Application of the Similarity Theory to Analysis of Photocatalytic Hydrogen Production and Photocurrent Generation


 
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2023, vol. 10(2), No. 202310203 
DOI: 10.15826/chimtech.2023.10.2.03 

 

1 of 21 

Application of the similarity theory to analysis  
of photocatalytic hydrogen production  
and photocurrent generation 

Dina V. Markovskaya * , Ekaterina A. Kozlova  

Department of heterogeneous catalysis, Boreskov Institute of Catalysis, Novosibirsk 630090, Russia 

* Corresponding author: madiva@catalysis.ru  

 
 

This paper belongs to a Regular Issue. 

 

 

Abstract 

In this research some methods of the similarity theory were quantitatively 

applied to the description of the relationship between the efficiencies of 
the photocatalytic hydrogen production and photocurrent generation for 
the first time. Two possible similarity criteria, namely, such as the ratio 

of the number of electrons involved in the photocatalytic reaction to the 
generation of photocurrent ones and the ratio of energies transformed in 
the case of photocatalytic hydrogen evolution to the photocurrent, were 

obtained by the dimensional analysis. The literature data allow checking 
the first criterion. The application of the first possible similarity criterion 
to the samples with different chemical nature, solid solutions, series, in 

which the synthesis time or the ratio of catalyst components, electrolyte 
amount or its nature is changed, was analyzed. It was shown that the ratio 

of electrons may serve as the similarity criterion only under the conditions 
of geometric and physical similarities.   

Keywords 

photocatalysis 

hydrogen evolution 

photocurrent generation 

theory of similarity 

similarity criterion 

dimension theory 

 

 

Received: 13.02.23 

Revised: 20.03.23 

Accepted: 26.03.23  
Available online: 04.04.23 

Key findings 

● Photocatalytic hydrogen production and photocurrent generation are the analogous phenomena.  

● Two possible similarity criteria were proposed.  

● Ratio of the electron numbers acts as a similarity criterion if the conditions of geometric and physical similarity are 

fulfilled.  

© 2023, the Authors. This article is published in open access under the terms and conditions of  

     the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). 
 

1. Introduction 

Nowadays different processes and phenomena whose real-

ization allows generating energy are of particular im-

portance. The traditional method of burning fuel resources 

has a significant disadvantage associated with the limited 

reserves of the corresponding resources. Accordingly, the 

search for alternative fuels is known to be an urgent task of 

modern science [1]. Since the 70s, the idea of using hydro-

gen as a fuel has gained particular popularity among re-

searchers [1, 2]. Hydrogen is known to be one of the most 

common elements on Earth and can be obtained from vari-

ous compounds. When hydrogen is burned, eco-friendly wa-

ter is formed, and the large amount of heat is realized. How-

ever, in this case the question arises about new methods of 

hydrogen synthesis, because the main methods either use 

non-renewable energy sources or are quite energy intensive 

[1]. One of the promising alternative ways to produce hy-

drogen is the photocatalytic method, implemented in the 

presence of photocatalysts based on semiconductors. An 

important feature of this method is the use of sunlight. 

Thus, in fact, we are talking about the conversion of light 

energy into the energy of chemical bonds occurring on the 

semiconductor surface [3]. 

It should be noted that the energy from light can be gen-

erated in the photoelectrochemical cells. These processes 

are often carried out on electrodes made of semiconductors. 

It is noteworthy that in the case of photocatalytic hydrogen 

production and photocurrent generation, the same physico-

chemical processes such as the formation of exciton, the 

formation of an electron-hole pair, the spatial separation of 

charge carriers during their migration to the boundaries of 

the phase interface, interphase transfer to the components 

of the reaction medium occur on the semiconductor surface 

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[4–7]. The main difference lies only in the fact that in the 

case of photoelectrochemical cells, besides participating in 

various transformations, electrons are transferred to coun-

ter electrodes, and for photocatalytic hydrogen evolution, 

the reaction occurs directly on the surface of semiconductor 

particles [7]. The similarity of the principles of functioning 

of these two phenomena can be useful in the development 

of various strategies for improving the target characteris-

tics of materials. It should be noted that the development of 

scientific branches related to photoelectrochemical cells 

and photocatalytic processes takes place in parallel. How-

ever, the scientific results of each of these fields may be 

useful in another one. For example, some materials such as 

metal phosphides were originally used for the electrocata-

lytic hydrogen evolution. However, these compounds are ac-

tive co-catalysts for photocatalytic hydrogen production [8]. 

Titania may be successfully used both as the material for the 

photoelectrochemical cell and as the photocatalyst [9]. 

To take into account the achievements in different 

branches, it is necessary to have a tool that allows compar-

ing some characteristics of the two phenomena. As such a 

tool, similarity theory can be used, which makes the transi-

tion between quantitative characteristics of phenomena of 

the same nature. The methods of similarity theory are suc-

cessfully used to describe physical processes in the field of 

engineering and mechanical engineering. In hydrodynam-

ics, the phenomena of thermal conductivity, diffusion and 

electrical conductivity in liquids are studied using the sim-

ilarity theory [10]. The aim of this paper is to determine the 

possibility of using similarity theory methods to describe 

the phenomena of photocatalytic hydrogen evolution and 

photocurrent generation. With the help of the dimension 

theory, potential similarity criteria were obtained in this 

work, after which they were used to analyze the literature 

data.  

2. Search of parameters which may be 

used as similarity criteria 

In the study of physical phenomena, a system of concepts 

and a system of units are introduced. The system of con-

cepts includes the quantities characterizing various aspects 

of the studied processes, while the system of units deter-

mines the numerical values of the introduced characteris-

tics. There are a number of correlations between these 

characteristics. Any physical relationship between different 

quantities can be formulated as a relationship between di-

mensionless quantities. This postulate underlies the theory 

of dimension [11]. With the help of dimension theory, the 

parameters that may serve as similarity criteria can be 

identified. Within the framework of this approach, at the 

first stage it is necessary to identify the defining system of 

parameters. At the second stage, linearly independent di-

mensionless combinations, which are potential similarity 

criteria, are formed from this system of parameters by 

analyzing dimensions [11]. At the third stage, the obtained 

parameters are verified by the experimental data.  

Let us apply the theory of dimension to the discussed 

processes. In the case of photocatalysis, it is necessary to 

describe quantitatively the reaction system (concentration 

and nature of reagents, volume of the reaction mixture, 

concentration of the catalyst or its mass), the light source 

and the photocatalytic activity of the catalyst. In the case of 

generating a photocurrent, we will take into account the 

characteristics of the light source and the photoelectro-

chemical cell. The irradiation source can be characterized 

by a set of independent quantities that determine the num-

ber of incident light quanta and their energy: the irradia-

tion power and wavelength, the number of incident photons 

and the wavelength of radiation, the number of incident 

photons and the energy of one photon, etc. The parameters 

describing the target properties of the photocatalyst and 

the photoelectrochemical cell are of the greatest interest. 

2.1. Parameters characterizing the photocatalytic 

activity 

The photocatalytic activity describes to what extent the 

studied system is a photocatalyst. In the literature several 

parameters describing the catalyst productivity are men-

tioned, including the catalytic activity [12–21], the turno-

ver number [20–22], the quantum yield [12, 19–21], the 

quantum efficiency [12, 19–21], the STH (solar-to-hydro-

gen) [14, 22]. The ways of their calculation were summa-

rized in Table 1.  

The catalytic activity, just as in the traditional catalysis, 

is defined as the rate of the photocatalytic process (W) di-

vided by the catalyst mass (m) [20, 23]. The catalytic activ-

ity is often measured in μmol·h–1·g–1. The catalytic proper-

ties of the samples can be characterized by the turnover 

number (TON).  

Table 1 Quantities characterizing the photocatalytic activity of 

samples. 

Quantity  Symbol Formula 

Catalytic 

activity 
CA CA = 𝑊/𝑚 (1) 

Turnover 
number 

TON 

TON =
𝑊

𝑁active sites
 or 

 TON =  
𝑊

𝑆catalyst surface
 

(2) 

Quantum 
yield 

φ, Φ Φ =
𝑁disappearing molecules

𝑁absorbed photons
· 100% (3) 

Quantum 

efficiency 

AQE, 

QE, PE 

AQE =
𝑁disappearing molecules ∙ 100%

𝑁incident photons
= 

𝑊 ∙ ℎ ∙ 𝑐 ∙ 𝑁𝐴 ∙ 100%

𝑃irradiation ∙ 𝑆irradiation ∙ 𝜆
 

(4) 

Solar-to-

hydrogen 
STH 

𝑆𝑇𝐻 =
∆𝐺° ∙ 𝑊 ∙ 100%

𝑃irradiation ∙ 𝑆irradiation
= 

=
𝐴𝑄𝐸 ∙ 𝜆 ∙ ∆𝐺°

ℎ ∙ 𝑐 ∙ 𝑁𝐴
 

(5) 

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The TON is the ratio of the number of photoinduced 

transformations for a given period of time to the number of 

active sites (Nactive sites) [21]. However, in heterogeneous ca-

talysis it is difficult to determine the number of active sites; 

it is often unknown. Therefore, for certainty, when calcu-

lating TON, normalization is carried out on the surface area 

of the catalyst (Scatalyst surface). 

Since the photocatalytic activity of the samples is di-

rectly related to the lighting conditions (type and power of 

illumination, wavelength), the quantum yield is used to 

evaluate the photocatalyst productivity and their compari-

son with each other [12, 19–21]. The quantum yield is a 

number of defined events, occurring per photon absorbed 

by the system at a specified wavelength [20, 21]. In hetero-

geneous photocatalysis, determining the number of ab-

sorbed photons is quite difficult: photocatalyst particles re-

flect and scatter light, and the contribution of this effect is 

difficult to measure. In practice, apparent quantum effi-

ciency is commonly used; it is normalized per photon inci-

dent in the system instead of a photon absorbed by the sys-

tem. Table 1 shows the formulas for the quantum yield and 

quantum efficiency calculation when monochromatic light 

is used.  

The photocatalytic reaction is often considered as 

transformation of the energy of the incident light to the 

energy of the chemical bonds. From this point of view, the 

photocatalyst producibility may be estimated using solar-

to-hydrogen (STH). During the reaction, ∆𝐺° ∙ 𝑊 J trans-

forms to the chemical energy per unit of time, while 

𝑃irradiation ∙ 𝑆irradiation J enters the system per unit of time 

[24]. In general, the ratio between these values is the ef-

ficiency of energy conversion during the photocatalytic re-

action.  

Note that the quantities characterizing the photocata-

lytic activity can be expressed in terms of a basic set of the 

certain parameters. This basis includes the photocatalytic 

reaction rate, the Gibbs energy, the mass and surface area 

of the catalyst, the irradiation power, and the area of the 

irradiation surface. Table 1 shows the relationship be-

tween these basic parameters and the parameters charac-

terizing the photocatalytic activity. For a complete de-

scription of the reacting system, it is necessary to add to 

these parameters the concentration and nature of the re-

agents, the volume of the reaction mixture, and the geo-

metric characteristics of the reactor. The example of a 

basic set of parameters is given in Table 2. This list may 

be completed as mentioned in the paper [25]; however, 

this basic set is sufficient for the tasks in the present 

work.  

Special attention should be paid to the values of quan-

tum efficiency and solar-to-hydrogen. They are dimension-

less; therefore, they can act as similarity criteria if the con-

ditions of geometric and physical similarity of two reaction 

systems are fulfilled, for example, for the photocatalytic hy-

drogen production in reactors of different volumes but the 

same geometry. 

Table 2 Parameters describing the photocatalytic hydrogen pro-

duction. 

Part of the reaction system  Characterizing parameters 

The basic set of parameters 

Reagents Reagent concentration, vol-

ume of the reaction mixture  

Light source Irradiation power, surface of 

irradiation, wavelength  

Working photocatalyst Mass, catalyst surface,  
reaction rate 

Chemical reaction Gibbs energy  

Chemical reactor Geometric parameters 

Similarity criteria 

Reaction system Quantum efficiency, STH 

2.2. Parameters characterizing the efficiency of 

the photoelectrochemical cell 

To describe the efficiency of the photoelectrochemical cells, 

researchers often use short-circuit current density (Jsc) 

[26–36], open-circuit potential (Voc) [26, 27, 30, 31, 33, 35–

37], fill factor (FF) [30, 33, 35, 36, 38], power conversion 

efficiency (PCE, η) [26–31, 33, 35, 37, 38], incident photon-

to-current efficiency (IPCE, external quantum efficiency, 

EQE) [32, 37–39], solar-to-hydrogen (STH) [26, 28, 31, 39]. 

Let us consider each of the values in more details.  

The short-circuit current density, open-circuit voltage, 

fill factor, and power conversion efficiency are calculated 

from the voltammograms (see Figure 1) [40]. The short-cir-

cuit current density is known to be the current normalized 

to the area of illumination that occurs in the cell without 

any potential [41, 42]. The physical meaning of this value is 

the highest current density which may be obtained in the 

photoelectrochemical cell. The short-circuit current density 

is dependent on the rate of electron-hole pair formation, 

their diffusion into the semiconductor and in the external 

circuit [41, 42]. One can say that the Jsc indirectly depends 

on the nature of the semiconductor and electrolyte and the 

characteristics of the irradiation source. 

The open-circuit voltage is the voltage occurring in the 

cell without any current [40–42]. For the discussed cell 

whose voltammogram is given in Figure 1 the open-circuit 

voltage equals ~0.6 V. The open-circuit voltage shows the 

highest potential which may be obtained in the cell. 

 
Figure 1 Example of calculation of several characteristics describ-

ing the effectivity of the photoelectrochemical cell according to 

[40]. 

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The physical meaning of the open-circuit voltage is the 

efficiency of light energy transformation in one act of pho-

toelectrochemical reaction. This parameter is largely deter-

mined by the nature of the chemical processes occurring in 

the electrolyte solution and at the interface of the elec-

trode/electrolyte [42]. 

The fill factor is the value reflecting the impact of the 

resistance of the photoelectrochemical cell and showing 

the degree of deviation of the produced cell power from 

the possible one without any resistance. The fill factor is 

calculated as the ratio of maximum power to the product 

of the short-circuit current density and the open-circuit 

voltage:  

FF =
𝐽MPP ∙ 𝑉MPP

𝐽SC ∙ 𝑉OC
∙ 100%, 

(6) 

where FF is the fill factor, JMPP is the current density in 

which the highest power is generated, VMPP is the potential 

in which the highest power is generated, Jsc is the short-

circuit current density, and VOC is the open-circuit potential. 

As shown in Figure 1, the plot of the produced power from 

potential was constructed, after which the maximum point 

(MPP) was found. The higher the fill factor, the closer the 

shape of the current-voltage curve to a rectangular one. The 

deviation from this shape is caused by resistance in the pho-

toelectrochemical system, recombination of electron-hole 

pairs [42], and changing resistance at the interface elec-

trode/electrolyte [41]. Because the fill factor is a dimen-

sionless quantity, it can be used as the similarity criterion 

for the photoelectrochemical systems, for example, in case 

of scaling the photoelectrochemical cells.  

The power conversion efficiency of the photoelectro-

chemicall cell shows the ratio of the electrical energy pro-

duced in the cell to the energy of the incident light [43]:  

𝜂 =
𝐽𝑀𝑃𝑃 ∙ 𝑉𝑀𝑃𝑃
𝑃𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

∙ 100% =
𝐽𝑆𝐶 ∙ 𝑉𝑂𝐶 ∙ 𝐹𝐹

𝑃𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
∙ 100%, 

(7) 

where η is the power conversion efficiency, JMPP is the cur-

rent density in which the highest power is generated, VMPP 

is the potential in which the highest power is generated, 

Рirradiation is the power of the irradiation which incidents on 

the photoelectrochemical cell, Jsc is the short-circuit current 

density, VOC is the open-circuit potential, and FF is the fill 

factor. The power conversion efficiency shows the effi-

ciency of the energy transformation. PCE is a dimensionless 

quantity and can act as the similarity criterion for the pho-

toelectrochemical systems.  

The incident photon-to-current efficiency is defined as 

the number of produced electrons divided by the number of 

photons incident in the system [43]. By simple transfor-

mations, one can obtain Equation (8), relating the short-

circuit current density and irradiation power. Of practical 

value is the dependence of IPCE on the wavelength, which 

makes it possible to optimize the irradiation conditions of 

the photoelectrochemical cell.  

𝐼𝑃𝐶𝐸 =
𝑁electrons
𝑁photons

∙ 100% =
𝐽SC ∙ ℎ ∙ 𝑐

𝑃irradiation ∙ 𝑒 ∙ 𝜆
∙ 100%, 

(8) 

where IPCE is the incident photon-to-current efficiency,  

Nelectrons is the number of electrons generated in the cell, 

Nphotons is the number of photons incident in the system,  

Jsc is the short-circuit current density, Pirradiation is the power 

of irradiation incident on the photoelectrochemical cell, h 

is Planck's constant, c is the speed of light, e is the electron 

charge, and λ is the wavelength of the incident irradiation.  

If additional water decomposition and hydrogen evolu-

tion occur in the photoelectrochemical cell, the efficiency of 

this process can be estimated using solar to hydrogen (STH), 

which may be calculated according to the following equation: 

STH =
𝐽SC ∙ 1.23 ∙ 𝜂F

𝑃irradiation
∙ 100%, 

(9) 

where Jsc is short-circuit current density, ηF is the Faraday 

efficiency factor for hydrogen evolution, and Pirradiation is the 

power of irradiation incident on the photoelectrochemical 

cell. It should be noted that the STH parameter can also 

characterize the photocatalytic hydrogen production (see 

2.1 and Equation 5). In this case, STH shows the relation-

ship between the energy of hydrogen production over the 

photocatalyst and the energy of incident light. In the case 

of the photoelectrochemical cell, STH reveals the share of 

the light energy which was used for the water decomposi-

tion and contained the product of the rate of electrochemi-

cal hydrogen production (𝐽𝑆𝐶 ∙ 𝜂𝐹) and the Gibbs energy of 

this reaction (1.23 V for water decomposition), as shown in 

the Equation 9. So, these values have the same physical 

meaning for both different processes. 

As in the case of the photocatalytic hydrogen evolution, 

the quantities characterizing the efficiency of the photoe-

lectrochemical cell can be expressed in terms of the basic 

set of several parameters. The short-circuit current density, 

the open-circuit potential, the current density at which the 

cell generates maximum power (in this case, VMPP is deter-

mined from the experimental data, the maximum cell 

power can act as the similarity criterion), the irradiation 

power, the area of the illuminated part of the photoelectro-

chemical cell, the irradiation wavelength (for simplicity, we 

restrict our consideration to monochromatic radiation). To 

fully characterize the reacting system, it is necessary to add 

to these parameters the concentration and nature of the 

electrolyte, the nature of the electrodes, and the geometric 

design of the cell.  

Among the quantities used by researchers to describe 

the efficiency of the photoelectrochemical cell, several di-

mensionless parameters can be selected: the fill factor, the 

power conversion efficiency, the incident photon-to-cur-

rent efficiency, and the solar-to-hydrogen. These parame-

ters can act as the similarity criteria provided that the con-

ditions of geometric and physical similarity of two photoe-

lectrochemical cells are met. 

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2.3. Derivation of the similarity criteria that may 

be used for the description of relation be-

tween the efficiencies of the photocatalytic 

hydrogen production and the photoelectro-

chemical cell 

The analysis of the nature of the photocatalytic hydrogen 

production and the photocurrent generation shows that 

these phenomena are analogous to each other [7]. Therefore, 

their quantitative description uses analogous values whose 

combination may be serve as the similarity criteria making 

the transition between the descriptions of both phenomena. 

Let us consider the list of the analogous quantities (see 

Table 3) in detail. The quantities used for the description of 

the photocatalytic hydrogen evolution and the photoelec-

trochemical cell allow defining the change in the number of 

molecules or the number of the electric charges per unit of 

time. In both cases, these changes are caused by the change 

in the number of electrons taking part in the target pro-

cesses. Based on the dimensions, the changing electron 

amount during the photocatalytic hydrogen production per 

unit of time per unit of irradiation surface may be calcu-

lated as 2 ∙ 𝑊 ∙ 𝑁𝐴 ∙ 𝑆𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
−1  , while the changing electron 

amount during the photocurrent generation per unit of time 

per the surface of the photoelectrochemical cell may be de-

fined as 𝐽𝑆𝐶 /𝑒. The ratio of these quantities will be dimen-

sionless and may act as the similarity criterion. The validity 

of this statement will be verified below by analyzing the lit-

erature data. It should be noted that voltammograms are 

often not presented in the literature, while most articles are 

accompanied by the data on the change in current density 

over time generated at the constant potential. This quan-

tity, e.g., at the first cycle, may be used instead of the short-

circuit current density, because it was measured at the con-

stant potential and has the same dimension. In this case, 

the similarity criterion was labeled as Q1’.  

The photocatalytic hydrogen production and the photo-

current generation are considered as the conversion of light 

energy into chemical bond or electrical energy. Therefore, 

these phenomena may be characterized by the energy con-

verted per unit of time. As in the previous case, for the pho-

tocatalytic reaction, it is necessary to normalize by the area 

of the illuminated part of the reactor, since such accounting 

occurs when the efficiency parameters of the photoelectro-

chemical cell are measured. Based on dimensions, we ob-

tain formulas for estimating the amount of energy con-

verted per unit of time per unit of area of the illuminated 

systems. They will be 
∆𝐺°∙𝑊

𝑆𝑖rradiation
 and Jsc·Voc for the photocata-

lytic hydrogen production and the photoelectrochemical 

cell, respectively. The ratio of these quantities will be di-

mensionless and may serve as the similarity criterion Q2. 

The studied phenomena occur in the light. From this 

point of view, the photocatalytic hydrogen evolution may 

be characterized by the quantum efficiency, while the pho-

tocurrent generation is described by ICPE. Both values are 

dimensionless, and their ratio is dimensionless too and may 

serve as a similarity criterion:  

𝑄3 =
𝐴𝑄𝐸

𝐼𝑃𝐶𝐸
=

𝑊 ∙ 𝑁𝐴 ∙ 𝑒

𝐽SC ∙ 𝑆irradiation
=

𝑄1
2

, (10) 

𝑄3
′ =

𝐴𝑄𝐸

𝐼𝑃𝐶𝐸
=

𝑊 ∙ 𝑁A ∙ 𝑒

𝐽 ∙ 𝑆irradiation
=

𝑄1
′

2
. (11) 

Note that the criteria Q1 and Q3 differ a constant mul-

tiplier. It is known that multiplying the similarity crite-

rion by a number allows getting another similarity crite-

rion [11]. 

The efficiencies of the photocatalytic hydrogen produc-

tion and the photocurrent generation are characterized by 

the solar-to-hydrogen and the power conversion efficiency, 

respectively.  

Table 3 Quantities describing the similar aspects of the photocatalytic hydrogen production and the photocurrent generation in the 

photoelectrochemical cell. 

Quantity 
Hydrogen  

production 

Photocurrent  

generation in the cell 
Possible similarity criterion 

Change in electron amount per unit 

of time per irradiation surface 

2 ∙ 𝑊 ∙ 𝑁𝐴
𝑆𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

 

𝐽𝑆𝐶
𝑒

 Q1 =
2 ∙ 𝑊 ∙ 𝑁𝐴 ∙ 𝑒

𝐽𝑆𝐶 ∙ 𝑆𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
 

𝐽

𝑒
 Q1

′ =
2 ∙ 𝑊 ∙ 𝑁𝐴 ∙ 𝑒

𝐽 ∙ 𝑆irradiation
 

Energy converted per unit of time 

per unit of irradiation surface 

∆𝐺° ∙ 𝑊

𝑆𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛
 𝐽𝑆𝐶 ∙ 𝑉𝑂𝐶  Q2 =

∆𝐺° ∙ 𝑊

𝑆irradiation ∙ 𝐽𝑆𝐶 ∙ 𝑉𝑂𝐶
 

Efficiency of using light Quantum efficiency IPCE 

Q3 =
AQE

IPCE
=

𝑊 ∙ 𝑁𝐴 ∙ 𝑒

𝐽SC ∙ 𝑆𝑖rradiation
=

𝑄1
2

 

Q
3
′ =

AQE

IPCE
=

𝑊 ∙ 𝑁𝐴 ∙ 𝑒

𝐽 ∙ 𝑆
irradiation

=
𝑄

1
′

2
 

Efficiency of energy conversion STH η Q4 =
𝑆𝑇𝐻

𝜂
 

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Dividing these two parameters by each other yields the 

similarity criterion Q4:  

𝑄
4

=
𝑆𝑇𝐻

𝜂
=

∆𝐺° ∙ 𝑊

𝑆irradiation ∙ 𝐽𝑆𝐶 ∙ 𝑉𝑂𝐶 ∙ 𝐹𝐹
. (12) 

Thus, four potential similarity criteria were obtained. 

Since the first and the third, the second and the fourth cri-

teria differ by a constant multiplier, in order to find out 

whether the proposed values are the similarity criteria, it 

is enough to verify only the parameters Q1 and Q2.  

3. Checking the possibility of applying the 

criterion Q1’ as the similarity criterion 

To check whether the proposed values are similarity crite-

ria, some literature data was analyzed [45–81]. It should be 

noted that the data of linear voltammetry either were not 

given by the authors or differ from the form shown in Fig-

ure 1. So, the current density in the cell at the constant po-

tential value, measured by chronoamperometry, will be 

used for comparison instead of the short-circuit current 

density. From the point of view of dimension theory, such 

substitution is correct due to the same dimensions of both 

quantities (mA/cm2). Thus, in most of the reviewed data, 

the possibility of using the parameter Q1' as the similarity 

criterion was verified.  

In the theory of similarity, a geometric level of similar-

ity and a physical one are often distinguished [44]. The ge-

ometric level implies an identical shape of particles and/or 

elements of the reaction set-up, its characteristic sizes [44]. 

When moving from the study of photocatalytic hydrogen 

evolution to measuring photocurrents for two different 

samples, the similarity at the geometrical level is often pre-

served. It is due to the comparable particle sizes of the 

tested samples, the experimental set-ups for studying the 

photocatalytic hydrogen evolution and the photoelectro-

chemical properties are the same. Special attention should 

be paid to the morphology of the samples: in case of its 

change, the conditions of the geometric similarity are vio-

lated. If the geometric similarity is observed for the studied 

systems, then the similarity of phenomena can also be taken 

place at the physical level. Two phenomena are similar if all 

parameters characterizing them are similar [44]. It means 

that the samples should be tested under the same condi-

tions, such as power irradiation, its wavelength, the com-

position of electrochemical cells and electrolyte, the com-

position of catalysts, etc. If these conditions are fulfilled, 

the question of similarity of the photocatalytic hydrogen 

production and the photocurrent generation for the studied 

samples can be considered.  

Below there are data on catalysts of various chemical 

nature, solid solutions of different compounds, the series of 

samples in which the mass ratio of the components is 

changed; the photocatalytic and photovoltaic characteris-

tics were studied in solutions of different electrolytes. All 

discussed data are given in Tables 4–7. Each table contains 

the experimental conditions; the criterion Q1’ was calcu-

lated. The error in calculating the parameter was deter-

mined taking into account the instrumental errors of the 

methods. They were either for 10% (if quantitative data 

were taken from tables or from the text), or for 15% in the 

case of getting data from the figures.  

3.1. Solid solutions of different compounds  

The data on the photocatalytic hydrogen production and 

photocurrent generation over some solid solutions are 

given in Table 4 [45–52]. The solid solutions of cadmium 

sulfide and zinc sulfide were described in a number of 

works. The short-circuit current densities were measured 

in [45] and [46], and the similarity criterion Q1 was calcu-

lated from obtained data. The ratio of the number of elec-

trons used for the photocatalytic hydrogen evolution and 

those to the number of electrons taking part in the photo-

current generation remained constant within experimental 

errors for all samples, except for zinc sulfide in [45]. Prob-

ably, zinc sulfide should be considered separately due to 

low absorbance of visible light and different chemical na-

ture (see Section 3.2). The authors of [46] studied a wider 

range of the solid solution composition; however, in this 

case, no indication of change in the parameter Q1 could be 

identified. Perhaps, it was caused by different composition 

of the electrolytes used in the experiments. The mixture of 

Na2S and Na2SO3 was used for the photocatalytic hydrogen 

production while sodium polysulfide was chosen for the 

photoelectrochemical experiments. In both cases, chemical 

transformations occurred between charge carriers and 

electrolytes. However, various chemical processes were re-

alized, so the changes in the target parameters vs. the pho-

tocatalyst composition were different. In this case, it was 

impossible to apply the similarity theory due to the viola-

tion of the condition of physical similarity. S. Du et al. stud-

ied the solid solutions of cadmium sulfide and cadmium 

selenides with low Se content [47]. The dependences of the 

photocatalytic hydrogen production rate and the current 

density on selenium concentration have a bell-shaped form, 

while the electron ratios expressed by the criterion Q1’ 

stayed the same and were 300–400 within the experi-

mental errors.  

The solid solutions of CdS and MnS were described in 

[48]. The dependences of both target characteristics on the 

solid solution composition went through a maximum. The 

Q1’ criteria were calculated for the tested samples and given 

in Table 4. One can see that Q1’ doubles when cadmium sul-

fide forms solid solutions with manganese sulfide. It may 

be associated with the changes in the rate constants of pho-

tochemical processes and charge recombination depending 

on the chemical nature of semiconductor. The ratio between 

the numbers of electrons used for the photocatalytic hydro-

gen evolution and those taking part in the photocurrent 

generation remained constant for all samples, excluding the 

photocatalyst with x = 0.9. For the mentioned sample, the 

deviation was due to its chemical nature. This photocatalyst 

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was a composite consisting of MnS and the solid solution of 

cadmium sulfide and manganese sulfide [48]. So, in this 

case, we deal with the non-compliance with the conditions 

of the physical similarity of the systems discussed. The 

same behavior was found for MnxCd1–xS [49]. For the solid 

solutions with different ratios of manganese to cadmium, 

the Q1’ criterion remained a constant within the experi-

mental error, while it increased by almost two times in the 

transition from CdS to the solid solution of cadmium and 

manganese sulfides. 

The solid solutions of more complex composition such 

as Cd1–xZnxS and Cd1–xZnxMoyS1+2y were mentioned in [50]. 

The introduction of the solid solution in the structure 

changed its chemical composition, affecting both the 

change in the target characteristics and their ratios. In this 

case, the condition of the physical similarity of the samples 

was violated, and it is incorrect to talk about the application 

of similarity theory. The ZnFe2O4 and ZnGaO4 spinels and 

their solid solutions were described in [51]. The ratio be-

tween the numbers of electrons used for the photocatalytic 

hydrogen evolution and those taking part in the photocur-

rent generation varied for these samples due to different 

chemical nature. For the solid solutions based on ZnFe2O4 

and ZnGaO4, ratios of the number of electrons used for the 

photocatalytic hydrogen evolution to the number of elec-

trons taking part in the photocurrent generation were less 

than those for individual compounds. However, their dif-

ferences between each other were more than 10%, which 

may be due to the formation of oxygen vacancies for the 

samples with x>1. Therefore, four samples demonstrated 

different physicochemical properties, and the similarity 

theory is not applicable to this case. In the work [52], the 

authors studied the photocatalysts consisting of the solid 

solutions of zinc sulfide, chromium sulfide, indium sulfide 

with different Q1’ values.  

Note that for the samples with adjacent values of metal 

content (e.g., Zn:Cr = 85:15 and Zn:Cr = 75:25) the target 

criteria are the same within the experimental errors. Per-

haps, it is connected with a stronger influence on the elec-

tronic structure of small changes in the composition of the 

triple solid solutions, which cause significant changes in the 

physicochemical properties and do not allow considering 

the samples similar. In the case of small fluctuations in the 

chemical composition, we can only talk about partial simi-

larity of the discussed systems. 

To sum up, for binary solid solutions, the criterion Q1’ 

can serve as the similarity criterion in case of compliance 

with the conditions of physical and geometric similarity. 

For triple solid solutions, the change in the photocatalyst 

composition has a stronger effect on its physicochemical 

properties, as a result of which we can only talk about par-

tial similarity for the samples similar in composition. For 

transition from individual compounds to their solid solu-

tions, the Q1’ criterion may both retain its value and change. 

Such cases should be considered individually.  

3.2. Samples whose chemical nature were different 

The data obtained over the samples whose chemical compo-

sition was changed during the preparation were given in Ta-

ble 5 ([53–74]). For compounds with different chemical na-

ture, the transition from the photocatalysts to the photoelec-

trodes was accompanied by the different ratio of the number 

of electrons used for photocatalytic hydrogen production to 

the number of electrons taking part in the photocurrent gen-

eration. For instance, in [53] NH2-UiO-66 and ZnIn2S4 were 

studied, and for them the Q1’ criterion differed by 7 times, 

while for CdS and ZnS – by 5 times [45]. This result was not 

surprising because the number of electrons was largely de-

termined by the balance between the rate of charge genera-

tion, their recombination, and consumption in various pro-

cesses. For samples with different chemical nature, the rate 

constants of these stages differed, and the ratios also diverged. 

In terms of the similarity theory, one can say that in this case 

the conditions of physical similarity were violated. More inter-

esting were the cases in which the chemical composition of the 

catalyst was changed by loading additional compounds or 

doping. Did the Q1’criterion change in this case? 

A special case of modification of the semiconductor was 

capping some ligands on the photocatalyst surface. In [54] 

titanium dioxide with capped quantum dots based on cad-

mium selenide and the solid solution of cadmium sulfide 

and zinc sulfide using ammonium thiocyanide and mercap-

topropionic acid was described. The scheme for the func-

tioning of these photocatalysts was proposed, in which pho-

togenerated holes were transferred from the valence band 

of quantum dots to the highest occupied molecular orbital 

of the ligand [54]. As a result, the target characteristics of 

the photocatalysts prepared with diverse ligands differed. 

Simultaneously, the Q1’ criteria showing the number of 

electrons used for the photocatalytic hydrogen evolution di-

vided by the number of electrons taking part in the photo-

current generation differed. Possibly, it may be assisted 

with strong differences in the transfer constants of the pho-

togenerated holes, which had an indirect effect on the num-

ber of electrons in the discussed systems. 

The photocatalyst surface was often modified by loading 

compounds and forming the composite catalysts. The re-

searchers extensively studied the composites with different 

composition. In [55] cadmium sulfide whose surface was 

modified with Nb2CT was studied. This deposition led to the 

increase in the reaction rate by 1.7 times, while the photo-

current grew by 1.8 times. The ratio of the number of elec-

trons occurring in the photocatalytic hydrogen production to 

the number of electrons used for the photocurrent genera-

tion was the same for these samples. In [56] copper nanopar-

ticles and their role in the photocatalysis after deposition on 

the surface of bohrium nitride, polyaniline, and the compo-

site photocatalyst consisting of bohrium nitride and polyani-

line were discussed. Copper nanoparticles and copper nano-

particles deposited on BN demonstrated the same catalytic 

activity.  

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Table 4 Verifying the possibility of using Q1’ as the similarity criterion for the series of different solid solutions. 

No. Sample Photocatalyst 
Sacrificial 

agent 

W 

(μmol/min) 

Counter and ref-

erence electrodes 
Electrolyte 

Current density 

(mA/cm2) 

Light 

source 
Q1’ Ref 

1 

CdS 

Solid solutions of CdS  
and ZnS 

0.24 M Na2S, 
0.35 M Na2SO3 

0.08 

Pt/C 

10 vol.% 

ethanol,  

0.5 M NaOH 

0.150 

Xe lamp 

0.14±0.02 

[45]a 

Cd0.25Zn0.75S 0.62 0.767 0.22±0.03 

Cd0.35Zn0.65S 0.48 0.992 0.13±0.02 

Cd0.65Zn0.35S 0.57 0.958 0.16±0.02 

ZnS 0.10 0.975 0.027±0.004 

2 

CdS 

Solid solutions of CdS  
and ZnS 

0.1 M Na2S,  
0.1 M Na2SO3 

0.12 

Cu2S/brass 
1 M Na2Sn,  
0.1 M NaCl 

0.881 

450-LED 

0.44±0.06 

[46] 

Cd0.9Zn0.1S 0.29 0.901 1.0±0.1 

Cd0.8Zn0.2S 0.37 2.21 0.54±0.08 

Cd0.7Zn0.3S 0.47 1.37 1.1±0.2 

Cd0.6Zn0.4S 0.39 0.33 3.8±0.5 

Cd0.5Zn0.5S 0.55 0.067 26±4 

Cd0.4Zn0.6S 0.96 0.139 22±3 

Cd0.3Zn0.7S 2.25 0.984 7±1 

Cd0.2Zn0.8S 0.96 0.259 12±2 

Cd0.1Zn0.9S 0.56 0.128 14±2 

ZnS 0.025 0.024 3.3±0.5 

3 

CdS 

Solid solutions of cadmium 

sulfide and cadmium selenide 

5 vol.% lactic 

acid 

0.35 

Pt, Hg|Hg2Cl2|Cl
– 0.5 M Na2SO4 

0.0036 

Xe lamp 

308±43 

[47]a 

CdS0.99Se0.01 0.55 0.0038 466±66 

CdS0.975Se0.025 0.61 0.0058 335±47 

CdS0.95Se0.05 1.22 0.0100 391±55 

CdS0.925Se0.075 0.61 0.0064 306±43 

CdS0.9Se0.1 0.36 0.0027 425±60 

4 

x = 0 

MnxCd1–xS 
10 vol.% lactic 

acid 

0.35 

Pt, AgCl|Ag|Cl– 0.2 M Na2SO4 

0.015 

Xe lamp 

74±10 

[48] 

x = 0.3 1.02 0.021 155±22 

x = 0.5 1.50 0.024 199±28 

x = 0.6 1.88 0.032 188±26 

x = 0.9 0.59 0.002 939±132 

5 

CdS 

Solid solutions of cadmium 

sulfide and manganese sulfide 

20 vol.% lactic 

acid 

0.055 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.03 

Xe lamp 

5.9±0.8 

[49] 

MCS-1 0.152 0.043 11±2 

MCS-2 0.178 0.065 9±1 

MCS-3 0.127 0.04 10±1 

MCS-4 0.117 0.035 10±2 

6 
ZCS Solid solutions of ZnS, CdS, 

MoS2 

0.35 M Na2S, 

0.35 M Na2SO3 

0.0003 
Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.00014 
Xe lamp 

8±1 
[50] 

ZCM5S 0.0038 0.00021 58±8 

 

 

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Table 4 Verifying the possibility of using Q1’ as the similarity criterion for the series of different solid solutions (continued). 

No. Sample Photocatalyst Sacrificial agent 
W 

(μmol/min) 

Counter and ref-

erence electrodes 
Electrolyte 

Current density 

(mA/cm2) 

Light 

source 
Q1’ Ref 

7 

x = 0 

ZnFe2–xGaxO4 
10 vol.% trieth-

anolamine 

4.63 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.0002 

Xe lamp 

(7±1)·104 

[51] 
x = 0.5 5.40 0.00075 (2.3±0.3)·104 

x = 1.5 5.85 0.00050 (3.7±0.5)·104 

x = 2.0 5.98 0.0017 (11±2)·104 

8 

ZIS 
Solid solutions of zinc sul-

fides, chromium sulfide, in-

dium sulfide 

0.25 M Na2S,  
0.35 M Na2SO3 

0.74 

С, Hg|Hg2Cl2|Cl
– 0.5 M Na2SO4 

0.00007 

Xe lamp 

(3.4±0.5)·104 

[52] 
Z0.85C0.15IS 1.35 0.00015 (2.9±0.4)·10

4 

Z0.75C0.25IS 1.71 0.00022 (2.5±0.4)·10
4 

Z0.55C0.45IS 1.09 0.00008 (4.4±0.6)·10
4 

a In this work the short-circuit current densities were presented, Q1 was calculated. 

 

Table 5 Verifying the possibility of using Q1’ as the similarity criterion for the series of samples with different chemical nature. 

No. Sample Photocatalyst 
Sacrificial 

agent 

W 

(μmol/min) 

Counter and ref-

erence electrodes 
Electrolyte 

Current 

density 

(mA/cm2) 

Light source Q1’ Ref 

Different chemical compounds 

1 

NU66d NH2-UiO-66 decarboxylated 

0.25 M 

Na2S/0.35 M 

Na2SO3 

0.050 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.0028 

Xe lamp, 

λ ≥ 420 nm 

57±8 

[53] 

ZIS ZnIn2S4 0.072 0.0058 395±56 

NU66/ZIS-30 ZnIn2S4 deposited on NH2-UiO-66 0.85 0.0078 349±49 

NU66-d/ZIS-30 
ZnIn2S4 deposited on decarbox-

ylated NH2-UiO-66 
1.22 0.0091 428±60 

2 
CdS CdS 0.24 M Na2S, 

0.35 M Na2SO3 

0.08 
Pt/C 

10 vol.% etha-
nol, 0.5 M NaOH 

0.150 
Xe lamp 

0.14±0.02 
[45] 

ZnS ZnS 0.10 0.975 0.027±0.004 

Capping ligands on the photocatalyst surface 

3 

SCN 
TiO2 with capping quantum dots 

using NH4SCN 0.1 М ascorbic 

acid 

4755 

Pt, AgCl|Ag|Cl– 
0.1 М ascorbic 

acid 

0.053 

AM-1.5G 

(2.9±0.4)·105 

[54] 

MPA 
TiO2 with capping quantum dots 

using mercaptopropionic acid 
470 0.028 (53.7±0.8)·103 

Deposition of different compounds 

4 

CdS CdS 
10 vol.% lactic 

acid 

0.52 

Pt, AgCl|Ag|Cl– 1 M Na2SO4 

0.033 
Xe lamp,  

λ ≥ 420 nm 

501±71 [55] 

CdS/Nb2CT-60 
CdS with deposited Nb2CT 

(60 mg) 
0.90 0.062 465±65 

5 

Cu/BN@PANI-
2.5 wt.% 

2.5% Cu deposited on BN and 
polyaniline 

14 vol.% lactic 

acid 

0.52 

Pt 0.1 M KOH 

49 

Xe lamp, λ ≥ 

420 nm 

0.034±0.005 

[56] Cu-PANI/2.5% 2.5% Cu deposited on polyaniline 0.25 30 0.027±0.004 

Cu/BN-2.5% 2.5% Cu deposited on BN 0.19 19 0.032±0.005 

Cu NPs Cu 0.165 15 0.035±0.005 

 

 
 

          

           

 
 

          

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Table 5 Verifying the possibility of using Q1’ as the similarity criterion for the series of samples with different chemical nature (continued). 

 No. Sample Photocatalyst 
Sacrificial 

agent 

W 

(μmol/min) 

Counter and ref-

erence electrodes 
Electrolyte 

Current 
density 

(mA/cm2) 

Light source Q1’ Ref 

6 

NiCo-LDH 
Nickel-cobalt double layered hy-

droxides 
0.2 M Na2S, 0.2 

M Na2SO3 

0.13 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.48 

AM-1.5G 

0.9±0.1 

[57] CoO CoO 0.20 0.88 0.7±0.1 

CoO/NiCo-LDH 
CoO deposited on nickel-cobalt 

double layered hydroxides 
1.00 3.15 1.0±0.1 

7 
ZnS/PDA1 Polydopamine deposited on ZnS 0.35 M Na2S, 

0.25 M Na2SO3 

0.36 
Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.002 
Xe lamp 

577±81 
[58] 

ZnS ZnS 0.16 0.001 526±74 

8 

UiO-66 UiO-66 
10 vol.% trieth-

anolamine 

0.067 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.02 
Xe lamp, 

λ ≥ 420 nm 

11±2 

[59] 
UiO-66/NiS2-5 

UiO-66 with deposited 5 wt.% 

NiS2 
0.30 0.07 14±2 

9 
CPt-14 Pt/g-C3N4 10 vol.% trieth-

anolamine 

3.38 
Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.00014 Xe lamp, 

λ ≥ 400 nm 

(8±1)·104 
[60] 

CPtO-6 PtO/g-C3N4 4.46 0.00020 (7±1)·10
4 

10 

CdS CdS 0.35 M 

Na2S/0.25 M 

Na2SO3 

198 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.0024 
Xe lamp, 

λ ≥ 420 nm 

(2.6±0.4)·105 

[61] 
0.4QD/CdS 

0.4 wt.% C (quantum dots)  

deposited on CdS 
309 0.0048 (2.1±0.3)·105 

11 
Pt/SiO2 RP/Pt/SiO2 

– 
200.4 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 
0.0030 Xe lamp, 

λ ≥ 420 nm 

21±3 
[62] 

CoP2-6 RP/CoP2(6)/SiO2 401.4 0.0032 40±6 

12 
20 WN/CdS 20 WN/CdS 10 vol.% lactic 

acid 

4.02 
Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.0021 Xe lamp, 

λ ≥ 420 nm 

6218±877 
[63] 

CdS CdS 0.43 0.0005 2771±391 

13 

3DOMM-TiO2 
TiO2 prepared by the template 

method 

10 vol.% meth-
anol 

0.136 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.20 

Xe lamp, 
λ ≥ 420 nm 

2.2±0.3 

[64] 

3DOMM-TiO2–x 
TiO2 prepared by the template 

method and reduced by NaBH4 
0.173 0.31 1.8±0.3 

3DOMM-TiO2–

x@PANI 

TiO2 prepared by the template 

method with deposited polyaniline 
0.264 0.80 1.1±0.1 

Ag@3DOMM-

TiO2–x@PANI 

TiO2 prepared by the template 

method with deposited 
 polyaniline and Ag 

0.281 1.12 0.8±0.1 

14 

BCN 
C3N4 prepared by the thermal 

polymerization 

20 vol.% trieth-

anolamine 

0.01 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.0002 

Xe lamp 

160±23 

[65] CAN 
C3N4 prepared by the template 

method 
0.02 0.0004 173±24 

10% Co/CAN 
10% Co3O4 deposited on C3N4 pre-

pared by the template method 
0.04 0.0013 97±13 

15 
In2S3 In2S3 10 vol.% lactic 

acid 

0.0015 
Pt, Hg|Hg2Cl2|Cl

– 0.5 M Na2SO4 
0.00055 

Xe lamp 
9±1 

[66] 
25MPIS 25% MoP/In2S3 0.24 0.0016 481±68 

16 
CdS CdS 20 vol.% lactic 

acid 

0.44 
Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.005 Xe lamp, 

λ ≥ 420 nm 

(2.8±0.4)·102 
[67] 

11% Fe2P/CdS 11% Fe2P/CdS 34.6 0.070 (1.6±0.2)·10
3 

           

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Table 5 Verifying the possibility of using Q1’ as the similarity criterion for the series of samples with different chemical nature (continued). 

 No. Sample Photocatalyst 
Sacrificial 

agent 

W 

(μmol/min) 

Counter and ref-

erence electrodes 
Electrolyte 

Current 

density 
(mA/cm2) 

Light source Q1’ Ref 

17 
TiO2 TiO2 0.5 M 

Na2S/Na2SO3 

0.009 
Pt, AgCl|Ag|Cl– 

0.5 M 
Na2S/Na2SO3 

0.10 
Xe lamp 

0.29±0.04 
[68] 

CBT-0 CdS/TiO2 0.489 0.52 3.0±0.4 

18 

LTO La2Ti2O7 

10 vol.% trieth-

anolamine 

0.06 

Pt, AgCl|Ag|Cl– 1 M NaOH 

0.012 

AM-1.5G 

15±2 

[69] 

rGO/LTO 
71 wt.% reduced graphene oxide 

deposited on La2Ti2O7 
0.29 0.026 36±5 

LTO/Ni-Fe 
La2Ti2O7 deposited on nickel-iron-

double layered hydroxides 
0.36 0.034 33±5 

rGO/LTO/NiFe 

Graphene oxide deposited on 

La2Ti2O7 deposited on nickel-iron-
double layered hydroxides 

0.53 0.068 25±4 

Doping 

19 
CdS CdS 20 vol.% 

С3Н6О3 

0.84 
Pt, Hg|Hg2Cl2|Cl

– 0.5 M Na2SO4 
0.027 Xe lamp, 

λ ≥ 420 nm 

100±14 
[70] 

Mo-CdS CdS:Mo (25 mol.%) 4.87 0.116 134±19 

20 

ZnO 

ZnO doped with Al – 

0.034 

Pt, AgCl|Ag|Cl– 0.1 M NaOH 

0.06 
Light source 

simulating 

solar light / 
sunlight 

1.8±0.3 

[71] 
ZnO/Al/0.5 0.056 0.11 1.6±0.2 

ZnO/Al/1 0.122 0.24 1.6±0.2 

ZnO/Al/5 0.183 0.38 1.5±0.2 

21 

BCN Carbon nitride 
20 vol.%  

methanol 

0.054 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.00036 
Xe lamp, 

λ ≥ 420 nm 

476±67 

[72] 
PTCN 

Carbon nitride doped by  

phosphorous 
0.092 0.00043 685±97 

22 

GCN-B Carbon nitride 

20 vol.% trieth-

anolamine 

0.0024 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.18 

Xe lamp, 

λ ≥ 420 nm 

(4.3±0.6)·10–2 

[73] 
GCN-NS Carbone nitride, nanosheets 0.0083 0.43 (6±1)·10–2 

B,Cs CN-B Carbon nitride doped with B and Cs 0.0027 0.175 (5.0±0.7)·10–2 

B,Cs CN-NS 
Carbon nitride doped with B and 

Cs, nanosheets 
0.0189 0.63 (10±1)·10–2 

23 

CN Carbon nitride 
10 vol.% trieth-

anolamine 

0.29 

Pt, AgCl|Ag|Cl– 0.2 M Na2SO4 

0.11 
Xe lamp, 

λ ≥ 420 nm 

8±1 

[74] 
BQCN 

Carbon nitride with benzoqui-

none as linker 
0.66 0.25 8±1 

 

 

 

 

 

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Table 6 Verifying the possibility of using Q1’ as the similarity criterion for the series of samples with different weight ratio of the components or preparation time. 

No. Sample Photocatalyst 
Sacrificial 

agent 

W 

(μmol/min) 

Counter and 

reference 

electrodes 

Electrolyte 

Current 

density 

(mA/cm2) 

Light 

source 
Q1’ Ref 

1 
CoP2-4 RP/CoP2(4)/SiO2 

– 
401.4 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 
0.032 

Xe lamp, 

λ ≥ 420 nm 

40±6 
[62] CoP2-6 RP/CoP2(6)/SiO2 707.4 0.052 44±6 

CoP2-8 RP/CoP2(8)/SiO2 622.8 0.048 42±6 

2 
6% MoS2/CdS 6% MoS2/CdS 10 vol.% lactic 

acid 

10.62 
Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.0036 Xe lamp, 

λ ≥ 420 nm 

(9±1)·103 
[75] 

20% MoS2/CdS 20% MoS2/CdS 5.80 0.0018 (10±2)·10
3 

3 

0% LaVO4 

Carbon nitride with different wt. 

content of deposited LaVO4 

10 vol.% trieth-

anolamine 

0.027 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.00045 

Xe lamp 

190±40 

[76] 

10% LaVO4 0.061 0.0010 196±42 

15% LaVO4 0.093 0.0013 230±49 

20% LaVO4 0.041 0.00075 176±37 

25% LaVO4 0.015 0.00034 144±31 

4 

SIS-ZIS-0.1 
Composites based on ZnIn2S4 

and SnIn4S8, number shows ½ 
mmol of added tin chloride dur-

ing the preparation stage 

10 vol.% trieth-
anolamine 

0.61 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.0048 

Xe lamp, 
λ ≥ 400 nm 

404±73 

[69] 

SIS-ZIS-0.2 0.76 0.0080 302±54 

SIS-ZIS-0.3 1.00 0.0094 339±61 

SIS-ZIS-0.4 0.85 0.0083 329±59 

SIS-ZIS-0.5 0.67 0.0072 297±53 

5 

CdS 

CdS with different amount of de-

posited titanium carbide 

20 vol.%  

methanol 

0.25 

Pt, AgCl|Ag|Cl– 0.5 M Na2SO4 

0.005 

Xe lamp 

0.16±0.03 

[77] 

CdS@Ti3C2-5 0.48 0.009 0.17±0.02 

CdS@Ti3C2-10 0.67 0.010 0.21±0.03 
CdS@Ti3C2-15 1.07 0.017 0.20±0.03 

CdS@Ti3C2-20 0.90 0.0095 0.30±0.04 

CdS@Ti3C2-25 0.88 0.009 0.31±0.04 

CdS@Ti3C2-50 0.50 0.0046 0.35±0.05 
CdS@Ti3C2-100 0.22 0.0025 0.28±0.04 

6 

1% CoSe2 

CdS0.95Se0.05 with different 
amount of deposited CoSe2 

5 vol.% lactic 
acid 

2.95 

Pt, Hg|Hg2Cl2|Cl
– 0.5 M Na2SO4 

0.011 

Xe lamp 

(9±1)·102 

[47] 

2.5% CoSe2 11.96 0.022 (1.7±0.3)·10
3 

5% CoSe2 23.16 0.057 (1.3±0.2)·10
3 

7.5% CoSe2 19.31 0.047 (1.3±0.2)·10
3 

10% CoSe2 12.60 0.028 (1.4±0.2)·10
3 

12.5% CoSe2 9.96 0.017 (1.9±0.3)·10
3 

7 

HD-TiO2 3 h 
Defected titania prepared during 

different time of hydrothermal 

treatment 

20 vol.%  

methanol 

11.1 

Pt, Hg|Hg2Cl2|Cl
- 2 M Na2SO4 

0.00036 

Xe lamp, 

λ ≥ 420 nm 

(10±1)·104 

[78] 
HD-TiO2 4 h 12.7 0.00046 (9±1)·10

4 

HD-TiO2 5 h 15.0 0.00056 (9±1)·10
4 

HD-TiO2 6 h 10.0 0.00029 (11±2)·10
4 

8 

PTCN/CN-1 
Ti3C2/P-doped g-C3N4, obtained 

for different time of mixturing 

20 vol.%  

methanol 

0.19 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.0006 
Xe lamp, 

λ ≥ 420 nm 

995±140 

[72] PTCN/CN-2 0.28 0.0012 753±106 
PTCN/CN-3 0.21 0.00077 881±124 

9 

NiS/CdS-10 

NiS/CdS, number shows time of 

mixturing of CdS suspension 

20 vol.% lactic 

acid 

0.75 

Pt, Hg|Hg2Cl2|Cl
– 

No infor-

mation 

1.0 

Xe lamp, 

λ ≥ 420 nm 

2.4±0.5 

[79] 

NiS/CdS-30 1.75 1.5 3.7±0.8 

NiS/CdS-60 3.80 2.8 4.3±0.9 
NiS/CdS-90 6.24 5.9 3.4±0.7 

NiS/CdS-120 4.67 4.0 3.7±0.8 

10 

CBT-30 
CdS/TiO2,number shows water 

share in water-alcohol solution 

put into the autoclave 

0.5 M 

Na2S/Na2SO3 

2.07 

Pt, AgCl|Ag|Cl– 
0.5 M 

Na2S/Na2SO3 

3.0 

Xe lamp 

2.2±0.3 

[68] 
CBT-50 3.57 4.3 2.7±0.4 

CBT-70 2.67 3.5 2.4±0.3 
CBT-100 1.68 2.6 2.1±0.3 

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Table 7 Verifying the possibility of using Q1’ as the similarity criterion for the series of samples with different electrolytes and their concentration. 

No. Photocatalyst Sacrificial agent 
Hydrogen production 

rate (μmol/min) 

Counter and refer-

ence electrodes 
Electrolyte 

Current density 

(mA/cm2) 

Light 

source 
Q1’ Ref 

1 

CuFe1.6Mn0.4O4 

Na2S 

3.39 

Pt, AgCl|Ag|Cl– 0.1 M Na2SO4 

0.090 

Xe lamp 

121±17 

[80] 

CuFe1.2Mn0.8O4 3.57 0.018 635±90 

CuFe0.8Mn1.2O4 3.62 0.065 178±25 

CuFe1.6Mn0.4O4 

Na2SO3 

0.80 0.090 29±4 

CuFe1.2Mn0.8O4 3.57 0.018 635±90 

CuFe0.8Mn1.2O4 1.56 0.065 77±11 

CuFe1.6Mn0.4O4 

Oxalic acid 

0.54 0.090 19±3 

CuFe1.2Mn0.8O4 0.58 0.018 103±15 

CuFe0.8Mn1.2O4 5.8 0.065 286±40 

2 

Cd0.8Zn0.2S 20 vol.% C2H5OH,  

0.1 M NaOH 

0.04 

Cu2S/brass 

20 vol.% C2H5OH, 0.1 M 

NaOH 

0.008 

 

16±2 

[81] 

1% CuS/ Cd0.8Zn0.2S 0.01 0.015 2.1±0.3 

Cd0.8Zn0.2S 
0.1 M Na2S 

0.10 
0.1 M Na2S 

0.082 3.9±0.6 

1% CuS/ Cd0.8Zn0.2S 0.35 0.1 11±2 

Cd0.8Zn0.2S 
0.1 M Na2S + 0.1 M Na2SO3 

0.59 
0.1 M Na2S + 0.1 M Na2SO3 

0.259 7±1 

1% CuS/ Cd0.8Zn0.2S 0.79 0.837 3.0±0.4 

Cd0.8Zn0.2S 

0.02 M Na2S, 0.1 M Na2SO3 0.18 0.02 M Na2S, 0.1 M Na2SO3 0.033 17±2 

0.05 M Na2S, 0.1 M Na2SO3 0.35 0.05 M Na2S, 0.1 M Na2SO3 0.168 7±1 

0.2 M Na2S, 0.1 M Na2SO3 0.82 0.2 M Na2S, 0.1 M Na2SO3 0.184 14±2 

0.3 M Na2S, 0.1 M Na2SO3 0.97 0.3 M Na2S, 0.1 M Na2SO3 0.297 10±2 

0.4 M Na2S, 0.1 M Na2SO3 1.15 0.4 M Na2S, 0.1 M Na2SO3 0.240 15±2 

0.1 M Na2S, 0.02 M Na2SO3 0.38 0.1 M Na2S, 0.02 M Na2SO3 0.125 10±1 

0.1 M Na2S, 0.05 M Na2SO3 0.54 0.1 M Na2S, 0.05 M Na2SO3 0.183 9±1 

0.1 M Na2S, 0.2 M Na2SO3 0.47 0.1 M Na2S, 0.2 M Na2SO3 0.211 7±1 

0.1 M Na2S, 0.3 M Na2SO3 0.41 0.1 M Na2S, 0.3 M Na2SO3 0.184 7±1 

1% CuS/ Cd0.8Zn0.2S 

0.02 M Na2S, 0.1 M Na2SO3 0.36 0.02 M Na2S, 0.1 M Na2SO3 0.219 5.3±0.7 

0.05 M Na2S, 0.1 M Na2SO3 0.62 0.05 M Na2S, 0.1 M Na2SO3 0.461 4.3±0.6 

0.2 M Na2S, 0.1 M Na2SO3 0.89 0.2 M Na2S, 0.1 M Na2SO3 0.727 3.9±0.6 

0.3 M Na2S, 0.1 M Na2SO3 0.83 0.3 M Na2S, 0.1 M Na2SO3 0.624 4.3±0.6 

0.4 M Na2S, 0.1 M Na2SO3 0.88 0.4 M Na2S, 0.1 M Na2SO3 0.444 6.3±0.9 

0.1 M Na2S, 0.02 M Na2SO3 0.48 0.1 M Na2S, 0.02 M Na2SO3 0.192 8±1 

0.1 M Na2S, 0.05 M Na2SO3 0.59 0.1 M Na2S, 0.05 M Na2SO3 0.424 4.5±0.6 

0.1 M Na2S, 0.2 M Na2SO3 0.62 0.1 M Na2S, 0.2 M Na2SO3 0.718 2.8±0.4 

0.1 M Na2S, 0.3 M Na2SO3 0.44 0.1 M Na2S, 0.3 M Na2SO3 0.605 2.3±0.3 

 

 

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14 of 21 DOI: 10.15826/chimtech.2023.10.2.03 

Copper loaded on polyaniline showed a higher catalytic 

activity (24% greater than 2.5% Cu/BN). The composite 

photocatalysts based on copper, bohrium nitride, and poly-

aniline were the most active in this set. Figure 2 demon-

strates the criteria Q1’ and Q3’ calculated for all samples. In 

this particular case, the parameter values are the same and 

can be considered the similarity criteria. 

In [57] nickel-cobalt double layered hydroxide photocata-

lysts were studied. Another discussed object was cobalt ox-

ide. Because of chemical composition similarities, the ratio 

between the numbers of electrons used to the photocatalytic 

hydrogen evolution divided and those taking part in the pho-

tocurrent generation was the same and equaled 0.7 and 0.9 

for cobalt oxide and double layered hydroxides, respectively. 

The formation of the composite catalyst from these compo-

nents allowed enhancing the photocatalytic hydrogen pro-

duction by 5–8 times and increasing the photocurrent gener-

ation by 4–7 times compared with pristine compounds [57]. 

The Q1’ criterion retained the value obtained for nickel-cobalt 

double layered hydroxides whose surface was modified with 

CoO by the hydrothermal method. The same result was 

reached for zinc sulfide and one deposited with polydopa-

mine described in [58]. Such modification allowed improving 

the target characteristics of the photocatalysts and photoe-

lectrodes and keeping Q1’ within experimental error. The 

same behavior was demonstrated for metal-organic frame-

works discussed in [59]. The deposition of 5% NiS led to the 

increase of the photocatalytic hydrogen production rate from 

aqueous solution of triethanolamine by 4.5 times, while the 

generated current density was enhanced by 3.5 times. The 

ratio of the electrons occurring in these processes remained 

the same. In [53] ZnIn2S4 was deposited on NH2-UiO-66 and 

decarboxylated NH2-UiO-66. The Q1’ criteria differed for 

pristine samples, while Q1’ was the same for the composite 

photocatalysts and ZnIn2S4. Finally, the same values of Q1’ 

were calculated for graphitic carbon nitride modified with 

platinum or platinum oxide [60]. The same behavior was 

found for CdS whose surface was modified with carbon quan-

tum dots. The photocatalytic hydrogen production rate and 

the photocurrent density doubled in these systems while the 

Q1’ criterion was the same within the experimental errors [61].  

The contrary trend was characterized for other systems 

described earlier. For instance, in [62] the photocatalysts 

based on silicon dioxide and the co-catalyst modified with 

red phosphorous were studied. The replacement of plati-

num co-catalyst with cobalt phosphide led to the growth of 

the catalytic activity and the ratio of the number of elec-

trons used for the photocatalytic hydrogen evolution to the 

number of electrons taking part in the photocurrent gener-

ation. Probably, different co-catalysts significantly changed 

the rate constants of the corresponding processes, which 

leads to the observed changes in the system. The same be-

havior was found in the case of CdS whose catalytic prop-

erties were improved with deposition of 20 wt.% WN [63]. 

The co-catalyst addition allowed enhancing the hydrogen 

production rate by 9.3 times while the photocurrent 

generation was increased by 4.2 times, the Q1’ criterion 

grew by 2.2 times. In [64] researches discussed titanium 

dioxide prepared by the template method. The reduction of 

titania by sodium borohydride led to an increase in the re-

action rate of hydrogen photoproduction from aqueous 

methanol solution by 20%; the studied ratio of the elec-

trons occurring in the photocatalytic and the photovoltaic 

properties did not change in this case. Additionally, the au-

thors improved the target characteristics by the deposition 

of polyaniline and polyaniline and silver on the photocatalyst 

surface. Such modifications favored the photocatalytic hy-

drogen production; however, the Q1’ criteria were different 

for the obtained samples as shown in Figure 3.  

The authors of [65] compared the target properties of gra-

phitic carbon nitride prepared by different methods such as 

thermal polymerization and template synthesis. At whole, the 

template method allowed getting more active samples; the ra-

tio between the number of electrons used for the photocata-

lytic hydrogen evolution and the number of electrons taking 

part in the photocurrent generation was the same within ex-

perimental errors. The subsequent modification of carbon ni-

tride with cobalt oxide changed the electronic properties of the 

semiconductor, improved the target characteristics of the pho-

tocatalytic and photovoltaic phenomena; the Q1’ parameter 

was also changed. 

 
Figure 2 Parameters Q1’

 and Q3’ calculated for the Cu-containing 

photocatalysts described in [56].  

 
Figure 3 The catalytic activities, current densities, and parameters 

Q1’ calculated for the titania-based photocatalysts discussed in [64]. 

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Chimica Techno Acta 2023, vol. 10(2), No. 202310203 REVIEW 

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The illustration of the significant change in the param-

eter Q1’ was the work [66] in which molybdenum phosphide 

(25 wt.%) was deposited on the surface of indium sulfide. 

It caused the increase in the rate of the photocatalytic hy-

drogen production from lactic acid, the photocurrent gen-

eration, and Q1’ value by 160, 2.9, and 53 times, respec-

tively. The same result was found for CdS modified with 

11 wt.% iron phosphide, where the co-catalyst addition led 

to the growth of the reaction rate, the photocurrent gener-

ation, and Q1’ by 79, 14, and 5.7 times, respectively [67]. 

In [68] titania and the composite samples based on tita-

nia and cadmium sulfide were tested in 0.5 M Na2S/Na2SO3. 

The composite photocatalysts were more active under visi-

ble light than pristine titania or cadmium sulfide due to the 

heterojunction formation. Perhaps, the heterojunctions 

changed the number of electrons taking part in the photo-

catalytic reaction and photocurrent generation, and its ra-

tio defined by Q1’. In [69] reduced graphene oxide deposited 

on La2Ti2O7, La2Ti2O7 deposited on nickel-iron-double lay-

ered hydroxides, the composite material consisting of gra-

phene oxide, nickel-iron-double layered hydroxides, and 

La2Ti2O7. Figure 4 reveals that as for CdS/TiO2, the reaction 

rates, the current density, and Q1’ differed for the composite 

photocatalysts. 

Thus, in the case of combining materials of different 

composition, the parameter Q1’ can either preserve the con-

stant value of the pristine material or change. Probably, the 

specific values of the parameter are related to the balance 

of various rate constants that described the processes of 

electron-hole generation, their transfer and recombination. 

Generally, the condition of physical similarity is not met for 

the catalysts having different chemical nature. However, in 

several cases, we can talk about partial similarity. 

Doping. The authors [70] studied the doping of cad-

mium sulfide with molybdenum. The introduction of 

25 wt.% of MoS2 led to an increase in the reaction rate and 

the photocurrent generation, while the ratio of the number 

of electrons used for the photocatalytic hydrogen evolution 

to the number of electrons taking part in the photoelectro-

chemical processes was the same. The introduction of Al to 

zinc oxide (up to 5 wt.%) improved the target characteris-

tics, while the Q1’ criteria were the same within experi-

mental error [71] as shown in Figure 5. 

The researchers studied doped graphitic carbon nitride. 

In [72] phosphorous was used as the dopant; its introduc-

tion in the structure allowed improving the target charac-

teristics; however, the ratio of electrons did not remain 

constant and grew during the doping. Probably, this behav-

ior was related to reaction rate constants of the processes 

occurring when P was introduced into the electronic struc-

ture of carbon nitride. The authors [73] discussed carbon 

nitride doped by B and Cs simultaneously for different 

forms such as nanoparticles and nanosheets. It should be 

noted that the introduction of these elements into the struc-

ture allowed improving both the photocatalytic and photo-

voltaic characteristics of the materials. However, Figure 6 

shows that the ratio of the number of electrons used to the 

photocatalytic hydrogen evolution to the number of elec-

trons taking part in the photoelectrochemical processes 

was the same for the nanoparticles and differed for the 

nanosheets.  

 
Figure 4 The catalytic activities, current densities, and parameters 

Q1’ calculated for the LTO-based samples mentioned in [69].  

 
Figure 5 The Q1’ parameter calculated for the Al-doped ZnO sam-

ples described in [71].  

 
Figure 6 The Q1’

 parameter calculated for the samples based on 

carbon nitride (GCN) discussed in [73]. NS denotes nanosheets.  

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In [74] the effect of benzoquinone on the target charac-

teristics of carbon nitride obtained by crosslinking polymer 

chains of carbon nitride was described. In this case, the 

change in the electronic properties was similar to ones oc-

curring during doping because the additional impurity level 

was formed in the electronic structure, which improved 

charge separation. The appearance of this level contributed 

to the increase in the reaction rate and photocurrent gener-

ation by a factor of 2.3 while the Q1’ was the same and 

equaled 8 [74]. Thus, in the case of doping, the parameter 

Q1' can both keep constant during the transition between 

samples and change. 

3.3. Samples in which weight ratios of  

components were changed  

Table 6 contains the data obtained for the samples during 

whose preparation the weight ratio of components or reac-

tion time were changed. This case was considered on the 

example of ten series of samples with different chemical 

nature. In [62] the composite photocatalysts based on co-

balt phosphide deposited on the silica surface for different 

time periods (the time in hours is written in the sample la-

bel in Table 6) with subsequent deposition of red phospho-

rous were studied. The ratio of electron amount used in the 

target processes was the same and equaled ~40 for all sam-

ples. In the case of the samples based on cadmium sulfide 

and molybdenum sulfide [75], the same result was found; 

increasing MoS2 amount from 6 to 25 wt.% led to the halv-

ing of the photocatalytic hydrogen production rate and the 

photocurrent density, while the Q1’ criterion remained con-

stant. The authors [76] discussed the composite photocata-

lysts consisting of lanthanum vanadate and graphitic car-

bon nitride; the photocatalytic and photovoltaic properties 

were studied for samples with w(LaVO4) from 0 to 25%. 

The changes in the target properties had a bell-shaped char-

acter, while their ratio was the same within the experi-

mental error. For the sample with 25 wt.% LaVO4, a slight 

decrease in this parameter was observed. Possibly, it was 

related to the change in the geometric structure of the cat-

alyst. The excess (relative to the optimal) content of lantha-

num vanadate was associated with the location of particles 

that block the photocatalyst’s active centers. During the 

transition between catalysts of different geometric struc-

tures, the conditions of geometric and/or physical similar-

ity were violated, as a result of which the potential similar-

ity criteria, as seen in Figure 7, will not be preserved.  

In [69] the composite photocatalysts based on ZnIn2S4 

and SnIn4S8 were described. The dependences of the hydro-

gen production rate and the photocurrent density on the 

catalyst composition went through a maximum. The ratio 

of the electron number used in the target processes re-

mained the same for the transition from one sample to an-

other and was 300–400 within experimental error. Another 

situation was found for CdS whose surface was modified 

with titanium carbide (Figure 8) [77]. The dependences of 

the reaction rate and the current density on the titanium 

carbide content was domed, the maximum values were ob-

served for 15 wt.% of titanium carbide. However, the Q1’ 

criteria were the same values within experimental error for 

the samples with 15% Ti3C2 (Q1’ ~ 0.16) and greater than 

15% Ti3C2 (Q1’ ~ 0.28). Such difference may be due to the 

textural characteristics of the samples or the number of in-

terfacial contacts; the increase in the Ti3C2 content led to 

the growth of the interfacial contacts and the surface area. 

After achieving the optimal structure of CDs@Ti3C2-15, the 

number of contacts between titanium carbide and cadmium 

sulfide decreased, and the surface area and pore volume 

also declined. Thus, in this case, the appearance of two 

groups of samples with different similarity criteria was 

connected with the change in their geometric structure; the 

theory of similarity within each group was fulfilled. 

In [47] the photocatalysts based on the solid solution of 

cadmium sulfide and cadmium selenide with deposited co-

balt selenide were studied. As for other deposited photo-

catalysts, the dependences of the hydrogen production rate 

and the photocurrent density on the co-catalyst content had 

a wide peak shape, as shown in Figure 9. 

 
Figure 7 The Q1’

 parameter calculated for the photocatalysts LaVO4/CdS 

with different LaVO4 content (based on data described in [76]). 

 
Figure 8 The dependence of Q1’

 on the co-catalyst content for the 

composites CdS@Ti3C2 discussed in [77].  

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Chimica Techno Acta 2023, vol. 10(2), No. 202310203 REVIEW 

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The ratio of the target characteristics denoted as Q1’ was 

the same within experimental error for all samples, exclud-

ing one with 1% CoSe2. Unfortunately, it was difficult to de-

termine the reasons for such deviation due to the lack of 

information about the texture and structure of the men-

tioned sample.  

In [78] the defect-containing titania prepared by the hy-

drothermal treatment at 3–6 h was studied. The hydrother-

mal treatment allowed obtaining the samples with oxygen 

vacancies whose amount impacted the hydrogen production 

and the photocurrent generation. The ratio of the electros 

taking part in the target processes was the same for all sam-

ples. The Q1’ criterion may serve as the similarity criterion 

in case of the composite materials based on graphitic car-

bon nitride doped by P and titanium carbide; the catalyst 

components were mixed at different time [72]. In [79] CdS 

with deposited NiS was described, and the crystallization 

time of CdS was varied. Figure 10 showed that for this set 

of samples the Q1’ value remained constant, excluding the 

first sample. This was probably due to the low crystalliza-

tion time and the resulting deviations in the structure of the 

catalyst in relation to other samples.  

Another way of changing the synthesis conditions, indi-

rectly related to the change in the mass ratios of the catalyst 

components, was the variation of the solvent composition 

during the synthesis [68]. The number of electrons occur-

ring in the photocatalytic hydrogen production divided by 

the number of electrons taking part in the photocurrent 

generation was the same for transition between the sam-

ples in this set.  

To sum up, if the conditions of geometric and physical 

similarity are fulfilled, the parameter Q1’ revealing the ratio 

of electrons taking part in the target processes can act as 

the similarity criterion revealing the relation between the 

efficiencies of the photocatalytic hydrogen production and 

the photocurrent generation for different samples.  

3.4. Studying photocatalytic and photovoltaic 

properties in different electrolytes  

Table 7 showed the data obtained over samples in different 

electrolytes [80, 81]. Unfortunately, little attention has 

been paid to the study of this issue in the literature. In [80] 

the authors described photocatalytic processes of the solid 

solution of copper oxide, iron oxide, and manganese oxide 

in aqueous solutions of sodium sulfide, sodium sulfite, and 

oxalic acid. For comparison, the photocurrent generation 

was carried out in 0.1 M Na2SO4 solution. In case of inor-

ganic salts, the dependence of hydrogen production rate on 

the solid solution composition went through a maximum, 

while for the photocurrent generation this dependence 

went through a minimum. In case of oxalic acid, the reac-

tion rate increased for the discussed samples. This behavior 

of the target characteristics was connected with electrolyte 

nature and different transformations in various media. So, 

it was difficult to identify any features for the ratio of elec-

trons taking part in target processes.  

 
Figure 9 The dependences of target values and Q1’

 on the CoSe2 

content for the photocatalysts CoSe2/CdS0.95Se0.05 described in [47].  

 
Figure 10 The dependence of Q1’ on the mixturing time of CdS sus-

pension obtained for NiS/CdS samples discussed in [79]. 

The Q1’ criterion did not remain the same for transition 

between different solutions and catalysts.The solutions of 

distinct nature or concentration possessed different prop-

erties such as dielectric constant, density, viscosity, etc., 

that impacted the charge transfer and current generation. 

Therefore, the condition of physical similarity of the dis-

cussed systems was not fulfilled; the transition between 

different solutions for the same sample cannot be consid-

ered using the similarity theory. The same conclusion may 

be made based on the results described in [81]. In that pa-

per the photocatalytic and photovoltaic properties were 

studied in 20 vol.% C2H5OH, 0.1 M NaOH, 0.1 M Na2S,  

0.1 M Na2S + 0.1 M Na2SO3. As in the previous case, the fea-

tures of the photocatalytic hydrogen production and photo-

current generation were different in various media. 

Figures 11 and 12 reveal that when the ratio of salts in 

the solution varied, the dependences of the target charac-

teristics on the composition of the electrolyte remained at 

a qualitative level. However, the Q1’ criterion changed from 

7 to 17 and from 2 to 8 for Cd0.8Zn0.2S and 1% 

CuS/Cd0.8Zn0.2S, respectively. Thus, in terms of the similar-

ity theory, consideration of the question of transferring the 

dependence of photocatalytic hydrogen production on pho-

tovoltaic parameters was incorrect. 

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Chimica Techno Acta 2023, vol. 10(2), No. 202310203 REVIEW 

18 of 21 DOI: 10.15826/chimtech.2023.10.2.03 

 
Figure 11 The dependence of the target characteristics of 

Cd0.8Zn0.2S measured in Na2S/Na2SO3 [81]. The electrolyte compo-

sition was labeled as a/b, where a is the concentration of Na2S, M, 

b is the concentration of Na2SO3, M.  

 
Figure 12 The dependence of the target characteristics of 
1% CuS/Cd0.8Zn0.2S measured in Na2S/Na2SO3 [81]. The electrolyte 

composition was labeled as a/b, where a is the concentration of 

Na2S, M, b is the concentration of Na2SO3, M.  

4. Limitations 

The topic of the transfer from the photocatalytic reaction to 

the photocurrent generation has some promising research 

directions such as the calculation and verification Q2 and 

Q4, getting more information about rate constants and in-

terpretation of the criterion values, discussing other photo-

catalytic reactions besides hydrogen production, etc.  

5. Conclusions 

The photocatalytic hydrogen production and photocurrent 

generation in the photoelectrochemical cell are analogous 

phenomena; so, one can use the similarity theory for their 

description. Using dimension theory, two parameters 

which could potentially act as the similarity criteria re-

vealing relation between efficiencies of the photocatalytic 

hydrogen evolution and the photocurrent generation were 

obtained. The first parameter is the ratio of the number of 

electrons involved in the photocatalytic hydrogen produc-

tion to the number of electrons taking part in the photo-

current generation. The latter value takes into account the 

energy aspects of converting light energy into chemical 

bond and electrical energy. The analysis of the literature 

data allowed verifying the first criterion and showed that 

the ratio of the number of electrons did act as a similarity 

criterion if the conditions of geometric and physical simi-

larity were fulfilled. In practice, this means that the ratio 

between the quantitative indicators of the photocatalytic 

hydrogen production and photocurrent generation re-

mained constant in the case of the same chemical nature 

of the samples, for example, in the set with different ra-

tios of the catalyst components, with the same morphol-

ogy and texture, or in the case of the solid solutions for-

mation with a similar composition. Generally, if the pho-

tocatalyst modification by chemical compounds changes 

the physicochemical properties of samples, such cases, as 

well as data analysis in various media, cannot be consid-

ered in the similarity theory and should be studied indi-

vidually.  

● Supplementary materials 

No supplementary materials are available. 

● Funding 

This work was supported by the Ministry of Science and 

Higher Education of the Russian Federation within the gov-

ernmental order for Boreskov Institute of Catalysis, project 

no. AAAA-A21-121011390009-1. 

● Acknowledgments 

None. 

● Author contributions 

Conceptualization: E.A.K., D.V.M. 

Data curation: D.V.M. 

Formal Analysis: D.V.M. 

Funding acquisition: E.A.K. 

Investigation: D.V.M. 

Methodology: D.V.M. 

Project administration: E.A.K. 

Resources: E.A.K. 

Software: E.A.K. 

Supervision: E.A.K.,D.V.M. 

Validation: D.V.M.,E.A.K. 

Visualization: D.V.M. 

Writing – original draft: D.V.M. 

Writing – review & editing: E.A.K.,D.V.M. 

● Conflict of interest 

The authors declare no conflict of interest. 

https://doi.org/10.15826/chimtech.2023.10.2.03


Chimica Techno Acta 2023, vol. 10(2), No. 202310203 REVIEW 

19 of 21 DOI: 10.15826/chimtech.2023.10.2.03 

● Additional information 

Author IDs: 

Dina V. Markovskaya, Scopus ID 55895307200;  

Ekaterina A. Kozlova, Scopus ID 12244601300. 

 

Website: 

Boreskov Institute of Catalysis, https://catalysis.ru. 

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