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

Kim, J. U. and Matsen, M. W. (2007) Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes. European Physical Journal E, 23 (2). pp. 135-144. ISSN 1292-8941

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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 $\mu \propto L^{-1}$ 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 $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.