Metal speciation dynamics in colloidal ligand dispersions. Part 3: Lability features of steady-state systems

Abstract

A lability criterion is developed for dynamic metal binding by colloidal ligands with convective diffusion as the dominant mode of mass transport. Scanned stripping chronopotentiometric measurements of Pb(II) and Cd(II) binding by carboxylated latex core-shell particles were in good agreement with the predicted values. The dynamic features of metal ion binding by these particles illustrate that the conventional approach of assuming a smeared-out homogeneous ligand distribution overestimates the lability of a colloidal ligand system. Due to the nature of the spatial distribution of the binding sites, the change in lability of a metal species with changing ligand concentration depends on whether the ligand concentration is varied via manipulation of the pH (degree of protonation) or via the particle concentration. In the former case the local ligand density varies, whereas in the latter case it is constant. This feature provides a useful diagnostic tool for the presence of geometrically constrained binding sites.

Lability of nanoparticulate metal complexes in electrochemical speciation analysis

“…These results are basically similar to the correction coefficient for the overall association and dissociation rate constants k a and k d as proposed by Pinheiro et al [23] and experimentally verified using metal complexes with silica NPs and surface-functionalized latex NPs [35,36]. As is clear now from the present analysis, the derived "lability" is actually an expression of the local chemodynamics of the particle in the surrounding medium.…”

Impact of Electrostatics on the Chemodynamics of Highly Charged Metal–Polymer Nanoparticle Complexes

“…The system is said to be dynamic or static when the rates of these volume reactions are fast or slow, respectively, on the effective time scale t of the experiments, that is, k a * ρ L V t , k d * t ≫ 1 or k a * ρ L V t , k d * t ≪ 1. ,,, For the former situation, we further distinguish nonlabile and labile complexes, that is, cases where the flux J T of metal species is predominantly controlled by the dissociation kinetic flux and by the diffusive flux of complexes, respectively. , The ratio between kinetic and diffusive flux (denoted as J kin * and J dif * , respectively) is expressed by the lability criterion defined by scriptL * = J kin * / J dif * . Equivalently, scriptL * may be written in the concise form scriptL * = ( δ̅ / μ r − 1 ) / ( 1 + ε K * ′ ) where ε = D p / D M stands for the ratio between the diffusion coefficient of the particle and that of M, μ r = [ D M /( k a * ρ L V )] 1/2 is the so-called reaction layer thickness defined by the mean lifetime of free metal ion M and derived from the rate constant k a * = K * k d * for the (re)association reaction with the colloidal ligand particle. − Under the condition adopted here for the SSCP electrochemical measurements, the steady-state diffusion layer thickness is fixed by gentle hydrodynamic conditions so that δ̅ = 1.61 D̅ 1/3 ω –1/2 υ 1/6 , , where D̅ is the effective diffusion coefficient defined by D̅ = D M (1 + εK *′)(1 + K *′) −1 , ω is the rotation speed of the working electrode, and υ is the kinematic viscosity of water. The limiting dynamic situations of labile and nonlabile particulate metal complexes correspond to scriptL * ≫ 1 and scriptL * ≪ 1, respectively .…”

“…Equivalently, scriptL * may be written in the concise form scriptL * = ( δ̅ / μ r − 1 ) / ( 1 + ε K * ′ ) where ε = D p / D M stands for the ratio between the diffusion coefficient of the particle and that of M, μ r = [ D M /( k a * ρ L V )] 1/2 is the so-called reaction layer thickness defined by the mean lifetime of free metal ion M and derived from the rate constant k a * = K * k d * for the (re)association reaction with the colloidal ligand particle. − Under the condition adopted here for the SSCP electrochemical measurements, the steady-state diffusion layer thickness is fixed by gentle hydrodynamic conditions so that δ̅ = 1.61 D̅ 1/3 ω –1/2 υ 1/6 , , where D̅ is the effective diffusion coefficient defined by D̅ = D M (1 + εK *′)(1 + K *′) −1 , ω is the rotation speed of the working electrode, and υ is the kinematic viscosity of water. The limiting dynamic situations of labile and nonlabile particulate metal complexes correspond to scriptL * ≫ 1 and scriptL * ≪ 1, respectively . In the Supporting Information, we briefly recall the strategy to experimentally derive scriptL * from SSCP data …”

Evaluation of nanometer thick mercury film electrodes for stripping chronopotentiometry

“…We are especially interested in the application in trace metal binding in colloidal dispersions [21][22][23].…”