Chemodynamics of Metal Complexation by Natural Soft Colloids: Cu(II) Binding by Humic Acid

The chemodynamics of Cu­(II) complexation by humic acid is interpreted in terms of recently developed theory for permeable charged nanoparticles. Two opposing electric effects are operational with respect to the overall rate of association, namely, (i) the conductive enhancement of the diffusion of Cu²⁺, expressed by a coefficient <i>f</i>_el, which accounts for the accelerating effect of the negative electrostatic field of the humic particle on the diffusive transport of metal ions toward it, and (ii) the ionic Boltzmann equilibration with the bulk solution, expressed by a factor <i>f</i>_B, which quantifies the extent to which Cu²⁺ ions accumulate in the negatively charged particle body. These effects are combined in the probability of outer-sphere metal–site complex formation and the covalent binding of the metal ion by the complexing site (inner-sphere complex formation) as in the classical Eigen mechanism. Overall “experimental” rate constants for CuHA complex formation, <i>k</i>_a, are derived from measurements of the thermodynamic stability constant, <i>K</i>*, and the dissociation rate constant, <i>k</i>_d*, as a function of the degree of metal ion complexation, θ. The resulting <i>k</i>_a values are found to be practically independent of θ. They are also compared to theoretical values; at an ionic strength of 0.1 mol dm^–3, the rate of diffusive supply of metal ions toward the particles is comparable to the rate of inner-sphere complex formation, indicating that both processes are significant for the observed overall rate. As the ionic strength decreases, the rate of diffusive supply becomes the predominant rate-limiting process, in contrast with the general assumption made for complexes with small ligands that inner-sphere dehydration is the rate-limiting step. The results presented herein also resolve the discrepancy between experimentally observed and predicted dissociation rate constants based on the above assumption