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

材料科学中晶格气体模型的非微扰数值研究

• 批准号: 9315969
• 负责人: Per Arne Rikvold
• 金额: $ 15.6万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-02-15 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9315969&HistoricalAwards=false
• 关键词: Non; Perturbative; Numerical; Studies; Lattice

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. ***

9315969 Rikvold拟议的研究由两个主要部分组成：晶格气模拟电化学吸附中的相变，和一阶相变附近的亚稳性的研究。 这两个项目采用非微扰统计力学数值方法，即蒙特卡罗模拟，有限尺寸缩放和转移矩阵计算。 (1)将模拟尿素、乙酸和草酸分子以及氯离子和磷酸根阴离子在单晶铂表面上的电化学吸附，并直接与实验观察进行比较。 (2)在简单的模型系统中，一阶相变附近的亚稳性将通过产生复值自由能的传递矩阵技术进行检查-虚部与亚稳状态的寿命成比例（据信）。这些寿命将与通过更直接的数值方法获得的寿命进行比较。 这项工作涉及相变的理解-在基本水平和系统特定的水平。 在后一种情况下，分子和带电离子在溶液中的电极上的吸附将被建模并直接与实验进行比较。 在前一种情况下，突变相变附近的亚稳性（如低于熔点的水的过冷）将通过一种新的数学方法，直接给出这些状态的寿命进行研究。 这些寿命将与成核理论和直接数值模拟的估计进行比较。 ***