Bragg-Williams mean-field lattice model

Figure 26.1 7 (a) Theoretical predictions for the heat capacity C near the critical temperature, for two-dimensional systems. The Bragg-Williams mean-field lattice model of Chapter 25 leads to a triangular function, while the exact solution of the two-dimensional Ising model shows a sharp peak. Source R Kubo, in cooperation with H Ichimura, T Usui and N Hashitsome, Statistical Mechanics, Elsevier Pub. Co., New York (1 965). (b) Experimental data for helium on graphite closely resembles the Ising model prediction. Source RE Ecke and JC Dash, Phys Rev B 28, 3738 (1983). 

The results shown in Figures 2 and 4 are intuitively obvious, and reflect the well known fact that the critical temperature in the system depends primarily on the strength of molecular interactions. In particular, in the lattice gas models the maximum of Tc is reached for the system of particles characterized by a" corresponding to the highest interaction between adsorbed particles. This can be readily demonstrated by considering the prediction of a very simple mean-field theory in the Bragg-Williams approximation. 

The individual variants of the lattice model differ fi om each other in the way the spatial distribution of the molecules of the individual components is taken into account. The simplest solution is the Bragg-Williams (B-W) approach which assumes a random distribution of molecules within the bulk phase. The thermodynamical meaning of this assumption is that the mixture is regular. In the adsorption layer, however, it is only in two dimensions (i.e., within the individual sublayers that a statistical distribution of molecules is assumed). Pioneering work in this field was published by Ono [92-94] and Ono and Kondo [95,96]. The method was later applied to the description of L/G interfaces by Lane and Johnson [97] and later taken up by Altenberger and Stecki [98]. Analytic isotherm equations have also been derived from the above... 

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