Layer compression modulus of electrostatically stabilized lyotropic lamellar phases revisited : Application to the quantitative analysis of a polymer induced critical SmA-SmA phase separation

We present a calculation of the smectic compression modulus B of a lyotropic lamellar phase stabilized by electrostatic interactions. This calculation, based on a numerical solution of the Poisson-Boltzmann equation, shows that the classical analytical expressions of B given in the literature in the two asymptotic limits (absence of added salt, or large added salt concentration) are valid under very restrictive conditions only. The motivation of this study lies in the understanding of the physical behavior of a doped amphiphilic lamellar phase formed from a mixture of non ionic surfactants (Triton X100/Triton X35), cationic surfactant (cetylpyridinium chloride), water, decane and water-soluble polymer (polyvynilpyrolidone). A critical lamellar/lamellar phase separation observed in our system is quantitatively well-explained by using both the present calculations and a recent model proposed by Ligoure et al. which predicts the polymer-mediated intermembrane interaction contribution to the smectic compression modulus.