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Du fait de leurs exceptionnelles propriétés, un très vaste champ d'applications s'ouvre aux nanotubes de carbone. La connaissance de leur toxicité est un enjeu primordial afin de connaître les risques et les dangers que ces objets représentent.Le travail présenté dans cette thèse vise à la synthèse de dérivés ayant pour but de favoriser les interactions entre les nanotubes et le milieu vivant.La synthèse d'une série de dérivés du cholestérol utilisables pour la fonctionnalisation des nanotubes de carbone a été mise au point. L'utilisation de tels dérivés a pour but de favoriser les interactions entre les objets greffés et les membranes cellulaires.Par ailleurs, de nombreux intermédiaires de synthèse présentent des propriétés mésomorphes. Celles-ci ont été étudiées au moyen de différentes méthodes telles que la microscopie optique, la calorimétrie différentielle à balayage et la diffusion des rayons X.Des nanotubes HiPco ont pu être purifiés et fonctionnalisés. L'analyse de leur cytotoxicité a été abordée, celle-ci a permis de mettre en avant une diminution de la toxicité des nanotubes greffés comparée à celles de nanotubes purifiés. / Synthesis and study of mesomorphic properties of grafts for carbon nanotubes functionalizationIn order to study the toxicity of carbon nanotubes, cholesterol based derivatives were synthesized. Due to their exceptional properties, a wide field of applications is opened for carbon nanotubes. Regarding this field, knowing their toxicity becomes a key issue.The work presented here aims towards the synthesis of chemical derivatives designed to increase interactions between carbon nanotubes and a biological environment. The synthesis of a series of cholesterol derivatives aimed for the functionalization of carbon nanotubes has been developed. Such derivatives are intended to interact with cell membranes.Moreover, many synthetic intermediates have mesomorphic properties. These properties have been studied using different methods such as polarized optical microscopy (POM), differential scanning calorimetry (DSC) and X-ray scattering (MWAXS).HiPco nanotubes have been purified, functionalized and characterized with techniques such as Raman spectroscopy and X-ray diffraction (XRD).Finally, a study of carbon nanotubes toxicity is presented.

This thesis presents results of novel methodologies applied to oriented systems. Both pure liquid crystalline materials as well as molecules oriented in liquid crystalline matrices have been studied. In particular this thesis presents investigations related to various aspects of NMR in liquid crystalline media, such as, assignment of resonances and the study of director dynamics of spinning liquid crystals in different phases and with different symmetry. Simplified methods for structure determination of solutes dissolved in liquid crystal solvents have been proposed. Diffusion ordered spectroscopy has been used to study a mixture of liquid crystals of opposite diamagnetic susceptibility at its coexistent phase. The methods presented represent novel techniques to characterize the liquid crystalline phase. NMR spectroscopy which has become a method of choice for understanding ordering mechanisms of mesogens requires a robust method for obtaining assignments of the NMR spectra of various nuclei that are found in the mesogens [1, 2]. It turns out that the spectra in the isotropic phase and in the nematic phase of a liquid crystal molecule are very different due to the presence of chemical shift anisotropy in the mesophase spectrum. There are a host of methodologies available for assigning spectra in the isotropic phase [3]. These methods however fail, when applied to the spectrum of the molecules in the mesophase due to the dominating role of strong anisotropic interactions, such as homonuclear couplings among protons. Problems arising while assigning spectral lines of liquid crystals in their nematic phase have been dealt with in chapter 2. To circumvent these problems, a property of the liquid crystal molecules under off-magic angle sample spinning can be utilized. It has been shown by Courtieu et al. [4] that the director/symmetry axis of a Δχ + ve liquid crystal aligns along the spinning axis for θ between 0 ° and θm, where θ is the angle between the spinning axis and the magnetic field and θm = 54.7° is the magic angle. It may be noted that the spectrum of θ = 0° spinning angle corresponds to the normal static spectrum, while the spectrum of θ = θm corresponds to the isotropic spectrum. In an earlier study, Teearr et al. [5] had recorded the 13C liquid crystal spectra as a function of very closely spaced θ values from 90° all the way up to 0°. From these plots of chemical shift versus the angle of spinning, it is possible to follow the trajectory of each 13C line from its position from θ = θm to θ = 0° and then match the spectrum in the isotropic phase (equivalently the magic angle sample spinning spectrum of the nematic phase) to the spectrum of the static sample in the nematic phase. However this method requires recording spectra at closely spaced angle intervals, so that one can unambiguously follow the trajectory of each of the lines without missing out any crossover of trajectories. However, this operation is time consuming. In this thesis we propose an alternate method, where we utilize the fact that the above trajectory has a very distinct relationship to the isotropic and anisotropic chemical shift and the problem of assignment does not require a continuous variation of angles, but just a few selected experiments should enable the assignment of the spectrum in the anisotropic phase. Thus the method of assignment has been made simpler and faster. It is shown that in addition to the assigned isotropic spectrum, only one other Off-magic angle spinning spectrum whose spinning angle θ is accurately known is necessary to obtain the complete assignment of the static spectrum. This procedure is non-trivial due to possibilities of errors in assignments arising out of inaccuracies in the knowledge of chemical shifts and the spinning angle. A computational procedure is proposed to take into account deviations arising out of non-ideal experimental conditions. A discussion regarding the details of the procedure and also situations where there can be ambiguities and how they can be resolved has been elaborated. The developed method has been demonstrated on a well known thermotropic liquid crystalline system, N-(4-ethoxybenzylidene)-4-n-butlyaniline [EBBA]. Since assignment of resonances in the nematic phase is a primary requirement for any further analysis regarding the ordering and deeper understanding of the role of various substituents in the mesogens we believe our novel prescription will be of immense use and utility. The third chapter presents the study of director dynamics in a lyotropic liquid crystal composed of Potassium laurate, 1-Decanol and D2O [6] under variable angle sample spinning using 2H NMR spectrum of D2O. A very interesting interplay of the magnetic orienting torque due to interaction of the liquid crystal director with the magnetic field and viscous torque arising from the viscosity of the sample on the director comes to fore. The relative magnitude of these torques has a direct bearing on the spectral pattern and line shapes observed, providing valuable insights into magnetohydrodynamics of the spinning liquid crystals. This study leads to even more interesting behavior for liquid crystals which deviate from uniaxial symmetry. This competition between magnetic and viscous torques has been quantitatively visualized by simulation of the 2H spectrum. It has been possible to visualize the observed spread in the director distribution arising out of viscous torque in terms of the energetics of the system under fast spinning. If the magnetic torque dominates over the viscous torque, then the equilibrium corresponds to the director orientation of δ = 0° where the energy is at its minimum. However the viscous and magnetic torques can become comparable as it may happen if the spinning angle is close to the magic angle or when the Δχ of the system is small. In those circumstances additional energy from the viscous torque causes the distribution of the director orientation to spread further away from δ = 0° for a positive Δχ liquid crystal. The trigonometric factor [P2(cosθ)∗P2(cosδ)] being proportional to the total energy of the system has been plotted against the spinning angle. The spectrum of the biaxial phase [7] as a function of the spinning angle shows more interesting director distribution. Here the patterns of the director distribution are observed on either side of the magic angle due to the presence of more than one director. The patterns observed also have information about the symmetry of the phase. This work provides insights into magnetohydrodynamics of spinning liquid crystals and can also be of relevance to samples of biological interest such as bicelles with protein oriented in them [8]. The fourth chapter deals with a novel characterization method relevant for the biaxial phase [9]. As an off shoot of the previous chapter, it effectively overcomes the disadvantages of the previous experimental methods which require simulation and line shape fitting to extract useful parameters. The chapter also presents the measurement of geometrical parameters of oriented solutes in phases exhibiting biaxial symmetry. The measured parameters show the effect of the onset of biaxiality as significant deviation in the value of the measured parameter. The utility of liquid crystalline media as solvents in high resolution NMR spectroscopy has been very rewarding since the pioneering work of Saupe and Englert [6]. The intramolecular interactions within solutes are only partially averaged. As a result one obtains a liquid like spectrum while at the same time very useful anisotropic interactions such as dipolar couplings, chemical shift anisotropies, quadrupolar couplings and anisotropic part spin-spin J couplings are extracted [10]. NMR spectra of molecules dissolved in thermotropic liquid crystals have long been used to obtain structural and orientational information. As the same time the complexity of the spectrum increases with the increase in the number of spins and the reduction in symmetry of the molecule, which can make the spectral analysis forbidding. Generally proton spectra have been used to obtain the geometry of the proton skeleton of the molecule and the information that includes dilute X nuclei such as 13C and 15N are available only from satellites which are buried in the intense proton spectrum. Different inequivalent dilute spins coupled to protons form different coupled spin systems in their natural abundance and appear as satellites in the proton spectra. Identification of transitions belonging to each of the spin system is essential to determine heteronuclear dipolar couplings, which is a formidable task. The fifth chapter deals with development of the techniques to obtain the complete structure of the dissolved molecules including nuclei other than protons in their natural abundance. The use of inverse experiments has been elaborated to overcome the problems of sensitivity and complexity for solute molecules having larger number of spins. In the present study using HSQC and HMQC experiments, we have selectively detected spectra of each inequivalent rare spin coupled to protons in pyrazine, pyrimidine and pyridazine dissolved in thermotropic Phase 4 and Phase 5 liquid crystal solvents. This way we could obtain enhancement in the intensity of satellites signals without the interference from the signals connected to the major isotopomers. Besides, we could resolve a complex spectrum into its sub-spectra corresponding to individual 13C and 15N isotopomers. This separation of the spectra corresponding to individual sub-spin systems makes analysis easy and helps analyze larger systems with higher number of spins and lower symmetry. Besides 1H-1H dipolar couplings, 13C-1H and 15N-1H dipolar couplings have been determined in natural abundance, thereby giving the complete dipolar coupling network between all the spins in the molecule. In this treatment pyrazine, pyrimidine and pyridazine have been used as examples of methodology developed. It is expected that the method will be of wider use for several other similar systems. Chapter six describes the diffusion ordered spectroscopic investigation [11] of a phase arising out of mixing together two liquid crystals having opposite signs of diamagnetic susceptibility anisotropy [12]. Towards this end we have used CH3CN as a probe molecule. The spectrum of CH3CN has with it the information about the parallel or perpendicular orientation of the phase. Such a mixture of liquid crystals have shown interesting behavior at the critical temperature where the two phases seem to coexist. It has been an interesting question to understand what exactly happens for the molecular orientation when the macroscopic anisotropy Δχ vanishes. Earlier Jokisaari et al. [13] have varied the temperature very finely taking due precautions to maintain homogeneity and stability of temperature to the tune of ±0.05K across the sample volume. Their observation of a powder pattern exactly in the critical temperature was interpreted as arising out of a distribution of directors equally oriented in all directions. In our experiments we have measured the diffusion coefficient of the probe molecule i.e. acetonitrile as we change the temperature of the system through the critical temperature. At the critical temperature we have a situation of being able to measure the parallel and perpendicular orientational diffusion coefficients simultaneously. The measurements show that the parallel component of the diffusion coefficient has reduced and the perpendicular component has increased in comparison to the trend in the immediate neighboring temperatures, thereby indicating that at the exact critical condition the liquid crystal mixture consists of an isotropic distribution of molecules. As a check to rule out any exchange of molecules in different domains of parallel and perpendicular orientations an EXSY experiment was conducted with a mixing time which was same as that of the diffusion delay in the DOSY experiment. The EXSY spectrum showed no exchange cross peaks between the two orientations, this confirms that the anisotropy of the diffusion vanishes at the critical temperature. Nematic liquid crystals exhibit a rich variety of phases and properties. NMR is a very powerful tool to study the various phases at the microscopic and molecular level. It has also turned out that some of these properties can be usefully utilized for investigation of both small and large molecules by NMR. Thus this thesis has attempted to expand several of the techniques already available for various applications and extend the utility of NMR for the study of partially ordered systems.

The present thesis reports computer simulation studies of several phase transition related phenomena in a range of soft-condensed matter systems. A coherent unifying theme of the thesis is the understanding of dynamics of phase transitions through free energy calculations using recently developed efficient non-Boltzmann sampling methods. Based on the system/phenomena of interest, the thesis has been classified into four major parts: I. Isotropic-nematic (IN) phase transition in liquid crystals. II. Nucleation phenomena in gas-liquid transition with particular emphasis on the systems close to the spinodal curve. III. Collapse transition in linear hydrocarbon (n-alkane) chains for a varying range of length, solvent and temperature. IV. Crystallization of unbranched polymer chains in dilute solution, with particular emphasis on the temperature dependent crossover between the rod-like crystalline state and spherical molten globule state. The thesis has been further divided into ten chapters running through the four parts mentioned before. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with the power law relaxation and glassy dynamics in thermotropic liquid crystals close to the IN transition and consists of two chapters. To start with, Chapter I.1 provides an introduction to thermotropic liquid crystals. Here we briefly introduce various liquid crystalline phases, the order parameter used to characterize the IN transition, a few well established theoretical models, and we conclude with describing the recent experimental and computer simulation studies that have motivated the work described in the next chapter. In Chapter I.2, we present our molecular dynamics simulation studies on single particle and collective orientational dynamics across the IN transition for Lebwohl Lasher model, which is a well-known lattice model for thermotropic liquid crystals. Even this simplified model without any translational degrees of freedom successfully captures the short-tointermediate time power law decay recently observed in optical heterodyne detected optical Kerr effect (OHDOKE) measurements near the IN transition. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a sub-diffusive regime which is followed by a super-diffusive regime before the onset of the longtime diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in the orientational motion particularly at lower temperatures. Interestingly, this behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of recently developed transition matrix Monte Carlo (TMMC) method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order transition, hence allowing for large scale, collective, and correlated orientational density fluctuations. We attribute this large scale fluctuations as the reason for the observed power law decay of the orientational time correlation functions. Part II consists of three chapters, where we focus on the age old problem of nucleation and growth, both from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter II.1. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter II.2) we attempt to elucidate the mechanism of nucleation near the gas-liquid spinodal from a microscopic point of view. Here we construct a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. The free energy, as a function of the size of the largest cluster, develops a pronounced minimum at a subcritical cluster size close to the spinodal. This signifies a two step nature of the process of nucleation, where the rapid formation of subcritical nuclei is followed by further growth by slower density fluctuations on an uphill free energy surface. An alternative free energy pathway involving the participation of many subcritical clusters is envisaged near the spinodal where the growth of the nucleus is found to be promoted by a coalescence mechanism in contrast to the single particle addition assumption within CNT. The growth of the stable phase becomes progressively collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches. In this chapter we present our studies both in 3dimensional Lennard-Jones (LJ) system and Ising model (both 2and 3dimensions). Our general findings seem to be independent of the model chosen. While the previous chapter focuses on relatively well-studied 3-dimensional (3D) LJ system, in Chapter II.3 we present our studies on the characteristics of the nucleation phenomena in 2dimensional (2D) Lennard-Jones fluid. To the best of our knowledge this is the first extensive computer simulation study to check the accuracy of CNT in 2D. Using various Monte Carlo methods, we calculate the free energy barrier for nucleation, line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinoidal limit). In 2D, a surprisingly large cutoff (rc ≥ 7.0σ where σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. Note that typically 2.5σ is sufficient for 3D LJ fluids. We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by as much as 50% at the saturation ratio S = 1.1(defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T* = 0.427(defined as T* = KBT/ ε, where ε is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even without any cutoff to make the simple CNT inaccurate. Part III again consists of three chapters and focuses on the conformational equilibria. Collapse transition and self-organized structures of n-alkanes in solution. In Chapter III.1 we carry out a brief survey of the existing theories of polymer in solution, with particular emphasis on the collapse process in poor solvents. We also introduce the concept of “hydrophobicity” and “hydrophobic collapse”, which is now a subject enormous interest, partly because it my help in understanding the initial processes involved in protein folding. We briefly discuss the subject of formation of beautiful self-organized structures by block copolymers, and also simple homopolymers which is essentially the focus of the work embodied in the next two chapters. In Chapter III.2 we demonstrated a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures o the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like(circular) for small chains(CnH2n+2; n ≤ 20) and spherical for very long ones( n = 100), we find the emergence of ordered helical structures at intermediate lengths (n ~ 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation(characterized by well-developed 1/f noise, where f is the frequency ) between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier. This appears to support a weakly first order phase transition between the extended and the collapsed states. Chapter III.3 extends the study of previous chapter to much longer chains (n ≥ 100), which irreversibly collapse in water into globular forms. Even though the collapsed form has a nearly spherical shape, close inspection shows a propensity towards local ordering in the alignment of the polymer segments. This tendency to maintain alignment in order to maximize the number of contacts leads to a core-shell like structure, where the shell is often characterized by a bent rod-like shape consisting of two adjacent segments running in parallel. A key event associated with the initial stage of collapse seems to be the formation of a skewed ring (or loop) that serves as a “nucleation center” for rest of the chain to collapse into. Time evolution of the radial distribution function of water surrounding the polymer, shows that the density of neighboring water decreases by only about 15-20% from that of bulk water. Even though interior of the ting-like structures is fully devoid of water, solvent accessible surface representation shows that these regions are geometrically/spatially inaccessible to water molecules. We suggest that the role of water is to stabilize such ring-like structures once formed by natural conformational fluctuations of the polymer chain. This view is confirmed by observation of spontaneous formation and melting away of such ring-like entities in a polar aprotic solvent(DMSO). We also comment on the role of the flexibility of polymer chains in determining the collapse kinetics. The last part(Part IV) of the thesis consists of two chapters that deal with the crystallization of linear polymer chains from dilute solution. The way long chain polymers crystallize is drastically different from their small molecule counterparts due to their topological connectivity. Linear polymers often crystallize from dilute solution in the form of thin lamellae with well-defined crystallographic features. In Chapter IV.1 we briefly survey the current theoretical understanding and confusions associated with the highly debated field of polymer crystallization. While the last few decades have seen the development of many successful phenomenological theories, the molecular mechanism of formation of such self-organized lamellae is extremely complex and very poorly understood. There are clearly two distinct steps in polymer crystallization. Firstly, the individual linear polymers must self-organize into bundles of somewhat regular structures. These structures then further aggregate to lamellar form and crystallize into a lattice. In this respect , it has marked similarity to the problem of protein crystallization. In chapter IV.2 we present Brownian dynamics simulation studies of a single polythelene chain of length 500. Such systems can reasonably mimic the process of crystallization from dilute solutions. Our simulations could successfully reproduce some of the interesting phenomena observed in experiments and very recent computer simulation studies, including multi-center nucleation of rod-like structures within a single polymer chain, an inverse relation between lamellar thickness and temperature etc. But our primary focus has been to understand the nature of the phase transition as one traverses along the melting temperature and the underlying free energy surface. Near the melting temperature we observe a very intriguing fluctuation between the disordered molten globule state and the ordered rod-like crystalline, where these two forms have highly different shape and structure. These fluctuations have strong signature of 1/f noise or intermittency. This clearly indicates the existence of a weakly first order transition, where two widely different states with large difference in values of order parameter are separated by a rather small free energy barrier. This can be related to the experimentally observed density fluctuations that resemble spinodal decomposition. It is important to note that very similar fluctuations have been observed in our previous studies on liquid crystals (Chapter 1.2) and intermediate sized alkalines in water(Chapter III.2) that signifies a universal underlying energy landscape for these systems. We have discussed the scope of future work at the end of each chapter whenever appropriate.

This thesis, which contains fourteen chapters in two parts, presents theoretical and computer simulation studies of dynamics in supercooled liquids and thermotropic liquid crystals. These two apparently diverse physical systems are unified by a startling similarity in their complex slow dynamics. Part I consists of six chapters on supercooled liquids while Part II comprises seven chapters on thermotropic liquid crystals. The fourteenth chapter provides a concluding note. Part I starts with an introduction to supercooled liquids given in chapter 1. This chapter discusses basic features of supercooled liquids and the glass transition and portrays some of the theoretical frameworks and formalisms that are widely recognized to have contributed to our present understanding. Chapter 2 introduces a new model of binary mixture in order to study dynamics across the supercooled regime. The system consists of an equimolar mixture of the Lennard-Jones spheres and the Gay-Berne ellipsoids of revolution, and thus one of its components has orientational degrees of freedom (ODOF). A decoupling between trans-lational diffusion and rotational diffusion is found to occur below a temperature where the second rank orientational correlation time starts showing a steady deviation from the Arrhenius temperature behavior. At low temperatures, the optical Kerr effect (OKE) signal derived from the system shows a short-to-intermediate time power law decay with a very weak dependence on temperature, if at all, of the power law exponent as has been observed experimentally. At the lowest temperature investigated, jump motion is found to occur in both the translational and orientational degrees of freedom. Chapter 3 studies how the binary mixture, introduced in the previous chapter, explores its underlying potential energy landscape. The study reveals correlations between the decoupling phenomena, observed almost universally in supercooled molecular liquids, and the manner of exploration of the energy landscape of the system. A significant deviation from the Debye model of rotational diffusion in the dynamics of ODOF is found to begin at a temperature at which the average inherent structure energy of the system starts falling as the temperature decreases. Further, the coupling between rotational diffusion and translational diffusion breaks down at a still lower temperature, where a change occurs in the temperature dependence of the average inherent structure energy. Chapters 4-6 describe analytical and numerical approaches to solve kinetic models of glassy dynamics for various observables. The β process is modeled as a thermally activated event in a two-level system and the a process is described as a β relaxation mediated cooperative transition in a double-well. The model resembles a landscape picture, conceived by Stillinger [Science 267, 1935 (1995)], where the a process is assumed to involve a concerted series of the β processes, the latter being identified as elementary relaxations involving transitions between contiguous basins. For suitable choice of parameter values, the model could reproduce many of the experimentally observed features of anomalous heat capacity behavior during a temperature cycle through the glass transition as described in chapter 4. The overshoot of the heat capacity during the heating scan that marks the glass transition is found to be caused by a delayed energy relaxation. Chapter 5 shows that the model can also predict a frequency dependent heat capacity that reflects the two-step relaxation behavior. The high-frequency peak in the heat capacity spectra appears with considerably larger amplitude than the low-frequency peak, the latter being due to the a relaxation. The model, when simplified with a modified description of the a process that involves an irreversible escape from a metabasin, can be solved analytically for the relaxation time. This version of the model captures salient features of the structural relaxation in glassy systems as described in chapter 6. In Part II, thermotropic liquid crystals are studied in molecular dynamics simulations using primarily the family of the Gay-Berne model systems. To start with, chapter 7 provides a brief introduction to thermotropic liquid crystals, especially from the perspective of the issues discussed in the following chapters. This chapter ends up with a detail description of the family of the Gay-Berne models. Chapter 8 demonstrates that a model system for calamitic liquid crystal (comprising rod-like molecules) could capture the short-to-intermediate time power law decay in the OKE signal near the isotropic-nematic (I-N) phase transition as observed experimentally. The single-particle second rank orientational time correlation function (OTCF) for the model liquid crystalline system is also found to sustain a power law decay regime in the isotropic phase near the I-N transition. On transit across the I-N phase boundary, two power law decay regimes, separated by a plateau, emerge giving rise to a step-like feature in the single-particle second rank OTCF. When the time evolution of the rotational non-Gaussian parameter is monitored as a diagnostic of spatially heterogeneous dynamics, a dominant peak is found to appear following a shoulder at short times, signaling the growth of pseudonematic domains. These observations are compared with those relevant ones obtained for the supercooled binary mixture, as discussed in chapter 2, in the spirit of the analogy suggested recently by Fayer and coworkers [J. Chem. Phys. 118, 9303 (2003)]. In chapter 9, orientational dynamics across the I-N transition are investigated in a variety of model systems of thermotropic liquid crystals. A model discotic system that consists of disc-like molecules as well as a lattice system have been considered in the quest of a universal short-to-intermediate time power law decay in orientational relaxation, if any. A surprisingly general power law decay at short to intermediate times in orientational relaxation is observed in all these systems. While the power law decay of the OKE signal has been recently observed experimentally in calamitic systems near the I-N phase boundary and in the nematic phase by Fayer and coworkers [J. Chem. Phys. 116, 6339 (2002), J. Phys. Chem. B 109, 6514 (2005)], the prediction for the discotic system can be tested in experiments. Chapter 10 presents the energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals by determining the inherent structures of a family of one-component Gay-Berne model systems. This study throws light on the interplay between the orientational order and the translational order in the mesophases the systems exhibit. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures. The inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the I-N transition and this breakdown is found to occur at a temperature below which the system explores increasingly deeper potential energy minima. There exists a remarkable similarity in the manner of exploration of the potential energy landscape between the Gay-Berne systems studied here and the well known Kob-Andersen binary mixture reported previously [Nature, 393, 554 (1998)]. In search of a dynamical signature of the coupling between orientational order and translational order, anisotropic translational diffusion in the nematic phase has been investigated in the Gay-Berne model systems as described in chapter 11. The translational diffusion coefficient parallel to the director D// is found to first increase and then decrease as the temperature drops through the nematic phase. This reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant for the first time. The non-monotonic temperature behavior of D// can thus be viewed from an energy landscape analysis as a dynamical signature of the coupling between orientational and translational order at the microscopic level. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion. Chapter 12 investigates the validity of the Debye model of rotational diffusion near the I-N phase boundary with a molecular dynamics simulation study of a Gay-Berne model system for calamitic liquid crystals. The Debye model is found to break down near the I-N phase transition. The breakdown, unlike the one observed in supercooled molecular liquids where a jump diffusion model is often invoked, is attributed to the growth of orientational pair correlation. A mode-coupling theory analysis is provided in support of the explanation. Chapter 13 presents a molecular dynamics study of a binary mixture of prolate ellipsoids of revolution with different aspect ratios interacting with each other through a generalized Gay-Berne potential. Such a study allows to investigate directly the aspect ratio dependence of the dynamical behavior. In the concluding note, chapter 14 starts with a brief summary of the outcome of the thesis and ends up with suggestion of a few relevant problems that may prove worthwhile to be addressed in future.

Spin selective MQ-SQ correlation has been demonstrated by either selective pulses in homo-nuclear spin systems in isotropic and weakly orienting chiral media or by nonselective pulses in hetero-nuclear spin systems in strongly aligned media. As a consequence of the spin selective correlation, the coherence transfer pathway from MQ to SQ is spin state selective. This two dimensional approach enables the utilization of the passive couplings (remote couplings) to break a complex one dimensional spectrum into many sub spectra. Each sub spectrum contains fewer transitions and hence fewer couplings (active couplings). The role of the passive couplings is to displace the sub spectra and measurement of the displacements taking into account their relative tilt provides the magnitude of the passive couplings along with relative signs. Further possibility of a spin state selective MQ-SQ resolved experiment to determine very small remote couplings otherwise buried within linewidth in one dimensional spectrum has been demonstrated. The resolution of the multiple quantum spectrum in indirect dimension has also been exploited to separate the sub spectra. The technique renders the analysis of complex spectrum in isotropic system much simpler. The potentialities of the technique have also been demonstrated for discrimination of optical enantiomers and derivation of the residual dipolar couplings from very complicated spectrum. The second order spectrum in strongly aligned media restrict selective excitation, however in hetero-nuclear spin system the nonselective pulses on protons do not interact with the hetero-nuclear spins. Thus the weakly coupled part of a strongly coupled spectrum has been exploited for simplifying the second order spectrum and thereby its analysis. Thus several methodologies derived from spin selective correlation has been demonstrated. Enantiopure spectrum has been recorded from a mixture of R and S enantiomers by a novel pulse scheme called Double Quantum Selective Refocusing Experiment. The dipolar coupled methyl protons in weakly orienting media are utilized. The selective excitation of double quantum coherence reduces the three spin system into a two spin system and remote couplings are refocused which otherwise leads to broadening. The sum of passive couplings being different for the enantiomers resolution in the DQ dimension is enhanced and thereby their discrimination. Finally several decoupling schemes has been compared in the indirect dimension of HSQC experiment to resolve 13C satellite spectra otherwise buried within line width for increased confidence in determining hetero-nuclear framework information.