This paper presents a study on the relationship between transport
properties and geometric free volume for dense hard sphere (HS) systems.
Firstly, a generic free volume distribution function is proposed based
on recent molecular dynamic (MD) simulations for the HS geometric free
volume1,2. Combining the new distribution function with a local particle
transportation model, we obtain a power law for the HS transport
properties. Then a relation between the geometric free volume and
thermodynamic free volume is established, which makes it possible to
obtain the expressions of the geometric free volume. The new models are
tested with MD results for HS viscosity, diffusivity, respectively and
the results are very satisfactory. Using the power law we are able to
reproduce equations obtained from different approaches, such as the
entropy scaling laws3, mode coupling theory4 or empirical correlations5.
In particular, A long-standing controversy regarding the
Cohen-Turnbull-Doolittle free volume model6,7 is resolved.