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

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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. ***