Polyelectrolyte brush bilayer under shear at linear and nonlinear response regimes: A combination of the density functional theory framework and the scaling theory

ABSTRACT The density functional theory framework and the scaling theory are employed to approach the problem of the Polyelectrolyte brush bilayer under shear. It turns out that, the system at shear rates larger than a critical shear rate undergo a global restructuring during which chains stretch in the shear direction. In the absence of the electrostatic interactions as well as the hydrodynamic interactions, this global restructuring causes a sublinear scaling of the shear stress with the shear rate which makes the shear thinning effect. Nevertheless, in the presence of the hydrodynamic interactions, not only there is no sublinear regime but also a weak superlinear regime which makes a weak shear thickening effect. In the presence of the electrostatic interactions, the stress tensor components change by their second Virial coefficients, however, their shear rate power law are untouched. Nonetheless, the kinetic friction coefficient is independent of the electrostatic interactions. This suggests that the lubrication is not very much different than the neutral bilayers and the electrostatic interactions do not change that. The results of this study offers that maybe nature uses another mechanism to reduce friction coefficient in synovial joint and other biological systems. SIGNIFICANCE The significance of this study is that it strongly criticizes the theoretical approach to the same system which is already published (T. Kreer, Soft Matter , 12 , 3479 (2016)). Moreover, the results of this study may help our understanding from Biological systems and optimization of artificial synovial joint which is the core of this study.