Stress in a polymer brush

We study the stress distribution in a polymer brush material over a range of graft densities using molecular dynamics (MD) simulations and theory. Flexible polymer chains are treated as beads connected by nonlinear springs governed by a modified finitely extensible nonlinear elastic (FENE) potential in MD simulations. Simulations confirmed the quartic variation of the normal stress parallel to the substrate, within the bulk of the brush, as predicted in our previous work, for low graft densities. However, in the high graft density regime, the Gaussian chain elasticity assumption is violated by finite extensibility effects (force-extension divergence) and the restriction to binary interaction among monomers is insufficient. This motivated us to extend a semi-analytical strong stretching mean field theory (SST) for polymer brushes, based on Langevin chains and a modified Carnahan-Starling equation of state to model monomer interactions. Our extended theory elucidates the stress and monomer density profiles obtained from MD simulations, as well as reproduces Gaussian chain results for small graft densities. A good agreement is observed between predictions of MD and Langevin chain SST for monomer density profile, end density profile and stress profile in high graft density regime, without fitting parameters (virial coefficients). Quantitative comparisons of MD results with various available theories suggest that excluded volume correlations may be important.