Article pubs.acs.org/est
The Dissolution Rates of SiO2 Nanoparticles As a Function of Particle Size Tamara Diedrich,†,* Agnieszka Dybowska,‡ Jacques Schott,† Eugenia Valsami-Jones,‡,§ and Eric H. Oelkers† †
GET-Université de Toulouse-CNRS-IRD-OMP, 14 Avenue Edouard Belin, 31400 Toulouse, France. Department of Mineralogy, Natural History Museum, Cromwell Road, London, SW7 5BD, United Kingdom
‡
ABSTRACT: There is a critical need to better define the relationship among particle size, surface area, and dissolution rate for nanoscale materials to determine their role in the environment, their toxicity, and their technological utility. Although some previous studies concluded that nanoparticles dissolve faster than their bulk analogs, contradictory evidence suggests that nanoparticles dissolve more slowly. Furthermore, insufficient characterization of the nanoparticulate samples and the solution chemistry in past studies obscures the relationship between particle size, surface area, and dissolution rate. Here we report amorphous SiO2 dissolution rates in aqueous solutions determined from complementary mixed-flow and closed reactor experiments at 6.9 ≥ pH ≥ 11.2 and 25 °C as a function of particle diameter from 25 to 177 nm. Experiments were performed at far-fromequilibrium conditions to isolate kinetic effects from those of changing the reaction driving force on overall dissolution rates. Measured far-fromequilibrium mass normalized dissolution rates are nearly independent of particle size, but corresponding BET surface area normalized rates decrease substantially with decreasing particle size. Combining these observations with existing established kinetic rate equations allows the prediction of nanoparticle dissolution rates as a function of both particle size and aqueous fluid saturation state.
1. INTRODUCTION The effect of nanoparticles on the environment and human health is strongly related to their dissolution rate behavior in aqueous fluids.1−9 Dissolution rates can be influenced by the chemical saturation state of the fluid with respect to the dissolving particles,10−12 degree of aggregation,13−15 surface area,16 particle shape,13 particle size,17−19 the density of defects and kink sites,18 ordering of the hydration layer at the surface,19 and differences in crystalline structure.20 The large number of factors influencing these rates has made it challenging to (1) determine the individual contribution of each, and (2) to generate a general equation describing dissolution rates as a function of particle size. This study is designed to overcome this challenge by measuring as a function of particle diameter, the dissolution rates of spherical amorphous SiO2 nanoparticles in aqueous solutions at far-from-equilibrium conditions. All experiments are performed at pH substantially above the zero point of charge to avoid aggregation. The purpose of this paper © 2012 American Chemical Society
is to report the results of this study and use them to improve our understanding of nanoparticle dissolution rates. This study focuses on the dissolution behavior of amorphous SiO2 nanoparticles. Amorphous silica nanoparticles are common in natural environments.21 These particles have received growing attention to their potential toxicity.22−25 Dissolution rates of solids are a function of both the distance from equilibrium (providing the driving force for dissolution) and the forward dissolution rate (reflecting the dissolution mechanism and the strength of bonds critical to maintain the structure). This concept is consistent with10−12 r = r+(1 − exp(−Δr G /σRT )) Received: Revised: Accepted: Published: 4909
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December 15, 2011 March 21, 2012 April 6, 2012 April 6, 2012 dx.doi.org/10.1021/es2045053 | Environ. Sci. Technol. 2012, 46, 4909−4915
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where r refers to the overall dissolution rate, r+ denotes the forward or far-from-equilibrium dissolution rate, R stands for the gas constant, T designates temperature in Kelvin, σ represents Temkin’s average stoichiometric number equal to the ratio of the rate of destruction of the activated or precursor complex relative to the overall rate (equal to 1 for amorphous SiO2), and ΔrG corresponds to the Gibbs free energy for the dissolution reaction (a measure of the distance from equilibrium and the chemical driving force for the reaction). As ΔrG for the reaction decreases, dissolution slows, stopping when ΔrG equals zero. At far-from-equilibrium conditions, rates are independent of the chemical driving force and are only a function of r+, the forward dissolution rate. For single metal oxides like SiO2, the forward dissolution rate is constant in constant pH aqueous solutions such that r+ = k+, a rate constant.10 Decreasing particle size enhances solubility by increasing the surface free energy of the particle. For spherical particles this effect can be described using a modified Kelvin equation:11 ⎡ 4γV̅ ⎤ s = exp⎢ ⎥ ⎣ RTd ⎦ s0
(2)
where s0 and s designate the solubility of a particle of infinite diameter and of diameter d, respectively, γ refers to the surface free energy, and V̅ stands for the solid phase molecular volume. Following eq 2, the solubility of fine particles increases at the nanoscale. An increase in particle solubility increases the driving force of the dissolution reaction at constant reactive fluid composition by increasing ΔrG. An increase in particle solubility can, therefore, lead to increased dissolution rates at near-to-equilibrium conditions as it increases ΔrG term in eq 1. In contrast, an increase in ΔrG will negligibly affect dissolution rates at far-from-equilibrium conditions. This study has been designed to identify the effects of particle diameter on forward dissolution rates independent from the effects of chemical driving force through the measurements of amorphous SiO2 nanoparticle dissolution rates in aqueous solutions at 6.9 ≥ pH ≥ 11.2 and 25 °C at far-from-equilibrium conditions (exp(−ΔrG/σRT) ≤ 0.05).
Figure 1. TEM images of the four amorphous SiO2 samples considered in this study. Samples before (left) and after (right) dissolution at a pH of 7 for approximately 24 h. The mean particle diameter, as determined by measuring 100 particles on TEM images, is shown in yellow, with the standard deviation given within parentheses.
nologies dynamic light scattering instrument, giving a close representation of condition during the dissolution experiment. Fifty individual measurements were made to form the distribution. Zeta potential measurements were performed using a Malvern Instruments Zetasizer Nano series dynamic light scattering instrument. The measurements were made in aqueous 0.01 m NaCl solutions by adding reagent grade NaOH and HCl to vary pH. Zeta potentials were obtained from measured electrophoretic mobilities using the Smoluchowski equation.27 The uncertainties in reported zeta potentials range from 5 to 20%, being highest near the isoelectric point. As dissolution is a surface mediated reaction, rates are often normalized to surface area.28 Defining surface areas is nontrivial in any case and for nanoparticles in particular. Dissolution rates are routinely normalized to the BET surface area, an expression of surface area based on the Brunauer−Emmett−Teller method29 where the surface area is determined by gas absorption. This process requires first drying the sample, which could alter the surface properties and cause agglomeration. BET surface areas were measured using a Micrometrics Gemini surface area analyzer linked to a FlowPrep 060 degasser by nitrogen adsorption using five adsorption points with P/P0 of 0.05−0.3. Samples were degassed overnight at 100 °C for at least 12 h prior to analysis. Uncertainties associated with resulting surface areas are ±7%. This uncertainty represents
2. MATERIAL AND METHODS Nanoparticle Synthesis and Characterization. Four samples of amorphous SiO2 were synthesized using the Stöber et al.26 method. Consistent with this method, reagent-grade ethanol, deionized H2O, and reagent-grade ammonia were mixed at room temperature. Tetraethyl (ortho)silicate (TEOS) was added drop by drop, and resulting solutions were stirred by magnetic stir bar at 500 rpm for at least 48 h. Powder X-ray diffraction confirmed that the samples were amorphous. Subsamples of particles before and after dissolution were diluted, in ethanol and in the reactive solution, respectively, and mounted on 300 mesh Cu grids with carbon film from Agar Scientific. Images of these particles were collected on a Hitachi H-7100 transmission electron microscope with an accelerating voltage of 100 kV. Images of the resulting synthetic amorphous silica nanoparticles are shown in Figure 1. Particle size for all samples was determined by measuring the diameter of 100 particles on digital images. Particle diameters are listed in Figure 1 and range from 25 to 177 nm. The hydrodynamic diameter of particles was measured immediately after dissolution in the same reactive fluid as during the dissolution experiment using a Cordouan Tech4910
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95% confidence limits of regular machine calibrations made using Quantachrome Instruments alumina standards. Alternatively, dissolution rates can be normalized to geometric surface area, determined by calculating surface area from particle size and shape.30 BET and geometric surface areas can differ by orders of magnitude depending on the surface roughness and internal porosity of the sample.31 Dissolution Experiments. Dissolution rate experiments were performed in both open-system mixed-flow reactors and closed-system reactors. Open-system dissolution experiments were performed in 250 mL Azalon beakers, following the method described by Kohler et al.32 The samples were contained in Cellu-Sep dialysis tubing sealed with clamps. The solutions were injected into the reactors at a constant rate varying from 2.49 to 3.05 ± 4% g/min using Gilson peristaltic pumps. The inlet solutions were comprised of demineralised H2O and reagent-grade NaCl, HCl, NaOH, and KH2PO4. The HCl, NaOH, and KH2PO4 were used to adjust aqueous solution pH, whereas NaCl was used to maintain its ionic strength constant. All experiments were performed at 25° and an ionic strength of 0.01M. Experiments ran from 10 to 24 h, until steady-state was reached and verified. Steady-state was verified with a minimum of three constant Si concentrations in the outlet fluid samples obtained over several residence times; the residence time is defined as the volume of the reactor divided by the reactive fluid flow rate. Dissolution rates were determined from these experiments by the difference in the inlet and outlet concentration of dissolved Si, according to
r=
ΔmSi F vSi
Table 1. Surface Areas and Roughness of Nanosilica Samples surface area (m2/g) average diameter (nm)
BET
geometric
roughness
25 39 101 177
301 232 57 30
91 59 23 13
3.3 3.9 2.5 2.3
areas increase from 30 to 301 m2/g with decreasing particle size from 177 to 25 nm, respectively. Similarly, geometric surface areas (Ageo), calculated assuming the solid consists of identically sized spheres using Ageo = 6/(d ρ), where again d stands for the particle diameter and ρ refers to its density, range from 13 to 91 m2/g. The surface roughness, defined as the ratio of the B.E.T to geometric surface area of the samples varies from 2.3 to 3.9. This low surface roughness value is consistent with the smooth, homogeneous, spherical texture exhibited by these amorphous SiO2 samples as shown in Figure 1. Moreover, as the surface roughness varies only slightly among the samples, the variation with particle size of BET surface area normalized rates is similar to those of geometric surface area normalized rates. The temporal variation of open and closed-system experiments is illustrated in Figure 2. As can be seen in Figures 2a and c, the Si concentration in the aqueous fluid of the closed-system experiments increase slowly initially and then more rapidly, attaining a constant rate consistent with steady-state dissolution, after ∼6000 s of elapsed time. Similarly, as shown in Figures 2b and d, instantaneous amorphous SiO2 dissolution rates in open-system reactors increase for the first ∼2 h or 7200 s attaining a near steady-state thereafter. A summary of all dissolution experiments and results is provided in Table 2. Rates normalized to particle mass, geometric surface area, and BET surface area are provided in this table. Dissolution rates obtained from this study are compared with previously reported amorphous silica dissolution rates36,37 as a function of pH in Figure 3. The dashed curves were calculated using the average particle diameters reported in the literature to obtain geometric surface area normalized dissolution rates. The dissolution rates from this study at a pH of 7 ± 0.2 are consistent with those of previous studies. At higher pH, our results are in agreement with the rates from Wirth et al.31 but diverge from those of Seidel et al.36 that are constant at pH > 7, a behavior inconsistent with available literature data. The agreement between our data and most published results demonstrates a consistency among the results obtained in different laboratories using a variety of experimental techniques. Both mass and BET surface area normalized amorphous SiO2 dissolution rates are shown as a function of particle diameter in Figure 4. Rates measured at pH 6.9 in the presence of KH2PO4 are ∼0.2 log units less than corresponding rates measured in pH 7.2 aqueous NaCl solutions. Although this difference is close to the uncertainty in the rate measurements, this observation suggests that these rates are slightly inhibited by the presence of aqueous phosphate. Mass normalized dissolution rates are independent of particle size within statistical uncertainty. Although the mass normalized dissolution rates of 25 nm particles are 0.15−0.3 log units faster than those of 177 nm particles, this difference is nearly within the uncertainty of the measurements and the coefficients of determination of the linear fits shown in Figure 4 a and b are low. BET surface area normalized rates, however, decrease
(3)
where ΔmSi stands for the Si concentration difference between inlet and outlet fluids, F designates fluid mass flow rate, vSi refers to the stoichiometric number of moles of Si in one mole of the dissolving solid, which in this case is equal to 1. Additional dissolution experiments were performed using closed-system reactors.23 In these experiments, the samples, again contained in dialysis bags, were placed with the reactive aqueous fluid in 1 L Nalgene bottles and samples of the fluid were collected approximately every 10 min. Dissolution rates were determined from the change dissolved Si concentration in the collected fluids as a function of time. The Si concentration of the reactive fluids was determined using the molybdate colorimetric method.34 Uncertainties associated with Si measurements are ±5%. The pH of the outlet fluids was measured at 25 °C using a 713 Metrohm pH meter coupled to a Mettler Toledo Inlab 422 with an uncertainty of ±0.02 units. Uncertainty estimates on Si and pH measurements are based on repeated reanalysis of standard solutions. Overall uncertainties on rates are difficult to quantify rigorously. Uncertainties in reported rates stem directly from uncertainties in the Si measurement, fluid flow rate, and surface area measurement, each of which have an uncertainty of 4−7%. In addition, measured rates may also be affected by uncertainties in pH and variations in particle surface area during the experiments. Consideration of the combined effect of all of these potential sources suggests a total experimental uncertainty in reported rates of approximately ±20%.35
3. RESULTS AND DISCUSSION Measured BET and geometric surface areas of the synthesized amorphous SiO2 are listed in Table 1. Measured BET surface 4911
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Figure 2. Temporal variation of fluid compositions and instantaneous rates during representative open and closed system experiments. Green triangles, red squares, and blue diamonds refer to results obtained for the 177, 101, and 39 nm solids, respectively. a and b) Mass-normalized fluid Si concentrations and instantaneous dissolution rates calculated using eq 3 from closed and flow-through experiments, respectively, conducted at a pH ∼11. The uncertainties of the values shown in these plots are smaller than the symbols. c and d) Results from the same experiments as above, but normalized to geometric surface area. The error bars in this case are ±0.1 log units, again consistent with an error of ±20%. The R2 values for all linear fits are greater than 0.99.
Table 2. Summary of Experimental Conditions and Resultsa surface area (cm2)
mixedflow reactors
average diameter, d (nm)
solution composition (per L soln.)
39
20 mL 0.1 M NaOH; 0.47 g NaCl
101 177 39 101 177 177 25
0.58 g NaCl
0.49 g NaCl; 3.7 mL 0.1 M NaOH; 6.3 mL 0.1 M KH2PO4
39 101 177 Batch reactors
25 39 101 177 39 101 177
a
20 mL 0.1 M NaOH; 0.47 g NaCl
[Si] M
flow rate (g/min)
log(r+,mass)/ (mols/g/s)
log(r+, BET)/ (mols/cm2/ s)
log(r+,Geo)/ (mols/cm2/ s)
5.78 × 10−4
2.60
−6.6
−12.9
−12.3
10−4 10−4 10−5 10−5 10−5 10−5 10−5
2.90 2.49 2.71 3.05 2.81 2.63 3.30
−6.7 −6.7 −7.3 −7.5 −7.7 −7.5 −7.4
−12.4 −12.2 −13.7 −13.3 −13.1 −13.0 −13.9
−12.0 −11.8 −13.1 −12.9 −12.8 −12.6 −13.4
5.00 × 10−5 2.90 × 10−5 3.35 × 10−5
3.30 3.38 3.27
−7.5 −7.8 −7.7
−13.9 −13.6 −13.2
−13.3 −13.2 −12.8
90 566
−6.5
−13.1
−12.6
53 417 24 136 12 035 53 417 24 136 12 035
−6.5 −7.0 −6.6 −6.6 −6.8 −6.8
−12.9 −12.8 −12.0 −13.0 −12.6 −12.3
−12.3 −12.4 −11.7 −12.4 −12.2 −11.9
pH
sample weightb (g)
BET
geometric
11.1
0.091
21 1275
53 417
11.2 11.2 7.2 7.2 7.2 7.2 6.9
0.107 0.094 0.091 0.107 0.094 0.094 0.085
61 066 28 240 211 275 61 066 28 240 28240 255 850
24 136 12 035 53 417 24136 12 035 12 035 76 981
4.51 4.29 9.23 6.56 4.48 7.15 6.00
6.9 6.9 6.9
0.091 0.107 0.094
211 275 61 066 28 240
53 417 24 136 12 035
10.4
0.085
301 000
10.3 10.6 10.5 10.7 10.8 10.7
0.091 0.107 0.094 0.091 0.107 0.094
211 275 61 066 28 240 211 275 61 066 28 240
c
× × × × × × ×
Uncertainties on the log r+ values are estimated to be ±0.1. bWeight of sample before experiment. cSteady-state concentration. 4912
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reason for the contrasting behaviors between our observations and those of past work is unclear as numerous factors including degree of aggregation and fluid phase composition of the past studies are unavailable. The decrease of surface area normalized dissolution rates with particle size, as observed in this study and others,13 have been attributed to a number of factors: • Particle aggregation. Aggregation has been shown to slow dissolution;14 the properties of fluids in nanospaces limit diffusion of dissolution products from the adjoining surfaces of particles in aggregates. This has the same effect as decreasing the surface area of the sample available for dissolution. Zeta potential measurements performed in this study, however, indicate that the zero point of charge for the nanoparticles investigated in this study is ∼2 (see Figure 5) so that aggregation is likely limited under our experimental conditions. This is confirmed by the results of hydrodynamic particle diameter measurements. The hydrodynamic diameters of the three largest amorphous Si samples, measured after their dissolution in pH 11 aqueous fluids, were 203, 121, and 78 nm, which match closely the diameters of these particles measured from transmission electron microscopy (177, 101, and 39 nm, respectively). • The particle size is approaching the critical radius for etch pit formation. A dissolution mechanism that depends on the migration of terraces away from etch pits has been invoked to describe a dependence of dissolution rate on particle size.40 According to this theory, as particle size
Figure 3. Steady-state geometric surface area normalized far from equilibrium amorphous SiO2 dissolution rates. Rates as a function of pH from this study are plotted as symbols whereas rates reported from Seidel et al.36 and Wirth et al.37 are represented by dashed and dotted curves respectively. Rates from these previous studies are recalculated using geometric surface area. Dissolution rates for this study and previous studies were measured in fluids with an ionic strength of 0.01 M.
substantially with decreasing grain size; B.E.T surface area normalized dissolution rates of 25 nm particles are ∼0.8 log units slower than those of 177 nm particles. These results contrast with those of past studies of the variation of amorphous SiO2 dissolution rates with particle diameter. Goto38 and Iler39 reported that the surfaces of smaller particles are more reactive than those of larger particles. In contrast, Rimer et al.20 reported that the dissolution rates of nanoparticle amorphous SiO2 are independent of particle surface area. The
Figure 4. Variation of measured mass and BET normalized amorphous SiO2 dissolution rates as a function of particle size. (a) Mass normalized rates measured at 6.9 < pH < 7.2, (b) mass normalized rates at 10.3 > pH > 11.1, (c) BET surface area normalized rates at 6.9 < pH < 7.2, and (d) BET surface area normalized rates at 10.3 > pH > 11.1. Open triangles, squares, and circles correspond to rates measured in open systems at pH 6.9, 7.2, and 11.1 respectively, whereas filled circles represent rates measured in open systems at 10.3 > pH > 10.8. Dashed lines illustrate least-squares fits of the data illustrated in the figure. The equations and R2 goodness of fit parameters are provided. 4913
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free energy driving the dissolution reaction. As this driving energy is readily calculated from the solubility of the nanoparticle using eq 2 and the reactive fluid composition, the combination of eqs 1 and 2 can provide a simple means to predict nanoparticle dissolution rates over a wide variety of conditions relevant to natural and industrial processes.
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AUTHOR INFORMATION
Corresponding Author
*Phone +33 5 61 33 25 75; fax+33 5 61 33 25 60; e-mail:
[email protected]. Present Address §
Figure 5. Results of zeta potential measurements for the four amorphous SiO2 samples synthesized in this study. The error bars show standard deviation of each measurement. When no error bars are present, standard deviation is less than the symbol size. The zero point of charge, the pH for which the zeta potential is zero, is ∼2 for all particle sizes.
School of Geography, Earth and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom.
approaches the critical radius for pit formation, the migration of terraces is suppressed and dissolution slows. The critical radius is a function of the degree of undersaturation in the system, as well as, the surface free energy and molar volume of the particle.41,42 Since the experiments in this study are conducted under extremely undersaturated conditions, the critical radii are significantly smaller than any of the particles sizes. For example, at pH of 7.2, using published surface energy and molar volume values,43 the critical radii for the samples in the experiments range from 1.1 to 1.2 nm, far smaller than the size of the particles used in our experiments; therefore, it is unlikely to have a significant impact on the dissolution rates. • The surfaces of the smaller particles contain fewer >SiO− groups. The dissolution rate of both quartz and amorphous silica has been described as a function of the concentration of the surface species that participate in dissolution (>SiOH2+, >SiOH, and >SiO−),44,45 which is reflected in surface charge density of the particle. While we do not have direct measurements of the surface speciation or charge of our solids, insight can be gained from their zeta potentials. Measured zeta potentials of the amorphous SiO2 used in this study is shown in Figure 5. Zeta potentials of all samples are similar in value at pH < 5, but diverge at higher pH. The zeta potentials of the smallest diameter particles tend have smaller absolute values at pH > 6. Since the zeta potentials, at equal pH and ionic concentration, reflect surface charge density, this observation suggests that if there is a relationship between particle size and dissolution rate, it may be due to a process that reduces the surface charge of the smallest particles. The results presented above indicate that far-from-equilibrium surface area normalized amorphous SiO2 rates decrease systematically with decreasing particle size in aqueous solutions at both neutral and basic pH. In contrast, mass normalized dissolution rates are close to independent of particle size at farfrom-equilibrium conditions. This latter observation suggests that r+ for mass normalized rates in eq 1 can be assumed to a first approximation to be particle size independent. If r+ is constant, the only factor influencing rates as a function of particle size and reactive fluid composition is ΔrG, the Gibbs
ACKNOWLEDGMENTS This work was supported by the National Science Foundation International Research Fellowship Program, and the European Commission through the Marie Curie Initial Training Network DELTA-MIN (ITN-2008-215360).
Notes
The authors declare no competing financial interest.
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