The Kinetics of First Order Phase Transitions

该奖项支持处理相分离动力学的几个密切相关问题的理论研究。第一个问题是蛋白质结晶的研究，其中紧密的蛋白质纳米颗粒从溶液中自组装形成结晶液滴。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的x射线衍射。因此，目的是确定从溶液中获得高质量蛋白质晶体所需的条件。重整化基团技术将用于精确确定当前溶液中蛋白质模型的热力学性质和相边界，特别是在成核增强的亚稳临界点附近。密度泛函方法将用于计算蛋白质结晶液滴的成核速率和生长。第二个主题是Lennard-Jones流体的结晶；目的是为了更好地从理论上理解这一重要的动力学过程。有限尺寸缩放方法将用于确定液固相变的自由能图，这是理解相分离动力学的先决条件。本研究还将把伦纳德-琼斯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被研究，基于一个具有序参数的模型，该模型不断地将具有fcc对称的晶体扭曲为具有bcc对称的晶体。这些对称性在结晶过程中很重要。研究的一小部分将涉及复杂流体中三相共存动力学的广义模型的研究，这是最近研究的主题。目的是为了更好地理解三相共存的动力学途径。该奖项支持处理相分离动力学的几个密切相关问题的理论研究。这项研究将提高我们对许多材料中常见相变的理解。我们感兴趣的一个系统是从溶液中结晶蛋白质晶体。这可能会导致更好的晶体，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.***