Rozprawy doktorskie na temat „Soft matther polymer physics”

Recent years have seen remarkable progress in our understanding of physical aging in nondisordered systems with slow, i.e. glassy-like dynamics. In many systems a single dynamical length L(t), that grows as a power-law of time t or, in much more complicated cases, as a logarithmic function of t, governs the dynamics out of equilibrium. In the aging or dynamical scaling regime, these systems are best characterized by two-times quantities, like dynamical correlation and response functions, that transform in a specific way under a dynamical scale transformation. The resulting dynamical scaling functions and the associated non-equilibrium exponents are often found to be universal and to depend only on some global features of the system under investigation. We discuss three different types of systems with simple and complex aging properties, namely reaction diffusion systems with a power growth law, driven diffusive systems with a logarithmic growth law, and a non-equilibrium polymer network that is supposed to capture important properties of the cytoskeleton of living cells. For the reaction diffusion systems, our study focuses on systems with reversible reaction diffusion and we study two-times functions in systems with power law growth. For the driven diffusive systems, we focus on the ABC model and a related domain model and measure two- times quantities in systems undergoing logarithmic growth. For the polymer network model, we explain in some detail its relationship with the cytoskeleton, an organelle that is responsible for the shape and locomotion of cells. Our study of this system sheds new light on the non- equilibrium relaxation properties of the cytoskeleton by investigating through a power law growth of a coarse grained length in our system.
Ph. D.

De nombreuses études théoriques et expérimentales ont été menées au cours des 30 dernières années afin d'établir le lien entre les propriétés d'interaction des protéines, leurs transitions de phase et leur auto-assemblage. Des avancées significatives ont ainsi été permises grâce à l'application de concepts et méthodes de la physique des polymères et des colloïdes. Ces études ont, pour la majeure partie d'entre elles, été limitées à des protéines d'intérêt médical et à des protéines animales. Ce travail de thèse vise à appliquer ce type d'approche aux protéines végétales afin de mieux comprendre leurs propriétés d'interaction à l'origine de leurs propriétés fonctionnelles au sein des grains et dans les matrices alimentaires. Ce travail a été mené sur un isolat de protéines de réserve du blé composé principalement de la fraction monomérique: les gliadines. Nous avons étudié les transitions de phase des gliadines afin de mieux comprendre leurs propriétés d'interaction d'une part et les structures associées d'autre part. Dans un premier temps, une procédure d'extraction a été développée afin de travailler sur un isolat de composition contrôlée dont les masses moléculaires sont comprises entre 20 kDa et 300 kDa. Le comportement de phase de cet isolat a ensuite été étudié en diminuant la qualité du solvant. Nous avons ainsi déterminé le diagramme de phases (T-Φ), où T est la température et Φv la fraction volumique des gliadines. Cette étude a mis en évidence une séparation de phase de type liquide-liquide dans le système par diminution de la température. Une analyse détaillée de la répartition des protéines au sein des deux phases en fonction de leur masse moléculaire a permis d'identifier une masse moléculaire critique séparant des protéines de comportement de type colloïdal et des protéines de comportement de type polymérique. A partir du diagramme de phase, deux études structurales ont été effectuées. La première a étudié les cinétiques de séparation de phase lors de la diminution de la température pour caractériser la dynamique locale de séparation de phase et identifier les mécanismes qui génèrent les systèmes concentrés. Deux grands types de mécanismes de séparation de phase ont été identifiés : nucléation-croissance et décomposition spinodale. La seconde étude structurale a consisté à établir l'équation d'état pression osmotique vs concentration dans des conditions de bon solvant et à caractériser la structure des dispersions de protéines associée. La relation pression osmotique vs fraction volumique a permis de mettre en évidence l'existence de plusieurs régimes de structuration, associés à des changements de structure secondaire et de propriété rhéologique. La discussion générale permet de mettre en relation les propriétés thermodynamiques déduites de cette approche expérimentale et les changements structuraux observés à différentes échelles
A substantial body of theoretical and experimental studies has been conducted over the last 30 years to establish the link between protein interaction properties, phase transitions and self-assembly. Both colloidal and polymer physics provide a new framework for understanding the driving force for proteins phase behaviour. Such studies have been limited to health-related proteins and to a few food proteins, mainly animal proteins such as casein, whey proteins. This thesis aims to apply this approach to plant proteins to better understand their interactions properties, at the basis of their functional properties within grains and food matrices. This work was carried out on a wheat storage protein isolate mainly composed of the monomeric fraction: gliadins.The objective of this PhD thesis is to investigate the phase transitions of wheat proteins to develop our knowledge on their interaction properties and the associated structures. We organized our experimental approach in five steps. First, we developed an extraction procedure to work on a protein isolate of controlled composition with molecular weight ranging from 20 to 300 kg mol-1. Then, we investigated the phase behaviour of the protein isolate by decreasing the solvent quality, here the temperature. We determined the T-Φ phase diagram, where T is the temperature and Φv the protein volume fraction, that maps the phase and structural transitions of the proteins. This study showed the existence of a liquid-liquid phase separation in the system upon a temperature decrease. We evidenced two different behaviours among proteins as a function of their MWs and highlighted a critical protein size above which the molecular weight is the key determinant of the protein properties. From the phase diagram, two structural studies were conducted. The first one studied the kinetics of phase separation upon temperature decrease to characterize the local dynamics of phase separation and to identify the mechanisms that generate concentrated systems. Two main mechanisms of phase separation have been identified: nucleation-growth and spinodal decomposition. The second one studied the effect of protein concentration on the multi-scale structure of wheat gliadins in good solvent. The integration of all these results allowed us to build the phase diagram of wheat gliadins, integrating thermodynamic and structural data

Nous avons étudié la friction de SBR (Styrene Butadiene Rubber) fondu sur des surfaces de faible rugosité portant des chaines ancrées de SBR, par mesures simultanées de la vitesse locale à la paroi (techniques de vélocimétrie laser par photolyse, mises au point au laboratoire pour des écoulements Couette-plan) et de la contrainte transmise. Le SBR est très enchevêtré par rapport aux études précédentes : ceci entraîne que les taux de cisaillement accessibles dans la fenêtre expérimentale peuvent être supérieurs à l'inverse du temps de reptation des chaines. Afin d'obtenir des surfaces avec des chaines de longueur et de densité contrôlées, nous avons d'abord utilisé des SBR fonctionnalisés monochlorosilane. Cette voie n'a pas abouti en raison d'impuretés résiduelles de synthèse créant des défauts dans les couches. Nous avons alors adsorbé des copolymères diblocs SBR-PDMS dont le bloc PDMS court s'adsorbe plus fortement a la surface que le bloc SBR. Dans toutes les expériences de friction sur des surfaces portant des chaines de SBR, nous avons observé le passage progressif d'un régime de glissement faible vers un régime de glissement fort en fonction du taux de cisaillement. Nous avons observé de manière quasi systématique un blocage de la contrainte sur une large gamme de vitesses de glissement, d'où une friction non linéaire, correspondant à la plage des vitesses de la transition faible -- fort glissement. La comparaison avec les modèles de Brochard-de Gennes ou d'Ajdari et al. reste qualitative compte tenu du nombre restreint de couches contrôlées, mais ces transitions de glissement et le blocage de contrainte correspondent bien an mécanisme d'étirement progressif et d'extraction des chaines ancrées en surface.

En dépit de leur importance pratique considérable, et bien que de nombreuses expériences établissent une corrélation certaine entre les hétérogénéités d'interaction de surface (rugosité ou inhomogénéités chimiques) et les propriétés de friction des surfaces, le rôle de ces interactions sur la friction n'est encore pas bien décrit par les modèles et les expériences existants. Dans ce travail de thèse, nous nous sommes intéressés à l'identification des mécanismes moléculaires de la friction aux interfaces polymères souples. Dans ce contexte, nous avons réalisé deux études complémentaires. La première partie du travail concerne le mouvement d'une ligne triple solide-liquide-vapeur qui se déplace sur une surface solide sous l'effet de différentes forces (gravité, forces capillaires et tensions interfaciales), et en particulier le lien entre le piégeage et le dépiégeage de la ligne triple et l'hystérèse de l'angle de contact. Cette méthode permet de mesurer des angles de contact d'avancée et de reculée avec une précision sans précédent (0,1°)et s'avère être particulièrement sensible aux mécanismes qui tendent à ancrer la ligne triple. Ceci en fait un outil de choix pour étudier la friction liquide/solide. Dans la seconde partie du travail, nous avons cherché à comprendre comment des chaînes de polymère flexibles, fortement ancrées sur une surface solide, dans le régime des fortes densités de greffage affectent la friction entre une telle surface et un élastomère réticulé constitué du même polymère. Nous avons montré que le comportement en friction de cette couche confinée suit exactement le comportement rhéofluidifiant observé pour des couches de fondu de masses molaires équivalentes mais avec un temps de relaxation beaucoup plus long que celui des chaînes en fondu,la reptation n'étant pas permise pour les chaînes ancrées. Enfin, en comparant les résultats obtenus pour des couches greffées chimiquement à une extrémité et des couches fortement adsorbées, ayant par ailleurs les mêmes caractéristiques moléculaires (masse molaire des chaînes et épaisseur de la couche ancrée), nous avons mis en évidence que la friction est remarquablement sensible à l'organisation moléculaire au sein de la couche ancrée.

Le confinement nanométrique permet d'obtenir la frustration des fluctuations et/ou des transitions de phases spontanées qu'un fluide moléculaire présente en volume (i.e. en " bulk "). Le confinement au sein de matrices poreuses est donc une voie usuelle de stabilisation de phases métastables. Nous détaillons ici les propriétés structurales, dynamiques et thermodynamiques de deux systèmes moléculaires confinés : dans un premier chapitre, nous nous intéressons au cas de l'eau puis, dans un deuxième chapitre, nous traitons le cas spécifique d'un polymère semi-cristallin. Le confinement permet d'abaisser considérablement le point de fusion du fluide confiné. Cette propriété a été récemment mise à profit dans la cadre de nombreux travaux visant à tester l'existence d'un hypothétique point critique à basse température dans l'eau volumique à 228 K and 100 MPa. Dans cette contribution, nous mettons en évidence des propriétés dynamiques surprenantes de l'eau interfaciale à basse température (de 100 à 300 K). Nous proposons un modèle de percolation décrivant les transitions dynamiques et thermodynamiques que nous observons à 150, 220 et 240 K. Nous proposons une description cohérente de cette eau à deux dimensions et de ses propriétés. Nous invoquons le rôle dominant des interactions de surface pour remettre en cause la pertinence de l'utilisation de l'eau confinée pour prouver l'existence d'un point critique à basse température dans l'eau volumique. Cette étude met cependant en évidence l'existence d'une transition liquide-liquide (l'une des conditions pour observer un point critique) impliquant des molécules d'eau. Récemment, un " effet corset " a été proposé : le confinement induirait une réduction d'un ordre de grandeur du diamètre du tube de reptation d'un polymère (quelques nanomètres en volume contre quelques angströms sous confinement). Dans le second chapitre, nous utilisons une approche par diffusion de neutrons pour accéder à une description multi-échelles de la dynamique d'un polymère (en volume puis sous confinement) de l'échelle atomique à temps court (picosecondes) jusqu'à une dizaine de nanomètres, à temps long (600 nanosecondes). Cette étude détaillée de la dépendance spatiale de la relaxation temporelle des chaînes de polymère ne permet pas de mettre en évidence d'"effet corset ". De façon générale, lorsque l'on cherche à tirer profit du confinement nanométrique pour obtenir des "effets de volume", en plus d'"effets de surface" parasites décrits dans le premier chapitre, on est également confronté à une perte significative d'information induite par la moyenne spatiale des observables spectroscopiques. Nous décrivons dans le deuxième chapitre comment utiliser des matrices de confinement orientées macroscopiquement pour s'affranchir de ces effets indésirables et/ou limitants. Dans le troisième et dernier chapitre, nous définissons un système de confinement nanométrique qui permet d'associer i) une orientation macroscopique des pores et ii) une absence totale d'interactions de surface. Un tel système permet d'envisager des effets de volume unidimensionnels très significatifs et ayant une portée sur des distances macroscopiques. Nous discutons pourquoi de tels " tuyaux nanométriques" peuvent potentiellement intéresser à la fois la recherche fondamentale et l'industrie.

The recent development of a framework called non-affine lattice dynamics made it possible to calculate the elastic moduli of disordered systems directly from their microscopic structure and potential energy landscape at zero temperature. In this thesis different types of disordered systems were studied using this framework. By comparing the shear modulus and vibrational properties of nearest neighbour spring networks based on depleted lattices we were able to show that the dominating quantity of the system’s non-affine reorganisation during shear deformation is the affine force field. Furthermore we found that different implementation of disorder lead to the same behaviour at the isostatic point. Later we studied the effect of long range interaction in such depleted lattices with regard to spatial correlation local elasticity. We found that the implementation of long springs with decaying spring constant reproduced the spatial correlation observed in simulations of Lennard-Jones glasses. Finally we looked at simple freely rotating polymer model chains by extending the framework to angular forces and studied the dependence of the shear modulus and the vibrational density of states (VDOS) and length and bending stiffness of the chains. We found that the effect of chain length on the shear modulus and the vibrational density of states diminishes as it depends on the number of backbone bonds in the system. This number increases fast for short chains as many new backbone bonds are introduced but slows down significantly when the chain length reaches 50 monomers per chain. For the dependence on the bending stiffness we found a rich phenomenology that can be understood by looking at specific motions of the monomers relative the the chain geometry. We were able to trace back the different regimes of the VDOS to the simple model of the triatomic molecule. We also explored the limits of non-affine lattice dynamics when describing systems at temperatures T > 0 and gave an approximate solution for the shear modulus in this case.

Ce manuscrit présente les résultats d'expériences illustrant différentes manifestations de la présence de polymères dans un écoulement. Pour chacune d'elles, nous étudions l'interaction entre la structure microscopique et l'écoulement.Lorsqu'une goutte se détache d'un capillaire, la colonne de liquide liant la goutte au capillaire doit se rompre. Pour les liquides simples, l'amincissement suit des lois universelles bien établies. La dynamique de détachement d'une goutte de fluide complexe est très différente. Pour les solutions de polymères, après une phase de décroissance rapide du diamètre de cette colonne, il se forme un long filament cylindrique entre la goutte et le capillaire. Afin de mieux comprendre comment les polymères présents en solution donnent naissance à ce filament, nous avons observé leurs conformations au cours du détachement. Ces observations confirment que l'étirement des polymères est à l'origine du ralentissement du processus de détachement. Cependant, lors de l'amincissement du filament, la distribution des longueurs reste inchangée. Ce résultat inattendu, nous a amené à mettre en place une nouvelle méthode pour estimer la viscosité élongationnelle.D'autres expériences sont présentées, l'une porte sur un effet de déplétion qui apparait lors de l'écoulement confiné d'une solution de polymères, alors que l'autre porte sur l'écoulement instable d'une solution concentrée de polymères dans une conduite rectiligne.

Le mouillage d'un substrat soluble est une situation couramment rencontrée dans la vie de tous les jours les jours. Par exemple, les motivations pratiques de cette étude concernent la préparation de boissons à partir de poudres déshydratées, constituées de substances solubles dans l'eau telles que les glucides. Les modèles hydrodynamiques décrivant le mouillage sur un substrat non soluble ne peuvent pas expliquer les observations expérimentales dans le cas d'un liquide s'étalant sur un substrat soluble. Tay et al.(1) ont émis l'hypothèse que la fraction d'eau à la ligne de contact contrôle la valeur de l'angle de contact et ils ont montré l'importance du processus d'évaporation/condensation du solvant lors du mouillage. Dans cette étude, nous montrons que d'autres transferts de matière doivent être considérés pour améliorer la compréhension du processus de mouillage d'une couche soluble; ainsi la diffusion dans le polymère de l'eau condensée, ou directement depuis la goutte sont des processus qui contribuent à hydrater le substrat et modifier l'angle de contact de la goutte. Nous avons utilisé l'approche suivante pour réaliser cette étude: (i) pour prendre en compte la diffusion dans le substrat, nous avons réalisé des simulations en éléments finis qui permettent de valider nos arguments théoriques, (ii) des expériences d'étalement de goutte sur des couches minces de maltodextrine ont été réalisées afin d'étudier le mouillage et l'hydratation en avant de la ligne de contact. Ce travail nous permet de mettre en avant l'influence de la diffusion dans la couche qui complexifie les profils d'hydratation en avant de la ligne de contact, avec notamment l'apparition d'une région de diffusion où de l'évaporation est observée. Un diagramme de mouillage épaisseur-vitesse (e − U) avec différents régimes est établi. Nous validons ces régimes expérimentalement et plus particulièrement un régime où l'angle de contact est une fonction du produit eU. Par ailleurs, nous montrons l'influence de la transition vitreuse du polymère sur l'angle de contact et l'hydratation. Enfin, une étude préliminaire est réalisée pour comprendre l'influence de la dissolution du polymère lors du mouillage.

Un polymère thermoplastique fondu glisse sur une surface solide lisse et non-adsorbante : la vitesse est non nulle à l'interface. Le glissement est réduit si l'on greffe des macromolécules à la surface. Dans ce travail théorique, nous modélisons cette réduction du glissement à l'aide de mécanismes moléculaires, donc à l'échelle nanométrique. Le comportement microscopique des molécules et la réponse rhéologique macroscopique de l'interface sont décrits. Les prédictions du modèle présenté et celles d'autres modèles moléculaires sont confrontées aux résultats des expériences menées par une équipe du lavoratoire. Un certain nombre des lois de comportement sont expliquées, mais la gamme explorée des paramètres ne permet pas de départager tous les modèles. Un test différent est proposé, utilisant des polymères en étoile. D'autres problèmes ont été abordés : conformation d'une macromolécule unique dans un fondu chimiquement différent, statique d'une brosse polymère et d'une étoile dans les mêmes conditions, pénétration partielle d'un fondu dans une brosse chimiquement identique très dense, généralisation aux polymères branchés statistiques d'une méthode de séparation de polymères en étoile en solution diluée, détermination du point de gel pour une structure constituée de polymères en anneau (gel "olympique"), dynamique d'étalement d'une goutte d'hélium superfluide analogue à celle d'une goutte de polymère liquide. Présentation (PDF p. 6, English p. 8) Partie I. Statique et dynamique de polymères liquides (PDF p. 10) Chapitre 1. Généralités sur les polymères (PDF p. 11, English p. 12, français p. 16) Chapitre 2. Polymères fondus : propriétés et mise en oeuvre (PDF p. 39, English p. 40, français p. 42) Chapitre 3. Polymères fondus : éléments de théorie (PDF p. 58, English p. 59, français p. 66) Partie II. Statique et dynamique de chaînes greffées (PDF p. 153) Chapitre 4. Statique de chaînes greffées (PDF p. 154, English p. 155, français p. 158) Chapitre 5. Glissement d'un polymère fondu sur une surface greffée (PDF p. 200, English p. 201, français p. 223) Partie III. Autres problèmes (PDF p. 313) Chapitre 6. Caractérisation de polymères branchés par perméation (PDF p. 314, français p. 315, article in English p. 318) Chapitre 7. Gel olympique (PDF p. 332, English p. 333, français p. 338) Chapitre 8. Étalement d'une goutte par effet Josephson (PDF p. 358, français p. 359, article in English p. 361) Conclusion (PDF français p. 370, English p. 372) Bibliographie (PDF p. 374) Table des matières / Table of contents (PDF p. 380)

Les défauts créés dans les polymères soumis aux rayonnements ionisants, en atmosphère inerte, suivent pratiquement tous la même évolution en fonction de la dose. Lorsque la dose augmente, leur concentration augmente puis se stabilise. L'hypothèse retenue pour expliquer ce comportement est la mise en place de transferts d'énergie vers les défauts macromoléculaires créés aux faibles doses. Ceux-ci agissent comme des pièges à énergie et conduisent donc à la radio-stabilisation du polymère. Au cours de cette thèse, nous nous sommes attachés à la quantification de l'apport de l'insaturation trans-vinylène dans le comportement sous rayonnements ionisants du polyéthylène. Avec le dihydrogène, ce groupement compte parmi les défauts majoritaires créés dans ce polymère. Du fait de la variété des défauts et de la simultanéité de leur création, nous avons choisi une méthodologie nouvelle consistant à insérer par voie de synthèse, de manière spécifique et à différentes concentrations, des insaturations de type trans-vinylène, dans les chaînes de polyéthylène. Les polymères résultants ont été irradiés, en atmosphère inerte, avec des rayonnements de faibles TEL (gamma, bêta) et de forts TEL (ions lourds). Tant les défauts macromoléculaires que l'émission de dihydrogène ont été quantifiés. Il apparaît, sur la base des résultats expérimentaux, que l'apport des groupements trans-vinylènes est prédominant dans la radio-stabilisation du polyéthylène en atmosphère inerte.

Cette étude a porté sur l'effet de différents fluidifiants (plus particulièrement le PolyNaphatalène Sulfonate : PNS et PolyCarboxylatePolyéthoxylé : PCP) sur la rhéologie d'une suspension de particules de gypse. Cette rhéologie a été caractérisée essentiellement par la contrainte seuil, par la viscosité dynamique et les modules de cisaillement. Nous avons montré, en utilisant différentes tailles de particules et différentes longueurs pour les molécules de fluidifiant, que la contrainte seuil était inversement proportionnelle au diamètre des particules et au carré de la distance entre les surfaces de particules. Un modèle nous a permis de remonter à l'épaisseur de la couche de polymère adsorbée sur la surface du gypse. Nous avons observé une diminution de l'efficacité du fluidifiant avec l'augmentation de la fraction volumique de particules de gypse qui a été associée à une diminution de l'écart entre les surfaces des particules. La viscosité dynamique d'une suspension de gypse broyé reste importante malgré la présence de fluidifiant et reflète la présence d'agrégats contenant plusieurs dizaines de particules. Les impuretés (ions divalents : Mg2+, trivalents : Al3+ et Fe3+) ainsi que la température (T>45°C) entraînent une dégradation de l'efficacité du PCP soit en réduisant l'interaction entre le polymère et la surface des particules dans le cas des cations, soit en réduisant la solvatation des polymères dans le cas de l'élévation de température.

Je suis un physicien, théoricien de la matière molle. Dans des domaines assez variés (polymères, mouillage, adhésifs, mousses), j'ai abordé des problématiques très différentes~: enchevêtrements dynamiques à l'échelle moléculaire, conformation de polymères aux interfaces, interactions visco-élastiques autour d'hétérogénéités (cavitation dans les adhésifs), capillarité, pression osmotique et dilatance dans les mousses liquides, dilatance et mécanismes locaux dans les granulaires mous immergés, formulation tensorielle de la plasticité à partir des grandes déformations élastiques dans les mousses. Depuis que je suis au laboratoire Matières et Systèmes Complexes, je m'intéresse aux travaux menés par plusieurs équipes sur la mécanique du vivant à différentes échelles, depuis le cytosquelette et la cellule entière jusqu'aux agrégats cellulaires et aux organismes en développement.

Polymers embedded with nanoparticles polymer nanocomposites (PNCs) have emerged as a new class of hybrid materials, which combine the unique electronic, mechanical, magnetic, catalytic, and optical properties of nanoparticles with the flexibility and processability of polymers, resulting in materials with novel and much improved properties. Experimental investigations accompanied by various theoretical and computational efforts have contributed to the fundamental understanding of the thermal, mechanical, and rheological properties of such PNCs, especially at lower NP loadings. Given the diverse properties of such materials, several potential applications have also emerged. Apart from their varied applications, the soft nanoparticle-polymer composites are a platform of rich physics involving subtle entropic and enthalpic effects which eventually determine their thermo-mechanical properties. In this thesis, we studied complex interplay of interfacial entropic-enthalpic effects and nanoparticles on temperature and time-dependent dynamical changes in PNCs. A short description of the works presented in this thesis is given below. In Chapter 1, we discuss various types of interactions present in polymer nanocomposite mixtures. The theoretical background of entropic and enthalpic interactions in a binary mixture is discussed in this chapter. A brief discussion on polymer dynamics and confinement-induced finite-size effects have been introduced. Chapter 2 deals with the materials and methods used in this thesis. In Chapter 3, we discuss a systematic study of segmental dynamics in polymer nanocomposites of polystyrene (PS) and 5 nm diameter polymer grafted nanoparticles (PGNPs) using quasi-elastic neutron scattering (QENS). It provides spatial and temporal information about small length scales (~1 nm) and fast time scales (~1 ns) and, therefore, at temperatures above the glass transition. For athermal PNCs, consisting of PGNPs embedded in chemically identical polymers, interface wettability and matrix chain penetration into the grafted chain layer (or thickness of interface layer, IL) is enhanced with increasing entropic compatibility between the graft and matrix chain. The IL properties are altered by changing the grafted to matrix polymer size ratio, f which in turn changes the extent of matrix chain penetration into the grafted layer. So, the interfacial length between matrix polymer on these length PGNPs are playing a crucial role for the dynamics and time scales polymer segmental motion in bulk PNCs. In Chapter 4, we extend the discussions into a confined PNC system. Since it is widely known that various properties of these thin films, especially their thermo-mechanical behavior, can be considerably different from the bulk depending on the thickness and interaction with surrounding media, it is imperative to study these properties directly on the films. However, quite often, it becomes difficult to perform these measurements reliably due to a dearth of techniques, especially to measure mechanical or transport properties like the viscosity of thin polymer or PNC films. Here we explore the complex interplay of two interfacial widths -film/substrate interface and graft/matrix chain interface - on the viscosity of confined PNC thin films through careful atomic force microscopy (AFM). We demonstrate a new method to study the viscosity of PNC thin films using atomic force microscopy-based force-distance spectroscopy. Using this method, we investigated viscosity and the glass transition, Tg, of PNC thin films consisting of polymer grafted nanoparticles (PGNPs) embedded in un-entangled homopolymer melt films. The PGNP–polymer interfacial entropic interaction parameter, f, operationally controlled through the ratio of grafted and matrix molecular weight, was systematically tuned while maintaining good dispersion even at very high PGNP loadings, ϕ. We observed a significant reduction (low f) and giant enhancement (high f) in the viscosity of the PNC thin films, with the effect becoming more prominent with increasing ϕ. This work thus not only demonstrates the tunability of the interfacial entropic effect to facilitate a dramatic change in the viscosity of PNC coatings, which could be of great utility in various applications of these materials but also suggests a new regime of viscosity variation in athermal PNC films indicating the possible need for a new theoretical model. In Chapter 5, we discuss a facile method to prepare PGNPs-based high-density functional polymer nanocomposites using thermal activation of a high-density PGNPs monolayer to overcome entropic or enthalpic barriers to the insertion of PGNPs into the underlying polymer films. The key challenge is to attain a high loading while maintaining reasonable dispersion to attain the maximum possible benefits from the functional nanoparticle additives. We monitor the temperature-dependent kinetics of penetration of a high-density PGNP layer and correlate the penetration time to the effective enthalpic/entropic barriers. Repeated application of the methodology to insert nanoparticles by appropriate control over temperature, time and graft-chain properties can lead to enhanced densities of loading in the PNC. This method can be engineered to produce a wide range of high-density polymer nanocomposite membranes for various possible applications, including gas separation and water desalination. In Chapter 6, we discuss the potential application of such nanostructured polymer thin film membranes for water desalination. Membranes with high water flux and large salt rejection are necessary to desalinate water at scale. While polyamide composite (PA-TFC) membranes are the benchmark, there is a continuing need to improve performance systematically. Here, we discuss a novel, transformative paradigm using thin films of pure PGNPs with fixed grafting density but varying chain lengths assembled on PA-TFC membranes through the venerable Langmuir-Blodgett method. The water permeance (A), and flux (J), show a non-monotonic dependence on graft chain molecular weight, likely driven by the modification of osmotic compressibility, which goes through a minimum at 88 kDa. In contrast to most separations, the membrane transport of components of saline solutions is driven by different physics, thus providing us with two distinctly different control handles to optimize these important phenomena opening a new direction in affordable water desalination technologies. Finally, Chapter 7 summarizes the results obtained in this thesis and expresses the future scope of this work.

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.

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 has been concerned with a few problems in systems driven at the scale of particles. The problems dealt with here can be extended and elaborated upon in a variety of ways. In 2 we examine the dynamics of a fluid membrane in contact with a fluid containing active particles. In particular, we show that such a membrane generically enters a statistical steady state with wave-like dispersion. While the numerical results are satisfying, a one-step coarse-graining calculation, in line with [66,93], will, we expect, yield a pair of coupled stochastic differential equations (probably KPZ like at least in one dimension) with wave-like dispersion. This calculation in of interest from a theoretical point-of-view. Further, the numerical exploration of the full set of equations is also left for future work, but can be relevant to many biological systems. In 3 we show that an active fluid confined in an annular channel starts to rotate spontaneously. Further, we predict the existence of banded concentration profile. Such profiles have not yet been observed in experiments. Further, it will be interesting to study what happens to our conclusions if we include the effect of treadmilling in our calculation. In 4 we describe a solid driven by active particles. Specifically, we only concern ourselves with the polar elastomeric phase of the material. However, the questions regarding the transition into that phase are interesting and have not been explored. How exactly does a polarisation transition happen in an active polar elastomer? Is it the same as in an active nematic elastomer? What is the nature of the gelation transition in an active polar fluid? What is the dynamics of nematic defects in an elastomer? Can the presence of the elastomer prevent defect separation? We are at present trying to answer these questions. In 5 we examine the dynamics of an active fluid confined in a channel. It will be interesting to test the prediction about fluctuations in a confined active system, which we show will be normal, in experiments on highly confined actomyosin systems. In 6 we write down the coupled equations of a conformation tensor and the apolar order parameter. This is a generic framework for studying viscoelastic active fluids. A fuller study of the effect of increasing the cross-linker density in such system remains to be done, both theoretically and experimentally. In general, we have shown in the thesis that the understanding of active systems can provide a mechanistic explanation of various biological observations. However, at times the comparison between theory and biological experiments become complicated due to the inherently complicated nature of the experimental systems. Thus, for a more rigorous experimental test of the theory, it is necessary to construct cleaner reconstituted systems with possibly as few as three components. Efforts in this direction have recently borne fruit [129]. However, a complete theoretical understanding of the rich behaviour evinced in these systems is as yet lacking. We expect that the conformation tensor theory we developed in chapter 6 will provide an explanation for the anomalous rheological behaviour observed in these systems. Even in the theoretical front, lot of questions remain to be answered. The dry polar active system, described by the Toner-Tu equations have been shown to undergo a transition to a state with LRO. However, though mean-field theory predicts a second order transition [151, 152, 156], detailed numerical analysis suggests that it is actually first-order with pre-transitional solitonic bands. This has been recently examined by Chate et al. [26] who mapped it to a dynamical system, but a complete theory is still lacking. Apolar systems present another set of challenges. First, the concentration coupling with the order parameter should create similar pre-transitional effects at the order-disorder transition for this system also. This has been studied to a certain extent [133]. However, the more interesting question concerns the role of defects in apolar systems and whether they allow for the possibility of even QLRO in two dimensions. The +1/2 nematic defect has a polarity, and can thus move balistically [51, 108, 115, 149] in a dry system. However, the −1/2 defect has a three-fold symmetry [27] and its motion is thus purely diffusive. Now consider a pair of +1/2 and −1/2 defect pair that can form due to noise in the system (since it does not violate charge conservation). Depending on the configuration and the kind of activity, this defect pair can unbind at zero temperature. Unbound defects would imply that the order is short-ranged. However, it appears from detailed simulations of an agent based Vicsek-like model of active nematics, that there exists a QLRO nematic in two dimensions [111]! How does an active nematic escape being destroyed by defect unbinding? Does concentration have a major role to play? If so, does making the concentration a non-conserved, and thus fast, variable by, for example, including evaporation-deposition rules in the model studied by Chate et al. [28] destroy the QLRO? Also, does the hydrodynamic theory for Malthusian (i.e. one in which the concentration relaxes fast to a steady value) nematics show only short-ranged order, while the one in which mass is conserved show QLRO? These questions are being studied at present by simulating both the agent-based model due to Chate with evaporation-deposition and the dynamical equation for the active nematic order-parameter. These studies should clarify the role of concentration in assisting apolar order. It must be borne in mind, however, that numerical simulations of active models are more difficult than their passive counterparts due to the larger number of parameters present in the problem. In passive systems Onsager symmetry relations constrain some parameters. However, the absence of an equivalent rule for systems far away from equilibrium implies that the spatial symmetry allowed couplings will all have independent kinetic coefficients. This increases the size of the parameter space in many problems. Also, many techniques like Monte Carlo have to be carefully modified to suit such systems. A new and exciting area of research from the point of view of statistical mechanics of active systems is an examination of collective behaviour of run-and-tumble particles pioneered by Tailleur and Cates [25]. This has led to fruitful active generalisations of models of dynamic critical phenomena like model B and model H. Also, it has led to an exploration of rules for selecting a state in a region of phase coexistence – an out of equilibrium generalisation of the Maxwell construction. Another interesting avenue is building up active matter equations from microscopics. This has been done for Vicsek model by Thomas Ihle [64,65], for a simple generalisation of Vicsek-type model for both polar and apolar alignment interactions by Bertin et al. and Chate et al. [15, 16, 107], and for a model of hard rods by Marchetti et al. [10, 11]. The issues of closure still remain to be fully resolved however in deriving the macroscopic equations. A particularly exciting new system that has been recently studied extensively is a collection of chemotactic Janus particles [127]. The far-field interaction in this case does not promote polar order but state with proliferation of asters. The coarse-grained hydrodynamic equations have been derived in this case starting from a microscopic picture of colloids coated axisymetrically with a catalyst in an inhomogeneous concentration of reactants by Saha et al. [127]. Another theoretical issue that plagues the derivation of hydrodynamic equations is that of noise. So far most theories have modelled the noise as Gaussian and white, akin to equilibrium systems, but with unknown strength. However, it is likely that the noise also depends on activity, thus requiring a microscopic picture treating the active forces as stochastic quantities. It is known that multiplicative character of the noise induces interesting features at least in the case of active nematics [104]. Thus, a lot of questions need to be answered if theories of active matter have to graduate from merely offering qualitative explanations of biological experiments to becoming the prototypical theory of systems in which energy input and dissipation both occur at a scale smaller than the coarse-graining volume.

This thesis has been concerned with a few problems in systems driven at the scale of particles. The problems dealt with here can be extended and elaborated upon in a variety of ways. In 2 we examine the dynamics of a fluid membrane in contact with a fluid containing active particles. In particular, we show that such a membrane generically enters a statistical steady state with wave-like dispersion. While the numerical results are satisfying, a one-step coarse-graining calculation, in line with [66,93], will, we expect, yield a pair of coupled stochastic differential equations (probably KPZ like at least in one dimension) with wave-like dispersion. This calculation in of interest from a theoretical point-of-view. Further, the numerical exploration of the full set of equations is also left for future work, but can be relevant to many biological systems. In 3 we show that an active fluid confined in an annular channel starts to rotate spontaneously. Further, we predict the existence of banded concentration profile. Such profiles have not yet been observed in experiments. Further, it will be interesting to study what happens to our conclusions if we include the effect of treadmilling in our calculation. In 4 we describe a solid driven by active particles. Specifically, we only concern ourselves with the polar elastomeric phase of the material. However, the questions regarding the transition into that phase are interesting and have not been explored. How exactly does a polarisation transition happen in an active polar elastomer? Is it the same as in an active nematic elastomer? What is the nature of the gelation transition in an active polar fluid? What is the dynamics of nematic defects in an elastomer? Can the presence of the elastomer prevent defect separation? We are at present trying to answer these questions. In 5 we examine the dynamics of an active fluid confined in a channel. It will be interesting to test the prediction about fluctuations in a confined active system, which we show will be normal, in experiments on highly confined actomyosin systems. In 6 we write down the coupled equations of a conformation tensor and the apolar order parameter. This is a generic framework for studying viscoelastic active fluids. A fuller study of the effect of increasing the cross-linker density in such system remains to be done, both theoretically and experimentally. In general, we have shown in the thesis that the understanding of active systems can provide a mechanistic explanation of various biological observations. However, at times the comparison between theory and biological experiments become complicated due to the inherently complicated nature of the experimental systems. Thus, for a more rigorous experimental test of the theory, it is necessary to construct cleaner reconstituted systems with possibly as few as three components. Efforts in this direction have recently borne fruit [129]. However, a complete theoretical understanding of the rich behaviour evinced in these systems is as yet lacking. We expect that the conformation tensor theory we developed in chapter 6 will provide an explanation for the anomalous rheological behaviour observed in these systems. Even in the theoretical front, lot of questions remain to be answered. The dry polar active system, described by the Toner-Tu equations have been shown to undergo a transition to a state with LRO. However, though mean-field theory predicts a second order transition [151, 152, 156], detailed numerical analysis suggests that it is actually first-order with pre-transitional solitonic bands. This has been recently examined by Chate et al. [26] who mapped it to a dynamical system, but a complete theory is still lacking. Apolar systems present another set of challenges. First, the concentration coupling with the order parameter should create similar pre-transitional effects at the order-disorder transition for this system also. This has been studied to a certain extent [133]. However, the more interesting question concerns the role of defects in apolar systems and whether they allow for the possibility of even QLRO in two dimensions. The +1/2 nematic defect has a polarity, and can thus move balistically [51, 108, 115, 149] in a dry system. However, the −1/2 defect has a three-fold symmetry [27] and its motion is thus purely diffusive. Now consider a pair of +1/2 and −1/2 defect pair that can form due to noise in the system (since it does not violate charge conservation). Depending on the configuration and the kind of activity, this defect pair can unbind at zero temperature. Unbound defects would imply that the order is short-ranged. However, it appears from detailed simulations of an agent based Vicsek-like model of active nematics, that there exists a QLRO nematic in two dimensions [111]! How does an active nematic escape being destroyed by defect unbinding? Does concentration have a major role to play? If so, does making the concentration a non-conserved, and thus fast, variable by, for example, including evaporation-deposition rules in the model studied by Chate et al. [28] destroy the QLRO? Also, does the hydrodynamic theory for Malthusian (i.e. one in which the concentration relaxes fast to a steady value) nematics show only short-ranged order, while the one in which mass is conserved show QLRO? These questions are being studied at present by simulating both the agent-based model due to Chate with evaporation-deposition and the dynamical equation for the active nematic order-parameter. These studies should clarify the role of concentration in assisting apolar order. It must be borne in mind, however, that numerical simulations of active models are more difficult than their passive counterparts due to the larger number of parameters present in the problem. In passive systems Onsager symmetry relations constrain some parameters. However, the absence of an equivalent rule for systems far away from equilibrium implies that the spatial symmetry allowed couplings will all have independent kinetic coefficients. This increases the size of the parameter space in many problems. Also, many techniques like Monte Carlo have to be carefully modified to suit such systems. A new and exciting area of research from the point of view of statistical mechanics of active systems is an examination of collective behaviour of run-and-tumble particles pioneered by Tailleur and Cates [25]. This has led to fruitful active generalisations of models of dynamic critical phenomena like model B and model H. Also, it has led to an exploration of rules for selecting a state in a region of phase coexistence – an out of equilibrium generalisation of the Maxwell construction. Another interesting avenue is building up active matter equations from microscopics. This has been done for Vicsek model by Thomas Ihle [64,65], for a simple generalisation of Vicsek-type model for both polar and apolar alignment interactions by Bertin et al. and Chate et al. [15, 16, 107], and for a model of hard rods by Marchetti et al. [10, 11]. The issues of closure still remain to be fully resolved however in deriving the macroscopic equations. A particularly exciting new system that has been recently studied extensively is a collection of chemotactic Janus particles [127]. The far-field interaction in this case does not promote polar order but state with proliferation of asters. The coarse-grained hydrodynamic equations have been derived in this case starting from a microscopic picture of colloids coated axisymetrically with a catalyst in an inhomogeneous concentration of reactants by Saha et al. [127]. Another theoretical issue that plagues the derivation of hydrodynamic equations is that of noise. So far most theories have modelled the noise as Gaussian and white, akin to equilibrium systems, but with unknown strength. However, it is likely that the noise also depends on activity, thus requiring a microscopic picture treating the active forces as stochastic quantities. It is known that multiplicative character of the noise induces interesting features at least in the case of active nematics [104]. Thus, a lot of questions need to be answered if theories of active matter have to graduate from merely offering qualitative explanations of biological experiments to becoming the prototypical theory of systems in which energy input and dissipation both occur at a scale smaller than the coarse-graining volume.

Binary mixtures of polymers and soft nanocolloids, also called as polymer nanocomposites are well known and studied for their enormous potentials on various technological fronts. In this thesis blends of polystyrene grafted gold nanoparticles (PGNPs) and polystyrene (PS) are studied experimentally, both in bulk and in thin films. This thesis comprises three parts; 1) evolution of microscopic dynamics in the bulk(chapter-3),2) dispersion behavior of PGNPs in thin and ultra thin polymer matrices (chapter-4) 3) effect of dispersion on the glass transition behavior (chapter-5). In first part, the state of art technique, x-ray photon correlation spectroscopy is used to study the temperature and wave vector dependent microscopic dy¬namics of PGNPs and PGNP-PS mixtures. Structural similarities between PGNPs and star polymers (SPs) are shown using small angle x-ray scatter¬ing and scaling relations. We find unexpected (when compared with SPs) non-monotonic dependence of the structural relaxation time of the nanoparticles with functionality (number of arms attached to the surface). Role of core-core attractions in PGNPs is shown and discussed to be the cause of anomalous behavior in dynamics. In PGNP-PS mixtures, we find evidence of melting of the dynamically arrested state of the PGNPs with addition of PS followed by a reentrant slowing down of the dynamics with further increase in polymer frac¬tion, depending on the size ratio(δ)of PS and PGNPs. For higher δ the reen¬trant behavior is not observed with polymer densities explored here. Possible explanation of the observed dynamics in terms of the presence of double-glass phase is provided. The correlation between structure and reentrant vitrifica¬tion in both pristine PGNPs and blends are derived rather qualitatively. In the second part, the focus is shifted to miscibility between PGNPs and polymers under confinement i.e., in thin films. This chapter provide a compre¬hensive study on the different parameters affecting dispersion viz., annealing conditions, fraction of the added particles, polymer-particle interface and more importantly the thickness of the films. Changes in the dispersion behavior with annealing is shown and the need for annealing the films at temperatures higher than the glass transition temperature of the matrix polymers is clearly elucidated. Irrespective of the thickness of the films( 20 and 65 nm) studied, immiscible particle-polymer blends unequivocally prove the presence of gradi¬ent in dynamics along the depth of the films. To our knowledge for the first time, we report results on confinement induced enhancement in the dispersion of the nanoparticles in thin polymer films. The enhanced dispersion is argued to be facilitated by the increased free volume in the polymer due to confinement as shown by others. Based on these results we have proposed a phase diagram for dispersibility of the nanoparticles in polymer films. The phase diagram for ultra thin films highlights an important point: In ultra thin films the particles are dispersed even with grafting molecular weight less than matrix molecular weight. In the third part, we have studied the glass transition of the thin films whose structure has been studied earlier in the earlier part. Non-monotonic variation in glass transition with the fraction of particles in thin films has increased our belief on the gradient in the dynamics of thin polymer films. En¬hanced dispersion with confinement is captured with the enhanced deviation in glass transition temperature of ultra thin films. Effect of miscibility param¬eter on Tgis studied and the results are explained with the subtle interplay of polymer-particle interface and confinement.

Binary mixtures of polymers and soft nanocolloids, also called as polymer nanocomposites are well known and studied for their enormous potentials on various technological fronts. In this thesis blends of polystyrene grafted gold nanoparticles (PGNPs) and polystyrene (PS) are studied experimentally, both in bulk and in thin films. This thesis comprises three parts; 1) evolution of microscopic dynamics in the bulk(chapter-3),2) dispersion behavior of PGNPs in thin and ultra thin polymer matrices (chapter-4) 3) effect of dispersion on the glass transition behavior (chapter-5). In first part, the state of art technique, x-ray photon correlation spectroscopy is used to study the temperature and wave vector dependent microscopic dy¬namics of PGNPs and PGNP-PS mixtures. Structural similarities between PGNPs and star polymers (SPs) are shown using small angle x-ray scatter¬ing and scaling relations. We find unexpected (when compared with SPs) non-monotonic dependence of the structural relaxation time of the nanoparticles with functionality (number of arms attached to the surface). Role of core-core attractions in PGNPs is shown and discussed to be the cause of anomalous behavior in dynamics. In PGNP-PS mixtures, we find evidence of melting of the dynamically arrested state of the PGNPs with addition of PS followed by a reentrant slowing down of the dynamics with further increase in polymer frac¬tion, depending on the size ratio(δ)of PS and PGNPs. For higher δ the reen¬trant behavior is not observed with polymer densities explored here. Possible explanation of the observed dynamics in terms of the presence of double-glass phase is provided. The correlation between structure and reentrant vitrifica¬tion in both pristine PGNPs and blends are derived rather qualitatively. In the second part, the focus is shifted to miscibility between PGNPs and polymers under confinement i.e., in thin films. This chapter provide a compre¬hensive study on the different parameters affecting dispersion viz., annealing conditions, fraction of the added particles, polymer-particle interface and more importantly the thickness of the films. Changes in the dispersion behavior with annealing is shown and the need for annealing the films at temperatures higher than the glass transition temperature of the matrix polymers is clearly elucidated. Irrespective of the thickness of the films( 20 and 65 nm) studied, immiscible particle-polymer blends unequivocally prove the presence of gradi¬ent in dynamics along the depth of the films. To our knowledge for the first time, we report results on confinement induced enhancement in the dispersion of the nanoparticles in thin polymer films. The enhanced dispersion is argued to be facilitated by the increased free volume in the polymer due to confinement as shown by others. Based on these results we have proposed a phase diagram for dispersibility of the nanoparticles in polymer films. The phase diagram for ultra thin films highlights an important point: In ultra thin films the particles are dispersed even with grafting molecular weight less than matrix molecular weight. In the third part, we have studied the glass transition of the thin films whose structure has been studied earlier in the earlier part. Non-monotonic variation in glass transition with the fraction of particles in thin films has increased our belief on the gradient in the dynamics of thin polymer films. En¬hanced dispersion with confinement is captured with the enhanced deviation in glass transition temperature of ultra thin films. Effect of miscibility param¬eter on Tgis studied and the results are explained with the subtle interplay of polymer-particle interface and confinement.