Zero-Point-Of-Charge Prediction from Crystal Chemistry and Solvation Theory

0016-7037(94)00092-l

LETTER

Zero-point-of-charge prediction from crystal chemistry and solvation theory

DIMITRI A. SVERJENSKY

Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 2 I2 18. USA

(Received March 1, 1994, accepted in revised form May 9, 1994)

Abstract-The pristine point of zero charge (pH rrzc) is a property of each solid in water that is widely used in the interpretation of adsorption processes and dissolution rates. Considerable effort has gone into attempting to calculate the pH rrzc values of oxides and silicates based on crystal chemistry and electrostatic models of the interaction between protons and OH surface groups. However, substantial discrepancies remain between calculated and measured values of the pH rpzc even for simple oxides such as quartz. This implies that the widespread use of real and fictive components (e.g., Si’v02 and A12iV03) to interpret the surface characteristics of silicates is unwarranted. In the present paper, I show that by adding electrostatic solvation theory to crystal chemical and electrostatic models, the differences between pH rrzc values of crystalline solids can be accurately quantified. The new model sums free energy contributions associated with proton solvation, electrostatic repulsion of protons by cations underlying the surface, and electrostatic attraction of protons by oxygen anions near the surface. It results in a theoretical dependence of the pH rpzc on the dielectric constant of the kth solid (Q) and the ratio of the Pauling electrostatic bond strength to the cation-hydroxyl bond length (s/ rM_oH),according to the equation pHppzC = -0.5(AQ2,/2.303RT)( l/t/J - B(~/r~_ou) + log Kh+,

in which An,, B, and XL+ are constants. This relationship describes the pHppzC values of oxides and silicates to better than +-0.5 and enables prediction of surface protonation reactions from the properties of the underlying crystal structure alone. These results suggest that the bonding of protons at the crystal- water interface is more analogous to the bonding in the bulk crystal structure than to the bonding in analogous aqueous complexes emphasized in other studies.

INTRODUCTION and

THE CONCEPT OF SURFACE protonation of solids in contact log &,, = log [XSOH;/&OHQH:~, (4) with aqueous solutions has proved to be a considerable help where Xso-, Xsou, Xsour represent mole fractions of the sub- in interpreting the adsorption of cations and anions on sur- scripted species and au: represents the activity of the proton faces and the dissolution rates of solids (summaries by near the surface. Other models of surface complexation in- SCHINDLER and STUMM, 1987; WIELAND et al., 1988; DAVIS volve more than one type of protonation site (e.g., HIEMSTRA and KENT, 1990; DZOMBAK and MOREL, 1990; PARKS, 1990; et al., 1989a,b). Although such multisite models are not ex- HAYES et al., 199 1). Single-site surface protonation reactions plicitly addressed here, it is expected that the theory developed can be represented for a surface S by the reactions below will also apply to them. The values of the individual intrinsic protonation constants SO- + H: = SOH (1) log Kin,,, and log K,“?..l are dependent on the particular elec- and trostatic model adopted (e.g., constant capacitance, diffuse double layer, triple layer; see the summary by HAYES et al., SOH + H: = SOH;, (2) 1991) the sum of Eqns. 1 and 2 is simply related to the pristine point of zero charge (pHPPzC, DAVIS and KENT, 1990) where SO-, SOH, and SOH; represent surface species, and which is experimentally measured, independent of electro- H: represents a proton near the charged surface. The species static models of the solid-water interface. For any given model Hz is simply related to the proton in the bulk solution, of the solid-water interface, the pHppzc is traditionally rep- H&,, by the work done in transfering the proton through the resented by the protonation reaction potential difference between the bulk solution and the charged interface (DZOMBAK and MOREL, 1990). The corresponding SO- + 2H: = SOH;, (5) intrinsic equilibrium constants are given by which is the sum of Eqns. 1 and 2. When the concentrations log Kc”,.,2 = log [XSOH/~.YO-~H~~ (3) of the charged surface species are equal, i.e., a zero-charge

3123 3124 D. A. Sverjensky surface, the pHppzC is related to the intrinsic equilibrium log Kint..H+,k= 2A - 2B(sh-d (11) constant for Eqn. 5 according to where A represents the sum of a Coulombic attraction term PH~~zc = 0.5 log Kint..H.+,k= 0.5 log KHf.,),k, (6) (between the adsorbing protons and the surface oxygen) and a chemical bonding term, and B represents a Coulombic re- where Kint..H:,k refers to the adsorption of H,+ onto the kth solid which is equal to KHf,,,k for the adsorption of Hf,,, onto pulsion term (between the adsorbing protons and the surface the h?h solid at a surface potential of zero. oxygen). In practice, both A and B have been treated simply In a landmark paper, PARKS ( 1965) showed that a simple as constants established by regression (YOON et al., 1979). as electrostatic description of the interaction between protons originally developed by PARKS (1965, 1967). Equations 10 and M-OH surface groups made it possible to express a major and 11 were then combined to express the pHppzC in terms part of the differences between the pHppzc values of simple of s/rM_OHand s: oxides in terms of charge and radius of the cation(s) in the pHppzC = A - B(s/rM_OH) - 0.5 log [(2 - s)/s]. (12) solid (see also STUMM et al., 1970). Major exceptions to this model included quartz and amorphous silica, both containing This approach to calculating the zero point of charge of oxides IV-coordinate silicon (S?02). The model was extended to still leaves major discrepancies between calculated and mea- silicates (PARKS, 1967) by taking the pHppzC values of silicates sured values of pHppzC (e.g., 3.7 units for SiO2, and 2.0 for to be the weighted sum of pHppzC values of the individual BeO; YOON et al., 1979). These discrepancies are substantial oxides. Experimental rather than calculated pHppzC values enough to indicate that perhaps there is an additional effect for real species such as Si”02 were used, but calculated values that is not accounted for in the above crystal chemical/elec- for fictive species such as Al’V203 had to be used, even though trostatic model of surface protonation. Although covalent the theory could not predict Si’v02. Despite this problem, effects have been emphasized in other more recent theoretical which was discussed and emphasized by PARKS (1967), and studies (RUSSO and NOGUERA, 1992a,b), there is an addi- despite the experimental studies of SPRYCHA (1982) and tional effect that has been almost completely neglected, that TCHAPEK et al. ( 1974) for Zn2Si04 and kaolinite, which were can be treated electrostatically, and that will account for the very critical of the idea of combining oxide components to above discrepancies. It will be shown below that this effect is generate silicate properties, the idea has had widespread ap- associated with the solvation of aqueous protons. STUMM et plication in recent studies of surface protonation and in in- al. (1970) and BLESA et al. (1990) have discussed possible terpretations of the mechanisms of dissolution rates of silicates solvation effects during protonation, and solvation effects (CARROLL-WEBB and WALTHER, 1988; BRADY and have been demonstrated to be of importance for predicting WALTHER, 1989; BLUM and LASAGA, 1991; WOGELIUS and cation adsorption (SVERJENSKY, 1993). WALTHER, 199 1; and below). Finally, because the pH ppzc values of silicate minerals have In order to try to improve upon the basic electrostatic been approximated as the sum of simple oxides (as discussed model developed by PARKS (1965, 1967), YOON et al. (1979) above), the discrepancies described above that are associated developed a combined crystal chemical and electrostatic the- with the calculation of the pHppZC values for the simple oxides ory of protonation. Instead of Eqn. 5, which relies on analogy must lead to much greater uncertainties in calculating and with aqueous complexation reactions, YOON et al. (1979) predicting the surface protonation of silicates. As noted above, suggested that protonation should be represented from a the oxide summation concept has been widely applied to aid crystallographic standpoint by addition of the protons to a mechanistic interpretation of surface titration and dissolution dangling oxygen with residual charge s, according to rate data for silicates (e.g., CARROLL-WEBB and WALTHER, S-O’*-“‘- + 2H+ = S”+_OH 1988; BRADY and WALTHER, 1989; BLUM and LASAGA, 2, (7) 199 1; WOGELKJS and WALTHER, 199 1). It will be shown be- where s represents the Pauling bond strength. For a crystal low that a more appropriate concept for silicates is to express with a single cation type and site with valence Z and coor- surface protonation in terms of fundamental parameters dination number V, characteristic of each bulk, individual silicate crystal structure. s = z/v. (8) For more complex structures with i cations and sites in equal INCLUSION OF SOLVATION THEORY INTO A abundances, THEORETICAL MODEL FOR SURFACE PROTONATION The similarity of the adsorption of near-surface protons S = z(Zi/Vi)/i. (9) (Eqn. 1) with the representation of the adsorption of near- Accordingly, the effective charges on the positive and negative surface cations according to sites of the surface are not + 1 and - 1, respectively, as implied by Eqn. 5, but instead are represented by +s and 2 - s re- SO- + M:+ = SOM+ (13) spectively, as shown in Eqn. 7. From Eqn. 7, a Law of Mass suggests that the recent application of Born solvation theory Action expression can be derived for the zero point of charge to cation adsorption (SVERJENSKY, 1993) may also be useful condition (YOON et al., 1979): in treating protonation reactions. Following JAMES and HEALY’S (1972) treatment of Born solvation, the free energy log Kint..H+,k= log { [(2 - J)/s~/(uH+)~}. (10) associated with solvation during adsorption can be repre- Specifically, YOON et al. (1979) combined crystal chemical sented in terms of the dielectric constants of the solid (ck), theory and electrostatic theory to express Ki”t.,H+,kin terms the interfacial water (tint.), and bulk water (eW). It follows of Pauling bond strength (s) and metal-OH bond length (SVERJENSKY, 1993) that the intrinsic equilibrium constants (TM-OH,see Table 1) by for adsorption of the M++ cation on the kth solid (log Prediction of zero-point-of-charge 3125

m Crystal structure properties and rem point of charge values at Kint..M:+,k) can be broken up into a fundamental salvation 25 C and 1 bar. cont~bution and a cont~but~on characteristic of the sorbing cation (log K&+), resulting in a dependence of log PHASE ek8 s/rM_cHb Exptl. Calc. 7 PHPPZ? P~FPZC K ,nt.,M:+,kon the inverse of the dielectric constant for the ,%th &ii02 4.578 0.3818 2.9 2.91 solid ( I/Q) according to A12Si~0&IH)4 11.8 0.2754 4.5 4.66 a-TiO:, 120.91 0.2246 5.6 5.21 Kint.,M:+,k = - (AQ,/2.303Rn( l,&) + log K&++r Fe304 20000 0.1766 6.6 7.to log (14) a-Fe203 25.0 0.f645 8.5 6.47 a-A1203 10.43 0.17f‘I 9.1 9.37 where the terms involving l/tinI. and l/c, are included in the a-AI 6.4 0.3716 10.0 9.84 log K:i_M++term. The success of this approach suggests that hng3 9.83 0.1070 12.4 12.24 l/~;~~.is a constant in these systems (SVERJENSKY, 1993). In PHASE @a s/rM_OHb Exptl. Cab. PHZ& pkvc Eqn. 14, the Born solvation term An, defined by z 11.957.16 0.18900.0976 10.2 12.39.5 An, = RsoM+ - Qso- = Q;&+ - $@. (1% NiO Il.9 0.1077 9,85-Il.3 Il.6 rxo 78.1 0.1686 9.5 8.6 replaces the term GM++in Eqn. 6 of SVERJENSKY (1993) in F$H) 8.4911.7 0.16760.165 9.0-9.78.7-9.3 10.09.4 order to emphasize a dependence on the overall Eqn. 13 amorphous SiO2 3.807 0.3818 3.5 3.9 above. The absolute values of QTbs,for each jth species are i+MnOz 10000 0.2301 4.6-7.3 4.8 Sr& 9.0 0.2177 7.3 7.7 defined in terms of (7~/4)Zj/r,_~, where 17is equal to 166.027 ZrO2 22.0 0.1803 7.9 kcal - A - mole-‘, Zj is the charge of thejth species, and r,,j is

2 24.0f8.9 0.14560.1480 9.0-9.3 9.69.2 an effective electrostatic radius (S~E~JEN~KY, 1993 and ref- CaTi 165.0 0.1409 8.8 erences therein). MgAtzOd 8.3 0.1703 9.9 The similarity of Eqns. 5 and 13 suggests that log FeAIZ04 40.0 0.1693 7.9 ZrSiOa 11.5 0.1559 9.8 &tt..ti+,k (or log KHsqbk) in Eqn. 6 should also depend on l/Q Zn&iOd 12.99 0.2389 7.4 6.1 according to ANDALUSITE 6.9 0.2531 5.2-7.6 6.9 KYANITE 7.8 0.2402 5.2-7.9 7.t StL~tMANlTE I f .0 0.2736 5.6-6.8 4.9 log K%&,.k = -(A~~/2.303R~(l~f~) -t log Kli.H+, (16) FORSTERITE 7.26 0.t972 10.5 9.1 GROSSULAA 8.53 0.2113 8.1 where ALMANDINE 4.3 0.2135 10.4 OH-TOPAZ 5.0 0.2413 6.6 AR, = Qso,.,; - Rso- (17) JADEITE 10.0 0.1930 6.5 A’OLLASTONITE 3.6 0.2370 7.0 and QsoH; and Qso- are individual Born coefficients. Con- DIOPSIDE 8.02 0.2336 7.3 ~~~~ 17.4 0.2333 5.9 sequently, PHPP~~ values for a series of solids should also \NTHOPHYLLIlE 8.0 0.2497 6.6 depend on I/Q. Again, it is assumed here that l/~~,,~.and l/ TREMOLKE 6.0 0.2402 7.0 TALC 5.8 0.2634 7.0 E, are constant and can thus be included in the term log MUSCOVITE 7.6 0.2539 6.6 Kii,H+. The calculations discussed below are consistent with PHLOGOPllE 7.6 0.2194 8.0 LOW ALBITE 6.95 0.2920 6.8 5.2 this assumption. H-ALBITE 8.95 0.3533 2.0 2.6 Experimental pHppZC values of selected crystalline oxides MAXINE 5.48 0.2889 6.3 ~-MIC~~LINE 5.48 0.3549 2.4 3.3 and silicates are summarized in Table 1 and Fig. la. It can ANORMlTE 7.14 0.2B09 5.6 be seen in Fig. la that, although there is a dependence on I/ +, solids containing tetravalent cations and/or tetrahedrally The first eight phases in the table and their properties were regressed coordinated cations are displaced down to low values of with Eqn. 18 togenerate -OS(AQ,/2.303RT) = 21.1158, B = 42.9148, and logI& = 14.6866. Ail other calculated values of pHppZC were pHPPZc. This suggests that the fundamental dependence on predicted using these coefficients in Eqn. t8. crystal chemistry described in earlier studies (PARKS, 1965, aDielectric constants from OLHOEFT ( 198 f ) except for EkO, MgO, 1967; YWN et al., 1979) could be linked to the salvation CaO, and ZnO {Shannon et al., 1992b), Si02, A1203, and grossular theory described above for a more complete description of (Shannon and Rossman, 1992), ZrO2 and ZrSi04 (Subramanian and surface protonation. Shannon, 1989). MgA&O, (Shannon and Rossman, 1991), diopside and anorthite (Shannon et aI., 1992a), amorphous silica (Shannon, In the present study, I combine the electrostatically based 1993). Values for H-albite and H-microcline were assumed to be crystal chemical approach (YOON et al., 1979) with electro- the same as for albite and microcline. The value for wiflemite statically based salvation theory (SVERJENSKY, 1993). There (ZnlSi04) was estimated following the procedure in Shannon ( 1993). are two ways to do this in the context of the present paper: b Computed by averaging all cation sites(i) with malar abundance Ni using S/TM-OH= [I: [(S/rM.on)iNi]]/[~Ni], where s for the ith site by ( 1) adopting the traditional representation of surface charge (Eqns. 5 and 6) and then combining Eqns. 6, 11, and 16, or was obtained using bqn. 8, and r,.o& for the ith site is calculated from r&OH = r&&O+ 1.Ol Angs (Yoon et al., 1979). Values of s and (2) by adopting the fractional charge representation of mean values of rMeo were obtained from Smyth and Bish (1988). ref. 6 (Eqns. 7 and 10) and then combining Eqns. 12 and 16, Values for H-albite and H-micro&e were calculated a5 for albite Be&ause the sofvation theory already developed (SVERJENSKY, and microdine omitting consideration of the alkali sites. 1993) refers to the traditional representation ofsurface charge, ’ From Davis and Kent { 1990): except for A12Si205(OH)4,A1(OH)S, BeO, and MgO which are from Carroll-Webb and Walther (1988) it is more consistent to consider an equation of the form Hiemstra et al. (1987), and Parks (1965); NiO (Parks, 1965; Tewari and Campbell, 1976); CaO, ZnO, and SnOz (Parks, 1965); Mn9 pHppZC = -0.5(AQ,/2.303RT)(l/~,) (Balistrieri and Murray, I%&!);amorphous silica (Bolt, 1957);goethite (Evans et al., 1979; Zeltner and Anderson, f 988); willemite (Sprycha, - 3(~~~~_~~~ + log KG+. ( I8) 1982); andalusite, kyanite, and sitlimanite (Parks, 1967); forsterite (Wogelius and Walther, 193 1);albite (Blum and tasaga, 199 1); H- The first term on the right hand side of this equation refers albite and H-microcline (Parks, 1967). to the part of the solvation contribution which depends 3126 D. A. Sverjensky

23.0 , I I , , @) 22,0 _ ~HPPZC CORRECTED FOR 13.0 21,. : PAULING BOND STRENGTH 12.0

10.0

p 9.0 HEMATITE 0  g 8.0

7.0 MAGNETITE

6.0 RUTILE t 1  KAOLINITE 13.0 -

QUARTZ 14 .O 1 MAGNETITE I’11 12.0 - 0 11.0 .“““‘I, “‘I”“““‘_ 2.0”‘..“.““‘..“““““’ 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25

1 IE 1 IE FIG. 1. Correlation and prediction of pH rpzc values of selected crystalline oxides and silicates versus values of the inverse of the dielectric constant (l/c). (a) Experimental values of pH rpzc vs. I/e. Note that solids with higher charged cations and/or lower coordination numbers are displaced to lower values of pHppzc. For example, progressively higher charged cations occur in the following VI-fold coordinated species: MgO (+2 cations), hematite, corundum and gibbsite (+3 cations), and rutile (+4 cations). Magnetite and kaolinite contain mixtures of IV-fold and VI-fold cations; and quartz contains the unusual combination of +4 cations (only) in IV-fold coordination. (b) Values of pHppzC corrected for the ratio of the Pauling bond strength (s) to the metal-OH radius (r,+on). The line represents a regression of the data with Eqn. I8 and coefficients given in Table 1.

strongly on the properties of the solid (i.e., l/tk), the second It can be seen in Figs. 1 and 2 and Table 1 that Eqn. 18 term refers to the electrostatic repulsion of the surface proton gives a remarkably close agreement between calculated and by the cations immediately underlying the surface (see Eqn. measured values of the pHPrZC, typically less than 0.5 of a 11). The final term is a combination of a general intrinsic pH unit even for solids as diverse as MgO and kaolinite. It binding constant for the proton on the surfaces of all oxides appears that the combination of crystal chemical theory with and silicates (this includes all nonelectrostatic effects), together an electrostatic theory of proton-M-OH interaction and sim- with the remaining part of the solvation contribution that ple solvation theory can account completely for the differences depends on l/~int, and l/t, (see above) and the term for the between the adsorption of protons on different solids. It can electrostatic attraction of the surface proton to the oxygen also be noted from Figs. 1 and 2 that the values of (Q) and anions at the surface (the “A” term in Eqn. 11). According the ratio of Pauling bond strength to radius (.s/rM_oH)for sim- to Eqn. 18, the surface protonation reaction associated with ple oxides and the more complex silicates are sufficient to the zero point of charge should depend linearly on both the characterize the surface protonation of these solids. Conse- bulk dielectric constant of the solid (Q) and the ratio of Paul- quently, it appears to be possible with Eqn. 18 to characterize ing bond strength to radius (s/rM_OH).Equation 18 expresses crystalline solids of all types simultaneously, based on the the strength of binding of protons to the surface in terms of crystal structure of each individual solid. There is no need to properties of the bulk crystal structure underlying the surface. regard the surface properties of silicates as the sums of the simple oxides. RESULTS Predicted values of pHppZC for a number of solids of geochemical interest are also summarized in Table 1. Most of Although numerous values of the zero point of charge these are plotted in Fig. 3a which displays where many solids (pHz& of many different kinds of solids abound in the lit- of geochemical interest lie in terms of the fundamental vari- erature, few accurate values of the pristine point of zero charge ables in the theoretical model developed in this paper. The (pHppzc) for well-characterized crystalline solids are available parameter s/r is, of course, just the averaged Pauling electro- (e.g., DAVISand KENT, 1990). The problems associated with static bond strength per angstrom (see Table 1). The param- poorly characterised and/or noncrystalline solids have been eter tk is the averaged low frequency permitivity of the solid, extensively discussed by PARKS (1965, 1967). In the present which can be related to, and in fact predicted from, atomic study, I have used the critical compilation of DAVIS and KENT polarizabilities (SHANNON, 1993). Consequently, provided (I 990), supplemented with a few other data as summarized that the crystal structure is known, both s/r and rk can be in the eight values of pHppzc given at the top of Table 1. obtained. It can be seen that most silicates are predicted to These data were regressed using Eqn. 18 and values of (t,J have pHppZC values in the range 5 to 9, whereas many oxides and the ratio of Pauling bond strength to radius (,s/~~_~n) lie in the range 8 to 10. It should perhaps be emphasized that given in Table 1 resulting in the calculated line shown in Fig. in the present study both s/rand ck refer to bulk values because 1b and the calculated values of pHppzC in Table 1 and Fig. the zero points of charge considered here also refer to bulk 2a and b. values. However, both s/r and tk are actually directional Prediction of zero-point-of-charge 3127

13.0 2 , , . , , I I , I I I (b) ‘: . Residuals 12.0 z 1.5 - vs. 11.0 Z - , ~HPPZC (expt.) 10.0 I? 9.0 i 0.5 - . RUTILE GIBBSITE hQJ - . 6.0 QUARTZ 0 HEMATlTEm 0’

7.0 - 2 = 0 g -0.5 - KAOLINITE 0

6.0 -  m MAGNETITE 0

d -1.5-‘:

-2 .‘,‘.‘.‘,‘,‘.‘.‘.‘,‘, 2.0 3.0 4.0 5.0 6.0 7.0 6.0 9.0 10.011.012.013.0 2.0 3.0 4.0 5.0 6.0 7.0 6.0 9.0 10.011.012.013.0

~HPPZC (cwt.) ~HPPZC (wt.)

FIG. 2. Comparison of experimental and calculated values of pH ppzc. (a) Experimental vs. calculated values of pHppz. (b) Residual values of pHppzC (expt). - pHppzc (talc.) vs. I/Q.

properties for anisotropic solids. Consequently, it can be ex- tainty still surrounds the interpretation of immersion pH pected that surface protonation reactions will also be highly values for feldspars (BRANTLEY and STILLING& 1994). anisotropic in general. In general, it can be seen in Fig. 3b that despite the fact Although accurate measured values of the pHppzc for many that the predicted values are not strictly comparable to the of these solids, particularly the silicates, are not yet available, experimental values there is close agreement between the two, it is possible to make a crude comparison of the predicted which lends further support to the utility of Eqn. 18. It is pHppzc values with experimental values of the pH at the zero particularly noteworthy that there is excellent agreement be- point of charge for systems in which either H+ is not the only tween the predicted and measured values for goethite potential determining species, or the solids are not well char- (FeOOH). Reported values of the zero point of charge of acterized, or the pH is simply an immersion pH, as discussed goethite vary by more than two units, depending on whether by PARKS ( 1965, 1967). For example, values of the completely or not the goethite has been purged of COz (EVANS et al., exchanged H-albite and H-microcline cited by PARKS ( 1967) 1979; TELTNER and ANDERSON, 1988). For example, PARKS are included for interest in Fig. 3b, but the immersion pH ( 1965) cited a value of 6.7, DAVIS and KENT (1990) selected determined for a partly exchanged albite by BLUM and LA- 7.3, HAYES et al. (199 1) reported 8.6, and EVANS et al. (1979) SAGA ( 199 I), although close to the value predicted for pure reported 9.3 for goethite. The zero point of charge of COz- albite (Table l), was not included because substantial uncer- free goethite is 9.0-9.7 (EVANS et al., 1979; ZELTNER and

fb)

13.0 0.26

L 0.22 . v)

pyROLUSrE&ralLLIMANITE 0.17 I

0.12 0.00 0.05 0.10 0.15 0.20 0.25

1 IE Zero point of charge (expt.)

FIG. 3. Predicted values of pH ppzc: (a) pHppzc as a function of the inverse of the dielectric constant (l/e) and the Pauling bond strength per angstrom (s/rM_oH). (b) Comparison of predicted pH ppzc values with experimental zero point of charge values from the literature (see Table I). Note the excellent agreement for goethite (CO*-free) and amorphous silica (see text). 3128 D. A. Sverjensky

ANDERSON, 1988) which agrees extremely well with the Gary Olhoeft, Jack Salisbury, and Bob Shannon helped me with the theoretical value of 9.4 calculated here. It should also be noted dielectric constant literature. Reviews by Sue Brantley and Pat Brady helped substantially. Financial support was provided by Du Pont that few poorly crystalline or amorphous solids are considered (through Noel Scrivner) and the National Science Foundation. here. Although excellent agreement between theory and measurement was obtained in the case of amorphous silica Editorial handling: J. D. Macdougall (Table 1 and Fig. 3b), it is difficult to define values of s/TM_ OH and/or tk for solids such as amorphous ferric hydroxide, REFERENCES birnessite, and y-alumina. ANDERSENT. N. and BOCKRISJ. O’M. (1964) Forces involved in the “specific” adsorption of ions on metals from aqueous solution. CONCLUSIONS Electrochim. Acta 9, 347-311. BALISTRIER~L. S. and MURRAYJ. W. (1982) The surface chemistry Several more results of interest follow from the practical of 6-Mn02 in major ion seawater. Geochim. Cosmochim. Acta 46, application of Eqn. 18 summarized above. First, the constant 1041-1052. B is simply related to the effective dielectric constant near BLESAM. A., MAROTOA. J. G., and RECAZZONIA. E. (1990) Surface the mineral-water interface in the context of Eqn. 5 (YOON acidity of metal oxides immersed in water: A critical analysis of et al., 1979; D. A. Sverjensky et al., unpubl. data). Because thermodynamic data. J. Colloid Inte$zce Sci. 140, 287-290. BLUMA. E. and LASAGAA. C. ( I99 I) The role of surface speciation the present study shows that B appears to be a constant for in the dissolution of albite. Geochim. Cosmochim. Acta 55,2193- all oxide and silicate minerals (B = 42.9148, Table I), it 2201. follows that the @ective dielectric constant near the mineral- BOLTG. H. 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