MORPHOLOGICAL THERMODYNAMICS OF COMPOSITE MEDIA

The homogeneous spatial domains of phases on a mesoscopic scale are a characteristic feature of many composite media such as complex fluids or porous materials. The thermodynamics and bulk properties of such co mposite media depend often on the morphology of its constituents, i.e. , on the spatial structure of the homogeneous domains. Therefore, a st atistical theory should include morphological descriptors to character ize the size, shape and connectivity of the aggregating mesophases. We propose a new model for studying composite media using morphological measures to describe the homogeneous spatial domains of the constituen ts. Under rather natural assumptions a general expression for the Hami ltonian can be given by extending the model of Widom and Rowlinson [B. Widom, J.S. Rowlinson, J. Chem. Phys. 52 (1970) 1670-1684] for penetr able spheres. The Hamiltonian includes energy contributions related to the volume, surface area, mean curvature, and Euler characteristic of the configuration generated by overlapping sets of arbitrary shapes. A general expression for the free energy of composite media is derived and we find that the Euler characteristic stabilizes a highly connect ed bicontinuous structure resembling the middle-phase in oil-water mic roemulsions for instance. (C) 1998 Elsevier Science B.V. All rights re served.