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Surface Tensions of Molten Salt Mixtures
(3) A. J. Kertes and H. Gutman, Surface Colloid Sci., 8, 193 (1975). (4) J. H. Fendler, E. J. Fendler, R. T. Medary, and 0. A. El Seoud, J . Chem. Soc., Faraday Trans. 7, 69, 280 (1973). (5) E. J. Fendler, J. H. Fendler, R. T. Medary, and 0. A. Ei Seoud, J . Phys. Chem., 77, 1432 (1973). (6) 0. A. El Seoud, E. J. Fendler, J. H. Fendler, and R. T. Medary, J . Phys. Chem., 77, 1876 (1973). (7) F. Y.-F. Low, B. M. Escott, E. J. Fendler, E. T. Adams, Jr., R. D. Larsen, and P. W. Smith, J. Phys. Chem., 79, 2609 (1975). (8) C. A. Parker, "Photoluminescence of Solutions", Elsevier, Amsterdam, 1968. (9) U. B. Birks, "Photophysics of Aromatic Molecules", Wiley, New York, N.Y., 1970. (10) E. L. Wehry, "Modern Fluorescence Spectroscopy", Plenum Press, New York, N.Y., 1976. (11) P. S. Sheih, Dissertation, Texas A&M University, May, 1976. (12) A. Romero, J. Sunamoto, and J. H. Fendler, ColloidInterface Sci., V, 111 (1976). (13) L. A. Shaver and L. J. C. Love, Appl. Spectrosc., 29, 485 (1965). (14) I. Isenberg and R. Dyson, Siophys. J., 9, 1337 (1969). (15) J. L. Armstrong, Appl. Polym. Symp., No. 8, 17 (1969). (16) E. A. Collins, J. Bares, and F. W. Billmeyer, Jr., "Experiments in
Polymer Science", Wiiey-Interscience, New York, N.Y., 1973. (17) J. B. Birks, D. J. Dyson, and I.H. Munro, Proc. R. SOC.London, Ser. A , 275, 575 (1963). (18) J. B. Birks and L. G. Christophorou, Spectrochim. Acta, 19, 401 (1963). (19) E. L. Frankevich, T. Morrow, and S. A. Salmon, Proc. R. SOC.Lodon, Ser. A , 328, 445 (1972). (20) F. Nome, S. A. Chang, and J. H. Fendler, J. Chem. Soc., faraday Trans. 1 , 72, 296 (1976). (21) M. M. Davis, J . Am. Chem. Soc., 84, 3623 (1962). (22) M. M. Davis, Natl. Bur. Stand. (U.S.), Monogr., No. 105 (1968). (23) C. de Boor, J . Approx. Theory, 6, 50 (1972). (24) W. J. Hemmerle, "Statistical Computations on a Digital Computer", Blaisdell Publishing Co., Waltham, Mass., 1967, Chapter 2. (25) J. B. Birks, M. D. Cumb, and I. H. Munro, Acta Phys. Polon., 26, 379 (1964). (26) J. B. Birks, J . Phys. Chem., 68, 439 (1964). (27) B. K. Selinger, Arstr. J. Chem., 19, 825 (1966). (28) R. Calas, R. Lalande, J. G. Gangere, and F. Moulines, Bull. SOC.Chim. Fr., 119 (1965). (29) F. Nome, S. A. Chang, and J. H. Fendler, J . Colloid Interface Sci., 56, 146 (1976).
Regular Solution Theory and the Surface Tensions of Molten Salt Mixtures. 2. Thallium Nitrate-Lithium Nitrate and Thallium Nitrate-Potassium Nitrate D. A. Nissen Sandia Laboratories, Livermore, California 94550 (Received May 3 1, 1977) Publication costs assisted by the U S . Department of Energy
The isothermal surface tensions of the binary, charge-symmetrical mixtures T1N03-LiN03and TlN03-KN03 are compared with values calculated from equations based on regular solution theory. The deviations found are attributed to the presence of significant non-Coulombic interactions in the melt which invalidate the random mixing assumption implicit in the theoretical equations.
Introduction We have shown' that it is possible to make very accurate calculations of the isothermal surface tension for a number of binary, charge symmetrical, molten salt mixtures using an equation based on the simplest realistic model of a molten salt solution and without the necessity of evaluating arbitrary parameters. However, pronounced deviations between calculated and experimental values of the surface tension were seen for mixtures which contained AgN03. It was postulated that the basis for this equation, regular solution behavior, began to fail in these melts because of significant non-Coulombic interaction^.^,^ It is the purpose of this paper to explore the limits of applicability of regular solution theory to the calculation of isothermal surface tension curves and, at the same time, to suggest a possible reason for the discrepancy. As previously,' we assume a quasi-lattice model and random distribution of the species, both in the bulk and on the surface of the liquid (zeroth approximation). On this basis, the surface tension of a binary mixture is given by7,' hT x I 1 wl wm y = y1 + - In - + -[(x,')'- (x2)'] - -(x2)' = a x1 a a hT x,' w1 y z +In+ -[(xl')' - ( x ~ )- ~-w]( xm ~ ) ~ a
x2
a
a
0022-3654/78/2082-0429$01 .OO/O
In this equation y;is the surface tension of the pure ith component a t the temperature of the experiment; xiis the mole fraction of the ith component, the primes referring to the surface; w is the interaction parameter in the theory of regular solutions; and 1 and m refer to the fraction of nearest neighbors which occupy the lattice plane and an adjacent lattice plane and satisfy the relationship 1 2m = 1. For a simple cubic lattice, Z = 6 and m = 1/6; in a close packed lattice, Z = 12 and m = 1/4. The parameter a is the mean surface area of the molecules and is given by
+
where N is Avogadro's number and vL is the molar volume of the ith component. For the calculation of the molecular surface area, we shall assume, as we have done previously,l that the molten salt mixtures discussed here can be considered, on a time-average basis, as though they were composed of ion pairs or neutral molecules rather than as an assemblage of individual anions and cations. Results The isothermal surface tensions of the mixtures T1N03-LiN03 and T1N03-KN03 as a function of composition were not available in the literature and so they were measured in this laboratory. Since the purpose of 0 1978 American Chemical Society
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The Journal of Physical Chemistry, Vol. 82, No. 4,
D. A. Nissen
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TABLE I: Value of t h e Interaction Parameter and Mean Molecular Surface Area for TlN0,-LiNO, and TlN0,-KNO,
TI NOg+ NOg
w = 4AHO.$,a, cm2 X System
cal/mol
lo1'
T , "C
TlN0,-LiNO, TlN0,-KNO,
-880 1-440
18.6 20.5
350 350
1
1
5
1
TABLE 11: Comparison of Calculated and Experimental Values of the Surface Tension of TlNO,-JiNO, and TINO,-KNO, ( T =360 "C) A. TINO,-LiNO, LiNO,, mol% 0
20 40 50 60 80 100
r(calcd), dyn/cm
r(expt.1): dyn/cm
99.9 99.7 100.1 100.4 101.0 102.7 110.7b B. TINO,-KNO,
100.7 102.0 102.9 103.9 106.7
KNO,, r(calcd), r(exptl),' mol % dyn/cm dyn/cm 0 99.9 20 101.2 99.8 40 102.7 99.9 50 103.6 100.5 60 104.6 101.9 80 107.0 105.0 100 109.9 ' Reference 9. Reference 14.
A, %
1.0 1.9 2.5 2.9 3.9 95
1
A, % 90
1.4 2.8 3.1 2.6 1.9
this paper is to compare calculated surface tensions with those determined experimentally, we refer the interested reader to the original p u b l i c a t i ~ n s for l ~ ~a detailed explanation of the experimental method and results. In order to calculate the surface tension from eq 1, it is necessary that we have a value for the interaction parameter w. This can be obtained from heat-of-mixing data of Kleppa and Hersh.2 The mean surface area, eq 2, was calculated for each molten salt pair using density data taken from Janz' tabulation.1° In Table I we list the values of the interaction parameter, evaluated at x1 = x 2 = 0.5, and the mean molecular surface area used in our calculation. The calculated and experimental values of the surface tension are shown in Table 11. The percent deviation of the calculated value from the experimental value is shown in the fourth column. In Figures 1 and 2 we have plotted both the experimental and the calculated surface tension curves for each mixture. Values of the surface tension were calculated for m = 1/4 and 1 / 6 since we had no particular reason for choosing one crystallographic orientation over another. The difference between the surface tension calculated for the two values of m was less than 1'70. The values shown in Table I1 are for m = 1/4. Discussion As was the case with the AgN03-MN03 mixtures,' we find a pronounced deviation between the Calculated and experimentally measured surface tension values for the T1N03-LiN03 and T1N03-KN03 mixtures. It has been suggested that the discrepancy between the calculated and experimental surface tension values is the result of two approximations implicit in eq 1. These approximations are (1)the interaction parameter is independent of concentration, and (2) the molecular surface
I
0
10
20
30
40
50 60 MOLE %TI NO3
70
80
90
0
Figure 1. Isothermal surface tension of the system TIN03-LiN03 as a function of composition. T = 350 O C . TINOl - KN03
115
1
I
90;
io
il
3'0
40
o;
60
70
a0
Po
MOLE B TIN03
Figure 2. Isothermal surface tension of the system TIN03-KN03 as a function of composition. T = 350 O C .
area is independent of composition. Before addressing these questions, however, we should point out that we have shown' by using eq 1, with its inherent approximations, it is possible to calculate values of the surface tension for a large number of molten salt mixtures which are in excellent agreement with those measured. The assumption of concentration independence of the interaction parameter is quite incorrect as shown by heat
Surface Tensions of Molten Salt Mixtures
of mixing data.15 That is, most molten salt mixtures are not, in the strictest sense, regular solutions. The T l N 0 3 mixtures discussed here are no exception.' Although for the two systems discussed here, T1N03-LiN03 and T1N03-KN03, the deviation of the heat of mixing from the value a t 50 mol % is less than 20% and, in fact, for the T1N03-KN03 it is less than 5%. We have previously shown that eq 1is not particularly sensitive to the value of the interaction parameter; a variation of 20% in the value of w causes a change of less than 2% in the calculated value of the surface tensi0n.l A more comprehensive discussion can be found in ref 1. Finally, there is no theoretical justification for adjustment of the interaction parameter with composition. Equation 1 is restrictive in the sense that no allowance is made for variation of the molecular surface area with composition in contrast, for example, to Hoar and Melford's more general treatment.16 However, this is entirely in keeping with the assumptions Guggenheim made in deriving eq 1;that the ratio of molecular sizes is close to unity.7 On this basis, it would seem reasonable to assume that, when there is a large discrepancy in molecular size, as, for example, between TlN03 and LiN03 (UINO~ = 16.4 X cm', aTiNO3 = 20.9 X cm2),deviations between calculated and experimental values of the surface tension would occur. We note, however, that examples have been given in which the discrepancy in molecular size is even greater than in the T1N03-LiN03 system, e.g., LiN03cm2, a c s ~ 0=3 23.7 X CsN03 (aLiNo8 = 16.4 X cm2), and yet the agreement between calculated and experimental values of the surface tension is excellent, better than 1%.l Furthermore, we have shown that a variation of 10% in the value of a causes less than a 1%change in the calculated value of the surface tension.' The result is that explanations of the deviations observed between calculated and experimental values of the surface tension, based on inherent limitations in eq 1,are not tenable and we must look elsewhere. If there is a nonzero heat of mixing, the assumption of random distribution of the components of a mixture cannot be strictly correct. That is, in such a mixture, there will be a greater proportion of certain anion-cation contacts than would be expected on the basis of a random distribution; which is the quasi-chemical approximation.ll In general, however, differences between thermodynamic quantities, e.g., free energies of mixing and activity coefficients, calculated from either a regular solution model or a quasi-chemical model of the molten salt, tend to be rather small.12 That the difference between the more correct quasi-chemical approximation and the zeroth or random mixing model is trivial is further shown by the excellent agreement between the experimental surface tension values and those calculated from a model based on random mixing of the c0mponents.l If, however, the departure from random mixing begins to become appreciable as the result of an increase in short-range order, caused by non-Coulombic interactions between anion-cation pairs or next nearest neighbors, we would expect to begin to see significant differences between the results calculated from eq 1 and those observed experimentally. Furthermore, we would expect these differences to increase as the interactions become stronger. It is well known from NMR4 and spectral studies5 on molten thallium nitrate, as well as on thallium halide-alkali halide mixtures,6 that there is a significant degree of non-Coulombic interaction, generally attributed to covalent contributions, in this salt.
The Journal of Physical Chemistry, Vol. 82,No. 4, 1978 431
TABLE 111: Comparison of Calculated and Experimental Surface Tension Values for TINO,-KNO, and AgN0,-KNO, ( T = 350 C) KNO,, dcalcd), dexptl), mol % dynlcm dynlcm A, % A. TINO,-KNO,a 20 101.2 99.8 1.4 40 102.7 99.9 2.8 50 103.6 100.5 3.1 60 104.6 101.9 2.6 80 107.0 105.0 1.9 B. AgNO,-KNO,b 20 131.8 125.8 4.8 5.5 40 124.9 118.4 60 119.5 115.0 3.9 80 114.9 112.7 4.8 Reference 9. Reference 1.
From heat-of-mixing studies on binary thallium nitrate-alkali nitrate systems, Kleppa' postulates the existence of significant non-Coulombic forces in these systems, and, in fact, he calculates a value of 16 kcal/mol as the non-Coulombic contribution to the lattice energy of pure thallium nitrate. Blander13 has calculated the extent of cation-cation dispersion interactions in thallium nitrate-alkali metal nitrate, as well as silver nitrate-alkali metal nitrate mixtures and finds that dispersion forces may account for most of the observed departure of the heat of mixing from that calculated assuming only Coulombic interactions. These considerations, coupled with the NMR4,6and spectral data5 cited earlier, lead to the conclusion that, while T1N03-LiN03 and T1N03-KN03 melts are ionic in nature, they must possess a certain structured character as the result of non-Coulombic contributions leading to significant departures from the random mixture assumed by regular solution theory. As a consequence, one would expect to see nontrivial departures from the calculated values of the surface tension, precisely what has been observed here. A similar situation may be expected to apply in silver nitrate mixtures, and indeed Table I11 shows that the greater differences between the calculated and experimental values of the surface tension are observed for AgN03-KN03 melts than for T1N03-KN03. This is in keeping with the results of Kleppa,2who calculated a value for the non-Coulombic contribution to the lattice energy of silver nitrate of 21 kcal/mol, 5 kcal/mol larger than that for thallium nitrate.
Conclusion While equations based on regular solution theory can be used to calculate successfully the surface tension of a large number of binary, charge-symmetrical molten salt mixtures, there are certain ones, e.g., those containing TlNO, and AgNO,, in which pronounced deviations between calculated and experimental results are seen. We have shown that these deviations are not inherent in the equations, but result instead from interactions in the solution itself. The available evidence suggests that, in addition to the normal Coulombic forces, appreciable contributions from dispersion forces and covalent bonding are present in TlN03 and AgN03 containing melts. These latter contributions cause departures from the random mixing assumption of regular solution theory, in which case the present equations become inadequate.
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Acknowledgment. The author expresses his gratitude to B. H. Van Domelen for helpful discussions.
References and Notes (1) D. A. Nissen and B. H. Van Domelen, J. Phys. Cbem., 79, 2003 (1975). (2) 0. J. Kleppa and L. S. Hersh, J . Cbem. Pbys., 36, 544 (1962). (3) L. S. Hersh and 0. J. Kleppa, J . Cbem. Pbys., 42, 130a (1965). (4) S.Hafner and H. H. Nachtrieb, J. Cbem. Pbys., 40, 2891 (1964). (5) S.C. Wait, A. T. Ward, and G. J. Janz, J. Cbem. Pbys., 45, 133 (1966). (6) S.Hafner and H. H. Nachtrieb, J . Cbem. Pbys., 42, 631 (1965). (7) E. A. Guggenheim, "Mixtures", Oxford University Press, London, 1952, p 29.
P. D. Fleischauer and J. K. Allen (8) R. Defay, I. Priogogine, A. Bellamans, and D. H. Everett, "Surface Tension and Adsorption", Wiley, New York, N.Y., 1966, p 171. (9) D. A. Nissen, J . Cbem. Eng. Data, 22, 389 (1977). (10) G. J. Janz, F. W. Dampier, G. R. Lakshminarayanan,P. K. Lorenz, and R. P. T. Tomkins, M I . Stand. Ref. Data Ser., Natl. Bur. Stand., No. 15 (1968). (11) E. A. Guggenheim, ref 7, p 38. (12) F. D. Richardson, "Physical Chemistry of Melts in Metallurgy", Vol. 1, Academic Press, New York, N.Y., 1974, p 147. (13) M. Blander, J. Cbem. Pbys., 36, 1092 (1962). (14) G. J. Janz, C. G. M. Dijkhuis, G. R. Lakshminarayanan, R. P. T. Tomkins, and J. Wong, Natl. Ref. Data Ser., Natl. Bur. Stand., No. 28 (1969). (15) 0. J. Kleppa and L. S. Hersh, J. Cbem. Pbys., 34, 351 (1961). (16) T. P. Hoar and D. A. Melford, Trans. Faraday SOC.,53, 315 (1957).
Photochemical Hydrogen Formation by the Use of Titanium Dioxide Thin-Film Electrodes with Visible-Light Excitationt Paul D. Fleischauer" and John K. Allen The Ivan A. Getting Laboratories, The Aerospace Corporation, Ei Segundo, California 90245 (Received May 6, 1977) Publication costs assisted by The Aerospace Corporation
TiOz thin-film electrodes were sensitized to visible light (X 1630 nm) with concomitant formation of Hz at a Pt counter electrode. A divided cell was used with the sensitizer at ambient pH (-4) in the anode chamber and 1N HzSO4 in the cathode side. Transparent TiOzelectrodes were made for this process by the radio-frequency sputtering of -250-nm thick films onto conductive substrates, Le., Sn-doped Inz03on glass. Two types of sensitization process were demonstrated: (1)nonabsorbing supersensitizerswere found that sufficiently amplify photocurrents in reduced TiOz films to obtain Hz with excitation in the 400-500-nm region and (2) true dye sensitization of the Hz formation reaction was obtained with a combination of the supersensitizers and the dye rhodamine B (A 500-630 nm). An applied bias voltage (10.2 V) was necessary for visual observation of sensitized Hz formation on the cathode. A five-film-stacked electrode configuration was designed and used to produce Hz at rates of -0.1 mL/h for A,, 2500 nm and 0.2 mL/h for A,, 2400 nm with a 200-W Hg arc lamp.
The photochemical decomposition of water to produce H2 and O2 with the aid of semiconductor electrodes has received a great deal of attention recently as a potential process for converting solar energy into a usable combination of electrical and chemical energy. Many materials have been used successfully as candidates for the semiconductor photoassistance electrode, e.g., TiOz,1-4SrTi03,5-7 and SnOz(Sb).8 With the use of these materials, the photon energy requirement for the decomposition reaction has been reduced from -6 eV (the energy of the first water absorption band) to -3 eV. This improvement in spectral utilization results in relatively low solar-energy-conversion efficiency in terrestrial applications since only -3% of the incident solar flux for air mass 1 is a t energies 2 3 eV (A 600 nm with accompanying hydrogen generation which was accomplished through the use of a combination of highly absorbing dye sensitizers, selected surface additives (supersensitizers), and pretreatment of thin-film TiOz electrodes. The sensitization of electron-transfer processes in semiconductor materials by visible and near-infrared +Thisresearch was supported by The Aerospace Corporation w i t h company-financed funds. 0022-3654/78/2082-0432$01 .OO/O
absorbing dyes has been investigated extensively.11-20 These studies have dealt with the sensitization of image f~rmation'l-'~or of photocurrents in electrochemical cells.15-20Silver halide (conventional photographic film) can be made sensitive to -1.2 pm with dyes that are added to the photographic emulsion.'',l2 Polymethine cyanine dyes often are used for this application because their absorption maxima can be adjusted by alteration of the length of the polymethine chain. Unconventional TiOz imaging films have been rendered sensitive to beyond 700 nrn.l3J4 Cationic cyanines are typically the best sensitizers for TiOz emulsions,13but, when the oxide surface is covered with a layer of adsorbed metal ions, anionic dyes are more effe~tive.'~Rhodamine B, eosin, and erythrosin were ineffective image sensitizers on both types of TiOz surface, even though they are very effective on ZnO. Dye sensitization of photoelectrochemical processes on ZnO, SnOz, and TiOz electrodes is well known. Typically, the photocurrent vs. excitation wavelength spectra are analogous to the absorption spectra of the dyes. These observations have been used to support the theory that electrons are transferred from excited dyes to the semiconductor substrate in photographic image forrnaton.l4-l6 In an electrochemical cell composed of a sensitized semiconductor anode and a Pt cathode, this electron transfer results in cell current and, hence, a net electrolysis process. However, prior to the present study, the cell currents achieved in such systems were too small to drive the potential of a Pt electrode in an air-equilibrated solution to that of the H2couple. The nature of the electrode reactions has been ignored in such studies. Certain re@ 1978 American Chemical Society
