Kinetics of amorphous silica dissolution andthe paradox of the silica polymorphsPatricia M. Dove*†, Nizhou Han*, Adam F. Wallace*, and James J. De Yoreo†‡

*Department of Geosciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061; and ‡Molecular Foundry, Lawrence Berkeley NationalLaboratory, Berkeley, CA 94720

Communicated by James K. Mitchell, Virginia Polytechnic Institute and State University, Blacksburg, VA, April 22, 2008 (received for reviewOctober 19, 2007)

The mechanisms by which amorphous silica dissolves have provenelusive because noncrystalline materials lack the structural order thatallows them to be studied by the classical terrace, ledge, kink-basedmodels applied to crystals. This would seem to imply amorphousphases have surfaces that are disordered at an atomic scale so that thetransfer of SiO4 tetrahedra to solution always leaves the surface freeenergy of the solid unchanged. As a consequence, dissolution rates ofamorphous phases should simply scale linearly with increasing driv-ing force (undersaturation) through the higher probability of detach-ing silica tetrahedra. By examining rate measurements for two amor-phous SiO2 glasses we find, instead, a paradox. In electrolytesolutions, these silicas show the same exponential dependence ondriving force as their crystalline counterpart, quartz. We analyze thisenigma by considering that amorphous silicas present two predom-inant types of surface-coordinated silica tetrahedra to solution. Elec-trolytes overcome the energy barrier to nucleated detachment ofhigher coordinated species to create a periphery of reactive, lessercoordinated groups that increase surface energy. The result is aplausible mechanism-based model that is formally identical with theclassical polynuclear theory developed for crystal growth. The modelalso accounts for reported demineralization rates of natural biogenicand synthetic colloidal silicas. In principle, these insights should beapplicable to materials with a wide variety of compositions andstructural order when the reacting units are defined by the energiesof their constituent species.

biogenic silica � demineralization � glass � nucleation � surface energy

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 scientificinvestigations. Of particular interest is the demineralization kineticsof biogenic silicas, reservoirs of highly reactive silica produced bysilicifying phytoplankton and terrestrial plants (1). In parallel, thematerials and medical communities are increasingly investigatingthe corrosion of silicas in efforts to design advanced covalent solidsand decipher the pathological basis for silicosis.

A mechanistic understanding of how amorphous silica dissolu-tion occurs is complicated by the structural, and sometimes com-positional, variability of noncrystalline solids (2–4). Although short-range structural order is recognized in amorphous materials atlength scales up to 20Å (2), amorphous silica lacks the regularlong-range order that can be studied with classical terrace, ledge,and kink-based models of crystal growth and dissolution. Despitevariations in Si–O–Si bond lengths and angles, low-pressure silicasshare the same fundamental chemical unit, the silica tetrahedron.By using the theoretical Kossel crystal construct, it has been shownthat silica tetrahedra on quartz surfaces have distinct bondingcoordinations at terraces and steps (5, 6). Gratz and Bird (6) definedtwo predominant types of sites available for reaction with water as� and � groups, or Q2 and Q3, respectively. Fig. 1a shows that ata step edge on the (100) quartz surface, Q2 groups are bonded totwo bridging oxygens. The Q3 groups of a terrace have a higherconnectivity to the solid through binding to three bridging oxygens.Q2 and Q3 species could be further subdivided into more ‘‘posi-

tions’’ through variations in Si–O bond lengths and angles, but theadded detail does not appear to be justified (6).

Reported dissolution rate data for crystalline and amorphousSiO2 support the idea that quartz and amorphous silicas havereaction pathways similar to dissolution and growth. All silicapolymorphs undergo hydrolysis by the overall reaction:

SiO2(s) � 2H2O � H4SiO4° [1]

In particular, previous studies show that the dissolution rates of bothquartz and the amorphous silicas are increased 50–100 times whenalkaline or alkaline earth cations are introduced to otherwise puresolutions (7–10). This large enhancement has significant implica-tions for the durability of inorganic and biological silicas in naturalwaters. The behavior is unique to SiO2 phases and not exhibited bysilicate minerals (11). We recently found this ‘‘salt effect’’ for quartzarises by a transition from dissolution at preexisting step edges anddislocation defects to the nucleated removal of units across theentire surface (10). That is, CaCl2 and NaCl solutions promoteremoval of Q3 species to create vacancy islands, each with aperiphery of new surface groups enriched in the reactive Q2 species.The transition to homogeneous nucleation, or ‘‘plucking’’ of Q3species gives quartz dissolution rates an exponential dependence onincreasing chemical driving force (undersaturation). This depen-

Author contributions: P.M.D., N.H., A.F.W., and J.J.D.Y. designed research; P.M.D., N.H., andA.F.W. performed research; P.M.D., N.H., A.F.W., and J.J.D.Y. analyzed data; and P.M.D.,N.H., A.F.W., and J.J.D.Y. wrote the paper.

The authors declare no conflict of interest.

†To whom correspondence may be addressed. E-mail: dove@vt.edu or jjdeyoreo@lbl.gov.

© 2008 by The National Academy of Sciences of the USA

Fig. 1. Illustration of quartz (a) and amorphous silica (b) showing Q2 and Q3species as tetrahedra with two and three coordinations to the surface, respec-tively. The physical model holds that amorphous surfaces are repeatedly,atomically roughened at a length scale that is the average distance over whichQ2 groups must be removed to return to a Q3-enriched SiO2 surface.

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dence is the hallmark of a nucleated process and has its roots in theincrease of surface free energy associated with creating new steps,that is, Q2 sites. The relationship between the surface free-energybarrier, chemical driving force, and temperature is described by theclassical nucleation theory developed for crystal growth (12, 13) andextended to dissolution (10).

This study asks the question of why dissolution rates of amor-phous silicas should also be significantly enhanced by electrolytes.From a mechanistic standpoint, congruent demineralization ofnoncrystalline silica should scale linearly with the increasing prob-ability of detaching silica tetrahedra from an atomically roughsurface. A nucleation process is not allowed because classicalnucleation theory is rooted in the concept that dissolution or growthoccurs by overcoming a free-energy barrier to forming a new phasewithin an existing phase (14). Because the atomically disorderedsurfaces of amorphous materials are presumed to be near themaximum in surface free energy for stable SiO2, the origin of acomparable energy barrier is not easy to understand. With detach-ment of any unit from an amorphous solid, the same averagesurface is produced. In other words, without the order imposed byterraces and kink sites, there is no additional free-energy barrier todrive a nucleated process. For amorphous silica, the physical resultis that, as chemical driving force increases, silica production fromthe surface should similarly increase (15, 16). Indeed, this is whatwe measure for amorphous silica dissolution in salt-free solutions(Fig. 2a). In electrolytes, however, we find a paradox. Just as seenfor quartz, the kinetics of amorphous silica dissolution exhibits astrong exponential dependence on driving force (Fig. 2 b and c). Weargue that the data are best explained by a crystal-based theory fora nucleated process even though a high degree of structural orderand periodicity are absent.

We analyze this surprising result by considering a physical modelbased on differences in site-specific energies of Q2 and Q3 tetra-hedra. To do this, we examine the hypothesis that it is possible fornoncrystalline SiO2 to undergo dissolution and growth by nucleatedprocesses when the reactions are viewed as attachments anddetachments of differently coordinated silica tetrahedral groups.This tests the idea that measured kinetic behavior is a consequenceof differences in the reactivity of Q2 and Q3 surface species at thesolid–solution interface. In doing so, we arrive at a plausiblemechanism-based model that is formally identical with classicalpolynuclear theory developed for crystal growth. By using thisapproach, we can also explain dissolution kinetics reported forsynthetic colloidal silica and natural biogenic silica. Our findingsraise the question of whether traditional crystal growth modelsbased in structure may be extended to discern the species-specific

roles of individual surface chemical groups during dissolution andgrowth across a spectrum of soluble materials. Correlations be-tween surface structure and chemical reactivity have long beenrecognized (17), but these insights suggest that a common mech-anistic and theoretical basis underlies the demineralization of bothamorphous and crystalline materials.

Results and DiscussionIn the absence of electrolytes, dissolution rates of fused quartz silicahave the expected linear dependence on increasing undersatura-tion, C/Ce (Fig. 2a), where C and Ce are measured and equilibriumconcentrations of H4SiO4°, respectively. Rates scale with chemicaldriving force through the increasing probability of detaching silicaunits from the surface as predicted by traditional theory. Data showno evidence for the ‘‘plateau’’ at large undersaturations (Fig. 2aInset) reported for quartz (10) in similar solutions, aluminumoxyhydroxides (18), and silicates at low temperatures (19). Forcrystalline materials, plateau behavior was explained by rates thatare dominated by step generation at dislocation defects, which areabsent in vitreous silica. Fitting the data to the classical power lawexpression for crystal growth and dissolution

rate � k��1 � C/Ce�n [2]

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 CaCl2solutions show a strong exponential dependence on driving force(Fig. 2b). Because this behavior seemed improbable, a second setof experiments was conducted by using a synthetic silica preparedby SiCl4 pyrolysis. This obtained a similar result (Fig. 2c). Rates inwater and electrolyte solutions diverge with increasing departurefrom equilibrium, such that at C/Ce � 0.1, electrolytes increase ratesby �50 times. Thus, the salt effect recognized for quartz (Fig. 2bInset), is also active in these vitreous silicas (Fig. 2 b and c).

The superlinear dependence indicates that a simple detachmentprobability model cannot explain silica dissolution in electrolytesolutions. Previous studies of crystalline materials conclude thatwhen rates obey Eq. 2 with n 2, growth or dissolution is occurringby a nucleated process (20). This would seem to be the case for thesesynthetic 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 superlineardependence (e.g., Fig. 2b Inset) is explained by a nucleation process(10). However, the assumptions of classical nucleation theory donot allow this explanation to be applied readily to amorphousmaterials.

a b c

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

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Physical Model. Despite the obvious lack of long-range order inamorphous silica, the exponential dependence of dissolution rateson chemical driving force leads us to propose a physical model forhow a nucleated process could occur. To do this, we first recall thatnucleation-driven dissolution of crystalline materials involves cre-ating a vacancy island followed by retreat of the newly created stepedges. By considering relative rates of these processes, two types ofend-member nucleation phenomena involving spreading can occur(12, 13): (i) The classical birth and spread model applies when thetime between nucleation events is short compared with the longtime required for the new steps to retreat (spread) across thesurface to the edge of the crystal. That is, regions affected byindividual pits are overlapping and the rate is limited by a combi-nation of pit birth and step spread. This model is widely applied incrystal growth and was found to also explain quartz dissolution bya nucleation process (10). (ii) The opposite end-member, themononuclear model, applies when the time between nucleationevents is long compared with the time to remove the affected area.

An intermediate nucleation process is described by the polynu-clear model. The theory assumes multiple nucleation sites that donot overlap. In the original conception, polynuclear theory definesthe area affected by each nucleation site as the critical radius of thematerial (20, 21). To apply polynuclear theory to amorphousmaterials, we instead consider the affected region of dissolution isequal to the average area, S, around the site of nucleation. Thecondition for applying the polynuclear model therefore is that thetime between detachment events from the complete surface overregion S is greater than the time required to remove the newlyexposed step in that region. For amorphous silica, S is the averagesize of the region for which removal of a Q3 species then creates aperiphery of Q2 groups on the surface. For example, with theremoval of a Q3 group from an amorphous silica surface (Fig. 1b),S covers the number of resulting Q2 groups that need to be removedto return the surface to a Q3-enriched state. Although we recognizethat amorphous materials may lie along a continuum between thebirth and spread vs. mononuclear end-members, the polynuclearmodel would seem to give the most likely description of amorphoussilica.

By therefore considering nucleation as a process that overcomesan energy barrier to removing a surface species of lower chemicalreactivity (Q3) that subsequently creates a number of more reactivesurface species (Q2), the traditional requirement for long-rangecrystalline order is overcome. That is, physical models of growthand dissolution by terrace, step, and kink constructs become moregeneral when viewed in terms of chemical bonding. Our applicationof the polynuclear model to amorphous silica dissolution (andgrowth) is given below.

Nucleation on a Rumpled Surface. By using crystalline silica as astarting point, we consider a physical picture for how amorphoussilica could undergo dissolution in a way that increases surface freeenergy—the requirement for a nucleated process. Quartz showsdifferent reactivities for Q3- and Q2-coordinated groups andcorresponding differences in surface energies (10). In the absenceof electrolytes, rates are dominated by removing Q2 groups atpreexisting step edges and dislocation defects. Q3 sites are kinet-ically inaccessible because of the high activation barrier for remov-ing this higher coordinated surface species from a terrace. Withelectrolytes, the energy barrier to detaching the less reactive Q3groups is reduced, increasing the probability of forming vacancyislands as driving force increases. This is a nucleated processbecause each vacancy island creates the equivalent of new step edgeon a crystal—an expanding perimeter of Q2 sites. As expected, theexcess free-energy barrier to creating pits by removing Q3 groupsfrom a quartz surface at homogeneous regions (�I) is higher thanfor groups coordinated with compositional defects (�II).

A similar picture of dissolution for amorphous silica againassumes that Q3 and Q2 species are the reacting units. We

recognize the variability of Si–O–Si bond lengths and angles andwhy they should ideally be statistically defined. Yet, comparisons ofthe differently arranged groups (Fig. 1 a and b) show Q2 and Q3species in amorphous silica may be thought of as pseudocrystallo-graphic surface sites. That is, the disordered surface of amorphoussilica is a ‘‘rumpled’’ structure of differently coordinated Si surfacegroups without terrace, ledge, or kink (Fig. 3a).

On a ‘‘fresh’’ surface of this rumpled structure, one would predictdissolution initially involves rapid removal of the most reactivegroups. Assuming that, just as seen for quartz, the lower coordi-nated Q2 groups are the most reactive, dissolution would beexpected to first proceed at preexisting defects such as scratches andother areas of curvature with a large number of highly underco-ordinated and strained groups. Once these sites are largely re-moved, dissolution proceeds at a steady-state rate because surfacescontinue to supply Q2 groups at particle edges, areas of highcurvature, and sites where impurity defects are removed. In thepresence of electrolytes, the energy barrier to detaching a Q3 groupis reduced, thus increasing its probability of release. As seen in Fig.3b, each time a Q3 group is ‘‘plucked’’ from the surface, adisordered Q2-enriched perimeter is generated to create a higher-energy region, S, on the surface. These Q2 groups subsequentlyretreat (Fig. 3c) until a lower-energy, Q3-enriched surface (Fig. 3d)is reestablished. Multiple nucleation events across the surface leadto the result that steady-state dissolution rates display the expo-nential dependence on driving force because the probability ofnucleated detachment of Q3 groups increases exponentially withincreasing departure from equilibrium.

Energy Barrier to Removing a Unit of Material. To quantify the rateof nucleated detachment, we begin by considering that the proba-bility of removing a unit of material is proportional to the expo-nential of the free energy barrier height divided by kT (22). Thus,the nucleation rate, J, is given by

J � A exp�� GCritn

kT � [3]

a

b

c

d

Fig. 3. Illustrationofamorphous silicadissolutionbyasimple rumpledstructureconcept. (a) After initial rapid dissolution of highly coordinated groups, a steady-state surface develops. (b) With each nucleated detachment of a highly coordi-nated Q3 species from the surface, a perimeter of higher-energy Q2 species isformed (Fig. 1b). (c) Reactive Q2 groups retreat over area, S, until (d) the affectedsurface returns to the lower-energy Q3-rich surface and the process regeneratesnew reactive vacancies at nucleation rate, J, by Eq. 8.

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where the preexponential, A, gathers a number of terms and GCritis the free-energy barrier to nucleating 2D vacancies. RewritingGCrit

n in terms of its dependence on chemical driving force fordissolution gives:

GCritn � �

��2�hkT ln�C/Ce�

���2�hkT � � , [4]

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

� ln�C/Ce� . [5]

Eq. 4 shows the energy barrier to nucleation decreases as solutionundersaturation increases or interfacial energy decreases. Substi-tuting Eq. 4 into Eq. 3 obtains an expression for 2D nucleation rate:

J � A exp�� ��2�h�kT�2 �

1� �� . [6]

Thus, nucleation rate depends on undersaturation, interfacial freeenergy, and temperature. � represents the increase in interfacialfree energy per molecule that is created by removing material fromthe surface over an area whose size is determined by the criticalradius, rc. In a crystalline material, � is the step edge free energy perunit 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, rc,by nucleation is given by:

rc � ���

kT ln�C/Ce�. [7]

Substituting Eq. 7 into Eq. 6 shows that the nucleation rate alsodepends on the energy barrier to creating a nucleus (pit) withradius, rc such that

J � A exp� ��hrc

kT � . [8]

For vitreous silica at 150°C in C/Ce � 0.1 (highly undersaturated),rc ranges from �2.5 to 4 Å by using accepted interfacial free-energyvalues of 37–62 mJ/m2, respectively (calculated from this studyassuming a hemispherical pit). That is, at far from equilibrium, thetheory estimates rc is 1–3 silica tetrahedral units. Although crude,the estimate suggests the assumption of using a Q3 species as thenucleation unit is a reasonable approximation. This is importantbecause, for the polynuclear model to apply, rc must be muchsmaller than the region (S) over which Q2 sites are available forsubsequent removal.

Polynuclear Dissolution. For conditions where nuclei are continu-ously removed from a surface, the normal retreat rate, R, isdetermined by the volume of microscopic nuclei formed at thesurface. Thus, R is expressed as the volume of nuclei formed perunit area of surface and time (12, 13, 21) such that for the generalmodel:

R � �hS�J, [9]

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

R � �hS��A exp�� ��2�h�kT�2 �

1� �� . [10]

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

ln R � ln�hS �A� ���2�h�kT�2 �

1� � . [11]

By presenting supersaturation as an absolute value, Eq. 11 is generalto dissolution and growth rates as discussed elsewhere (10). Eq. 11shows that the logarithm of the rate of removing a unit of materialfrom the surface has a squared dependence on the energy barrierto creating new surface (�) and T. Moreover, the natural logarithmof rate should increase with a linear dependence on inverseundersaturation with increasing � or T.

The fit of Eq. 11 to experimental measurements gives goodagreement with the dissolution behavior of the synthetic and fusedsilica glasses (Fig. 4 a and b). In highly undersaturated solutions,rates show a strong linear dependence on 1/ with a high slope, justas seen for quartz (10). From the model fit to the data, we estimate

σ σ

σ σ

σ

a b

c

d

Fig. 4. Polynuclear model (Eq. 11) describes the dependence of dissolutionrate on undersaturation for the two synthetic silicas and reported data forstudies of biogenic and synthetic colloidal silicas. Model fits (Table 1) showthat, in electrolyte solutions, all silicas exhibit a steeply sloped linear trend atfar from equilibrium conditions and suggest one or more lower-sloped de-pendencies at lower driving force: fused quartz glass (a); synthetic silica (b);biogenic (diatomaceous) silica at pH 8 (7) (c); Dissolution and growth rate ofsynthetic colloidal silica at pH 7 (25) in undersaturated and supersaturatedsolutions (d), respectively.

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interfacial energy as �I. If the model is valid, � represents theincreased interfacial energy associated with removing a silica unitfrom the surface by homogenous nucleation (12, 13). We assign h �2.17 Å as an approximation of the height of a silicon tetrahedronand other parameters are given in Table 1. Although crude, Table1 shows �I � 52 � 10 and 49 � 2 mJ�m�2 for the synthetic and fusedquartz silicas, respectively. As expected for these disordered silicas,�I values are significantly lower than the 79 � 14 mJ�m�2 obtainedfor quartz, their crystalline counterpart, in the same solutions at200°C (10).

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

Relationships in Fig. 4 a and b suggest a second, lower-sloperegion at low driving force but the number of data is insufficient toconclude whether this is one or a number of shallow-sloped trends.Previous studies of crystal growth and dissolution by nucleationreport a single, lower-sloped dependence for ADP, thaumautin,and quartz (10, 13, 23). At high temperatures, kaolinite andK-feldspar also show this behavior (10). Malkin and others (13)attributed this behavior to compositional defects that lower theenergy barrier to nucleation. In their ‘‘defect-assisted’’ model, smallamounts of impurities induce localized strain to give lower free-energy barriers than for 2D nucleation at perfect surfaces. Domi-nance of one defect type seems to be common to these crystallinesystems. Because these vitreous silicas contain up to 0.2% iron asFe2O3 and 0.03% aluminum as Al2O3 (9), a similar interpretationbased on Fe and/or Al as compositional defects is consistent withan analogous explanation. Although we are uncertain that the dataare expressing a single trend, our fit of the nucleation model to thosedata presenting the lower slope obtains �II � 22 and 18 � 7 mJ�m�2

for the synthetic and fused quartz silicas, respectively (Table 1).These estimates of �II show the expected lower values than thosedetermined for the analogous compositional defect-based valuesestimated for quartz.

Whether there is a single slope or continuum of shallow-slopedtrends for the conditions where driving force is lower, a nucleation-based model can again explain dissolution when reacting units areviewed in terms of their surface coordination. When compositionalimpurities are present, disruption or weakening of the intermolec-ular bonds can destabilize the solid, which means its free energy isincreased. Thus, the excess free-energy �II associated with nucle-

ating a new dissolution site is reduced from �I, whether the solid iscrystalline or amorphous. Lower driving forces are then sufficientto overcome the reduced free-energy barrier to nucleation at sitesof compositional impurities. But also, when compositional impu-rities are present, the free energy of the solid, whether amorphousor crystalline, and thus the energy penalty (ie, interfacial energy) isreduced. Presumably this occurs through local strain that raises theenthalpy of the solid.

AFM examination of surfaces treated in the absence and pres-ence of CaCl2 for the same extent of reaction suggest electrolytesprogressively smoothen the amorphous silica surface at very shortlength scales. By using 2D power spectral analyses, electrolytesproduce dissolution surfaces that are depleted in roughness featuresover the 2- to 50-nm length scale. Smoothening may be occurringat still-shorter lengths but our estimate is limited by the 2-nmresolution of AFM cantilevers. This gives the reasonable result thatS is probably less than �50 nm, which is consistent with the modelfor progressive smoothening of a rumpled surface structure.

Further Tests of Nucleation Model. Agreement of the experimentaldata with the physical model and the comparisons with quartz ledus to further test Eq. 11 by using dissolution rate data for two othersilicas that also reported an exponential dependence on drivingforce. Using cleaned biogenic silica, Van Cappellen and Qiu (7, 8)reported dissolution rates for this natural material in a 0.7 M NaClsolution at pH � 8.0 and T � 25°C. The samples, collected from theAntarctic Ocean at 1 and 4 cm below the seafloor sediment–waterinterface, are primarily a siliceous ooze, composed largely of brokendiatom valves (8). The material is 89% opaline silica with thebalance as biogenic CaCO3 (0.3%), organic matter (2.6%), andmineral detritus (10.8%). Dissolution rate measurements wereconducted at controlled saturation states. Eq. 11 gives a good fit totheir kinetic data; again showing a strong linear trend at highundersaturations and possible single trend at smaller departuresfrom equilibrium (Fig. 4b). By using parameters given in Table 1,we estimate �I � 46 � 4 mJ�m�2 at far from equilibrium conditions.At lower driving force, �II � 6 � 2 mJ�m�2. Although �I is similarto our estimates for the vitreous silicas, �II is significantly lower,which is consistent with the idea that nucleation at impurity defectscontributes to the rate dependence at low driving force because thesilica 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 dissolutionand growth kinetics of Ludox, a synthetic colloidal silica (25). Ludoxis a nonporous, monodisperse suspension of SiO2 particles withdiameters �19.2 � 4.2 nm and contains 0.05–0.5% Al. Experimentswere 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 andgrowth rates and emphasizes that both obey the same relations oneither side of the driving force (equilibrium). Estimates of �I and �IIfor dissolution at high and low driving force are 39 � 2 and 27 �3 mJ�m�2, respectively (Table 1). For growth, we estimate �I and �II

Table 1. Summary of experimental conditions and the constants used to estimate surface energy, �

Process Material Solution Temp, °C Ce, molecules cm�3 (ppm SiO2) �, cm3 �I*, mJ�m�2 �II*, mJ�m�2

Dissolution Synthetic silica 0.0167 M CaCl2 150 4.19 � 1018 (417) 4.53 � 10�23 52 � 10 22Fused quartz 0.0167 M CaCl2 150 4.19 � 1018 (417) 4.53 � 10�23 49 � 2 18 � 7Biogenic silica† 0.7 M NaCl 25 9.6 � 1017 (95) 4.74 � 10�23 46 � 4 6 � 2Colloidal silica‡ 0.01 M NaCl 25 1.30 � 1018 (130) 4.74 � 10�23 39 � 2 27 � 3Quartz§ 0.0167 M CaCl2 200 2.37 � 1018 (236) 3.77 � 10�23 79 � 14 32 � 10Quartz§ 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.

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are 29 � 1 and 15 � 4 mJ�m�2, for homogeneously and defect-promoted nucleation, respectively.

Additional Insights. For conditions farthest from equilibrium, theformalism in Eq. 11 estimates excess interfacial free energy forvitreous silica to be lower than reported for quartz (Table 1). Thisis consistent with the expectation that a crystalline polymorph hasa lower free energy of solution than its amorphous counterpart. Butwhereas the lower free energy results in a higher probability ofmaking sites susceptible to dissolution, it should not be confusedwith the lower activation energy barrier arising from the greaterstrain of Si–O–Si bonds. This strain gives lower barriers to detach-ment of Q2 or Q3 groups presented at the mineral–water interfaceto decrease the durability of amorphous phases.

Second, the polynuclear model appears to explain the dissolutionof glassy silicas in electrolyte solutions at 150°C and amorphoussilicas at ambient temperature. At first, this would seem to conflictwith the finding that quartz and aluminosilicates undergo dissolu-tion by a nucleated process only at higher T and (for quartz) insolutions containing electrolytes (10). The explanation for thisdifference in behavior comes from three coupled effects, onestructural and two kinetic. In quartz, the presence of dislocationsthat provide continuous sources of Q2 sites introduces an alternatedissolution mechanism that requires no nucleation. At low temper-ature, pit nucleation is too slow compared with the rate of removalat dislocations. But the 1/T dependence of the thermodynamicbarrier to pit stabilization (Eq. 7) leads to a T2 dependence in theexponent of Eq. 11. This drives a crossover to a nucleation-dominated regime with increasing temperature. Alternatively, elec-trolytes reduce the kinetic barrier to dissolution site initiation byremoving Q3 sites. This barrier is in the exponential of a term withinthe prefactor A in Eq. 11 (see ref. 10). Thus, addition of electrolytesalso drives a switch from a dislocation to a nucleation-dominatedregime. The lack of dislocations in glasses eliminates these cross-overs; once initial topography is removed, nucleation dominates atall temperatures and compositions. It is notable, however, that themononuclear model breaks down when vacancies are formed atsuch a high rate that they never have a chance to spread. In thissituation, the birth and spread model begins to apply.

By holding chemistry invariant and examining the influence ofstructure, SiO2 materials reveal the ability of a structure-basednucleation model to describe both amorphous and crystallinephases. Long-range order is not a requirement for a crystal-based

model to describe behavior when the reacting units are defined interms of coordination. That is, the primary property that unifies thebehavior of these materials is their constituent species. This suggestsintriguing parallels between the approach presented here andlong-standing surface species-based models of mineral dissolutionthat are prevalent in the geochemical community. Perhaps bylinking structure-based theory with species-based correlations, anew mechanistic understanding can emerge.

MethodsGlasses. Synthetic silica and fused quartz glass were obtained from Corning andQuartzScientific, respectively.Propertiesandpretreatmentofthesematerialsaredescribed elsewhere (9). Specific surface area of final crushed and cleaned syn-thetic and fused materials were 0.030 and 0.029 m2/g, respectively, as determinedby single-point Brunauer–Emmett–Teller (B.E.T.) method (Micromeritics). Ramanspectroscopyandx-raydiffractionof thefinalmaterialdidnot showevidenceanycrystalline phases.

Experiments. Dissolutionratemeasurementusedmixedflow-throughreactors todetermine the steady-state rate of silica production at 150°C for the overallreaction (Eq. 1) by established methods (9, 10). Rates were measured across byusing solutions with characterized levels of monomeric silicic acid, H4SiO4° atcircumneutral pH and calculated in situ pH (pHT) �5.7. Some silica solutions alsocontained reagent-grade CaCl2�2H2O (Aldrich) at 0.0167 M (ionic strength �0.05). Simple linear and exponential fits to rates measured in the absence andpresence of electrolytes estimated solubility values of 417 � 19 and 418 ppm,respectively, by determining the silica concentration where the dissolution ratediminished to zero. In this article, we set Ce � 417 ppm SiO2 at 150°C (Fig. 2a). Thisvalue is lower than the 620–660 ppm reported for amorphous silica solubility(26–28) but we offer three possible explanations for the difference: (i) Mostprevious studies were conducted by using silica gel that is hydrated and colloidal.We expect this material to have a higher Ce than our SiO2 glasses. (ii) Ourexperiments were careful to contain only the monomeric form of aqueous silica.To ensure this, we used freshly prepared solutions. At 150°C, C/Ce � 0.85 was themost concentrated solution that we could use and be assured that all silica was inthe monomeric form. Polymeric forms are likely present for the conditions andanalysis techniques used by some previous studies. (iii) It is possible that traceamounts of iron from the fused quartz glass that was used to generate inputsolutions loweredtheapparentsolubility,but theminute levelsand lowsolubilityof ferric iron at near-neutral pH make this explanation unlikely.

ACKNOWLEDGMENTS. We thank Alex Chernov and Peter Vekilov for thought-ful discussions. This work was supported by Department of Energy Award FG02-00ER15112 and National Science Foundation Awards OCE-052667 and EAR-0545166 (to P.M.D.). This work was performed under the auspices of Departmentof Energy Contract W-7405-Eng-48 at the University of California, LawrenceLivermore National Laboratory (to J.D.Y.).

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