Fluctuation pressure of biomembranes in planar confinement

The fluctuation pressure of a lipid-bilayer membrane is important for the stability of lamellar phases and the adhesion of membranes to surfaces. In contrast to many theoretical studies, which predict a decrease of the pressure with the cubed inverse distance between the membranes, Freund suggested very recently a linear inverse distance dependence [Proc. Natl. Acad. Sci. USA 110, 2047 (2013)]. We address this discrepancy by performing Monte Carlo simulations for a membrane model discretized on a square lattice and employ the wall theorem to evaluate the pressure for a single membrane between parallel walls. For distances that are small compared with the lattice constant, the pressure indeed depends on the inverse distance as predicted by Freund. For intermediate distances, the pressure depends on the cubed inverse distance as predicted by Helfrich [Z. Naturforsch. A 33, 305 (1978)]. Here, the crossover length between the two regimes is a molecular length scale. Finally, for distances large compared with the mean squared fluctuations of the membrane, the entire membrane acts as a soft particle and the pressure on the walls again depends linearly on the inverse distance.