936
ANALYTICAL CHEMISTRY, VOL. 50, NO. 7, JUNE 1978
W.J. Wheeler and C. M. Amling in developing the carbon
dependent current recorded in the blank buffer solution. Similar behavior was observed with both ac-treated glassy carbon and carbon film electrodes. Pretreatment appears to renew the electroactive surface and the PRV technique permits separation of the transport-dependent current signal from background current transients. The procedure appears t o be a workable approach to overcoming a surface fouling problem. The oxidation of NADH appears to have a significantly greater over-potential on the carbon film, but the very broad, well-defined plateau indicates considerable analytical promise for the carbon film electrode.
coating process.
LITERATURE CITED L. B. Rogers and S. S. Lord, Jr., Pittsburgh Conference on Analytical Chemistry, March 1952. H. E. Zittel and F. J. Miller, Anal. Chem., 37, 200 (1965). R. E. Panzer and P. J. Elving, J . Electrochem. Soc., 119, 864 (1972). H. A. Laitinen and D. R. Rhodes, J. Electrochem. Soc., 109, 413 (1962). T. Noda, M. Inagaki, and S. Yamada, J . Non-Crystalline Solids. I,285 (1969). G. M. Jenkins, K. Kawarnura, and L. L. Ban, Proc. R . Soc., London(A), 327, 501. (1972). R. N. Adams, "Electrochemistry at Sola Electrodes", Marcel Dekker, New York, N.Y., 1969. A. L. Beilby, W. Brooks, Jr., and G. L. Lawrence, Anal. Chem., 36, 22 (1964). R. E. Panzer and P. J. Elving, Electrochim. Acta, 20, 635 (1975). J. S . Mattson and C. A. Smith, Anal. Chem., 47, 1122 (1975). T. P. DeAngelis, R. W. Hurst, A. M. Yacynych, H. B. Mark, W R. Heineman, and J. S. Mattson. Anal. Chem., 49, 1395 (1977). W. J. Blaedel and R. A. Jenkins, Anal. Chem., 47, 1337 (1975). J. Jordan, Anal. Chem., 27, 1708 (1955). J. Jordan and R. A. Javick, Electrochim. Acta, 6, 23 (1962). W. J. Blaedel and G. W. Schieffer, J . Electroanal. Chem., 80, 259 (1977). J. E. B. Randles, Can. J . Chem., 37, 238, (1959). S . N. Deming and S. L. Morgan, Anal. Chem.. 45, 278A (1973). W. J . Blaedel and R. C. Engstrom, Anal. Chem., 5 0 , 476 (1978). W. J. Blaedel and R. A. Jenkins, Anal. Chem., 46, 1952 (1974).
C0NCLUS I ON S An adherent, shiny, black carbon film can be formed on quartz surfaces simply, inexpensively, and in a variety of shapes. As yet, no attempt has been made to study the structure of the film,but electrochemical experiments indicate that it compares moderately well with glassy carbon as an electrode material. It appears to be a practical tool for electrochemical studies. Well-defined, reproducible current-voltage curves can be obtained by conditioning the surface with an ac-treatment of 1 4 V a t -70 Hz before the current measurement.
RECEILTD for review December 27, 1977. Accepted March 22, 1978. This work has been supported in part by a grant (No. CHE76-15128) from the National Science Foundation.
ACKNOWLEDGMENT The authors appreciate the assistance of glass technicians
Exchange Kinetics at Potassium-Selective Liquid Membrane Electrodes Karl Cammann' Department of Chemistry, University of Chicago, Chicago, Illinois 60637
The ion exchange between a valinomycin-containing organic phase and aqueous solutions was studied. Estimates of apparent exchange current densities with potassium salt solutions as well as with solutions containing various interfering ions demonstrate a high correlation of this exchange current density and the corresponding Nernstian behavior.
This study continues the work described earlier in this journal ( I ) . T h e similarity of ion-transfer reactions a t ionselective membranes with redox reactions a t metal electrodes was demonstrated. In the theoretical treatment of ion-selective electrodes, one among other assumptions is that of a thermodynamic equilibrium a t the interfaces (2-5). Deviations from an ideal Nernstian behavior may then be explained by additional diffusion potentials inside the ion-selective membrane. Another explanation would be a deviation from the equilibrium situation at the interface of interest. The importance of the ion-exchange rate constants, their potential dependences, and the resulting linearized charge transfer resistances has already been pointed out by Buck (6) in the case of solid Present address, University of Munich, Institut fur Mineralogie und Petrographie, Theresienstr. 41, 8 Munchen 2, West Germany. On leave at the University of Chicago during 1976. 0003-2700/78/0350-0936$01.00/0
electrodes and by Gavach (7-9) in the case of liquid ionexchanger electrodes. Buck (10) has also given an experimental criterion for cases where the effect of surface rate shows up. Jaenicke and Haase (11) already determined the cationand anion-exchange current density at silver halide electrodes. They found deviations from the equilibrium a t the interface if the silver salt was solvated by complexing agents even in the case of exchange current densities in the order of 0.1 A/cm2. Tadros and Lyklema (12) demonstrated several aspects of nonequilibrium behavior a t glass electrodes. The determination of exchange current densities of different ions a t the same ion-selective membrane is therefore relevant to understanding whether thermodynamic equilibrium is achieved or not. The exact experimental determination of the exchange current density a t membranes with high bulk resistances however is difficult. According to the previous article ( I ) and Equation 79 of (13), the charge transfer resistance which is assumed t o be very low, is in series to bulk resistance Rhf. Lev et al. (14) determined the sum of the two charge transfer resistances a t a membrane by varying the membrane thickness and thereby 2Mand extrapolation. This study uses the concentration dependency of one charge transfer resistance to extrapolate to a term which is assumed to be constant in Equation 79, a t least over short time intervals. This technique, however, works only if the charge transfer resistance is comparable to the bulk resistance at least a t low concentrations of the potential determining ion. C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO 7, JUNE 1978
EXPERIMENTAL Apparatus. The experimental setup was much the same as that described earlier ( I ) . But, in addition to the galvanostatically controlled current step technique (15), a potentiostaticallg controlled voltage step technique was also applied. The total voltage across the membrane was held below 50 mV. Because of the high bulk resistance of the membranes studied (-1 MQ), nearly the whole of the voltage corresponds to the iR drop. Thus the absolute overvoltages at the two interfaces were held well below 5 mV in order to apply Equation 6 from the last study (I). The electrodes studied were prepared by loading an Orion series 92 liquid membrane electrode with the nonaqueous solutions mentioned in the captions. The supporting membranes used were those delivered with the Orion 92-19-00 potassium electrode. These were washed in petroleum ether and pentane beforehand. Internal filling solution was an aqueous 0.01 M KC1 solution. The reference electrode in the three-electrode setup was an Orion Ag/AgCl double junction electrode with a sleeve diaphragm. Sometimes, a supporting electrolyte of 0.05 M MgC1, or LiCl was used to hold the bulk solution resistance constant. If only single salts were measured, this varying resistance was determined using a second reference electrode instead of the potassium electrode and corrected for. The corrections were small because the current path was held short and the voltage measurement was done with an amplifier having an input impedance of >lo" R. All emf and R, values were taken after 2 min, where a stable emf reading was achieved in most cases. Reagents. Monodistilled water was used. Chemicals were analytical reagent grade. The valinomycin was obtained from Serva (Heidelberg, West Germany), and was used without further purification.
RESULTS Concerning the method of evaluation of the obtained current-respective voltage-time curves, it should again be mentioned that with respect t o the simplified equivalent circuit described in the earlier work ( I ) , all parameters which are not related to the interface studied (phase boundary: ion-selective membrane/solution) were regarded as being constant during the time of measurement. Only in the case of potassium picrate solutions, a linear extrapolation back to the time of measurement was necessary. This treatment assumes that the double layer capacity also remains constant. Calculations of the respective term in Equation 6 in ( 2 ) show t h a t with an extremely high value of C in the order of 10 pF/cm2 (insulator electrodes show typical capacities of 0.01 t o 1 pF/cm2 (16-18)) and the worst case of dilute solutions of M and 2 = 1, an error of only approximately 25%: would be introduced if io lies in the order of 1 0 ~A/cm2. 3 If a high concentration of a supporting electroljTe is used, such a high error is unlikely. In addition, the exchange current density of the respective anion was neglected. A comparison between measurements performed with a high concentration of a non-interfering supporting electrolyte and solutions containing only the measured ion and the same anion showed t h a t both assumptions were justified (exception: picrate). The detailed evaluation procedure was described earlier (see Figure 5 in ( I ) ) . According to Equation 6 of ( I ) , the recorder trace was extrapolated back to t = 0 via a plot vs. t l i 2 in order t o correct for diffusion processes. This results in the total resistance of the circuit including the effect of the electronic equivalent circuit of the inner reference half cell. By varying the concentration of the potential determining ion (here: potassium) in the outer solution, a change in this total resistance was detectable. According to our simplified model, this can be attributed only to a corresponding change of the outer charge transfer resistance which is known to be concentration dependent (13). Starting with dilute potassium salt solutions and increasing the concentration, it was possible t o reach the point where the change in this total resistance was within the experimental error. This lower value was then taken as the sum of all constant remaining parameters of the
937
total circuit. This value was then subtracted from the others found with more dilute solutions of the ion under study in order to gain the charge transfer resistance of the interface of interest. In the case of measurements with interfering ions, this value was redetermined with 0.1 and 1.0 M KC1 solutions after each single R, determination in order t o correct for a slowly changing membrane bulk resistance Rhl. Because the difference between the total resistance in 0.1 M KCl and 1.0 M KC1 was within the experimental error, no data point in the Figures could be obtained in this case. The experimental error was approximately 5% so that only changes larger than 5% of the total resistance could be measured. Because the total resistance was on the order of 1 MR.this corresponds to values of R, = >50 kR, which are obtained in 0.1 M solutions of some interfering ions however. Before going into detail, some general comments have to be made. In applying the theory developed for metal electrodes to ion-selective electrodes ( I , 9, I3), several limitations must be considered. (a) Unlike metal electrodes, the composition of the membrane surface may be altered by the current flow, thus resulting in a change in the chemical potential in that area. (b) Diffusion processes may also occur in the membrane phase, thereby influencing the effective potential difference across the interface which controls kinetic processes. (c) In case of a high ohmic membrane bulk resistance, a corresponding ohmic drop voltage develops which is difficult to separate from the small overvoltage caused by low charge transfer resistances (high exchange current densities). Because of the first two limitations, all results have to be regarded as apparent values. T h e Last limitation results in a n increase in already high measuring errors corresponding with decreasing charge transfer resistances (when measuring in the direction of more concentrated solutions of the potential determining ion, two large values have to be subtracted). Therefore the results can be considered only as estimates. Freshly loaded electrodes were found to be noisy, slow in response, and sub-Nernstian. Electrodes soaked several hours in M KCl solution gave more rapid response and better slopes. The same observation was reported by Boles and Buck (19)in the case of commercial potassium electrodes without information over the exact composition of the organic phase. This study showed that this behavior can be attributed to a too high membrane bulk and charge transfer resistance, e.g., decreases the bulk resistance from -20 MR to -5 MR and the charge transfer resistance for a 1 M KC1 solution from lo4 kR to lo2 kR in the case of a 6 X M valinomycin in 1-decanol organic phase during soaking in M KC1 overnight! In some instances (e.g., measuring high concentrations of interfering ions or solutions containing lipophilic anions, such as picrate), the membrane bulk resistance changes in time intervals long compared to the response time. In the case of a high concentration of potassium picrate, the membrane bulk resistance changed reversibly (e.g. in 3 h from -5 MI2 to -0.2 MR in the case of 2.7 X valinornycin in diphenyl ether) and the supporting membrane yellowed. This uptake of picrate by the membrane phase was also discussed on a quantitative basis earlier (19)but still under the assumption of a thermodynamic equilibrium a t the interface. T h e electrode potential in potassium picrate solutions is very unstable and shows a large sensitikity toward stirring even a t high concentrations. According to Jaenicke and Haase (111, this can be due to some deviation from equilibrium a t the interface. Measurements with potassium iodide and phthalate solutions result in only slightly reduced charge transfer resistances compared to other anions (C1 , Rr , F , NO? ). This
-
-
938
ANALYTICAL CHEMISTRY, VOL. 50, NO. 7, JUNE 1978
MV
-103-3L
l
.
3
p2
1
K% 0
1
A 2
3
p L
5
1
9
K
L
3
2
CONCENTRATION
Figure 1. EMF and log R, vs. log cdiagrams with different concentrations of valinomycin in 1-decanol as liquid membrane. (A) 6 X lo-’ M valinomycin; (6)6 X 10-4 M valinomycin, (C) 6 X 10-3 M valinomycin; KCI solutions of various concentrations
was connected with a reduced slope of 47 to 55 mvldecade compared to a normal 55 to 59 mV/decade. The results are summarized in Figures 1 to 3 and Table I. In these Figures the apparent charge transfer resistances (inversely proportional to the exchange current density, see Equation 4 of ( 1 ) ) are plotted on a logarithmic scale vs. the logarithm of the respective ion concentration in order to extrapolate to the standard charge transfer resistance (1 M solution). This is equivalent to a plot of log io vs. log c which in the case of metal electrodes allows the determination of the charge transfer coefficient p. The straight lines obtained in these diagrams are a strong indication that this treatment, following the model of kinetics at metal electrodes, is justified in a first approximation. This was also found previously by Gavach et al. (9) and Koryta (20) using different methods. The evaluation of nearly 100 different experiments showed t h a t the apparent standard exchange current density of potassium ions a t an ion-selective membrane containing 2.7 X M valinomycin in diphenyl ether lies in the order of 2 mA/cm2. Using unwashed Orion potassium membranes, a five times higher value was found. I t seems that the membrane already contains some valinomycin. T h e above mentioned organic phase was better than the ones of Figure 1 with respect to selectivity. An explanation for this behavior was given by Morf and Simon (21).
DISCUSSION Figure 1 shows a comparison between the emf vs. log c curves and the corresponding log R, vs. log c plots in the case of different concentrations of the electroactive compound (valinomycin) in 1-decanol. The best Nernstian response is obtained with an intermediate concentration. Such a concentration may be optimal in the saturation of the surface of the organic phase, assuming that valinomycin reacts like a surface active compound. But another explanation is also possible. According to Kedem et ai. (22),the millipore filter material used as supporting membrane contains about 10-4mol/L negative fixed charges. Taking into account the formation of a 1:l complex between potassium ions and valinomycin, an equivalent concentration of valinomycin would be sufficient to bring predominately potassium ions into the membrane phase. In the case of a higher valinomycin concentration, however, the membrane phase can extract appreciable amounts of the corresponding ion pair. Since the concentration of the anion in the membrane phase is increased by this process, its exchange current density becomes higher (see also Equations 71 and 7 2 of (13))and can no longer be neglected. By this, the slope of the emf vs. log c curve becomes
1
PION -21 , 0 1 2 CONCENTRATION I
,
,
3
L
PION
5
Figure 2. EMF and log R, vs. log c diagrams of a membrane containing 2.7 X M valinomycin in diphenyl ether; all solutions were prepared with the chloride sans: TMA = tetramethyl ammonium;TAA = tetraaethyl ammonium: H,O values were initial values
1
--@(2-20
2
3
5
L
PK
C 0 N C E N TRATION
Figure 3. EMF and log R, vs. log c diagrams of a membrane containing 2.7 X M valinomycin in diphenyl ether in mixed solutions and in solutions containing strongly interfering ions. (A) KCI, (B) KCI constant 0.1 M NaCI, (C) KCI constant 0.1 M MgCI,, (D) KCI constant 0.1 M NH,CI, (E) potassium picrate
+
+
+
increasingly more sub-Nernstian. In addition, the selectivities obtained with 1-decanol as a solvent were rather poor (e.g. KK.Li 5 0.1; mixed solution method). Therefore all other experiments were performed with the more unpolar solvent, diphenyl ether. Figure 2 shows results obtained with a nonaqueous phase of 2.7 X M valinomycin in diphenyl ether. The selectivity coefficient is related in a complex manner (see below and be aware that the charge transfer resistances are only estimates) to the ratio of the charge transfer resistance of the ion to be measured to the charge transfer resistance of the interfering ion (see Table I). Because of the different slopes of the log R, vs. log c lines of different ions, the concentration dependence of the selectivity coefficient is now understood as is the lack of selectivity when the exchange current density of the ion to be measured falls into the range of the unspecific adsorption and desorption processes. Because of clearance reasons, not all data points are drawn out into a line. All ions listed in Table I start a t M with nearly the same value, which reflects the detection limit of the electrode studied. The data points for pure water are initial values which change quickly to the values of the detection limit. The dissolution of potassium ions out of the membrane phase into the solution seems responsible for this behavior. Figure 3 shows results using mixed solutions containing interfering ions in addition to the ion to be measured. From curves B and C, it follows that sodium and magnesium ions
ANALYTICAL CHEMISTRY, VOL. 50, NO. 7, JUNE 1978
Table I. Estimates of Apparent Standard Exchange Current Densities i o o,’ Coefficients Obtained by Different Methodsb
Exchange Current Ratios
0.1 M solutions I
2.1 x 10-3 4.7 x 10-3
1 3.2
CSCl
5 . 3 x 10-4
0.32
NH,Cl
4 . 2 x 10-5
4 x 10-2
4.2 X 2.6 X
M solutions KK-I
1091/ioqK
10-3
1 2.4 2.5 0.34 0.32 2 x 10-2 1.4 X 10-’C 2 x 10-4 4 x 10-5
lom6
Selectivity
.
Solution KC 1 RbCl
NaCl
i o o A/cm’
i o , I / o , K and
939
7 x
2.1 x
6.6 X lo-‘
1.2 x
2.5 X lo-‘
2.5 x 10-5= 5 . 3 x 10-5 2 x 10-5 4 . 6 x 10-5 1.7 X l o - ’ 6.7 x 10-5 3.1 X
iO,IliO,K
0.6 1 0.5 0.6
KK-I
1 0.5 0.4 0.5 0.4
0.1 0.08
0.5
5x 3 x 10-2
0.4
3.4 2x 3x 2x
0.3
0.2
3x 2x
x
lo-2
10-2
lo-’ 10-2
lo-2
Membrane phase, 2.7 x 10.) M valinomycin in diphenyl ether; geometrical surface, -0.012 cm’. First value, separate solution of the same concentration; second value, separate solution with the same potential; third value, mixed solution method. Constant concentration of the interfering ion, I = 0.1 M. do not interfere seriously. Interestingly, they all result in the same standard charge transfer resistance for the potassium ion. The different slopes are due to the parallel array of charge transfer resistances. I t was found that in the case of less interfering ions, the corresponding R, values could be treated as if they were components of an electronic circuit. This, however, is not the case with curve D (constant background of 0.1 M NH,Cl). There are several reasons for the lower potassium exchange current density. First, the ammonium ions could bind a certain amount of valinomycin at the surface. Second, a mixed potential could be built up raising the actual overvoltage above 10 mV where the linearization of the charge transfer resistance is no longer valid (see p 349 of (13)). T h a t the exchange current density for potassium picrate solutions was one order of magnitude higher than normally found with potassium solutions containing other anions (F-, C1-, Br-, NO3-) can be explained by a corresponding increase in the anion exchange current density. The latter causes according to the model used (1,23,24) a loss of the selectivity for potassium ions. In the mixed potential model, the equilibrium potentials of potassium and picrate ions a t the interface interact with each other, resulting in a mixed potential located between both. The estimated standard exchange current density is, of course, that of the mixed potential. Here again the linearization of R, can fail. This may explain why the value found is higher by a factor of ten rather than by a factor of two. In the case of potassium iodide and phthalate solutions, only negligible higher exchange current densities could be estimated. The electrode still functions as a potassium sensor; however the slope was reduced by about 10%. The reason why less interfering ions do not show the typical dependence of R, from the concentration is because the R, value of the potassium ion detection limit lies in parallel to the charge transfer resistance of the respective ion. The actual values can be much higher. This may also explain why the exchange current density ratio describes the selectivity more correctly a t higher exchange current densities (see Table I) than a t lower densities.
CONCLUSIONS This study and the work of others (1, %11,20) have shown that the kinetic relationships originally developed for redox reactions a t metal electrodes hold also for ion-selective membranes. I t is therefore justified to use all of the infor-
mation we have about metal electrode processes to describe ion-selective electrodes from this point of view also. Normally, ion-selective electrodes give stable readings also in solutions containing only interfering ions. Sometimes they even show a Nernstian behavior in these solutions. The interfering ions must establish a thermodynamic equilibrium a t the interface with an exchange current density many orders higher than the input current of the amplifier. In mixed solutions containing an interfering ion and the ion to be measured, two different equilibrium potentials have to interact with each other as if an external overvoltage is applied to each ion exchange equilibrium. For this the theory predicts a mixed potential located in between both the equilibrium potentials. In this model (25, 26), the location of the mixed potential depends on the thermodynamic parameters (equilibrium potentials) as well as on the kinetic parameters (exchange current densities) according to Equation 11.27 of (27). The establishment of a thermodynamic equilibrium may be prevented for one or both reactions, depending on the course of the interacting current-voltage curves. In such a situation, deviations from an ideal Nernstian behavior are possible in both directions. The occurrence of a super-Nernstian behavior (after taking into account possible variations of the liquid junction potential at the reference electrode) can be a strong indication for a mixed potential. Concerning the selectivity coefficient defined in an extended Nernst equation (28), it becomes obvious that the relationship between the different equilibrium potentials and their exchange current densities is too complex to be described only by a one-parameter equation. An exact treatment would require a knowledge of all current-voltage curves of all parallel electrode reactions involved a t the respective interface. I t is known that the selectivity coefficient depends upon the method of determination (29). The separate solution method will better reflect the situation of a thermodynamic equilibrium. Thus a correlation between the selectivity and thermodynamic parameters can be expected ( 5 ) . The mixed solution method suggested by the IUPAC (30),however, better reflects the real situation of measurements with normal samples which almost always contain more than one ion pair. According to our model, a mixed potential can occur in this case. The result will depend upon the respective course of the current-voltage curves involved a t the interface. T h e dependence of the selectivity on the polarity of the nonaqueous solvent or on the concentration of some
940
ANALYTICAL CHEMISTRY, VOL. 50, NO. 7, JUNE 1 9 7 8
"mediator" (29) in the case of PVC membrane electrodes must be considered as important factors affecting the exchange current ratios of the different ions. This effect is produced by the varying amounts of ions in the membrane phase and/or a change in the effect of the two or more equilibrium potentials upon each other due to varying membrane "resistances on a molecular scale" depending on the permittivity of the solvent used. T h e strong influence upon the response time caused by more interfering ions can be qualitatively explained. In the above suggested model, the response time of an ion-selective electrode is exactly the time needed to establish the steady-state configuration of the mixed potential. Strongly interfering ions disturb the equilibrium potential of the ion to be measured to a greater extent than less interfering ions and therefore draw a higher current through the interface. This may lead t o diffusion controlled processes (square root dependence of the response function) which are slower than the double-layer charging process. T h e decrease of the charge transfer resistance during the conditioning procedure of soaking the electrode in a solution containing the ion to be measured, corresponds to an uptake of this ion into the membrane phase (according to the extraction equilibrium) resulting in a higher exchange current density of that ion. This is the working principle of the coated wire electrodes (31) which all use the same electroactive compound (Aliquat 336 S ) but nevertheless yield different selectivities depending on the preparation step. Kozlowski (32) already successfully applied the mixed potential theory (25,26) used in corrosion research to amalgam electrodes which can be viewed as standing between metal electrodes and ion-selective electrodes. It is therefore justified to describe ion-selective electrodes also from this point of view. In order to be a selective Nernstian sensor, the same criterion as for a good reference half cell should be applied, which is in this case: The current-voltage curve a t the interface of interest should approach a vertical line up to high current densities a t the equilibrium potential of the ion to be measured and flat lines for all other ions.
and for many fruitful discussions. He thanks Heinz Gerischer for his helpful criticisms and suggestions.
ACKNOWLEDGMENT
RECEIVED for review November 1,1977. Accepted March 3,
T h e author is indebted to Stephen Mazur for his kind invitation to perform this work a t the University of Chicago
1978. This work was generously supported by the Deutsche Forschungsgemeinschaft (grant: Ca 69/3).
LITERATURE CITED (1) (2) (3) (4)
(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32)
K. Cammann and G. A. Rechnitz, Anal. Chem., 48, 856 (1976). S.Ciani, G. Eisenman, and G. Szabo, J . Membrane Blol., 1, 1 (1969). T. Teoreli, Discuss. Faraday Soc., 21, 9 (1956). K. H. Meyer and J. F. Sievers, He&. Chim. Acta, 19, 649, 665, 987 (1936). W. E. Morf, D. Ammann, E. Pretsch, and W. Simon, Pure Appl. Chem., 36, 421 (1973). R. P. Buck, Anal. Chem., 40, 1432, 1439 (1968). C. Gavach and F. Henry, J , Nectroanal. Chem., 54, 361 (1974). C. Gavach and B. D'Epenoux, J . Electroanal. Chem., 55, 59 (1974). C. Gavach, B. D'Epenoux, and F. Henry, J . Nectroanal. Chem., 64, 107 (1975). R. P. Buck, Anal. Chim. Acta, 73, 321 (1974). W. Jaenicke and M. Haase, 2. Elektrochem., 63, 521 (1959). T. F. Tadros and J. Lyklema, J . Hectroanai. Chem., 22, 91 (1969). R. P. Buck, Anal. Chem. Crlt. Rev., 5 , 323 (1976). A. A. Lev, V. V. Malev, and V. V. Osipov, in "Membranes", Vol. 2, G. Eisenman, Ed., Dekker, New York, N.Y., 1973. D. Inman, J. 0'. M. Bockris, and E. Blomgren, J . Electroanal. Chem., 2, 506 (1961). K. Bohnenkamp and H. J. Engell, 2 . Elektrochem., 61, 1184 (1957). J. F. Dewaid, Bell Syst. Techn. J . , 39,615 (1960). M. J. D. Brand and G. A. Rechnitz, Anal. Chem., 41, 1185 (1969); 42, 478 (1970). J. H. Boles and R. P. Buck, Anal. Chem., 45, 2057 (1973). J. Koryta, P. Vanqsek, W. Khalii. and M. Brezina, paper presented at the conference on ion-selective electrodes, 5-9 September, Budapest, Hungary, 1977. W. E. Morf and W. Simon, Hung. Sci. Instrum., 41, 1 (1977). 0. Kedem, M. Perry, and R. Bioch, paper presented at the IUPAC symposium on selective ion-sensitive electrodes, 9-12 April, Cardiff, Enaland. 1973. K. b m h a n n , paper presented at the IUPS sateiilte symposium on "Theory and application of ion-selectlve electrodes in physiology and medlclne", 27-29 July, Dortmund, W. Germany, 1977. K. Cammann, paper presented at the conference on ion-selective electrodes, 5-9 September, Budapest, Hungary, 1977. C.Wagner and W. Traud, Z . Nektrochem., 44, 391 (1938). G. Kimball and A. Glassner, J . Chem. Phys., 8, 815 (1940). J. 0'. M. Bockrls and A. K. N. Reddy, "Modern Electrochemistry", Vol. 2, Academic Press, New York, N.Y., 1970. B. P. Nikoisky, M. M. Shultz, N. V. Peschechonowa, A. I.Parfenov, A. A. Belijustln, and V. V. Bobrov, Vestn. Leningrad. Univ., 4, 73 (1963). G. J. Moody and J. D. R. Thomas, "Selective Ion Sensitive Electrodes", Merrow Publishing Co., Watford, England, 1971. Pure Appl. Chem., 48, 129 (1976). H. James, G. Carmack, and H. Freiser, Anal. Chem., 44, 856 (1972). M. T. Kozlowski, T r . Soveshch. Nektrokhlm., 4th, Moscow, October 1956, Academy of Sciences of the USSR, Moscow, 1959, p 704.
