Second virial coefficient of Kihara molecules with variable range

This work presents solutions to the second virial coefficient of Kihara molecules with a soft variable range of interaction given by a generalized Lennard-Jones four-parameter function. Regarding the four parameters, there are drawbacks in the mathematical procedure, since to find the virial solution two expansion series are used for which only the first coefficients are obtained and their radii of convergence are numerically computed. It is possible to dispense with a parameter of the potential in order to find an exact analytical expression for the virial of soft convex bodies, without a loss of generality. Alternatively, the Kihara square well fluid is used to define the sticky hard convex bodies limit of the virial and a comparison with the respective result from the continuous pair potential is made. The geometrical parameters of infinitely thin rods are used to show the behavior of the virial and the dependence of the Boyle temperature with the range. In addition, the exact formulas are corroborated by comparing with numerical results, which are obtained using Conroy's method.