Fluctuations and Phase Behavior of Passages in a Stack of Fluid Membranes

The collisions of neighboring membranes in lamellar phases leads to the formation of passages, or “wormholes”. We study the shape and the fluctuations of theses passages, based on the curvature model of membranes. In particular, we calculate the average radius, the fluctuations of the radius, the asphericity, and the free energy of a wormhole. This requires a careful analysis of the translational zero modes. The free energy of a single wormhole is then used to obtain the density of passages in the low-density limit. We find that the density increases as $d^{4/3}$ with increasing membrane separation $d$ of the stack, decreases exponentially with increasing saddle-splay modulus $\bar \kappa$, and also decreases rapidly with increasing bending rigidity $\kappa$