Anal. Chem. 1994,66,4519-4524
Thermodynamic Origin of the Sub-Nernstian Response of Glass Electrodes Friedrich 0. K. Baucke* Schott Glaswerke, D-55 122 Mainz, Germany
A thermodynamic explanation of the sub-Nernstian response of pH glass electrodes is presented on the basis of the dissociation mechanism, which attributes the functioning of glass electrodes to the phase boundary equilibriumof functional groups at the glass surface and ions in the solution. It is found that the activity change of the functional surface groups caused by pH variations, which basically reduces the electrode slope, cannot be neglected and results in a measurable electromotive efficiency below 1. All membrane glasses, independent of composition and response, have a comparable electromotive efficiency, which is confirmed by the equal magnitude of measured and reported data. This adds a thermodynamic meaning to this quantity and yields detailed quantitative information on the phase boundary equilibrium, i.e., the pH dependence of the activity of negative surface groups (which actually determine the membrane potential) and the dependence of the membrane potential on the activity of the negative groups (“internal slope”), which amounts to several tens of volts per decade. The sub-Nemstianresponse is characteristic of glass electrodes and is not expected for redox, metalmetal ion, and crystal membrane electrodes. pH glass electrodes exhibit a subNemstian pH response at medium pH values outside the acid and sodium error range. The deviation is normally not noticed since it is included in the slope factor when glass electrodecontaining cells with transference are standardized. However, it is measured by directly comparing the glass electrode potential with that of the Pt, Hz electrode, which is known to exhibit the theoretical slope, k = (RT In lO)/F, in cell I without transference,
0
Pt,H2/buffers(pHl, pHJ/glass electrode
and when the glass and Pt, Hz electrode potentials are indirectly compared by a reference electrode in cells IIa and 1% with transference,’
ref el/KCl(m
2 3.5 mol kg-’)//buffers(pH,,
pHJ/glass el OIa)
and
ref el/KCI(m L 3.5 mol kg-’)//buffers(pH,,
pHJ/Pt, H,
0%) The practical slope, k,], of the glass electrode is usually referred to the theoretical slope by the electromotive efficiency, a = kgl/ Chairman, DIN Committee Technical pH Measurements. (1) Bates, R G. Determination ofpH. n e o y andpractice, 2nd ed.; Wdey: New York, 1973. 0003-2700/94/0366-4519$04.50/0 0 1994 American Chemical Society
k,’ but is also characterized in this paper by the electromotive loss factor, n = 1 - a. For example, Kratz, as early as in 1951, cited several papers from which a L 0.996 for various electrodes could be estimated,2 Bates reported that electromotive efficiencies could be as small as a = 0.995 in the intermediate pH range,’ and Covington, describing high-precision measurements in cell I, published emf‘s which yielded a L 0.997.3 Also, recent measurements on cells IIa and IIb employing multiplepoint calibration with linear regression resulted in a = 0.997-0.998 for a glass electrode with a lithium silicatebased membrane glass4 Surprisingly, the reported data have a comparable magnitude around 0.997, independent of the membrane glass applied. A cause of the subNemstian response has neither been suggested nor reported. Cell I and cells IIa and IIb exclude liquid junction potentials, the buffer solutions applied rule out acid and sodium errors, and accidental shunts of the glass electrodes, which also cause a pH-independent decrease of the slope factor, cannot account for a slope reduction by up to 0.5%because of the large insulation resistance of modem glass electrodes; see, for example, ref 5. Besides, diffusion potentials in subsurface layers of electrode membranes are independent of pH at 100%pH selectivity? which also excludes irreversible processes at the glass surface. Since indirect causes are thus obviously ruled out, it must be suspected that the subNemstian response is connected with the functioning of the glass membrane and represents a fundamental property of glass electrodes. We have applied the dissociation mechanism of glass elect r o d e ~and ~ , have ~ found that the response of pH glass membranes, in principle, is subNemstian for thermodynamic reasons; Le., glass electrodes with a thermodynamically correct function exhibit an electromotive efficiency below 1. Besides, the subNemstian response is characteristic of pH as well as pM glass electrodes, and a has a comparable magnitude for all membrane glasses and selectivities, independent of the glass composition. Since this gives a thermodynamic meaning to the experimental electromotive efficiency,we have carried out measurements on several pH glass electrodes with negligible shunts yielding results in agreement with the average of the reported data. The electromotive efficiency gives detailed information on the phase boundary equilibria, which are the basis of the dissociation mechanism.6 (2) Kratz, L. In Die Glaselektrode und ihre Anwendungen, Jiiger, R, Ed.; WissenschaftlicheForschungsberichte, NaturwissenschaftlicheReihe; Steinkopff: Frankfurt, 1950; Vol. 59. (3) Beck, W. H.; Bottom, A E.; Covington, A K Anal. Chem. 1968.40,501. (4) Baucke, F. G. K; Naumann, R; Alexander-Weber, C. Anal. Chem. 1993, 65, 3244. (5) Glass Electrodes, British Standard Spec@cation BS 2586 (1979);British Standard Institution: London, 1979. (6)Baucke, F. G. K Fresenius J. Anal. Chem. 1994,349,582. (7) Baucke, F. G. K J. Non-Ctyst. Solids 1985,73,215.
Analytical Chemisty, Vol. 66, No. 24, December 15, 1994 4519
In the following,equations for the electromotive efficiency are derived, the measurement of a is described and critically discussed, and resulting details of the phase boundary equilibrium are given. PHASE BOUNDARY EQUILIBRIUM AND pH RESPONSE OF MEMBRANE GLASSES
According to the dissociation mechanism, the functioning of glass electrodes is based on an electrochemical equilibrium between functional (anionic) groups of the glass at the interface glass/solution and cations in the solution.6 This interfacial equilibrium also determines the species and relative concentrations of the cations that are bound to the surface groups of the glass. The pH response of the silicatebased pH glass electrode, for instance, reflects the dissociation equilibrium of acidic silanol (=SOH) groups, eq 1, where s and soln denote surface and =SOH($
+ H,O(soln)
--L
=SiO-(s)
+ H30f(soln)
(1)
solution, respectively, and the three bars in front of silanol and siloxy (=SO-) mark the bonds to other (oxygen) atoms of the glass. Correspondingly, the alkali or pM response is caused by an association, or salt-forming, equilibrium with cations, eq 2, =SO- (s)
+ M’(so1n)
== ZSiOM (s)
(2)
resulting in ESiOM groups, by which the membrane is covered, if a silicate glass is again chosen as an example despite its limited alkali response. The transition range between 100%pH and 100% pM response is characterized by dissociation, eq 1, and association, eq 2, and by a surface containing both =SOH and ESiOM groups, eq 3, besides much smaller concentrations of =SO=SiOH(s)
+ M+(soln) + H,O(soln) * =SiOM(s) + H30+(soh) (3)
groups, which cancel in eq 3 but are actually present. The relative pH and pM functions and surface concentrations of =SOH and =SiOM groups, respectively, are determined by the pH and pM of the solution and the product of the dissociation and association constants of the equilibria eqs 1and 2. Simultaneous irreversible reactions, for instance, interdiffusion of ions from the surface and the bulk of the glass causing diffusion potentials that are independent of pH at 100% pH response? slow hydration and dissolution of the glass network, and formation of leached subsurface layers, do not disturb the surface equilibria since their current densities are much smaller than the exchange current densities of the equilibria eqs 1 and 2 (see ref 6) and are of no concern for the present discussion. The equilibrium of interest here is the dissociation of silanol groups, eq 1,which, depending on glass and solution composition, prevails at pH values below 9-12. It is characterized by zero change of electrochemical free energy, eq 4, where G is the
chemical free energy of the species indicated, cm = qgl - qs0his the potential of the membrane glass, Le., the difference of the 4520 Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
internal electrical potentials of glass, qgl,and solution, qs0h,and F is the Faraday constant. The minus sign in front of the potential term in eq 4 results from writing the dissociation, eq 1, opposite to the direction of cell I, where the membrane potential is em according to IUPAC. Introduction of the chemical free standard energy AG“ of dissociation and of activities, a, and surface activities, a’, results in
and, after rearrangement,
which presents the pH dependence of the membrane potential. KD,His the thermodynamic dissociation constant, and log refers to the basis 10. Equations 5 and 6 describe rigorously the interfacial dissociation equilibrium. An increase of the hydronium activity, for instance, increases the silanol activity, U’S~OH, decreases the siloxy activity, a’sio-, since AC’S~OH = -Ac’sio- (where c’ is the surface concentration), and, in turn, increases the potential of the glass membrane because of the reduced density of negative charges at the surface. Because of the strong dependence of the potential on the surface charge of a phase: however, the siloxy concentration (and activity) is much smaller than the silanol concentration, and its change caused by a pH variation is even smaller,6eq 7 ,
where c’o is the total surface concentration of functional groups. The second term on the right side of eq 6, consequently, can be assumed constant as a first approximation and can be combined with the first term to give the pH standard potential of the glass membrane,
so that eq 6, with this approximation, can be written as eq 9, which
reflects the well-known linear dependence of the glass electrode potential on pH and corresponds to the general assumption that, ideally, the glass electrode should exhibit the theoretical slope, eq 10,
as does, for instance, the Pt, Hz electrode. However, the experimental pH response of glass electrodes is generally less than theoretical (see, for example, refs 1-4), which is taken into account by introducing the practical slope, kgl, in order to adapt eqs 9 and 10 to the practical results. Thus, (8) Guggenheim, E. A. Thermodynamics; North-Holland, Wiley: Amsterdam, New York, 1967.
describes the practical dependence of the membrane potential on PH, and
represents the practical slope. The term nk in eq 12, which may be termed electromotive loss, is the difference of the ideally expected Nemstian, eq 10, and the practical slope according to
The origin of the sub-Nemstian pH response has not been reported. However, eq 6 offers a thermodynamic explanation in that changes of the activities in the second term of its right side caused by pH variations may not be sufficiently small to justify the approximation yielding eqs 8-10. This is significant since, fjrst, the ratio of the activities appears in the log term of the equation describing the potential difference as a function of the pH difference,
and
which show the thermodynamic meaning of the electromotive loss factor, n, and of the electromotive efficiency, a,respectively. The thermodynamically correct pH response of glass electrodes, consequently, is basically subNemstian, eq 16, and eqs 18 and 19 give quantitative information on the phase boundary equilibrium if other causes are excluded. It was thus of interest to measure a and n of glass electrodes that, particularly, were free of shunts since short circuits cause pH-independent reductions of the potential slope as does the electromotive loss factor. Such measurements were carried out by means of cell I and cells IIa and IIb. The equations for n and a of glass electrodes measured in these cells, which differ slightly from eqs 18 and 19, respectively, are derived in the following section. “IDEAL” ELECTROMOTIVE EFFICIENCES OF GLASS ELECTRODES AS OBTAINED BY CELL I AND CELLS IIA AND IIB
The emf E4gl of cell I is the sum of the potentials cg] and C P ~ H ~ of the glass and the Pt, Hz electrodes, respectively,
and second, the ratio of the doxy activities (which are much smaller than the activities of the silanol groups, eq 7, and of water, which is nearly unity in dilute solutions) is larger than the ratio of these larger activities, eq 15. A change of pH for determining
the practical slope of a glass electrode according to eq 14 is thus connected with an activity term whose magnitude may well be a measurable contribution to the potential difference. In addition, this term always reduces the Nemstian response, eq 14, because changes of pH and siloxy activity have the same sign. The thermodynamically correct slope of pH glass membranes is obtained by differentiating eq 6 with respect to pH,
where the derivative of the log term is constant because of the constant slope (dc,/dpH) in the intermediate pH range.’ The difference of the Nemstian, eq 10, and the thermodynamic pH response, eq 16, is thus given by
whose combination with eq 13, finally, yields
or
where cog] is the (constant) sum of the potentials of the internal reference electrode and internal membrane surface of the glass electrode. The potential of the outer membrane surface is given by eq 6, that of the Pt, Hz electrode is established by equilibrium eq 22, where g denotes gas and the standard potential of the Pt,
1/2H2(g)+ H20(soln) -H,O+(soln)
+ e-(Pt)
(22)
Hz electrode is defined zero at all temperatures. Thus,
or, after rearranging,
Differentiating eq 24 with respect to pH at constant hydrogen pressure p~~ and rearranging yields eq 25, which shows that Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
4521
measurements on cell I result in what may be called the “ideal” electromotive loss factor n’ (and “ideal” electromotive efficiency a’),
Table 1. “Ideal” Electromotive Efficiencies, a’,of Three pH Glass Electrodes (1-3) (Schott N 1120) As Measured in NIST/DIN Standard Buffer Solutions Citrate, 1:l Phosphate, and Carbonate at 25 and 50
25
3.776 6.865 6.865 10.012
which differs from n by the lack of the activity of water, 3.776 10.012
n’ = n f d Oog UHzO) /dpH
(27)
1 2 3 1 2 3 1 2 3
-179.70 -183.75 -182.03 -179.44 -183.35 -181.59 -179.70 -183.75 -182.03
-179.44 -183.35 -181.59 -178.83 -182.88 -181.01 -178.83 -182.88 -181.01
1 2 3 1 2 3 1 2 3
-173.20 -175.14 -173.35 -172.58 -174.38 -172.79 -173.20 -175.14 -173.35
-172.58 -174.38 -172.79 -172.04 -173.73 -172.08 -172.04 -173.73 -172.08
average However, n’ can be approximated to n as long as the glass electrode is transferred between dilute solutions, e.g., standard buffer solutions, whose water activity is close to unity. A corresponding derivation for cells IIa and IIb yields
50
3.749 6.833 6.833 9.828 3.749 9.828
average or for two individual buffer solutions with pH1 and pH2,
0.9986 0.9978 0.9980 59.04 0.9976 0.9967 0.9975 0.9971 58.99 0.9969 0.9976 0.9976 0.9975 59.02 0.9972 0.9976 k0.0005 0.9981 0.9988 0.9982 64.00 0.9978 0.9972 0.9966 0.9967 63.91 0.9963 0.9970 0.9964 0.9967 63.91 0.9967 0.9972 k0.0008
a Ept 1 is the emf of cell I, is the average value of the practical slope of the glass electrode. The electromotive efficiencies were confirmed by emfs of cells IIa and IIb due to the presence of a Thalamid reference electrode in the cell vessel.
where Egland E ~ areHthe~emfs of cells IIa and IIb at the indicated pH values, respectively. A further derivation shows that the electromotive efficiency and loss factor as obtained from cells IIa and IIb do not contain the activity of water either and are thus also ideal values. An equation for a’ corresponding to eq 29 was given by Bates.’ EXPERIMENTAL SECTION
A thermostated, jacketed, glass vessel with seven NS 14.5 ground glass joints was equipped with three glass electrodes (Schott Gerate Hofheim, N 1120 with Thalamid internal reference electrodes and 100 MQ membrane resistance at 25 “C), one reference electrode (Schott Gerate Hofheim B 2930, Thalamid with 3.5 mol kg-l KCl and Pt diaphragm), one double Pt wire electrode (Schott Gerate Hofheim, Pt 1200), a combined hydrogen inlet and outlet tube carrying a glass disk (Schott Glaswerke, 6 mm diameter, porosity D 3), and a thermometer with 0.1 K graduation. The hydrogen flow rate was approximately 500 mL h-l; the vertical distance between glass disk and Pt electrodes was at least 20 mm. Hydrogen (99.998%;Linde) was used; emf measurements were referred to a hydrogen pressure of 1013.25 hPa according to ref 1. Platination and treatment of the Pt electrodes before platination were conducted as recently described in detaiLg Buffer solutions used were NIST/DIN standard buffers citrate (0.05 mol kg-l), 1:l phosphate (KHzPO4 and Na2HP04,0.025 mol k g ’ each), and carbonate (NaHCO3 and NaZC03,0.025 mol kg-l each).’O pH values at the measuring temperatures are given in Table 1. (9) Baucke, F. G. I C J . ElectroanaL Chem. 1994, 368, 67. (10)Deutsches Institut fiir Nomung; pH-Messung,Standardpufferlosungen,DIN 19 266. Beuth-Verlag: Berlin, 1979.
4522
Analytical Chemistry, Vol. 66, No. 24,December 15, 1994
An electrometer (Keithley, Model 617 Programmable Electrometer, resolution 10 pV, input impedance > 2 x 1014 Q) was used for the emf measurements. RESULTS AND DISCUSSION
Ideal electromotive efficiencies, a’, of three glass electrodes were measured in three buffer solutions within the intermediate pH range 3-10 in cell I at 25 and 50 “C and were confirmed by emfs of cells IIa und IIb due to an additional reference electrode in the cell vessel. The results given in Table 1 show that, within experimental error, a’ is independent of the individual electrodes, the pH range, and the temperature and obviously represents the thermodynamic electromotive efficiency according to eq 26 because the following conditions were met: (I) The cells excluded any influence of liquid junction potentials. (2) The narrow pH range and the type of glass electrode chosen ruled out contributions from acid and sodium errors. This is also confirmed by the independence of the obtained electromotive efficiencies of the pH range. (3) Electric shunts of the glass electrodes were negligible. The insulation resistance, including connecting cables and plugs, was R, > 10l2 Q (25 “C) and nearly independent of the solution temperature, while the membrane resistance was R, = lo8 Q at 25 “C and = lo7 Q at 50 “C, yielding ratios RJR, L lo4 Q (25 OC) and RJR, L lo5 (50 “C). Electromotive efficiencies resulting from these resistances are aR = R,/(R, + R 3 r0.9999 (25 “C) and ~ 0 . 9 9 9 9 9(50 “C). Besides, a’ is independent of the measuring temperature despite the temperature-dependent ratios RJR,,,, Table 1. (4) Diffusion potentials in leached layers of pH glass membranes are independent of pH at 100%pH sensitivity as predicted
Table 2. Detailed Information on the Phase Boundary Equilibrium Qlasr/SoiutionAs Obtained from Several Assumed Electromotive Efficienciesa of pH Qlars Electrodes
- d d
dOog 9)/ dOog 9) = (U’sio-,l/dsio-,d (Ac‘Sio-/c’Sio-.2)/% dpH = ‘zt ak/n Ob for ApH = -1 for ApH = -lC
a 0.9990 0.9985 0.9975 0.9960 0.9950
0.0010 0.0015 0.0025 0.0040 0.0050
59.10 39.38 23.61 14.73 11.77
0.9977 0.9966 0.9943 0.9908 0.9886
the change of the d o x y activity because of eqs 7 and 15) is only one to five thousandths of the pH change. For example, it amounts to a four hundredth of the pH change for a’ = 0.9975, Le., for the average a’ determined in this paper, Table 1, which agrees approximately with the average of the reported data. Table 2 also presents ratios of the siloxy activities (fourth column) and approximate relative changes of the siloxy concentration, eq 33,
-0.23 -0.34 -0.57 -0.92 -1.14
’d Oog Q)/dpH = dOOg(U’SiO-/U’SiOHUH,O)) Id Oog a’sio-)/dpH. (Wcolumn) both for ApH = - 1. (A constant activity coefficient d 4 d O o g 9) = dem/dOog U’sio-) = “internal slope” of membrane of siloxy is assumed in eq 33 because of the small relative potentd (Ac‘so-/~‘so-,~= (c‘so-,~- CSO-,~/C‘SO-~ I(Mso-/c#so-,~.
by Eisenman” and contimed experimentally for several membrane glasses including the one of the glass electrode applied in this work.6 (5) The equal magnitude of a’ of the individual glass electrodes, Table 1, excludes accidental causes of the results. Equation 19 gives detailed information on the phase boundary equilibrium. Generally, only the overall dependence of the electrode potential on the cation activity is given by the Nemst equation. This is also the case with the dissociation mechanism as long as the activity ratio of the functional surface groups is assumed constant, eq 11. However, eqs 18 and 19 yield the extent to which the surface activity of the siloxy groups, whose charge actually determines the glass membrane potential, depends on the pH value of the solution. For the homogeneous dissociation of a monobasic acid, e.g., AH in water, AH(so1n)
+ H,O(soln) -- A-(soln) + H,O+(soln)
concentration changes.) These data show the small change of the siloxy concentration relative to the pH change. For a = 0.9975,for instance, a l(lfo1d increase of the hydronium ion activity results in a siloxy concentration decrease of only -0.57%. Also, the strong effect of the membrane potential on the siloxy activity is described by the electromotiveloss factor. Thus, writing the potential slope according to the chain rule,
where Q
(u’~~o-/u’~~oH U H ~ O )rearranging , eq 34 to form
and inserting the known derivatives, eqs 12 and 18, yield the “internal slope”of the membrane potential, i.e., the slope referred to the siloxy activity,
(30)
with the dissociation constant KD,
the derivative of the logarithm of the activity ratio of the participating particles with respect to pH is unity,
For the phase boundary equilibrium, i.e., for the heterogeneous dissociation of silanol groups at the glass surface, eq 1, on the contrary, the corresponding derivative is given by the electrome tive loss factor, eq 18. It is much smaller since the siloxy activity is not only determined by the chemical driving force (as the Aactivity in eq 32) but also by the counteracting negative potential of the glass surface. Table 2 presents derivatives according to eq 18 (second column, Q denotes the surface activity ratio) for several values of a in the range reported in the literature. It is seen that the change of log Q (which can be approximated by (11) Eisenman, G. In Advances in Analytical Chemist9 and Instrumentation; Reilley, C. N., Ed.; Wiley-Interscience: New York, 1925 Vol. 4.
As seen in Table 2 (third column), it amounts to several tens of volts per decade of the siloxy activity and, for example, is 23.61 V for Afi(Si0) = 1 at a‘ = 0.9975 if the definition p(Si0) E -log uho- is used. As expected, the product of the derivatives, eqs 18 and 36, yields the overall practical slope of pH glass membranes, eq 12. While eq 6 represents the membrane potential as a function of pH, the corresponding eq 37, derived in a similar way, describes
the potential dependence on P M . ~ ( K ~ M is the association constant.) The slopes obtained by differentiating eqs 6 and 37 with respect to pH and pD (to which glass electrodes respond in a way similar to pH’) and pM, respectively, do not contain individual equilibrium constants and can thus be represented by general expressions, i.e., by
for the pH (and pD) function and by Analytical Chemistry, Vol. 66,No. 24, December 15, 1994
4523
for the pM response of the membrane glass. R-, RH, and RM denote the dissociated, acidic, and associated, or salt, forms, respectively, of a general functional surface group R,and H stands for hydrogen and deuterium in eq 38. Since the practical slopes of the pH, pD, and pM response of glass electrodes are known to be near-Nemstian,’it must be concluded that, apart from the water activity in eq 38, the electromotive loss factors represented by the derivatives in eqs 38 and 39 depend on activity coefficients but are approximately equal for all membrane glasses, for the pH, pD, and pM response, and for the transition pH range. For pH glasses, this conclusion seems to be confirmed by the narrow range of the measured, Table 1, and reported electromotive efficiencies. Because of its general thermodynamic meaning, however, this quantity should be measured for more electrodes with different membrane glass compositions. In addition, eq 39 should be verified, for instance, by comparing pNa glass electrodes with a sodium amalgam electrode in standard pNa solutions using cells of types I and IIa and IIb. These measurementts are to be carried out in the near future. In general, a thermodynamically caused sub-Nemstian response is observed in any electrode if two conditions are met: (1) The electrode functioning must be the result of a phase boundary equilibrium between located functional groups at the electrode surface and ions in the solution so that the concentration of the charged form of the groups, which is given by the activity of the dissolved ions, determines the electrode potential. (2) The activity change of the charged groups caused by an (opposite) activity change of the dissolved ions must be sufficiently large to reduce the theoretical potential slope measurably, and other causes of the sub-Nemstian response must be excluded. Glass electrodes obviously meet these conditions as the dissociation mechanism, by which the sub-Nemstianresponse is explained in this paper, was verified experimentally6 (first condition) and other causes of the effect are excluded by measurements and literature data (second condition). The ion exchange theory, on the other hand, fails to offer an explanation since it is based on an unspecified exchange of different cations between glass and solution,’2which does not meet the first condition. Si02 and A l 2 0 3 , used in ion-sensitive field effect transistors (ISFETs) also exhibit a sub-Nernstian response, which has been discussed in great detail; e.g., see ref 13. The site-binding theory proposed by Yates et al.I4 assumes differently charged surface groups in equilibrium with the dissolved cations and thus meets the first condition, and it may well be that the second condition is also met, which, (12) Eisenman, G., Ed. Class Electrodesfor Hydrogen and Other Cations, Principles and Practice; Dekker: New York, 1967. (13) Bousse, L.; Bergfeld, P. Sens. Actuators 1984,6, 65. (14)Yates, D. E.; Levine, S.; Healy, T. W. J. Chem. SOC.,Faraday Trans. 1974, 70, 1807. (15) Osch, U.;Drzo, Z.; Xu,A; Rusterholz, B.; Suter, G.; Than, H, V.; Weltin, D. H.; Ammann, D.; Retsch, E.; Simon, W. Anal. Chem. 1986, 58, 2285.
4524
Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
however, necessitates a rediscussion of the points made in ref 13 and probably additional experiments. The mechanism of PVCbased ion-selective electrodes (ISEs), which also show subNemstian behavior,15is based on diffusion and does not seem to meet the first condition so that the nonideality most probably has a different origin. Finally, a subNernstian response is neither observed nor expected with redox, metal-metal ion, and crystal membrane electrodes since the electrons and cations, respectively, which establish the potential, do not represent located charges and thus exclude the first condition. The derivatives and differences of potentials mainly treated in this paper are independent of individual equilibrium constants. It is noted, however, that membrane potentials are determined also by the dissociation and/or association constants, eqs 6 and 37, and thus differ appreciably for different glasses. These differences, however, are undetectable since the potentials of the opposite surfaces of membranes are controlled by the same constants. whose influence thus cancels. CONCLUSIONS A thermodynamic explanation of the subNernstian response of pH glass electrodes has been given. It is based on the experimentally verified phase boundary equilibrium between functional surface groups of the glass and ions of the solution, which is the central equilibrium of the dissociation mechanism of glass electrodes! It involves negatively charged groups, whose activity ratio is sufficiently large to cause a measurable reduction of the theoretical slope. These findings add a thermodynamic meaning to the experimental electromotive efficiency and yield detailed quantitative information about the phase boundary equilibrium, i.e., the pH dependence of the activity of the negative surface groups (the origin of the membrane potential) and the dependence of the membrane potential on the activity of these groups (“internal slope”), which is in the order of several tens of volts per decade of activity. These numbers distinguish the phase boundary equilibria of glass membranes quantitatively from homogeneous dissociation equilibria. It is concluded that the electromotive efficiency must have the same magnitude for different membrane glasses and sensitivities, which should also be verified experimentally for alkali-sensitive glass electrodes. The thermodynamic subNemstian response is not explained by the ion exchange theory because of the insufficiently detailed nature of the latter. It is a unique effect of glass electrodes and of other membrane electrodes whose response is also established by the dissociation mechanism. It is not expected for redox, metal-metal ion, and crystal membrane electrodes. Received for review May 13, 1994. Accepted September 9, 1994.@ @
Abstract published in Advance ACS Abstracts, October 15, 1994.
