Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Unveiling the Role of Electrostatic Forces on Attraction between Opposing Polyelectrolyte Brushes

Electrostatic interaction and molecular excluded-volume effects are responsible for a plethora of nonintuitive phenomena in soft-matter systems, including local charge inversion and attraction between similar charges. In the current work, we study the surface forces and swelling behavior of opposing polyelectrolyte brushes using a classical density functional theory that accounts for electrostatic and excluded-volume correlations. We observe that the detachment pressure between similarly charged brushes is sensitive to salt concentration in both the osmotic and salted regimes and can be negative in the presence of multivalent counterions. A comparison of the theoretical results with the mean-field predictions unravels the role of correlation effects in determining the surface forces and brush structure. For systems containing multivalent counterions, the detachment pressure attains negative values at an intermediate brush-brush separation, and the attractive region in the pressure vs distance plot is magnified in terms of both the depth and width of attraction with increasing counterion valency. However, the interbrush attraction vanishes when the size-induced correlations are switched off. We also investigated the role of counterion size and polymer chain length on the detachment pressure. It is found that smaller counterions are more effective in neutralizing the polymer charge than bigger counterions, leading to a reduced interbrush repulsion and, in some cases, attraction between like-charged brushes at intermediate distances. Meanwhile, varying the chain length of the grafted polymers only shifts the location of the attraction basin, with little influence on the interaction strength. The theoretical predictions show qualitative agreement with experimental observations and offer valuable insights into the interaction between similarly charged polymer brushes in the presence of multivalent ions.

Self-consistent field theory of polyelectrolyte brushes with finite chain extensibility

Polyelectrolyte brushes are formed by charged macromolecules tethered by the end segment to a solid-liquid interface. At low ionic strength of the solution, the intermolecular electrostatic interactions lead to strong stretching of the macromolecules that may, as a result, approach the limit of their extensibility (the contour length). Here, we present an analytical theory of polyelectrolyte brushes developed within the Poisson-Boltzmann approximation which explicitly accounts for finite extensibility of the brush-forming chains. In contrast to earlier theories based on the approximation of Gaussian elasticity of the brush-forming chains, the current approach enables avoiding artificial result of stretching of the chains beyond the contour length at high degrees of ionization or/and large grafting densities.

Single-chain-in-mean-field simulations of weak polyelectrolyte brushes

Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pK_a value of the polymer.

Curvature elasticity of a grafted polyelectrolyte brush

The curvature elasticity of a polyelectrolyte brush monolayer attached to curved surface is investigated theoretically. An analytical method based on the strong-stretching theory for a Gaussian chain is developed to calculate the elastic modulus induced by a polyelectrolyte brush. In particular, the scaling relations for the bending or Gaussian modulus with respect to system parameters related to the electrostatic interaction (degree of ionization and salt concentration) are derived. Using the numerical self-consistent-field theory, the inner structural, free-energy, and elastic moduli are computed for the polyelectrolyte brush with excluded-volume interactions. Compared to the analytical result, the curvature elasticity has a weaker dependence on the system parameters, which is attributed to the linearization for the Poisson-Boltzmann equation in the analytical treatment. Furthermore, our results are compared to the curvature elasticity of a bare charged surface, wherefrom the unique polyelectrolyte brush effect on the surface elasticity is clarified clearly. The scaling relations derived in our paper can serve as a guide to experimental studies on the related systems.