4175
ION-EXCHANGE EQUILIBRIA BETWEEN GLASSAND MOLTEN SALTS of the homologous series of compounds studied. However, the E derived from the Maxwell relation is the infinite-wavelength value and contains no contribution from permanent dipoles. Therefore, this relation must be considered only as an approximation. Table I1 shows film refractive index, dielectric constant, and surface dipole moment calculated according to eq 1. The refractive indices are higher than the 1.5 expected for closely packed, Langmuir-Blodgett-type films. This is probably because the retracted films measured by the ellipsometer include not only the organic molecules adsorbed but also some of the surface oxide and the metal itself, Ellipsometer measurements on closely packed, Langmuir-Blodgett films gave refractive indices close to the expected value^.^ The dielectric constant values in Table I1 seem reasonable for the types of films studied. According to Powles and Smyth,’O e for nonionic solids and liquids usually lies between 1.9 and 2.3 and for ionic solids between 4 and 10. The surface dipole moments, p p ’ , are higher than the originally calculated values and are all closer to the expected dipole moments for these molecules.
Summary Relative polarities of six homologous series of organic compounds adsorbed on chromium have been determined. Surface dipole moments were calculated by the Helmholtz equation, for the adsorbed films, assuming the dielectric constant as unity. Assuming the condenser analogy, the optical dielectric constant was used in the Helmholtz equation to obtain revised surface dipole moments. These moments were close to those expected for the 18-carbon compounds of each of the homologous series. The remaining discrepancies can be explained by dipoles induced in and by the metal and metal oxide and by lateral interactions between the adsorbed dipoles.
Acknowledgment. The authors thank Mr. C. J. Quilty for helpful discussions during the preparation of this paper. (9) B. J. Bornong, presented at the Conference on Recent Developments in Ellipsometry, University of Nebraska, Lincoln, Neb., August 1968. (10) J. G. Powles and C. P. Smyth in “Physical Methods of Organic Chemistry,” A. Weissberger, Ed., Interscienoe Publishers, New York, N. Y., 1960, pp 2555-2656.
Ion-Exchange Equilibria between Glass and Molten Salts by H. M. Garfinkel Research and Development Laboratorks, Corning Glass Works, Corning, New York l&?SO
(Received M a y $0,1968)
Equilibrium-sorption isotherms were determined for the Na+-Lif, Ag+-Li+, Ag+-Na+, and K+-Na+ ionexchange reactions. These systems were found to exhibit n-type behavior, with the exception of Na+-Li+ exchange in a crystallized glass. The results are similar to those reported for zeolites in aqueous solution. Thermodynamic results are presented for these systems, and the n-type behavior is discussed in terms of the regular-solution model.
Introduction When an ion exchanger such as glass is placed in contact with a mollten salt that contains a counterion different from that in the ion exchanger, equilibrium is attained. That is, given sufficient time, a condition is reached such that there are no gradients of concentration in the exchanger. This equilibrium can be represented by
X+Y-’X+Y
for several exchange reactions according to eq 1 as a function of the composition of the exchanger. Only a few studies of this kind have been reported in the literature. Schulzel reported the ratio of sodium to silver ions in a soda-lime-silica glass as a function of the composition of the sodium nitrate-silver nitrate bath. Callahan and Kay2 discussed their results on the ionexchange characteristics of several zeolitic materials in fused sodium nitrate. RowelP investigated the use of
(1)
where X and ‘Ir are the counterions in the exchanger phase and X and Y are the counterions in the liquid phase. In this paper, equilibrium results are presented
(1) G. Schulze, Ann. Phys., 40, 335 (1913). (2) C. M. Callahan and M. A. Kay, J. Inorg. Nucl. Chem., 2 8 , 233 (1966). (3) M. H. Rowell, J . Inorg. Chem., 5 , 1828 (1966).
Volume 78, Number 1.2 November 1968
H. M. GARFINKEL
4176 borate-glass ion exchangers for fused salts. He reviewed the suitability of a number of inorganic solids for ion-exchange or chromatographic separations of cations in fused salts.4 Recently, equilibrium measurements were reported between @-alumina and various binary nitrate melts containing NaX03 and the nitrates of silver, thallium, potassium, rubidium, lithium, and cesium.6 i\.Iost of these studies, however, were concerned only with measurements of the distribution coefficients, although some thermodynamic results were presented in the extensive work involving @-alumina. A study of the thermodynamics of ion exchange is of fundamental importance in deciding upon the form of the thermodynamic “forcesJ7 acting on the exchange system as a whole. It is also pertinent to understanding the origin of glass membrane potentials in molten salts and the related problem of selectivity. Ion exchange between glass or ceramics and molten salts has proved to be of interest because of the large changes in mechanical properties that can be effected by the process.
Experimental Section The equilibrium-sorption isotherm can be determined either directly by a measurement of the distribution of ions between the solution and the exchanger phase or by an indirect determination involving the selectivity of a glass electrode from measurement of its electrical potential. Since the former method is preferable, it was used exclusively for the data presented here. The two methods have actually been compared, and these results will be presented in a separate paper.6 The direct measurement can be done either with equilibrated powders or exchanged glass rods. The compositions of the glasses are shown in Table I in mole per cent of oxide. Most of the data were collected by equilibrating powdered glass samples in various binary mixtures of molten salt at constant temperature. Usually ten molten salt mixtures were prepared ranging from 0.1 to 1.0 cation fraction of the exchangeable species. These mixtures were contained in Vycor-brand beakers; 200-250 g of vacuum-dried salt was added to each beaker. Then 3 g of glass that had passed either a -270 (53 p ) or -325 (44 p ) mesh screen was added to each beaker of molten salt. The samples were
equilibrated for 200-500 hr, depending upon the system and the temperature of exchange. The mixture was stirred continuously with a Corning Code 7900 glass stirring rod. After equilibration, the glass sample and salt were separated, and the glass was washed in an ultrasonic cleaner to remove adsorbed salt. The glass was then analyzed; sodiun, potassium, and lithium analyses were done with the flame photometer, while silver analyses were done both with flame photometry and titrimetry. Since interdiffusion and self-diffusion coefficients were known for all the systems investigated,6 the time required to reach, say, 99% equilibration of a spherical particle could be calculated.’ To check this calculation experimentally, a glass rod was placed in a mixed fused salt; in most cases the salt was doped with the radiotracer of the foreign counterion. After the sample was held for a measured time at temperature, it was removed from the bath, cleaned ultrasonically, and weighed. Layers of glass were etched off in HFHzS04 solution with ultrasonic agitation. The solutions were analyzed either by liquid counting or with a flame photometer. The concentration was determined from the weight change, density of the glass, and the results of the analysis; for the case in which radiotracers were used, the specific activity of the tagged bath was required also. A concentration-distance plot was constructed, and the concentration was extrapolated back t o the surface II: = 0. Measurements were made for different times in the melt to ensure that the exchange at the surface had gone to equilibrium. The enthalpy change of two of the ion-exchange reactions studied was determined by a solution-calorimetry technique.* The equilibrium mixtures of glass and salt were prepared as described above. The heat of solution in hydrofluoric acid was determined for the products and reactants at 26.9”. The heat of reaction was calculated at 26.9” from the difference of the sum of the heats of solution of the products and reactants according to eq 1.
Results The rational equilibrium constant for the exchange reaction given by eq 1 is
Table I : Composition of Glasses Used in This Study Mol% A
B
C
D
Liz0 NazO AlzOs
11.4
5.86
...
...
...
16.3 13.2
Bz03
...
...
...
11.4 5.82 18.7
3.81
...
...
3.78 4.09 74.7
...
16.5
Ti02 MgO
...
Si02
71.5
11.5
The Journal of Physical Chemistry
...
...
66.7
64.1
(4) M. H. Rowell, U. S. Naval Radiological Defense Laboratory Technical Report, USNRDL-TR-1091, San Francisco, Calif., Sept 1966. (5) Y.-F. Y . Yao and T. J. Kummer, J. Inorg. Nuc2. Chem., 29, 2453 (1967). (6) H. M. Garfinkel, to be submitted for publication. (7) J. Crank, “Mathematics of Diffusion,” Oxford University Press, London, 1956. (8) R. E. Tischer, Rev. Sci. Instrum., 37, 431 (1966).
ION-EXCHANGE EQUILIBRIA BETWEEN GLASS AND
4177
MOLTEN SALTS
The value of K depends upon the choice of reference states. It is most convenient with molten salts to use the pure material as standard state, SO that 0.8
lim yi = 1 Ni-+l
for component i. The standard state used for the solid exchanger is that in which all of the exchangeable cations are of the ion in question. Rothmund and Kornfeldg suggested that the ratio of the activities of the ions in an ion exchanger is given by
P
I2
O0.4. I
p"
(3) where mi is the cation fraction of component i. This has been referred to as n-type behavior.lO Most of the molten nitrate mixtures used can be characterized approximately as regular (symmetric) Although the heat of mixing of the alkali nitrates is a slight function of composition, for our purposes here, this approximation is quite satisfactory. Therefore, we may write
where A is a constant independent of temperature. Values of the parameter A given in the literature12for systems of interest here are shown in Table 11. Substituting eq 3 and 4 into eq 2 yields log
E)-
A (1 % m T
- 2Ny)
=
Equation 5 is similar to the semiempirical relation proposed by Kielland for aqueous exchangers.l3
Table I1 : Values of the Parameter A for Systems of Interest System
NaNO,-LiNOa NaN03-KNOa NaNOa-AgNOs LiN03--AgN03 a
A, oal/mola
-470 -442
I
0 "a*
Figure 1. The exchange Na+-Li+ in composition A: 0, 400"; 0 , 451".
equilibrium in terms of the experimental conditions used. Na+-Li+ Exchange in Composition A. The isotherm for the exchange reaction Li+(glass)
+ Na+(melt) Jr Na+(glass)
+ Li+(melt)
(6)
with glass composition A at 400" is shown in Figure 1; the cation fraction of sodium in the glass is plotted as a function of the cation fraction of sodium in the melt. The two features to note are the sigmoid character of the exchanger and the failure to.reach greater than 90% = 1. This isotherm is usually conversion at characterized as S type;I4 Le., the selectivity is reversed in the course of conversion. The most probable explanation for the irregular behavior of composition A is that proposed by Barrer and Falconer.16 In the Na+-Li+ exchange irregular behavior arises from the fact that occupancy of an exchange site by Na+ influences the relative affinities of the adjacent sites for these ions. Since accommodation of Na+ becomes increasingly more difficult as conversion proceeds, occupancy of two neighboring sites by
590
650
Obtained from ref 12.
If the assumtptions made in arriving at eq 5 are correct, then a plot of the left-hand side of eq 5 vs. log ( R x / ~ Yshould ) give a straight line with slope equal to n and intercept equal to log (l/K). Each system studied is covered individually. The results are characterized by the ion-exchange isotherm, which is a graphical representation of the ion-exchange
(9) V. Rothmund and G. Kornfeld, 2.Anorg. Allg. Chem., 103, 129 (1918). (10) G. Karreman and G. Eisenman, Bull. Math. Biophys., 24, 413 (1962). (11) J. G. Kirkwood and I. Oppenheim, "Chemical Thermodynamics,'' McGraw-Hill Book Co., Inc., New York, N. Y., 1961. (12) T. Ffirland in "Fused Salts," B. R. Sundheim, Ed., McGrawHill Book Co., Inc., New York, N. Y . ,1964. (13) J. Kielland, J. SOC.Chem. Ind., 54, 2321' (1935). (14) F. Helferrich, "Ion Exchange," McGraw-Hill Book Go., Inc., New York, N. Y., 1962. (15) R. M. Barrer and J. D. Falconer, Proc. Roy. SOC.,A236, 227 (1956). Volume 78, Number 18 November 1968
4178
H. M. GARFINKEL
P
0.8
-1.2 I -0.8
I -0.4
I
I
0.0
L0P(iiN,+/
* 0.4
I
~ 0.8
I
R,,,)
Figure 2. Test of n-type behavior for Na+-Lit exchange in composition A a t 400'.
Log
( I + /I,,,I
Figure 4. Test of n-type behavior for Ag+-Li+ exchange in composition A a t 300'.
necessary to bring the reactants and products to 400". It was assumed that the specific heat datal6 for the liquid are independent of temperature and that the specific heats of the exchanged and base glass are essentially the same. This procedure yielded -1 f 1 kcal/g-ion of Na+ exchanged as the heat of reaction at 400". Although the value is not very reliable, it does suggest that the ion-exchange reaction is not very sensitive to temperature in agreement with our observations. Ag+-Li+ Exchange in Composition A. The ionexchange isotherm for the exchange
* I,."
Li+(glass) 0
0.2
0.6
04
0.8
1.0
NAg
Figure 3. The exchange Ag+-Lit in composition A: 0, 300"; X, 350".
two Na+ ions is energetically less favorable than occupancy by one Na + and one Li + or by two Li + ions as in basic cancrinite. l5 Because of space requirements, conversion may even remain incomplete. Although the structure of glass is less regular than the structure of zeolites, it seems plausible that a similar explanation might hold for the glass. Figure 2 shows the data in Figure 1 plotted according to eq 5 . A least-squares analysis gave n = 1.9 and K = 0.28. Since K < 1, the glass prefers lithium. The heat of reaction of the hypothetical exchange
+ 0.500 g of LiG = 0.0900 g of LiNOa + 0.521 g of NaG
0.111 g of NaN03
at 26.9" was found to be - 1.7 i 1.4 kcaI/g-ion of Na+ exchanged. The actual heat effect at 400" was determined by calculating the difference in heat content T h e Journal of Physical Chemistry
+ Ag+(melt) 1_ Ag+(glass)
+ Li+(melt)
(7)
is shown in Figure 3 for composition A. The isotherm is again sigmoid in shape. The results obtained at 300 and 350" indicate little temperature variation, and conversion appears incomplete. The data in Figure 3 are shown plotted in Figure 4 according to eq 5. A least-squares analysis gave n = 2.2 and K = 3.2 at 300". The equilibrium constant for the Ag+-Na+ exchange is at least K = 11 at 300". Preliminary results with potassium show it is even less preferred in glass composition A than sodium. Therefore, the selectivity order with composition A is Ag+ > Li+ > Na+ > K+. Nu+-Li+ Exchange in Composition B. Composition B forms a stable glass, which can be crystallized by the proper heat treatment to yield a nonporous, finegrained polycrystalline material called a glass ceramic. '' This glass ceramic is characterized as a solid solution of (16) M. Blander, Ed., "Molten Salt Chemistry," Interscience Publishers, New York, N. Y., 1964. (17) S. D. Stookey, Ind. Eng. Chem., 51, 805 (1959).
ION-EXCHANGE EQUILIBRIA BETWEEN GLASSAND MOLTEN SALTS
r
0
4179
1
0.2
0.6
0.4
0.8
1.0 Log (RNo*IRL,+)
"a
+
Figure 5. The exohange Na+-Lit in composition B a t 400': 0, glass; 0 , glass ceramic.
@-spodumene and the metastable polymorph of silica called keatite. The ion-exchange isotherm for the exchange given by eq 6 is shown in Figure 5 for both the glass and the glass ceramic. The isotherm for glass B is similar to that for glass A, showing both the sigmoid character and incomplete conversion. However, the results for the glass ceramic B show that the crystalline material very much prefers to remain in the lithium form over the entire range in bath composition. This represents the most extreme behavior observed in these studies. I n this case, it is evident that the large selectivity for lithium reflects the preferred crystal structure. The selectivity coefficientsfor the exchange reaction given by eq 6 are shown in Table 111. The data in Figure 5 for the glass ceramic could not be represented adequately by eq 5. Instead, two straight-line segments were obtained. The glass ceramic is about 95% crystalline and 5% amorphous (glass). Chemical analysis has shown that
Table I11 : Selectivity Coefficients K' for Cryst'allized Composition B as a Function of N N , + K' "a+
0.998
0,888 0.791 0.676 0,576 0.498 0.407 0 333 0.210 0.100 I
(=
(W,,tFNLi-)/(~Lii."al.))
0.0176 0.0123 0.0129 0.0169 0 I0221 0.0256 0.0387 0.0432 0.0811 0.1479
Figure 6. Test of n-type behavior for Nat-Li+ exchange in glass B a t 400".
95% of the total cation content is lithium and 5% is sodium, and it is most likely that the sodium exists in the glass phase. The results for the glass ceramic can be described by assuming that there are two types of exchange sites in the material. With this assumption, we find that K1 = 2 X lov2 and n = 0.6 for the Li+ sites and K z = 2 X low6and n = 4 for the sodium sites from the two straight-line segments. It is probably somewhat fortuitous that the value of n for the sodium sites is approximately equal to the value of n for the base glass. These results show that the sodium sites in the glassy phase prefer Li+ about lo4 times more than do the Li+ sites in the crystalline phase. The Li+-]Sa+ exchange in sodiumcontaining glasses is being investigated presently to determine the magnitude of K . Figure 6 shows the data in Figure 5 for glass B plotted according to eq 5 . The equilibrium constant K was found by least-squares analysis to be equal to 0.273 with n = 3.2. Again the lithium-containing glass is lithium preferring. K+-Nu+ Exchange in Composition C. The K+-Ka+ exchange was studied with glass composition C. The ion-exchange isotherm at 500" for the exchange Na+(glass)
+ K+(melt) 1_ K+(glass)
+ Na+(melt)
(8)
is shown in Figure 7 for composition C. I n this case the isotherm is almost ideal with close to lOOyo conversion. The data are plotted according to eq 5 in Figure 8. Least-squares analysis gave K = 0.94 with n = 1.2. Thus the glass exhibits almost equal preference for the two ions at this temperature, with sodium being slightly favored. Volume 73, Number 12
NovembeT 1968
4180
H. M. GARFINKEL
0.8
-
0.6
-
0.2r,
P -
I2
0.4
-
I
,
I
,
,
,
I
I
0.
0.2
04
Figure 7.
-
0.4
-
Figure 9. The exchange Agi-Nai a t 300': 0, powder; 0 , tracer.
Y
t0 +
-
7 0 z z \ .
0.0
5
-0.4-
1.0
in composition D
/
2
z
0.9
Ag'
The exchange K + - N a + in composition C a t 500'.
0.8
0.6
N
NK'
x
cc
-0.8
/ I
-0.8
,
I
I
-0.4
00
Lo9
mN+/"o'
I
0.4
I
0.8
Figure 8. Test of n-type behavior for Ki-Na+ exchange in composition C a t 500".
The heat of reaction of the hypothetical exchange 0.194 g of K N 0 3
+ 0.400 g of KaG = 0.163 g of NaN03 + 0.431 g of KG
at 26.9' was found to be -0.69 i 0.31 kcal/g-ion of
K + exchanged. Using the same procedure as outlined previously yielded a value of 3.8 f 0.6 kcal/g-ion of K + for the heat of reaction at 500". Since this value of the heat of reaction should approximate AH" at 500°, the selectivity is a slight function of temperature; above 520', the glass mould prefer K + over Na+. Ag+-Na+ Exchange in Composition D. Since much of our work on preparation of photochromic glass by silver ion exchange18was conducted with glass composition D, a detailed study of the Ag+-Na+ exchange reT h e Journal of Phusical Chemistry
LogtE ,/iiN0*l A0
1
Figure 10. Test of n-type behavior for Ag+-Na+ exchange in composition D a t 300'.
action was conducted with this glass composition. The ion-exchange isotherm at 300" for the exchange Na+(glass)
+ Ag+(melt) Ag+(glass)
+ Naf(me1t)
(9)
is shown in Figure 9. Although sigmoid behavior is obtained, conversion is almost complete. At 266", conversion is 96% complete from tracer diffusion studies in tagged AgN03. From self-diffusion studies of silver in composition D with sodium nitrate dilute in radioactive silver, a partition factor of 500 was obtained, which is similar to results reported for silver exchange in soda-lime-silica glass. l g (18) H. M. Garfinkel, J . App2. Optics, 7, 789 (1968). (19) R. H. Doremus, J . P h y s . Chem., 68, 2212 (1964).
ION-EXCHANGE EQUILIBRIA
BETWEEN
GLASSAND MOLTEN SALTS
4181
Table IV : Summary of Ion-Exchange Results Exchange
Temp,
pair
Glass
OC
N a +-Li + Ag +-Li +
A A
K +-Na + K +-Na +
C Code 7740”
Na+-Li+ N a +-Li +
B
400 300 500 465 400 400
Ag+-Na+
B (cryst)
D
300
Based on a two-phase model (ref 6).
K
0.28 1.9 3.17 2.2 0.94 1.2 1.2 ... 0.27 3.2 (2 X 10-Z)b (0.6)b (2 x 10-9* (4)b 2.55 1.4
WA-B,
AHv,
AS?,
kcal/mol
kcal/mol
eu
Preference
...
Lithium Silver Sodium Keither Lithium Lithium Lithium Silver
-1
-2.4 -2.7 -0.6
1
,..
...
3.6 + 0.6 (16Ib
...
-5.9
(Ob
...
... 4.5
... ... ...
(-7)b
...
...
-0.9
..,
.,.
Numbers in parentheses indicate uncertain values.
The data in .Figure 9 are shown in Figure 10 plotted according to eq 5. The equilibrium constant K was found to be 2.51,and n was found to be 1.4 by a leastsquares analysis. Thus the glass is silver preferring. It is interesting that little difference was noted with calorimetrically or electrochemically determinedz0 values of A , which in fact do differ, in the results of the analysis of the data for the Ag+-Li+ or Ag+-Xa+ exchange reactions.
Discussion The results obtained for the various exchange reactions are suinmarized in Table IV. Although the results for Code 7740 borosilicate glass were not included in this paper, the results were added to Table IV for completenes#s. It is interesting that the relationship given by eq 3 fits so many exchange systems so well. The results indicate that either the glasses are homogeneous, or if two or more phases coexist, all the phases have the same selectivities. Garrels and Christ2’ demonstrated that this description is related to the regular-solution theory of binary mixtures, used so successfully to describe ion-exchange equilibria.22 The assumption that the exchanger is a regular solution gives the ratio of the activity coefficients of species A and E) in the binary mixture as
From eq 3 and the definition of the rational activity coefficient, we find that
Expansion of the In (LTA/RB) gives
‘/3(1 - 2flB)3
n
+ ‘/5(1 - 2nB)6 + . . .
(12) Since only the first term of eq 12 need be considered for the concentrations used in this study, we find that
Calculated values of WA-B, the excess interactionenergy of neighboring A and B ions, are shown in Table IV.
Since a negative value of WA-B indicates repulsion between the A and B ions, inspection of Table IV shows that the deviations from ideality of the ion-exchanged glasses are caused by repulsions of the counterions. Surely, the strain around the exchanged site also affects this behavior. Unfortunately, there are no heat-of-mixing data available for these systems. TischeP investigated the heats of mixing in the binary Li2Si307-Ei2Si307 system. Although he found that the heats of mixing depended upon composition, the sodium-potassium silicate system showed smaller (negative) deviations from ideality than the sodium-lithium silicate system, in qualitative agreement with the results in Table IV. It can be shown, under the assumption that the selfdiffusion coefficient is the same in the presence or absence of a concentration gradient, that for a binary exchange the interdiffusion coefficient D is given in terms of the individual self-diffusion coefficients Di bylg
D=-
DADB _ _ b 1_n_C ~ N A D A NBDBb In CA
+
(14)
We have shown that b In aA/bln CA = n for some of the glass systems for which we know D,DA, and D g . Therefore, we are now in a position to test the original assumption used to arrive at eq 14. Moreover, this will allow a comparison of the n-type and regular-solution models. Acknowledgment. The author wishes to acknowledge the technical assistance of R. J. Kerr. (20) J. Lumsden, ”Thermodynamics of Molten Salt Mixtures,” Academic Press, London, 1966. ( 2 1 ) , R . M. Garrels and C. L. Christ, “Solutions, Minerals, and Equilibria,” Harper and Row, New York, N. Y., 1965. (22) C. B. Amphlett, “Inorganic Ion Exchangers,” Elsevier Publishing Co., Amsterdam, The Netherlands, 1964. (23) R. E. Tisoher, to he submitted for publication.
Volume 7.9. Number 1.9 November 1968
