ELECTRICAL POTENTIALS OF GLASSELECTRODES IN hJOLTEN SALTS
2877
Electrical Potentials of Glass Electrodes in Molten Salts by R. H. Doremus General Electric Research and Development Center, Schenectady, New York
(Received February 6 , 1988)
Electrical potentials across fused silica and Vycor glass tubes in molten sodium-silver nitrates were measured. The mobility ratio of sodium and silver ions in the silica glass and the distribution coefficient for these ions between the glass and melt were calculated from electrolyses of the ions into the glass. The potential of this glass electrode as calculated from equations based on the ion-exchange theory for membrane potentials agreed with the measured potential. Thus the ion-exchange theory, based on ionic mobilities and ionic preference in the bulk of the glass, was verified for glass electrodes.
Introduction Many theories have been presented to explain the electrical potentials of glass electrodes. Reviews of early theories were given by Dole,’iZ and some later theories were described by Eisenman. a Dole’ classified the theories into phase-boundary, ion-adsorption, and diff usion-potential categories. Recently an ionexchange theory for potentials of glass electrodes has been utilized and is described in ref 4 and 5. This theory was developed from those for potentials of biological and synthetic membranes in aqueous solution.6 I n virtually all of these theories, it is found that the potential, V , of a glass electrode when it is sensitive to only one ion A is given by
RT
V=Vo+--lna F where Vois independent of concentration, R is the gas constant, T is the absolute temperature, F is the faraday, and a is the thermodynamic activity of the ion A in the solution in contact with the glass electrode. When another ion B also has an influence on the potential, the following equation is found in almost all of the theories
V
=
+ RT In (a + Pb)
VO
where P is another constant independent of ionic concentration and b is the activity of B in the solution. A theory of the glass electrode in which this equation does not result is discussed in a later section. It is clear that to decide between the various theories it is not sufficient to show that the functional dependence of eq 2 is followed, as has been done by various author^;'^^^^ it is also necessary to relate the constant P to the properties of the glass and to show that it is correctly given by the theory. For example, Eisenman measured membrane potentials of a sodium aluminosilicate glass sensitive to sodium and potassium ions in aqueous solution and
found agreement between values of P calculated from the potentials and from the properties of the glass, using the equations of the ion-exchange theory.9 In aqueous solution, silicate glasses are covered with a hydrated layer with different properties than the dry glass. This thin, hydrated layer, rather than the dry bulk of the glass, determines the potential of a glass electrode in aqueous solution. The main aim of this work was to test the equations of the ion-exchange theory for the unhydrated bulk of a glass. For this purpose potentials across fused-silica glass immersed in molten nitrate melts were measured. There was good agreement between the measured potentials and those calculated from the properties of the glass and the equations of the ion-exchange theory. Therefore, this theory was confirmed for potentials of glass electrodes. Another aim of this work was to establish the relations between solution activities and potentials across fused silica to aid in the development of reference electrodes for molten salts. Such electrodes might be useful in determining thermodynamic properties of fusedsalt solutions and in analyzing for ions in these solutions. (1) M. Dole, J. Amer. Chem. Soc., 53, 4620 (1931). (2) M. Dole, “Glass Electrode,” John Wiley and Sons, Inc., New
York, N. Y., 1941, p 256 ff. (3) G. Eisenman in “Advances in Analytical Chemistry and Instrumentation,” Vol. 4, C. N. Reilly, Ed., Interscience Division of John Wiley and Sons, New York, N. Y., 1965, p 305. (4) G. Karreman and G. Eisenman, BUZZ. Math. Biophys., 24, 413 (1962). ( 5 ) R. H. Doremus in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Marcel Dekker, Inc., New York, N. Y., 1966, Chapter 4, p 101. (6) An extensive discussion with earlier references is given in F. Helfferich, “Ion Exchange,” McGraw-Hill Book Co., Inc., New York, N. Y., 1962, p 368 ff. (7) B. P. Nicolsky, M. M. Schults, A. A. Belijustin, and A. A. Lev in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Marcel Dekker, Inc., New York, N. Y., 1966, chapter 6, p 174, and earlier references in this article. (8) K. Nots and A. G. Keenan, J.Phys. Chem., 70, 662 (1966). (9) G. Eisenman in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Marcel Dekker, Inc., New York, N. Y., 1966, Chapter 6, p 133. Volume 72, Number 8 August 1968
R. H. DOREMUS
2878 In the following sections are presented the equations for glass-electrode potentials, the experimental methods used, experimental results, and a discussion of t’he results and those of other workers.
Equations for Glass-Electrode Potentials This section is based on ref 5 , which should be consulted for further details. I n the ion-exchange theory, the potential developed across a “ fixed-charge” membrane with different solutions on either side of it can be separated into two portions, a phase boundary (Donnan or surface) potential and a diffusion potential. The surface potential arises because of differences in activities of ions between the solutions and the glass, while the diffusion potential results from differences in mobilities of different ions in the glass. In most silicate glasses, only monovalent cations can exchange and contribute to the membrane potential, so the present treatment is limited to these ions. The equilibrium distribution of A and B ions exchanging between solution and glass can be represented by the coefficient a%’’
KAB = b‘a”
(3)
where a and b are the ionic activities in the solution (one prime) and the glass (two primes). When two ions of different mobility interdiffuse in the glass, an electrical-potential gradient is set up to maintain equal ionic fluxes and, thereby, electrical neutrality. The flux of diffusing ions is given by the Nernst-Planck equations, from which the interdiffusion process can be described in terms of the mobilities Ui of the two ions and their mole fractions N1.l’ If a glass membrane separates two solutions, 1 and 2, containing different ionic concentrations of ions A and B, the diffusion potential VD set up in the glass is6tlo
The diffusion potential, therefore, depends only upon the ionic concentrations in the glass at its surfaces, the mobility ratio, UB/UA, and the (‘thermodynamic factor,” b In aA/b In NA. If the activity coefficient y (a = N y ) is constant with concentration, the thermodynamic factor is 1. With this condition and a constant mobility ratio, eq 4 can be integrated, and the diffusion potential can be related to the solution activities through the coefficient K from eq 3. The total membrane potential, V u , is the sum of the surface and diffusion contributions, and in the case of constant activity coefficients and mobility ratio in the glass is4~6
where the subscripts 1 and 2 refer to the two different The Journal of Physical Chemistry
solutions. This equation has the same form of eq 2 with P = KAB(UB/UA), if the activities in solution 2 are held constant and so contribute to Vo, If the mobility ratio and thermodynamic factor are functions of concentration, eq 4 cannot be integrated without knowledge of this functionality. Even in this case, the membrane potential is constant with time as soon as equilibrium between the solutions and glass surfaces is established and does not depend upon the concentration profile of diffusing ions. Eisenman has extended eq 5 by allowing the activities in the glass to vary with mole fractions, N , in the glass with the functionality a”/b” = ( N A / N B ) with ~, n a c o n ~ t a n t . ~This relation is equivalent to the assumption of regular solution behavior when the mole fractions are not too different. With this relation the thermodynamic factor is equal to n. If one side of the glass is covered with a layer of different properties that is thin enough to come to equilibrium with the solution in the time taken to make experimental measurements, the layer will not affect the total membrane potential of the glass. If the layer is at equilibrium with the solution, there can be no concentration gradients in it and hence no diffusion potential in the layer. Furthermore, at equilibrium the electrochemical potentials of ions in the thin layer at its two surfaces must be equal, so there will be no net Donnan potential across the layer. These elect,rochemical potentials of the ions will be the same throughout the layer as in the solution, so at the interface between the bulk of the glass and the layer the ions will also have these potentials; thus the equations of the last paragraph still apply t o the bulk of the glass. This analysis shows that specific surface adsorption should not affect the membrane potentials. The thickness of such a thin surface layer determines the time needed to reach equilibrium between the bulk of the glass and the solution. At the temperatures of the present experiments, the potential was constant with time when the bath was well mixed, showing that equilibrium was reached before the first measurement was made. T o test eq 5 , the membrane potential, distribution coefficient, and mobility ratio were measured in separate experiments.
Experimental Methods Tubes of General Electric 204A fused silica, (0.d. = 1.01 cm; wall thickness, 0.13 cm) and Corning Vycor glass (0.d. = 1.10 cm; wall thickness, 0.10 cm) were used. Their density was 2.2 g/cma. The electrical potential across the glass was measured with a cell consisting of an inner tube of silica or Vycor about 30 cm long and an outer container of fused silica about 12 cm high and with i.d. = 2 cm. The
(io) R. H. Doremus,
J . m y s . Chem., 68, 2212 (1964)
ELECTRICAL POTENTIALS OF GLASSELECTRODES IN MOLTEN SALTS salt levels ranged from 5 to 9 cm. For the potential measurements, the inside tube contained pure silver nitrate, while mixed silver-sodium nitrates were the outer solution. The composition of this solution was determined by weighing the salts as they were successively added to the outer melt, A portion of the melt was withdrawn at each composition, and its alkali content was determined with a flame photometer to check the composition value. The solution was stirred by bubbling argon through it to ensure uniform composition; without this precaution, mixing was very slow. To maintain a constant and uniform temperature in the cell, the cell was placed in another salt bath of mixed p0tassiu.m and lithium nitrates in a silica cup of larger diameter. The entire assembly was placed in an electric furnace with about 5 cm of insulating brick in the furnace mouth, with a small hole for the inner tube and outer electrode. The temperatures of the cell melts, as measured by platinum-platinum-rhodium thermocouples immersed in them, could be held constant to within a few tenths of a degree. The electrodes were thin silver wires wound on fine silica tubes, which also served as electrical insulation. Cell potentials were measured with a Keithley 610B electrometer or with a Rubicon potentiometer with the electrometer as a null indicator when more accuracy was desired. With these arrangements cell potentials were reproducible to about 3t 1 mV. The main source of this variation was probably inadequate shielding of the electrometer leads. With pure silver nitrate on both sides of the inner tube, its “asymmetry potential” was less than 2 mV. The experiments with Vycor were done before those with G.E. fused silica. The temperature was not controlled as carefully, nor were as many precautions taken, so that the readings were reproducible only to about & 3 mV. The mobility ratio for two ions was found by measuring the electrical conductivity of the glass when it contained only one ion or the other. The ionic concentration in the glass was fixed by electrolyzing it in a bath of the desired composition. For example, a sample tube was first electrolyzed in sodium nitrate at 337” and a constant voltage of 220 V until the resistance of the glass, after several days electrolysis, no longer changed. Then this tube was electrolyzed in silver nitrate, again until the resistance was constant. The ratio of the current through the glass in the two states (using the same voltage) is equal to the mobility ratio for the ions in these states, if all of the first ion is replaced by the second. Complete replacement was confirmed by intercomparing the mobility ratios of different ion pairs, such as sodium-silver, lithium-silver, and sodium-lithium. The total ionic concentration could be calculated from the time dependence of the current during electrolysis; the same concentration was found for different ion pairs, again indicating complete replacement of ions. The currents in the glasses were
2879
measured with the Keithley 610B electrometer. For a particular pair of ions, the same glass tube was used for both the potential and electrolysis measurements to avoid any possible variations from one glass sample to another. The distribution coefficient K for sodium and silver ions was determined from the electrical conductivity of the glass after electrolysis in a bath of mixed sodiumsilver nitrate. The total conductivity UT of the glass is then made up of contributions from the two ions QT
+
= NAUA NBQB
(6)
where ui is the conductivity of the glass containing only one kind of ion and Ni is the mole fraction of this ion (NA N g = 1). I n using this equation it is assumed that the total ionic concentration in the glass is constant for different ionic ratios. If the glass initially contained A ion, the ratio of the current after electrolysis to that at the start is proportional to QT/UA, and since UB/U.A is known from experiments of the type described in the last paragraph, the mole fractions of the ions can be calculated from eq 6. Since the activities of the ions in the melt are known, K can be calculated from eq 3 if the activity ratio YB/YA of the ions in the glass is 1. This latter condition is equivalent to assuming that the kinetic thermodynamic factor is 1, which was done to integrate eq 4. The comparison of various experimental measurements made in the next section shows is close to 1 in fused silica. that indeed This method of determining the distribution of ions between melt and glass is also based on other assumptions. The first is that the ionic concentration in the glass is uniform and constant with time. These conditions were established from the time course of the electrolysis and comparisons of the total electrical conductivity after successive electrolyses. Another assumption is that the mobilities of the ions in the glass are constant with varying ionic mole fraction in the glass. This assumption seems reasonable, in view of the very low ionic concentrations in the fused silica and Vycor glass, and is confirmed by the constancy of the K(UB/UA)values calculated from the membrane potentials at different melt concentrations and from the agreement between these values and those measured in the electrolysis experiments.
+
Experimental Results and Discussion I n order to calculate K ( U B / U Avalues ) from the me% sured cell potentials and K values from electrolyses, it was necessary to know the thermodynamic activities of the ions in the melts of silver-sodium nitrates. Several investigators have measured the activity of silver nitrate in these m e 1 t ~ ; ~ l -unfortunately l~ the most de-
w.
(11) R. Laity, J. Amsr. Chem. Soc., 79, 1849 (1967). (12) M.Bakes and J. Guion, Compt. Rend., 258,1223 (1964); EEectrochim. Acta, 10, 1001 (1965).
Volume Y??, Number 8 August 1968
It. H. DOREMUS
2880 tailed of these studies, in ref 13, deviates somewhat from the others. Furthermore, in ref 13 there is evidence that this mixture is not precisely a regular solution, as the other authors assumed. For the present calculations the solutions were considered to be regular, the activity coefficients being given by
0
210 2bO ZAO 3bo 3AO 3;O 3:O 30 where X is the mole fraction. The value 840 was found TEMPERATURE 'C in ref 11, 12, and 14, assuming no diffusion potentials Figure 1. Potential of a Vycor tube in a melt of in the cells with transference that were used t o measure sodium-silver nitrates containing 0.831 mole fraction of silver nitrate, with pure silver nitrate inside the tube, as a electrode potentials. A very small diffusion potential function of temperature. Line drawn was reported in ref 14 using cells with arid without proportional to absolute temperature. transference. Equation 7 is used for the ionic activities in K , since these activities always occur in ratios, so that the activities of the nitrate anions cancel. membrane potential V , is the difference between the It is possible t o test eq 5 with the experiments demeasured cell potential and the electrode potential. scribed in the last section without knowing the acSome measurements of the potential across Vycor tivity coefficients in the melt, as shown below, so their glass at different temperatures, for the melt given in reliability will not affect this test. However, the abTable I, are shown in Figure 1. Within experimental ) solute magnitudes of the calculated K and K ( u A ~ / u N ~ error, the temperature dependence is given by the values will be functions of the activities chosen. Errors Nernst slope, which shows that K ( U A ~ / U NisJ not a in these values resulting from incorrect activity costrong function of temperature. efficients should be greatest in solutions dilute in one The product K ( U B / U Awas ) calculated from the meaion, especially the alkali ion. sured cell potential V , and eq 8 and 11, with sodium as The cell potentials measured for fused silica in various ion A and silver as ion B. Then mixtures of silver-sodium nitrates are given in Table I, together with the calculated electrode and membrane
and since b2 = 1 and a2is small
Table I : Potentials of Fused Silica Tubes Containing Silver Nitrate and Immersed in Melts of Sodium-Silver Nitrates at 333' Mole fraction of AgNOa
Measured potential ( V d ,mV
Electrode potential (Vd,mV
K(UA~/UN~ (calcd from eq 9)
Membrane potential ( V d ,mV
General Electric 204 0.836 0.700 0.536 0.440 0.339
8.2 15.1 22.9 31.4 40.6
49.0 73.8 90.0 108 121
41.8 58.7 67.1 76.6 80.4 Av
0.831
58.0
Vycor 8.2
50.0
0.202 0.181 0.178 0.179 0.171 0.182 0.157
potentials. The electrode potentials V , were calculated from the usual equation
V, =
RT
bz
F
bi
- In -
where the b's are the thermodynamic activities of the silver ions in the two solutions. Since one solution was pure silver nitrate, it was taken as the standard state and considered positive, so that bz = 1. The The Journal of Physical Chemistry
The values calculated in this way are given in Table I. The deviation from the average value of K ( U A ~ / U N is& ) small for the concentration range investigated, implying that this term is constant with changing ionic mole fraction in the glass. The results of several successive electrolyses at a constant 220 V on one fused silica tube are given in Table 11. The currents from one run to the next do not agree exactly because the levels of the melts were slightly different. The mole fractions of silver in the glass were calculated from eq 6, as described in the last section. The ratio of sodium to silver mobility can be calculated from electrolyses 3 and 4 and number 5 ; the average value is 13.70. Values of K can be calculated with eq 3 from the known activities in the melt and the ratios of the silver to sodium concentrations found in runs 1 and 2, and 3 and 4, assuming that the ratio of activity coefficients in the glass is 1. The average of (13) M. Liquornik and Y . Marcus, Israel Atomic Energy Commission Rehovoth, Israel, Report 742-2,June 1964. (14) J. A. A. Ketelaar, J . Chim. Phya., 61,44 (1964).
ELECTRICAL POTENTIALS OF GLASSELECTRODES IN MOLTEN SALTS Table I1 : Electrolysis of General Electric 204 Fused Silica in Melts of Sodium-Silver Nitrates a t 337’ and a t a, Voltage of 220 V
No.
1 2 3 4
5 a
Mole fraction of silver nitrate in the melt
--Current, Initial
0.253 0 0.284 1.000 0
... 2.96 5.41 2.79 0.398
PA---Final
... 5.84 3.08 0.357 5.42
Mole fraction of silver in the glass Initial Final
1,000 0.532‘ 0 0.464’ 1,000
0.532“ 0 0. 474a 1.000
0
2881
glass electrode in aqueous solution, this “bulk” of the glass is actually a hydrated layer that is hundreds of atom layers thick. Since diffusion distances are very short at room temperature, exchanging ions do not diffuse far into this layer, and it serves the same function as the whole of the glass membrane in the measurements in fused salts at higher temperatures.
Discussion of Results of Others Results on membrane potentials in glass have been interpreted16-lg with the usual equation for potentials of cells with transference
Calculated from eq 6.
these two K’s is 2.10. These two averages give a K . ( u A g / u ~of* 0.156, ) in reasonably good agreement with the value of 0.182 found for G.E. fused silica from the potential measurements. The value of K(uA~/uN.) for Vycor given in Table I agrees closely with the one calculated from the electrolyses of fused silica, indicating that Vycor has similar ionic properties to the G.E. fused silica. The above agreement between the two K(uAg/uNa)values confirms the validity of eq 5 for potentials of glass electrodes. It also supports the assumptions of constant mobilities and unit activity coefficients for silver and sodium ions in fused silica, since these assumptions led to eq 5 and were involved in the experimental determination of K . Some experiments were conducted with fused silica that had different surface treatments. Experiments with a radioactive silver tracer showed that a silica surface that had been soaked in concentrated nitric acid absorbed a large amount of silver tracer from a sodium nitrate melt. The glass surface was covered with SiOH groups from reaction with the acid, and silver exchanged with the H+ ions because it was strongly held by the SiO- group. Treatment of this surface with an aqueous potassium cyanide solution removed some adsorbed silver tracer quickly, but a considerable amount of the tracer dissolved only slowly into the cyanide solution, indicating that the silica surface was hydrated at least several atom layers deep by the acid treatment. When this surface was placed in 8% H F for a few seconds, all the adsorbed silver was removed. The H F removed the hydrated layers and also substituted some SiF groups for the SiOH groups. This surface did not adsorb silver from the nitrate melt. Glasses treated in these two ways gave similar results for membrane potentials and in the electrolysis experiments, supporting the contention in the Introduction that specific ion adsorption in a thin surface layer does not affect the measured membrane potentials. It also shows that potentials of glass electrodes are related to the bulk properties of the glass, as reflected in the distribution coefficients and mobility ratios. I n a
in which t i and Zi are the transference number and number of unit charges of ion i. Since the definition of t i is ti
= ciui/Cciui i
(11)
eq 10 is equivalent to eq 4 for the diffusion potential. In cells with transference in aqueous solution there are no boundary potentials, since the medium is a continuous aqueous phase. However, in a glass electrode the solution and glass are two separate phases, and a phase-boundary potential can arise, which has been neglected in ref 15-19. In using eq 10 these authors assumed that the transference number of sodium is constant in the glass. However, from eq 11 and the present work it is clear that this assumption will be true for fused silica only if all or none of the monovalent cations in the glass are sodium. In the general case of contact with melts with two or more exchanging ions, their transference numbers will be strong functions of ionic concentration in the glass, because of the ci factor in the numerator of eq 11. In ref 16 Stern found agreement between eq 10 and his data for sodiumsilver exchange potentials in Vycor glass with a constant sodium “transport number’’ of 0.95. This comparison was made by assuming that the activities in the melts of sodium-silver chlorides were equal to the concentrations; however, the results of Panish, et ~ 1 . ~ 2 0 showed that this solution is not ideal. When the correct activities are used, eq 10 is satisfied with a sodium transport number of 1.00. The reason eq 10 works in this case is that K ( U B / U Ais) small; if this term in eq 5 is very much larger or smaller than 1, this equation is (15) R. Littlewood, EZectrochim. Acta, 3 , 270 (1961). (16) K.H.Stern, J . Phys. Chem., 67, 893 (1963). (17) K. H. Stern and J. A. Stiff, J. Electrochem. SOC.,111, 893 (1964). (18) K. H.Stern and S. E. Meador, J . Res. Nut. Bur. Stand., A69, 553 (1965). (19) K.H.Stern, Chem. Rev., 66, 355 (1966). (20) M. B. Panish, F. F. Blankenship, R. F. Newton, and W. R. Grimes, J. Phys. Chem., 62, 1325 (1958). Volume 79,Number 8 August 1968
IVANHALLER
2882 the same as eq 4 with a large or small value of UB/UA. Thus the use of eq 10 with a constant and neglect of the phase-boundary potentials is not justified. The
experiments described in the previous section show that both surface and diffusion potentials must be taken into account in describing membrane potentials in glasses.
Thermal Isomerization of Hexafluorobicyclo[2.2.0] hexa-2,5-diene by Ivan Haller I B M Watson Research Center, Yorktown Heights, New York 10608 (Received February 6, 1068)
The kinetics of the vapor-phase thermal isomerization of hexafluorobicyclo[2.2.0]hexa-2,5-diene to hexafluorobenzene was studied in the high-pressure region in the temperature range of 35-76', The reaction is clean an3 homogeneous and it follows first-order kinetics with a rate constant k = 1018.'8*o.llexp[(-Z8.45 & 0.16 kcal)/RT] sec-l. The heat of reaction, measured approximately by differential scanning calorimetry in the liquid state, was found to be 51 f. 3 kcal/mol.
Introduction Thermal valence isomerization reactions of smallring compounds have received a great deal of recent interest, as they are important sources of data for the understanding of energetics in chemical bonding.'-' Rearrangement reactions of valence isomers of benzene and of its derivatives to the corresponding aromatic compounds are particularly interesting, as the driving force for these reactions includes a substantial resonance energy in addition to the more common terms occurring in other valence isomerization reactions; measurements in these systems, however, are exceedingly rare. van Tamelen and Pappass observed that bicyclo [2.2.0]hexadiene isomerizes to benzene without side reactions with a half-life of approximately 2 days in pyridine solution at room temperature. Kinetic measurements of the gas-phase isomerization of this compound have not, however, been reported, probably due to the difficulties in the synthesis of sufficient quantities of this material. Hexafluorobicyclo [2.2.0]hexa~ ' ~paper 2,5-diene (I) is more readily a ~ a i l a b l e ; ~this presents our measurements of the kinetics and reaction calorimetry of its isomerization to hexafluorobenzene (reaction 1).
It was shown earlier" that ultraviolet irradiation of hexafluorobenzene in the vapor phase results in a rapid isomerization to vibrationally excited compound I, which reverts to hexafluorobenzene unless it is deactivated in collisions. Quantum-yield measurements The JOUTnal of Physical Chemistry
at various pressures and irradiating wavelengths resulted in rate constants for isomerization of the vibrationally excited species as a function of energy. An additional motivation for the present investigation has been the fact that a comparison12between rates obtained from the photochemical studies and the predictions of nonequilibrium unimolecular rate theory can only be made if the appropriate kinetic and thermodynamic parameters are available.
Experimental Section Materials. Hexafluorobenzene
(Pierce Chemical Co.) was purified by gas chromatography. Compound I was preparedev1O by irradiating hexafluorobenzene vapor (36 torr) for 16 hr in a 2-1. quartz bulb in the presence of nitrogen (-900 torr). The bulb was rotated in front of the lamp (Hanovia 73-A-10) t o mini(1) s. W.Benson and W. B. DeMore, Ann. Rev. Phys. Chem., 16, 397 (1965). (2) G. R. Branton, H. M. Frey, and R. F. Skinner, Trans. Faraday SOC.,6 2 , 1546 (1966). (3) R. Criegee, D. Seebach, R. E. Winter, B. Borretzen, and H. A. Brune, Chem. Ber., 9 8 , 2339 (1965). (4) H.M. Frey and I. D. R. Stevens, Trans. Faraday Soc., 6 1 , 90 (1965). ( 5 ) R. Srinivasan, A. A. Levi, and I. Haller, J. Phys. Chem., 6 9 , 1775 (1965). (6) C. Steel, R. Zand, P. Hurwitz, and 8. G. Cohen, J . Amer. Chem. SOC.,8 6 , 679 (1964). (7) J. P. Chesick, ibid., 8 8 , 4800 (1966). (8) E.E.van Tamelen and S. P. Pappas, ibid., 85, 3297 (1963) (9) I. Haller, ibid., 88, 2070 (1966). (10) G. Camoggi, F. Gonzo, and G. Cevidalli, Chem. Commun., 313 (1966). (11) I. Haller, J . Chem. Phys., 47, 1117 (1967). (12) I. Haller, to be submitted for publication.
