Primitive models of chemical association. I. Theory and simulation for dimerization

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Abstract
The structure and thermodynamic properties of a model of associating particles that dimerize into fused-sphere dumbbells are investigated by MC simulation and by integral-equation theory. The model particles, introduced by Cummings and Stell, associate as a result of shielded attractive shells. The integral equation theories are of two types. The first is an extension of Wertheim’s associative Percus–Yevick (APY) equation to the case of the shielded sticky shell model, which is the limiting case of the shielded attractive shell model that can be handled analytically. The second is the extended mean spherical approximation (EMSA) of Zhou and Stell applied to the shielded sticky shell model. In the case of partially associated systems, the EMSA requires as input the equilibrium association constant, which is obtained here using an exact relation between monomer density and a cavity correlation function, together with an equation of state due to Boublik. The structure obtained from the EMSA is in good agreement with the predictions of the MC simulation over a substantial density range that includes liquid-state densities, while the thermodynamic input from Boublik’s equation is in excellent agreement with the simulation results for all densities. Predictions of the APY approximation are also in good agreement with the simulation results as long as the density of the system is relatively low or, at high density, when the hard-core volume of a dimer is not substantially less than that of the two free monomers from which it is formed. There is an intermediate density range in which neither integral-equation theory gives correlation functions of high quantitative accuracy.