Membrane pinning on a disordered substrate

TL;DR

This paper studies how a disordered substrate affects an elastic membrane, revealing a transition from a hovering to a pinned state influenced by substrate disorder and interaction potentials.

Contribution

It demonstrates that substrate disorder causes a transition from a single DLVO minimum to two distinct membrane states, introducing a new understanding of membrane-substrate interactions.

Findings

Disorder transforms the DLVO minimum into two states.

The transition between states is continuous.

The transition depends on interaction and substrate parameters.

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.