MODELING DYNAMICS lN SELECTED POLYMER SYSTEMS

Abstract

Chapter 1 introduces the selected problems I undertake in this thesis. The following two chapters discuss calculations on a model polymer system that attempts to explain the relative motion of surfaces at the single polymer level. Chapter 2 discusses the solution of a steady state, a stationary state independent of time, analogous to creep states in frictional systems and rupture termination states in earthquakes. The generic one-dimensional rupture model includes the rebinding of interconnecting bonds between a flexible transducer (bead-spring polymer) and a rigid fixed plate. The interconnecting bonds described as harmonic springs rupture and rebind stochastically when a constant force pulls the flexible transducer. The formulated mean field equations facilitate analytical tractability. A distinct steady state results in stochastic simulations of the model, which agrees with the numerical solution of the mean field equations for specific parameter sets. The chapter discusses analytical steady state solutions within the homotopy analysis method, which converges and agrees well with the numerical results. Chapter 3 explores the possibility of a generic steady state that spans early to later times for all parameter states in agreement between the two sets of numerical solutions. One attempt is to rewrite, in particular, the mean field bond equation of motion so that it is close to the rupture and rebinding mechanism of the stochastic model. The chapter also discusses some results with different functions for rebinding rate as an attempt at further generalization. Chapter 4 discusses applying the ”Rouse model with diffusing diffusivity” in polymeric liquids, particularly the united atom molecular dynamics simulation trajectories of unentangled polyethylene melts. The model accurately estimates scaling relations for c.m. and monomer mean square displacement with time interval t. The corresponding c.m. and monomer diffusion coefficients as a function of t confirm diffusing diffusivity in polymer melts. The analysis of velocity autocorrelation functions and their discrete cosine transform provides further congruence with the current understanding of anomalous dynamics in unentangled melts. The analysis shows that the test of the theory is on simulation trajectories of polymer melts with friction. The results indicate that the Rouse model with diffusing diffusivity may find scope as an alternate theoretical formalism for polymeric liquids. Chapter 5 concludes and provides a future scope of the thesis studies.