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\DOI{10.5802/crchim.454}
\datereceived{2025-11-27}
\daterevised{2026-02-18}
\datererevised{2026-02-21}
\dateaccepted{2026-04-21}
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\section*{Declaration of interests}
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\COI{The authors do not work for, advise, own shares in, or receive
funds from any organization that could benefit from this article, and
have declared no affiliations other than their research organization.}

\dateposted{2026-08-17}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Photocatalytic degradation of azo food dye tartrazine using
TiO\textsubscript{2} in aqueous solution: an innovative removal method by
Box--Behnken design optimization and kinetic modeling}

\alttitle{D\'{e}gradation photocatalytique du colorant alimentaire
azo\"{i}que tartrazine par TiO\textsubscript{2} en solution aqueuse : une
m\'{e}thode innovante d'\'{e}limination par optimisation du plan
d'exp\'{e}riences selon Box--Behnken et mod\'{e}lisation de la
cin\'{e}tique}

\author{\firstname{Lydia} \lastname{Hihat}}
\address{Materials Technology and Process Engineering Laboratory,
University of Bejaia, 06000 Bejaia, Algeria}               

\author{\firstname{Laila} \lastname{Mahtout-Ait Braham}\CDRorcid{0009-0005-2664-954X}}
\addressSameAs{1}{Materials Technology and Process Engineering
Laboratory, University of Bejaia, 06000 Bejaia, Algeria}               

\author{\firstname{Hayet} \lastname{Belkacemi}\CDRorcid{0000-0002-0523-1495}\IsCorresp}
\addressSameAs{1}{Materials Technology and Process Engineering
Laboratory, University of Bejaia, 06000 Bejaia, Algeria}               
\email[H. Belkacemi]{hayet.belkacemi@univ-bejaia.dz}

\author{\firstname{Daouia}\nobreakauthor\lastname{Ingrachen-Brahmi}\CDRorcid{0000-0001-8454-3800}}
\addressSameAs{1}{Materials Technology and Process Engineering
Laboratory, University of Bejaia, 06000 Bejaia, Algeria}               

\keywords{\kwd{Photocatalysis}\kwd{Adsorption}\kwd{Tartrazine}\kwd{Food
dye}\kwd{Box--Behnken design}\kwd{Wastewater}}

\altkeywords{\kwd{Photocatalyse}\kwd{Adsorption}\kwd{Tartrazine}
\kwd{Colorant alimentaire}\kwd{Plan d'exp\'{e}riences de
Box--Behnken}\kwd{Eaux de rejets}}

\begin{abstract}
In this study, the heterogenous photocatalytic degradation of the azo
food dye tartrazine (TRZ) was investigated using a TiO\textsubscript{2} catalyst
under UV light in contaminated water. A Box--Behnken experimental
design with three factors at three levels was applied, considering pH,
catalyst mass, and dye concentration as the main variables. The
response was the TRZ photodegradation rate (\%), statistically
controlled by ANOVA and response surface method (RSM). The model
developed demonstrated a strong correlation between predicted and
experimental values. Furthermore, a kinetic study was carried out to
determine the reaction order and rate constants, and a photocatalytic
degradation mechanism was proposed. The optimal values of the operating
conditions were found: pH 5.7, TiO\textsubscript{2} mass 48.4 mg, and dye
concentration 5 mg/L, corresponding to a photodegradation rate of
89.3\% as predicted by the model, with a coefficient of linear
regression around \textit{R}\textsuperscript{2} = 98.9\%. 
\vspace*{-2.5pt}
\end{abstract}

\begin{altabstract}
Dans cette \'{e}tude, la d\'{e}gradation photocatalytique
h\'{e}t\'{e}rog\`{e}ne du colorant alimentaire azo\"{i}que tartrazine
(TRZ) a \'{e}t\'{e} \'{e}tudi\'{e}e en utilisant du TiO\textsubscript{2} comme
catalyseur sous rayonnement UV dans de l'eau contamin\'{e}e. Un plan
d'exp\'{e}riences de Box--Behnken \`{a} trois facteurs et trois niveaux
a \'{e}t\'{e} appliqu\'{e}, consid\'{e}rant le pH, la masse du
catalyseur et la concentration du colorant comme principales variables.
La r\'{e}ponse mesur\'{e}e \'{e}tait le taux de photod\'{e}gradation
(\%) de la TRZ, analys\'{e} statistiquement par ANOVA et la m\'{e}thode
des surfaces de r\'{e}ponse (MSR). Le mod\`{e}le d\'{e}velopp\'{e} a
montr\'{e} une forte corr\'{e}lation entre les valeurs pr\'{e}dites et
exp\'{e}rimentales. De plus, une \'{e}tude cin\'{e}tique a \'{e}t\'{e}
men\'{e}e pour d\'{e}terminer l'ordre de la r\'{e}action et les
constantes de vitesse et un m\'{e}canisme de d\'{e}gradation
photocatalytique de la TRZ a \'{e}t\'{e} propos\'{e}. Les conditions
op\'{e}ratoires optimales ont \'{e}t\'{e} d\'{e}termin\'{e}es : pH 5,7,
masse de TiO\textsubscript{2} 48,4 mg et concentration du colorant 5 mg/L,
correspondant \`{a} un taux de photod\'{e}gradation de 89,3 \%
pr\'{e}dit par le mod\`{e}le, avec un coefficient de r\'{e}gression
lin\'{e}aire d'environ \textit{R}\textsuperscript{2} = 98,9 \%.
\end{altabstract}

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\section{Introduction}\label{sec1}

The dye industry is one of the activities that produces the most toxic
industrial waste and represents a great risk to human health and
environment. Globally, dye production is estimated at around 700\,000
tons per year~\cite{1,2,3}, about 70\% of which are azo dyes, widely
used in textile, paper, pharmaceutical, food, cosmetics, and leather
industries~\cite{4}. Some studies have established a link between
tartrazine (TRZ) and sensitivity to food dyes, and recent research
suggests a possible link between ingestion of TRZ and the worsening of
behavioral disorders, especially in children, including symptoms such
as hyperactivity and irritability. In addition, TRZ can induce
oxidative stress and contribute to cellular damage, where it presents a
potential role in carcinogenesis~\cite{5}. The release of azo dyes into
aquatic systems is a major environmental concern due to their
persistent nature and toxicity~\cite{6,7}. Their complex molecular
structure renders them stable and largely non-biodegradable~\cite{8,9}.

In recent years, significant progress has been achieved in developing
various treatment methods for the removal of azo dyes from industrial
wastewater. Physical methods such as adsorption~\cite{10,11,12},
membrane filtration~\cite{13}, forward osmosis~\cite{14},
coagulation--flocculation~\cite{15,16} are considered simple and
efficient for dye removal. However, they do not achieve complete
degradation of the \mbox{contaminants.} Biological methods using
microorganisms~\cite{17,18} or enzymes~\cite{19} mainly lead to
decolorization rather than complete degradation of azo dyes, resulting
in the formation of aromatic amines, which are often toxic and
resistant to further biodegradation. Chemical methods such as advanced
oxidation processes, including Fenton processes~\cite{20,21},
ozonation~\cite{22}, electrochemical  processes~\cite{23,24},
photocatalysis~\cite{25,26} have been widely studied for the
degradation of azo dyes and have shown the greatest potential to
achieve complete mineralization. The efficiency of photocatalytic
processes for decolorization and mineralization of azo dyes is strongly
influenced by multiple parameters. Factors such as initial pollutant
concentration, catalyst dosage, pH of reaction medium, and intensity of
UV--Vis irradiation may exert both individual and interactive effects
on the degradation kinetics. However, optimizing this process by
varying only one factor at a time (OFAT) is not only inefficient and
resource-consuming, but also unable to reveal the interaction among
parameters, which may lead to overlooking the truly optimal operating
conditions. To overcome this limitation, the design of experiments
(DOE) approach provides a rigorous and systematic statistical
framework. It enables the simultaneous evaluation of the effects of
several critical factors and their interactions on the degradation
efficiency while minimizing the number of experiments required. This
method is therefore essential for accurately modeling the
photocatalysis.

\section{Results and discussion}\label{sec2}

The objective of this work is to use an experimental design to optimize
the operating conditions for the heterogenous photocatalysis of the azo
food dye tartrazine. A Box--Behnken design was employed to evaluate the
impact and interactions of the main factors (TiO\tsub{2} mass, initial
TRZ concentration, and pH) on the degradation efficiency response (\%).
The analysis of the results provides a basis to develop a predictive
model and the determination of the optimal conditions to maximize the
degradation efficiency.\looseness=1

Tartrazine (E102) or
4,5-dihydro-5-oxo-1-(4-sulfophenyl)-4-[(4-sulfophenyl)azo]-1H-pyrazole-3-{\ubreak}carboxylic 
acid, trisodium salt is a water-soluble mono-azo yellow dye that
undergoes tautomerism between its enolic (hydroxy) and keto (oxo) forms
(Figure~\ref{fig1})~\cite{27,28}.

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Chemical structure of tartrazine in its two
tautomeric forms, (1) enolic and (2) keto.}
\end{figure*}

\subsection{Photocatalysis}\label{ssec21}

Photocatalytic degradation experiments were carried out in a reactor
(see Figure~S1).
For each trial, a TRZ solution was prepared with
varying concentrations by adding a mass $m$ of TiO\tsub{2} at different
pH levels. The practical removal photodegradation yield ($Y$\%) of the
dye was calculated according to Equation~(\ref{eq1}):
{\begin{equation}\label{eq1}
Y(\%) = \dfrac{C_{0}-C_{t}}{C_{0}} \times 100,
\end{equation}}\unskip
where $C_{0}$ is the initial TRZ concentration (mg/L) and $C_{t}$ is
the concentration after reaction time $t$ (mg/L).\looseness=1

The factors studied, the low (${-}$1), central (0), and high (${+}$1)
levels of each factor are presented in Table~\ref{tab1}. The response
variable considered in the optimization process was the practical
removal--degradation yield, determined for each run after
photocatalysis testing. The combinations of experimental conditions for
each run were generated using the Minitab program, and statistical
analysis was performed to evaluate the effects and interactions of the
parameters studied. 

%tab1
\begin{table*}
\caption{\label{tab1}Parameters and levels of controlled factors for
photocatalysis optimization}
\begin{tabular}{cccc}
\thead
Factors & Low (${-}$1) & Central (0) & High (${+}$1) \\
\endthead
\textit{X}\tsub{1}: initial concentration of TRZ (mg/L) & \05 & 15 & 25 \\
\textit{X}\tsub{2}: mass of TiO\tsub{2} (mg) & 10 & 30 & 50 \\
\textit{X}\tsub{3}: pH & \05 & \07 & \09
\botline
\end{tabular}
\end{table*}

The experimental design was developed according to a Box--Behnken
Design (BBD) with three factors--three levels (Table~\ref{tab2}) and
three repetitions at the central points, resulting in fifteen
experimental runs. The experimental conditions were optimized by the
design of the response surface method (RSM). Initial dye concentration
(\textit{X}\tsub{1}), photocatalyst mass (\textit{X}\tsub{2}), and pH of the
solution (\textit{X}\tsub{3}) were examined as key factors affecting TRZ
removal efficiency ($Y$). The quadratic response model, which
represents all linear terms, square terms, and interaction elements,
can be presented as follows (Equation~(\ref{eq2})):
{\begin{equation}\label{eq2}
Y = \beta _{0} + \sum \beta _{i}X_{i} + \sum \beta _{ii}{X}_{i}^{2} + 
\sum \sum \beta _{ij}X_{i}X_{j},
\end{equation}}\unskip
where $Y$ is the response, $\beta_{0}$ is a constant, $\beta_{i}$ is
the linear coefficient, $\beta _{ii}$ is the quadratic coefficient,
and $\beta_{ij}$ is the interaction coefficient, while $X_{i}$ and
$X_{j}$ are  the coded values of the independent factors.

%tab2
\begin{table*}
\caption{\label{tab2}Box--Behnken design matrix with TRZ removal yield
$Y$}
\begin{tabular}{ccccccccc}
\thead
\multicolumn{4}{c}{Coded variables} & 
\multicolumn{3}{c}{Uncoded variables} & 
\multicolumn{2}{c}{Response} \\\cline{1-4}\cline{5-7}\cline{8-9}
Assay & $X_{1}$ & $X_{2}$ & $X_{3}$ & [TRZ] (mg/L) &
$m_{\mathrm{TiO}_{2}}$ (mg) & pH & Observed ($Y$\%) & Predicted
($Y'$\%) \\
\endthead
\0{1} & ${-}$1 & ${-}$1 & \mn0 & \05 & 10 & 7 & 53.5 & 53.7 \\ 
\0{2} & ${+}$1 & ${-}$1 & \mn0 & 25 & 10 & 7 & 18.0 & 19.4 \\ 
\0{3} & ${-}$1 & ${+}$1 & \mn0 & \05 & 50 & 7 & 87.3 & 85.9 \\ 
\0{4} & ${+}$1 & ${+}$1 & \mn0 & 25 & 50 & 7 & 45.1 & 45.0 \\ 
\0{5} & ${-}$1 & \mn0 & ${-}$1 & \05 & 30 & 5 & 83.0 & 80.3 \\ 
\0{6} & ${+}$1 & \mn0 & ${-}$1 & 25 & 30 & 5 & 36.9 & 33.9 \\ 
\0{7} & ${-}$1 & \mn0 & ${+}$1 & \05 & 30 & 9 & 59.1 & 62.1 \\ 
\0{8} & ${+}$1 & \mn0 & ${+}$1 & 25 & 30 & 9 & 31.7 & 33.3 \\ 
\0{9} & \mn0 & ${-}$1 & ${-}$1 & 15 & 10 & 5 & 25.8 & 27.3 \\ 
{10} & \mn0 & ${+}$1 & ${-}$1 & 15 & 50 & 5 & 55.2 & 58.3 \\ 
{11} & \mn0 & ${-}$1 & ${+}$1 & 15 & 10 & 9 & 23.1 & 20.0 \\ 
{12} & \mn0 & ${+}$1 & ${+}$1 & 15 & 50 & 9 & 48.2 & 46.7 \\ 
{13} & \mn0 & \mn0 & \mn0 & 15 & 30 & 7 & 57.0 & 55.0 \\ 
{14} & \mn0 & \mn0 & \mn0 & 15 & 30 & 7 & 55.9 & 55.0 \\ 
{15} & \mn0 & \mn0 & \mn0 & 15 & 30 & 7 & 52.2 & 55.0 
\botline
\end{tabular}
\tabnote{Experimental values were obtained from the mean of repeated
measurements ($n=3$). Predicted values were derived from the fitted
model (see ANOVA section for details).}
\vspace*{2pt}
\end{table*}

Unlike a conventional OFAT strategy, the experimental design and the
operating protocol in this work are intrinsically linked. Each trial
corresponds to a specific point in the BBD matrix.

\begin{figure*}
\vspace*{-2pt}
\includegraphics{fig02}
\vspace*{-2pt}
\caption{\label{fig2}Calibration curves of TRZ (a) UV--Vis absorption
spectra of TRZ, (b) at different pH values.}
\vspace*{-2pt}
\end{figure*}

\subsection{Structural characterization of the TiO\tsub{2} catalyst and
tartrazine}\label{ssec22}

The X-ray diffraction pattern of the commercial TiO\tsub{2} catalyst is
represented in Figure~S2 (SI). The dominant diffraction peaks observed
at 2${\theta}$ values of approximately 25.52\textdegree,
37.96\textdegree, 48.23\textdegree, 54.04\textdegree, 55.27\textdegree,
and 62.86\textdegree\ correspond to the (101), (004), (200), (105),
(211), and (204) crystal planes of the anatase phase respectively. They
match the theoretical pattern for the anatase phase of TiO\tsub{2} from
Crystallography Open Database (COD, ID 1526931). A weak peak at
27.64\textdegree\ with an intensity of 4.06\% can be attributed to the
rutile (110) plane (COD ID 1534781), indicating the presence of a trace
amount of rutile. The significant density of surface hydroxyl groups is
critical to the material's photocatalytic activity, providing active
sites for the generation of radical species responsible for the
degradation of organic dyes. The Fourier-transform infrared
spectroscopy (FTIR) spectrum of the commercial TiO\tsub{2} catalyst
(Figure~S3 in SI) identifies key surface functional groups, such as
hydroxyl groups and Ti--OH bonds. 

The molecular structure of TRZ was verified using FTIR spectroscopy
(Figure~S4 in SI), and the calibration curves of TRZ were established
at three different pH values (5, 7, and 9) using UV--Vis
spectrophotometry. A linear relationship between absorbance and
concentration was observed at all pH values, confirming the validity of
the Beer--Lambert law, as shown in Figure~\ref{fig2}a. Standard
solutions with known concentrations were prepared, and their absorbance
was measured at the dye's maximum absorption wavelength (426~nm), which
was confirmed by preliminary UV--Vis spectra presented in\break
Figure~\ref{fig2}b. 

\subsection{Model fitting and statistical analysis}\label{ssec23}

Results for the efficiency of TRZ photodegradation are presented in
Figure~\ref{fig3}. The best yields are obtained for Assay 3 with 87.3\%
and 85.9\% for the experimental and predicted values, respectively.

\begin{figure*}
\vspace*{1pt}
\includegraphics{fig03}
\vspace*{1pt}
\caption{\label{fig3}The observed and predicted amounts of TRZ removal
by photocatalysis.}
%\vspace*{2pt}
\end{figure*}

Experiments under the various working conditions are presented in
Table~\ref{tab2}, which gives the coded and uncoded values for each
assay, including both observed and predicted responses. 

In order to evaluate the effect of the factors on the response (the
removal of TRZ), a second-order polynomial model was developed based on
the experimental data, where $Y$ represents the removal yield; as
presented in Equation~(\ref{eq3}).
{\begin{eqnarray}
\hspace*{-.5pc}
Y (\%) 
&
=
&
-12.2 - 4.713 X_{1} + 2.409 X_{2} + 22.27 X_{3} 
\nonumber \\&& 
+\, 0.0513 X_{1}^{2} -0.02296 X_{2}^{2} - 1.940 X_{3}^{2}
\nonumber \\ && 
-
\,
0.00831 X_{1}X_{2} + 0.2206 X_{1}X_{3} - 0.0264 X_{2}X_{3}. 
\nonumber \\ 
\label{eq3}
\end{eqnarray}}\unskip

\subsubsection{Statistical analysis and ANOVA}\label{sssec231}

The adequacy and statistical significance of the regression model were
assessed using analysis of variances (ANOVA) which included evaluation
of the $F$-value, $p$-value, and lack-of-fit test. The results are
reported in Table~\ref{tab3}.

%tab3
\begin{table*}
\caption{\label{tab3}Analysis of variance (ANOVA) and model summary}
\tabcolsep 11pt
\begin{tabular}{cccccc}
\thead
Source & DF & Adj SS & Adj MS & $F$-Value & $p$-Value \\ 
\endthead
Model & 9 & 5410.74 & \0601.19 & \047.80 & 0.000 \\ 
Linear & 3 & 4671.22 & 1557.07 & 123.81 & 0.000 \\ 
$X_{1}$ & 1 & 2824.51 & 2824.51 & 224.59 & 0.000 \\ 
$X_{2}$ & 1 & 1667.82 & 1667.82 & 132.62 & 0.000 \\ 
$X_{3}$ & 1 & \0178.89 & \0178.89 & \014.22 & 0.013 \\ 
Square & 3 & \0646.13 & \0215.38 & \017.13 & 0.005 \\ 
$X_{1}^{2}$ & 1 & \0\097.14 & \0\097.14 & \0\07.72 & 0.039 \\ 
$X_{2}^{2}$ & 1 & \0311.39 & 311.39 & \024.76 & 0.004 \\ 
$X_{3}^{2}$ & 1 & \0222.25 & 222.25 & \017.67 & 0.008 \\ 
2-Way interaction & 3 & \0\093.39 & \0\031.13 & \0\02.48 & 0.176 \\ 
$X_{1}X_{2}$ & 1 & \0\011.06 & \0\011.06 & \0\00.88 & 0.391 \\ 
$X_{1}X_{3}$ & 1 & \0\077.88 & \0\077.88 & \0\06.19 & 0.055 \\ 
$X_{2}X_{3}$ & 1 & \0\0\04.45 & \0\0\04.45 & \0\00.35 & 0.578 \\ 
Error & 5 & \0\062.88 & \0\012.58 &  &  \\ 
Lack-of-fit & 3 & \0\050.37 & \0\016.79 & \0\02.68 & 0.283 \\ 
Pure error & 2 & \0\012.52 & \0\0\06.26 &  &  \\ 
Total & 14\0 & 5473.62 &  &  &  \\ 
Model summary & \multicolumn{5}{c}{$S=3.54631\quad R^{2}=98.9\%\quad
R^{2}$(adj) ${=}$\ 96.8\%\quad $R^{2}$(pred) ${=}$\ 84.8\%}
\botline
\end{tabular}
\end{table*}

The statistical significance of the model terms depends on the
$F$-values and corresponding $p$-values. Significant terms are
characterized by large $F$-values coupled with small $p$-values
($p<0.05$), while non-significant terms have low $F$-values and high
$p$-values ($p>0.05$)~\cite{31}.  The $F$-value for the model as
reported in Table~\ref{tab3} is 47.8 and the $p$-value is less than
0.05, indicating that the model is significant. This suggests that the
model is statistically useful and accurately represents the form of the
relationship between the variables and the response. Therefore, the
model can be considered reliable.

Statistical adjustment indicates that the model adequately describes
the experimental data. This is further confirmed by the high value of
$R^{2}$ (98.9\%), adjusted $R^{2}$ (96.8\%), and predicted $R^{2}$
(85.8\%) as shown in Figure~\ref{fig4}, indicating the model's high
ability to explain and predict the response variable.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Predicted data versus observed data.}
\end{figure}

The model terms $X_{1}$, $X_{2}$, $X_{3}$, $X_{1}^{2}$,  $X_{2}^{2}$,
and $X_{3}^{2}$ are significant ($p$-value ${<}$ 0.05), whereas the
interaction terms $X_{1}X_{2}$, $X_{1}X_{3}$, and $X_{2}X_{3}$ are not
significant ($p$-value ${>}$ 0.05). The $p$-value of the lack-of-fit is
non-significant ($p=0.283>0.05$). 

\subsubsection{Analysis of response surface and effects of the factors}
\label{sssec232}

From the fitted model, a 3D response surface plot and contour plot were
generated to investigate two-way interactions between the factors
affecting the removal of TRZ (response) as shown in Figure~\ref{fig5}.

\begin{figure*}
\vspace*{-2pt}
\includegraphics{fig05}
\vspace*{-2pt}
\caption{\label{fig5}3D surface and contour plot of factor
interactions: (a,b) Initial TRZ concentration--pH vs $Y$ (\%). (c,d)
Initial TRZ concentration--mass of photocatalyst vs $Y$ (\%).  (e,f)
Mass of photocatalyst--pH vs $Y$ (\%).}
\vspace*{-2pt}
\end{figure*}

The interaction effect between pH and initial TRZ concentration on the
removal efficiency is depicted in Figure~\ref{fig5}a,b. For any range
of pH (from 5 to 9), degradation efficiency increases as the initial
TRZ concentration decreases. For an initial TRZ concentration of
25~mg/L, degradation efficiencies of 31.6\% and 36.9\% were obtained at
pH ${=}$\ 9 and pH ${=}$\ 5, respectively. As the initial concentration
increases, the number of active sites required at the catalyst surface
also increases. Since illumination time and amount of catalyst are
constant, the OH$^{\bullet}$ radical (primary oxidant) formed at the
surface of TiO\tsub{2} is also constant.

Therefore, the relative number of free radicals interacting with TRZ
decreases as the amount increases~\cite{32}. In contrast, a significant
effect of pH was observed at a lower concentration (5~mg/L); yields of
59.1\% and 81.7\% were obtained for pH ${=}$\ 9 and pH ${=}$\ 5,
respectively, which represents a significant increase compared to the
yield values at a higher concentration (25~mg/L). When pH is too high,
competitive adsorption occurs between OH\tsup{\tminus} and the
negatively charged material surface. The predominant OH\tsup{\tminus}
groups interact primarily with TRZ molecules, reducing the interaction
efficiency of the materials~\cite{33};  that could explain the
difference in degradation efficiency between pH ${=}$\ 9 and pH ${=}$\ 5.
The highest degradation efficiency was observed for initial TRZ
concentrations in the range 5--8~mg/L and for pH values between 5
and~6.

The interaction effect of initial TRZ concentration and photocatalyst
mass on removal efficiency is presented in Figure~\ref{fig5}c,d. As
it can be seen in the 3D response surface plot of Figure~\ref{fig5}c,
as soon as the initial TRZ concentration decreases and the mass of
TiO\tsub{2} increases, degradation efficiency increases. For an initial
concentration of 25~mg/L, removal efficiency increases from 18.0\% to
45.1\% when TiO\tsub{2} mass is increased from 10 to 50~mg. Similarly,
when the initial concentration of TRZ is lower (5~mg/L), removal
efficiency rises from 53.5\% to 87.3\% when TiO\tsub{2} mass is
increased from 10 to 50~mg. The dark red area in the contour plot
presented in Figure~\ref{fig5}d shows that the highest removal
efficiencies (78.7\%--87.3\%) were observed for the lowest initial TRZ
concentrations (5--8~mg/L) and highest TiO\tsub{2} mass (40--50~mg). A
comparable trend was also observed by Buu et~al.\ and Rostami-Javanroudi
et~al.~\cite{34,35}. Increasing the amount of catalyst led to an
increase in the number of photons absorbed and, consequently, improved
degradation efficiency~\cite{36,37}. In contrast, the ``colder'' areas
in the contour plot, where degradation efficiency remains below 40\%,
can be explained by a much more significant absorbance of UV light by
TRZ itself at higher TRZ concentrations. As a result, fewer photons
reach the surface of TiO\tsub{2} and the hydroxyl radical flux on the
catalyst surface is thus reduced~\cite{38}. Certain adsorption
phenomena promote competition between adsorbed molecules and the
solvent, which can slow down or prevent the formation of a large
quantity of OH$^{\bullet}$ radicals on the surface of the catalyst.
Consequently, the photocatalytic effect of these radicals on TRZ will
also\break decrease.

The interaction effect of pH and photocatalyst mass on TRZ removal is
presented in Figure~\ref{fig5}e,f. Below 35~mg TiO\tsub{2},
degradation efficiency increases with photocatalyst mass across the
entire pH range. It can be attributed to the enhanced adsorption of
photons, which promotes the generation of reactive species. Degradation
efficiency decreases beyond 35~mg TiO\tsub{2} at pH 5.0--5.5, beyond
45~mg TiO\tsub{2} at pH 6.0--7.5. This behavior is likely due to an
increase in solution \mbox{opacity,} which leads to a reduction in photon flux
penetration, thereby decreasing the photocatalytic degradation
rate~\cite{39}. Moreover, a loss in surface area by agglomeration
(particle--particle interactions) at high solid concentration is also
observed~\cite{40}. The highest degradation efficiency was observed at
pH 6.0--7.5 and photocatalyst mass 40--45~mg.

Optimizing the conditions for photocatalytic degradation is essential.
In this study, the optimal levels of the process variables leading to
maximum degradation efficiency were determined using an approach based
on the concept of desirability. The composite desirability score is
based on transforming the response variable into a scale-free value
that reflects how desirable a particular outcome is: 0 (completely
undesirable) to 1 (fully desirable)~\cite{41}.

%tab4
\begin{table*}
\caption{\label{tab4}Optimal conditions and corresponding predicted
response value\vspace*{3pt}}
\begin{tabular}{cccccc}
\thead
\multicolumn{3}{c}{Optimal conditions} & 
\xmorerows{1}{Desirability} & \xmorerows{1}{Predicted} & \xmorerows{1}{Error} \\ 
\cline{1-3}
\parbox[t]{8pc}{\centering Initial concentration of TRZ (mg/L)} & 
\parbox[t]{5pc}{\centering Photocatalyst mass (mg)}\vspace*{2pt} & pH & & &  \\ 
\endthead
5.0 & 48.4 & 5.7 & 1 & 89.3 & 3.27
\botline
\end{tabular}
\vspace*{3pt}
\end{table*}

According to Table~\ref{tab4}, the conditions for initial TRZ
concentration, TiO\tsub{2} mass, and pH that yielded the highest
degradation rate predicted (89.3\%) were: 5~mg/L, 48.4~mg, and 5.7,
respectively. Under similar conditions (Assay~3), the experimental
response was 87.3\% which confirms accuracy of the predicted value.

\subsection{Kinetic study of photocatalytic degradation}\label{ssec24}

The kinetics of the photocatalytic degradation for many organic
compounds in TiO\tsub{2} suspensions exposed to intense UV light has
been modeled using the equation of Langmuir--Hinshelwood (L--H) applied
for heterogeneous catalytic processes according to the work reported by
Kiani et~al.~\cite{42}. The model considers that the reaction rate $v$
is proportional to the photocatalyst surface fraction covered by the
substrate ($\theta$). In order to study the mechanism of photocatalysis
degradation, a first-order kinetic model was applied in accordance with
the following equations (Equations~(\ref{eq4})--(\ref{eq8})):
{\begin{equation}\label{eq4}
v = - \dfrac{\mathrm{d}C_{t}}{\mathrm{d}t} = k \theta
\end{equation}}\unskip
with 
{\begin{equation}\label{eq5}
\theta = \dfrac{KC_{t}}{(1+KC_{t})}.
\end{equation}}\unskip
Then we can write the final equation as follows: 
{\begin{equation}\label{eq6}
v = - \dfrac{\mathrm{d}C_{t}}{\mathrm{d}t} = k
\dfrac{KC_{t}}{(1+KC_{t})},
\end{equation}}\unskip
where $v$ is the rate (mg\tsup{\tminus 1}${\cdot}$L${\cdot}$min\tsup{\tminus 1}),  $k$ the
rate constant, and $K$ the adsorption equilibrium constant.  When
$KC_{t} \ll 1$ (diluted solution), the reaction follows an apparent 
first-order equation model:
{\begin{equation}\label{eq7}
-\dfrac{\mathrm{d}C_{t}}{\mathrm{d}t} = k K C_{t} =
k_{\mathrm{app}}C_{t}.
\end{equation}}\unskip
By integrating the previous equation, we obtain:
{\begin{equation}\label{eq8}
\ln \left(\frac{C_{0}}{C_{t}}\right) = k_{\mathrm{app}} t,
\end{equation}}\unskip
where $C_{0}$ is the initial TRZ concentration (mg/L) and $C_{t}$ the
concentration (mg/L) at time $t$. $k_{\mathrm{app}}$ (min\tsup{\tminus 1}) is
the first order kinetic constant corresponding to the slopes of the
linear regression curves depicted in the graph of $\ln(C_{0}/C_{t})$ as
a function of time. The kinetic profiles of TRZ photodegradation
($C_{t}/C_{0}$ versus time) are presented in Figure~\ref{fig6}.

\begin{figure}
\vspace*{3pt}
\includegraphics{fig06}
\caption{\label{fig6}Kinetic profiles of TRZ photodegradation with
TiO\tsub{2} (see Table~\ref{tab2} for conditions 1--15) and control
tests (TRZ/TiO\tsub{2}, TRZ/UV).} 
\end{figure}

A significant decrease in TRZ concentration, confirming the high
performance and efficient TRZ removal within two hours only,
particularly for Assay 3 conducted with a TRZ concentration of 5~mg/L
(${-}$1), a TiO\tsub{2} mass of 50~mg (${+}$1), and at pH 7 (0). The
results also demonstrate that efficient degradation occurred only when
both TiO\tsub{2} and UV irradiation were combined, emphasizing the
photocatalytic nature of the process.

Most of the runs exhibited good linearity with correlation coefficients
$R^{2}$ ranging from 0.88 to 0.99, confirming the suitability of this
model under the conditions studied (Table~\ref{tab5}). 

%tab5
\begin{table}
\caption{\label{tab5}First-order kinetic parameters of TRZ
photocatalysis under various experimental conditions}
\tabcolsep=3pt
\begin{tabular}{cccccc}
\thead
\morerows{1}{\raisebox{-12pt}{Assay}}
& \multicolumn{3}{c}{Design conditions} & 
\multicolumn{2}{c}{Kinetic parameters} \\ \cline{2-4}\cline{5-6}
 & \parbox[t]{3pc}{\centering [TRZ] (mg/L)} & 
\parbox[t]{3pc}{\centering $m_{\mathrm{TiO}_{2}}$ (mg)} & pH & 
\parbox[t]{3pc}{\centering $k_{\mathrm{app}}$ (min\tsup{\tminus 1})}\vspace*{2pt} & 
$R^{2}$ \\ 
\endthead
\01 & \05 & 10 & 7 & 0.0007 & 0.93 \\ 
\02 & 25 & 10 & 7 & 0.0019 & 0.92 \\ 
\03 & \05 & 50 & 7 & 0.0019 & 0.92 \\ 
\04 & 25 & 50 & 7 & 0.0049 & 0.99 \\ 
\05 & \05 & 30 & 5 & 0.0121 & 0.74 \\ 
\06 & 25 & 30 & 5 & 0.0035 & 0.95 \\ 
\07 & \05 & 30 & 9 & 0.0072 & 0.94 \\ 
\08 & 25 & 30 & 9 & 0.0028 & 0.98 \\ 
\09 & 15 & 10 & 5 & 0.0027 & 0.97 \\ 
10 & 15 & 50 & 5 & 0.0072 & 0.93 \\ 
11 & 15 & 10 & 9 & 0.0021 & 0.85 \\ 
12 & 15 & 50 & 9 & 0.0062 & 0.95 \\ 
13 & 15 & 30 & 7 & 0.0061 & 0.97 \\ 
14 & 15 & 30 & 7 & 0.0061 & 0.94 \\ 
15 & 15 & 30 & 7 & 0.0063 & 0.99 
\botline
\end{tabular}
\end{table}

However, among the tests, two kinetic profiles (Assays 5 and 11 in
Table~\ref{tab5}) showed lower correlation value, suggesting partial
deviation from the pseudo-first-order behavior. These discrepancies can
be attributed to non-ideal adsorption--desorption equilibrium on the
TiO\tsub{2} surface, variation in catalyst dispersion, or light
intensity fluctuations during the reaction~\cite{43}.

The kinetic data were fitted to the pseudo-first-order model by
plotting $\ln(C_{0}/C_{t})$ versus time $t$ (Figure~\ref{fig7}).

TiO\tsub{2} photocatalysis is a heterogeneous kinetic process,
comprising several successive steps initiated by the electron--hole
pair formation reaction (e\tsup{\tminus}/h$^{+}$), which depends on the value
of the energy gap, according to the following equation at the point of
zero charge (PZC) of the photocatalyst (6.3) and close to it in a
neutral medium:
{\begin{equation*}
\mathrm{TiO}_{2} \overset{h\nu(\mathrm{UV})}{\longrightarrow}
\mathrm{TiO}_{2} (\mathrm{h}_{\mathrm{VB}}^{+} + \mathrm{e}_{\mathrm{CB}}^{-}).
\end{equation*}}\unskip

But in an acidic medium at a pH lower than the photocatalyst's PZC
(6.3), the TiO\tsub{2} surface is positively charged by protonation of
the oxygens oriented toward the surface, producing the TiOH\tsup{2+}
form, favorable to the adsorption of anionic functional groups or
electronegative ones (electron donors such as nitrogen or oxygen
doublets). Conversely, in a basic medium or at pH ${>}$ PZC,  the surface
is negatively charged (TiO\tsup{\tminus}) and preferentially attracts cations.

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Linearized kinetic curves according to the
pseudo-first-order of Langmuir--Hinshelwood (L--H) model for
photocatalyzed TRZ degradation (see Table~\ref{tab2} for conditions
1--15, with TRZ/TiO\tsub{2} and TRZ/UV control tests).}
\end{figure}

Furthermore, since TRZ possesses lone electron pairs on the oxygens of
functional groups, such as sulfonates (SO\tsub{3}\tsup{2\tminus}),
carboxylate (COO\tsup{\tminus}) and azo N${=}$N, the photocatalytic
activity of TiO\tsub{2} and its adsorption property toward TRZ increase
significantly in acidic medium, while they decrease in neutral and
basic medium (Table~\ref{tab2}). In addition, H\tsup{\tplus} excess promotes
the formation of a large number of holes, by recombining more with the
mobile electrons of the photoconduction band (CB). This increases the
number and speed of hopping of the electrons from the valence band (VB)
to the CB and thus increases the number of active holes with respect to
the adsorbed pollutant.
{\begin{eqnarray*}
\mathrm{TiO}_{2} + \mathrm{H}_{2}\mathrm{O} & \longrightarrow &
[\mathrm{TiO}{-}\mathrm{OH}] + \mathrm{H}^{+} \quad \mbox{at } 
\mathrm{pH} = 6.3 \\
{}[\mathrm{TiO}{-}\mathrm{OH}] + \mathrm{H}^{+} &\longrightarrow&
[\mathrm{TiO}{-}\mathrm{OH}_{2}]^{+} \quad \mbox{at } \mathrm{pH} < 6.3 \\
{}[\mathrm{TiO}{-}\mathrm{OH}] + \mathrm{OH}^{-} &\longrightarrow&
[\mathrm{TiO}{-}\mathrm{O}]^{-} + \mathrm{H}_{2}\mathrm{O} \quad 
\mbox{at } \mathrm{pH} > 6.3 \\
{}[\mathrm{TiO}{-}\mathrm{OH}]^{+} &\overset{h\nu}{\longrightarrow}&
[\mathrm{TiO}{-}\mathrm{OH}]^{+} 
(\mathrm{h}_{\mathrm{VB}}^{+} +
\mathrm{e}_{\mathrm{CB}}^{-}) \\
\mathrm{H}_{2}\mathrm{O}_{\mathrm{ads}} + \mathrm{h}_{\mathrm{VB}}^{+} 
&\longrightarrow&  \mbox{}^{\bullet}
\mathrm{OH}_{\mathrm{ads}} + \mathrm{H}_{\mathrm{ads}}^{+} \\
\mathrm{OH}_{\mathrm{ads}}^{-} + \mathrm{h}_{\mathrm{VB}}^{+}
&\longrightarrow&  \mbox{}^{\bullet}
\mathrm{OH}_{\mathrm{ads}} \\  
\mathrm{O}_{2\mathrm{ads}} + \mathrm{e}_{\mathrm{CB}}^{-} &\longrightarrow&
\mathrm{O}_{2}^{\bullet -}
\end{eqnarray*}}\unskip
and,
{\begin{eqnarray*}
&& 
\left.\begin{array}{ccl}
[\mathrm{TRZ}]_{\mathrm{ads}} + {}^{\bullet}\mathrm{OH}_{\mathrm{ads}} & \longrightarrow & 
[\mathrm{TRZ}{-}\mathrm{OH}]^{\bullet}_{\mathrm{ads}}  \\[3pt]  
{}[\mathrm{TRZ}]_{\mathrm{ads}} + \mathrm{O}_{2\,\mathrm{ads}}^{\bullet -} &\longrightarrow& 
[\mathrm{TRZ}]^{\bullet-}_{\mathrm{ads}} + \mathrm{O}_{2} \\[3pt]
{}[\mathrm{TRZ}]_{\mathrm{ads}} + \mathrm{h}_{\mathrm{VB}}^{+} &\longrightarrow& 
[\mathrm{TRZ}]^{\bullet+}_{\mathrm{ads}} \\[3pt]
{}[\mathrm{TRZ}]_{\mathrm{ads}} + 
\mathrm{e}_{\mathrm{CB}}^{-} &\longrightarrow& 
[\mathrm{TRZ}]^{\bullet-}_{\mathrm{ads}}                                                           
\end{array}\right\} 
\\&& \qquad\quad 
\longrightarrow \mbox{Photodegradation products.}     
\end{eqnarray*}}\unskip

It appears that the main factor influencing the photocatalytic activity
and the photocatalyst surface is the pH of the solution. Indeed, one of
the intrinsic properties of the molecule is its acid--base dissociation
equilibrium in aqueous solution. In the case of TRZ, three dissociation
equilibria are observed, characterized by their p$K_{\mathrm{a}}$
values of 2, 5, and 10.86, attributed to the sulfonate
(SO\tsub{3}\tsup{2\tminus}), carboxylate (COO\tsup{\tminus}), and azo
(N${=}$N) attracting groups, respectively~\cite{44,45}.

In this study, TRZ most often exists in anionic sulfonate form (the
most stable), for all our tests of the experimental design, since, as
the pH ranged between 5 and 9, that is higher than the first value of
p$K_{\mathrm{a}}=2$. For some tests carried out at pH ${=}$\ 5, an
equilibrium between the anionic carboxylate and neutral carboxylic form
could make the two forms coexist in solution. For the tests at pH ${=}$\
 9, the values are higher than that of the second p$K_{\mathrm{a}}=5$, 
hence the predominance of the anionic carboxylate form. Conversely, the
tests at pH ${=}$\ 9 could favor the cationic form of the azo group 
(N${=}$NH\tsup{\tplus}) by protonation of the latter. For tests at pH ${=}$\ 7,
slightly higher than the PZC, the surface of the photocatalyst has both
positive and negative charges, so that both forms [TiO--OH]\tsup{\tplus} and
[TiO\tsup{\tminus}] can exist at the same time and adsorb anionic and cationic
groups, respectively. At the same time, for tests at pH ${=}$\ 5 (${<}$
PZC ${=}$\ 6.3), the dispersion of the photocatalyst in solution promotes
the formation of positives charges on the catalyst surface by
protonation of the Ti(IV) sites, producing the [TiO--OH]\tsup{\tplus} species,
which orients the hydroxyl cation (OH\tsup{\tplus}) outside of the TiO\tsub{2}
surface. 

Attractive electrostatic forces and hydrogen bonds can thus be created
with the anionic sulfonate and carboxylate groups, which further
promotes the adsorption and subsequently the interaction of these
groups with the $\mathrm{h}_{\mathrm{VB}}^{+}$ holes (Intermediate
\textbf{I}) in a Kolbe reaction and the radical species ${}^{\bullet}$OH
formed (Intermediates \textbf{II}, \textbf{III}, \textbf{IV}, and
\textbf{V}). This increases the speed and efficiency of the
photocatalytic reaction with respect to TRZ, which could react more
easily and in a more quantitative manner with the photocatalyst 
(Figure~\ref{fig8}).

\begin{figure*}
\vspace*{-1pt}
\includegraphics{fig08}
\vspace*{-2pt}
\caption{\label{fig8}Photodegradation mechanism of TRZ by TiO\tsub{2}
at pH ${\leq}$ PZC and under optimal conditions.}
\vspace*{-1pt}
\end{figure*}

Therefore, it is likely that the mechanism of
adsorption--photocatalysis of TRZ on TiO\tsub{2} involves a series of
steps as follows:

A schematic diagram is presented in Figure~\ref{fig9} which summarizes
the processes involved in the adsorption--photocatalysis of TRZ under
optimal pH conditions (pH ${=}$\ 5 and 7). The photocatalytic activity
increases with the interactions created on the one hand between TRZ and
the ${}^{\bullet}$OH radical (therefore, with the lower energy species
$\mathrm{h}_{\mathrm{VB}}^{+}$) and on the other hand with
$\mathrm{e}_{\mathrm{CB}}^{-}$ of high energy. These different
combinations as well as the recycling of the ${}^{\bullet}$OH,
O\tsub{2}\tsup{\textbullet \tminus}, and ${}^{\bullet}$H radical species
increase the photocatalytic efficiency of the process.

\begin{figure*}
\vspace*{-4pt}
\includegraphics{fig09}
\vspace*{-4pt}
\caption{\label{fig9}Diagram of TRZ photodegradation by TiO\tsub{2}/UV
under optimal pH conditions.}
\vspace*{-4pt}
\end{figure*}

Furthermore, the photoproducts formed at the end of the process are
essentially gas and water molecules with stable polymerization
bioproducts (lignin) of the phenoxy radical, which do not present any
risk to the environment. Recent work by Klett et~al.~\cite{45} has
shown that the number of negatively charged sites increases
significantly when the solution's pH is higher than PZC. Therefore, the
repulsion between TRZ's anionic groups and the negatively charged sites
on the surface of the photocatalyst is significantly favored. This
decreases the adsorption capacity with increasing pH of TRZ solutions.

Moreover, at pH ${=}$\ 9, the only cationic group formed is the azo group
by protonation of one of the two nitrogens (N${=}$NH\tsup{\tplus}). However,
because this group is directly linked to two bulky substituents, the
sulfophenyl and pyrazole rings, this creates steric constraints that
prevent the approach of the N${=}$NH\tsup{\tplus} group toward the negative
sites of the catalyst surface and its adsorption/photocatalysis. 

\section{Conclusion}

To prove the efficiency of the heterogeneous TiO\tsub{2}-catalyzed
photocatalytic degradation of azo food dye tartrazine, a method based
on statistical control using a design of experiments was developed. The
application of the Box--Behnken design of experiments significantly
reduced the number of experiments required, while simultaneously
revealing key interactions between operating parameters and overcoming
the limitations of the traditional ``one-factor-at-a-time'' approach.

Statistical analysis, performed using ANOVA and response surface method
(RSM), confirmed the relevance and reliability of the model developed.
The high coefficients of determination ($R^{2}=0.98$,
$R^{2}_{\mathrm{adj}}=0.96$, and $R^{2}_{\mathrm{pred}}=0.85$) showed
excellent correlation between experimental and predicted values, thus
validating the model and confirming its predictive power for optimizing
operating conditions. The optimal factor values and the associated
model-predicted response were as follows: dye concentration 5~mg/L,
catalyst mass 48.4~mg, and pH 5.7, resulting in a degradation
efficiency of 89.3\%. Furthermore, the kinetic study indicated that the
reaction followed a pseudo-first-order model, corresponding to a
photocatalytic mechanism under ideal and optimized conditions.

These results confirm the reliability of the model proposed and the
effectiveness of the statistical optimization method for designing
high-performance photocatalytic treatment systems.

Ultimately, this research highlights the effectiveness of statistical
optimization in improving the photocatalytic degradation of azo dyes
and contributes to promoting the sustainable and \mbox{economical}
\mbox{treatment} of industrial wastewater containing food dyes that are
highly toxic to the environment and human health.

\vspace*{-2pt}

\section{Experimental section}
\vspace*{-2pt}
\subsection{Materials and methods}
\vspace{-2pt}
\subsubsection{Reagents}

Reagents and catalysts employed in this work, including titanium
dioxide (TiO\tsub{2}, 99\%), sodium dioxide (NaOH, 97\%) were purchased
from Biochem Chemopharma. Nitric acid (HNO\tsub{3}, 52.4\%) was given
by ProLabo. Tartrazine (TRZ), with chemical formula
C\tsub{16}H\tsub{9}N\tsub{4}Na\tsub{3}O\tsub{9}S\tsub{2} and molecular
weight 534.4~g${\cdot}$mol\tsup{\tminus 1}, was supplied by an agri-food industry
(Algeria). 

\vspace{-2pt}

\subsubsection{Photocatalytic reactor and experimental procedure}

Photocatalytic degradation experiments were carried out in a reactor
that included a magnetic stirrer with a 100~mL beaker placed at 10~cm
below two UV lamps (250--365~nm) as shown (Figure~S1 in the SI).
Kinetic monitoring was performed over a 2-hour period, with 5 mL
aliquots withdrawn at 10~min \mbox{intervals} followed by centrifugation at
6000~rpm for 20~min. Residual dye concentration was determined by
UV--Vis absorbance measurements using a Thermo Scientific Genesys 10S
spectrophotometer at $\lambda_{\max}=426$ nm, using a calibration curve
at different pH values.

\vspace*{-3pt}

\subsection{Characterization of TiO\tsub{2} and tartrazine}
\vspace*{-3pt}
\subsubsection{X-ray diffraction (XRD) analysis}

The crystal structure of the commercial TiO\tsub{2} photocatalyst was
determined by XRD (Figure~S2 in the SI). The analysis was performed
using an Empyrean diffractometer equipped with a
reflection--transmission spinner configuration. Cu K${\upalpha}$
radiation was employed as the X-ray source, with wavelengths of 1.54
(K$\upalpha_{1}$) and 1.54~\AA{} (K$\upalpha_{2}$) and a 
K$\upalpha_{1}$/K$\upalpha_{2}$ intensity ratio of 0.5. The diffraction
patterns were collected in a 2$\theta$ range of 8--80\textdegree\ with
a step size of 0.02626 and a counting time of 27.54 s per step. The
patterns were then compared to reference patterns from Crystallography
Open Database (COD).

\vspace*{-2pt}

\subsubsection{Fourier-transform infrared (FTIR) analysis}

FTIR Spectroscopy was employed to identify the characteristic
functional groups present in \mbox{commercial} TiO\tsub{2} and TRZ, using an
IR-ATR Nicolet Thermos Scientific iS5 spectrometer. The solid samples
were prepared as potassium bromide (KBr) pellets. The spectra were
acquired in transmittance mode over a wavenumber range of
4000--500~cm\tsup{\tminus 1}.

\paragraph{TiO\tsub{2} (Figure~S3 in SI)}

The broad band at 3420 cm\tsup{\tminus 1} is characteristic of O--H stretching
vibrations from surface hydroxyl groups (Ti--OH). A distinct peak at
1635 cm\tsup{\tminus 1} is attributed to the in-plane angular deformation
vibrations of physisorbed water molecules ($\updelta$ H--O--H). The peak
at 1413 cm\tsup{\tminus 1} can be attributed to deformation vibrations of
Ti--O--H. The intense broad absorption below 1000 cm\tsup{\tminus 1} centered
around 726~cm\tsup{\tminus 1} corresponds to the deformation vibrations of Ti--O
bonds within the TiO\tsub{2} lattice under a tetrahedral TiO\tsub{4}
structure.

\paragraph{TRZ (Figure~S4 in SI)}

The broad band at ${\sim}$3459~cm\tsup{\tminus 1} correspond to O--H
stretching, while the peak at ${\sim}$1635 cm\tsup{\tminus 1} is
assigned to C${=}$O stretching. Critically, the strong absorption at
${\sim}$1560 cm\tsup{\tminus 1} signals the N${=}$N azo bond stretch,
TRZ's key chromophore and the main target for photocatalytic
degradation~\cite{29}. The aromatic C${=}$C stretching shows at
${\sim}$1480 cm\tsup{\tminus 1} confirming the presence of benzene
rings in the structure. And the strong bands between 1250 and 1000
cm\tsup{\tminus 1} are attributed to S${=}$O stretching of the
sulfonate groups, which contribute to the dye's
hydrosolubility~\cite{30}.

\section*{Acknowledgements}

We wish to express our gratitude to the staff of the PTAPC research
center at the University of Bejaia, and more particularly to its
director, for their invaluable support and for their valuable
analyses.

\printCOI

\section*{Supplementary materials}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crchim-454-suppl.pdf}}

\back{}

\printbibliography
\refinput{crchim20250956-reference.tex}

\end{document}
