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Les nanocomposites polymère intéressent depuis de nombreuses années la communauté scientifique, du fait, notamment, de leurs bonnes propriétés mécaniques. Il est établi que l'amélioration des propriétés mécaniques observées dans les nanocomposites est principalement due à des effets de structure (dispersion des particules) et à des effets d'interface (interactions particule/matrice et particule/particule). Cependant, de nombreux résultats expérimentaux restent difficiles à expliquer. Dans ce contexte, nous avons synthétisé des nanocomposites modèles constitués de nanoparticules de silice greffées de chaînes de polystyrène (PS) (ou de PS-b-poly(acrylate de tertio-butyle)) par polymérisation radicalaire contrôlée par les nitroxydes (NMP) et réparties dans une matrice de PS. Ces nanocomposites ont ensuite été caractérisés en couplant la diffusion de rayons X et la microscopie électronique à transmission. En variant la taille des chaînes de la matrice, nous sommes parvenus à obtenir différentes répartitions spatiales de particules allant de la dispersion totale à l'agrégation en passant par un état intermédiaire s'apparentant à un réseau connecté aux fractions volumiques élevées. Les propriétés mécaniques de ces nanocomposites ont été étudiées par des mesures de cisaillement aux faibles fréquences puis reliées aux différentes dispersions observées. Enfin, nous avons mesuré la dynamique locale et intermédiaire des chaînes de polymères greffées dans les matériaux préparés en couplant la diffusion quasiélastique des neutrons (rétrodiffusion et écho de spin) et la résonance magnétique nucléaire. Ces mesures ont ensuite été reliées aux propriétés mécaniques des nanocomposites. / Polymer nanocomposites interest for many years the scientific community, due in particular, to their good mechanical properties. It is established that the improvement of these properties observed in nanocomposites are mainly due to structural effects (particles dispersion) and interfacial effects (particle/matrix and particles/particles interactions). However, many experimental results are difficult to explain. In such a context, we have synthesized model nanocomposites based on silica nanoparticles grafted with polystyrene (PS) chains (or PS-b-poly(ter-butyl acrylate)) by nitroxide mediated polymerization and dispersed in a PS matrix. Then, these nanocomposites have been characterized by combining X-ray scattering and transmission electronic microscopy. By varying the length of the matrix chains, we have obtained different fillers structure going from individual nanoparticles dispersion to aggregate, up to an intermediate state (equivalent to an interconnected network for high volume fraction). Mechanical properties of these nanocomposites were studied by the mean of shear measurements at low frequency and linked to the different states of dispersion observed. Finally, we have measured local and intermediate dynamics of the grafted polymer chains by combining quasielastic neutron scattering (backscattering and spin echo) and nuclear magnetic resonance. Then, we have linked these measurements with the mechanical properties of the materials.

This thesis presents our recent study of few interesting problems involving activated processes. This chapter gives an overview of the thesis. It is now possible to do single molecule experiments involving enzyme molecules. The kinetics of such reactions exhibits dynamic disorder associated with conformational changes of the enzyme-substrate complex. The static disorder and dynamic disorder of reaction rates, which are essentially indistinguishable in ensemble-averaged experiments, can be determined separately by the real-time single-molecule approach. In our present work we have given a theoretical description of how rate of reactions involving dynamic disorder is studied using path integral approach. It is possible to write the survival probability and the rate of the process as path integrals and then use variational approaches to get bounds for both. Though the method is of general validity, we illustrate it in the case of electronic relaxation in stochastic environment modeled by a particle experiencing diffusive motion in harmonic potential in presence of delta function sink. The exact solution of corresponding Smoluchowski equation was found earlier[1] analytically in Laplace domain with sink having arbitrary strength and position. Exact evaluation of path integral calculation to survival probability is not possible analytically. Wolynes et al.[2] have done an approximate calculation to get bounds to the survival probability in the Laplace domain. A bound in the Laplace domain is not as useful as a bound in the time domain and hence we use the direct approximate variational path integral technique to calculate both lower and upper bound of survival probability in time domain. We mimic the delta function sink by quadratic sink for which the path integral can be solved exactly. The strength of the quadratic sink is treated as variational parameter and using the optimized value for it, one can estimate the optimized lower as well as upper bound of survival probability. We have also calculated a lower bound to the rate. The variational results are compared with the exact ones, and it is found that the results for the two parameter case are better than those of one parameter case. To understand how good our approximation is, we calculate the bounds in survival time and found them to be in good agreement with exact results. Our approach is valid for any arbitrary initial distribution that one may start with. We consider the Kramers problem for a long chain polymer trapped in a biased double well potential. Initially the polymer is in the less stable well and it can escape from this well to the other well by the motion of its N beads across the barrier to attain the configuration having lower free energy. In one dimension we simulate the crossing and show that the results are in agreement with the kink mechanism suggested earlier. In three dimensions, it has not been possible to get analytical “kink solution”for an arbitrary po-tential; however, one can assume the form of the solution of the non-linear equation as a kink solution and then find a double well potential in three dimensions. To verify the kink mechanism, simulations of the dynamics of a discrete Rouse polymer model in a double well in three dimensions were done. We find that the time of crossing is proportional to the chain length which is in agreement with the results of kink mechanism. The shape of the kink solution is also in agreement with the analytical solution in both one and three dimensions. We then consider the dynamics of a short chain polymer crossing over a free energy barrier in space. Adopting the continuum version of the Rouse model, we find exact expressions for the activation energy and the rate of crossing. For this model, the analysis of barrier crossing is analogous to semiclassical treatment of quantum tunneling. Finding the saddle point for the process requires solving a Newton-like equation of motion for a fictitious particle. The analysis shows that short chains would cross the barrier as a globule. The activation free energy for this would increase linearly with the number of units N in the polymer. The saddle point for longer chains is an extended conformation, in which the chain is stretched out. The stretching out lowers the energy and hence the activation free energy is no longer linear in N . The rates in both the cases are calculated using a multidimensional approach and analytical expressions are derived using a new formula for evaluating the infinite products. However, due to the harmonic approximation made in the derivation, the rates are found to diverge at the point where the saddle point changes over from the globule to the stretched out conformation. The reason for this is identified to be the bifurcation of the saddle to give two new saddles. A correction formula is derived for the rate in the vicinity of this point. Numerical results using the formulae are presented. It is possible for the rate to have a minimum as a function of N . This is due to the confinement effects in the initial state. We analyze the dynamics of a star polymer of F arms confined to a double well potential. Initially the molecule is confined to one of the minima and can cross over the barrier to the other side. We use the continuum version of Rouse-Ham model. The rate of crossing is calculated using the multidimensional approach due to Langer[3].Finding the transition state for the process is shown to be equivalent to the solution of Newton’s equations for F independent particles, moving in an inverted potential. For each star polymer, there is a critical total length N Tc below which the polymer crosses over as a globule. The value of NTc depends on the curvature at the top of the barrier as well as the individual arm lengths. So we keep the lengths of (F -1) arms fixed and increase the length of the F th arm to get the minimum total length NTc. Below NTc the activation energy is proportional to the total arm length of the star. Above N Tc the star crosses the barrier in a stretched state. Thus, there is a multifurcation of the transition state at NTc. Above NTc, the activation energy at first increases and then decreases with increasing arm length. This particular variation of activation energy results from the fact that in the stretched state, only one arm of the polymer is stretched across the top of the barrier, while others need not to be. We calculate the rate by expanding the energy around the saddle upto second order in the fluctuations. As we use the continuum model, there are infinite modes for the polymer and consequently, the prefactor has infinite products. We show that these infinite products can be reduced to a simple expression, and evaluated easily. However, the rate diverges near N Tc due to the multifurcation, which results in more than one unstable mode. The cure for this divergence is to keep terms upto fourth order in the expansion of energy for these modes. Performing this, we have calculated the rate as a function of the length of the star. It is found that the rate has a nonmonotonic dependence on the length, suggesting that longer stars may actually cross over faster.

Entangled polymeric fluids subjected to shear display a stress plateau through a range of shear rates. The formation of this plateau is often attributed to an entanglement-disentanglement transition in scientific literature. However, to our best knowledge in situ studies recovering the intermediate scattering function of polymer dynamics under shear have until now never been performed. This thesis documents the successful development of a high viscosity shear device whose interaction with polarized neutrons is small enough to allow use for Neutron Spin Echo spectroscopy. Further, first measurements towards the direct observation of the variation of the degree of entanglement throughout increasing shear are documented, albeit yet for too short Fourier times to measure beyond Rouse dynamics.

One of the important dynamic parameter characterizing the properties of polymer nanocomposite is viscosity. It is a quantity of interest on macroscopic scale also. A thorough study of viscosity in case of polymer nanocomposite has not been carried out in the existing literature. In this work we used atomic force microscope, force-distance spectroscopy to experimentally measure the viscosity of polymer and polymer nanocomposite thin films. In particular we try to tune viscosity by changing the nature of interface of polymer grafted nanoparticle and polymer melt. The interface nature in varied by changing the miscibility parameter ( f ), defined as the ratio of grafted chain length to the matrix chain length. Using coarse-grained molecular dynamic simulations, dynamics at the nanoparticle-matrix interface is explored by calculating slip length and mobility at the interface. Equilibrium molecular dynamic simulation is employed to calculate the viscosity of nanocomposite. Chapter 1 We introduce some basic models for polymer chain conformation and dynamics. The known facts about the structural and dynamics of polymer grafted nanoparticle are also described. Chapter 2 We present our experiment method and results for various nanocomposite systems for two different volume fractions of nanoparticles and for two different thicknesses. We show that introduction of nanoparticles causes reduction in viscosity of thin film with respect to the neat polymer films. Further for the low volume fraction system (0:5%) the extent of reduction decreases with increasing f -value and almost matching the neat system at the highest f . At high volume fraction (1%), for lower f we observe a reduction in viscosity and for highest f surprisingly there is an increase in viscosity of nanocomposite with respect to the neat system with a cross-over for intermediate f . We attribute the effects to possible slip at the nanoparticle-matrix interface. A rough estimation of slip length from the measured value of viscosity of nanocomposite and pure polymer is provided which strongly supports our idea of slip at the interface Chapter 3 Briefly discusses some basic aspects of molecular dynamic simulation. Chapter 4 Using MD simulation we calculate the slip-length at the grafted nanoparticle-matrix interface for various systems with different f values. A spherical core grafted with atoms same as the matrix is kept fixed at the canter of simulation box. The particle is rotated for calculating slip length. We also look at the mobility variation of matrix chains as a function of radial distance from the centre of nanoparticle. From both slip-length and mobility calculation we observe that slip length as well as mobility is higher for lower f systems as compared to higher f thus supporting our assertion of slip as the most likely cause for our experimental observations. Chapter 5 Now instead of single grafted nanoparticle we have multiple nanoparticles which are free to move in the matrix. Using Green-Kubo formalism we calculate the equilibrium viscosity for pure polymer and nanocomposite systems from MD simulations. We observe increase in viscosity for nanocomposite system as compared to the pure polymer system. We also look at various structural and dynamical changes, that occurs in the filled system with respect to neat system, that leads to such increase in viscosity.

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This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.