Quiz 7

Conceptually construct the layout of the anode, electrolytic solution, and cathode of an ideal regenerative photovoltaic oxygen cell from relatively oxidizing single redox couple \(}_/}_\text\), using a negative inverse overvoltage for photosensitized anodic oxidation, driven by a photoexcited minority carrier hole in the n-type anode in combination with a counter metal cathode.

(a)

Distinguish the anode and cathode and briefly clarify their related electrochemical reactions. Give the best candidate material for the counter cathode.

(b)

Predict the photocurrent I vs photovoltage V curve using the concept of the quasi-Fermi level underlying the negative overvoltage, \(_}^,\text}<0\), for the photoexcited anodic oxidation, caused by the VB minority holes in the n-type anode.

Answer 7

(a)

The term “anode” originally comes from “anion.” A cation is usually newly created as an oxidant at the anode/solution interface during oxidation in the dark by producing the redox electron left behind in the metal anode, and hence another partner "anion" there must compensate for the newly created cation, diffusing through the electrolyte from the counter cathode/electrolyte interface toward the anode/solution interface, to maintain the charge neutrality condition as a whole.

As an alternative, an anion is newly consumed as a reductant at the anode/solution interface during oxidation under illumination by consuming the photoexcited VB hole coming from the n-type anode interior. Hence, another partner “cation” must simultaneously be consumed at the counter metal cathode by the redox electron to compensate for the anion consumed.

Special attention needs to be paid to the two facts: (1) an oxidative operation of consuming a photoexcited VB hole during illumination is physically equivalent to another oxidative operation of producing a redox electron left behind in the metal anode in the dark; (2) on the whole, in any redox system, an electron or hole lost by the anode is simultaneously gained by the counter cathode.

In contrast, the term, “cathode” is named after “cation.” A cation is usually consumed at the cathode/solution interface during reduction by either injecting the photoexcited CB electron coming from the p-type cathode surface or injecting the redox electron from the metal cathode surface in the dark. Therefore, the newly created cation must compensate for the “depleted cation,” diffusing through the electrolyte from the counter anode/electrolyte interface to maintain the charge neutrality condition as a whole.

The overall cell reaction is divided into a partial anodic oxidation at the n-type anode/electrolyte interface and a partial cathodic reduction at the metal cathode/electrolyte interface, given by

$$}_\text+2\text\left(\text\right)=}^+\frac}_,\text$$

(24)

$$}^+\frac}_+2\text\left(_}^}\right)=}_\text,\text,$$

(25)

respectively, giving the total overall reaction

$$\text\left(_}^}\right)+\text\left(\text\right)=0,\text\left(\text\right)$$

(26)

The n-type anode under illumination is from the beginning compensated by the metal Ni anode usually used in the dark, having the best positive catalyst for electrolytic oxygen evolution, while the classical raney-Ag (an Ag–Al alloy) [12] is one of the best candidates for the counter metal cathode, having a relatively low overvoltage for cathodic oxygen reduction, following Eq. (25).

(b)

Refer to Fig. 7b and related texts.

Fig. 7

A hypothetical ideal regenerative wet photovoltaic oxygen cell designed from a relatively oxidative single redox couple \(}_/}_\text\), using a negative overvoltage for photosensitized anodic oxidation by a photoexcited minority carrier hole in the n-type anode combined with a counter metal cathode such as an Ag–Al alloy: a shift of equilibrium (the alignment of \(_}\) on either side) to closely approach the flat band situation (generation of photocurrent/voltage) on the energy band diagram; b resulting photocurrent I vs photovoltage V polarization curve predicted on a qualitative base. The term “regenerative” means no net chemical change in the electrolytic solution occurs

The redox couple \(}_/}_\text\) is shown to have moderate/poor reversibility [the charge transfer resistance, \(_}=0\), an extremely low value, \(_} \left[\text}^\right]=\frac_}\), z \(=\) the oxidation number \(\left[\text\right]\), \(F=\text=\text\left[}^\right]\) and the exchange current density (the rate of charge transfer is referred to as an idle rate at zero overvoltage), \(_=\infty\), a considerably large value, \(_ \left[\text}^\right]=zF_}\), \(_}=\text\left[\text}^}^\right]\) are responsible for ideal reversibility], and it is expected to give a small exchange current and relatively high charge transfer resistance, accordingly delivering relatively high anodic/cathodic overvoltages on either side. Therefore, it cannot be used as a good reversible redox couple, unlike the reversible redox couple \(}^}\right)}_\right]}^\left(\text\right)/}^}\right)}_\right]}^\left(\text\right)\left(\text\right)\) on the Pt electrode, \(}_\)(the chlorine gas as an oxidant)/\(}^\)(chloride as a reductant) couple, and the reversible hydrogen ion/gas redox couple. It is usual practice to write the oxidized species (oxidant) of the couple first [13].

We have conceptually designed a hypothetical regenerative photovoltaic oxygen cell, relative to an ideal regenerative hydrogen cell, like the Daniell cell, only for instructive use, not for a practical application.

To avoid any confusion, we will think of the reference potential of the negative (cathodic) and positive (anodic) overvoltages delivered or measured regarding \(_}^}\) [14] during any spontaneous electrochemical oxidation/reduction, respectively, in the dark; in comparison, that reference potential of the negative and positive inverse overvoltages (better called ‘photoexcited hole and electron overvoltages’) delivered regarding \(_}^}/_}^}\) during photosensitized oxidation/reduction, respectively. Both reference potenials should be taken as the well-defined electrode potential, \(_}^}\), and the flat band potential, \(_}^}/_}^}\), respectively, by definition.

The negative and positive overvoltages regarding their reference potential usually give the driving force for the occurrence of the cathodic reduction and anodic oxidation, respectively, in the dark. In comparison, the negative and positive inverse overvoltages occur during illumination as consequences of the single shift of their electrode potential to their flat band potential, which must necessarily be performed only by the photo-enhanced minority hole in the n-type and minority electron in the p-type, respectively, based on the band diagram. In this respect, neither any further negative overvoltage regarding \(_}^}\), caused by the photo-enhanced minority hole in the n-type, nor any further positive overvoltage regarding \(_}^}\), driven by the photo-enhanced minority electron in the p-type, which can make sense during illumination.

From our previous work [6] dealing with the relationship of a power producing dry photovoltaic cell at n/p junction to a power consuming n/p junction, it is recognized that the electric field strength present over the depleted space charge transition region is responsible for simultaneous migration (drift) of photoexcited minority EHP (electron and hole) across the transition region into the n-type and p-type regions, respectively, before recombining there and finally delivering a photocurrent and a photovoltage to the external load.

As shown in Fig 7a, a photosensitized anodic oxidation current at the n-type anode/solution interface, driven by a minority VB hole enhanced by illumination, simultaneously occurs only when an appreciable electric field exists across the transition region, along with a photo-sensitized cathodic reduction current at the counter metal cathode/solution interface, caused by the majority CB electron flowing from the n-type anode through the external load toward another counter metal cathode.

The same is true of a photo-sensitized cathodic reduction current at the p-type cathode/solution interface, as depicted in Fig 8a.

Fig. 8

A hypothetical ideal regenerative wet photovoltaic hydrogen cell designed from a relatively reductive single redox couple \(}^/}_\), using a positive overvoltage for photosensitized cathodic reduction by a photoexcited minority carrier electron in the p-type cathode in combination with a counter metal anode such as an Ni–Al alloy: a shift of equilibrium (the alignment of \(_}\) on either side) to closely approach the flat band situation (generation of photocurrent/voltage) on the energy band diagram; b resulting photocurrent I vs photovoltage V polarization curve predicted on a qualitative base. The term “regenerative” means no net chemical change in the electrolytic solution occurs

No photocurrent appears at the flat band potential, \(_}\), because the electric field that is necessarily required to separate the photoexcited EHP, finally delivering a photo reaction current and a photovoltage, is absent. The photocurrent appears at any other potentials up/down to \(_}^}\) compared with the \(_}\); hence, the \(_}\) can be interpreted as the unique potential for photocurrent onset.

Therefore, it follows that photosensitized anodic oxidation, driven by the minority VB hole of the n-type anode, enhanced by illumination, may appear at potentials from \(_}^}\) up to \(_}^}\text_}\) in a more positive direction of potential (Figs. 7b, 9b and 13c), relative to photosensitized cathodic reduction, caused by the minority CB electron of the p-type cathode, enhanced by illumination at potentials from \(_}^}\) down to \(_}^}\) (Figs. 8b and 10b) at which the occurrence of those anodic oxidations and cathodic reductions is thermodynamically impossible in the dark.

Fig. 9

An ideal regenerative wet photovoltaic cell composed of an n-type, an electrolyte containing such a single redox couple as \(}^/}^\) and a counter metal cathode, using a negative overvoltage for photosensitized anodic oxidation by photoexcited minority carrier hole in the n-type: a at equilibrium (the alignment of \(_}\) on either side) and during illumination (generation of photocurrent/voltage) on the energy band diagram; b resulting photocurrent I vs photovoltage V polarization curve predicted on a qualitative basis. The term “regenerative” means no net chemical change in the electrolytic solution occurs

Fig. 10

An ideal regenerative wet photovoltaic cell composed of a counter metal anode, an electrolyte containing such a single redox couple as \(}^/}^\) and a p-type cathode, using a positive overvoltage for photosensitized cathodic reduction by photoexcited minority carrier electron in the p-type: a at equilibrium (the alignment of \(_}\) on either side) and during illumination (generation of photocurrent/voltage) on the energy band diagram; b resulting photocurrent I vs photovoltage V polarization curve predicted on a qualitative base. The term “regenerative” means no net chemical change in the electrolytic solution occurs

The photo-enhanced minority hole necessarily needs to shift the equilibrium potential of the redox couple to the flat band potential in the negative direction (the negative inverse overvoltage, \(_}^,\text}<0\), for photosensitized anodic oxidation) based on the band diagram as suggested in Answer 5(e) to Quiz 5 and in Fig. 6a. This shift makes it thermodynamically possible for oxygen evolution to proceed above the flat band potential by anodic transfer of the photoexcited hole, whose occurrence is thermodynamically impossible in the dark. Thus, the photo-I vs V curve in this cell behaves as those of the self-driven Galvanic cell, for instance, the Daniell cell and hydrogen/oxygen fuel cell, etc., as indicated in Fig. 7b. The same is true of the positive inverse overvoltage, \(_}^,\text}>0\), for cathodic reduction, driven by a photoexcited minority electron, as mentioned in Fig. 8b.

Notably, there are two kinds of sign conventions concerning the anodic oxidative current/cathodic reductive current: one is IUPAC (European) convention 1953, saying that an oxidative current is negative owing to the loss of a redox electron, while a reductive current is positive owing to the gain of a redox electron. In this respect, remember the acronym 'OIL RIG', which spells out the initial letters of 'oxidation is loss, reduction is gain' of electrons. Another is the non-IUPAC convention, saying that following the traditional definition of the anodic overvoltage being positive regarding the electrode potential \(\left[_}=\left(_}-_}^}\right)>0\right]\), and the cathodic overvoltage being negative regarding the electrode potential \(\left[_}=\left(_}-_}^}\right)<0\right]\); the oxidative current and reductive current should be positive and negative, respectively, so that their product, power \(\left(W=\eta \times I>0\right)\), never should always be negative (the second principle of electrochemical thermodynamics [15]). The latter non-IUPAC convention is adopted throughout the article.

In Fig. 7a at equilibrium, namely after dipping the electrode into the electrolytic solution containing the single redox couple, \(}_/}_\text\), the alignment of the Fermi level on the n-type anode, electrolyte, and the counter metal cathode gives rise to a downward concave band bending in the direction of the interior of the n-type. Under illumination, photo-enhanced minority holes having quasi-Fermi level,\(_}^}\), going upward along the concave-up band bending from the n-type toward the interface between the n-type and electrolyte, drive an anodic oxidation at the n-type electrode on the left side like in Eq. (24).

In contrast, the majority electrons enhanced by illumination with their quasi-Fermi level, \(}_}^}\), coming downward along the concave-up band bending from the n-type through the external load toward another counter metal cathode, drive a cathodic reduction at the counter metal electrode on the right side like in Eq. (25).

This simultaneous oxidation/reduction processes produce a photocurrent as well as a photovoltage despite zero electrochemical emf (Gibbs free energy change, \(\Delta G=-zF\times \text=0\), \(\text=0 \left[\text\right]\)) with no net chemical change, thus providing the photocurrent for the external load. The separation of the two quasi-Fermi levels, \(\left(_}^}-_}^}\right)\), divided by the electronic charge is the limiting photo emf.

Notably, the separation of the quasi-Fermi levels, \(\left(n_}^}-p_}^}\right)\text\left[\text\right]\), in the n-type anode under illumination is responsible for generation of a negative photovoltage (compared to the counter cathode, \(_}^,\text}<0 \text\left[\textvs\text\right]\)). At equilibrium in the dark, this photovoltage is zero. This negative photovoltage provides the driving force for the photo-generated current. At the same time, this quasi-Fermi level separation also causes a shift in the negative inverse overvoltage, \(_}^,\text}<0 \text\left[\text\right],\) at the n-type anode/solution interface. Like the photovoltage, this overvoltage is zero at equilibrium in the dark. Under illumination, however, it enables photosensitized anodic oxidation, driven by photoexcited minority holes. This behavior is a fundamental feature of n-type-based photovoltaic cells and photo-electrochemical cathodic protection cells, as illustrated in Fig. 7, and further discussed in Figs. 9 and 13.

Quiz 8

Conceptually construct the layout of the anode, electrolytic solution, and cathode of an ideal regenerative photovoltaic hydrogen cell from a relatively reducing single redox couple \(}^/}_\), aided by a positive inverse overvoltage for photosensitized cathodic reduction, caused by a photoexcited minority carrier electron in the p-type combined with a counter metal electrode.

(a)

Distinguish the anode and cathode and clarify their related electrochemical reactions briefly. Give the best candidate material for the counter anode.

(b)

Predict the photocurrent I vs photovoltage V curve using the concept of the quasi-Fermi level underlying the positive overvoltage, \(_}^,\text}>0\) for the photoexcited cathodic reduction, driven by the VB minority electron in the p-type.

Answer 8

(a)

The overall cell reaction is divided into a partial anodic oxidation at the metal anode/electrolyte interface and a partial cathodic reduction at the p-type anode/electrolyte interface, given by

$$}_+2\text\left(_}^}\right)=}^,\text$$

(27)

$$}^+2\text\left(\text\right)=}_,\text,$$

(28)

respectively, giving the total overall reaction

$$\text\left(\text\right)+\text\left(_}^}\right)=0,\text\left(\text\right),$$

(29)

where the electron acts as a minority \(\text\left(\text\right)\) in the p-type during the migration (drift) over the space charge transition region, and it also functions as a redox electron during cathodic reduction; the hole \(\left(_}^}\right)\) usually acts as a conduction electron in the current collector, and it also acts as a redox electron (flow of the hole in the opposite direction of the redox electron) during anodic oxidation.

From the beginning, the p-type cathode under illumination compensated for the metal Pt cathode usually used in the dark, having the best positive catalyst for electrolytic hydrogen evolution, while the classical raney-Ni (an Ni–Al alloy) [12] is one of the best candidates for the counter metal anode, having a relatively low overvoltage for anodic hydrogen ion oxidation, following Eq. (27).

(b)

Refer to Fig. 8b and related texts.

The redox couple \(}^/}_\) has excellent reversibility (\(_}=0\) and \(_=\infty\) are responsible for ideal reversibility), and it is expected to give a large exchange current \(_\) and an extremely low charge transfer resistance \(_}\), accordingly delivering extremely low anodic/cathodic overvoltages on either side. Therefore, it can be used as a good reversible redox couple, like the reversible redox couple, ferricyanide/ferrocyanide \(\left(\text\right)\) on Pt electrode, as well as the chlorine gas/chloride redox couple in electrochemical perspectives, but it is not usually utilized for a practical application for economical reasons [13].

The photo-enhanced minority electron necessarily needs to shift the equilibrium potential of the redox couple to the flat band potential in the positive direction (the positive inverse overvoltage, \(_}^,\text}>0\), for photosensitized cathodic reduction) based on the band diagram, as suggested in Answer 6(e) to Quiz 6 and in Fig. 6b. This shift makes it thermodynamically possible for hydrogen evolution to proceed below the flat band potential by cathodic transfer of photoexcited electrons; the occurrence is thermodynamically impossible in the dark. Thus, the photo-I vs V curve in this cell behaves as those of the self-driven Galvanic cell, for instance, the Daniell cell and hydrogen/oxygen fuel cell, etc., as indicated in Fig. 8b.

In Fig. 8a at equilibrium, namely after dipping the electrode into the electrolytic solution containing the single redox couple,\(}^/}_\), the alignment of the Fermi level on the counter metal electrode, electrolyte, and p-type cathode gives rise to an upward convex band bending in the direction of the interior of the p-type. Under illumination, photo-enhanced minority electrons having quasi-Fermi level, \(_}^}\), coming downward along the concave-down band bending from the p-type toward the interface between the p-type and electrolyte, drive a cathodic reduction at the p-type cathode on the right side like in Eq. (28).

In contrast, majority holes enhanced by illumination with their quasi-Fermi level, \(_}^}\), going upward along the concave-down band bending from the p-type through the external load toward another counter metal anode, drive an anodic oxidation at the counter metal anode on the left side like in Eq. (27).

These simultaneous oxidation/reduction processes produce a photocurrent and a photovoltage despite zero electrochemical emf (Gibbs free energy change, \(\Delta G=-\text\times \text=0\), \(\text=0 \left[\text\right]\)) with no net chemical change, thus providing the photocurrent for the external load. The separation of the two quasi-Fermi levels, \(\left\_}^}-_}^}\right)>0\right\}\), divided by electronic charge is the limiting photo emf.

It seems adequate to mention that the separation of the quasi-Fermi levels, \(\left\_}^}-_}^}\right)>0\right\}\text\left[\text\right]\), in the p-type cathode under illumination is responsible for providing the positive photovoltage regarding the counter anode, \(_}^,\text}>0 \text\left[\textvs\text\right]\), essential for the driving force of the photocurrent, and it is also responsible for the shift of positive inverse overvoltage, \(_}^,\text}>0 \text\left[\text\right]\), for photosensitized cathodic reduction at the p-type cathode/solution interface, driven by a photoexcited minority electron, which is a common characteristic of p-type-based photovoltaic cells, as shown in Fig. 8, mentioned below in Figs. 10 and 11 as well.

Fig. 11

An ideal regenerative wet photovoltaic cell composed of an n-type anode having a negative overvoltage for photosensitized anodic oxidation by photoexcited minority carrier hole in the n-type, an electrolyte containing such a single redox couple as \(}^/}^\) and a p-type cathode having a positive overvoltage for photosensitized cathodic reduction by photoexcited minority carrier electron in the p-type: a at equilibrium (the alignment of \(_}\) on either side) and during illumination (generation of photocurrent/voltage) on the energy band diagram; b resulting photocurrent I vs photovoltage V polarization curve predicted on a qualitative base. The term “regenerative” means no net chemical change in the electrolytic solution occurs

In comparison, the migration (drift) of minority EHP enhanced by illumination is responsible for the separation of the Fermi levels on either side, \(\left(_}^}-_}^}\right)\approx \left(n_}^}-p_}^}\right)>0\text\left[\text\right]\), along the concave-up bending/concave-down bending across the depleted space charge transition region into the n-type and p-type regions, respectively, before recombination there, without any electrochemical reaction, eventually delivering a photocurrent and a positive photovoltage regarding the n-type negative pole region, \(_}^,\text}>0 \text\left[\textvs\text\right]\), which is characteristic of the dry photovoltaic cell at the n/p junction, as shown in Fig. 12.

Fig. 12

The working principle of an n-p-type junction dry photovoltaic cell: a at equilibrium (alignment of the equilibrium Fermi level \(_}\) on either side) on the energy band diagram; b during illumination (the separation of the equilibrium Fermi level \(_}\) on either side) on the energy band diagram; c non-linear current I vs voltage V characteristic in the dark and under illumination; d typical resulting photo I vs V characteristic