Study of cadmium–humic interactions and determination of stability constants of cadmium–humate complexes from their diffusion coefficients obtained by scanned stripping voltammetry and dynamic light scattering techniques

Abstract

Diffusion coefficients of Cd–humate complexes are dependent on pH and [Cd]/[Humic] Acid (HA)] ratio in a Cd–HA system. These two factors mainly control the mass transport and complexation kinetics of Cd that may influence bioavailability and toxicity of Cd species in environmental systems. Determination of diffusion coefficients of Cd–HA systems by Scanned stripping voltammetry and dynamic light scattering techniques can provide a better understanding of the systems and can be very useful for extracting other speciation parameters of the systems. This study revealed that Cd²⁺ ion along with small dynamic Cd complexes was predominantly present in a Cd–HA system at pH 5 with high diffusion coefficients. HA molecules were in aggregated form at pH 5. However, HA molecules were in disaggregated form at pH 6 and concentrations of Cd²⁺ ion and small Cd-dynamic complexes decreased with a decrease in diffusion coefficients of Cd complexes at this pH due to formation of Cd–humate complexes. No further decrease in the hydrodynamic radii of HA was observed with the increase of pH from 6 to 7. The Cd–humate system partially lost its lability at pH 7. Conditional stability constants were calculated for Cd–humate complexes by combining the diffusion coefficient data obtained by two techniques. The log K values calculated in this study are in good agreement with the data available from the literature.

Introduction

One of the most important properties in an environmental system is the diffusion coefficient, which determines the mass transport, complexation kinetics, bioavailability and toxicity of a metal species. Unfortunately, determination of diffusion coefficient of a single metal species is extremely difficult in natural systems where metal complexes are polydisperse and chemically heterogeneous [1]. However, it is possible to determine an average diffusion coefficient of all dynamic metal complexes by using different techniques such as diffusive gradients in thin films technique (DGT) [2], stripping voltammetry (SV) [3], gel permeation chromatography [4], [5], ultra-filtration [6], diffusion through activated carbon column [7], and dynamic light scattering (DLS) [8], [9]. SV techniques have been applied widely to determine average diffusion coefficients ($\overline{D}$) of metal complexes in natural water systems because of their simplicity. Pinheiro et al. [10] applied the SV technique to determine an average diffusion coefficients of nanoparticles and humic substances. Despite a large numbers of attempts [11], [12], [13] using different techniques to determine the average diffusion coefficient of metal complexes in natural aqueous systems, this important speciation parameter has not been used to help understand the basic chemistry involved in metal–humic interactions in natural systems.

Metals in natural waters are predominantly found in complexes with ligands including humic substances, polysaccharides, and proteins. Humic substances are physically and chemically heterogeneous [1] and thus metal–humic complexes also become polydisperse and different in thermodynamic stability. Due to unknown nature of humics, determination of absolute diffusion coefficient of a single species is impossible. In general, the reported diffusion coefficient of metal complexes in natural systems by different techniques is an average diffusion coefficient of all dynamic metal complexes (including metal aqua complexes) in the system. The average diffusion coefficient ($\overline{D}$) [14], [15] of a metal M is represented by

$$\overline{D}=\frac{D_{\text{M}}{c}_{\text{M}}+D_{\text{ML}}{c}_{\text{ML}}}{c_{\text{M},\text{T}}^{*}}$$

where, C_MC_ML and $c_{\text{M},\text{T}}^{*}$ are the concentrations of the free metal ion, dynamic metal complexes and total metal, D_M and D_ML represents the diffusion coefficient of free metal ion and metal–ligand complexes. This equation suggests that the formation of free metal ion or labile complexes from the strong complexes increase either C_M or C_ML and as a result $\overline{D}$ of the species increases. Similarly, complexation of free metal ion with strong complexing sites of humics, i.e. formation of inert complexes and formation of weak bulky complexes, may decrease $\overline{D}$. It is important to mention that the detection of C_ML depends on the analytical detection window of the technique applied.

Thus, the following equation [14] was introduced to express the average diffusion coefficient and explain the above phenomenon:

$$\overline{D}=D_{\text{M}}\frac{(1+\epsilon K^{\prime })}{(1+K^{\prime })}$$

where, ɛ = D_ML/D_M and K′ = KC_L (K is the conditional stability constant of ML complexes and C_L is the uncomplexed ligand concentration).

The above equation can be reduced to

$$K^{\prime }=\frac{D_{\text{M}}-\overline{D}}{\overline{D}-D_{\text{ML}}}$$

Thus, the determination of $\overline{D}$ and D_ML of a system can be very effective to understand the metal complexation with a heterogeneous ligand in aqueous system. The objective of this work was to develop a better understanding of metal speciation by determining $\overline{D}$ and D_ML of metal complexes (which includes metal–humate and other complexes) by using two independent techniques. The interaction of cadmium and humic acid was studied in model solutions with a well-characterized humic acid by using scanned stripping voltammetry (SSV) and DLS.