Stress in a polymer brush
M Manav and M Ponga and AS Phani, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 127, 125-150 (2019).
We study the stress distribution in a polymer brush material over a range of graft densities, using theory and molecular dynamics (MD) simulations. MD simulations confirmed the quartic variation of the normal stress within the bulk of the brush, as predicted in our previous work. However, in the high graft density regime, further improvements to the theory are needed, as it is known that finite extensibility effects (force-extension divergence) invalidate Gaussian elasticity of chains, and the restriction to binary interaction among monomers is insufficient. This motivated us to extend a semi-analytical strong stretching theory (SST) for polymer brushes that use Langevin force- extension relation for chains and a modified Carnahan-Starling (CS) equation of state to model monomer interactions. Our extended theory elucidates the stress profiles obtained from MD simulations. It reproduces Gaussian chain results for small graft densities, and shows a good qualitative agreement with MD results for monomer density profile, end density profile and stress profile for high graft densities without the need for fitting parameters (virial coefficients). Quantitative comparisons of MD results with various available theories suggest that excluded volume correlations may be important. (C) 2019 Elsevier Ltd. All rights reserved.
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