BHS THEORY AND COMPUTER-SIMULATIONS OF LINEAR HETERONUCLEAR TRIATOMIC HARD-SPHERE MOLECULES

As an extension to a recent study of model diatomic molecules, an equation of state is determined for linear heteronuclear triatomics formed from three tangent hard spheres with diameters sigma-1, sigma-2 and sigma-3. Spheres 1 and 3 are positioned at each end with sphere 2 in the centre so that the 1-2 and 2-3 bond lengths are l12 = (sigma-1 + sigma-2)/2 and l23 = (sigma-2 + sigma-3)/2. The bonded hard-sphere (BHS) approach provides a route to the thermodynamic properties of the triatomic fluid. An equation of state is obtained from the corresponding expression for an equimolar ternary mixture of different-sized hard spheres with bonding sites. In the limit of complete bonding, the heteronuclear triatomic molecules are formed. The cases investigated are the homonuclear system with sigma-1 = sigma-2 = sigma-3, the symmetrical heteronuclear system with sigma-1 = sigma-3 = sigma-2/4, sigma-1 = sigma-3 = 3-sigma-2/5 and sigma-1 = sigma-3 = 4-sigma-2, and the asymmetrical heteronuclear system with sigma-1 = sigma-2 = 2-sigma-3 and sigma-1 = 2-sigma-2 = 4-sigma-3. Isothermal-isobaric Monte Carlo (MC-NPT) simulations are performed for these systems and the results used to test the BHS theory for a range of densities in the fluid state. Comparisons are also made with existing semi-empirical scaled particle theories (SPT). The BHS and SPT equations of state are in excellent agreement with the "exact" simulation data for all but one case which shows small deviations at high densities. It is also interesting to note that the simulation data for the linear symmetrical system with sigma-1 = sigma-3 = 3-sigma-2/5 are virtually identical to existing data for an equivalent nonlinear molecule with a bond angle of 105-degrees. In general, the BHS approach is easier to extend to larger polyatomic molecules and their mixtures than SPT. The BHS approach provides the basis of a general equation of state for arbitrary polyatomic molecules modelled by fused hard spheres.