# Accelerating the Design of Photocatalytic Surfaces for Antimicrobial Application: Machine Learning Based on a Sparse Dataset

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## Abstract

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## 1. Introduction

_{2}O

_{2}), at low concentrations (e.g., 0.5%), is known as a fast biocidal agent, including for severe acute respiratory syndrome (SARS) coronavirus, Middle East respiratory syndrome (MERS) coronavirus or endemic human coronaviruses (HCoV) [12], and H1N1 influenza virus [13].

_{2}) loaded with metallic co-catalysts have been tested in many applications, including the removal of organic contaminants [15]. This technology relies on the production of reactive oxidative species (ROS) such as hydroxyl radicals, superoxide radical ions, and hydrogen peroxide (H

_{2}O

_{2}) in response to light excitation with energy greater than the band gap of the photoactive catalyst (see Figure 1).

_{2}O

_{2}would attack and oxidize key proteins leading to their inactivation [17]. To ensure the large-scale deployment of such photoactive antimicrobial nanocoatings, additional efforts are needed to explore the possibility of replacing rare and expensive co-catalysts such as platinum (Pt), palladium (Pd), and gold (Au) with less expensive metals such as silver (Ag), copper (Cu) and iron (Fe).

_{2}nanoparticles, determines not only ROS generation but also ROS degradation [18,19,20,21,22]. Therefore, because the overall reaction rate determines the efficacy of the photocatalyst, we explore the efficiency of ROS generation and degradation rates on the surface of the photocatalysts while targeting antimicrobial applications.

## 2. From-Experiment-to-Machine-Learning Scheme

#### 2.1. Handling Small Dataset with Machine Learning

_{2}O

_{2}production rates via TiO

_{2}photocatalyst loaded with different amounts of metallic Au

_{x}Ag

_{(1-x)}nanoparticle co-catalysts, where $0\le x\le 1$. Because the dataset consists of a small number (∼15) of entries, we build our model using three input variables, which are the most physically and chemically relevant in this application. GAM is a generalization of the generalized linear model (GLM) in which the relationship between some input(s) ${x}_{1}$, ${x}_{2}$,$\cdots $ and ${x}_{p}$ and target $Y$ is not linear and for which an ordinary least squares (OLS) estimator does not capture the relationship very well. In this situation, one needs to relate nonlinear inputs to the expected value $\mathsf{\mu}=\mathrm{E}\left(Y|x\right)=\mathrm{g}\left(x\right)$, with a non-predefined link function $\mathrm{g}$ that might be appropriate. In other words, we can write the GAM structure as:

#### 2.2. Dataset Preparation and ML Training

_{2}/H

_{2}O

_{2}[20,31,32,33,34,35,36,37]. (see “Mechanism of photocatalytic hydrogen peroxide production” in the Supplementary Information (SI)) While the reaction is expressed as ${\mathrm{O}}_{2}+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_{2}{\mathrm{O}}_{2}$, it is understood that the reduction occurs through either a sequential two-step single-electron indirect reduction (${\mathrm{O}}_{2}\to {\mathrm{O}}^{\u2022-}\to {\mathrm{H}}_{2}{\mathrm{O}}_{2}$) or a one-step two-electron direct reduction (${\mathrm{O}}_{2}\to {\mathrm{H}}_{2}{\mathrm{O}}_{2}$) route [38,39]. Moreover, the reaction is related to a decrease of H

^{+}as well, and the redox potential level of O

_{2}/H

_{2}O

_{2}is more negative than the level of H

^{+}/H

_{2}by 0.69 V [34]. The trapped charges in the nanoparticles should transfer favorably to a reactant forming H

_{2}O

_{2}, while we keep the H

^{+}oxidation reaction, preventing it from the backward reaction of $2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_{2}$. Thus, it is challenging to determine with confidence the key factors governing the overall reaction mechanism. Moreover, one might need to take into consideration the adsorption of reactants on the surface of Au-Ag nanoparticles [18,19,20] since adsorbed reactants on the surface induce the rearrangement of charges at the interface between the molecule and Au-Ag nanoparticles, hence affecting the overall reaction rate.

_{2}O

_{2}, respectively, with respect to the vacuum level, and ${\mathsf{\Phi}}_{{\mathrm{Au}}_{x}{\mathrm{Ag}}_{\left(1-x\right)}}$ is the work function of the Au-Ag co-catalyst. The work function of Au-Ag alloy was obtained from the geometric mean between pure metals; in the case of Au

_{x}Ag

_{(1−x)}, the work function is given by:

_{2}/H

_{2}O

_{2}redox level. In contrast, for the pure Ag nanoparticles, $\Delta {E}_{\mathrm{M}-{\mathrm{H}}_{2}{\mathrm{O}}_{2}}=0.99$. At the same time, this metric reflects the high coverage of Ag on the nanoparticle active site as the values are significant. Thus, it represents the relative positions of work functions as well as the proportionate coverage of adsorbed nanoparticles. We employed an additional input variable $NP$ for the metallic nanoparticle loading. In addition to nanoparticles loading, we considered $\mathrm{exp}\left({\mathsf{\phi}}_{\mathrm{B}}\right)$ and $\mathrm{exp}\left(\Delta {E}_{\mathrm{M}-{\mathrm{H}}_{2}{\mathrm{O}}_{2}}\right)$ as the input variable during the GLM and GAM model training.

_{2}O

_{2}formation rate (${k}_{\mathrm{f}}$) and decomposition rate (${k}_{\mathrm{d}}$).

## 3. Results and Discussion

_{x}Ag

_{(1−x)}/TiO

_{2}photocatalysts having as target values the formation of H

_{2}O

_{2}and decomposition rates (${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$) as well as the overall produced concentration ([H

_{2}O

_{2}]) at a few discreet co-catalyst compositions and loadings. We used the root mean square error (RMSE) and ${R}^{2}$ as metrics to evaluate the accuracy of each trained model. Rather than building one regression model for [H

_{2}O

_{2}], two separate models were built for ${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$ separately. Subsequently, [H

_{2}O

_{2}] is computed according to the formula $\left[{\mathrm{H}}_{2}{\mathrm{O}}_{2}\right]=\left({k}_{\mathrm{f}}/{k}_{\mathrm{d}}\right)\left\{1-\mathrm{exp}\left(1-{k}_{\mathrm{d}}t\right)\right\}$ as in Ref. [31]. Our decision is well grounded by examining the Pearson correlation coefficients, as shown in Figure S3 in the Supplementary Materials. We found a significantly strong correlation between the input variables ($NP$, $\Delta {E}_{\mathrm{M}-{\mathrm{H}}_{2}{\mathrm{O}}_{2}}$ and $\Delta {E}_{{\mathrm{TiO}}_{2}-\mathrm{M}}$) and target variables (${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$). While attempting to build a model to predict [H

_{2}O

_{2}] directly from the experimental data, we found a negligible correlation with $\Delta {E}_{\mathrm{M}-{\mathrm{H}}_{2}{\mathrm{O}}_{2}}$ and $\Delta {E}_{{\mathrm{TiO}}_{2}-\mathrm{M}}$, confirming that our adopted approach for performing two separate regressions for ${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$ is well justified.

_{2}O

_{2}, in particular for ${k}_{\mathrm{f}}$ prediction (see Figure S4 in the Supplementary Materials for the GLM model). The computed ${R}^{2}$ values of ${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$ are 0.62 and 0.75, while the errors for ${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$ values are $\pm $0.1 mM ${\mathrm{h}}^{-1}$ and $\pm $0.05 ${\mathrm{h}}^{-1}$, respectively. Because these GLM models behave poorly when the nonlinear correlation is dominant, the accuracy is worse when we assess the [H

_{2}O

_{2}] production via two-step $\left({k}_{\mathrm{f}}/{k}_{\mathrm{d}}\right)$ computation or by simply building a GLM predictive model for [H

_{2}O

_{2}]. GLM model gives large residual errors because it fails to capture the non-linear relationship between the input and target. Subsequently, we moved to the GAM method, which, as shown in the next section, demonstrates significantly improved predictive power.

_{2}O

_{2}production rate can be expressed as $\left[{\mathrm{H}}_{2}{\mathrm{O}}_{2}\right]=\left({k}_{\mathrm{f}}/{k}_{\mathrm{d}}\right)$, (when $\mathrm{t}=\infty $ in $\left[{\mathrm{H}}_{2}{\mathrm{O}}_{2}\right]=\left({k}_{\mathrm{f}}/{k}_{\mathrm{d}}\right)\left\{1-\mathrm{exp}\left(1-{k}_{\mathrm{d}}\mathrm{t}\right)\right\}$. We thus combine the output of the GAM models we trained for ${k}_{\mathrm{f}}$ and ${k}_{\mathrm{d}}$ to generate a predictive model for [H

_{2}O

_{2}].

_{2}O

_{2}production.

_{2}O

_{2}production rates and explains why GLM performed poorly as shown earlier. Thus, GAM models reproduce well both rates and capture their non-linear dependence on the input variables.

_{2}O

_{2}production reaches its maximum when the amount of nanoparticle loading is at $NP=0.55$ (0.41 mol %). On the other hand, the H

_{2}O

_{2}degradation rate ${k}_{\mathrm{d}}$ reaches its minimum when $NP=0.20$ (0.09 mol %) and its maximum when no co-catalysts are loaded, namely, when $NP=0.0$. Interestingly, this implies that one could target the desired H

_{2}O

_{2}production for a given application guided by the results of our models by exploring the predicted H

_{2}O

_{2}production over the entire range of nanoparticle loading and Au-Ag compositions. Such heatmaps of ${k}_{\mathrm{f}}$ and ${k}_{d}$ are presented in Figure 2c,d.

_{2}O

_{2}] at discrete Au-Ag nanoparticle loading, while Figure 4b illustrates the calculated [H

_{2}O

_{2}] production map produced in this work. Despite a handful of data points of experimentally reported data our calculated [H

_{2}O

_{2}] production is consistent with the reported results: the maximum predicted [H

_{2}O

_{2}] production of 3.4 mM is recorded for Au

_{0}.

_{16}Ag

_{0}.

_{84}alloy. Interestingly, we found that very high [H

_{2}O

_{2}] values could be achieved using nanoparticle loading as small as $NP=0.1$ mol %. The model predicts a high production rate at this concentration and loading while the decomposition rate is at its minimum, leading to an overall maximum efficiency in the [H

_{2}O

_{2}] production. Using this model, we constructed a full landscape of the photocatalytic production of [H

_{2}O

_{2}] by varying the nanoparticle loading and Au-Ag composition.

_{2}O

_{2}production that achieves high accuracies in individual predictions between the observed and produced H

_{2}O

_{2}concentrations as indicated by ${R}^{2}=0.95$, while the RMSE is as low as 0.22 mM. Therefore, the GAM models we built can capture the main trends governing [H

_{2}O

_{2}] as a function of the properties of the metallic co-catalyst concentration in the Au

_{x}Ag

_{y}/TiO

_{2}system.

_{2}O

_{2}as efficiently as the TiO

_{2}catalyst with Au

_{0.2}Ag

_{0.8}$NP=0.5$ mol %. The H

_{2}O

_{2}production may be sustained by incorporating a smaller amount of Au and Ag since ${k}_{\mathrm{d}}$ is suppressed by reducing the loading while ${k}_{\mathrm{f}}$ is less affected by the loading reduction. Interestingly, Yang et al. recently reported the synthesis of the colloidal Au-Ag/TiO

_{2}, which shows an excellent photocatalytic efficiency for the degradation of methylene blue [40]. The Au-Ag loading ranged from 0.4 to 1.0 mol % and the maximal photoactivity was achieved by using Au

_{0.21}Ag

_{0.79}with $NP=0.82$ mol % TiO

_{2}catalyst. Such a high nanoparticle loading also supports the prediction made by our model, which was kept blind to this information, pointing out the strongest photocatalytic activity properly.

_{x}Ag

_{y}/TiO

_{2}photocatalysts can be used effectively as an antimicrobial surface. Disinfection of influenza virus on a steel surface achieved a 3 log

_{10}pathogen reduction within 15 min using 10 ppm (0.6 mM) of H

_{2}O

_{2}in vapor. Increasing the concentration of H

_{2}O

_{2}to 90 ppm (5.2 mM) boosted the pathogen reduction to 4.5 log

_{10}[13]. On the other hand, Fenton photocatalysts used for water treatment systems led to the degradation of dyes and pollutants in periods of time in the range of 30–200 min when used in solution containing a H

_{2}O

_{2}concentration ranging from 4 mM to 90 mM depending on the used Fenton catalyst and illumination conditions [32].

_{2}triphase system has been tested against the inactivation of Klebsiella pneumoniae Gram-negative bacteria (KPN) [41,42]. The system offered an H

_{2}O

_{2}generation rate of 1003 ± 52 μM ${\mathrm{h}}^{-1}$ (∼1 mM ${\mathrm{h}}^{-1}$), which is 18 times higher than its corresponding diphase system. The G-L-S TiO

_{2}disactivated the KPN colony concentration with the following efficiency: at 10 min, the survival ratio was quickly reduced to 35% and within 30 min irradiation with ultraviolet light (UV), it achieved over 99% light-triggered removal efficiency. Hence, it is possible to increase the level of H

_{2}O

_{2}production by at least one order of magnitude by using an G-L-S triphase photocatalytic system where the Au

_{x}Ag

_{y}/TiO

_{2}photocatalysts are immobilized on porous superhydrophobic substrate to ensure a maximal flow of O

_{2}system and overcome the slow kinetics of O

_{2}in solution. The triphase system allows reactant O

_{2}to reach the reaction interface directly from the ambient atmosphere, greatly increasing the interface O

_{2}concentration, which in turn simultaneously enhanced the kinetics of H

_{2}O

_{2}formation and suppresses the unwanted electron-hole recombination and the kinetics of H

_{2}O

_{2}decomposition reaction.

_{x}Ag

_{y}bi-metallic nanoparticles photocatalysists to combat the spread of infection via the deployment of antibacterial coatings requires a careful analysis of the involved reaction kinetics [43]. For instance, accordingly, we estimate that for the efficient inactivation of enveloped viruses such as SARS-CoV-2, within 30 min, we need a material capable of producing at least 1 mM ${\mathrm{h}}^{-1}$ ${\mathrm{mg}}^{-1}$ using O

_{2}and H

_{2}O from the air and releasing not more than 30 $\mathsf{\mu}$M of H

_{2}O

_{2}. Still, it is also important to account for various competing phenomena: (i) the affinity of the microorganism to water and to a particular surface [44]; (ii) the competition between the microorganism, water layer on the surfaces, and organic pollutant present in the air; and (iii) the spontaneous decomposition rate of ${\mathrm{H}}_{2}{\mathrm{O}}_{2}\to {\mathrm{H}}_{2}\mathrm{O}+\frac{1}{2}{\mathrm{O}}_{2}$ on the surface as a function of temperature and humidity.

_{2}O

_{2}production rate, Au

_{x}Ag

_{y}/TiO

_{2}photocatalysts could be used as a sustainable and continuous source of hydrogen peroxide in heterogeneous Fenton catalytic systems, ensuring a controlled production of H

_{2}O

_{2}upon illumination [32]. It might find application for water and air decontamination as well as self-cleaning coating with the controlled release and degradation of H

_{2}O

_{2}upon illumination, ensuring that the level of H

_{2}O

_{2}never exceeds the internationally agreed health safety levels (1 ppm) [45]. The plasmonic effects due to the response of Au and Ag nanoparticles to visible light excitation are expected to increase the photocatalytic activity for Au

_{x}Ag

_{y}/TiO

_{2}photocatalysts [46]. If combining with Fenton catalysts, one might expect to broaden the visible light absorption of the hybrid material under visible light illumination and hence its disinfection efficiency for indoor settings.

## 4. Conclusions

_{2}O

_{2}to enable its level to be kept within safe ranges. If tailored adequately, we estimate that the photocatalytic system proposed in this work could be efficient for the continuous inactivation of bacteria and possibly viruses. In addition, the proposed composition would give a balanced production of reactive oxygen species (ROS) upon controlled illumination, offering an opportunity for continuous disinfection of water, surfaces, and air, facilitating its integration in indoor environments such as offices, buildings, offices, malls, and airports.

## Supplementary Materials

_{2}/Metal) with the electrolytes, Figure S2. Schematic energy-band diagrams, Figure S3. Pearson correlation coefficient between input and target variables, Figure S4. Pair-wise comparison between the experimental and GLM-predicted values for the models.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Mechanism of ROS generation on the surface of semiconducting nanoparticles and the effects of ROS activity on organic substances and microorganisms.

**Figure 2.**Pair-wise comparison of the accuracy between the experimental observation of H

_{2}O

_{2}(

**a**) production rate ${k}_{\mathrm{f}}$ and (

**b**) decomposition rate ${k}_{\mathrm{d}}$ as function of the Au

_{x}Ag

_{(1–x)}co-catalyst nanoparticle composition and nanoparticle loading (mol %) within TiO

_{2}. Heatmap of predicted reaction rate by GAM for (

**c**) ${k}_{\mathrm{f}}$ and (

**d**) ${k}_{\mathrm{d}}$.

**Figure 3.**Fitted smooth functions (solid lines) for (

**a**) ${k}_{\mathrm{f}}$ and (

**b**) ${k}_{\mathrm{d}}$ illustrate relationship between the input and target variables of the GAM models. Dots represent the data, while the dashed red lines indicate the confidence intervals.

**Figure 4.**(

**a**) Heatmap of reported [H

_{2}O

_{2}]. (

**b**) Heatmap of the calculated [H

_{2}O

_{2}] in this work. (

**c**) Pair-wise comparison of the accuracy of the amount of produced H

_{2}O

_{2}in mM. For H

_{2}O

_{2}concentration, $\left[{\mathrm{H}}_{2}{\mathrm{O}}_{2}\right]=\left({k}_{\mathrm{f}}/{k}_{\mathrm{d}}\right)\left\{1-\mathrm{exp}\left(1-{k}_{\mathrm{d}}t\right)\right\}$, and $\mathrm{t}=\infty $.

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## Share and Cite

**MDPI and ACS Style**

Park, H.; Bentria, E.T.; Rtimi, S.; Arredouani, A.; Bensmail, H.; El-Mellouhi, F.
Accelerating the Design of Photocatalytic Surfaces for Antimicrobial Application: Machine Learning Based on a Sparse Dataset. *Catalysts* **2021**, *11*, 1001.
https://doi.org/10.3390/catal11081001

**AMA Style**

Park H, Bentria ET, Rtimi S, Arredouani A, Bensmail H, El-Mellouhi F.
Accelerating the Design of Photocatalytic Surfaces for Antimicrobial Application: Machine Learning Based on a Sparse Dataset. *Catalysts*. 2021; 11(8):1001.
https://doi.org/10.3390/catal11081001

**Chicago/Turabian Style**

Park, Heesoo, El Tayeb Bentria, Sami Rtimi, Abdelilah Arredouani, Halima Bensmail, and Fedwa El-Mellouhi.
2021. "Accelerating the Design of Photocatalytic Surfaces for Antimicrobial Application: Machine Learning Based on a Sparse Dataset" *Catalysts* 11, no. 8: 1001.
https://doi.org/10.3390/catal11081001