Soft matter encompasses a diverse set of materials from colloids and polymers to biological cells and materials. In this thesis, we study two distinct problems using new and existing tools of theoretical soft matter physics. In Part I of this thesis, we study the steady-states of a paradigmatic non-equilibrium system, Active Brownian Particles, in two dimensions. We develop a theoretical approach to approximate the many-body probability distribution of interacting Active Brownian Particles. We use this distribution to calculate the pressure and a spatial correlation function of the active Brownian particle system, and compare our theory to direct simulation. In Part II of this thesis, we develop a model of polymer dynamics in the presence of a phase separating binary fluid, and numerical techniques to simulate the resulting equations of motion. We apply use this model to study a polymer-droplet complex with polymer ends attracted to the droplet. We find that droplet interactions restrict polymer diffusion in the direction perpendicular to the droplet, create non-zero average bending in the polymer and subsequently increased rates of contact between polymer endpoints. The numerical software developed in Part II can be easily extended to simulate multi-polymer, multi-droplet systems.
Non-equilibrium statistical mechanics of Active Brownian Particles & dynamics of semiflexible polymers in the presence of phase separation
Cameron, S. (Author). 23 Jan 2024
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)