Electrostatic repulsion between two parallel plates covered with polyelectrolyte brush layers. Effects of interdigitation

Swelling and shrinking of two opposing polyelectrolyte brushes

Salt concentration and confinement effects affect the configuration of polyelectrolyte (PE) brushes due to electrostatic interactions. In this work, we develop a new theoretical model to analyze the electrostatics and swelling-shrinking behavior of two opposing PE brushes. By comparing three length scales, i.e., equilibrium brush height, separation distance, and Debye length, we obtain distinct scaling laws for brush height in different regimes. We provide explanations for the anomalous shrinkage of the PE brush with added salt reported in experiments and simulations, the applicability of the homogeneous brush assumption, and the confinement effect on the brush height. Our model can be used to shed light on the configuration and functionalities of PE-grafted interfaces, which play important roles in ion selective membranes and organism lubrication. We also anticipate that our method will be useful to understand the functionalities of other charged soft matter systems, such as hydrogel swelling and colloidal stability.

Lubrication in polymer-brush bilayers in the weak interpenetration regime: Molecular dynamics simulations and scaling theories

We conduct molecular dynamics (MD) simulations and develop scaling laws to quantify the lubrication behavior of weakly interpenetrated polymer brush bilayers in the presence of an external shear force. The weakly interpenetrated regime is characterized by 1<d_{g}/d_{0}<2, where d_{g} is the gap between the opposing surfaces (where the brushes are grafted) and d_{0} is the unperturbed brush height. MD simulations predict that in the shear thinning regime, characterized by a larger shear force or a large Weissenberg number (W), R_{g}^{2}∼W^{0.19} and η∼W^{-0.38}, where R_{g} is the chain extension in the direction of the shear and η is the viscosity. These scaling behaviors, which are distinctly different from that witnessed in strongly compressed regime (for such a regime, characterized by d_{g}/d_{0}<1, R_{g}^{2}∼W^{0.53}, and η∼W^{-0.46}), match excellently with those predicted by our scaling theory.

Polyelectrolyte brush bilayers in weak interpenetration regime: Scaling theory and molecular dynamics simulations

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 δ∼N^{1/2}(2-d_{g}/d_{0})^{1/2} (where δ is the interpenetration length and N is the number of Kuhn segments in PE brush). MD simulations excellently recover this dependence of δ 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.

Interaction between two parallel plates covered with a polyelectrolyte brush layer in an electrolyte solution

An approximate analytic expression is derived for the interaction energy between two parallel plates covered with a polyelectrolyte brush layer in an electrolyte solution. The interaction energy has three components: electrostatic interaction energy between two brush layers before and after their contact, steric interaction energy between two brush layers after their contact, and the van der Waals interaction energy between the cores of the plates. It is shown that these three components are of the same order of magnitude and contribute equally to the total interaction energy between two polyelectrolyte-coated plates in an electrolyte solution. On the basis of Derjaguin's approximation, an approximate expression for the interaction energy between two spherical particles covered with polyelectrolyte brush layers is also derived.

Compression of polymer brushes in the weak interpenetration regime: scaling theory and molecular dynamics simulations

We employ scaling theory and Molecular Dynamics (MD) simulations to probe the compression of the semi-dilute polymer brush bilayers (BBLs) in the weak interpenetration (IP) regime. Such a regime is characterized by two layers of interacting polymer brushes grafted on opposing planar surfaces having a separation d_g, such that d₀ < d_g < 2d₀, with d₀ being the unperturbed brush height. Currently, scaling theories are known for polymer BBLs with a much larger degree of IP (i.e., d_g < d₀) - in such regimes, the brush height can be quantified by the corresponding IP length δ. On the other hand, we show that in the weak IP regime, the brush height is not solely dictated by δ. We develop new scaling theories to show that δ in this weak IP regime is different from that in the strong IP regime. Secondly, we establish that the compressed brush height in this weakly IP regime can be described as d ∼ N^χ with χ < 1 and varying monotonically with d_g/d₀. MD simulations are carried out to quantify δ and χ and the results match excellently with our new scaling theory predictions. Finally, we establish that our scaling theory can reasonably predict the experimentally witnessed variation of the interaction energy dictating the compressive force between the interpenetrating brushes in this weakly IP regime.

Electrostatic interaction of soft particles

Theories of the electrostatic interaction between two soft particles (i.e., particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution are reviewed. Interactions of soft particles after contact of their surface layers are particularly discussed. Interaction in a salt-free medium and the discrete-charge effect are also treated.

Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates

A new theory quantifies the effect of finite ion size in osmotic pressure (Πosm) between two soft charged plates.