On the stability of lyotropic lamellar liquid crystals and the thicknessesof their lamellae

The stability of lamellar lyotropic liquid crystals was investigated using a thermodynamic formalism. The interfacial tension gamma was expressed in t erms of the thicknesses delta (1) and delta (2) of the two kinds of lamella e. For given thicknesses, the system might be stable if gamma greater than or equal to 0. In adition, the derivatives partial derivativef/partial deri vative delta (i) of the excess free energy f, due to van der Waals. hydrati on, steric, electrostatic, and undulation interactions, must be negative fo r the lamellar structure to be stable. The thermodynamic conditions employe d show that the domain of existence of the lamellar phase is restricted to narrow ranges of layer thicknesses and parameters of interaction. The effec t of the bending modulus and of the ionic strength on the stability was exa mined. The thicknesses of the two kinds of lamellae were calculated using e quilibrium and mass balance equations. It was shown that the nonlinearity o f these equations could be responsible for the observed deviations from the "ideal dilution law". A comparison between the calculated and experimental results was made.