Complete unbinding of fluid membranes in the presence of short-ranged forces.

Abstract

Lipid or surfactant bilayers which are bound by an external pressure and intereact via an additional short-ranged potential are studied theoretically. If the latter potential is not strong enough to bind the lamellae by itself, it has asymptotically no effect on the (complete) unbinding transition, which occurs in the limit of vanishing pressure; the separation and correlation lengths diverge as power laws as a function of the pressure, with the amplitudes being determined by characteristic amplitude ratios. If the potential strength exceeds the critical value, the bilayers are bound even for zero external pressure (incomplete unbinding). Exactly at the critical potential strength, all length scales again diverge as a function of the pressure. The critical exponents are found to be identical to those for a less attractive potential, but the asymptotic amplitude ratios have different values; also, the fluctuation amplitude, which measures the strength of the fluctuation-induced repulsion between the bilayers, is reduced by a factor of 12 as compared to the subcritical case. These results are obtained directly by Monte Carlo simulations of two fluid membranes and agree with exact calculations for the analogous system of two strings in 1+1 dimensions. Experimentally, the effects of short-ranged van der Waals attraction on the fluctuation amplitude ${\mathit{c}}_{\mathrm{fl}}$ should be observable for suitable systems by small-angle x-ray scattering on lamellar phases.