J. Phys. Chem. 1981, 85,289-294
I
”
”
/
1
t,,
I
/’
1
/ “
? ..: 0
I
/
O.8t
I
eo
.:--, , -- ---,__ _ 60
40
I
80
,
I
100
x, pm
Concentration profiles for the system of eq 1 with kf = lo5 s-’ M-’,kb = 10 s-’, Cb = 1 mM. Solid lines, 7 = 5.47 s; dashed lines, 7 = 0.36 s. FI ure 5.
-
is 130 pm, and the concentration profiles for Re and R2 are much flatter. On the time scale of the pulse, for t, = 1 ms the diffusion layer thickness is -2 pm. As shown in the inset of Figure 5, the concentration profiles are quite flat on this distance scale for T = 5.47 s. Estimation of the equilibrium constant using the surface concentrations at 7 = 5.47 s gives K’Cb = 8.1, whereas the true value is 10. The simulation yields for this case K’Cb = 7.9.
289
Limits of Application. It has already been shown in the discussion leading to the choice of tp = 1 ms that this treatment is restricted to reactions which have sufficiently large values of KCb or sufficiently small values of [kbt / (KCb)1/z]1/2 that the homogeneous reaction is frozen on t i e time scale of the pulse. On the other hand, during the period T - t, there must be sufficient approach to equilibrium to see a measurable effect if K is to be determined. For a first-order reaction we could describe the approach to homogeneous equilibrium by In [C(O)- C ( ~ ) ] / [ C (-T ) C(m)] = k~ where C(0) and C(m) are the initial and equilibrium concentrations, respectively. If we require that [C(O)- C ( ~ ) ] / ( C (-TC) ( - ) ] > 1.1, then for measurement of K we must have log ( k ~ >) -1. There are also experimental limits on the value of log (KCb). From eq 6 and 9, it is necessary to obtain accurate measurements of iRp,D and iRP,R or of i ~ p~ ,D C ,and i w , to ~ calculate K ! For small values of log (K’Cb),iRP,,-,becomes small and is difficult to measure accurately even if it can be measured directly rather than by resorting to eq 9. We choose as a conservative experimental limit the requirement iRp,D 2 O.liNp. Then, since under those conditions iRp,R iNP,log (K’Cb) L -1.3. On the other hand, if K is large, LRP,D N tNp, and measurement of iRp,R becomes difficult. Again we choose a conservative limit, iRp,R 2 iDc/2, which gives log (K’Cb)5 4. Thus this treatment is experimentally accessible over the range -1.3 5 log (K’Cb) I 4. Acknowledgment. This work was supported in part by the National Science Foundation under Grant No. CHE 7917543.
Mixed-Alkali Effect in Aqueous Silicate Solutlons Malcolm D. Ingram, * Klrwan Klng, Davld Kranbuehl, Department of Chemlstty, College of Wllllam and Maws Wllllamsburg, Virginia 23 185
and Mohamad Adel-Hadadl Vitreous State Laboratoty, Catholic University of America, Washington, D.C. 20064 (Received: May 16, 1980)
The fluidity (4) and the conductivity ( 0 ) of strongly supercooled solutions of sodium and potassium metasilicate and their mixtures, of general formula xK2SiO3-(l-x)NazSiO3-7Hz0, have been measured to -70 “C. The Arrhenius plots were curved, and both 4 and u data were fitted to the equation 4 (or a) = A exp[-B/(T - To)], where Tois a “zero mobility temperature” obtained by an iterative least-squares method. The viscosity data were measured over nine orders of magnitude and were well described for all solutions by this three-parameter equation. When the conductivity was plotted as a function of composition at constant fluidity, a conductance minimum was found at low temperatures which was identified as the appearance of the “mixed-alkali”effect. The results offer quantitative support for the idea that the mixed-alkali effect is only found when the structural relaxation time, ( 7g), is much longer ( 100 times) than the conductivity relaxation time, ( 7 c ) . N
Introduction The “mixed-alkali effect’’1,2covers a number of remarkable properties of glass, but the most spectacular effect involves the ionic conductivity (a). Thus in glasses of constant alkali content, e.g., xK20-(1-x)Na20-3Si02 where all of the current is carried by Na+ and/or K+ ions, the conductivity of mixed glasses can be reduced by a factor of lo4 or lo5 compared with single-alkali glasses measured at the same temperature. Such large departures (1) J. 0. Isard, J.Non-Cryst. Solids, 1, 235 (1969). (2) D. E. Day, J. Non-Cryst. Solids, 21, 343 (1976).
0022-3654/81/2085-0289$01 .OO/O
from additivity clearly constitute a major breakdown of the principle of independent migration of ions, which works well for dilute aqueous electrolytes. In an attempt to bridge these two extremes of behavior and also to get an improved understanding of the mixed-alkali effect, we have examined the behavior of highly supercooled alkali silicate solutions. As a starting point, we have taken the recent paper by Moynihan3 which discusses conductivity in hydrate melts of composition xNaN03-(0.2-x)MN03-0.8Ca(N03)z~
~~
(3) C. T. Moynihan, J. Electrochem. SOC.,126,2144 (1979).
0 1981 American Chemical Society
290
The Journal of Physical Chemistty, Vol. 85, No. 3, 1981
4.09H20, where M = K or T1. No significant departures from additivity were found by Moynihan, but extrapolations of the conductivity data using the Vogel-Tammann-Fulcher equation (see below) suggested that a mixed-alkali effect might have been detected had the data been extended to lower temperatures. Moynihan suggested that a mixed-alkali effect in conductivity can only occur if the time scale for ionic transport is short compared with that required for relaxations in liquid structure; this condition was not satisfied in his experiments. The object of the present investigation was to look for mixed-alkali effects in concentrated silicate solutions and to see whether the results were consistent with the known properties of these systems and Moynihan’s time-scale hypothesis. Aqueous silicates seemed a promising choice because of their widespread industrial use in adhesives and ~ e m e n t sand ~ * their ~ tendency to form hard glasslike substances on drying.6 However, we found experimentally that the majority of commercially available alkali silicate solutions readily crystallized on cooling, but, by a process of trial and error (adjusting the composition of proprietary silicate solutions in stepwise amounts), it was found that both aqueous sodium and potassium silicates of approximately “metasilicate” composition could be readily supercooled to form glasses. The solutions used in the present investigation of conductivity and viscosity effects had the general formula xK,SiO,-( 1-x)Na2SiO3-7Hz0, where it was possible to study the complete range from 100% sodium to 100% potassium compositions. Experimental Section Preparative Work. Various alkali silicate solutions were provided by the PQ Corp. Sodium and potassium metasilicate solutions were prepared as needed by adding appropriate amounts of finely divided SiOz powder (dried a t 500 OC for 12 h) and NaOH and KOH pellets to the proprietary solutions. The strongly exothermic reaction yielded supersaturated solutions of the required composition, and, after being left to clarify overnight, these stock solutions were mixed to provide a range of sodium/potassium solutions for immediate use. ViscositylFluidity Measurements. Viscosities up to 400 P were measured by using a capillary Cannon-Ubbelohde viscometer (NBS standardized). For viscosities in the range 102-107 P, a Brookfield Synchro-Lectric rotating cylinder viscometer (Model No. RVT) was used in its customary mode,’ a stationary outer cylinder with an inner cylinder rotating at a known angular velocity. The range of the Brookfield viscometer was extended by using a relaxation technique.8 For viscosities of lo6-log P, the inner cylinder was rotated away from its equilibrium position. The rate of return to equilibrium due to the torque of the solution was measured over time periods which ranged from several minutes to hours depending on the viscosity. The relaxation time of this first-order rate process is proportional to the viscosity. Calibration constants for the relaxation measurements were separately determined for each solution by overlapping relaxation measurementswith the conventional rotating-cylinder results. The maximum variation in the viscosity on separately prepared solutions of the same composition was 15%. In general, the viscosity (4)J. G. Vail and J. H. Wills, “Soluble Silicates, Their Properties and Uses”, ACS Monogr., Reinhold, New York, 1952. (5) H. H. Weldes and K. R. Lange, Ind. Eng. Chem., 61, 29 (1969). (6)L. S.Dent Glasser and C. K. Lees, J.Appl. Chem. Biotechnol., 21, 127 (1971);25,427 (1975). (7)C. T. Moynihan and S. Cantor, J . Chem. Phys., 48,115 (1968). (8)R. Weiler, S. Blaser, and P. B. Macedo, J.Phys. Chem., 73,4148 (1969).
Ingram et al. T ( O C )
20
I
0
-50
-40
-20
-60
-70
1
34
36
38
40
42
44
46
40
50
10~(~-1)
T Figure 1. Arrhenius plots (log q5 vs. 1 / T ) for fluidity in seven alkali metasilicate solutions where the numbers indicate (1) 0% K, (2) 10% K, (3) 18% K, (4) 40% K, (5) 60% K, (6) 90% K, and (7) 100% K using (0)capillary viscometers and (0)rotating cup viscometers.
was independent of the shear rate, consistent with an earlier reportg of Newtonian behavior in sodium silicate solutions. Conductivity Measurements. Conductivities were measured in standard conductivity cells, with cell constants of 0.3-0.4 cm-‘. At higher temperatures, the conductivity was measured by using a Universal Instruments conductance bridge with fixed frequencies of 1and 3 kHz. For conductivities less than lo4 cm-l a General Radio 1615 bridge was used, with external source (General Radio 1610-B) and detector (General Radio 1232-A) taking readings over a frequency range from 30 Hz to 1kHz. Care was taken to obtain values in the frequency-independent regime, avoiding both electrode polarization at high temperatures and low frequencies, and the conductivity dispersions (or dielectric losses) at low temperatures and high frequencies.1° The low-temperature limit of conductivity measurement was reached when the latter conductivity dispersion spread out over the available frequency range; in practice, measurements were discarded when the conductivity varied by more than 10% between 30 and 50 Hz. Both the viscosity and conductivity cells were immersed in a FTS Multi-Cool temperature bath which maintained the temperature to f O . l “C. The temperature was monitored by using a Hewlett Packard quartz thermometer. Experimental Results Fluidity-Composition-Temperature Trends. Figure 1 contains “Arrhenius”plots for fluidity (6= v-l) for a series of solutions with different proportions of Na’ and K+ ions, expressed as the percentage of K+ ions, % K = 1 0 0 n ~ / ( n , + nNa). The pronounced curvature in these plots is (9)R. Grant and C. R. Masson, J. Colloid Interface Sci., 41, 606 (1972). (10)J. H. Ambrus, C. T. Moynihan, and P. B. Macedo, J. Phys. Chem., 76,3287 (1972).
Mixed-Alkali Effect in Aqueous Silicate Solutions
The Journal of Physical Chemistty, Vol. 85, No. 3, I981 291
TABLE I : Best Fit VTF Parameters for Alkali Silicate Solutions soln 7% K b A& B& To(@) SDln@ 83 9 21gU 0.225 0 91 5 6400 1083 207 0.06 7 10 201 0.074 19770 1214 18 40 18515 190 0.125 1231 1109 183 0.185 60 7343 1102 167 0.1 58 90 8214 161 0.188 100 8631 1092 To= 209 if lowest-temperature data point is omitted (see Figure 2).
A0 11745 6060 1.585 209 44 29 113 37
1 2 3 4 5 6 7
I
’
‘
%
BU
To(u)
SDln u
1174 1611 1461 1130 1721 1035 86 0
183 182 181 181 152 159 161
0.254 0.113 0.095 0.053 0.087 0.282 0.104
= 100qK/(vNa + RK).
%K
I
Potassium
Figure 2. Best-fii (fluidity) To parameters as a function of potassium content, where % K = 100qK/(qN,4- qK). (0 is the Tovalue for 0% K solution when the lowest-temperature data point is omitted).
noteworthy, but this has been found previously in other molten salts and hydrate m e l t ~ . ~ J The ~ - ~data ~ can be fitted to the Vogel-Tammann-Fulcher (VTF) equation, where
4 = A , exp[-B,/(T
-
To)]
(1)
and Tois understood as a “zero mobility” temperature. Equation 1 describes the data remarkably well, the solid lines in Figure 1 being drawn from the “best-fit’’ values of A,B, and Toin Table I. It is apparent from Table I and Figure 2 that Todecreases smoothly with increasing potassium content (especially if the lowest data point for solution 1 is omitted) and that the B parameter is effectively constant. The fluidity of these solutions can be expressed as a simple function both of temperature and of the fraction of K+ ions; thus
where the values of B, TO,Na, and C are ca. 1100,210, and 50 K (see below). This variation in Toparameter has a decisive effect on the shape of the isothermal fluidity plots (interpolated from Figure 1) shown in Figure 3. Close to room temperature, where T >> To, log 4 varies almost linearly with composition;the slope (e.g., 1.85 K at 278 K and 100% K) agrees well with the value [d log 4/dXKIT= BC/[2.30(T - TOY]= 1.9 K which can be calculated by differentiating eq 2 with respect to XK. The steep rise in fluidity at lower temperatures, found on initial replacement of Na+ by K+ ions, simply reflects (11)C.A. Angell, J . Phys. Chem., 68,218, 1917 (1964). (12)R. Bose, R. Weiler, and P. B. Macedo, Phys. Chem. Glasses, 11, 117 (1970). (13)H . Tweer, N.Laberge, and P. B. Macedo, J. Am. Ceram. Soc., 54, 121 (1971).
0
10
20
30
40
50
60
70
80
90
100
% Potassium
Figure 3. Fluidity isotherms for mixed-alkali silicate solutions.
the greater proximity to Toin the case of the sodium-rich solutions. The smooth decrease in To,on replacing Na+ by K+ ions, means that the mixed-alkali effect must be absent in the case of fluidity. Indeed, we do not find in the isothermal plots either fluidity maxima as reported for anhydrous silicate and germanate melta14J6or fluidity minima found earlier in mixed-alkali silicate solutions much richer in SiOz, typically with mole ratios Si02:M20 = 3.3:l (the so-called “double water glasses”).la As a check on the reliability of the present results, an attempt has been made to compare the measured fluidities (or viscosities) with existing literature values. However, very little work has been done with such highly concentrated, highly alkaline solutions, although the NazO-Si02-H20 system has received most attention. If one takes the data of Bacon and McKinneyl’ and extrapolates to 25 wt. % Na20 (i.e., the NazSi03-7H20 composition), viscosity q = 200 P can be estimated. When one considers the strong dependence of the viscosity on composition and temperature, the agreement with the experimental value of 80 P (this study) is satisfactory (a 1% error in the water content, for example, would account for the difference). Conductivity-Composition-Temperature Trends. The Arrhenius and isothermal conductivity plots in Figures 4 and 5 resemble the corresponding fluidity plots, Figures 1and 3,and it seems that the conductivity follows closely the trends in fluidity. Thus, in the isothermal plots, replacement of Na+ by K+ causes an increase in conductivity. At ambient temperatures log u varies linearly with the (14)J. P.Poole, J. Am. Ceram. Soc., 32, 230 (1949). (15)J. E.Shelby, J. Appl. Phys., 46,193 (1975). (16)Reference 4,Vol. 2,p 324. (17)Figure 11, ref 5.
The Journal of Physical Chemistry, Vol. 85,No. 3, 1981
292
T 0
20
-2
--‘5 2
v
Ingram et ai.
conduction mechanism and, as a consequence, the onset of the mixed-alkali effect.
(OC)
-50
-40
-20
-60
-70
Discussion Structural Aspects of Silicate Solutions. The available evidence from NMRl9l2Oand trimethylsilation/chromatographic techniques21indicates that there are no long-chain polymeric species in “metasilicate” solutions; the predominant anionic species are orthosilicate monomers (H2Si0z-) and substantial amounts of dimer, linear trimer, and cyclic tetramer. Hydrolysis is a further complication, and the strongly alkaline reaction of these solutions arises from reactions of the kind [HzSiO4lZ-+ H 2 0 == [H3Si04]-+ OH(3)
-
-3-4
-
-5
-
b 0
2 -6-7 -8-
-9 -
I 34
36
37
40
42
4 4
46
50
40
Flgure 4. Arrhenius plots (log u vs. 11T ) for conductivity for the same seven solutions given in Figure 1. I
I
- 4
-2t
-r / -9
I
0
From the standard it appears that concentrated metasilicate solutions will have a pH = 14, and so, if one negleds activity coefficients, the concentration of OH- ions could be taken as approximately 1 M. In testing for the mixed-alkali effect, it is necessary to assume that a high proportion of the current is carried by alkali cations. In the early work of HarmanF2Hittorf-type experiments on sodium metasilicate solutions were performed in the range 0.1-2.0 M, and tOHand tNa values of 0.53 and 0.37 were calculated, respectively. However, this work was done before the 4-coordination of silicon in aqueous solutions was recognized and also before the importance of polymerization reactions was properly appreciated, so these data could certainly be reevaluated in the light of modern knowledge. It seems likely that the transport by Na+ ions will be more important in the conductivity experiments described in the present investigation. A straightforward calculation based on the density of Na2SiO3-7HzO solution at 0 “C (1.68 g ~ m - shows ~ ) the solution to be ca. 13.5 M with respect to Na+ ions. In these systems, which can be regarded as ionic melts somewhat diluted with HzO, the OHions may lose their “anomalous mobility” (associated in aqueous solution with the Grotthus mechanism) and make only a small contribution to the electrical conductivity. A more serious problem arises, however, from the differing extents of hydration of Na+ and K+ ions. The obvious dissimilarity in behavior between the sodium and potassium metasilicates is the enormous disparity in viscosities, 80 P for NazSi03-7Hz0 and 0.5 P for K2Si037Hz0 at 20 “C. GlasserZ3has suggested that this reflects the small concentration of “free water” in sodium as compared with potassium silicate solutions. Indeed, it is probable (although the necessary thermodynamic data are not available to support this argument) that the increase in the conductivity and fluidity which occurs when sodium is replaced by potassium in paralleled by an increase in the water activity. This does seem to be a markedly different situation from the NaN03-KN03-Ca(N03)2-4H20 melts used by Moynihan? where all of the HzO molecules could be presumed to be tightly bound to the Ca2+ions. Moynihan’ Time-Scale Criterion. It was suggested3that the mixed-alkali effect occurs in liquids (as well as in crystals and glasses) only when a “solidlike” conduction mechanism is operating and that the mobile cations can “hop” from one recognizable site to another before the anion framework has time to rearrange. Under these conditions the relaxation time for structural rearrangement
10
20
30
I 40
50 Ole
60
70
80
90
100
Potassiur
Flgure 5. Conductivity isotherms for mixed-alkali silicate solutions.
mole fraction of potassium, but curvature develops at lower temperatures as in the case of the fluidity. There is also no obvious mixed-alkali effect in this system, in the sense that at any temperature the conductivity goes through a minimum value. Inspection of the besbfit VTF parameters listed in Table I, however, reveals some interesting features. Only for the pure potassium metasilicate solution do the Toparameters for fluidity and conductivity agree exactly. In all other cases, To(a)< To(4).Behavior like this has been reported before for nitrate melts, where there was a “return” to an Arrhenius region at low temperatures.l2,le No obviously linear region on the Arrhenius plots appears in Figure 4, and the actual changes in curvature required to displace the Tovalue are probably quite small. Thus, when the data are fitted to eq 1, any decrease in To is automatically compensated for by increasing the value of the B parameter. Nevertheless, theee (small) irregularities in the VTF parameters may signal a change toward a “glasslike” (18)F.S.Howell, R. A. Bose, P. B. Macedo, and C. T. Moynihan, J. Phys. Chem., 78,639 (1974).
(19)H. C.Marsmann, 2.Naturforsch. B, 29,495(1974). (20)R. 0.Gould, B. M. Lowe, and N. A. MacGilp, J. Chem. SOC., Chem. Commun., 720 (1974). (21)L.S.D.Glasser and S. K. Sharma, Br. Polym. J.,6 , 283 (1974). (22)R.W.Harman, J. Phys. Chem., 30, 359 (1926). (23)L.S.D.Glasser, private communication.
Mixed-Alkali Effect in Aqueous Silicate Solutions
The Journal of Physical Chemistry, Vol. 85, No. 3, 198 1 293
TABLE 11: Isothermal lon ( o n ) Productsa
ternn. K
a
103/T, K-’
% ’ Dotassium
294 3.4 278 3.6 263 3.8 250 4.0 244 4.1 233 4.3 222 4.5 213 4.7 208 4.8 204 4.9 Taken from Figures 1 and 4.
0
10
18
40
-0.70 -0.50 +0.10 +1.40
-0.90 -0.70 -0.35 +0.60 +1.50
-1.00 -0.75 -0.30 +0.40 +0.90
-1.25 -1.00 -0.60 -0.20 +0.15 +1.05
’
60 -1.10 -0.95 -0.60 -0.35 +0.75 +1.55
90
100
-1.15 -1.00 --0.90 -0.65 -0.30 +0.25 +0.65 +1.15
- 1.35
- 1.25 - 1.15 - 1.00
-0.75 -0.40 -0.15 +0.05
must be much longer than for the decay of the electric field by means of the conduction processes, where the ratio ( 7 8 ) / ( ~ , ) is given by eq 4,18 where G, is the solidlike ?/G-( 7=8 -) (4) (7,)
E o d Q
(high-frequency) sher modulus of the melt, E , is the limiting high-frequency dielectric constant, and €0 = 8.854 X F cm-’ is the permittivity of free space. If one takes typical values for ionic melts and glasses of G, = 10” dyn cm-2 and E , = 6 , this gives eq 5, where g (P) and a (W (5)
-6t -
-e -1
$ = l o p
1
7t----4 I
I
0
20
I
40 60 80 ‘1. Potassium
100
cm-’) are in cgs units. The appeal of this concept is that it leads directly to the prediction that the mixed-alkali Figure 8. Isofluidii-conductivii plots for mixed-alkali silicate solutions. effect should appear in melts with large qa products (or a/$ ratios) and might become detectable when ag > 5, i.e., content (cf. the increase found in the isothermal plots). when the ratio of relaxation times is -1OO:l. Second, there is a shallow minimum in the conductivity, The relevant ag values for the silicate solutions axe given appearing at the lowest fluidities (ca. P-’1, where the in Table 11. For each solution, the ag product increases ag value is -20. This conductance minimum can be taken with decreasing temperature, and, at any given temperaas evidence for the onset of the mixed-alkali effect. ture, the ag value increases with increasing sodium content. Mechanistic Interpretations. Elsewhere, Ingram and Broadly speaking, ag increases as Tois approached. Moynihan25@have proposed that glasses should be classed Judging by the high ag value (30 P 0-’cm-’) for the as weak electrolytes, in the sense that only a fraction of sodium metasilicate solution at 250 K, the mixed-alkali the available cations (in Na20-3Si02 glasses typically 3% effect should be expected, as evidenced by a decrease in depending on temperature) are actually mobile. In one conductivity on addition of potassium. Figure 5 shows that theory, these mobile cations have been assumed to be the opposite is true, and apparently the theory has broken paired,25 Le., residing within some 2-3 A of each other, down. However, the rise in conductivity is accompanied instead of at the average interionic distance, which is -4 by a rise in fluidity (see Figure 3) and can be attributed A in anhydrous silicate glasses and 5 8, in these concento the general enhancement of ionic mobilities associated trated silicate solutions. The pairing of cations is supposed with a decrease in the structural relaxation time. to lead to mutual destabilization (viewed either in terms Isofluidity Plots. We propose that the “best” procedure of electrostatic repulsions or local ”overbonding”), and for identifying mixed-alkali effects is to look for minima migration proceeds by a “paired interstitialcy” mechanism in conductivity-composition curves plotted under condias in p-alumina crystal^.^' On this basis, a mixed-alkali tions of constant fluidity. This is equivalent (see eq 4) effect arises when “unlike-pairs”, e.g., (NaK)2+,are formed to following changes in the conductivity relaxation time and (perhaps because of a favorable polarization energy) ( 7,),under conditions of constant structural relaxation become immobilized in the glass structure. This time ( 7 8 ) . Since the B parameter for the fluidity is ef“interstitial pair” concept can be used to provide a simple fectively constant for all of these metasilicate solutions, basis for explaining the shape of the isofluidity plots in the constant-fluidity criterion amounts to comparing Q Figure 6. values at constant reduced temperatures (T- To).A High-Fluidity Region ($ = ca. P’). Here, transport similar procedure was adopted by Easteal and H ~ d g for e ~ ~ processes follow the pattern typical of ionic melts and salt locating the conductance minima in molten KC1-PbC12 hydrates generally? Over the whole range of compositions, mixtures. the ag value is -0.1, and the ratio of structural to conIsofluidity plots are given in Figure 6. At high fluidities ductivity relaxation times ( T ~ ) / 76) ( remains small ( ~ 2 ) . ($ = P-’1, the conductivity is almost independent of The absence of any conductivity irregularities (maxima or composition, but, as the fluidity decreases, deviations apminima) suggests that the weak electrolyte (e.g., interstitial pear. These deviations are of two kinds. First, there is a (25)M. D.Ingram, J.Am. Ceram. SOC.,63,248 (1980). (26) M.D.Ingram, A. V. Lesikar, and C. T. Moynihan, J. Non-Cryst. general decrease in conductivity with increasing potassium (24) A. J. Easteal and I. M. Hodge, J. Phys. Chem., 74,730 (1970).
Solids, 38 and 39, 371 (1980). (27) J. C. Wang, M. Gaffari, and S. Choi, J. Chem. Phys., 63, 772 (1975).
294
J. Phys. Chem. 1981, 85, 294-300
pair) mechanism is probably not operating, and conduction involves the cooperative rearrangement (and possibly migration) of all of the ions present in the solution (Na+, K+, OH-, “silicate”, etc.). Low-Fluidity Region (4 = Pl).In this region, the high 07 values (-20 for the 100% Na composition) and high ( r 8 )/ ( 7,) ratios (-400) suggest that the current is being carried by only one type of ion (e.g., cations). This suggestion is based on the argument that when ( ~ ~ ) / ( 7 , ) is greater than unity, there exists a substantial difference in mobility between the component ions in the solutions.l8 The fast-moving ions determine 7, and the slower ions determine the slower rate of overall structural rearrangement. It is useful to consider how the concentrations of (NaJ2+, (NaKl2+and (KJ2+might vary with concentration, in order to explain the conductivity trends. Using the interstitial pair concept discussed above, we speculate that, when % K = 0, all of the current is carried by (Na2)2+pairs. The relatively high a value (as compared with 4) reflects the relatively high abundance of paired cations in solutions where, it has been argued, the water activity is low and hydration of unpaired Na+ ions would be incomplete. Addition of K+ ions would lead to the formation of immobile (NaKl2+pairs, and the appearance of a conductivity minimum around 40% K. The subsequent rise in conductivity seen at 60% K would arise from an increasing contribution from mobile (K2)2+pairs (the formation of which is perhaps encouraged by the greater success of Na+ ions in acquiring the water molecules of hydration). Finally, in solutions containing 90% or more K+ ions, sufficient water would now be present for all of the K+ ions to be fully hydrated. The concentration of (K2)2+ions therefore decreases and the conductivity falls off markedly.
It is interesting to recall (Table I) that only in the case of the 100% potassium metasilicate solution do the To values for fluidity and conductivity agree. The difference in Toparameters (To($)- To( a)) correlates remarkably well with the “excess conductivities” attributed in the present discussions to the existence of the glasslike conduction process. General Conclusions (1)Moynihan’s relaxation-time criterion seems to provide a sound basis for predicting the onset of the mixedalkali effect in hydrate melts, provided appropriate assumptions regarding “corresponding states” are made. In the case of the alkali silicate solutions, isofluidity (isoviscous) plots seemed to be quite satisfactory in this respect. (2) Sodium and potassium metasilicate solutions differ markedly in their properties. It is difficult to find clear evidence for the mixed-alkali effect in these aqueous silicate solutions. Only in the sodium-rich solutions (where the cations are thought to be incompletely hydrated) is a mixed-alkali effect observed similar to that found in anhydrous silicate melts and glasses. The effects observed are not nearly so pronounced as in anhydrous melts and glasses. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial financial support of two of us (K.K. and D.K.). We thank also Me. Ardemiss Ayanian (PW Corp.) for supplying a selection of sodium and potassium silicate solutions and Professor C. T. Moynihan and Dr. L. S. D. Glasser for helpful discussion.
Temperature Dependence of Bragg Scatterlng from Crystallized Suspensions of Macroions John 0. Dalyt and R. Hastlngs” Department of Physics, North Dakota State University, Fargo, North Dakota 58105 (Recelvd: June 24, 1980)
Measurements of the temperature dependence of the Bragg scattering intensity from crystallized suspensions of 1090-A diameter latex polystyrene spheres are reported. Body-centered cubic crystals with lattice constants ranging from 4000 to 7000 A are examined. In most samples the intensity drops with temperature, falling rapidly to zero as the crystals melt. Some samples show an initial rise in intensity. The data are described qualitatively in the screened Coulomb model for the potential of interaction between macroions. However, the least-squares fitting parameters yield ionic strengths which appear to be unreasonably small for these systems. Theoretical refinemenk are suggested and experiments are proposed which will detect crystallization in other ionic solutions.
I. Background The possibility that the ions in aqueous electrolytic solutions may form a crystal lattice has been discussed in the literature for many years. Early speculation wm based upon discontinuities or instabilities in calculations of the thermodynamic properties of ionic solutions. More recently, neutron scattering and viscosity measurements International Laser Systems, 3404 Orange Blossom Terrace, Orlando, FL 23804.
indicate that the nickel ions in concentrated aqueous NiC12 solutions form a lattice in equilibrium at room temperature.172 The most direct evidence for crystalline phases of ionic solutions is provided by suspensions of negatively charged latex polystyrenespheres neutralized by hydrogen ion^.^-^ Delicate, opalescent crystals form in these sus(1)R.A. Howe, W. s.Howells, and J. E. Enderbu, J. Ph.ys. C, 7,Llll (1974). (2) G. Maisano, P. Migliardo, and F. Wanderlingh, J. Chern. Phys., 68, 5594 (1978). (3) P. A. Hiltner and I. M. Krieger, J. Phys. Chern., 73,2386(1969).
0022-3654/81/2085-0294$01 .OO/O 0 1981 American Chemical Society
