Cluster kinetics modeling of glassforming materials
In this work, a new model relating temperature and pressure to dielectric relaxation or viscosity of a glassformer is developed. The model is based upon cluster kinetics, reaction-like mechanisms describing interactions between glassformer monomers and their clusters. Mathematical solutions of population balance equations for monomer and cluster lead to molar concentrations in terms of rate coefficients of the reaction-like mechanisms. These are then related to viscosity or dielectric relaxation time through free volume theory. The resulting equations are tested against data for a variety of pure glassformers, fragile, non-fragile, large, and small molecules over a wide range of temperatures, pressures, and dielectric relaxation times. It is found that the parameters of the cluster kinetics model are invariant to temperature and pressure and can be used to predict dielectric relaxation at other conditions. The parameters can thus be considered properties of the glassformer compound. Given this understanding of the parameters, the cluster kinetics model is then demonstrated to predict binary glassformer dielectric relaxation times for mixtures exhibiting a single relaxation in response to temperature, by application of a simple mixing rule to determine mixture parameters from the pure component parameters. For binary mixtures exhibiting two distinct relaxations in response to temperature, the pure component parameters are demonstrated to have predictive ability for the mixture. The same is demonstrated for glassformer solutions. Thus, the cluster kinetics model is shown to have broad applicability and to successfully predict dielectric relaxation behavior for pure glassformers, glassformer mixtures, and glassformer solutions.
cluster kinetics, modeling, glass transition, dielectric relaxation, glass
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