Monte Carlo Simulations of Growth Kinetics and Phase Transitions at Interfaces: Some Recent Results
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MONTE CARLO SIMULATIONS OF GROWTH KINETICS AND PHASE TRANSITIONS AT INTERFACES: SOME RECENT RESULTS P.NIELABA AND K.BINDER Institut fiir Physik, Johannes-Gutenberg-Universitit Mainz, Staudingerweg 7, D-6500 Mainz, FRG ABSTRACT In the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble. INTRODUCTION Monte Carlo simulations play a vital role both in the study of thermal equilibrium properties of adsorbed monolayers and multilayer structures [1] and in the study of growth phenomena near thermal equilibrium [2]. Such studies, which mostly imply simplified lattice gas- type models, will not be discussed here. Rather we focus attention to two areas where significant recent progress has been made, namely the study of far from equilibrium irreversible growth kinetics at flat substrates, and the study of phase transitions in off- lattice continuum models of adsorbed monolayers, including cases where internal quantum- mechanical degrees of freedom play a role. PART I Irreversible deposition in monolayers has attracted significant theoretical effort [3]. Experiments in which the relaxation time scales are much longer than the times of the formation of the deposit include the adhesion of proteins and colloidal particles on uniform surfaces, as well as certain other systems [4]. Recent theoretical and experimental results suggest that in packed-bed colloid experiments multilayer adhesion can be studied systematically. Theoretical description of the statistical mechanics of multilayer deposition was limited to the mean-field theory and certain rate-equation approximations in the ID deposition models [5]. Here we report on a systematic Monte Carlo study of the irreversible deposition in miultilayers [6]. We consider 1D and 2D models without screening (to be defined below). In irreversible deposition, the most profound correlations are due to the blocking by the already deposited particles of the available area for deposition of new particles. This infinitememory effect was studied extensively in the monolayer case [3], under the term "random sequential adsorption". The deposition process stops at a certain jamming coverage which is less than close-packing. Another effect present only in the multilayer case is the screening of the lower layers by the particles in the higher layers. Models without blocking but with screening allowed, fall in the class of the ballistic deposition [7,3] or diffusion-limited aggregation [8,3], depending on the mechanism of the particle transport to the surfac
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