J . Phys. Chem. 1991, 95,95 13-95 18 simple tool to understand the condensation processes and the effect of long-range nonideality effects in those media. The same kind of investigations will be continued on other -polyelectrolytic or . complex electrolyte solutions.
Acknowledgment. We acknowledge with gratitude helpful
9513
discussions with Luc Belloni, Werner Kunz, and Patricia Tivant. L.B. acknowledges support from NSF Grants CHE 89-01 597 and EPSCOR RII-86-10677. Registry No. NaCI, 7647-14-5; CaCI2, 10043-52-4; LaC13, 1009958-8; sodium heparinate, 9041-08-1.
Effects of Organic and Alkali Metal Cations on the Distribution of Silicate Anions in Aqueous Solutions W. M. Hendricks, A. T. Bell,* and C. J. Radke Center for Advanced Materials, Lawrence Berkeley Laboratory, and Department of Chemical Engineering, University of California, Berkeley, California 94720 (Received: March 12, 1991; In Final Form: July I , 1991)
The effects of tetraalkylammonium (TAA) cations on the equilibrium distribution of silicate oligomers in aqueous alkaline silicate solutions have been investigated using 29SiNMR spectroscopy. The results indicate that intrinsic differences exist in the interactions involving TAA cations and those involving alkali metal cations. The large size of the TAA cations precludes significant ion pairing; however, hydrophobic solvation and ion crowding play important roles in determining silicate speciation at equilibrium.
Introduction Zeolites are usually synthesized from a gel comprised of an insoluble solid phase and an entrapped liquid phase. The liquid phase contains an equilibrium distribution of silicate and aluminosilicate anions, the supply of which is maintained by dissolution of the solid phase. Studies by a number of researchers suggest that the anions present in the liquid phase participate in zeolite nucleation and crystal growth.l-* Since the composition of the cations in solution is known to affect the distribution of anionic species and the structure of the zeolite formed,2 there is considerable interest in identifying the structure-directing effects of cations. A very effective tool for this purpose is 29SiN M R spectroscopy. This technique is noninvasive and can provide quantitative determinations of the concentration of specific anions. The distribution of silicate species in alkaline metal silicate solutions is quite different from that observed in tetraalkylammonium (TAA) silicate solutions.*I2 Alkali metal silicate solutions contain a broad spectrum of silicate species, ranging from monomeric silicate anions to oligomeric anions containing as many as 12 silicon atoms. The extent of oligomerization increases with size of the cation, a trend that has been attributed to the formation of cationanion pai13.l) By contrast, TAA silicate solutions exhibit a highly specific and much narrower distribution of anions, and ( I ) Barrer, R. M. Zeolites 1981, I , 131. (2) Barrer, R. M. The Hydrothermal Chemistry . of . Zeolites; Academic Press: London, 1983. (3) Ueda, S.: Kageyama, H.; Koizumi, M. In Proceedings of rhe Internarional Zeolire Conference.6rh: Bisio. A.. Olson. D. H.. Eds.: Butterworth: Guildford, U.K., 1984; p 905. (4) Zhdanov, S. P.; Samulevich, N. N. In Proceedings ojrhe International Zeolife Con/erence, Srh; Rees, L. V. C.,Ed.; Heyden: London, 1980. ( 5 ) Kerr, G. T. J . Phys. Chem. 1960, 70, 1047. (6) Flanigen, E. M. In Proceedings of the International Zeolite Conference, 5th; Rees, L. V. C., Ed.: Heyden: London, 1980; p 760. ( 7 ) Dodwell, G.W.; Sand, L. B. Energy Fossil Report DE84016264, US. Department of Energy, 1984. (8) McNicol. B. D.; Pott, G. T.; Loos, K. R. J . Phys. Chem. 1972, 76, 3388. (9) Marsmann. T. 2.Naturforsch. 1974. 295. 495. (IO) Engelhardt, G.Z . An&g. Allg. Chem. 1975,418, 17. (11) Harris, R. K.; Knight, C. T. G. J . Chem. Soc., Faraday Trans. 2 1983. 79. 1525 and 1539. (12) McCormick, A. V.; Bell, A. T.; Radke, C. J. Zeolites 1987, 7, 183. (13) McCormick, A. V.; Bell, A. T.; Radke, C. J. J . Chem. Phys. 1989, 93, 1733.
0022-365419112095-95 13$02.50/0
the effects of cation size cannot be explained by the same arguments. In the earliest studies of TAA cation effects, Engelhardt et al. observed the preference of double four-membered rings (D4R) in TMA silicate solution^,^^*^^ the preference of double threemembered rings (D3R) in TEA silicate solution^,'^ and the near absence of double-ring structures in TPA and TBA silicate sol u t i o n ~ . ' ~ !The ' ~ interpretation given these observations was that "clathrate-like" water structures form in both TMA and TEA solutions and these in turn stabilize double-ring silicates. It was also concluded that these "clathrate" structures do not form in TPA or TBA solutions since they contain only small amounts of double-ring silicates. Harris and KnightI9 have used 29SiNMR spectroscopy to study TAA silicate solutions prepared with 29Si-enriched silica. They were able to identify definitively the double four-membered ring (D4R) and to note the relatively large amounts of D4R present in TMA silicate solutions. The presence of D4R anions with TMAOH has also been confirmed by Raman spectroscopyZoand by trimethylsilation followed by chromatography and mass spectroscopy.21 At the concentration studied ([SO,] = 2 M, R = [Si0,]/[(TAA)20] = 2), D4R structures were not observed in solutions containing larger TAA ions. Other researchers have observed enhancement of D3R silicates in solutions containing TEA and TBA.22*23Thouvenot et have observed stabilization of D4R by trimethylphenylammonium (TMPhA), albeit to a lesser extent than with TMA. The striking differences between the effects of inorganic and organic cations on silicate speciation has led to a great deal of confusion in the literature, especially when the organic cations 14) Engelhardt, G. 2.Anorg. Allg. Chem. 1982, 484. 22. 15) Engelhardt, G. Z . Anorg. Allg. Chem. 1982, 494, 31. 16) Engelhardt, G. 2.Anorg. Allg. Chem. 1980, 465, 15. 17) Engelhardt, G.2.Anorg. Allg. Chem. 1984, 509, 85. 18) Engelhardt, G.2.Anorg. Allg. Chem. 1985, 521, 22. 19) Harris, R. K.; Knight, C. T. G. J . Mol. Struct. 1982, 78, 273. 20) Dutta, P. K.; Shieh, D. C. J. Roman Spertrosc. 1985, 16, 312. 21) Engelhardt, G.; Rademacher, 0. J . Mol. Liq. 1984, 27, 125. 22) Hoebbel, D.; Vargha, A.; Fahlke, B.; Engelhardt, G. 2.Anorg. - Allg. Chem. 1985, 521, 61. (23) Cavell, K. J.; Masters, A. F.: Wilshier, K. G. Zeolites 1982,2, 244. (24) Thouvenot, R.; Hew€. G.; Guth, J. L.;Wey, R. Nouu. J . Chim. 1986, 10, 479.
0 1991 American Chemical Society
9514 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
are viewed as merely larger members of a class that begins with the alkali metal cations. To gain a deeper understanding of the different ways in which alkali metal and tetraalkylammonium cations influence silicate oligomerization, it is necessary to understand the intrinsic differences between organic and inorganic cations and the nature of their interactions with the solvent and with other ions. The purpose of this study is to clarify the role of organic cations in aqueous silicate solutions and to compare and contrast the behavior of these cations with alkali metal cations. A conceptual framework is developed to explain the differences between alkali metal and TAA silicate solutions, and the influence of cation size on the distribution of silicate anions.
Experimental Section Tetraalkylammonium (TAA) silicate solutions containing 1-2 mol % Si02 were prepared using fumed silica (Cabot Corp. C a b - O W ; grade EH-5). This form of silica was found to be higher in purity than other reagent-grade silica products such as silica gel, waterglass, silicic acid, and pyrogenic silica. TAA concentrations of 0.5-2.0 mol % were produced using 25% tetramethylammonium hydroxide (TMAOH) and 25% tetrapropylammonium hydroxide (TPAOH) solutions obtained from Kodak and 40% tetraethylammonium hydroxide (TEAOH) and 55% tetrabutylammonium hydroxide (TBAOH) solutions obtained from Alfa Products. Solutions of asymmetric analogues of TMAOH where one of the methyl groups is replaced by ethyl (4.53 M), n-propyl (4.56 M), or neopentyl (1.02 M) were supplied by Chevron Research Co. In all cases dilutions were made with deionized water and 99.8% deuterium oxide (used as a field frequency lock for N M R spectroscopy). All 29SiNMR measurements were recorded on a Bruker AM500 spectrometer at 99.365 MHz. Spectra were collected in 32K data sets with a 70’ pulse of about 8 p s and a 12-s delay between pulses. Experimental measurements of T,relaxation times by inversion-recovery were found to be between 1 and 2 s; the presence of paramagnetic impurities (oxygen and carbon dioxide) causes these relaxation times to be lower than some of the published values.24 The pulse sequence described above results in N M R spectra that are quantitative with respect to the concentration of 29Sinuclei in different environments. Neither 29Si homonuclear coupling nor proton coupling was observed due to the low natural abundance of 29Siand rapid exchange of silanol protons. For purposes of comparison, each spectrum is referenced to the peak corresponding to monomeric silicate. In an aqueous silicate solution, the chemical shift of a given silicate spin is influenced most strongly by its silicon connectivity (number of nearest neighbor silicon atoms) and to a lesser extent by its S i 4 bond lengths and Si-0-Si bond angles. The influence of connectivity separates all of the observed spins into bands indicated by Q, where n denotes the connectivity of the spin in question; n = 0 for the monomer, n = I for Si end groups, n = 2 for a Si with two Si nearest neighbors, and n = 3 for a Si atom with three Si nearest neighbors. When the Si spin is in a three-membered ring, the added bond strain results in a downfield shift that creates two new bands designated by n = 2A, 3A. Further resolution within the bands results from differences in Si-0 bond lengths and Si-0-Si bond angles, and this provides the basis for identification of Si atoms in specific oligomeric structures. Assignments for the 29Sipeaks observed in this work are presented in Table I . These assignments are based on comparison with previous work done with enriched 29Siin potassium silicate sol u t i o n ~ ~ and ~ - ~at ’ natural abundance in alkali metal silicate solutions.28 (25) Kinrade, S. D.: Swaddle, T. W. J. Am. Chcm. Soc. 1986,108,7159. (26) Harris, R. K.;OConnor, M. J.; Curzon, E. H.; Howarth, 0. W.J. Magn. Reson. 1984. 57. 1 1 5.
(27) Knight, C. T. G.;Kirkpatrick, R. J.; Oldfield, E. J. Mugn. Reson. 1988, 78, 3 1, (28) McCormick, A. V. Ph.D. Dissertation, Department of Chemical gineering, University of California, Berkeley, CA, 1987.
En-
Hendricks et al.
I
2 ”
I
2
12
I
1 4
13 “w+v
3b,5b
43 I
i
42
2 4
6 (7b
methyl
n-propyl alkyl group
ethyl
neopentyl
Figure 2. Connectivity histogram obtained by integrating ’9Si NMR spectra of silicate solutions ([!SO2] = 1 mol %, R = 2) prepared with [(alkyl)(CH,),N]OH; alkyl = methyl, ethyl, n-propyl, and neopentyl. The error associated with each bar is f 2 % .
Results Figure 1 shows 29SiNMR spectra of silicate solutions ( [SO2] = 1 mol %; R = 2) prepared with [(alkyl)(CH3)3N]OH(alkyl = methyl, ethyl, n-propyl, or neopentyl). The proportion of Si in each connectivity class is shown in Figure 2 for each of the four organic bases. The principal species observed in a TMA silicate solution (Figure 1 a) are monomer, dimer, cyclic trimer, D3R, and D4R anions. Small amounts of linear trimer and tetramer are also observed. When one of the methyl groups in TMA is substituted by a larger substituent, the intensity of the peak for the D4R rapidly decreases relative to the intensities of the peaks for smaller
Effects of Cations on Silicate Oligomers
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9515
:2 I L
4
I
I'
0
I ' I
I
J l I I I
0
1 1
Figure 5. Plot of percent of total silicon contained in (a) cyclic trimer and (b) cyclic tetramer anions as a function of cation in TAA silicate solutions ([SiO,] = 1 mol %, R = 2).
1 1 1 1 1 1 1 1 I I I l l 1 1 1 1 1 I l l 1 1 I I
-5
-10
-15
-20
-25
111
10
-30
PPm Figure 3. 79SiNMR spectra of silicate solutions ([SiO,] = 1 mol %, R = 2) prepared with [(alkyl),N]OH; alkyl = (a) methyl, (b) ethyl, (c)
n-propyl, and (d) n-butyl.
4
(a) D3R
-
iij m c
co
c
0
c C
a
z
\
[ C
TMA
TEA
TPA
TBA
Figure 4. Connectivity histogram obtained by integrating 29SiNMR spectra of silicate solutions ([SiO,] = I mol %, R = 2) prepared with [(alkyl)3N]OH;alkyl = methyl, ethyl, n-propyl, and n-butyl. The error associated with each bar is i2%.
oligomeric species. This trend is also evident in Figure 2, which shows a decline in the proportion of Si in Q3environments and a corresponding increase in the proportion of Si in Qo,Q,. QZA, and Q2 + Q3,, environments when a methyl group is replaced by an ethyl group. When a methyl group is substituted by an n-propyl group, the presence of Q, is completely suppressed, and the proportion of QI atoms increases. Further incre'asing the size of the substituent to neopentyl results in a decrease in the proportion of Si atoms in Q2+ Q3Aenvironments and an increase in the proportion of Si in Qoand Q,environments. 29SiNMR spectra of silicate solutions ([SiO,] = I mol %; R = 2) prepared with [(alkyl)4N]OH (alkyl = methyl, ethyl, npropyl, and n-butyl) are presented in Figure 3. The effect of alkyl
g
a
(b) D4R
10
\ Figure 6. Plot of percent of total silicon contained in (a) D3R and (b) D4R anions as a function of cation in T A A silicate solutions ([SiO,] = 1 mol %, R = 2).
substituent size on the distribution of Si in different connectivity environments is given in Figure 4, whereas Figures 5 and 6 illustrate the effects of substituent size on the proportion of Si atoms found in cyclic trimer, cyclic tetramer, D3R, and D4R anions. Several trends can be observed as the size of the alkyl group increases. It is evident from Figures 5 and 6 that, in progressing
9516 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
Hendricks et al.
'5 30 c t
E
Q
20
10 Na
LI
0 1
2 R
3
Figure 7. Connectivity histogram obtained by integrating 29SiNMR spectra of TMA silicate solutions ( [Si02] = 1 mol 56)for R = I , 2, and 3. The error associated with each bar is +2%.
50
I
ma,
Rb
cs
MOH;M = lithium, sodium, potassium, rubidium, and cesium. The error associated with each bar is *2%. Q3 environments increases and the proportion of Si atoms in Q2 + QsAenvironments decreases. Discussion The results of the present study indicate that the distribution of silicate anions in TAA silicate solutions is a function of both silicate ratio (pH) and cation structure. For a given cation, the degree of oligomerization increases with increasing silicate ratio. This trend has been observed in all previous studies of alkali metal and TAA silicate solutions and can be readily explained by considering the effects of hydroxyl ion concentration on the equilibrium distribution of silicate species. For example, the formation of dimer silicate anions from monomer anions can be represented by the three equilibria:
M1
K
Figure 9. Connectivity histogram obtained by integrating 29Si NMR spectra of silicate solutions ([SiO,] = 1 mol I, R = 2) prepared with
2
+ H20 = M + OH-
(1)
3
R
Figure 8. Connectivity histogram obtained by integrating 29SiNMR spectra of TPA silicate solutions ([SiO,] = 1 mol %) for R = 1, 2, and 3. The error associated with each bar is *2%.
from TMA to TBA, the proportion of Si in cyclic trimer and cyclic tetramer anions increases and the proportion of Si in D3R and D4R anions decreases. Figure 4 shows that the proportions of Si atoms in Qoand Q, environments pass through maxima as the size of the alkyl group increases, whereas the proportion of Si atoms in Q, environments passes through a minimum. The proportion of Si atoms in Q2 QsAenvironments rises initially and then becomes more or less constant as the size of the alkyl groups increases. The effects of silicate ratio (R) on the NMR spectra of TMA, TEA, TPA, and TBA silicate solutions were investigated. Plots of the distribution of Si atoms as a function of silicate ratio for TMA and TPA silicate solutions are shown in Figures 7 and 8. It is evident from Figures 7 and 8 that, with rising silicate ratio, the silicon connectivity rises. This is a direct consequence of the decrease in pH. The increase of Si atoms in Q2 Q3,, and Q3 environments in the case of the TMA silicate solution comes at the expense of Si in monomer and cubic octamer silicate anions. In the case of TPA silicate solutions, the increase in the proportion of si in Q2 Q3Aand Q3 environments is accompanied by a depletion of Si in Qo, Q,, and QZAenvironments. To compare the distribution of silicate anions present in TAA silicate solutions with the distribution of anions in alkali metal silicate solutions, spectra were collected for Li, Na, K, Rb, and Cs silicate solutions. The distribution of Si atoms in different environments is shown in Figure 9. It is evident that, at the same Si02concentration and silicate ratio, the spectra of the alkali silicate solutions contain a much greater fraction of the Si atoms in Q2 + Q3Aand Q3 environments than any of the TAA silicate solutions. Figure 9 shows that as the size of the alkali metal cation increases from Li+ to Cs+, the proportion of Si atoms in Q, and
+
+
+
where M and D refer to the silicate monomer and dimer. It is apparent that dimer formation will increase as the pH decreases. Reactions similar to those shown above can be written to represent higher levels of oligomerization. From these it can be generalized that the degree of oligomerization increases with decreasing pH. The influence of cation structure on the distribution of silicate anions at a fixed silicate ratio is complex and not well understood. Consideration of physical-chemical phenomena in ionic solutions suggests that at least three processes may be relevant: cation-anion pair formation, water structuring, and cation crowding. The role that each of these processes might play is examined next. Coulombic interactions between cations and anions are known to result in the formation of cation-anion pairs in concentrated ionic solutions. McCormick et a1.28have proposed that the formation of such pairs stabilizes anions toward hydrolysis and that larger anions are stabilized relative to smaller ones with increasing size of the cation. Evidence in support of this conclusion was obtained by cation NMR spectroscopy of alkali metal silicate solutions. Silicate oligomers were found to shield Cs+ more efficiently than Na+, and from 29SiN M R spectroscopy it was deduced that the selectivity for large silicate oligomers is higher in the presence of Cs+ than Na+. Additional support for the conclusion that large alkali metal cations stabilize large silicate anions preferentially can be drawn from the work of Liebau, who has demonstrated that large, polarizable cations, such as Cs+, are better able to bind with ring and cage silicates than small cations, such as Li+.29 The second way in which cations might influence the distribution of silicate anions is through their effect on the structuring of water. The interaction of alkali metal cations with water has (29) Liebau, F. The Structurul Chemisfry ofdilicates; Springer-Verlag: Berlin, 1985.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9517
Effects of Cations on Silicate Oligomers TABLE I: 5 1Perk Assignments oligomer (1) monomer (2) dimer
(3) linear trimer
Qo
a
-
A
(5) linear tetramer
a b
(6)
cyclic tetramer
X
(7)
branched cyclic trimer
'P
(8)
bridged cyclic tetramer
42
Q ~ A
Q ~ A
Q3
0.0
H
cyclic trimer
(4)
QI 8.3-8.5 8.1-8.3
16.8-17.0 10.1-10.3 16.5-17.0
8.1-8.3
16.2-16.5 8.1-8.3
18.2-18.4
9.8-1 0.1 14.2
21.9
16.4
17.0
(10) tricyclic hexamer
16.1
16.7, 17.3
(1 1) doubly bridged cyclic tetramer
14.6
(9) bicyclic pentamer
9.9-10.0
21.2
(1 2) prismatic hexamer
17.2 27.2-27.5
(1 3) cubic octamer (14)
tricyclic octamer
(1 5 ) tetracyclic nonamer
been modeled by treating the cation as a charged sphere and the water as a series of dipoles (or in some cases quadrapoles).M This type of model predicts heats of hydration to within 10% for the series Na+ through Cs+ and to within 20% for Li+. Since the strength of the interaction between water and an alkali metal cation falls off with the square of the distance between centers, the influence of the cation would not be expected to extend much beyond one or two water molecules and to decrease with increasing cation size. The relative strength of water-cation interactions can be observed by measuring the rotational correlation time of the hydrating water molecule^.^' As seen in Figure 10, the rotational correlation time of the hydrating water molecules relative to the bulk value, 7*/ib, decreases inversely with cation size for the series Li+ to Cs+. Longer correlation times indicate that the waters of hydration are more tightly held. For TAA anions, one might expect the rotational correlation times to be even shorter than that for Cs+, since the radii of all of the TAA cations are significantly larger than that of Cs+. Instead, Figure IO shows that the rotational correlation time of the hydrating water increases rapidly with increasing cation size. Another indicator of the differences in the effects of alkali metal cations and TAA cations on the properties of water can be drawn from the work of Worley and K l o t ~ . Near-infrared ~~ spectra of HOD-D20 solutions containing various bromide salts were used to calculate the ratio of hydrogen-bonded to nonbonded water. This ratio increased in the order (values are normalized to 1 .OOO for pure solvent): KBr (0.822) < NaBr (0.827) < LiBr (0.893) < TMABr (1.000) < TEABr (1.034) < TBABr (1.339) (30) Bockris, J. 0.;Reddy, A. K.N . Modern Electrochemistry; Plenum Press: New York, 1970. (31) Desnoyers. J. E.; Jolicoer, C. In Comprehensive Treatise of Electrochemistry; Conway, B. E., Bockris, J. O., Yeager, E., Eds.; Plenum Press: New York, 1983; Vol. 5 , p 82. (32) Worley, J. D.; Klotz, I . M. J . Chem. Phys. 1966, 45, 2868.
24.7
?
24.7
?
25.0
L
.
TBA+
3-0 -
2-
-
0 0
. ...
Li+
-
-
OTMA+
1cs+ I
I
I
ChargelRadius, 8;' Figure 10. Plot of rotational correlation times of hydrating water molecules relative to the bulk value ( T * / T ~ )for TAA and alkali metal cations as a function of the charge to radius ratio.
This indicates that the concentration of bonded water molecules rises with decreasing alkali metal cation size and with increasing tetraalkylammonium size. The effects of cation structure on the rotational correlation time of water and the extent of hydrogen bonding can be attributed to "hydrophobic interactions". The underlying principle is that organic functional groups promote the formation of a three-dimensional hydrogen-bonded structure of water. Thus, if one imagines that water molecules exist in a two-state equilibrium: (4)
then the presence of organic molecules in solution shifts the equilibrium of reaction 4 to the right. The influence of hydrophobic interactions on the condensation of silicate anions can be envisioned by the equilibrium: 2(-SiOH) = -SiOSi- + H20 (5)
'1
4 i .-0
s
+d
a,
-E, P
a,
e!
LL
2 4 6 8 Cation Radius (Unhydrated), A Figure 11. Plot of free volume per cation as a function of cation radius in a solution that is 1 M in cation. Upper curve represents free volume per cation for unhydrated cations whereas the bottom curve represents the free volume per cation for hydrated cations. For purposes of comparison the unhydrated radii of Li', Cs', TMA', and TBA' and the volumes of D3R and D4R are shown.
-0
If the introduction of organic solutes causes the chemical potential of water to decrease, then the equilibrium for reaction 5 will shift to the right and the extent of silicate condensation will increase. The third mechanism by which cations can exert an influence on the distribution of silicate anions is through a process that we shall refer to as ionic crowding. Due to Coulombic repulsion, the cations in solution tend to distribute so as to produce the maximum cation-cation separation. The free volume per cation can then be defined as the total solution volume per cation minus the volume of the cation. In the absence of strong cation-anion interactions, as is likely to be the case with TAA cations, the anions in solution must have volumes that are equal to or smaller than the free volume associated with each cation. If this condition is not met, local crowding of cations will occur and this will set up an electrostatic field that disperses the cations. On the basis of these considerations, one may postulate that the maximum size that silicate anions can achieve in solution is constrained by the free volume per cation. It follows therefore that, for a fixed silicate ratio and cation concentration, cation crowding will work toward decreasing the size of silicate anions as the size of the cation is increased. In a 1 M solution the average distance between cation centers is 12 A. Figure I I shows how the free volume per cation varies with cation size. For reference, the unhydrated radii of Li+, Cs+. TMA, and TBA are shown at the bottom ofjhe figure. The upper curve represents the free volume assuming that all cations are unhydrated, whereas the lower curve represents the free volume assuming a single layer of cation hydration. The estimated volumes for fully hydrated D3R and D4R anions are indicated on the ordinate. It is immediately evident that for cations with radii equivalent to or smaller than TMA' the free volume in solution is sufficient to accommodate D4R anions and all smaller structures. When the unhydrated cation radius is increased to 5 A, the frce volume becomes insufficient to accommodate D4R anions. The effects of cation size and structure on the distribution of silicate species can now be examined in light of the preceding discussion. All of the alkali metal cations are small enough so that, at I M concentration, the free volume per cation is sufficient to accommodate D4R and all smaller anions. As a consequence, effects of ionic crowding should not be observable for alkali metal cations. Since these cations do not induce water structuring, the only influence of cation size is on the extent of cation-anion pairing. Consequently, the increase in Si connectivity with cation size, observed in Figure 9, can be attributed to the preferential interaction of large silicate anions with large alkali metal cations. This conclusion and the trends observed in Figure 9 are similar to those reported earlier by McCormick et al." All of thc TAA cations are sufficiently large that cation-anion pairing should not be extensive. In this case, the effects of cation
Hendricks et al. size should be expressed through changes in the hydrophobicity of the cation and the extent of cation crowding. With increasing cation size, the hydrophobic effect of TAA cations on the structuring of water increases and the free volume per cation decreases. As discussed above, these two effects influence the distribution in opposing ways: for rising cation size the increased hydrophobic effect increases the extent of silicate oligomerization, while the decrease in cation free volume decreases the extent of oligomerization. The trends observed in Figures 1 and 2 suggest that even the relatively small increases in cation size caused by replacement of a single methyl group by a larger alkyl substituent result in a significant change in the distribution of silicate anions. It is interesting to observe in Figures 2 and 4 that, by the time one reaches the species C3H7(CH3)3N+,the distribution of Si connectivities becomes equivalent to that observed in solutions prepared with (C3H7)4N+cations. The trends in the distribution of Si between single and double-membered rings with increasing size of TAA cations can also be attributed to the opposing effects of hydrophobicity and cation free volume. Thus, we see in Figures 3 and 4 that as the size of the TAA cation rises, there is a monotonic increase in the proportion of Si in single three- and four-membered rings due to the hydrophobic effect, and a corresponding decrease in the proportion of Si in double three- and four-membered rings due to the ion crowding effect. Finally, we note that the results presented in Figures 7 and 8 indicate that the effects of cation size are most pronounced at R = 2, and less evident at R = 1 and R = 3. These trends can be ascribed to the effects of pH and cation concentration. At low silicate ratio, the pH is high and so is the concentration of cations. The high pH reduces the extent of silicate oligomerization. While this is partially offset by the hydrophobic effect caused by the high concentration of cations, the influence of pH appears to be the dominant factor affecting the distribution of silicate anions. At R = 3, the pH is lower than at R = 2, causing the distribution of silicate species to shift toward more highly oligomeric species. The lower concentration of cations at the higher silicate ratio reduces the extent of water structuring due to the cations and, hence, the extent to which cation size influences the distribution of silicate species.
Conclusions For the same silica concentration and silicate ratio, intrinsic differences are found in the distribution of silicate anions in alkali metal silicate and tetraalkylammonium silicate solutions. Alkali metal silicate solutions exhibit a broad spectrum of silicate anions. The extent of silicate anion oligomerization increases with increasing size of the alkali metal cation. In agreement with previous investigation^,'^ the effects of cation size can be attributed to cation-anion pair formation, large silicate anions being stabilized preferentially by large cations. TAA silicate solutions contain a smaller number of silicate anions than alkali metal silicate solutions. The effects of cation size are subtle and do not correspond to a simple extension of the reasoning for alkali metal cations. The large size of the TAA cations precludes significant cation-anion pairing. It is proposed that with increasing size hydrophobic solvation effects lead to a greater degree of water structuring. This promotes the oligomerization of monomeric silicate anions. Counteracting this trend is the influence of ion crowding. With increasing cation size, the free volume available per silicate anion decreases. For cations the size of TBA, the free volume per cation is comparable to that required to accommodate the largest silicate anions observed. Crowding of the cations by the accommodation of large anions is envisioned to produce an electrostatic stress which is compensated by a reduction in the anion size. This is the likely origin of D3R and D4R silicates with TMA but not for larger TAA analogues. Acknowledgment. This work was supported by the Director, Office of Basic Energy Sciences, Material Sciences Division of the U.S. Department of Energy, under Contract DE-AC0376SF00098, and a grant from W. R. Grace and Co.
