Eur. Phys. J. E (2007) 23: 135-144
https://doi.org/10.1140/epje/i2007-10188-1

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

Department of Mathematics, University of Reading, Whiteknights, Reading, RG6 6AX, UK

^* e-mail: j.kim@reading.ac.uk
^** e-mail: m.w.matsen@reading.ac.uk

Received: 6 March 2007
Published online: 6 June 2007

Abstract

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance μ∝L^-1 from the substrate, where L is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance ξ∝L^-1/3. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.