This award supports theoretical research that deals with the kinetics of phase separation for several closely related problems. The first problem is a study of protein crystallization, in which compact protein nanoparticles self-assemble from solution to form crystal droplets. Understanding protein function is a major field of activity; determining the structure of protein molecules is essential to an understanding of the structure-function relationships. The primary tool for protein structure remains the diffraction of X-rays by protein crystals. Therefore the objective is to determine the conditions necessary to obtain high quality protein crystals from solution. Renormalization group techniques will be used to determine accurately the thermodynamic properties and phase boundaries of current models of proteins in solution, particularly in the vicinity of the metastable critical points where nucleation is enhanced. Density functional methods will be used to calculate the nucleation rate and growth of the protein crystal droplets. The second topic is the crystallization of Lennard-Jones fluids; the objective is to obtain a better theoretical understanding of this important kinetic process. Finite size scaling methods will be used to determine the free energy landscape for the liquid -solid phase transition, which is a prerequisite to understanding the kinetics of phase separation. This study will also link microscopic and mesoscopic length scales for Lennard-Jones fluids. The dynamics of crystal growth will also be investigated, based on a model with an order parameter that continuously distorts a crystal with fcc symmetry to one with bcc symmetry. These symmetries are important in the crystallization process. A smaller part of the research will involve a study of a generalized model for the kinetics of three-phase coexistence in complex fluids, which has recently been the subject of investigation. The objective is to gain a better understanding of the kinetic pathways to three-phase coexistence. %%% This award supports theoretical research that deals with the kinetics of phase separation for several closely related problems. The research will improve our understanding of common phase changes in a number of materials. One system of interest will be the crystallization of protein crystals from solution. This may lead to better crystals and, subsequently, a better understanding of the properties of proteins. ***
