Bonded hard-sphere theory and computer simulations of polyatomic hard-sphere models of alkanes and their derivatives

Abstract

The equation of state of the first two members of a homologous series of model alkane-like molecules which incorporate the identities of the backbone and substituent atoms as hard-sphere sites is examined. These polyatomic molecules are formed from tangentially bonded hard spheres with diameters σ₁ and σ₂, where spheres of type 1 make up the backbone of the chain, and spheres of type 2 represent the substituent atoms. The spheres are bonded together in a tetrahedral geometry so that all of the bond angles are ω = 109°; for the second and higher homologues dihedral angles χ about the 1–1 bonds also have to be specified. In order to test the predictions of a recent bonded hard-sphere (BHS) theory, isothermal-isobaric Monte Carlo (MC-NPT) simulations are undertaken for methane- and ethane-like molecules with different diameter ratios σ₂/σ₁ over a range of densities in the fluid state. In the case of the ethane-like molecules trans (χ = 30°) and freely rotating geometries are examined. The simulation data are found to be in excellent agreement with the BHS theory although the theory becomes less accurate at high densities for the systems with large substituent spheres. The assumption inherent in the BHS approach that different conformations and structural isomers of a hard-sphere polyatomic molecule have the same thermodynamical properties is found to be a good approximation for low to moderate fluid densities. The BHS theory is one of the simplest, most accurate and versatile presently available for the properties of polyatomic molecules formed from hard-sphere sites, and could find a use in perturbation and group contribution theories of more realistic models of polyatomic molecules.