Mean curvatures, polymer morphological

In spatially evolving multiphase media (e.g., during dissolution of a porous medium, or phase separation in a polymer blend), the mean curvature of the interface between two phases is of interest. Curvature is a sensitive indicator of morphological transitions such as the transition from spherical to rod-like micelles in an emulsion, or the degree of sintering in a porous ceramic material. Furthermore, important physicochemical parameters such as capillary pressure (from the Young-Laplace equation) are curvature-dependent. The local value of the mean curvature K — (1 /R + 1 /Ri) of an interface of phase i with principal radii of curvature Rx and R2 can be calculated as the divergence of the interface normal vector ,... 

The local shape of the interface in each of the 3D images provided in Fig. 30 can be described by the probability densities of the mean and Gaussian curvatures—Ph(H) and PxiK), respectively—and can be calculated from P(H,K) [72]. The curvature is arbitrarily chosen to be positive if the center of the osculating circle resides within the I microphase of the copolymer or the PB phase of the polymer blend. To facilitate comparison, Ph(H) and Pk K) have been scaled in the same manner as described in Sect. 4.4. E was equal to 0.070 nm for the copolymer and 0.136 for the blend. The Ph h) and Pk k) determined from the two bicontinuous morphologies shown in Fig. 30 are displayed in Fig. 31 and exhibit surprising similarity. 

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