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Dynamics of silicate exchange in highly alkaline potassium silicate solutions Eva Vallazza, Alex D. Bain, and Thomas W. Swaddle
Abstract: The problem of measuring the kinetics of Si exchange between aqueous silicate species by 29Si NMR has been revisited, using highly alkaline KOH solutions (2.8 mol SiIV per kg solvent, [SiIV]/K2O = 0.43) at 60–90°C to minimize the number of silicate species present. Longitudinal 29Si relaxation times T1 and apparent rate constants estimated from line-shape analysis (LSA) varied markedly with the degree of purity of the KOH used, but rate constants k obtained by selective inversion–recovery (SIR) using the CIFIT data-fitting program were independent of the source of KOH and were smaller than those obtained from LSA by at least an order of magnitude. Although only four kinetically significant silicate anions (monomer M, dimer D, linear trimer L, and cyclic trimer C) were present, overlap of the D and L resonances prevented complete analysis of the SIR data. True rate constants could therefore be obtained only for the M–D exchange (for formation of D, k1 (90°C) = 0.13 ± 0.01 kg mol –1 s–1, ∆H1‡ = 67.4 kJ mol–1, ∆S1‡ = –78 J K–1 mol–1; for dissociation of D, k–1 (90°C) = 1.4 ± 0.1 s–1, ∆H–1‡ = 64.7 kJ mol–1, and ∆S1‡ = –66 J K–1 mol–1). Models that included L as the precursor of C (MDLC mechanism) showed, within the limitations imposed by D–L band overlap, that the reactivities of M, D, L, and C in Si-O-Si link formation or dissociation were all roughly comparable. Good fits of the experimental data, however, and equally reliable rate constants for the M–D exchange, could be obtained with models that ignored the presence of L entirely (MDC mechanism). The simple MDC model also provides consistent apparent rate constants kC and k–C for the overall formation of C from M + D and the reverse process, respectively, by SIR of either M or C (∆HC‡ = 76.5 kJ mol–1, ∆SC‡ = –57 J K–1 mol–1; ∆H–C‡ = 88.6 kJ mol–1, and ∆S–C‡ = –7 J K–1 mol–1). Key words: kinetics, silicates, 29Si NMR. Résumé : On a réexaminé le problème associé à la mesure de la cinétique de l’échange du Si entre des espèces silicates aqueuses à l’aide de la RMN du 29Si; à cette fin, opérant à des températures allant de 60 à 90°C, on a utilisé des solutions extrêmement alcalines de KOH (contenant 2,8 mol SiIV par kg de solvant, [SiIV]/K2O = 0,43) afin de minimiser le nombre d’espèces de silicate. Les temps de relaxation longitudinale du 29Si, T1, ainsi que les constantes apparentes de vitesse évaluées sur la base d’une analyse de la forme de la raie («LSA») varient beaucoup avec le degré de pureté du KOH utilisé; toutefois, les constantes de vitesse k, obtenues par une récupération sélective de l’inversion («SIR») en utilisant le programme «CIFIT» d’ajustement des données, sont indépendantes de la source de KOH et elles sont au moins 10 fois plus faibles que celles obtenues par la méthode de «LSA». Même si seulement quatre anions silicates (monomère, M; dimère, D; trimère linéaire, L; trimère cyclique, C) cinétiquement significatifs sont présents, le recouvrement des résonances des entités D et L rend impossible l’analyse complète des données «SIR». On n’a donc pu obtenir les vraies constantes de vitesse que pour l’échange M–D (pour la formation de D, k1 (90°C) = 0,013 ± 0,01 kg mol–1 s–1, ∆H1‡ = 67,4 kJ mol–1 et ∆S1‡ = –78 J K–1 mol–1; pour la dissociation de D, k–1 (90°C) = 1,3 ± 0,1 s–1, ∆H–1‡ = 64,7 kJ mol–1 et ∆S–1‡ = –66 J K–1 mol–1). Les modèles qui incluent L comme précurseur de C (mécanisme MDLC) démontrent, sujet aux limitations imposées par le recouvrement des bandes D–L, que les réactivités de M, D, L et C sont assez semblables pour la formation et la dissociation de la liaison Si-O-Si. Toutefois, de bons accords avec les données expérimentales et des constantes de vitesse également fiables pour l’échange M–D pourraient aussi être obtenus à l’aide de modèles qui ignoreraient complètement la présence de L (mécanisme MDC). Le modèle MDC simple fournit aussi des constantes de vitesse apparentes kC et k–C cohérentes respectivement pour la formation globale de C à partir des entités M + D ainsi que pour le processus inverse, par «SIR» des entités soit M ou C (∆HC‡ = 76,5 kJ mol–1 et ∆SC‡ = –57 J K–1 mol–1; ∆H–C‡ = 88,6 kJ mol–1 et ∆S–C‡ = –7 J K–1 mol–1). Mots clés : cinétique, silicates, RMN du 29Si. [Traduit par la rédaction]
Received August 20, 1997. E. Vallazza and T.W. Swaddle.1 Department of Chemistry, The University of Calgary, Calgary, AB T2N 1N4, Canada. A.D. Bain. Department of Chemistry, McMaster University, Hamilton, ON L8S 4M1, Canada. 1
Author to whom correspondence may be addressed. Telephone: (403) 220-5358. Fax: (403) 289-9488. E-mail:
[email protected]
Can. J. Chem. 76: 183–193 (1998)
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Introduction Aqueous solutions of silicates and aluminosilicates are important in a wide variety of technological, geological, and biomedical contexts, as noted in a recent review (1). Silicate anions occur in alkaline aqueous solution in at least 25 oligomeric forms, in addition to the orthosilicate monomer (HO)4−zSiOzz− . In their pioneering studies, Harris et al. (2–5) identified most of these oligomers by 29Si NMR spectroscopy, a technique that, along with 17O NMR, also reveals that the oligomers (other than special cases such as the cubic cage 8− (6)) undergo rapid intermolecular Si–Si site species Si8O20 exchange (7–13). It has proved difficult, however, to obtain reliable rate constants for exchange between specific silicate species in typical solutions with pH around 11, where the average charge per Si atom is about –1, because of the excessive number of species present. The number of detectable oligomeric species diminishes as the pH and temperature are raised (14), whereas the rates of Si site exchange increase with rising temperature but decrease with rising pH (10). Thus, the most favorable conditions for the quantitative study of Si–Si exchange kinetics by NMR are high pH and elevated temperatures — conditions that have some intrinsic technological interest in relation to the synthesis of zeolite catalysts and the carryover of silicate in the Bayer process for bauxite refining (1). An added complication, however, is that traditional NMR line-shape analysis (LSA) methods of determining exchange rates are subject to error because of nonkinetic contributions to the line widths, particularly line broadening by adventitious paramagnetic contaminants (8, 10), and this problem can be expected to worsen with the addition of high concentrations of alkalis that inevitably contain traces of paramagnetic substances (15). Fortunately, the kinetics of Si–Si chemical exchange can be studied without these complications by the technique of selective inversion–recovery (SIR) (8, 10, 12), in which the magnetization of the population of one exchanging species is inverted and the propagation of the magnetic perturbation to the other species through chemical exchange is monitored. The rate of disappearance of the imposed perturbation of magnetization is then a function of the chemical exchange rates and nuclear spin-lattice relaxation times T1 of the species involved in exchange, and numerical analysis can, in principle, separate these parameters to yield unambiguous chemical exchange rate constants. Rigorous analysis of the evolution of the observed spectral changes with time t is not trivial, particularly for intermolecular processes such as silicate–silicate exchange, and was not attempted in our previous report on this topic (10). The original 29Si SIR study by Harris and co-workers (8) gave rate constants only for the dimerization of orthosilicate (0.21 and 1.06 kg mol–1 s–1 at 83 and 107°C, respectively) in a solution of 2.8 mol kg–1 SiO2 in aqueous KOH (K:Si = 3.8:1). Bell and co-workers (12) considered the interconversion of the monomer M, the dimer D, and the cyclic trimer C (Fig. 1) in SIR experiments on solutions of 3 mol% SiO2 in 10 mol% aqueous KOH, but only for a single unspecified temperature, and the possible involvement of other oligomers was not taken into account. Thus, there is need for a reexamination of the problem of silicate exchange kinetics. The present article describes an attempt to extract reliable rate constants k by the SIR and LSA methods for silicate
Can. J. Chem. Vol. 76, 1998 Fig. 1. Schematic representation of structures of silicate species detectable in this study. Each black dot represents a silicon atom, tetrahedrally surrounded by oxygens; the lines represent Si-O-Si links.
M
D
L
C
B
exchange at 60–90°C in highly alkaline potassium silicate solutions, in which the only detectable silicate species present were the monomer (HO)4−zSiO zz− (M), the dimer (HO)6−z(Si2O)Ozz− (D), the “linear” or acyclic trimer (HO)8−z(Si3O2)Ozz− (L), the cyclic trimer (HO)6−z(Si3O3)Ozz− (C), and the branched tetramer (HO)8−z(Si4O4)Ozz− (B) (Fig. 1). We focus upon results from two particular samples, called I and II, that were almost identical except for the source of the KOH used. Numerical analysis of SIR data was carried out using the CIFIT program (16–18), which is based on Muhandiram and McClung’s SIFIT procedure (19). The rate constants so obtained are subject to uncertainties arising from the irreducible chemical complexity of the exchanging silicate system, but nevertheless the results present a more complete picture than previously published studies (8, 10, 12). Comparison is made with rate constants estimated from complete line-shape analyses. In particular, it is shown that trace impurities in the alkali lead to substantially shortened longitudinal relaxation times T1 and to apparent rate constants for Si–Si exchange from LSA that are too large.
Experimental Materials All alkaline solutions were prepared in Teflon–FEP containers, which were soaked successively in dilute solutions of HCl, HNO3, and Na2H2EDTA prior to use. Amorphous silica was prepared by dropwise hydrolysis of freshly distilled silicon tetrachloride (Fisher, technical grade) in water. The resulting gel was dried, crushed, and washed with water. Potassium hydroxide solutions were prepared by dissolving solid KOH (BDH ACS grade for sample I, or Alfa Aesar, 99.995% pure on the basis of metals content, for sample II) in freshly boiled solvent consisting of approximately 75% D2O (Aldrich, 99.9 at.% D) and 25% deionized distilled H2O. Sample preparation Samples were prepared directly in Teflon–FEP NMR tube liners by dissolving a known quantity of silica (dried at 250°C) in a weighed portion of KOH solution that had been standardized with potassium hydrogen phthalate. Dissolved oxygen was purged from the sample with N2, then the tube was closed with a Teflon stopper and sealed with Parafilm. The compositions of samples I and II are given in Table 1 in various ways to facilitate comparison with other published work. NMR measurements Silicon-29 spectra were obtained at 59.624 MHz on a Bruker AMX2-300 spectrometer using a 10 mm probehead with spin rate of 10 Hz. The glass coil supports of the probe and the NMR glass tube gave rise to a broad signal centered around –40 ppm relative to the orthosilicate resonance. Spectra were © 1998 NRC Canada
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Vallazza et al. Table 1. Composition of solutions. IV
–1
[Si ]/mol (kg solvent) [SiIV]/mol% [K+]/mol (kg solvent)–1 [K+]/mol% K/Si R = [Si]/[K2O] Source of KOH [M]/mol kg–1 (60°C) [D]/mol kg–1 (60°C) [L]/mol kg–1 (60°C) [C]/mol kg–1 (60°C) [M]/mol kg–1 (90°C) [D]/mol kg–1 (90°C) [L]/mol kg–1 (90°C) [C]/mol kg–1 (90°C)
Sample I
Sample II
2.80 4.17 13.0 9.67 4.64 0.431 BDH, ACS grade 2.134 0.401 0.1002 0.1646 2.140 0.438 0.0962 0.1255
2.79 4.17 12.9 9.63 4.62 0.433 Alfa Aesar, 99.995% 2.127 0.399 0.0998 0.1640 2.133 0.436 0.0958 0.1250
recorded over a temperature range from 4.5 to 90°C. Temperature calibration was carried out using the proton spectra of neat ethylene glycol (Fisher, ACS Certified) (20). The 29Si 90° pulse width was determined for each temperature and was between 22 µs (at 4.5°C) and 45 µs (at 90°C). Longitudinal relaxation times T1 (Table 2) were estimated by nonselective inversion–recovery measurements (180°–τ–90°–FID–td), and pulse intervals were chosen to be greater than 5 times the maximum measured T1, i.e., intervals of 30–75 s for sample I and 75–300 s for sample II. Selective inversion–recovery (SIR) experiments were conducted as described by Morris and Freeman (21). A DANTE sequence of 18 pulses of 5 µs with 0.4–0.7 ms interpulse delay was used to invert selectively the Q0 Si spins2 of the monomeric silicate anion M, the Q1 spins of Si of the dimer D and linear trimer L (overlapping bands), or the Q2 Si spins in three-membered rings of cyclic trimer C and branched tetramer B (overlapping bands). Results of M-, (D + L)-, and C-SIR experiments on sample I at 90°C, and sample II at 60 and 90°C, have been deposited as supplementary material.3 Calculations Complete line-shape analyses (LSA) were carried out using the Fortran program GNMR derived from the exchange-modified Bloch equations (10). For each sample, the low-temperature (4.5°C) unbroadened spectrum was simulated manually by iterating the positions, line widths, and areas of five computer-generated Lorentzian peaks. Reaction models were tested to find appropriate sets of rate equations (kinetic matrices (22)) that would replicate the observed line broadening. SIR curves were calculated using the C program CIFIT (16, 17), designed to fit data from SIR experiments of systems undergoing slow chemical exchange. CIFIT searches for the set of parameters (rate constants k, relaxation times T1, and initial 2
3
The connectivity n of a silicon center is denoted as Qn ; thus, the connectivity of a terminal SiO4 unit is Q1, and that of the Si centers in the cubic octamer Si8O208- is Q3. Tables S1–S9 (10 pages), giving integrated signal intensities as functions of delay time for M-, (D + L)-, and C-SIR experiments on sample I at 90°C, and on sample II at 60 and 90°C, may be purchased from: the Depository of Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, Canada K1A 0S2.
Table 2. Longitudinal 29Si relaxation times from nonselective inversion–recovery. Sample
I II II
Temp./°C
90 90 60
Longitudinal relaxation times T1/s M peak
Combined D/L band
Combined C/B band
7 20 16
6 21 9
6 17 13
and equilibrium band intensities M0 and M∞) that best fits the experimental data. Since the three observed peaks have different line widths, peak areas were used to describe changes in z-magnetizations. They were calculated by integrating the simulated peaks obtained by deconvoluting spectra processed with an artificial line broadening of 1 Hz using the Bruker WINFIT program. For each SIR experiment the normalized peak areas were fitted optimally using the CIFIT program with various mechanistic models. Since the number of parameters was large, it was generally necessary to allow only the M0 and M∞ values and limited sets of k and T1 to vary in a given computation; the best-fit values of k and T1 and the associated uncertainties were then determined by manual iteration (18). In cases where the propagated SIR effect on a particular peak was weak, k and T1 values determined for that peak by its direct inversion were inserted as fixed parameters.
Results It can be inferred immediately from the experimental spectra shown in Figs. 2 and 3 that there is a much larger intrinsic line broadening for sample I (that with the less pure KOH) than for sample II, and hence that line-shape analysis for sample I is likely to overestimate the chemical exchange rates. Furthermore, although the spectra at 90°C (the optimum temperature for SIR experiments on the samples used in this study) for both samples show a single band at chemical shift δ ≈ –7.0 ppm, it is clear from the low-temperature spectra that this feature includes intensity from the minor but not negligible band at δ ≈ –6.9 ppm due to the Q2 silicons of the linear trimer L, as well as from the dimer D. Extrapolation from spectra run at lower temperatures indicated that the band comprised 80% D with 20% L at 60°C, and 82% D with 18% L at 90°C. These and other relative integrated band intensities allowed calculation of the actual concentrations of M, D, L, and C in the two samples at 60 and 90°C (Table 1). On the other hand, the resonance expected for the Q2 silicon of L at δ ≈ –16.6 ppm (14) was not observable (probably because of strong kinetic line broadening) and was of necessity neglected. The small feature discernible at δ ≈ –9.5 ppm, attributable to the branched tetramer B, remained distinct from 4.5 to 90°C for sample II at least, and therefore corresponded to exchange processes slow enough to be disregarded in calculating the integrated C signal intensity. Longitudinal 29Si relaxation times T1 calculated from nonselective inversion experiments are listed in Table 2. Values of T1 obtained at 90°C may be partly averaged by chemical exchange (23); Kinrade et al. (15) report that onset of averaging of T1 occurred above 50°C for a sample containing 2.2 mol kg–1 of each of NaOH and SiO2 but, in the present study © 1998 NRC Canada
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Fig. 2. Comparison of experimental (dotted lines) and simulated (solid lines) spectra for sample I at various temperatures. The simulations are based on the assumption that the spectrum at 4.5°C shows no chemical exchange. Small variations in resonance frequencies caused by phenomena other than spin–site exchange, as well as shifts in population equilibria, were corrected manually. The branched tetramer peak at about –9.5 ppm was neglected in line-shape analyses and in the interpretation of selective inversion–recovery experiments.
with higher alkalinity and consequently slower chemical exchange, T1 data obtained at 60°C should be reasonably close to the values for independent silicate centers. When fitting the data in both line-shape analysis and selective inversion–recovery, two main mechanisms were considered: MDC mechanism: [1]
kD
M+MCD k−D
Table 3. Equilibrium constants, and associated enthalpies and entropies of reaction, for the MDLC reaction scheme under the i=1
Parameter Ki (60°C) Ki (90°C) ∆Hi/kJ mol–1 ∆Si/J K–1 mol–1 a
i=2 a
0.088 0.096a +2.7 –12
i=3 a
0.117 0.103a –4.4 –31
1.64 1.305 –7.7 –19
Units: kg mol–1.
kD′ = kD[M] = k–D[D]/[M]; KD = kD/k–D = [D]/[M]2 [2]
kC
M+DCC k−C
kC′ = kC[D] = k–C[C]/[M]; KC = kC/k–C = [C]/[D][M] MDLC mechanism: [3]
k1
M+MCD k−1
k1′ = k1[M] = k–1[D]/[M]; K1 = k1/k–1 = [D]/[M]2 = KD [4]
k2
M+DCL k−2
k2′ = k2[D] = k–2[L]/[M]; K2 = k2/k–2 = [L]/[D][M]
[5]
k3
LCC k−3
k3 = k–3[C]/[L]; K3 = k3/k–3 = [C]/[L]; K2K3 = KC. Here, the various ki are rate constants and the Ki are equilibrium constants. Values of Ki and the associated enthalpies (∆Hi) and entropies (∆Si) estimated from the data of Table 1 and cognate data for lower temperatures are given in Table 3. The MDC mechanism differs from the MDLC mechanism in that participation of the linear trimer L in the exchange processes is discounted, i.e., either addition of monomer to dimer and subsequent ring closure to form the trimer can be © 1998 NRC Canada
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Fig. 3. Comparison of experimental (dotted lines) and simulated (solid lines) spectra for sample II at various temperatures. Details as for Fig. 2.
represented by a single rate constant kC or, contrary to chemical intuition, L is not an intermediate in the D–C exchange process.
[6]
0 −1 M ∞ −1 M M∞ D∞ M d ′ = k D D D + kC′ 0 −2 D M dt ∞ 1 − ∞ C M∞ D∞ 2 1 D∞
Selective inversion–recovery analysis As is shown in the Appendix, the kinetic equation for the MDC mechanism is
M∞ C∞ M M∞ 2 D C∞ C M∞ −3 C∞
where the italicized quantities M, D, and C are the magnetizations of the monomer M, dimer D, and cyclic trimer C, respectively. The subscripts ∞ indicate equilibrium values, and these are proportional to the corresponding concentrations multiplied by the number of nuclei per molecule of the particular kind observed. The branched tetramer was excluded and the
area of the peak at –9.7 ppm was attributed to the cyclic trimer alone. If the participation of the linear trimer as the precursor of the cyclic trimer in the exchange processes is included (MDLC mechanism), and it is assumed that all three Si nuclei in L were represented in the (D + L) band, the kinetic equation becomes © 1998 NRC Canada
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[7]
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0 −1 M ∞ M −1 M∞ D∞ M d D = k1′ + k2′ 0 −2 M dt L D∞ 1 − ∞ D M∞ D∞ C 2 1 D∞
M∞ L∞ L∞ −1 M∞ C∞ L 2 L C L∞ 1 − ∞ M∞ C∞ −3 L∞
In fact, only the two Q1 nuclei in L are expected to contribute to the intensity of the (D + L) band, but for computational purposes the signal of the unobservable third (Q2) nucleus had to be assumed to be included to conserve the number of NMRactive sites in eqs. [4] and [5]. It should be noted that, while reaction [5] involves three NMR-active nuclei, it is also mechanistically triply degenerate, i.e., any of the three Si-O-Si links in C may be broken to form L. Because the overlap of the D and L resonances prevents rigorous numerical analysis of the SIR data, several approximate approaches with more or less faulty assumptions were tried with the object of producing consistent, accurate fits of the experimental results in terms of a mechanistic picture, as well as meaningful rate constants for those reaction steps for which these could be defined. Model (i) The (D + L) band was assumed to represent the major component D alone, and the MDC model was applied; that is, we feigned ignorance of the composite character of this band for expediency in computation (the true concentrations of D and L were, however, used in calculating KC, KD, k–C, and k–D). Separate experiments involving, respectively, selective inversion of the M, (D + L), and C bands can be accommodated by the CIFIT program for the MDC mechanism (Figs. 4–7). Model (ii) The minor component L of the (D + L) band was assumed to be inactive in Si exchange on the time scale of the M–D and D–C exchanges; the MDC model was then applied to data sets in which the integrated (D + L) signal intensities were uniformly reduced by an amount L∞ corresponding to the stoichiometric concentration of Q1 L nuclei. The M-SIR data of sample I are well represented by this approach, but the assumption that L is inactive cannot be correct since no sharp resonance corresponding to the Q2 nucleus of L was detectable and no inverted signal corresponding to the L component persisted in SIR of the combined (D + L) band. Model (iii) As a variant of (ii), the MDC mechanism was applied with all (D + L) signal intensities reduced by a factor of L∞/(D∞ + L∞). This implies that the time dependence of L follows that of D, as could happen if equilibration of L with D + M were rapid on a time scale on which the formation of C is slow. Model (iv) D–C exchange was assumed to proceed through L as an intermediate, and the MDLC mechanism was invoked. To achieve this in an approximate way, the integrated (D + L) band intensity was divided proportionally into magnetizations
D and L, as in model (iii), on the basis of the known equilibrium concentrations of D and L (Table 1). This dissection is exact for the equilibrium magnetizations D∞ and L∞ that appear in the CIFIT matrices of eq. [7] and is accurate enough for the zero-time magnetizations required by the CIFIT program, but it is unlikely to reflect accurately the evolutions of D and L over time during spin inversion–recovery unless they are fortuitously similar. This assumption is reasonable, however, since the pseudo-first-order reactions of M with another M and with D are likely to be mechanistically similar and, besides, the change in the intensity of the L signal with time will be small relative to the concurrent changes in M, D, and C. Since the CIFIT program cannot handle SIR of the (D + L) band if it is divided into two contributions, only M-SIR and C-SIR data can be analyzed with this model. To reduce the number of parameters, a reasonable approximation, viz., that T1 values for the Q1 silicons of D and L are the same, was made. Typical results of this approach are shown in Figs. 8 (sample II) and 9 (sample I, with scales expanded to show detail). Model (v) The fraction of the (D + L) band allocated to L as in model (iv) was augmented by 50% to represent a contribution from the missing Q2 resonance of L, and the MDLC mechanism was applied. The kinetic and NMR parameters so obtained for a given sample and temperature were essentially the same as those obtained in model (iv); thus, the numerical analysis of the SIR results was insensitive to the number of active nuclei assigned to the L resonance when preparing the data files. The numerical results of the various SIR analyses are collected in Tables 4 and 5. Adopted (in most cases, averaged) values of the kinetic parameters are listed in Table 6. The inconsistency of rate constants derived from D-SIR reflects the composite nature of the (D + L) band. Line-shape simulations Line-shape simulations were carried out for spectra acquired from 4.5 to 90°C, with the assumption that there was no observable chemical exchange at 4.5°C and therefore the line widths at this low temperature represent natural line widths. Line positions, populations, and rate constants were adjusted manually to describe the experimental spectra. It became evident that the apparent rate constants for LSA were much greater than for SIR, but also that no self-consistent set of rate constants corresponding to the MDC or MDLC mechanisms could be derived. The monomer and dimer peaks could not both be accurately reproduced simultaneously unless an additional line- broadening factor for the monomer was arbitrarily included. This excess broadening of the M signal was more evident in sample I than in sample II, and experiments with samples not described in Table 1 showed that the broadening © 1998 NRC Canada
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Fig. 4. M-SIR of sample I at 90°C, MDC model. (M): M signal; (): (D + L) signal; (): C signal. Fitted curves yield T−1 1 =0.101, 0.25, and 0.14 s–1 for M, (D + L), and C, respectively; kD′ = 0.282 s–1, and kC′ = 0.037 s–1.
Fig. 6. D-SIR of sample II at 90°C, MDC model. Legend as for –1 Fig. 4. Fitted curves correspond to T−1 1 = 0.037, 0.080, and 0.035 s for M, (D + L), and C, respectively; kD′ = 0.28 s–1, and kC′ = 0.25 s–1.
Fig. 5. M-SIR of sample II at 90°C, MDC model. Legend as for –1 Fig. 4. Fitted curves yield T−1 1 = 0.035, 0.080, and 0.024 s for M, –1 (D + L), and C, respectively; kD′ = 0.31 s , and kC′ = 0.029 s–1.
Fig. 7. C-SIR of sample II at 90°C, MDC model. Legend as for Fig. 4. The broken curves represent best fits and yield T−1 1 = 0.016, 0.084, and 0.044 s–1 for M, (D + L), and C, respectively, kD′ 0.034 s–1, and kC′ = 0.044 s–1. The solid curves are constructed with fixed parameters derived in other calculations: T−1 1 = 0.037, 0.080, and 0.044 s–1 for M, (D + L), and C, respectively, and kD′ = 0.28 s–1; these give kC′ = 0.040 s–1.
was greater the more ACS Reagent-grade alkali that was present, despite the fact that increasing [OH–] is known to retard the Si–Si exchange rate (10). The excess broadening was arbitrarily expressed as an apparent rate constant kcorr, which may represent a process, other than simple silicate–silicate exchange, in which the monomer interacts preferentially with
paramagnetic impurities brought in with the alkali. To facilitate LSA simulations based on the MDLC mechanism for the © 1998 NRC Canada
190 Fig. 8. M-SIR of sample II at 90°C, MDLC model (iv). (M): M signal; (): estimated D signal; (O), estimated L signal; (): C signal. Fitted curves correspond to T−1 1 = 0.036, 0.070, 0.070, and 0.053 s–1 for M, D, L, and C, respectively; k1′ = 0.26 s–1, k2′ = 0.089 s–1, and k3′ = 1.4 s–1. The dimer signal intensities have been increased by 1.0 unit for clarity.
sake of order-of-magnitude comparison with the SIR results, k1′was set equal to k2′, giving the approximate data of Table 7.
Discussion The conditional ∆Hi values of Table 3 illustrate the general observation (14) that, at a given [OH–], higher temperatures disfavor the larger oligomers; the monomer–dimer equilibrium, however, is almost thermoneutral. It is not possible at present to apportion contributions to the thermodynamic parameters between proton ionization of Si-O-H groups (relatively few of which should remain in the highly alkaline solutions used in this study) and Si-O-Si bonding changes. A salient feature of the SIR results is that T1 values for the various 29Si nuclei are in reasonable agreement between different experiments for a particular sample and temperature but are about three times as long for sample II as for sample I, as may be seen in the nonselective inversion results of Table 2 as well as in the SIR data of Tables 4 and 5 and by visual inspection of Figs. 4 and 5 (noting the different time scales). Since samples I and II differ significantly only in the source of KOH used, we may conclude that paramagnetic contaminants are present in sufficiently high levels in typical concentrated aqueous KOH solutions to exert important influences on the 29Si NMR spectra of silicates. These observations are consistent with those of Creswell et al. (8) and Kinrade et al. (15). Consequently, rate constants for Si exchange in alkaline solution estimated by line-shape analyses will almost inevitably be too large. This is borne out by the SIR results, which gave rate constants an order of magnitude lower than did LSA even for sample II (that with the purer KOH). Furthermore, it proved impossible to obtain accurate LSA fits for all the major
Can. J. Chem. Vol. 76, 1998 Fig. 9. Early stages of M-SIR for sample I at 90°C, MDLC model (iv). Legend as for Fig. 8. Fitted curves correspond to T−1 1 = 0.101, 0.29, 0.29, and 0.084 s–1 for M, D, L, and C, respectively; k1′ = 0.24 s–1, k2′ = 0.097 s–1, and k3′ = 1.5 s–1.
bands simultaneously on the basis of silicate–silicate exchange alone; excess broadening of the monomer band may represent a preferentially rapid interaction of the monomer with some impurity. In the SIR analyses, selective inversion of the strong M band gave much more reliable SIR data than did inversion of the (D + L) band (which is composite as well as much weaker than the M signal) or of the C band (the weakest; the C-SIR spectra of sample I were of especially poor quality, and those of sample II could not be analyzed unambiguously, as shown in Fig. 7). Unfortunately, complications due to the overlap of the D and L signals could not be avoided, and the results of the computations, summarized in Tables 4–6, are therefore necessarily tentative. Furthermore, our failure to observe the Q2 center of L serves as a warning that other undetected Si centers could have contributed to the dynamics of a network of Si–Si exchanges. Nevertheless, there is encouraging consistency in the rate constants for M–D exchange (±10% of the average in Table 6) for the two samples and different modes of analysis. Clearly, kD and k–D are identical with k1 and k–1, respectively, and are the true reaction rate constants governing monomer–dimer exchange under the given conditions. Thus, at 90°C, k1 = 0.13 ± 0.01 kg mol s–1 and k–1 = 1.4 ± 0.1 s–1, with corresponding activation parameters ∆H1‡ = 67.4 kJ mol–1, ∆S1‡ = –78 J K–1 mol–1, ∆H−1‡ = 64.7 kJ mol–1, and ∆S−1‡ = –66 J K–1 mol–1. Creswell et al. (8) reported first-order rate constants kD of 0.21 and 1.06 kg mol–1 s–1 at 83 and 107°C, respectively, obtained with an MDC model for a solution containing 2.8 mol kg–1 SiO2 with K/Si = 3.8. These values are 2.6–2.9 times faster than calculated for these temperatures from our activation parameters, in accordance with the general observation that Si exchange rates become slower with rising alkalinity. If each Si center is associated with two negative charges, as is © 1998 NRC Canada
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Vallazza et al. Table 4. Interpretation of SIR data via the MDC (three-site) mechanism.a T1–1/s–1 Temp./°C
SIR
M
D
C
kD′/s–1
kC′/s–1
I
90
II
90
II
60
M Mb Mc D C M Mc D C C M D C
0.104 (0.15) 0.12 0.094 0.104 0.034 0.043 0.042 (0.016) 0.037 0.063 0.069 0.067 d
0.27 (0.12) 0.26 0.21 0.21 0.080 0.077 0.086 0.084 0.080 0.20 0.20 0.20 d
0.10 0.14 0.083 0.13 0.102 0.024 0.034 0.067 0.043 0.043 —d 0.103 0.105
0.298 0.280 0.256 0.278 0.28 0.312 0.280 0.300 (0.034) 0.28 0.039 0.039 0.039 d
0.035 0.026 0.033 0.08 0.038 0.032 0.034 0.07 0.044 0.034 —d 0.006 0.0030
Sample
a Model (i), except as indicated; parentheses denote an unreliable result, excluded from final averaging; italicized data are fixed parameters taken from other experiments. b Model (ii). c Model (iii). d SIR effect too small.
Table 5. Interpretation of SIR data via the MDLC (four-site) mechanism.a T1/s Sample
Temp /°C
SIR
I
90
II
90
II
60
M C M C M C
M 9.9 9.9 28 28 16 16c
Db
Lb
C
k1′/s–1
k2′/s–1
k3 /s–1
3.4 3.4 14 14 4.5 4.5c
3.4 3.4 14 14 4.5 4.5c
12 12 19 29 (22)c 10.8
0.243 0.29 0.261 0.261 0.030 0.030c
0.097 0.097 0.089 0.089 0.009 0.009c
1.5 1.6 1.4 2.1 (0.06)c 0.11
a
Model (iv); parentheses denote an unreliable result, excluded from final averaging; italicized data are fixed parameters taken from other analyses. b T1 for D and L were taken as equal to reduce the number of parameters. c SIR effect too small.
likely at such high pH, then the concentration of free OH– was about 5.4 mol kg–1 in our samples I and II, as compared with 3.0 mol kg–1 in the solutions of Creswell et al. (8), but no simple relationship between k1 and stoichiometric [OH–] can be expected in these highly concentrated solutions in which interionic interactions will be strong and the activity of solvent water will be far removed from unity. McCormick et al. (12) used an MDC model to obtain kD = 0.05–0.1 L mol–1 s–1 and kC = 0.1–0.2 L mol–1 s–1 (see Appendix) for a solution containing 3 mol% SiO2 with SiO2/K2O = 0.6, but the temperature was not reported; very short (
