Structural and dynamical properties of liquid and solid phases of ionic liquids confined inside nanoporous materials

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1 Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2012 Structural and dynamical properties of liquid and solid phases of ionic liquids confined inside nanoporous materials Ramesh Singh Louisiana State University and Agricultural and Mechanical College, Follow this and additional works at: Part of the Chemical Engineering Commons Recommended Citation Singh, Ramesh, "Structural and dynamical properties of liquid and solid phases of ionic liquids confined inside nanoporous materials" (2012). LSU Doctoral Dissertations This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please

2 STRUCTURAL AND DYNAMICAL PROPERTIES OF LIQUID AND SOLID PHASES OF IONIC LIQUIDS CONFINED INSIDE NANOPOROUS MATERIALS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor in Philosophy In The Gordon A. and Mary Cain Department of Chemical Engineering By Ramesh Singh B.Tech., Indian Institute of Technology, Roorkee, 2001 M.S.,SUNY-ESF, Syracuse, 2007 M.S., Louisiana State University, 2010 May 2012

3 ACKNOWLEDGEMENTS First and foremost I would like to express my deepest gratitude to my advisor Dr. Francisco R. Hung, for his invaluable guidance, consistent encouragement, and support. I have been fortunate to gain the benefit of his expertise in the field of molecular modeling and simulation. He has always been a patient listener to my research ideas and constantly gave me positive feedback in order to implement them. His delightful nature taught me that serious research work can be done in a light and charming environment. I sincerely thank dean s representative Dr. Jeffrey C. Clayton and my thesis committee members Dr. John C. Flake, Dr. Krishnaswamy Nandakumar, and Dr. Dorel Moldovan for their invaluable suggestions on my research work. My special thanks to Dr. Erik Santiso who patiently guided me in the studies of solid phases of ionic liquids from time to time. I am also very thankful to Dr. Joshua D Monk, my fellow group members and my friends for their support and for making my life easy. I would also like to thank all those in the Cain Department of Chemical Engineering at LSU. I gratefully acknowledge funding from the American Chemical Society Petroleum Research Foundation (ACS-PRF), the LONI Institute and the Cain Department of Chemical Engineering, LSU. I also thank the Cain Chemical Engineering Department at LSU for giving me opportunity to pursue my Ph.D degree here. I also thank all the professors, staff members and other graduate students of the department. I am indebted to my parents, brother Suresh Kumar Singh, and sister Lakshmi Chaudhary for their ever-present love and support. Last but not the least, I would thank my loving, and patient wife Geeta and son Nilesh who faithfully supported me during my Ph.D. ii

4 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ii ABSTRACT... v CHAPTER 1 INTRODUCTION Background and Motivation Outline of Dissertation... 3 CHAPTER 2 A COMPUTATIONAL STUDY OF THE BEHAVIOR OF IONIC LIQUID [BMIM + ][PF6 - ] CONFINED INSIDE MULTI-WALLED CARBON NANOTUBES Introduction Computational Details Results and Discussion Structural Properties Dynamical Properties Concluding Remarks CHAPTER 3 HETEROGENEITY IN THE DYNAMICS OF THE IONIC LIQUID [BMIM + ][PF 6 - ] CONFINED IN A SLIT NANOPORE Introduction Computational Details Results and Discussion Mean Squared Displacement (MSD) and Self-diffusion Coefficients Self-part of the Van Hove Correlation Function Incoherent Intermediate Scattering Function Relaxation Times Radial Distribution Functions Concluding Remarks CHAPTER 4 MOLECULAR DYNAMIC SIMULATIONS OF IL [EMIM + ][TFMSI - ] CONFINED INSIDE RUTILE (110) NANOPORE: EFFECT OF PORE LOADING ON STRUCTURAL AND DYNAMICAL PROPERTIES Introduction Computational Details Results and Discussion Structural Properties Dynamical Properties Concluding Remarks CHAPTER 5 EFFECT OF ACETONITRILE SOLVENT ON THE STRUCTURAL AND DYNAMICAL PROPERTIES OF IL [EMIM + ][TFMSI - ] CONFINED INSIDE SLIT-LIKE GRAPHITIC PORE: A MOLECULAR DYNAMIC SIMULATION STUDY Introduction Computational Details Results and Discussion iii

5 5.3.1 Density Profiles Radial Distribution Function Preferential Orientation Mean Square Displacement Concluding Remarks CHAPTER 6 CONCLUSION AND FUTURE WORK Conclusion Proposed Work Defining Order Parameters to Characterize Local and Global Degree of Crystallinity Study of the Effect of Charged Electrodes on the Properties of the Confined ILs REFERENCES APPENDIX A: PERMISSION LETTERS A.1 Permission for Chapter A.2 Permission for Chapter APPENDIX B: SUPPORTING INFORMATION (CHAPTER 3) B.1 Representative Gromacs Input File with MD Parameters (.mdp file) B.2 Relaxation Times VITA iv

6 ABSTRACT The purpose of this research is to investigate the physical properties of ionic liquids (ILs) confined inside nanopores of different materials and morphologies. We are interested to study the effect of pore material, morphology and addition of organic solvents on the properties of confined ILs. Understanding the behavior of ILs inside nanopores is relevant to potential applications of these systems in electrochemical double layer capacitors (EDLCs) and dye sensitized solar cells (DSSCs). Such a fundamental understanding is also crucial to optimize the synthesis of hard-templated 1D nanostructures (nanorods, nanotubes, nanowires) based on organic salts, which may be imparted properties (e.g., magnetic, optical) that are desirable for different applications (magnetic hyperthermia cancer treatment, medical imaging, sensors). In this work we have used molecular dynamics (MD) simulations to investigate systems of representative ILs, [BMIM + ][PF - 6 ] and [EMIM + ][TFMSI - ], inside several model materials (e.g., slit-shaped graphitic and titania pores, carbon nanotubes). Formation of different layers of ions was observed for the confined ILs irrespective of variations in pore size, shape, material and amount of solvent. In all cases, change in pore loading leads to lower densities of ions in the center of the pore. The cations close to the pore walls tend to align with their imidazolium rings parallel to the pore surface in the case of carbon materials, and multiple preferential orientations are observed in the case of titania pores. For all porous materials studied, the dynamics of the ions depend strongly on their location with respect to the surface; bulk-like dynamics are generally observed for the ions in the center regions of the pore, with the dynamics becoming slower as the ions get closer to the pore surfaces. Addition of acetonitrile solvent also shows similar layering behavior for ILs and solvent near the pore wall with less variation in the center of the pore. Preferential orientations of the ions remain unaffected and solvent molecules tend to v

7 align flat near the pore surface. The dynamics of the ions and molecules increases linearly with increase in IL molar concentration both near the wall and in the center of the pore. vi

8 CHAPTER 1 INTRODUCTION 1.1 Background and Motivation Ionic liquids (ILs) are salts composed of an organic cation and an organic or inorganic anion with melting point below 100 C. Their unique properties such as great thermal, chemical, and electrochemical stability and their nonvolatile, nonexplosive and nonflammable nature have gained them immense attention in recent years [1-10]. Because of their numerous applications and unique properties, there is a rapidly growing scientific and commercial interest in ILs. It has been observed that properties of ILs changes drastically under confinement. It has been reported that the melting points and the thermal decomposition temperature of several ILs increase by more than 200 C when confined inside multi-walled carbon nanotubes (MWCNTs) [2, 3]. Experimental results [11] suggest that organic cations are strongly adsorbed on surfaces with negative charges (e.g., mica, silica), and interact strongly with graphitic surfaces; surface roughness is also observed to affect the structure of ILs at the interface. Understanding the behavior of ILs inside nanopores is relevant to potential applications of these systems in electrochemical double layer capacitors (EDLCs) [12-19]. These devices have specific power higher than batteries and fuel cells but lack in specific energy. The conventional electrolytes that are used in these devices are only stable up to 2.5 volts hence limiting the performance in terms of both specific power and specific energy. ILs with their unique properties, especially higher electrochemical window (up to 6.0 volts) have the potential to replace the conventional electrolytes that are used in these devices. ILs also have potential to replace the conventional electrolytes in dye sensitized solar cells (DSSCs), a class of solar cell based on a semiconductor formed between a photo-sensitized anode and an electrolyte. The major problems with the conventional electrolytes in DSSCs are 1

9 that they catch fire, are explosive and evaporate with time [20-22]. This not only undermines the performance of the device, but also causes environmental hazards. Current research suggests that ILs with their unique properties have potential to tackle these problems and improve the performance of DSSCs [22-25]. Understanding the behavior of ILs confined inside nanopores is also relevant to the development of nanoparticles based on organic salts. Recently, Warner et al. synthesized nonmagnetic [26, 27], magnetic [27] and optically-active (fluorescent) [28] nanoparticles based on ILs that are in solid phase at room temperature. They called these nanoparticles GUMBOS (Group of Uniform Materials Based on Organic Salts). These nanomaterials have potential uses in biomedical applications ranging from magnetic hyperthermia cancer treatment to medical imaging [29-37]. As further tunability of the magnetic and optical properties can be achieved by introducing shape anisotropy [29-37], the Warner group also synthesized 1D nanomaterials (e.g., nanorods, nanotubes and nanowires) based on organic salts, by introducing these compounds inside hard templates with cylindrical nanopores, e.g., multi-walled carbon nanotubes (MWCNTs), and anodic aluminum oxide membranes (AAO). Nanomaterials based on ILs hold enormous promise, due to their highly tunable properties [5] and the fact that they can be prepared from FDA-approved compounds [38-41], and thus could be free of the toxic effects that other nanomaterials currently considered for biomedical applications may have [42, 43]. The properties of a nanoconfined fluid phase can be different from those of bulk phase [44]. It is very complicated to gain a molecular-level picture of the behavior of ILs inside nanopores from experiments alone. Characterization techniques usually give an incomplete picture of the pore morphology and surface chemistry of the porous material. Moreover, in experiments it is difficult to determine the individual effects of each variable (e.g., pore size, 2

10 shape, interconnectivity) on the system s properties. Molecular simulations, on the other hand, allow us to work with a model porous material that is completely characterized (the positions and chemical identities of all the atoms are known a priori). In consequence, molecular simulations are well suited to perform a systematic study of the relevant physical variables and determine their individual effects on the system. A reliable computational model can assist in the interpretation of experimental results and provide accurate predictions of the behavior of the system, eliminating the need for costly trial-and-error experiments. Furthermore, molecular simulations of confined ILs will be fundamental to develop theories for the electric double layer for ILs, which are lacking [45] and will be useful to obtain rapid predictions for these systems. 1.2 Outline of Dissertation As stated before, the main objective of this work is to use molecular simulation techniques to study the structural, dynamical and thermodynamic properties of ILs confined in nanopores of different geometries and materials. Chapter 2 is published work (Singh, R., J. Monk, and F.R. Hung, A Computational Study of the Behavior of the Ionic Liquid [BMIM + ][PF - 6 ] Confined Inside Multiwalled Carbon Nanotubes, The Journal of Physical Chemistry C, 2010, 114(36): p ) in which we have performed molecular dynamics (MD) simulations to study the structural and dynamical properties of a typical (IL) [BMIM + ][PF - 6 ] confined inside multi-walled carbon nanotubes with inner diameters ranging between 2.0 and 3.7 nm. Chapter 3 is published work (Singh, R., J. Monk, and F.R. Hung, Heterogeneity in the Dynamics of the Ionic Liquid [BMIM + ][PF - 6 ] Confined in a Slit Nanopore, The Journal of Physical Chemistry C, 2011, 115(33): p ) in which we have performed MD simulations to study the dynamics of the IL [BMIM + ][PF - 6 ] confined in a slit nanopore of pore 3

11 size 5.4 nm. The main focus of this work was to study the effect of temperature on the dynamics the ions and different time regimes that are present in the MSD plots. Chapter 4 includes our MD simulation study of the IL [EMIM + ][TFMSI - ] confined inside rutile (110) pore of pore size 5.2 nm. We studied the effect of pore loading on the structural and dynamical properties of the ILs, and contrast those against our results obtained for the same IL inside a slit graphitic nanopore of the same size. Chapter 5 includes our MD simulation study of mixtures of acetonitrile and varying concentrations of the IL [EMIM + ][TFMSI - ] confined inside slit-like graphitic pore of pore size 5.2 nm. We studied the effect of organic solvent on the structural and dynamical properties of the IL at various IL molar concentrations. Chapter 6 has the summary of the main finding of this work. Ideas for future research in this area are also discussed. 4

12 CHAPTER 2 A COMPUTATIONAL STUDY OF THE BEHAVIOR OF IONIC LIQUID [BMIM + ][PF6 - ] CONFINED INSIDE MULTI-WALLED CARBON NANOTUBES 1 Contents of this chapter have already been published (Singh, R., J. Monk, and F.R. Hung, A Computational Study of the Behavior of the Ionic Liquid [BMIM + ][PF - 6 ] Confined Inside Multiwalled Carbon Nanotubes. The Journal of Physical Chemistry C, 2010, 114(36): p ). In this chapter, we report molecular dynamics (MD) results of the structural and dynamical properties of the IL [BMIM + ][PF - 6 ] confined inside multi-walled carbon nanotubes with inner diameters ranging between 2.0 and 3.7 nm. The main objective of this study was to understand the effect of pore size and pore filling on the structural and dynamical properties of the confined IL. The rest of this chapter is structured as follows. Section 2.1 is the introduction. Section 2.2 contains a description of our computational models and methods. In Section 2.3 we present results and discussion of the structural and dynamic properties of the confined ILs, and in Section 2.4 we summarize our main findings Introduction Ionic liquids (ILs) have attracted extensive attention in recent years for applications ranging from green solvents for chemical synthesis, catalysis and separations, to electrolytes for electrochemistry and photovoltaics, among others [1-10]. When confined inside nm-sized pores, ILs exhibit physical properties that are different from those observed in bulk systems. For example, the melting points and the thermal decomposition temperature of several ILs have been reported to increase by more than 200 C when confined inside multi-walled carbon nanotubes (MWCNTs) [2, 3]. In contrast, when confined inside nanoporous silica [46], ILs can exhibit 1 Reprinted with permission from Singh, R., J. Monk, and F.R. Hung, The Journal of Physical Chemistry C, (36).Copyright (2010) American Chemical Society. 5

13 similar mobility as the bulk phases, and their melting points decrease significantly [1, 47]. This melting point depression is enhanced by decreasing the pore size. Experimental results [11] also suggest that organic cations are strongly adsorbed on surfaces with negative charges (e.g., mica, silica), and interact strongly with graphitic surfaces; surface roughness is also observed to affect the structure of ILs at the interface. All these observations agree with prior studies considering simpler molecules adsorbed inside nm-sized pores [48-50]. Understanding the behavior of ILs inside nanopores is relevant to potential applications of these systems in electrochemical double layer capacitors (EDLCs) [12-19]. These devices have a structure similar to a battery, consisting of two carbon-based nanoporous electrodes, an electrolyte and an ion-permeable separator. EDLCs store charge in the interface between a nanoporous electrode and an electrolyte; during the charging process, a difference of potential induces charges in the negative and positive electrodes, attracting the cations and the anions in the electrolyte. EDLCs can store more energy than traditional capacitors, since the nanoporous electrodes exhibit a large surface area, and the thickness of the electric double layer has nanoscale dimensions. EDLCs cannot store as much energy as fuel cells and batteries, but exhibit fast charge/discharge times and can provide bursts of energy very quickly. As a result, EDLCs can complement the capabilities of internal combustion engines, fuel cells and batteries in hybrid vehicles, industrial equipment and electronic devices. Understanding the behavior of ILs confined inside nanopores is also relevant to the development of nanoparticles based on organic salts. Recently, Warner et al. synthesized non-magnetic [26, 27], magnetic [27] and opticallyactive (fluorescent) [28] nanoparticles based on organic salts that are in solid phase at room temperature. These nanomaterials have potential uses in biomedical applications ranging from magnetic hyperthermia cancer treatment to medical imaging [29-37]. As further tunability of the 6

14 magnetic and optical properties can be achieved by introducing shape anisotropy [29-37], the Warner group also synthesized 1D nanomaterials (e.g., nanorods, nanotubes and nanowires) based on organic salts, by introducing these compounds inside hard templates with cylindrical nanopores, e.g., multi-walled carbon nanotubes (MWCNTs), and anodic aluminum oxide membranes (AAO). Nanomaterials based on organic salts hold enormous promise, due to their highly tunable properties[5] and the fact that they can be prepared from FDA-approved compounds,[38-41] and thus could be free of the toxic effects that other nanomaterials currently considered for biomedical applications may have.[42, 43] Optimization of the applications mentioned above therefore requires a fundamental understanding of the behavior of ILs when confined inside nm-sized pores. In this study, we have used molecular simulation to investigate systems of ILs inside multi-walled carbon nanotubes (MWCNTs). There has been several simulation studies of ILs adsorbed on surfaces such as rutile and graphite [51-55]. A few simulation studies have been published on ILs confined inside nanopores with slit-like [52, 56-61], and cylindrical geometry [62-64]. Only three of these previously mentioned reports considered the formation of solid phases inside nanopores [59, 60, 63]. In these prior studies, the authors considered very narrow pores (pore widths or diameters < 1.4 nm) and very small system sizes (in some cases, only four ion pairs were inside the nanopores). Although understanding the solidification of organic salts inside nanopores is relevant to optimize the synthesis of 1D-nanostructures based on organic salts [26, 28], as a first step we have concentrated on studying liquid phases of organic salts confined inside MWCNTs. The main objective of this study is to understand the effect of pore size and pore filling on the structural and dynamical properties of the confined IL 1-butyl-3- methylimidazolium hexafluorophosphate, [BMIM + ][PF - 6 ]. Recent studies of ILs confined inside 7

15 carbon nanotubes [62-64] have either considered other ILs, or have not studied their dynamical properties Computational Details The software Nanotube Modeler (JCrystalSoft, 2009) was used to generate the xyz coordinates of the carbon atoms in the multi-walled carbon nanotubes (MWCNTs). The MWCNTs were kept Figure 2.1 Schematic representation of the IL [BMIM + ][PF - 6 ]. in fixed positions and were filled with varying amounts of the IL 1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM + ][PF - 6 ]. A scheme of the IL is presented in Figure 2.1. Constant volume and temperature (NVT) molecular dynamics simulations have been performed using the GROMACS MD package [65]. The carbon atoms in the MWCNTs were modeled as LJ spheres with σ c = nm and ε c /k = 28.0 K. The IL was modeled using the all-atom force field developed by Lopes et al. [66-68], which is based on the optimized potential for liquids simulation/all atom (OPLS-AA) of Jorgensen et al.[69] Prior to studying confined systems, we carried out preliminary MD simulations of bulk [BMIM + ][PF - 6 ] in the NVT and NPT ensembles. From these simulations we obtained a value of 1.35 g/cm 3 for the bulk liquid density, and 42.2 kcal/mol for the heat of vaporization at 25 C (this last quantity was determined following the 8

16 procedure detailed by Morrow and Maginn).[70] These simulated values are comparable to results from previous simulations, [70] and to reported experimental values (1.36 g/cm 3 ; and 37.0 kcal/mol and 45.8 kcal/mol). [71, 72] For our simulations with confined ILs, we considered four different multi-walled carbon nanotubes (MWCNTs) having a length of L = 5.0 nm and internal pore diameters D equal to 2.0, 2.5, 3.0 and 3.7 nm. These pore diameters D are measured as the center-to-center distance between diametrically-opposed carbon atoms in the inner wall of the MWCNTs. In our first set of simulations, we placed a total of 33, 60, 96 and 147 ion pairs initially arranged in an arbitrary lattice inside the MWCNTs mentioned above. These numbers of ion pairs were chosen for the confined [BMIM + ][PF - 6 ] to have a density of 1.35 g/cm 3. We also performed additional simulations at different degrees of pore loadings, where we reduced the number of ion pairs inside the MWCNTs to 80% and 65% of the bulk density. These densities for the confined IL were calculated using a volume Vmin D c L 4 2. Our results for the radial density profiles (Figure 3) indicate that the density of the confined ions reach a value of zero at r D 2 ~ c. Such an observation leads us to believe that the volume we have used in our calculations give an accurate estimate of the density of the confined IL in our systems. We also ran several simulations considering longer MWCNTs (L = 10 nm), obtaining results similar to those obtained with L = 5.0 nm. In all our simulations, the Lennard-Jones interactions were cut off at 1.2 nm, and the long range coulomb interactions were handled by the particle-mesh Ewald (PME) method[73] with a cutoff of 1.0 nm and a grid spacing of 0.1 nm. Periodic boundary conditions were applied in the x, y, and z directions. The ILs/nanotube system was kept in vacuum in the center of the 9

17 orthorhombic box in such a way that one side of the box was equal to the length of the nanotube (5.0 nm), and the length of the other two sides of the box (12.0 nm) was long enough to avoid any artificial effect caused by the periodic boundary conditions. From preliminary simulations it was determined that a 5.0 nm axial length was long enough to remove any finite-size effects due to periodic boundaries in the system. The improved velocity-rescaling algorithm recently proposed by Parrinello et al.[74, 75] was used to mimic weak coupling at 300 K with a coupling constant of 0.1 ps. D =2.0 nm D =2.5 nm D =3.0 nm D =3.7 nm Figure 2.2 Representative simulation snapshots of [BMIM + ][PF 6 - ] confined inside MWCNTs of different diameters. 10

18 We first minimized the energy of our initial configurations using the steepest descent method. Afterwards, we ran MD simulations using a time step of 0.5 fs. All of the systems were run for 2 ns at 600 K, and then annealed from 600 to 300 K in six stages: 200 ps at 550 K, 300 ps at 500 K, 300 ps at 450 K, 200 ps at 400 K, 500 ps at 350 K and 6.5 ns at 300 K. Afterwards, we took the final configuration of our systems and repeated the above steps two additional times. We subjected our systems to a total of three cycles of simulated annealing in an attempt to overcome the difficulties posed by the slow dynamics of ILs, which are likely to be exacerbated when these compounds are confined inside nanopores. Our final run at 300 K was further extended to up to 40 ns, and our measured properties were averaged over the final ~30 ns of simulation time. Representative simulation snapshots for our systems are depicted in Figure Results and Discussion Structural Properties In Figure 2.3 we present the radial density profiles of the ions (in kg/m 3 ) confined inside MWCNTs of different diameters, when the confined IL has a density similar to that of a bulk IL (ρ bulk ). The density profiles of the ions are calculated from the individual atomic positions. The mass density profiles of the confined IL are found to be oscillatory with a local maximum in the density close to the pore walls, due to the stacking of the ions near the wall surface. Layering behavior is observed for both the cations and anions and all pore diameters considered. The oscillation patterns observed in the radial density profiles depend strongly on the diameter of the MWCNTs. The number of layers of IL increases from two to four as the diameter of the nanotubes increases from 2.0 nm to 3.7 nm. Another interesting observation regards the positions and the widths of the peaks of the radial density profiles for the ions. The peaks for both the cations and anions are observed in similar positions, and the peak width is about nm, 11

19 Mass density (Kg/m 3 ) Electron density (e/nm 3 ) Mass density (Kg/m 3 ) Electron density (e/nm 3 ) Mass density (Kg/m 3 ) Electron density (e/nm 3 ) Mass density (Kg/m 3 ) Electron density (e/nm 3 ) showing that the cations and anions stack together inside the MWCNTs. The results presented in Figure 2.3 are in good agreement with previous results obtained for a different IL inside single D = 2.0 nm Cation Anion Radial distance (nm) D = 2.5 nm Cation Anion Radial distance (nm) D = 3.0 nm Cation Anion Radial distance (nm) D = 3.7 nm Cation Anion Radial distance (nm) D = 2.0 nm Cation Anion Radial distance (nm) D = 2.5 nm Cation Anion Radial distance (nm) D = 3.0 nm Cation Anion Radial distance (nm) D = 3.7 nm Cation Anion Radial distance (nm) Figure 2.3 Mass density profiles (left) and electron density profiles (right) of the confined ions along the radial direction. In all cases, the confined IL has a density similar to ρ bulk. 12

20 Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) and double-walled carbon nanotubes [62]. These observations are also similar to what was obtained for the density profiles of ILs inside pores of slit-like geometry [56]. We also present in Figure 2.3 the electron density profiles for the cations and anions in the radial direction, which were calculated by the procedure described by Bhargava and Balasubramanian.[76] X-ray reflectivity experiments have been used in the past to measure the electron density profiles as a function of depth at the [BMIM + ][PF - 6 ]-vapor interface [77]. The electron and the mass density profiles in the radial direction are very similar. Both profiles show oscillatory patterns, with the positions of the peaks for the cations and anions completely in phase (i.e., the peaks for the cations and anions in both electron and mass density profiles are observed at similar radial positions). These observations are in contrast to what was found in simulation studies for the ρ ~ 0.45ρ Bulk Cation Anion ρ ~ 0.65ρ Bulk Cation Anion Radial distance (nm) Radial distance (nm) ρ ~ 0.80ρ Bulk Cation Anion Radial distance (nm) ρ ~ ρ Bulk Cation Anion Radial distance (nm) Figure 2.4 Mass density profiles along the radial direction of the cations and anions confined with a MWCNT of D = 3.7 nm, for different pore loadings (expressed as percentages of ρ bulk ). 13

21 Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) Mass density (Kg/m 3 ) [BMIM + ][PF - 6 ]-vapor interface,[76] where the positions of all of the ion peaks were out of phase with the exception of the one that was exactly at the vapor-il planar interface. These differences in behaviors can be attributed to the important differences in geometry (cylindrical vs. planar) and the confinement effects due to the MWCNT walls D =2.0 nm Axial distance (nm) 1500 D =2.0 nm Axial distance (nm) 1500 D =2.0 nm Axial distance (nm) 1500 D =3.7 nm Axial distance (nm) 1500 D =3.7 nm Axial distance (nm) 1500 D =3.7 nm Axial distance (nm) Figure 2.5 Mass density profiles along the axial direction of the ions confined inside MWCNTs of D = 2.0 nm (left) and D = 3.7 nm (right) and different pore loadings: ρ ~ ρ bulk (top), ρ ~ 0.8 ρ bulk (center) and ρ ~ 0.65 ρ bulk (bottom). Continuum and dashed lines represent the densities of cations and anions. 14

22 Orientation (Cos (θ)) In Figure 2.4 we present mass density profiles in the radial direction for both cations and anions confined inside a MWCNT with D = 3.7 nm at different pore loadings. Our results show that reductions in the pore loading lead to a decrease in the mass density near the center of the nanotube, and to an increase in the local density near the surface of the nanotube. We also studied the axial density profiles of the confined cations and anions at different pore loadings; results for the case of D = 2.0 and 3.7 nm are shown in Figure 2.5. When the confined IL has a density similar to ρ bulk, the axial density profiles are relatively uniform for both pore sizes, but as the pore loading decreases, we observe local variations in the axial density profiles, which exhibit regions of high and low densities (Figure 2.5). The variations in the axial density are particularly pronounced for the confined cations nm nanotube 3.0 nm nanotube 3.7 nm nanotube Radial distance (nm) Figure 2.6 Orientation distribution profile (continuum lines) of the imidazolium ring of the cation as a function of radial position for different pore sizes and ρ ~ 0.8 ρ bulk. Cos(θ) is defined as the angle between the radial vector and the vector perpendicular to the imidazolium ring. The radial position of the inner surfaces of the carbon atoms at the pore walls are represented as dotted lines. 15

23 In order to understand the structure of the ILs near the nanotube surface, we determined the orientation of the cations as measured by cos(θ), where θ is the angle between the radial vector and the vector normal to the imidazolium ring. In Figure 2.6 we present results for the average value of cos(θ) as a function of the radial position for MWCNTs of different diameters when the confined IL has a density similar to 80% of ρ bulk. Our results show that cos(θ) has a relatively large value near the surfaces of the MWCNTs, indicating that the imidazolium ring of the cations tend to align parallel to the surface when close to the walls. Another factor that affects the ordering of the cations is the available surface area, which increases as the nanotube diameter becomes larger. For the MWCNTs with D = 3.0 and 3.7 nm, the average values of cos(θ) drop as we approach the center of the nanotube (Figure 2.6), suggesting a loss in orientational order with increasing distance from the pore walls. These results are consistent with similar findings obtained for ILs confined inside slit-like pores [56], as well as inside single- and double-walled nanotubes [62] Dynamical Properties In Figure 2.7 we present results for the mean square displacements in the axial direction of [BMIM + ][PF - 6 ] confined inside MWCNTs of D = 3.7 nm and 3.0 nm at 300 K and different pore loadings (expressed as a percentage of the bulk density of the IL at the same temperature). These MSD results suggest that the cations move faster than the anions, in analogy to previous studies for bulk systems [70, 78-83]. At any given value of t, the MSD for the bulk cations and anions are larger than those observed for the confined ions, indicating that the dynamics for bulk systems are faster than for confined systems. Our results also suggest that, for a given pore size, the dynamics are faster when the confined IL has a density lower than the bulk density. Systems at lower pore loadings have larger MSDs and reach the diffusive regime (MSD ~ t) faster; in 16

24 MSD, Axial Direction (nm 2 ) MSD,Axial Direction (nm 2 ) 1 D = 3.0 nm 0.1 Fickian Time ( ns ) 1 D = 3.7 nm 0.1 Fickian Time ( ns ) Figure 2.7 Mean square displacement in the axial direction for the ions confined inside MWCNTs with D = 3.0 nm (top) and D = 3.7 nm (bottom), and different pore loadings: ρ ~ ρ bulk (red), ρ ~ 0.8 ρ bulk (green) and ρ ~ 0.65 ρ bulk (blue). Black lines represent the bulk behavior. Continuum and dashed lines represent the MSDs of cations and anions. The continuous purple line indicates the behavior expected for the Fickian regime (MSD t). contrast, systems at the largest pore loading have barely reached the Fickian regime close to the end of our simulations. Also, for all pore loadings considered, it is apparent that there is a long 17

25 time interval in which the MSD increases slowly with t, which is a signature of the so-called cage effect where ions are temporarily trapped by their surrounding neighbors. The cage effect has been observed in bulk ILs [78, 84], as well as in supercooled LJ liquids confined in nanopores [85]. The time intervals for this cage regime are larger for confined systems, as compared to those observed for bulk systems. Our results suggest that for a given pore loading, there is a non-monotonic dependence of MSD with pore size. Our results suggest that, for pore loadings equivalent to 100% and 80% of the bulk density, the axial MSD decreases with increasing degree of confinement. However, for a pore loading equivalent to 65% of the bulk density, the axial MSD observed for D=3.0 nm is larger than that observed for D=3.7 nm. Furthermore, our results suggest that for a given pore size, there is a non-monotonic dependence of MSD with pore loading. For a MWCNT with D = 3.0 nm, the axial MSD increases with decreasing pore filling, but for the MWCNs with D = 3.7 nm, the smaller MSD is observed when the density of the confined IL is similar to the bulk density, and the largest MSD is observed at ~80% of the bulk density. Intermediate values of the axial MSD are observed when the confined IL has a density similar to 65% of the bulk density. Furthermore, for this latter pore size, when the IL has a density similar to 80% of ρ bulk it reaches the diffusive regime faster than when it has a density similar to 65% of ρ bulk. The axial MSDs for an IL confined inside a MWCNT with D = 3.0 nm (data not shown) have a behavior similar to that we have described for a MWCNT with D = 3.7 nm. These non-monotonic behaviors of the axial MSD for varying pore sizes and fixed pore loadings, and for fixed pore sizes and varying pore loadings, may be due to strong local fluctuations in the axial density profile of the confined IL, as the pore filling decreases (Figure 2.5). We intend to study this behavior in more detail in an upcoming manuscript. 18

26 C(t)/C(0) MSD, Axial Direction (nm 2 ) C(t)/C(0) MSD, Axial Direction (nm 2 ) 1.2 D =3.0 nm (ρ ~0.80 ρ Bulk ) Time ( ns ) 1.2 D =3.0 nm (ρ ~ ρ Bulk ) Time ( ns ) Cr Cr (NN) Cr (NH) Cv Cr Cr (NN) Cr (NH) Cv 0.03 D =3.0 nm (ρ ~0.80 ρ Bulk ) Time ( ns ) D =3.0 nm (ρ ~ ρ Bulk ) Time ( ns ) Cation Anion Cation Anion Figure 2.8 Single-particle time correlation functions for the cations (left panel) and mean square displacement in the axial direction for cations and anions (right panel). The IL is confined inside a MWCNT with D = 3.0 nm and two pore loadings are considered: ρ ~ 0.8ρ bulk (top panel) and ρ ~ ρ bulk (bottom panel). The correlation functions depicted are the following: Cv = velocity of the center of mass of the cation (Cv); Cr = reorientation of the cation around an axis perpendicular to the imidazolium ring; Cr (NN) = reorientation of the cation around an axis in the same plane as the imidazolium ring, but perpendicular to the vector joining the N atoms (see Figure 1); and Cr (NH) = similar to Cr (NN), but now the vector is in the direction of the C-H bond of the CR carbon (Figure 2.1). Motivated by the simulation results presented by Urahata and Ribeiro [79] for bulk ILs, in Figure 2.8 we present several single-particle time correlation functions of the cations, as well 19

27 as the axial MSD of the cations and anions confined within a MWCNT of D = 3.0 nm and two different pore loadings. These results indicate that for both pore fillings, the velocity of the center of mass of the cations decorrelate very quickly, as this correlation function reaches a value close to zero in less than 1 ns of simulation time. In contrast, the reorientational motion of the ring of the cations around different rotation axes is orders of magnitude slower. In particular, when the confined IL has a density similar to that of a bulk IL, ~30 ns of simulation time are not enough for these rotational motions to completely decorrelate. Nevertheless, reducing the density of the confined fluid to about 80% of ρ bulk allow the reorientational motion of the imidazolium ring of the cations to decorrelate after ~30 ns. Even though the translational and the angular velocities of the cations are not directly compared here, the single-particle time correlation functions presented serve as a suitable measure of different timescales involved in the translational and rotational motion of the cations for different pore loadings. Previous simulations for bulk ILs also pointed out large differences in characteristic timescales for the translational and rotational motions of the cations of ILs [78, 79]. In Figure 2.9 we present data for the axial MSD of the cations and anions according to their radial position within a MWCNT of D = 3.0 nm and a density similar to that of a bulk system. There are slight differences in the MSDs for the different layers of ions. The cations in the inner layer (center of the pore) move faster than those in the middle layer, which in turn have faster dynamics than the cations close to the walls of the nanotube (outer layer). These results are in agreement with those observed for supercooled LJ fluids in confinement [85]. Similarly, the anions close to the walls have slower dynamics as compared to those in the inner and middle layers. 20

28 MSD,Axial Direction (nm 2 ) D =3.0 nm Time ( ns ) Cation (0 < r < 0.5) Cation (0.5 < r <1.0) Cation (1.0 < r <1.5) Anion (0 < r < 0.5) Anion (0.5 < r < 1.0) Anion (1.0 < r < 1.5) Figure 2.9 Mean square displacement in the axial direction for the cations and anions in different layers according to their radial position (Figures 2 and 3). The ions are confined inside a MWCNT of D = 3.0 nm and have ρ ~ ρ bulk. Thick, continuous lines represent the cations, and thin, dashed lines represent the anions. All r distances are in nm. Nevertheless, the axial MSD of the anions in the inner and middle layers are similar in magnitude. The cations in the inner and outer layers have larger MSDs than the anions in those layers; in contrast, the MSDs of cations and anions in the middle layers are comparable in magnitude. Similar results are observed in our simulations for MWCNTs of different sizes when the density of the confined IL is similar to that of a bulk IL (data not shown). These results suggest that the local dynamics of the confined ions are heterogeneous and depend strongly on their radial position. 2.4 Concluding Remarks We have studied the structural and dynamical properties of the IL [BMIM + ][PF 6 - ] confined inside MWCNTs of different diameters. Our results indicate that the diameter of the MWCNT and the pore loading have a profound influence on the structural and dynamical 21

29 properties of the confined IL. The mass density profiles of the ions in the radial direction show layering behavior, with the peaks of the cations and anions taking place at similar values of r. Increasing the pore diameter results in an increase in the number of layers from two (D = 2.0 nm) to four (D = 3.7 nm). Reductions in the pore loading lead to regions of low density in the center of the pore. The density profiles in the axial direction also exhibit important variations, with regions of high and low densities as the pore loading decreases. Our simulations also indicate that cations close to the pore surface tend to align with their imidazolium ring parallel to the surfaces. Our MSD results in the axial direction indicate that the confined ions show dynamics that are slower than those observed in bulk systems. The confined cations move faster than the anions, in analogy to bulk systems; however, the confined ions spend a significantly larger amount of time in the cage regime than bulk systems, before finally reaching the Fickian (diffusive) regime. In analogy to bulk systems, there are large differences in the characteristic timescales for the translational and rotational motion of the confined cations. The former decorrelate very quickly (much less than 1 ns of simulation time), but the rotational motion of the cation is orders of magnitude slower. The rotation of the imidazolium ring of the cation decorrelates faster when the pore loading is reduced. Our results also suggest that the cations in the center of the pore tend to move faster than those close to the pore walls, in analogy to the behavior observed for simple fluids in confinement. A similar behavior is observed for the distinct layers of anions, although the differences in dynamics are not as marked as those observed between layers of cations. Finally, our results suggest that for some pore sizes, the axial MSD increases with decreasing pore filling; however, for some pore sizes, the axial MSD seems to have a non-monotonic dependence with pore loading. Likewise, there is a non-monotonic 22

30 dependence of MSD with pore size and fixed pore loadings. These non-monotonic behaviors are possibly due to the presence of local variations in the axial density profile of the IL as the pore loading decreases. We intend to study this behavior in more detail in an upcoming manuscript. Similarly, in upcoming studies we will consider confinement of ILs in pores of different geometries, as well as studying the behavior of solid phases of organic salts inside nanopores. 23

31 CHAPTER 3 HETEROGENEITY IN THE DYNAMICS OF THE IONIC LIQUID [BMIM + ][PF 6 - ] CONFINED IN A SLIT NANOPORE 2 Contents of this chapter have already been published (Singh, R., J. Monk, and F.R. Hung, Heterogeneity in the Dynamics of the Ionic Liquid [BMIM + ][PF - 6 ] Confined in a Slit Nanopore, The Journal of Physical Chemistry C, 2011, 115(33): p ). In this chapter, we report molecular dynamics (MD) results of the structural and dynamical properties of the IL [BMIM + ][PF - 6 ] when confined inside an uncharged slit-like graphitic pore of width H = 5.4 nm, in the temperature range K. The main objective of this work was to study in detail the dynamical properties of the same IL, [BMIM + ][PF6 - ], when confined inside a much simpler pore geometry, namely an uncharged slit-like graphitic pore. The rest of this chapter is structured as follows. Section 3.1 is the introduction. Section 3.2 contains a description of our computational models and methods. In Section 3.3 we present results and discussion of the structural and dynamic properties of the confined ILs, and in Section 3.4 we summarize our main findings. 3.1 Introduction Ionic liquids (ILs) are organic salts with a melting temperature below the boiling point of water.[86] The properties of ILs are highly tunable; as many as 10 9 to ILs could be formed by varying the cations or the anions.[86] ILs have applications as green solvents for chemical synthesis, catalysis and separations, and as electrolytes for electrochemistry and photovoltaics, among others.[6, 7, 86] A fundamental understanding of the properties of ILs inside nanopores is relevant for applications of ILs as electrolytes for energy storage in electric 2 Reprinted with permission from Singh, R., J. Monk, and F.R. Hung, The Journal of Physical Chemistry C, (33).Copyright (2011) American Chemical Society. 24

32 double-layer capacitors (EDLCs),[12, 13, 87-93] and in dye-sensitized solar cells (DSSCs) for conversion of solar energy.[93-95] Furthermore, ILs confined inside sol-gels (ionogels) have potential applications as electrolyte membranes and in optics, catalysis and biocatalysis, drug delivery and sensing and biosensing.[10, 96-98] In addition, very recently nanoparticles (NPs) based on frozen ILs with interesting magnetic[26, 27] and optically-active (fluorescent)[28, ] properties were synthesized. As further tunability of the magnetic and optical properties can be achieved by introducing shape anisotropy,[29-37, 102] the Warner group has also synthesized 1D-nanomaterials (e.g., nanorods, nanotubes and nanowires) based on organic salts,[101] by introducing these compounds inside hard templates with cylindrical nanopores, e.g., anodized alumina membranes. Nanomaterials based on organic salts hold enormous promise, because they share the inherent functionality and highly tunable properties of ILs,[7, 86] and can be prepared via simple procedures.[26-28, ] Furthermore, nanomaterials based on organic salts can be prepared from FDA-approved compounds,[38-41] and thus could be free of the toxicity effects that other nanomaterials may have.[ ] Possible applications of these organic salts-based nanomaterials are envisioned in fields as diverse as optoelectronics, photovoltaics, separations, analytical and biomedical. The macroscopic performance of IL-based EDLCs and DSSCs, as well as the macroscopic properties of ionogels and IL-based 1D-nanomaterials, are determined by the structural and dynamical properties of the IL confined inside the nanopores. Nevertheless, a fundamental understanding of the structural and dynamical properties of ILs inside nanopores is still lacking. Such knowledge is crucial for the rational design of EDLCs, DSSCs, ionogels and IL-based nanomaterials with optimal properties. Molecular simulations, in close interplay with 25

33 experiments, are well positioned to provide such fundamental understanding and advance those technologies well beyond their current state of the art. Several studies have reported simulations of ILs and molten salts adsorbed on surfaces such as rutile, graphite, quartz and sapphire.[51-55, ] A few simulation reports have been published on ILs confined inside nanopores with slit-like,[52, 56-58, 61, 113, ] cylindrical[62-64, 113, 122] and complex pore geometries.[123] In a recent paper,[122] we have studied the structural and dynamical properties of the IL [BMIM + ][PF - 6 ] confined inside multiwalled carbon nanotubes of diameters ranging from 1.5 to 4.7 nm. In this study, we found that the dynamics of the confined cations and anions are heterogeneous and depend strongly on their distance to the pore walls; for example, the cations and anions in the center of the pore had faster dynamics than those close to the pore walls. However, in that study we used the force field proposed by Lopes et al.,[66-68] which has important limitations in reproducing experimental values of the transport properties of bulk ILs. For example, the diffusion coefficients of bulk [BMIM + ][PF - 6 ], as predicted by the force field of Lopes et al., are on average about 6 times smaller than reported experimental values in the temperature range between 300 K and 450 K.[124, 125] Although the absolute values of the dynamics of the confined IL as estimated in our previous study[122] are likely to be off, we expect that the trends observed for the dynamics of the confined IL as a function of pore size and pore loading, as well as the heterogeneities observed in the dynamics of the confined ions as a function of their distance to the pore walls, are still going to be consistent with the trends observed in a similar real system. The aim of our present work is to study in detail the dynamical properties of the same IL, [BMIM + ][PF - 6 ], when confined inside a much simpler pore geometry, namely an uncharged slitlike graphitic pore. We have modeled the IL using the non-polarizable force field developed by 26

34 Bhargava and Balasubramanian,[124] which can give accurate predictions of the structure and dynamics of bulk [BMIM + ][PF - 6 ]. Furthermore, this force field was used recently to study heterogeneity in the dynamics of [BMIM + ][PF - 6 ] in the bulk.[87] In addition to mean squared displacements (MSDs), we also report results for the radial distribution function, self-part of the time-dependent van Hove correlation function G s (r,t), and the incoherent intermediate scattering function F s (q,t). These properties have been used to detect and characterize dynamical heterogeneities in previous studies of bulk ILs (see ref. [78] for a recent review) and supercooled Lennard-Jones (LJ) liquids in a slit pore.[85] Heterogeneities in the dynamics are explained in terms of structural properties, namely local density profiles and radial distribution functions. Previous simulation studies of ILs and molten salts confined in slit pores [52, 56-58, 61, 113, ] have not placed a special focus on dynamical heterogeneities. 3.2 Computational Details Constant volume and temperature (NVT) molecular dynamics simulations have been performed using the GROMACS MD package.[65] We considered a slit-like graphitic pore of size H = 5.4 nm, where the two pore walls are formed by three graphene layers of area (5.70 nm 5.61 nm) fixed in space (Figure 3.1). The carbon atoms in the graphite sheets were modeled as LJ spheres with σ c = nm and ε c /k = 28.0 K. Regarding the force field for the IL 1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM + ][PF - 6 ], in our previous study[122] we used the model proposed by Lopes et al. [66-68] to study the structural and the dynamical properties of the IL inside carbon nanotubes. However, this force field has important limitations in reproducing experimental values of the transport properties of bulk ILs; for example, the diffusion coefficients of the cation and anion of [BMIM + ][PF - 6 ] as predicted by the force field of Lopes et al. are on average about 6 times 27

35 smaller than reported experimental values in the temperature range between 300 K and 450 K.[124, 125] In the present work, the IL was modeled using the non-polarizable force field developed by Bhargava and Balasubramanian.[124] In this model, charges on the cations and anions are chosen to be 0.8e and -0.8e respectively (see refs. [124] and [78] for a discussion of the reasons behind this choice of net charges for the ions). Bhargava and Balasubramanian have reported simulated density values within 1.4% of the experimental values, and diffusion coefficients that are within 20% of experimental values in the temperature range between 300 K and 500 K. Prior to studying confined system, we carried out preliminary MD simulations of bulk [BMIM + ][PF - 6 ] in the NVT and NPT ensembles. From these simulations we obtained a value of 1.38 g/cm 3 for the bulk liquid density at 25 C; diffusion coefficients for the cations and anions were found to be m 2 s -1 and m 2 s -1 respectively. Our simulated values are comparable to results from previous simulations, and to reported experimental values.[87, 124] In our simulations, the slit pore was filled with a varying number of ion pairs so that our systems had a density similar to the bulk density at the temperatures of interest. Therefore, the number of ion pairs we used were 486, 470 and 455 at 300 K, 350 K and 400 K, so that the confined IL had a density of 1.37 g/cm 3, 1.33 g/cm 3 and 1.28 g/cm 3 at these temperatures. The temperature range considered in our simulations ( K) is well above the experimental glass transition temperature of K reported for [BMIM + ][PF - 6 ].[126] The density for the V xy z confined IL was calculated using a volume min c. Our results for the mass density profile (Figure 1) indicate that the density of the confined ions reach a value of zero at z ~ c 2. We have also run simulations at different temperatures keeping constant the number of ion pairs, 28

36 and the results were very similar to those obtained when our confined IL had a density similar to the bulk value at the temperatures of interest. In all our simulations, the Lennard-Jones interactions were cut off at 1.2 nm, and the long range coulomb interactions were handled by the particle-mesh Ewald (PME) method [73] with a cutoff of 1.0 nm and a grid spacing of 0.1 nm. Periodic boundary conditions were applied in the x, y, and z directions. The ILs/graphite sheet system was kept in vacuum in the center of the orthorhombic box in such a way that two sides of the box were equal to the sides of the graphite sheets (5.70 nm 5.61 nm), and the length of the other one side of the box (10.0 nm) was long enough to avoid any artificial effect caused by the periodic boundary conditions. The improved velocity-rescaling algorithm recently proposed by Parrinello et al.[74, 75] was used to mimic weak coupling at different temperatures with a coupling constant of 0.1 ps. We first minimized the energy of our initial configuration using the steepest descent method. Afterwards, we ran MD simulation using a time step of 0.5 fs. The systems were melted at 600 K for 2 ns, and then annealed from 600 to 300 K in stages: 200 ps at 550 K, 300 ps at 500 K, 300 ps at 450 K, 200 ps at 400 K, and 500 ps at 350 K. Afterwards, our systems were equilibrated and the properties of interest were sampled for 6.5 ns at 300 K. In order to make sure that our systems were properly equilibrated, apart from monitoring standard variables (e.g., energy), we also examined the mean squared displacement (MSD) and confirmed that the confined IL has reached the diffusive regime (Figures 3.3 and 3.4). In addition, and as we did in our previous study,[122] we also monitored several single-particle time correlation functions for the cations (namely, the correlation functions for the velocity of the center of mass of the cation, and the reorientation of the cation around different rotation axes). These results (not shown for 29

37 brevity) indicate that our simulation times are long enough to decorrelate the reorientational motion of the ring of the cations around different rotation axes. After finishing this first production run, we took the final configuration of our system and repeated the above steps (melting, annealing, equilibration and averaging) at least one additional time. Our reported results were averaged over at least two independent realizations of the same system. Such a procedure was adopted in an attempt to overcome the difficulties posed by the slow dynamics of ILs, which are likely to be exacerbated when these compounds are confined inside a nm-sized slit pore. A similar procedure was used to carry out simulations of the confined IL at 350 and 400 K; likewise, we also performed simulations of the bulk IL at 300, 350 and 400 K using a similar procedure. A representative simulation snapshot of the IL confined at 300 K is depicted in Figure Results and Discussion Prior to the study of the dynamics of the confined system, we measured the mass density profile of the ions in the IL for different temperatures ranging from 300 to 400 K (Figure 3.1). Layering behavior was observed at all temperatures, with two density peaks close to each of the graphite sheets and a region in the center of the pore where the IL has a density similar to the bulk density (Figure 3.1). It is also observed that the positions of the peaks do not change appreciably with variations in the temperature; however, the heights of the peaks decrease as the temperature increases. According to our previous simulation study of ILs confined in cylindrical nanopores,[122] the dynamical properties of the ions will depend strongly on their position from the pore walls. As a result, and based on the density profiles shown in Figure 3.1, we split the ions into three different layers/regions according to their distance from the pore walls: the first layers (closest to the pore walls), the second layers and the center regions. We monitored the 30

38 Mass Density (Kg/m 3 ) coordinates of the ions as a function of time during the sampling period from the simulation trajectories, and we did not observe significant exchange of ions within the different layers/regions. The fact that ions remain in their layers/regions during the sampling period allowed us to accurately sample and report the properties of each layer/region of the confined IL, as indicated below K 350 K 400 K Z (nm) Figure 3.1 Left panel: Representative simulation snapshot of the IL [BMIM + ][PF 6 - ] confined inside a slit-like graphitic pore of size H = 5.4 nm at 300 K. Cations and anions are depicted in purple and green. The density of the confined IL is similar to that of the bulk IL at the same temperature. Right panel: Mass density profile of the IL along the z direction at different temperatures. 31

39 MSD (nm 2 ) MSD (nm 2 ) 10 First layers 10 Center region Time (ps) Time (ps) Figure 3.2 Parallel (x- and y-) and z-component of the mean square displacements of the ions in the first layers (left panel) and in the center region of the pore (right panel) at 400 and 300 K. Solid and dashed lines represent cations and anions. Red and purple lines depict the parallel and z-components of the MSD at 400 K; black and green lines represent the parallel and z- components of the MSD at 300 K Mean Squared Displacement (MSD) and Self-diffusion Coefficients In Figure 3.2, we show a semi-log plot of the MSDs of the ions in the first layers and in the center region for 300 K and 400 K. Depicted in this figure are the parallel and the z- component of the MSD of both cations and anions. Results for the second layers are in-between those for the first layers and the center region, and thus are not shown. As expected, the dynamics of the ions increase with increase in temperature. It is also observed that cations move faster than anions independent of their distance from the pore walls. The dynamics of the ions in the z-direction are slower as compared to those in the parallel direction due to the presence of the 32

40 MSD (nm 2 ) MSD (nm 2 ) Cation, first layers Cation, second layers Cation, center region Diffusive regime Cation,bulk Sub-Diffusive regime Ballistic regime Time (ps) Anion, first layers Anion, second layers Anion, center region Diffusive regime 0.01 Anion, bulk Sub-Diffusive regime Ballistic regime Time (ps) Figure 3.3 Parallel component of the mean squared displacement for the cations (top panel) and anions (bottom panel) at 300 K, as a function of their distance from the pore walls. The continuous blue lines depict the slopes expected for the ballistic and diffusive regimes. 33

41 walls and confinement effects. As expected, the dynamics of the confined IL become faster with an increase in the temperature. In Figure 3.3 we show a log-log plot of the parallel component of the MSD of the confined cations and anions in the different layers/regions at 300 K, and compare against the simulated MSD for the bulk IL at the same temperature. The dynamics of the confined ions are heterogeneous: the slowest dynamics are observed for the ions in the first layers (closest to the pore walls), and the dynamics of the ions in the center of the pore are very similar to those observed for the ions in the bulk IL. These results agree with our previous findings for an IL confined in a cylindrical pore,[122] as well as with previous results for a supercooled LJ liquid confined in a slit pore with rough walls.[85] All MSDs exhibit the three dynamic regimes (ballistic, sub-diffusive and diffusive or Fickian).[85, 127] The ballistic regime occurs in the first few picoseconds when the molecules have not interacted with other neighbors, and thus the dynamics are faster than in the other regimes, MSD t 2.[85, 127] After the ballistic regime, a plateau is observed and the system is in the sub-diffusive regime. In this regime the dynamics slow down due to the ions becoming temporarily trapped by a cage formed by their neighbors. The time window in which this plateau is observed is slightly larger for the ions close to the pore walls, and becomes shorter for the ions in the center of the pore and for the ions in the bulk IL (Figure 3.3). Eventually, particles escape the cage formed by their neighbors, the MSDs become proportional to t and the dynamics reach the diffusive regime. An interesting observation is that the bulk and the ions in the center of the pore reach the diffusive regime faster than the ions closer to the pore walls; the ions in the first layers (closest to the pore walls) spend the longest time in the sub-diffusive regime. As temperature increases, the plateau corresponding to the sub-diffusive regime becomes weaker and the ions tend to reach the diffusive regime faster, as can be observed in Figure 3.4. In this figure we depict the variations in the overall MSD for 34

42 MSD (nm 2 ) MSD (nm 2 ) K 350K 300K Cation, center region Diffusive regime 0.01 Sub-Diffusive regime Ballistic regime Time (ps) K 350K 300K Anion, center region Diffusive regime 0.01 Sub-Diffusive regime Ballistic regime Time (ps) Figure 3.4 Overall mean square displacement of the cations (top panel) and anions (bottom panel) in the center region of the pore at 300 K, 350 K and 400 K. The continuous blue lines depict the slopes expected for the ballistic and diffusive regimes. 35

43 the ions in the center region of the pore as the temperature changes. Similar trends with temperature are observed for the ions in the first and second layers (results not shown). The self-diffusion coefficients of the ions are obtained from the MSDs in the diffusive regime by using the appropriate Einstein relation.[128, 129] The obtained values of the diffusion coefficient of the confined ions in the parallel direction are compared with the bulk values at 300 K, 350 K and 400 K and are reported in Table 3.1. Only for comparison purposes, we also show in this table the self-diffusion coefficients in the parallel direction that would be obtained for the ions in the different layers/regions of the pore. Results from this table indicate that at all temperatures, the self-diffusivities of the confined ions in the parallel direction are always smaller than the bulk values (or at most equal, within the reported uncertainties). In addition, and consistent with our MSD results (Figures ), the ions close to the graphite have the slowest dynamics and the ions in the center of the pore have dynamics similar to those in the bulk IL. Table 3.1 Diffusion coefficient of the confined ions in the parallel direction at different temperatures. Bulk results obtained from simulation and experiment (parentheses) are taken from Bhargava and Balasubramanian.[124] Cation, Ds (m 2 s -1 ) T [K] first layers second layers center region overall Bulk (+/-0.8) 6.4 (+/-0.1) 7.2 (+/-0.5) 6.1 (+/-0.8) 6.7 (8.0) (+/-1.2) 23.3 (+/-0.7) 48.6 (+/-1.2) 36.1 (+/-0.8) 77.6 (64.2) (+/-18.9) (+/-2.1) (+/-2.6) (+/-3.4) (209.2) Anion, Ds (m 2 s -1 ) T [K] first layers second layers center region overall Bulk (+/-0.8) 3.6 (+/-0.2) 4.7 (+/-0.7) 4.0 (+/-0.6) 4.7 (5.9) (+/-2.7) 13.0 (+/-1.8) 32.5 (+/-0.4) 23.8 (+/-3.3) 52.7 (51.4) (+/-1.7) 76.3 (+/-10.5) (+/-3.1) 94.4 (+/-1.5) (178.6) 36

44 Self-part of the Van Hove Correlation Function The results presented in the previous section indicate that the dynamics of the confined ions are heterogeneous and depend on their distance to the pore walls. Further insights of these dynamical heterogeneities can be obtained by studying the time-dependence of the self part of the van Hove correlation function of the ions.[130, 131] G s (r,t) represents the probability of finding a particle at time t a distance r away from the place it was at t = 0. Figure 3.5 represents the G s (r,t) of the center of mass of the confined cations and anions in the different layers/regions of the pore as a function of r at 300 K and three different characteristic times. These results are compared against the G s (r,t) of the bulk ions at the same temperature. At time t = 0.10 ps, the ions in all regions of the pore and in the bulk system are in the ballistic regime (Figure 3.3). Therefore, G s (r,t) decays to zero rapidly at a very short distance, and G s (r,t) is very similar for all confined ions independently of their distance from the pore walls. G s (r,t) for the bulk ions is also similar to those observed for the confined ions in all layers/regions; slightly larger differences are seen for the cations than for the anions, but this fact is consistent with the larger differences observed between the MSDs of the cations in bulk and in confinement, as compared to the bulk and confined anions (Figure 3.3). For the intermediate time t =10 ps, when the bulk and confined systems are in the subdiffusive regime (Figure 3.3), we observe different behaviors for G s (r,t) for the confined ions depending on their distance from the graphitic walls. At this time, G s (r,t) for the anions in the center of the pore have its maximum at r ~ 0.06 nm. In contrast, the anions in the first layers (closest to the pore walls) have a G s (r,t) with a maximum at r ~ nm, which highlights again that the dynamics of the confined anions depend on their distance to the pore walls. The short distances at which the maxima are observed in G s (r,t), when coupled with the results for the 37

45 G s (r,t) G s (r,t) G s (r,t) G s (r,t) G s (r,t) G s (r,t) t=0.1ps,t= 300 K Cation, bulk Cation, first layers Cation, second layers Cation, center region r (nm) t=0.1ps,t= 300 K Anion, bulk Anion, first layers Anion, second layers Anion, center region r (nm) t=10 ps, T= 300 K t=10 ps, T= 300 K r (nm) r (nm) 10 8 t=2500 ps,t= 300 K 10 8 t=2500 ps,t= 300 K r (nm) r (nm) Figure 3.5 Time dependence of the self part of the van Hove correlation function G s (r,t) for the confined cations (left) and anions (right) in the different layers/regions of the pore at 300 K. Results of G s (r,t) for the bulk cations and anions at the same temperature are also presented. 38

46 MSDs (Figure 3.4) suggests that at t = 10 ps the anions have not yet escaped the initial cage formed by their neighbors at t = 0. Another observation is that G s (r,t) for the anions in the second layers has properties in between those observed for G s (r,t) for the anions in the center of the pore and the first layers. A surprising observation is that, at this time, G s (r,t) for the anions in the second layers is very similar to the G s (r,t) of the bulk anions. The qualitative trends described for the anions is also observed in the G s (r,t) of the cations, with differences observed in the specific values of G s (r,t) and the positions of the peaks (since the cations move faster than the anions). At t = 2500 ps, G s (r,t) for the bulk ions becomes similar to G s (r,t) for the ions in the center of the pore. However, G s (r,t) for the ions in the layers near the pore walls are significantly different from those of the ions in the center of the pore or the bulk system, highlighting the fact that the ions closer to the pore walls exhibit dynamics that are much slower than those of the ions in the center of the pore or in a bulk system at the same temperature Incoherent Intermediate Scattering Function The space Fourier transform of G s (r,t), which is better known as the incoherent or selfintermediate scattering function, F s (q,t) can be measured experimentally, for example using inelastic neutron scattering. In Figure 3.6 we show F s (q,t) for the center of the mass of the ions as a function of time, for the bulk system at 300 K and for the confined ions in the different layers/regions of the pore, and at different wave vectors (in the case of the confined system, the wave vectors were parallel to the graphitic walls). F s (q,t) for the bulk system agrees with simulated values reported previously,[87] and shows the features typically observed in supercooled liquids and other ILs.[78, 84, 85, 87, ] First, at very short timescales, F s (q,t) F q, t 1 t 2 can be described by s s 2, where Ω s is the microscopic frequency 39

47 (a) First layers (b) Second layers (c) Center region (d) Bulk Figure 3.6 Incoherent intermediate scattering function F s (q,t) of the center of the mass of the ions with time (log scale) at 300 K in the different layers/regions of the pore. The scattering functions are calculated at the wave vectors q = 5.0, 10.0, 15.0, 20.0, 25.0 and 30.0 nm -1 (shown from top to bottom). (a) First layers (b) second layers (c) center of the pore and (d) bulk. Cations and anions are represented by solid and dashed lines. k T 1 2 defined as s q B.[135] This corresponds to the ballistic regime, when ions are free to move. Following the ballistic motion of the ions at short time, F s (q,t) decays to a plateau, 40

48 which corresponds to the cage effect described before in which ions are temporarily trapped in a cage formed by their neighbors. The time window in which F s (q,t) is in this plateau represents the β-relaxation regime, in which the ions diffuse only inside the cage formed by their neighbors. Afterwards, at longer timescales, F s (q,t) falls below the plateau, which corresponds to a second relaxation process (α-relaxation) in which the ions escape the cage and reach the diffusive regime. From Figure 3.6, it is observed that, independently of wave vector, the F s (q,t) for the cations decays to zero faster than that of the anions in the bulk system and for all layers/regions of the pore. Such a result indicates that cations relax faster than the anions. In addition, the plateau corresponding to the β-relaxation regime is more noticeable for certain values of the wave vector (Figure 6). Furthermore, results for F s (q,t) for the confined ions in the center of the pore are similar to those observed for the bulk IL. All these observations are consistent with the MSD results reported in Figure 3.3. Figure 3.7 shows F s (q,t) as a function of time at 350 K for the confined ions in the different layers/regions of the pore. The scattering functions are calculated at the wave vector q = 15.0 nm -1 (maximum of the structure factor for the bulk IL). For this wave vector, the correlation function decays to zero within the length of the MD trajectory (Figure 3.6), which suggests that the run is long enough to equilibrate the system.[136] From Figure 3.7, the ions in the center regions of the pore have a F s (q,t) that decays faster as compared to the layers of ions closer to the pore walls, which is consistent to the results presented in Figures 3.3 and 3.5. Furthermore, the results for the center region and for the bulk system are very similar. In Figure 3.8 we show the time dependence of F s (q,t) of the confined ions in the second layers at different temperatures (results for the other layers/regions exhibit similar trends and are not shown for brevity). It is observed that as temperature decreases, the length of the plateau becomes longer; afterwards, 41

49 F s (q,t) decays very fast with increase in the temperature, which indicates that the confined ions reach the diffusive regime faster as temperature increases, in agreement with the results presented in Figures 3.2 and 3.4. Figure 3.7 Comparison of the incoherent intermediate scattering function F s (q,t) of the confined cation (left panel) and anion (right panel) with time (log scale) at 350 K for the different layers/regions of the pore. The scattering functions are calculated at the wave vector q = 15.0 nm -1 (maximum of the structure factor). Results of F s (q,t) for the bulk cations and anions at the same temperature are also presented. 42

50 Figure 3.8 Incoherent intermediate scattering function F s (q,t) of the center of the mass of cation (left panel) and anion (right panel) with time (log scale) for the second layers at different temperatures. The scattering functions are calculated at the wave vector q =15.0 nm Relaxation Times To quantify the times associated with the β- and α-relaxation processes, we fitted F s (q,t) to a modified Kohlrausch-Williams-Watts (KWW) function at the wave vector q =15 nm -1, following the methodology used by Sarangi et al.,[87] who modeled bulk [BMIM + ][PF - 6 ] using the same force field used by us. In particular we used the following equation:[87, 134] F s t t exp q, t Aexp 1 A (3.1) Where A and (1 A) represent the amplitudes of the β- and α-relaxation processes, and β is the stretching parameter of the α-relaxation. Following Sarangi et al.,[87] the time parameter associated with the α-relaxation process, <τ α >, was obtained using the following relation: 43

51 <τ α > or τ β (ps) β 1 (3.2) In Figure B-1 (Appendix B) we show the original F s (q,t) data and the fitted equation (3.1) for the cations in the center regions of the pore at 350 K. The fitted parameters, standard errors, R 2 values and other relevant statistical parameters are also presented in this figure. In the Cation First layers Second layers Center region Anion First layers Second layers Center region z (nm) Figure 3.9 Time associated with α and β relaxation along the z direction at 350 K. The values are calculated at the wave vector q = 15.0 nm -1 (maximum of the structure factor). The top and bottom curves denote values for <τ α > and τ β respectively. Inset: variation of the KWW stretching parameter β of the α-relaxation regime. Dotted lines are drawn as a guide to the eye. 44

52 case we obtained an excellent value for R 2 = Similar fit qualities were obtained for all of our results, which are summarized in Figures All numerical fits were performed using the OriginPro 8.5 software. In Figure 3.9 we present the time parameters associated with the α- and β-relaxation processes, <τ α > and τ β. These time parameters are determined for the confined cations and anions in the different layers/regions of the pore at 350 K. The time parameters <τ α > and τ β for the confined ions exhibit a decreasing trend as we move from a position close to the pore walls toward the center of the pore. This trend is consistent with results observed for a supercooled Lennard-Jones fluid confined in a slit pore.[85] The fitted time parameters <τ α > and τ β for the confined cations and anions are very similar in magnitude to those reported by Sarangi et al.[87] in their simulation study for bulk [BMIM + ][PF - 6 ]. The relaxation times for the confined anions are slightly larger than those of the cations in all regions of the pore, which is consistent with the results reported in Figs In contrast, Sarangi et al.[87] report τ β values that are slightly larger for the cation, and <τ α > values that are larger for the anion. These results suggest that in the bulk IL, at short timescales the anion relaxes slightly faster than the cation, but the trend reverses at longer timescales. In the inset of Figure 3.9 we show the variation of β, the stretching parameter of the α-relaxation process for the confined ions in the different layers/regions of the pore. In analogy to <τ α > and τ β, the stretching parameter β decreases as we move towards the center of the pore. In Figure 3.10 we show the effect of temperature on the relaxation of the confined cations and anions in the second layers. Results for the other layers/regions of the pore follow similar trends and are not reported here for brevity. As expected, increases in the temperature causes a reduction in both the α- and β-relaxation times <τ α > and τ β. The inset in the figure 3.10 shows the variation of the KWW stretching parameter β of the relaxation regime for the ions. It is observed 45

53 <τ α > or τ β (ps) β that the value of β increase with increase in temperature. These findings are consistent with what has been reported by Sarangi et al. for the bulk IL.[87] In Figure 3.11 we show the dependence of <τ α > and τ β with the wave vectors, for the confined ions in the center of the pore. It is observed 10, , Cation Anion Temperature (K) Figure 3.10 Time associated with α and β relaxation for the second layers at different temperature along the z direction. The values are calculated at the wave vector q = 15.0 nm -1. At every point, higher and lower values are <τ α > and τ β respectively. Inset: variation of the KWW stretching parameter β of the α relaxation regime. Dotted lines are drawn as a guide to the eye. 46

54 <τ α > or τ β (ps) β 1, Cation Anion q (nm -1 ) Figure 3.11 Time associated with α and β relaxation for the center region along the z direction at 300 K. The values are calculated at the wave vectors q = 10.0, 15.0, 20.0, 25.0 and 30.0 nm -1. At every point, higher and lower values are <τ α > and τ β respectively. Inset: variation of the KWW stretching parameter β of the α relaxation regime. Dotted lines are drawn as a guide to the eye. that both relaxation times decrease with an increase in the wave vectors. τ β shows a much weaker dependence than <τ α > similar to what has been found in the bulk.[87] The inset of Figure 3.10 shows the variation of the KWW stretching parameter β of the α-relaxation regime for the confined ions in the center of the pore. β decreases with an increase in the wave vectors, in analogy to what was found for the bulk IL. 47

55 Radial Distribution Functions Insights on the structure of the confined IL can be obtained from analysis of relevant radial distribution functions g(r). In Figure 3.12 we have depicted the g(r) for cation-cation, anion-anion and cation-anion for the IL in the different layers/regions of the slit pore, and for the bulk IL at 300 K. To obtain these g(r) we used the N atom bonded to the butyl group in the cation, and the P atom in the anion. All radial distribution functions reported in Figure 3.12 were calculated in 3D. Strictly speaking, the first and second layers of IL inside the pore are not 2D systems, because the density profiles of Figure 3.1 show that these layers have non-negligible thickness (rather, they are quasi-2d systems). The IL in the center regions of the pore is a 3D system; however, it exhibits a slab geometry (i.e., its size in the z-direction is smaller than its size in the x- and y-directions). Because we are carrying out a conventional 3D g(r) calculation for the IL in these quasi-2d and slab systems, we observe some distortions in the height of the peaks, and the g(r) of the confined IL do not go to unity at large distances (Figure 3.12). These distortions are examples of excluded volume effects.[ ] These excluded volume effects affect mainly the height of the peaks in g(r) and the value of g(r) at large distances [for example, compare Figures 5-7 in ref. [137], which show as-measured g(r) for water inside Vycor glass nanopores, against Figures 3-5 in ref. [138], which show the same g(r) corrected for excluded volume effects]. Excluded volume effects do not change the location of the peaks of g(r); furthermore, these effects do not produce additional, artificial peaks or features to arise in g(r). In Figure 3.12, we are mostly interested in comparing the position of the peaks/features of g(r) between the bulk ions and the confined ions in the different layers/regions, rather than in comparing the height of the peaks/features. 48

56 g (r) g (r) g (r) K Cat-Cat (first layers) Cat-Cat (second layers) Cat-Cat (center region) Cat-Cat (bulk) Distance (nm) K An-An (first layers) An-An (second layers) 6 An-An (center region) 4 An-An (bulk) Distance (nm) K Cat-An (first layers) Cat-An (second layers) Cat-An (center region) Cat-An (bulk) Distance (nm) Figure 3.12 Radial distribution function g(r) of cation-cation (top panel), anion-anion (center panel) and cation-anion (bottom panel) for different layers/regions at T=300 K. Results of the bulk ILs at the same temperature are also presented. 49

57 From Figure 3.12, it is apparent that the cation-cation, anion-anion and cation-anion g(r) for the confined ions in the center of the pore and for the bulk ions are very similar, suggesting that the ions in the center of the pore have a structure that closely resembles that of the bulk IL. In contrast, the g(r) for the confined ions in the first layers exhibit marked differences with respect to their counterparts for the bulk IL. In particular, more correlation at longer distances is observed for the confined ions in the first layers as compared to the ions in the bulk IL; also, the first peak in the cation-cation and anion-anion g(r) are observed at somewhat longer values of r as compared to those in the bulk IL. The g(r) for the confined ions in the second layers exhibit features that are in between those observed in the g(r) for the bulk ions and for the ions in the first layer. The results shown in Figure 3.12 suggest that the confined ions in the first and second layers and in the center of the pore have marked structural differences. Such structural heterogeneity is likely linked to the dynamical heterogeneity described by the results shown before, in analogy to what was observed for bulk ILs.[84, 87] 3.4. Concluding Remarks We have studied the dynamics of the IL [BMIM + ][PF - 6 ] when confined inside an uncharged slit-like graphitic nanopore of width H = 5.4 nm, in the temperature range K. We have modeled the IL using the non-polarizable force field of Bhargava and Balasubramanian,[124] which has been shown to give accurate predictions for the structural and dynamical properties of bulk [BMIM + ][PF - 6 ]. The same force field was used recently to study heterogeneity in the dynamics of [BMIM + ][PF - 6 ] in the bulk.[87] For the particular pore size considered by us, the local density profile (Figure 3.1) for the confined cations and anions show three distinct regions: a first layer closest to the pore walls, a second layer and a center region. Our results for the MSDs, self-diffusivities, self-part of the van Hove correlation functions, and 50

58 incoherent intermediate scattering functions for the confined ions in the different regions of the pore indicate that the dynamics of the confined IL are highly heterogeneous, and depend strongly on the distance of the ions with the pore walls. In particular, the ions in the center regions of the pore have dynamics and relaxation times that are very similar to those observed in a bulk IL at the same temperature. In contrast, the dynamics slow down appreciably as the ions get closer to the pore walls, and their relaxation times increase markedly. Ions closer to the pore walls spend a significantly larger amount of time inside a cage formed by their neighbors ( cage regime ), as compared to their counterparts in the center of the pore, before finally reaching the diffusive (Fickian) regime. The diffusivities in the parallel (x, y) direction for the confined ions in the different layers/regions of the pore are found to be always smaller (or at most equal, within the numerical uncertainties) than the diffusivities of the bulk ions at the same temperature. The overall diffusivities in the parallel (x, y) direction for the confined ions are found to be always smaller than the bulk diffusivities. Inspection of the radial distribution functions g(r) suggests that these dynamical heterogeneities are linked to structural features. Although the g(r) of the ions in the center of the pore are similar to those of the bulk IL, marked differences were observed between these g(r) and those of the confined ions in the first and second layers. We also studied the effect of temperature on the dynamics, observing that in analogy to bulk systems, an increase in temperature cause the confined IL to have faster dynamics and smaller relaxation times. It is interesting to compare the simulation results presented in this paper with those obtained for the same IL (with a different force field, however) confined inside a cylindrical multi-walled carbon nanotube (MWCNT).[122] The pore diameters considered in that study (up to D = 3.7 nm) were significant smaller than the pore size considered here (H = 5.4 nm). 51

59 Significant layering was observed for the IL inside the two different pore geometries. Likewise, in both pore geometries, in general the cations exhibited faster dynamics than anions, and the dynamics of the ions decrease monotonically as we go from the center of the pore to the IL layer near the pore walls. However, evidence of complex dynamics was observed for the IL inside a cylindrical pore. MSD results observed for the IL inside a MWCNT of D = 3.0 nm (for which three layers of ions are observed) indicate that in the second layer, the MSD of the cations and anions are similar in magnitude; furthermore, the anions in this second layer have dynamics that are similar to those observed for the anions in the center of the pore (see Figure 9 in ref. [122]). Evidence of similar complex dynamics was not observed for the same IL inside a slit pore in this study. It is also interesting to note that the dynamic properties of the confined IL in the center region of the pore (which is only ~1.25 nm away from the walls) are very similar to bulk-like. Similar results have been observed experimentally in other glass-forming systems inside nanopores or near surfaces, including polymer thin films[143] and organic glass-formers.[49, 144] 52

60 CHAPTER 4 MOLECULAR DYNAMIC SIMULATIONS OF IL [EMIM + ][TFMSI - ] CONFINED INSIDE RUTILE (110) NANOPORE: EFFECT OF PORE LOADING ON STRUCTURAL AND DYNAMICAL PROPERTIES In this chapter, the structural and dynamical properties of the IL [EMIM + ][TFMSI - ] confined inside a rutile (110) pore are investigated by means of classical molecular dynamics simulations. The simulations are carried out at different pore loading ranging from 0.1ρ bulk to ρ bulk with the pore size (H) of 5.2 nm at 333 K. Various equilibrium and time dependent properties such as density profiles, radial density profiles (RDF), orientation, auto-correlation functions and mean square displacements (MSDs) are calculated and the effect of the confinement on the above properties are studied. We contrast these results against those obtained by us for the same IL confined inside a slit graphitic nanopore of the same width. The rest of this chapter is structured as follows. Section 4.1 is the introduction. Section 4.2 contains a description of our computational models and methods. In Section 4.3 we present results and discussion of the structural and dynamic properties of the confined ILs, and in Section 4.4 we summarize our main findings. 4.1 Introduction Ionic liquids (ILs) are molten salts that are usually composed of bulky organic cations and smaller organic or inorganic anions. Due to their bulky structure and loose packing IL remain liquid at or near room temperature. ILs are also considered green chemicals for properties such as low vapor pressure (non-volatile), nonflammability, low viscosities, high conductivity, excellent thermal and chemical stabilities. These unique properties make them potential candidates for the replacement of the conventional chemicals in diverse fields such as green solvents for the synthesis [6, 145, 146], in CO 2 sequestration [ ], in extraction [156, 157] and as electrolytes in electrochemical double layer capacitors (EDLCs) [ ] and dye 53

61 sensitized solar cells (DSSCs) [20, 22-25, ]. The latter is a class of solar cell based on a semiconductor formed between a photo-sensitized anode and an electrolyte. A schematic diagram of a DSSC is given in Figure 4.1. The major problems with the conventional electrolytes in DSSCs are that they catch fire, are explosive and evaporate with time [20-22]. This not only undermines the performance of the device, but also causes environmental hazards. Current research suggests that ILs with their unique properties have potential to tackle these problems and improve the performance of DSSCs [22-25]. It is possible to synthesize ILs with the desired properties by selecting the right combination of cation and anion while keeping in mind that the properties of ILs strongly depend on the structure of the ions. Previous experimental [ ] and simulation studies [52, 56-64, 113, , ] have helped in understanding these complex ions under confinements; however the effect of the structure and dynamics of ILs on the performance of the device is not well understood yet. Electrodes are the other main components of the DSSCs; the characteristics of the electrodes determine the overall performance and life of these devices. Some of the semiconductor materials that have potential as an anode are TiO 2, ZnO and CuO [20-22, ]. Among these TiO 2 is one of the most extensively studied materials over the last few decades due to its unique chemical, electrical, optical, and photochemical properties [184, ]. The ability to harness the solar energy can be further improved by the choice of electrode material and IL electrolyte. Many IL/solid interfaces have been studied [175, 176, 178, 180, 181, 183, ]; however it is not possible to test all possibilities experimentally [ , , 205, 206]. Computer simulations enable us to have atomic-level understanding at the IL/solid interface. A few simulation studies have been published on ILs near TiO 2 surface [180, 208]. In these prior studies only structural properties and preferential orientation of the ILs 54

62 [BMIM + ][PF - 6 ] and [BMIM + ][NO - 3 ] have been discussed. The main objective of this work is to study in detail the structural as well as dynamical properties of the IL [EMIM + ][TFMSI - ] near TiO 2 electrode. In the present study we considered the interaction between the IL [EMIM + ][TFMSI - ] and the rutile (110) surface at different pore loadings. In this work molecular dynamics simulations are performed with the goal of predicting and understanding the behavior of the IL [EMIM + ][TFMSI - ] as an electrolyte near TiO 2 electrodes. Achieving such an objective is crucial in developing new electrolytes by choosing the most appropriate cation-anion combination for applications in DSSCs and other devices such as fuel cells and EDLCs. The rest of this paper is structured as follows. Section 4.2 contains a description of our computational models and methods. In section 4.3, we present results and a discussion of the structural and dynamic properties of the confined ILs, and in section 4.4, we summarize our main findings. 4.2 Computational Details The ionic liquid [EMIM + ][TFMSI - ] (Figure 4.2) was confined inside two parallel (110) rutile TiO 2 walls with a pore size of H = 5.2 nm and simulations were performed at a temperature of 333 K to characterize its structural and dynamical properties. Various pore loadings ranging from 0.1ρ bulk to ρ bulk are considered by changing the IL pairs inside the fixed pore volume. The numbers of IL pairs at 0.1ρ bulk, 0.2ρ bulk, 0.4ρ bulk, 0.6ρ bulk, 0.8ρ bulk, and ρ bulk loadings are 36, 73, 145, 218, 290, and 363 respectively. Classical molecular dynamic simulations at constant volume and temperature (NVT) ensemble were performed using the GROMACS MD package [65]. A temperature higher than the melting point of [EMIM + ][TFMSI - ], T m = K, was chosen to ensure significant ionic displacement. The two pore walls are formed by repeating the rutile unit cell along the [100], [010], and [001] and then cutting the box 55

63 Electric bulb e e e e Solar energy e e e Electrically conductive FTO glass electrode TiO2 nanowires loaded with dye Ionic liquid electrolyte Counter Pt electrode Figure 4.1 Schematic diagram of a dye sensitized solar cell (DSSC). H1 H1 HA H1 HA NA CR NA CE C1 C2 HA CW CW HA HA HE HE HE FJ FJ CJ OJ FJ SJ OJ NJ FJ SJ OJ OJ FJ CJ FJ [EMIM + ] [TFMSI - ] 1-ethyl-3-methylimidazolium Bis-(trifluoromethanesulfonyl)imide Figure 4.2 A schematic representation of the IL [EMIM + ][TFMSI - ]. The labels are atom notations used throughout in this work. 56

64 Oxygen atoms Titanium atoms Figure 4.3 Representative snapshot of the rutile (110) surfaces. Oxygen and titanium atoms are colored red and white respectively. A vector perpendicular to the surface is shown. along the (110) plane to form a slab (Figure 4.3) of the dimensions (5.60 nm 5.10 nm). The oxygen and titanium atoms in the rutile surface were modeled as LJ spheres with σ o = 0.303, σ Ti = 0.392, nm, ε o = 0.12 kcal/mol, and ε Ti = kcal/mole [209, 210]. The partial charges on oxygen and titanium atoms are e and 2.196e respectively[211]. The force field parameters for the cations [EMIM + ] and anions [TFMSI - ] were taken from Maginn et al. [212]. Partial charges were located on cations and anions according to the values reported by Maginn et al. Force field parameters for [EMIM + ][TFMSI - ] from Maginn et al. adequately reproduced the experimental density, heat of vaporization and diffusion coefficient of the bulk system. The density for the confined IL was calculated using a volume V min xy z c. Our results for the number density profile (Figure 4.5) indicate that the density of the confined ions reach a value of zero at z 2. ~ c 57

65 (a) (b) (c) Z X (d) (e) (f) Figure 4.4 Representative simulation snapshots of the IL [EMIM + ][TFSI - ] confined inside a rutile (110) surfaces (H = 5.2 nm) at 333 K and different pore loadings: (a) ρ = 0.1ρ bulk, (b) ρ = 0.2 ρ bulk, (c) ρ = 0.4 ρ bulk, (d) ρ = 0.6 ρ bulk, (e) ρ = 0.8 ρ bulk and (f) ρ = ρ bulk. Cations and anions are depicted in purple and green. In all our simulations, the Lennard-Jones interactions were cut off at 1.2 nm, and the long range coulomb interactions were handled by the particle-mesh Ewald (PME) method[73] with a cutoff of 1.0 nm and a grid spacing of 0.1 nm. Periodic boundary conditions were applied in all directions. The ILs/rutile system was kept in vacuum in the center of the orthorhombic box in such a way that two sides of the box were equal to the sides of the graphite sheets (5.60 nm 5.10 nm), and the length of the other one side of the box (12.0 nm) was long enough to avoid any artificial effect caused by the periodic boundary conditions. The improved velocity-rescaling algorithm recently proposed by Parrinello et al.[74, 75] was used to mimic weak coupling at different temperatures with a coupling constant of 0.1 ps. 58

66 We first minimized the energy of our initial configuration using the steepest descent method. Afterwards, we ran MD simulation using a time step of 1.0 fs. The systems were melted at 600 K for 1 ns, and then annealed from 600 to 333 K in stages: 400 ps at 550 K, 400 ps at 500 K, 200 ps at 450 K, 200 ps at 400 K, 200 ps at 350 K, and 200 ps at 333 K. Afterwards, our systems were equilibrated and the properties of interest were sampled for 20.0 ns at 333 K. Afterwards, we took the final configuration of our system and repeated the above steps (melting, annealing, equilibration and averaging) at least one additional time. Our reported results are averaged over at least two independent realizations of the same system. Such a procedure is adopted in an attempt to overcome the difficulties posed by the slow dynamics of ILs, which are likely to be exacerbated when these compounds are confined inside a nm-sized slit pore. Representative simulation snapshots of the ILs confined inside a rutile(110) pore at 333 K and different loadings are depicted in Figure Results and Discussion Structural Properties We studied the mass and number density profiles of the ions along the pore length. The density profiles of the ions are calculated by computing the average in different bins inside the pore. Figure 4.5 presents the number density profiles of the ions (ions/nm 3 ) confined inside the rutile (110) pore, when the confined IL has a density ranging from 0.1 ρ bulk to bulk density (ρ bulk ) at 333 K. It is found that both cations and anions have the highest density near the surface with layering behavior evident throughout the system. The oscillations are observed to reduce in amplitude away from the surface and are minimal at the center of the pore. It can be summarized that the increased density profiles near the surface are due to a strong interaction between the ions and the titanium and oxygen atoms that form the surface shown in Figure 4.5. At lower pore 59

67 loadings, the intensity of the fluctuations decrease monotonically in the center of the pore; the density of the ions in the first layer is minimally affected by pore loadings above 20%. At a density equal to 0.1 ρ bulk, the height of the peak drops down due to less number of ions in the pore which results in the IL s inability to cover the entire surface. It is also observed that anions have higher mass densities than cations in every pore loading study. The mass density profiles of the ions are also examined (not reported for brevity). Similar profile characteristics are observed with the exception that the anions have a higher mass density peaks than the anions. This is explained by the higher molecular weight of the anions. Both mass density and number density profiles show that the local maxima (first peak) for both the ions were present at the same position from the wall. This indicates that both ions are stacking at the same distance from the wall, forming a layer of average thickness nm. The results presented in Figure 4.5 are in good agreement with previous results obtained for different ILs inside the slit like pores of different materials such as graphite, silica, mica, quartz, sapphire and rutile [52, 56-58, 61-64, 113, ]. To further understand the structural differences of the ions in different regions and at different pore loading, we studied the radial distribution function g(r) of the ions inside the pore. The RDFs of the ions are calculated by taking the CR atom of the cation and the NJ atom of the anion. Figure 4.6 represents the site-site intermolecular RDF for cation-cation, anion-anion and anion-cation confined inside a rutile (110) pore of 5.2 nm at 333 K. The results for the first layers are shown in the left panel and right panel shows the results of the center regions at different pore loadings. We observed drastic change in the liquid structure of IL in the first layers at different pore loadings indicating structural heterogeneity inside the pore. Highly ordered structure is observed at lower pore loadings as there are very few ions in the center of the pore. 60

68 Number Density (ions/nm 3 ) Number Density (ions/nm 3 ) Cation Anion Distance (nm) Distance (nm) Figure 4.5 Number density profiles of the confined ions along the z-direction at different pore loading. The confined IL has a density similar to bulk density (1.49 g/cm 3 ). The vertical dotted lines indicate how the confined ions were divided into different layers/regions for further study. Different color lines are used for different loadings: gray (ρ = 0.1ρ bulk ), orange (ρ = 0.2 ρ bulk ), green (ρ = 0.4 ρ bulk ), purple (ρ = 0.6 ρ bulk ), red (ρ = 0.8 ρ bulk ) and blue (ρ = ρ bulk ). In the center of the pore we observed increase in the height of the peaks with decrease in pore loading but the position of peaks remains same at different pore loadings. This indicates that the pore loading does not affect the overall 3D structure of IL in the center of the pore. The results are similar to our previous studies of ILs confined inside the graphitic slit like pore. The RDF results in the center of the pore at different loading are similar and indicate homogeneous structure in the center of the pore at various pore loadings. No such similarities are observed in the first layers with more ordered structure at lower loadings. 61

69 g(r) g(r) g(r) g(r) g(r) g(r) 10 8 First layers (a) Distance(nm) (b) Center region Distance(nm) 10.0 ρ ~ ρ bulk 8.0 ρ ~ 0.80 ρ bulk 6.0 ρ ~ 0.60 ρ bulk 4.0 ρ ~ 0.40 ρ bulk ρ ~ 0.20 ρ bulk 2.0 ρ ~ 0.10 ρ bulk Distance(nm) (c) Distance(nm) Distance(nm) Distance(nm) Figure 4.6 Radial distribution functions g(r) of (a) cation cation, (b) cation anion, and (c) anion anion for the different regions of [EMIM + ][TFMSI - ] confined inside a slit pore of H = 5.2 nm and different pore loadings at 333 K. Left panel shows the results for the first layers and right panel for the center region. 62

70 Cation Anion Figure 4.7 Left panel shows the center of mass of cations and anions in the first layer. Different colors are used to show different orientation. In case of cations orange dots indicates [EMIM + ] laying parallel (θ <25 0 ) to surface and blue indicates [EMIM + ] tilted (θ >25 0 ) to the surface. In case of anions green dots indicates ions laying parallel to surface (θ <25 0 ) and purple indicates ions tilted to surface (θ >25 0 ). In the right panel, two vectors are shown that are used in orientation calculations. Right panel shows multiple preferential orientations of the cations (top) and anions (bottom) at the rutile (110) surface at 333 K. The orientation of the cations near the rutile surfaces was determined by calculating cos(θ), where θ is the angle between the vector normal to the slab surface and the vector normal to the imidazolium ring. Similarly, the orientations of the anions are determined by calculating the cos(θ), where θ is the angle between the vector normal to the slab surface and the vector formed by joining the atoms CJ and CJ of the ion (see Figure 4.2 for the nomenclature). Figure 4.7 (left panel) shows the center of mass of the ions in the first layer; two different color dots are used to distinguish the ions that are laying parallel to the surface (θ <25 0 ) we use orange for cations and green from anions. Any ion that is not parallel, thus is tilted or perpendicular to the surface (θ>25 0 ) are identified by blue for cations and purple for anions. It is interesting to note 63

71 that, although most cations orient tilted or perpendicular to the surface, a significant fraction of them arrange parallel to the surface. This heterogeneous layering behavior is not common in imidazolium based cations and these results present new layering arrangements not observed in previously reported results where ions are definitively flat or perpendicular near carbon and rutile surfaces [122, 123, 180, 208]. Since ions can have multiple orientations, it would be interesting to know the most preferred orientation of ions. Figure 4.7 (right panel) shows the arrangement of the ions near the surface. In case of the cations, the most common orientation results is the interaction of the rutile oxygen atoms and both hydrogen atoms connected to CW atoms (Figure 4.2). The second most common orientation is found when the hydrogen atom connected to CR atom is attracted to the rutile oxygen (Figure 4.2). This is due to the partial positive charge on the ring hydrogen atoms and partially negatively charged oxygen atoms. The most preferential arrangements of the anions have a strong interaction between the anions OJ and the titanium in the rutile (110) surface and are also shown in the right panel of figure 4.7. No preferential orientation of the cations and anions are observed in the center region of the pore (results not shown) Dynamical Properties Although extensive research has been done on confined fluids, there are only few studies where dynamics of the ions has been studied in detail. From our previous studies where we mainly focused on carbon based pores of different morphologies [122, 123, 183, 213], we found that dynamics of the ions inside the pore are very complex and heterogeneous. It is found that the ions near the surface have the slowest dynamics and the behavior changes non-monotonically with pore loadings. The ions in the center of the pores behave very similar to the bulk if the pore size is larger than 5.0 nm [183]. It was also observed that lower loadings slow down the 64

72 C(t)/C(0) C(t)/C(0) C(t)/C(0) C(t)/C(0) Cation (First layers) Anion (First layers) Time (ns) Time(ns) Cation (Center region) Anion (Center region) Time (ns) Time (ns) Figure 4.8 Single-particle time correlation functions for the cations (left panel) and anions (right panel) in different layers/regions. In case of cations, reorientation around an axis perpendicular to the imidazolium ring. In case of anion, reorientation around a vector formed by joining the atoms CJ and CJ of the ion (see Figure 4.2). Different color lines are used for different loadings: gray (ρ = 0.1ρ bulk ), orange (ρ = 0.2 ρ bulk ), green (ρ = 0.4 ρ bulk ), purple (ρ = 0.6 ρ bulk ), red (ρ = 0.8 ρ bulk ) and blue (ρ = ρ bulk ). dynamics due to the formation of the void spaces inside the pores. In the present work, we want to extend our previous efforts to understand the dynamics inside rutile (110) pore. The study of the ions inside rutile pore is more relevant for DCSCs application where the internal resistance and charge screening entirely depends on the dynamic of the ions. The dynamical behavior of [EMIM + ][TFMSI - ] was first observed by plotting single-particle time auto correlation functions for the reorientation of the ions as presented by Urahata and Ribeiro [214]. Figure 4.8 shows the single-particle time correlation functions of the cations (left panel) and anion (right panel) at different loadings in different layers/regions at 333 K. In case of cations, reorientation motion is 65

73 calculated around an axis perpendicular to the imidazolium ring. The results indicate that for cations at ρ~ ρ bulk, the reorientation in the center region decorrelate very quickly. The correlation function reaches a value close to zero in less than 1.0 ns of simulation time. In contrast, cations near the surface hardly decorrelate after 20 ns due to their strong interaction to the surface. The reorientation motion of the anions is calculated around a vector formed by joining the atoms CJ and CJ of the ion (see Figure 4.2); similar results are obtained at ρ~ ρ bulk. Correlation functions for the center ions reach a value close to zero in less than 1 ns of simulation time. Reduction in pore density causes slower dynamics for both cations and anions in the center of the pore and ions take longer time to decorrelate with the longest time at 0.1ρ bulk since the ratio of surface ions to center ions increases with decreasing loading. In case of the first layers, there is a nonmonotonic decorrelation for both ions at different pore loading. The results are consistent with our previous studies of ILs inside graphitic slit-like pores. Mean square displacements (MSDs) of the ions in the direction perpendicular to the confinement (x- and y- direction) are calculated. The dynamics of the ions in different layers/regions are compared in the above mentioned direction. Figure 4.9 shows the dynamics of the cations (left panel) parallel to the surface (x- and y- direction) in the center of the pore at three different pore loadings. It is found that lowering the loading slows down the mobility if the ions. It is due to the formation of the void spaces inside the pores. Figure 4.9 (right panel) shows the dynamics of the anions in the center of the pore at different loading and similar behavior is observed. Dynamics of cations and anions are faster along the x and y direction as compared to the z direction (results are not shown for brevity). This indicates that the confinement hinders the motion of the IL in the confined direction. These findings are in analogy to our previous results of IL under 66

74 MSD (nm 2 ) MSD (nm 2 ) MSD (nm 2 ) MSD (nm 2 ) 0.08 Cation (First layers) 0.08 Anion (First layers) Time (ns) 5.0 Cation (Center region) Time (ns) 5.0 Anion (Center region) Time (ns) Time (ns) Figure 4.9 Mean square displacements (MSDs) of the ions in the first layers and center region of the pore. Left panel shows the parallel (x- and y-) component of cation MSDs and right panel shows the parallel (x- and y-) component of anion MSDs. Different color lines are used for different loadings: gray (ρ = 0.1ρ bulk ), orange (ρ = 0.2 ρ bulk ), green (ρ = 0.4 ρ bulk ), purple (ρ = 0.6 ρ bulk ), red (ρ = 0.8 ρ bulk ) and blue (ρ = ρ bulk ). confinement. [122, 183] The results also indicate that MSD values haves a strong correlation to the distance of ions from the surface. To visually represent the slower dynamics near the surface, the displacement in nm between the initial and final timesteps are represented (Figure 4.10) for three pore loading systems, 0.4 ρ bulk, 0.6 ρ bulk, and 1.0 ρ bulk. It can be observed that the mobility of the cations and anions in the first layers are slower and the dynamics are very complex as compared to the central region and are not shown for brevity. 67

75 (a) (b) (c) Figure 4.10 (Color) Displacement of the each atom was calculated between T = 0 ns and at 20 ns for the systems with a) 0.4 ρ bulk b) 0.6 ρ bulk and c) 1.0 ρ bulk. The legend on the right indicates the coloring scheme where blue has minimal displacement and red has the maximum displacement. Titanium is white and oxygen is red in rutile (110) structure Concluding Remarks Structural and dynamical properties of IL [EMIM + ][TFMSI - ] inside a titania slit nanopore is studied. It is found that both cations and anions form local density maxima near the pore surface with slight oscillation in the center of the pore, consistent with our previous studies of ILs inside slit-like graphitic pores, nanotubes and CMK-3. We observed drastic change in the liquid structure of IL in the first layers at different pore loadings; however the overall 3D structure of IL in the center of the pore remains unchanged. It is interesting to see the orientation of the ions, especially near the surface; our results indicate that cations have multiple orientation preferences near the surface with most of the cations tilted. Cations are oriented in such a way that the hydrogen atoms of the imidazolium ring attracted to the partially negatively charged surface oxygen atoms. Similar results are observed for anions with oxygen atoms of the ions attracted to the titanium atom of the rutile surface. Self autocorrelation results indicate that at a density equal to bulk density, ions in the center of the pore decorrelate faster than the ions on the 68

76 surface. Reduction in the pore loading results in slower decorrelation. The ions in the first layers are strongly attached to the surface and have very poor decorrealtion at all different loadings. We studied the dynamics of the ions by measuring the mean square displacements of the ions. We find that the ions in the center of the pore have the fastest dynamics at a density equal to bulk density. At lower pore loading, dynamics slows down linearly due to the formation of the void space in the center. The dynamics in the first layers is the slowest, complex and non-monotonic with pore loadings. The dynamical behavior of ILs inside rutile pores is similar to our previous studies of ILs confined inside carbon nanopores at different pore loadings. However the mobility of the ions is much slower in rutile pores indicating stronger interaction of ions for the rutile surface. We have gained atomic level insight on the rutile (110) pore. However there are several aspects of ILs and pore materials that need further attention. Pore surface plays an important role in determining the behavior of the ILs, it is essential to consider other surfaces of the same polymorph of titania. It is also important to understand the effect of the charged surface on the behavior of ILs, especially on the dynamics of the ions to enhance the performance of DSSCs. 69

77 CHAPTER 5 EFFECT OF ACETONITRILE SOLVENT ON THE STRUCTURAL AND DYNAMICAL PROPERTIES OF IL [EMIM + ][TFMSI - ] CONFINED INSIDE SLIT-LIKE GRAPHITIC PORE: A MOLECULAR DYNAMIC SIMULATION STUDY In this chapter we studied the effect of acetonitrile (ACN) solvent on the properties of the IL [EMIM + ][TFMSI - ] inside an uncharged slit-like graphitic pore. The effect of different concentrations of IL (1.0 M, 2.0M, and 3.0M) on the structural and dynamical properties of the system is considered. The rest of this chapter is structured as follows. Sections 5.1 and 5.2 contain an introduction and a description of our computational models and methods. In Section 5.3 we present results and discussion of the dynamic properties of the confined ILs, and in Section 5.4 we summarize our main findings. 5.1 Introduction Electrochemical double layer capacitors (EDLCs) have attracted extensive attention due to very fast charging and discharging ability, which results in high specific power [12, ]. However, these devices have low specific energies as compared to batteries. Carbon-based materials have been extensively used as electrode materials due to their low cost and properties such as high electrical conductivity, large surface area, stiffness and chemical and thermal inertness [ , ]. The conventional electrolytes used in these devices are either aqueous solution of sulfuric acid and potassium hydroxide or organic electrolytes based on acetonitrile (ACN) and propylene carbonate (PC) solvent[226, 238]. There are also some studies on using polymer gel electrolytes for EDLCs [239]. It is found that aqueous electrolytes have the problem of decomposition at higher voltage whereas organic electrolytes suffer due to low ion conductivity limiting the performance of the device. Ionic liquids (ILs), which are organic salts with melting points below C, have the potential to replace conventional electrolytes, due to unique properties such as very low vapor pressure (non-volatile), excellent thermal and chemical 70

78 stability, non-toxicity, non-flammability and wide electrochemical window. When compared to conventional electrolytes that are only stable up to 2.5 volts, ILs are stable up to 6 volts and have the potential to improve the efficiency of EDLCs in term of both specific power and specific energy. Some of these simulations [61, 64, 113, , 121, ] suggest that the electrode capacitance attains maxima at certain specific conditions of pore size, pore geometry, surface charge density and electrode potential. These simulation and theoretical studies also supported and provided rational explanations to the experimental findings that the specific (or area-normalized) capacitance of nanopores filled with organic electrolytes or ILs increased anomalously as the pore size decreased[ ] (however, a recent experimental study[251] reports a relatively constant specific capacitance for the electrolyte (C 2 H 5 ) 4 NBF 4 /acetonitrile inside carbons with pore sizes ranging between 0.7 and 15 nm). Furthermore, very recent simulation and theoretical studies[ ] suggest that the specific capacitance has a decaying oscillatory behavior as the pore size increases. Both experimental and computational studies have been done in order to understand the microscopic and macroscopic behavior of ILs near electrodes of different materials (e.g. silica, quartz, rutile, and graphite) and morphologies (e.g. slit-like pore, nanotube, and CMK-3) [51-58, 60-64, , 122, 183, 213, ]. It has been observed that nm-size confinements have profound effect on both structural and dynamical properties. Previous computational studies on ILs inside nanopores suggest a layering behavior of ILs near the wall due to strong interaction forces exerted by the wall atoms. The dynamics of the confined cations and anions are heterogeneous and depend strongly on distance from the pore walls; for example, cations and anions in the center of the pore have faster dynamics than those close to the pore walls. 71

79 The purpose of using organic solvents in EDLCs is to reduce viscosity of ILs in order to improve the mobility of ions inside the pores. It is important to understand the effect of solvent and variation in IL concentration on the molecular level properties of EDLCs. Previous experimental study has shown that acetonitrile can reduce the viscosity of ILs and improve the performance of EDLCs [256]. Although many computational studies have considered pure ILs near electrodes of different materials [51-58, 60-64, , 122, 183, 213, 252, 253], very limited attention has been given on the effect of organic solvents on the behavior of ILs [179, ]. Some of the computational studies that have been done in this area show a change in the capacitance with changing the ion size and concentration. It is also observed that addition of solvent affects the ion distribution and orientation inside the pore. However, a fundamental understanding of how the structure and dynamics of the ions inside the pore change with variations in IL concentrations is still missing. Following our previous work on pure IL inside nanopores of different pore size, pore morphology and pore material, we extend our efforts at understanding the effect of organic solvent on the properties of confined ILs. In the present work, we intend to study the effect of varying concentrations of acetonitrile (ACN) solvent on the properties of the IL [EMIM + ][TFMSI - ] inside an uncharged slit-like graphitic pore. IL at different ionic concentration (1.0M, 2.0M, and 3.0M) is considered and both structural and dynamical properties are measured. We aim at understanding the atomic distribution of the ions and ACN molecules inside the slit-like pores. We are also interested in understanding the effect of the IL concentrations on the mass and number density profiles. Orientation of the ions plays a crucial role in determining the electrical double layer at the electrode; preferential orientation of the ions will be calculated. Dynamics of the ions will be analyzed by calculating the mean square displacement (MSD) of the ions at different concentrations. 72

80 The rest of this paper is structured as follows. Section 5.2 contains a description of our computational models and methods. In Section 5.3 we present results and discussion of the dynamical properties of the confined ILs, and in Section 5.4 we summarize our main findings. H1 H1 HA H1 HA NA CR NA CE C1 HA CW CW HA C2 HA HE HE HE FJ FJ CJ OJ FJ SJ OJ NJ FJ SJ OJ OJ FJ CJ FJ HT HT HT CT CB NB [EMIM + ] [TFMSI - ] (ACN) 1-ethyl-3-methylimidazolium Bis-(trifluoromethanesulfonyl)imide Acetonitrile (a) (b) (c) Figure 5.1 A schematic representation of the IL [EMIM + ][TFMSI - ] (panel a and b)and acetonitrile (ACN) molecule (panel c). The labels are atom notations used throughout in this work. Vectors shown are used to define the orientation of the ions/molecule. 5.2 Computational Details GROMACS molecular dynamics simulation package was used to study the effect of ACN solvent on the properties of the IL [EMIM + ][TFMSI - ] inside graphitic slit-like pore of pore size H = 5.2 nm. A schematic representation of the IL [EMIM + ][TFMSI - ] and ACN molecule are shown in Figure 5.1. The ensemble of choice was NVT due to the fixed dimensions (5.70 nm 5.61 nm 5.2 nm) of the pore. The pore walls were modeled by taking three carbon sheets and fixing them in space keeping the pore size H =5.2 nm. The carbon atoms in the graphite sheets were modeled as LJ spheres with σ c = nm and ε c /k = 28.0 K. Three different IL molar concentrations 1.0 M, 2.0M and 3.0M including pure ACN were considered in this study. The number of IL pairs and ACN molecules in different cases are reported in table

81 Table 5.1 Detail description of the IL ion pairs and ACN molecules in different cases. System [EMIM + ][TFMSI - ] pairs ACN molecules 1.0 M IL M IL M IL Pure ACN H= 5.2 nm Z Y Figure 5.2 A snapshot of 3.0 M IL [EMIM + ][TFMSI - ]electrolyte in ACN solvent confined inside a slit-like graphitic pore of size H = 5.2 nm at 333 K. Cations, anions, ACN molecules are colored in green, purple, and red respectively. The non-polarizable force field force field parameters for IL [EMIM + ][TFMSI - ] used in this work are taken from Maginn et al. [212]. The force field parameters for ACN molecules are taken form Nikitin et al. [261]. A representative simulation snapshot of the slit-like graphitic pore containing 3.0 M IL at 333 K is depicted in Figure

82 Most of the simulation procedure used in this work is similar to our previous work and a detailed description could be found in recent publications [122, 123, 183, 213]. In all our simulations, the Lennard-Jones interactions were cut off at 1.2 nm, and the long range coulomb interactions were handled by the particle-mesh Ewald (PME) method with a cutoff of 1.0 nm and a grid spacing of 0.1 nm. Periodic boundary conditions were applied in the x, y, and z directions. The ILs/ACN/graphite sheet system was kept in vacuum in the center of the orthorhombic box in such a way that two sides of the box were equal to the sides of the graphite sheets (5.70 nm 5.61 nm), and the length of the other one side of the box (12.0 nm) was long enough to avoid any artificial effect caused by the periodic boundary conditions. The improved velocity-rescaling algorithm recently proposed by Parrinello et al. was used to mimic weak coupling at different temperatures with a coupling constant of 0.1 ps. 5.3 Results and Discussion Density Profiles Density of the ions near the electrode surface affects the electrical double layer formation. In case of pure IL near an uncharged surface, higher density is reported close to wall than in the center of the pore [56, 80, 183, 213, 252, 253]. Figure 5.3 shows the mass density profiles along the length of the pore (Z- direction, Figure 5.2) of ions and ACN molecules at three different IL molar concentrations (1.0M, 2.0M and 3.0M) including pure ACN molecules. From the density profile, the confined ions were divided into two different layers/regions: the first layers (closest to the pore walls), the center region. In case of pure ACN molecules (case (a), Figure 5.3), a strong layering behavior is observed throughout the pore length with highest density near the pore wall caused by strong surface forces; density decreases linearly as we move toward the center of the pore. The density in the first layer is roughly five times higher 75

83 Mass Density (Kg/m 3 ) Mass Density (Kg/m 3 ) Mass Density (Kg/m 3 ) Mass Density (Kg/m 3 ) 5000 (a) 2500 (b) Distance (nm) 2000 (c) Distance (nm) 2000 (d) Distance (nm) Distance (nm) Figure 5.3 Mass density profiles of the IL [EMIM + ][TFMSI - ] in acetonitrile (ACN) solvent at different molar concentrations along the length of the pore: (a) Pure ACN, (b) 1M [EMIM + ][TFMSI - ], (c) 2M IL [EMIM + ][TFMSI - ], and (d) 3M IL [EMIM + ][TFMSI - ]. Cations, anions and ACN molecules are shown in green, purple and red color respectively. Dotted horizontal line in case (a), represent bulk ACN density (780 Kg/m 3 ) and dotted vertical lines distinguish the first layers. than the bulk density. It is observed that the higher density in the first few layers induces a void space in the center of the pore; the density in the center is lower than the bulk density (780 Kg/m 3 ). The thicknesses of the layers are approximately nm and are consistent inside the pore. At different IL molar concentration (case (b), (c) and (d), Figure 5.3), significantly different density profiles for ILs and ACN molecules are observed. Addition of ions in the 76

84 system starts replacing ACN molecules that are present in the first layers. At 1.0M concentration, ACN molecules dominate first layers; the density in the first layer is two times higher than the bulk density. Anions have second highest density (850 Kg/m 3 ) followed by cations (410 Kg/m 3 ). In the center, densities are lower for the ions/molecules than in bulk. At 2.0 and 3.0 M, the density of the ions in the first layer is higher than ACN molecules with cations and anion have the maximum densities of 900 and 1400 Kg/m 3 (2.0M) and 1000 and 1500 Kg/m 3 (3.0M) respectively. The density of the ACN molecules in the first layers decreases from 1000 Kg/m 3 to 500 Kg/m 3 after changing the concentration form 2.0M to 3.0M. Density results in the center of the pore at 2.0M and 3.0M are fluctuating, similar to 1.0M and depend on the size and shape of the void formed. We also studied number density profiles at various IL molar concentrations (Results are not show for brevity). Observations from the number density profiles are similar to mass density results and are consistent with our previous studies of confined ILs [213] Radial Distribution Function To understand the local structure of IL confined inside slit pore at different molar concentration, the radial distribution function (RDF) was computed. Figure 5.4 represents the site-site intermolecular RDF of anion anion, cation cation, cation anion, anion ACN, and cation ACN for the first layers and the center region at 333 K. CR carbon atom of [EMIM + ], NJ nitrogen atom for [TFMSI - ] and CB atom for ACN were chosen for plotting RDF. Result indicates that structural heterogeneity is observed in the RDF of ions at different molar concentrations and this heterogeneity in the structure is more significant at the surface as compared to the center region. We observed loss of the first coordinations shell of anion-anion and formation of first coordination shell of anion-acn with increase in concentration in the first layers. In the first layers the RDF of cation-cation shows upto three coordination shells at 1 M 77

85 g (r) g (r) g (r) g (r) g (r) g (r) g (r) g (r) g (r) g (r) 6.0 (a) First layers 3.0 Center region Distance (nm) 6.0 (b) Distance (nm) Distance (nm) 12.0 (c) Distance (nm) Distance (nm) 8.0 (d) Distance (nm) 8.0 (e) Distance (nm) Distance (nm) Distance (nm) Distance (nm) Figure 5.4 Radial distribution functions g(r) of the (a) anion anion, (b) cation cation, (c) cation anion, (d) anion CAN, and (e) cation ACN for the first layers/center region of [EMIM + ][TFMSI ] confined inside a slit pore of H = 5.2 nm at different concentrations. Red, green and purple colors are used to show the results of 1.0M, 2.0M, and 3.0M respectively. 78

86 3.5 nm 2.5 nm 1.2 nm Top view Side view Figure 5.5 Snapshots of the top and side views of the ions and ACN molecules in the center of the pore at different IL molar concentrations. Side views show the width of the void formed at different concentrations. Top panel shows 1.0M [EMIM + ][TFMSI - ], center panel 2.0M [EMIM + ][TFMSI - ], and bottom panel 3.0M [EMIM + ][TFMSI - ]. Cations, anions and ACN molecules are shown in green, purple and red color respectively. 79

87 concentration however at 2 and 3 M concentration only one broader and weaker peak is observed suggesting weak structuring of cation-cation at 2 and 3 M concentrations. The results show that the local structure of anion-anion and cation-cation at 1M concentrations is significantly different from 2M and 3M concentrations at the surface indicating that presence of high number of ACN molecules at the surface affect the interaction among cations and anions. Unlike our previous findings RDF of cation-cation, cation-anion and anion-anions shows some structural heterogeneity in the center [183, 213]. This could be due to formation of void at the center by ACN molecules where IL is trapped. As seen from Figure 5.5 that width of void formed in 1M concentration is more as compared to 2 and 3 M, hence more ions close to the surface gets affected by the void in 1 M concentration Preferential Orientation Preferential orientations of the ions/molecules inside the pore are studied by calculating the average P 1 (Cos θ), where θ is the angle between a vector normal to the pore surface and a vector defining the orientation of the ions/molecules. The pore is sliced into bins and averaged P 1 (Cos θ) is calculated for 20 ns long trajectories (frames are saved after every 50 ps). In case of cations, we defined a vector that is perpendicular to the imidazolium ring as shown in panel (a) of figure 5.1. Panel (b) of figure 5.1 shows the orientation vector for anions; the vector is defined by joining the CJ- CJ atoms of the anions. Similarly CT and NB atoms are used to define the orientation vector for the ACN molecules (panel (c), figure 5.1). Figure 5.6 shows the average P 1 (Cos θ) for the ions/molecules at 1.0M and 3.0M IL concentrations. Results at 2.0M are similar and are not reported. In all different cases, the ions/ molecules that are in the center of the pores, have no preferential orientation; the average P 1 (Cos θ) value is in between 0.45 to The average P 1 (Cos θ) value for cations that are close to the surface, is close to 1 and for anions and 80

88 P 1 (Cos θ) P 1 (Cos θ) M IL [EMIM + ][TFMSI - ] M IL [EMIM + ][TFMSI - ] First layer Center First layer Figure 5.6 Orientation of the ions and ACN molecules at 1.0M and 3.0M [EMIM + ][TFMSI - ] concentrations. Average P 1 (Cosθ) are calculated using a vector perpendicular to the pore surface and orientation vectors as shown in figure 5.1. Average P 1 (Cosθ) for cations, anions and ACN molecules are shown in green, purple and red color respectively. ACN molecules is close to 0, showing that ions/molecules tend to align themselves parallel to the surface. The results can be further confirmed by looking at the snapshots of the first layer ions/molecules shown in Figure 5.7. These finding are consistent with other reported and our previous studies of the confined ILs inside the graphitic slit pore [183, 213, 252]. 81

89 MSD (nm 2 ) MSD (nm 2 ) (a) (b) (c) Figure 5.7 Snapshots of the ions and ACN molecules in the first layers at different IL molar concentrations: (a) 1.0M [EMIM + ][TFMSI - ], (b) 2.0M [EMIM + ][TFMSI - ], and (c) 3.0M [EMIM + ][TFMSI - ]. 0.3 First layers 0.9 Center region Time (ns) Time (ns) Figure 5.8 Lateral (x and y direction) mean square displacement of the ions and ACN molecules in the first layer (left panel) and in the center region (right panel) of the pore at various concentration. Solid lines, dashed lines and dotted lines are used to represent 3.0M, 2.0M and 1.0M [EMIM + ][TFMSI - ] concentrations respectively. Results for cations, anions and ACN molecules are shown in green, purple and red color respectively. 82

90 5.3.4 Mean Square Displacement Dynamics of the electrolyte play a very crucial role in determining the performance of electrochemical devices; faster dynamics results in less internal resistance and improved specific power. Mean square displacements (MSDs) of the ions and ACN molecules are calculated in the plane parallel to the wall surface at various IL concentrations. Figure 5.8 shows the MSDs of the ions and ACN at 1.0 M, 2.0 and 3.0M IL concentrations. Left panel shows the behavior of the ions/molecules in the first layers and right panel in the center of the pore. It is interesting to find that dynamics of the ions/molecules decreases linearly with decrease in the molar concentration form 3.0M to 1.0M in the center of the pore. The result contradicts the previous studies of ILs solvent mixtures in bulk [262]. The dynamics of the ACN molecules is found to be between the ions, consistent at different concentrations. The slower dynamics is the result of the clustering of the ions/molecules and large size void formation in the center of the pore. Among the ions/molecules, cations have the fastest dynamics and anion slowest. Figure 5.5 shows the top and side view of ions/molecules in the center of the pores. It is found that at 1.0M concentration, there is a large void formation caused by local clustering of the ions and molecules. The thickness of the void is approximately 3.5 nm. As we increase the IL concentration, the size of the void decreases results in improved dynamics. From our previous studies, it has been observed that void formations are the results are local clustering and dynamics slow down drastically once voids are formed. It is also interesting to see that ions prefer to cluster themselves at the liquid/air interface. At 3.0M, void diminishes results in improved dynamics. The dynamics in the first layer is much slower than in the center of the pore but follows the same trends as in the center of the pore. 83

91 5.4 Concluding Remarks We performed MD simulations to study the effect of acetonitrile solvent on the properties of the IL [EMIM + ][TFMSI ] confined inside uncharged slit-like graphitic nanopores of pore width 5.2 nm. The structural and dynamical properties of the confined IL were studied at three different IL molar concentrations including a case when pure ACN was confined inside the nanopore. Mass density results indicate a very strong layering pattern throughout the pore width in case when pure ACN solvent is confined. The density of the solvent decreases linearly as we move toward the center of the pore. Addition of IL in the solvent continued showing similar behavior for ILs and solvent near the pore wall with less variation in the center of the pore. Variation in the density depends strongly on the concentration of the confined IL. In all cases some very low density region (cavity) formation is observed due to the clustering of the ions/molecules near the pore wall. Variations in the concentration do not cause significant changes in the overall (local) 3-d liquid structure of the confined IL and solvent in the center of the pore. Significant change is observed in the structure of the first layers showing structural heterogeneity under confinement at different concentrations. These finding are consistent with our previous studies of ILs in slit-like pores [183, 213]. Structural heterogeneity could be further confirmed by looking at the preferential orientation of the ions/molecules at different concentrations. Irrespective of the concentration, the ions/ molecules in the first layer like to align themselves parallel to the wall surface whereas no preferential orientation is observed in the center of the pore. The dynamics of the IL/ACN at various concentrations is studied from the mean square displacement (MSD) results. It is interesting to find that dynamics of the ions/molecules decreases linearly with decrease in the molar concentration form 3.0M to 1.0M. It is due to clustering of the ions/molecules and large size void formation in the center of the pore 84

92 in the center of the pore. At higher concentration, clustering diminishes results in improved dynamics. Among the ions/molecules, cations have the fastest dynamics and anion slowest. The dynamics of the ACN molecules is found to be between the ions, consistent at different concentrations. Surprisingly the results obtained in this chapter indicate that addition of solvent deteriorate the dynamics of the ions inside the nanopores. A factor that needs to be considered in future simulation studies in this area is to increase the solvent concentration to avoid formation of voids at different IL molar concentration. These studies are currently in progress and will be described in detail in an upcoming paper. 85

93 CHAPTER 6 CONCLUSION AND FUTURE WORK 6.1 Conclusion In this work we have used molecular dynamics (MD) simulation to investigate systems of representative ILs, [BMIM + ][PF - 6 ] and [EMIM + ][TFMSI - ], inside several model materials (e.g., slit-shaped graphitic and titania pores, carbon nanotubes) having pores of different sizes and morphologies. Our goal was to understand how several properties of the ILs (e.g., local density profiles, radial distribution functions, orientation of the ions, diffusivities and mean squared displacements) depend on variables such as pore size and shape, porous material and the amount of IL inside the pore. We also studied the effect of mixing varying amounts of the IL [EMIM + ][TFMSI - ] with an organic solvent, acetonitrile (ACN), on the properties of the confined ILs inside a slit-like graphitic pore. In general, we observed that the ILs exhibit similar layering effects near the surface of the nanoporous irrespective of the pore size, shape and morphology. Variation in the pore loading (pure ILs) and IL molar concentration (IL-ACN mixtures) had a similar effect on the structural properties, with the IL having similar oscillations in the density profiles with lower densities in the center. The densities close to the wall surface depend on the pore loading and IL molar concentration. Orientation distribution profiles indicate that the imidazolium ring of the cations tend to align parallel to the surface when close to the walls in case of slit-shaped graphitic pores, and carbon nanotubes. In case of titania pores, cations tend to have multiple preferential orientations near the surface. Varying molar concentration of IL has no effect on the preferential orientation of the ions near the wall surface. MSD results show that the dynamics of the ions depend strongly on their location with respect to the surface, with slower dynamics generally observed near the pore surfaces in all studied model materials. 86

94 It is interesting to compare the simulation results of ILs inside a slit-like graphitic pore [183] with those obtained for the same IL (with a different force field, however) confined inside a cylindrical multi-walled carbon nanotube (MWCNT) [122]. Significant layering was observed for the IL inside the two different pore geometries. Likewise, in both pore geometries, in general the cations exhibited faster dynamics than anions, and the dynamics of the ions decrease monotonically as we go from the center of the pore to the IL layer near the pore walls. However, evidence of complex dynamics was observed for the IL inside a cylindrical pore. MSD results observed for the IL inside a MWCNT of D = 3.0 nm (for which three layers of ions are observed) indicate that in the second layer, the MSDs of the cations and anions are similar in magnitude; furthermore, the anions in this second layer have dynamics that are similar to those observed for the anions in the center of the pore (compare Figures 2.9 and 3.3). Evidence of similar complex dynamics was not observed for the same IL inside a slit pore. It is also interesting to note that the dynamical properties of the confined IL in the center region of the pore are very similar to bulklike. Similar results have been observed experimentally in other glass-forming systems inside nanopores or near surfaces, including polymer thin films[143] and organic glass-formers.[49, 144] When comparing the properties of ILs confined inside slit-like graphitic and rutile pore, significant difference in both structural and dynamical properties was observed. Multiple preferential orientations for the ions were observed near the rutile wall. However, for slit-like graphitic pores ions prefer to align flat at the pore wall. No preferential orientation was observed in the center region for both pore materials. We also observed that 3-d structure of ions in the center region remains unchanged. The dynamical behavior of ILs inside rutile pores is similar to our previous studies of ILs confined inside carbon nanopores at different pore loadings. However 87

95 the mobility of the ions is much slower in rutile pores indicating stronger interaction of ions for the rutile surface. Addition of solvent in IL does not affect the preferential orientation of the ions near the wall and in the center of the pore when compared with neat IL; most of the ions tend to align flat near the surface. We observed that solvent molecules also lie flat at the surface. Unexpectedly the dynamics of confined IL slows down with addition of solvent. This may be due to the clustering of the ions/molecules and large size void formation in the center of the pore. 6.2 Proposed Work Defining Order Parameters to Characterize Local and Global Degree of Crystallinity A proposed research in this area could be studying the solid phases of ILs in bulk and under confinement. A fundamental understanding of the solidification of organic salts inside cylindrical nanopores is essential to optimize the properties of the resulting 1D-nanoGUMBOS. One important aspect of the proposed simulation studies is establishing a suitable set of collective variables (order parameters) that can accurately characterize the nanocrystalline structure of the ILs in bulk and under confinement. These order parameters should allow us to distinguish between different crystal polymorphs and liquid/amorphous phases, as well as permit the detection of local order in nm-sized regions. A method to calculate the order parameters have been recently proposed by Santiso and Trout,[263, 264] which are based on the generalized pair distribution function of molecular fluids. This method has been tested successfully to study the nucleation of α-glycine crystals in solution, the crystallization of benzene from the melt, and the polymorph transformation of terephthalic acid in bulk systems.[263, 264] This methodology could be extended to study the solidification of organic salts in bulk and inside nanopores. 88

96 Figure 6.1 Snapshot from a preliminary MD simulation of bulk [DMIM + ][Cl - ]. Cations are color-coded by their locally-averaged bond orientation order parameter [eqn. (7)]. Red = liquidlike, white/blue = crystal-like. The calculations of local, locally- and globally-averaged order parameters is already implemented in C++ libraries for NAMD [265] and available under the GNU Lesser General Public License [266]. These local parameters usually take larger values for crystal-like configurations and small values for liquid-like/amorphous configurations. One then could calculate local and global averages of these concentration parameters and use those as a measure of the local and global degree of crystallinity in our simulated systems. In Fig. 6.1 we show a snapshot from a preliminary MD simulation of bulk [DMIM + ][Cl - ] exhibiting distinct liquid-like (disordered) and crystal-like regions. The cations are color-coded according to their locallyaveraged bond orientation order parameter. These preliminary results strongly suggest that the proposed order parameters can indeed be used to distinguish between crystalline and amorphous nm-sized regions in systems of ILs. 89

97 6.2.2 Study of the Effect of Charged Electrodes on the Properties of the Confined ILs Another proposed research in this area could be the study of confined ILs in which pore surfaces are positively/negatively charged. It will be interesting to study the effect of charge on the structural and dynamical properties of the confined ILs inside nanopores of different pore material and morphology. The study could be further extended to the case where solvents are used along with ILs inside confinement. This will give a more realistic picture of the relations between electrode/electrolyte surface and its ability to store charge at the interface. A more complex model of electroactive potential can also be studied [240, 267]. By fundamentally understanding how the electrical, structural and dynamical properties of ILs are affected by the properties of nanoporous materials (i.e pore size and shape, surface density of electrical charge, presence of chemical functional groups at the pore surfaces, and various degree of heterogeneities in these properties), a solid platform will be in place to rationally design EDLCs, DSSCs, ionogels and IL-based electrochemical systems with optimal properties. A very simple approach can be used to study how the properties of the ILs are affected by different values of surface charge density (σ) in the nanopores. A charged nanoporous material can be modeled by uniformly distributing a constant charge q= ±ne among the wall atoms (where e is the charge of one electron; n=0 for an uncharged porous material).[57, 61, 62, 64, 268]. A system with an uncharged porous material will contain an equal number of cations and anions. In contrast, a system where the porous material has a charge, q= ±ne, n/2 randomly selected cations (anions) can be replaced by anions (cations) for the case of positively (negatively) charged nanopores, to ensure that the whole system is electrically neutral. The total charge q will be kept fixed throughout the simulations. Replacing cations for anions and vice 90

98 versa will lead to variations in the density of the IL, and therefore different system sizes will be evaluated in an attempt to minimize the effects of these variations. A number of dynamical properties such as MSD, self part of van Hove correlation function, intermediate scattering function can be determined in the proposed simulations for charged systems in order to understand the dynamics of ILs inside nanopores at the molecular level. 91

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125 APPENDIX A: PERMISSION LETTERS A.1 Permission for Chapter 2 118