Evaluating Rosenfeld's Conjecture On the Relation Between Entropy and Diffusivity

Rosenfeld has suggested a relationship between the self-diffusivity and the entropy departure function

Δs = (S-Sid)/R.[1] The suggested correlation is:

ρ⅓D/T½ ~ Bexp(A*Δs)

This relationship is largely empirical, but it has been investigated by Mittal et al.[2] They found that the correlation was quite accurate for hard spheres and Lennard-Jones spheres, but less so for square well spheres. If successful, such a correlation would provide a valuable link between thermodynamic properties and transport properties. Whereas perturbation theories of thermodynamic properties have been quite successful, no comparable theory exists for transport properties.

We have recently developed a correlation for diffusivity on n-alkane chains ranging from ethane to C60. The correlation is based on molecular simulations of the fused-hard sphere chains as reference fluids combined with an empirical correction for the effects of attractive forces. It is accurate to 8.6% average absolute deviation (AAD), despite the diffusivity being very sensitive to variations in temperature and density. Similarly, Elliott and Gray have published relations to characterize the terms of thermodynamic perturbation theory (TPT) for n-alkane chains.[3] Combined, these results provide a basis for evaluating Rosenfeld's conjecture. In particular, the entropy departure for hard chain fluids (given by A0) can be compared to their simulated self-diffusivities. The entropy departure for the complete atomistic potential can be computed from second order TPT using the terms for A1, A2. The trends of the self-diffusivity vs. entropy can thus be evaluated for both the reference fluids and their full potentials. We report the results of this comparison and its implications for the relation between thermodynamics and transport properties.

Reference:

1. Rosenfeld, Y., Phys. Rev. A 1977, 15, 2545.

2. Mittal, J.; Errington, J. R.; Truskett, T. M., Relationships between Self-Diffusivity, Packing Fraction, and Excess Entropy in Simple

Bulk and Confined Fluids. J. Phys. Chem. B 2007, 111, 10054-10063.

3. Elliott, J. R.; Gray, N. H., Asymptotic Trends in Thermodynamic Perturbation Theory. J. Chem. Phys. 2005, 123, 184902.