Abstract.
By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R , viscosity (\( \eta\) , and shear force (F over a wide range of Weissenberg numbers, W . In agreement with our theory, the simulation reveals simple power laws, R ∼ W 0.53 , \( \eta\) ∼ W -0.46 , and F ∼ W 0.54 , for the non-Newtonian regime.
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In this context, the limit of ``strong'' compression does not imply melt conditions. Instead, we refer to a semidilute bilayer with a uniform monomer density profile
In fact, previous investigations kreer, where hydrodynamic interactions were strongly screened due to the application of a different (Langevin) thermostat, report a somewhat larger exponent, $R^2/R^2_0 \sim W^{0.6}$. This can be understood from our approach by reformulating eq. (Fwet.eq) for ``dry'' bilayers. Without hydrodynamic interactions, the force per area in linear response is proportional to the number of monomers in the interpenetration zone, $F/A \sim cL\dot{\gamma} D$. Repeating our analysis we obtain $R^2/R^2_0 \sim W^{0.65}$, $F/F(W = 1)$ $\sim W^{0.73}$, $\eta/\eta_0 \sim W^{-0.27}$ for the non-Newtonian response of semidilute, dry bilayers. Note that these exponents clearly differ from the present approach giving rise to the assertion that hydrodynamic interactions are represented in our simulations for all solvent models used. Dry bilayers, as modeled in ref. kreer, are physically much less relevant, of course
Note that experimental shear rates are usually much smaller than in the simulation. On the other hand, simulations typically work with much smaller chain lengths. Equation (tau.eq) suggests that both effects partially cancel, such that the related Weissenberg numbers become comparable
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Spirin, L., Galuschko, A., Kreer, T. et al. Polymer-brush lubrication in the limit of strong compression. Eur. Phys. J. E 33, 307–311 (2010). https://doi.org/10.1140/epje/i2010-10674-3
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DOI: https://doi.org/10.1140/epje/i2010-10674-3