Structure and tension of the boundary line between amphiphilic layers

The structure and tension of the region of contact where an oil phase, a water phase and a microemulsion phase meet, is theoretically investigated. The analysis has as a starting point a Landau-theory-like expression for the free energy in which, besides the usual gradient of the density squared term, a term proportional to the second derivative of the density squared is present. The coefficient of the squared gradient term is taken to be negative in the microemulsion phase (cf. G. Gompper and M. Schick, Phys. Rev. Lett. 65 (1990) 1116). In a closely related model, we show that a first order wetting transition exists at which point infinitely many (n = 0, 1, 2,…) surface phases can coexist, each described by the presence of a different thickness (ℓn = (2n + 1)ℓ0) of the microemulsion phase between the oil and water phase. This situation physically describes the coexistence of layers of amphiphilic molecules with different thicknesses between a water and an oil bulk phase, the thickness of one amphiphilic layer being equal to ℓ0. We present the calculation of the density profile and the boundary tension of the contact region of a coexisting n = 0 and n = 1 surface phase, e.g. between the oil-water interface with a single amphiphilic layer present and the oil-water interface where three amphiphilic layers are present. Also, an approximate analysis is made for the calculation of the boundary tension between surface phases consisting of three or more amphiphilic layers.