pH Glass Electrode and Its Mechanism - ACS Symposium Series (ACS

Chapter 20

pH Glass Electrode and Its Mechanism K. L. Cheng

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Department of Chemistry, University of Missouri-Kansas City, Kansas City, M O 64110 The past major mechanisms are briefly reviewed. The generally accepted ion exchange theory failed to explain the origin of the electrode potential. The newly proposed double-layer and double-capacitor theory emphasizes the importance of electrode surface, double layers, adsorption of both cations and anions on the zwitterionic surfaces, surface active sites, charge density, Boltzmann distribution, etc. The acid and alkali errors, the suspension effect, the membrane thickness, the charging and discharging, and the pH relationship to the membrane capacitance are discussed. It is a pH electrode in acid solutions but a pOH electrode in basic solutions. A challenging view on the validity of applying the Nernst equation to the non-faradaic pH electrode is presented. Since 1906 when Cremer (1) first observed the potentiometric relationship of a glass membrane with a pH solution and the first systematic study of the glass electrode for pH measurement was by Haber and Klemenciewicz (2) in 1909, many investigators have attempted to explain the glass membrane potential. Table I lists major investigators and their mechanisms for the past 80 years. The pH glass electrode is one of the most widely used analytical tools, yet it has been perhaps one of the least understood. Many quantitative analysis textbooks have presented its theories, but none have given a clear or definitive explanation of the mechanism relating to the origin of the glass membrane potential. The development and the theories of the pH glass electrode have been discussed in many books (5-8). Previous mechanisms have been briefly reviewed by Dole (3), Durst (4), Buck (44), and Cheng (9). Dole explained that the potential of a thin glass film is attributed to the selective permeability or mobility of the H+ ion across the glass-aqueous solution interface. The concept of an

0097-6156/89/0390-0286$06.00/0 © 1989 American Chemical Society

In Electrochemistry, Past and Present; Stock, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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pH Glass Electrode and Its Mechanism

287

Table I


Major Mechanisms for pH Glass Electrode Year

Proposed by

Origin of Potential

1909

Haber

Phase boundary potential or Donnan potential

1925 1926

Gross, Halpern Hughes

1923 1924 1937

Horovitz Schiller Haugaard

Ion adsorption or ion exchange between Na+ and H +

16 26 27

1906 1926 1928

Cremer Michaelis Quittner

Membrane or diffusion potential, glass membrane permeable to H+

1 28 12

1931

Lengyel

Adsorption and capacitor of quartz electrode

43

1941

Haugaard

Disproved H+ diffusion through membrane by chemical analysis

10

1961

Schwabe and Dahms

Disproved H+ diffusion by tritium

11,14

1941

Dole

Disproved Lengyel's quartz capacitor No OH- ions taking part

3,5

1984

Cheng

21

1985

Cheng

pH electrode in acid medium, pOH electrode in alkaline medium. Double-layer and doublecapacitor model

Reference

2

24 25

29



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ELECTROCHEMISTRY, PAST AND PRESENT

actual penetration through the glass membrane by hydrogen ions has been definitely disproved by the work of Haugaard (10) and the work of Schwabe and Dahms with tritium (11). It is surprising that in 1985 some chemists still believed that the glass membrane was permeable to the H+ ion (15). The adsorption-potential theory postulates an adsorbed layer of hydrogen ions on the glass surface causing a potential drop at the glass-solution interface, corresponding to the difference in chemical potential between the free and adsorbed ions (12). The most generally accepted ion exchange equilibrium theory proposes that the gel layer of the glass membrane acting as an ion exchanger produced a phase boundary potential at which the H+ ion exchanges with the Na+ ion (13,16,43). Such an ambiguous proposal has never been supported by experimental results. If such an exchange did occur, there would be no net change in interfacial charges. Furthermore, the sodium ion in the gel layer of membrane would be eventually depleted after a long time use/resulting in the failure of the glass electrode. But the pH glass electrode can be used for a long time. It is also known that a quartz glass membrane containing no sodium could act as a pH glass electrode (43). Addition of sodium oxide to the glass is only to increase the conductivity of the membrane (10,17,18). Prior to the ion exchange theory, the mechanism of a concentration gradient of the proton suggests that the potential arose due to the proton concentration difference on both sides of the thin semipermeable glass membrane. The Donnan equilibrium with mathematical formulas and equations was used to support the theory where a Donnan theory term was proposed. It seems that the failure of previous theories is caused by erroneous assumptions. Many investigators claimed that their theories were based on thermodynamics using the Nernst equation to explain the logarithm relationship between the potentials and the concentrations. Previous investigators devoted too much time interpreting the glass electrode in terms of thermodynamics. Haugaard commented that, ". . .most of the previous experiments in this direction have failed because the investigators have tried to deduce their theories from the thermodynamic treatment of systems in equilibrium. But we know that thermodynamics alone can not tell us the mechanism of a process. . . Potentials of glass electrode systems not in equilibrium have been measured and compared. . ." (10). In the past, it seemed fashionable to explain the mechanism with thermodynamics. As a whole, thermodynamics is always right. However, its usefulness depends on how it is applied to a particular system. In commenting on the historic development before 1947 in the treatment of electrochemical reactions across interfaces, Bockris (19) stated that most electrochemists were still trying to do the impossible, i.e., to treat the highly thermodynamically irreversible electrode reactions by a series of misconceptions and approximations on the basis of reversible thermodynamics. This fundamental error and lack of conceptualization held a dead hand on the mode of achieving electrochemical reactions and on the electrochemical energy conversion for 4 to 5 decades. He called this period in electrochemistry


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"The Great Nernst Hiatus." In direct potentiometry using membrane electrodes, a similar situation has occurred in the past 8 decades. Every quantitative and instrumental analysis textbook has treated the glass electrode as a battery obeying the principles of reversible thermodynamics and the Nernst equation. We may follow the similar case and call the period of 8 decades as "The Great Nernst Hiatus of Direct Potentiometry." This paper summarizes a new concept based on capacitances as an attempted explanation.


Battery and Capacitor A battery is a device containing no insulator and producing an electric current through chemical redox reactions that occur in cells that are placed in series. Each cell contains an anode and a cathode that are immersed in an electrolyte medium. Connecting the anode and the cathode to the external circuit causes an electric current flow until chemical reactions cease. Mostly it is reversible, following the principles of equilibrium thermodynamics, i.e., the Nernst equation. On the other hand, a capacitor is a device for storing electric charges through two conducting plates between which there is a dielectric in which no reversible redox reaction takes place. By connecting two charging plates, no significant current flows. For a capacitor, C = q/V, where C is the capacitance, q is the charge, and V is the potential difference. In the literature the pH electrode is generally represented in a cell as follows (30,44).

It has been known for a long time that there are no redox reactions involved in the potential development of glass electrode (3,6,10). Based on the definitions of battery and capacitor shown above, it is difficult to accept the statement, "The electrode component of a pH measuring system is comparable to a battery whose voltage changes with pH" (15). We would like to point out that the pH glass electrode is comparable to a capacitor rather than to a battery. It is extremely important to have a correct assumption and concept before deducing any mechanism. Capacitor Figure 1 (a) illustrates a capacitor used in a common electric device that is able to hold charges on applying a potential with a battery or power source. In Figure 1 (b) and (c), the membrane electrodes may have their arrangements as shown. This depends on what functional group is present on the surface and whether the cations or anions are adsorbed. The glass electrode or other membrane electrodes may be represented by Figure 1(c) which is the zwitterionic surface structure where both cations and anions may



290


Figure 1.

Capacitors with different charges.



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291

be adsorbed simultaneously. For instance, Na+ and OH- can be adsorbed simultaneously on the pNa electrode as discussed in the latter part of this paper. Each side of membrane interface potential exists due to the presence of the net charges. When the glass electrode is immersed in an electrolyte solution a double layer is formed that contains surface charges. Since both layers (inner and outer) of the membrane are in touch with the electrolyte solutions, two double layers are formed on both sides with the same membrane. Helmholtz considered the double layer as a capacitor (20). A membrane with double layers may be considered as double-capacitor electrode. The potential difference (Δ E) is that between the outer and inner interfacial potentials (Figure 2 ) . An electrode capacitor may be considered as a membrane material made from either a dielectric or a semiconductor which can adsorb cations and anions on its active sites. The membrane potential is believed to derive from the two interfaces that hold charges on the surface through double layer adsorptions. The glass electrode potential follows the capacitance law.

there k is the dielectric constant of the glass membrane, ε is the permittivity, A is the membrane area, d is the membrane thickness, q is the charge, and C is the capacitance of the membrane. When ε , K, A, d, and C are constant for the same glass membrane, E is then proportional to q (q+ is the positive charge, and q- is the negative charge). Then,

where K is a new constant. If only cations (H+) are adsorbed on the membrane surface, Σ q- = 0, resulting in the potential increasing with increasing positive charges; if only anions are adsorbed (OH-), Σ q+ = 0, resulting in the potential decreasing with increasing negative charges; and if both cations and anions are adsorbed simultaneously, the result is the sum of positive and negative charges (net charges). From equation (3), besides the charges, the membrane potential is affected by the surface area (A) and the thickness (d), which have been demonstrated ( 2 1 , 2 2 ) . We have measured the capacitance of the glass membrane as a function of pH as discussed in the last part of this paper. The membrane electrodes behave definitely as capacitors. Tubular pH Glass Electrode Tests have been made with a tubular pH glass electrode for quantitative determination of the charge density effect on potential. A cylindrical and pH sensitive glass electrode of 1.0 cm X 1.5 cm was specially prepared and used as a substitute for a pH bulb electrode. The whole section of the tube was sensitive to pH, when sealed, and the tube contained a pH 7 phosphate buffer



292


Figure 2.

Electrode double layers.



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solution and a Ag/AgCl reference electrode. The outer surface of the tubular electrode exposed to the test solution was controlled by the depth of immersion, i.e., the amount of charge on the same whole membrane surface area varied as a function of immersion depth. The results are shown in Figure 3. Different amounts of H or OH- ions are adsorbed on the surface as a result of varying depth of immersion of the tubular electrode into the same solutions. In acid solutions the potentials increase with increasing depth of immersion. Similarly, in basic solutions the potentials decrease with increasing depth of immersion. At approximately pH 5.5 (isoelectric point of the glass membrane), the potential remains the same regardless of the depth of immersion (the point of zero change, pzc). In acid media, the increased positive potentials are the result of the increased adsorption of H+ ions on the electrode surface. In basic media, the increased negative potentials are the result of the increased adsorption of 0H~ ions on the electrode surface (or possibly neutralizing the surface proton). It emphasizes the fact that the pH glass electrode is a pH electrode in an acid medium, but it is a truly pOH sensor in a basic medium. It should be logically called as a pOH electrode in basic solutions. This has been evidenced by the negative charges of the glass membrane in basic solutions, (Figures 3 and 6 ) . This is one of the fundamental differences between the capacitor theory and the past theories which do not consider the role of 0H~ ions in the potential development. The concentration of OH- has never been included in the cell diagram and the Nernst equation. A correct concept dealing with the actual measurements using a pH glass electrode is very important; otherwise, misleading conclusions may be made (9, 23). Tubular pNa Electrode A similar experiment with a tubular pNa electrode at different depth of immersion was carried out in a pH 10.5 buffer (ethylenediamine) with different concentrations of sodium nitrate. For dilute sodium solutions, the potentials decreased to more negative values with increasing depths of immersion, at higher sodium ion concentrations in the same buffer solutions (above 1 M) (Figure 4), the slope changed to positive values. This shows that the pNa glass electrode is also a pH and pOH electrode with a zwitterionic surface which can adsorb both OHand Na + ions (9). The potential response by the pNa electrode is the result of Equation (3). This explains the reason that the determination of sodium ion with a pNa electrode must be done in a basic buffer solution. Double Layers The double layer or triple layer has been known for a long time (19). When an ionic solid, in particular an oxide, is placed in an electrolyte solution, cations or anions are adsorbed on the surface depending on the surface charges or the functional groups at the surface. For a quartz or glass surface, when it is



294


Figure 3. Effect of electrode surface contact in the solution on the potential.

Figure 4. Effect of pNa electrode surface contact in the solution on the potential.



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295

hydrated, the surface contains polymerized silicic-acid which is weakly ionized and can interact with H+ and OH- ions. The adsorption of H + ion on the glass has been known in the past (10), but the adsorption of OH- ion or reaction of 0H~ ion with undissociated proton on the glass surface has not been reported. We believe that the appearance of a double layer or triple layer yields a capacitor. The glass surface becomes either positively charged or negatively charged, while the solution (the bulk) is oppositely charged. A preliminary estimate of the distance (d) of the capacitor (Equation 2) is approximately in the range of 0.030.8 μm, much larger than the commonly calculated double layer thickness. It could be that the distance which we calculated differs from what other investigators calculated with different equations. Since the membrane has both inner solution and outer solution, there is an inner double layer and an outer double layer. The Eo (emf from the outer capacitor) and Ei (emf from the inner capacitor) are formed through the double layers. The measured potential is Δ E = Eo - Ei (Figure 2 ) . An interface may acquire a charge by several possible means. According to Ottewill, the charge on a glass surface is controlled by the ionization of chemical groupings on the surface (35). It is called an ionogenic surface. The distribution of ions close to the surface (in the socalled diffused layer) is commonly given by the Boltzmann distribution equation (35,36).

where Ψ is the potential difference, ni is the number of ions of type i per unit volume in the vicinity of the surface, and nio is the concentration of ions far from the surface (bulk concentration). The valence number zi is either a positive or negative integral, e the fundmental unit of charge, k the Boltzmann constant, and T the absolute temperature. The charge density, p* , is related to the ion concentration as follows:

Confining attention to a planar interface, if P is the volume charge density in the diffused layer, the Poisson-Boltzmann equation may be applied in the form

where x is the separation of two plates. The derivation of the Poisson equation implies that the potentials associated with various charges combine in an additive manner. On the other hand, the Boltzmann equation involves an exponential relationship between the potential and the charges. We should realize that these equations are approximations (36).


296


The Boltzmann equation has been applied to the derivation of relationship betwwen potential and pH (9,45).


Adsorption of Hydrogen and Hydroxyl Ions by Glass The adsorption of hydrogen ion by Corning glass powder has been studied by Haugaard (10). Since the previous investigators (3) did not believe that the OH" ion could take part, they never tried to measure the OH- ion adsorption by the glass. They used the term "absorption" instead of "adsorption". We carried out the experiments for adsorption of both H + and OH- ions (9). The results are shown in Figure 5. At pH 6.2, there was no significant adsorpton of H + or OH- ions. It was also noted that at the same pH and the same pOH, equal number of H+ and OH- were adsorbed. At pH 3 or pOH 3, approximately 13 H+ and OH- ions per nm2 were adsorbed. The pH 6.2 is therefore isoelectric point of the glass, and no ions can be adsorbed on the surface (42). Acid and Alkaline Errors The acid and alkaline errors of the pH measurements by the glass electrode have baffled chemists ever since the glass electrode was created. After many studies, the conclusion has been that it is too complicated to be understood (30). The Nernst equation cannot explain the nonlinearity at the very low and very high hydrogen ion concentrations. If we accept the following concepts, the acid and alkaline errors are easily understood. 1. The glass surface has a limited number of active sites, and cannot accommodate an unlimited mnumber of H + and OH - ions. 2. Concentrated alkali solutions damage the glass surface. 3. The H + and OH- adsorptions follow the ion adsorption isotherm. 4. At very high concentrations of NaOH, not only the adsorption of OH- is nonlinear with the concentration, the Na+ ion may also be adsorbed to offset the negative charges. As mentioned previously, the glass can act as a zwitterionic surface. 5. The electrode is a capacitor. Chemical Amplification of Potential A membrane electrode acting as a parallel capacitor should follow the capacitance law as shown in Equation (2). The E t o t a l resulting from connecting the capacitors in series with multimembrane electrodes is the sum of each capacitor potential, E

total - E1 + E2 + E3 + E4 +......

for the same solution. The results of 4 pH glass electrodes in series connections are shown in Figure 6. The emf after amplification for both pH 1.0 and 13.0 exceeded one volt. This is a remarkable chemical potential amplification. We further verify that the increase in the positive potential is due to the



20.

CHENG


Figure 5. Adsorption of H + and OH- ion on pH glass.

Figure 6. Chemical potential amplification through electrode connection in series.


297

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ELECTROCHEMISTRY, PAST A N D PRESENT

adsorption of an increased number of H+ ions, and the increase in the negative potential is due to the adsorption of an increased number of OH- ions. A multimembrane pH glass electrode can be constructed with higher sensitivity.


Charge and Discharge of pH Glass Electrode The results in Figure 7 indicate that by grounding the glass electrode, it took less than 3 seconds to discharge completely to zero potential. On the other hand, it took 1-2 min. to charge the glass electrode because of the relatively slow process of chemical charging by the migration of ions to the electrode surface. Qualitatively, one can see a dramatic charging effect by injecting the positive or negative particles on the electrode surface through a zerostat gun (available from Aldrich Chemical Co.) which is used to neutralize the static charges. Suspension Effect The suspension effect on the pH measurements by the pH glass electrode has been known for a long time (31,32). This effect can not be explained by the Nernst equation or ion exchange theory. It is generally attributed to the change in the junction potential of the reference electrode (33,34). We carried out an experiment to separate the reference electrode of Ag/AgCl in a clear NaCl solution from the colloid solution in which the glass electrode was immersed. The two solutions were connected through a piece of copper wire. We found that the colloid particles affected the potential measurements instead of the reference electrode. The suspension effect is caused by the charged colloid particles which have their own double layers and potential from their single capacitors. These tiny colloid particles nearby the glass electrode surface will play an important part in the development of the whole electrode potential. The remedy for eliminating the suspension effect is to measure the pH of the supernatant portion or to coagulate the suspended charged particles with a neutral and polyvalent salt (43). Difficulties encountered in the pH measurement of emulsions have been reported (37). Glass is capable of taking up other substances than water, for instance, alcohol and acetone (10). It is plausible that some interfering substances in the emulsions may be adsorbed on the glass, reducing the effective surface area, or changing the charge density. The emulsion effect may be the same in nature as the suspension effect caused by the charged particles. Solid State pH Glass Electrode Solid state electrodes for copper (38) and for fluoride (39) have been reported. A solid state pH glass electrode has also been reported (40), contrary to the previous belief that a membrane electrode must have an internal solution which contains an ion to be determined in the external solution. Now, we know that this is not so. The above reports further show that even the internal



20. CHENG


Figure 7.

Charge and discharge of pH glass electrode.


299

300


solution is not required. This means that the cell diagram and the Equation (1) lose their significance. According to the capacitor theory, the presence of an internal solution is immaterial, so long as there is a charge contact at the inner layer of the membrane for the emf measurement. The coated wire electrodes are another example without an internal solution.


Capacitance of Glass Electrode at Different pH The capacitance of the flat pH glass membranes was measured at pH 1, 4, and 7, with an internal solution of pH 1, 4, 7, 10 at 140 Mohms. When both the external and internal solutions were pH > 7, a same value of 90 pF/cm2 was obtained. When both the external and internal solutions were pH < 7, the same value of 60 pF/cm2 was obtained. If the pH of the internal solution was pH < 7 and the external solution was pH > 7, or vice versa, the capacitance was from 72 to 75 pF/cm2. Based on the capacitance relationship,

C s = 36, for half of the average capacitance. The average of individual capacitance will be 36 x 2 = 72 pF/Cm2. This is in good agreement with the experimental results. Conclusion The historical development of the pH glass electrode mechanism has been briefly reviewed. Special attention is directed to the fact that membrane electrodes including the pH glass electrode are not a battery as previously believed, but a capacitor. The correct concept is of utmost importance in the understanding of the origin of electrode potentials. Experimental results are presented to support the notion of ionic adsorptions and double layers in electrode potential development. The pH glass electrode is truly a pH electrode in acid media, but it is a pOH electrode in basic media. An electrode with both the internal and external solutions contains a double-layer and double-capacitor membrane. The chemical amplification of potential has been demonstrated, suggesting the device of multi-membralla electrodes for higher emf signals. The acid and alkaline errors, the suspension effect, and the emulsion effect have been discussed. The capacitance of pH glass membrane is measured as a function of pH. The Nernst equation was misused in the past for the pH glass electrode. Its partial success in the quantitative relationship between the potential and the pH may be coincidental. The development of the capacitor theory for the membrane electrodes should stimulate further studies in the double layers and membrane electrodes. Acknowledgments The author is grateful to H. A. Droll, G. D. Christian, and E. W. Hellmuth for helpful discussions and to H. Z. Song, Susie X. R. Yang, and Cynthia Ferrendelli for their potential measurements.


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8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

31. 32. 33. 34. 35. 36.

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pH Glass Electrode and Its Mechanism - ACS Symposium Series (ACS

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