Statistical mechanical models of chemical reactions

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Abstract
The formalism and model introduced in a previous paper [1984, Molec. Phys., 51, 253] and used there to study the inhomogeneous association reaction A + B⇌AB is used here to consider the homogeneous association reaction 2A⇌A 2. Two approximations are introduced to obtain an analytic theory. The first is the Percus-Yevick approximation. The second is the neglect of rigid polygonal n-mers, n ⩾ 3. (These are sterically possible in our model, but can be expected in most cases to form only rarely because of their restricted geometry.) Representative quantitative results for association probabilities, association constants and radial distribution functions as functions of thermodynamic state are given and discussed. Our model has a dimension-less association parameter τ that is a combined measure of association strength and temperature; for a given atomic number density ρA there is a value of τ at which diatomic association is complete. Under the assumptions of our theory one then has a fluid of homonuclear diatomics, the hard dumbell fluid. It is found that in this case our theory reduces to the zero pole approximation of Morriss and Cummings for this fluid.