Introduction

Information on gas composition is important in many applications ranging from control of combustion processes to environmental monitoring. To meet these needs, gas sensors have been developed using a variety of different sensing approaches [1–9]. One approach is built on the pioneering work of Kiukkola and Wagner [10], who demonstrated the use of solid electrolytes for measurement of chemical potentials. Solid electrolytes are particularly useful in sensors for high-temperature applications and can be used in several different ways [11–18].

The most direct use of solid electrolytes in gas sensors is for measurement of a gas species corresponding to the ion that is mobile in the solid electrolyte. A common example of this is the use of an oxygen ion conductor, such as yttria-stabilized zirconia (YSZ), for the measurement of oxygen partial pressure, as in the exhaust gas from an internal combustion engine. Fortunately, however, detection is not limited to the mobile species because an auxiliary electrode can be added to provide sensitivity to another species by equilibrating between the desired target species and the ion that is mobile in the electrolyte. For example, the addition of sulfates or carbonates to various solid electrolytes (including oxygen-, sodium-, and lithium-ion conductors) can be used for the measurement of SO2 and CO2 gases [19]. However, this approach requires that the auxiliary electrode material be stable in the sensing environment, which limits the species that can be measured [20].

Although the Nernst potential on which potentiometric sensors are based is established by equilibration between the gas, electrolyte, and electrode, solid electrolytes can be used in non-equilibrium conditions, in which a steady state between electrochemical reactions establishes a potential that can be used as the sensor signal. The establishment of this potential can be described by the mixed potential theory that is commonly used to describe the corrosion of metals [21].

Mixed potential theory

The mixed potential sensing mechanism is based on the establishment of a steady state in which all the electrons produced by an oxidation reaction are consumed by a reduction reaction [22–25]. This is essentially the same process that occurs in an equilibrium sensor except that for an equilibrium sensor the oxidation and reduction reactions are the same reaction but in opposite directions, whereas for a mixed potential sensor the oxidation and reduction reactions are for different species.

The establishment of a mixed potential is illustrated schematically in Fig. 1. The voltage in polarization plots is often plotted as the abscissa, which is appropriate for the results from a polarization experiment where the current is measured at a fixed voltage. However, current is used as the abscissa in Fig. 1 to reflect the idea that the currents associated with the rates of the two reactions establish the voltages. The upper two curves in Fig. 1a represent the oxidation

$$ 2{O^{2 - }} \to {O_2} + 4{e^{-} } $$
(1)

and reduction

$$ {O_2} + 4{e^{-} } \to 2{O^{2 - }} $$
(2)

reactions for the equilibration between oxygen gas and oxygen ions in the electrolyte. The solid lines represent the net current in each direction, which approach zero as the voltages asymptotically approach the equilibrium redox potential. The linear portion of the curve represents the activation polarization, and the extrapolation of that linear curve to the equilibrium potential (indicated by a broken line) is the exchange current, which represents the rates of the forward and reverse reactions at equilibrium. The bottom portion of the figure shows a polarization curve for the oxidation of CO

$$ 2CO + 2{O^{2 - }} \to 2C{O_2} + 4{e^{-} } $$
(3)

and a small portion of the polarization curve for the reduction of CO2

$$ 2C{O_2} + 4{e^{-} } \to 2CO + 2{O^{2 - }} $$
(4)

which establish a lower equilibrium potential than that established by oxygen gas.

Fig. 1
figure 1

Schematic CO and O2 polarization curves. a Establishment of mixed potential. b Effect of changing CO concentration on mixed potential

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The potentials for both reactions depend on the concentrations of the species. Using the reduction potentials, the concentration dependence of the potential (E) is given by

$$ E = {E_{\rm{o}}} - \frac{{RT}}{{nF}}\ln K{,} $$
(5)

where E o is the standard reduction potential, R is the gas constant, T is temperature, F is Faraday's constant, and n is the number of electrons in the reduction reaction with equilibrium constant K. If CO and O2 are both present at non-equilibrium conditions, such as those represented in Fig. 1a, the gases would react according to

$$ 2CO + {O_2} \to 2C{O_2} $$
(6)

which would decrease the CO and O2 concentrations and increase the CO2 concentration. These changes in concentration would lead to an upward shift in the CO polarization curve (i.e., K for Reaction 4 decreases) and a downward shift in the O2 polarization curve (i.e., K for Reaction 2 increases) until the equilibrium potentials become equal. In most practical applications of CO sensors, this does not occur (i.e., the gases do not equilibrate) so a mixed potential is established. The mixed potential is labeled in Fig. 1a and is the potential at which all the electrons from Reaction 3 are consumed by Reaction 2. The effect of the CO concentration on the mixed potential is shown in Fig. 1b. As indicated by Eq. 5, a decrease in the CO concentration will increase the reduction potential which will lead to an increase in the mixed potential (E M).

Since only voltage differences rather than absolute voltages can be measured, a reference electrode is needed. The link to the reference electrode is provided by the solid electrolyte in which ions are mobile, so that the concentration of ionic defects (e.g., oxygen vacancies in YSZ) is the same throughout the bulk of the electrolyte and provides a link between the equilibria at the two electrode surfaces [11, 12]. In this paper, the voltages are reported with the reference electrode as the negative terminal. Although not always used, this convention is common, so if the signs of the electrodes were not specified in a paper from the literature, the reference electrode was assumed to be the negative terminal. The reference electrode can be based on an equilibrium potential, but in that case the reference and sensing electrodes must be separated by a gas-tight seal. However, if the reference potential is also based on a mixed potential, both electrodes can be exposed to the test gas, which, by eliminating the need for separate gas streams and a gas-tight seal between the two electrodes, simplifies the sensor design and thus reduces cost.

The differential response between the reference and sensing electrodes in a mixed potential sensor is achieved by selecting materials with different polarization behaviors. Figure 2 shows the polarization curves for the oxidation of CO (Reaction 3) and reduction of O2 (Reaction 2) on two different electrodes: Reference electrode (Pt) and sensing electrode (SE). Linear polarization curves and equal exchange currents for the two electrodes are used in Fig. 2 to simplify the diagram and more clearly illustrate the trends in the mixed potentials established with different overpotentials and gas compositions. Platinum is typically used as the reference electrode, since it is a good catalyst, which results in a low overpotential (shallow slope). In Fig. 2a, the overpotentials for both the oxidation and reduction reactions on the sensing electrode are increased similarly (relative to Pt), in which case the mixed potential is not changed, so the potential difference between the reference and sensing electrodes is approximately zero. However, if the overpotentials for the two reactions change differently, the mixed potential is changed as shown in Fig. 2b and c. Figure 2b shows the case where the overpotential for the oxidation reaction on the sensing electrode increases more than the reduction reaction on the same electrode. In this case, the mixed potential on the sensing electrode is higher than that on the Pt reference electrode, so a positive voltage will be generated. The reverse case, where the overpotential for the oxygen reduction reaction is increased more than the overpotential for the oxidation reaction, is shown in Fig. 2c. In this case, the potential at the sensing electrode is lower than that at the Pt reference electrode, so a negative voltage will be generated. The oxidation of CO is used as the example in Figs. 1 and 2, but the same mechanism would apply to any reducing gas (such as hydrocarbons) that would be oxidized by oxygen.

Fig. 2
figure 2figure 2

Effect of electrode overpotential reducing gas (CO). a Oxidizing and reducing overpotentials affected similarly. b Oxidizing overpotential of sensing electrode increased more than reducing overpotential. c Reducing overpotential of sensing electrode increased more than oxidizing overpotential

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A mixed potential can also be generated with an oxidizing gas, such as NO2, which is illustrated in Fig. 3. In this case, the relevant reactions are the oxidation of NO

$$ 2NO + 2{O^{2 - }} \to 2N{O_2} + 4{e^{-} } $$
(7)

and the reduction of NO2

$$ 2N{O_2} + 4{e^{-} } \to 2NO + 2{O^{2 - }} $$
(8)

which are analogous to Reactions 3 and 4, but occur at a higher potential than the polarization curves for oxygen. The result of this is that the mixed potential is established between the oxidation of O2− by Reaction 1 and the reduction of NO2 by Reaction 8. Figure 3a shows that when the overpotential for the oxidizing reaction on the sensing electrode increases more than that for the reduction reaction, the mixed potential on the sensing electrode is higher than that on the reference Pt electrode, so the voltage difference is positive. As with the reducing gas shown in Fig. 2, a change in which reaction overpotential is most affected by the electrode material reverses the sign of the voltage. Figure 3b shows that a negative voltage is generated when the overpotential for the reduction reaction on the sensing electrode is increased more than the overpotential for the oxidation reaction. Thus, the sign of the response depends on the relative equilibrium voltages of the two reactions (i.e., oxidizing or reducing gas) and the overpotential that is most increased on the sensing electrode.

Fig. 3
figure 3

Effect of electrode overpotential oxidizing gas (NO2). a Oxidizing overpotential of sensing electrode increased more than reducing overpotential. b Reducing overpotential of sensing electrode increased more than oxidizing overpotential

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Figure 1b shows how the mixed potential on an electrode is changed by a change in gas composition. However, if the reference electrode is placed in the sample gas, which as noted above is a major advantage of mixed potential based sensors, the mixed potentials at both the sensing and reference electrodes will be affected. This is illustrated in Fig. 4, which includes the polarization curves for the oxidation of CO for two different CO concentrations. If the oxygen partial pressure is not changed, then the polarization curves for O2 reduction will not change. Since both the reference and sensing potentials increase, the difference between the two mixed potentials is smaller than the difference between the two mixed potentials at the sensing electrodes for the two CO concentrations.

Fig. 4
figure 4

Effect of gas concentration on mixed potential

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The electrochemical reaction rates can be limited by other factors, such as mass transport from the bulk gas to the electrode surface. In this case, the polarization curve is affected as illustrated in Fig. 5. In particular, at a certain overpotential, the current becomes limited by transport of gas to or from the electrode surface and does not increase with further increase in overpotential. Figure 5a shows a case in which the oxidation of CO reaches a plateau. Even though, in this example, the saturation current is the same for the two electrodes, the mixed potential is different because of the different overpotentials for the oxygen reduction reaction. Figure 5b shows the effect of a change in CO concentration in the case of concentration polarization. In addition to the shift in the potential of the polarization curves (lower potential for higher CO concentration), as in Figs. 1b and 4, the limiting current can also change, since the maximum rate of supply of CO (in this example) will depend on the CO concentration in the bulk gas (larger current for higher CO concentration). This change in the limiting current is the same as that used in amperometric sensors based on solid electrolytes. The result of these two factors is a larger (more negative) voltage with increasing CO concentration.

Fig. 5
figure 5

Mixed potential with concentration overpotential. a Establishment of mixed potential. b Effect of changing CO concentration on mixed potential

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Non-equilibrium sensor performance

One of the simplest uses of a mixed potential is in a sensor with a Pt reference electrode and an Au sensing electrode for the measurement of CO. Figure 6 shows that the overpotential for the reduction of O2 on a cerium gadolinium oxide (CGO) electrolyte with an Au electrode is higher than that with a Pt electrode [26]. The schematic in Fig. 2c indicates that an increase in the overpotential for oxygen reduction leads to a decrease in the mixed potential voltage, which would result in generation of negative voltage. A negative voltage has been observed for CO sensors with Pt and Au electrodes as shown in Fig. 7 [26–33]. The increased response with decreasing temperature of the sensors with CGO electrolytes shown in Fig. 7 correlates with the increasing overpotential with decreasing temperature shown in Fig. 6. In addition to the oxygen ion conducting electrolytes shown in Fig. 7 (e.g., samarium-doped ceria and YSZ), a sodium ion conducting electrolyte, beta alumina, has also been used in CO sensors with Au and Pt electrodes [34–36]. The sodium ion conducting electrolyte can be used for measurement of the mixed potential because the equilibrium between sodium oxide in the sodium beta alumina acts as an auxiliary electrode by providing equilibration between oxygen and sodium.

Fig. 6
figure 6

O2 reduction overpotential for Au and Pt electrodes on cerium gadolinium oxide (CGO) [26]

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Fig. 7
figure 7

Outputs for CO sensors with Pt and Au electrodes [26–33]

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The addition of an oxide can inhibit microstructural changes in the Au electrode and thus improve sensor stability, particularly at high temperatures where sintering can occur [33]. Semiconducting oxides can also be used as the electrodes, some examples of which are shown in Fig. 8 [27, 37–43]. Several of these oxides generate negative voltages similar to Au electrodes, but there have been reports of positive voltages for LaFeO3, La0.8Sr0.2O3, and La2CuO4 electrodes [41–43]. Although the responses for sensors with LaFeO3 or La0.8Sr0.2O3 electrodes are relatively small, the response with a La2CuO4 electrode is large.

Fig. 8
figure 8

Outputs for CO sensors with Pt and oxide electrodes [27, 37–43]

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The largest response for a LaCu2O4 electrode was found at 300 °C, but this signal was not stable, in that the signals for increasing and decreasing gas concentration were different [43]; 300 °C was also the temperature at which the rate of CO desorption, according to temperature-programmed desorption (TPD) results, was maximum. As the temperature increased above 300 °C, the desorption and sensor signal decreased, so the response was attributed to adsorbed species. 300 °C was also the temperature above which the oxidation of CO occurred more slowly on La2CuO4 than on Pt according to temperature-programmed reaction (TPR) experiments. The slower oxidation on CO could lead to a mixed potential response with a positive sign if the slower rate were due to an increased overpotential for the oxidation of CO (see Fig. 2b) on La2CuO4.

The response of a sensor with Au and Nb2O5-covered Au has also been attributed to CO adsorption based on the absence of any catalysis of the CO oxidation for either electrode material as measured with TPR [44]. The response is attributed to a shift in the Fermi level of the semiconducting electrode due to adsorption on the electrode surface, but the mechanism by which this change relates to the electrochemical potentials in the solid electrolyte has not been described. Although both Au and Nb2O5-covered Au do not catalyze CO oxidation, there could still be a difference in their polarization behaviors, so a mixed potential response is possible. The changes in mixed potentials generally increase as the magnitude of the overpotential increases (i.e., steeper slopes in Figs. 1, 2, 3, 4, and 5), so even a relatively small difference in overpotentials may generate a measurable response.

As mentioned above, the mixed potential mechanism can be applied to other reducing gases, some examples of which are shown in Fig. 9 [32, 45–50]. Sensors with Pt and Au electrodes respond to hydrocarbon gases and the response increases with increasing molecule size (i.e., C2H4 to C4H8). A similar trend is observed using an oxide electrode (In2O3+MnO2), but the response of the oxide electrode is larger. An oxide electrode (In2O3) has also been shown to respond to very small (sub parts per million) levels of C3H6. Figure 9 also shows that the sensor response can be changed by doping the electrolyte. In particular, the addition of titanium to the electrolyte leads to an increased response to C3H6, which illustrates the importance of the electrode–electrolyte interface in the polarization behavior. In addition to changes in the magnitude of the sensor response, changes in the sign can occur, as has been observed between CO and C3H6 for an Nb2O5 electrode [51]. The differences between the responses of different electrodes change with temperature, which provides an additional variable in the design of sensing systems for mixed gases, since multiple sensitivities can be obtained, even for a single sensing element, by varying the test temperature. The ability to respond to multiple gases expands possible sensor applications and also creates challenges in obtaining satisfactory selectivity in multicomponent gases.

Fig. 9
figure 9

Outputs for CO and hydrocarbon sensors with YSZ electrolytes [32, 45–50]

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Another important application of non-equilibrium-based sensors is for the measurement of NO x . Although equilibrium-based NO x sensors have been reported, they have limited applicable ranges, so non-equilibrium-based sensors are more promising [52]. The equilibrium between the two common NO x gases

$$ 2NO + {O_2} \rightleftharpoons 2N{O_2} $$
(9)

indicates that the NO2 is favored at low temperatures and high oxygen partial pressures. In particular, the Gibbs energy for Reaction 9 is 0 at 491 and 235 °C for oxygen partial pressures of 105 and 103 Pa, respectively [53]. Since these conditions are similar to common sensing conditions, measurement of both gases by non-equilibrium sensors is possible.

The polarization behavior of NO2 sensors was discussed above in Fig. 3, while that of NO would be analogous to CO described in Fig. 2. Although both sensors are based on the same reactions, the positions of the polarization curves relative to those of oxygen are different due to the different gas compositions (i.e., NO/NO2 ratio). The responses of mixed potential gas sensors for NO and NO2 are typically opposite in sign. The generally observed negative potential for NO and positive potential for NO2 is consistent with the discussion above and indicates that the oxygen reaction controls the sensor response [54]. However, by applying a potential between the reference and sensing electrode, effectively shifting the relative positions of the polarization curves, the relative response to NO and NO2 can be changed [55–58], which provides means for optimizing the sensor selectivity for a particular application.

The outputs of some NO2 sensors with YSZ electrolytes and WO3 electrodes are shown in Fig. 10 [41, 42, 59–67]. In one case [63], a tubular configuration, in which the electrodes were separated so the reference electrode could be exposed to a separate gas, was used to increase the sensor output. As discussed above, the potential of a reference electrode in the test gas, as in a planar sensor, is affected by changes in the test gas composition, so the sensor output may be smaller than that for a sensor with separated electrodes. In another case [65, 66], deposition of WO3 on both the Pt and YSZ in a planar configuration was found to improve sensor response. The improvements were attributed to an interfacial layer inhibiting catalysis, which would increase the overpotential and thus increase the response as discussed above.

Fig. 10
figure 10

Outputs for NO2 sensors with Pt and WO3 electrodes at 600 °C [41, 42, 59–67]

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Another commonly used electrode material for NO2 sensors is NiO, and the outputs of some sensors with NiO electrodes and YSZ electrolytes are shown in Fig. 11 [68–72]. As with the CGO-based CO sensors in Fig. 7, the magnitude of the response decreases with increasing temperature, which is expected for a sensor based on kinetic limitations, since those kinetic barriers are more easily overcome with the increased thermal energy at higher temperatures. The temperature dependence is also shown by the comparison in Fig. 12 of the sensitivities (millivolt per decade) of NO2 sensors with WO3 and NiO electrodes [41, 42, 59–63, 69–75].

Fig. 11
figure 11

Outputs for NO2 sensors with Pt and NiO electrodes [68–72]

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Fig. 12
figure 12

Sensitivities of NO2 sensors with Pt and WO3 or NiO electrodes [41, 42, 59–63, 69–75]

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According to Fig. 3a, a positive sensor response to an oxidizing gas, like NO2, indicates an increased overpotential for the oxidation of O2−. The anodic polarization curves for doped and undoped NiO electrodes in Fig. 13 show that the overpotential for O2− oxidation is increased with cobalt additions, but decreased with chromium additions [75, 76]. Figure 14 shows, consistent with Fig. 3a, that the increased overpotential (i.e., Ni0.9Co0.1O) generates a larger response, while the decreased overpotential (i.e., Ni0.95Cr0.03O1-δ) leads to a smaller response [71, 72, 74–76]. A similar increase in both polarization and sensor response has been observed with the addition of CuO to NiO [77].

Fig. 13
figure 13

O2− oxidation overpotential for doped and undoped NiO electrodes at 800 °C [75, 76]. The NiO polarization curves were used to normalize the currents for direct comparison on a single graph

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Fig. 14
figure 14

Outputs of NO2 sensors with Pt and doped/undoped NiO electrodes at 800 °C [71, 72, 74–76]

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There have been some reports of NO2 sensors with responses that are opposite in sign to those of the WO3- and NiO-based sensors discussed above. In particular, negative potentials have been observed for La0.8Sr0.2FeO3 [41, 42, 60] and La2CuO4 [43] sensing electrodes with Pt reference electrodes and YSZ electrolytes. Because these are both p-type semiconductors, as compared to WO3 which is an n-type semiconductor, the opposite signs of the responses have been related to the semiconductor nature of the electrode materials. However, NiO [78] as well as lanthanum chromite [79] and (La,Sr)(Co,Fe)O3 [80] are also p-type semiconductors and generate a positive response when used in NO2 sensors, as shown in Fig. 15 [41–43, 69, 81–83]. Although the p-type conduction does not alone explain the opposite sign, there is a difference in the response mechanism.

Fig. 15
figure 15

Outputs for NO2 sensors with Pt and oxide electrodes [41–43, 69, 81–83]

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The response of sensors with La2CuO4 electrodes has been attributed to an absorption mechanism [43] based in part on infrared and X-ray photoelectron spectroscopy, which indicate that absorbed NO and NO2 species lead to anionic species on the La2CuO4 surface [84]. The adsorbed species are suggested to lead to the formation of oxygen vacancies with electrons for NO adsorption and holes for NO2 adsorption, which cause shifts in the Fermi level. The maximum response occurs at the same temperature at which NO2 is reduced on both Pt and La2CuO4 surfaces as indicated by TPR results. The response decreases with increasing temperature, but a response is observed at temperatures at which TPD results indicate that most of the NO and NO2 would have desorbed from the surface. There is a recent report of a NO2 sensor based on the surface plasmon resonance of Au nanoparticles in a YSZ matrix [85], which suggests that NO2 adsorption could affect the electronic state in the electrode. In addition, although generally considered to cancel out for symmetric Pt electrodes, the chemical potential of electrons in the electrode contributes to the measured potential of an electrochemical cell [11]. Changes in the Fermi potential could generate a sensor response, but for that response to be measured with a solid electrolyte, the change in potential needs to be related to the mobile ions in the solid electrolyte. This interaction would occur by redox reactions at the YSZ–La2CuO4 interface, which could be established by a mixed potential mechanism. According to TPR results, the reduction rates of NO2 on Pt and La2CuO4 are similar [43]. However, the presence of adsorbed species or related inhibiting gas–solid interactions could affect the polarization behavior of the electrode, similar to the way that mass transport limitation can lead to concentration polarization, and establish a mixed potential on the electrode surface. The observed negative value of the response voltage would suggest that, according to Fig. 3b, whatever the inhibiting effect, the NO2 reduction reaction is affected more than the O2− oxidation reaction.

Electrode microstructure is particularly important in non-equilibrium-based sensors, since factors such as surface area and morphology affect reaction rates. For example, small grains [86] or small particles [87] have been shown to improve response. However, the effect of surface area in a non-equilibrium potentiometric sensor is different from that in many other sensors, such as semiconductor resistance-based sensors where high surface area is desired to enhance gas–solid interaction. For a mixed potential sensor, an increase in the electrode surface area would increase the rates of both reactions, so, at least under activation polarization, the mixed potential would not be changed. However, if the reaction was under concentration polarization, the rate would be limited by mass transport from the bulk gas to the electrode surface, which would not be affected by the increased surface area. Thus, a mixed potential between one reaction under activation polarization control and another under concentration polarization control can be affected by a change in the electrode surface area. For example, a NO2 sensor based on two platinum electrodes with different surface morphologies responded to 40 ppm NO2 and generated a signal of 80 mV at 800 ppm NO2 [88].

The usual approach in electrochemical devices is to have a dense electrolyte to separate the gases at the two electrodes with porous electrodes to increase the active surface area. However, in the case of mixed potential sensors, separation of the gases is not needed and high reaction rates are not desired for all reactions. Thus, sensors with porous electrolytes and dense La0.8Sr0.2CrO3 [82, 89, 90] or (La,Sr)MnO3 [39] electrodes have been reported. The advantage of the dense electrode is that heterogeneous catalysis by the electrode is minimized due to the low surface area, while the porous electrolyte allows for gas transport to the electrode–electrolyte interface.

Conclusions

Non-equilibrium-based electrochemical sensors provide the ability to sense gases, such as NO x , CO, and hydrocarbons, that are difficult, if not impossible, to measure with equilibrium-based electrochemical sensors. The theory most often used to describe the sensing mechanism is the mixed potential theory, for which the sensor output is based on a steady state between four different electrochemical reactions. The sensor response is most often attributed to differences in the overpotential for oxygen reduction or oxygen-ion oxidation, but this explanation does not explain all observed sensor responses. Processes, such as adsorption, may inhibit the electrochemical reactions at the electrode surfaces, which may increase overpotentials and thus affect the electrode potentials. The multiple factors that can affect the outputs of non-equilibrium sensors provide opportunities for the development of new sensors, but also create challenges in understanding and controlling the sensor responses.