A new expression for radial distribution function and infinite shear modulus of Lennard-Jones fluids

Molecular dynamics simulations are applied to generate an expression for the radial distribution function (RDF) of Lennard-Jones fluids for 165 reduced temperature-isochors in the range of 1.4 ⩽ T∗ ⩽ 4.2 and 0.35 ⩽ ρ∗ ⩽ 0.85. Due to the impossibility of presenting a single general expression with few adjustable parameters for the whole distance range, one function is presented for the first peak of the RDF and a second function for the other peaks. The calculated pressure is very sensitive to the shape of RDF and is used as a criterion for the investigation of convergence of the simulation and the accuracy of the simulated RDF. The parameters in the function are adjusted to precisely reproduce of the first peak and thus to accurately predict the pressure of the Lennard-Jones fluids with a relative mean error about 1.6%. Based on the simulated RDF, the infinite-frequency shear modulus, G∞ of the Lennard-Jones fluid is calculated and a simple expression is presented for G∞ in the range of 1.0 ⩽ T∗ ⩽ 4.2 and 0.35 ⩽ ρ∗ ⩽ 0.85.