Polymer brush bilayer under stationary shear motion at linear response regime: A theoretical approach

Abstract

Statistical mechanics is employed to tackle the problem of polymer brush bilayers under stationary shear motion. The article addresses, solely, the linear response regime in which the polymer brush bilayers behave very much similar to the Newtonian fluids. My approach to this long-standing problem split drastically from the work already published Kreer, T, Soft Matter, 12, 3479 (2016). It has been thought for many decades that the interpenetration between the brushes is source of the friction between the brush covered surfaces sliding over each other. Whiles, the present article strongly rejects the idea of interpenetration length in that issue. Instead, here, I show that structure of the whole system is significant in friction between brush covered surfaces and the interpenetration is absolutely insignificant. The results of this research would blow one's mind about how the polymer brush bilayers respond at small shear rates.

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

“…In the other words, the collision time is the duration of a mean free path. The collision time for the PBBs is calculated as mean free path squared divided by diffusion constant (7,(10)(11)(12).…”

“…The DFT framework calculations, also, show that the shear and normal stress components at linear response regime are given as follows (7). Note that, to calculate the shear stress one need to calculate the intrinsic viscosity which needs the collision time.…”

“…( 1) the system resides in the linear response regime and at ( 1) it resides in the nonlinear response regime. The DFT framework calculations show that, at linear regime, the shear and normal chain extensions are given as follows (7,8), The DFT framework calculations, also, show that the shear and normal stress components at linear response regime are given as follows (7). Note that, to calculate the shear stress one need to calculate the intrinsic viscosity which needs the collision time.…”

“…( 1) the system resides in the linear response regime and at ( 1) it resides in the nonlinear response regime. The DFT framework calculations show that, at linear regime, the shear and normal chain extensions are given as follows (7,8),…”

“…The most straight answer to this question would be because vanishing of the interpenetration zone does not cause the shear thinning effect. In contrast, the chains which get stretched strongly in the shear direction and the system undergoes a global restructuring is the key effect (7). In the present study, I shall address these issues by extrapolating my theory to the Polyelectrolyte brush bilayers (PEBs) in the presence of the hydrodynamic interactions (HIs).…”