In 1909, based on observations of Cremer (1906) at glass membranes, F. Haber and Z. Klemensiewicz developed the pH glass electrode [4]: a glass bubble filled with strong electrolyte and a silver|silver chloride electrode inside (Figure 1-a). Improved pH selective glasses were found by Mcinnes in 1930. Present glasses contain, e.g., 63% SiO₂, 28% Li₂O, 5% BaO, 2% La₂O₃ [5]. UO₂ and TiO₂ improve the performance in alkaline solutions [6]. A. Beckman's practical pH meter (1934) used a high-gain vacuum tube amplifier in order to replace the earlier used sensitive galvanoscope by a cheap milliamperemeter. Swiss chemist W. Ingold (1952) created the single-rod measuring chain, which finally combined working electrode and reference electrode in one shaft. Advanced potentiometric measuring chains have become commercially available since the 1970s. In 1986, Ingold replaced the liquid inner electrolyte by a gelled electrolyte, in order to slow down the loss of electrolyte through the junction between reference electrode and external solution, however, at the cost of lifetime.

The double junction electrode introduced an additional chamber between reference electrode and external solution to save the reference electrolyte from external contamination (Figure 1-b). The potential difference Δφ_I–II across the thin glass membrane reflects the difference between the H⁺ activities a on both sides, and can only be determined by means of two reference electrodes. The less than 0.5 μm thick soaking layers on both sides of the membrane enable the exchange of cations in the silicate framework against H₃O⁺ from the surrounding solutions and vice versa. The two soaking layers are connected by the cationic conductivity of the thin glass membrane. The measured chain voltage E is made up of the membrane contribution and the diffusion potentials at the liquid junction between each reference electrode and the ambient solution: (2a) Δ ϕ I − I I = R T F ln a ( H + , glass I ) a ( H + , solutionI ) − R T F ln a ( H + , glass II ) a ( H + , solutionII ) = R T F ( p H I I − p H I ) + Δ ϕ a s (2b) E = R T F ( p H II − p H I ) + E a s + E d

The measured voltage E consists of (1) the H⁺ activity-dependent potential drop Δφ₁ between glass membrane and outer solution I, (2) Δφ₂ between glass and inner electrolyte II, (3) Δφ₃ at the inner reference electrode, (4) Δφ₄ at the external reference electrode, (5) the diffusion potential at both reference electrodes, E_d = Δφ_d,I + Δφ_d,II, which is caused by small amounts of various ions passing the diaphragm in both directions with different velocity, driven by concentration gradients between the adjacent solutions. Even at the same pH of inner electrolyte and outer test solution, the measured chain voltage does not equal zero, because the slightly different soaking layers on both glass sides cause an instable asymmetry voltage E_as = Δφ_as. Due to the dissociation of functional groups at the glass surface, the slope of the E vs. pH function may be smaller than the theoretical Nernst response, dE/dpH = ln 10 · (RT/F) ≈ 0.059, at 25 °C.

The practical chain zero-point, U = 0 V, in commercial glass electrodes is at about pH 6.84, and drifts to slightly higher pH values the more the membrane glass corrodes in the inner electrolyte. The offset voltage at pH 7 is determined mainly by the diffusion potential in the test solution. The intersection point of the isotherms (pH_iso|U_iso) in Figure 1-c is calculated by means of the pH measurements in two buffer solutions (A and B) at two different temperatures (1 and 2): (3a) U iso = U B 1 S 2 − U B 2 S 1 − S 1 S 2 ( p H B 2 − p H A 2 ) S 2 − S 1 ; S 1 = U B 1 − U A 1 p H B 1 − p H A 1 (3b) p H iso = U iso − U A 1 S 1 − p H A 1 ; S 2 = U B 2 − U A 2 p H B 2 − p H A 2

Hence the terminal voltage of a pH meter is not absolutely defined; it must be calibrated against standardized pH buffer solutions [7]; e.g. hydrochloric acid (0.1 mol/L, pH 1.094), potassium hydrogen phthalate (0.05 mol kg^–1, pH 4.005), Na₂HPO₄/KH₂PO₄ (each 0.025 mol kg^–1, pH 6.865), sodium tetraborate (0.01 mol kg^–1, pH 9.180), NaHCO₃/Na₂CO₃ (each 0.025 mol kg^–1, pH 10.012) at 25 °C.

Solutions of strong acids, such as 0.001 molar HCl (pH 3.00), exhibit nearby no temperature dependence of pH, because the H⁺ concentration is determined by the dissociation of the acid. In alkaline solutions, however, the pH value is determined by the autoprotolysis of water, and decreases with rising temperature; e.g. 0.001 molar NaOH: pH 11.94 at 0 °C; 11.00 (25 °C); 10.26 (50 °C).

The cross-sensitivity of the pH electrode is described by the Nikolsky-Eisenman equation, containing the selectivity coefficients k_i for all other single charged ions present [8,9]: (4) E = E 0 + R T F ln ( a H + + k 1 a Na + + k 2 a K + + … )

The cross-sensitivity is measured in different solutions after adding rising amounts of NaClO₄, e.g., 0, 0.01, 0.1, and 1 mol/L, respectively. Useful solutions for this purpose are [10]: a)

2,2-Bis(hydroxyethyl)amino-tris(hydroxymethyl)methane, 20.924 g/L, in HCl, 0.05 mol/L; pH 6.58

The Harned cell [11] is a primary method of measurement [12] in order to incorporate pH determinations into the SI system, based on a well-defined measurement equation in which all of the variables can be determined experimentally in terms of SI units. The Harned cell, a cell without transference, defined by (–) Pt|H₂|solution, KCl|AgCl|Ag (+), consists of a hydrogen electrode (dry hydrogen at atmospheric pressure p) and a silver-silver chloride electrode, and exhibits no diffusion potential, which usually occurs at any two adjacent liquid phases. The measurement comprises three steps:

The cell (–) Pt|H₂|HCl(m)|AgCl|Ag (+) is filled with hydrochloric acid (e.g. m_HCl = 0.01 mol kg^–1, γ_±HCl = 0.904 at 25 °C), and the potential difference according to the spontaneous cell reaction, ½H₂ + AgCl → Ag_(s) + H⁺ + Cl^– is measured. From this E⁰ is calculated (p⁰ = 101 325 Pa):

(5) Δ E 1 = E K C 1 | AgC 1 | A g 0 − R T ⋅ ln 10 F lg ( m H C 1 ⋅ γ ± H C 1 ) 2 p / p 0 ⋅ ( 1 molkg − 1 ) 2

For non-aqueous solvents [13], having an water-like autoprotolysis, LH + LH ⇌ [LH₂]⁺ + L^–, the ⇌ neutral point, similar to pH 7 in pure water, is defined by n = − lg K, wherein K is the equilibrium constant of the autoprotolysis. Such a specific pH_n scale for each solvent does not allow the direct comparison with aqueous solutions.

A universal scale of acidity for all media must be based on the activity of free protons, pH = –lg a_H [14], and can be measured relative to a standard hydrogen electrode in this medium as shown above. For concentrated sulfuric acid (pH = −10), and saturated KOH solution (pH 19), the usual range between pH 0 and 14 is reached again by dilution.

The fabrication of an all-solid-state glass electrode [15] is complicated by the internal reference electrodes, which do not work precisely in the absence of a buffer solution. Trials to coat platinum wires with glass were not successful. Silver layers, amalgams (of sodium, lithium or cadmium), metal alloys and tungsten bronzes on the inner porous glass membrane are known (see Section 7).

Ion Selective Field Effect Transistors (ISFET) have been developed since the 1970s [16], but have not yet reached the precision of the pH glass electrode. ISFET pH sensors are limited to a pressure of about 2 bar and temperatures up to about 85 °C.

Basically, the current flowing between two semiconductor electrodes (drain and source) is controlled by the electrostatic field generated by the protonated third electrode (gate), which is placed between drain and source. Usually the gate is coated by (i) a ceramic material such as Al₂O₃, Si₃N₄, Ta₂O₅, ZrO₂, GaN (Table 1); (ii) an organic material, e.g. valinomycin in a resin; (iii) a polymer such as PTFE, polypyrrol or polyethylene naphthalate (PEN), or (iv) a catalytical metal layer, e.g. Pt. Instead of measuring the potential difference on two sides of a glass membrane, the current flowing through the transistor (MOSFET) is observed. For practical measurements in liquids, the electrical circuit must be closed with a reference electrode (Figure 2). On any change of pH value and thus the gate potential, the voltage supply to the reference electrode is re-adjusted by electronic feedback in order to keep the measured drain current constant to a predefined value – usually the current at the isothermal point in order to avoid the influence of temperature. Highly accurate amperometers are required (< 1 μA) to measure the drain-source current, while the gate voltage is increased.

pH-sensitive films of RuO₂ can be sputtered or screen-printed on silicon, alumina, pyrex, or polyester foil (Figure 3-a). The electrochemical sensor exhibits three basically nonideal characteristics:

Drift effect: The slow nonrandom change of output voltage with time (by some mV h^–1) in a solution with constant composition and temperature. Measurement circuit, reference electrode, and device body are greatly affected.

A pH-sensitive enamel zone, deposited on a sturdy steel tube, can be used for pH measurements under mechanical stress [20]. A flat steel diaphragm, at the end of the tube, is connected to the reference electrode. The probe has an individual slope around 55 mV pH^–1; the working range is between pH 0 and pH 10. The sodium error, especially at elevated temperatures, limits applications to pH 6–8 at temperatures above 140 °C. pH_iso (see Figure 1-c) lies around pH 2.

The composition of a glass having a similar thermal expansion coefficient than steel was reported as (by weight): 68.61% SiO₂, 18.41% Na₂O, 6.44% MgO, 6.54% UO₂ [2]. Mixed electronically and ionically conducting glasses in order to connect two pH glass layers, may contain iron oxide; such as 36.9% SiO₂, 16.1% Na₂O, 43.4% Fe₂O₃, 2.6% Al₂O₃ [2].

Proton-sensing compounds – such as N-octadecylmorpholine – in a polymer matrix [21] are suitable for pH measurements in a narrow pH range [22].

Redox-active groups in a receptor adsorbate on a conducting substrate may indicate pH changes. Thioethers adsorb strongly on a gold surface through the sulfur atom; the alkyl groups may be linked to a ferrocene group and a carboxyl acid group, e.g. (C₅H₅)Fe(C₅H₄)–(CH₂)₆–S–(CH₂)₇COOH. On a change from pH 6.5 to pH 1, the redox peak of ferrocene in the cyclic voltamogram is shifted by about 200 mV [23]. Cyclodextrins, calixarenes, and cavitands are able to bind organic guest molecules in a hydrophobic cavity, which can be used for biosensors.

Advantages and disadvantages of different pH monitoring methods are compiled in Table 2. The use of optical sensors for spectroscopy and light scattering measurements is restricted to nearby colorless solutions without substantial changing of transparency. pH indicators require the absence of strongly oxidizing or reducing agents. For pH measurements in biological media, quinoline derivates have been reported as a fluorescence probe.

Platinum black, purged with pure hydrogen (Section 2.2), is most corrosion resistive, but it is readily poisoned by CN^–, H₂S, and As₂O₃. Platinum absorbs oxygen if not stored under hydrogen permanently, and heavy metal ions, nitrate, and nitrophenols are reduced on its surface.

Palladium, ruthenium, and osmium, if resaturated with hydrogen periodically, work as pH probes, without it being necessary to maintain them permanently in a current of hydrogen (such as platinum). It holds E = −0.0591 pH, or pH = −16.92·E (at 25 °C).

The standard potential of the half-cell reveals whether a redox system is stable in aqueous solution or works as an oxygen electrode (E⁰′ > 0.815 V at pH 7) or a hydrogen electrode (E⁰′ < −0,414 V at pH 7). For example, the redox system Cr³⁺ + e^–⇌Cr²⁺, due to the ínstable Cr²⁺, decomposes water and is therefore a hydrogen electrode, H⁺ + e^–⇌½H₂, which, however, can be stabilized at pH 7.

The quinhydrone electrode [25] consists of an equimolar mixture of benzoquinone and 1,4-dihydro-xybenzene, which is contacted by a platinum rod. The standard redox potential E⁰ = – (RT/F) ln [p_H2]^1/2 ≈ +0.70 V corresponds to the low hydrogen pressure of about 2·10^–24 bar. This quasi-hydrogen electrode is restricted to diluted acid solutions. At pH ≥ 8 it is decomposed by oxygen.

Metal surfaces which form unsoluble hydroxides in aqueous solution can be used for pH determinations. The redox potential of the antimony electrode [26, 27] – see Table 4 – depends directly on the proton activity of the solution in the range between pH 3 and pH 11: (9) E = E 0 + R T 3 F ln a ( Sb 3 + ) = E 0 + R T 3 F ln K L K W + R T F ln a ( H + ) = E 0 ′ − R T 0.4343 ⋅ F ⋅ p Hwhere K_w = a(H⁺)·a(OH^–) denotes the ionic product of water. K_L is the solubility product of antimony hydroxide according to Sb₂O₃ + 3H₂O ⇌ 2Sb(OH)₃ ⇌ 2Sb³⁺ + 6OH^–. The surface of antimony wires can be oxidized anodically or in a potassium nitrate melt. An immediate electrode response is achieved if Sb₂O₃ is added to the melt when puring the antimony electrode, too. The potential of the antimony electrode depends on the oxygen partial pressure and parasitic electrode reactions; mechanical cleaning of the electrode surface is uncritical.

The measured cell voltage of the antimony electrode against a reference electrode is disturbed by reducing and oxidizing agents in the solution – a problem of all metal electrodes. pH_iso of the highly asymmetric cell (see Figure 1-c) lies at a negative pH value of -3.

In alkaline solutions the bismuth electrode was described [28]. Approximately linear functions of potential versus pH were observed with Sn, W, Fe, Ir, Os, Ag, Cu, Zn, and other metals, mainly in oxygen-free buffer solutions. Mostly, the slope does not equal the theoretical value of (ln 10) RT/F, and is limited to a narrow pH window, and depends on the anions present in the solution. These electrodes are not simply hydrogen electrodes; several simultaneous potential-determining processes give rise to a mixed potential which may come close to the reversible hydrogen potential.

Since the late 1970s mixed platinum metal oxides [31], coated on titanium supports, have been developed for dimensionally stable electrodes (DSA) for chloralkali electrolysis [32]. The RuO₂ electrode works as a quasi-hydrogen reference electrode (cf. Section 3), and is sensitive for dissolved oxygen. First, in the 1980s, oxygen intercalation [33] was assumed, with a proton activity in the liquid phase, and an oxygen activity in the solid phase: RuO₂ + 2z (H⁺ + e^–)⇌RuO_2–z + zH₂O. However, platinum oxide surfaces were found to be able to exchange protons with aqueous solutions [34]. The mechanism in Equation 10 was found, among others, by investigating the point of zero charge and the exchange of tritium ions on the inner surface of the porous material [35,36]: (10) R u O x ( O H ) y + z e − + z H + ⇌ R u O x − z ( O H ) y + z (11) Simplified : R u I V O 2 + e − + H + ⇌ R u III O ( O H )

The pseudocapacitance C(U) = dQ/dU of the RuO₂ electrode [37] arises from kinetically inhibited redox processes at the metal oxide-liquid interface, and depends strongly on frequency, temperature, and the applied voltage U.

The Helmholtz double-layer capacitance is always superimposed by faradaic delivered charges Q from the battery-like redox steps involved in the potential-determining charge-transfer reaction across the interface. Water molecules saturate the free valences in the disturbed rutile lattice. By dissociative adsorption of water – as shown in Figure 3-a – the RuO₂ surface is covered by hydroxide groups, which try to form oxide sites by the release of protons. The process might be driven by the goal to compensate the oxygen defect stoichiometry of the oxide.

The cyclic voltammogram in Figure 3b shows the overlapping, highly reversible, redox processes of Ru(IV), a small amount of Ru(III) and other species. The thermodynamically calculated standard potential of the redox reaction 2RuO₂ +2H⁺ +2e⁻ ⇌ Ru₂O₃ + H₂O at E⁰ = 0.937 V [39] corresponds to a current peak in the cyclic voltammogram, which arises during the precipitation reaction according to: 2RuCl₃ + 6KOH + ½O₂ → 2(RuO₂·1.5H₂O) + 6KCl [40].

Tetravalent ruthenium, e.g. in K₂Ru(OH)Cl₅, can be reduced to Ru(III) with hydrogen; and “Ru(OH)₃” can be oxidized in the air to RuO₂·2H₂O. The peak currents, I = C v, in the oxidation wave at about 0.7–0.9 V in Figure 3-b increase if oxygen is blown on the RuO₂ electrode. Solutions of RuCl₃·3H₂O, which are reduced electrochemically to pink [Ru(H₂O)₆]²⁺ ions, are immedeately oxidized back to the yellow [Ru(H₂O)₆]³⁺ by oxygen, or less fast by the decomposition of water. Ru(II), with hydrogen bound side-on, is known as a proton source, [Ru(H₂O)₅(H₂)]²⁺→[Ru(H₂O)₅H]⁺ +H⁺.

A RuO₂ film that is electrochemically oxidized on a quartz crystal microbalance loses a mass of 56.3 u per electronic charge, which corresponds roughly to [H(H₂O)₃]⁺ (mass 55) [41], cf. Equation 11. To explain the ionic conductivity of RuO₂, a bulk diffusion process including H₃O⁺ species was suggested [42]; later the low activation energy of 4–5 kJ mol⁻¹ was attributed to a Grotthus-type proton hopping mechanism. The protons (or hydroxide sites), formed by dissociative adsorption of water, can penetrate into the porous electrode material. The impedance spectrum in Figure 3-c shows a diffusion branch at low frequencies which depends clearly on the thickness of the active layer.

The voltammetric charge Q increases with rising RuO₂ mass until the film gets too thick; solid-phase redox reactions in the bulk material contribute by less than 10% to the overall capacitance. In particles larger than 30 nm, therefore, most of the charge capability will remain unused in the particle core.

Usual thick film sensors are prepared by three inks or pastes which are screen-printed onto alumina: Ag-Pd paste as conductor, metal oxide paste as active surface and an overglace paste as protector. In recent years, finely dispersed platinum metal oxides were coated on carbon particles or bound in polymers [54,55,56]. Polymer bound metal oxide electrodes can be fabricated by coating metal plates with a thin layer of a mixture of metal oxide powder in commercial varnish based resins. The best pH sensitivity is achieved by a mixture of 10% sol-gel RuO₂·xH₂O (water content ∼7.2%) in a matrix of epoxy or polyester [57]. Reactive sputtering of platinum metal targets in argon-oxygen atmospheres is used to produce 1 μm thick oxide electrodes on alumina and silicon substrates; palladium and platinum oxides were found to be less stable than ruthenium oxide [58]. An overview of applications [59] is given in Table 5. Both potentiometric and amperometric sensors [60] have been used.

IrO₂ [73] promises to be a superior material for pH measurements in technical media, such as fuels [74], food applications [75], and in biological media [76]. Irdium oxide provides: (i) a wide linear pH response range, with negligible interference of ions and complexing agents, (ii) a fast and stable response in aqueous, nonaqueous, non-conductive, and even corrosive media, (iii) high conductivity, low temperature coefficient, and no requirement for pretreatment.

The Ag|AgCl|Cl^– electrode works basically without any AgCl on its surface; AgCl can be dispersed in the solution, but the response to the chloride ions is slow according to the equilibrium: Ag⁺_(s) + Cl^–_(s) ⇌ AgCl_(s).