Metal speciation dynamics in soft colloidal ligand suspensions. Electrostatic and site distribution aspects.

The theory for metal speciation dynamics in dilute, monodisperse suspensions of spherical core-shell colloidal ligand particles is extended with the impact of the electric double layer (EDL) field and inhomogeneous site distribution inside the particle. The latter is defined by a diffuse, radial distribution for the density of charged polymer segments supporting the ligands L. The site distribution at the scale of the particle suspension and within the colloidal shell results in association/dissociation rate constants (denoted as k(a)* and k(d), respectively) that may significantly differ from their homogeneous solution counterparts (k(a) and k(d)). The differences arise from intertwined kinetics of metal-ligand (ML) complex formation/dissociation in the particle shell and diffusive transport of free metal ions M within/outside the shell in the electric field set up by the EDL at the core-shell/electrolyte interphase. The relationship between k(a,d) and k(a,d) is derived from the numerical evaluation of the spatial, time-dependent distributions of free and bound metal as governed by coupled Nernst-Planck equations corrected by appropriate chemical source term and written in a Kuwabara cell geometry. The average interphasial electrostatic field stemming from the formation of the EDL at the complexing colloidal interphase is obtained from the solution of the nonlinear Poisson-Boltzmann equation. The EDL composition is exclusively governed by ions from indifferent background electrolyte present in large excess over free metal species M. The dependences of k(a,d)* on rate constants k(a,d), geometrical details of particle, particle charge, concentration of indifferent background electrolyte, and ligand distribution within the shell are thoroughly discussed within the context of dynamic features for colloidal complex systems. Examination of the chemical equilibrium regime allows addressing explicitly the impact of electrostatics on colloidal complex stability (polyelectrolyte effect). The numerical study is further supported by an approximate analytical expression based on Donnan partitioning and valid under the quasi-steady-state approximation (nonequilibrium chemical regime). The analysis covers the limiting cases of charged rigid particles where binding sites are located at the very surface of the core (e.g., functionalized latex colloids) and polyelectrolyte particles devoid of a hard core (e.g., polysaccharide macromolecules, gel particles).