  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.
