Theory and computer simulations of heteronuclear diatomic hard-sphere molecules (hard dumbbells)

Abstract

The isothermal-isobaric Monte Carlo (MC-NPT) method is used to determine the PVT behaviour of model heteronuclear diatomic molecules. The systems of particular interest are hard-dumbbell models consisting of two tangent hard spheres with diameters σ₁ and σ₂ so that the bond distance between the centres of the spheres is l = (σ₁ + σ₂)/2. Computer simulations are performed for molecules with diameter ratios of R = σ₂/σ₁ = 1/4, 1/2, 3/4, and 1 over a range of packing fractions in the fluid state (η = π(σ³ ₁ + σ³ ₂)N _m/(6V) = 0·0 to 0·45). The ‘exact’ results obtained from the simulations are compared with an equation of state derived using a thermodynamic perturbation theory for fluids with highly directional bonding forces. The diatomic hard-sphere molecules can be constructed by bonding together the two components of an equivalent binary mixture of hard spheres with bonding sites. In the limit of infinite bonding, an equation of state for the heteronuclear hard-dumbbell fluid is obtained in terms of g ^hs ₁₂(σ₁₂), the contact value of the 1–2 sphere-sphere radial distribution function of the reference hard-sphere mixture. Theoretical predictions are in excellent agreement with the simulation data for all of the systems studied. The theory includes an accurate expression for the hard-sphere correlation function of the underlying reference mixture, thus the approach is more rigorous than currently available theories, and offers a basis from which to develop more accurate perturbation theories for larger polyatomic molecules and mixtures.