(63f) Theoretical Phase Diagram of Self-Assembled Patchy Particles: Fluid and Solid Phases

Patchy particles, such as associating molecules and patchy colloids, provide building blocks for soft materials with designed structure and explain the properties of protein crystallization and of gas hydrates. A simple model of patchy particles are hard cores decorated with discrete patches of varying size and geometry. Since the size, the number or the local arrangement of the patches on colloids can be tuned, key questions arise including: what is the relation between target structure and patchy interactions and how does the patchy interaction favor the formation of a target structure, such as diamond structure or Kagome lattice. Wertheim’s theory in the form of the SAFT equation of state has been widely used to predict self-assembly and thermodynamics of patchy colloids and associating molecules in solution. Less work has considered self-assembly to form soft materials. Further Wertheim’s perturbation theory and SAFT have been limited to independent association sites that can bond only once. Recent development of a new cluster distribution theory by Bansal, et al and Marshall and Chapman has enabled description of multi-bonding sites of general geometry that include multibody interactions. In this work, we extend these theories to predict equilibrium between the fluid and solid states. This has the potential to enable a free energy analysis of soft material structure based on patch size and geometry for pure and mixed systems. In this work, we present the effect of patchy interactions on the phase diagram of patchy particles in the fluid and solid states .