Dual promotional effect of CuxO clusters grown with atomic layer deposition on TiO2 for photocatalytic hydrogen production

The promotional effects on photocatalytic hydrogen production of CuxO clusters deposited using atomic layer deposition (ALD) on P25 TiO2 are presented. The structural and surface chemistry study of CuxO/TiO2 samples, along with first principles density functional theory simulations, reveal the strong interaction of ALD deposited CuxO with TiO2, leading to the stabilization of CuxO clusters on the surface; it also demonstrated substantial reduction of Ti4+ to Ti3+ on the surface of CuxO/TiO2 samples after CuxO ALD. The CuxO/TiO2 photocatalysts showed remarkable improvement in hydrogen productivity, with 11 times greater hydrogen production for the optimum sample compared to unmodified P25. With the combination of the hydrogen production data and characterization of CuxO/TiO2 photocatalysts, we inferred that ALD deposited CuxO clusters have a dual promotional effect: increased charge carrier separation and improved light absorption, consistent with known copper promoted TiO2 photocatalysts and generation of a substantial amount of surface Ti3+ which results in self-doping of TiO2 and improves its photo-activity for hydrogen production. The obtained data were also employed to modify the previously proposed expanding photocatalytic area and overlap model to describe the effect of cocatalyst size and weight loading on photocatalyst activity. Comparing the trend of surface Ti3+ content increase and the photocatalytically promoted area, calculated with our model, suggests that the depletion zone formed around the heterojunction of CuxO–TiO2 is the main active area for hydrogen production, and the hydrogen productivity of the photocatalyst depends on the surface coverage by this active area. However, the overlap of these areas suppresses the activity of the photocatalyst.


The details of XPS analysis and approximation of Cu x O content
The surface chemistry of the ALD synthesized Cu x O/TiO 2 samples were studied using the XPS technique. The content of different copper species (Cu 1+ and Cu 2+ ) was quantified based on the method that Biesinger has proposed [1,2]. This method uses the shake-up peaks that are present in the spectra of Cu 2+ but are absent Cu 0 or Cu 1+ spectra. The shake-up peaks are the result of the interaction of the outgoing photoelectrons with the valance electrons, leading to the excitation of the valance electrons to a higher energy level. As a result of such inelastic interactions, the outgoing core photoelectron loses few electron volts of energy, producing shake-up peaks. Figure S1 shows the 2p 3/2 spectra of two samples with low and high Cu 2+ content (1.19 and 3.79 wt. %, respectively). The different copper species, Cu 0 , Cu 1+ , and Cu 2+ , contribute to the main emission line of copper (region A in Figure S1), while the shake-up satellite peaks (region B in Figure S1) stem from Cu 2+ . Accordingly, the shake-up satellite peaks of region B can be assumed as the fingerprint of Cu 2+ , and its absence indicates the presence of Cu 0 /Cu 1+ only. Biesinger suggests that the content of different copper species should be calculated by taking the signal of the main emission line and the shake-up peaks. It is worth noting that the metallic copper (Cu 0 ) and Cu 1+ in Cu 2 O show a very close 2p 3/2 peak at binding energies of 932.6 eV and 932.4 eV for Cu 0 and Cu 1+ , respectably. The distinction of these two species is challenging using XPS; however, they can be clearly distinguished using the LMM Auger peak. Since in our samples, the main matrix is TiO 2 , and this spectral region overlaps with Ti 1s, we cannot employ Auger spectroscopy for this purpose [3]. Also, since the size of the ALD synthesized Cu x O clusters observed using TEM imaging is ~2 nm or smaller, and the synthesis process had an oxidative atmosphere at 250°C, we assumed that the ALD deposited copper is oxidized to some degree, and the Cu x O/TiO 2 samples are Cu 0 free.
Biesinger [1,2] has proposed the following equations to calculate the relative concentration of Cu 1+ and Cu 2+ on the surface of a copper-containing sample: (Equation S1) ) where A1 is the peak area of the main signal of Cu 2+ , A2 is the peak area of the main signal of Cu 1+ , and B is the peak area of shake-up satellite peaks. The accuracy of these two equations depends on the accurate determination of the ratio between the main peak/shake-up peak areas (A1 s /B s ) for a 100% pure Cu 2+ sample. We used 1.89 for the A1 s /B s , reported for Cu 2+ by Biesinger for our calculations [1]. The relative concentrations of Cu 1+ and Cu 2+ in Cu x O/TiO 2 samples were calculated using equations S1 and S2, and the results are summarized in Table 2 of the main text.
Using the calculated values for Cu 1+ and Cu 2+ content in ALD synthesized Cu x O/TiO 2 samples, the average oxidation state of copper is calculated: Using the average oxidation state of copper and assuming a stoichiometric ratio between copper and oxygen, the weight loading of Cu x O in the ALD synthesized Cu x O/TiO 2 samples were calculated: where M w, O is the molar mass of oxygen assumed to be 15.999 g·mol -1 and M w, Cu is the molar mass of the copper assumed to be 63.546 g·mol -1 . The oxidation state of oxygen is assumed to equal 2. The calculated weight loadings of ALD synthesized Cu x O/TiO 2 samples are presented in Table 2 of the main text.

Formulations and parameters of Modified expanding photocatalytic area and overlap model
The Modified expanding photocatalytic area and overlap (M-EPAO) model uses similar formulations that the original EPAO model uses [4], and the equations are modified to satisfy the assumption/condition of the M-EPAO model. In addition to the main difference between the M-EPAO model and the original EPAO model described in the main text, the M-EPAO model takes the photoactivity of pristine P25 TiO 2 into account. In contrast, the original EPAO model has associated the rate of hydrogen generation with the total photocatalytically promoted area, A T [4]. During stages I and II of the M-EPAO model, the number of cocatalyst clusters is increasing, then during stage III, the clusters start growing.
The parameters used in the M-EPAO model are listed in Table S1. These parameters are obtained in different ways. Some parameters are defined using the experimental data, and others are calculated. The parameters a, b', and k are obtained via fitting the model to the experimental data via minimizing the sum of square errors using the Globalsearch function in Matlab. Calculating these parameters directly is difficult or not possible, and for that reason, they are optimized.
As explained in the main text, the M-EPAO model is divided into three different sections. The first section is defined as the system before the theoretical ideal weight loading; at this point, there is no photocatalytically promoted area (PPA, A T ) overlap. The second section of the model is defined as the system after the ideal weight loading where the PPA overlap occurs. The third section of the model is characterized by the increase of the cocatalyst clusters size. The moment when certain sections of the model are in effect is dependent on the nucleation and growth behavior. The base equation of the M-EPAO model is the hydrogen production rate:

Equation S5
considers the activity of the PPA (A T ) and the unpromoted area of P25 TiO 2 (pristine area -A base ). It calculates the rate of hydrogen production based on a rate constant of k and k base per area of photocatalytically promoted and the unpromoted area, respectively. The specific surface area of P25 TiO 2 (SA) is employed to change the unit of the rate from to .
The first stage of the M-EPAO model deals with the situation that the increase of the number of cocatalyst clusters results in the rise in A T and consequently increases the hydrogen production rate.  (Figure S5-a). The growth Cu x O constant (c) was obtained using linear fitting of the particle size measured using TEM images as a function of Cu x O content.
The photocatalytically active area around Cu x O clusters is calculated using parameters a and b'. The parameter a defines the active area based on the initial constant surface island size. As the surface islands' size changes, the size of the PPA will change as well. This change in PPA size is due to a change of surface islands' size and is defined using the b' parameter. The radius of photocatalytically active area around Cu x O cocatalyst clusters (r z ) is calculated using equations below for three stages of the M-EPAO model: For hexagonal and square packing, the interparticle distance can be calculated using equations S9 and S10, respectively: During stage I, the interparticle distance is large enough to avoid PPA overlap (R≥2r z ); hence the overlapped area is zero (∆A=0). Accordingly, A base can be calculated as: where f is the packing factor of Cu x O clusters on the surface of P25 TiO 2 with the value of 4 and 6 for square and hexagonal packing, respectively.
The highest Cu x O content in which the hydrogen rate is maximum, the loading/packing of Cu x O particles is optimum/ideal so that the highest surface coverage with PPA can be achieved. Above this Cu x O content, the PPA overlap outweighs the promotional effect of Cu x O clusters. Figure S2 shows how the PPA overlap is defined in the model. The overlapped area (∆A) can be calculated using the equation below: (Equation S12) Equation S12 is adapted based on the solution provided by Assencio for the intersection area of two circles [5].
By having the overlap area, the photocatalytically promoted area (A T ) can be calculated using Equation S13: (Equation S13) Having the A T and A base , we can calculate the hydrogen rate using Equation S5.
A Matlab code is developed to fit the model using these equations to the experimental data and optimize the three model parameters, i.e., a, b', and k (the code is provided). The optimized values are summarized in Table S2. The M-EPAO model fits well with the experimental data using the values presented in Table S2. The model's average absolute relative deviation (AARD) from the experimental data (calculated using Equation S14 ) indicates that the model using square packing of Cu x O clusters fits better with the experimental data.
(Equation S14) where θ E,i is the experimental data, and θ m,i is the corresponding value obtained from M-EPAO model.  Figure S3.     Figure S7. The cumulative hydrogen production after 20 hours of reaction as a function of copper loading in Cu x O/TiO 2 photocatalysts. Figure S8.