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Summary: The Influence of Substrate Structure on Membrane
Adhesion
Peter S. Swain, and David Andelman*,
Max-Planck Institut fu¨r Kolloid- und Grenzfla¨chenforschung, Am Mu¨hlenberg, 14476 Golm,
Germany, and School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of
Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
Received April 21, 1999. In Final Form: July 29, 1999
We consider a membrane that adheres both weakly and strongly to a geometrically structured substrate.
The interaction potential is assumed to be local, via the Deryagin approximation, and harmonic.
Consequently, we can analytically describe a variety of different geometries; such as, smooth substrates
interrupted by an isolated cylindrical pit, a single elongated trench, or a periodic array of trenches. We
present more general expressions for the adhesion energy and membrane configuration in Fourier space
andfindthat,comparedwithplanarsurfaces,theadhesionenergydecreases.Wealsohighlightthepossibility
ofovershootsoccurringinthemembraneprofileandlookatitsdegreeofpenetrationintosurfaceindentations.
1. Introduction
The statistical mechanics of membranes is an important
branch of soft-condensed matter physics, not least because
of its application to biological systems. Examples of
membranes that can be studied experimentally include
those of liposomes or vesicles, microemulsions, lamellar
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