time for the electrode process in the case of potentiometric end point detection. In short, it should be possible to find an optimum compromise between the sensitivity at the null point and the kinetics of the various processes involved. This advantage of coulometric titrations in trace analysis does not seem to be fully recognized. Another advantage of the method in trace work is that it offers an optimal possibility to prevent loss of sought for constituent by adsorption on the walls of the vessel used for the determination. This is so because the ionic strength of the solution is very high corhpared with the concentration of sought for constituent and the adsorption sites may already be occupied. Furthermore, there is always some of the sought for constituent present prior to the addition of a sample. In view of the results presented it seems reasonable that in a fully automated constant current coulometric analyzer system, the number of samples handled per unit time would be limited primarily by the length of time required to change samples. It is possible that coulometric systems could be devised to handle well over a thousand samples in a 24-h period. Considerable simplification in plumbing might also occur since the supporting electrolyte could be premixed, no further reagents in solution are necessary, and a number of determinations can be made sequentially in the same supporting electrolyte. The present instrument is capable of generating a 10-ps current pulse containing pC of charge within an accuracy of 10% relative. The measurement of equiv of material is orders of magnitude beyond the capabilities of present end point detection systems. New approaches are needed. A report of our efforts using fluorescent indicators for coulometric acid-base titrations has been published (31).
(4) J. K. Taylor and S. W. Smith, J. Res. Natl. Bur. Stand., Sect. A, 63, 153 (1959). (5) V. V. Mironenkov and L. Sh. Malkin, Zavod. Lab., 35, 289 (1969). (6) J. A. Pike and G. C. Goode, Anal. Chim. Acta, 39, 1 (1967). (7) J. C. Quayle and F. A. Cooper, Analyst (London), 91, 355 (1966). (8) K. W. Kramer and R. B. Fischer, Anal. Chem., 26,415 (1954). (9) Y. Maekawa and L. Okasaki, Yakugaku Zasshi, 80, 1411 (1960). (10) M. Lindstrom and G. Sundholm. J. Chem. Educ., 49,847 (1972). (11) I. Slavicek and J. Soucek, Chem. Prum., 20, 334 (1970). (12) R. E. Karcher and H. L. Pardue. Clin. Chem. ( Winston-Salem, N.C.), 17, 214 (1971). (13) J. Loiselet and G. Srouji, SOC.Chlm. Bid. Bull., 50, 219 (1968). (14) L. Meites, Anal. Chern., 24, 1057 (1952). (15) J. S. Parsons, W. Seaman, and R. M. Amick. Anal. Chem., 27, 1754 (1955). (16) K. Jeffcoat and M. Akhtar, Analyst(London), 87, 455 (1962). (17) R . G. Clem and W. W. Goldsworthy, Anal. Chem.. 43, 918 (1971). (18) R. G. Clem, lnd. Res., 15, 50 (1973). (19) W. D. Cooke, C. N. Reilley, and N. H. Furman, Anal. Chem., 23, 1662 (1951). (20) Burr-Brown Research Corp., "Operational Amplifiers: Design and Applications", J. G. Graeme, G. E. Tobey, and L. P. Huelsman. Ed., McGrawHill, New York, N.Y., 1971, p 229. (21) Fairchild Semiconductor Corp., Mountain View, Calif., "Integrated Circuit Data Catalog", 1970, pp 5-34. (22) Philbrick Researches, "Application Manual for Computing Amplifiers", Nimrod Press Inc., Boston, 1966, p 82. (23) D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry", Holt, Rinehart and Winston, New York, N.Y., 1963, p 435. Chemistrv". 2nd ed, Interscience. New (24) J. J. Lingane. "Electroanalvtical . York, N.i'., 1958, p 362. (25) W. G. Parks, J. Am. Chem. SOC.,53, 2045 (1931). (26) N. H. Furman, C. N. Reilley. and W. D. Cooke, Anal. Chern., 23, 1665 119511. (27) i. Meites, "Polarographic Techniques", 2nd ed, Interscience, New York, N.Y., 1965, pp 546-556. (28) W. D. Cooke, C. N. Reilley, and N. H. Furman, Anal. Chern., 24, 205 (1952). (29) H. A. Laitinen. "Chemical Analysis", McGraw-Hill, New York. N.Y., 1960, pp 332,368-372. (30) V. T. Athavale, R. G. Dhaneshwar, and D. A. Sarang, Talanta, 14, 1333 (1967). (31) L. E. Jaycox, G. E. Cadwgan, and D. J. Curran, Anal. Left, 6, 1061 (1973).
ACKNOWLEDGMENT The authors wish to thank C. E. Puleston of Fairchild Semiconductor Corp. for supplying the analog switch.
RECEIVEDfor review July 16, 1975. Accepted February 9, 1976. One of the authors (L.B.J.) expresses his appreciation of an NSF Traineeship for part of the work and the authors are grateful for partial support by the Research Council of the University of Massachusetts in the form of a Faculty Research Grant. Presented in part a t the 163rd National Meeting of the American Chemical Society, Boston, Mass., April 9-14, 1972, and at the 7th Materials Research Symposium, NBS. Taken in part from the Ph.D. thesis of L. B. Jaycox.
LITERATURE CITED (1) J. J. Lingane. "Electroanalytical Chemistry", 2nd ed. Interscience. New York, N.Y., 1958. (2) F. Vorstenburg and A. W. Loffler, J. Electroanal. Chem., 1, 422 (1959/ 60). (3) G. E. Gerhardt. H. C. Lawrence, and J. S. Parsons, Anal. Chem., 27, 1752 (1955).
Response Time Curves of on-Selective Electrodes Ern6 Lindner, Klara Tbth, and Ern0 Pungor* lnstitute for General and Analytical Chemistry Technical Ur Iersity, Budapest, Hungary
The response characteristics of different types of ion-selective electrodes were investigated thoroughly for obtaining kinetic information for the electrode response. On the basis of response time data or supposed electrode mechanisms, the ion-selective electrodes have been divided into different groups. For the evaluation of the response time curves of electrodes, at which the rate-determining step is the diffusion of the appropriate ion in the electrode membrane phase (neutral carrier-, and covered surface electrodes), a dlff usion model has been used. The response characteristics of electrodes operating on ion-exchange equilibria (e.g., precipitate based electrodes etc.) have been interpreted with the help of a first-order kinetic equation. In addition to this, a so-called
multielectrode model has been worked out for the general interpretation of the electrode response if the rate determining sequence of the overall potential determining step is covered by a diffusion process through the adhering laminary layer at the electrode surface.
In order to understand the kinetics of ion-selective electrodes, the steps of the overall potential determining process are of fundamental importance. Since the thermodynamic treatment considers only the energetic conditions of the initial and the final states, the intermediate potential determining steps are irrelevant from the thermodynamic point of view. ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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However, for the further development of the field of ion-selective electrodes, it would be necessary to know the sequences of the individual steps of an organic or inorganic compound, resulting in an electrode potential difference, described thermodynamically. I t seems to be obvious that the transient signals providing kinetic information on the electrode processes are used for studying the individual steps. Similarly, it would also be obvious if the irreversible thermodynamic treatments were employed for studying the charge transport a t the boundary layer and in the bulk of the electrode membrane. Within the transient signals, the response time of the electrodes is of theoretical and practical importance. Since the 1960’s,several authors have investigated first the response time of glass electrodes and, later on, that of other ion-selective electrodes (1-6). By applying different mathematical models for the explanation of the response characteristics of the electrodes, the final results were almost the same; the electrode response has been approximated with one exponential equation. Our investigations carried out with precipitate-based ionselective electrodes date back also into the late 1960’s (7). The same measuring set-up (8) has been used since, which was developed for studying the fast potential response of the potentiometric electrodes in order to eliminate the difficulties of obtaining results for the electrode characteristics (2). From our studies it can be concluded that the potential vs. time curves of the electrodes caused by a fast concentration jump can be described with any first-order kinetic equations, such as ion-dehydration, chemisorption, or complex formation reaction. However, a t solving the differential equation of the first-order reactions, the integration must be done between the activity of the so-called conditioning solution (aio)and the newly introduced solution (ai’)as limits to be able to describe the differing behavior of the response time curves of electrodes depending on the direction of the activity change in the sample solution. Accordingly, the activity change in the boundary layer of the electrodes can be given as follows:
where ai‘ is the activity in the boundary-face of the solution a t time t > 0, ai0 is the activity in the bulk of the solution a t the time t < 0, and ai is the activity in the bulk of the solution causing the transient signal a t the time t 3 0. This equation, formally the same as that derived by Buck on the basis of current-voltage-time curves of glass electrodes (5, 6), or by Markovic and Osborn (12), and others (9-11) employing a diffusion model based on the assumption that the ion-transport through the adhering laminary layer (Prandtl layer) is the slowest electrode process. This is because the nature of the rate-determining individual steps affects only the constants of the mathematical final equation. However, it is quite difficult to distinguish between the assumed rate-determining steps on the basis of the constants relevant to the electrode process-obtained by curve fitting-since their real values are not found in the literature. For electrodes with ionic transport either in their swollen boundary layer or in the bulk of the electrode membrane, a diffusion kinetic model is also valid which was described by Morf, Lindner, and Simon (9-11) for the neutral carrier electrodes by the consideration of the parameters of the membrane phase and the experimental conditions (Le. K , 6 . . .). In this case, the activity of the potential-determining ion in the boundary phase of the solution is given by the following equation: 1072
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
where 7 is the time constant ( I 1, Equation 20). By substituting ai’ values of Equations 1 and 2 into the Nernst equation, one can get the time dependence of the electrode potential for electrodes operating on either electron-, and ion-exchange equilibria, or neutral carrier principle, respectively:
where E is the emf of the cell, Eo is the standard potential of the electrode assembly, and S is the Nernstian slope of the response function; E vs. log ar’ (59.16 mV/z, a t 25 “C). S must be replaced with S,ff if Equations 3 and 4 are used for describing the response time curves of electrodes with nonNernstian response. S,ffis the slope of the electrode calibration graph. The aim of our present study was to select experimentally an appropriate model for describing the response time curves. Accordingly, the response time experiments have been carried out with different types of electrodes under various conditions (temperature, flow-rate, surface area, etc.). To survey the wide range of electrodes studied, the following classification of the electrodes are given: *l.Electrodes operating on electron-exchange reaction, e.g. siIver rod electrode. 2. Ion-selective electrodes operating on chemisorption (precipitate exchange reaction). 2.1. Silver and iodide ion-selective electrodes prepared from silver iodide crystals (Radelkis type OP-I-7111C). 2.2. Silver and iodide ion-selective electrodes made of a 1:l mixture of silver iodide and silver sulfide crystals. 2.3. Silver and iodide ion-selective electrodes prepared by incorporating silver iodide crystals into a silicone rubber supporting material. 2.4. Lanthanum fluoride single crystal fluoride ion-selective electrode (Orion type 94-09). 3. Neutral carrier electrodes. 3.1. Valinomycin-based potassium ion-selective membrane electrodes in silicone rubber. 3.2. Valinomycin-based potassium ion selective liquid membrane electrode. In addition to this, in the case of the electrodes belonging to group 2.3, the effect of the electrode’s surface phenomena on the response time curves has also been investigated. The potential-time responses of the electrodes were tested under various surface conditions: without previous pretreatment; with polished electrode surface; with covered surface electrodes, using silicone rubber, cellophane or dialysis membrane; with electrodes, on the surface of which a diffusion layer is formed by soaking the iodide selective electrode in relatively concentrated cyanide solutions. EXPERIMENTAL
Measuring Cell. The cell Hg,Cl,, satd KC1 .Hg, li reference electrode
1 membrane 1
sample solution activity ai
internal filling solution, AgC1, Ag ion-selective electrode
ts
*-.
50ms EMF (mV)
Figure 1. Schematic diagram of the measuring set-up showing the profile of the flow at the electrode surface (1) Indicator electrode, (2) reference electrode, (3) jet, (4) differential amplifier (Keithley, Type 604), (5) storage oscilloscope (Philips PM 3251) or an X-Y recorder (Bryans 26000A 3)
Figure 2. Effect of flow rate on the responsetime curves of an iodide selective electrode (Electrode membrane 1:1 AgpS Agl; 4 = 12 mm)
-+
was used throughout. The reference electrode was manufactured by Radiometer (Type K401). The contact between the external reference electrode and the indicator one was assured with a thin solution layer (Figure 1). The indicator electrodes belonging to groups 1,2.2,2.3,3.1, (23) and 3.2 ( 2 4 ) were prepared in our Laboratory according to the procedures given in the literature. All response time measurements were carried out with the measuring set up (Figure 1)described in our earlier paper (8). Reagents. All chemicals used were of analytical grade. Apparatus. An impedance converter, Keithley Differential Amplifier, model 604; a storage oscilloscope, Philips model P M 3251; and an X-Y recorder, Bryans model 26000 A3 were used.
D*
1/2
(16)
for laminar flow parallel to the electrode surface; 6 % 10.1 urn-0.9. u17/30. D* 1/3 ( 1 7 )
.
for turbulent flow parallel to the electrode surface;
(5) (6)
- a
(7) for the so-called wall-jet electrode, where u , is the flow velocity of the solution flowing parallel to the electrode surface, in the direction of the coordinate 1, at great (infinite) distance from the surface; Y is the kinematic viscosity; D* is the diffusion coefficient in the laminar adhering layer; R e is the Reynolds number R e = d, USTR/”( 1 8 ) ;d, is the diameter of the jet (see Figure 1);USTR is the flow-rate (see Figure 1).
-
U S T R = 6.4 u , *~d,/(x
Precipitate-Based Ion-Selective Electrodes and the Silver Rod Electrode. In agreement with our earlier studies and literature data ( 1 1 , 1 4 , 1 5 ) ,it was found that in a certain range of flow, the response time of the electrodes decreases on increasing the rate of flow. As examples, characteristic curves are shown (Figure 2, u and b). If the ion-transport through the adhering Prandtl layer is the slowest process, then the time-constant of Equation 1 depends to a great extent on the thickness of the laminary diffusion layer (11, 1 2 ) . In order to find out the rate-determining role of the diffusion through the laminary Prandtl layer, calculations were made on the basis of the relationships used in voltammetry for the determination of the thickness of the Prandtl layer. Our measuring device, however, did not correspond completely to any of those employed for deriving Equations 5 , 6 , and 7, and, therefore, only qualitative conclusions could be drawn. In the literature the following relationships are found for the calculation of the thickness of the adhering layer: 1112. ~ ~ - 1 1 2y1/6. .
-
---
-
RESULTS AND DISCUSSION
6= 3.
---
M KI. a, = M KI. - v1 = 117 ml/min, - vp = 54 ml/min. (a) ai0 = (6) a? = lo-* M KI, ai = M KI, - -vl = 30 ml/min, - .v2 = 54 ml/min, v3= 117 I/min, -vn = 138 ml/min
+ 1 ) (18)
(8)
where u x is the flow-rate perpendicular to the surface and x is the distance between the jet and the electrode. Under the measuring conditions of our experimental device (Figure 1) ( 1 9 ) , the layer thickness increases outward from the center of the eletrode surface and the newly introduced solution (ai)has to pass through an evenly increasing diffusion thus, different points of the electrode surface are layer (aio); a t the same time instances in contact with solutions of different concentrations [ui,( t , 1 ) ] . The dependence of layer thickness on parameter 1 can also be seen from Equations 5 , 6, and 7. From these, it follows a t the same time, that at different points of the electrode surface, different response time values exist, only the average of which can be measured. Considering this, it seemed interesting to study the effect of the surface area on the response time values. Results are shown in Figure 3, from which it can be seen that the larger the relative measuring surface area (measuring surface of the electrode is related to the jet area at the orifice), the longer response time values were measured in accordance with the theoretical expectation. Consequently, if the elimination of the effect caused by the nonhomogeneous layer thickness is required-which means that the real response time value is intended to be measured-then point-like electrode surface and solution jet placed as near to the electrode surface as possible, must be assured (Equation 8). ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
1073
Table I. Corrected Initial Slope Response Time Curves
(m,ff)
Recorded in Ag+ solutions, m V / m s Temperature, T
tlmtl
Figure 3. Effect of electrode surface area on the response time curve of a silver selective electrode (Electrode membrane 1:l Ag2S Agl) v = 117 mllmin, ai0 = M AgN03, ai = lo-' M AgN03. - I#J = 12 mm,
+
-
b=6mm
20m
t lrnsl
Figure 4. Comparison between the silver ion response of various types of silver sensitive ion-selective electrodes
-
M AgN03,4 = 6 mm. silver v = 117 ml/min, af' = M AgN03, ai = rod electrode, silver ion-selective electrode (1:lAgl -I-Ag2S), silicone rubber based silver selective electrode. - Silver ion-selectiveelectrode (Ag2S).- - - - - Silver ion-selective electrode (Agl)
t[msl
Flgure 5. Response time curves of different types of iodide ion-selective electrodes
-
v = 117 ml/min, af' = M KI, ai = M KI, I#J = 6 mm; Iodide selective electrode made of a 1:l mixture of Agl Ag2S. - - Agl based iodide selective electrode. - Iodide ion-selective electrode made by incorporating Agl into silicone rubber
+
-
In the course of the experiments carried out with electrodes of relatively large surface area ( 4 = 12 mm), especially in the case of lower flow-velocities (u, = 60 ml/min); it was found that well separable sections appeared on the response time curves (e.g., Figures 2, b and 3). An explanation for this can be given by considering that under such conditions the concentration profile a t the electrode surface is inhomogeneous as a result of uneven layer thickness and remixing. At high flow-rates (u, 3 100 ml/min), the response time curves of electrodes of different surface areas hardly differ from each other. The delaying effect of the surface area is not so significant, which is in accordance with Equation 6 and 7 (6 10.1). The dynamic behavior of the potential-time response of silver iodide-based electrodes has been investigated in both silver and iodide ions (Figures 4 and 5 ) .
-
1074
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
Electrode t y p e
2 5 OC
6 5 "C
Ag (metal) Ag,S & I + Ag,S AgI &I (SR) Average meff values of different types of electrodes
5.5
7.5
4.8 5.9 3.7 5.5 5.1
8.3 9.4 8.4
of the Recorded i n Isolutions, rnV/rns Temperature, T 2 5 OC
6 5 "C
4.1
7.0
3.7 3.3 3.7
8.1 7.8 7.6
As can be seen from the results presented in Figures 4 and 5, there is no significant difference between the response time curves and values [e.g., 95% of the equilibrium potential (20)] and they are in the order of a few tenths of milliseconds. However, the problems owing t o the measuring technique resulted in a relatively high standard deviation of the extremely short response time values measured. In addition to this, it was found that if the role of the diffusion of the potential-determining ion through the Prandtl layer cannot be eliminated, then a relatively small change in the layer thickness results in a relatively large difference in the response time values. If the response of the silver iodide-based ion-selective electrodes to both silver and iodide ions is compared, then it can be seen clearly that the initial slope of the response time curves to silver ions is greater (Figure 4), than that to iodide ions (Figure 5 and Table I). This phenomenon cannot be explained by a diffusion model considering the relative ionmobilities of silver and iodide ions in the adhering layer ( U A ~ + = 50.2 cm2/R; U p = 62.7 cm2/fl (22)). This is because the experimental conditions were chosen in such a way, that the liquid film adhering to the electrode surface was kept as thin as possible, so the role of the diffusion process through the Prandtl layer was minimized. We have evaluated the initial slope of the response time curves, because, according to our opinion, this can be used only for obtaining information on the kinetics of the electrode response, For comparing the initial slope of different response time curves of electrodes with Nernstian-, or non-Nernstian response, or that of univalent or divalent ion-selective electrodes, a so-called meffinitial slope value has been introduced
where m is the initial slope of the appropriate response time curve and S and Seffhave the meaning given earlier. If the end of the response time curves is studied, then it must not be forgotten, that a t this part of the response time curves, the diffusion of potential-determining ion through the adhering layer will become the most important step in the electrode process. The extrapolation (14) of the response time values recorded a t given flow velocities to the "infinite" flow velocity (considering an infinitely thin diffusion layer), does not necessarily give the real response time of the electrode; this gives only the capability of the appropriate measuring set-up. To investigate the effect of the temperature, response time curves have been recorded in solutions of different temperatures. As examples, some results are shown in Figure 6 and
~
;MF[mVI,
I
,
1
,
-L-
I
'm 4 -I---
+
I
I
:'/-----
I I
I
2 -
Table I. Unfortunately, these data did not give significant information on the process governing the electrode response, because almost all parameters, which may influence the response characteristics of an electrode (e.g., v, D*, k, S,Seff, etc.) are altered by temperature. Consequently, the increase in the slope of the initial part of the response time curves cannot be rendered unambiguously to only one parameter; but it was useful to learn that the temperature influences first of all the initial slope. General Interpretation of the Results: The So-called Multielectrode Model. In the course of our investigations, it was stated that in spite of the emphasized influence of various parameters; e.g. measuring conditions, the surface area, and the pretreatment of the electrodes, on the response time curves, the response characteristics of the precipitatebased solid-state membrane electrodes may be treated in the same way. For the general interpretation of the response time curves, one has to consider that after introducing a concentration jump a t the electrode surface, the electrode a t a given time instant is in contact with solutions of different activities. This can be interpreted by assuming the electrode as a multielectrode system formed by dividing the electrode surface into small parts, resulting in many elementary electrodes. (According to our definition, the elementary electrode is a point-like electrode, on the surface of which a homogeneous concentration distribution exists.) Consequently, the resultant of the potentials of the elementary electrodes, the so-called mixed potential, is measured, and the response time curves show the time dependence of the so-called mixed potentials of the multielectrode system. So, to understand the response characteristics of these electrodes, the time-dependence of the resultant mixed potential values must be studied. For this, replacement models have been worked out (Figures 7 and 8). In Figure 7 , a measuring set-up is shown for modeling the multielectrode system. The surface of the indicator electrode (4 = 12 mm) is divided into equal parts, which are separately connected with the help of a salt bridge to the same reference electrode. This arrangement allowed us to make a model experiment for measuring mixed potential values of an indicator electrode of large surface area if solutions of different activities are placed in each half cell. For modeling another way is shown in Figure 8. In this case, the emf values of electrode couples immersed in solutions of different concentrations are measured separately and after joining the individual cells in parallel. Both models approximate a dynamic system with a static model and, therefore, it holds information only at a given point of the response time curve. Consequently, the model is suitable for obtaining qualitative information on the mixed potential values established as a result of nonhomogeneous concentration distribution on electrodes with relatively large surface areas.
Figure 7. Measuring set-up for modeling the nonhomogeneous concentration distribution at the boundary of an electrode of relatively large surface area. (1) Ion-selective membrane, (2) Outer reference electrode, (3) Inner reference electrode, (4) Salt-bridge, (5)Wall for separating the different sections of the electrode surface
1E-Figure 8. Measuring set-up for modeling the nonhomogeneous concentration distribution at the boundary of an electrode of relatively large surface area 11.2.
= an indicator electrode. R1.2
= reference electrode
For evaluating the experimental results a physical model was used (Figure 9). As a zero-order approximation, the calculation was carried out by assuming Zi to be constant, which is identical to that of Ri >> ( R , R s ) ,and it leads to the following result:
+
n
5 Fi
i=l
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
1075
Table 11. Comparison between the Activity Values Calculated from the Mixed Potential Values and with Equation 10b ~~~
Figure 9. Equivalent circuit of the multielectrode system if the various impedances are considered
Surfaces :overed with solutiIns of diffe *ent activiies
iypothetic acti fit ies calcula t ec rom potential ralues measurec
Z '-i
Em ( t )is the so-called mixed potential, €is the emf value of a cell, Z,is the impedance of a cell, Ri is the internal resistance of a cell, Rc is the charge transfer resistance, R s is the resistance of the solution in the cell, ( t ) means the time dependence of the parameters indicated, and R is the number of the cell studied
1.33
1.22
1.67
1.65
1.67
1.33
2.33
2.01
2.50
2.24
2. 25
2.06
2.75
2.41
or
5 Fi(-log - log a = 5 Fi i=l
ai)
(lob)
i=l
where 2; is the sum of R i , R,, and R, (See Figure 9); Fi is the area of the electrode surface in one of the individual cells; ai is the activity of the solution in one of the individual cells; a is a hypothetic activity value which would result in the mixed potential value (E,(t)) if the electrode surface was covered with a solution having this activity value. However, on the basis of the results (Table 11), the assumption that Z i is constant, had to be neglected because, as the measured data show, the hypothetic activity values calculated from the measured potential values differ from those calculated with Equation lob, namely, it is always closer to the activity of the more concentrated one. Consequently, if the charge transfer (R,), and the solution resistance (R,) cannot be neglected in comparison with the internal resistance ( R i ) of the cell, then the resistance values varying with solution concentrations must be taken into consideration to obtain the so-called mixed potential values established on coupling electrode pairs in parallel and immersed in solutions of different concentrations. To prove the validity of the physical model shown in Figure 9, two cells were connected in parallel in an appropriate set-up (Figure 8). In one of the cells a silver rod electrode, whiIe in another one a silver-sensitive ion-selective electrode were placed. If the two cells were connected in parallel, then the mixed potential value was always found closer to the potential of the silver rod electrode, which means the solution concentrations (their resistance values) do not play so important a part. This is in accordance with the model shown in Figure 9 where the Rimed
@ lo-'
lo-'
gion / I
Table 111. Comparison between Measured and Calculated Activity Data for Multielectrode Systems Solution concn No, of M/1 cells AgNO,
Data o b t a i n e d after coupling cells 1 a n d 2 in parallel Electrode couples
EMF,
mV
E,mV
-log Qcalcd
-log Qmeasd
373 314
371
3.5
3.03
314 373
340
3.5
3.56
1
Agmet-SCE
The corresponding experimental values are shown in Table 111. On the basis of the experimental results, it can be stated that the physical model gives a good approximation of the hypothetical multielectrode system obtained by considering a nonhomogeneous solution distribution a t an electrode with a relatively large surface area. For the further development of the model, the polarization of the electrodes as a result of the current flowing through the parallelly coupled cells of different emf values, must also be taken into consideration. The mixed potential values may also be interpreted on the basis of current-voltage polarization curves since the slope of the polarization curves depends on concentrations also. N e u t r a l C a r r i e r Electrodes. (Modeling experimentally the ionic diffusion through the membrane phase). In the course of our study, the response characteristics of the vali-
2
AgI,,,b.-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
I-
-
