Non-Perturbative Numerical Studies of Lattice-Gas Models in Materials Science

提出的研究包括两个主要部分：电化学吸附相变的晶格气体模拟和一阶相变附近亚稳性的研究。两个项目均采用非微扰统计力学数值方法；即蒙特卡罗模拟，有限大小缩放和转移矩阵计算。(1)模拟尿素、乙酸和草酸分子以及氯离子和磷酸阴离子在单晶铂表面的电化学吸附，并与实验观察结果进行直接比较。(2)简单模型系统一阶相变附近的亚稳态将通过产生复值自由能的转移矩阵技术进行检验——虚部与亚稳态的寿命成正比（据信）。这些寿命将与用更直接的数值方法得到的寿命进行比较。这项工作涉及到对相变的理解——既在基础层面，也在系统特定层面。在后一种情况下，分子和带电离子在溶液电极上的吸附将被模拟，并直接与实验进行比较。在前一种情况下，将通过一种新的数学方法来研究突变相变附近的亚稳态（例如熔点以下的水过冷），该方法直接给出这些状态的寿命。这些寿命将与核成核理论和直接数值模拟的估计进行比较。＊＊＊

9315969 Rikvold The proposed research consists of two main parts: lattice gas modelling of phase transitions in electrochemical adsorption, and the study of metastability near first-order phase transitions. Both projects employ non-perturbative statistical mechanical numerical methods; ie Monte Carlo simulation, finite-size scaling and transfer matrix calculations. (1) The electrochemical adsorption of urea, acetic and oxalic acid molecules and of chloride and phosphate anions onto single crystal platinum surfaces will be simulated and directly compared with experimental observations. (2) Metastability near first order phase transitions in simple model systems will be examined via transfer matrix techniques which produce complex valued free energies - the imaginary part being proportional (it is believed) to the lifetime of the metastable state. These lifetimes will be compared with those obtained by more direct numerical methods. %%% This work involves the understanding of phase transitions - both at the fundamental level and at the system-specfic level. In the latter case, the adsorption of molecules and charged ions at electrodes in solution will be modelled and compared directly to experiment. In the former case, metastability near abrupt phase transitions (eg supercooling of water below the melting point) will be studied via a new mathematical method which gives the lifetime of these states directly. These lifetimes will be compared with estimates from nucleation theory and from direct numerical modelling. ***