Journal de Physique II

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DOI: 10.1051/jp2:1996142
J. Phys. II France 6 (1996) 1465-1481

Elastic Properties of Polymer-Decorated Membranes

Christin Hiergeist and Reinhard Lipowsky

Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Kantstr. 55, 14513 Teltow-Seehof, Germany

(Received 11 March 1996, revised 13 May 1996, accepted 13 June 1996)

Abstract
Polymers attached to one side of a fluid membrane induce a spontaneous curvature $M_{\rm sp}$ of the membrane and change its elastic constants. For an ideal polymer in the mushroom regime, we determine $M_{\rm sp}$ and the elastic constants $\kappa$ and $\kappa_{\rm G}$ by an explicit calculation of the entropy gain of a polymer anchored onto a curved surface. For anchored polymers in the brush regime, a scaling picture is used to determine $M_{\rm sp}$ which increases monotonically with the coverage $\overline{\Gamma}$ . For small and large $\overline{\Gamma}$ , one has $M_{\rm sp}\sim N^{2} \overline{\Gamma}^$ and $M_{\rm sp}\sim N^\overline{\Gamma}^$ , respectively. Both in the mushroom and in the brush regime, the polymers increase the bending rigidity, whereas the Gaussian bending rigidity is decreased.