Second virial coefficient properties of the n-m Lennard-Jones/Mie potential

The second virial coefficient (B), Boyle temperature (TB), and temperature maximum (Tmax) are determined for the n-m Lennard-Jones/Mie (LJ/M) potential. The full range of n, m behavior is investigated between the 5-4 LJ/M, hard sphere (n = ∞) + attractive (m ≥ 4) term (HSAm), and hard sphere potential limits. The (n = m + 1)-m LJ/M potential has an important role in characterising the overall behavior of second virial coefficient properties. Different TB, Tmax behavior is observed for n(constant)-m LJ/M and n-m(constant) LJ/M potentials. In the former case, there are two distinct linear (5 ≤ n ≤ 30) and non-linear regions (n > 30). In the latter case, there is a minimum in Tmax in two distinct non-linear regions (4 ≤ m ≤ 34 and 35 ≤ m ≤ 150) followed by a maximum TB region (m ≥ 151). Analytical relationships for some of the behavior are determined and numerical values of TB for a range of n and m values are reported. Molecular simulation data are used to determine simple relationships between TB and both the critical temperature and triple point temperature for the special case of the n-6 LJ/M potential.