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Parallel and Perpendicular Lamellae on Corrugated Surfaces Yoav Tsori*

Summary: Parallel and Perpendicular Lamellae on Corrugated Surfaces
Yoav Tsori*
Laboratoire Matie`re Molle & Chimie (UMR 167), ESPCI, 10 rue Vauquelin,
75231 Paris Cedex 05, France
David Andelman
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv 69978, Israel
Received April 15, 2003; Revised Manuscript Received August 12, 2003
ABSTRACT: We consider the relative stability of parallel and perpendicular lamellar layers on corrugated
surfaces. The model can be applied to smectic phases of liquid crystals, to lamellar phases of short-chain
amphiphiles, and to lamellar phases of long-chain block copolymers. The corrugated surface is modeled
by having a single q-mode lateral corrugation of a certain height. The lamellae deform close to the surface
as a result of chemical interaction with it. The competition between the energetic cost of elastic
deformations and the gain in surface energy determines whether parallel or perpendicular lamellar
orientation (with respect to the surface) is preferred. Our main results are summarized in two phase
diagrams, each exhibiting a transition line from the parallel to perpendicular orientations. The phase
diagrams depend on three system parameters: the lamellar natural periodicity, the periodicity of surface
corrugations and their corresponding amplitude. For a fixed lamellar periodicity (or polymer chain length),
the parallel orientation is preferred for surfaces having small-amplitude corrugations at long wavelengths.
For a fixed corrugation periodicity, the parallel orientation is preferred for small corrugation amplitude


Source: Andelman, David - School of Physics and Astronomy, Tel Aviv University


Collections: Materials Science; Physics