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Anal. Chern. 1985, 57, 1506-1511
Theoretical Interpretation of Transient Signals Obtained with Precipitate-Based Ion-Selective Electrodes in the Presence of Interfering Ions Miklds Gratzl, Ern6 Lindner, and Ern6 Pungor* Institute for General and Analytical Chemistry, Technical University of Budapest, Gelldrt tdr 4, Budapest, 1111 Hungary F
Preclpltate-based Ion-selectlve electrodes respond to sudden changes In the lnterferlng Ion actlvlty with nonmonotonic, overshoot-type transient slgnals, when a certaln amount of prlmary Ion Is also present In the solution and when the respectlve selectlvlty factor Is much less than one. A slmpllfled and more detalled quantilatlve description of these slgnals Is presented In terms of diffusion processes In the adherent solution layer and of adsorptlon/desorptlon equillbrla on the electrode membrane surface. The valldlty of thls descrlptlon Is proved by excellent flttlngs to experlmental signals In cases of (i) lncreaslng and decreasing lnterferlng Ion actlvlty steps, (11) subsequent changes in lnterferlng Ion actlvlty, (111) interfering Ion actlvlty steps at different prlmary Ion actlvlty levels. The selectlvlty factor, the dlffuslon layer thlckness values, and the amount of Ions adsorbed or desorbed provldlng good flttlng were In agreement wlth the experlmental values delermlned by other methods, wlthln the respectlve experlmental and calculatlon errors.
A contribution by Morf (1)has recently appeared in Analytical Chemistry. In this work Morf actually responded to an earlier publication of Lindner et al. (2) in which it was demonstrated, for the first time, that precipitate-based ionselective electrodes respond to sudden changes in interfering ion concentration (activity) by potential overshoot type transient functions (Figure 1). To support his theoretical model Morf (1) fitted the function he has derived to the experimental curves obtained by Hulanicki (3) and Lindner (2) and aimed at a general description of the phenomenon. Hulanicki (3) and Lindner (Z), however, reported on investigations performed under essentially different conditions, of which only the fmt one (3) correspondedto the assumptions the theoretical model of Morf was based on. This becomes evident even when the quality of fittings published by Morf is considered (compare Figure 1 and Figure 2 in ref 1). The aim of the present paper is to clear up the incoherences concerning this phenomenon of both practical and theoretical interests, by giving the quantitative version of our earlier qualitative model. In the literature the attempts at the qualitative and quantitative interpretations of the overshoot type transients (4-14) were related first to glass electrodes (4-8) and later to ion-exchanger based liquid membrane electrodes (9, 11). When interpreting the nonmonotonic transient functions obtained with precipitate based ion-selective electrodes, we believe it would not be correct to use assumptions valid for other systems (i.e., for glass electrodes) and applied to earlier models (i.e., different mobilities of primary and interfering ions in the membrane phase (4,8,14) and layers characterized by different selectivity factors in the membrane (1, 13)) as these assumptions cannot be based on a realistic physical picture in the case of precipitate-based electrodes. Conse-
quently a new model was set up in accordance with the physical properties (2). It is based on the assumption that following the sudden increase in the activity of interfering ions, primary ions are desorbed from the electrode surface in quantities depending on the concentration level of the interfering ions or in the opposite case, Le., when the activity of the interfering ions suddenly decreases, after the interfering ion desorption primary ions are adsorbed in certain quantities on the electrode membrane surface. Due to the desorption or adsorption of primary ions from or at the electrode surface, respectively, ionic activities in the adhering solution layer, which determine the instantaneous values of the electrode potential, temporarily differ from those in the bulk of the sample. The difference in primary ion concentration thus created by the interfering ion activity step initiates diffusion precesses toward equalization. In our opinion, the transient signals in question are the results of the following processes taking place consecutively or simultaneously at the electrode/solution interface (the increase of interfering ion activity is discussed here): (1)diffusion of interfering ions (electrolyte) from the bulk of the solution to the electrode membrane surface; (2) adsorption (chemisorption) of interfering ions; (3) desorption of primary ions; (4)diffusion of excess primary ions into the bulk of the sample solution; (5) change of chemical composition and morphology of the electrode membrane surface, and related diffusion processes. Of the processes described above the first three are assigned to the fast increasing section of transient signals (Figure 1, phase A; 0.1 s range). However, during the decreasing relaxation section (Figure 1,phase B, seconds range) and the slowest, drift type signal range (marked by C in Figure 1,minutes range), the fourth or fifth process prevail over the others, respectively. This model was sharply criticized by Morf (1)who was of the opinion that our model “would imply strongly disparate diffusion rates for the two ionic species” and “it would be in conflict with the zero current condition”. In this work (1)Morf developed his segmented membrane model (13)further in such a way that-making use of Hulanicki’s (3) equation on the apparent selectivity coefficient-he derived an equation describing the time dependence of the apparent coverage factor, which is essentially also a description of the time dependence of the apparent selectivity coefficient. Before making a comparison between the two models discussed above, based on experimental data, and rejecting some of Morf s statements, we consider it useful to present the description we suggest in a more detailed form, and to compare the fit of theoretical equations (derived in the course of this work and reported by Morf (1))to experimental data.
EXPERIMENTAL SECTION In this work the experimental results of our earlier publication (2)were used for the model calculations; i.e., the measuring setup
(15),the electrochemical cell, and the activity steps were identical with those published earlier (2). The data were analyzed with a HP-85 type desk-top computer.
0003-2700/85/0357-1508$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
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c, i x - 0 . t i
I
m
... .I
time
IV L
a
K--
c i IX.0.tl
I
Time Flgure 1. Typical nonmonotonic transient signals following interfering Ion actlvity Increase 01 decrease: (A) overshoot phase (0.1 s range), (B) relaxation phase (second range), (C) slow surface transformation phase (minute range).
THEORETICAL SECTION As already mentioned both in the introduction and in our earlier publication (2),the transient function, following the stepwise change in the activity of interfering ions, consists of three phases of different rates (Figure 1). The quantitative description discussed in the present paper is limited to the first two sections of transient signals (Figure 1,phases A and B). Here we do not intend to deal with the slowest section of the curves (Figure 1, phase C ) where we assume chemical changes to take place a t the electrode membrane surface (2, 16,17). Neither do we want to deal here with cases where the interfering ions form, with the cations or anions of the membrane, precipitates of lower solubility than that of the membrane material itself, because in such cases: (a) the nonmonotinic potential overshoot type transient functions discussed above cannot be observed, but rather the opposite happens; i.e., the electrode potential varies according to a monotonic, asymptotic function (e.g., in the case of AgCl based electrodes in the presence of Br- or I- ions (1,3,18));(b) an irreversible change of the membrane material occurs, and in this respect the phenomenon is to a certain extent analogous to the processes determining the third phase of transient signals (16-18). In our treatment, it is assumed that the sorption and ionexchange processes are much faster than the transport processes, Le., diffusion processes arising after the change in interfering ion activity. Hence, a dynamic description is needed for the diffusion only. The response of precipitate-based ion-selective electrodes in the presence of interfering ions can be described by the Nicolsky equation (19)
E = EiO - RT In (a{ + ~ ~ ~ a : ) (1) F where E is the cell potential, E? is a reference potential characteristic of the cell, and R, T , and F have their usual meanings. The activities measured by the electrode (a[ and a{) refer to the boundary solution layer being in contact with
the electrode membrane surface. According to our treatment it is supposed that this boundary layer is in a thermodynamic equilibrium with the membrane surface. The theoretical selectivity factor Kij is the equilibrium constant of the basic ion exchange equilibrium Me1 3. J- = MeJ + Iwhich can be calculated from the solubility products of the respective precipitates. In this chemical equation Me+ represents the metal cation and I- and J- stand for the primary and interfering anions, respectively. In connection with the theoretical selectivity factor it has to be emphasized that under the experimental conditions discussed here (Kij > 1 case discussed by Morf, where (as it has already been pointed out by several authors (3,20-22)) the apparent selectivity factor may vary between D//D{and Kjjvalues (D{ and Dj’ are the diffusion coefficients of primary and interfering ions, respectively, in the boundary solution layer). The extension of an equation derived for the limiting case of Kij >> 1 to the opposite limiting case of Ki,
