Determination of diffusion coefficients of nanoparticles and humic substances using scanning stripping chronopotentiometry (SSCP)

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Abstract

A methodology, based on a labile metal ion probe using stripping chronopotentiometry at scanned deposition potential (SSCP), is presented for the determination of the diffusion coefficients of nanoparticles and humic matter. The novel methodology was successfully applied to the determination of diffusion coefficients (and thus hydrodynamic diameters) of eight standard nanoparticles with radii ranging from 5 to 129 nm and two samples of colloidal humic substances with hydrodynamic radii of ca. 1 nm. Good agreement was found between the SSCP determinations and results obtained by dynamic light scattering (DLS), transmission electron microscopy (TEM) and fluorescence correlation spectroscopy (FCS). The SSCP technique is critically analysed with respect to its use for the determination of diffusion coefficients of colloidal complexes.

Introduction

Diffusion coefficients can also be used to infer: the importance of mass transport in environmental systems, conformational changes of macromolecules and aggregation kinetics and aggregate structures. Unfortunately, size or diffusion coefficient determinations are extremely difficult to obtain in natural systems where compounds are always chemically heterogeneous and polydisperse. For example, for humic substances (HS), size determinations (often via D measurements) have been performed using gel permeation chromatography [1], [2], ultra-filtration [3], viscosimetry [4], diffusion through activated carbon columns [5], dynamic light scattering (DLS) [6], [7], small angle neutron scattering [8], vapor phase osmometry [9], flow field flow fractionation [10], [11], [12], fluorescence correlation spectroscopy (FCS) [13], [14], atomic force microscopy [15], transmission electron microscopy (TEM) [16], low angle X-ray scattering [17] and electrochemical techniques [18], [19], [20]. Nonetheless, no consensus on the structure, diffusion coefficients or molar masses of the HS is yet available due to the large number of analytical techniques, source materials and isolation and fractionation procedures that have been employed. Another complicating factor is the dependence of molecular size on the ionic strength and pH of the system [21]. In addition, some observed size variations may be related to the dynamic character of the HS and their ability to adsorb to particle surfaces or to disaggregate then re-aggregate when crossing dialysis or filtration membranes [22].

Metals in natural waters are predominantly found in complexes with ligands including HS [23], polysaccharides [24], cell exudates [25], aluminosilicates [26], oxyhydroxides [27] and biological cells. In recent years, there has been a growing interest in taking trace metal speciation into account when legislating the impacts of trace metals on natural waters [28]. Within this framework, much of the traditional work focusing on the determination of distribution coefficients (KD) is not sufficiently precise to allow for the modeling of trace metal speciation or the correct interpretation of speciation data under a variety of environmental conditions. Unfortunately, the majority of analytical techniques that are able to quantitatively determine trace metal speciation require some additional information on the chemical lability or physical mobility of the trace metal complexes. For example, chemical speciation techniques including diffusive gradients in thin films (DGT) [29], permeation liquid membranes (PLM) [30] and stripping electrochemical techniques, such as anodic stripping voltammetry (ASV) [31] and scanned stripping chronopotentiometry (SSCP) [32] require diffusion coefficients of the colloidal metal complexes in order to rigorously interpret the analytical signal. While ASV [19], [20] can be employed to simultaneously evaluate the lability and mobility of trace metal complexes, it is cumbersome due to the need to know the exact value of the binding constant for the macromolecular trace metal complex. On the other hand, in SSCP [33], the shift in the half-wave deposition potential is directly related to the complex stability constant (K) irrespective of the lability of the metal complex. The limiting transition time, τ*, quantifies the metal species that have accumulated in the electrode, and depends on both the lability and mass transport of the metal complexes in solution. Discrepancies between potential derived and transition time derived K values indicate a loss of lability. For fully labile complexes the diffusion coefficient of the metal complex can be determined directly from the decrease in τ*.

In this paper, diffusion coefficients of colloidal metal complexes are determined by SSCP. Three model colloidal systems are employed to demonstrate the feasibility of the technique: spherical latex nanoparticles with radii ranging from 15 to 129 nm; gold and silver nanoparticles with radii smaller than 10 nm and two colloidal HS (one humic and one fulvic acid). The results from SSCP are compared with the results obtained from DLS (latex nanoparticles), TEM (gold and silver nanoparticles) and FCS (humic substances). The advantages and limitations of SSCP for the determination of diffusion coefficients in environmental media are discussed critically.

Section snippets

Theory

The objective of this work is to use a trace metal ion as a probe to determine the diffusion coefficient of a macromolecular ligand by means of an electrochemical stripping technique (SSCP). Electrochemical stripping techniques are two step processes. The first step consists in the application of a deposition potential (Ed) over a fixed period of time (deposition time, td). For a sufficiently negative deposition potential (limiting conditions), both the free metal and labile complexes are

Reagents and colloids

All solutions were prepared in ultrapure water from a Barnstead EasyPure UV system or a Millipore Simplicity 5 unit (resistivity >18 MΩ cm). Cd(II) solutions were prepared from solid Cd(NO3)2 (Merck, p.a.) and those for Pb(II) from the dilution of a certified standard of 0.100 M Pb(NO3)2 (Metrohm). The KNO3 and NaNO3 solutions were prepared from solid KNO3 and NaNO3 (Merck, suprapur). Stock solutions of MES (2-(N-morpholino)ethanesulfonic acid) and MOPS (3-(N-morpholino)propanesulfonic acid)

Results and discussion

Results were first obtained for the interactions of lead and cadmium with carboxyl modified latex particles in order to better understand the SSCP signal and the limitations of the technique for determining diffusion coefficients in well defined macromolecular systems. In particular, the detection window and associated errors were carefully evaluated. The ability of SSCP to determine diffusion coefficients of complexed metals in labile systems depend on D¯ and K′. Eq. (4) can be re-written as

Conclusions

The proposed methodology to determine the diffusion coefficients of nanoparticles and humic matter by means of a labile metal probe and SSCP produced reliable results for both the nanoparticles and humic substances. Particle sizes of six different latex samples with radii ranging from 15 to 129 nm were found to be in good agreement with reported sizes corresponding well to light scattering measurements. Sizes of silver and gold nanoparticles determined by SSCP showed good agreement with sizes

Acknowledgements

We thank Dr. Joxe Sarobe and Ikerlat Polymers (Spain) for the cleaning and characterization (conductimetric and potentiometric) of the 40, 60.5 and 129 nm carboxylated latex particles. This work was performed within the framework of the projects POCI/QUI/56845/2004, Ph.D. grant (RD) SFRH/BD/8366/2002 and Post-Doctoral fellowship (RL) SFRH/BPD/20176/2004, Fundação para a Ciência e Tecnologia, Portugal. This work was partially supported by the Swiss National Science Foundation and the Natural

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