Competitive calcium ion binding to end-tethered weak polyelectrolytes

Polymer-coated nanoparticles have many biomedical applications ranging from sensing as imaging contrast agents to delivery platforms for therapeutics. Hence, it is important to understand how multivalent ions found in biological environments influence the coating. Here we use a molecular theory that explicitly includes the size, shape, and charge distribution of all species, as well as the conformations of the end-tethered polyelectrolytes to theoretically describe the structural changes and potential collapse of weak polyelectrolyte layers end-tethered to nanoparticles as a function of pH and divalent ion concentrations. Also, explicitly considered into the theory are the following chemical reactions: the acid-base equilibrium, ion condensation, and calcium bridging. End-grafted poly(acrylic acid) (pAA) layers collapse in the presence of sufficient amounts of Ca²⁺ ions, while poly arcrylamido-2-methylpropane sulfonate layers will not collapse. The collapse of end-tethered pAA is due to the formation of calcium bridges between two acrylic acid monomers and one calcium ion. The collapse of pAA layers is strongly dependent on the pH as well as divalent and monovalent salt concentrations of the environment and the curvature or radius of the nanoparticle.