Model lamellar-lamellar phase equilibria

We study some examples of lamellar-lamellar phase equilibria in a previously introduced lattice model of surfactant solutions. The model is treated in a local mean-field approximation. The emphasis is on the properties of the interfaces between coexisting phases. We present an example in which iamellar phases of periods two and four lattice spacings are of equal free energy and both locally stable as bulk phases but metastable with respect to a phase of period three. The interface between the former two is then unstable and nucleates the formation of the latter, which spreads through the entire mass. We conjecture that the period-three phase, had it coexisted as a bulk phase with those of periods two and four, would have wet the period-two/period-four interface, and that this may be a general mechanism for the destruction of metastability. An example is also given of a phase of period three and its antiphase, each being stable as a bulk phase and with a stable interface between them. This case illustrates an ambiguity in the definition of interfacial tension between ordered phases. In general we establish stability both of bulk phases and of interfaces by showing that all the eigenvalues of the matrix of second derivatives of the free energy with respect to the densities are positive.