Diffusion and Glass Transition in Simple Liquids

Abstract

The free volume theory of diffusion for hard spheres, earlier developed by Cohen and Turnbull, is modified for simple van der Waals type liquids. The modified theory fits the self-diffusion data for argon, krypton, and xenon fairly well and predicts glass transition for these liquids at approximately one-third of their normal boiling points. It is found that a more accurate model for the free volume diffusion in liquids should include a redistribution energy for voids arising from the nonlinear behavior of the pair potential. The agreement found by Cohen and Turnbull between their hard sphere theory and the self-diffusion data of some large organic molecules is interpreted as evidence that the simple Lennard-Jones potential does not accurately describe their interaction with each other. This situation is reflected in the failure of these molecules to obey the same corresponding states relationship as the simple liquids of argon, krypton, and xenon.

Phosphorus Diffusion in Partially Crystallized Films of SiO[sub 2]

“…Under these conditions, a free volume model (17)(18)(19)(20) successfully accounts for the viscosity of some fluids; organic liquids are one example (21). Under these conditions, a free volume model (17)(18)(19)(20) successfully accounts for the viscosity of some fluids; organic liquids are one example (21).…”

Molecular diffusion in polymer solutions

“…Chung (1966) put the Macedo-Litovitz expression on a firmer theoretical basis by deriving it from statistical mechanical arguments. Naghizadeh ( 1964) obtained another extended version of the Cohen-Turnbull result by including a redistribution energy for the voids in the system, as contrasted to the random distribution of voids assumed by Cohen and Turnbull. Finally, Fujita (1961) utilized the CohenTurnbull equation as a starting point for a free volume interpretation of polymer-solvent diffusion.…”

“…In the derivation of the above expression, it has been assumed that a jump occurs only when a volume greater than the critical hole free volume T I ' is available. Also, it has been assumed that the free volume available for molecular transport can be redistributed with no change in energy, Bueche ( 1 9 6 2~) and Naghizadeh (1964) have derived different versions of Equation ( Berry and Fox (1968) have pointed out that there should be no significant differences between either of these results and Equation (39) for the temperature intervals usually considered.…”

Self-Diffusion and Glass Transition of the Soft-Core Model

“…This result enables us to put C= 0.54 and v 0 * =0.57 at high p*. It should be noted, on the other hand, that for p*;S0.9 C never behaves constant and even its behavior (to increase as p* decreases) cannot be compatible with a simple consideration to take account that C is proportional to z.Thus we conclude that at high p* D can be well fitted by ln D = -1.242-0.82/ ( v*-0.57) + 0.54 (-v*-0.57) jv*6 …”

“…(2) (solid curve) with the molecular dynamics result (clotted curve).The constant A in Eq. (1) was set equal to -ln U3 /6) 6 ). B was taken to be 0.82, the same value as that of Naghizadeh for argon.…”