J. Phys. Chem. 1982, 86, 5234-5237
5234
TABLE 11: Static and Kinetic Parameters of Intercalation-Deintercalation of Ions in Layered Intercalation Compounds at 25 “C n-Zr.P-H+
2.9
-1.9
y-%r P-H’
7.3
2.8 x 10
6.0 18
9.0 x l o 3 1.4 x l o 3
Ni-HT(Cl)-OHNi-HT(CI)-CI-
5.8 x 10-1 present work 2.6 x lo-‘ present work 6.7 x 15 1.3 x 10 15
related linearly to K,, while the deprotonation rate constants in these suspensions are independent of K,. On the other hand, in silica-alumina and y-Zr.P, the values of both rate constants are 1 order of magnitude smaller than the corresponding values in the former group, which may be due to the difference of the acidities caused by double oxide in the silica-alumina and densely linked structure in the r-ZPP.
Among the rate constants of the intercalation-deintercalation process in various systems listed in Table 11, the intercalation rate constants depend on the equilibrium constants, K1. Further discussion is impossible because of the lack of kinetic data. Preliminary relaxation experiments in aqueous suspensions of zirconium phosphates containing various alkalimetal hydroxides using the pressure-jump technique were performed and similar relaxations were found. Further studies of these systems will lead to quantitative clarification of the intercalation-deintercalation of various guest species.
Acknowledgment. We thank Dr. S. Yamanaka in the Faculty of Engineering of Hiroshima University for the supply of the a-and y-zirconium phosphate samples, and for his useful suggestions and important information on acidities.
Surface Tension of Binary Molten Salt Mixtures J. D. Pandey’ and Usha Gupta Department of Chemistry, University of Aiiahabad, Allahabad-2 1 1002, U.P., India (Received: February 8, 1982; I n Flnai Form: August 5, 1982)
The surface tension of binary molten salt mixtures has been evaluated by utilizing the Flory theory, the Eberhart equation, and the Brock-Bird relationship as a function of composition. The agreement between the theoretical and experimental values was satisfactory. The Eberhart relation overestimates surface tension values, whereas the Flory theory, in most of the systems, underestimates it. The maximum deviations were observed in the case of the Brock-Bird relation.
Introduction Among the various physical properties which have been investigated to elucidate ionic interactions in binary molten salt mixtures, surface tension is the one of the few which has been treated theoretically. Guggenheim,’ using a quasi-crystalline model, has derived equations for ideal and regular solutions. The thermodynamic method of Guggenheim has been used by Heymann et al.2to test whether certain molten salts are noninteracting or whether they contain certain complexes. An improved derivation was developed by Hoar and M e l f ~ r d . ~ The work of Bertozzi and Sternheim4p5showed that, by calculation of the surface tension of alkali nitrates and binary halide systems from previous derivations, remarkable deviations were seen. To find good agreement with the experimental results, they introduced a parameter in these derivations, called the “Tobolsky parameter” [ ( d , d2)/(d1+ d2)],2Le., a function of interionic distances of the respective pure salts only. In a later paper Nissen and D ~ m e l e npointed ~ , ~ out that an equation based on regular (1) E. A. Guggenheim, “Mixtures”, Clarendon Press, Oxford, 1952. (2) N. K. Board, A. R. Palmer, and E. Heymann, Trans. Faraday SOC., 51, 277 (1955). (3) T. P. Hoar and D. A. Melford, Trans. Faraday Soc., 53,315 (1957). (4) G . Bertozzi and G. Sternheim, J . Phys. Chem., 68, 2908 (1964). (5) G. Bertozzi, J . Phys. Chem., 69, 2606 (1965). (6) D. A. Nissen and B. H.Van Domelen, J. Phys. Chem., 79, 2003 (1975). (7) D. A. Nissen, J . Phys. Chem., 82, 429 (1978). 0022-3654/82/2086-5234$01.25/0
solution theory, assuming the quasi-lattice model and random distributions of species both in the bulk phase and in the surface phase, can be used to calculate the surface tension of binary molten salt mixtures. Results of these models were in good agreement with the experimental values and the deviations are attributed to non-Coulombic interactions, which invalidate the random mixing assumption implicit in the theoretical equations. In these calculations the surface tension of binary molten salt mixtures was obtained from a knowledge of surface tension, density of the pure components, and the interaction parameter, which can be obtained from the heats of mixing. Flory’s statistical t h e 0 r 9 ~with certain assumptions has been applied to evaluate the surface tension of binary liquid mixtures. RecentlylO its applicability has been extended for the calculation of the surface tension of pure molten salts, the sound velocity of binary molten halides,” the viscosity of binary molten nitrates,I2 and pseudoGriineisen parameters of pure molten salts and their binary mixtures.13 However, no attempt has been made to apply (8) P. J. Flory, J. Am. Chem. Soc., 87, 1833 (1965). (9) A. Abe and P. J. Flory, J. Am. Chem. SOC.,87, 1838 (1965). (IO) J. D. Pandey, B. R. Chaturvedi, and R. P. Pandey, J. Phys. Chem., 85, 1750 (1980). (11) J. D. Pandey and Alec D. M. David, Chem. Scr., in press. (12) J. D. Pandey and Alec D. M. David, J . Phys. Chem., 85, 3151 (1981). (13) J. D. Pandey and Alec D. M. David, J. Chem. Phys., in press.
0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 26, 1982 5235
Surface Tension of Binary Molten Salt Mixtures
Flory's statistical theory for estimating the surface tension of binary molten salt mixtures. This work is initiated to test the applicability of Flory's theory in calculating the surface tension of binary molten salts. In addition, the surface tension of molten salts has been evaluated theoretically by using the Eberhart equation14 and the Brock-Bird semiempirical relation.15 These methods have not, so far, been used for the binary molten salts. For the present study, the following molten salt mixtures were selected: NaC1-NaBr, KC1-KBr, RbC1-RbBr, NaC1-KC1, LiCl-KC1, KC1-NaI, NaN03-KN03, AgN03NaN03, and AgN0,-KNO,, mainly because of their spherical shape and diminutive free volume difference, both factors being essential to describe the good agreement of calculated and experimental values.
Theoretical Section A close connection between Flory theory and the corresponding state theory of Prigogine et al.,16 employing a simple cell model of the liquid state, was shown by Patterson et al.17-19 They obtained the following equation for the characteristic surface tension = k1/3P*2/3T*1/3
(1)
where k is the Boltzmann constant, and PC and T* are the characteristic pressure and temperature given by T* = T / F
PC = y p T F
(2)
Here yp is the thermal pressure coefficient, !i the ' reduced temperature, and V the reduced volume. Prigogine and SaragaZ0formulated the reduced surface tension
where M is the fractional decrease in nearest neighbors which a molecule loses on going from the bulk phase of the liquid to the surface phase. Thus, on the basis of the corresponding state principle, the surface tension of a liquid is given by the expression a = a*?@)
(4)
In the evaluation of the surface tension of binary mixtures, characteristic parameters used are given by the following expressions:
+ x2v,* P* = [(cplP1*Ol)l/2+ (P,*(0202)'/2]2 T* = P*/(cplPl*/Ti* + @Pz*/T2*) v* = XlV1*
(5)
(Pc2Tc)
= (-0.951
+ 0.432/&)(1
- Tr)l1l9 (8)
Here, Pc, Tc, Vc, Zc, and T, stand for critical pressure, critical temperature, critical volume, compressibility factor, and reduced temperature. The critical compressibility factor and the reduced temperature are given by
zc = PcVc/(RTc)
(9)
T, = T/Tc (10) The extended form of the Brock and Bird relation for mixtures may be written as ~ , i , / ( P c , ~ T c , ) ~ /=~ (-0.951 + 0.432/2cm)(1- Trm)ll/' (11)
Characteristic parameters Pc,, Tc,, and Vcm for the mixtures are calculated from the critical constants of pure liquids. In the case of a binary mixture pc, = X l P C , + x2pc, VC" X l V C , + xzvc, Tc, = X l T C , + XZTC,
(12)
where x1 and x 2 are the mole fractions of the pure components. The critical compressibility factor of the mixture was evaluated from eq 9 by using critical constants of the mixture, which were computed computed with the aid of eq 12. EberhartI4 assumed that the surface tension of a binary mixture is a linear function of the surface layer mole fractions, i.e. a = Y l U l + Yza2
(13) using a semiempirical constant (S),which he defined as the surface enrichment factor for the component having the lower surface tension:
s = (YZ/Yl)/(X2/Xl)
(14)
where y1 and y2 are surface mole fractions and xl and x 2 are bulk mole fractions. When y1 + y2 = 1 and x1 x2 = 1, then a can be expressed in terms of the bulk liquid composition of the mixture
+
a = (x1a1
+ xpSa,)/(x, + SXZ)
(15)
This is Eberhart's equation. By definition
F=
(0- a2)/(01
- 02)
r = (xl/xJ
(16) (17)
(6)
where E is the surface tension on a dimensionless scale and r is the bulk mole ratio. Combining eq 15 and 17 we get
(7)
5 = -S(F/r) + 1
where (al, (a2 are the segment fractions and 01, 8, are site fractions. The values of these parameters have been discussed in Flory's original publication. The values of PC, however, have been based on Berthelot's approximaion for homopolar specie^.^,^ According to Brock and Bird,15 the surface tension (a) is given by the relation (14)J. G.Eberhart, J.Phys. Chem., 70, 1183 (1966). (15)J. R. Brock and R. B. Bird, AIChE J., 1, 174 (1955). (16)I. Prigogine, "Molecular Theory of Solutions", North-Holland Publishing Company, Amsterdam, 1957. (17) D. Patterson, S. N. Bhattacharya, and P. Picker, Tram. Faraday SOC.,64,648 (1968). (18)D.Patterson and G. Delmas, Trans. Faraday SOC.,65,708(1969). (19)D. Patterson and A. K. Rastogi, J.Phys. Chem., 74,1067 (1970). (20)I. Prigogine and L. Saraga, J. Chim. Phys., 49, 399 (1952).
(18)
Ramkrishna and S u r P described the nature of the constant S on a thermodynamic basis as
- S = exp(a, - a2)A2/RT (19) XZ/% Here A, is the molar surface area of the second component of the mixture. The above equation is based upon the assumptions that (i) the molar area of mixing is zero and (ii) the activity coefficient is nearly equal to 1.
--
Y2/Y1
Results and Discussion The results of comparative studies of the surface tension of binary molten salt systems from the Flory theory, the Eberhart equation, and the Brock and Bird relation are (21)V. Ramkrishna and S. K. Suri, Indian J. Chem., 5, 310 (1967).
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The Journal of Physical Chemistry, Vol. 86, No. 26, 1982
Pandey and Gupta
TABLE I : Comparison of Calculated and Experimental Values of Surface Tension of Various Binary Molten Salt Mixtures o(calcd), dynlcm system 1 + 2 NaC1-NaBr (800 " C ) b KCl-KBr (800 o C ) b RbC1-RbBr (800 oC)b NaC1-KCI ( 8 2 5 oC)",b
LiCl-KC1 (800 "C)"
KCl-Nal (800 "C)"
NaN0,-KNO, (400 ' C P d AgN0,-NaNO, (300 "C)", AgN0,-KNO, (300 oC)c,d
a
Reference 6.
component 2, mol 9i
u(exptl), dyn/cm
Flory theory
Eberhart's eq
50 50 50 20 40 60 80 20 40 60 80 15 33 50 66.7 .8 5 20 40 60 80 20 40 60 80 20 40 60 80
107.7 93.1 85.0 109.5 105.2 101.8 98.8 107.2 102.9 98.7 98.1 82.4 77.6 76.1 74.0 72.0 111.4 110.0 108.8 107.8 133.5 127.2 123.8 120.2 124.1 120.5 117.6 116.3
104.89 90.83 81.33 101.98 101.88 102.42 89.28 109.86 103.91 100.25 100.83 71.99 65.10 6 5.36 75.90 75.62 110.57 108.94 109.19 107.15 137.70 125.44 116.36 110.83 133.66 123.60 126.6 106.42
112.49 92.63 86.49 110.63 107.00 103.20 99.16 110.55 104.48 100.78 98.45 90.60 85.40 81.94 79.19 76.91 111.77 110.65 109.29 107.60 136.97 131.05 125.74 120.95 136.88 130.34 123.99 117.51
Reference 5.
Reference 30.
% deviation
Brock and Bird relation 177.63 117.42 65.45 107.69 84.79 59.28 54.80
Flory theory
Eberhart's eq
-2.6 -2.43 -4.3 -6.8 -3.1 0.6 -9.6 2.4 0.9 1.5 2.7 -12.6 -10.9 -14.1 2.5 4.7 -0.74 -0.96 -0.35 -0.60 3.05 -1.3 -6.0 -7.7 6.8 2.5 7.1 - 8.4
4.2 0.5 1.7 1.02 1.6 1.3 0.36 3.03 1.5 2.06 0.35 9.0 9.1 7.1 6.5 6.4 0.3 0.5 0.4 0.2 2.5 2.9 1.5 -0.6 9.3 7.5 5.1 1.2
Brock and Bird relation 39.3 20.7 - 22.4 - 1.6 -19.4 -41.7 -44.5
Reference 4.
listed in column four, five, and six, respectively, of Table I. The characteristic parameter V*, PC and T* for binary mixtures are evaluated from eq 5-7. These parameters are calculated by utilizing the values of the thermal expansion coefficient and isothermal compressibility taken from the l i t e r a t ~ r e . ~ ~The - ~ ~reduced volume of binary molten mixtures, needed in calculating the reduced surface tension from eq 3, is computed from the knowledge of molar volumes of these binary melts which are taken from the literat~re.~"~' The critical temperature, the critical pressure, and the critical volume of binary molten mixtures were obtained from eq 12 by utilizing critical data of pure molten salts.28*29 The enrichment constant (S) of the Eberhart equation for the systems NaCl-KCl, LiC1-KC1, KC1-NaI, NaN03-KNOB,AgN03-NaN03, and AgN03-KN03 were calculated with the aid of eq 18. For the remaining systems NaC1-NaBr, KC1-KBr, and RbC1-RbBr eq 19 was used. The values of the surface tension of pure molten salts were taken from the l i t e r a t ~ r e . *It~ ~means ~ ~ that the values of S in the Eberhart equation are adjusted for the components having lower values of surface tension. These values have been used to calculate theoretical values of surface tension at different concentrations for the corresponding binary mixtures using eq 15. (22) R. Vilcu and C. Misdolea, J . Chem. Phys., 46, 906 (1967). (23) S.Sternberg, Reu. Roum. Chim., 15, 1665 (1970). (24) G. J. Jan,, 'Molten Salts Hand Book", Acadamic Press, New York, 1967. (25) H. Bloom and D. C. Rhodes, J. Phys. Chem., 60, 791 (1956). (26) E. R. Van Arstdalen and I. S. Yaffe, J. Phys. Chem., 59, 118 (1955). (27) S. Sternberg and V. Vasilescu, Reu. Roum. Chim., 12,1187 (1967). (28) A. D. Krishnenbaum, J. A. Chaill., P. J. Malgonical, and A. V. Grosse, J. Inorg. Nucl. Chem., 24, 1287 (1962). (29) M. J. Gillan, "Thermodynamics of Nuclear Materials, 1974", Val. I, International Atomic Energy Agency, Vienna, 1975, p 269. (30) H. Bloom, F. G. Davis, and D. A. James, Tram. Faraday Soc., 56, 1179 (1960).
A perusal of Table I reveals that the calculated values from the Flory theory and the Eberhart equation are in good agreement with the experimental values of surface tension. The largest discrepancy is seen in the computed values of surface tension obtained from the Brock and Bird relation. The precentage deviations in the calculated surface tension values from the Flory theory, the Eberhart equation, and the Brock and Bird relation, respectively, are as follows: -2.6, 4.2, 39.3, in NaC1-NaBr; -2.4, 0.5, 20.7 in KC1-KBr; and -4.3, 1.7, -22.4 in RbC1-RbBr. The average percentage deviations in the NaCl-KCl system are respectively -4.13, 1.07, and -26.8. These results show that the Flory theory and the Eberhart equation are found to be superior to the Brock and Bird relation for calculating the surface tension of binary molten salt mixtures. The minimum average discrepancy in the surface tension values obtained from the Flory theory is -0.66 in the NaN03-KNO3 system and -4.3 in RbC1-RbBr. The largest deviation in the KCl-NaI system (-12% at 15 mol % of NaI and -14% at 50 mol % of NaI) may be attributed to the fact that the law of corresponding states is not strictly obeyed by this system which has been usedz0 as a basis in the e ~ a m i n a t i o n of ' ~ the Flory the0ry~8~ to calculate surface tension. Larger discrepancies in the values of surface tensionlo of molten alkali bromides and iodides than chlorides calculated from the Flory theory are in support of this view. However, the possibility of the formation of complex ions (C1NaI)- cannot be ruled Theoretical values of the surface tension of binary molten salt systems are very much sensitive to the value of M , the fractional decrease in the neighbor of a cell in the surface phase as compared to the bulk phase, and have valueslg ranging from 0.25 to 0.29 on the basis of close-packed structure. Recently Pandey et and others32used a higher value (31) J. D. Pandey, J. Chem. Soc., Faraday Trans. 1,75,2160 (1979); 76, 1215 (1980). (32) R. P. Pandey and B. R. Chaturvedi, Chem. Scr., 18, 65 (1981).
J. Phys. Chem. 1982, 86, 5237-5243
of M in their calculations. Auxillary calculations show that for the systems under investigation the overall agreement can be improved by using a value of 0.325 for the parameter M , as described in a previous paperaloObserving the results of Eberhart's equation, one finds that 0.37% is the minimum average discrepancy obtained in the NaNO,-KNO3 system and 7.62% is the maximum deviation in the KC1-NaI system. In the case of molten electrolytes, a high degree of Coulombic interaction would be expected in the near and next to near neighbors, resulting in ordering effects. The success of the Eberhart method in these cases is probably due to the quotient of mean activity coefficients vanishing according to the equation (61/62)/(71/Y2) 1 (20) where 6 and y are surface layer and bulk activity coefficients, respectively. The percentage deviation between experimental and calculated surface tension values of NaC1-KC1, KC1-KBr, RbC1-RbBr, and NaC1-NaEh from the Brock and Bird relation is higher and for NaCl-KC1 lies in the range of -1.6 to -44. The deviation in this system increases with an increase in percent mole concentration of KC1. The semiempirical relation of Brock and Bird is simpler to operate and only a knowledge of critical parameters is needed; therefore, uncertainties in the critical constants available in the l i t e r a t ~ r e ~are ~v~~ considered as a part of the discrepancy in this method. The greater discrepancy is attributed to the fact that these systems do not obey the theorem of corresponding states which has been used as a base in the derivation of the relation under investigation. Surface tensions of remaining systems from the Brock and Bird relation were not calculated, owing to the lack of critical data.
5237
On the basis of the above discussion, it may be concluded that both the Flory theory and the Eberhart equation predict surface tension values of molten salt mixtures to a substantial extent. However, values from the Flory theory are lower than the theoretical surface tension values obtained from the Eberhart relation. The deviation in surface tension values of all the binary mixtures can be qualitatively explained by the fact that the surface layer of the liquid is enriched in the component of the lower surface tension, thereby minimizing the surface tension of the mixture. This factor has been considered in the Eberhart relation and due to this fact the Eberhart equation gives a better fit to the observed surface tension values than do equations based on the Flory theory. The discrepancy in values of the Flory theory may be attributed partly to the nonorthodoxy of the theory, since the application of eq 3 to an equivalent single-component liquid effectively ignores differences in concentration occurring at the surface of the mixture. On the basis of our calculations, it can be concluded that the theory affords a useful estimate of the surface tension of binary molten salt mixtures without considering such concentration effects and without adjusting any parameter to fit the surface properties of the mixture. Furthermore, the basic advantage of the Flory theory in calculating surface tension is that all the necessary parameters, e.g., densities, isothermal compressibilities, and coefficients of thermal expansion for the pure components, can be determined experimentally.
Acknowledgment. we are grateful for the laboratory facility provided by the Chemistry Department of the University of Allahabad.
An ESR Study of Intrachannel Mobility in DOCA Clathrates. Effects due to Photochemical Reactivity between Guest and Host Eva Meirovitch The Weizmann Instkute of Sclence, 76 100 Rehovot, Israel (Received: March 22, 1982; I n Final Form: July 26, 1982)
ESR spectra of deoxycholic acid channel type inclusion compounds doped with 2,2,5,5-tetramethyl-3-carbamidopyrrolinyl-1-oxy1 (Tempyo)and 2,2,6,6-tetramethylpiperidinyl-l-oxyl-4-ol (Tanol) free radicals were recorded as a function of temperature, radical concentration, and photochemically triggering UV irradiation. A t room temperature the spin probes are immobile and isotropically dispersed within the channels. Onset of isotropic molecular reorientation is observed upon increasing the temperature to 50-70 "C and nearly complete motional averaging is achieved between 120 and 140 "C with activation energies of the order of 6-8 kcal/mol. For 5-30% molar enrichment of the guest with the paramagnetic dopant, second-order rate constants for bimolecular encounters of 1.65 X lov M-' s-l at 130 "C and a related activation energy of 5 kcal/mol are measured from concentrdtion-dependent spin exchange effects on the ESR line shape. Clustering is observed for radical concentrations relative to the guest of the order of 0.2 M. With acetophenone as guest we find that, following the photochemical reaction between host and guest, the rate for rotational reorientation and the rate constant for bimolecular encounters are slowed down considerably.
I. Introduction Inclusion compounds are built of host molecules which form vacancy-containing frameworks (either cavities or channels) wherein guest molecules are trapped.'-3 Par-
ticular conformational requirements have to be fulfilled by a molecule to serve as guest, i.e., to interact physically with the host and form a clathrate. Once trapped within the cavities or the channels, it may also interact chemically with the host or with other guest molecules, these being
(1)S.G.Frank, J.Pharmacol. Sci., 64,1585 (1975). (2)D.D.McNicol, J. J. McKendrick, and D. R. Wilson, Chem. SOC. Reu., 7,65 (1978).
(3) N. G. Parsonage and L. A. K. Staveley, "Disorder in Crystals", Clarendon Press, Oxford, 1978.
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0 1982 American Chemical Society
