The Kinetics of First Order Phase Transitions

该奖项支持有关几个密切相关问题的相分离动力学的理论研究。第一个问题是蛋白质结晶的研究，在这个过程中，致密的蛋白质纳米颗粒从溶液中自组装形成晶滴。了解蛋白质的功能是一个主要的活动领域；确定蛋白质分子的结构对于理解结构-功能关系是必不可少的。研究蛋白质结构的主要工具仍然是蛋白质晶体对X射线的衍射。因此，目标是确定从溶液中获得高质量蛋白质晶体所需的条件。重整化群技术将被用来精确地确定蛋白质在溶液中的热力学性质和当前模型的相边界，特别是在亚稳临界点附近，那里的成核作用被增强。用密度泛函方法计算了蛋白质晶滴的成核率和生长速度。第二个主题是Lennard-Jones流体的结晶；目的是从理论上更好地理解这一重要的动力学过程。有限尺寸标度方法将被用来确定液-固相变的自由能图景，这是理解相分离动力学的前提。这项研究还将把Lennard-Jones流体的微观和介观长度尺度联系起来。晶体生长的动力学也将基于一个有序参数的模型，该模型将fcc对称性的晶体连续扭曲为bcc对称性的晶体。这些对称性在结晶过程中很重要。这项研究的较小部分将涉及对复杂流体中三相共存动力学的通用模型的研究，该模型最近一直是研究的主题。该奖项的目的是为了更好地了解三相共存的动力学途径。%该奖项支持几个密切相关问题的相分离动力学的理论研究。这项研究将提高我们对许多材料中常见相变的理解。一个令人感兴趣的系统将是蛋白质晶体从溶液中结晶。这可能会导致更好的结晶，并随后更好地理解蛋白质的性质。

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.***