Temperature dependence of the specific volume of Lennard-Jones potential and applying in case of polymers and other materials

Based on solutions of the Ornstein-Zernike equation, we derive analytical formula for the specific volume of polymers interacting through Lennard-Jones potential. We use mean spherical approximation assuming that the system is of low density, homogeneous, isotropic and composed of one component. The specific volumes of some polymers in addition to the minimum volumes of Lennard-Jones potential and the specific volumes of proteinogenic amino acids: A, R, N, D, C, Q, E, G, H, I, L, K, M, F, P, S, T, W, Y and V, are calculated according to that formula. We show that the simple formula we derive is reliable and agrees well with results obtained from experimental and fitting reported in other studies. We believe that it can be used for many systems described by Lennard-Jones potential such as biological systems, soft matter systems, large molecules such as polymers and inert gases fluids like liquid argon.