The Influence of Substrate Structure on Membrane Adhesion

We consider a membrane both weakly and strongly adhering 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: as well as randomly rough self-affine surfaces, smooth substrates interrupted by an isolated cylindrical pit, a single elongated trench or a periodic array of trenches are investigated. We present more general expressions for the adhesion energy and membrane configuration in Fourier space and find that, compared to planar surfaces, the adhesion energy decreases. We also highlight the possibility of overshoots occurring in the membrane profile and look at its degree of penetration into surface indentations.