A Computational Investigation of the Thermodynamics and Structure in Colloid and Polymer Mixtures

Abstract

In this dissertation I use computational tools to study the structure and thermodynamics of colloid-polymer mixtures. I show that fluid-fluid phase separation in mixtures of colloids and linear polymers cannot be universally reduced using polymer-based scaling principles since these assume the binodals exist in a single scaling regime, whereas accurate simulations clearly demonstrate otherwise. I show that rethinking these solutions in terms of multiple length scales is necessary to properly explain the thermodynamic stability and structure of these fluid phases, and produce phase diagrams in nearly quantitative agreement with experimental results. I then extend this work to encompass more geometrically complex "star" polymers revealing how the phase behavior for many of these binary mixtures may be mapped onto that of mixtures containing only linear polymers.

I further consider the depletion-driven crystallization of athermal colloidal hard spheres induced by polymers. I demonstrate how the partitioning of a finite amount of polymer into the colloidal crystal phase implies that the polymer's architecture can be tailored to interact with the internal void structure of different crystal polymorphs uniquely, thus providing a direct route to thermodynamically stabilizing one arbitrarily chosen structure over another, e.g., the hexagonal close-packed crystal over the face-centered cubic. I then begin to generalize this result by considering the consequences of thermal interactions and complex polymer architectures. These principles lay the groundwork for intelligently engineering co-solute additives in crystallizing colloidal suspensions that can be used to thermodynamically isolate single crystal morphologies.

Finally, I examine the competition between self-assembly and phase separation in polymer-grafted nanoparticle systems by comparing and contrasting the validity of two different models for grafted nanoparticles: "nanoparticle amphiphiles" versus "patchy particles." The latter suggests these systems have some utility in forming novel "equilibrium gel" phases, however, I find that considering grafted nanoparticles as amphiphiles provides a qualitatively accurate description of their thermodynamics revealing either first-order phase separation into two isotropic phases or continuous self-assembly. I find no signs of empty liquid formation, suggesting that these nanoparticles do not provide a route to such phases.