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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Dans cette thèse nous étudions la relation entre la conformation et la dynamique de la chromatine en nous basant sur une classe de modèles de polymères aléatoirement réticulé (AR). Les modèles AR permettent de prendre en compte la variabilité de la conformation de la chromatine sur l’ensemble d’une population de cellules. Nous utilisons les outils tels que les statistiques, les processus stochastiques, les simulations numériques ainsi que la physique des polymères afin de déduire certaines propriétés des polymères AR a l’équilibre ainsi que pour des cas transitoires. Nous utilisons par la suite ces propriétés afin d’élucider l’organisation dynamique de la chromatine pour diverses échelles et conditions biologiques. Dans la première partie de ce travail, nous développons une méthode générale pour construire les polymères AR directement à partir des données expérimentales, c’est-à-dire des données de capture chromosomiques (CC). Nous montrons que des connections longue portées persistantes entre des domaines topologiquement associés (DTA) affectent le temps de rencontre transitoire entre les DTA dans le processus d’inactivation du chromosome X. Nous montrons de plus que la variabilité des exposants anormaux – mesurée en trajectoires de particules individuelles (TPI) – est une conséquence directe de l’hétérogénéité dans la position des réticulations. Dans la deuxième partie, nous utilisons les polymères AR afin d’étudier la réorganisation locale du génome au point de cassure des deux branches d’ADN (CDB). Le nombre de connecteurs dans le modèle de polymère AR est calibré à partir de TPI, mesurées avant et après la CDB. Nous avons trouvé que la perte modérée de connecteur autour des sites de la CDB affecte de façon significative le premier temps de rencontre des deux extrémités cassées lors du processus de réparation d’une CBD. Nous montrons comment un micro-environnement génomique réticulé peut confiner les extrémités d’une cassure, empêchant ainsi les deux brins de dériver l’un de l’autre. Dans la troisième partie nous déduisons une expression analytique des propriétés transitoires et a l’équilibre du modèle de polymère AR, représentant une unique région DTA. Les expressions ainsi obtenue sont ensuite utilisées afin d’extraire le nombre moyen de connexions dans les DTA provenant des données de CC, et ce à l’aide d’une simple procédure d’ajustement de courbe. Nous dérivons par la suite la formule pour le temps moyen de première rencontre (TMPR) entre deux monomères d’un polymère AR. Le TMPR est un temps clé pour des processus tels que la régulation de gènes et la réparation de dommages sur l’ADN. Dans la dernière partie, nous généralisons le modèle AR analytique afin de prendre en compte plusieurs DTA de tailles différentes ainsi que les connectivités intra-DTA et extra-DTA. Nous étudions la dynamique de réorganisation de DTA lors des stages successifs de différentiations cellulaires à partir de données de CC. Nous trouvons un effet non-négligeable de la connectivité de l’inter-DTA sur les dynamiques de la chromatique. Par la suite nous trouvons une compactification et une décompactification synchrone des DTA à travers les différents stages. / In this dissertation we study the relationship between chromatin conformation and dynamics using a class of randomly cross-linked (RCL) polymer models. The RCL models account for the variability in chromatin conformation over cell population. We use tools from statistics, stochastic process, numerical simulations and polymer physics, to derive the steady-state and transient properties of the RCL polymer, and use them to elucidate the dynamic reorganization of the chromatin for various scales and biological conditions. In the first part of this dissertation work, we develop a general method to construct the RCL polymer directly from chromosomal capture (CC) data. We show that persistent long-range connection between topologically associating domain (TAD) affect transient encounter times within TADs, in the process of X chromosome inactivation. We further show that the variability in anomalous exponents, measured in single particle trajectories (SPT), is a direct consequence of the heterogeneity of cross-link positions. In the second part, we use the RCL polymer to study local genome reorganization around double strand DNA breaks (DSBs). We calibrate the number of connectors in the RCL model using SPT data, acquired before and after DSB. We find that the conservative loss of connectors around DSB sites significantly affects first encounter times of the broken ends in the process of DSB repair. We show how a cross-linked genomic micro-environment can confine the two broken ends of a DSB from drifting apart. In the third part, we derive analytical expressions for the steady-state and transient properties of the RCL model, representing a single TAD region. The derived expressions are then used to extract the mean number of cross-links in TADs of the CC data, by as simple curve fitting procedure. We further derive formula for the mean first encounter time (MFET) between any two monomers of the RCL polymer. The MFET is a key time in processes such as gene regulation. In the last part, we generalize the analytical RCL model, to account for multiple TADs with variable sizes, intra, and inter-TAD connectivity. We study the dynamic reorganization of TADs, throughout successive stages of cell differentiation, from the CC data. We find non-negligible effect of inter-TAD connectivity on the dynamics of the chromatin. We further find a synchronous compaction and decompaction of TADs during differentiation.

<p>This dissertation includes my research works during Ph.D. career about three different kinds of random walks in (dynamical) random environments. It includes my two published papers “Functional weak limit of random walks in cooling random environments” which has been published in electronic communications in probability in 2020, and “Variable speed symmetric random walk driven by the simple symmetric exclusion process” which is the joint work with Peterson and Menezes and has been published in electronic journals of probability in 2021. This dissertation also includes my two other projects, one is the joint work with Janjigian and Emrah about moderate deviation and exit time estimates in integrable directed polymer models. The other one is the joint work with Peterson and Conrado that extends the weak limit of random walks in cooling randon environments with underlying environment is in the transient case.</p>