On swelling and structure of composite materials. Some theory and applications of lyotropic mesophases

Abstract

Swelling relations linking structural dimensions to composition in two-phase composite materials are derived as a function of domain shape and swelling mode. Planar, cylindrical, globular and hyperbolic (“sponge”) monodisperse shapes are analysed and compared in detail. The effect of small variations in domain shape about some average form is also shown to modify the swelling exponent from that associated with the shape parameter of monodisperse (and “homogeneous”) domain morphologies. Both exponential and polynomial variations of characteristic dimensions of the composite with concentration arise, depending on the swelling mode. Swelling exponents are shown to be simply related to a shape parameter, which is a useful index of the shape of domains within the composite. It is shown that the usual relation used to identify lamellar structures holds equally well for other morphologies, particularly sponges, in certain situations. Applications of the swelling theory are presented to re-investigate the mesostructures of a cubic phase, hexagonal phases and a sponge phase in lyotropic lipid assemblies. The analysis forcefully demonstrates the paradoxical nature of swelling as a probe of domain structure in composite materials. On the one hand, the swelling behaviour of a single composite structure is exquisitely sensitive to the detailed mechanism of composite swelling, such as the occurrence of neutral surfaces within the material during swelling. On the other, many different composite geometries can display identical swelling behaviour, given distinct specific swelling mechanisms for each morphology.