Elasticity of polymer-anchored membranes

The renormalization of the elastic constants of a polymer-anchored membrane is investigated by means of systematic Monte Carlo simulations. Our results indicate that when polymers are grafted on both sides, and are in the brush regime, the excess bending rigidity scales as N(3)sigma(alpha) (N and sigma being the number of statistical segments and grafting density, respectively) with 7/3 < α < 5. When the membrane is grafted on one side only, the induced excess bending modulus depends on the bare membrane bending modulus, kappa(0), and approaches a value of (3/2)kappa(0). These results are largely in agreement with the self-consistent field theory and scaling arguments using the blob picture.