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

Colloids and Surfaces A: Physicochem. Eng. Aspects 295 (2007) 200–208

Determination of diffusion coefficients of nanoparticles and humic substances using scanning stripping chronopotentiometry (SSCP) Jos´e P. Pinheiro a,∗ , Rute Domingos b , Rocio Lopez b , Roberta Brayner c , Fernand Fi´evet c , Kevin Wilkinson d a

Centro de Biomedicina Molecular e Estrutural (CBME), Departamento de Qu´ımica e Bioqu´ımica/FCT, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal b Centro de Multidisciplinar de Qu´ımica Ambiental (CMQA), Departamento de Qu´ımica e Bioqu´ımica/FCT, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal c Interfaces, Traitements, Organisation et Dynamique des Syst` emes (ITODYS), UMR-CNRS 7086, Universit´e Paris, 7 Denis Diderot, case 7090, 2 Place Jussieu, 75251 Paris, Cedex 05, France d Department of Chemistry, University of Montreal, P.O. Box 6128, Succ. Centre-Ville, Montreal (QC), H3C 3J7, Canada Received 17 June 2006; received in revised form 17 August 2006; accepted 28 August 2006 Available online 1 September 2006

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. © 2006 Elsevier B.V. All rights reserved. Keywords: Diffusion coefficients; Nanoparticles; Humic matter; Stripping chronopotentiometry; Fluorescence correlation spectroscopy

1. 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 [10–12], fluorescence correlation spec-

∗

Corresponding author. Tel.: +351 289 800905; fax: +351 289 800066. E-mail address: [email protected] (J.P. Pinheiro).

0927-7757/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2006.08.054

troscopy (FCS) [13,14], atomic force microscopy [15], transmission electron microscopy (TEM) [16], low angle X-ray scattering [17] and electrochemical techniques [18–20]. 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 reaggregate 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

J.P. Pinheiro et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 295 (2007) 200–208

Nomenclature A ci∗ ∗ ci,T

¯ D DM DML Ed Ed,1/2 F Id∗ Is ka kd K K n r0 td

electrode area (m2 ) concentration of species i in bulk solution (mol m−3 ) total concentration of species i in bulk solution (mol m−3 ) average diffusion coefficient (m2 s−1 ) diffusion coefficient of the free metal in solution (m2 s−1 ) diffusion coefficient of the metal complex in solution (m2 s−1 ) deposition potential (V) SSCP shift of the half-wave potential (V) Faraday constant (C mol−1 ) limiting reduction current (A) stripping current (A) formation rate constant of the complex ML (mol−1 m3 s−1 ) dissociation rate constant of the complex ML (s−1 ) complexation constant (mol−1 m3 ) effective complexation constant (= KcL∗ ) number of electrons involved in the faradaic process radius of the electrode (m) deposition time (s)

Greek symbols α hydrodynamic parameter of the mass transport to the electrode δM “planar” diffusion layer thickness in the absence of complexing ligands (m) δ¯ “planar” diffusion layer thickness in the presence of complexing ligands (m) ε =DML /DM , dimensionless diffusion coefficient γ part of δ that does not depend on the diffusion coefficient τ SSCP transition time (or wave height) (s) τ* SSCP limiting transition time (s) ∗ τM limiting transition times obtained in the absence of a complexing ligand (s) ∗ τM+L limiting transition times obtained in the presence of a complexing ligand (s)

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 tech-

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niques, 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. 2. 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 reduced at the surface of the electrode and a reduction current (Id∗ ) is obtained. The second step is a measuring step, which aims to determine the concentration of the metal in the amalgam. The difference with stripping chronopotentiometry, as compared to the other stripping techniques, is that the accumulated metal is reoxidized by application of a low constant oxidizing current (stripping current, Is ) rather than a potential scan. When the stripping current is sufficiently low, the accumulated metal is completely depleted from the electrode and application of Faraday’s law will yield a direct relationship between the transition time, τ * , and the reduction current: τ∗ =

Id∗ td IS

(1)

This technique is simpler to use than other electrochemical techniques (e.g. square wave voltammetry), in that it allows a straightforward determination of the “limiting current”. For a

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spherical electrode in the presence of labile complexes [34], the “limiting current” is given by:   1 1 ∗ ∗ ¯ M,T (2) Id,M+L = nFADc + r0 δ¯ while in absence of ligand, this equation reduces to:   1 1 ∗ ∗ Id,M = nFADM cM,T + δM r0 ∗ ∗ ¯ = (DM cM + DML cML ) D ∗ cM,T

(3) (4)

¯ is the mean diffusion coefficient of the free metal (M) where D and its complex (ML) in solution [35], c* is the concentration of metal complex (ML) or total metal (M,T) in solution, n is the number of electrons involved in the process, F is Faraday’s constant, A is the electrode area, r0 is the electrode radius and δ¯ and δM are the “planar” diffusion layer thicknesses (average and free ion). The diffusion layer thickness depends on the hydrodynamic conditions during the deposition step. It can be evaluated from a power function of Dα : δ = γDα

(5)

where α is related to the hydrodynamic nature of the mass transport [36] and γ corresponds to the constant part of δ¯ that does not depend on the diffusion coefficient. In a previous work [37], an α value of 1/3 was obtained using the same electrochemical cell and conditions as in this work. For a given total metal concentration, the mean diffusion coef¯ can be computed from the limiting transition times ficient, D, ∗ ∗ ) (calobtained in the presence (τM+L ) (titration) and absence (τM ibration) of ligand: ∗ ¯ ¯ 1/3 ) + (1/r0 )) τM+L D((1/γ D = ∗ 1/3 τM DM ((1/γDM ) + (1/r0 ))

which for macroelectrodes, i.e. 1/r0  1/δ, reduces to:   ∗ ¯ 2/3 D τM+L ∗ = D τM M

(6)

(7)

For spherical electrodes under mixed diffusional control, it is necessary to solve Eq. (6), which can be performed by using the ¯ 1/3 to obtain a cubic equation [38] variable substitution y = D   ∗ r0 1 r0 2 τM+L 3 y + y − ∗ DM (8) α +1 =0 γ τM γ DM Under conditions of ligand excess (most often the case in environmental systems), it is usual to define the stability constant K as: cML (9) K = KcL,T = cM where K is the stability constant of ML and cL,T corresponds to the total concentration of ligand. K can be determined from the potential shift, Ed,1/2 , corrected for the decrease in transition

Fig. 1. Schema of SSCP calculations. Two waves are shown: one for the metal without ligands (calibration) and the other in the presence of ligands. The poten∗ tial shift (Ed,1/2 ) and the transition times obtained in the presence (τM+L ) and ∗ ) of ligands are indicated. absence (τM

time using an expression that is equivalent to the DeFord–Hume expression [33] (Fig. 1):   ∗   nF τ  ln(1 + K ) = − (10) ΔEd,1/2 − ln M+L ∗ RT τM The diffusion coefficient of the complex, DML , can be obtained from the stability constant (K ), computed using Eq. (10) and the mass balance for the metal: ¯ − DML = D

1 ¯ (DM − D) K

(11)

3. Experimental section 3.1. Reagents and colloids All solutions were prepared in ultrapure water from a Barnstead EasyPure UV system or a Millipore Simplicity 5 unit (resistivity >18 M 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-(Nmorpholino)propanesulfonic acid) buffers were prepared from the solids (Fluka, Microselect, >99.5%). HNO3 (Merck, suprapur), KOH (0.1 M standard, Merck) and NaOH (Riedel–de Ha¨en) were used to adjust the pH. For the synthesis of the aqueous solutions of colloidal Ag and Au, HAuCl4 was kindly supplied by Engelhard France, AgNO3 was purchased from Prolabo, 11-mercapto-undecanoic acid (11-MUA) was purchased from Aldrich and polyvinylpyrrolidone (PVP) and NaBH4 were purchased from Sigma. Three samples of monodisperse carboxylated latex nanospheres (P(S/V-COOH)) were obtained from Bangs Labs (Fishers, IN, USA): a = 15 nm, cL,T = 0.65 × 10−4 mol COOH per gram; a = 35 nm, cL,T = 1.68 × 10−4 mol COOH per gram and a = 65 nm, cL,T = 1.60 × 10−4 mol COOH per gram (a corresponds to the radius of the nanoparticles). The

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nanospheres were cleaned by a mixed bed resin method [39] to eliminate surfactant. Another three samples were obtained from Ikerlat Polymers (Spain): a = 40.0 nm, cL,T = 5.2 × 10−5 mol COOH per gram; a = 60.5 nm, cL,T = 5.1 × 10−5 mol COOH per gram and a = 129 nm, cL,T = 5.9 × 10−5 mol COOH per gram. These nanospheres were cleaned by the manufacturer, who provided a conductimetric and potentiometric characterization of each sample. Due to the low concentration of the dispersions that was used (0.01–0.4% w/w) the maximum expected change in viscosity was on the order of 0.3% [40]. Au and Ag nanoparticles were synthesized in aqueous solution. The procedure involved addition of HAuCl4 and AgNO3 salts to 20 mL of distilled water to reach a final concentration of 10−4 M. To control particle size and shape, 11-MUA and PVP were added to aqueous solutions of Au and Ag salts to attain final concentrations between 10−4 and 10−2 M. Finally, 600 ␮L of 0.1 M NaBH4 was added to the solutions under vigorous stirring at room temperature. Formation of the Au colloids turned the solution from yellow to purple while the presence of Ag colloids caused a color change from transparent to orange. A fulvic (AF:Hf) and a humic acid (AH:Hf) sample were extracted from a Galician soil (ombrotrophic peat bog, Sierra de Buio) in NW Spain following IHSS recommendations [41]. The elemental compositions of the samples were: FA (52.79% C, 0.65% N, 41.90% O and 4.66% H) and HA (57.73% C, 1.60% N, 36.55% O and 4.48% H), which are typical values for these types of substances [42]. Both samples have been extensively characterized by spectroscopy (UV–vis; Infrared; 13 C nuclear magnetic resonance) and potentiometry (pH; Cu, Pb and Cd ion selective electrodes) [43,44]. 3.2. Colloidal characterization SSCP experiments were performed using an Autolab PGSTAT 12 System (Eco Chemie) coupled to a Metrohm 663 VA Stand and a personal computer using the GPES 4.8 software (Eco Chemie). Electrodes included a static drop mercury electrode (working electrode), a saturated calomel electrode with a 0.1 M NaNO3 or KNO3 salt bridge (reference electrode) and a glassy carbon counter electrode. A Lauda E100 thermostatization unit was used to maintain the temperature at 25 ◦ C. An oxidizing current, Is , of 1 × 10−9 A (latex and humic experiments) or 0.75 × 10−9 A (gold and silver nanoparticles) was applied in quiescent solution until the potential reached a value sufficiently beyond the transition plateau (−0.40 V for Cd and −0.15 V for Pb). The Is values corresponded to conditions that approached complete depletion. SSCP waves were constructed from a series of measurements made over a range of deposition potentials, Ed . The potential was held at Ed for the duration of the deposition time, td , after which the oxidizing current was applied. The raw signal is a measurement of the variation of potential with time that is automatically converted to the dt/dE versus E format. Each SSCP experiment included a calibration plot for which the SSCP curve was measured at a given concentration (2.0–8.0 × 10−7 M) of lead or cadmium. Calibration was performed at low pH (<4) in order to avoid losses to the container

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walls. The sample was then added directly to the calibration solution, together with a pH buffer (MES or MOPS). The pH was adjusted using NaOH or HNO3 and the SSCP data were acquired. Each experiment was performed at three or four different pH values or at constant pH with several ligand concentrations. Experiments were performed between pH 6 and 8 using MOPS (Cd) and between pH 4.5 and 6.5 using MES (Pb). The concentration of latex varied between 0.01 and 0.4% (w/w). Nanoparticle experiments were performed using dilutions from the stock solution 2:100 and 4:100 for Au-PVP and 1:100 and 3:100 for Ag-11-MUA. Humic substances experiments were performed at 5 mg L−1 . Experiments using the nanoparticles were performed at an ionic strength of 0.01 M while experiments with the HS were performed at ionic strengths of 0.01 and 0.1 M using Cd(II) at pH 5.5, 6.0 and 6.5. Dynamic light scattering measurements were performed using an ALV apparatus with an Ar ion laser (514 nm). All scattering data were acquired at 90◦ . Intensity fluctuations from a single run were analysed automatically on a ALV-2000 digital correlator. Transmission electron microscopy (TEM) was performed on a JEOL 100 CXII microscope operating at 100 kV. Surface average particle diameters were obtained after digitization and image analysis using the SAISAM and TAMIS software (Microvision Instruments). Diffusion coefficients of the humic substances were acquired using fluorescence correlation spectroscopy (FCS) [45–47]. Experiments were carried out using a Confocor instrument (Zeiss) that employed an Ar ion laser. In the absence of chemical reactions or other dynamic processes, temporal fluctuations in the measured fluorescence intensity in the confocal volume can be attributed to the translational diffusion of the fluorophore [48]. Diffusion coefficients, D, are calculated from measured diffusion times following calibration with rho¯ Organics), which has a known damine 6G (R6G from ACROS diffusion coefficient of 2.8 × 10−10 m2 s−1 [49]. For each data point, fluorescence intensity fluctuations were measured over 2 min. Values are presented as the mean and standard deviation for 15 replicates. NaNO3 (Merck, suprapur) was used to adjust the ionic strength of the samples and NaOH (Riedel–de Ha¨en) and HNO3 (Merck, suprapur) to adjust the pH. Humic substances were examined at 10 mg L−1 for two different ionic strengths (0.01 and 0.1 M), each at five different pH values (4.5, 5.0, 5.5, 6.0 and 6.5). Where necessary, for comparative purposes, particle radii were calculated from diffusion coefficients using the Stokes–Einstein equation for hard spheres.

4. 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 ¯ and K . Eq. (4) can be re-written in labile systems depend on D

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Table 1 Computed K values necessary to obtain a contribution of 10 or 50% of the complexed metal to the total metal reduced at the electrode during the deposition step for different particle sizes Particle radius, a (nm)

DML (10−12 m2 s−1 )

DML /DM

K (50%)

K (10%)

1 3 10 30 100

223 74.4 22.3 7.44 2.23

0.319 0.106 0.032 0.011 0.003

3.1 9.4 31.0 94.0 313

0.3 1.0 3.5 10.3 34.5

A diffusion coefficient of 7.0 × 10−10 m2 s−1 was used for Cd2+ (DM ) [54].

as function of K :  ¯ = DM (1 + (DML /DM )K ) D 1 + K

(12)

which has two important limits, i.e. for DML = DM or K  1, ¯ = DM and for (DML /DM )K  1, D ¯ = DML . Although it D might intuitively appear that the ideal situation for the deter¯ = DML , a very high K would mination of DML would be for D be necessary under these conditions, almost certainly resulting in a non-labile system. In addition, this lower limit is of little interest to this work since it corresponds to the presence of a small ligand. Therefore, the most accurate measurements of the diffusion coefficient will be obtained when a significant part of the metal that is reduced at the electrode during the deposition ∗ is of the same order of step is in its complexed form, i.e. DM cM ∗  magnitude asDML cML or (DML /DM )K ≈ 1. For example, K values that are required to have either a 10 or 50% contribution of particulate bound Cd(II) to the reduction during the deposition step can be calculated using Eq. (12) (Table 1). As expected, K values that were necessary to maintain a given proportion of reduced bound to free metal increased linearly with the particle radius. This calculation suggests that the sensitivity of the technique to determine DML will be better for smaller particles due to the possible loss of lability at higher K . SSCP was used to determine average diffusion coefficients of the labile metal complexes with the latex nanospheres (Fig. 2, Table 2). Errors are given for a 95% confidence level based upon a Student distribution [50]. For the latex particles with radii of 15, 35 and 65 nm, diffusion coefficients of (1.5 ± 0.2) × 10−11 m2 s−1 , (7.0 ± 0.2) × 10−12 m2 s−1 and (3.8 ± 0.2) × 10−12 m2 s−1 were obtained, in good agreement with their reported radii and with results obtained from dynamic light scattering [33]. No aggregation was observed by DLS, neither in the stock solution, nor in measurements obtained in

Fig. 2. Calculated vs. measured particle radii (nm). The SSCP calculated values are averages of several measurements obtained from the interaction of Pb(II) and Cd(II) with latex nanoparticles, using different pH values (pH 5.4–7.6) and latex concentrations (0.01–0.4% w/w) at ionic strength 0.01 M. The errors bars correspond to a 95% error based upon a Student’s distribution.

the media used for the voltammetric experiments. In general, there was good agreement between the reported and calculated particle radii, with relative errors situated between 2.8 and 13%. Nonetheless, for the 129 nm latex particle, it was quite difficult to perform the experiment due to the high K values required and the small signal obtained for these systems due to their very low DML . Based upon these results, it would appear that the upper limit for the determination of particle sizes (diffusion coefficients) using SSCP is about 100 nm. Some caution is required in interpreting the errors reported in Table 2 since they are obtained for different numbers of measurements under different experimental conditions, i.e. different K values. Larger values of K gave rise to smaller errors on the individual measurements (Eq. (12); Fig. 3). For example, while the 95% error for 16 measurements made on the 35 nm particle was ±1.2 nm (Fig. 3),

Table 2 Diffusion coefficients calculated using SSCP from the interaction of Pb(II) and Cd(II) with latex nanoparticles Particle radius, a (nm)

Number of measurements

DML (10−12 m2 s−1 )

95% std. error on DML (10−12 m2 s−1 )

SSCP particle radius, a (nm)

95% std error on a (nm)

Relative error (%)

15.0 35.0 40.5 60.5 65.0 129

6 16 8 10 4 4

15.3 6.76 5.84 3.62 3.60 1.74

1.8 0.13 0.22 0.11 0.44 0.02

14.2 33.2 38.3 61.9 62.2 128.7

1.1 1.2 1.4 2.1 8.2 3.7

8.0 3.6 3.8 3.4 13 2.8

The values are an average of results obtained using different latex concentrations (0.01 up to 0.4% (w/w)) and different pH values, ionic strength = 0.01M.

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Table 3 Particle sizes, diffusion coefficients and K values calculated using SSCP and TEM for Ag-11-MUA and Au-PVP Particle

TEM (nm)

SSCP DML (10−11 m2 s−1 )

Ag-11-MUA

6.2 ± 0.5

8.30 8.11

Au-PVP

13.4 ± 2.5

2.13 1.84

Fig. 3. Calculated particle radius, a (nm), as a function of the stability constant, K , for the 35 nm latex nanoparticles. The SSCP values correspond to several measurements obtained for the interaction of Pb(II) and Cd(II) with the 35 nm latex nanoparticles using different latex concentrations (0.01 up to 0.3% w/w) and pH values at an ionic strength of 0.01 M. The errors bars correspond to the ±1 mV error of the potential shift in SSCP.

deviations as large as ±5 nm were observed for individual measurements. For an accurate size determination, measurements should be replicated and performed at sufficiently high K values. While the latex particles are an interesting model system, it is very difficult to study small diameters due to aggregation and a significant polydispersity. For example, the 15 nm particles aggregated at ionic strengths >0.01 M or pH < 5.0. For the nanoparticle size range, a hybrid functional material [51] was synthesized. Preliminary results obtained for a silver particle

SSCP interval range (nm)

SSCP K

5.4 5.5

3.1–19 4.4–7.3

0.36 1.07

10.5 12.1

– 7.9–28

1.24 2.70

SSCP particle radius, a (nm)

covered with 11-MUA (Ag-11-MUA) and a gold particle covered with PVP (Au-PVP) gave reasonable agreement between the SSCP and TEM measurements (Fig. 4, Table 3). Nonetheless, results obtained several days later for the Ag nanoparticles gave a similar value of K but a lower diffusion coefficient, indicating that the sample did not suffer a chemical modification but had begun to aggregate. Since the first results for the Ag-11MUA particles were obtained within 1 week of synthesis while the second measurements were performed a week later, these particles are likely not sufficiently stable to maintain in solution for more than a week. For the Au nanoparticles, there was good reproducibility for first measurements made on different days but not among consecutive replicas on the same day. In the latter case, the value of Ed,1/2 shifted to more negative potentials while the limiting transition time increased and the shape of the SSCP wave became distorted, approaching a shape indicative of an irreversible reduction [52]. These results indicate that the suspension may have been chemically modified, likely due to desorption of PVP from the particle surface and its subsequent adsorption at the surface of the mercury electrode. Adsorption, leading to fouling, would be consistent with the observation of electrode irreversibility. The presence of PVP in solution would cause a higher transition time due to the higher diffusion coefficient of the polymer. While these examples clearly demonstrate the potential of the SSCP technique, they also indicate some of its limitations (best for small particles, some chemical and electrochemical knowledge of system required, etc.). The technique was also tested on two soil humic substances for which no prior size characterization was available. Good agreement was obtained for DML values measured

Fig. 4. TEM micrographs of (a) Au-PVP and (b) Ag-11-MUA colloids.

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Fig. 5. Diffusion coefficient as function of pH determined for the humic acid by SSCP () and FCS () at ionic strengths (a) 0.01 M (b) 0.1 M.

by SSCP and FCS, although SSCP results had larger associated errors (Figs. 5 and 6). DML values ranged from 2.30 to 2.83 × 10−10 m2 s−1 , corresponding to hydrodynamic diameters of 1.5–1.8 nm, in good agreement with previous FCS [12,14] and AFM [15] results where reported hydrodynamic diameters ranged between 1.5 and 2.5 nm for the Suwannee River HA and FA. Agreement between the sizes of soil and aquatic humic substances has been observed previously and is generally attributed to the normalizing effects of the purification procedure. While larger errors were associated with the SSCP measurements as compared to FCS, the error was nonetheless estimated differently. In SSCP, each data point corresponded to a pH-ionic strength combination that was performed on different days. The error was computed by assuming an uncertainty of ±1 mV on the value of Ed,1/2 . In Figs. 5 and 6, the mean values were plotted with their standard deviations. For more measurements, the statistical error should become significantly smaller. A more serious problem arose from the fact that for some of the Cd-HS systems, some loss of lability was observed for relatively low K values. This loss of lability manifested itself at higher pH values such that only one of the results obtained at pH 6.5 could be used. Diffusion coefficients obtained by FCS are those obtained for the humic matter, DL , while those obtained by SSCP correspond to the complex species, DML . The similarity of the values that were obtained suggests that Cd binding did not produce a noticeable change diffusion coefficient of the humic matter,

Fig. 6. Diffusion coefficient as function of pH determined for the fulvic acid by SSCP () and FCS () at ionic strengths (a) 0.01M (b) 0.1M.

i.e. DML ≈ DL , in good agreement with previous results for Pbhumic complexes [52]. Diffusion coefficients obtained for the humic and fulvic materials were quite similar, in spite of a significantly higher charge density for the fulvic acid and a higher aromatic content of the humic acid. Interestingly, the diffusion coefficient increased with pH for the fulvic acid (Fig. 6). For the humic acid, DML values remained practically constant with pH at 0.01 M ionic strength but decreased slightly at 0.1 M ionic strength for pH values below pH 6.0. This slight decrease has been observed previously [14] where it was attributed to a slight association of the humic molecules due to a reduction of the intermolecular repulsion as the molecules were protonated (for pH values near and below the pKa of approx. 4) [53]. A decrease in D at higher pH values due to the deprotonation of the macromolecules and a higher intramolecular repulsion was not observed here, i.e. aggregation predominated over molecular compression. Nonetheless, it is likely that these humic substances are sufficiently reticulated and sufficiently small that size variations due to an increasing molecular charge (for pH > pKa ) would be too small to be detected by the FCS technique. 5. 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

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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 determined by TEM measurements. While, the SSCP signal could be used to evaluate the state of aggregation of the nanoparticles, a fairly detailed knowledge of the electrochemical behavior of the system was necessary for rigorous interpretation in more complex matrices. The diffusion coefficient of a humic acid and a fulvic acid were determined by SSCP at different pH and ionic strength. Diffusion coefficients ranged from 2.30 to 2.83 × 10−10 m2 s−1 , in good agreement with FCS measurements. Overall, the results demonstrate that SSCP is a useful technique to determine diffusion coefficients/particle sizes for particle radii between 1 and 100 nm. The technique is especially useful for simultaneous determinations of trace metal complexation and diffusion coefficients. 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, Fundac¸a˜ o para a Ciˆencia e Tecnologia, Portugal. This work was partially supported by the Swiss National Science Foundation and the Natural Sciences and Engineering Research Council of Canada. References [1] Y.P. Chin, G. Aiken, E. O’Loughlin, Environ. Sci. Technol. 28 (1994) 1853. [2] I. Perminova, F.H. Frimmel, A.V. Kudryavtsev, N.A. Kulikova, G. AbbtBraun, S. Hesse, V.S. Petrosyan, Environ. Sci. Technol. 37 (2003) 2477. [3] J. Buffle, D. Perret, M. Newman, The use of filtration and ultrafiltration for size fractionation of aquatic particles, colloids and macromolecules, in: J. Buffle, H.P. van Leeuwen (Eds.), Characterization of Environmental Particles, vol. 2, IUPAC Environmental Analytical Chemistry Series, vol. 1, Lewis, 1993. [4] M.J. Avena, A.W.P. Vermeer, L.K. Koopal, Colloid Surf. A: Phys. Eng. Aspects 151 (1999) 213. [5] P.K. Cornel, R.S. Summers, P.V. Roberts, J. Colloid Int. Sci. 110 (1986) 149. [6] P. Schurtenberger, M. Newman, in: J. Buffle, H.P. van Leeuwen (Eds.), Characterization of Biological and Environmental Particles Using Static and Dynamic Light Scattering, vol. 2, Lewis, 1993 (chapter 2 in Environmental Particles). [7] J.P. Pinheiro, A.M. Mota, J.M.R. d’Oliveira, J.M.G. Martinho, Anal. Chim. Acta 329 (1996) 15. [8] R. Osterberg, I. Lindqvist, K. Mortensen, Soil Sci. Soc. Am. J. 57 (1993) 283. [9] G.R. Aiken, R.L. Malcolm, Geochim. Cosmochim. Acta 51 (1987) 2177. [10] R. Beckett, Z. Jue, J.C. Giddings, Environ. Sci. Technol. 21 (1987) 289. [11] M. Benedetti, J.F. Ranville, M. Ponthieu, J.P. Pinheiro, Org. Geochem. 33 (2002) 269. [12] J.R. Lead, K.J. Wilkinson, E. Balnois, C. Larive, B. Cutak, S. Assemi, R. Beckett, Environ. Sci. Technol. 34 (2000) 3508.

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