Hydrogel Mesh Size and Its Impact on Predictions of Mathematical Models of the Solute Diffusion Coefficient

A mathematical model that can provide good predictions of the solute diffusion coefficient in hydrogels would be highly beneficial in designing hydrogels for biomedical and industrial applications, and a number of such models have been derived. Mesh size plays a prominent role in determining the solute diffusion coefficient within a hydrogel. However, in assessing the predictive ability of models derived for this purpose, we have employed various values of the mesh size, i.e., the correlation length or the mesh radius. Herein, a systematic examination of the use of the correlation length or the mesh radius as the mesh size was performed in assessing the predictive quality of four recent models: a semiempirical Cukier hydrodynamic model, an obstruction model, an obstruction-exclusion model, and a combined free volume/obstruction model. The use of the correlation length as the mesh size along with the obstruction model yielded the most consistent agreement between experimental data and model predictions. In contrast, use of the mesh radius did not yield good agreement with the experimental data when used with any of the models.