A new model for the coarsening of cocontinuous morphologies

Abstract

The coarsening of fluorescently labeled polystyrene/ styrene-ran-acrylonitrile copolymer symmetric blends with cocontinuous morphologies was studied with 3D imaging. Blends with three different interfacial tensions were analyzed. Two regimes of coarsening were observed: a linear growth of the characteristic size followed by a gradual decrease of the rate of coarsening. Only the linear regime was explained by the classical analysis of phase separating systems by Siggia (Phys. Rev. A, 1979, 20, 595). Here, we propose a new model which considers both the characteristic size and the interfacial curvature. This model is a generalization of Siggia's analysis, after including the contribution of the local curvature on the capillary pressure within the interconnected domains. Our capability to compute curvature data from 3D images of the blend microstructure allowed us to test our model. Additionally, a general expression for the coarsening rate proposed by Scholten et al. (E. Scholten, L. M. C. Sagis and E. van der Linden, Macromolecules, 2005, 38, 3515) was, for the first time, assessed here. Both early and late stages of coarsening were predicted with the new model, while Scholten et al. and Siggia's expressions are able to adequately describe only one stage. A crossover between the two regimes of coarsening took place at a single value of capillary number (Ca ∼ 0.003) for all three blends, as predicted by our new expression.