Aqueous Solubility Diagrams for Cementitious Waste Stabilization

Environ. Sci. Technol. 1996, 30, 2286-2293

Aqueous Solubility Diagrams for Cementitious Waste Stabilization Systems. 1. The C-S-H Solid-Solution System M. KERSTEN* Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH-8600 Du ¨ bendorf, Switzerland

The major component in cementitious waste solidification/stabilization (S/S) systems is an amorphous calcium silicate hydroxide hydrate phase (C-S-H) phase according to cement chemistry nomenclature), but the behavior of this gel phase in aqueous solution is not well understood. In this paper, a thermodynamic model is suggested for predicting aqueous solubility of C-S-H as a function of the Ca/ Si ratio based on a solid solution-aqueous solution (SSAS) subregular equilibrium model for a binary nonideal mixing of the end-member phases calcium hydroxide and calcium silicate, with known pK values and a miscibility gap at Ca/Si > 3. A maximum in Gibbs free energy of mixing (GM) of -3.2 kJ/mol is predicted to occur at a Ca/Si ratio of 1.5. Predicted Ca and Si solubility, pH, and solid Ca/Si values agree with experimental data on C-S-H solubility reported from the literature. The thermodynamic basis of this SSAS model is superior to those based on empirical Ksp values vs Ca/Si ratio relationships or on ideal solid solution models yet used in cement chemistry. It opens access to predicting the solubility of trace metals bound into the C-S-H host phase when the Ksp values and possible mixing gaps of the end-member phases are known.

Introduction Solidification/stabilization (S/S) is the process whereby hazardous materials are treated in a way to reduce their toxicity and to prevent dissolution of the toxic components and their release into the environment. Stabilization is generally defined as the process to chemically transform soluble contaminants into a less soluble form. Common S/S technologies utilize cementitious material to stabilize the hazardous components (1). The principal binding agent in ordinary Portland cement pastes (about 60% by weight) is an amorphous calcium silicate hydrogel (termed C-S-H in cement chemistry nomenclature) with a Ca/Si composition ratio varying roughly between 0.8 and 2.5. The C-S* Present address: Baltic Sea Research Institute, Marine Geology Section, Seestrasse 15, D-18119 Rostock, Germany; e-mail address: [email protected].

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H-H2O system has been the subject of research in the field of cementitious S/S technology for many years. Despite the importance of solubility data for any predictive evaluation of the stabilization effectivity, only a few attempts have been made to model the aqueous solubility of trace elements incorporated chemically in this gel material or at least the solubility of the host material itself. The major reason is the complex dissolution behavior of C-S-H. For those (minor) components that exhibit congruent dissolution (e.g., ettringite or hydrogarnet), their solubilities may be calculated simply from their solubility products and an aqueous thermodynamic model to characterize the aqueous phase composition, especially with respect to the extent of ion pairing and/or complexation with other ions in the alkaline solution (2, 3). The C-S-H-H2O system considered here is a threecomponent system, which may be taken to be CaO-SiO2H2O. According to Gibbs phase rule, a system containing three components in which a solid and a solution are at equilibrium at a fixed temperature and pressure has only one degree of freedom. Thus, when pairs of concentrations of the two dissolved components in the third phase (H2O) are plotted against each other, the result is a smooth curve (4). If the concentration of one dissolved component is changed, the concentration of the other must also change in a well-defined manner. If equilibria were established with samples of C-S-H having a variable composition (i.e., Ca/Si ratio), the concentration data would fall on a curve, but the shape of that curve would not necessarily imply a single value for the equilibrium constant. At a solid Ca/Si > 1, C-S-H dissolves incongruently in pure water, with aqueous Ca concentrations being much higher than those of Si. Moreover, the extent of the incongruent dissolution behavior of C-S-H is gradually increasing with the Ca/Si ratio of the solid phase. Lime-rich C-S-H (Ca/Si > 2) equilibrates with aqueous solutions of very high Ca/Si concentration ratios (>10 000), whereas low-lime C-S-H (Ca/Si e 1) produces solutions having Ca/Si ratios less than 1 (4). In spite of this nonstoichiometric dissolution behavior, a close inspection of the data published over a period of 50 years revealed that the concentration of Ca and Si in the aqueous phase must be guided by a thermodynamic equilibrium (4). Greenberg (5) was among the first to conclude from that behavior that C-S-H (with Ca/Si > 1) is essentially a solid solution of Ca(OH)2 in an imaginary low Ca/Si ratio calcium silicate component (e.g., CaH2SiO4), now a generally accepted compositional model (6). Two main approaches to model the complex dissolution behavior of C-S-H gels have been published in the last decade. The first approach proposed by Glasser et al. (7) is based on the assumption that the aqueous solubilities in the CaO-SiO2-H2O solid-solution system are recalculated to unique solubility products involving activities raised to fractional powers as a function of the Ca/Si ratio. This approach is widespread in applied chemistry but is not justified by thermodynamic principles. By virtue of the additivity of chemical potentials, which contain the logarithms of the activities of individual reactants in stoichiometric proportion, the stoichiometric coefficients appear as exponents in the mass action expression (i.e., the

S0013-936X(95)00681-X CCC: $12.00

 1996 American Chemical Society

solubility product). Integer coefficients are self-evident as long as one considers the formation of molecular compounds to which the law of mass action is applied. In the same way, arithmetric solutions of the electroneutrality condition in terms of fractional stoichiometric numbers, taken from applying conventional thermochemical formalism to the chemical composition of a mixed component, are also not a meaningful description of the saturation equilibrium. Consequently, nonfractional exponents should result for the solubility product of complex ionic components by virtue of the electroneutrality condition because charges are integers according to atomic theory. Moreover, a solubility product will give a meaningful description of the saturation equilibrium only when the composition of the solid phase remains invariant over a certain range of activity ratios in the aqueous phase, provided that thermodynamic equilibrium is indeed the governing aspect here. All these thermodynamic principles are violated by a “basic assumption” for the C-S-H-H2O system, where “the solid is considered to be a nonideal mixture of two congruently soluble components; each congruently soluble component is associated with a variable solubility product, which depends on the particular C/S ratio of the solid” (8). This model is otherwise appealing because it is possible to use the nonconstant solubility product as a fitting parameter to describe experimental data on equilibria in the C-S-HH2O system and also useful for speciation modeling purposes involving ion association (using MINEQL; 8) or ion interaction models (using Pitzer equations; 2). Prediction capabilities of this empirical approach, however, are necessarily limited to the range of homogeneous experimental data sets on solubilities and compositions used for the parameter estimation. It is not possible to extend this model to multicomponent systems in a predictive sense, if the adequate fitting parameters (i.e., composite solubility product vs composition relationships) have previously not been measured for that system (3). Phase diagrams depicting the stability field of C-S-H and related components, which have been calculated from noninteger stoichiometric exponents in the solubility products (9), are also of limited value when both the intercepts and the slopes of the phase boundaries delimiting this field have been determined from such nonthermodynamic assumptions. Application of the Gibbs-Duhem equation as the second approach currently enjoys the greatest support in cement chemistry to fit the available experimental data for the relationship between the C-S-H solubility curve and the Ca/Si ratio of the solid (10, 11). For the threecomponent system CaO-SiO2-H2O, the Gibbs-Duhem equation can be applied to each phase (i) (at dT ) dP ) 0):

XiC dµiC + XiS dµiS + XiH dµiH ) 0

(1)

The region of interest here is a two-phase region in which solid C-S-H is in a state of (metastable) equilibrium with a dilute aqueous solution containing the components CaO and SiO2. Since, in the aqueous phase, the mole fraction of these solutes never exceeds 5 × 10-4 (in a pure CaOSiO2-H2O system), it is reasonable for a first approximation to set XaqH equal to unity. In that case, eq 1 can be simplified for the aqueous phase:

- dµaqH ) XaqC dµaqC + XaqS dµaqS ) (maqC dµaqC + maqS dµaqS) × 1/55.51 (2) where m denotes units of molality (since the aqueous phase is very dilute in this system, molarity and molality can be equated). At equilibrium, the chemical potential of each component must be equal in both phases. Thus, for the C-S-H solid, using eqs 1 and 2 yields

XsC dµsC + XsS dµsS ) XsH(maqC dµaqC + maqS dµaqS) × 1/55.51 (3) which can be rearranged to give an expression for the molar ratio of CaO to SiO2 (RC/S) of the C-S-H solid, as follows (11):

RC/S )

XsC XsS

)

-dµS 1 - maqSRH/S maqCRH/S + dµC 55.51 55.51

(4)

where RH/S is the molar H2O/SiO2 ratio of the solid. For the C-S-H system, the first term of eq 4 is more than 2 orders of magnitude larger than the other terms, because RH/S never exceeds 5 even in fully saturated C-S-H gels (11). Excess H2O may be considered as bulk porewater and eq 4 can be approximated by the following expression:

RC/S ) -dµS/dµC

(5)

which reduces the problem to a two-component system as derived by Fujii and Kondo (10). The remaining problem is to calculate the chemical potentials in eq 5 from the activities of all ions in the solution, given only the total concentrations of CaO and SiO2, as exemplified by Gartner and Jennings (11). Moreover, a potential phase diagram can be drawn showing the position of the chemical potential solubility isotherms for C-S-H with respect to various other compounds of interest in the CaO-SiO2-H2O system. The success of this approach, however, was limited. Values of calculated RC/S vs CaO concentration and experimental RC/S vs CaO concentration in solution agreed only for a single case of data reported for a “tobermorite-like” C-S-H phase precipitated from soluble salts in the range 1 < RC/S < 2 (11). The major drawback of this approach is that it still does not incorporate any structural information such as the nonideal mixing behavior and mixing gaps known for the C-S-H solid-solution system, although it appears that the calculated values of RC/S are sensitive to both the positions and slopes of the solubility curves representing at least two different equilibria in the potential phase diagram (commonly termed as C-S-H(I) or tobermoritelike C-S-H and C-S-H(II) or jennite-like C-S-H; 12). A new approach will therefore be introduced in this theoretical paper based on both a generalized Gibbs-Duhem equation and structural information for the C-S-H gel, to derive a thermodynamic equilibrium relationship between the composition of the solid solution and the respective aqueous phase.

New Thermodynamic Model A general model for the structure and composition of C-S-H gel in hardened tricalcium silicate pastes has been described by Richardson and Groves (6) as

Ca2nHwSi(3n-1)O(9n-2)‚Cany/2(OH)w+n(y-2)‚mH2O (6)

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where D, the distribution coefficient, is given by

TABLE 1

D ) KCSλCS/KCHλCH

Thermodynamic Database: Aqueous Species aqueous species OH-

formation reaction

log β

H+

-14.00 -9.86 -22.91 -12.78

H2O H4SiO4 - H+ H4SiO4 - 2H+ Ca2+ + H2O - H+

H3SiO4H2SiO42CaOH+

Equation 11 is the classical expression of a SSAS system at thermodynamic equilibrium. Another expression for the SSAS equilibrium is obtained by simply adding eqs 9 and 10 to give

with fixed interrelations between the stoichiometric coefficients, e.g., for

0 e y e 2; 2 e y e 4; 4 e y e 6;

n(2 - y) e w e 2n 0 e w e 2n 0 e w e n(6 -y)

The model is based on a highly disordered layer structure comprising finite dreierketten silicate chains of length 3n - l in solid solution with a variable amount of Ca(OH)2, where for individual structural units n ) 1, 2, 3, etc. In immature cement pastes, the dimer is the most common silicate species, while in aged cement pastes an increasing proportion of higher polymers has been found in the silicate anion structure (6). A special case of this model based on very specific structural considerations (jennite-like C-S-H) is the model developed by Taylor (12), which will not be considered here. The simplest possible silicate endmember composition with integer stoichiometry (Ca/Si ) 1) is tobermorite-like C-S-H, which can be formulated as Ca2H2Si2O7‚3H2O (with n ) 1, w ) 2, and m ) 3). This end-member (abbreviated as CS) is assumed to be congruently soluble with a solubility product given by Berner (8). For the formulation of a solid solution-aqueous solution (SSAS) equilibrium model, first the solubility products of the pure end-members assumed to compose the solid solution have to be determined by the following mass action laws:

Ca2H2Si2O7‚3H2O ) {H3SiO4-}2{CaOH+}2 ) KCS2 (7) Ca(OH)2 ) {CaOH+}{OH-} ) KCH

(8)

The solubility products have been recalculated with activities of the monovalent Ca species CaOH+ as a common cation to give values of pKCH ) 4.0 and pKCS ) 7.8, using the thermodynamic database listed in Table 1. The thermodynamic equilibrium in the pseudobinary C-S-H-H2O system is described by the equivalence of the chemical potentials of the solid and aqueous phase components, that is, by the appropriate mass action expressions:

{H3SiO4-}{CaOH+} ) KCS(1 - XCH)λCS

(9)

{CaOH+}{OH-} ) KCHXCHλCH

(10)

and

The solid-phase activities are given as the product of their respective mole fraction, X, and activity coefficient, λ. Dividing eq 9 by eq 10 and removing the common cation yields the Berthelot-Nernst distribution law:

XCH/1 - XCH ) D{OH-}/{H3SiO4-}

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(12)

(11)


ΣΠeq ) ({H3SiO4-} + {OH-}){CaOH+} ) (aCHKCH) + (aCSKCS) (13) where the left term is the “total solubility product” variable ΣΠ, which is fixed by the right term to the total solubility product constant ΣΠeq at thermodynamic equilibrium (13, 14). The latter is dependent on the composition of the solid solution, while the variable ΣΠ does not depend on the solid-phase composition. The ΣΠeq constant can be calculated (using eq 13), if the individual activities of the components in the solid phase (aCH and aCS) are known at thermodynamic equilibrium. Alternatively, ΣΠeq can be calculated if the activity fractions of the substituting ions in the aqueous phase are known at thermodynamic equilibrium. The activity fractions for the C-S-H-H2O system are defined as

χOH- ) {OH-}/({H3SiO4-} + {OH-})

(14)

χH3SiO4- ) {H3SiO4-}/({H3SiO4-} + {OH-}) (15) Substituting these two relations into eq 13 and rearranging by expressing the activities of the solid-phase components in terms of their activity coefficients and mole fractions yields

ΣΠeq )

1 χH3SiO4χOH+ KCHλCH KCSλCS

(16)

From eqs 14-16, a “generalized Gibbs-Duhem equation” of the aqueous phase can be derived, which is topologically equivalent to eq 2 (15):

(1 - χOH-) d[ln{H3SiO4-}{CaOH+}] + χOH- d[ln{OH-}{CaOH+}] - d[ln ΣΠ] ) 0 (17) Note, however, that χaq is not a molar quantity in the sense of Xaq but can be set as equivalent in the present case of diluted solutions (γ ≈ 1). Lippmann ΣΠ - X - χ phase diagrams can now be constructed from total solubility product expressions 13 and 16 together with the appropriate mole and activity fractions as coordinates (13, 14). Analogous to phase diagrams for binary gas/binary liquid systems or for solid/ melt systems, a Lippmann phase diagram is a plot of a solidus curve (the total solubility product defined by eq 13) and a solutus curve (the isothermal crystallization curve defined by eq 16), with the ΣΠ variable as the ordinate. Both the solidus and solutus curves form a characteristic loop common in other phase diagrams involving (complete) solubility of two phases. The loop becomes wider when the difference in the solubility products of the end-members increases. Similar to the phase diagrams used for binary solid/melt systems, horizontal tie-lines (conodes) can be drawn between the solutus and solidus curves, thereby

giving the solid-phase and aqueous-phase compositions for the series of possible thermodynamic equilibrium states. A Lippmann diagram differs from traditional phase diagram representations in that it uses aqueous activity products and activity fractions rather than elemental concentrations and mole fractions (and partial pressures in the case of gas/liquid equilibria) to define the composition of all phases in the system. For the present case, two different scales are used for the abscissa: an activity-fraction scale χOH relating to the aqueous-phase composition and a mole-fraction scale XCH defining the solid-phase composition. The benefit of the activity-fraction scale is that there is no necessity to consider the extent of ion pairing and/or complexation with other ions in the aqueous solution. The effect of speciation is important in the alkaline solutions of cementitious S/S systems, where ion pairs that form complete or nearly-complete solid-solution series may not have similar complexing affinities. As a result, a speciation model of ion complexation in the aqueous solution will be required in the construction of Lippmann diagrams from experimental concentration data. The solidus and solutus curves can be plotted and used to predict the solubility of any ideal solid solution at thermodynamics equilibrium (i.e., at ai ) Xi). The description of the thermodynamic properties of a nonideal solid solution, and consequently of the solid-phase activity coefficients vs solid composition relations, requires knowledge of the excess free energy of mixing of the solid solution, that is, of the deviation of its free energy of mixing from that of an ideal solid solution:

GE ) GM + GM,id

(18)

The Gibbs free energy of mixing GM of a solid solution can be considered to be the difference between the actual free energy of the solid solution and that of a compositionally equivalent mechanical mixture of the end-member components. For an ideal binary solid solution, the free energy of mixing for end-member components i and j will be

GM,id ) RT(Xi ln Xi + Xj ln Xj)

(19)

No experimental data exist, however, on Gibbs free energy of mixing functions of the C-S-H composition and therefore on solid-phase activity coefficients for that system. Empirical relationships for the compositional dependence of the solid-phase activity coefficients obtained from a Gibbs-Duhem integration, using the Guggenheim subregular model for the excess free energy of mixing of a binary solid solution, has been successfully used to fit laboratory solubility data for a variety of binary SSAS systems (14):

GE ) RT(Xi ln λi + Xj ln λj) ) XiXjRT[R0 + R1(Xi - Xj)] (20) with the dimensionless empirical parameters R0 and R1, from which the following expressions for the solid activity coefficients in the C-S-H system can be derived:

ln λCS ) XCH2[R0 - R1(3XCS - XCH)] ) XCH2[R0 - R1(3 - 4XCH)] (21) and

ln λCH ) XCS2[R0 + R1(3XCH - XCS)] ) XCS2[R0 + R1(4XCH - 1)] (22) Structural information of the C-S-H solid-solution behavior can be used to estimate the R0 and R1 parameters as a better approximation than the commonly used assumption of an ideal solid solution (i.e., GM ) 0). Complete solid-solution series in the C-S-H system are not known; i.e., this system deviates from ideality, because the solubility of the two end-members is limited in the limerich part and the partial solid-solution series is not isomorphous. Although initial dissolution of Ca3SiO5 (C3S) is congruent, the hydrated solid has always a Ca/Si ratio less than 3, and no C-S-H could be synthesized from salts beyond a Ca/Si > 3 (i.e., XCH > 0.67; 8). This miscibility gap information can be exploited to calculate the Guggenheim R0 and R1 parameters using the MBSSAS computer code (16). If the equilibrium compositional boundaries of a miscibility gap XCH,1 and XCH,2 (or XCS,1 and XCS,2) are known, MBSSAS will calculate the Guggenheim parameters R0 and R1 by solving the following set of transcendental equations:

XCH,1/XCH,2 ) exp{R0(XCS,22 - XCS,12) + R1[3(XCS,22 - XCS,12) - 4(XCS,23 - XCS,13)]} (23) XCS,1/XCS,2 ) exp{R0(XCH,22 - XCH,12) + R1[3(XCH,22 - XCH,12) - 4(XCH,23 - XCH,13)]} (24) No information on the solubility of the silicate endmember in Ca(OH)2 is available. However, it may be assumed to be negligible as a first approximation, because the portlandite lattice has no structural units where the silicate chains could fit in. The upper boundary was arbitrarily set to XCH ) 0.95 because the MBSSAS program system becomes unstable at higher values. With this miscibility gap information for the C-S-H solid-solution system, a value of -2.3 for the R0 and 3.4 for the R1 coefficient at 25 °C can be obtained. A Lippmann phase diagram can now be drawn to describe the SSAS equilibrium behavior of the C-S-H-H2O system (Figure 1).

Discussion Verification of the model and thermodynamic implications can be done using experimental data published in the literature upon the necessary recalculations. As mentioned above, an aqueous speciation and activity coefficient model is required in order to determine aqueousphase compositions from the ion activity scale of the solutus (eq 14) at a given solid-solution composition (and vice versa, solid-solution composition at a given aqueous-phase composition for verfication with experimental data). For the vertification of the model, experimental data published by Fujii and Kondo (10) and Greenberg and Chang (17) were selected because the authors used C-S-H precipitates for their solubility evaluations, obtained by stirring hydrated silica and calcium hydroxide in a suspended state at 50 °C for several weeks. The final aqueous equilibrium at 25-30 °C was determined under the absence of any unreacted calcium silicates such as C3S. One of the most important experimental precautions published by these teams, but not by many others, is that care was taken to exclude the formation and to verify the absence of surface layer products different in composition from the bulk during equilibration, although it is difficult to prove this because there is no


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reactivity of this amorphous solid with a very high specific surface (values of >100 m2/g on dried gel have been reported). Kinetic conditions that cause multicomponent solid solutions to react as metastable one-component solids of fixed composition as used in the stoichiometric or primary saturation concepts seem not to play a significant role in the C-S-H-H2O system. Aqueous solutions that plot below the solutus curve are undersaturated with respect to any solid phase, including the pure end-member solids, whereas solutions plotted above the solutus are supersaturated with respect to a series of solid solutions. It should be noted that, although it is numerically possible to draw the solidus over the entire compositional range, equilibrium cannot occur with solids of composition inside the miscibility gap (0.67 < XCH < 1). Another striking fact is that the solutus part corresponding to solids with XCH < 0.67 plots very close to χOH- ) 1, which is consistent with the high pH value and very low concentration of the aqueous SiO2 component in equilibrium with C-S-H. Saturation curves for the CS and CH endmember solids can also be drawn on the diagram by applying the respective equations given by Lippmann (13, 14): FIGURE 1. Calculated Lippmann diagram for the pseudobinary C-SH-H2O system. Unlike traditional phase diagrams, ΣΠ values for the solid and the aqueous phase are plotted on the ordinate against two superimposed scales on the abscissa: XCa(OH)2 refers to the concentration of Ca in the solid, and χOH- refers to the activity of hydroxyl ions in the aqueous solution. The loop lines show the equilibrium compositions of the coexisting solid (upper solidus curve calculated from eq 13) and the aqueous solution (lower solutus curve calculated from eq 16). The equilibrium values of ΣΠ for the coexisting solid and aqueous composition are related by the thermodynamic solubility products of the pure end-members: calcium silicate and portlandite, involving the Ca species CaOH+ as a common cation in the total solubility product expression (eq 13). The asymmetric, nonideal mixing behavior is represented by a mixing gap at Ca/Si > 3, which has been used to calculate the solid activity coefficients by eqs 21 and 22 and the computer code MBSSAS (17). Black dots represent some of the most cited experimental data on aqueous suspensions of C-S-H components with varying Ca/Si ratios for verification of this model (b, ref 10; O, ref 17).

analytical method for determining the equilibrium composition of a hydrated surface layer in contact with a solution of a certain composition. The published total concentrations of the components were transferred to the respective species activities with the thermodynamic database listed in Table 1 and the reported pH and ionic strength data. Ion activity coefficients were calculated using the Davies equation by help of the MacµQL program (18). MacµQL is a simplified Macintosh version of the more common program MINEQL developed by Westall and co-workers (19). As a result of this verification, both the solidus and solutus curves in the Lippmann diagram are perfectly matched by the experimental data (Figure 1). Data pairs on solid and solution composition lie on the solidus and solutus curves, respectively, and can in fact be bound with a horizontal tie-line (not indicated in Figure 1). The perfect match with the Lippmann solutus and solidus curves verifies also the assumption of thermodynamic equilibrium for the experimental data on the C-S-H-H2O system published by the above-mentioned teams. The C-S-H gel seems to be a solid-solution system capable of adjusting its composition in response to the aqueous solution composition within relatively short time. This is not surprising given the high

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ΣΠCH ) KCH/χOH-

(25)

ΣΠCS ) KCS/χH3SiO4-

(26)

and

which define the conditions for which a solution containing CaOH+, OH-, and H3SiO4- ions will be at saturation with respect to pure portlandite and calcium silicate. The endmember solubility products in this system differ by 4 orders of magnitude. The solutus curve and the curve representing saturation with respect to the silicate end-member closely follow each other except in the region where χH3SiO4- is close to zero. In that region, the pure CS curve approaches an infinitely high value of ΣΠ, while the solutus curve intercepts the ΣΠ axis at a value equal to the pure Ca(OH)2 solubility product. The pure Ca(OH)2 solubility curve is consistently above the solutus (except at XCH ) 1); therefore a solution at thermodynamic equilibrium with respect to any C-S-H solid will always be undersaturated with respect to pure portlandite. Such a solution will also always be undersaturated with respect to pure CS, but in this case only by a relatively small amount. Recall the definition of the solutus curve (eq 16); since the value of KCH is considerably greater than that of KCS and if the solid-phase activity coefficients were unity (in case of an ideal solid solution), the term (χOH-/KCHλCH) would be insignificant compared to the value of (χH3SiO4-/KCSλCS), and the solutus equation would essentially be identical to the pure CS solubility curve (eq 24). Increasing the solid-phase activity coefficient λCS [such as by increasing the term R0 + R1(4XCS - 1) in eq 21], however, causes the solutus curve to move downward, further away from the pure-phase saturation curves. In corresponding behavior, the negative excess free energy of mixing (corresponding to the negative value of R0) lowers the position of the solutus relative to that of an ideal solidsolution series, indicating that intermediate solid solutions are more stable than would be predicted from ideal mixing. Figure 2 shows the Gibbs free energy of mixing (GM) curve calculated for this C-S-H-H2O system with eqs 18-20. Calorimetric measurements to prove this plot experimen-

FIGURE 2. Gibbs free-energy of mixing (GM) curve for the C-S-HH2O system at 25 °C, calculated from eq 18. Note that the right slope of the GM curve is slightly concave due to the miscibility gap. The two intersection points of a common straight tangent applied to that curve part represent the boundaries of the miscibility gap assumed at 0.66 < XCH < 0.95.

tally are not known to the author. New electrochemical techniques introduced for experimental evaluation of mixing energy terms are available (10, 21), but experimental conditions are difficult because the necessary glassware is less inert in that alkaline milieu but also due to the complexity and number of different more or less crystalline hydrated phases belonging to the C-S-H-H2O system. Implications for Cement Chemistry. From the results of the SSAS model of the C-S-H-H2O system, some important insights emerge for the understanding of the complex processes that occur during hydration of cement. The model is in fact quite appealing because it is capable of explaining some unique features of the C-S-H-H2O system that have not yet been understood. In cement pastes, the reaction of C3S with water yields C-S-H gel and portlandite. Except in the very early stages of reaction, the average Ca/S ratio of the gel is constant at 1.5-1.8, though the ratio appears to vary markedly on a submicrometer scale (12). This value represents in fact simply the minimum in the Gibbs free energy of mixing (GM curve, Figure 2). The gain in ∆G for solid solutions below or above that value must therefore decrease when approaching that mole ratio leading to a cease in further reactivity of the C-S-H gel formed. This relation explains also the well-known empirical fact that it is difficult to prepare C-S-H gels with a Ca/Si ratio of above 1.5 in the laboratory by the reaction of, for example, calcium hydroxide with silica gel or calcium nitrate and tetraethylorthosilicate (22). Clearly, this SSAS equilibrium approach enables one to predict the dependence of the incongruent solubility of the C-S-H component on the Ca/Si ratio. The excellent model fit of the experimental data is hard to see from Figure 1. The extremely low solubility of the calcium silicate endmember compared to portlandite implies a strong pref-

FIGURE 3. Lippmann equilibrium diagram of the aqueous solubility in the pseudobinary SSAS system C-S-H-H2O, enlarged from Figure 1 for the solute activity fraction χOH- > 0.99, with the model solidus (upper) and solutus (lower) curve, and dots representing some of the most cited experimental data on solute composition of aqueous C-S-H suspensions with varying solid Ca/Si ratios (b, ref 10, O, ref 17).

erential partitioning of Si in the solid phase. As a consequence, the solutus curve in the Lippmann plot shows a strong asymptotic behavior due to the dominance of the hydroxyl ions in the activity fraction χOH- (eq 14). This part of the Lippmann plot has thus been enlarged in Figure 3, showing that the Si concentration in solution can in fact still be predicted given the Ca/Si ratio of the solid (conode from the solutus) and the pH of the solution. In the same manner, total Ca concentrations can be calculated given the Ca/Si ratio of the solid (conode from the solutus), the pH of the solution, and the total solubility product ΣΠ (eq 13). Only a narrow range of aqueous-phase compositions can coexist in equilibrium with solid mole fractions in the Ca/Si range of 1.1-2.0. The range of pH values of aqueous C-S-H solutions, for example, have been reported to lie in-between 12.0 ( 0.3 (5, 8). Within this range, small changes in the aqueous composition imply drastic changes in the solid equilibrium composition. This behavior might thus explain the appearance of compositional variations on a micrometer scale recognized by SEM studies of C-S-H phases (e.g., ref 12). The much greater solubility of portlandite leads to the result that even from a Ca-rich solution [saturated with respect to Ca(OH)2] the equilibrium precipitate is low in Ca/Si ratio. Only when the Si concentration in the aqueous solution becomes by more than 3 orders of magnitude lower than the corresponding Ca concentration, which occurs in later stages of Ca3SiO5 reaction due a hindrance of Si diffusion into solution through the reactant rim, will a more Ca-rich C-S-H phase (Ca/Si g 1.5) precipitate. It should be stressed that the total solubility product ΣΠ (eq 13) gives the activities of the ions CaOH- and H3SiO4from which the total Ca and Si concentrations have to be recalculated. As the result of these calculations, Figure 4 shows a nomogram of total dissolved Si concentrations (in


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by cementitious S/S technology. In the portlandite crystal structure, the Ca2+ cation can be replaced isomorphously by, for example, Zn2+ or Cd2+ ions without significant deformation of the hexagonal lattice (23). It is thus not surprising that these bivalent cations may also substitute at a crystal-chemical level in the octahedrally coordinated Ca(OH)2 layers of C-S-H phases. The aqueous solubility of such trace metal “impurities” in the C-S-H host phase can therefore be represented by a ternary Lippmann diagram of the metal hydroxide-calcium hydroxide-calcium silicate system that will be detailed in a subsequent paper. This finding is also important for the assessment of long-term fate of cementitious S/S systems, because the effect of carbonation of these systems may then be represented as a change from the ternary hydroxide to a binary carbonate SSAS system for a variety of bivalent metals. Some minor but important ternary phases in cementitious S/S systems like ettringite, monosulphate, hydrogarnet, and hydrotalcite also form extended multicomponent solid-solution series. Lippmann diagrams of the binary and even ternary SSAS equilibria in these systems may also be drawn, because most of the end-member components are congruently soluble and the mixing gaps are relatively well known.

Acknowledgments FIGURE 4. Plot of predicted total concentrations of the components SiO2 and CaO in an aqueous phase in equilibrium with tobermoritelike C-S-H gel, calculated for two different pH values and a range of Ca/Si ratio in the solid between 1.1 and 1.5. The speciation program MacµQL (18) has been used to calculate the species activities by the Davies equation for an ionic strength of I ) 0.04 given by Greenberg and Chang (7, 17). The logarithmic scale for total Si concentrations is used to help separate the points at high total Ca concentration. The model curve for tobermorite-like C-S-H of Gartner and Jennings (curve 2 in ref 11) plots in-between both curves as well as the many experimental data points taken from the literature (b, ref 10; O, ref 17; 9, ref 22; +, ref 24).

µM on a logarithmic scale) vs total dissolved Ca concentrations (in mM) in suspensions of C-S-H gels with solid compositions in the range 1.1 < Ca/Si < 1.5 at pH values of 11.7 and 12.3. The pH is a sensitive parameter that had not been previously accounted for. Both model curves span approximately the range of experimental values given by Jennings (curve A in ref 4) and bracket the model curve calculated by Gartner and Jennings (curve 2 in ref 11) for tobermorite-like C-S-H using the Gibbs-Duhem eq 4. The experimental data from various sources plot in-between both curves. Data were chosen only from suspension experiments that yield tobermorite-like C-S-H as represented, e.g., by the lower solubility curve A in ref 4. Note that the two solubility curves A and B in ref 4 never cross, and as a consequence, jennite-like C-S-H having the upper solubility curve B is always metastable with respect to tobermorite-like C-S-H having the lower solubility curve A (4). Applications in S/S Technology. There are two main applications for SSAS theory in the chemical modeling of cementitious solidification/stabilization technology: (i) prediction of solid-solution solubilities as shown above and (ii) prediction of the distribution of trace components between solid and aqueous phases. The latter is the main application of the present model, because it is possible to extend this model to multicomponent systems in a predictive sense, e.g., by calculation of ternary Lippmann SSAS phase diagrams in the case of solid solution of a trace toxic element (heavy metal or radionuclide) into the C-S-H gel

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A fellowship grant from the DFG allowed the author to prepare this work at EAWAG. I am grateful to Peter Baccini and Annette Johnson for encouragement and discussions. Valuable suggestions and software were provided by Pierre Glynn (MBSSAS) and Beat Mu ¨ ller (MacµQL).

Notation C S H CH CS C3S D [A] {A} ai γi λi I Ki

ΣΠ Xsi Xaqi χi R0,1

GM

CaO SiO2 H2O Ca(OH)2 Ca2H2Si2O7‚3H2O Ca3SiO5 Berthelot-Nernst distribution coefficient molality of species A (mol of A/kg of H2O) activity of species A, molality basis (mol kg-1) activity of component i in the solid phase, mole fraction basis (ai ) Xsiλi) activity coefficient of component i in the aqueous phase activity coefficient of component i in the solid phase ionic strength of the solution, molality basis (mol kg-1) solubility product of the pure end-member solid phase i (pKi, its negative decadic logarithm value) Lippmanns total solubility product mole fraction of component i in the solid phase mole fraction of component i in the aqueous phase activity fraction of the component i in the aqueous phase Guggenheim parameters in the subregular excess free-energy model for solid-solution activity coefficient calculation Gibbs free energy of mixing

GE GM,id

Gibbs excess free energy of mixing for a real solid solution Gibbs free energy of mixing for an ideal solid solution

Literature Cited (1) Spence, R. D., Ed. Chemistry and Microstructure of Solidified Waste Forms; Lewis: Boca Raton, FL, 1993. (2) Reardon, E. J. Cem. Concr. Res. 1990, 20, 175. (3) Bennet, D. G.; Read, D.; Atkins, M.; Glasser, F. P. J. Nucl. Mater. 1992, 190, 315. (4) Jennings, H. M. J. Am. Ceram. Soc. 1986, 69, 614. (5) Greenberg, S. A.; Chang, T. N.; Anderson, E. J. Phys. Chem. 1960, 64, 1151. (6) Richardson, I. G.; Groves, G. W. Cem. Concr. Res. 1993, 23, 131. (7) Glasser, F. P.; Lachowski, E. E.; Macphee, D. E. J. Am. Ceram. Soc. 1987, 70, 481. (8) Berner, U. R. Radiochim. Acta 44/45, 387. (9) Djuric, M.; Komljenovic, M.; Petrasinovic-Stojkanovic, L.; Zivanovic, B. Adv. Cem. Res. 1994, 6, 19. (10) Fujii, K.; Kondo, W. J. Chem. Soc. Dalton Trans. 1981, 2, 645. (11) Gartner, E. M.; Jennings, H. M. J. Am. Ceram. Soc. 1987, 70, 743. (12) Taylor, H. F. W. Z. Krist. 1992, 202, 41.

(13) Lippmann, F. N. Jb. Min. Abh. 1980, 139, 1. (14) Glynn, P. D.; Reardon, E. J. Am. J. Sci. 1990, 290, 164. (15) Ko¨nigsberger, E.; Gamsja¨ger, H. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 734. (16) Glynn, P. D. Comput. Geosci. 1991, 17, 907. (17) Greenberg, S. A.; Chang, T. N. J. Phys. Chem. 1965, 69, 182. (18) Mu ¨ ller, B. MacµQL Manual and Program. EAWAG: Du ¨ bendorf, 1993. (19) Westall, J.; Zachary, J. L.; Morel, F. F. M. Technical Note No. 18. Ralph M. Parsons Lab, MIT: Cambridge, 1976. (20) Ko¨nigsberger, E.; Gamsja¨ger, H. Mar. Chem. 1990, 30, 317. (21) Rock, P. A.; Casey, W. H.; McBeath, M. K.; Walling E. M. Geochim. Cosmochim. Acta 1994, 58, 4281. (22) Suzuki, K.; Nishikawa, T. Cem. Concr. Res. 1985, 15, 213. (23) Shpynova, L. G.; Melnik, S. K. Izv. Vyssh. Uchebn. Zaved., Khim. Khim. Tekhnol. 1985, 28, 83; Chem. Abstr. 1985, 102, 20837d. (24) Brown, P. W.; Franz, E.; Frohnsdorff, G.; Taylor, H. F. W. Cem. Concr. Res. 1984, 14, 257.

Received for review September 12, 1995. Revised manuscript received March 21, 1996. Accepted March 27, 1996.X ES950681B X

Abstract published in Advance ACS Abstracts, May 15, 1996.


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Aqueous Solubility Diagrams for Cementitious Waste Stabilization

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