Entropic interactions between polymerized membranes

We consider the problem of elastic (e.g., polymerized) membranes whose undulations are constrained by the presence of other membranes, or by a wall. Monte Carlo simulation shows that in the low-temperature, ordered phase the fluctuation-driven ‘‘steric’’ potential decreases as a power of the mean distance between membranes, 1/$l^{\tau }$, with the exponent τ=3.1±0.2. This result, very different from that predicted and measured for the case of fluid membranes (τ=2), suggests possible experiments on the swelling of polymerized lamellar phases which would demonstrate the existence of an ordered phase below a crumpling transition.