(197b) Chain Bridging Contributions to Polyelectrolyte Brush Collapse in the Presence of Multivalent Ions

Surface modification using polyelectrolyte brushes is becoming increasingly common for colloidal stabilization and lubrication, both for biomedical and materials science applications. The unique properties of polyelectrolyte brushes result from the stretching of the chains away from the surface, which allows the brush to adopt an extended conformation. Electrostatic and excluded volume interactions between chain segments and osmotic pressure from counterions in the brush volume counteract the polymer chain elasticity to result in extension normal to the tethering surface. For polyelectrolyte brushes in the presence of monovalent counterions, this behavior is well understood both theoretically and experimentally, but a full understanding of brush extension in the presence of multivalent ions has not yet been reached. Multivalent ions are commonly present in industrial colloid formulations, coming from water sources in the form of calcium and magnesium, and are also present within the human body, so affect many applications of polyelectrolyte brushes. It has been shown experimentally that the brush height decreases sharply with increasing multivalent ion concentration, and this transition occurs at low ion concentrations. Previous experiments in our group on opposing polyelectrolyte brushes in the presence of multivalent counterions have shown an attractive force between the brushes as they are pulled apart, indicating that there is an attractive interaction between chains on the two different brushes, which is expected to be the bridging of polyelectrolyte chains by the multiple charges of multivalent ions. Using a phenomenological mean-field term, we introduce the attractive bridging interaction to a current model of a polyelectrolyte brush. Using an energy balance represented by the sum of electrostatic, polymeric and entropic mean-field terms, we minimize the free energy with respect to the ion populations and the brush height. Consistent with experimental observations, the brush height decreases sharply with an increase in the multivalent ion concentration, even in mixtures of multivalent and monovalent ions. Considering the bridging effect is essential to understanding the behavior of polyelectrolyte brushes in biological applications and industrial formulations, and may lead to the use of multivalent ions as a tuning parameter for new stimuli-responsive materials.