Electrode differential potentiometric

Figure 2.3 Differential potentiometric electrode system for titrations. After each addition of titrant and reading, the solution in the dropper is exchanged with the bulk solution.

Potentiometric titration curves normally are represented by a plot of the indicator-electrode potential as a function of volume of titrant, as indicated in Fig. 4.2. However, there are some advantages if the data are plotted as the first derivative of the indicator potential with respect to volume of titrant (or even as the second derivative). Such titration curves also are indicated in Figure 4.2, and illustrate that a more definite endpoint indication is provided by both differential curves than by the integrated form of the titration curve. Furthermore, titration by repetitive constant-volume increments allows the endpoint to be determined without a plot of the titration curve the endpoint coincides with the condition when the differential potentiometric response per volume increment is a maximum. Likewise, the endpoint can be determined by using the second derivative the latter has distinct advantages in that there is some indication of the approach of the endpoint as the second derivative approaches a positive maximum just prior to the equivalence point before passing through zero. Such a second-derivative response is particularly attractive for automated titration systems that stop at the equivalence point. 

Differential potentiometric titration — means the experimental recording of the first derivative of potential over volume of added titrant of a -> potentiometric titration curve. This can be achieved with a -> retarded electrode as developed by - Maclnnes. In a broader sense this term also covers the mathematical derivation of potentiometric titration curves. 

Potentiometric titration — A - titration method based on the measurement of the potential of a suitable -> indicator electrode as a function of - titrant volume. Usually the -> cell voltage or a - p-function associated with the concentration of the - analyte is plotted as a function of the volume of -> titrant added [i]. See also -> differential potentiometric titration, and - retarded electrode. 

Nicholson proposed a differential potentiometric tltrator involving two indicator electrodes for the automatic control of processes in industrial plants [35]. As can be seen from Fig. 7.20, the sample and reagent streams are split and led to two half-cells via capillary tubes adjusted to provide slightly different titrated fractions. The potential difference (AE) between the two indicator electrodes Is transmitted to a control and detection system (D) which regulates the flow of titrant in an automatic fashion by means of valve V, thereby maintaining the preselected AE between the two ends of the cell. The speed of titrant addition, reflected by the flow meter (M), is a measure of the sample composition. An evaluation of the instrument carried out by the titration of dichromate with iron(II) revealed that the conditions to be used must be carefully selected. Thus, stable electrode responses are only obtained in the zone where Fe(II) prevails, and not in that where dichromate prevails over the former as the process determining the potential obtained in such a zone is irreversible. This method therefore has limited application in the control of slow reactions. 

Recently, a novel two electrode differential potentiometric cell for enzyme electrode systems has been described that provides enhanced substrate sensitivities compared to conventional cells composed of a single enzyme electrode and reference (Cha, G.S. Meyerhoff, M.E. Electroanalysis, in press). The cell employs two working enzyme electrodes, one which responds to the analyte in the positive potential direction via detection of cations, and one which responds to the same analyte but in a negative direction owing to anion detection. A similar approach can be applied in the design of new two electrode gas-selective sensors with enhanced gas sensitivity. 

Macinnes invented the use of a retarded electrode for differential potentiometric titrations [vii]. Macinnes also wrote an influential textbook [viii]. 

A Standard one-electrode configuration for potentiometric measuranents consists of the potentio-metric electrode connected to a voltage follower and the reference electrode connected to electrical ground. To improve noise level and drift, a differential potentiometric mode can be employed in a three-electrode configuration consisting of the SECM potentiometric probe and two independent external references. For example, the potential difference between the potentiometric probe and a large inert Pt electrode is compared to the potential difference between a large reference electrode of the same nature as the potentiometric probe and the Pt electrode The Pt wire... 

A continuous potentiometric determination of sulphate in a differential flow system160 consisted of a flow cell with two Pb2+-selective electrodes in series. All solutions contained 75% of methanol and were adjusted to pH 4 a standard solution of Pb(II) passes the first sensor and, after being mixed with the sulphate sample stream, yielding a PbS04 precipitate in addition to excess of Pb(II), it passes the second sensor from the potential difference between the sensors the sulphate content of the sample can then be derived. 

New polymer membrane-based ISEs for nitrate and carbonate exhibit detection limits and selectivities that may be applicable for ocean measurements. In addition, a number of these ISEs can be used as internal transducers for the design of useful potentiometric gas sensors. For example, dissolved C02 can be detected potentiometrically by using either a glass membrane electrode or a polymer-based carbonate ISE, in conjunction with an appropriate reference electrode, behind an outer gas permeable membrane. Novel differential pC02 sensors based on two polymer membrane-type pH sensors have also been developed recently. 

Because each enzyme sensor has its own unique response, it is necessary to construct the calibration curve for each sensor separately. In other words, there is no general theoretical response relationship, in the same sense as the Nernst equation is. As always, the best way to reduce interferences is to use two sensors and measure them differentially. Thus, it is possible to prepare two identical enzyme sensors and either omit or deactivate the enzyme in one of them. This sensor then acts as a reference. If the calibration curve is constructed by plotting the difference of the two outputs as the function of concentration of the substrate, the effects of variations in the composition of the sample as well as temperature and light variations can be substantially reduced. Examples of potentiometric enzyme electrodes are listed in Table 6.5. 

SPMBE = screen-printed microband electrode, ASV = anodic stripping voltammetry, HCMV = human cytomegalovirus, PGE = pencil-graphite electrode, DPV = differential pulse voltammetry, SPEs = screen-printed electrodes, PSA = potentiometric stripping analysis, M-GECE = magnetic graphite-epoxy composite electrode. 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

Differential Titration.—The object of potentiometric titration is to determine the point at which AEjAv is a maximum, and this can be achieved directly, without the use of graphical methods, by utilizing the principle of differential titration. If to two identical solutions, e.g., of sodium chloride, are added v and v + 0.1 cc. respectively of titrant, e.g., silver nitrate, the difference of potential between similar electrodes placed in the two solutions gives a direct measure of AEjAVy where Av is 0.1 cc., at the point in the titration corresponding to the addition of t + 0.05 cc. of silver nitrate. The e.m.f. of the cell made up of these two electrodes will thus be a maximum at the end-point. 

By differentiating the titration curve twice and then equating the second derivative to zero, it can be shown that for a symmetrical titration curve ( i = the point of maximum slope theoretically coincides with the equivalence point. This conclusion is the basis for potentiometric end-point detection methods. On the other hand, if 2> the titration curve is asymmetrical in the vicinity of the equivalence point, and there is a small titration error if the end point is taken as the inflection point In practice the error from this source is usually insignificant compared with such errors as inexact stoichiometry, slowness of titration reaction, and slowness of attainment of electrode equilibria. 

Figure 4-5 Differential planar PCO2 potentiometric sensor design, based on two identical polymeric membrane pH electrodes, but with different internal reference electrolyte solutions. Both pH sensing membranes are prepared with selective ionophore.

Wachsman, E.D. (2003) Selective potentiometric detection of NOx ky differential electrode equilibria. Proceedings of the Electrochemical Society, 2000-32 Solid-State Ionic Devices II Ceramic Sensors, The Electrochemical Society, Penrrington, New Jersey, pp. 215-21. 

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