ANALYST, JANUARY 1993, VOL. 118 41 Glass pH Electrodes With Improved Temperature Characteristics Part 2.* Systems With Conventional Inner Reference Electrodes Derek Midgleyt National Power pic, Technology and Environmental Centre, Kelvin Avenue, Leatherhead, Surrey, UK KT22 7SE Glass electrodes with internal filling solutions containing zwitterionic buffers are shown to have standard potentials that vary linearly with temperature over a wide range (at [east 5-50 "C). This reduces the errors of temperature compensation compared with the proprietary electrodes currently available. A judicious choice of buffer and inner reference element yields an electrode with almost the ideal characteristics of isopotential pH (=7) and zero-point pH (=7), which enable it to be used with all pH meters.Other electrodes could readily be used with modern microprocessor-based meters. In other aspects of their performance (slope factor, hysteresis, response time) the new electrodes are at least as good as commercial sensors. Keywords: pH; glass electrode; temperature compensation; isopotential; zwitterionic buffer In industrial and environmental analysis, where monitoring may be required over extended periods of time and where control of sample temperature may be impractical, tempera- ture compensation is an important factor. This has long been true in potentiometry,lJ and problems with commercial glass pH and reference electrodes have been identified.3-5 Seven requirements for ideal temperature compensation have been enumerated,h the outstanding problem being for a pH cell that shows a truly linear variation with temperature, so that effective compensation can be applied over a wider tempera- ture range than at present.An inner reference system consisting of a metal-metal oxide electrode enabled this requirement to be met substantially,h but the use of the resulting electrode would have been impractical with most pH meters, which require the isopotential pH (at which the e.m.f. is invariant with temperature) and zero-point pH (at which the e.m.f. is 0 mV) to coincide at pH 7. This paper describes the use of internal filling solutions that show a linear variation of pH with temperature while allowing all other parts of the pH cell to be conventional.7 Theory The derivation of the following eqns., (1)-(6), has been presented in a review of the effect of temperature on pH measurements .3 The e.m.f. of a potentiometric cell for measuring pH is given by a form of the Nernst equation: E = Eocell - kpH (1) where k is the slope factor theoretically equal to RTln(lO)/F, R being the gas constant, T the absolute temperature, and F the Faraday constant.EOcell is the standard potential of the cell, but is only quasi-thermodynamic as it includes a number of factors controlled by the experimental conditions, notably the concentrations of the inner and external reference electro- lytes, and assumes that liquid-junction potentials are constant. The e.m.f. can be represented in a way that allows for convenient temperature compensation by pH meters: E = E, - k(pH - pH,,,) (2) where E, contains all the temperature-independent com- ponents of EOccll, and pH,,, all the temperature-dependent * For Part 1.see rcf. 6. -1 Present address: Hillcroft Research, 41 St Mary's Road, Leatherhead, Surrey, UK KT22 8HB. ones; pHiso is the isopotential pH at which the e.m.f. is, ideally, independent of temperature. It follows that 6 E('ce11/6 T 1 pHiS,6k/6 T (3) Most practical pH cells contain a glass electrode with an Ag-AgCI or, less commonly, an Hg-HgC1 inner reference element; the inner filling solution therefore contains a chloride salt as well as a pH buffer. Reference half-cells contain the same reference elements in concentrated KCI solutions. A detailed analysis of such cells3 shows that +-- 6EO k6logac1 [ 6 T 6 T AEo + EL k pH,,, = pH') - 6AEV6T + 6E,/bT + kbpH'/bT bk/6 T + - ilogac., ( 5 ) where i = 0 or 1 for isothermal and non-isothermal cells, respectively.pH0 = pH' + AEo + EJ + log (U&'(-I) k where EO' and Eo are the standard potential of the internal and external reference electrodes, respectively, a'c, and acl are the activities of CI- inside the glass and reference electrodes, respectively, and pH' is the pH of the solution inside the glass electrode. E, is the liquid-junction potential, AEO = EO' -Eo, and pH0 is the pH at which E = 0 mV (at 25 "C). Non-linearity of the temperature response mainly arises from the term k6pH'lGT in eqn. (4) and this in turn depends on 6pK/6Tfor the buffer component inside the electrode. The values of 6pK/6T required for isothermal and non-isothermal combinations of Ag-AgCI and calomel reference electrodes to yield the desired pH,,, = pH0 = 7.00 can be calculated,3 and Table 1 shows the requirements for external reference electrodes filled with 3 mol dm-3 KCI.The properties of most inorganic and carboxylic acid buffers are such that 6pH/6T is neither zero nor constant. The zwitterionic 'biological' buffers developed by Good and co-workerss-10 contain one or more amino groups, and studies11312 on three of these indicate excellent constancy of 6pK/6T for these groups, which control the pH in the desired buffer range (6-8). Other members of this group have been studied less extensively, but for most of them 6pK/6T lies in42 ANALYST, JANUARY 1993, VOL. 118 Table 1 Characteristics required of solutions inside glass electrodes to yield pH,,, = pH0 = 7.0.(Calibration at 25 "C versus reference electrodes containing 3 mol dm-3 KCI solution) Reference element Buffer. Glass Reference 6p Kl6 T electrode half-cell pH' - log a',-, (isothermal) AgCl AgCl 6.77 0 AgCl Hg2C12 7.54 3.5 x 10-3 HgzC12 Hg2C12 6.77 0 Hg2C12 AgCl 5.99 -3.5 x 10-3 Buffer, 6p Kl6 T (non- isothermal) -2.7 X lo-' -5.3 x 10-3 -8.8 x 10-3 -6.2 X 1 W 3 the range -0.01 to -0.02. Comparison of these data with the results in Table 1 shows that an isothermal cell with the desired characteristics is unattainable with these buffers and the usual reference electrodes (a difference of 0.0033 in 6pK/6T is equivalent to 1 in pHis,). With a non-isothermal cell having calomel inner and external electrodes, the desired value is closely approached by PTPESS (-0.0085).A number of buffers have 6pK/6T = -0.0011, and two with a convenient pH range were chosen for investigation in non-isothermal cells with an external calomel electrode. The values of 6pK/6T required are not strongly influenced by the concentration of chloride in the reference electrode.3 Experimental Apparatus Potentials were measured with a digital pH meter reading to 0.1 mV and were simultaneously displayed on a chart recorder. Electrodes were fixed in B14 ground-glass sockets in the lids of water-jacketed glass cells connected to a C-100 thermo-circulator and a Model 1000 cooler (Techne, Cam- bridge, UK). Reference Electrode A modified Kent 1352 calomel electrode (ABB Kent-Taylor, Stonehouse, Gloucestershire, UK) with a remote ceramic frit junction was used.The main body of the electrode was fitted with a water jacket connected to a Techne C-100 thermo- circulator at 25 "C. The filling solution of the electrode was 3 rnol dm-3 KCI. Experimental Glass Electrodes Bodies from Kent 1070-1 standard glass electrodes were filled with various buffer solutions and fitted with appropriate reference electrodes (see below) driven through soft silicone- rubber bungs fitted into the open end of the glass body. Connection to the exposed ends of the reference electrodes was made by means of a screened cable fitted with a crocodile clip. This arrangement was suitable for experimental pur- poses, enabling solutions and reference electrodes to be changed easily. The signals were surprisingly free of noise.Inner Reference Electrodes Silver-silver chloride electrodes Irradiated polyolefin tubing (Radiospares 399-899, Corby , Northamptonshire, UK) was heat-shrunk onto 1 mm diameter silver wire, leaving about 1 cm exposed at each end. The wire was then driven through a silicone-rubber bung. One end was cleaned in aqueous ammonia, de-greased with acetone and etched in nitric acid; it was then anodized in 0.01 mol dm-3 HCI at 0.01 mA cm-2 for 18 h. Calomel electrodes Irradiated polyolefin tubing (Radiospares 399-899) was heat- shrunk onto 1 mm diameter platinum wire, leaving a 1 cm overlap at one end and 1 cm of wire exposed at the other. The wire was then driven through a silicone-rubber bung and clamped vertically with the overlapping tubing uppermost. A small drop of mercury was injected from a syringe with a fine stainless-steel needle.Electrolytic calomel (BDH, Poole, Dorset, UK) was applied to the top of the mercury, and the tube was plugged with cotton wool soaked in the appropriate glass-electrode filling solution. The mercury and calomel stayed in place when the electrode was turned the right way up and contact with the platinum wire was maintained. Electrode Filling Solutions All materials were obtained from BDH; NaOH and KCl were AnalaR grade. Solutions were prepared in de-ionized water. MES solutions. These were prepared to contain 0.05 rnol dm-3 2-morpholinoethanesulfonic acid (MES) , 0.025 rnol dm-3 NaOH and 0.453 rnol dm-3 KCI. The observed and calculated pH of this solution was 6.10 at 25 "C. ADA solutions. These contained 0.05 rnol dm-3 acet- amidoiminodiacetic acid (ADA), 0.075 mol dm-3 NaOH and 0.140 rnol dm-3 KCI.The pH observed at 25 "C was 6.59 compared with 6.57 calculated. PIPES solutions. These contained 0.05 rnol dm-3 pipera- zine-N, N'-bis(ethanesu1fonic acid) (PIPES), 0.075 rnol dm-3 NaOH and either 0.226 rnol dm-3 KCl (for Ag-AgCI inner reference electrodes) or 1.16 rnol dm-3 KCI (for calomel electrodes). The pH at 25 "C was 6.73 compared with 6.76 calculated. Commercial Glass Electrodes Orion 91-01 (Cambridge, MA, USA) Corning 3111015 (Corning, NY, USA) and Orion 81-02 electrodes were included in the tests as before.6The first two were used versus the same external remote reference electrode as the experimental electrodes, and the last was a combination electrode of the 'Ross' type with Pt-12-I- reference elements.Reagents National Institute of Standards and Technology (NIST) buffers were prepared from BDH AnalaR chemicals: 0.05 rnol kg-1 potassium hydrogen phthalate (pH 4.005 at 25 "C) and 0.025 rnol kg-1 each of potassium dihydrogen phosphate and disodium hydrogen phosphate (pH 6.865 at 25 "C). Procedure As the temperature of the cell was varied, the e.m.f. values were monitored on a chart recorder, and the steady values at each temperature were noted. The steps in temperature was usually 10 "C and both increasing and decreasing trends were followed. The electrodes were first calibrated at 25 "C in pH 4 and 6.86 buffers. Results The results for seven experimental electrodes are shown in Table 2. Results for three commercial electrodes6 are included for comparison.Slope Factor The slope factors for all the electrodes were slightly sub- Nernstian, but quite acceptable.5.13 The temperature cycles did not cause the slope factors to change with time. The standard deviation for the PIPES-calomel electrode was muchANALYST, JANUARY 1993, VOL. 118 43 P C C C Table 2 Results for experimental and commercial pH electrodes Mean slopc factor SD" El) pH (calc.) Mean EOpH (obs.) SD Mean pH,,,, (obs.) SD pH,,, (talc.) ADA/ AgC1-Ag 58.85 0.29(7) 7.0 7.2 0 . 00( 9) 5.5 5.9 0.24( 9) MES/ AgCI-Ag 58.80 0.28(3) 7.0 7.0 5.3 5.8 0.13(4) 0.05( 3 ) PIPES/ AgCI-Ag 58.89 0.4(2) 7.0 7.2 6.3 5.0 0.1(2) 0.1(2) ADA/ Hg2C12 59.08 0.17(2) 7.8 8.0 7.3 7.2 0.46(3) 0. O( 2) MES/ Hg2Cl2 59.051- 58.77 0.19(3) 0.21(2) 7.87 7.0 7.81- 7.1 0.0(4) 0.0(3) 7.11- 6.4 7.51- 6.5 0.15(5) 0.2(3) PIPES/ 58.49 0.07( 9) 7.0 7.3 0.03( 8) 7.4 6.8 0.28(9) Hg2C12 Corning/ AgCl 58.77 0.33(6) 6.98 - 0.03( 7) - 7.9 0.20(8) Ross/ Pt-12-1- 58.31 0.17(5) 7.0 6.8 0.06(5) 7.0 6.6 0.20(5) Orion/ AgCl 58.92 0.20( 3) 0.05 (3) - 6.13 - 6.3 0.98(4) 1 .000 0.999 - - 1.006 - 1.005 1 .001 - 1 .004 (6klb7') (obs.) (6kl67') (theor.) SD 0.005(3) 0.004(2) - - 4 1 ) - -(1) 0.006(2) - -(I) * SD = standard deviation (numbcr of results in parentheses).t With a chloride concentration appropriate for the Ag-AgC1 electrode. I I - C A A iomin Time - Fig. 1 Response to gradual temperature changes. A, PIPES- Hg2C12, B Corning and C ADA-AgCl smaller than those of the others. In a few instances the slope factors were checked at 45 and 9.5 "C, and the experimental ratios of the slope factors were found to be close to the theoretical values.The variations of slope factor were not a function of time, at least over periods of 3 months (MES- calomel) or 6 months (ADA-AgCl). These results indicate that the slope factors were unlikely to be a major cause of uncertainty in the assessment of temperature effects. Zero-point pM Zero-point pH could be predicted fairly accurately by means of eqn. (6), considering the assumptions made about activity coefficients in the moderately complicated and concentrated buffer solutions, the constancy of liquid-junction potentials and the absence of asymmetry potentials. Further empirical adjustment of pHO to the desired value of 7, by changing the chloride concentration, should not be difficult.For instance, the ADA-calomel and the first MES-calomel electrodes had fillings for Ag-AgC1 reference electrodes and so had higher pHO values than desirable. The second MES-calomel elec- trode shows that adjustment was quite straightforward. I n general, the values of pH0 were very reproducible, even after several temperature cycles, and changed by less than 0.1 over a period of up to 6 months (e.g., the ADA-AgCI electrode). Temperature Response The variation of the slope factor with temperature has already been shown to agree with the theoretical value. Time course of e.m.f, change with temperature Figs. 1 and 2 show how the e.m.f. values of a selection of electrodes change in response to gradual and sharp changes in 250c I 50 "C D Time - I I & '10 min' I I Time - Fig.2 (a) Response to sharp changes in temperature. B, Corning; C, ADA-AgCI; and D, MES-Hg2CI2. ( h ) PIPES-Hg2C12 temperature, respectively. When the temperature changed gradually, there was little practical difference between the rates of response of the various electrodes; the experimental electrode with a calomel inner reference was slightly slower to respond than that with the Ag-AgC1 reference, but the commercial electrode was no better. With sharp changes in temperature, the more rapid response of the Ag-AgC1 references was more clearly evident, but electrodes with calomel inner elements came to equilibrium as quickly as the commercial electrode, which was one of the best in previous tests.4 It is noteworthy that the e.m.f. changes for the experimental electrodes were monotonic, without the over- shoot observed for some commercial combination electrodes .5 The experimental electrodes, therefore, are at least equal to most currently available commercial electrodes in this aspect of performance.Hysteresis Electrodes were calibrated at 25 "C and then cycled between solutions maintained at 25 and 49 "C. The changes from the initial e.m.f. in phthalate buffer at 25 "C are shown in Table 3. The changes show no pattern and are generally less than 1 mV (0.017 pH). (The scatter of points around 25 "C in Fig. 5 is another example of the randomness associated with measure- ments at varying temperatures.) The experimental electrodes, including those with calomel elements, were no worse than the44 ANALYST, JANUARY 1993, VOL.118 Table 3 Thermal hysteresis of clectrodes in phthalatc buffer Change in e.m.f.*/mV Electrode 1st cycle-1 2nd cycle? ADA/AgCI MES/Hg?Cl? PIPES/Hg?Cl? Corning Orion 91 -0 1 -0.2 +0.5 + 1 .o +0.3 +0.3 -0.2 -0.9 -0.4 +0.7 +1.1 +0.1 * With respect to initial reading at 25 "C on first cycle. 1 One cycle involves a change from 25 to 49 "C and back again. TPC 0 10 20 30 40 50 440 - 430 - > E I' a 420 - Y + W 410 - 400 - 390 . I 1 I I I I 55 57 59 61 63 Slope factor/mV pH-' Fig. 3 Determination of pH,,, for experimental electrodes with Ag-AgCI inner rcference clemcnts. Filling solutions: A, ADA; B. MES; and C. PIPES commercial designs and were better than some commercial combination electrodes previously tested,s Variation of EO with temperature From eqn.(2), it follows that a plot of E + kpH versus k is (ideally) linear with a slope equal to pH,,,, which is related to 6E/6T by eqn. (3). Plots for a variety of electrodes are shown in Figs. 3 and 4, and the pH,,, values are listed in Table 2. It has been shown that the dependence of the slope factor on temperature is ideal and it is, therefore, permissible to plot slope factor versus temperature if desired, as shown on the upper horizontal axes. The slope is then (2.3R/F)pHI,, = 0. 198pH,,,. Figs. 3 and 4 show that the experimental electrodes with Ag-AgC1 reference elements displayed excellent linearity for 6EBT and that those with calomel elements were little worse. Similar plots for proprietary electrodes4,6 were considerably more curved.Table 2 shows that the experimental electrodes with Ag-AgC1 reference elements had lower than ideal values of pH,,,, whereas those with calomel elements approached the target value of 7 quite closely, and at least as closely as the commercial electrodes. The calculated values of pH,,, were obtained from eqn. ( 5 ) with the observed value of pH0 (thereby correcting for asymmetry potential, liquid-junction potential and inaccurac- ies in activity coefficients). With MES and ADA buffers the agreement between observed and calculated values is very good, but PIPES afforded lower values than expected. As 500 490 480 470 > 460 E 9 a 450 + Y 440 W 430 420 41 0 400 390 TPC 0 10 20 30 40 50 I I 1 I I 55 57 59 61 63 65 Slope factor/mV pH-1 Fig.4 Dctermination of pH,,, for expcrimental electodes with calomel inner reference clcmcnts. Filling solutions: A, ADA; B, MES; and C, PIPES there appears to be nothing significantly wrong with the electrodes in the other examples, it could be that bpH'/6T for PIPES is in error (0.3 in pHiSo corresponds to 0.001 in 6pH'/6T). The observed and calculated pHiSO values would agree if 6pH'/6T = -0.013 or -0.011 for AgCl and calomel inner reference electrodes, respectively, compared with -0.0085 in the literature.8 Errors caused by adopting a fixed pHis(, value Many pH meters lack an adjustment for isopotential and operate at a fixed value of pHibo = 7 (k0.5). The error caused by using an electrode with a different pHiso is T - T (7) where T, is the temperature at which the electrode was calibrated and T is the temperature of measurement.Fig. 5 shows the error for three electrodes when used with a meter set at pH,,, = 7.00. Data from two to four runs with each electrode are included. The solid lines show the errors predicted by eqn. (7). The experimental points show very similar trends to those predicted, but are subject to random and, in some instances, systematic error. The starting tem- perature was always 25 "C, but these data are not shown; the points at 25 "C are for a return to that temperature. The deviations from the predicted line could arise from: ( i ) non-linearity of the variation of EO with temperature; (ii) drift of the standard potential; (iii) experimental errors in the slope and standard potential; ( i v ) changes in room temperature affecting the electrodes, which cannot be in perfect thermal equilibrium with the solution; and ( v ) errors in temperature measurement.Tt can be assumed that effect ( v ) was small, because the thermometers had been checked against a standard. Experimentally, effect (iv) would be included in the drift (ii). The experimental points were obtained with two different pH meters, which exhibited no bias between them. IfANALYST, JANUARY 1993, VOL. 118 4s 0.03 0 I d -0.03 0.02 0 -0.03 0.08 0.04 0: -0.04 -0.08 5 15 25 35 45 T/”C Fig. 5 Error caused by assuming pH,,, = 7 for calibration at 25 “C. B, PIPESXalomel electrode with pH,,,, = 6.8; A, ADA-Ag-AgCl electrode with pH,,, = 5.9; C, Ross clcctrode with pH,,, = 6.6; solid lines are calculated from cqn.(7). Open symbols for decreasing temperatures, closed symbols for increasing temperatures the meters had been set to the mean observed pHiso for each electrode, the errors would not have exceeded 0.01 pH. Discussion Glass pH electrodes having standard potentials with linear temperature characteristics can be prepared by using ‘bio- logical’ (aminosulfonic acid or iminocarboxylic acid) buffers to control the pH of the inner filling solution. This confers linear temperature characteristics on the whole pH cell when conventional inner and external reference electrodes are used. The linearity arises from the constancy of 6pK/6T (and, hence, bpHlb7’) for these buffers. The desired zero-point pH (7.0) can easily be obtained by adjustment of the pH and CI- concentration of the filling solution , for both Ag-AgCI and calomel reference elements.the best approximation to an isopotential pH of 7.0 is obtained for PIPES buffer with a calomel inner reference element and a remote calomel external reference electrode. Calomel ele- ments are not generally favoured for varying temperatures, because of hysteresis and slow response, but the experimental glass electrodes with calomel elements were no worse in these respects than commercial electrodes with Ag-AgCI elements. The temperature coefficients of pK for the buffers of this sort, reported so far, are too large for other permutations of Ag-AgC1 and calomel elements to approach the ideal characteristics; e.g., to use an Ag-AgC1 inner element and a remote calomel reference electrode requires a buffer with 6pK/6T of approximately -0.006, compared with the reported ranges-12 of -0.0085 to -0.027.The linearity of the temperature characteristics iq better than has been observed for commercial pH electrodes44 and for experimental electrodes with Hg-HgO inner reference elements.h The pH0 = pH,,, = 7 condition has been achieved before14 by use of amine buffers inside glass electrodes. As the buffers also contained carboxylic, phosphoric or phenylphosp- honic acids, linearity could have been compromised, although not as much as with conventional electrodes. Other improve- ments in temperature characteristics have been achieved by careful matching of inner and external reference electrodes as to geometry and thermal ~apacity~ls-17 but this does not compensate for non-linear pH changes in the inner reference solution and does not make pH cells independent of temperat- ure, as is sometimes implied.The ‘ideal’ characteristics are set by limitations of pH meters with fixed settings for temperature compensation. Meters with microprocessors can often cope with isopotential and zero-point pH values that differ from each other and from the standard value of 7.0. However, optimal use of such meters probably requires an experienced operator. The literature value8 for the temperature coefficient of PIPES buffer appears to be in error and requires further investigation. No such large discrepancies were observed for ADA or MES buffers and the reported value for PIPES is considerably lower than those reported for all the other ‘biological’ buffers. 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Method5 for the Examination of Waters and Associated Materials, The Determinution of p H in Low Ionic Strengtlz Water5 1988, HM Stationery Office, London, 198% p. 14. Simon, W.. and Wcgmann, D., U.S. Pat., 3445363, 1969. Ross, J . W., U . S. Par., 4495 050, 19x5. Buhler, H., and Galster, H., Ger. Put., DE 3405401, 1985. Torrance, K., Analyst, 1984, 109, 1555. NorE-Rcf. 6 is to Part 1 of this scries. Paper 2102750J Received May 27, 1992 Accepted June 16, 1992