Modeling Speciation in Highly Concentrated Alkaline Silicate

Comment on “Structure-Directing Role of Counterions in the Initial Stage of Zeolite Synthesis”. Claire E. White , John L. Provis. The Journal of P...
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Ind. Eng. Chem. Res. 2005, 44, 8899-8908

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Modeling Speciation in Highly Concentrated Alkaline Silicate Solutions John L. Provis,† Peter Duxson,† Grant C. Lukey,† Frances Separovic,‡ Waltraud M. Kriven,§ and Jannie S. J. van Deventer*,† Department of Chemical and Biomolecular Engineering and School of Chemistry, The University of Melbourne, Victoria 3010, Australia, and Department of Materials Science and Engineering, The University of Illinois at UrbanasChampaign, Urbana Illinois 61801

A model describing the distribution of silicate sites in concentrated alkali metal silicate solutions used in the synthesis of geopolymeric gels is presented. The model is based on a free energy minimization algorithm, using free energy of formation data obtained from the literature. A simplified form of the Pitzer method (Pitzer, K. S. J. Phys. Chem. 1973, 77, 26) is used to calculate activity coefficients, with interaction parameters calculated from known values for ions of similar size and charge type. Ion pairing effects are incorporated into the model formulation by a simple approximation, whereby larger cyclic or cagelike ions form strong ion pairs with dissolved alkali metal cations, and smaller monomeric (Q0) or end-group (Q1) sites pair less strongly with the cations. The model is able to describe accurately the speciation data obtained from a systematic 29Si NMR investigation of sodium, potassium, and mixed (1:1) sodium/potassium silicate solutions. The model is also tested against a large data set from the literature on sodium silicate solutions with a wide range of compositions. The model provides understanding of the speciation of silicate solutions and a basis for further understanding and modeling of the geopolymerization process. Introduction It has long been recognized that the observed physicochemical and spectroscopic properties of alkaline silicate solutions may only be explained by the presence of a variety of monomeric and small polymeric species.1-3 The nature and relative abundances of the different possible species are believed to be of particular importance in analysis of the mechanisms of geochemical and hydrothermal processes involved in mineral weathering and dissolution4 and synthesis of zeolites,5 sol-gel derived glasses or ceramics,6 and silicate or aluminosilicate binders such as geopolymers.7 In addition, gelation and condensation of silicates and aluminosilicates is poorly understood from a mechanistic standpoint, which causes difficulties in the processing of a variety of alkaline radioactive waste streams.8,9 The lability of the anionic silicate species present in alkaline solution means that the structures observed in solution are unlikely to be fully representative of the solid phases formed upon solidification.5,10 However, a fully quantitative description of any of these solidification processes can only be developed by use of a model based upon an understanding of the speciation equilibrium in the solution from which the solid phases form. Furthermore, from the point of view of geopolymer research,11,12 a reaction mechanism must be able to incorporate the effects of impurities and ionic contaminants that are present in both the alkali silicate solutions, which may be obtained from waste streams of other industrial processes, and the solid aluminosilicate sources, such as fly ash and blast furnace slag. * To whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemical and Biomolecular Engineering, The University of Melbourne. ‡ School of Chemistry, The University of Melbourne. § The University of Illinois at UrbanasChampaign.

Various experimental techniques have been used in an attempt to determine the structures and distribution of silicate species in aqueous solution, including potentiometry,2 SAXS,13 tetramethylsilylation/chromatography,14 and FTIR.15 However, the method that is best able to provide simultaneous identification and quantification of all the species present in highly concentrated alkaline silicate solutions is 29Si NMR.3,16-19 At least 25 distinct silicate structures have been identified by use of NMR spectroscopic techniques, including isotopic enrichment of both 29Si 20 and 17O 21 nuclei, twodimensional22 and Si-Si decoupling experiments.16 Although some of the 29Si NMR spectral peak assignments remain uncertain,23,24 this does not affect the precise quantification of the composition of these solutions. Previous attempts at modeling the speciation in alkaline silicate solutions have employed an equilibrium-based description of the system. This approach was originally introduced by Lagerstro¨m almost 50 years ago2 and has been revised and extended since that time.6,17,25,26 However, there are two primary difficulties in the application of an equilibrium-based model of this type to describe silicate speciation in an alkaline solution. The first is that the implementation of such a model usually involves the assumption of ideality, i.e., setting all activity coefficients to unity. The second is that in complex speciation problems where a multiplicity of species are present, equilibrium constants must be generated for each species with respect to one or more of the other species present in the system, which is often far from a simple undertaking. The assumption that all activity coefficients are equal to unity is inappropriate for the highly concentrated solutions of interest here. This must therefore be overcome by the use of an appropriate formulation for calculating activity coefficients if truly representative

10.1021/ie050700i CCC: $30.25 © 2005 American Chemical Society Published on Web 10/14/2005

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equilibrium constants are to be calculated. The inherent difficulties are typified by the results of Svensson et al.,17 whose calculated set of equilibrium constants varied strongly with the solution ionic strength. However, Felmy et al.8 implemented the Pitzer model27 to calculate activity coefficients and overcome this difficulty, producing a model valid for relatively dilute ([SiO2] < 0.1 M) alkali silicate solutions. The equilibrium constants calculated with use of the Pitzer model differ by several orders of magnitude from those of Svensson et al.,17 Sjo¨berg et al.,25 and Caullet and Guth,26 who assumed unity activity coefficients. Clearly, a more accurate activity coefficient treatment is required for a better description of silicate speciation equilibria. Implementation of an equilibrium constant-based model requires that the equilibrium constants are of necessity written for the formation of particular selected species and describe their relative abundance with respect to other species present in the system. This requirement represents a second major difficulty, which is inherent in this modeling approach.28 The selection of a subset of species from all known silicate species is required for use in calculations, and a set of equations is developed to describe their formation from other species present. In alkaline silicate systems, these reactions have traditionally been written to represent formation of deprotonated polynuclear species from Si(OH)4 by condensation polymerization of the neutral monomer with expulsion of protons. This is a convenient way of representing these reactions and provides a basis from which equilibria may be computed. However, the actual reaction mechanisms are expected to differ significantly from these idealized representations. Furthermore, the quantities of Si(OH)4 and H+ actually present in a concentrated alkaline silicate solution will often be small or negligible, particularly at low SiO2/ M2O (M: alkali metal) ratios. This can cause significant computational difficulties in evaluation of these equilibria, because the system composition must be determined using a very small step size in any iterative procedure if accuracy and non-negative values are to be assured. Caullet and Guth26 noted that the calculated parameter values are strongly dependent on the experimental determination of the level of monomeric silicate present, and this cannot always be determined with high accuracy. In their development of an equilibriumbased model, Busey and Mesmer4 used equations written in terms of Si(OH)4 and OH-, in conjunction with the Brønsted-Guggenheim activity coefficient formulation, to describe potentiometric data showing formation of polynuclear silicate species. However, their chosen subset of species is not sufficient to fully describe the range of silicate site coordinations observable by NMR. The difficulties associated with developing a representative set of equilibrium relationships within a complex reaction system led White et al.28 to suggest an alternative formulation of the equilibrium conditions based on a free energy minimization approach. This has been shown29 to be mathematically equivalent to the equilibrium-based formulation but is more convenient to apply to a complex mixture and involves fewer inherent assumptions regarding reaction pathways. An implementation of this approach based on a modified version of the SOLGASMIX code30 was used by Weber and Hunt9 to describe speciation in the system NaOHNaNO3-SiO2-H2O. However, data obtained at rela-

tively low silica concentrations were used as well as selected results from the literature, and, therefore, a systematic set of values was lacking at high concentrations. Furthermore, as will be discussed in more detail below, the implementation of the Pitzer model suffered from some difficulties in parameter estimation. The primary aim of the current work is to develop a model for the speciation of silicates in the alkaline silicate solutions used in the synthesis of aluminosilicate binders, known as ‘geopolymers’31-34 or ‘inorganic polymer glasses’.35 These activating solutions generally contain a high level of NaOH and/or KOH with varying amounts of dissolved silica (0-10 molal, depending on desired binder properties), which plays a significant role in controlling the setting rate and product characteristics. To develop a more accurate model for the speciation of silicates over the entire compositional range of interest in geopolymerization, a systematic set of quantitative 29Si NMR data spanning the full range of possible activating solution compositions has been obtained. Geopolymeric binders are formed at ambient or slightly elevated temperature by reaction of a solid aluminosilicate source with alkaline silicate solutions of composition H2O/M2O ∼ 11 and SiO2/M2O ∼ 0-2, where M is usually Na and/or K. Therefore, this investigation has focused on the description of silicate speciation around this compositional range in the presence of various alkali cations at 25 °C. This temperature enables comparison of the model with quantitative speciation data that have previously been published for a wide variety of solution compositions in addition to the quantitative 29Si NMR data presented here. The effects of different alkali cations on silicate speciation have been investigated experimentally36-38 but not modeled. However, different cations and cation mixtures are commonly used in geopolymer synthesis and accordingly are investigated here. The approach adopted in this investigation provides a framework by which the effects of different cations on silicate speciation may be described by an ion pairing-based formulation. The issues associated with overcoming parameter estimation problems are explored, and a simple method is proposed by which meaningful values of the Pitzer model parameters may be obtained. Furthermore, in adopting a Pitzer-type implementation, the possibility exists, in the future, to couple a description of alkali silicate solutions with other ionic species, such as aluminates and impurities. This will allow the effect of ionic species on silicate speciation to be explored, which is of great importance in developing a mechanistic understanding of geopolymerization and other alkali aluminosilicate syntheses utilizing impure feedstocks. Experimental Section Sodium, potassium, and mixed (1:1) sodium/potassium silicate solutions with composition SiO2/M2O ) R (0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, and 2.0) and H2O/ M2O ) 11 were prepared by dissolving appropriate quantities of amorphous silica (Cabosil M5, 99.8% SiO2) in alkali metal hydroxide solutions of the required concentration until clear. Hydroxide solutions were prepared by dissolution of NaOH pellets (Merck, 99.5%) and/or KOH pellets (Merck, >85%, remainder primarily H2O) in a mixture of Milli-Q and deuterated water (Aldrich, 99.99%) to provide solutions with an overall D2O enrichment of 40% of all water. Solutions were stored for a minimum of 24 h prior to use to allow

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equilibration. All containers were kept sealed wherever possible to minimize contamination by atmospheric carbonation. 29Si NMR spectra for solutions with R ) 0.5, 1.0, 1.5, and 2.0 were obtained at a Larmor frequency of 119.147 MHz with a Varian (Palo Alto, CA) Inova 600 NMR spectrometer (14.1 T). Spectra were collected using a 10 mm Doty (Columbia, SC) broadband probe. Between 128 and 256 transients were acquired using a single 70° pulse of about 8 µs and recycle delays of typically 20 s to ensure full relaxation of all species. The spectra of all other compositions were collected using a Varian (Palo Alto, CA) UnityPlus 400 NMR spectrometer (9.4 T) at 79.412 MHz using a 5 mm broadband probe. Between 2048 and 4096 transients were acquired using a single 90° pulse of about 10 µs and 20 s recycle delay. This pulse sequence results in NMR spectra that are quantitative with respect to the concentration of 29Si in different environments. The spectral quantification of high and low concentration solutions was measured on both NMR spectrometers using different field strengths to ensure field-independent analysis, and the results were found to be consistent. All spectra were referenced to monomeric silicate, Si(OH)4.

therefore have a negligible effect on the free energy minimization procedure. The Pitzer model formulation used in the current work for anionic species is given by eqs 2-5.27 Nc

ln γi ) zi2F + 2

(2)

Here, mj is the molality of species I, Bci is the second virial coefficient term describing interactions between cation c and anion i, and λj,i is a parameter representing the short-range interaction between neutral species j and anion i. The dummy summation index c represents a sum over all Nc different alkali metal cations present. The term F is a combination of a Debye-Hu¨ckel term and terms incorporating the dependence of the second virial coefficients on ionic strength, as given by eq 3

F ) -Aφ

[

xI

1 + 1.2xI

+

ln(1 + 1.2xI) 0.6

]

+

Nc N+K

∑∑

mcmaB′ca (3)

c)1a)N+1

The free energy minimization approach for determination of equilibria is based on solving the constrained optimization problem presented in eq 1.29 N+K m

mjλj,i ∑ j)0

c)1

Outline of the Model

min G* )

∑

N

mcBci + 2

(

µi0

mi + ln γimi ∑ RT i)0

)

(1a)

where Aφ is a lumped combination of physical and solvent parameters equal to 0.392 for water at 25 °C; I is the solution ionic strength, and the sum over a includes all anionic (i.e. silicate + hydroxide) species. The second virial coefficient terms B and their ionic strength derivatives B′ follow the functional form given by Pitzer.39

N+K-1

subject to:

∑ i)0

mi ) mSi,total

(1b)

N+K

∑

zimi ) mM+,total

(1c)

i)N

mi g 0, i ) 0, 1, ..., N + K

(1d)

Here m is the composition vector, with m0, m1, ..., mN being the molalities of neutral silicate species present, mN+1, mN+2, ..., mN+K-1 the molalities of the K - 1 distinct anionic silicate species under consideration, and mN+K the molality of free OH-. G* is the total reduced Gibbs energy of the system ()G/RT), µi0 is the standard Gibbs energy of formation of species i, and zi is the magnitude of the charge on anionic species i. Constraint 1b is a mass balance constraint, (1c) ensures electroneutrality, and (1d) non-negativity of all concentrations. It should be noted that in the systems of interest, at pH g 11, the concentration of free H+ is not significant and so may be assumed negligible in determining electroneutrality. Activity coefficients of anionic and neutral species, γi, are calculated by a simplified form of the Pitzer model. The Pitzer model provides a semiempirical framework for the calculation of activity coefficients of electrolytes from dilute through to high concentrations. The activities of the alkali cations and the solvent are not calculated explicitly, as they are only weakly dependent on the exact speciation of the dissolved silicate and

β(1) MX [1 - (1 + 2xI) exp(-2xI)] 2I

(4a)

[-1 + (1 + 2xI + 2I) exp(-2xI)]

(4b)

BMX ) β(0) MX + B′MX )

β(1) MX 2I2

The full formulation of the Pitzer model for mixed electrolyte systems involves parameters describing third virial coefficients (CMX), pairwise interactions between species of like charge (θij), and interactions of up to 3 different ions (ψijk). The θ and ψ parameters are often neglected for mixtures only involving mono- and divalent electrolytes, due to the relatively weak interactions between like-charged species in these systems. For this reason θ and ψ will not be included here.27 Also, it has been shown that the parameters β(1) and C are strongly correlated40 and that the accuracy of the model is not significantly diminished by omission of the C parameter provided that correctly determined values of β(0) and β(1) are used.41 Therefore, a simplified form of the model requiring only β(0) and β(1) parameters is used in this investigation. This form of the Pitzer model has been shown41 to be approximately equivalent under certain circumstances to the SIT model,42 another widely used empirical approach for prediction of activity coefficients. The SIT model is discussed further in the section entitled ‘Determination of Pitzer Ion Interaction Parameters’. The Pitzer activity coefficient expression for neutral species j is given by eq 5.27,43

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Ind. Eng. Chem. Res., Vol. 44, No. 23, 2005 Nc

ln γj ) 2(

Table 1. Species Modeled in the Current Investigationa

N+K

∑mcλj,c + a)N+1 ∑ maλj,a)

(5)

coordination

c)1

Q0

neglected,27

Ionic strength dependence of λ terms is as are neutral-neutral interactions. The system of eqs 1-5 was solved by a combination steepest descent/Monte Carlo method using Microsoft Visual C++ 6.0. Constraints 1b-d were incorporated into the analysis by a penalty function method, with the penalty function chosen so as to ensure continuous first derivatives throughout the domain of interest. An equilibrium point was considered to have been reached if every first partial derivative of the objective function changed sign within an interval of 2 × 10-4 molal centered on the current best point. This slightly nonstandard stopping criterion (stationary point determination) was required due to the uneven ‘energy surface’ introduced by the penalty function method. Accurate and reproducible results were obtained by initializing the minimization from a sufficiently close-to-feasible initial guess, which was achieved by simply using the experimental data to distribute the silicon present between the possible connectivity types with some consideration of the charge states expected at different SiO2/Na2O ratiosi.e., initializing the model with primarily highly charged species at low SiO2/Na2O and vice versa. Applying the charge balance constraint by the penalty function method rather than as a strict constraint also accounted for any possible formation of M+OH- ion pairs. This approach was found to be satisfactory for the strongly basic systems of interest here, but revision will be required if relatively weaker bases are to be treated accurately by this model. Description of Different Silicate Sites Implementation of an equilibrium constant-based model for silicate speciation requires the selection of a subset of the known silicate species for inclusion in the model. However, the free energy minimization model removes this requirement and allows treatment of each site according to its connectivity type rather than specifying how every single site is located in each species.9 The definition of a ‘species’ used in this investigation is designed to remove the difficulties in calculation of the effective ionic strength of systems containing large multicharged species.8 Rather than a description based on oligomeric silicate species, the ionic strength and connectivity distribution are calculated by considering each silicon site as an individual solvated charged species. Hence the calculated ionic strength, with z2 dependence on the charge of dissolved species, is not skewed unreasonably by the presence of large multinuclear species with multiple distributed charged sites. The connectivities and free energies of formation of silicon sites for solutions analyzed in this investigation are given in Table 1. Sites are represented by the Q notation of Engelhardt et al.,3 where a Qn site is a tetrahedral silicate center connected to n bridging oxygens and (4-n) nonbridging oxygens. The free energies of formation presented in Table 1 were calculated from literature data as noted and represent the free energy of formation per silicon atom of small symmetric silicate anions containing only the connectivity site of interest. Where data were not available for particular connectivity or deprotonation states, values were cal-

Q1

Q2c Q2 Q3c Q3 OH-

z

representative species

µ0/RT

ref

0 1 2 3 0 1 2 3 0 1 2 0 1 2 0 1 0 1 1

Si(OH)4 Si(OH)3OSi(OH)2O22Si(OH)O331/ (Si (OH) O) 2 2 6 1/ (Si (OH) O 2-) 2 2 4 3 1/ (Si (OH) O 4-) 2 2 2 5 1/ (Si O 6-) 2 2 7 1/ (Si (OH) O ) 3 3 6 3 1/ (Si (OH) O 3-) 3 3 3 6 1/ (Si O 6-) 3 3 9 1/ (Si (OH) O ) 4 4 8 4 1/ (Si (OH) O 4-) 4 4 4 8 1/ (Si O 8-) 4 4 12 1/ (Si (OH) O ) 6 6 6 9 1/ (Si O 6-) 6 6 15 1/ (Si (OH) O ) 8 8 8 12 1/ (Si O 8-) 8 8 20 OH-

-527.55 -504.96 -474.30 -437.08 -480.54 -457.86 -427.35 -391.77 -434.20 -409.94 -379.70 -435.69 -411.21 -380.64 -408.84 -383.93 -437.26 -412.17 -63.49

48 48 48 6,48 6,48 48 26,48 26,48 6,48 48 6,48 26,48 48 26,48 8,26,48,49 8,26,48,49 7,26,48,49 7,48,49 49

a

Qn represents a tetrahedral silicate center connected to n bridging and (4-n) nonbridging oxygens.

culated using published equilibrium constants for formation and deprotonation reactions. Sites present as part of three-membered rings are included separately from acyclic or larger cyclic species, as they are able to be distinguished from other sites by NMR spectroscopy due to the strained nature of these rings.3 These sites are denoted Qnc , where n ) 2 or 3. It is well-known that a wide range of silicate species, not restricted to the fully symmetric representative species presented in Table 1, are formed in alkali silicate solutions.23 However, it is not currently possible to accurately predict individual free energies of formation for the individual connectivity types within every single possible structure, so the sites within small symmetric species are taken to be representative of the same connectivity types in other species. Table 1 presents a full array of site types in silicate solutions, with all possible deprotonation states of all connectivities except the z ) 4 monomer considered. The concentration of this fully deprotonated monomer will be negligible in the solutions considered in this study, since pKa,4 of silicic acid is believed to be approximately 18.8.6 Incorporation into the model of all sites listed in Table 1 is required for an accurate description of experimental data over the entire composition range of interest. Smaller arrays of possible site types, as used in all previous quantitative descriptions of silicate speciation equilibria, are able to describe limited compositional ranges. However, the use of a comprehensive array of sites allows accurate description of systems covering a much larger range of concentrations and compositions, while introducing few additional complications into the model formulation used here. The focus of this study was to model the distribution of dissolved species in alkali metal silicate solutions. Therefore, the presence of Q4 silicate sites (colloidal silica) in these solutions was not incorporated into the model. The degree of formation of colloidal silica, which is observed primarily in very high SiO2/M2O ratio solutions, has been shown to be strongly and sometimes unpredictably dependent on the silica source.44,45 The presence of Q4 sites in dissolved (as opposed to colloidal) species has only been observed in tetraalkylammonium silicate solutions, in very small quantities,46,47 and so their inclusion is not required for an accurate description of the alkali metal silicate solutions in the current

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work. When applying the model to literature data for systems reported to contain Q4 sites, these sites were discounted in analysis, and the calculated compositions are based on dissolved species only. Inclusion of Ion Pairing Effects Ion pairing between alkali metal cations and deprotonated (anionic) silicate species has been observed to take place in alkali silicate solutions.38,50,51 However, the study of these interactions in concentrated alkali silicate solutions has to date largely been motivated by the possible utilization of templating properties in zeolite synthesis.38,50 Cagelike silicate anions are known to form pairs with certain cations.38,50 Association between alkali cations and monomeric silicate anions has also been noted but is believed to be relatively weak compared to the pairing involving larger anions.52 Therefore, to avoid the need to introduce an entire set of empirical parameters into the model for description of ion pairing effects, a simple treatment was developed to account for variation in pairing strength with anion size. Each anionic site in a cyclic or cagelike species was assumed to pair with a number of cations equal to the charge on the site, while Q0 and Q1 sites formed ion pairs with half this number of cations. This treatment resulted in a simple and accurate prediction of speciation in the alkali metal silicate systems of interest here. The effects of the inclusion of ion pairing effects on speciation predictions were relatively minor, only affecting calculated speciation predictions by up to 2% in most cases. However, the purpose of the inclusion of these effects is to allow simple model extension to more complex systems, in particular tetraalkylammonium silicate solutions, in which cation-selective templating effects are highly significant.53,54 The model framework provides scope for variation in association behavior in the presence of different cations, but this was found not to be required for description of the sodium and potassium systems reported here. However, accounting for the association behavior of different cations may become important in determining ion pairing effects when dealing with cations with large differences in properties as has been observed previously.38,50 The effect of ion pairing on the properties of each anionic silicate species is assumed to be purely energetic. Sanchez and McCormick55 calculated the change in energy associated with replacement of H2O by a deprotonated silanol group in the first coordination shell of different alkali cations, finding values of -42.1 kcal/ mol for Na and -45.4 kcal/mol for K.55 In the mixed Na/K solutions, Na+ and K+ were assumed to participate equally in ion pairing. These energies were incorporated into the µ0/RT term for anions participating in ion pairing in all calculations, thereby stabilizing the ion-paired sites relative to other nonpaired silicate sites. For every cation associated with a particular connectivity type, the replacement of one water molecule in the solvation shell of the cation by Si-O- causes the µ0/RT value of that silicate site to decrease by the amount noted above. All ions were treated as independent for the purposes of activity coefficient calculation via the Pitzer model. Determination of Pitzer Ion Interaction Parameters There are few published Pitzer ion interaction parameters available for use in the description of alkali

metal silicate systems. Parameters appropriate for the description of the interactions of monomeric56,57 or neutral43,58 silicate species with alkali metal cations have been presented. Rather than the site-based approach used in this work, Felmy et al.8 developed a set of parameters based on the description of entire silicate anions, which therefore are not directly transferable to this investigation. Weber and Hunt9 attempted to fit a full set of Pitzer parameters, including third virial coefficient terms and anion-anion interaction parameters, using a site-based ionic strength calculation approach similar to that used here. However, these authors treated the Gibbs energy of formation for each silicate site type, µ0, as an adjustable parameter, and obtained a set of values significantly different to those calculated from literature data in the current investigation. The calculated Pitzer parameter values9 differ significantly from those generally applicable to interactions between ions of similar size and charge type.27,41 In particular, the large negative values of the β(1) parameter calculated by Weber and Hunt are very different to the small positive values shown by Plyasunov et al.41 to be generally applicable to 1-1 and 1-2 charge-type interactions. The magnitudes of the mixing (anion-anion interaction) parameters calculated by Weber and Hunt9 are also larger by a factor of approximately 100 than those appearing elsewhere in the literature27 for anions of comparable charge type and size. The approach of Weber and Hunt9 and that of the current work require further examination in order to reveal critical differences, in particular the parameter estimation procedure. The parameters calculated by Weber and Hunt9 were used in calculations with the current model formulation, using the same subset of possible sites as was chosen by those authors. The activity coefficients calculated from the Pitzer equations based on the parameters of Weber and Hunt9 were in many cases either too large or small to be plausible. The sensitivity of the actual model output to these parameters is in many cases very low, so it is possible to obtain close agreement with experimental results from erroneous Pitzer parameters by using different values of µ0. However, comparison of the calculated activity coefficients using the parameter set of Weber and Hunt9 with those calculated using the parameters obtained in this investigation reveals significant differences, and the use of µ0 values different to those that are generally accepted to be correct is considered undesirable here. Therefore, the µ0 and Pitzer parameter values calculated by Weber and Hunt9 were not used in the current work. The complications involved with fitting Pitzer cationanion interaction parameters based on speciation data, even for simple systems, have been discussed in detail by Plyasunov et al.41 The use of a single representative β(1) value for reactions of each charge type was found to be sufficiently accurate under most circumstances.41 Plyasunov et al.41 also developed a method for converting tabulated  parameters from the SIT model to Pitzer β(0) values. This method is applied here for the calculation of Pitzer β(0) parameters in preference to attempting to fit directly to experimental data. However, tabulated  values for silicate species are not themselves readily available and so must be estimated based on known values for oxoanions of similar size and charge type. Grenthe et al.48 suggest the use of phosphate species as a model for monomeric silicates with different

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Table 2. Pitzer Ion-Ion Interaction Parameters Used in Modeling Silicon Speciationa coordination Q0 Q1 Q2c Q2 Q3c Q3 OH-

z

β(0) (Na+)

β(0) (K+)

β(1)

1 2 3 1 2 3 1 2 1 2 1 1 1

0.162 0.369 0.700 0.162 0.369 0.700 0.0465 0.357 0.0465 0.357 0.0235 0.0235 -0.0111

0.208 0.327 0.470 0.208 0.327 0.470 0.0465 0.380 0.0465 0.380 0.0235 0.0235 -0.0571

0.34 1.56 4.29 0.34 1.56 4.29 0.34 1.56 0.34 1.56 0.34 0.34 0.34

a Values of β(0) were calculated from  parameters of Ciavatta42 by the method of Plyasunov et al.,41 and values of β(1) are those recommended by Plyasunov et al.41 for each charge type.

Table 3. Pitzer Ion-Neutral Interaction Parametersa

a

k

λneutral,k

Na+ K+ z ) 1 silicate site z ) 2 silicate site z ) 3 silicate site

0.09250 0.03224 -0.0094 -0.1396 -0.2

Figure 1. 29Si NMR spectra of potassium silicate solutions with H2O/M2O ) 11 and SiO2/K2O ) (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0.

was determined based on extrapolation from the other interaction parameters. However, the actual value of this parameter has little effect on the modeling results given the low levels of uncharged silicate sites that would be present in solutions that are sufficiently alkaline to produce triply deprotonated sites.

From ref 58.

degrees of deprotonation, while Reardon57 prefers the use of sulfates. The approach adopted here differs slightly, in that each silicate species is compared to an oxoanion with the same number of sites available for deprotonation. So, parameters for charged Q0 and Q1 sites were calculated based on H2PO4-, HPO42-, and PO43-, according to the degree of deprotonation. Parameters for Q2 and Q2c sites were taken from HSO4- and SO42- and those for Q3 and Q3c from NO3-. The  values of Ciavatta42 (denoted b in the original work and calculated directly from isopiestic measurements) were used throughout, and β(0) values were calculated from these using the equations developed by Plyasunov et al.41 Where a parameter was available for the interaction of an anion with Na+ but not with K+, the Na+ parameter was assumed to be a reasonable estimate of the K+ value, as suggested by inspection of the parameter set of Pitzer.27 The parameters for ion-ion interactions used in the present investigation are presented in Table 2. Notably, the parameters used for M+-OH- interactions are not equal to those found explicitly by other authors to be optimal for describing these interactions.27,40 These small differences had little effect on the overall model output, and by adopting these parameters a more consistent parameter set could be maintained. A consistent parameter set that best describes the global system is therefore provided, rather than the most accurate possible description of each interaction. The parameter values used to describe the interactions between ions and neutral silicate sites are those of Azaroual et al.58 for interactions involving the neutral SiO2(aq) species. The ion-neutral interaction parameters used in the model are presented in Table 3. The same parameter values are used for all neutral silicate sites regardless of coordination, with the values for anion-neutral interactions based on those published for oxoanions of similar charge, NO3- for z ) 1 sites and SO42- for z ) 2 sites. An estimated z ) 3 parameter

Results and Discussion 29Si

NMR spectra for a selection of potassium silicate solutions, with H2O/K2O ) 11, are shown in Figure 1. The designation of the more than 20 different silicate oligomers that have been identified by 29Si NMR is described elsewhere.23 The regions of the spectra relating to each of the different types of Q-centers are indicated in Figure 1. Subscript c indicates that the sites are in a three-membered ring, the resonances being observed separately from chains or larger rings due to the deshielding effects. As the concentration of silicon increases, the number of larger oligomers increases. Integration of the peak areas in each spectrum thus directly provides speciation data for comparison to model predictions. Comparisons of the model predictions to the experimental speciation data for systematic sets of sodium, potassium, and mixed (50:50) sodium/potassium silicate solutions are shown in Figures 2-4. The model output data were calculated as the sum over all different protonated and deprotonated sites for each coordination type of Si. Summation over all protonated and deprotonated sites is required since the degree of deprotonation cannot readily be determined due to insufficient spectral resolution at even the highest field NMR instruments available. The model fits the experimental data reasonably well over the entire compositional range of interest (Figures 2-4). In general, regardless of cation, the model underestimates the Q0 site in the most highly alkaline (lowest silica content) systems and Q1 in the least alkaline (highest silica content) systems. The most significant differences are in the low-silica region, where the model predicts significantly more Q1 and less Q2c than observed experimentally. The reasons for these discrepancies at very low silica content are not entirely clear and may be due to difficulties in the numerical solution procedure. However, the model generally predicts the experimental observations with a high degree of accuracy for SiO2/M2O g 0.75. This is particularly notable considering that the parameter set used in model

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Figure 2. Comparison of model calculations (lines) and quantitative Na2O ) 11.

29Si

Figure 3. Comparison of model calculations (lines) and quantitative H2O/K2O ) 11.

NMR data (symbols) for sodium silicate solutions with H2O/

29Si

NMR data (symbols) for potassium silicate solutions with

Figure 4. Comparison of model calculations (lines) and quantitative 29Si NMR data (symbols) for mixed (1:1) sodium/potassium silicate solutions with H2O/M2O ) 11.

development was based on literature values, rather than attempting to fit the model directly to the data set. The experimental results show that the amount of each connectivity type in the mixed Na/K system generally fell between the values for the pure Na and pure K systems. The simplified Pitzer equations used here gave purely additive effects when the two cations were mixed, with neither cation-cation interactions nor selectivity in the treatment of ion pairing being taken into account. Despite these simplifications, however, the

model is able to reproduce the observed trends in speciation with different cations. Speciation in alkali metal silicate solutions has been studied experimentally over a wide range of concentrations and compositions. In particular, NMR studies of sodium silicate solutions have produced a set of quantitative data17,19,45,59-61 which may be used to validate the model proposed here. These data cover a range of silica concentrations from 0.40 to 16.44 molal and SiO2/ Na2O ratios from 0.5 to 3.88. In modeling these data

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sets, Q4 (colloidal) silica sites were neglected, as described earlier, and the total dissolved Si concentrations used as model input were adjusted to reflect this. The model fits these data with a maximum error margin of better than (10% in total composition. Spectral resolution often did not separate Q2 and Q3c centers in early NMR studies, where lower field strengths reduced resolution and signal-to-noise ratios. In those instances the model results for the two sites were summed and are presented in Figure 5 as a single category denoted Q2 + Q3c . The model overpredicts the proportions of Q0 and Q2c sites in several cases in Figure 5, in particular where these species are present only as minor system components. This is different to the trend observed in Figures 2-4, where the Q2c site is underpredicted in the lowsilica region and accurately described otherwise. Some of the differences between the literature data and the experimental results obtained in this investigation may be due to the improvements in NMR technology and field strengths over the past two decades, allowing acquisition of spectra with better spectral resolution and higher signal-to-noise ratios. More accurate quantification of the smaller spectral peaks, which are often barely distinguishable from the noise present in spectra obtained at low field strengths, is now possible. Therefore, the fact that the model does not exactly fit low field NMR data is not cause for significant concern. Largely because of the overprediction of the Q2c site, most other sites were slightly underpredicted by the model (Figure 5). However, the model was considered to be adequate so that revision of the model parameters solely on this basis was not justified, particularly considering the uncertainties in the data as noted earlier. Difficulties in prediction of the Q0 and Q2c connectivity types when present in small quantities were also encountered by Weber and Hunt.9 Geopolymerization is a complex process, which for the purposes of this discussion may be simplified by description as simultaneous dissolution, solution phase structural reorganization, polymerization, and hardening. This model serves as a tool in the understanding of alkali silicate solution speciation prior to geopolymerization and may be extended toward understanding the effects of ion pairing interactions and incorporation into more extensive modeling of concentrated alkali aluminosilicate solutions. Furthermore, experimental determination of pH in highly concentrated alkali metal silicate solutions is a nontrivial task and prone to significant uncertainties. Therefore, the ability to predict pH accurately from a model would provide new and valuable data. However, the greatest drawback of the free energy minimization modeling approach used here when compared to the more common equilibrium-based formulations is that prediction of pH by this method is prone to large errors, particularly in high SiO2/Na2O ratio systems. Because OH- is treated as a system component in the modeling process rather than deriving all other calculations from equilibrium expressions involving either OH- or H+, the concentration of OHis generally not calculated to a degree of accuracy sufficient for meaningful pH calculations. In high SiO2/ Na2O ratio systems, where the pH is lowest, a constant absolute error in OH- concentration is several orders of magnitude more significant in terms of the pH scale than at a pH closer to 14, typical of low SiO2/Na2O ratios. Furthermore, there are little available data with

Figure 5. Comparison of model calculations and sodium silicate speciation data obtained from refs 17, 19, 45, and 59-61 for (a) Q0 and Q1 sites, (b) Q2c and Q2 sites, and (c) Q3c and Q3 sites as well as the summed Q2 + Q3c category where these sites were not distinguished in the original experimental work. The solid diagonal line represents a perfect model fit, and the light diagonal lines represent (10% error bounds.

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which to compare pH predictions generated by the model and therefore such predictions have not been attempted. It must be noted that the model of Weber and Hunt9 does, by use of the SOLGASMIX energy minimization algorithm, provide relatively accurate pH predictions. However, the issues relating to parameter values in the work of Weber and Hunt, as previously discussed, do raise some questions regarding the validity of these predictions. Conclusion A model for description of speciation over a wide compositional range of concentrated alkali metal silicate solutions has been presented. The model is based on free energy minimization, with activity coefficients calculated by the Pitzer method. Ion pairing plays an important role in determining the formation of different silicate species, with larger cyclic or cagelike ions forming stronger ion pairs with dissolved alkali metal cations. Model output satisfactorily described a data set obtained from a systematic 29Si NMR investigation of sodium, potassium, and mixed (1:1) sodium/potassium silicate solutions. The model also described data obtained from the literature for sodium silicate solutions varying in concentration by a factor of more than 40 and in SiO2/M2O ratio by a factor of almost 10. The exclusive use of parameters and free energies of formation obtained from the literature was found to satisfactorily reflect the behavior of these systems, removing the requirement for a parameter-fitting process, which previously has been observed to result in unphysical parameter values. The implementation of the Pitzer model for the determination of speciation of alkali silicate systems is an important step toward a greater understanding of more complex systems incorporating aluminum and trace impurities such as calcium, magnesium, and iron. Ultimately, this type of model may lay a foundation for the building of a more complete reaction kinetic model of alkali aluminosilicate gel synthesis. The current work presents a methodology for determining appropriate and reasonable Pitzer parameters, valid for describing both single- and mixed-cation alkali metal silicate solutions over a wide range of compositions. Furthermore, the incorporation into the model of ion-pairing effects demonstrates that description of these systems can be used to determine the importance of ionic interactions, which will become more important in understanding the effects of aluminum and other ionic contaminants on silicate speciation. Acknowledgment Financial support is gratefully acknowledged from the Australian Research Council (ARC) and the Particulate Fluids Processing Centre (PFPC), a Special Research Centre of the Australian Research Council. Part of this work was carried out at the University of Illinois at UrbanasChampaign, supported by a University of Melbourne Postgraduate Overseas Research Experience Scholarship awarded to P.D. and by an AustralianAmerican Fulbright Postgraduate Scholarship awarded to J.L.P.. The authors also thank Dr. Paul Molitor, School of Chemical Sciences, The University of Illinois, for assistance in acquisition of some of the NMR spectra. Supporting Information Available: Comparisons of model predictions and activity coefficients to those

calculated using the parameter set of Weber and Hunt9 as well as full tables of experimental speciation data. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Vail, J. G. Soluble Silicates: Their Properties and Uses; Reinhold: New York, 1952; Vol. 1. (2) Lagerstro¨m, G. Equilibrium studies of polyanions. III. Silicate ions in NaClO4 medium. Acta Chem. Scand. 1959, 13, 722. (3) Engelhardt, G.; Zeigan, D.; Jancke, H.; Hoebbel, D.; Wieker, W. 29Si NMR Spectroscopy of Silicate Solutions. II. On the Dependence of Structure of Silicate Anions in Water Solutions from the Na:Si Ratio. Z. Anorg. Allg. Chem. 1975, 418, 17. (4) Busey, R. H.; Mesmer, R. E. Ionization equilibria of silicic acid and polysilicate formation in aqueous sodium chloride solutions to 300°C. Inorg. Chem. 1977, 16, 2444. (5) Knight, C. T. G. Are zeolite secondary building units really red herrings? Zeolites 1990, 10, 140. (6) Sˇ efcˇ´ık, J.; McCormick, A. V. Thermochemistry of aqueous silicate solution precursors to ceramics. AIChE J. 1997, 43, 2773. (7) Phair, J. W.; van Deventer, J. S. J.; Smith, J. D. Interaction of sodium silicate with zirconia and its consequences for polysialation. Colloid. Surf. A 2001, 182, 143. (8) Felmy, A. R.; Cho, H.; Rustad, J. R.; Mason, M. J. An aqueous thermodynamic model for polymerized silica species to high ionic strength. J. Solut. Chem. 2001, 30, 509. (9) Weber, C. F.; Hunt, R. D. Modeling alkaline silicate solutions at 25°C. Ind. Eng. Chem. Res. 2003, 42, 6970. (10) Knight, C. T. G.; Kinrade, S. D. Comment on “Identification of precursor species in the formation of MFI zeolite in the TPAOHTEOS-H2O system”. J. Phys. Chem. B 2002, 106, 3329. (11) Duxson, P.; Lukey, G. C.; Separovic, F.; van Deventer, J. S. J. The effect of alkali cations on the incorporation of aluminum in geopolymeric gels. Ind. Eng. Chem. Res. 2005, 44, 832. (12) Provis, J. L.; Lukey, G. C.; van Deventer, J. S. J. Do geopolymers actually contain nanocrystalline zeolites? - A reexamination of existing results. Chem. Mater. 2005, 17, 3075. (13) Gaboriaud, F.; Nonat, A.; Chaumont, D.; Craievich, A.; Hanquet, B. 29Si NMR and small-angle X-ray scattering studies of the effect of alkaline ions (Li+, Na+, and K+) in silico-alkaline sols. J. Phys. Chem. B 1999, 103, 2091. (14) Lentz, C. W. Silicate minerals as sources of trimethylsilyl silicates and silicate structure analysis of sodium silicate solutions. Inorg. Chem. 1964, 3, 574. (15) Couty, R.; Fernandez, L. Variations of 29Si NMR and Infrared Spectra between Colloid and Ionic Sodic Silica Solutions. C. R. Acad. Sci. Paris IIa 1995, 320, 823. (16) Harris, R. K.; Knight, C. T. G. Silicon-29 nuclear magnetic resonance studies of aqueous silicate solutions. Part 6. Secondorder patterns in potassium silicate solutions enriched with silicon29. J. Chem. Soc., Faraday Trans. II 1983, 79, 1539. (17) Svensson, I. L.; Sjo¨berg, S.; O ¨ hman, L. O. Polysilicate equilibria in concentrated sodium silicate solutions. J. Chem. Soc., Faraday Trans. I 1986, 82, 3635. (18) Kinrade, S. D.; Swaddle, T. W. Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria. Inorg. Chem. 1988, 27, 4253. (19) Bahlmann, E. K. F.; Harris, R. K.; Say, B. J. Method for the quantification of silicon-29 NMR spectra, developed for viscous silicate solutions. Magn. Reson. Chem. 1993, 31, 266. (20) Harris, R. K.; Jones, J.; Knight, C. T. G.; Pawson, D. Silicon-29 NMR studies of aqueous silicate solutions. Part II. Isotopic enrichment. J. Mol. Struct. 1980, 69, 95. (21) Knight, C. T. G.; Thompson, A. R.; Kunwar, A. C.; Gutowsky, H. S.; Oldfield, E.; Kirkpatrick, R. J. Oxygen-17 nuclear magnetic resonance spectroscopic studies of aqueous alkaline silicate solutions. J. Chem. Soc., Dalton Trans. 1989, 275. (22) Harris, R. K.; O’Connor, M. J.; Curzon, E. H.; Howarth, O. W. Two-dimensional silicon-29 studies of aqueous silicate solutions. J. Magn. Reson. 1984, 57, 115. (23) Swaddle, T. W.; Salerno, J.; Tregloan, P. A. Aqueous aluminates, silicates, and aluminosilicates. Chem. Soc. Rev. 1994, 23, 319.

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Received for review June 14, 2005 Revised manuscript received August 29, 2005 Accepted September 7, 2005 IE050700I