Rheological Modeling of Spherical Polymeric Gels and Dispersions Incorporating the Influence of Particle Size Distribution and Surface Forces

Polymer gels are cross-linked polymer particles that are finding applications in coatings, controlled drug delivery, consumer products, etc. A simple model for predicting the viscosity of spherical polymeric gels and dispersions which can help in the formulation of dispersions in terms of solids content, particle size distribution (PSD), pH, ionic strength, etc. is developed. The model is based on an extended Krieger−Dougherty (K−D) equation, which incorporates the influences of both PSD and interparticle surface forces. The two important parameters in the model are the maximum packing fraction and the interaction energy between the particles. Unlike previous models which treated them as adjustable parameters, they are computed as functions of particle, solvent, and suspension characteristics. The maximum packing fraction is calculated as a function of PSD using linear packing theory while the interaction energy is computed using well-established surface force theories. The hydrodynamic thickness of the polymer layer and the mean distance between the chain attachment points on the hard core particle surface are treated as adjustable parameters. The model predictions are in close agreement with the experimentally observed viscosity values for microgel and latex suspensions reported in the literature. The effect of PSD on the suspension viscosity was found to be more pronounced at high particle volume fractions than at low volume fractions.