Relating Dynamics to Free Volumes

Because efficient methods for computing free volumes from molecular simulations were introduced only recently, their connections to the dynamical properties of liquids have yet to be explored systematically. Nonetheless, initial investigations have already allowed scrutiny of some historical notions about these properties. Here, we briefly discuss two of these initial studies. Their results illustrate that some early free-volume based ideas about the origins of dynamics are consistent with simulation data, but those ideas will need significant revision if they are to be applied in a general way. 

To fully understand the anomalous dynamics of an attractive colloidal fluid from a free-volume perspective, one must consider two effects of attractions on free volumes.75 First, attractions increase the average local space available to the particles and render the free-volume distribution more inhomogeneous than when no attractions exist. These changes act to increase the mobility of the fluid. Second, strong attractions also lead to long-lived 

To measure such time scales, the free-volume autocorrelation function CV can be calculated.75 This quantity, defined as, 

Another static quantity, the entropy, is also thought to be intimately related to various dynamic properties of liquids such as the viscosity p and the self-diffusivity D. In the next section, we discuss some of the main ways in which computer simulations have been used to probe this connection in recent years. 

A well-known prediction connecting thermodynamics to dynamics appeared in the seminal work of Adam and Gibbs (AG),90 where semiempiri-cal arguments led to the following exponential relationship  

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