Numerical Results and Approximate Theories

Numerical Results and Approximate Tlieories.— The phase diagram and structure of a model colloidal dispersion has been studied by computer simulation.The Monte Carlo results have been supplemented by predictions from two approximate analytic theories cell theoryand perturbation theory. 

In an attempt to imitate the latex dispersions in which phase transitions have been observed,Snook and van Megen simulated an assembly of between 32 and 108 particles. The pair potentials were of the DLVO form given in equations (1)—(4). In a Monte Carlo simulation, the radial distribution function is calculated from 

The properties of a concentrated, disordered dispersion may be described by perturbation theory. In the approach of Barker and Henderson,the pair potential is assumed to be of the form 

Gaylor, W. van Megen, and I. K. Snook, J. Chem. Soc., Faraday Trans. 2, 1979, 75, 451. J. A. Barker, Lattice Theories of the Liquid State , Pergamon, Oxford, 1963. 

In the theory of Weeks, Chandler, and Andersen (WCA), equation (29) is replaced by 

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