Applicability of the Reaction Layer Principle to Nanoparticulate Metal Complexes at a Macroscopic Reactive (Bio)Interface : A Theoretical Study

The reaction layer concept is commonly adopted to estimate the contribution of metal complexes to the flux of free metal ions (M) toward a macroscopic M-accumulating (bio)interface, e.g., a biosurface (microorganism) or a sensor (electrode). This concept is well-established for molecular ligands homogeneously distributed in solution. However, the case of (nano)particulate complexants carrying metal binding sites within their body or at their surface has so far received scant attention. In this study, a formalism is elaborated to evaluate the thickness λ of the reaction layer that is operational for (nano)particulate metal complexes at a macroscopic metal-sensing (bio)interface. The theory integrates the relevant chemodynamic properties of nanoparticulate metal complexes as governed by the interplay between M conductive diffusion to/from the nanoparticulate complexants and the dissociation kinetics of inner-sphere complexes between M and particle-supported binding sites. The intricate dependence of λ on particle size, particle type, particle charge, the density/number of metal binding sites, and the nature of the metal ion is physically interpreted with the aid of computational illustrations. Analytical formulations are further derived in the extremes where reaction layer properties are dominated by either diffusion-controlled or kinetically controlled dissociation of nanoparticulate metal complexes. The results constitute a solid physicochemical basis for elaboration to lability of nanoparticulate complexes at macroscopic reactive (bio)interfaces, a central theme in biouptake and toxicity of metals. In particular, the here-reported formalism is shown to successfully predict the lability of metal-polymer nanoparticle complexes as determined from voltammetric measurements. It is further evidenced that conventional approaches ignoring particle body exclusion from the reaction layer may dramatically overestimate, by several orders of magnitude, the true kinetic flux arising from the rate of dissociation of nanoparticulate metal species at a macroscopic reactive interface