Membrane pinning on a disordered substrate

¹ LPSB/NICHD, Bld. 12A Rm. 2041, National Institutes of Health Bethesda, MD 20892-5626, USA
² Department of Physics, Faculty of Mathematics and Physics University of Ljubljana - SI-1000 Ljubljana, Slovenia and Department of Theoretical Physics, J. Stefan Institute - SI-1000 Ljubljana, Slovenia
³ MEMPHYS - Center for Biomembrane Physics, Department of Chemistry University of Southern Denmark - Campusvej 55, DK-5230 Odense M, Denmark

Received: 20 August 2002
Accepted: 30 January 2003

Abstract

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.