Accumulation Mechanism for Metal Chalcogenide Nanoparticles at

Jan 10, 2008 - A multistep mechanism is proposed on the basis of accumulation experiments with polydisperse copper sulfide (CuxS) nanoparticles. Parti...
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Anal. Chem. 2008, 80, 742-749

Accumulation Mechanism for Metal Chalcogenide Nanoparticles at Hg0 Electrodes: Copper Sulfide Example Damir Krznaric´,† George R. Helz,*,‡ Elvira Bura-Nakic´,† and Darija Jurasˇin§

Center for Marine and Environmental Research, Institute Ru[er Bosˇ kovic´ , Bijenicˇ ka 54, 10000 Zagreb, Croatia, Department of Chemistry and Biochemistry and Department of Geology, University of Maryland, College Park, Maryland 20742, and Department of Physical Chemistry, Institute Ru[er Bosˇ kovic´ , Bijenicˇ ka 54, 10000 Zagreb, Croatia

Mercury electrodes preconcentrate metal chalcogenide nanoparticles effectively, enabling their detection at submicromolar concentrations (as ∑chalcogenide) by adsorptive cathodic stripping voltammetry. Understanding the unique behavior of nanoparticle analytes during preconcentration is critical for lowering detection limits and for quantification. A multistep mechanism is proposed on the basis of accumulation experiments with polydisperse copper sulfide (CuxS) nanoparticles. Particles first diffuse and adsorb at the Hg0 surface. When both the electrode and particles have negative surface potentials, this process resembles charge-impeded coagulation, obeying the Schulze-Hardy rule at various electrolyte strengths. Consequently, accumulation rates are surprisingly sensitive to electrolyte concentration. Choosing accumulation potentials where the electrode and particles have opposite surface potentials greatly improves collection efficiency, especially for the smallest particles. After adsorption, particles undergo transformations. One product is a more stable (harder to reduce) form of CuxS, interpreted to consist of adclusters or adlayers. A very significant (∼0.3 V) negative shift in reduction potential results from this transformation. Loss of analyte to at least one nonelectroactive product is also observed. Loss is greatest for the smallest particles and is sensitive to choice of accumulation potential. To improve accumulation efficiency, accumulation potentials more positive that the potential of zero charge of Hg electrodes are advantageous but care must be taken to remove dissolved chalcogenides under these conditions in order to avoid artifacts. Nanoparticulate chalcogenides (MenXm, Me ) metal and X ) S, Se, or Te) have promising applications as fluorescent tags in biology and medicine,1 and they are interesting photocatalysts.2 * Corresponding author. E-mail: [email protected]. † Center for Marine and Environmental Research, Institute Ru[er Bos ˇ kovic´. ‡ University of Maryland. § Department of Physical Chemistry, Institute Ru[er Bos ˇ kovic´. (1) Parak, W. J.; Gerion, D.; Pellegrino, T.; Zanchet, D.; Micheel, C.; Williams, S. C.; Boudreau, R.; Le Gros, M. A.; Larabell, C. A.; Alivisatos, A. P. Nanotechnology 2003, 14, R15-R27. (2) Zhang, X. V.; Ellery, S. P.; Friend, C. M.; Holland, H. D.; Michel, F. M.; Schoonen, M. A. A.; Martin, S. T. J. Photochem. Photobiol., A 2007, 185, 301-311.

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The most useful optical properties are obtained when the particles are monodisperse and in the quantum size range (so-called quantum dots). However, these materials are displaying unexpected biological properties. They are capable of penetrating cells, of passing to different organs in living mice, and of persisting there for considerable periods.3 They also exhibit toxic behavior which is not yet fully understood.4-7 These findings have raised questions about whether synthetic chalcogenide nanoparticles could become hazardous in the environment as nanotechnology is more widely commercialized.6,8,9 Surprisingly, growing evidence suggests that chalcogenide (specifically, sulfide) nanoparticles of natural origin already exist in some aquatic environments, even in the presence of dissolved oxygen.10-18 These nanoparticles’ production mechanisms, lifetimes, and biological effects, if any, are unknown. They might play an important role as mediators of trace metal nutrition and toxicity in aquatic ecosystems.19 The elegant fluorescence-based analytical methods, which are so useful for detecting synthetic, monodisperse quantum dots, are likely to be troublesome or impractical for studying chalcogenide (3) Ballou, B.; Lagerholm, B. C.; Ernst, L. A.; Bruchez, M. P.; Waggoner, A. S. Bioconjugate Chem. 2004, 15, 79-86. (4) Derfus, A. M.; Chan, W. C. W.; Bhatia, S. N. Nano Lett. 2004, 4, 11-18. (5) Lovic´, J.; Cho, S. J.; Winnik, F. M.; Maysinger, D. Chem. Biol. 2005, 12, 1227-1234. (6) Hardman, R. Environ. Health Perspect. 2006, 114, 165-172. (7) Cho, S. J.; Maysinger, D.; Jain, M.; Ro ¨der, B.; Hackbarth, S.; Winnik, F. M. Langmuir 2007, 23, 1974-1980. (8) Oberdo ¨rster, G.; Oberdo¨rster, E.; Oberdo¨rster, J. Environ. Health Perspect. 2005, 113, 823-839. (9) Robichaud, C. O.; Tanzil, D.; Weilenmann, U.; Wiesner, M. R. Environ. Sci. Technol. 2005, 39, 8985-8994. (10) Rozan, T. F.; Benoit, G. Geochim. Cosmochim. Acta 1999, 63, 3311-3319. (11) Rozan, T. F.; Luther, G. W.; Ridge, D.; Robinson, S. Environ. Sci. Technol. 2003, 37, 3845-3852. (12) Moreau, J. W.; Webb, R. I.; Banfield, J. F. Am. Mineral. 2004, 89, 950960. (13) Sukola, K.; Wang, F.; Tessier, A. Anal. Chim. Acta 2004, 528, 183-195. (14) Slowey, A. J.; Johnson, S. B.; Rytuba, J. J.; Brown, G. E. Environ. Sci. Technol. 2005, 39, 7869-7874. (15) Hsu-Kim, H.; Sedlak, D. Environ. Sci. Technol. 2005, 39, 4035-4041. (16) Ciglenecˇki, I.; Krznaric´, D.; Helz, G. R. Environ. Sci. Technol. 2005, 39, 7492-7498. (17) Tsang, J. J.; Rozan, T. F.; Hsu-Kim, H.; Mullaugh, K. M.; Luther, G. W. Environ. Sci. Technol. 2006, 40, 5388-5394. (18) Bura-Nakic´, E.; Krznaric´, D.; Jurasˇin, D.; Helz, G. R.; Ciglenecˇki, I. Anal. Chim. Acta 2007, 594, 44-51. (19) Mann, R. M.; Ernste, M. J.; Bell, R. A.; Kramer, J. R.; Wood, C. M. Environ. Toxicol. Chem. 2004, 23, 1204-1210. 10.1021/ac071180z CCC: $40.75

© 2008 American Chemical Society Published on Web 01/10/2008

nanoparticles in natural waters. The latter can be expected to be diverse in both size and composition (and therefore also in optical properties). Further, they come dispersed in a matrix which is rich in naturally fluorescent organic materials.20 Systematic studies of chalcogenide nanoparticles in natural waters therefore await development of new analytical methods. Considerable previous research has been devoted to the electrochemistry of nanoparticulate chalcogenides.21-24 Most of this research concerns catalytic or photocatalytic processes. In these studies, nanoparticles, themselves, were not subject to voltammetric characterization and quantification, which are the goals of our current research. Previously, we have shown that nanoparticles composed of several different sulfides (CuS, PbS, HgS) readily sorb and concentrate at mercury surfaces.16,18,25 Subsequently, their integrated mass can be quantified in cathodic scans that reduce them to amalgams plus free HS-. Not much is known about the mechanism of accumulation, which is the key step in the determination of nanoparticles at trace concentrations. Using polydisperse copper sulfide nanoparticles as the example, we investigate the mechanism here. We will show that polydispersity is a significant aspect of the analytical problem. METHODS Stock solutions were prepared from Milli-Q water and reagent grade chemicals: Na2EDTA‚2H2O, CuSO4‚2H2O, and Na2S‚9H2O, the latter dissolved in N2-deaerated 0.2 mM NaOH. A supporting electrolyte consisting of 0.1 M NaClO4 and 0.03 M NaHCO3 (pH 8.5-9.0) was used except where stated otherwise. Under the conditions of these experiments, NaClO4 is redox-inert. Copper sulfide nanoparticles were prepared by well-established methods involving precipitation of Cu2+ or CuEDTA2- with bisulfide.26-32 When Cu2+ and HS- are mixed, a brown sol is observed immediately. If a strong (i.e., slowly disassociating) chelate, like CuEDTA2-, is mixed with HS-, the brown color appears slowly, over a period of minutes. The previously reported transformation of the brown sol to a green sol having spectral characteristics of CuS (covellite) is slow under the conditions of our experiments (no O2, mildly alkaline pH)30,33 and was not observed. The exact composition of the precipitates is not known and might vary with experimental conditions, so the product will (20) Del Vecchio, R.; Blough, N. V. Environ. Sci. Technol. 2004, 38, 38853891. (21) Texter, J. In Electrochemistry in Colloids and Dispersions; Mackay, R. A., Texter, J., Eds.; VCH Publishers: New York, 1992; pp 3-21. (22) Scholz, F.; Meyer, B. Electroanal. Chem. 1998, 20, 1-86. (23) Heyrovsky´, M.; Jirkovsky´, J. Langmuir 1995, 11, 4288-4292. (24) Bard, A. J.; Ding, Z.; Myung, N. Struct. Bonding 2005, 118, 1-57. (25) Krznaric´, D.; Helz, G. R.; Ciglenecˇki, I. J. Electroanal. Chem. 2006, 590, 207-214. (26) Chiu, G. J. Colloid Interface Sci. 1977, 62, 193-194. (27) Horzempa, L. M.; Helz, G. R. Geochim. Cosmochim. Acta 1979, 43, 16451650. (28) Helz, G. R.; Horzempa, L. M. Water Res. 1983, 17, 167-172. (29) Shea, D.; Helz, G. R. J. Colloid Interface Sci. 1987, 116, 373-383. (30) Silvester, E. J.; Greiser, F.; Sexton, B. A.; Healy, T. W. Langmuir 1991, 7, 2917-2922. (31) Sugimoto, T.; Chen, S.; Muramatsu, A. Colloids Surf., A 1998, 135, 207226. (32) Privman, V.; Goia, D. V.; Park, J.; Matijevic´, E. J. Colloid Interface Sci. 1999, 213, 36-45. (33) Pattrick, R. A. D.; Mosselmans, J. F. W.; Charnock, J. M.; England, K. E. R.; Helz, G. R.; Garner, C. D.; Vaughan, D. J. Geochim. Cosmochim. Acta 1997, 61, 2023-2036.

be described below with the generic formula, CuxS. Published data suggest that x ) 1.0-1.4 typically.34 All Cu-HS mixtures employed in our work, including those starting with CuEDTA2-, were supersaturated by orders of magnitude with respect to known crystalline and amorphous copper sulfide phases. Therefore, the stoichiometrically limiting reagent in any mixture ought to be precipitated quantitatively. However, inhibited precipitation allows CuEDTA2- and HS- to persist together.28,29 In this situation, electrode-mediated precipitation of CuxS adlayers can occur, leading to a potential artifact that may be of concern in natural water analyses.25 Dissolved Cu in natural waters is strongly bound to organic ligands that are not well-characterized,35 and in this work EDTA is used as a model for them. Apparent hydrodynamic diameters, d, of nanoparticles were determined by dynamic light scattering using a photon correlation spectrometer (Zetasizer Nano ZS, Malvern) equipped with a 532 nm laser; measurements were made at a 173° scattering angle. The intensity correlation function was analyzed using CONTIN,36 and the number-average particle size was estimated using the Einstein-Stokes equation, assuming spherical shape. Transmission electron microscopy (JEOL, JEM-2100; run at 200 kV) was used to cross-check particle sizes obtained by dynamic light scattering. Samples for electron microscopy were prepared by pipetting a 10 µL drop of sol onto a carbon film; after a ∼1 min of exposure, excess solution and salts were wicked away by touching a piece of filter paper to the drop. Samples for both light scattering and electron microscope tests were prepared under anaerobic conditions but were unavoidably exposed to air during their introduction into the measuring instruments. Electrochemical measurements were made with a µ-Autolab (Electrochemical Instruments Eco Chemie) voltammetric analyzer connected to a 663 Stand Metrohm mercury electrode. An Ag/ AgCl (3 M KCl) reference electrode and a platinum auxiliary electrode were used. The electrode surface area (5.4 × 10-3 cm2) was measured by detaching 10-20 Hg drops, weighing them, and calculating the area per drop by assuming spherical shape. Solutions were continuously deaerated with O2-free nitrogen. Continuous stirring was employed during accumulation of nanoparticles at the electrode surface. RESULTS Characteristics of the Experimental System. Figure 1 gives particle size information for precipitates. Solution 1 (ionic strength controlled by 0.03 M NaHCO3 buffer) contains particles that are 5-10 nm in mean diameter according to dynamic light scattering and do not grow appreciably during an hour. In good agreement with these results, diameters of ∼80 particles that were measured in electron micrographs were 6.5 ( 2.5 nm (mean ( standard deviation). On the other hand, on the basis of the highly variable dynamic light scattering data, particles in solutions 2 and 3 (ionic strength controlled by 0.1 M NaClO4 plus 0.03 M NaHCO3) appear to undergo significant growth during an hour. Presence or absence of EDTA has no particle size effect that is discernible outside the (34) Shea, D.; Helz, G. R. Geochim. Cosmochim. Acta 1989, 53, 229-236. (35) Xue, H.; Sigg, L. In Environmental Electrochemistry: Analysis of Trace Element Biogeochemistry; Rozan, T. F., Taillefert, M., Eds.; American Chemical Society: Washington, DC, 2002; Vol. 811, pp 326-370. (36) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 229-242.

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Figure 1. Left panel: mean hydrodynamic particle diameters ((standard deviation) from dynamic light scattering as a function of aging time, which was measured from when 3 × 10-4 M HS- was introduced into deaerated solutions containing 1 × 10-4 M Cu2+ and 0.03 M NaHCO3. The upper two curves are for higher ionic strength solutions (see key). The solution represented by solid triangles contained 1 × 10-3 M HEDTA3-, whereas the other two solutions contained no HEDTA3-. Right panels: transmission electron micrographs; both are at the same scale.

range of variability in the dynamic light scattering data. In these high ionic strength solutions, electron micrographs reveal a number of flocs having diameters in the 30-50 nm range. Therefore, particle growth is most likely due to electrolyte-induced floc formation. At higher magnification than shown in Figure 1, lattice fringes were observed in some of the larger grains in the flocs. This implies that flocs contain at least some crystalline material. Whether the 0 causes suppression of both A2 and C2. One reason is that CuxS adlayers compete for space with HgS adlayers on the electrode. Another reason is that HgS can be consumed by any residual Cu0 according to25

HgS(s) + xCu0 T CuxS + Hg0

(3)

The copper sulfide produced by reaction 3 is not readily distinguished from that contributed by nanoparticles. In order to quantify CuxS nanoparticles using C3, we previously recommended (38) Krznaric´, D.; Ciglenecˇki-Jusˇic´, I. Electroanalysis 2005, 17, 1317-1324.

Figure 3. Effect of accumulation time on (A) C3 peak charge and (B) C3 peak potential. All solutions contain 1 × 10-4 M CuSO4, 3 × 10-4 M Na2S, 0.03 M NaHCO3. Additionally, solution 1 (9) contains 0 M EDTA, 0 M NaClO4; solution 2 (0) contains 0 M EDTA, 0.1 M NaClO4; solution 3 (b) contains 1 × 10-3 M EDTA, 0.1 M NaClO4; solution 4 (O) contains 1 × 10-3 M EDTA, 0.1 M NaClO4. For all measurements, ED ) -0.9 V and v ) 0.1 V s-1. Although C3 peaks for solution 1 are very small (upper panel), they are not zero and their potentials (lower panel) are well-defined in the voltammograms.

that accumulation potentials should be kept on the negative side of C2, thus preventing reaction 3 by depriving the electrode of HgS. Effect of Analytical Variables on the C3 Peak. Figure 3 shows that increasing tD affects the C3 peak’s cumulative charge, Q(C3), and potential in an unexpected, nonlinear way. The different solutions represented in the figure contain different concentrations of EDTA and NaClO4 but identical concentrations of copper and sulfide. These compositions are the same as those for which particle diameters are given in Figure 1, but practical limitations prevented us from performing both voltammetric and particle sizing experiments on the same samples. At low ionic strength (i.e., no NaClO4; particle diameters -0.55 (positive electrode surface charge), Q(C3) is immensely larger at the lowest electrolyte concentrations but slightly suppressed at the highest electrolyte concentration. (We attribute the suppression to gradual sorption of particles on the Teflon stir bar and container walls while the points in Figure 6 were being collected; for each curve, data collection began at -0.7 V and continued in +0.05 V steps toward more positive potentials.) DISCUSSION Mechanism of CuS Accumulation. We find that Q(C3) behaves in unusual ways; for example, it exhibits nonlinear variation with tD, a strong dependence on the kind and concentration of electrolyte, and a marked accumulation potential dependence that differs in direction and magnitude at different electrolyte concentrations. Figure 7 depicts a proposed accumulation mechanism that can explain some of these features. The first step in this mechanism is simply Brownian diffusion of particles through the hydrodynamically stagnant layer surrounding the electrode in the stirred solution. The rate of this

Figure 7. Schematic of proposed CuxS accumulation mechanism. The sequence at the top shows particles diffusing to, and becoming sorbed by, the Hg0 surface, then either reordering to adlayers (upper path) or being reduced to Cu amalgam before the cathodic scan (lower path). The lower left diagram shows that, with increasing tD, adsorbed particles reach a steady state; further analyte accumulation involves secondary adlayer growth. The lower right diagram shows the resulting concentration of particles as a fraction of total analyte. These schematics illustrate how observed patterns, including plateaus, in Figure 3 would arise, assuming (a) that the electrode measures the sum of analyte in both adsorbed particles and adlayers and (b) that adsorbed particles have a reduction potential of about -0.95 V, whereas adlayers, which are more stable, have a reduction potential of about -1.25 V.

process should depend critically on whether the chosen accumulation potential is above or below the electrode’s potential of zero charge. At accumulation potentials more negative than -0.55 V, where both the electrode and the particles have negative surface potentials, particles must penetrate an electrostatic potential energy barrier to reach the electrode. Under these circumstances, accumulation of nanoparticles is analogous to coagulation of hydrophobic colloids. Figure 4A shows that the effects of CaCl2 versus NaCl electrolytes on accumulation seem to obey the Schulze-Hardy rule. As interpreted within the framework of Dejagrien-Landau-Verwey-Overbeek (DLVO) theory,40 the Schulze-Hardy rule predicts that electrolyte concentrations necessary to induce rapid colloid coagulation are proportional to Z-6, where Z is the counterion charge (i.e., cation charge in the case of sulfide minerals with negative surface potentials). The relative concentrations of Na+ and Ca2+ at the maxima in Figure 4A are reasonably consistent with this prediction. Furthermore, the concentrations of Na+ and Ca2+ necessary for rapid coagulation of CuS nanoparticles27 correspond reasonably well to maxima in Figure 4A. Declines in Q beyond the maxima can be explained by hydrodynamic shear-promoted sorption of particles onto the stirring apparatus. Figure 1 demonstrates that higher electrolyte concentrations promote growth of nanoparticles in solution, as would be expected for colloids undergoing coagulation. Nonetheless, Figure 4B implies that electrolyte concentration also affects accumulation (40) Overbeek, J. T. G. In Colloid Science; Kruyt, H. R., Ed.; Elsevier Publishing Co.: Amsterdam, 1952; pp 302-341.

independently of particle growth in solution. The latter figure shows that the analyte accumulation rate remains roughly constant during short time intervals when electrolyte concentration is constant, even though aging processes, including coagulation, would be progressing. Furthermore, increasing the electrolyte concentration immediately increases the accumulation rate with no detectable lag for aging processes. When ED is more positive than the electrode’s potential of zero charge, the electrostatic interaction between the electrode and particles is attractive. (This assumes that surface potentials of particles do not undergo sign changes near the electrode as a result of electron tunneling.) For particles and an electrode having opposite surface charges, the accumulation rate will be limited by diffusion of particles to the point where their double layers begin to intersect the electrode’s double layer; there electrostatic attraction will take effect. By suppressing double layer thicknesses, increasing counterion concentrations would be expected to reduce the capture cross section of particles and to diminish accumulation rates. Thus whether increasing counterion concentration enhances or suppresses accumulation should depend on the electrode’s surface charge. The expected inversion in the effect of counterion concentration near the electrode’s zero point of charge in fact is observed in Figure 6, although additional processes, discussed below, are also involved. Striking features of the Q versus tD curves in Figure 3A are their plateaus at intermediate accumulation times. Plateau heights are well below reported values for CuxS monolayers (210 µC cm-2)41 and vary with experimental conditions. As shown by the following calculation, the plateaus cannot be explained by particle crowding on the surface. The integrated charge, Qp, required to reduce a single spherical particle is

Qp )

4 × 106πnF(1 - p)r3 3Vm

(in µC)

(4)

where n ) 2 according to reaction 2 stoichiometry, F is the Faraday constant, p is the particle’s porosity (fraction of open space), r is the particle radius (cm), and Vm is the volume of solids per mole of sulfur. Because most of the volume of crystals is occupied by anions, Vm for CuxS phases is not very sensitive to x and can be taken as 24 ( 3 cm3. The number of particles per square centimeter of electrode surface that must be reduced to explain an observed plateau value of Q(C3) is given by Q(C3)/ Qp, and the footprints of these particles per square centimeter of electrode surface are obtained by multiplying this number by πr2. From these relationships, a plateau of 100 µC cm-2 (Figure 3) can be explained if the electrode surface is only 3% covered with 3 nm radius nonporous particles or only 0.5% covered with 20 nm radius nonporous particles. High porosity (e.g., 50%) would only double these percentages. Average distances between particle centers would be far larger than double layer thicknesses (reciprocals of the Debye parameter, κ, are less than 2 nm at the electrolyte concentrations used in this study.) Therefore, electrostatic repulsion between particles would be completely screened and could not explain the wide particle separations. (41) Basa, A.; Krogulec, T.; Baranski, A. S. J. Electroanal. Chem. 1999, 463, 200-211.

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Rather than invoking particle crowding to explain the plateaus in Figure 3A, we propose that the plateaus mark attainment of a steady state in which the rate of loss of adsorbed CuxS particles on the electrode becomes equal to the rate of arrival of new particles from the solution. Loss of adsorbed particles probably does not involve simply the reverse of the adsorption process (i.e., achievement of adsorption equilibrium). Reversible adsorption is generally regarded as unlikely when colloidal particles are in direct contact with an adsorbing surface (i.e., trapped in the primary potential energy minimum of DLVO theory40). For particles to be detected electrochemically they would need to be in direct contact with the electrode; reducing particles that are not in direct contact implausibly would require metallic Cu0 transport to the electrode through an aqueous phase. Instead, we suggest that two other processes contribute to loss of adsorbed particles, setting up a steady state in adsorbed particle concentration on the surface. These processes compete, and their relative importance is size-dependent. One process involves transformation of adsorbed particles into another electroactive form of analyte, probably a CuxS adlayer. A lag may occur in this process before adlayers nucleate. The evidence for appearance of a second electroactive form of analyte is the negative shift in the C3 peak potential with increasing tD (Figure 3B). This shift indicates that a relatively easily reduced form of analyte (e.g., adsorbed particles) declines in importance compared to a less easily reduced form (e.g., adlayers) as total analyte accumulates. The negative shift in reduction potential implies that adlayers are thermodynamically more stable (harder to reduce) than adsorbed particles. The free energy to drive this process could come in part from reduction in the surface energy inherent in nanoparticles. Additional contributions could come from favorable chemical interactions between CuxS adlayers and underlying Hg0 as well as from amorphous f crystalline transitions as adlayers become thicker. The lower diagrams in Figure 7 illustrate schematically how this mechanism can reproduce the observed patterns in Figure 3. The second competing process involves loss of electroactive analyte from the electrode. In plots of Q(C3) versus tD (Figure 3A), key evidence for loss is the very marked difference in the initial slope at tD < 10 s compared to the ultimate slope at tD > 60 s (illustrated schematically in Figure 7). This discrepancy in accumulation rate implies that a loss mechanism becomes active as the concentration of adsorbed particles grows. The simplest explanation for why some analyte reaching the electrode surface is lost is that a certain particle fraction becomes prereduced by reaction 2 while accumulation is taking place. This fraction is then not included when Q(C3) is measured during the subsequent cathodic scan. Generally, the smallest particles, owing to their high specific surface, would have the least negative free energy per mole and, therefore, would be most likely to be lost in this manner. Consistent with this, Figure 3A shows that small particles, those formed in electrolyte lacking 0.1 M NaClO4, are very inefficiently accumulated at Ed ) -0.9. Furthermore, Figure 6 shows that making ED less negative, and therefore less effective at reducing CuxS, produces the greatest Q(C3) enhancement in the lowest ionic strength solution, which contains the smallest particles. 748 Analytical Chemistry, Vol. 80, No. 3, February 1, 2008

Figure 8. Particle diameter effect on reduction potential for a nanoparticulate analyte consisting of spheres with a surface energy of 0.5 J/m2. The solid curve shows the magnitude of the positive reduction potential shift as a function of particle diameter. Dashed curves are hypothetical size distributions for two populations of particles. Aging can transform the left population into the right one, which is more stable and thus less susceptible to prereduction to Cu amalgam before the cathodic scan. As a result, aging can increase the recovery of CuxS analyte.

Surface energies of copper sulfide precipitates have not been measured, to our knowledge, but values near 0.5 J/m2 are reasonable based on other sulfides.12,42,43 This surface energy would contribute substantially to the total free energy of CuxS nanoparticles and should make smaller particles much easier to reduce. The solid curve in Figure 8 shows a hypothetical reduction potential shift relative to that of bulk analyte assuming that particle stability affects reduction potential according to ∆G ) nF∆E. This figure illustrates why analyte loss by prereduction is expected to be greatest for the smallest particles. As shown in Figure 8, if an accumulation potential was set at +50 mV relative to the bulk analyte’s C3 reduction potential, most of the particles represented by left-hand size spectrum (5 nm mean diameter) would be reduced and lost during the accumulation process. This corresponds to solution 1 in Figure 3. On the other hand most of the aged particles represented by the right-hand size distribution (20 nm mean diameter; e.g., solutions 2 and 3) would accumulate without loss to reduction. Elsewhere,18,25 we have shown examples where recovery of nanoparticulate analyte increases with aging time, most probably due to growth of small, inefficiently detected particles into larger, more efficiently detected particles. Analytical Implications. Previously,25 we concluded that the best accumulation potential for determining CuxS nanoparticles would lie between C2 and C3. In this range, production of CuxS adlayers by reaction 3 was blocked because no HgS could accumulate. Thus, all analyte accumulated would come only from nanoparticles. The present work reveals a problem with this strategy. Figure 8 implies that the C3 potential is size-dependent, (42) Barton, P. B. In Fluid-Mineral Equilibria in Hydrothermal Systems; Henley, R. W., Truesdell, A. H., Barton, P. B., Eds.; Reviews in Economic Geology, Vol. 1; Society of Economic Geologists: El Paso, TX, 1984; pp 191-201. (43) Daskalakis, K. D.; Helz, G. R. Environ. Sci. Technol. 1992, 26, 2462-2467.

and for the smallest nanoparticles in a polydisperse sol, there may be no useable interval betweenC2 and C3. Additionally, accumulation efficiency is much poorer on the negative side of C2 than on the positive side (Figure 6). The present work suggests that accumulation potentials on the positive side of C2 would be better. To prevent the analytical artifact from reaction 3, it would be necessary in this situation to remove dissolved sulfide prior to the accumulation step. Gas stripping is a reasonably effective strategy for accomplishing this. For most sulfide nanoparticles, removing sulfide would prompt them to dissolve, but CuxS and HgS nanoparticles are sufficiently insoluble that dissolution is quite slow.10 Although our work here has been restricted to CuxS, it is reasonable to assume that this study could be expanded to develop useful analytical procedures for additional metal chalcogenides,

and we have already taken steps in that direction.18 The attractiveness of voltammetry in this area is rooted in the strong affinity between Hg0 and all chalcogenides, making the Hg electrode a promising tool for preconcentrating as well as quantifying metal chalcogenide nanoparticles. ACKNOWLEDGMENT The authors thank the Ministry of Science and Technology (Croatia), the National Science Foundation (United States; EAR 0229387), and the Fulbright Scholar Program for the financial support that made this work possible. Received for review June 4, 2007. Accepted November 3, 2007. AC071180Z

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