This Dissertation is devoted to computational study of the solidification, dynamics and mechanics of model semiflexible polymers with variable chain flexibility as well as a computational investigation of the clogging phenomena observed in granular materials.

Chain stiffness is an intrinsic factor that governs single-chain flexibility. It plays a critical role in the physics of polymeric materials. In this work, we employ a coarse-grained polymer model in which chain stiffness can be tuned by a single parameter (bending stiffness kb) that yields chain shape ranging from coil-like to rod-like in the flexible and very stiff limit respectively. In chapter 2, we focus on how chain stiffness affects how polymer melts solidify under thermal cooling. We observe a strong dependence of the solid-state morphology (formed after cooling) upon chain flexibility. In the flexible limit, we find that monomers possess crystalline order while chains retain random-walk like structure. In higher stiffness regime glass formation is obtained while nematic ordering typical of lamellar precursors coexists with close-packing in the rod-like limit. Surprisingly we observe various structures ranging from spiral, to multi-domain nematic phases in the intermediate values of kb.

In chapter 3 we go a step further to relate the solidification behaviors of chains discussed in chapter 2 to their melt dynamics. We probe the microstructure and the dynamics of flexible, intermediate-stiffness and rod-like chains. We find that melts of flexible and stiff chains that crystallize under cooling show simple and fast dynamics with Arrhenius temperature dependence. Interestingly, the intermediate-stiffness chains exhibit Vogel-Fulcher dynamical relaxation typical of fragile glass-formers even though their ground states is a nematic-close-packed crystal. There is no compelling argument based on static micro-structure change explaining this dynamical arrest to be found. However, we find that the dynamics of intermediate-stiffness chains is dominated by the stringlike cooperative motion that correlates along their chain backbones. This cooperative rearrangement which is absent in other systems appears to be the main cause of the dynamical arrest observed for intermediate-stiffness chains.

In chapter 4, we turn to another class of materials where the negligible contribution of thermal fluctuations gives rise to an interesting phenomenon, i.e. the clogging transition. Clogging is a probabilistic event that occurs through a transition from a homogeneous flowing state to a heterogeneous or phase separated jammed state. The granular system under study is an assemble of bidisperse disks externally driven through a two dimensional periodic substrate. We find that the probability for clogging strongly depend on particle packing, obstacle number and the driving direction. Surprisingly, under relevant conditions we observe a size-specific clogging transition in which the smaller species get trapped while the larger species keep flowing.

Chapter 5 returns to discuss the polymer solidification in the context of isostaticity. Results from the simulations of semiflexible polymers described in chapter 2 allow us to derive a generalized isostaticity criterion that can be applied to finite-stiffness chains. The new criterion is based on the characteristic ratio Cinfinity which characterizes the slow freezing out of configurational freedom of chains as chain stiffness increases. The results of the average coordination number at solidification Z(Ts) suggest a link between jamming in athermal systems and solidification in their thermal counterparts.

Finally, in chapter 6 we study the effect of chain stiffness on the mechanical response of glassy polymers. We investigate shear deformation of three systems with a different degree of entanglement. We find that loosely entangled chains display strong shear banding and undergo fracture via chain pullout. In contrast, tightly entangled chains fail at high enough strain along a well-defined plane via chain scission shortly after chains are pulled taut. We explain these chain-stiffness-dependent behaviors qualitatively using the segmental packing efficiency argument and quantitatively using modern plasticity measures.