracted. This was done by determining the bulk gas phase contributions in separate experimen ts performed on an NMR tube containing only CF 4 gas at a comparable pressure. As already discussed earlier i n the case of unrestricted and isotropic diffusion PFG NMR attenuation curves are expected to follow a mono exponential behaviour given by the E quation 1.25 However, in the present case the diffusion is restricted to one dimensional channels that are randomly oriented H ence isotropic 3 dimensional diffusion cannot be expected for such a system. Consequently, t he attenuation curves in Fig ure 3 2 show significant deviations from the monoexponential behaviour. I n the studied sample, there are many nanotubes (or nanotube bundles) present that are shorter ( ) than the distances travelled by the molecules during the observation time. Due to this reason, in addition to intra channel diffusion, it is expected that there is an ensemble of CF 4 molecules diffusing according to the mechanism of long range diffusion. Under the conditions of t he long range diffusion there is fast

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47 exchange 54 between the interiors of the nanotubes and the gas phase surrounding t he nanotubes or (nanotube bundles). Hence the attenuation curve is expected to contain two terms with contributions from both the diffusion mechanisms i.e., intra channel as well as long range (3.1) where is the fraction of molecules that undergo long range diffusion with the diffusion coefficient being and represents the fraction of adsorbed molecules that never leave the tubes during the observation time. For intra channel diffusion within randomly oriented one dimensional channels, the attenuation function can be expressed as follow s 55 (3.2) Equation 3. 2 results in the following expression (3.3) w here and are the diffusivities along the directions parallel and perpendicular to the channel axis, respectively. The dashed line in Figure 3 2 is a fit obtained by using E quation 3. 1. I t was found that E quation 3. 1 can be used to obtain good fits to all of the experimental data. Figure 3 3 presents the diffusion attenuation curve extended to larger gradients for effective diffusion time of 4 ms T he dashed red curve shows the best fit using Equation 3.1 and for comparison the result of the double exponential fit is also shown (blue solid li ne).

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48 For all three diffusion times used, the corresponding best fit parameters were found to be the same within the limits of experimental uncertainty. The values obtained for these parameters were and The Einstein relation (E quation 1.9) was used to find the limiting values of the root mean square displacements for diffusion insid e the nanotubes and these values were estimated to be approximately 4 m for 4 ms and 8 m for 16 ms. These results are consistent with the observation of many sufficiently large (>10 m) nanotub e bundles in the studied sample (Fig ure 3 1) The presence of large nanotube bundles proves that it is possible for the molecules to cover distances of up to 8 m without leaving a nanotube channel.

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49 Fig ure 3 2. Attenuation curves for diffusion measurements of tetrafluoromethane in aluminosilicate nanotubes obtained for different effective diffusion times. The dashed line represents the best fit result using E q uation 3. 1 The inset shows the diffusion data for t eff = 8 ms for the larger gradient range. The empty and filled circles in the insert show the attenuation curves measured for different delays between the first and second pulses of the PGSTE LED sequence ( = 2.7 and 1.3 ms).

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50 Fig ure 3 3 PFG NMR attenuations for tetrafluoromethane in alumino silicate nanotubes at eff ective diffusion time of 4 ms extended to larger gradients. The dashed red curve shows the best fit using Eq uation 3 1. F or comparison, the result of the double exponential fit is shown (blue solid line). The e mpty and filled diamonds in the figure show the attenuation curves measured for different delays between the first and second pulses of the PGSTE LED sequence ( = 2.7 and 1.3 ms). Another important result indicated by the data obtained is that the intra channel diffusivity remains independent of diffusion time within the limits of experimental error. Thus it can be concluded that the measured intra channel diffusivity is not significantly affected by possible transport restrictions at the channel margin, i.e. it represents the true intra channel diffusivity Also, the observed independence of the value of on diffusion time for the studied range of can be explained by the existence of a broad distribut ion of nanotube bundle lengths. The diffusivity along the direction of the channels was found to be at least 4 orders of magnitude larger than that in the direction

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51 perpendicular to the channels, indicating that the density of defects that would allow diffusion of CF 4 molecules in the direction perpendicular to the channel direction is negligible. In order to rule out possible influence of magnetic susceptibility effects on the measured diffusion data, additional PFG NMR measurements were performed for the same effective diffusion time ( t eff = 8 ms) but with different values of the delays between the first and second pulses of the used sequence ( = 2.7 and 1.3 ms). The observed coincid ence of the PFG NMR attenuation curves measured for different values of confirms that susceptibility effects are negligible u nder our measurement conditions 56 Conclusions 13 C PF G NMR at high field and high gradients was used to study diffusion of tetrafluoromethane in novel aluminosilicate nanotubes. The data provide evidence for one dimensional diffusion within non intersecting channels. The measured PFG NMR diffusion data yield ed the self diffusion coefficient of CF 4 along the channel direction in the nanotube interior as well as the corresponding diffusivity of CF 4 molecules undergoing fast exchange between many nanotubes. The intra channel diffusivity was found to remain independent of diffusion time within the limits of experimental error.

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52 LIST OF REFERENCES (1) Fick, A. E. Ann. Phys. 1855 94 59. (2) Fick, A. E. Phil. Mag. 1855 10 30. (3) Crank, J. The Mathematics of Diffusion ; Claredon Press: Oxford, 1975. (4) Krger, J.; Vasenkov, S.; Auerbach, S. M. Diffusion in Zeolites. In Handbook of Zeolite Science and Technology ; Auerbach, S. M., Carrado, K. A., Dutta, P. K., Eds.; Marcel Dekker, Inc.: New York, Basel, 2003; pp 341. (5) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987 19 1. (6) Krger, J.; Pfeifer, H.; Heink, W. Advances in Magnetic Resonance; Academic Press: New York, 1988. (7) Krger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Micro porous Solids ; Wiley & Sons: New York, 1992. (8) Levitt, M. H. Spin dynamics : basics of nuclear magnetic resonance 2nd ed.; John Wiley & Sons: Chichester, England ; Hoboken, NJ, 2008. (9) Keeler, J. Understanding NMR spectroscopy 2nd ed.; John Wiley and Sons: Chichester, 2010. (10) Callaghan, P. T. Principles of nuclear magnetic resonance microscopy ; Clarendon Press Oxford University Press: Oxford England New York, 1991. (11) Gibbs, S. J.; Johnson, C. S. Journal of Magnetic Resonance (1969) 1991 93 395 (12) Cotts, R. M.; Hoch, M. J. R.; Sun, T.; Markert, J. T. J. Magn. Reson. 1989 83 252. (13) Galvosas, P.; Stallmach, F.; Seiffert, G.; Krger, J.; Kaess, U.; Majer, G. J. Magn. Reson. 2001 151 260. (14) Wu, D. H.; Chen, A. D.; Johnson, C. S. Journal of Magnetic Resonance, Series A 1995 115 260. (15) Wider, G.; Dotsch, V.; Wuthrich, K. Journal of Magnetic Resonance, Series A 1994 108 255. (16) Levitt, M. H.; Forsterling, F. H. Medical Physics 2010 37 406. (17) Price, W. S. Concepts in Magnetic R esonance 1997 9 299.

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56 BIOGRAPHICAL SKETCH Aakanksha Katihar was born in 1984 at Ajmer India to Govind Singh and Meena Katihar. She grew up with her parents and younger brother Akshay Singh Katihar. All her early schooling was done in Ajmer itself. During her school years, she was a bright student and was recognized for merit for her exceptional performanc e in high school and senior secondary school examinations. She won badminton championship at state levels and performed well at various national talent search exams. She attended the Malaviya National Institute of Technology, Jaipur India (formerly MREC) a nd earned Bachelor of Technology in Chemical Engineering in 2008. After that, she attended graduate school at University of Florida (UF) Gainesville and earned a Master of Science in chemical e ngineering in 2011