Membrane pinning on a disordered substrate

We investigate interactions between an elastic membrane and a substrate characterized by quenched positional disorder in the height function. We show that the positional disorder transforms the standard secondary DLVO minimum into two separate states: the hovering state characterized by a planar membrane at a finite separation from the interface and a pinned state where the membrane follows closely the asperities of the substrate and is as a consequence quite corrugated. The transition between the two states is continuous and depends on the parameters of the underlying DLVO potential as well as the parameters describing the quenched height-height correlation function of the substrate. pacs87.16.DgMembranes, bilayers, and vesicles pacs68.15.+eLiquid thin films In the DLVO theory one usually assumes that when a membrane or in general an elastic manifold interacts with a rigid substrate, the membrane is modelled as flat and the substrate is envisioned as featureless [1]. This leads in a straightforward manner to the secondary minimum of the DLVO theory and to an equilibrium spacing between the membrane and the substrate. Taking into account the elastic degrees of freedom of a membrane can alter this picture drastically, leading to the emergence of Helfrich interaction which may induce an unbinding transition of the membrane. This transition has been clearly shown to be a consequence of the interplay between elastic fluctuations of the membrane and DLVO interactions between the membrane and the substrate [2]. In the present work we are motivated by recent experiments on deposited lipid multilayers on atomically smooth vs. rough surfaces [3]. These experiments reveal differences in equilibrium lamellar spacings of lipid multilayers in proximity of a substrate that seem to correlate with molecular roughness of the substrate [3]. In order to lay ground for understanding effects of this type it is desirable to relax the