The second virial coefficient and critical point behavior of the Mie Potential.

Aspects of the second virial coefficient, b2, of the Mie m : n potential are investigated. The Boyle temperature, T0, is shown to decay monotonically with increasing m and n, while the maximum temperature, Tmax, exhibits a minimum at a value of m which increases as n increases. For the 2n : n special case T0 tends to zero and Tmax approaches the value of 7.81 in the n → ∞ limit which is in quantitative agreement with the expressions derived in Rickayzen and Heyes [J. Chem. Phys. 126, 114504 (2007)] in which it was shown that the 2n : n potential in the n → ∞ limit approaches Baxter’s sticky-sphere model. The same approach is used to estimate the n − dependent critical temperature of the 2n : n potential in the large n limit. The ratio of T0 to the critical temperature tends to unity in the infinite n limit for the 2n : n potential. The rate of convergence of expansions of b2 about the high temperature limit is investigated, and they are shown to converge rapidly even at quite low temperatures (e.g., 0.05)...