Web Release Date: December 23,
On the Curvature Energy of a Thin Membrane Decorated by Polymer Brushes
and
Institute of Macromolecular Compounds of the Russian Academy of Sciences, 199004 St. Petersburg, Russia, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6307 HB Wageningen, The Netherlands
Received June 12, 2007
Revised Manuscript Received October 25, 2007
Abstract:
In this work, we present approximate analytical predictions for the contribution to the free energy
of curvature of a thin (flexible) membrane rising from a polymer brush, which is grafted to both sides of the
membrane. The influence of the approximations is revealed by a detailed comparison with numerically exact
self-consistent field (SCF) calculations. We consider both the quenched case, i.e., when the grafting density is
the same on both sides, and the annealed case, i.e., when the polymer chains can translocate upon bending from
one side of the membrane to the other. It is found that the analytical predictions give the correct sign for the
brush contribution to the free energy of curvature. Moreover, for spherically curved membranes, a reasonably
accurate scaling with the grafting density 
and the chain length N is obtained. However, in the case of a cylindrical
curvature, the analytical models overestimate the dependence on the polymer chain length. It is shown that the
mean bending modulus is positive, which implies that the grafting of polymers onto membranes makes these
stiffer. The Gaussian bending modulus is negative and scales with the chain length in the power three, whereas
the mean bending modulus scales with the chain length with a power two. This is in contrast with the analytical
predictions which point to the same power-law dependence of three. Our results imply that for sufficiently long
polymers the flat conformation becomes unstable in favor of bending.
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