Mechanistic Studies of Ion-Selective Glass Membrane Electrodes M. J. D. Brand and G. A. Rechnitz Chemistry Dept., State University of New York, Buffalo,N . Y. 14214
The properties of several ion selective glass membrane electrodes are studied by impedance and galvanostatic measurements. Using methods of electrical network analysis, an equivalent circuit for glass membranes is proposed. It is shown that the electrical double layer at the membrane interface is similar to that of semiconductor electrodes rather than metallic electrodes. The results of galvanostatic measurements are also in agreement with the proposed model. This investigation provides the basic information necessary for an understanding of the electrochemical properties of glass membranes, essential for the measurement of the kinetics of processes at such electrodes.
Figure 1. Equivalent circuit of glass membrane with hydrolyzed surface film according to Buck (12)
R, is glass resistance, C,/i double layer capacity, R,, series resistances, and Frepresent transmission lines
GLASSMEMBRANE electrodes are of analytical importance for the potentiometric determination of hydrogen ions and other monovalent cations and the properties of such electrodes have been extensively characterized ( I ) . Commercially available glass electrodes fall into three main types (2); ( i ) pH electrodes showing greatest selectivity to protons, (ii) sodium electrodes, which may be 1000 times more sensitive to sodium than to potassium ions, and (iii) cationic electrodes which show a response to a range of monovalent cations but may be about 30 times more sensitive to potassium than to sodium ions. The mechanism of response of such electrodes is thought to depend upon ion exchange reactions at the membrane interfaces together with mobility of the cations in a lattice of fixed anion sites within the membrane. Such membrane systems never reach a state of true thermodynamic equilibrium in practice and ions migrate under the influence of the gradient of their electrochemical potentials. Thus the time invariant behavior of glass membranes has been obtained by integration of the Nernst-Planck equations (3)
for each mobile species present a t zero current ( 4 ) and a t fixed currents (5). Extension of this treatment to include the time variable properties by which the membrane steady state is established requires the simultaneous solution of the coupled continuity condition
A general analytical solution to these equations has not been given except under certain simplifying conditions. Helfferich and Plesset (6, 7) have obtained a numerical solution to the related problem of the time dependence of ion permeation into spherical ion exchange resin beads. Rechnitz and Hameka (1) G. Eisenman, “Glass Electrodes for Hydrogen and Other Cations: Principles and Practice,” M. Dekker, N. Y., 1967. (2) G. A. Rechnitz, Chem. Eng. News, 43(25), 146 (1967). (3) F. Helfferich, “Ion Exchange,” p 267, McGraw-Hill, N. Y., 1962. (4) F. Conti and G. Eisenman,. Biophysical Journal,. 5,247 (1965). _ . . . . (5j Zbid., p 511. (6) F. Helfferich and M. S . Plesset, J . Chem. Phvs.. 28. 418 (1958). (7) M. S. Plesset, F. Helfferich, and J. N. Franklin, ibid., 20, 1064 (1958). 1788
(8) have given a solution for the zero current time response of an electrode to a step change in activity E(t) = E” (1
- e-lIT)
(3)
and Buck (9) has confirmed the form of this equation. An exponential response time equation has also been obtained (10) by application of the theory of electrode kinetics of charge transfer reactions to the ion exchange reactions at a glass membrane. The response time of an ion selective electrode is of considerable practical importance. While a relatively slow response time may be tolerable for laboratory potentiometric measurements in solutions a t equilibrium, for automatic titrations and continuous analysis, a fast response is desirable. Also, if the electrode is to be successfully employed in measuring reaction kinetics, the response time must be fast in comparison with the reaction rate. Rechnitz and Kugler (11) have measured the response times of several glass electrodes using a rapid-mixing flowing stream to obtain a step change in activity. Typically the electrode potential reached a limiting value following a change in principal counter ion activity in a time of the order of 10 to 100 msec. Johansson and Norberg (10) have measured response times of pH electrodes in water and organic solvents and reported response times of the order of tens of msec. in aqueous solution. As the amplifier used for this work had a time constant of 20 msec, it is probable that these results are not meaningful. Both the steady state and dynamic properties of a glass membrane electrode should be predictable from a detailed knowledge of the mechanism of the electrode response. It is useful to consider each property of the electrode as its electrical analog and to represent the entire membrane electrode as an equivalent electrical circuit. Buck (12) has proposed the equivalent circuit of a glass membrane with a hydrolyzed surface film shown in Figure 1. In this model the surface film is represented as a finite transmission line and the glass membrane as a parallel array of resistance, double layer capacitance, and Warburg diffu(8) G. A. Rechnitz and H. F. Hameka, 2. Aria/. Chem., 214, 252
(1965). (9) R. P. Buck, J. Electroanal. Chem., 18, 363 (1968). (10) G. Johansson and K. Norberg, ibid., 18, 239 (1968). (11) G. A. Rechnitz and G. C. Kugler, ANAL.CHEM., 39, 1682 (1967). (12) R. P. Buck, J. Electroar?al.Chem., 18, 381 (1968).
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
OSCILLOSCOPE OR RECORDER DIFFERENTIAL HORIZONTAL AMPLIFIER
4vr
dG-q GENERATOR
VOLTME SOURCE
EIFIER .
Figure 2. Schematic of apparatus for impedance measurements
\
IOOC
60
D.C.VOLTAGE
OSCILLOSCOPE VERTICAL AMPLIFIER
FOLLOWER AMPLIFIER
40
01
' IO2
OSCILLOSCOPE EXTERNAL TRIGGER
Figure 3. Schematic of apparatus for current step measurements
sional impedance. Measurement of the impedance of glass membranes (13) supported this model. The finite transmission line representing finite diffusion across the surface film reduced to a pure resistance at high and low frequencies. After subtraction of the high frequency series resistance, the impedance at high frequencies showed equal real and imaginary components, resembling a Warburg impedance with a 45" phase angle (14). In this paper we report on a re-examination of the electrical properties of glass membranes using impedance measurements. Standard methods of electrical network analysis are used to obtain an equivalent circuit of the membrane which is verified by a galvanostatic technique.
lo"
lo"
Id FREQUENCY Hz
Figure 4. Frequency dependence of impedance of glass electrodes 0 pH electrode in 10-2M HCI; A sodium electrode in 10-zM NaCl 0monovalent cation electrode in 10-2MKCl
90
f FREQUENCY Hz
EXPERIMENTAL
The electrodes used in this study were a pH electrode (No. 41263) and a sodium ion electrode (No. 39278) (Beckman Instruments Inc., Fullerton, Calif.), and a monovalent cation electrode (No. 476220) (Corning Glass Works, Medfield, Mass.). The counter electrode was a silver billet electrode (No. 39261) (Beckman Instruments, Inc., Fullerton, Calif.) which was brightly polished and in solutions of fixed chloride ion activity served as a nonpolarizable electrode with a moderate current capacity. All measurements were made at room temperature. Impedance measurements were made by the procedure described previously (15) but with the considerably improved instrumentation shown schematically in Figure 2. AC signals were obtained from a Model 203A Variable Phase Function generator (Hewlett-Packard, Palo Alto, Calif.). A dc offset to the ac signal was provided, when required, from the Kelvin-Varley output of a Model AC-1lOB-1 Precision ac-dc voltmeter (Precision Standards Corp., San Marino, Calif.). Because the output impedance of this source was a function of output level and had a value up to 10 K Q, it was isolated by the voltage follower amplifier 3, a Model 143A operational amplifier (Analog Devices, Cambridge, Mass.). Amplifier 1 was one of a pair forming a Type 3A8 plug-in unit, the second amplifier, 2, being used as a variable gain preamplifier. The plug-in was used as (13) R. P. Buck and I. Krull, J . Electroanal. Chem., 18,387 (1968). (14) D. C. Grahame, J . Electrochem. SOC.,99, 37OC (1952). (15) M. J. D. Brand and G . A. Rechnitz, ANAL.CHEM., 41, 1185 (1969).
Figure 5. Frequency dependence of phase angle of glass electrodes Data as in Figure 4
the vertical amplifier in a Type 564 storage oscilloscope equipped with a Type 3A3 differential input horizontal amplifier (Tektronix, Beaverton, Ore.). The oscilloscope was used to display signals with frequencies 2 1 Hz,while lower frequencies were displayed on a Model 7590 CMR X-Y recorder (Hewlett-Packard, Palo Alto, Calif.). The horizontal display amplifier was driven by the variable phase output of the Function generator and the vertical display amplifier by the output of amplifier 2. Phase angles were read directly from the Function generator by adjusting the phase-lag control until the displayed ellipse collapsed to a straight line indicating zero phase difference between the vertical and horizontal signals. Impedance values were obtained from the vertical deflection. Apparatus for current step measurements is shown in Figure 3. The electrochemical cell formed the feedback path of the operational amplifier 1, part of the Type 3A8 plug-in unit. Application of a fixed potential through a fixed input resistor forced a constant current through the cell. The dc potential was obtained from the Precision ac-dc voltmeter, isolated through the follower amplifier 2. A step current was obtained by closing the switch and it was found that rapid, noise free, switching could be obtained by manually touching together two solid brass contacts. The potential across the cell was obtained from the output of amplifier 1 and potential-time curves were recorded on the
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
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Figure 6. Complex impedance plane plot of monovalent cation electrode in 10-2MKCl
Figure 7. Complex impedance plane plot of pH electrode in 10-2M HCI
storage oscilloscope, using a Type 3B4 time base. An external trigger signal was obtained by amplifying the dc potential 100 times with amplifier 3.
40
-
35
-
30
-
RESULTS Impedance Measurements. The variation of the impedance of each electrode with frequency is shown in Figure 4, and Figure 5 shows the corresponding variations in phase angle. The impedance loci of the monovalent cation, pH, and sodium electrodes in the complex impedance plane (16) are shown in Figures 6 , 7, and 8. At the highest frequencies attainable the real (resistive) impedance, ZR, of each electrode reached a finite value of about 10 KQ while the imaginary (capacitative) impedance, Z,, tended toward zero. The locus of the complex impedance of the monovalent cation electrode was a distorted arc of a circle having a centre below the real axis, and was similar to that reported previously for liquid ion exchange resin membranes (15). Impedance loci for the pH and sodium electrodes also showed this behavior at high frequencies but at lower frequencies there appeared a second distorted circular arc, which was most pronounced for the pH glass. This low frequency series impedance corresponds to the presence of a nonionic hydrolyzed surface film on the glass, which was not present to an appreciable extent on the monovalent cation glass. The impedance of each glass electrode was found to depend to a small extent on the chemical and electrical pretreatment of the electrode. Thus impedance measurements were not reproducible from day to day although the shapes of the complex plane plots were the same. Slow changes in electrode properties were small in comparison to the time required to complete a series of measurements. The impedances of the glass membranes were found to be independent of the dc potential across the membrane over the range =tlO V. This indicated a rectilinear cell current-potential curve and dc measurements in the absence of an ac signal confirmed that this was so. The use of a 1-V peak to peak ac signal for impedance measurements is therefore justifiable in this case. The variation of membrane impedance with solution conditions was investigated but any effect was found to be less than the reproducibility of the measurements. The equivalent circuit of a glass membrane can be considered as a series circuit consisting of the resistance of the (16) J. H. Sluyters, Rec. Trau. Chim. Pays-Bas, 79, 1092 (1960).
1790
z,
25-
Mn 20
-
I5
-
IO
30
I
I
40
XI
I
60
70
80
Z, Ma Figure 8. Complex impedance plane plot of sodium electrode in 10-2MNaCl
reference electrodes and solutions, R,,the impedance of the intact non-hydrolyzed glass, Z,, and the hydrolyzed film, Z,, if present. From the complex impedance plane plots 2, and 2,can be extrapolated to high frequencies to intercept the real axis at R, and R8’, respectively. The net impedances 2, and 2,can then be defined from measured values of ZRand Z,,
2, = (ZR - R,)
-j Z ,
(4)
( i ) FILMIMPEDANCE. Transformation of the complex impedance of the surface film, 21,to the complex admittance plane (17) resulted in a straight line admittance locus for both the pH and sodium electrodes. The equations of these lines were calculated by a least squares method as
pH electrode: Na electrode:
Yc = 1.02 YR - 0.0032 (r = 0.998)
(6)
Y, = 0.99 YR - 0.000089 (r = 0.998) (7)
where YRand Y,, the real and imaginary admittances, are in 10-6 52-l. The correlation coefficient, r, is givenin parentheses. (17) E. Brenner and M. Javid, “Analysis of Electric Circuits,” McGraw Hill, N. Y.(1959), p. 405.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
I
Ra
I
Rt
GLASS IMPEDANCE FILM IMPEDANCE
‘“I 30
Figure 10. Equivaient circuit of glass membrane electrode
I
p/
R, series resistance, R, glass resistance, Rj
film resistance
R,, space charge region resistance, C,, space charge capacitance, W Warburg impedance
YR
Figure 9. Complex admittance plane plot for intact glass impedance 0 pH electrode in 10-ZMHCI; A sodium electrode in 10 -ZMNaCl 0 Monovalent cation electrode in 10-2M KCI
The reciprocal of the intercept on the real admittance axis, YR’ (obtained by solving for YE with Yc = 0 in Equations 6 and 7) gives the magnitude of the parallel resistance component of the film impedance, 318 MQ for the pH electrode and 11,100 Mi2 for the sodium electrode. The slope of the complex admittance plot for the film impedance is equal to 1 within experimental error, which is characteristic of a Warburg diffusional impedance. Further confirmation that the film is equivalent to a shunted Warburg impedance is obtained from the linear dependence of ( Y R - YE’)on the square root of frequency for both the pH and sodium electrodes. The calculated lines of best fit were pH electrode: (YR
- YR‘) = 0.0519 w 1 / 2
Na electrode: ( Y z
+ 0.000333 (r = 0.981)
(8)
- 0.00228 (r = 0.998)
(9)
- YR’) = 0.0679 wl/’
where YE and YR’are in 10-6Q-l and w is radian frequency. ’ predicted ~ by Equations The small intercepts on the ~ 1 axis 8 and 9 are less than the experimental errors. From these results it may be concluded that the equivalent circuit of the glass film is a Warburg impedance in parallel with a large resistance. (ii) GLASSIMPEDANCE. Transformation of the complex impedance of the intact glass, Z,, into the complex admittance plane gave a curved admittance locus, shown in Figure 9 for each electrode. The impedance plane locus of 2, intercepts the real axis at 0 at high frequencies (after subtraction of series resistances, R,) and at an extrapolated finite resistance R, at low frequencies. The corresponding admittance plane locus therefore intercepts the real axis at 1/R, and also goes to infinity. The intercept on the real axis therefore corresponds to the admittance of the resistance R,, which is in parallel with another impedance. The locus for the sodium electrode was best defined and the dependence of the admittance on frequency was examined. Below 20 KHz the admittance was directly proportional to frequency but deviated from linearity at high frequencies. At 60 KHz, the admittance was 2 0 z greater than required for direct proportionality. An admittance directly proportional to frequency is characteristic of a capacitance, but Figure 9 shows that a resistive compo-
nent is also present. The membrane solution interface must exhibit a double layer capacitance due to separation of charge in two phases; the presence of such a charge has been assumed in previous theoretical treatments (10,12) and estimates have been made of its value (13). A glass membrane, however, is a poor conductor and it is not surprising that the double layer at the interface is rather different from that observed at, for example, mercury electrodes. A better analogy might be provided by a semiconductor rather than a metallic conductor electrode. Such capacity measurements as have been made at semiconductor electrodes (18, 19)have indicated a frequency dependent capacitance. The structure of the excess charge in a semiconductor phase is not the two dimensional layer found at metal interfaces, but rather a three dimensional structure extending into the bulk of the semiconductor. Such a model seems quite plausible for a glass membrane and the frequency dependence of the capacity would arise from the distributed properties of the space charge. The data of Figure 9 suggest that a frequency dependent resistance is in series with the space charge capacitance and we propose the equivalent circuit of a glass membrane electrode shown in Figure 10. At low frequencies the magnitude of the series resistance tends to zero, and the double layer capacitance can then be calculated from the slope of an admittance-frequency graph. A value of 159 pf was obtained for the sodium electrode, many orders of magnitude lower than the capacity at a mercury electrode of equal surface area. Current Step Measurements. Measurement of the potential-time curve for each electrode when the cell current was stepped from zero to a constant value showed that following an initial rapid rise, the potential eventually reached a limiting value. Figure 11 shows typical curves obtained for each electrode and in Figure 12 the initial potential rise is shown on an expanded time scale. The monovalent cation electrode reached a limiting potential in less than 1 sec, but the pH and sodium electrodes required a longer time. Over the range 0.01 pA to 1 pA, the shapes of the potentialtime curves were independent of current and a linear relationship existed between limiting potential and current. After passing a current through the electrodes, however, long periods were required before the electrode potential returned to its original zero current value. In general, therefore, the dc resistance values obtained from the ratio of limiting potential to cell current were not in complete agreement with the limit(18) M. Green, in “Modern Aspects of Electrochemistry,” J. O M . Bockris, Ed., Butterworths Scientific Publications, London, (1959) No. 2 p. 343. (19) H. Gerischer, in “Advances in Electrochemistry and Electrochemical Engineering,” P. Delahay, Ed., Interscience, N. Y . (1961) Vol. I, p. 233.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
1791
Oi
5
IO
15
20
25
t
SEC
30
35
40
0 I 2 3 4 5 6 7 8 9 IO II 12 13 I4 1516 17 18 t mSEC
45
Figure 11. Potential time curves obtained by application of 0.1 PA current.
Figure 12. Potential time curves of initial potential rise
Data as in Figure 11
0 pH electrode in 10-2M HCI; A Na electrode in 10-2M NaCI; 0 monovalent cation electrode in 10-2MKCI
ing low frequency resistances obtained by impedance measurements. A qualitative description of the shape of the potentialtime curve for the monovalent cation electrode can be obtained by assuming that the total cell current is divided between the current required to charge the double layer spacecapacitance and the current due to ion transport across the membrane. However, it is difficult to make this treatment quantitative because of the nonlinearity of the double layer capacitance. Caplan and Mikulecky (20) have discussed a theoretical treatment due to Teorell in which the resistance of a membrane under constant current conditions varies as 0.01
dR _ -- - k ( R dt
- R”)
Under these conditions the cell potential is obtained as a constant multiple of R , and Equation 10 has as solution an equation of the form of (3). A test of this equation is shown in Figure 13, in which the function log [(V - Vm)/-Vml is plotted against t for each electrode. The deviations from a straight line are a result of the nonlinear space charge capacitance. This treatment is only applicable to the pH and sodium electrodes at short times; at longer times concentration polarization in the hydrolyzed surface film on the glass resulted in the time dependent behavior shown in Figure 11. If the transport of ions through the membrane film is diffusion controlled, the potential should be dependent on the square root of time. A test of this condition is shown in Figure 14 and confirms that a limiting time-independent potential is reached as predicted by the glass film equivalent circuit. DISCUSSION The transient response time of a membrane electrode may be defined for the present purpose as the time required for the cell potential to reach a constant value following a step change in activity of the principal counter ion on one side of the membrane, assuming a complete absence of any potential change associated with the reference electrode. It has been shown (3) that a constant cell potential is reached as soon as (20) S. R. Caplan and D. C. Mikulecky, in “Ion Exchange,” J. A. Marinsky, Ed., Marcel Dekker, N. Y.(1966) Vol. I, p. 50. 1792
0
I I
I
I
I
I
I
I
0
2
4
6
8
IO
12
I
I
I
I
14 16 18 20
t mSEC
Figure 13. Test of Equation 10. Data as in Figure 12
Data as in Figure 12
a steady state is established at the membrane-solution interface. Therefore, the response time of the electrode will be determined by the kinetics of the ion exchange reaction at the interface and by transport processes occurring within the membrane. It has been the purpose of the investigation to obtain a clearer insight into these effects. Impedance measurements have shown that the equivalent circuit of a glass membrane in the absence of a surface film, Figure 10, is a resistance R , in parallel with a nonlinear space charge capacitance. The theory of charge transfer reactions at metallic electrodes interprets such a resistance as the polarization resistance from which the exchange current can be calculated and hence the kinetic parameters (21). For an ion (21) B. B. Darnaskin, “The Principles of Current Methods for the Study of Electrochemical Reactions,” McGraw Hill, N. Y. (1967) p. 73.
ANALYTICAL CHEMISTRY, VOL. 4 1 , NO. 13, NOVEMBER 1969
I
”
”
”
”
hydrolyzed surface film, a parallel RC charging curve is obtained which deviates from an exponential growth curve due to dispersion of the double layer capacitance. Electrodes having surface films also show this response at short times, while over a period of seconds concentration polarization within the film is observed. For electrodes without surface films, the time required for the potential to change from the zero current to the constant current steady state will also be equal to the response time of the electrode-i.e., less than 20 msec. The potential-time curve on application of a current step will be different from the potential-time curve obtained by an activity step because in the former, charging of the nonlinear double layer capacitance is involved. In the presence of a surface film it would seem that the response time should be limited by diffusion of ions through the film and it is widely believed that old glass electrodes are sluggish in response. Attempts at the direct measurement of electrode response times (6, 7) do not support this view. The mechanism of ion transport across the film cannot be said to be well understood. Clearly, the film is porous and it may be that under vigorous stirring conditions mass transport is not diffusion limited. For a complete understanding of the time dependence of electrode potentials it is essential that measurements be made of both the kinetics of the ion exchange processes at the membrane interface and of the mobilities of ions within the membrane. It is apparent from this investigation that distinction between these two cannot be made by steady state measurements. The use of pulse perturbations could lead to measurements of kinetic data of the ion exchange processes, providing a more exact description of the membrane double layer capacity can be obtained.
wyTs!rr 2
&
0
1.0
2.0
30
4.0
5.0
6.0
7.0
8.0
4 SEC”2
Figure 14. Test of diffusion control in surface film
Data as in Figure 11 exchange reaction at a membrane permeable to the exchanging ions, R , in fact represents the sum of two resistances in series, one related to the kinetics of the ion exchange reaction and the second representing the mobility of the counter ions in the membrane. Where the glass membrane is coated by a surface-hydrolyzed film, the equivalent circuit has, in addition to that described above, a series Warburg diffusional impedance shunted by a resistance. It is, perhaps, surprising that under an applied electric field the counter ions show any diffusion at all as they are the major charge carrier present in solution. The large resistance in parallel with the Warburg impedance is interpreted as representing the effects of electromigration through ‘pores’ in the surface film. The results of the current step measurements of potentialtime curves are compatible with the equivalent circuit model obtained by impedance measurements. In the absence of a
RECEIVED for review July 7, 1969. Accepted August 21, 1969. This work was supported by a grant from the National Science Foundation. Electronic equipment was provided by the University Program for Scientific Measurement and Instrumentation.
Silver-Silver Nitrate Couple as Reference Electrode in Acetonitrile Byron Kratochvil, Esther Lorah, and Carl Garber Department of Chemistry, University of Alberta, Edmonton,Alberta, Canada The silver-0.01M silver nitrate couple has been investigated as a reference electrodefor potentiometric measurements in acetonitrile. The thermal temperature coefficient of the standard silver-silver(l) couDle in acetonitrile is estimated to be 0.9 mV/OC. The’extent of silver nitrate association was measured and evaluated. The couple is reversible, and its potential is relatively unaffected by those impurities commonly found in acetonitrile.
STANDARD REFERENCE COUPLES normally used in water are not satisfactory in acetonitrile. The hydrogen electrode is unstable and easily poisoned (1). The mercury-mercury(1) halide couples are unsuitable because large mercury(I1) halide formation constants in this solvent cause extensive mercury(1) disproportionation (2). Silver chloride slowly forms a Series of anionic and polynuclear complexes which cause drifting (1) D. J. G. Ives and G. J. Janz, “Reference Electrodes: Theory and Practice,” Academic Press, New York, p 446 (1961). (2) K. Cruse, E. P. Goertz, and H. Petermoeller, 2.Elektrochem., 55, 405 (1951).
potentials in silver-silver chloride electrodes (3); to minimize this drift for polarographic studies, Popov and Geske used a silver-silver chloride reference in which the electrolyte was a saturated solution of silver chloride and trimethylethylammonium chloride (4). We have observed, however, that this electrode is also somewhat subject to drift and, therefore, is not completely satisfactory for potentiometric work (5). Aqueous saturated calomel electrodes have been used as external reference electrodes, particularly for polarography. However, the use of any external reference couple in another solvent gives unknown and variable junction potentials, and introduces the possibility of contamination with the second solvent during accurate measurements (6). (3) G. J. Janz and H. Taniguchi, Chem. Reus., 53, 397 (1953). (4) A. 1. POPOV and D. H. Geske, J . h e r . Chem. SOC.,79, 2074
(1957). ( 5 ) B. Kratochvil and J. Knoeck, unpublished work, Univ. of
Wisconsin (1965). (6) J. F. Coetzee and G . R. Padmanabhan, J. Phys. Chem., 66, 1708 (1962).
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