Elastic Properties of Polymer-Decorated Membranes

Polymers attached to one side of a fluid membrane induce a spontaneous curvature Msp of the membrane and change its elastic constants. For an ideal polymer in the mushroom regime, we determine Msp and the elastic constants κ and κG 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 Msp which increases monotonically with the coverage $\overline{\Gamma}$. For small and large $\overline{\Gamma}$, one has $M_{\rm sp}\sim N^{2} \overline{\Gamma}^{13/6}$ and $M_{\rm sp}\sim N^{1/7}\overline{\Gamma}^{13/21}$, respectively. Both in the mushroom and in the brush regime, the polymers increase the bending rigidity, whereas the Gaussian bending rigidity is decreased