reactant. The reason for such an order of reaction is that the adsorbed species is in a lower free energy state than is the dissolved material. In the case of sulfide exchange between mercuric sulfide and cadmium(II), the energy state of the electrode, mercuric sulfide, as well as that of the cadmium(I1) must be considered. Adsorbed cadmium(I1) would be-in a lower energy state than diffusing cadmium(II), but the mercuric sulfide associated with the adsorbed cadmium(I1) might well be in a higher energy state than mercuric sulfide not closely associated with a cadmium(I1) species. If the adsorption process can be schematically represented as the polarization of the bond between a mercury(I1) and a sulfide, Hg(I1)-S-Cd(II), there will be a tendency for the mercuric sulfide bond to be weakened as the cadmium sulfide bond is formed. Thus the affected mercuric sulfide molecule would be more readily reduced than mercuric sulfide reacting with diffusing cadmium(I1). Adsorption would thus produce the observed pre-peak anodic to the main, diffusion controlled, exchange peak. Further evidence for surface control of the pre-peak is offered by the effect of surfactants on the pre-peaks of three metal ions. Saturated solutions of uncharged camphor completely surpressed the pre-peak while not affecting the shape or height of the main exchange peaks of cadmium(II), lead (11), or zinc(I1). The presence of camphor shifted the main exchange peaks for these ions by only 10 to 20 millivolts in the cathodic direction, a much smaller shift than was experienced by the process for the reduction of the metal ion to the amalgam. Charged strychinine-H+, added as the nitrate salt, produced the same effect on the pre- and main-exchange waves of cad-
mium(II), and lead(I1) as did neutral camphor. However, strychnine nitrate at a concentration of 2.5mM, while suppressing the pre-wave of zinc(II), also caused the main exchange of zinc(I1) to appear very irreversible. The potential of the zinc(I1) exchange in the presence of strychnine nitrate was forced cathodic to very near the region for direct reduction of mercuric sulfide. Plots of logarithm current us. potential for the direct reduction of mercuric sulfide still demonstrated reversible slope in the presence of strychnine nitrate, and the peak potential of the HgS reduction curve was shifted less than 0.01 V by the surfactant. Kolthoff has shown that the strychnine cation adsorbed on freshly precipitated mercuric sulfide is associated with specific sites (9). He assumed that these sites are adsorbed sulfide ions since zinc(I1) could replace the adsorbed strychnine in a 1 to 1 fashion. The fact that the strychnine cation inhibited the induced exchange of zinc(I1) but not the exchange of lead(I1) or cadmium(I1) cannot be fully explained. However, the effect is certainly coupled to the charge on the strychnine-H+ since uncharged camphor does not affect the main zinc wave. Also, the association of strychnine-H+ with specific sites may be a factor. It is possible that zinc(II), to accept a sulfide, must first adsorb on the electrode at specific sites, which can be partially blocked by strychnine cations. RECEIVED for review November 6, 1969. Accepted January 19, 1970. This research was supported by National Science Foundation grant NSF GP 7773. Additional support in the form of an American Chemical Society Analytical Division Summer Fellowship is gratefully acknowledged by J. H. Carney. (9) I. M. Kolthoffand D. R. Moltzau, Chem. Rec., 17, 293 (1935)
Mechanistic Studies on Crystal-Membrane Ion-Selective Electrodes M. J. D. Brand and G. A. Rechnitz Chemistry Department, State University of New York, Buffalo, N .
Y.14214
The properties of several ion-selective electrodes having single-crystal, polycrystalline, and mixedcrystal membranes are examined. Measurements of the electrode impedance are used to derive e uivalent circuit models of each type of electrode. he lanthanum fluoride electrode is shown to have a surface film resembling the hydrolyzed surface film on glass membrane electrodes. A distinction i s made between electrodes in which ion transport occurs across the membrane and those in which ion-blocking is found at the electrode. All of the electrodes are found to exhibit nonlinear space charge effects. The resulting equivalent circuit models point the way to a possible means of measuring the kinetics of ion exchange at a membrane-solution interface.
fluoride membrane to sense the activity of fluoride ion in solution (2). Subsequently, membrane electrodes have become commercially available in which silver halide and silver sulfide membranes are used to measure the activity of halide ions ( 3 , 4 ) , silver and sulfide ions (5,6). More recently, solid state membrane electrodes have been introduced which respond selectively to the activities of the divalent ions of copper (7), lead (8),and cadmium (9). The membrane in these elec-
'f
AMONG THE MORE significant advances in analytical potentiometry in recent years has been the development of ion selective electrodes using solid state inorganic crystals as membranes. The first, and perhaps the most remarkable of these electrodes, was introduced by Frant and Ross ( I ) who used a lanthanum 478
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
(1) M. S.Frant and J. W.Ross, Science, 154, 1553 (1966). (2) K. Srinivasan and G. A. Rechnitz, ANAL.CHEM.,40, 509 (1968). (3) D. A. Katz and A. K. Mukherji, 'Microchemical J., 13, 604 (1968). (4) J. C. VanLoon, Analyst, 93,788 (1968). ( 5 ) T. M. Hseu and G. A. Rechnitz, ANAL.CHEM., 40, 1054 (1968). (6) T.S.Light and J. L. Swartz, Anal. Lett., 1,825 (1968). (7) G.A. Rechnitz and N. C. Kenny, ibid., 2, 395 (1969). (8) J. W.Ross and M. S. Frant, ANAL.CHEM., 41,967 (1969). (9) M. J. D. Brand, J. J. Militello, and G. A. Rechnitz, Anal. Lett., 2,523 (1969).
Table I. Equivalent Circuit Values for Lanthanum Fluoride Membrane Electrodes
Manufacturer Model No. Rs, M a Beckman 39600 0.20 Corning 476042 0.14 IIIb Orion 94-09 0.23 1vc Orion 94-09 0.008 Limiting high frequency value. * Early model distinguished by white plastic electrode body. c Recent model distinguished by black plastic electrode body. I I1
trodes consists of a mixture of silver sulfide and the divalent metal ion sulfide. The properties of solid state membrane electrodes are analytically attractive. ’ Their sensitivity is limited in pure dilute solutions primarily by the low solubility product of the membrane salt. Selectivities for this type of electrode can be extremely favorable; thus hydroxide ions represent the only significant interference for the fluoride electrode. The electrodes are compatible with organic solvents (7, 9) and are mechanically robust. The mechanism of response of solid state electrodes is not so well understood as that of glass or liquid ion exchanger membrane electrodes. It is appealing to apply the ion exchange theory (10) of electrode operation directly to the solid state membrane case. Thus, Buck (11, 12) has presented such a theory assuming rapid, reversible ion exchange at the membrane interfaces and mobile defects within the membrane crystal. While it is at least highly probable that these are necessary conditions for the operation of a solid state ionselective membrane electrode, experimental evidence supporting this view is not available for many solids now in use as membrane materials. Pungor (13) used radiochemical methods to investigate the exchange of iodide ions at silver iodide crystals dispersed in a silicone rubber matrix and reported that the exchange rate is fast. The ion exchange reaction depends upon ion adsorption at the membrane surface as it may be postulated that adsorption is the primary step in the mechanism of ion exchange, M+
+ IS (cryst)
-+
M+ - - - IS (cryst) + I+
+ MS.
The possibilities of interference in the potentiometric response by a mechanism of mixed crystal formation and by simple adsorption without mixed crystal formation have been recognized by Buck (11) and by Ross and Frant (14). An attempt has also been made to correlate the selectivity coefficients, k l , for interfering ions with the solubility products of their corresponding silver or sulfide salts for a mixed sulfide electrode (9). Although the restilts were somewhat scattered, it was apparent that a relationship existed, at least in the simpler cases. Deviations were attributed to uncertainty in solubility product data and to the operation of other mechanistic effects. The importance of accurate selectivity data for ion selective electrode cannot be overemphasized. A critical study of selectivities for solid state electrodes, comparable to those carried out on anion selective liquid membranes (15), would be of (10) G. Eisenman, ANAL.CHEM., 40, 310 (1968). (11) R. P. Buck, ibid., 40, 1432 (1968). (12) Ibid., p 1439. (13) E. Pungor, ibid., 39 (13), 28A (1967). (14) J. W. Ross, Jr., and M. S. Frant, Electrochemical Society Meeting, New York, May 1969. (15) K. Srinivasan and G. A. Rechnitz, ANAL.CHEM.,41, 1203 (1969).
RM, M a
Csc,’ p F
RF, Ma
C F ,pF ~
1.6 0.15 0.46 0.006
6 x 10-6 0.056 0.014 0.006
2.2 0.38
3 x 10-6 6.3
...
... ...
0.005
immense value to an understanding of solid state membrane response. The requirement that the membrane must be electrically conducting can be met in theory by ion transport, by electronic conduction, or by a mixture of both mechanisms. Experimental studies of conductivities in solids have most frequently been made at high temperatures (16-19) often near the crystal melting point, as this condition allows the intrinsic conductivity to be observed. At lower temperatures, the extrinsic conductivity region corresponds to the motion of crystal defects introduced by impurities. The extrinsic conductivity may be very much greater than that which would be observed for a pure crystal at the same temperature (20). In silver halide crystals, the intrinsic conductivity is due to mobility of both Ag+ (21-23) and electrons (24). Silver sulfide also exhibits mixed conductivity; in the low temperature form, ionic conduction by migration of Ag+ may be a considerable fraction of the total, whereas above 177 “C electronic conduction predominates (25, 26). Sher et al. (27) have examined the conductivity of lanthanum fluoride over the temperature range 27-727 “Cand found a value of lo-’ ohm-’ cm-* at the lowest temperature. The main contribution to the conductivity was thought to be migration of the fluoride anion, LaF3
+ molecular hole
+
LaF2+
+ F-
Previously we have examined the properties of ion selective electrodes with liquid ion exchange resin (28) and glass (29) membranes by measuring their impedance as a function of frequency. Plotting the impedance locus in the complex impedance plane (30) allowed graphical methods to be used to obtain an equivalent circuit of the membrane electrode and to
(16) K. Kiukkola and C. Wagner, J . Electrochem. Soc., 104, 308, 379 (1957). (17) C. Wagner, in “Advances in Electrochemistry and Electrochemical Engineering,” P. Delahay, Ed., Interscience, N. Y., 1966, Vol. 4, p 1. (18) D. 0. Raleigh, in “Progress in Solid State Chemistry,” H. Reiss, Ed., Pergamon Press, Oxford, England, 1967, Vol. 3, p 83. (19) J. Kummer and M. E. Milberg, Chem. Eng. News, 47, 90 (1969). (20) J. H. Beaumont and P. W. M. Jacobs, J. Chem. Phys., 45, 1496 (1966). (21) E. Koch and C. Wagner, 2.Phys. Chem., B38,295 (1937). (22) R. J. Friauf, J . Chem. Phys., 22, 1329 (1954). (23) C. Tubandt, 2.Anorg. Allgem. Chem., 115, 105 (1921). (24) B. Ilschner, J. Chem. Phys., 28, 1109 (1958). (25) M. H. Hebb, ibid., 20, 185 (1952). (26) C. Wagner, ibid., 21,1819 (1953). (27) A. Sher, R. Solomon, K. Lee, and M. W. Muller, Phys. Reo., 144,593 (1966). (28) M. J. D. Brand and G. A. Rechnitz, ANAL.CHEM.,41, 1185 (1969). (29) Ibid., p 1788. (30) J. H. Sluyters, Rec. Truv. Chim. Pays-Bas, 79,1092 (1960). ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
479
Table 11. Equivalent Circuit Values for Silver Chloride Membrane Electrodes GC,'
Manufacturer Model No. Rs, MQ V Beckman 39604 0.07 VI Corning 476126 0.08 VI1 Orion 94-17 0.10 a Limiting high frequency value. * Prototype electrode.
R M ,MQ 0.97 10 22
pF 8 7
7
characterize membrane processes. This approach is extended here to the case of ion selective electrodes with solid state membranes.
output by 100. The attenuator was a resistor potential divider, the output of which was buffered with a voltage follower amplifier P85 AU (Philbrick-Nexus Research Inc., Dedham, Mass.). For the higher impedance electrodes, ac amplitudes of up to 1 V peak to peak were used. All ac signals were used without external dc offsets. The oscilloscope vertical amplifier was dc coupled to minimize phase shift errors within the oscilloscope. Some of the cells studied exhibited such large potentials that it was not possible to display the ac signal at full sensitivity using the oscilloscope vertical position control. In these cases an external, variable dc voltage of the correct polarity was summed into the preamplifier and was used as a coarse vertical position control. Treatment of Results. Experimentally determined values of impedance Z and phase angle 0 were plotted in the complex impedance plane ZR,ZCwhere ZR
=
z COS e
Zc
=
Z sin 8
z
=
ZB
EXPERIMENTAL.
Apparatus. The ion selective electrodes used in this study are listed in Tables I to IV. The counter electrode used was a silver billet electrode No. 39261 (Beckman Instruments Inc., Fullerton, Calif.). Impedance measurements on the fluoride, chloride, bromide, iodide, and sulfide electrodes were made with cells of the type
Ion-Selective Electrode
Solution
!
Silver Electrode
All values of Z c were negative (capacitative reactance) but were plotted in the first quadrant of the complex plane for convenience. Graphical extrapolation of the impedance locus to high frequencies gave an intercept on the real axis, Rs,
RS = Z R ( w -+
For the fluoride electrode, the solution was 10-2M in NaF and 10-2M in NaCl. For the other halide and sulfide electrodes, solutions used were 10-2M in the sodium or potassium salt of the anion. A 10d2Msilver nitrate solution was also used with the silver electrode. Impedance measurements on the mixed sulfide electrodes were made with cells of the type,
1M Potassium Silver Chloride Solution Electrode
The liquid junction between the metal ion solution and the potassium chloride solution was formed across a sintered glass frit with large surface area. Metal ion solutions used in this case were 10-2M in copper, lead, or cadmium nitrate. The apparatus and procedure for impedance measurements has been described previously (29). Where possible, the amplitude of the ac signal used was 10 mV peak to peak; this signal was obtained by attenuating the signal generator
=zc
Z' = ZR'
+j Z c '
Transformation of the complex impedance Z ' , 8' to the complex admittance plane YR, YCgave the equivalent admittance Y , e', where Y
=
l/Z'
=
YR
+j
YC
YR = Y cos 8' YC = Y sin 8'
Table 111. Electrical Parameters of Silver Bromide, Iodide, and Sulfide Electrodes A log 2 1 Membrane Manufacturer Model No. Rs, KQ A log w 39602 64 -0.394 AgBr Beckman 94-35 1.5 -0.400 AgBr Orion 39606 6.4 -0.500 AgI Beckman AgI Orion 94-53 12 -0.454 AgZS Beckman 39610 4.4 -0.554 AgzS Orion 94-16 6 -0.415
VI11 IX X XI XI1 XI11
XIV
xv
Q
m)
corresponding to an equivalent series resistance. Subtraction of this resistance from the impedance 2,0 gave the magnitude of the equivalent series impedance Z', e',
ZC'
Ion-Selective Metal Ion Electrode Solution
+j Z c
Table IV. Electrical Properties of Mixed Sulfide Electrodes Membrane Manufacturer Model No. Rs, KQ . . . 4 Beckmaw CuS/AgzS
CuS/AgiS
Orion
94-29
0.8
2 1( W
=
1) KQ
3.1 4.6 19.4 5.3 15.8 8.9
Comments Z, Almost independent
of
w
Zl Almost independent of w log21 -0.79 log w logZ1 a -0.74log w
XVI PbS/AgiS Orion 94-82 0.2 XVII CdS/AgiS Orion 94-48 0.8 Prototype electrode. This electrode contained no internal filling solution; metallic contact was made to the inner membrane surface.
480
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
i
f
'\
I
\
1
ZC. M ii
zi I
0
05
I3
20
1.5
Z2
2.5
30
3.5
Figure 2. Equivalent circuits for solid state membrane electrodes
I
4.0
Mr.
( A ) Lanthanum fluoride membrane ( B ) Silver chloride membrane
Figure 1. Complex impedance plane locus for Beckman Fluoride Electrode Model No. 39600. Z1bulk electrode impedance; Zz impedance of surface film
(C) Silver sulphide membrane 51.
RESULTS Lanthanum Fluoride Membranes. Four types of fluoride electrode were examined. The complex impedance plane locus for electrodes I, 11, and IV showed that the cell was equivalent to a series circuit comprising a resistance, Rs, and two frequency dependent impedances Zl and Zz (Figure 1). In the case of electrode 11, Zz was not well defined and this was attributed to imperfect sealing between the membrane and the electrode body. The precision of measurement was low for electrode IV because the magnitude of the impedance was 100 to 1000 times lower than for the other electrodes. The general shape of the complex impedance locus was similar to that observed for glass electrodes with hydrolyzed surface films (29), therefore, it is not improbable that Zz also represents a surface layer on the membrane of a fluoride electrode. It is apparent from the impedance locus that both ZIand ZZat very low frequencies are equivalent to resistances RMand RF. Transformation of the impedance, after subtracting the series resistance, to the complex admittance plane gave loci making positive intercepts on the real axis for both Z1 and Z Z . At high frequencies, the admittance loci tended toward infinity, but the loci were not the straight vertical lines characteristic of a simple parallel RC circuit. Instead, at low frequencies, the real and imaginary parts of the admittance increased linearly together while at higher frequencies only the imaginary admittance increased. We have suggested previously (29) that these effects arise from nonlinearity in the space charge capacitance of semi-conducting solids. Graphs of log YICand log YZcagainst log w for electrode I had a slope of unity but for electrode I1 has a slightly lower slope of 0.68. Values of the imaginary admittance of Z 1 and Zz at the highest frequencies were used to estimate values of the capacitances in parallel with RF and R M . The proposed equivalent circuit for a lanthanum fluoride membrane electrode is shown in Figure 2A and estimated values for the network components are given in Table I. Silver Chloride Membranes. The complex impedance plane locus of each of the three silver chloride membrane electrodes examined showed that the cell was equivalent to a series circuit comprising a resistance Rs and a frequency dependent impedance Zl (Figure 3). At very low frequencies electrode
MCI zc
\-[:'
32 -
111
?.u
Figure 3. Complex impedance plane locus for Corning Chloride Electrode Model No. 476126
V showed a slight decrease in impedance at constant phase angle with increase in frequency; this was attributed to small leaks between the membrane and the electrode body which under normal potentiometric conditions would not affect the electrode response. It is apparent from Figure 3 that Zl intercepts the real axis at low frequencies, becoming equivalent to a pure resistance. The loci of ZI in the complex admittance plane for each electrode were similar to those observed for lanthanum fluoride membranes. Figure 2B shows an equivalent circuit for a silver chloride membrane cell and Table 11 lists calculated values for the network components. Silver Bromide, Iodide, and Sulfide Membranes. In contrast to the lanthanum fluoride and silver chloride membranes, the complex impedance loci of membranes of silver bromide, iodide, and sulfide showed no tendency to intercept the real axis at very low frequencies (0.005 Hz), as shown in Figure 4. As before, the membrane was equivalent to a series circuit comprising Rs and Z I , a frequency dependent impedance (Figure 2C). ZI decreased to zero at high frequencies. For electrode VIII, the total impedance was almost independent of frequency, while for electrodes IX and XI1 the imaginary part of ZI became frequency independent at low frequencies. For a silver sulfide membrane, XIII, the general behavior of Zl was almost independent of whether the solution contained Ag+ or Sz-ions, although the value of Rs varied as shown in Figure 4. For each electrode, a graph of log Zl us. log w was found to be a straight line with a negative slope of near 0.5; Zl was approximately proportional to w-li2. Table 111lists values of ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
481
SOLUTION
MEMBRANE
I
SOLUTIOY
2
28r
c+RhJ2
20-
A
ZC
csc,
CSC*
RM
RM2
K c* 12;
+.=\
R2
i,r\r\p--
-+ CSCl
1
0
4
B
12
16
20 2,
24
28
32
36
,
-
40
KC,
Figure 4. Complex impedance plane loci for Orion Sulfide Electrode Model 94-16 0 Ag + solution 0 S2-solution Rs, the slope of the log 21us. log w graph and the value of ZI whenw = 1. Mixed Sulfide Membranes. The electrical properties of the two copper ion selective electrodes examined, XIV and XV, showed little dependence on frequency. The measured phase angle for XIV was 2 O over the frequency range 0.05 to 50 Hz, while for electrode XV a maximum phase angle of 7' was observed at -0.6 HZ. The impedance of electrode XIV decreased by about 10% over the measured frequency range while the impedance of electrode XV decreased to half its low frequency value. In contrast, the electrical properties of the lead (XVI) and cadmium(XVI1) eleitrodes were markedly dependent on frequency. The complex impedance plane loci resembled those of the silver sulfide membrane electrodes, showing that the membranes were equivalent to a series resistor Rs and a frequency dependent impedance Zl. As with the silver sulfide electrodes, graphs of log w os. log Zl were straight lines having negative slopes, but the gradient was significantly different from -0.5, being more nearly equal to -0.75. Table IV summarizes results for the mixed crystal membrane electrodes.
