Dissolution Kinetics and Solubility of ZnO Nanoparticles Followed by

Article pubs.acs.org/JPCC

Dissolution Kinetics and Solubility of ZnO Nanoparticles Followed by AGNES Calin A. David,† Josep Galceran,*,† Carlos Rey-Castro,† Jaume Puy,† Encarnació Companys,† José Salvador,† Josep Monné,† Rachel Wallace,‡ and Alex Vakourov‡ †

Departament de Química, Universitat de Lleida, Rovira Roure 191, 25198 Lleida, Catalonia, Spain Centre for Molecular Nanoscience (CMNS), School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom

‡

S Supporting Information *

ABSTRACT: There is a current debate on whether the toxicity of engineered ZnO nanoparticles (NPs) can be traced back to their nanoscale properties or rather to the simple fact of their relatively high solubility and consequent release of Zn2+ ions. In this work, the emerging electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping), which is specially designed to determine free metal ion concentration, is shown to be able to measure the Zn2+ concentration resulting from dissolution of ZnO nanoparticles dispersed in aqueous salt solutions. Three NP samples from different sources (having average primary particle diameters of 6, 20, and 71 nm) were tested and compared with bulk ZnO material. The enhanced solubility of the nanoparticles with decreasing primary radius allows for an estimation of the surface energy of 0.32 J/m2. AGNES also allows the study of the kinetics of Zn2+ release as a response to a change in the solution parameters (e.g., pH, ZnO concentration). A physicochemical model has been developed to account for the observed kinetic behavior. With this model, only one kinetic parameter is required to describe the time dependence of the free Zn2+ concentration in solution. Good agreement with this prediction is obtained when, starting from an equilibrated NP dispersion, the pH of the medium is lowered. Also, the independence of this parameter from pH, as expected from the model, is obtained at least in the pH range 7−9. When dissolution is studied by dispersing ZnO nanoparticles in the medium, the kinetic parameter initially decreases with time. This decrease can be interpreted as resulting from the increase of the radius of the clusters due to the agglomeration/ aggregation phenomena (independently confirmed). For the larger assayed NPs (i.e., 20 and 71 nm), a sufficiently large pH increase leads to a metastable solubility state, suggesting formation of a hydroxide interfacial layer.

1. INTRODUCTION Increased use of engineered nanoparticles has given rise to heightening concern for their biological activity. Nanoparticles (NPs) in aqueous dispersion have dimensions in between those of micrometer-sized particles and molecular-sized dissolved compounds.1 Their thermodynamics, transport, mechanical, and chemical properties are dependent on their small dimension and their large surface area that generates a considerable surface activity.2 As a result, the nanoparticles become highly active, even if they are made of inert material. In addition, the biological impact of nanoparticles depends on their size and structure in the solution environment as well as on their functionality, since a small cluster of metal atoms can have a different chemical potential than the bulk solid and be more easily dissolved.3 In fact, some nanoparticles can dissolve and release species which may itself be toxic. This, coupled with the putative ability of nanoparticles to cross cell membranes and enter cells (because of their small size3), will imply the presence of toxic species in the cell interior. Taking into account the full complexity of a nanoparticle’s toxicity, an initial step in a study of their biological activity will involve an investigation into the factors controlling the dissolution of specific nanoparticles. A known biologically active nanoparticle © 2012 American Chemical Society

species which dissolves in aqueous media is ZnO, and it remains equivocal whether the toxicity of ZnO stems from the particle or from the dissolved Zn2+. Deriving from the biological concern, an important consideration in nanotechnology is the impact of manufactured nanoparticles on the environment, which has further promoted the study of their characteristics and behavior.3−6 Dissolution of the NP in water has been pointed out as an important physicochemical property to be taken into account7,8 to assess the environmental impact. Similar to their behavior in biological media, ZnO NPs can dissolve in aqueous environments significantly, so that some studies attribute the toxicity mainly to the dissolved Zn2+,9−11 others to the nanoscale properties of ZnO,12,13 and still others to a combination of both factors (with a different weight).14−22 The dissolution process of nanoparticulate ZnO has been tackled in several studies.9−11,15,17,18,20−26 A particularly important thermodynamic question is the equilibrium concentration of Zn2+, while the main kinetic question addresses the Received: February 20, 2012 Revised: April 14, 2012 Published: April 26, 2012 11758

dx.doi.org/10.1021/jp301671b | J. Phys. Chem. C 2012, 116, 11758−11767

The Journal of Physical Chemistry C

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proved to be negligible in all samples. TEM images provided information about the size and morphology of the primary particles. The Sigma-Aldrich NPs showed a somewhat wide size distribution, and a range of various morphologies was present, including spherical, faceted, and elongated particles. The IoLiTec sample, on the contrary, showed a narrow size distribution with the majority of particles having a spherical morphology and a small proportion of elongated particles. The in-house-prepared sample displayed a very narrow size distribution, and all particles imaged were of a spherical morphology. Solid ZnO (Fluka) was also used to prepare solutions of the bulk material. All ZnO samples were kept in a desiccator to prevent humidity and CO2 adsorption. Concentrated stock suspensions of the nanoparticle powders used previously boiled Milli-Q water without any additive or background electrolyte and were sonicated for 30 min (Branson 3210, 100 W) to yield 1−4 g/L ZnO concentrations. Preparation and conservation of stock solutions was carried out under nitrogen atmosphere to avoid CO2 fixation. Solubility experiments (both equilibrium and kinetic measurements) were carried out by adding a suitable aliquot of this concentrated NP stock to a voltammetric cell containing the previously deoxygenated and buffered test medium under N2 atmosphere. The final particle concentration in the experiments was 50−100 mg ZnO/L, depending on pH. The test media were prepared with KCl or KNO3 (Fluka) and Tris (tris(hydroxymethyl)aminomethane) (Merck) or MOPS (3-(N-morpholino)propanesulfonic acid) (Sigma-Aldrich) pH buffers. Previous experiments discarded a possible influence of the buffer on the values of [Zn2+] measured. The total ionic strength was 0.1 M, with a buffer concentration of 0.02M. HCl (Merck) and KOH (Fluka) were used to adjust the pH, which was kept constant to different values within the range 7−9. To obtain a homogeneous dispersion in each experiment, the ZnO-NP stock dispersion was sonicated for 10 min just before addition to the buffer solution. Subsequent to the thermodynamic or kinetic experiment, the diluted ZnO nanoparticle solutions were standardized (i.e., via determination of total zinc) applying AGNES after acidification of the solution. 2.2. AGNES. AGNES has been applied for determination of the free concentration of Zn2+ in ZnO dispersions. AGNES is an electroanalytical technique consisting of two stages.30 In the first stage, a deposition potential E1 is applied for a long enough time (t1) to reduce metal into the mercury (Hg) until Nernstian equilibrium conditions. This E1 prescribes a preconcentration factor or gain Y = Y1 between [Zn0] in the amalgam and [Zn2+] in the solution. At the end of this first stage, a situation of no concentration gradient at either side of the electrode surface is attained. In the second stage, a reoxidation potential E2 under diffusion-limited conditions (associated to a gain Y2) is applied to quantify the metal accumulated in the amalgam. The free metal ion concentration in solution can be obtained from the faradaic current I, which results from subtraction of a suitable blank to the measured current at a fixed time t2, using

speed of the dissolution process. On the other hand, gaining this knowledge is not straightforward, due to the concomitance of other phenomena, such as aggregation or sedimentation.5,16,27,28 Measurement of ZnO NP solubility in previous work has usually relied on the separation of the solution phase from the NP via dialysis, filtration, or centrifugation.10,11,13,15−23,25,26 An analogous approach has been taken investigating the dissolution of CuO NP.29 However, the separation procedures could be inaccurate, as small nanoparticles might still remain in solution, when the total Zn analysis is performed in the supernatant of filtrate. Moreover, the total Zn analysis does not allow determination of the individual contributions of the different soluble species (e.g., complexes with buffer species) to the overall solubility. On the other hand, the slow crossing of metal ions through membranes can yield underestimations of the equilibrium Zn2+ value in the dialysis experiments. In any case, all methods involving solid− liquid separation procedures are relatively time consuming, which hinders the good time resolution needed for kinetic experiments. All these difficulties are easily avoided with the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping).30 This technique is specifically sensitive to the concentration of Zn2+ species (thus allowing discernment between free ions and the rest of soluble metal species), it can be applied in situ, i.e., without the need for particle separation, and each measurement takes place in the time scale of a few minutes. AGNES has been successfully applied to determination of free Zn2+ in seawater,31 freshwater,32 humic acid solutions,33 wine,34 and other matrices. AGNES has also been used in sensing Cd2+ released from quantum dots.35 The lack of commercial ion-selective electrodes (ISEs) for Zn2+ renders AGNES especially useful for measurement of the free metal ion concentration of this element. Once the free Zn2+ concentration is known, the solubility can be easily computed (see section 3.2 below), because they are just related by a proportionality factor. The aim of this work is to apply AGNES to wellcharacterized dispersions of ZnO NPs of different sizes in aqueous media with moderate ionic strength (0.1 M) in order to extract thermodynamic and kinetic information from the dissolution processes. Particular attention is addressed here to analysis of the size-dependent effects on the equilibrium free Zn2+ concentration and the solubility of dispersions of NP and bulk material. After the study of the equilibrium data, we turn toward the kinetic process, proposing a simple model which is checked against data from various experimental designs.

2. MATERIALS AND METHODS 2.1. Materials. Three different ZnO NP samples were used. Two of them were obtained as dry powders purchased from commercial sources: Sigma-Aldrich (71 nm nominal average primary particle diameter) and IoLiTec, Ionic Liquid Technologies GmbH (20 nm nominal average primary particle diameter). The third sample was from an academic source and consisted of particles of 6 nm delivered as a 4% w/v dispersion in ethanol solution. This sample was synthesized by a wet chemical method from LiOH and Zn(Ac)2 in ethanol (code EN-Z-5 within ENNSATOX project). All three samples were characterized by transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), electron diffraction (SAED), and X-ray diffraction (XRD) (see Supporting Information). The hexagonal wurtzite phase (characteristic of zincite) was confirmed, and the presence of impurities was

[Zn 2 +] =

I Yη

(1)

The proportionality factor η can be obtained from a calibration. AGNES has been applied with an Eco Chemie Autolab PGSTAT12 potentiostat attached to a Metrohm 663VA stand. The working electrode was a Metrohm multimode mercury drop electrode (selected drop radius around r0 = 1.41 × 10−4 11759



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equilibrium conditions can be ensured. The resulting values of free Zn2+ concentrations in equilibrium with each NP sample and bulk material are shown in Figure 1. In this figure, the

m). The auxiliary electrode was a glassy carbon electrode, and the reference electrode was Ag/AgCl/3 mol L−1 KCl, encased in a jacket containing 0.1 mol L−1 KCl or KNO3. A blanket of previously water-saturated N2 flows continuously through the voltammetric cell of the stand to avoid O2 interferences. The flow of N2 was regulated and decreased in order to avoid evaporation in long-term experiments. Due to its large influence on ZnO solubility, the pH of the dispersion was continuously controlled during the experiments using a combination glass electrode (Orion 9103) inserted in the voltammetric cell and attached to a Thermo Orion 720A ion analyzer. The glass electrode was previously calibrated using commercial pH standards. A glass-jacketed cell thermostatted at 25.0 °C was used in all measurements. ZnO NP 71 nm dispersions induced adsorption phenomena that lead to a falling of the Hg drop (at pH > 8.8). These phenomena were avoided using lower total ZnO NP concentrations (50 mg/L) and occasional cleaning of the capillary. Application of AGNES requires selection of the appropriate parameters (gains and times).30,36 The potentials (E1 and E2) associated to the various gains were computed from the peak potentials of differential pulse polarograms using eq 10 of ref 30. For the Y1 applied all along this work (from 0.01 to 10), equilibrium could be reached in a deposition time t1 less than 100 s (the general rule of thumb is t1 = 7 × Y1) and Y2 = 10−8. In order to remove other contributions different from the faradaic one, we subtracted the “shifted” blank,31 which consists of applying (to the solution containing the metal) a potential program shifted to a range in which there is no analyte deposition. 2.3. Other Experimental Methods. The size distributions of ZnO nanoparticles and their aggregates in solution were measured as hydrodynamic diameters using dynamic light scattering (DLS) at 173° on a Zeta Sizer Nano ZS equipment (Malvern, Bedford, MA), which employs a He−Ne laser of 633 nm wavelength. In the absence of an adequate experimental setup to distinguish between agglomeration (a loose interaction) and aggregation (strong bonds),37 for the sake of simplicity, we will use the term “aggregation” to indicate whichever of them is in operation. The number-weighted particle size distributions were calculated from the DLS autocorrelation function according to the ISO13321 standard using Malvern software package. The results allowed us to check the dispersion stability and follow the increase in the average diameter of the aggregates with time. The characteristic UV−vis absorption spectra of the NP dispersions as well as the changes in solid ZnO concentration during the solubility experiments (see Supporting Information) were recorded using Perkin-Elmer Lambda XLS and Specord 210 (from AnalytikJena UK) spectrophotometers. Total Zn in the supernatant of centrifugation experiments was measured with inductively coupled plasma (ICP-OES) (Activa-S, Horiba Scientific) after acidification with HNO3. pH was measured with a pH meter Thermo Electron Orion, 720A+.

Figure 1. Equilibrium free Zn2+ concentration in buffered aqueous dispersions of ZnO NPs and bulk solid at 0.1 M ionic strength and different pH values as measured with AGNES (markers): (red diamonds) bulk ZnO; (blue circles) 71 nm NPs; (green squares) 20 nm NPs; (brown triangles) 6 nm NPs. Solid and empty markers correspond to experiments carried out in KCl and KNO3, respectively. Lines correspond to the linear regression of results from each ZnO sample to eq 3: continuous red line for bulk ZnO; dashed blue line for 71 nm NPs; dotted green line for 20 nm NPs; dashed−dotted brown line for 6 nm NPs.

markers represent values obtained from independent individual experiments at a fixed pH, the different colors correspond to the different ZnO materials, and the lines represent the average solubility equilibria for each material, computed as explained in the following paragraphs. The dissolution process of ZnO material K sp

ZnOs,zincite + H 2O HooI Zn 2 + + 2OH−

(2)

can be described with the solubility product Ksp, which depends on the size of the NPs (as will be shown below). The solubility product expression can be written as a linear dependence of the logarithm of the free concentration with pH ⎛ K sp ⎞ ⎛ [Zn 2 +] ⎞ ⎟ − 2pH log⎜ ⎟ = log⎜⎜ 2⎟ ⎝ M ⎠ ⎝ γZn 2+K w ⎠

(3)

where γZn2+ is the activity coefficient for Zn ions and Kw is the ionic product of water. This equation was used for a leastsquares regression analysis of the experimental log([Zn2+/M]) vs pH data shown in Figure 1 for each ZnO sample in order to statistically assess if the experimental solubility product reflects an influence of the primary particle size. The fitted values of Ksp are listed in Table 1, together with the corresponding statistical estimates of error. The retrieved bulk value log Ksp = −16.90 ± 0.07 is in agreement with the literature value log Ksp = −16.8 ± 0.2.38 As can be seen in Table 1 (and in Figure 1), the solubility of the 71 nm and 20 nm diameter nanoparticles are, within experimental error, hardly distinguishable from the solubility measured in dispersions of the bulk ZnO material. This has an interesting practical implication: for ZnO NPs with primary diameter larger than 20 nm, the theoretical concentration can 2+

3. THERMODYNAMIC SOLUBILITY 3.1. Equilibrium Free Zn2+ Concentration. The free Zn2+ concentration in dispersions of ZnO and different pH values was measured with AGNES as a function of the time elapsed since their preparation until a constant value is reached (which takes place in less than a few hours), so that the solubility 11760



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Literature specifically focused on the role of surface energy on the size-dependent solubility of ZnO is scarce to date. We must highlight, however, the very recent paper published by Grassian and co-workers26 during submission of the present work. These authors reported solubility values of very well characterized ZnO particles (from 4 to 130 nm in size) at pH 7.5 and room temperature, which allowed them to estimate a value of γ = 0.06 J/m2, somewhat lower than expected from the literature. The authors justified this result on the basis of the possible influence of particle aggregation, exposed crystal planes, or the presence of surface-adsorbed acetate groups. Unfortunately, direct comparison of their results with the data shown in the present work is not possible as neither the ionic strength of the experiments nor a precise control of the temperature (below ±1 °C) was reported. Both parameters have a great influence on the solubility especially when divalent cations are involved. Moreover, these authors used a centrifugal ultrafiltration separation method, combined with ICP-OES elemental analysis, which yields values of the overall Zn solubility in the filtrate, rather than specific measurement of the concentration of Zn2+ species in the sample. 3.2. Solubility of ZnO. Once the free metal concentration, under the given conditions, is known, the solubility (S) of the ZnO NPs can be computed via summation of the concentrations all dissolved species containing Zn(II), which can be estimated from the known stability constants (see eq 6) in our solutions. The conclusion is that for the assayed conditions (i.e., excess of ligand and constant pH) the solubility is just proportional to the free metal ion concentration

Table 1. Retrieved Values of Thermodynamic Solubility Parameters for Bulk and Nanoparticlulate ZnO at pH 8, Interpolated from Experimental Data (Figure 1) using Eq 3a NP size bulk 71 nm 20 nm 6 nm a

log(Ksp/(γZn2+K2w)) 11.53 11.62 11.67 12.09

± ± ± ±

0.07 0.1 0.06 0.07

log Ksp −16.90 −16.81 −16.76 −16.34

± ± ± ±

0.07 0.1 0.06 0.07

Activity coefficients were calculated using the Davies model.

be computed with a thermodynamic speciation code, such as VMINTEQ,39 using formation constants for the bulk phase from the literature.38 However, the solubility of the 6 nm particles is clearly above the bulk one. This result is consistent with Ostwald−Freundlich equation, which predicts a higher equilibrium free metal concentration for the smaller nanoparticles23,40,41

⎡ 2γV̅ ⎤ S = exp⎢ ⎥ ⎣ RTr ⎦ S0

(4)

where S is the solubility in the NP dispersion, S0 is the bulk solubility, γ is the surface energy, V̅ is the molar volume, R is the gas constant, T is the temperature, and r is the primary radius of the NP. Reported values of γ in the literature are uncertain42 (and perhaps not even constant for different morphologies of the same size26), although most of the estimates lie within the range between 0.1 and 0.5 J/m2.43,44 An estimation of γ can be gained from the presented data in this work by recasting eq 4 as ⎛ [Zn 2 +] ⎞ ⎛ [Zn 2 +] ⎞ 2γV̅ bulk ⎟ log⎜ log e + log⎜ ⎟= RTr M ⎝ M ⎠ ⎝ ⎠

S = [Zn 2 +] + [Zn(OH)2 ] + [ZnNO+3 ] + ...

{

}

cond cond − +[NO ] + ... = [Zn 2 +] 1 + KZn(OH) [OH−]2 + K ZnNO 3 2 3

(5)

(6)

Figure 2 plots the free Zn2+ concentrations of the different ZnO materials interpolated at pH 8 (using the data in Table 1) versus the inverse of the primary particle radius (the radius of the bulk material is taken as infinity). From the fitted slope, γ = 0.32 J/m2 can be estimated, which satisfactorily lies in the above-mentioned range of 0.1−0.5 J/m2.

where the superscript “cond” indicates the conditional nature of the stability constant. For low pH values, free Zn2+ represents the larger fraction of dissolved Zn(II), although as pH increases the contribution of the hydroxo complexes increases. For instance, at pH 8.0 in 0.1 M KCl medium and 25 °C, [Zn2+] = 4.53 × 10−5 M and S = 5.47 × 10−5 M (or 4.45 mg of ZnO per liter). The slope of the plot in Figure 1 and eq 3 indicates that one-half a unit of pH leads to a change of 1 order of magnitude in the free metal concentration and, consequently, in the solubility. These results are relevant for ecotoxicological experiments, as pH should be carefully controlled and the amounts of ZnO assayed should be clearly above the solubility at that pH to avoid the possibility of a full dissolution of the added ZnO NPs. In order to compare AGNES against alternative methods for determining ZnO solubility we centrifuged (30 min at 3783 g) a dispersion of 20 nm diameter ZnO NPs in KCl 0.1 M + Tris buffer at pH = 8.3 and analyzed the supernatant. ICP-OES measurements of the supernatant yielded a value of total soluble zinc (4.07 mg ZnO/L) that was five times as large as the value predicted by VMINTEQ. On the other hand, AGNES measurement in the same sample yielded a free metal concentration leading to a total soluble zinc of 0.91 mg ZnO/L, which is practically the speciation code prediction. This disagreement between centrifugation and AGNES measurements is probably due to the existence of small NPs remaining in the supernatant after centrifugation (which are below the detection limit of UV spectroscopy). Leakage of small NPs as well as small differences in the control of pH and/

Figure 2. Dependence of the equilibrium free Zn2+ concentration with the average size of the primary particles (bulk ZnO is assumed to have a very large particle size). Symbols: values interpolated with eq 3 at pH 8 from experimental data. Dashed line: linear regression to eq 5, from which the ZnO surface energy can be estimated. 11761



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or temperature, the impact of nonexcluded CO2, or the use of NPs smaller than 20 nm could, perhaps, explain the fact that some of the values reported in the literature are actually higher than those predicted by speciation codes or experimentally measured in solutions in equilibrium with bulk ZnO. For instance, Wong et al. 201021 reported a solubility of 3.7 mg/L for 20 nm ZnO NPs, in contrast with their 1.6 mg/L measured with bulk ZnO. Both values were obtained in artificial seawater at pH 8 after filtration through 0.1 μm filters and ICP analysis. Another example of the apparent increase of the solubility with the decrease in particle size has been reported by Bian et al. 2011,23 who found solubility values (measured in centrifuged samples by ICP analysis) of 57, 22, and 10 mg/L for ZnO particles with average sizes of 4, 15, and 241 nm at pH 7.5, respectively. However, the exact medium composition and ionic strength were not explicitly reported. On the other hand, our equilibrium results are in agreement with those of Franklin et al.,9 who used dialysis and 0.1 μm filtration followed by ICP analysis. These authors reported similar values of total dissolved zinc for 30 nm NPs and bulk ZnO in 0.01 M Ca(NO3)2 and PIPES buffer at pH 7.5 ± 0.15 and 24 °C. Mudunkotuwa et al.26 found lower solubilities than those reported here for the smaller NPs. We must insist on the importance of an extremely careful control (and reporting) of the experimental conditions (pH, temperature, medium composition, etc.) during solubility experiments as well as detailed specification of the procedures carried out. Only in this way a meaningful comparison among the increasingly large amount of experimental results reported in the literature can be carried out.

leading to the following variation in the number of moles (nZn) of ZnO in this aggregate dnZn = 4πr02k in[Zn 2 +]r0 − 4πr02kout[H+]2 dt

For one aggregate, in steady state

dnZn = −J 4πr02 dt

[Zn 2 +]r0 =

r0 D Zn2 +

(11)

r0

= 4πNr02kout[H+]2 − 4πNr02k in[Zn 2 +]r0

(12)

3

where N is the number of aggregates in 1 m c ZnO N= 4 ρ 3 πr03

(

)

(13)

and cZnO is the analytical ZnO concentration. The accuracy of N can be improved by subtracting the amount of dissolved Zn(II) to cZnO, although this correction should be negligible if pH is not too acidic. Simple algebra leads to the differential equation ⎛ D 2 +[Zn 2 +] ⎞ kout[H+]2 + Zn r ⎟ d[Zn 2 +] 2⎜ 0 + 2 = 4πNr0 ⎜kout[H ] − ⎟ D Zn2 + dt ⎜ ⎟ 1+ k r in 0 ⎝ ⎠ = a − b[Zn 2 +]

(14)

whose solution is a [Zn 2 +] = − ([Zn 2 +]t = 0 − [Zn 2 +]eq )e−bt b

(7)

= [Zn 2 +]eq − ([Zn 2 +]t = 0 − [Zn 2 +]eq )e−bt 2+

(15)

2+

where [Zn ]eq and [Zn ]t=0 are the (final) equilibrium and initial concentration, respectively ⎛ k k [H+]2 r0 ⎞ ⎟ a = 4πNr02⎜kout[H+]2 − in out k inr0 + DZn 2+ ⎠ ⎝

kout k in

k in +

D Zn2 +[Zn 2 +]

dn d[Zn 2 +] = −N Zn dt dt

where DZn2+ is the diffusion coefficient of Zn2+ ions (other dissolved species being neglected) and [Zn2+] and [Zn2+]r0 indicate the bulk and surface concentrations, respectively. See the schematic representation in Figure 3. On the other hand, we can assume simple kinetics for the reactions at the aggregate surface ZnOs + 2H+ HooI Zn 2 + + H 2O

kout[H+]2 +

Taking into account all the aggregates

([Zn 2 +]r0 − [Zn 2 +]) r0

(10)

Thus, from previous equations, we can isolate the concentration of free Zn2+ at the nanoparticle surface

4. KINETICS OF DISSOLUTION 4.1. Kinetic Model. The model assumes that all nanoparticles are aggregated in spherical clusters with a fixed radius r0 (which is obviously much larger than the primary radius r). The flux from one aggregate toward the dispersion (when diffusive steady state is reached) can be expressed as J = DZn 2+

(9)

(8)

(16)

and ⎛ k inDZn 2+ ⎞ 3c ZnO ⎛ k inDZn 2+ ⎞ b = 4πNr02⎜ ⎟= ⎜ ⎟ ρr0 ⎝ k inr0 + DZn 2+ ⎠ ⎝ k inr0 + DZn 2+ ⎠ (17)

From eq 15, which can be seen as a kind of Noyes−Whitney equation,25 the parameter b can be interpreted as a rate of approach toward equilibrium. The solution 15 can also be recast in logarithmic terms as ⎛ ⎞ [Zn 2 +] ⎟ ln⎜⎜1 − = c − bt [Zn 2 +]eq ⎟⎠ ⎝

Figure 3. Schematic representation of the reaction−diffusion model. Radius of the cluster (arising from the aggregation of NPs) is r0. 11762

(18)



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is not sufficiently indicative of the changes in dissolution rate that can be in operation. On the other hand, when the representation suggested by the model is applied to data of Figure 4, we obtain Figure 5, where

where ⎛ [Zn 2 +]t = 0 ⎞ ⎟ c = ln⎜⎜1 − [Zn 2 +]eq ⎟⎠ ⎝

(19)

Notice that c can be interpreted as the initial separation from the equilibrium. According to this simple kinetic model, the plot of ln(1 − [Zn2+]/[Zn2+]eq) vs time should give a straight line whose slope, b, is independent from pH (see eq 17) but dependent on the radius of the aggregate and the concentration of NPs. The model could be extended to include other dissolved Zn species by assuming that the dissociation kinetics of the soluble zinc complexes is much faster than the dissolution/precipitation of ZnO, so that equilibrium relationships (i.e., lability conditions for the complexes) can be applied. 4.2. Addition of ZnO NPs to a Buffer solution. For the relatively high free Zn2+ concentrations at the explored pH values, AGNES measurements can be performed in a few minutes, so that this technique can follow the kinetics of ZnO dissolution, which, as seen in Figure 4, is on the order of a

Figure 5. Plot of ln(1 − [Zn2+]/[Zn2+]eq) (which is a measure of the proximity to equilibrium) vs time for the experimental data shown in Figure 4 (where NP is added to a buffer). According to the kinetic model, the plot for each series should be a straight line with slope b (see eq18). Markers as in Figure 4.

the expected linearity of the processed data is only reached for relatively long times (see dashed lines). In order to quantitatively analyze these results, we computed a kind of “instantaneous” b from every two consecutive experimental points (see Figure 6) by determining the slope of the line that

Figure 4. Evolution of the free Zn2+ concentration (as measured with AGNES) vs time elapsed after addition of a stock solution of ZnO NPs to the buffer solution: (filled markers) 71 nm primary diameter NPs; (open markers) 20 nm primary diameter NPs. pH of the experiment is indicated close to each series. ZnO concentration in solution is 10−3 M. Buffer solutions were prepared at 0.1 M ionic strength using Tris 0.02 M and KCl.

couple of hours. In this respect, AGNES is more suitable than small pore dialysis9 in which Zn2+ ions might take hours just to cross the membrane and reach equilibrium between the internal and the external solutions. In the experiments shown in Figure 4, we see that the stabilization of the measured [Zn2+], after addition of ZnO NPs to a buffer, is already achieved at ca. 100 min, a time much shorter than in some reported experiments, i.e., on the order of 72 h,9 much larger than 3 h,15 more than 1 day,11 and more than 10 h in the case of ultrapure water.10 It can also be observed that the stabilized (equilibrium) values decrease with increasing pH as prescribed by the thermodynamic expectations of Figure 1 and eq 3. In our experiments, the nonequilibrium regime is shorter for the smaller NPs (see open markers), which is consistent with the expected faster dissolution23 for smaller NPs, although this concentration vs time representation

Figure 6. Evolution of the instantaneous b values with time of dissolution in the same experiments reported in Figure 4 using the same markers. These b values are obtained from two consecutive AGNES measurements by considering that the line connecting these points is eq18. Dashed horizontal line indicates the b value obtained in the pH jump represented by open blue diamonds in Figure 8 (see section 4.3).

joins both points. The accuracy of the instantaneous b values is quite low for longer times, because of the proximity of the measured free Zn2+ concentration to the equilibrium value. The general trend of the instantaneous b values in all series (different pH values and different primary size of NP) is the same: a kind of exponential decay toward an asymptotic value. These changes in b indicate, again, that the model is not fully 11763



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the NPs are not completely monodisperse (in terms of the primary size), there could be a selective disappearance of the smallest particles due to their faster dissolution and higher solubility according to eq 4. This effect is rather difficult to support with independent measurements, since DLS intensity signal is proportional to the sixth power of the particle diameter, and therefore, the intensity size distributions of the polydisperse samples do not probably yield accurate information on the fraction of small particles or aggregates. Alternatively, the exposed surface of the NPs can change due to sedimentation and/or adsorption onto the walls of the glass cell. 4.3. Decrease of pH Value. In order to uncouple the dissolution process from aggregation, a new series of experiments was designed in which the NPs were already forming stable aggregates when the dissolution process was triggered due to addition of HCl. More specifically, (i) an aliquot of concentrated NP stock solution (ZnO 4 or 1 g/L in Milli-Q water) was added to the medium (KCl + TRIS 0.02 M, ionic strength 0.1 M) and the initial pH was adjusted, (ii) the dispersion was left stirring for at least 2 h, so that the NP aggregates reached a stationary size, and (iii) a small volume of HCl 0.1 M was added to induce a sudden “jump” in the pH, while AGNES measurements were run repeatedly to follow the variation of [Zn2+] with time up to the equilibrium concentration at the new pH value. The representation of the obtained kinetic data (depicted in Figure 8) shows the linearity predicted by eq 18. Regression

operational in this kind of experiments. One source of discrepancy is the change in the radius r0, which has been independently observed in DLS measurements (see Figure 7).

Figure 7. Evolution of the number-weighted average diameter of ZnO clusters (71 nm primary particle size, cZnO = 10−3 M) in buffer solution (Tris 0.02 M + KCl at 0.1 M ionic strength and pH 8.3 with stirring) showing the aggregation process concomitant to dissolution. Dashed line corresponds to the linear regression for t > 25 min.

Before addition, the concentrated NP stock solution (in Milli-Q water) is sonicated for 10 min, yielding a number-weighted average diameter of ∼140 nm for the 71 nm NPs and ∼85 nm for the 20 nm NPs. These relatively large initial sizes of the aggregates (compared with the primary particles) are due to incomplete redispersion of the commercial ZnO powders during ultrasonication or to partial aggregation in the concentrated stock dispersions. After adding the aliquot of NP stock to the buffered background electrolyte solution, we observed (Figure 7) an increase in the number-weighted average diameter up to ∼900 nm (for both kinds of NP) within 25 min, which supports our interpretations, even if measurements with DLS cannot be taken as accurate for particles close to the micrometer range. Similar fast aggregation behavior has been reported in the literature for ZnO NPs dispersed in media of moderate to high ionic strength.22,28 This means that we have, at least, 2 concomitant processes in operation after addition of NP to the buffer: the aggregation and dissolution process. Thus, the observed decrease in b (in Figures 5 and 6) can be ascribed to an increase of the aggregate radius r0 (see eq 17). In fact, computation of an instantaneous b can be seen as neglecting the radius variation (due to aggregation) during the short interval in between two consecutive AGNES measurements. In this way, the steeper slope observed in Figure 5 at the beginning of the experiments in the 20 nm NP dispersions, compared with the 71 nm NPs (and the consequent shorter dissolution transient), could be justified by their initially smaller aggregate size. Moreover, the convergence of all instantaneous b values toward a common value is consistent with the fact that the finally achieved effective r0 of both NP dispersions is practically the same (around 900 nm, see Figure 7 for the 71 nm case). The observed independence of b values (see Figures 5 and 6) from pH (in the relatively short probed range) is also consistent with the model (see eq 17). In addition to aggregation (for which we have independent evidence), other phenomena could account for the lack of linearity at the early stages of the addition. For instance, since

Figure 8. Plot of ln(1 − [Zn2+]/[Zn2+]eq) (which is a measure of the proximity to equilibrium) vs time in experiments with a pH jump in buffer solutions of 0.02 M Tris and KCl at 0.1 M ionic strength. Initial and final pH values as well as the concentration of nanoparticles and their primary size are indicated close to each line.

lines corresponding to the same NP concentration yielded the same slope (compare green solid bullets with red open squares), regardless of their primary size. This is consistent with eq 17 and the observation of a common effective aggregate size (DLS diameter of 900 nm) for both kinds of nanoparticles. The effect of the NP concentration on the dissolution kinetics also seems to be consistent with the model. Compare the two experimental data series marked with red and blue symbols in Figure 8: a 2-fold increase in the concentration cNP (blue open diamonds) yields a 2-fold increase in the absolute value of the slope of the regression line. The value of this slope (0.023 min−1) has been added to Figure 6 as a dashed line, and it coincides with the asymptotic long-time value of the 11764



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Figure 9. Evolution of the free Zn2+ concentration in 71 nm NP dispersions (two replicates with different markers) vs time elapsed after a sudden increase in pH. Total concentration of ZnO cZnO = 5 × 10−4 M. Lower dashed line stands for the expected free Zn2+ concentration in equilibrium with solid ZnO (zincite). Upper dashed line stands for the computed free Zn2+ concentration in equilibrium with β-Zn(OH)2 when this is the only allowed solid phase.

5. DISTINGUISHING ENHANCED SOLUBILITY DUE TO A SMALL RADIUS FROM THE HYDROXIDE SOLUBILITY As the observed free metal concentration in equilibrium with the 6 nm NPs is practically equal to the value predicted for bulk β-Zn(OH)2, we carried out specific UV−vis and AGNES experiments to confirm that the observed Zn2+ concentration actually corresponds to the equilibrium with ZnO-NP and not with some β-Zn(OH)2 phase. When the pH of a 20 nm NP dispersion is decreased from 8.8 to 7.7, there is a substantial decrease in the UV absorption around λ = 361 nm (see Figure SI-17, Supporting Information), indicating dissolution (and loss) of solid ZnO from the NPs. However, when the pH of the same dispersion is raised back from 7.7 to 9.3, the absorbance practically does not change, indicating that the newly deposited (or crystallyzed) material (which we ascribe to β-Zn(OH)2 due to the agreement between the experimental [Zn2+] and the theoretical solubility of β-Zn(OH)2) does not absorb in this UV region. When the pH of a 6 nm NP dispersion is decreased from 8.7 to 7.5 (see Figure SI-18, Supporting Information), there is again a substantial decrease of absorbance but it is essentially recovered (in around 2 h) when the pH is raised back to the starting value. We conclude that the recovered material is ZnO (because of the absorbance increase) and not β-Zn(OH)2, which barely absorbs in the region 340−360 nm. This recovery of the ZnO mass in the 6 nm NP dispersion is likely to involve the enlarging of the remaining particles, as this fact is also consistent with (a) a shift in the maximum of the spectrum to longer wavelengths (see Figure SI-20, Supporting Information), indicating a larger radius of the NP,47,48 and (b) a slight decrease in the solubility (see Figure SI-19, Supporting Information) with respect to the initial solubility of the 6 nm NP dispersion.

concentrations measured with AGNES, at certain time intervals, after addition of a small amount of 0.1 M KOH to a NP dispersion previously stabilized with respect to aggregation. The measured concentration decreases with time, but instead of tending toward the expected saturation value of zincite−ZnO (as in previous experiments) we observe a higher free Zn2+ concentration that remains constant for several days, which is compatible with the value predicted by VMINTEQ for saturated solutions of solid β-Zn(OH)2. These results suggest that perhaps an increase in pH could induce formation of a metastable layer of hydroxide around the ZnO NPs.23,45 When the pH increase is too small to reach the β-hydroxide formation (i.e., the [Zn2+] in equilibrium with zincite at the initial pH is below the [Zn2+] in equilibrium with β-hydroxide at the final pH), the system tends toward formation of zincite at an extraordinarily slow pace (of the order of days). The possibility of coexistence of solid Zn(OH)2 and ZnO phases in aqueous media in early stages of precipitation (and slow conversion from the less to the more stable phase) has been recently suggested by Wei and coauthors46 based on kinetic arguments. We must point out, however, that these hysteresis effects in the solubility were not observed in the case of the 6 nm NPs (see the following section). We conclude that pH increases could lead to erroneous (higher) solubility determinations, if the oversaturated concentration is taken as the concentration in true equilibrium with ZnO NPs.

6. CONCLUSIONS This work represents the first application of the electroanalytical technique AGNES to direct measurement of the Zn2+ concentration in aqueous dispersions of ZnO NPs. It also explores the influence of the primary particle size on the equilibrium and kinetic solubility results. For NPs with primary particle diameter above 20 nm, we obtained essentially the same solubility values as those for the bulk ZnO material (see Figure 1). On the other hand, in the samples of 6 nm primary particle we found a higher solubility, as predicted by the Ostwald−Freundlich expression (eq 4). From the variation in solubility with primary radius (see eq 5 and Figure 2) we estimated the surface energy of ZnO. Our kinetic studies have revealed that there is a nonequilibrium regime in the dissolution process, which could be on the order of 1 h (see Figure 4), so that freshly prepared ZnO dispersions can exhibit a free Zn2+ concentration far from equilibrium. The diffusion−reaction model presented in section 4.1 is a rough interpretative tool for experiments under wellcontrolled conditions (pH, aggregation, stirring, etc.). The main parameter of the kinetic model is the parameter b, the slope of a logarithmic representation of the proximity to equilibrium versus time (see eq 18 and Figures 5 and 8). This parameter can be interpreted as the rate of approach to the equilibrium and does not depend on pH or primary particle size but on the radius of the aggregates and the NP concentration (see eq 17).

instantaneous b values of experiments with NP added to the buffer. The dependence of b with the total concentration of NP, commented above, is observed only under extremely wellcontrolled conditions. If there is an important quantity of NP sedimented or adsorbed to the walls, the effective area of dissolution decreases and the direct proportionality between cNP and b is not found. 4.4. Increase of pH Value: Metastable State. Another set of pH-jump experiments explored an increase in the pH value, instead of a decrease. Figure 9 shows the free Zn2+

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Higher free Zn2+ concentrations than those thermodynamically expected can also correspond to metastable layers formed around ZnO NP when there is an increase in the pH of the dispersion (see Figure 9). The results of this work and from the literature highlight the large sensitivity of the solubility measurements to the particular experimental conditions (pH, temperature, medium composition, sample history, etc.) as well as to the procedures carried out prior to elemental analysis. Compared with separation methods (centrifugation, filtration, etc.), AGNES presents some advantages in the study of the thermodynamic and kinetic aspects of the dissolution of ZnO NP because it provides a method for in situ, direct, and robust measurements of the free Zn2+ concentration in a relatively short time and without manipulation of the sample.

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ASSOCIATED CONTENT

S Supporting Information *

(1) Characterization data on the three NP samples, obtained by TEM, EDX, SAED, XRD, and DLS; (2) combined UV−vis spectroscopy/AGNES study of dissolution/precipitation reversibility in ZnO NPs. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research leading to these results received funding from the European Union Seventh Framework Programme (FP7/20072013) under grant agreement no. 229244 (ENNSATOX), from the Spanish Ministry of Education and Innovation (Projects CTQ2009-07831 and CTM2009-14612), and from the “Comissionat per a Universitats i Recerca del Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya”. We thank L. Andrew Nelson for insightful discussions and guidance.

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