On the Stability of Lyotropic Lamellar Liquid Crystals and the Thicknesses of Their Lamellae

The stability of lamellar lyotropic liquid crystals was investigated using a thermodynamic formalism. The interfacial tension γ was expressed in terms of the thicknesses δ 1 and δ 2 of the two kinds of lamellae. For given thicknesses, the system might be stable if γ ≥ 0. In adition, the derivatives ∂ f/ ∂δ i of the excess free energy f, due to van der Waals, hydration, steric, electrostatic, and undulation interactions, must be negative for the lamellar structure to be stable. The thermodynamic conditions employed show that the domain of existence of the lamellar phase is restricted to narrow ranges of layer thicknesses and parameters of interaction. The effect of the bending modulus and of the ionic strength on the stability was examined. The thicknesses of the two kinds of lamellae were calculated using equilibrium and mass balance equations. It was shown that the nonlinearity of these equations could be responsible for the observed deviations from the “ideal dilution law”. A comparison between the calculated and experimental results was made.