The effect of rotational and translational energy exchange on tracer diffusion in rough hard sphere fluids

Thermodynamic properties of a molecular dipolar liquid using the two-phase thermodynamic approach

A modified version of the original two-phase thermodynamic approach has been extended to evaluate the thermodynamic properties of molecular systems. Its basic assumption states that the density of states can be decomposed into solid-like and gas-like components. The solid part has been approximated by that of a set of harmonic oscillators, whereas a subset composed of rough hard spheres has been considered for the gas part. In this new approach, molecules have been modelled as rotating hard spheres that experience elastic collisions. The technique has been tested on a system made up of dipolar diatomic molecules, and it leads to very good results for total entropy, potential energy reference and heat capacity. Translation and rotation solid components of the overall spectra have been compared to the real part of the instantaneous normal mode vibrational densities of states. Similarities between them reinforce the validity of the two-phase thermodynamic approach.

Diffusion of squalene in n-alkanes and squalane

Squalene, an intermediate in the biosynthesis of cholesterol, has a 24-carbon backbone with six methyl groups and six isolated double bonds. Capillary flow techniques have been used to determine its translational diffusion constant, D, at room temperature in squalane, n-C16, and three n-C8-squalane mixtures. The D values have a weaker dependence on viscosity, η, than predicted by the Stokes-Einstein relation, D = kBT/(6πηr). A fit to the modified relation, D/T = ASE/η(p), gives p = 0.820 ± 0.028; p = 1 for the Stokes-Einstein limit. The translational motion of squalene appears to be much like that of n-alkane solutes with comparable chain lengths; their D values show similar deviations from the Stokes-Einstein model. The n-alkane with the same carbon chain length as squalene, n-C24, has a near-equal p value of 0.844 ± 0.018 in n-alkane solvents. The values of the hydrodynamic radius, r, for n-C24, squalene, and other n-alkane solutes decrease as the viscosity increases and have a common dependence on the van der Waals volumes of the solute and solvent. The possibility of studying squalene in lipid droplets and membranes is discussed.

Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles

Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues.