ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978 (18) H. Stephen and T. Stephen, Ed., "Solubilities of Inorganic and Organic ComDounds", Macmillan Company, New York, N.Y., Vol. 1, Part 1, 1963, Table No. 1080, p 368. (19) W. J. Youden in "Treatise on Analytical chemistry", I.M. Kolthoff and P. J. Elving, Ed., Interscience, New York, N.Y., VOI. I, Part I, 1959, p 60. (20) H. S.Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions", Reinhold Publlshlng Corp., New York, N.Y., 3rd ed., 1958, p 531.
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(21) M. Randall and C. F. Failey, Chem. Rev., 4, 271 (1927).
RECEIVED for review April 17, 1978. Accepted July 10, 1978. This paper was presented in part a t The Pittsburgh Conference On Chemistry and Spectroscopy~ Cleveland, Ohio, 1978.
Response Time Studies on Neutral Carrier Ion-Selective Membrane Electrodes Erno Lindner, Kl5ra T6th, Erno Pungor," Werner E. Mort,' and Wilhelm Simon' Institute for General and Analytical Chemistry, Technical University Budapest, Hungary
In order to study the parameters affecting the dynamic characteristics of neutral carrier ion-selective electrodes, the response time curves of valinomycin-based potassium electrodes with different membrane compositions were recorded. The effect of membrane matrix, incorporated ion-exchange sites, and carrier concentration has been investigated thoroughly. The experimental results have been compared with theoretical models.
One of the most rapidly developing areas of the application of ion-selective electrodes is their use in streaming solutions (1-7). In such continuous or semicontinuous measurements, the response time of the electrodes must be considered as one of the most important characteristics (8-25). In spite of the importance of response time parameters, not much research has been devoted to the comprehensive critical evaluation of the response time curves of nonglass ion-selective electrodes (12, 13, 17, 18, 23, 25). This may be due to the complexity of the equilibration processes involved and, on the other hand, to the difficulties associated with the experimental study of corresponding theoretical models (see below). In this paper, we report on the dynamic response behavior of neutral carrier based membrane electrodes. The effect of the following parameters will be discussed in detail: the membrane matrix, the incorporated ion-exchange sites, the carrier concentration in the ion-selective membrane, and the anions present in the sample solution.
GENERAL CONSIDERATIONS I t was pointed out earlier (12, 23, 18,23)that response time curves are generally composed of two or more sections, due to the operation of different rate-determining mechanisms. However, these sections usually do not appear on the complete response time curve because of an insufficient resolution. Indeed, after a step change in the sample concentration, the electrode potential approaches 90% of the final value within 10 to 100 ms whereas the final steady-state is attained relatively slowly (Figure la). In order to check theoretical models by curve fitting methods, either the first section of 'Permanent address, Swiss Federal Institute of Technology, Department of Organic Chemistry, Universitatstrasse 16, 8006 Zurich, Switzerland.
the observed response time curve has to be recorded with a high resolution in respect to the time (Figure l b ) or the final asymptotical section with a high resolution in respect t o the potential (Figure l a , lower curve). If the initial portion of a response time curve is t o be recorded without distortions, an ideal step-change in the sample concentration as well as electronic equipment of very small time constant is required. However, it should be taken into account that even if a very fast concentration change is assured a t the electrode surface, different points of the electrode surface may still be in contact with solutions of different concentrations, especially in the case of macroelectrodes. Thus, the sensor is to be considered as a multielectrode system and the mixed potential so developed may also distort the response time curve (18). For recording the second, final section of the response time curve, usually amounting to only a few millivolts, a sensitive potential measurement is required. In this region, noise, drift, and the variation of the liquid junction potential may cause serious problems. In an earlier theoretical study ( 17) we classified ion-selective electrodes into two groups, according to their dynamic behavior: (1) Ion-exchanger electrodes (Ion-selective electrodes with constant membrane composition: glass, solid and liquid ion-exchanger based electrodes). (2) Neutral carrier electrodes. The response time curves of electrodes belonging to group 1 can generally be described in a given concentration range by an exponential type equation as follows:
7'
= a2/2D'
(2)
This has been interpreted: (a) in terms of a slow surface exchange rate (manifesting itself as a surface resistance (18) or (b) in term of transport through a high resistance surface film or inhomogeneous surface layer (17). Both effects combine with the double-layer capacitance to give a time constant and a decay of potential which involves t'/* at short times and becomes an exponential a t long times. These phenomena have been shown and discussed first by Buck (8-13). Whereas the dynamic response of neutral carrier electrodes is approximated by square-root type function (Equation 3),
0003-2700/78/0350-1627$01.00/0 0 1978 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
Table I. Steady-State Response Characteristics of Potassium Ion-Selective Electrodes sloDe of the calibration graph recorded in solumembrane composition tions, mV code for the lower detection matrix s, 7% R-,% DBP, 7% electrodes KCl KSCN limit, -log a m h PVC 2.2 70.2 K- 1 53.1 45.0 6.5 PVC 2.4 0.66 70.5 K- 2 56.1 52.7 6.1 PVC 0.28 61.8 K- 3 52.2 44.6 6.4 PVC 0.30 0.09 67.9 K-4 55.6 50.0 6.4 SR
4.16
-
-
K-SR
56.1
56.1
6.4
upper detection limit in KSCN solutions, -log Qmax 2.2 1.8 2.2 1.8 < 1.0
a, =lOa:iz=21
_ _ _ _ _ _ __ _ - - - -
Equl 0 0
- - - - - - - ._Equ3
2 7'
LT
67 TIME
27
47
6r
Figure 2. Theoretical response time curves of uni-, and divalent ion-selective electrodes. (---) Calculated with equation 3. (-) Calculated with equation 1. t,,, = the time required to attain 90% of the final potential value (€-). fE,-e = the time required to attain the final potential value to within f e
Flgure 1. Response time curves of valinomycin-based potassium ion-selective membrane electrodes marked K-2 in Table I. aio = M KCI. a,= lo-* M KCI. (a) Upper curve: x = 1 s/div; y = 10 mV/div. Lower curve: x = 1 s/div; y = 1 mV/div. (b) Curves are recorded at increasing and decreasing concentration jumps. x = 10 ms/div; y = 10 mV/div
because the rate of response is definitely controlled by transport processes within the membrane ( I 7):
E,=Em+slog[
l-(l-r)j] +1
(3)
T
(4) where E, = electrode potential measured at the time t after the sample activity change; E , = final potential, corresponding to the activity value ai;S = slope of the electrode response function; a?,ai = activity of the primary ion in the bulk of sample solution at t < 0 and t 2 0, respectively; D = mean diffusion coefficient in the membrane phase (17);D' = mean diffusion coefficient in the adhering aqueous layer (17);K = partition coefficient between the aqueous and the membrane phase (17);and 6 = thickness of the aqueous adhering layer. The corresponding theoretical response time curves of
electrodes of group 1 and 2 are shown schematically in Figure 2. In addition to the above, other mathematical expressions have been published ( 2 0 , 2 1 , 2 3 ) which sometimes may yield a better fit to experimental results than Equations 1 and 3 do. Since their time parameters are usually empirical ones, however, they do not provide any information on the electrode response mechanism. For reviews, see ( 1 2 , 13, 2 3 - 2 5 ) . As shown in Figure 2, the response rate of an ion-selective electrode can equally well be characterized by t50,tgO,or tg9 values, if a mathematical model describing the response time curve is given. Thus, the response time values determined according to diverse definitions can easily be converted into each other. At the same time, the IUPAC recommendation for the response time of an electrode (26) turns out to be not very fortunate-in spite of its practical usefulness-since it results in different response time values for univalent and divalent ion-selective electrodes even if the time constant of the mathematical equation describing the electrode response is the same (tE-e(r=l) > tE-e(z=2) in Figure 2 ) . In an earlier study of electrodes belonging to the first group, we used the initial slope of the response time curve for characterizing the electrode behavior (18). The aim was to obtain additional kinetic information. It was shown experimentally that at relatively high sample flow rates, the initial slopes of the potential vs. time characteristics are not determined exclusively by the diffusion processes across the adhering solution film. This simple method permitted a comparison of response time curves of different electrode types (responsive to uni- and divalent ions), even if the concentration changes are different, and the slope of the electrode calibration curve is not Nernstian (18).
EXPERIMENTAL In the course of the present work, the response characteristics
ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
L
1629
I
0
LO0
200
600
Tirnehs)
Figure 4. Response time curves of PVC-(K-1) and SR-(K-SR) based potassium ion-selective carrier electrodes (see Table I). ai0 = M KCI. a, = lo-‘ M KCI
Figure 3. Schematic diagram of the measuring setup showing the profile of the flow at the electrode surface. (1) Indicator electrode. (2) Reference electrode. (3) Jet. (4) Differential amplifier (Kiethley, Type 604). (5) Storage oscilloscope (Philips, PM 3251) or an XY recorder (Bryans 26000 A 3)
of neutral carrier electrodes with different membrane compositions were investigated. Valinomycin-based potassium ion-selective electrodes were prepared with PVC and SR (silicon rubber) matrices; the carrier concentration varied between 0.25 and 4.5 wt %. As membrane solvent dibutyl phthalate was used in PVC membranes. Into some of the PVC membranes an additional amount of tetraphenylborate was incorporated (27). The electrode membranes thus prepared were mounted into a Philips IS-560 electrode body (active membrane surface 0.126 cm2) and tested electrochemically. The calibration curves were obtained by the conventional method as well as by the continuous dilution method (28) in KC1 and KSCN solutions. The slopes of the calibration curves, S,, the lower detection limit, u-, and also the upper detection limit amaxin the case of KSCN solutions are given in Table I. The response time curves were recorded using the measuring setup constructed earlier in our laboratories (Figure 3) (18)which allows study of both the initial and asymptotic sections of the response time curve. The ionic strength of the solutions was adjusted to 0.1 M with sodium chloride. The measuring conditions were as follows: u, i= 300 cm/s; d N = 0.1 cm, x = 0.5 cm (explanation of symbols is given in Figure 3).
The response time curves were evaluated in two different ways: (1)The initial slope (mrnessd)was determined and was normalized using the following equation (18):
(5) (2) The time constant, 7 ,of Equation 3 giving the best fit of the second section of the response time curve was evaluated using the slope of the electrode calibration graph, Smeasd, and the initial and final potential values, Eo and E,.
RESULTS AND DISCUSSION Effect of the Membrane Matrix on the Response Characteristics of Valinomycin Based K+-Selective Electrodes. Since the K+-selective electrode was introduced (29),great efforts have been made by different research groups t o improve the characteristics of this electrode (30, 31). Different membrane matrices have been tested of which silicone rubber provides the advantage that lipophilic anions do not interfere with the electrode response (32,33) (Table 1)*
The dynamic response characteristics of PVC and SRsupported potassium electrodes were found to be different (Figure 4). The initial slope of the response time curve of silicone rubber valinomycin-based electrodes (at t = 0) is only one fifth of that obtained for PVC electrodes and one tenth
N , 0
1-11
4
coo
0
800
Time l m s )
Figure 5. Calculated and measured response time curves of a SR-based potassium ion-selective electrode. a,” = lov3M KCI. ai = lo-’ M KCI. (-) Values measured. (000)Values calculated with Equation 1 (7’ = 225 ms)
-
*< -1 _.
porous or swollen silicone layer
- _ - -bulk ~ - of the
- u n s t i r r d boundary layer h
-
~-
-
-
membrcne
