We employ molecular dynamics (MD) simulations and develop scaling theories to quantify the equilibrium behavior of polyelectrolyte (PE) brush bilayers (BBLs) in the weakly interpenetrated regime, which is characterized by $d_0<d_g<2d_0$, where $d_g$ is the gap between the opposing plates where the PE brushes are grafted and $d_0$ is the unperturbed height of a PE brush grafted at a single plate. Scaling predictions establish that, for the weakly interpenetrated osmotic PE BBLs $\delta \sim N^{1/2}{(2-d_g/d_0)}^{1/2}$ (where $\delta$ is the interpenetration length and $N$ is the number of Kuhn segments in PE brush). MD simulations excellently recover this dependence of $\delta$ on $N$ and the extent of interpenetration (quantified by $d_g/d_0$). These predictions, unlike the existing studies, establish a finite interpenetration for all values of $d_g/d_0$ as long as $d_g<2d_0$. Finally, we quantify the monomer and counterion concentration distributions and point out that these two distributions may quantitatively deviate from each other at locations very close to the channel centerline, where the interpenetration-induced monomer concentration can be significantly low.

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• Polymer behavior