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Why Do Certain Glasses with a High Dissolution Rate Undergo a Low Degree of Corrosion? Celine Cailleteau,*,†,^ Franc- ois Devreux,‡ Olivier Spalla,§ Frederic Angeli,† and Stephane Gin† †
Laboratoire d'etude du Comportement a Long Terme, CEA Marcoule, DEN, 30207 Bagnols-sur-Ceze, France Physique de la Matiere Condensee, UMR7643 Ecole Polytechnique-CNRS, 91128 Palaiseau, France § Laboratoire Interdisciplinaire sur l'Organisation Nanometrique et Supramoleculaire/SIS2M, UMR3299 CEA-CNRS, 91191 Gif-sur-Yvette, France ‡
bS Supporting Information ABSTRACT: Two series of borosilicate glasses were prepared for studying the influence of the substitution of (i) CaO for Na2O and (ii) ZrO2 for SiO2 on glass durability. They were corroded in buffered aqueous solution at pH 6.9 and pH 8.0. An inverse correlation was found between the initial dissolution rate and the final degree of corrosion in the saturation regime. It was observed as a function of pH for a given glass as well as a function of glass composition at a fixed pH. A ToF-SIMS study of the permeation of foreign ions in the corrosion layer, SAXS characterization of the layer reorganization, and Monte Carlo simulations of the corrosion provide the key to this paradoxical behavior: glasses with a fast dissolution rate undergo a fast restructuring of the corroded layer into a passivating film, which rapidly stops corrosion by porosity closure; on the contrary, the slow restructuring of glasses with a slow dissolution rate leads to a higher degree of corrosion.
I. INTRODUCTION A sound understanding of the mechanisms of aqueous glass corrosion is a major challenge for the predictions of the long-term behavior of nuclear waste confinement glasses.1-3 Indeed, in the case of geological storage, one of the main hazards is the permeation of underground water in storage tunnels, followed by the corrosion of the glass blocks and the dragging of radioelements toward the biosphere. More generally, aqueous corrosion of silicate-based glasses and minerals plays an important role in many areas of science and technology. Examples include the weathering of feldspar, which governs soil fertility;4,5 the natural or artificial leaching of various calcium silicates, which may trap part of atmospheric carbon dioxide;6,7 the biosolubility of rock-wool and glass-wool fibers used for insulation or reinforcement;8,9 and the alteration of archeological and historical glasses and ceramics.10,11 Elementary chemical mechanisms responsible for silicate aqueous corrosion are well-known: hydration, exchange of protonated species (Hþ, H3Oþ) with alkali or earth-alkali ions (interdiffusion), and hydrolysis of the covalent bonds, followed by a possible recondensation into another configuration.12-15 They are strongly coupled. Their efficiency, and consequently the rate and the degree of corrosion, greatly depends on the glass or mineral composition and on the conditions of corrosion (duration, flow rate, pH, temperature). In the frequent case of noncongruent dissolution, a corroded film depleted in the most soluble components forms at the surface. The structure and the thickness of the film, also called gel or gel layer, evolve with time and interfere in the progress of corrosion.16,14,17,18 The back and forth coupling between the chemical reactions and the geometrical and morphological properties of the film makes the problem quite r 2011 American Chemical Society
intricate. In particular, a minute change in material composition may lead to a major change in corrosion performance.19-21 Thus, to address the question of glass durability, we develop a strategy based on two main principles: (i) studying a series of glasses with controlled composition changes and (ii) coupling together leaching kinetics studies, morphological characterization of the gel layer, and Monte Carlo simulations of the corrosion. In particular, we have demonstrated the existence of abrupt changes in corrosion behavior in borosilicates22 and aluminosilicates.23 The transition was explained by the percolation of the soluble cation sublattice in the first case and by the nonpercolation of the silica sublattice in the second case. In the present paper, we study the impact on corrosion of the nature of network modifier cations by replacing alkali (Na) by earthalkali (Ca) and the influence of insoluble oxides by substituting zirconia for silica. Moreover, the effect of the solution pH was investigated by performing leaching experiments at two controlled pHs using buffered solutions. For each glass, the initial dissolution rate was measured and the long-term saturation regime was studied. The latter is specially important for assessing the durability of nuclear glasses, because their corrosion should be dominated by the one in the cracks of the glass blocks, where solution is expected to be readily saturated with silica. The composition of the corroded layer was characterized by time-of-flight secondary-ion mass spectroscopy (ToF-SIMS) and its morphology by small-angle x-ray scattering Received: December 2, 2010 Revised: January 26, 2011 Published: March 08, 2011 5846
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The Journal of Physical Chemistry C (SAXS). The structure factor measured by X-ray was compared to the one calculated for simulated corrosion layers obtained by Monte Carlo simulations of corrosion. A preliminary account of part of this work has been published elsewhere.24
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element X, and wX its mass fraction in the pristine glass. The normalized mass loss is defined as the normalized mass of the element released in solution per surface unit NLX ¼
II. EXPERIMENTAL SECTION A. Sample Preparation. The nominal glass compositions were
62 SiO2-2 ZrO2-17 B2O3-(19 - x) Na2O-x CaO with x = 0, 3, 6 and 9, and (61 - x) SiO2-x ZrO2-17 B2O3-18 Na2O-4 CaO with x = 0, 2, 4, and 8. The glasses of the two series are hereafter designated as xCa and xZr, respectively. The compositions were selected to approximate the proportions of the major oxides (with the exception of Al2O3) of the French R7T7 reference nuclear glasses. The glasses were prepared by melting appropriate mixtures of reagent grade SiO2, ZrO2, H3BO3, Na2CO3, and CaO at 1300 C in a platinum crucible. They were poured in a square-shaped (25 25 mm2) graphite crucible to be annealed at 600 C for 1 h. The compositions were controlled by ICP-AES. Monoliths (3 mm thick) were cut from the glass blocks and polished to obtain a surface roughness of less than 1 μm. Calibrated powders were prepared by crushing and grinding the glass blocks and sieving the resulting powders. Monoliths and powders were washed with acetone to remove fine particles. The specific surface areas of the calibrated powders, measured by BET krypton adsorption, were founded in the range of 0.1600 ( 0.0200 m2 3 g-1 for the 20-40 μm fractions and 0.0480 ( 0.0030 m2 3 g-1 for the 80-125 μm fractions. B. Leaching Procedures. The leaching experiments were performed at 90 C with two controlled pH solutions in closed PTFE reactors. The solutions were buffered by using tris-hydroxymethyl-aminomethane (TRIS) as a buffering agent (0.2 mol 3 L-1) and adding nitric acid to adjust the pHs to 6.9 ( 0.1 and 8.0 ( 0.1 (measured at 90 C). The initial dissolution rates were measured in short-term experiments (typically 8 h) using a low glass surface areato-solution volume ratio (SA/V) of 0.1 cm-1 (90 mg of calibrated powder from the 80-125 μm fraction in 450 mL of solution). The full kinetics, including the saturation regime, were studied in longterm experiments (up to 2 years) with a high SA/V ratio of 30 cm-1 for the xCa series (5 g of powder from the 20-40 μm fraction in 250 mL of solution) and 15 cm-1 for the xZr series (4 g from the 2040 μm fraction in 400 mL of solution). The solutions were sampled (typically 1 or 2 mL) at different times to monitor the leaching kinetics. The solution samples were filtered through a 0.45 μm filter and diluted with an equal volume of Milli-Q water. Concentrations in solution were measured by colorimetry (Varian Cary 50 scan) for silicon and calcium, by colorimetry (WTW Photolab S12) or capillary electrophoresis (water capillary ion analyzer) for boron, and by capillary electrophoresis (water capillary ion analyzer) or flame photometry (Jenway PFP7) for sodium. They were controlled by ICP-AES and ICP-MS at the end of the experiments. The measurement accuracy was 5% for silicon, boron, and calcium; 10% for sodium; and 2% for all elements in the final ICPAES and ICP-MS measurements. Dissolved fractions and normalized mass losses are deduced from the measured concentrations. The dissolved fraction is the ratio of the dissolved mass of each element (X = Si, B, Na, Ca) to its mass in the original glass. It is obtained as DFX ¼
VCX mwX
where V is the solution volume, m the initial mass of glass submitted to leaching, CX the measured concentration of the
1 VCX 1 ¼ DFX SA wX Σ
where SA is the initial glass surface area and Σ the specific surface area of the glass. C. ToF-SIMS Experiments. Time-of-flight secondary-ion mass spectroscopy (ToF-SIMS) was used to obtain the spatially resolved composition of the gel layers and to monitor the penetration of foreign ions inside the gels. The ToF-SIMS profiles were acquired with a spectrometer, TOF V IONTOF, at the Biophy Research Laboratory in Fuveau (France). An oxygen ion source (2 keV) was used for sputter-etching, the sputtered area being about 300 300 μm2. A bismuth gun with an ion energy of 25 keV was used as a primary ion source for the analysis. An area of 100 100 μm2 was analyzed in the center of the etched area. D. SAXS Experiments. Small-angle X-ray scattering (SAXS) is known as a powerful tool to characterize the structure of hydrated corrosion layers.25 SAXS experiments were performed here to follow the evolution of the gel morphology during the course of corrosion. Two homemade setups were used. The first one used a rotating molybdenum anode as an X-ray source with a wavelength of 0.709 Å and a flux of 15 106 photons 3 s-1. It covered the range of scattering vector modulus from 0.25 to 20 nm-1. The second setup used a rotating copper anode source with a wavelength of 1.54 Å and a flux of 106 photons 3 s-1. It slightly extended the detection to lower q values, ranging from 0.15 to 7 nm-1. The direct and scattered photon fluxes were measured using a 2D photographic plate as a detector. Both devices have been described in detail elsewhere.26,27 The calibration of the SAXS experiments required the measurement of standards, such as Lupolen and octodecanol. The pastes of wet glass powder, containing the glass powder and the leaching solution, were enclosed between two sheets of kapton. The thicknesses of the cell were optimized to 2 and 0.2 mm for the Mo and Cu setups, respectively. E. Monte Carlo Simulations. The principles of the Monte Carlo simulations of glass corrosion have been presented in detail elsewhere.28,29 Briefly, the glass structure is represented by a diamond lattice with the boron and silicon cations randomly distributed at the nodes of the lattice and the oxygen atoms at the middle of the bonds between two network-forming cations. Zirconium cations are placed in cages of six silicon tetrahedra. Sodium and calcium cations were disposed in interstitial positions either as charge-balancing cations for BIV and ZrVI units or as network modifiers inducing dangling bonds with nonbridging oxygens. The dissolution kinetics is modeled by introducing dissolution and condensation probabilities that depend on the nature and on the environment of the different cations, which are classified into three categories according to their solubility: soluble (B, Na, Ca), partially soluble (Si), and insoluble (Zr).
III. RESULTS A. Initial Dissolution Rate. The initial dissolution rate refers to the first hydrolysis of the silicate network. It is obtained by linear regression of the normalized silicon mass loss NLSi versus time in the short-term experiments at a low SA/V ratio (0.1 cm-1). The results at pH 6.9 and pH 8.0 are given in Table 1. The accuracy is about 8%, taking into account both the accuracy of concentration measurements and the precision of the linear regression. The dissolution rate of the glasses xCa was nearly constant at pH 6.9 and increased by a factor of 3 at pH 8.0 when 9 mol % Na2O was 5847
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Table 1. Initial Dissolution Rate, k0, Final Silicon Saturation Concentration, CSi*, and Final Boron Dissolved Fraction, DFB*, for the Two Series of Glassesa glass
k0 (g 3 m-2 3 d-1)
CSi* (mg 3 L-1)
DFB* (%)
0Ca
1.6/3.5
140/171
42/35
3Ca
0.9/6.3
130/173
34/25
6Ca
1.3/6.8
125/161
30/18
9Ca
1.4/11.1
125/164
30/19
0Zr 2Zr
26/18.7 4.4/-
133/160 140/-
24/40 42/-
4Zr
1.1/10.9
118/156
83/58
8Zr
0.09/1.8
87/92
87/75
The first number is the result at pH 6.9; the second one is the result at pH 8.0.
a
replaced by CaO. For the glasses xZr, there was a sharp drop (by a factor of 300) at pH 6.9 and a moderate one (by a factor of 10) at pH 8.0 when 8 mol % SiO2 is replaced by ZrO2, which pointed out that the Si-O-Zr bonds are more easily broken at increasing pH. The decrease of the dissolution rate as the zirconia content increases in glass is not amazing because zirconia is highly insoluble and is expected to reinforce the silicate network.30 Otherwise, the dissolution rate increased with the solution pH for all glasses (except 0Zr). This is also expected because a basic pH shift is known to favor the hydrolysis of siloxane bonds.31 B. Long-Term Corrosion. Figure 1 displays the full kinetics for the glasses xCa corroded at pH 6.9. The fractions of dissolved silicon reached a plateau at about 2%, whereas the fractions of dissolved boron, sodium, and calcium became variable and reached much higher values. Contrary to silicon, the plateau reached by the other elements did not result from thermodynamical equilibria, but rather from kinetics limitations due to strongly restricted diffusion. The fraction of dissolved boron, which is the yardstick of the degree of glass corrosion,32 decreased as the Ca content increased in the glass. The dissolutions of boron and sodium were almost congruent, except for a possible drift of the sodium concentrations at very long times. On the contrary, the fraction of dissolved calcium was less than those of sodium and boron, and it increased as the calcium content increased in the glass. This can be explained by the presence of a small amount of zirconia (2 mol %) in the glass composition. Indeed, tetravalent zirconium is known to be in an octahedral environment in both pristine33 and corroded34 glasses as long as there are enough charge compensators (sodium and calcium in the present case). Comparing the variations of the dissolved Na and Ca fractions as a function of calcium content clearly shows that calcium was the favored chargebalancing cation for the [ZrO6]2- units in the corroded layers. The kinetics at pH 8.0 are included in the Supporting Information (Figure S1). They are rather similar to the ones at pH 6.9. However, the dissolved B, Na, and Ca fractions decreased to a larger extent as the Ca content increased in the glass. Figure 2 displays the corrosion kinetics for the glasses xZr corroded at pH 6.9. The introduction of zirconia led to an important slowdown of the corrosion kinetics and also to increasing dissolved boron and sodium fractions. After the saturation of the solution with respect to silica, there was a sharp drop in the B and Na leaching rates, leading to a corrosion stop for the glasses with a low Zr content (0Zr and 2Zr). On the contrary, the dissolved B and Na fractions slowly continued to rise, leading to nearly complete corrosion for the glasses with a high Zr content (4Zr and 8Zr). Thus, substituting an insoluble
oxide, such as zirconia, for part of the silica surprisingly increased the degree of glass corrosion. The dissolution of calcium was congruent with the one of boron for the glass without zirconia and dropped as the zirconia content increased in the glass. This corroborated the above proposal that calcium plays the role of a charge-balancing cation for the zirconium octahedra in the corroded glasses. The corrosion kinetics at pH 8.0 are given in the Supporting Information (see Figure S2) for the glasses 0Zr, 4Zr, and 8Zr. They look like those at pH 6.9 with slightly smaller dissolved B and Na fractions. Table 1 summarizes the main results. The final silicon concentrations, CSi*, and the final dissolved boron fractions, DFB*, are given at pH 6.9 and pH 8.0 for the test glasses. In most cases, the silicon concentration corresponded nearly exactly to the amorphous silica solubility at the experimental temperature and pH.31 It was only smaller for the glasses with the highest Zr content, which reflected the reinforcement of the silicate network by the presence of zirconium. Substituting calcium for sodium decreased the degree of corrosion, in agreement with the widespread opinion that earth-alkali improve glass durability.35,36 Conversely, the partial replacement of silica by zirconia increased the degree of corrosion, which is quite surprising, as mentioned above. However, the most significant result was the systematic inverse correlation between the initial dissolution rate and the final degree of glass corrosion as measured by the dissolved boron fraction: the faster the dissolution, the smaller the degree of corrosion, and vice versa. This was observed as a function of pH for a given glass as well as a function of glass composition at a fixed pH (except for the Ca series at pH 6.9, for which the variation of the dissolution rate is quite small). The investigations of the gel morphology presented below will provide the key to this apparent paradox. C. Gel Composition and Pore Network Connectivity Probed by ToF-SIMS. The monoliths used in the ToF-SIMS experiments were corroded together with the powders in order to achieve the same corrosion conditions, especially the same SA/V ratio. Moreover, the corroded monoliths were disposed for 15 min in a silicasaturated solution containing Kþ ions and then washed before being dried for the ToF-SIMS analysis. The purpose of this process was to monitor the permeation of foreign ions inside the gel structure. Figure 3a,b shows the ToF-SIMS profiles as a function of the etched depth, d, in the gels of the glass 0Zr after 8 h and 2 months of corrosion at pH 6.9. Figure 3c,d displays the corresponding data for the glasses 4Zr and 8Zr after 2 months of corrosion at the same pH. The raw ToFSIMS intensities I(X,d) (where X = B, Na, Ca, K) were divided by I(Si, d) in order to overcome the possible variations of the ionization yield. This defines the relative intensity: IR(X,d) = I(X,d)/I(Si,d). Moreover, the relative intensity was divided by its mean value in the uncorroded glass for B, Na, and Ca. Thus, the normalized relative intensity, IN(X,d) = IR(X,d)/glass, characterizes the depletion or the enrichment of the element in the gel versus its concentration in the original glass. The results show that the gels were free of boron so that the boron profiles can be used to locate the borderline between the gel and the uncorroded glass. The frontier was very sharp in glasses 4Zr and 8Zr (Figure 3c,d), but it was quite soft in the 0Zr aged gel (Figure 3b). At a short corrosion time, the 0Zr gel (Figure 3a) displayed a two-step boundary, which may reflect the ongoing progress of corrosion. The 0Zr gels were also free of sodium and calcium, whereas the 4Zr and 8Zr gels retained calcium and partly sodium. The amount of retained sodium increased when the calcium content became insufficient to compensate for the increasing zirconium content, which again confirms the role of calcium as a favored charge-balancing cation for the zirconium octaedra. 5848
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Figure 1. Dissolved fractions of Si, B, Na, and Ca as a function of time for the glasses 0Ca (a), 3Ca (b), 6Ca (c), and 9Ca (d) corroded at pH 6.9. The continuous lines are guides for the eyes.
Figure 2. Dissolved fractions of Si, B, Na, and Ca as a function of time for the glasses 0Zr (a), 2Zr (b), 4Zr (c), and 8Zr (d) corroded at pH 6.9. The continuous lines are guides for the eyes.
The most outstanding outcome rests on the potassium profiles. K ions permeated the aged gels of the glasses with zirconium, but they did not enter the aged gel of the glass 0Zr. As potassium replaces þ
sodium or calcium in the gel structure, one actually expects a higher Kþ concentration in the gels of the glasses with zirconium that retain alkali and earth-alkali. However, there was also a sharp drop of the Kþ 5849
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Figure 3. K relative ToF-SIMS intensity (left scale) and the B, Na, and Ca normalized relative ToF-SIMS intensity (right scale) as a function of the etching depth for the glass 0Zr after 8 h (a) and 2 months (b) of corrosion at pH 6.9, and for the glasses 4Zr (c) and 8Zr (d) after 2 months at the same pH. Note that the scale is different for the K intensity between (a, b) and (c, d).
concentration for the glass 0Zr between 8 h (Figure 3a) and 2 months (Figure 3b) of corrosion. This demonstrates that the gel porosity closed in the course of corrosion in the glass without zirconia, whereas it remained open in the glasses containing zirconia, which explains quite well why corrosion stops in the former and keeps going in the latter ones. This result confirms preceding experiments made on the same glasses: dye impregnation, neutron scattering with index matching by H2O-D2O exchange, and the comparison pore surface areas as measured by SAXS and BET gas adsorption also led to the conclusions of closed porosity in the glass without zirconia and open porosity in the glasses containing zirconia.24 The ToF-SIMS profiles of boron and sodium also reflected this difference. The sharp B and Na profiles pointed out that the soluble cations were free to diffuse toward solution across the 4Zr and 8Zr gel layers. Conversely, the soft profiles indicated that the diffusion was impeded in the 0Zr aged gel. The variation of the gel thicknesses among the three samples as measured by ToF-SIMS was in agreement with the leaching data concerning the increase of the degree of corrosion with the Zr content. Finally, one notices that the 0Zr gel was thinner after 2 months of corrosion than after 8 h. On the basis of the Monte Carlo simulations of the corrosion (see below), this can be attributed to the densification and to the shrinkage that occur in the aged gels containing only silica (but not in gels including also insoluble oxides, such as zirconia). The ToF-SIMS experiments were repeated for the three glasses after 10 months of corrosion at pH 8. The results included in the Supporting Information (see Figure S3) present qualitatively the same features. The erratic behavior of the profiles around 1 μm for the glass 0Zr was probably an experimental artifact. D. SAXS Study of the Gel Restructuring. Small-angle X-ray Scattering (SAXS) was performed after different times of corrosion to monitor the evolution of the gel structure during the corrosion process. The times chosen for the measurements were fractions or multiples (τ/4, τ/2, τ, 2τ...) of the time τ characteristic of the leaching kinetics, which is deduced from the data in Figure 2 by fitting the
boron kinetics using DFB(t) = DFB*[1 - exp(-t/τ)]. Because they are performed on wet samples, SAXS experiments offer the advantage of preventing a possible change in gel morphology that otherwise could be induced by drying the powders. The absolute intensity scattered in a given direction 2θ is defined as the differential cross section per volume unit of glass. It can be obtained experimentally by counting the number ΔN(2θ) of photons collected in the solid angle ΔΩ IS ðqÞ ¼
1 dσ ΔNð2θÞ ð2θÞ ¼ φS Vs dΩ φS N0 eTΔΩ
ð1Þ
where q = (4π/λ)sin θ is the scattering vector modulus, Vs the sample volume, φS the volume fraction of glass in the sample, N0 the incoming flux of photons on the sample, e the cell thickness, and T the transmission coefficient.37 The scattering curves for the samples 0Zr, 2Zr, 4Zr, and 8Zr corroded at pH 6.9 were obtained with the Mo setup. They are displayed in Figure 4. The strong extra scattering observed for the corroded glasses versus the uncorroded ones is caused by the gel porosity on the nanometer scale. The rise of the scattering curves as a function of time reflects the growth of the gel layer. The profiles beyond the low q shoulder were tentatively fitted by a power law, I(q) ∼ q-u. Figure 5 displays the variation of the exponent u of the power law as a function of the relative corrosion time, t/τ. The evolution of the exponent provides a qualitative indication about the reorganization of the corrosion layer. Power laws between q-1 and q-3 refer to the scattering by a structured object with the exponent being equal to D, the (fractal or not) dimension of the structure.38 In our case, this corresponds to the dimensionality of the porous network. Power laws between q-3 and q-4 correspond to the scattering by an interface, which is, here, the surface of the pores. The exponent is then equal to 6-Ds, where Ds is the (fractal or not) dimension of the surface,39 which goes from 3 for a very rough surface to 2 for a regular soft surface. In 5850
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Figure 4. SAXS scattering curves for the glasses 0Zr (a), 2Zr (b), 4Zr (c), and 8Zr (d) after different times of corrosion at pH 6.9.
Figure 5. Variation of the exponent of the power law I(q) ∼ q-u as a function of the relative corrosion time, t/τ, for the glasses xZr corroded at pH 6.9. The relative corrosion time is the ratio of the actual corrosion duration to the characteristic time of the corrosion kinetics, which is defined by fitting the boron corrosion kinetics shown in Figure 2 by the relation DFB(t) = DFB*[1 - exp(-t/τ)]. The domains of scattering by the porous network and by the pore surface are shown.
the latter case, one recovers the celebrated Porod regime, I(q) ∼ q-4.40 Thus, Figure 5 highlights a transition from network scattering to surface scattering as corrosion proceeds. This is basically due to the increase of the pore size resulting from the ripening of the gel structure. When the typical pore size is less than the inverse scattering vector modulus, X-rays probe the structure of the pore network; when it is larger, they probe the surface of the pores. Initially, all the scattering curves in Figure 4 belonged to the network scattering regime (u < 3), which implies that the pore sizes were less than the inverse scattering vector modulus (typically 1 nm). This highlights the existence of a more or less ramified network of tight pores, which results from the extraction of the soluble components and from the hydrolysis of the weakest siloxane bonds. The network
dimension increased from D ≈ 1 (filaments) for 8Zr to D ≈ 2 (ramified) for 0Zr. As corrosion proceeded, the exponents increased progressively, which implies the increase of the pore size and the softening of the pore surface. This is a consequence of the restructuring of the gel layer caused by the hydrolysis-recondensation reactions of the silicate species within the gel. Figure 5 shows that the gel restructuring was strongly impeded by the presence of zirconium, implying a considerable slowing down of the hydrolysis-condensation mean reaction rate. At the longest reaction time, glass 8Zr was still in the network scattering regime after 403 days of corrosion (the dimension D ≈ 2.5 is close to the one of 3D percolation), glass 4Zr was just at the borderline between the two regimes after 132 days, and glass 2Zr still displayed a rough surface characterized by a dimension Ds ≈ 2.2 after 173 days. On the contrary, the glass without zirconia reached the Porod regime within less than 1 day. In the case where the scattering curves obey the Porod law (I(q) q4 = constant), it is possible to carry out a quantitative data analysis to determine the specific surface area of the porous network, the porous volume, and the mean pore size. The pore specific surface area ΣP and the porosity ΦP are obtained from the relations40,37 ½I ðqÞ q4 Porod ¼ ΦC 2πb2 ðFS - FW Þ2 d ΣP Zþ¥ I ðqÞ q2 d q ¼ ΦC 2π2 b2 ðFS - FW Þ2 ΦP
ð2Þ
0
where b is the Thomson scattering length, d the mass density of the corroded layer, FS its average electronic density, and FW the one of the solution within the pores. I*(q) is the intensity restricted to the extra scattering coming from the porous structure. It is obtained by subtracting the small contribution of the external surface of the powder grains from the measured intensity. ΦC is the volume fraction of corroded glass. It is introduced for taking into account the fact that 5851
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Figure 6. SAXS scattering curves for the glasses 0Zr, 4Zr, and 8Zr after 10 months of corrosion at pH 8.
the degree of corrosion is generally not equal to 100%. It is equal to DFB for the glasses that do not undergo shrinkage and to DFB - DFSi for those that display significant shrinkage.22 The pore diameter l is deduced from the porosity and from the specific surface area: l = 4ΦP/(d ΣP), assuming cylindrical pores, and l = 6ΦP/(d ΣP), assuming spherical pores. The specific surface area and the porosity were estimated using eqs 2 for the glasses in the Porod regime, that is, only for 0Zr after 16 h and more of corrosion (see Figure 5). The Porod plateau was taken in the range of q (0.9, 2.0 nm-1) because, at larger q, an extra contribution coming from the inner structure of the gel skeleton corrupted the scaling law. The specific surface area was 202 m2 3 g-1 after 16 h, 84 m2 3 g-1 after 39 days, and 69 m2 3 g-1 after 125 days. This reduction of the specific surface area is clearly visible in Figure 4a, where the scattering profiles measured after 39 days and 125 days of corrosion are under the profile at 16 h. In parallel, the porous volume decreased from 21.3% at 16 h to about 10% at long times. This corresponds to increasing pore diameters from 2.5 to 3.6 and, finally, 4.2 nm, assuming spherical pores. These data indicate that the gel morphology continued to evolve long after the corrosion blocking, which took place around 1 day for the glass 0Zr. Moreover, the decreasing porosity together with the increasing pore size suggests a phenomenon of pore coalescence. The gel morphology of the glasses corroded at pH 8.0 was also characterized by X-ray scattering. Figure 6 displays the scattering curves obtained for 0Zr, 4Zr, and 8Zr after 330 days of corrosion. The measurements were performed with the Cu SAXS device that extends the scattering range toward the low-q region. Only the samples 0Zr and 4Zr reached the pore surface scattering regime. For 4Zr, the pore surface remained quite rough (DS = 2.5), whereas the scattering profile of the sample 0Zr corresponded to the Porod regime with a specific surface area of 21 m2 3 g-1, a porosity of 6.9%, and a pore diameter of 8.5 nm. The softer 4Zr surface and the lower 0Zr surface area indicate that the ripening of the gel morphology was more important at pH 8.0 than at pH 6.9. E. Monte Carlo Simulations of the Gel Morphology. Starting from a dense 3D sample, the simulations generate a porous structure that results from the removal of the soluble cations and from the hydrolysis of the silicate network. After saturation of the solution with respect to silica, the morphology of the structure continues evolving, driven by the siloxane hydrolysis-condensation reactions, which progressively transforms the weakest silicon species into stronger ones (for example, doubled-bonded Q2 into triple bonded Q3). In turn, the induced morphological change influences the progress of
Figure 7. 2D longitudinal cross sections of the simulated corrosion layer after 3 105 computer steps for the glasses xZr (x = 0, 2, 4, 6 and 8). The silicon and boron lattice nodes are shown in red and yellow, respectively, and water in blue.
corrosion. In particular, porosity closure may inhibit the extraction of the soluble cations and eventually leads to stopping further corrosion.28 The corrosion of the glasses xZr (x = 0, 2, 4, 6, 8) was simulated with SA/V = 15 cm-1.41 The corrosion stop occurred after 2 104 simulation steps for 0Zr. As the experimental blocking time was around 1 day for this glass, this sets the correspondence between the experimental and simulation time scales to about 3-4 s per simulation step. Corrosion blocking was also observed for 2Zr after 4 104 steps and for 4Zr after 7 104 steps, but did not occur for 6Zr and 8Zr. Figure 7 displays the 2D longitudinal cross sections of the simulated corrosion layers after 3 105 simulation steps. Considering the morphology of the layers provides an explanation for the difference in behavior between glasses with low and high Zr contents. The samples with a low Zr content display a shrinkage due to the complete dissolution of the outer sample layers and to the densification of the external gel layers. Consequently, porosity decreases and the pore network becomes nonpercolating. This prevents the transport of the soluble species and stops the corrosion. In contrast, in the samples with a high Zr content, there is neither shrinkage nor densification because the presence of nearly insoluble clusters around zirconium atoms freezes the gel structure by inhibiting, or at least considerably slowing down, the restructuring. The porous network remains percolating, and the corrosion goes on. The structure factors of the simulated 3D corrosion layers were calculated with a view comparing to the SAXS experiments. It can be computed for either water (W) or solid (S) sites as follows ( 2 n 1 S 1 cosð~ q:ri Þ FS;W ð~qÞ ¼ nS n ¼ 1 NS i ¼ S or W 2 ) þ sinð~ q:ri Þ
∑
∑
∑
i ¼ S or W
where nS is the number of samples and NS the total number of solid sites in the sample. For a given ~q modulus, the structure factor is averaged over about 2000 samples by choosing randomly the orientation of the vector q~. It was checked that the results are independent of sample size and that computations using W or S sites gave the same result in the pore scattering region, in accordance 5852
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Figure 8. Simulated SAXS scattering for the composition 0Zr. (a) The simulated SAXS scattering curves after 104 and 107 computation steps. Inset: the variation of the exponent of the power law as a function of the computation step. (b) The variation of F(~q)~q4/(2πda) as a function of the scattering vector modulus at different computation steps. The plateau values give the simulated pore surface areas.
Finally, Figure 9 displays the exponents of the power law after 106 steps for the simulated glasses, together with those after 39 days for the real glasses. These times are almost equivalent, according to the correspondence of one simulation step for 3-4 s. Both curves show a decrease of the exponents, highlighting the slowing down of the gel reorganization as the Zr content increases in the glass. However, the exponents from the simulation are slightly lower, which indicates that the simulation modeling underestimates the restructuring, as mentioned above.
Figure 9. Exponent of the SAXS power law as a function of the ZrO2 content in glass composition after 106 computation steps for the simulated glasses and after 39 days of corrosion for the real glasses.
with the Babinet theorem. Calculations were then performed with the sites W, which are less numerous, to save computation time. The SAXS absolute intensity as defined by eq 1 was obtained from the calculated structure factor as IðqÞ ¼ b2 ðFS - FW Þ2 a3 Fð~qÞ with ~q = qa, where a = 0.32 nm is the Si-O-Si distance. Figure 8a gives the numerical scattering curves for two simulation times, before and after the corrosion stop for the sample 0Zr. These results are in agreement with the experimental ones in Figure 4a concerning the magnitude of the scattered intensities as well as regarding the increase of the slope of I(q) as a function of the corrosion duration. The inset in Figure 8a shows the variation of the exponent u of the power law I(q) ∼ q-u. This is also in qualitative agreement with the results in Figure 5, although the numerical ripening appears slower than the experimental ones. In the Porod regime (u = 4), the pore specific surface area was estimated from the computed structure factor by calculating F(~q)~q4/(2πda). The variation of this expression is shown for different simulation steps in Figure 8b. The plateau around 1 nm-1 corresponds to the Porod regime. Its extension toward the low-q region at long corrosion times reflects the growth of the pore sizes. The specific surface area reduced from 130 to 70 m2 3 g-1 by aging, in reasonable agreement with the values obtained from the SAXS experiments.
IV. DISCUSSION ToF-SIMS along with previous experiments24 showed that the glasses with high dissolution rates and a moderate degree of corrosion display porosity closure. Results from SAXS indicated that these glasses are also those for which the corrosion layer restructuring is the fastest. Monte Carlo simulations suggested that the same glasses undergo shrinkage and densification of the corrosion layer. Leaching and SAXS experiments also showed that dissolution and restructuring rates vary in the same direction as a function of solution pH. When put together, these results make it possible to build a scenario for understanding the inverse correlation between the initial dissolution rate and the ultimate degree of glass corrosion in the saturation regime. In the case of noncongruent glass dissolution, which is the problem presently under consideration, the final degree of glass corrosion results from a competition between the extraction of the soluble elements and the reorganization of the corrosion layer. The initial porous network is, by that very fact, percolating, and it develops a large surface area. The corrosion will continue as long as it remains percolating, permitting the transport of the soluble components from the uncorroded glass to the solution. In physical terms, the corrosion layer reorganization is due to surface tension forces, which tend to minimize the pore surface area by increasing the pore size, softening the pore surface, and favoring pore coalescence with possible expulsion of pores outside the corrosion film. In chemical terms, this mechanism rests on the hydrolysis-condensation reactions, which tend to minimize free energy by replacing poorly bounded species by more connected ones. Thus, the glasses with high dissolution rates, which exhibit fast hydrolysis, also undergo fast restructuring. The corroded layer rapidly turns into a passivating film that almost stops corrosion by closing the pores. Of course, corrosion may continue, however, at a considerably reduced rate, through mechanisms 5853
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The Journal of Physical Chemistry C involving solid-state diffusion.42 On the contrary, for the glasses with low dissolution rates, the correlative slow restructuring is not sufficient to close the pathways for the transport of the soluble elements of the glass to the solution, and the corrosion goes on. This explains why the introduction of insoluble oxides, such as zirconia, paradoxically leads to an increasing degree of corrosion. This paradox was stated 10 years ago.43 The present article and the preceding one24 fully confirm this prediction. In fact, the increase of the corrosion caused by the introduction of zirconia in borosilicate glasses is not completely new. It was already observed in experiments where increasing amounts of zirconia were added to the glass composition 70 SiO2-15 B2O3-15 Na2O.44,45 However, the effect was much less pronounced than in the present work. There was a small increase of the degree of corrosion up to 2% of zirconia, followed by a decrease for larger amounts. There are two reasons for the difference. First, as zirconia was added to the initial composition instead to be substituted for silica, the relative amount of soluble oxides decreased, which balanced out the increasing amount of zirconia. Moreover, the glass compositions were pretty remote from the composition 60 SiO2-20 B2O3-20 Na2O, for which the percolation of the soluble cation subnetwork occurs.22 This makes these glasses almost corrosion-resistant. Conversely, in the present work, the smaller amount of silica (61% in the glass without zirconia) makes the competition between the release of the soluble oxides and the reconstruction of the corroded layer much tighter. The slowing down of the restructuring induced by the presence of zirconia then comes out thoroughly, leading to a continuous increase of corrosion as the zirconia content increases in the glass.
V. CONCLUSION Leaching experiments were performed at two different controlled pHs (6.9 and 8.0) on two series of glasses obtained by replacing sodium oxide by calcium oxide (xCa series) and silica by zirconia (xZr series). They show that the glasses with the highest initial dissolution rates are those that undergo the lowest degree of corrosion in the saturation regime. Especially, the glasses with a low zirconia content went through a corrosion stop, whereas the ones with a high zirconia content sustained continuous corrosion. ToF-SIMS and SAXS experiments have been performed on the glasses xZr corroded at both pHs. ToF-SIMS shows that foreign Kþ ions permeated the corrosion layer of the glasses containing zirconia, but not the aged gel layer of the glass without zirconia, which is interpreted as resulting from porosity closure. Also, the sharp boron and sodium profiles in the former suggest free diffusion of the soluble species across the gel layer, whereas the loose profiles observed in the latter point out impeded diffusion. SAXS experiments highlight that the presence of zirconia considerably slows down the restructuring of the corrosion layers. Finally, the Monte Carlo simulations of glass corrosion show that glasses free of insoluble oxides display shrinkage and densification of the corrosion layer, unlike those containing insoluble oxides. The structure factors calculated for the simulated corrosion layers are in good agreement with the ones deduced from X-ray experiments. All these results lead to propose the following paradigm: glasses with high dissolution rates undergo fast restructuring and corrode slightly; glasses with low dissolution rates undergo slow restructuring and corrode deeply. This conclusion applies to the silicate glasses where the proportion of network-forming oxides more soluble than silica is sufficient to generate a substantial corrosion layer that can turn into a passivating layer. It can probably be extended to the silicate minerals that display noncongruent dissolution with the formation of an amorphous corrosion layer.
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’ ASSOCIATED CONTENT
bS
Supporting Information. Three supplementary figures are available. They display the corrosion kinetics at pH 8.0 for the glasses xCa (Figure S1) and xZr (Figure S2) and the ToF-SIMS profiles for the glasses 0Zr, 4Zr, and 8Zr after 10 months of corrosion at pH 8.0 (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Address
^ Structures et Proprietes d'Architectures Moleculaires, UMR5819 CEA/CNRS/UJF, 38054 Grenoble, France.
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