Kinetics of amorphous silica dissolution and the paradox of the silica polymorphs

Abstract

The mechanisms by which amorphous silica dissolves have proven elusive because noncrystalline materials lack the structural order that allows them to be studied by the classical terrace, ledge, kink-based models applied to crystals. This would seem to imply amorphous phases have surfaces that are disordered at an atomic scale so that the transfer of SiO₄ tetrahedra to solution always leaves the surface free energy of the solid unchanged. As a consequence, dissolution rates of amorphous phases should simply scale linearly with increasing driving force (undersaturation) through the higher probability of detaching silica tetrahedra. By examining rate measurements for two amorphous SiO₂ glasses we find, instead, a paradox. In electrolyte solutions, these silicas show the same exponential dependence on driving force as their crystalline counterpart, quartz. We analyze this enigma by considering that amorphous silicas present two predominant types of surface-coordinated silica tetrahedra to solution. Electrolytes overcome the energy barrier to nucleated detachment of higher coordinated species to create a periphery of reactive, lesser coordinated groups that increase surface energy. The result is a plausible mechanism-based model that is formally identical with the classical polynuclear theory developed for crystal growth. The model also accounts for reported demineralization rates of natural biogenic and synthetic colloidal silicas. In principle, these insights should be applicable to materials with a wide variety of compositions and structural order when the reacting units are defined by the energies of their constituent species.

Over the past 20 years, the essential roles of amorphous silica (SiO₂) dissolution in controlling biogeochemical cycling of silicon and carbon have emerged at the forefront of scientific investigations. Of particular interest is the demineralization kinetics of biogenic silicas, reservoirs of highly reactive silica produced by silicifying phytoplankton and terrestrial plants (1). In parallel, the materials and medical communities are increasingly investigating the corrosion of silicas in efforts to design advanced covalent solids and decipher the pathological basis for silicosis.

A mechanistic understanding of how amorphous silica dissolution occurs is complicated by the structural, and sometimes compositional, variability of noncrystalline solids (2–4). Although short-range structural order is recognized in amorphous materials at length scales up to 20Å (2), amorphous silica lacks the regular long-range order that can be studied with classical terrace, ledge, and kink-based models of crystal growth and dissolution. Despite variations in Si–O–Si bond lengths and angles, low-pressure silicas share the same fundamental chemical unit, the silica tetrahedron. By using the theoretical Kossel crystal construct, it has been shown that silica tetrahedra on quartz surfaces have distinct bonding coordinations at terraces and steps (5, 6). Gratz and Bird (6) defined two predominant types of sites available for reaction with water as β and γ groups, or Q2 and Q3, respectively. Fig. 1a shows that at a step edge on the (100) quartz surface, Q2 groups are bonded to two bridging oxygens. The Q3 groups of a terrace have a higher connectivity to the solid through binding to three bridging oxygens. Q2 and Q3 species could be further subdivided into more “positions” through variations in Si–O bond lengths and angles, but the added detail does not appear to be justified (6).

Fig. 1.

Illustration of quartz (a) and amorphous silica (b) showing Q2 and Q3 species as tetrahedra with two and three coordinations to the surface, respectively. The physical model holds that amorphous surfaces are repeatedly, atomically roughened at a length scale that is the average distance over which Q2 groups must be removed to return to a Q3-enriched SiO₂ surface.

Reported dissolution rate data for crystalline and amorphous SiO₂ support the idea that quartz and amorphous silicas have reaction pathways similar to dissolution and growth. All silica polymorphs undergo hydrolysis by the overall reaction:

In particular, previous studies show that the dissolution rates of both quartz and the amorphous silicas are increased 50–100 times when alkaline or alkaline earth cations are introduced to otherwise pure solutions (7–10). This large enhancement has significant implications for the durability of inorganic and biological silicas in natural waters. The behavior is unique to SiO₂ phases and not exhibited by silicate minerals (11). We recently found this “salt effect” for quartz arises by a transition from dissolution at preexisting step edges and dislocation defects to the nucleated removal of units across the entire surface (10). That is, CaCl₂ and NaCl solutions promote removal of Q3 species to create vacancy islands, each with a periphery of new surface groups enriched in the reactive Q2 species. The transition to homogeneous nucleation, or “plucking” of Q3 species gives quartz dissolution rates an exponential dependence on increasing chemical driving force (undersaturation). This dependence is the hallmark of a nucleated process and has its roots in the increase of surface free energy associated with creating new steps, that is, Q2 sites. The relationship between the surface free-energy barrier, chemical driving force, and temperature is described by the classical nucleation theory developed for crystal growth (12, 13) and extended to dissolution (10).

This study asks the question of why dissolution rates of amorphous silicas should also be significantly enhanced by electrolytes. From a mechanistic standpoint, congruent demineralization of noncrystalline silica should scale linearly with the increasing probability of detaching silica tetrahedra from an atomically rough surface. A nucleation process is not allowed because classical nucleation theory is rooted in the concept that dissolution or growth occurs by overcoming a free-energy barrier to forming a new phase within an existing phase (14). Because the atomically disordered surfaces of amorphous materials are presumed to be near the maximum in surface free energy for stable SiO₂, the origin of a comparable energy barrier is not easy to understand. With detachment of any unit from an amorphous solid, the same average surface is produced. In other words, without the order imposed by terraces and kink sites, there is no additional free-energy barrier to drive a nucleated process. For amorphous silica, the physical result is that, as chemical driving force increases, silica production from the surface should similarly increase (15, 16). Indeed, this is what we measure for amorphous silica dissolution in salt-free solutions (Fig. 2a). In electrolytes, however, we find a paradox. Just as seen for quartz, the kinetics of amorphous silica dissolution exhibits a strong exponential dependence on driving force (Fig. 2 b and c). We argue that the data are best explained by a crystal-based theory for a nucleated process even though a high degree of structural order and periodicity are absent.

Fig. 2.

Rates of vitreous silica dissolution vs. undersaturation, C/C_e show dependence on chemical driving force in the absence or presence of the simple electrolyte, CaCl₂·2H₂O at 150°C. Standard error of each measurement is determined from replicate samples and is smaller than the symbol diameter. (a) Rates of fused quartz silica dissolution in solutions without electrolyte show the expected linear dependence on C/C_e without evidence for the dissolution plateau reported for quartz (10) (Inset). In contrast, fused quartz glass (b) and synthetic silica (c) show dissolution rates in electrolyte solutions with an exponential dependence on undersaturation. Open symbols at bottom right of a, b, and c assume rate = 0 at C/C_e = 1.0.

We analyze this surprising result by considering a physical model based on differences in site-specific energies of Q2 and Q3 tetrahedra. To do this, we examine the hypothesis that it is possible for noncrystalline SiO₂ to undergo dissolution and growth by nucleated processes when the reactions are viewed as attachments and detachments of differently coordinated silica tetrahedral groups. This tests the idea that measured kinetic behavior is a consequence of differences in the reactivity of Q2 and Q3 surface species at the solid–solution interface. In doing so, we arrive at a plausible mechanism-based model that is formally identical with classical polynuclear theory developed for crystal growth. By using this approach, we can also explain dissolution kinetics reported for synthetic colloidal silica and natural biogenic silica. Our findings raise the question of whether traditional crystal growth models based in structure may be extended to discern the species-specific roles of individual surface chemical groups during dissolution and growth across a spectrum of soluble materials. Correlations between surface structure and chemical reactivity have long been recognized (17), but these insights suggest that a common mechanistic and theoretical basis underlies the demineralization of both amorphous and crystalline materials.

Results and Discussion

In the absence of electrolytes, dissolution rates of fused quartz silica have the expected linear dependence on increasing undersaturation, C/C_e (Fig. 2a), where C and C_e are measured and equilibrium concentrations of H₄SiO₄°, respectively. Rates scale with chemical driving force through the increasing probability of detaching silica units from the surface as predicted by traditional theory. Data show no evidence for the “plateau” at large undersaturations (Fig. 2a Inset) reported for quartz (10) in similar solutions, aluminum oxyhydroxides (18), and silicates at low temperatures (19). For crystalline materials, plateau behavior was explained by rates that are dominated by step generation at dislocation defects, which are absent in vitreous silica. Fitting the data to the classical power law expression for crystal growth and dissolution

gives a near-linear dependence on driving force with n = 0.91 ± 0.23 and rate constant, k₊ = 6.6 × 10⁻⁹ mol·m⁻²·s⁻¹.

In contrast, dissolution rates of fused quartz silica in CaCl₂ solutions show a strong exponential dependence on driving force (Fig. 2b). Because this behavior seemed improbable, a second set of experiments was conducted by using a synthetic silica prepared by SiCl₄ pyrolysis. This obtained a similar result (Fig. 2c). Rates in water and electrolyte solutions diverge with increasing departure from equilibrium, such that at C/C_e = 0.1, electrolytes increase rates by ≈50 times. Thus, the salt effect recognized for quartz (Fig. 2b Inset), is also active in these vitreous silicas (Fig. 2 b and c).

The superlinear dependence indicates that a simple detachment probability model cannot explain silica dissolution in electrolyte solutions. Previous studies of crystalline materials conclude that when rates obey Eq. 2 with n > 2, growth or dissolution is occurring by a nucleated process (20). This would seem to be the case for these synthetic and fused quartz silicas because a fit of Eq. 2 obtains n = 3.4 ± 0.6 and 2.9 ± 0.5, respectively. For quartz, this superlinear dependence (e.g., Fig. 2b Inset) is explained by a nucleation process (10). However, the assumptions of classical nucleation theory do not allow this explanation to be applied readily to amorphous materials.

Physical Model.

Despite the obvious lack of long-range order in amorphous silica, the exponential dependence of dissolution rates on chemical driving force leads us to propose a physical model for how a nucleated process could occur. To do this, we first recall that nucleation-driven dissolution of crystalline materials involves creating a vacancy island followed by retreat of the newly created step edges. By considering relative rates of these processes, two types of end-member nucleation phenomena involving spreading can occur (12, 13): (i) The classical birth and spread model applies when the time between nucleation events is short compared with the long time required for the new steps to retreat (spread) across the surface to the edge of the crystal. That is, regions affected by individual pits are overlapping and the rate is limited by a combination of pit birth and step spread. This model is widely applied in crystal growth and was found to also explain quartz dissolution by a nucleation process (10). (ii) The opposite end-member, the mononuclear model, applies when the time between nucleation events is long compared with the time to remove the affected area.

An intermediate nucleation process is described by the polynuclear model. The theory assumes multiple nucleation sites that do not overlap. In the original conception, polynuclear theory defines the area affected by each nucleation site as the critical radius of the material (20, 21). To apply polynuclear theory to amorphous materials, we instead consider the affected region of dissolution is equal to the average area, S, around the site of nucleation. The condition for applying the polynuclear model therefore is that the time between detachment events from the complete surface over region S is greater than the time required to remove the newly exposed step in that region. For amorphous silica, S is the average size of the region for which removal of a Q3 species then creates a periphery of Q2 groups on the surface. For example, with the removal of a Q3 group from an amorphous silica surface (Fig. 1b), S covers the number of resulting Q2 groups that need to be removed to return the surface to a Q3-enriched state. Although we recognize that amorphous materials may lie along a continuum between the birth and spread vs. mononuclear end-members, the polynuclear model would seem to give the most likely description of amorphous silica.

By therefore considering nucleation as a process that overcomes an energy barrier to removing a surface species of lower chemical reactivity (Q3) that subsequently creates a number of more reactive surface species (Q2), the traditional requirement for long-range crystalline order is overcome. That is, physical models of growth and dissolution by terrace, step, and kink constructs become more general when viewed in terms of chemical bonding. Our application of the polynuclear model to amorphous silica dissolution (and growth) is given below.

Nucleation on a Rumpled Surface.

By using crystalline silica as a starting point, we consider a physical picture for how amorphous silica could undergo dissolution in a way that increases surface free energy—the requirement for a nucleated process. Quartz shows different reactivities for Q3- and Q2-coordinated groups and corresponding differences in surface energies (10). In the absence of electrolytes, rates are dominated by removing Q2 groups at preexisting step edges and dislocation defects. Q3 sites are kinetically inaccessible because of the high activation barrier for removing this higher coordinated surface species from a terrace. With electrolytes, the energy barrier to detaching the less reactive Q3 groups is reduced, increasing the probability of forming vacancy islands as driving force increases. This is a nucleated process because each vacancy island creates the equivalent of new step edge on a crystal—an expanding perimeter of Q2 sites. As expected, the excess free-energy barrier to creating pits by removing Q3 groups from a quartz surface at homogeneous regions (α_I) is higher than for groups coordinated with compositional defects (α_II).

A similar picture of dissolution for amorphous silica again assumes that Q3 and Q2 species are the reacting units. We recognize the variability of Si–O–Si bond lengths and angles and why they should ideally be statistically defined. Yet, comparisons of the differently arranged groups (Fig. 1 a and b) show Q2 and Q3 species in amorphous silica may be thought of as pseudocrystallographic surface sites. That is, the disordered surface of amorphous silica is a “rumpled” structure of differently coordinated Si surface groups without terrace, ledge, or kink (Fig. 3a).

Fig. 3.

Illustration of amorphous silica dissolution by a simple rumpled structure concept. (a) After initial rapid dissolution of highly coordinated groups, a steady-state surface develops. (b) With each nucleated detachment of a highly coordinated Q3 species from the surface, a perimeter of higher-energy Q2 species is formed (Fig. 1b). (c) Reactive Q2 groups retreat over area, S, until (d) the affected surface returns to the lower-energy Q3-rich surface and the process regenerates new reactive vacancies at nucleation rate, J, by Eq. 8.

On a “fresh” surface of this rumpled structure, one would predict dissolution initially involves rapid removal of the most reactive groups. Assuming that, just as seen for quartz, the lower coordinated Q2 groups are the most reactive, dissolution would be expected to first proceed at preexisting defects such as scratches and other areas of curvature with a large number of highly undercoordinated and strained groups. Once these sites are largely removed, dissolution proceeds at a steady-state rate because surfaces continue to supply Q2 groups at particle edges, areas of high curvature, and sites where impurity defects are removed. In the presence of electrolytes, the energy barrier to detaching a Q3 group is reduced, thus increasing its probability of release. As seen in Fig. 3b, each time a Q3 group is “plucked” from the surface, a disordered Q2-enriched perimeter is generated to create a higher-energy region, S, on the surface. These Q2 groups subsequently retreat (Fig. 3c) until a lower-energy, Q3-enriched surface (Fig. 3d) is reestablished. Multiple nucleation events across the surface lead to the result that steady-state dissolution rates display the exponential dependence on driving force because the probability of nucleated detachment of Q3 groups increases exponentially with increasing departure from equilibrium.

Energy Barrier to Removing a Unit of Material.

To quantify the rate of nucleated detachment, we begin by considering that the probability of removing a unit of material is proportional to the exponential of the free energy barrier height divided by kT (22). Thus, the nucleation rate, J, is given by

where the preexponential, A, gathers a number of terms and ΔG_Crit is the free-energy barrier to nucleating 2D vacancies. Rewriting ΔG_Critⁿ in terms of its dependence on chemical driving force for dissolution gives:

where h = average height of this vacancy, ω = specific volume of molecule (cm³/molecule), α = local interfacial free energy, T = temperature. Degree of undersaturation, σ, is defined:

Eq. 4 shows the energy barrier to nucleation decreases as solution undersaturation increases or interfacial energy decreases. Substituting Eq. 4 into Eq. 3 obtains an expression for 2D nucleation rate:

Thus, nucleation rate depends on undersaturation, interfacial free energy, and temperature. α represents the increase in interfacial free energy per molecule that is created by removing material from the surface over an area whose size is determined by the critical radius, r_c. In a crystalline material, α is the step edge free energy per unit step length per unit step height around the new vacancy island. This usage is distinct from surface or bulk interfacial free energy, which is defined and recognized as an average over a surface area.

The minimum (critical) radius to removing a unit of material, r_c, by nucleation is given by:

Substituting Eq. 7 into Eq. 6 shows that the nucleation rate also depends on the energy barrier to creating a nucleus (pit) with radius, r_c such that

For vitreous silica at 150°C in C/C_e = 0.1 (highly undersaturated), r_c ranges from ≈2.5 to 4 Å by using accepted interfacial free-energy values of 37–62 mJ/m², respectively (calculated from this study assuming a hemispherical pit). That is, at far from equilibrium, the theory estimates r_c is 1–3 silica tetrahedral units. Although crude, the estimate suggests the assumption of using a Q3 species as the nucleation unit is a reasonable approximation. This is important because, for the polynuclear model to apply, r_c must be much smaller than the region (S) over which Q2 sites are available for subsequent removal.

Polynuclear Dissolution.

For conditions where nuclei are continuously removed from a surface, the normal retreat rate, R, is determined by the volume of microscopic nuclei formed at the surface. Thus, R is expressed as the volume of nuclei formed per unit area of surface and time (12, 13, 21) such that for the general model:

where h = step height; S = surface area affected by each nucleation event, and J = rate of 2D nucleation per area, to give R units of length/time. For an amorphous solid, h is the average height of a surface group (see below) and S is the area of the rumpled surface over which Q2 groups must be removed to return to a Q3-enriched surface. Substituting the expression for J from Eq. 6 gives

Rewriting Eq. 10 into a form that is linear in 1/σ gives the final expression:

By presenting supersaturation as an absolute value, Eq. 11 is general to dissolution and growth rates as discussed elsewhere (10). Eq. 11 shows that the logarithm of the rate of removing a unit of material from the surface has a squared dependence on the energy barrier to creating new surface (α) and T. Moreover, the natural logarithm of rate should increase with a linear dependence on inverse undersaturation with increasing α or T.

The fit of Eq. 11 to experimental measurements gives good agreement with the dissolution behavior of the synthetic and fused silica glasses (Fig. 4 a and b). In highly undersaturated solutions, rates show a strong linear dependence on 1/σ with a high slope, just as seen for quartz (10). From the model fit to the data, we estimate interfacial energy as α_I. If the model is valid, α represents the increased interfacial energy associated with removing a silica unit from the surface by homogenous nucleation (12, 13). We assign h = 2.17 Å as an approximation of the height of a silicon tetrahedron and other parameters are given in Table 1. Although crude, Table 1 shows α_I = 52 ± 10 and 49 ± 2 mJ·m⁻² for the synthetic and fused quartz silicas, respectively. As expected for these disordered silicas, α_I values are significantly lower than the 79 ± 14 mJ·m⁻² obtained for quartz, their crystalline counterpart, in the same solutions at 200°C (10).

Fig. 4.

Polynuclear model (Eq. 11) describes the dependence of dissolution rate on undersaturation for the two synthetic silicas and reported data for studies of biogenic and synthetic colloidal silicas. Model fits (Table 1) show that, in electrolyte solutions, all silicas exhibit a steeply sloped linear trend at far from equilibrium conditions and suggest one or more lower-sloped dependencies at lower driving force: fused quartz glass (a); synthetic silica (b); biogenic (diatomaceous) silica at pH 8 (7) (c); Dissolution and growth rate of synthetic colloidal silica at pH 7 (25) in undersaturated and supersaturated solutions (d), respectively.

Table 1.

Summary of experimental conditions and the constants used to estimate surface energy, α

Process	Material	Solution	Temp, °C	Ce, molecules cm−3 (ppm SiO2)	ω, cm3	αI*, mJ·m−2	αII*, mJ·m−2
Dissolution	Synthetic silica	0.0167 M CaCl2	150	4.19 × 1018 (417)	4.53 × 10−23	52 ± 10	22
	Fused quartz	0.0167 M CaCl2	150	4.19 × 1018 (417)	4.53 × 10−23	49 ± 2	18 ± 7
	Biogenic silica†	0.7 M NaCl	25	9.6 × 1017 (95)	4.74 × 10−23	46 ± 4	6 ± 2
	Colloidal silica‡	0.01 M NaCl	25	1.30 × 1018 (130)	4.74 × 10−23	39 ± 2	27 ± 3
	Quartz§	0.0167 M CaCl2	200	2.37 × 1018 (236)	3.77 × 10−23	79 ± 14	32 ± 10
	Quartz§	0.05 NaCl	200	2.37 × 1018 (236)	3.77 × 10−23	61 ± 6	18 ± 8
Growth	Colloidal silica‡	0.01 M NaCl	25	1.30 × 1018 (130)	4.74 × 10−23	29 ± 1	15 ± 4

*Assumes h = 2.17 Å for all silicas.

^†From ref. 7.

^‡From ref. 25.

^§From ref. 10.

The physical basis for this behavior can be understood by realizing electrolytes create an energetically different surface. Here, the thermodynamic barrier to Q3 detachment is more easily overcome such that total rate becomes dominated by the increasing frequency of homogeneously removing Q3 groups with increasing driving force. The resulting perimeter of lower coordinated groups (Fig. 3b) creates a higher-energy region that is quickly removed over the area S required to return to the Q3-enriched surface. Hence, the measured rate of silica production becomes controlled by the sum of rates of Q3 release and subsequent Q2 retreat. Although there is no crystallographically defined structural control, it is energetically similar to the nucleated formation of vacancy islands on a quartz surface, regardless of long-range order.

Relationships in Fig. 4 a and b suggest a second, lower-slope region at low driving force but the number of data is insufficient to conclude whether this is one or a number of shallow-sloped trends. Previous studies of crystal growth and dissolution by nucleation report a single, lower-sloped dependence for ADP, thaumautin, and quartz (10, 13, 23). At high temperatures, kaolinite and K-feldspar also show this behavior (10). Malkin and others (13) attributed this behavior to compositional defects that lower the energy barrier to nucleation. In their “defect-assisted” model, small amounts of impurities induce localized strain to give lower free-energy barriers than for 2D nucleation at perfect surfaces. Dominance of one defect type seems to be common to these crystalline systems. Because these vitreous silicas contain up to 0.2% iron as Fe₂O₃ and 0.03% aluminum as Al₂O₃ (9), a similar interpretation based on Fe and/or Al as compositional defects is consistent with an analogous explanation. Although we are uncertain that the data are expressing a single trend, our fit of the nucleation model to those data presenting the lower slope obtains α_II = 22 and 18 ± 7 mJ·m⁻² for the synthetic and fused quartz silicas, respectively (Table 1). These estimates of α_II show the expected lower values than those determined for the analogous compositional defect-based values estimated for quartz.

Whether there is a single slope or continuum of shallow-sloped trends for the conditions where driving force is lower, a nucleation-based model can again explain dissolution when reacting units are viewed in terms of their surface coordination. When compositional impurities are present, disruption or weakening of the intermolecular bonds can destabilize the solid, which means its free energy is increased. Thus, the excess free-energy α_II associated with nucleating a new dissolution site is reduced from α_I, whether the solid is crystalline or amorphous. Lower driving forces are then sufficient to overcome the reduced free-energy barrier to nucleation at sites of compositional impurities. But also, when compositional impurities are present, the free energy of the solid, whether amorphous or crystalline, and thus the energy penalty (ie, interfacial energy) is reduced. Presumably this occurs through local strain that raises the enthalpy of the solid.

AFM examination of surfaces treated in the absence and presence of CaCl₂ for the same extent of reaction suggest electrolytes progressively smoothen the amorphous silica surface at very short length scales. By using 2D power spectral analyses, electrolytes produce dissolution surfaces that are depleted in roughness features over the 2- to 50-nm length scale. Smoothening may be occurring at still-shorter lengths but our estimate is limited by the 2-nm resolution of AFM cantilevers. This gives the reasonable result that S is probably less than ≈50 nm, which is consistent with the model for progressive smoothening of a rumpled surface structure.

Further Tests of Nucleation Model.

Agreement of the experimental data with the physical model and the comparisons with quartz led us to further test Eq. 11 by using dissolution rate data for two other silicas that also reported an exponential dependence on driving force. Using cleaned biogenic silica, Van Cappellen and Qiu (7, 8) reported dissolution rates for this natural material in a 0.7 M NaCl solution at pH = 8.0 and T = 25°C. The samples, collected from the Antarctic Ocean at 1 and 4 cm below the seafloor sediment–water interface, are primarily a siliceous ooze, composed largely of broken diatom valves (8). The material is 89% opaline silica with the balance as biogenic CaCO₃ (0.3%), organic matter (2.6%), and mineral detritus (10.8%). Dissolution rate measurements were conducted at controlled saturation states. Eq. 11 gives a good fit to their kinetic data; again showing a strong linear trend at high undersaturations and possible single trend at smaller departures from equilibrium (Fig. 4b). By using parameters given in Table 1, we estimate α_I = 46 ± 4 mJ·m⁻² at far from equilibrium conditions. At lower driving force, α_II = 6 ± 2 mJ·m⁻². Although α_I is similar to our estimates for the vitreous silicas, α_II is significantly lower, which is consistent with the idea that nucleation at impurity defects contributes to the rate dependence at low driving force because the silica of diatomaceous organisms contain considerable aluminum (1.3–1.9% as Al₂O₃) (4, 24).

We also test the model by using data reported for the dissolution and growth kinetics of Ludox, a synthetic colloidal silica (25). Ludox is a nonporous, monodisperse suspension of SiO₂ particles with diameters ≈19.2 ± 4.2 nm and contains 0.05–0.5% Al. Experiments were conducted in 0.01 M NaCl solutions with pH = 7 and T = 25°C. Fig. 4d shows that Eq. 11 gives a good fit to dissolution and growth rates and emphasizes that both obey the same relations on either side of the driving force (equilibrium). Estimates of α_I and α_II for dissolution at high and low driving force are 39 ± 2 and 27 ± 3 mJ·m⁻², respectively (Table 1). For growth, we estimate α_I and α_II are 29 ± 1 and 15 ± 4 mJ·m⁻², for homogeneously and defect-promoted nucleation, respectively.

Additional Insights.

For conditions farthest from equilibrium, the formalism in Eq. 11 estimates excess interfacial free energy for vitreous silica to be lower than reported for quartz (Table 1). This is consistent with the expectation that a crystalline polymorph has a lower free energy of solution than its amorphous counterpart. But whereas the lower free energy results in a higher probability of making sites susceptible to dissolution, it should not be confused with the lower activation energy barrier arising from the greater strain of Si–O–Si bonds. This strain gives lower barriers to detachment of Q2 or Q3 groups presented at the mineral–water interface to decrease the durability of amorphous phases.

Second, the polynuclear model appears to explain the dissolution of glassy silicas in electrolyte solutions at 150°C and amorphous silicas at ambient temperature. At first, this would seem to conflict with the finding that quartz and aluminosilicates undergo dissolution by a nucleated process only at higher T and (for quartz) in solutions containing electrolytes (10). The explanation for this difference in behavior comes from three coupled effects, one structural and two kinetic. In quartz, the presence of dislocations that provide continuous sources of Q2 sites introduces an alternate dissolution mechanism that requires no nucleation. At low temperature, pit nucleation is too slow compared with the rate of removal at dislocations. But the 1/T dependence of the thermodynamic barrier to pit stabilization (Eq. 7) leads to a T² dependence in the exponent of Eq. 11. This drives a crossover to a nucleation-dominated regime with increasing temperature. Alternatively, electrolytes reduce the kinetic barrier to dissolution site initiation by removing Q3 sites. This barrier is in the exponential of a term within the prefactor A in Eq. 11 (see ref. 10). Thus, addition of electrolytes also drives a switch from a dislocation to a nucleation-dominated regime. The lack of dislocations in glasses eliminates these crossovers; once initial topography is removed, nucleation dominates at all temperatures and compositions. It is notable, however, that the mononuclear model breaks down when vacancies are formed at such a high rate that they never have a chance to spread. In this situation, the birth and spread model begins to apply.

By holding chemistry invariant and examining the influence of structure, SiO₂ materials reveal the ability of a structure-based nucleation model to describe both amorphous and crystalline phases. Long-range order is not a requirement for a crystal-based model to describe behavior when the reacting units are defined in terms of coordination. That is, the primary property that unifies the behavior of these materials is their constituent species. This suggests intriguing parallels between the approach presented here and long-standing surface species-based models of mineral dissolution that are prevalent in the geochemical community. Perhaps by linking structure-based theory with species-based correlations, a new mechanistic understanding can emerge.

Methods

Glasses.

Synthetic silica and fused quartz glass were obtained from Corning and Quartz Scientific, respectively. Properties and pretreatment of these materials are described elsewhere (9). Specific surface area of final crushed and cleaned synthetic and fused materials were 0.030 and 0.029 m²/g, respectively, as determined by single-point Brunauer–Emmett–Teller (B.E.T.) method (Micromeritics). Raman spectroscopy and x-ray diffraction of the final material did not show evidence any crystalline phases.

Experiments.

Dissolution rate measurement used mixed flow-through reactors to determine the steady-state rate of silica production at 150°C for the overall reaction (Eq. 1) by established methods (9, 10). Rates were measured across σ by using solutions with characterized levels of monomeric silicic acid, H₄SiO₄° at circumneutral pH and calculated in situ pH (pH_T) ≈5.7. Some silica solutions also contained reagent-grade CaCl₂·2H₂O (Aldrich) at 0.0167 M (ionic strength = 0.05). Simple linear and exponential fits to rates measured in the absence and presence of electrolytes estimated solubility values of 417 ± 19 and 418 ppm, respectively, by determining the silica concentration where the dissolution rate diminished to zero. In this article, we set C_e = 417 ppm SiO₂ at 150°C (Fig. 2a). This value is lower than the 620–660 ppm reported for amorphous silica solubility (26–28) but we offer three possible explanations for the difference: (i) Most previous studies were conducted by using silica gel that is hydrated and colloidal. We expect this material to have a higher C_e than our SiO₂ glasses. (ii) Our experiments were careful to contain only the monomeric form of aqueous silica. To ensure this, we used freshly prepared solutions. At 150°C, C/C_e = 0.85 was the most concentrated solution that we could use and be assured that all silica was in the monomeric form. Polymeric forms are likely present for the conditions and analysis techniques used by some previous studies. (iii) It is possible that trace amounts of iron from the fused quartz glass that was used to generate input solutions lowered the apparent solubility, but the minute levels and low solubility of ferric iron at near-neutral pH make this explanation unlikely.