may be compared with a maximum K + to N a + selectivity of about 30:1 for the best available glass electrode. Fur thermore, the valinomycin electrode has an 18000:1 selectivity for K + with re spect to H + ; this means that the elec trode should be usable in strongly acidic media, where cation-sensitive glass electrodes lose their effectiveness. The nonactin electrode, on the other hand, shows an interesting selectivity for N H 4 + over hydrogen ion and the alkali metal ions and may be of con siderable practical value in this con nection. I t is too early to say whether anti biotic electrodes will be of general util ity and give rise to a broad new class of ion electrodes; however, there is no question but that electrodes based upon the synthetic organic analogs of such compounds are worthy of serious in vestigation. Pedersen (18) recently synthesized a whole series of cyclic polyethers, so-called "Crown" com pounds, which bind (19) alkali metal ions selectively. These compounds can be tailor-made to display desired ion binding and transport properties; thus, they should play a major role in the development of new ion-selective elec trodes. Two U. S. manufacturers have recently announced potassium ion-selec tive, liquid-membrane electrodes. A K + to Na+ selectivity of about 5000:1 is claimed for one of these. New directions for ion-selective elec trodes are not limited, of course, to the development of electrodes. Novel and imaginative applications are of equal importance. Electrode development and application mutually stimulate one another, however, so that the present vigorous pace of research in this area assures ion electrodes a major place in modern measurement science.
Literature Cited (1) G. A. Rechnitz, Chem. Eng. News, 43 (25), 146 (1967). (2) G. Eisenman, (Editor) "Glass Elec trodes for Hydrogen and other Cat ions," Marcel Dekker, New York, Ν . Υ., 1966. (3) R. A. Durst, (Editor) U. S. Bureau of Standards Monograph on Ion-Selec tive Electrodes, Government Printing Office, Washington, D . C., 1969.
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(4) G. Eisenman, ANAL. C H E M . , 40, 310
(1968). (5) M. J . Brand and G. A. Rechnitz, ibid., 41, 1185 (1969). (6) F . A. Schultz, A. J . Petersen, C. A. Mask, and R. P . Buck, Science, 162, 267 (1968). (7) G. A. Rechnitz and Τ . Μ . Hseu, ANAL. C H E M . , 41, 111 (1969).
(8) J. W. Ross, paper presented at meet ing of the Electrochemical Society, New York, M a y 1969. (9) T. M. Hseu and G. A. Rechnitz, ANAL. C H E M . , 40, 1054 and 1661 (1968).
(10) G. A. Rechnitz and N . C. Kenny, Anal. Letters, 2,395 (1969). (11) J. W. Ross and M. S. Frant, ANAL. C H E M . , 41, 967 (1969).
(12) J. Kummer and Μ. Ε. Milberg, Chem. Eng. News, 47 (20), 90 (1969). (13) G. G. Guilbault and J. G. Montalvo, J. Am. Chem. Soc, 91, 2164 (1969). (14) G. G. Guilbault and J. G. Montalvo, Anal. Letters, 2, 283 (1969). (15) G. G. Guilbault, R. K. Smith, and J. G. Montalvo, ANAL. C H E M . , 41, 600
(1969). (16) L. A. R. Pioda and W. Simon, Chimia, 23, 72 (1969). (17) W. Simon, paper presented at meet ing of the Electrochemical Society, New York, Ν . Υ., M a y 1969. (18) C J. Pederscn, J. Am. Chem. Soc, 89,7017 (1967). (19) R. M . Izatt, J. H . Rytting, D . P . Nelson, B. L. Haymore, and J. J. Christensen, Science, 164, 443 (1969).
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-L-' is most stimulating and should convince analysts that continued re search and development of ion selective electrodes is a fertile field. What has been accomplished so far is impressive and very useful, but, as he has pointed out, the possibilities are almost unlimit ed. Dr. Rechnitz and his associates continue to contribute heavily to the subject and this discussion combines en thusiasm with extensive experience. It seems quite certain that a host of useful systems can be developed for in-
organic, organic, or biological systems. We are not too happy about the pres ent state of knowledge of the electrical behavior of selective ion electrodes. For example, what is the equivalent cir cuit of such systems? How are poten tial, current, capacitance, and resis tance related and how do they combine to account for the observed behavior? If this query reeks too much of the electrical engineer's "black box," it still seeks to get a practical answer. Knowledge about the attainment of equilibrium at the electrode is unsatis-
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INSTRUMENTATION factory. In practically all cases, no data are given and it is difficult to ana lyze the emf vs. time curves in any pre cise fashion. Dr. Rechnitz has made repeated pleas for more information (data), to which we would add, "always give the final value of the equilibrium potential, even if you have to wait hours or days for the answer." There is the temptation to quote the half-time (fin)—»•£·> the time required for the emf to attain half the final equilibrium value. In the usual analytical tech niques, this is an illusory constant, be cause the measurement, in the early stages, is a fruity mélange of mixing time and electrode equilibration. It is not unusual to encounter in the literature a statement that "the electrode had fast response with a half time of 1 second" and then followed by "the potentials were recorded after an interval of 2.5 minutes." This still gives no indication of the true potential equilibrium or what fraction thereof is attained in 2.5 minutes. There is an empirical approach which affords an accurate prediction of the equilibrium value, obtainable from a few values taken at moderately short times. We speak of this briefly because of its utility, particularly in kinetic studies. Basically, the object is not to delineate the entire emf vs. time curve, but to get an accurate prediction of the equilibrium value. But in simpler terms, "one is interested in where he is going rather than where he has been." For some time, here at Baton Rouge, we have looked into this matter in collaboration with Dr. Doris Miiller and Dr. Philip W. West. Measurements of emf to ±0.1 mV as a function of elapsed time were made with an Orion Ag2S membrane electrode for "jump" increments of Ag+ ion. The data were accurately represented by the equation: Ε = t/(a + bt) where Ε is the increase in potential caused by the sud den increment of Ag+ concentration. The curve is a hyperbola and a plot of t/E vs. t yields an excellent straight line, the slope of which is ο and the in tercept is a. The maximum value of Ε (for t = °° ) is equal to 1/5, the recip rocal slope. As expected, there is a small but progressive deviation from linearity for the lower values of ί in which range the experimental condi tions are ill-defined. The prediction of the equilibrium potential Ee does not involve any dubious extrapolation pro cedure because it is given by the recip rocal slope of a straight line and the de gree of linearity of this line is a reliable criterion of the confidence which can be placed in the calculation of Ee.
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For a given value of constant b, which defines Ee, an infinite number of hyperbolas can be drawn, all converg ing to Ee at t — » , depending upon the choice of constant a. These would range from almost instantaneous re sponse to almost infinitely slow or sluggish response. The ratio of these constants α (intercept) and 6 (slope) is a useful quantity; for example, the half-time, ti/, — alb. The time re quired to attain any desired fraction / of the equilibrium value Ee is simply: t, = [//(l - /)] X a/b. Beyond this, constant α is a reliable response speed measure of the electrode, but more use ful when used in the ratio alb. Some doubt may be expressed that Ee is attained only at infinite time. The apparent stabilization at finite and relatively short times is a function of the sensitivity of the detecting system, and simple "eyeballing" of a recorder trace is not reliable. At very long time intervals after apparent equilibrium had been attained, we could detect in crements in potential of the order of 10-50 μ,ν. We have examined several curves reported in the literature, as far as our patience in disinterring the data permitted, and they were found to yield well to this treatment. The empirical approach to this prob lem is useful because the calculated values agree with the observations with the same precision that the data are known. For want of better informa tion, such results are preferable to plausible theoretical derivations yield ing results in which the agreement be tween calculated and observed is called "encouraging." The hyperbolic relationship is not without significance for an ultimate un derstanding of the time-response phe nomenon. It bears a formal, if not ac cidental, similarity to the Langmuir ad sorption isotherm and is, at least circuitwise, akin to the equivalent re sistance of two resistors in parallel, one of which is changing uniformly with time. In the latter case, it is conceiv able that such an arrangement could be set up as a compensator to turn out an emf value corresponding to the true E0 value over a reasonable period of elapsed time. One might even drive it with an alarm clock. Data supporting these conclusions are being submitted to this Journal. We obtrude these few generalizations upon this commentary merely in the sense that there are other questions re lating to selective ion electrodes worthy of detailed inquiry. They should not detract from the larger design and vista which Dr. Rechnitz has outlined for us.
