This thesis deals with several aspects of translational and reorientational dynamics of water molecules confined inside narrow carbon nanotubes. Water molecules confined in a non-polar, nanoscopic pore exhibit extremely unusual structural and dynamical properties. Adding to the list of anomalies which are already present in bulk liquid water, the confined water “chains” and “shells” springs many more surprises. The relatively weak interaction with the surrounding walls in conjuction with the strong inter-water hydrogen bonds lead o several novel structural and dynamical features, very special to this “strange” phase of water. In this thesis, we present our findings on the detailed molecular level description of translational and reorientational dynamics of this novel phase of anomalously “soft” water. Chapter 1 introduces the varied theoretical, numerical and experimental attempts to demystify the properties of bulk, interfacial and confined water. It also motivates the aspects of diffusion in low dimensional systems, which are often termed “anomalous”. In Chapter 2, we study the structure and dynamics of water molecules inside an open ended carbon nanotube placed in a bath of water molecules. The size of the nanotube allows only a single file of water molecules inside the nanotube. The water molecules inside the nanotube show solid-like ordering at room temperature, which we quantify by calculating the pair correlation function. It is shown that even for the longest observation times, the mode of diffusion of the water molecules inside the nanotube is Fickian and not sub-diffusive. We also propose a one-dimensional random walk model for the diffusion of the water molecules inside the nanotube. We find good agreement between the mean-square displacements calculated from the random walk model and from MD simulations, thereby confirming that the water molecules undergo normal-mode diffusion inside the nanotube. We attribute this behavior to strong positional correlations that cause all the water molecules inside the nanotube to move collectively as a single object. The average residence time of the water molecules inside the nanotube is shown to scale quadratically with the nanotube length. In Chapter 3, we study the diffusion of water molecules confined inside narrow (6,6) carbon nanorings. The water molecules form two oppositely polarised clusters. It is shown that the effective interaction between these two clusters is repulsive in nature. The computed mean-squared displacement (MSD) clearly shows a scaling with time, which is consistent with single file diffusion (SFD). The time up to which the water molecules undergo SFD is shown to be the lifetime of the water molecules inside these clusters. The inter-cluster repulsive interactions are electrostatic and hence long-ranged, which is in complete contrast with shorter ranged steric repulsion in other systems which exhibit SFD. In Chapter 4, we study the anisotropic orientational dynamics of water molecules confined in narrow carbon nanotubes and nanorings. We find that confinement leads to strong anisotropy in the orientational relaxation. The relaxation of the aligned dipole moments, occurring on a timescale of nanoseconds, is three order of magnitude slower than that of bulk water. In contrast, the relaxation of the vector joining the two hydrogens is ten times faster compared to bulk, with a timescale of about 150 femtoseconds. The slow dipolar relaxation is mediated by the hopping of orientational defects, which are nucleated by the water molecules outside the tube, across the linear water chain. In Chapter 5, we study the reorientational dynamics of water molecules confined inside narrow carbon nanotubes immersed in a bath of water. Our simulations show that the confined water molecules exhibit bistability in their reorientational relaxation, which proceeds by angular jumps between the two stable states. The energy barrier between these two states is about 2kBT. The effect of non-Markovian jumps shows up in the ratio of the timescales o the first and second order reorientational correlation functions, which exceeds the value of the ratio in the diffusive limit. The analytical solution of a proposed model is also presented, which qualitatively explains this “unusual” relaxation. These results will have important implications in understanding proton conduction in water-filled ion channels. In Chapter 6, we report the thermodynamic aspects of the translational and re-orientational dynamics of the strongly confined water molecules. Considering the energetics it is surprising that the water molecules spontaneously fill up the nanotube. Thus the thermodynamics of entry of water molecules in the hydrophobic cavity of nanotube. This is generally attributed to the rotational entropy gain by the water molecules on entering the tube, a fact which has not been demonstrated quantitatively so far. We show that the gain in rotational component of the entropy compensates the loss of energy of the water molecules upon entering the nanotube. In Chapter 7, we conclude by summarising the work done in the previous chapters and discuss the future course of actions. We would like to extend the studies on the diffusion of water inside finite nanotubes in the presence of bathwater outside, to nanotube lengths, where it is possible to observe the cross-over from an initial “single file” to and eventual, centre of mass dominated, “normal” diffusion. The mean field estimate of the length of the nanotube required so that one observes a crossover from the initial “single file” to “normal” diffusion at 100 ps is about 700 ˚A. Simulation of such a system would possibly provide an unambiguous answer to the question, whether it is possible to observe SFD in finite carbon nanotubes, filled with water. Regarding the reorientational dynamics, we would like to extend our understanding of the reorientational relaxation of water chains to more more complicated structures. Depending on the diameter of the confining nanotube water molecules form polygons of ice. In the present situation each water molecule can be in only two possible states of orientation. Hence, it would be interesting to predict the reorientational dynamics for other ice structures, where each water molecule can be more “orientational states”. In Chapter 8, we report a work which is unrelated to the rest of this thesis. The work has been done in collaboration with Prof. T. V. Ramakrishnan and Prof. Vijay B. Shenoy. We report a novel method for the calculation of elastic constants of a solid in the frame work of Ramakrishnan-Youssouf density functional theory. The structural aspect of the liquid to solid transition and how it affects the elastic constants of the solids is brought out very clearly. The calculation is analytical and we obtain explicit expressions for the elastic constants. The description of the solid is in terms of the structure factor, S(G), of the coexisting liquid. The elastic constants are expressed as a function of equilibrium parameters, such as c(0), relatedto the compressibility of the liquid. Another important quantity on which the elastic constants depend is the curvature, c"(|G|), of c(|q|)curve at its peak (q= G). These quantities are known experimentally for many systems, and can also be calculated accurately. The shear modulus depends only on c"(|G|), while the bulk modulus has contributions from both c"(|G|) and c(0). The obtained elastic constants do not satisfy the Cauchy relations, in that C12 is not equal to C44. Calculations have been performed for two-dimensional square and triangular lattices as well as bcc and fcc lattices in three dimensions. It is seen that in order to get good agreement between the theoretical and the experimental results of the elastic constants, three body correlations have to be introduced in the calculations for the bcc and the fcc lattices. For the last, in which two shells of reciprocal lattice vectors are appropriate, we point out the modifications needed for choosing the lattice parameter in the unstrained freezing problem. We obtain a new, first principles, quasiuniversal relation for elastic constants, scaled by the melting temperature, that is experimentally satisfied. It is similar to the famous Verlet criterion that S(|G|) = 2.9 at freezing and is free of some of the unphysical aspects of previous work.

The thesis involves computer simulation and theoretical studies of dynamics of water under confinement and structural transformation in different complex systems. Based on the systems and phenomena of interest, the work has been classified in to three major parts: I. Dynamics of water under confinement II. Dynamics of water in presence of amphiphilic solutes III. Structural transformation in complex systems The three parts have further been divided into nine chapters. Brief chapter wise outline of the thesis is discussed below. Part I deals with the dynamics of water in confined systems. In Chapter I.1, we provide a brief introduction of water dynamics inc on fined systems. We also give a brief outline of relevant experimental and theoretical techniques used to study the water dynamics under confinement. Chapter I.2 describes a model based analytical study of dynamical correlation in confined systems. Here, we introduce a novel one dimensional Ising model to investigate the propagation and annihilation of dynamical correlations in confined systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles (RMs).In our model, the two spins located at the two end cells are oriented in the opposite directions to mimic the surface effects present in the real systems. These produce opposing polarizations which propagate from the surface to the center, thus producing bulk like condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm).We show that the model satisfactorily reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of the relaxation of spins undergoes a change with the emergence of homogeneous dynamics, where the decay is predominantly exponential. In Chapter I.3, layer-wise distance dependent orientation relaxation of water confined in reverse micelle s(RM)is studied using theoretical and computational tools. We use both a newly constructed spins on a ring (SOR) Ising-type model with modified Shore-Zwanzig rotational dynamics and atomistic simulations with explicit water. Our study explores the size effect of RMs and the role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the surface) dependence of water relaxation. The SOR model can capture some aspects of distance dependent orientation relaxation, such as acceleration of orientation relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond (H-bond) formation pattern clearly reveal that the H-bond arrangement of water at a certain distance away from the surface can remain frustrated due to interaction with the polar surface head groups. We show that this layer-wise analysis also reveals the presence of a non-monotonic, slow relaxation component which can be attributed to the frustration effect and is accentuated in small to intermediate size RMs. For larger RMs, the long-time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. In ChapterI.4, we present theoretical two dimensional infrared spectroscopic (2D-IR) studies of water confined within RMs of various sizes. Here we focus again mainly on the altered dynamics of confined water by performing a layer-wise decomposition of water. We aim to quantify the relative contributions to the calculated 2D-IR spectra by water molecules located in different layers. The spectra of 0-1 transition clearly show substantial elongation along the diagonal, due to in homogeneous broadening and incomplete spectral diffusion, in the surface water layer of different size of RMs studied in this work. Our study reveals that the motion of the surface water molecules is sub-diffusive, establishing the constrained nature of their dynamics. This is further supported by the two peak nature of the angular analogue of the van Hove correlation function. With increasing system size the motion of water molecules becomes more diffusive in nature and the structural diffusion is observed to be almost completed in the central layer of larger RMs. Comparisons between experiment and simulation help establishing the correspondence between the spectral decomposition available in experimental 2D-IR with the spatial decomposition of simulated 2D-IR. Simulations also allow a quantitative exploration of the relative role of water, sodium ions and sulfonate head groups in irrational dephasing. Interestingly, the negative cross correlation between forces on oxygen and hydrogen of O-H bond in bulk water significantly decreases in the surface layer of different RMs. This negative cross correlation gradually increases in the central layer with increasing size of the RMs and this is found to be partly responsible for the faster relaxation rate of water in the central layer. Part II consists of two chapters and focuses on the dynamics of water in presence of amphiphilic solutes. In Chapter II.1, we present a brief introduction of water – DMSO binary mixture and various anomalous properties of the same. In Chapter II.2, we present theoretical IR study of water dynamics in water–DMSO binary mixtures of different compositions. We show that with increasing DMSO concentration, the IR absorption peak maxima show the presence of structural transformation in similar concentration range, observed in earlier studies. Analysis of H-bonded network near hydrophilic and hydrophobic part of DMSO also suggests that average number of hydrogen bonds near the hydrophobic parts possess maxima at the same concentration range. We also show that with increasing DMSO concentration water dynamics becomes very slow. This has been supported by the diagonal elongation of the 2D-IR spectra and also the slow decay of frequency fluctuation correlation n function (FFCF) and the orientation time correlation function (OTCF). The decoupling of the OTCF establishes that water-DMSOH-bond is much stronger than that of water-water. The last part (Part III) consists of three chapters that deal with structural transformation in various complex systems. In Chapter III.1, we introduce polydisperse systems and present existing theoretical, computer simulation and experimental studies. It also contains the importance and diversity of polydisperse system in nature. In Chapter III.2, we present computer simulation study of melting of polydisperse Lennard-Jones (LJ) system with Gaussian polydispersity in size. The phase diagram reproduces the existence of an early temperature in variant terminal polydispersity (δt0.11), with no signature of re-entrant melting. The absence of re-entrant melting can be attributed to the influence of attractive part of the potential on melting. We find that at terminal polydispersity the fractional density change approaches zero that seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction system undergoes a sharp transition from crystalline solid to disordered state with increasing polydispersity. This has been quantified by second and third order rotational invariant bond orientational orders as well as by the average inherent structure energy. The translational order parameter also indicates similar structural change The free energy calculation further supports the nature of the transition. The third order bond orientational order shows that with increasing polydispersity, local cluster favors more icosahedral-like arrangements and thus the system loses its crystalline symmetry. In Chapter III.3, we present study of phase transition and effect of confinement on it in SOR model. This system is similar to our SOR model discussed in Chapter I.3. The spins execute continuous rotation under a modified XY Hamiltonian. In order to understand the nature of phase transition in such confined spin systems we have performed extensive Monte Carlo simulations. The system size dependence of Binders cumulant, specific heat, order parameter and finite size scaling of order parameter universally suggest the existence of a phase transition. The absence of hysteresis and Scaling of Binders energy cumulant minimum confirm the continuous nature of the transition. The finite size scaling analyses give rise to the mean field nature of the transition. Plausible applications of the proposed model in modeling dipolar liquids in confined systems are also discussed. In Appendix A, we discuss a preliminary study of front propagation in a non-equilibrium system. The model system analogous to the super cooled liquid shows non-Avrami domain growth during rejuvenation. The origin of the non-Avrami nature of the domain growth and the presence of cross over are also discussed. In Appendix B, we discuss umbrella a sampling technique and WHAM analysis which is used in ChapterIII.2 to get the free energy of polydisperse LJ system.