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Quantum chemical studies of the effects on silicate mineral dissolution rates by adsorption of alkali metals
Geochimica et Cosmochimica Acta, Vol. 61, No. 13, pp. X77-2587, 1997 Copyright G I997 ElsevierScienceLtd Printedin the USA. All rightsreserved oOl&7037/Y7 $17.00+ .OO
Pergamon
PI1 SOO16-7037( 97)00118-X
Quantum
chemical
HELENE STRANDH,
studies of the effects on silicate mineral by adsorption of alkali metals
dissolution
rates
’LARS G. M. PETTERSSON,2 LENNART SJOBERG,‘.* and ULF WAHLGREN’
and Geochemistry, University of Stockholm, S-106 91 Stockholm, Sweden ‘Department of Physics, University of Stockholm, Box 6730, S-l 13 85 Stockholm. Sweden
‘Department
of Geology
(Received
June 7, 1996; accepted
in revised form
Murch
I,
1997)
Abstract-Quantum chemical calculations at the density functional level (B3LYP functional) with full geometry optimisation have been performed on the effect of protonation and of adsorption of alkali cations (Li + , Na + , K + , Rb+ , and Cs ‘) on the siloxane bond strength in silicate minerals. The influence of pH was modelled by assuming a fully protonated surface model, (OH)&-0-Si( OH)l, at pH lower than the point of zero charge (pzc), while for pH = pzc and pH > pzc, the cation was assumed to interact with a deprotonated surface -O- site. At low pH, addition of cations is found to strengthen the siloxane bond in agreement with experiment for the alkali metals, but not for the interaction with H?O + At high pH, the siloxane bond is weakened by the addition of alkali, in agreement with experiment for feldspar dissolution. Inclusion of the surface hydroxyl groups is found to be important particularly when solvation of the ions at the surface is considered; up to three water molecules have been included in the geometry optimisation. Salvation of the ions interacting with the surface is found to give very important Co&right 0 1997 Elsevier Science Ltd _ contrib&o& to the computed reaction energies. 1. INTRODUCTION
dissolution is controlled by the surface speciation which itself is determined by the composition of the surrounding solution. Dove and Elston (1992) employed the triple layer electrostatic model, computing the distribution of predominant species on the surface to be able to get a better understanding of rate controlling processes. The calculations were performed using a set of parameters describing the electrostatic layer and the surface, and the results were included in a rate law fitted to experimental data. To avoid using parameters to describe the surface and its environment, one may use quantum chemical calculations. In a study of the mechanism of adsorption and hydrolysis of H,O+ and H’ + H20 at Si-0-Si and Si-O-Al bridges, Xiao and Lasaga ( 1994) calculated the intermediate transition state for the reactants and products using ab initio molecular orbital calculations. These model calculations showed that the Si-0 bond and, even more, the Al-0 bond are weakened by the adsorption of H30 ’ at the siloxane oxygen, which may explain the acid effect on the dissolution kinetics. i.e.. the observed increase in the rate for pH < pzc. The dissolution kinetics is furthermore dependent on the composition of the solvent, i.e., the presence of ions other than proton and hydroxide. Of particular interest for the present study is the influence on the dissolution process of the type and amount of alkali metal present; at pH values larger than pzc, it has been found that alkali metals enhance the dissolution of feldspar in the order Li > Na > K ( Schweda, 1990; SjGberg, 1989)) but for quartz, the effects indicate a different order (Li < Na = K) (Plettinck et al., 1994; Dove and Crerar, 1990). At pH less than pzc, dissolution is inhibited by the presence of alkali metals with the relative activities for feldspar Li < Na < K (Stillings and Brantley, 1995; Schweda, 1990: Sjiiberg. 1989). For quartz, the dissolution in this pH region has been reported to be inhibited by Li’ with a lower dissolution rate than in pure HCI solution (Bennett, 1995 ), but newer results ( Strandh et
The processes of weathering and dissolution of silicate minerals such as quartz and feldspar have become of particular interest during the last decades, due to the increased knowledge of the changes in the environmental chemistry caused by human activities. This change in chemistry has lead to an observed increase in the rate of these processes and has generated a concern for the preservation of historical treasures such as rock-carvings. In coastal regions, the rockcarving surfaces will be exposed both to a wide pH interval and to a relatively high concentration of salts, which both have a strong influence on the dissolution rate. Thus, in the present theoretical work, we will focus on models of the quartz surface and examine possible reaction mechanisms which include both the dependence on pH and the presence of alkali metal cations. The present studies have been accompanied by new experimental determinations of the rate constants of quartz dissolution as function of pH and salt (LiCl, NaCl, KC]) concentration (Strandh et al., 1996, and H. Strandh, unpubl. results). Interest in silicate mineral dissolution processes has been large and has been concerned with the mineral-solution interface reactions and with understanding the solution dependencies that dissolution kinetics studies show. The network silicate minerals quartz and feldspar have been observed to give similar results in the dissolution process with a rate minimum at about the same pH as the pH where the proton activity gives a zero net charge on the surface of the respective mineral, i.e., the point of zero charge (pzc) (Knauss and Copenhaver, 1995; Plettinck et al., 1994; Sverjensky, 1994; Hellmann, 1994; Bennett, 1991; Brady and Walther, 1990; Knauss and Wolery, 1988; Wollast and Chou, 1986). The observed pH dependence has lead to the conclusion that:
* Deceased. 2577
H. Strandh et al
2578
al., 1996, and H. Strandh, unpubl. results) show no effect from Li+ and Na+ and an inhibition by K’ In the present study, we investigate the effects of the alkali cations (Li+, Nat, K+, Rb’, and Cs’) on the siloxane bond strength using quantum chemical calculations on models of the siloxane bridge at different pH (acid, neutral, and basic) with respect to surface speciation and compare the trends between the different cations with those observed experimentally at different pH. In solution, the cations will naturally be solvated by, on average, six water molecules in the first solvation shell. At the surface, the solvation may be less efficient but can still lead to important effects on the energy differences between reactants and products. The solvation energies for alkali metal ions in solution are well-known experimentally, but at the liquid-solid interface, the situation is !ess clear, and we have thus also considered models including up to three water molecules. 2. MODELS In a model study of complicated reactions such as weathering, a number of assumptions have to be made about how the process occurs. There is general agreement that the ratedetermining step in the chemical weathering of both quartz and feldspar is the breaking of a siloxane bond between two Si atoms and that, at neutral and acid pH (relative to pzc), the process involves water as a reactant; in alkaline solution, hydroxide ions are assumed to participate in the bond breaking. In the present work, we assume this to be true also in the investigation of the effect of alkali cations on the strength of the siloxane bond. At least two silicon atoms must be included in a model which should describe the breaking of a siloxane bond. The Si atoms, having four possible bonds, must be bound to three additional groups in order to saturate the system. In bulk quartz, each Si atom is bound to four other silicon atoms through 0 bridges while at the surface, the exposed 0 will be protonated or form 0 groups. We have chosen to terminate all bonds with hydroxyl groups; at the surface, we have thus included the surface OH groups while the siloxane bridges to bulk-like Si atoms are replaced by OH groups as a simplest representation of these. Thus, the minimal model of the hydroxylated quartz surface consists of two Si( OH), groups bound together by an 0 bridge (a siloxane bond) (Fig. 1a). The deprotonated surface in alkaline solution was represented by removing a proton from a Si(OH)3 group (Fig. lb) while in acid solution, the surface instead can become protonated, and this was modeled by adding a proton to one of the Si ( OH)x groups (Fig. 1c) In order to consider the salt effects observed in silicate dissolution experiments, an alkali metal cation was added and allowed to interact with the model of the surface in alkaline and neutral (compared to pzc) solution. In the acidic solution, the surface charge was given either by a proton or by an alkali metal cation so that in this case, the model may be described by (OH),SiOHM’-0-Si(OH), (Figs. lc and 3). The structure was fully optimized using gradient techniques for each of the cases. Since the reactions occur in an electrolyte solution, the solvation of the ions and of the reactants and products must be considered. In the present work,
we have
investigated
these
effects
by optimising
se-
lected systems, including explicitly one, two, or three water molecules. The breaking of a siloxane bond must involve an attack by either a water molecule, a hydroxide ion, or a hydronium ion. We have assumed that the attack in the alkaline case is carried out by a hydroxide ion and in a neutral surrounding, by a water molecule. In the acidic case, it is reasonable to assume that the surface becomes protonated, which makes an attack by a hydronium ion unlikely due to the electrostatic repulsion. Xiao and Lasaga (1994) have earlier shown that performing the attack by H,O+ or by H+ + HZ0 produces the same results for the reaction energy and geometry. We have therefore assumed that the breaking of a siloxane bond in the acidic case occurs through an attack by a water molecule on a protonated surface. In the present model, the dissociation products leaving the surface into the solute are Si( OH)4 in the neutral and acid situations and Si( 0H)30m when the attack is made by a hydroxide ion (i.e., the alkaline case). 3. METHODS At the surface, three types of situations are relevance: the surface may be fully hydroxylated of zero as modelled by (OH)&-0-Si(OH), be deprotonated as (OH),Si-0-Si(OH)&
expected to be of with a total charge (Fig. la), it may
(Fig. 1b), or it may be protonated with a net positive surface charge as (OH)&0-Si( OH),OH; (Fig. I c). In alkaline solution, the deprotonated and neutral species are assumed to dominate while in the acid solution, the neutral and protonated species should dominate at the surface. At pzc, the net charge of zero may be achieved in two different ways: by regions with fully hydroxylated surface groups and by regions with equal numbers of positively and negatively charged groups. The bond strength of additional cations interacting with these surfaces is highest for the negatively charged species, followed by the neutral surface, and lowest for the positively charged sites; this has been the basis for the different reaction models described below. We assume that the reaction mechanisms in both alkaline and neutral solution involve an interaction with a deprotonated site at the surface. In a neutral solution, the reaction is assumed to occur with water so that we may write Si(OH)?OM-0-Si(OH),
+ Hz0 + Si(OH),OM
+ Si(OH),
where M is either a proton or an alkali metal cation, The corresponding model reaction in alkaline surrounding sumed to occur with a hydroxide ion: Si(OH),OM-0-Si(OH),
+ OH-
is as-
+ Si(OH),OM
+ Si(OH),O-
In acid surrounding, the model assumes that the surface fully hydroxylated and that the reaction is with water: (Si(OH)20MH-O-Si(OH),,+
(I)
(2) site is
+ Hz0 + (Si(OH),OMH)+
+ Si(OH),
(3)
For each model and for each of the cations (Li+, Na’, K’, Rb’, and Cs ‘), the geometries of reactants and products in the model of the dissolution mechanism were optimized at both the Hartree-Fock SCF and the density functional (DFT) levels, where the latter provides an estimate of the effects of electron correlation. The effects of going beyond the Hartree-Fock approximation in computing these reaction energies are large for the anionic products in the alkaline case and reduce the computed endothermicities by up to 21 kcal/ mol (Li’; 6-311G basis). For the neutral model, the effects are insignificant except for the smallest ions, e.g.. H+ (+4.6 kcal/mol) and Li+ (+7.3 kcallmol). The character of the optimised minima was established by fre-
Model of silicate dissolution
a
d b
Fig. 1. Cluster models of siloxane bridge at different pH: (a) Neutral model (pH = pzc), (b) alkaline solution (pH > pzc), (c) acid solution (pH < pzc), and (d) acid solution (pH < pzc). an alternative geometry of a proton associated to the bridging 0. All distances in angstrom units and angles in degrees.
quency analysis. In the DFT calculations, the B3LYP (Becke, 1988, 1993a,b) hybrid functional was used; this includes gradient corrections in the component functionals and part of Hartree-Fock exchange. The reaction energy was estimated by comparing the computed total energies for reactants and products. It should be noted that, due to the smallness of the model and the incomplete treatment of salvation, the trends within the series, i.e., the changes in computed reaction energies for different alkali metals, will be more signiticant than the computed absolute values. The geometry optimizations were performed using the 6-31 IG basis set with the heavier alkali atoms (K’, Rb’, and Cs’) described using the Hay-Wadt effective core potentials (Hay and Wadt, 1985) Extending the basis set to 6-3 I lG* * (investigated for the reactions with Li ‘) had relatively small effects (less than 3.4 kcall mol) on the computed reaction energies. The 6-3 I I G basis set represents an economical level to generate structures for the different components, but for the description of the solvation of the alkali metal cations, in particular in the alkaline region, a substantially larger basis set is required for reliable energetics. The 6-3 1 IG basis does not properly reproduce the dipole moment and polarisability of the water molecule. which results in a large overbinding between the alkali metal ions and the water molecule compared to experiment (Dzidic and Kebarle, 1970). For Rb’ , the difference between the calculated value and experiment is 4.8 kcal/mol, while for the smaller cation Li + with HzO, the difference is 14.3 kcal/mol. Thus, a substantially larger 0 ( I ls7p2d)/[4s3p2d] and H (6slp)/[ 3slp] basis set (Clementi and Ffabitz, 1983) was used in single-point calculations at the optimized geometries to give the final reaction energies. With this basis set, the difference from experimental solvation with one water molecule to Li + reduces to 1.9 kcal/mol due to the improved description of the dipole moment and polarizability of the water molecule. The most important improvement, however, is in the description of the hydroxide ion, resulting in a substantially lower energy for this ion and, as a consequence, the reactions at
high pH becoming substantially more endothermic. It should be noted, however, that, for a given pH, the computed effects of the electrolyte show the same trends with the two basis sets. Finally. the effects on the geometry from using the larger basis in the optimization were investigated by comparing the Clementi and Habitz ( 1983) basis set results for the 6-31 IG optimised geometry with the results, including reoptimization, of the structure with the larger basis set; only minor effects were found. The adopted procedure is thus to perform full geometry optimizations at the B3LYP level with the smaller 6-3 I IG basis set and, for the minimum structure, to obtain the reaction energies using the substantially larger Clementi and Habitz ( 1983) basis set. All calculations were performed using Gaussian 92 or Gaussian 94 (Frisch et al., 1995) running on a DEC Alpha workstation. 4. RESULTS Optimised
I988), only
for
previously
by a number of workers (Xiao
1994; and
Lasaga
the 6-3 lG* 1.652
and
basis
our
1991;
results
for
report
the
model
a mean
to the
experimentally Gibbs,
1980).
MP2
and
geometries la).
here Using
at the MP2-level, bond
value
(Geisinger The
have
and Gibbs,
(Fig.
siloxane
present
model
Lasaga
set in a full optimisation
A comparable and
hydroxylated
the computational
Lasaga
I .63 w reported Newton
the
and Gibbs,
we report
to establish
Xiao
DISCUSSION
structures
been reported Lasaga,
AND
of
length 1.66
and Gibbs, optimised
of
A and I98 1;
Si-0-Si
angle was 123.1’ ( Xiao and Lasaga, 1994) while the present result is 143”, which is in better agreement with the experimental range, 140- 152”, for Si-0-Si bond angles (Xiao and Lasaga,
1994,
and references
therein),
H. Strandh et al.
2580
In the model for the neutral and alkaline cases, one of the OH groups is deprotonated, which weakens the siloxane bond as shown by an increase of the Si-0 bond distance by 0.04 A on the deprotonated side of the system (Fig. lb). The Si-0-Si angle does not seem to be affected by the change in chaage state, but the Si-O- bond distance is reduced by 0.08 A compared to that of the hydroxyl groups. In the protonated surface model, there are two possible products where the proton is either bound to the hydroxyl groups (Fig. lc) or to the siloxane bridging 0 (Fig. 1d) In previous studies of the proton catalysed dissolution of siloxane bonds, only the structure where the proton was found to be directly bonded to the bridging 0 was considered (Xiao and Lasaga, 1994). The model used, H$i-0-SiH?, did not include the surface hydroxyl groups and thus no additional interactions with 0 were available. When the fully hydroxylated surface is considered, we find that the structure where the proton is bonded to the surface hydroxyl groups gives lower energy (by 7.9 kcal/mol), probably due to the extra O-H bond. For this structure, the proton has no direct interaction with the siloxane bridge and consequently has no effect on the siloxane bond distances (Fig. lc). The same chemisorption site is found to be preferred for the alkali cations independent of pH region, but for the alkali metals, we do find a direct interaction with the bridging 0, although with only minor effects on the Si-0 bond distances (Figs. 3 and 4). The structures obtained for the different cations follow the trends of the ionic radii with the shortest M’ distance to the siloxane oxygen for Li’ (2.36 A) and the longest (3.61 .&) for Cs ’ (Fig. 3, acid solution). For the alkaline and neutral models, the interaction with the 0 at the surface dominates, particularly for the smallest cation, Li + (Fig. 4). Compared with the neutral model, the distance to the siloxane 0 increases by 0.65 A; for Na, the increase is 0.29 A; for K, 0.14 A; while for Rb, no change is found and for Cs, the trend is reversed. The resulting structures for the dissociated products including the cation are shown in Figs. 5 and 6. We find the cation coordinated to two hydroxyl groups, again with bond distances following the ionic radii. The reaction products are Si(OH), and Si(OH),O in neutral/acid and alkaline solution, respectively. The optimised structures of these are given in Fig. 2a and 2b. Compared to the results, 1.65 A, of Xiao and Lasaga ( 1994), our computed Si-0 bond lengths for Si( OH), are slightly longer, 1.67 A, but still in good agreement with their MP2/ 6-3 1G * calculations. Having obtained the optimised structures for both reactants and products, we may compute the reaction energies, AE, by subtracting the total energies of the reactants from those of the products in Eqns. 2 and 3. To be specific, we have for the reaction with alkali cations at neutral pH AE = -EISi,O(OH)sOM]
+ E[Si(OH),OM] - E[H*O]
+ E[Si(OH),]
(4)
and at high pH: AE = -E[Si,O(OH),OM]
+ E[Si(OH),OM] - E[OH-]
and at low pH:
+ E(Si(OH),O-]
(5)
a
1.61
b
Fig. 2. Optimized structures of products (a) Si(OH), in neutral and acid solution and (b) Si(OH)?O- in alkaline solution. Distances in FmgstrBm.
AE = -E[Si,O(OH),OHM+]
+ E[Si(OH),OHM+] - E[H,O]
+ E[Si(OH),]
(6)
Determination of the total energy as described above estimates the energy change of the system and indicates the exothermicity. The activation energies of these reactions are not considered, but we assume that the difference in the activation barriers between the reactions are small so that a relative comparison between the reaction energy and the reaction rate can be applied. In the present work, the effects of both pH and addition of alkali metal cations are investigated, and thus, both the reaction energies at different pH values and the relative values from addition of electrolyte at fixed pH are calculated. The absolute values are given in Table 1, where it should be noted that for the reaction with OH _ in the alkaline case, the experimental energy of hydration, - 108 kcal/mol (Ball and Norbury, 1974), of the OH species has been added on the reactant side. For the solvation of the reaction product, Si ( OH)30 ~, no experimental value
Model of silicate dissolution
2581
1.89
Fig. 3. Optimized structures for alkali cation interacting with siloxane bridge of hydroxylated surface. Distances in Bngstrtim and angles in degrees. Fig. 5. Hydroxylated model. Optimized structures Distances in IngstrSm and angles in degrees.
of products.
of the hydration energy is known to us; we have thus computed it by modelling the effects of solvation by placing the anion in a cavity in a polarisable medium with the dielectric constant of water, which is 80.4, using Gaussian921DFT. This model of solvation of ions has some problems in treating the H bonds to the solvent. In order to get a reasonable estimate of the hydration energy of Si( OH)30-, one may compare with the perchlorate ion, which is of similar size, has a weak hydrogen bond interaction with the solution, as expected also of Si ( 0H)30-, and for which an experimental value has been determined. Computing the hydration energy of the Si (OH),0 and the ClO, ions gives energies of -50 and -49 kcal/mol, respectively (6-311G basis set), compared to the experimental value for Cl07 AH,,, = -54
kcal/mol (Ball and Norbury, 1974). Since the model does not include the H bond influence properly and the results on perchlorate hydration modelling show less negative hydration energy than experiment, we assume that the computed hydration energy for Si( OH)30m is an upper bound to the true hydration energy; thus the reaction energy in the alkaline pH region should become more exothermic with a more accurate value for the hydration energy. The computed hydration energy for Si(OH)?O‘ ( -50 kcal/mol) has been added to the product side of all entries for the alkaline region in Table I. It should be noted that without consideration of the solvation terms for the alkaline model. the reaction
Fig. 4. Optimized structures for alkali cation interacting ane bridge of deprotonated surface. Distances in angstriim in degrees.
Fig. 6. Deprotonated model. Optimized structures Distances in lngstrijm and angles in degrees.
with siloxand angles
of products.
H. Strandh
2582
Table I. Reaction energies (in kcal/mol) computed at the B3LYP level for siloxane bond breaking at different pH and with different electrolytes. 6-3 I I G values are given in parenthesis. Electrolyte
H Li Na K Rb CS
Low pH 5.8 21.6 14.7 I I.2 10.0 7.1 6.0
(5.1) (23.9) (19.1) (15.6) (16.6) (11.1) (9.8)
Neutral 16.4 5.8 14.8 15.7 15.4 15.2 14.9
High pH”.”
(18.0) (5.1) (14.4) (16.6) (17.2) (17.0) (16.4)
” OH energy of hydration. -108 kcallmol, Norbury, 1974). ” Si(OH)Q hydration energy, -50 kcal/mol, using Gaussian92/DFT). ’ No electrolyte added.
27.2 (16.8) 25.7 26.5 26.3 26.0 25.7
(13.4) (15.6) (16.2) (16.0) (15.3)
included
(Ball and
included
(modelled
energies would all have been strongly exothermic for the high pH region. We may now compare the reaction energies for the different pH regions without the electrolyte added. For the deprotonated model, we have a reaction energy of 16.4 kcal/mol for the reaction with water (pH = pzc), while the reaction with OH- gives an upper bound of 27.2 kcal/mol (pH > pzc). For the low pH case, we compare with the reaction energy of the protonated model reacting with water; this gives an endothermic reaction energy of 5.8 kcal/mol (same as the deprotonated model reacting with H+ and H20). Assuming that the barriers are similar for the different reactions so that the relative reaction energies could be used to estimate the reaction rates, the present results would give the highest rate for the low pH region followed by pH = pzc (“neutral”). The lowest rate would be expected for the alkaline solution which has the most endothermic reaction. Experimentally a minimum in the rate is found for pH around pzc, and the simple model that we have considered so far thus does not predict the correct order between neutral and alkaline solution. The treatment of the negatively charged species in the modelling of this pH region is, however, complicated, and, furthermore, large effects of solvation on the alkaline model could be expected. The relative values for a given pH (collected in Table 2 from Table 1 for easy reference) show the effects on the siloxane bond strength from addition of a proton (acidic/ neutral) or an alkali cation to the siloxane bond. Here, the reference value for the acidic solution was taken as the reaction energy, 5.8 kcal/mol, of the hydroxylated siloxane bond, (OH),Si-0-Si(OH),, reacting with water. For both the neutral and alkaline (relative to pzc) pH regions, the reference was taken as the partially deprotonated (OH),Si-O-Si(OH)20 surface mode1 interacting with water (16.4 kcal/mol) or OH(27.2 kcal/mol), respectively. Since the differences between the neutral and alkaline solution models do not involve the cations (cf. Eqns. 5 and 4), the trend for the different alkalis is by construction identical for the neutral and alkaline solutions. The largest effect from an alkali cation on the reaction energy is found for the reaction with Li’ and Cs’, which destabilise the siloxane bond by about 1.5 kcal/mol; the differences among the alkali ions are small, however. The results would indicate a larger
et al
destabilisation for Li+ than for Na+ and K+, while the trend is increasing from K to Cs; the energy differences are too small to allow firm conclusions, however. In comparison to experimental data on salt effects on dissolution rates of feldspar (Li > Na > K), the results show the expected trend. The reported (Dove and Crerar, 1990) experimental salt effects on quartz, however, indicate an opposite trend, Li < Na = K. The model of the dissolution process in acid solution gives some surprising results; for this model, contrary to what has been reported previously and termed proton catalysed siloxane bond breaking (Xiao and Lasaga, 1994), we find a stabilisation of the siloxane bond through the interaction with a proton. Two different structures were investigated: the direct interaction with the siloxane bridging 0, which has previously been studied by Xiao and Lasaga (1994), and the more favorable case (within the present model) where the proton interacts with the hydroxyl groups. In both cases, we find a stabilisation from the interaction with the proton: interaction with the siloxane bridging 0 gives a reaction energy of 13.8 kcal/mol (stabilisation by 8 kcal/mol) while interaction with the hydroxyl groups gives a larger stabilisation (by 15.8 kcal/mol). The origin of the stabilisation is the favorable interaction with the surface OH-groups, which was not included in earlier work. Furthermore, all of the cations are found to increase the endothermicity, i.e., to stabilise the siloxane bond; the magnitude of the effect decreases with increasing size of the cations. Experimentally, at low pH, addition of alkali has been found to inhibit the dissolution process of feldspar with the relative activities Li < Na < K. For quartz, the situation is less clear, but new data indicate no effect from Li+ and Na’ and inhibitory activity of K’ (Strandh et al., 1996, and H. Strandh, unpubl. results). Thus, the present results indicate a genera1 agreement with an inhibitory effect but give the wrong relative activities for the different ions. Furthermore, the comparison with the (fully hydroxylated, Fig. lc) neutral reference model shows a stabilisation of the bond from the interaction with a proton (+15.8 kcal/mol, Table 2), which is again contrary to what is normally assumed. These results indicate that, in particular for the acid model where the surface becomes charged, one must at least consider the effects of solvation. Ideally this should be done having the first salvation shell included and embedding the whole system in a polarisable dielectric medium. Since the solution is present on only one side of the system, the dielectric medium is not trivial to include. We have thus chosen to focus on the effects of adding the first few water molecules in order to qualita-
Table 2. Computed B3LYP level reaction energies relative to the respective models without electrolyte. Electrolyte
Low pH
-
5.8 + 15.8 +8.9 +5.4 +4.2 +1.3 +0.2
H Li Na K Rb CS
Neutral 16.4 -10.6 -1.6 -0.7 -1.0 - 1.2 -I .5
(in kcal/mol)
High pH 27.2 -1.5 -0.7 -0.9 -1.2 -1.5
Model of silicate dissolution tively describe energetics. 4.1. Solvated
the effects
of the presence
of water on the
Table 3. Computed B3LYP including effects of solvation.
The dissolution will occur at the liquid-solid interface where the liquid is an electrolyte of varying composition and PH. Thus, we must consider the effects of solvation of the surface, i.e., association of water molecules via H bonding to the OH-groups at the surface. Furthermore, the cations in the solution will be solvated by, on the average, six water molecules in the first solvation shell; part of this solvation shell may be expected to be lost when the ions are coordinated to the surface. The efficiency of the salvation may be different for the reactants and the products so that the solvation may affect the computed reaction energies. Finally, all reactions involving a proton should be expected to be very strongly affected by replacing the proton with a H,O’ rather than a free proton. Since the surface with cation in the acid model bears a positive charge, this is where the largest effects of solvation should be expected, and, in fact, qualitative effects of solvation may be seen already after adding the first few water molecules (Table 3). The results for Li+ and Rb’ for the acid model are shown in Figs. 7 and 8, which may be com-
Fig. 7. Optimized
structures
energies
Zero water
1 H,O
Acid Model H Li Rb
5.8 21.6 14.7 7.1
17.9 12.4 6.2
Neutral -
16.4
Electrolyte
Models
level reaction
2 H,O
13.4 9.8 5.5
model
H Li Alkaline
(in kcal/mol)
-
5.8 14.8
6.1 12.0
2.6 10.9
27.2 25.7
22.8
21.8
model
Li
-
pared with the unhydrated system in Fig. 3. The addition of the first water leads to an increase in the alkali to siloxane 0 distance for Li’ and Rb+ by 0.54 w and 0.05 A: respectively. The second water already has a much smaller effect on the Li+ structure and increases the distance by only 0.05 A; for Rb’, the effect is somewhat larger, 0.14 A. For the
with one water molecule
2584
H. Strandh et al
Fig. 8. Optimized structures with two water molecules.
products in the acid case, the main solvation effect will occur for the charged [Si(OH),M]+ system, and the structures resulting from the addition of one and two waters are shown in Figs. 9 and 10 (cf. Fig. 5); the result of the interaction with the water molecules is again a reduction in the strength of the interaction with the nearest 0. The structure around the larger cation, Rb’, is hardly affected by the addition of the second H20, while again for Li+, much larger changes are found; here the Li-0 distance increases from 1.89 to 1.93 to 2.01 A upon addition of one and two water molecules. Since the hydration effects on reactants and products involving Rb’ are small, the resulting effect on the reaction energy is very small. The solvation of the reactants and products including Li’ had a large impact on the structure and, consequently, a large effect on the reaction energy. The obtained results show that the hydration of the dissolution product, including an alkali metal ion, is more effective on the smaller ion Li+ than on Rb+. Solvation of the large cation Rb+ seems to be as effective on the surface model as on the dissolution product (Si(OH),OHM+). This result indicates that using full hydration, the model may produce a reversed trend for the alkali metal ion effect on the reaction energy, i.e., that the smaller ions have a smaller stabilising effect on the siloxane bond than the larger ions, yielding a better agreement with experimental data. In the alkaline and neutral solutions, the models of the surface and the dissolution prod-
uct with adsorbed alkali metal ions are uncharged, but still the solvation of the ion gives a less endothermic reaction. When including three water molecules in the hydration layer around the alkali metal ion, the water molecules start to interact by H bonds with the hydroxyl groups that represent the connection to the bulk structure on the surface model (Fig. 11). This would not be possible in reality, and it is clear that the surface model used in the present study has to be modified to be able to model a larger hydration layer on the adsorbed alkali metal ions. Work along this line has been initiated. The dissociation processes in the alkaline situation will be strongly affected by solvation processes due to the presence of charged species. The dominating solvation effects will thus occur for the hydroxide ion before the dissociation and for the dissociated Si acid ion, Si(OH)30-, after the process; these two contributions have been taken from experiment (OH-) or estimated from calculations (Si(OH),O-) in the present work. The first two terms, containing the alkali metal, are the same in Eqn. 5 and Eqn. 4 and thus the difference between the two reactions, for a given cation M, is just a constant term. Consequently, hydratization can not, in this simple model, affect the relative order of the bond energies as a function of the alkali atoms, and the same relative order of the effects should thus be expected. This does not seem to be in agreement with experiment, where no effect of addi-
Model of silicate dissolution
: . Y
0.97
Fig. 9. Optimized
structures
of products
with one water molecule.
Li 2.01 Rb 2.94
/1.65
Fig. 10. Optimized
structures
of products
with two water molecules.
2585
H. Strandh et al.
2586
Fig. Il. Optimized three water molecules.
structure
of surface
and adsorbed
Li + with
tion of alkali is reported for the neutral surface, while at high pH, the effects depend both on the metal and on the mineral (feldspar: Li > Na > K and quartz: Li < Na = K). This may be due to the charge distribution at the surface in alkaline and neutral solutions being different from what is assumed in the presents models. This would require larger models of the surface to be considered, where e.g., for the neutral solution, a model including both positively and negatively charged sites as in (OH),SiOH:-0-Si(OH),-OSi(OH)20and for the alkaline solution, (OH)$i-OSi(OH),-0-Si(OH),Ocould be used to differentiate between these two pH regions. In view of the differences in the effects of the different cations on feldspar and quartz dissolution rates found experimentally, it seems likely that the structural differences between feldspar and quartz must be taken into account in an extended model. Even though the breaking of the siloxane bond is considered the rate limiting step in the dissolution process, a minimal model including only the siloxane bond cannot be sufficient for a reliable comparison of the dissolution processes of the two minerals. 5. CONCLUSIONS The present theoretical study has been performed to investigate a connection of salt effects on the dissolution rates of quartz and similar minerals to adsorption at different pH of alkali metal ions on siloxane bonds. The adsorption of alkali metals was found to result in changes in both geometry and Si-0 bond strength, depending on which alkali metal that
was adsorbed. Calculated bond energies of the model used for the alkaline pH region imply that the adsorbed alkali metal ions weaken the Si-0 bond, which then is easier to break; consequently, a higher dissolution rate should be obtained, in agreement with experimental results. For pH < pzc, addition of alkali cations to the siloxane bond was found to stabilise the bond with a greater effect from the smaller cations; experimentally, this is what has been found, but with reverse dependence on the size of the ions compared to what is obtained from the calculations. Including the first few water molecules in the solvation shell around the cation coordinated to the surface and to the reaction product has the largest effects on the smaller ions and reduces the stabilisation of the bond. Thus. it seems likely that a fully solvated model should be able to reproduce also the relative ordering among the alkali cations; solvation of the ions at the surface makes significant contributions to the reaction energies and must be included in the model calculations. A critical fact when performing theoretical calculations on complex systems such as mineral surfaces is the size of the model. Earlier studies by Xiao and Lasaga (1994) on H30+ hydrolysis were performed using only H-terminated Si-0-Si models and the results indicated that a direct interaction between the proton and the bridging 0 could be the cause of the increased dissolution rate found in acid pH experiments. The effect of H,O’ hydrolysis is completely different when using larger systems more like the true surface, as the hydroxyl-terminated model used in the present study, with no interaction between the proton and the bridging 0. The increase in dissolution rate at pH < pzc is, as is the case for the alkali cations, indicated to be due to the relative hydration energy effect on the surface and the dissolved products. The main results of the present model study are the importance of solvation on the energetics of the siloxane bond breaking in different environments and also that, in spite of the smallness of the model, the main characteristics of the dissolution process have been captured. The model is, however, too small to be able to include the full hydration effect on the adsorbed ions since the hydration water and the groups representing the bulk mineral start to interact. Work has been initiated on larger models containing two siloxane bonds for which the effects of solvation on the surface and on the coordinated ions may be studied in more detail. Acknowledgments-Valuable discussions with M. Sandstrom on solvation energies of anions are gratefully acknowledged. This work was funded by The Swedish Central Board of National Antiquities.
Editorial
handling:
J. Tossell
REFERENCES Ball M. C. and Norbury A. H. (1974) Physical Data jbr Inorgunic Chemists. Longman. Becke A. D. (1988) Density-functional exchange-energy approximation with correct asymptotic ,behavior. Phys. Rev. A38, 3098. Becke A. D. (1993a) A new mixing of Hartree-Fock and local density-functional theories. J. C/rem. Phys. 98, 1372. Becke A. D. (1993b) Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Ph~v. 98, 5648. Bennett P. C. (1991) Quartz dissolution in organic-rich aqueous systems. Geochim. Cosmochim. Actu 55, 1781- 1797.
Model of silicate dissolution Bennett P. C. (1995) Dynamics of silicate dissolution in organic and inorganic electrolyte solutions. GSA annual meeting 27 (abstr.). Brady P. V. and Walther J. V. (1990) Kinetics of quartz dissolution at low temperatures. Chem. Geol. 82, 253-264. Clementi E. and Habitz P. (1983) A new two-body water-water potential. J. Phys. Chem. 87, 2815-2820. Dove P. M. and Crerar D. A. (1990) Kinetics of quartz dissolution in electrolyte solutions using a hydrothermal mixed flow reactor. Geochim. Cosmochim. Actu 54, 955-969. Dove P. M. and Elston S. F. (1992) Dissolution kinetics of quartz in sodium chloride solutions: Analysis of existing data and a rate model for 25°C. Geochim. Cosmochim. Acta 56, 4147-4156. Dzidic I. and Kebarle P. (1970) Hydration of the alkali ions in the gas phase. Enthalpies and entropies of reactions M+(HZO),,_, + HZ0 = M+(HZO),,. J. Phys. Chem. 74, 1466 1474. Frisch M. J. et al. (1995) GAUSSIAN 94. Revision A. I. Gaussian, Inc. Geisinger K. L. and Gibbs G. V. (1981) STO-3G molecular orbital (MO) calculated correlations of tetrahedral SiO and Al0 bridging bond lengths with p,, and f,. GSA Abstr. Prog. 13, 458 (abstr.). Hay P. J. and Wadt W. R. (1985) Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J. Chem. Phys. 82, 299-3 10. Hellmann R. (1994) The albite-water system: Part I. The kinetics of dissolution as a function of pH at 100, 200 and 300°C. Geochim. Cosmochim. Actu 58, 595-611. Knauss K. G. and Copenhaver S. A. (1995) The effect of malonate on the dissolution kinetics of albite, quartz, and microcline as a function of pH at 70°C. Appl. Geochem. 10, 17-33. Knauss K. G. and Wolery T. J. (1988) The dissolution kinetics of quartz as a function of pH and time at 70°C. Geochim. Cosmochim. Actu 52, 43-53.
2587
Lasaga A. C. and Gibbs G. V. (1988) Quantum mechanical potential surfaces and calculations on minerals and molecular clusters 1. STO-3G* and 6-31G* results. Phgs. Chem. Mined. 16, 29-41. Lasaga A. C. and Gibbs G. V. (1991) Quantum mechanical HartreeFock surfaces and calculations on minerals. II. 6-31G* results. Phys. Chem. Mined 17, 485 -49 1, Newton M. D. and Gibbs G. V. (1980) Ab initio calculated geometries and charge distribution for H,SiO? and H,Si?O, compared with experimental values for silicates and siloxanes. Phys. Chem. Mineral. 6, 22 I -246. Plettinck S., Chou L., and Wollast R. (1994) Kinetics and mechanism of dissolution of silica at room temperature and pressure. Mineral. Mug. 58A, 728-729. Schweda P. (1990) Kinetics and mechanism of alkali feldspar dissolution at low temperatures. Ph.D. thesis, Stockholm Univ. Sjoberg L. (1989) Kinetics and non-stoichiometry of labradorite dissolution. Proc. 6th Intl. Symp. Wuter-Rock Interaction, 609-612. Stillings L. L. and Brantley S. L. (1995) Feldspar dissolution at 25°C and pH 3: Reaction stoichiometry and the effect of cations. Geochim. Cosmochim. Actu 59, 1483- 1496. Strandh H., Sjoberg L., Pettersson L. G. M., and Wahlgren U. (1996) A theoretical and experimental study of quartz dissolution dependence on alkali metal cations. GFF 118, A55-A56 (abstr.). Sverjensky D. A. (1994) Zero-point-of-charge prediction from crysActu tal chemistry and salvation theory. Geachim. Cwnochim. 58, 3123-3129. Wollast R. and Chou L. (1986) Processes, rate and proton consumpTrans. XII Gong. of the Id SOL.. of tion by silicate weathering. Soil Sci. Xiao Y. and Lasaga A. C. (1994) Ab initio quantum mechanical studies of the kinetics and mechanism of silicate dissolution: H’(H,O‘) catalysis. Geochim. Cosmochim. Actu 58, 5379-5400.
Pergamon
PI1 SOO16-7037( 97)00118-X
Quantum
chemical
HELENE STRANDH,
studies of the effects on silicate mineral by adsorption of alkali metals
dissolution
rates
’LARS G. M. PETTERSSON,2 LENNART SJOBERG,‘.* and ULF WAHLGREN’
and Geochemistry, University of Stockholm, S-106 91 Stockholm, Sweden ‘Department of Physics, University of Stockholm, Box 6730, S-l 13 85 Stockholm. Sweden
‘Department
of Geology
(Received
June 7, 1996; accepted
in revised form
Murch
I,
1997)
Abstract-Quantum chemical calculations at the density functional level (B3LYP functional) with full geometry optimisation have been performed on the effect of protonation and of adsorption of alkali cations (Li + , Na + , K + , Rb+ , and Cs ‘) on the siloxane bond strength in silicate minerals. The influence of pH was modelled by assuming a fully protonated surface model, (OH)&-0-Si( OH)l, at pH lower than the point of zero charge (pzc), while for pH = pzc and pH > pzc, the cation was assumed to interact with a deprotonated surface -O- site. At low pH, addition of cations is found to strengthen the siloxane bond in agreement with experiment for the alkali metals, but not for the interaction with H?O + At high pH, the siloxane bond is weakened by the addition of alkali, in agreement with experiment for feldspar dissolution. Inclusion of the surface hydroxyl groups is found to be important particularly when solvation of the ions at the surface is considered; up to three water molecules have been included in the geometry optimisation. Salvation of the ions interacting with the surface is found to give very important Co&right 0 1997 Elsevier Science Ltd _ contrib&o& to the computed reaction energies. 1. INTRODUCTION
dissolution is controlled by the surface speciation which itself is determined by the composition of the surrounding solution. Dove and Elston (1992) employed the triple layer electrostatic model, computing the distribution of predominant species on the surface to be able to get a better understanding of rate controlling processes. The calculations were performed using a set of parameters describing the electrostatic layer and the surface, and the results were included in a rate law fitted to experimental data. To avoid using parameters to describe the surface and its environment, one may use quantum chemical calculations. In a study of the mechanism of adsorption and hydrolysis of H,O+ and H’ + H20 at Si-0-Si and Si-O-Al bridges, Xiao and Lasaga ( 1994) calculated the intermediate transition state for the reactants and products using ab initio molecular orbital calculations. These model calculations showed that the Si-0 bond and, even more, the Al-0 bond are weakened by the adsorption of H30 ’ at the siloxane oxygen, which may explain the acid effect on the dissolution kinetics. i.e.. the observed increase in the rate for pH < pzc. The dissolution kinetics is furthermore dependent on the composition of the solvent, i.e., the presence of ions other than proton and hydroxide. Of particular interest for the present study is the influence on the dissolution process of the type and amount of alkali metal present; at pH values larger than pzc, it has been found that alkali metals enhance the dissolution of feldspar in the order Li > Na > K ( Schweda, 1990; SjGberg, 1989)) but for quartz, the effects indicate a different order (Li < Na = K) (Plettinck et al., 1994; Dove and Crerar, 1990). At pH less than pzc, dissolution is inhibited by the presence of alkali metals with the relative activities for feldspar Li < Na < K (Stillings and Brantley, 1995; Schweda, 1990: Sjiiberg. 1989). For quartz, the dissolution in this pH region has been reported to be inhibited by Li’ with a lower dissolution rate than in pure HCI solution (Bennett, 1995 ), but newer results ( Strandh et
The processes of weathering and dissolution of silicate minerals such as quartz and feldspar have become of particular interest during the last decades, due to the increased knowledge of the changes in the environmental chemistry caused by human activities. This change in chemistry has lead to an observed increase in the rate of these processes and has generated a concern for the preservation of historical treasures such as rock-carvings. In coastal regions, the rockcarving surfaces will be exposed both to a wide pH interval and to a relatively high concentration of salts, which both have a strong influence on the dissolution rate. Thus, in the present theoretical work, we will focus on models of the quartz surface and examine possible reaction mechanisms which include both the dependence on pH and the presence of alkali metal cations. The present studies have been accompanied by new experimental determinations of the rate constants of quartz dissolution as function of pH and salt (LiCl, NaCl, KC]) concentration (Strandh et al., 1996, and H. Strandh, unpubl. results). Interest in silicate mineral dissolution processes has been large and has been concerned with the mineral-solution interface reactions and with understanding the solution dependencies that dissolution kinetics studies show. The network silicate minerals quartz and feldspar have been observed to give similar results in the dissolution process with a rate minimum at about the same pH as the pH where the proton activity gives a zero net charge on the surface of the respective mineral, i.e., the point of zero charge (pzc) (Knauss and Copenhaver, 1995; Plettinck et al., 1994; Sverjensky, 1994; Hellmann, 1994; Bennett, 1991; Brady and Walther, 1990; Knauss and Wolery, 1988; Wollast and Chou, 1986). The observed pH dependence has lead to the conclusion that:
* Deceased. 2577
H. Strandh et al
2578
al., 1996, and H. Strandh, unpubl. results) show no effect from Li+ and Na+ and an inhibition by K’ In the present study, we investigate the effects of the alkali cations (Li+, Nat, K+, Rb’, and Cs’) on the siloxane bond strength using quantum chemical calculations on models of the siloxane bridge at different pH (acid, neutral, and basic) with respect to surface speciation and compare the trends between the different cations with those observed experimentally at different pH. In solution, the cations will naturally be solvated by, on average, six water molecules in the first solvation shell. At the surface, the solvation may be less efficient but can still lead to important effects on the energy differences between reactants and products. The solvation energies for alkali metal ions in solution are well-known experimentally, but at the liquid-solid interface, the situation is !ess clear, and we have thus also considered models including up to three water molecules. 2. MODELS In a model study of complicated reactions such as weathering, a number of assumptions have to be made about how the process occurs. There is general agreement that the ratedetermining step in the chemical weathering of both quartz and feldspar is the breaking of a siloxane bond between two Si atoms and that, at neutral and acid pH (relative to pzc), the process involves water as a reactant; in alkaline solution, hydroxide ions are assumed to participate in the bond breaking. In the present work, we assume this to be true also in the investigation of the effect of alkali cations on the strength of the siloxane bond. At least two silicon atoms must be included in a model which should describe the breaking of a siloxane bond. The Si atoms, having four possible bonds, must be bound to three additional groups in order to saturate the system. In bulk quartz, each Si atom is bound to four other silicon atoms through 0 bridges while at the surface, the exposed 0 will be protonated or form 0 groups. We have chosen to terminate all bonds with hydroxyl groups; at the surface, we have thus included the surface OH groups while the siloxane bridges to bulk-like Si atoms are replaced by OH groups as a simplest representation of these. Thus, the minimal model of the hydroxylated quartz surface consists of two Si( OH), groups bound together by an 0 bridge (a siloxane bond) (Fig. 1a). The deprotonated surface in alkaline solution was represented by removing a proton from a Si(OH)3 group (Fig. lb) while in acid solution, the surface instead can become protonated, and this was modeled by adding a proton to one of the Si ( OH)x groups (Fig. 1c) In order to consider the salt effects observed in silicate dissolution experiments, an alkali metal cation was added and allowed to interact with the model of the surface in alkaline and neutral (compared to pzc) solution. In the acidic solution, the surface charge was given either by a proton or by an alkali metal cation so that in this case, the model may be described by (OH),SiOHM’-0-Si(OH), (Figs. lc and 3). The structure was fully optimized using gradient techniques for each of the cases. Since the reactions occur in an electrolyte solution, the solvation of the ions and of the reactants and products must be considered. In the present work,
we have
investigated
these
effects
by optimising
se-
lected systems, including explicitly one, two, or three water molecules. The breaking of a siloxane bond must involve an attack by either a water molecule, a hydroxide ion, or a hydronium ion. We have assumed that the attack in the alkaline case is carried out by a hydroxide ion and in a neutral surrounding, by a water molecule. In the acidic case, it is reasonable to assume that the surface becomes protonated, which makes an attack by a hydronium ion unlikely due to the electrostatic repulsion. Xiao and Lasaga (1994) have earlier shown that performing the attack by H,O+ or by H+ + HZ0 produces the same results for the reaction energy and geometry. We have therefore assumed that the breaking of a siloxane bond in the acidic case occurs through an attack by a water molecule on a protonated surface. In the present model, the dissociation products leaving the surface into the solute are Si( OH)4 in the neutral and acid situations and Si( 0H)30m when the attack is made by a hydroxide ion (i.e., the alkaline case). 3. METHODS At the surface, three types of situations are relevance: the surface may be fully hydroxylated of zero as modelled by (OH)&-0-Si(OH), be deprotonated as (OH),Si-0-Si(OH)&
expected to be of with a total charge (Fig. la), it may
(Fig. 1b), or it may be protonated with a net positive surface charge as (OH)&0-Si( OH),OH; (Fig. I c). In alkaline solution, the deprotonated and neutral species are assumed to dominate while in the acid solution, the neutral and protonated species should dominate at the surface. At pzc, the net charge of zero may be achieved in two different ways: by regions with fully hydroxylated surface groups and by regions with equal numbers of positively and negatively charged groups. The bond strength of additional cations interacting with these surfaces is highest for the negatively charged species, followed by the neutral surface, and lowest for the positively charged sites; this has been the basis for the different reaction models described below. We assume that the reaction mechanisms in both alkaline and neutral solution involve an interaction with a deprotonated site at the surface. In a neutral solution, the reaction is assumed to occur with water so that we may write Si(OH)?OM-0-Si(OH),
+ Hz0 + Si(OH),OM
+ Si(OH),
where M is either a proton or an alkali metal cation, The corresponding model reaction in alkaline surrounding sumed to occur with a hydroxide ion: Si(OH),OM-0-Si(OH),
+ OH-
is as-
+ Si(OH),OM
+ Si(OH),O-
In acid surrounding, the model assumes that the surface fully hydroxylated and that the reaction is with water: (Si(OH)20MH-O-Si(OH),,+
(I)
(2) site is
+ Hz0 + (Si(OH),OMH)+
+ Si(OH),
(3)
For each model and for each of the cations (Li+, Na’, K’, Rb’, and Cs ‘), the geometries of reactants and products in the model of the dissolution mechanism were optimized at both the Hartree-Fock SCF and the density functional (DFT) levels, where the latter provides an estimate of the effects of electron correlation. The effects of going beyond the Hartree-Fock approximation in computing these reaction energies are large for the anionic products in the alkaline case and reduce the computed endothermicities by up to 21 kcal/ mol (Li’; 6-311G basis). For the neutral model, the effects are insignificant except for the smallest ions, e.g.. H+ (+4.6 kcal/mol) and Li+ (+7.3 kcallmol). The character of the optimised minima was established by fre-
Model of silicate dissolution
a
d b
Fig. 1. Cluster models of siloxane bridge at different pH: (a) Neutral model (pH = pzc), (b) alkaline solution (pH > pzc), (c) acid solution (pH < pzc), and (d) acid solution (pH < pzc). an alternative geometry of a proton associated to the bridging 0. All distances in angstrom units and angles in degrees.
quency analysis. In the DFT calculations, the B3LYP (Becke, 1988, 1993a,b) hybrid functional was used; this includes gradient corrections in the component functionals and part of Hartree-Fock exchange. The reaction energy was estimated by comparing the computed total energies for reactants and products. It should be noted that, due to the smallness of the model and the incomplete treatment of salvation, the trends within the series, i.e., the changes in computed reaction energies for different alkali metals, will be more signiticant than the computed absolute values. The geometry optimizations were performed using the 6-31 IG basis set with the heavier alkali atoms (K’, Rb’, and Cs’) described using the Hay-Wadt effective core potentials (Hay and Wadt, 1985) Extending the basis set to 6-3 I lG* * (investigated for the reactions with Li ‘) had relatively small effects (less than 3.4 kcall mol) on the computed reaction energies. The 6-3 I I G basis set represents an economical level to generate structures for the different components, but for the description of the solvation of the alkali metal cations, in particular in the alkaline region, a substantially larger basis set is required for reliable energetics. The 6-3 1 IG basis does not properly reproduce the dipole moment and polarisability of the water molecule. which results in a large overbinding between the alkali metal ions and the water molecule compared to experiment (Dzidic and Kebarle, 1970). For Rb’ , the difference between the calculated value and experiment is 4.8 kcal/mol, while for the smaller cation Li + with HzO, the difference is 14.3 kcal/mol. Thus, a substantially larger 0 ( I ls7p2d)/[4s3p2d] and H (6slp)/[ 3slp] basis set (Clementi and Ffabitz, 1983) was used in single-point calculations at the optimized geometries to give the final reaction energies. With this basis set, the difference from experimental solvation with one water molecule to Li + reduces to 1.9 kcal/mol due to the improved description of the dipole moment and polarizability of the water molecule. The most important improvement, however, is in the description of the hydroxide ion, resulting in a substantially lower energy for this ion and, as a consequence, the reactions at
high pH becoming substantially more endothermic. It should be noted, however, that, for a given pH, the computed effects of the electrolyte show the same trends with the two basis sets. Finally. the effects on the geometry from using the larger basis in the optimization were investigated by comparing the Clementi and Habitz ( 1983) basis set results for the 6-31 IG optimised geometry with the results, including reoptimization, of the structure with the larger basis set; only minor effects were found. The adopted procedure is thus to perform full geometry optimizations at the B3LYP level with the smaller 6-3 I IG basis set and, for the minimum structure, to obtain the reaction energies using the substantially larger Clementi and Habitz ( 1983) basis set. All calculations were performed using Gaussian 92 or Gaussian 94 (Frisch et al., 1995) running on a DEC Alpha workstation. 4. RESULTS Optimised
I988), only
for
previously
by a number of workers (Xiao
1994; and
Lasaga
the 6-3 lG* 1.652
and
basis
our
1991;
results
for
report
the
model
a mean
to the
experimentally Gibbs,
1980).
MP2
and
geometries la).
here Using
at the MP2-level, bond
value
(Geisinger The
have
and Gibbs,
(Fig.
siloxane
present
model
Lasaga
set in a full optimisation
A comparable and
hydroxylated
the computational
Lasaga
I .63 w reported Newton
the
and Gibbs,
we report
to establish
Xiao
DISCUSSION
structures
been reported Lasaga,
AND
of
length 1.66
and Gibbs, optimised
of
A and I98 1;
Si-0-Si
angle was 123.1’ ( Xiao and Lasaga, 1994) while the present result is 143”, which is in better agreement with the experimental range, 140- 152”, for Si-0-Si bond angles (Xiao and Lasaga,
1994,
and references
therein),
H. Strandh et al.
2580
In the model for the neutral and alkaline cases, one of the OH groups is deprotonated, which weakens the siloxane bond as shown by an increase of the Si-0 bond distance by 0.04 A on the deprotonated side of the system (Fig. lb). The Si-0-Si angle does not seem to be affected by the change in chaage state, but the Si-O- bond distance is reduced by 0.08 A compared to that of the hydroxyl groups. In the protonated surface model, there are two possible products where the proton is either bound to the hydroxyl groups (Fig. lc) or to the siloxane bridging 0 (Fig. 1d) In previous studies of the proton catalysed dissolution of siloxane bonds, only the structure where the proton was found to be directly bonded to the bridging 0 was considered (Xiao and Lasaga, 1994). The model used, H$i-0-SiH?, did not include the surface hydroxyl groups and thus no additional interactions with 0 were available. When the fully hydroxylated surface is considered, we find that the structure where the proton is bonded to the surface hydroxyl groups gives lower energy (by 7.9 kcal/mol), probably due to the extra O-H bond. For this structure, the proton has no direct interaction with the siloxane bridge and consequently has no effect on the siloxane bond distances (Fig. lc). The same chemisorption site is found to be preferred for the alkali cations independent of pH region, but for the alkali metals, we do find a direct interaction with the bridging 0, although with only minor effects on the Si-0 bond distances (Figs. 3 and 4). The structures obtained for the different cations follow the trends of the ionic radii with the shortest M’ distance to the siloxane oxygen for Li’ (2.36 A) and the longest (3.61 .&) for Cs ’ (Fig. 3, acid solution). For the alkaline and neutral models, the interaction with the 0 at the surface dominates, particularly for the smallest cation, Li + (Fig. 4). Compared with the neutral model, the distance to the siloxane 0 increases by 0.65 A; for Na, the increase is 0.29 A; for K, 0.14 A; while for Rb, no change is found and for Cs, the trend is reversed. The resulting structures for the dissociated products including the cation are shown in Figs. 5 and 6. We find the cation coordinated to two hydroxyl groups, again with bond distances following the ionic radii. The reaction products are Si(OH), and Si(OH),O in neutral/acid and alkaline solution, respectively. The optimised structures of these are given in Fig. 2a and 2b. Compared to the results, 1.65 A, of Xiao and Lasaga ( 1994), our computed Si-0 bond lengths for Si( OH), are slightly longer, 1.67 A, but still in good agreement with their MP2/ 6-3 1G * calculations. Having obtained the optimised structures for both reactants and products, we may compute the reaction energies, AE, by subtracting the total energies of the reactants from those of the products in Eqns. 2 and 3. To be specific, we have for the reaction with alkali cations at neutral pH AE = -EISi,O(OH)sOM]
+ E[Si(OH),OM] - E[H*O]
+ E[Si(OH),]
(4)
and at high pH: AE = -E[Si,O(OH),OM]
+ E[Si(OH),OM] - E[OH-]
and at low pH:
+ E(Si(OH),O-]
(5)
a
1.61
b
Fig. 2. Optimized structures of products (a) Si(OH), in neutral and acid solution and (b) Si(OH)?O- in alkaline solution. Distances in FmgstrBm.
AE = -E[Si,O(OH),OHM+]
+ E[Si(OH),OHM+] - E[H,O]
+ E[Si(OH),]
(6)
Determination of the total energy as described above estimates the energy change of the system and indicates the exothermicity. The activation energies of these reactions are not considered, but we assume that the difference in the activation barriers between the reactions are small so that a relative comparison between the reaction energy and the reaction rate can be applied. In the present work, the effects of both pH and addition of alkali metal cations are investigated, and thus, both the reaction energies at different pH values and the relative values from addition of electrolyte at fixed pH are calculated. The absolute values are given in Table 1, where it should be noted that for the reaction with OH _ in the alkaline case, the experimental energy of hydration, - 108 kcal/mol (Ball and Norbury, 1974), of the OH species has been added on the reactant side. For the solvation of the reaction product, Si ( OH)30 ~, no experimental value
Model of silicate dissolution
2581
1.89
Fig. 3. Optimized structures for alkali cation interacting with siloxane bridge of hydroxylated surface. Distances in Bngstrtim and angles in degrees. Fig. 5. Hydroxylated model. Optimized structures Distances in IngstrSm and angles in degrees.
of products.
of the hydration energy is known to us; we have thus computed it by modelling the effects of solvation by placing the anion in a cavity in a polarisable medium with the dielectric constant of water, which is 80.4, using Gaussian921DFT. This model of solvation of ions has some problems in treating the H bonds to the solvent. In order to get a reasonable estimate of the hydration energy of Si( OH)30-, one may compare with the perchlorate ion, which is of similar size, has a weak hydrogen bond interaction with the solution, as expected also of Si ( 0H)30-, and for which an experimental value has been determined. Computing the hydration energy of the Si (OH),0 and the ClO, ions gives energies of -50 and -49 kcal/mol, respectively (6-311G basis set), compared to the experimental value for Cl07 AH,,, = -54
kcal/mol (Ball and Norbury, 1974). Since the model does not include the H bond influence properly and the results on perchlorate hydration modelling show less negative hydration energy than experiment, we assume that the computed hydration energy for Si( OH)30m is an upper bound to the true hydration energy; thus the reaction energy in the alkaline pH region should become more exothermic with a more accurate value for the hydration energy. The computed hydration energy for Si(OH)?O‘ ( -50 kcal/mol) has been added to the product side of all entries for the alkaline region in Table I. It should be noted that without consideration of the solvation terms for the alkaline model. the reaction
Fig. 4. Optimized structures for alkali cation interacting ane bridge of deprotonated surface. Distances in angstriim in degrees.
Fig. 6. Deprotonated model. Optimized structures Distances in lngstrijm and angles in degrees.
with siloxand angles
of products.
H. Strandh
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Table I. Reaction energies (in kcal/mol) computed at the B3LYP level for siloxane bond breaking at different pH and with different electrolytes. 6-3 I I G values are given in parenthesis. Electrolyte
H Li Na K Rb CS
Low pH 5.8 21.6 14.7 I I.2 10.0 7.1 6.0
(5.1) (23.9) (19.1) (15.6) (16.6) (11.1) (9.8)
Neutral 16.4 5.8 14.8 15.7 15.4 15.2 14.9
High pH”.”
(18.0) (5.1) (14.4) (16.6) (17.2) (17.0) (16.4)
” OH energy of hydration. -108 kcallmol, Norbury, 1974). ” Si(OH)Q hydration energy, -50 kcal/mol, using Gaussian92/DFT). ’ No electrolyte added.
27.2 (16.8) 25.7 26.5 26.3 26.0 25.7
(13.4) (15.6) (16.2) (16.0) (15.3)
included
(Ball and
included
(modelled
energies would all have been strongly exothermic for the high pH region. We may now compare the reaction energies for the different pH regions without the electrolyte added. For the deprotonated model, we have a reaction energy of 16.4 kcal/mol for the reaction with water (pH = pzc), while the reaction with OH- gives an upper bound of 27.2 kcal/mol (pH > pzc). For the low pH case, we compare with the reaction energy of the protonated model reacting with water; this gives an endothermic reaction energy of 5.8 kcal/mol (same as the deprotonated model reacting with H+ and H20). Assuming that the barriers are similar for the different reactions so that the relative reaction energies could be used to estimate the reaction rates, the present results would give the highest rate for the low pH region followed by pH = pzc (“neutral”). The lowest rate would be expected for the alkaline solution which has the most endothermic reaction. Experimentally a minimum in the rate is found for pH around pzc, and the simple model that we have considered so far thus does not predict the correct order between neutral and alkaline solution. The treatment of the negatively charged species in the modelling of this pH region is, however, complicated, and, furthermore, large effects of solvation on the alkaline model could be expected. The relative values for a given pH (collected in Table 2 from Table 1 for easy reference) show the effects on the siloxane bond strength from addition of a proton (acidic/ neutral) or an alkali cation to the siloxane bond. Here, the reference value for the acidic solution was taken as the reaction energy, 5.8 kcal/mol, of the hydroxylated siloxane bond, (OH),Si-0-Si(OH),, reacting with water. For both the neutral and alkaline (relative to pzc) pH regions, the reference was taken as the partially deprotonated (OH),Si-O-Si(OH)20 surface mode1 interacting with water (16.4 kcal/mol) or OH(27.2 kcal/mol), respectively. Since the differences between the neutral and alkaline solution models do not involve the cations (cf. Eqns. 5 and 4), the trend for the different alkalis is by construction identical for the neutral and alkaline solutions. The largest effect from an alkali cation on the reaction energy is found for the reaction with Li’ and Cs’, which destabilise the siloxane bond by about 1.5 kcal/mol; the differences among the alkali ions are small, however. The results would indicate a larger
et al
destabilisation for Li+ than for Na+ and K+, while the trend is increasing from K to Cs; the energy differences are too small to allow firm conclusions, however. In comparison to experimental data on salt effects on dissolution rates of feldspar (Li > Na > K), the results show the expected trend. The reported (Dove and Crerar, 1990) experimental salt effects on quartz, however, indicate an opposite trend, Li < Na = K. The model of the dissolution process in acid solution gives some surprising results; for this model, contrary to what has been reported previously and termed proton catalysed siloxane bond breaking (Xiao and Lasaga, 1994), we find a stabilisation of the siloxane bond through the interaction with a proton. Two different structures were investigated: the direct interaction with the siloxane bridging 0, which has previously been studied by Xiao and Lasaga (1994), and the more favorable case (within the present model) where the proton interacts with the hydroxyl groups. In both cases, we find a stabilisation from the interaction with the proton: interaction with the siloxane bridging 0 gives a reaction energy of 13.8 kcal/mol (stabilisation by 8 kcal/mol) while interaction with the hydroxyl groups gives a larger stabilisation (by 15.8 kcal/mol). The origin of the stabilisation is the favorable interaction with the surface OH-groups, which was not included in earlier work. Furthermore, all of the cations are found to increase the endothermicity, i.e., to stabilise the siloxane bond; the magnitude of the effect decreases with increasing size of the cations. Experimentally, at low pH, addition of alkali has been found to inhibit the dissolution process of feldspar with the relative activities Li < Na < K. For quartz, the situation is less clear, but new data indicate no effect from Li+ and Na’ and inhibitory activity of K’ (Strandh et al., 1996, and H. Strandh, unpubl. results). Thus, the present results indicate a genera1 agreement with an inhibitory effect but give the wrong relative activities for the different ions. Furthermore, the comparison with the (fully hydroxylated, Fig. lc) neutral reference model shows a stabilisation of the bond from the interaction with a proton (+15.8 kcal/mol, Table 2), which is again contrary to what is normally assumed. These results indicate that, in particular for the acid model where the surface becomes charged, one must at least consider the effects of solvation. Ideally this should be done having the first salvation shell included and embedding the whole system in a polarisable dielectric medium. Since the solution is present on only one side of the system, the dielectric medium is not trivial to include. We have thus chosen to focus on the effects of adding the first few water molecules in order to qualita-
Table 2. Computed B3LYP level reaction energies relative to the respective models without electrolyte. Electrolyte
Low pH
-
5.8 + 15.8 +8.9 +5.4 +4.2 +1.3 +0.2
H Li Na K Rb CS
Neutral 16.4 -10.6 -1.6 -0.7 -1.0 - 1.2 -I .5
(in kcal/mol)
High pH 27.2 -1.5 -0.7 -0.9 -1.2 -1.5
Model of silicate dissolution tively describe energetics. 4.1. Solvated
the effects
of the presence
of water on the
Table 3. Computed B3LYP including effects of solvation.
The dissolution will occur at the liquid-solid interface where the liquid is an electrolyte of varying composition and PH. Thus, we must consider the effects of solvation of the surface, i.e., association of water molecules via H bonding to the OH-groups at the surface. Furthermore, the cations in the solution will be solvated by, on the average, six water molecules in the first solvation shell; part of this solvation shell may be expected to be lost when the ions are coordinated to the surface. The efficiency of the salvation may be different for the reactants and the products so that the solvation may affect the computed reaction energies. Finally, all reactions involving a proton should be expected to be very strongly affected by replacing the proton with a H,O’ rather than a free proton. Since the surface with cation in the acid model bears a positive charge, this is where the largest effects of solvation should be expected, and, in fact, qualitative effects of solvation may be seen already after adding the first few water molecules (Table 3). The results for Li+ and Rb’ for the acid model are shown in Figs. 7 and 8, which may be com-
Fig. 7. Optimized
structures
energies
Zero water
1 H,O
Acid Model H Li Rb
5.8 21.6 14.7 7.1
17.9 12.4 6.2
Neutral -
16.4
Electrolyte
Models
level reaction
2 H,O
13.4 9.8 5.5
model
H Li Alkaline
(in kcal/mol)
-
5.8 14.8
6.1 12.0
2.6 10.9
27.2 25.7
22.8
21.8
model
Li
-
pared with the unhydrated system in Fig. 3. The addition of the first water leads to an increase in the alkali to siloxane 0 distance for Li’ and Rb+ by 0.54 w and 0.05 A: respectively. The second water already has a much smaller effect on the Li+ structure and increases the distance by only 0.05 A; for Rb’, the effect is somewhat larger, 0.14 A. For the
with one water molecule
2584
H. Strandh et al
Fig. 8. Optimized structures with two water molecules.
products in the acid case, the main solvation effect will occur for the charged [Si(OH),M]+ system, and the structures resulting from the addition of one and two waters are shown in Figs. 9 and 10 (cf. Fig. 5); the result of the interaction with the water molecules is again a reduction in the strength of the interaction with the nearest 0. The structure around the larger cation, Rb’, is hardly affected by the addition of the second H20, while again for Li+, much larger changes are found; here the Li-0 distance increases from 1.89 to 1.93 to 2.01 A upon addition of one and two water molecules. Since the hydration effects on reactants and products involving Rb’ are small, the resulting effect on the reaction energy is very small. The solvation of the reactants and products including Li’ had a large impact on the structure and, consequently, a large effect on the reaction energy. The obtained results show that the hydration of the dissolution product, including an alkali metal ion, is more effective on the smaller ion Li+ than on Rb+. Solvation of the large cation Rb+ seems to be as effective on the surface model as on the dissolution product (Si(OH),OHM+). This result indicates that using full hydration, the model may produce a reversed trend for the alkali metal ion effect on the reaction energy, i.e., that the smaller ions have a smaller stabilising effect on the siloxane bond than the larger ions, yielding a better agreement with experimental data. In the alkaline and neutral solutions, the models of the surface and the dissolution prod-
uct with adsorbed alkali metal ions are uncharged, but still the solvation of the ion gives a less endothermic reaction. When including three water molecules in the hydration layer around the alkali metal ion, the water molecules start to interact by H bonds with the hydroxyl groups that represent the connection to the bulk structure on the surface model (Fig. 11). This would not be possible in reality, and it is clear that the surface model used in the present study has to be modified to be able to model a larger hydration layer on the adsorbed alkali metal ions. Work along this line has been initiated. The dissociation processes in the alkaline situation will be strongly affected by solvation processes due to the presence of charged species. The dominating solvation effects will thus occur for the hydroxide ion before the dissociation and for the dissociated Si acid ion, Si(OH)30-, after the process; these two contributions have been taken from experiment (OH-) or estimated from calculations (Si(OH),O-) in the present work. The first two terms, containing the alkali metal, are the same in Eqn. 5 and Eqn. 4 and thus the difference between the two reactions, for a given cation M, is just a constant term. Consequently, hydratization can not, in this simple model, affect the relative order of the bond energies as a function of the alkali atoms, and the same relative order of the effects should thus be expected. This does not seem to be in agreement with experiment, where no effect of addi-
Model of silicate dissolution
: . Y
0.97
Fig. 9. Optimized
structures
of products
with one water molecule.
Li 2.01 Rb 2.94
/1.65
Fig. 10. Optimized
structures
of products
with two water molecules.
2585
H. Strandh et al.
2586
Fig. Il. Optimized three water molecules.
structure
of surface
and adsorbed
Li + with
tion of alkali is reported for the neutral surface, while at high pH, the effects depend both on the metal and on the mineral (feldspar: Li > Na > K and quartz: Li < Na = K). This may be due to the charge distribution at the surface in alkaline and neutral solutions being different from what is assumed in the presents models. This would require larger models of the surface to be considered, where e.g., for the neutral solution, a model including both positively and negatively charged sites as in (OH),SiOH:-0-Si(OH),-OSi(OH)20and for the alkaline solution, (OH)$i-OSi(OH),-0-Si(OH),Ocould be used to differentiate between these two pH regions. In view of the differences in the effects of the different cations on feldspar and quartz dissolution rates found experimentally, it seems likely that the structural differences between feldspar and quartz must be taken into account in an extended model. Even though the breaking of the siloxane bond is considered the rate limiting step in the dissolution process, a minimal model including only the siloxane bond cannot be sufficient for a reliable comparison of the dissolution processes of the two minerals. 5. CONCLUSIONS The present theoretical study has been performed to investigate a connection of salt effects on the dissolution rates of quartz and similar minerals to adsorption at different pH of alkali metal ions on siloxane bonds. The adsorption of alkali metals was found to result in changes in both geometry and Si-0 bond strength, depending on which alkali metal that
was adsorbed. Calculated bond energies of the model used for the alkaline pH region imply that the adsorbed alkali metal ions weaken the Si-0 bond, which then is easier to break; consequently, a higher dissolution rate should be obtained, in agreement with experimental results. For pH < pzc, addition of alkali cations to the siloxane bond was found to stabilise the bond with a greater effect from the smaller cations; experimentally, this is what has been found, but with reverse dependence on the size of the ions compared to what is obtained from the calculations. Including the first few water molecules in the solvation shell around the cation coordinated to the surface and to the reaction product has the largest effects on the smaller ions and reduces the stabilisation of the bond. Thus. it seems likely that a fully solvated model should be able to reproduce also the relative ordering among the alkali cations; solvation of the ions at the surface makes significant contributions to the reaction energies and must be included in the model calculations. A critical fact when performing theoretical calculations on complex systems such as mineral surfaces is the size of the model. Earlier studies by Xiao and Lasaga (1994) on H30+ hydrolysis were performed using only H-terminated Si-0-Si models and the results indicated that a direct interaction between the proton and the bridging 0 could be the cause of the increased dissolution rate found in acid pH experiments. The effect of H,O’ hydrolysis is completely different when using larger systems more like the true surface, as the hydroxyl-terminated model used in the present study, with no interaction between the proton and the bridging 0. The increase in dissolution rate at pH < pzc is, as is the case for the alkali cations, indicated to be due to the relative hydration energy effect on the surface and the dissolved products. The main results of the present model study are the importance of solvation on the energetics of the siloxane bond breaking in different environments and also that, in spite of the smallness of the model, the main characteristics of the dissolution process have been captured. The model is, however, too small to be able to include the full hydration effect on the adsorbed ions since the hydration water and the groups representing the bulk mineral start to interact. Work has been initiated on larger models containing two siloxane bonds for which the effects of solvation on the surface and on the coordinated ions may be studied in more detail. Acknowledgments-Valuable discussions with M. Sandstrom on solvation energies of anions are gratefully acknowledged. This work was funded by The Swedish Central Board of National Antiquities.
Editorial
handling:
J. Tossell
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