\makeatletter
\@ifundefined{HCode}
{\documentclass[screen,CRCHIM,Unicode,biblatex,published]{cedram}
\addbibresource{crchim20240510.bib}
\newenvironment{noXML}{}{}
\def\tsup#1{$^{{#1}}$}
\def\tsub#1{$_{{#1}}$}
\def\ndash{\text{--}}
\usepackage[T1]{fontenc}
\def\thead{\noalign{\relax}\hline}
\def\tbody{\noalign{\relax}}
\def\endthead{\noalign{\relax}\hline}
\def\tabnote#1{\vskip4pt\parbox{.91\linewidth}{#1}}
\def\xxtabnote#1{\vskip4pt\parbox{.78\linewidth}{#1}}
\def\mathbi#1{\text{\textbf{\textit{#1}}}}
\def\sfrac#1#2{{#1}/{#2}}
\def\sofrac#1#2{({#1}/{#2})}
\def\rmmu{\upmu}
\def\rmalpha{\upalpha}
\def\rmdelta{\updelta}
\RequirePackage{etoolbox}
\def\jobid{crchim20240510}
%\graphicspath{{/tmp/\jobid_figs/web/}}
\graphicspath{{./figures/}}
\newcounter{runlevel}
\let\MakeYrStrItalic\relax
\csdef{Seqnsplit}{\\}
\def\refinput#1{}
\def\back#1{}
\def\botline{\\\hline}
\def\mn{\phantom{$-$}}
\def\0{\phantom{0}}
\def\og{\guillemotleft}
\def\fg{\guillemotright}
\usepackage{multirow} 
\def\nrow#1{\@tempcnta #1\relax%
\advance\@tempcnta by 1\relax%
\xdef\lenrow{\the\@tempcnta}}
\def\morerows#1#2{\nrow{#1}\multirow{\lenrow}{*}{#2}}
\def\xmorerows#1#2{{#2}}
\usepackage{hyperref}
\makeatletter
\g@addto@macro{\UrlBreaks}{\UrlOrds}
\gappto{\UrlBreaks}{\UrlOrds}
\DOI{10.5802/crchim.404}
\datereceived{2024-06-21}
\daterevised{2024-12-04}
\datererevised{2025-03-26}
\dateaccepted{2025-05-20}
\ItHasTeXPublished
}
{\documentclass[crchim]{article}
\usepackage[T1]{fontenc}
\def\CDRdoi{10.5802/crchim.404}
\def\sfrac#1#2{{#1}/{#2}}
\def\sofrac#1#2{({#1}/{#2})}
\let\refinput\input
\def\xmorerows#1#2{\morerows{#1}{#2}}
\def\xxtabnote#1{\tabnote{#1}}
\makeatletter
\def\CDRsupplementaryTwotypes#1#2{}
}
\makeatother

\usepackage{upgreek}

\dateposted{2025-09-12}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Equilibrium isotherm, kinetic, and thermodynamic studies of
Safranin O adsorption on pomegranate (\textit{Punica granatum}) peels
as a low-cost adsorbent}

\alttitle{Isotherme d'\'{e}quilibre, \'{e}tudes cin\'{e}tiques et
thermodynamiques de l'adsorption de la Safranine O sur les \'{e}corces
de grenade (\textit{Punica granatum}) en tant qu'adsorbant \`{a} faible
co\^{u}t}

\author{\firstname{Amina} \lastname{Abbaz}}
\address{Environmental Process Engineering Laboratory (LIPE), 
Faculty of Process Engineering, University of
Salah Boubnider Constantine 3, Constantine, 25000, Algeria}
%\email[A. Abbaz]{amina.abbaz@univ-constantine3.dz}

\author{\firstname{Sihem} \lastname{Arris}}
\addressSameAs{1}{Environmental Process Engineering Laboratory (LIPE), 
Faculty of Process Engineering, University of
Salah Boubnider Constantine 3, Constantine, 25000, Algeria}

\author{\firstname{Abdeslam-Hassen} \lastname{Meniai}\CDRorcid{0000-0002-0357-3512}\IsCorresp}
\addressSameAs{1}{Environmental Process Engineering Laboratory (LIPE), 
Faculty of Process Engineering, University of
Salah Boubnider Constantine 3, Constantine, 25000, Algeria}
\email[A.-H. Meniai]{meniai@yahoo.fr}
         
\shortrunauthors

\keywords{\kwd{Pomegranate}
\kwd{Adsorption}
\kwd{Kinetics}
\kwd{Safranin O}
\kwd{Dye}
\kwd{Wastewater}}

\altkeywords{\kwd{Grenade}
\kwd{Adsorption}
\kwd{Cin\'{e}tique}
\kwd{Safranine O}
\kwd{Colorant}
\kwd{Eaux us\'{e}es}}

\begin{abstract}
The present study considered the adsorption capacity of Safranin O (SO)
dye onto pomegranate peel powder (PP). The effect of operating
parameters such as contact time, adsorbent dosage, initial
concentration, pH and temperature on the performance of the dye
adsorption process was also investigated. The PP was characterized by
Fourier transform infrared spectroscopy (FTIR), X-ray diffraction
(XRD), Thermogravimetric analysis (TGA), point of zero charge
(pH$_{\mathrm{pzc}}$), and Boehm titration. According to the results,
the dye removal rate increased proportionally to the amount of
adsorbent used. Langmuir, Freundlich, Temkin, and Dubinin--Radushkevich
isotherms in their linear and non-linear forms were tested to determine
the most appropriate model. The results showed an adsorption capacity
by PP of 44 mg/g at natural pH, room temperature, in 30 min, and with
an adsorbent dosage of 10 g/L. From the $R^{2}$, SSE, and RMSE values,
it was found that the pseudo-second-order model best fitted the kinetic
data and intraparticular diffusion was one of the rate-limiting steps.
Thermodynamic analysis revealed that SO adsorption on PP is endothermic
and favored. The results demonstrate that PP is a promising adsorbent
for removing cationic dyes, such as SO, from aqueous solutions.
\end{abstract}

\begin{altabstract}
La pr\'{e}sente \'{e}tude a consid\'{e}r\'{e} la capacit\'{e}
d'adsorption du colorant Safranine O (SO) sur la poudre de peau de
grenade (PP). L'effet des param\`{e}tres op\'{e}ratoires, tels que le
temps de contact, la quantit\'{e} d'adsorbant, la concentration
initiale, le pH et la temp\'{e}rature, sur la performance du
proc\'{e}d\'{e} d'adsorption du colorant a aussi \'{e}t\'{e}
\'{e}tudi\'{e}e. La PP a \'{e}t\'{e} caract\'{e}ris\'{e}e par
spectroscopie infrarouge \`{a} transform\'{e}e de Fourier (FTIR),
diffraction des rayons X (XRD), analyse thermogravim\'{e}trique (TGA),
point de charge z\'{e}ro (pH$_{\mathrm{pzc}}$) et titrage de Boehm.
D'apr\`{e}s les r\'{e}sultats, le taux d'\'{e}limination des colorants
augmente proportionnellement \`{a} la quantit\'{e} d'adsorbant
utilis\'{e}e. Les isothermes de Langmuir, Freundlich, Temkin et
Dubinin-Radushkevich dans leurs formes lin\'{e}aires et non
lin\'{e}aires ont \'{e}t\'{e} test\'{e}es pour d\'{e}terminer le
mod\`{e}le le plus appropri\'{e}. Les r\'{e}sultats ont montr\'{e} une
capacit\'{e} d'adsorption de la PP de 44 mg/g au pH naturel, \`{a} la
temp\'{e}rature ambiante, en 30 min et avec un dosage d'adsorbant de 10
g/L. D'apr\`{e}s les valeurs de $R^2$, SSE et RMSE, il a \'{e}t\'{e}
constat\'{e} que le mod\`{e}le du pseudo-second ordre a montr\'{e} la
meilleure repr\'{e}sentation des donn\'{e}es cin\'{e}tiques et la
diffusion intra-particulaire a \'{e}t\'{e} l'une des \'{e}tapes
limitant la vitesse. L'analyse thermodynamique a r\'{e}v\'{e}l\'{e} que
l'adsorption du colorant sur le PP est endothermique et favorable. Les
r\'{e}sultats d\'{e}montrent que la PP est un adsorbant prometteur pour
\'{e}liminer des solutions aqueuses les colorants cationiques tels que
le SO.
\end{altabstract}

\maketitle

\vspace*{10pt}

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec0}
Water is essential for sustainable and socio-economic development due
to its impact on most aspects of economy and society. For instance,
regardless of location, maintaining the quality of drinkable and safe
water is crucial for public  health~\cite{1,2}. The economy depends
heavily on manufacturing processes, which also release residues and
byproducts containing chemicals that, if improperly managed, could harm
the environment and contaminate water  sources~\cite{3}. In contrast to
all other types of 
\mbox{wastewaters,} dye wastewater has drawn a great deal
of attention. Over the past century, the printing and dyeing industries
have released huge amounts of dyes into the  environment~\cite{4}.
Organic dyes are compounds widely used in various sectors as coloring
agents in textiles, paper, rubber, leather, plastics, and other 
materials~\cite{5}. Nowadays, the textile industry uses over 700,000
tons of dyes and represents one of the three most significant sources
of  pollutants~\cite{6}. Most of the dyes used are organic compounds
that are both carcinogenic and  teratogenic~\cite{7}. Pharmaceutical
and biochemical industries use Safranin O (SO), also known as basic red
2, as a dye in their 
\mbox{histology} and cytology sectors. It is commonly
used to identify cartilage, mucin, and mast cell granules as well as to
stain gram-negative  bacteria~\cite{8}. Moreover, it is frequently used
in food products and for the coloration and processing of tannins,
cotton, fibers, wool, paper, and  leather~\cite{9}. 

Furthermore, SO may induce harmful health effects, including ocular
irritation, dermatitis, and respiratory allergies. Considering these
consequences, it is necessary to implement an appropriate wastewater
treatment  process~\cite{10}. Traditional remediating wastewater
methods include sedimentation, coagulation, and chemical and membrane
technologies. However, various drawbacks, including high costs, poor
reusability, and low efficacy, frequently constrain these 
methods~\cite{11}. Therefore, two approaches have attracted much
interest in the remediation of organic contaminants in wastewater. The
first approach involves the degradation of organic pollutants using
advanced oxidation processes. The degradation process produces highly
reactive species. These species oxidize toxic organic compounds,
breaking them into simpler, less harmful compounds, or entirely into
CO$_2$ and water. The second approach is adsorption, which has emerged
as a critical method for dye  removal~\cite{12}. Adsorption is a
flexible and inexpensive method to eliminate contaminants in
wastewater. It is based on the contact of the adsorbate and a solid
adsorbent for mass  transfer~\cite{13}. Consequently, this approach has
attracted interest in wastewater treatment because of its versatility
and efficiency in handling a wide range of dyes. Adsorption processes
have many advantages, including ease of use, performance in getting rid
of dyes, and possibly even regeneration of the adsorbent for further
use  again~\cite{14,15}. This method is beneficial for treating
wastewater persistently containing difficult-to-treat colors because it
provides a suitable solution when other approaches are 
\mbox{impractical.}

Adsorbents, such as polymer resins, clay minerals, biomaterials,
zeolites, carbon, and industrial solid waste, are used to remove
organic pollutants from  wastewater~\cite{13,14,15}. Adsorption is a
simple and inexpensive  process~\cite{16}. Activated carbon is the most
commonly used adsorbent in this field because of its effectiveness in 
adsorption~\cite{17}. However, its application is limited because of
its high cost and complex  operation~\cite{18}. Adsorbents have 
several \mbox{advantages} over conventional chemical adsorbents in 
\mbox{water} treatment.

Even with the efficiency of these inexpensive adsorbents, their use has
specific issues, like the difficulty of regeneration and treated water
separation of treated water; these materials are affordable,
biodegradable, readily available and manufactured. Adsorbents can be
obtained from various biomasses, such as bacteria, fungi, algae, and
industrial, natural, and agricultural  waste~\cite{19,20,21,22,23}.
These adsorbents are excellent at removing various contaminants from 
wastewater~\cite{24}.

Among food and agricultural wastes,~pomegranate (\textit{Punica
granatum}) peels (PPs) were considered to be highly effective in the
removal of methylene  blue~\cite{25}, amaranth  dye~\cite{26},
hexavalent chromium~\cite{27},  ciprofloxacin~\cite{28}, and malachite 
green~\cite{29} from aqueous solutions. PP surface has functional
groups like hydroxyl (--OH) and carboxyl (--COOH) that come from
carboxylic acid, phenol, alcohol, ketone, aldehyde, ether, and ester
parts. These groups are the main reason for its  efficiency~\cite{30}.
In 2020, the global area cultivated with pomegranates was approximately
300,000 hectares, producing about 3 million metric tons. The foremost
pomegranate-producing countries include India, Turkey, the United
States, China, Iran, Afghanistan, and Egypt. Since most of this
quantity is turned into juice, jam, and other products, a significant
amount of useless PP is  \mbox{generated~\cite{31}.}

Using PP as adsorbent for dye removal from aqueous solutions has gained
significant interest due to their sustainability and
cost-effectiveness. For instance, a study by Ahmed  et~al.~found that
PP was highly effective in removing dyes such as methylene 
blue~\cite{32}. 

This work investigates the removal of the SO dye using PPs, employing
both linear and non-linear kinetic and isotherm models. Preparation and
characterization of the PP adsorbent was the main focus of this work.
Investigations were conducted into the effects of pH, initial
concentration, temperature, and adsorbent mass. Equilibrium data were
analyzed using isotherm parameters from the Langmuir,
Freundlich,~Temkin, and D--R~linear and non-linear models. Different
types of models were used to look into how to remove the SO dye from
PPs. These included the pseudo-first-order, {pseudo-second-order,}
Elovich, and {intraparticle}  {diffusion} models. {Additionally,}
thermodynamic  parameters were analyzed to predict the adsorption
{process.}

\section{Materials and method}\label{sec1}

\subsection{Adsorbate and chemicals}\label{sec1.1}
Analytical grade chemicals were used in the present work without any
purification. Safranin O ($\lambda_{\mathrm{max}} = 522$~nm, 99.5\%),
sodium hydroxide (99\%), sodium chloride (99.5\%), and hydrochloric
acid (37\%) were supplied by Sigma-Aldrich. The experiments reported in
this paper used SO as the adsorbate, the chemical structure of which is
shown in\unskip\break Figure~\ref{fig1}. 

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Chemical structure of Safranin O.}
\end{figure}

\subsection{Adsorbent preparation}\label{sec1.2}
Pomegranate peels were collected from a market in Mila, Algeria. Raw
peels were washed with distilled water to remove any adhering
substances, followed by drying in an oven at  50~\textdegree C for two
hours. The dried PP was ground and sieved to achieve a uniform particle
size of  315~$\rmmu$m and the resulting PP powder was then further
oven-dried at 105~\textdegree C until a constant weight was obtained. 

\subsection{Adsorbent characterization}\label{sec1.3}
The surface functional groups of PP were studied 
\mbox{using} a Fourier
transform infrared (FTIR) JASCO FT/IR 4600 spectrometer. The FTIR
spectra of the powders were recorded at 4000 and  400~cm$^{-1}$
\mbox{frequencies.}

The X-ray diffraction (XRD) measurements were performed using a D2
PHASER-BRUKER AXS diffractometer with Cu K$\rmalpha$ radiation at a
generator voltage of 40~kV and a generator current of 40~mA. The
scattering angles (2$\theta$) ranged from 5 to 100.

{\advance\baselineskip by -.08pt

Thermogravimetric analysis (TGA) was conducted in an air atmosphere
using a Mettler TC-10 
apparatus,~from 30 to 700~\textdegree C, at a
heating rate of 10~\textdegree C/min. 

The equilibrium pH of the adsorbent was measured by immersing 1~g of PP
in 100 mL of distilled water. The whole was agitated for 24~h.
After filtering the suspension, the pH of the filtrate was determined
utilizing a pH meter.

The point of zero charge (pH$_{\mathrm{pzc}}$) of PP was determined
using the pH drift  method~\cite{33}. Fifty mL of a 0.01~N NaCl
solution was poured into six separate 250~mL Erlenmeyer flasks.
Solutions 0.1~M NaOH and 0.1~M HCl were then used to adjust the pH
between 2 and 12. Each flask was filled with 0.15~g of adsorbent and
thoroughly shaken for 24~h. The pH in each flask was then determined.
The pH$_{\mathrm{zpc}}$ value was then determined by plotting a graph
of final pH vs.\ initial pH, and the intercept was selected as the
pH$_{\mathrm{pzc}}$ of the PP surface.

}

The Boehm titration method was used to characterize functional groups
as described by Farahani  et~al.~\cite{34}. A small amount (0.1~g) of
PP adsorbent was mixed with 50 mL of solutions of 0.1~M NaOH, 0.1~M
NaHCO$_2$, and 0.05~M Na$_{2}$CO$_{3}$, then
shaken at room temperature for 96~h. Afterwards, the suspensions were
decanted and filtered. The solutions were then back titrated with a 
0.1~M HCl solution. An analogous procedure determined the basicity of the
adsorbent. The sample was contacted with a 0.1~M HCl, and 0.1~M NaOH
was used for the titration. The quantities of HCl and NaOH employed in
titration are used to calculate surface chemistry. Acidic groups
include lactones, phenolics, and carboxyls. The amount of 0.1~N HCl
used to titrate the NaHCO$_2$ solution was used to  figure out the
carboxyl groups. Lactone groups were quantified by the difference in
the consumed volume of 0.1~N HCl 
during the titration of
Na$_{2}$CO$_{3}$ and NaHCO$_2$. Phenolic groups
were identified by the difference in the consumed volume of HCl (0.1~N)
during the titration of NaOH and Na$_{2}$CO$_{3}$
solutions. The volume of NaOH (0.1~N) required for the titration of HCl
(0.1~N) was calculated to identify the basic groups. The quantity of
functional groups can be calculated as follows:
{\begin{eqnarray}
&&\displaystyle
\text{functional group}\ 
({\mathrm{mmol}}/{\mathrm{g}})
\nonumber\\&&\quad
= \frac{(\mathrm{Normality}\times
\mathrm{Volume}_{\mathrm{Consumed}})}
{\text{Adsorbent weight}}
\nonumber\\&&\qquad
\times \,
\frac{(\text{initial volume})}
{(\text{selected volume for titration})}
\label{eq1}
\end{eqnarray}}\unskip
The iodine number, which quantifies the micropore content of an
adsorbent (0--20~\AA{}), was determined using a standard 
method~\cite{35}. In a conical flask, 10~mL of a 0.1~N iodine solution
was titrated with a 0.1~N sodium thiosulfate solution. Two drops of a 
1~wt\% starch solution were employed as an indicator until the solution
turned colorless. Fifty milligrams of PP were introduced into a conical
flask containing 15~mL of a 0.1~N iodine solution, agitated for 4 min
and then filtered. Ten milliliters of filtrate were titrated with a
standard sodium thiosulfate solution, using two drops of starch
solution as an indicator. The iodine number was calculated using the
following\break equation: 
{\begin{equation}\label{eq2}
\text{Iodine number}=
\frac{(V_{\mathrm{b}}-V_{\mathrm{s}})\times N\times (126.9)\times (15/10)}{M}
\end{equation}}\unskip
where $V_{\mathrm{b}}$ (mL) and $V_{\mathrm{s}}$ (mL) are the volumes
of sodium thiosulfate solution required for blank and sample
titrations, respectively,  $N$ (mol/L) is the normality of the sodium
thiosulfate solution, 126.9 the atomic weight of iodine (g/mol), and 
$M$ (g) the mass of PP used. 

The methylene blue index (MBI) in~mg/g indicates the adsorption
capacity of medium-sized molecules for assessing mesopores and
macropores. It is based on the method from the European Centre of
Federations of the Chemical Industry  (1989)~\cite{36}. In a 100~mL
Erlenmeyer flask, 0.1~g of pre-dried PP~and  50~mL of a 50~mg/L
methylene blue solution were added. The mixture is agitated for 120~min
and subsequently filtered. The residual concentration of methylene blue
was measured using a UV--visible spectrophotometer at a wavelength of
665~nm. The methylene blue index was calculated according to the
following equation:
{\begin{equation}\label{eq3}
\mathrm{MBI}=
\frac{(C_{0}-C_{\mathrm{r}})\times V}{m}
\end{equation}}\unskip
where $C_{0}$  is the initial dye concentration (mg/L), $C_{\mathrm{r}}$~(mg/L)
the residual dye concentration, $V$ the solution volume (L) and $m$ the
mass of adsorbent (g).

The moisture content was determined by utilizing the oven-drying
method. Half a gram of PP~powder with an average particle size of 0.315
mm was placed in a weighed ceramic crucible. The samples were dried at
110~\textdegree C until they reached a stable weight. Subsequently, the
samples were weighted after being cooled to room 
temperature~\cite{37}. The moisture content was calculated using the
following\break formula:
{\begin{equation}\label{eq4}
\mathrm{moisture}~(\%)=
\frac{w_{3}-w_{2}}{w_{1}}\times 100
\end{equation}}\unskip
where $w_{3}$ (g) is the weight of the crucible containing PP before 
drying, $w_{2}$ (g) is the weight of the crucible containing the PP
after drying, and $w_{1}$ (g) is the weight of PP.

\subsection{Batch adsorption experiments}\label{sec1.4}
Adsorption of SO on PP adsorbent was investigated by varying the dye
concentration, pH, temperature, and adsorbent dose. The range of SO
concentration was 10 to 300~mg/L. Using 0.1~N HCl and 0.1~N NaOH, the
pH was adjusted from 2 to 12. The adsorbent dosage varied from 1 to
40~g/L. The experiment was carried out by changing the temperature from
298 to 333~K. Temperature variation is intended to determine
thermodynamic parameters. The amount of dye adsorbed onto PP~at time
$t$~$q_t$ (mg/g) was assessed using an OPTIZEN POP UV--Vis
spectrophotometer (K LAB Co., Ltd., Taejon, South Korea) at a
wavelength of  $\lambda = 522$~nm and calculated using the following
equation:
{\begin{equation}\label{eq5}
q_{t}=
\frac{(C_{0}-C_{t})}{m}\times V
\end{equation}}\unskip
Percentage removal  ($R$\%) was calculated by 
\text{Equation~(\ref{eq6}):}
{\begin{equation}\label{eq6}
R\% =\frac{(C_{0}-C_{t})}{C_{0}}\times 100
\end{equation}}\unskip
where $C_{0}$ is the initial dye concentration (mg/L), $C_{t}$ (mg/L)
is the dye concentration at any time $t$, $V$  is the volume of the
solution (L), and $m $ is the mass of adsorbent (g).

\subsection{Kinetic studies}\label{sec1.5}
The kinetic studies of SO adsorption on PP were conducted using
pseudo-first order, pseudo-second order, intraparticle diffusion, and
Elovich models.

\subsubsection{Pseudo-first-order model}\label{sec1.5.1}
According to Lagergren~\cite{38}, the adsorption \mbox{capacity} of an
adsorbent determines the solute's adsorption rate on it, which is
represented by 
\text{Equation~(\ref{eq7}).}
{\begin{equation}\label{eq7}
\frac{\mathrm{d}q_{t}}{\mathrm{d}t}=
k_{1}(q_{e}-q_{t})
\end{equation}}\unskip
The linearized form of the pseudo-first-order model is expressed by:
{\begin{equation}\label{eq8}
\ln (q_{e}-q_{t})= \ln q_{e}-k_{1}t
\end{equation}}\unskip
where $q_{e}$ and $q_{t}$ are the amounts of adsorbed dye (mg/g) at
equilibrium and at any time $t$ (min), respectively, and 
$k_{1}~(\mathrm{L}{\cdot}\mathrm{min}^{-1})$ is the pseudo-first-order
model rate constant. 

\subsubsection{Pseudo-second-order model}\label{sec1.5.2}
The rate-limiting step in the pseudo-second-order model's one-step
process is chemical adsorption, which creates valence forces by
exchanging or sharing electrons between the adsorbent and the 
adsorbate~\cite{39}. Kinetic theory best describes the phenomenon using
Equation~(\ref{eq9}).
{\begin{equation}\label{eq9}
\frac{\mathrm{d}q_{t}}{\mathrm{d}t}=
k_{2}({q_{e}}-{q_{t}})^{2}
\end{equation}}\unskip
The linearized form of the pseudo-second-order model equation is:
{\begin{equation}\label{eq10}
\frac{t}{q_{t}}=
\frac{1}{k_{2}{q}_{e}^{2}}+
\frac{1}{q_{e}}t
\end{equation}}\unskip
where $q_{e}$ and  $q_{t}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$
represent the amount of adsorbed dye at equilibrium and time $t$,
respectively, the pseudo-second-order model's rate constant is denoted
by $k_{2}~(\mathrm{g}{\cdot}\mathrm{mg}^{-1}{\cdot}\mathrm{min}^{-1})$.
The linearized relationship can be obtained by plotting $t/q_t$ against
$t$, with the intercept and the slope determining the values of $k_{2}$
and $q_{e}$, respectively.

\subsubsection{Intraparticle diffusion model}\label{sec1.5.3}
The intraparticle diffusion kinetic model (Equation~(\ref{eq11})) was
used to investigate the rate-controlling step of SO 
adsorption~\cite{40}. 
{\begin{equation}\label{eq11}
q_{t}=k_{\mathrm{i}}t^{1/2}+C_{\mathrm{i}}
\end{equation}}\unskip
where $k_{\mathrm{i}}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{1/2})$
is the intraparticle diffusion constant, and $C_{\mathrm{i}}$ is a constant
depending on the boundary layer thickness. By plotting the linear
determination between $q_{t}$ and $t^{1/2}$, the values of $k_{\mathrm{i}}$ and
$C_{\mathrm{i}}$ can be calculated by slope and intercept determination. 

The following equation can be used to determine the intraparticle
diffusion coefficient $D_{\mathrm{i}}$, for SO adsorption onto PP:
{\begin{equation}\label{eq12}
D_{\mathrm{i}}= \frac{0.3r^{2}}{t_{1/2}}
\end{equation}}\unskip
where $D_{\mathrm{i}}$ is the coefficient of the intraparticle diffusion
$(\mathrm{cm}^{2}{\cdot}\mathrm{s}^{-1})$, $t_{1/2}$ is the time
required to complete half the adsorption (s), and $r$ is the radius of
the adsorbent particle (cm). When the calculated value of $D_{\mathrm{i}}$ is
located in the range of  $10^{-5}$ to
$10^{-13}~\mathrm{cm}^{2}{\cdot}\mathrm{s}^{-1}$, it can be deduced
that intraparticle diffusion is the rate-controlling step. In contrast,
if it is between  $10^{-6}$ and
$10^{-8}~\mathrm{cm}^{2}{\cdot}\mathrm{s}^{-1}$, the rate-controlling
step is the film  diffusion~\cite{41}.

\subsubsection{Elovich model}\label{sec1.5.4}
The type of chemisorption kinetics (homogeneous or heterogeneous) and
the number of steps (one or multiple steps) contributing to the
adsorption rate can be determined by applying the Elovich model to
analyze adsorption rate  data~\cite{42}. It can be expressed using
Equation~(\ref{eq13}).
{\begin{equation}\label{eq13}
\frac{\mathrm{d}q_{t}}{\mathrm{d}t}=
\alpha \exp ^{-\beta {q_{t}}}
\end{equation}}\unskip
As $q_{t}\approx 0,
\sfrac{\mathrm{d}q_{t}}{\mathrm{d}t}\approx \alpha $, integrating and
applying the limits for  $t\; (0, t)$ and $q_{t}\; (0, q_{t})$, the
Elovich model can be linearized as: 
{\begin{equation}\label{eq14}
q_{t}=\frac{1}{\beta }
\ln [1+\alpha \beta t]
\end{equation}}\unskip
As the system approaches equilibrium $t\gg  \sfrac{1}{\alpha \beta }$,
thus Equation~(\ref{eq14}) becomes:
{\begin{equation}\label{eq15}
q_{t}=\frac{1}{\beta }
\ln (\alpha \beta )+
\frac{1}{\beta }\ln t
\end{equation}}\unskip
where the desorption constant
$\beta~(\mathrm{g}{\cdot}\mathrm{mg}^{-1})$ is related to surface
coverage and the activation energy of chemical adsorption,
$\alpha~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1})$ is
the initial adsorption, and $q_{t}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$
is the amount of dye adsorbed at time $t$ (min). Plotting $q_{t}$
versus  $\ln t$ provides both $\alpha $ and $\beta $
values.

\subsection{Isotherm adsorption experiment}\label{sec1.6}
Adsorption isotherm experiments were established by equilibrating PP
(0.5~g) in conical flasks holding 50~mL of dye solutions with various
initial dye concentrations
$(50\ndash300~\mathrm{mg}{\cdot}\mathrm{L}^{-1})$ at room temperature.
The mixture was magnetically stirred at 150~rpm until achieving
equilibrium. Samples were centrifuged once equilibrium was reached and
analyzed for the residual SO concentrations. The amount of SO adsorbed
by PP in each condition was calculated using Equation~(\ref{eq5}). The
adsorption parameters were determined by using the following isotherm
models:

\subsubsection{Langmuir isotherm model}\label{sec1.6.1}
The most widely used adsorption isotherm is the Langmuir 
isotherm~\cite{43}, which is based on three main assumptions: 
(i)~monolayer adsorbate coverage is created on the homogeneous
adsorbent surface; (ii)~there is no interaction between the molecules
that are retained; and (iii)~the molecules of the adsorbate are
connected to the adsorption active sites and are unable to migrate
across the surface. The expression~(\ref{eq16}) represents the Langmuir
equation.
{\begin{equation}\label{eq16}
q_{e}=\frac{q_mbC_{e}}{1+bC_{e}}
\end{equation}}\unskip
The linearized form of Langmuir isotherm equation is:
{\begin{equation}\label{eq17}
\frac{1}{q_{e}}=\frac{1}{q_m}+\frac{1}{bq_m}\cdot \frac{1}{C_{e}}
\end{equation}}\unskip
where $q_{e}$ is the amount of adsorbed SO at equilibrium (mg/g),
$C_{e}$ is the free SO concentration at equilibrium (mg/L), $q_m$ is
the maximum amount of adsorption for a complete monolayer (mg/g), and
$b$ is the constant associated with the binding site affinities and
adsorption energy (L/mg).

The favorability of the process was assessed using the Langmuir
isotherm's dimensionless constant separation factor 
$(R_{\mathrm{L}})$. It is calculated using Equation~(\ref{eq18}). The
isotherm's nature is indicated by  $R_{\mathrm{L}}$ values, which can
be either irreversible when $R_{\mathrm{L}} = 0$, favorable when it is
between 0 and 1, linear when  $R_{\mathrm{L}} = 1$, or unfavorable when
it is higher than 1~\cite{44}.
{\begin{equation}\label{eq18}
R_{\mathrm{L}}=\frac{1}{1+bC_{0}}
\end{equation}}\unskip
where $b$ is the constant of Langmuir, and $C_{0}$ is the initial SO
concentration in the solution.

\subsubsection{Freundlich isotherm model}\label{sec1.6.2}
The Freundlich isotherm is an empirical equation used to
describe~heterogeneous systems within a specific range. Furthermore,
different adsorption energies occur in the active  sites~\cite{45}. The
Freundlich equation can be expressed~as: 
{\begin{equation}\label{eq19}
q_{e}=K_f{C}_{e}^{\frac{1}{n}}
\end{equation}}\unskip
The linearized form of Freundlich isotherm equation is as follows:
{\begin{equation}\label{eq20}
\ln q_{e}=\ln K_f+\frac{1}{n}\ln C_{e}
\end{equation}}\unskip
where $q_e$ is the amount of adsorbed dye at equilibrium, 
$K_f~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}
(\mathrm{L}{\cdot}\mathrm{mg}^{-1})^{1/n})$ is the Freundlich constant
corresponding to the capacity of adsorption; for a given adsorbate, an
increase in $K_f$ generally leads to a rise in adsorption capacity;
$1/n$ is the Freundlich exponent associated with surface heterogeneity.
Generally, if  $1/n$ is between 0 and 1, it represents a favorable
process;  $1/n= 0$ indicates irreversible adsorption, and  $1/n$ higher
than 1 indicates unfavorable  adsorption~\cite{46}.

\vspace*{1pt}

\subsubsection{Temkin isotherm model}\label{sec1.6.3}
The Temkin isotherm considers the heat of adsorption over all molecules
in the layer, which decreases linearly with coverage; this could be due
to interactions between the adsorbate and  adsorbent~\cite{47}. The
Temkin isotherm can be represented as below.
{\vspace*{1pt}
\begin{equation}\label{eq21}
q_{e}=\frac{RT}{b_{\mathrm{T}}}
\ln a_{\mathrm{T}}C_{e}
\end{equation}}\unskip
The linearized form is described by the following equation:
{\vspace*{1pt}
\begin{equation}\label{eq22}
q_{e}=B\ln a_{\mathrm{T}}+
B\ln C_{e}
\end{equation}}\unskip
where  $q_e$ is the amount of adsorbed dye at equilibrium, 
$C_{e}~(\mathrm{mg}{\cdot}\mathrm{L}^{-1})$ is the equilibrium
concentration of SO at a constant temperature,
$q_{e}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ is the amount adsorbed at
equilibrium, $a_{\mathrm{T}}~(\mathrm{L}{\cdot}\mathrm{g}^{-1})$ is the
binding constant of the Temkin isotherm, and 
$B~(\mathrm{J}{\cdot}\mathrm{mol}^{-1})$ is the Temkin constant that is
controlled by~temperature. Calculating the intercept and slope of the
plot $q_{e}$ against $\ln C_{e}$  allows determining the values of $B$
and  $a_{\mathrm{T}}$. 

\vspace*{1pt}

\subsubsection{Dubinin--Radushkevich (D--R)}\label{sec1.6.4}
The D--R isotherm (Equation~(\ref{eq23})) can be used to distinguish
between chemisorption and physisorption. This isotherm explains the
development of multilayers of microporous adsorbents; this is broader
than the Langmuir isotherm because it does not require a homogeneous
surface. However, it can be utilized to describe the adsorbent's
surface heterogeneity at low coverage  levels~\cite{48}.
Equation~(\ref{eq23}) represents the D--R isotherm.
{\vspace*{1pt}
\begin{equation}\label{eq23}
q_{e}=Q_me^{-{K_{d}}{\varepsilon ^{2}}}
\end{equation}}\unskip
The linear form of the D--R model is presented by the following
equation:
{\vspace*{1pt}
\begin{equation}\label{eq24}
\ln q_{e}=\ln Q_m-K_{d}\varepsilon ^{2}
\end{equation}}\unskip
where $Q_m~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ is the adsorbed mass
per unit weight of adsorbent at equilibrium, and 
$K_{d}~(\mathrm{mol}^{2}{\cdot}\mathrm{kJ}^{-2})$ is the average
adsorption energy per mole. The Polanyi potential $\varepsilon $ can be
calculated using Equation~(\ref{eq25}).
{\begin{equation}\label{eq25}
\varepsilon =RT\ln 
\left(1+\frac{1}{C_{e}}\right)
\end{equation}}\unskip
where
$R~(8.314~\mathrm{J}{\cdot}\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$
and $T$ (K) are the gas constant and the absolute temperature,
respectively. The values of $Q_m$ and $K_{d}$ in Equation~(\ref{eq13})
can be acquired by obtaining the slope and intercept from a plot of
$\ln q_{e}$ against $\varepsilon ^{2}$. Equation~(\ref{eq26}) can be
used to determine the mean free energy.
{\begin{equation}\label{eq26}
E=\frac{1}{\sqrt{2K_{d}}}
\end{equation}}\unskip
Chemisorption occurs when  $E$ is between 8 and 
$16~\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$,  while physisorption occurs
when \mbox{$E<8~\mathrm{kJ}{\cdot}\mathrm{mol}^{-1}$~\cite{49}.}

\subsection{Thermodynamic studies}\label{sec1.7}
Thermodynamic studies provide information on the adsorption nature and
feasibility by 
\mbox{calculating} the variations of relevant thermodynamic
properties like enthalpy  $(\Delta
H)~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$, entropy  $(\Delta
S)$ ($\mathrm{J}{\cdot}\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1}$),  and
Gibbs free energy $(\Delta G)~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$
for dye absorption at various temperatures (20, 30, 40, 50, and
60~\textdegree C) using 
Equations (\ref{eq27})--(\ref{eq29})~\cite{50}:
{\begin{eqnarray}
\Delta G 
 &=&
-RT\ln K_{d}  \label{eq27}\Seqnsplit
\Delta G 
 &=& 
\Delta H-T\Delta S  \label{eq28}\Seqnsplit
\ln K_{d} 
 &=& 
\frac{\Delta S}{R}-\frac{\Delta H}{RT} \label{eq29}
\end{eqnarray}}\unskip
with  $R$ the universal gas constant
$(8.314~\mathrm{J}{\cdot}\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$,
$K_{d}~(q_e/C_e)$ the distribution coefficient and  $T$~(K) the
absolute temperature. Plotting  $\ln K_{d}$ versus $1/T$ leads to the
determination of the thermodynamic 
\mbox{parameters.}

\subsection{Error functions}\label{sec1.8}
A variety of mathematical error functions were used, including the
following: coefficient of determination ($R^2$), the sum of squares
errors (SSE), and root mean square error (RMSE).
These  functions were used to assess the reliability of linear and non-linear 
\mbox{regression}
methods and to determine the best fit model for the experimental 
data~\cite{50,51}.\pagebreak
{\begin{eqnarray}
&\displaystyle 
\mathrm{SSE}= \sum_{i=1}^{n} (q_{e,\mathrm{exp}}-
q_{e,\mathrm{cal}})_{i}^{2} \label{eq30}\Seqnsplit
&\displaystyle 
\mathrm{RMSE}= \sqrt{\sum_{i=1}^{n}
(q_{e,\mathrm{exp}}- q_{e,\mathrm{cal}})_{i}^{2}}  \label{eq31}
\end{eqnarray}}\unskip
where $q_{e,\mathrm{cal}}$ is the computed value of the solid phase
adsorbate concentration at equilibrium (mg/g) and $q_{e,\mathrm{exp}}$
is the experimental value. The number of data points is denoted by $n$.

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

\subsection{Characterization analysis}\label{sec2.1}
Figure~\ref{fig2}a shows the FTIR spectrum of the SO dye and PP powder
before and after SO adsorption. The spectrum of PP before and after
adsorption exhibits a large absorption peak at  3292~cm$^{-1}$,
indicating the presence of OH groups resulting from vibrations of
hemicellulose, cellulose, lignin, and adsorbed  water~\cite{52}. The 
2929~cm$^{-1}$ peak corresponds to the stretching vibration of C--H in
methyl groups. The stretching of C${=}$O group of ketones and aldehydes
is represented by the peak at   1720~cm$^{-1}$~\cite{53}. The peak at 
1602~cm$^{-1}$ is related to  CH$_{2}$ stretching in the aromatic ring
of hemicellulose. The phenolic, ether, ester, and carboxylic groups in
lignin, cellulose, and hemicellulose components are responsible for the
C--O stretching vibration at   1016~cm$^{-1}$~\cite{54,55}. Weak peaks
at 1322~and  1439~cm$^{-1}$ can be associated to $\rmdelta$CH$_{3}$
bending and $\rmdelta$CH$_{2}$ scissoring, respectively, in
hemicelluloses (H$_{3}$C--(C${=}$O)--O--) and lignin
(H$_{3}$C--O--Ar)~\cite{56}. Additionally, the peak at  1634~cm$^{-1}$
can be assigned to the aromatic ring, and the band at 1335~cm$^{-1}$
represents the aromatic--N bond. However, the PP--SO spectrum shows
important changes. A new peak appeared at 1216~cm$^{-1}$ and could be
assigned to the C--N stretching vibration in the amine group of 
SO~\cite{57}, whereas the peak at 1417~cm$^{-1}$ disappeared and the
peak at 1720~cm$^{-1}$ became more intense. These peaks are assigned to
lignin, cellulose, and hemicellulose compounds, suggesting that these
groups are mainly responsible for the adsorption of SO molecules on the
PP surface, as confirmed by similar results obtained by Mekhamer
et~al.~\cite{28} and Oyekanmi et~al.~\cite{58}.

\begin{figure*}
\vspace*{2pt}
\includegraphics{fig02}
\vspace*{4pt}
\caption{\label{fig2}(a)~FTIR spectrum of the SO dye, PP before
adsorption and PP after adsorption of the dye; (b)~XRD.}
\end{figure*}

The XRD pattern in  Figure~\ref{fig2}b shows a spectrum typical of the
amorphous zone of the cellulose
material. It has primary and secondary
peaks at $2\theta$ of 22 and 16, respectively, corresponding to the
(002) plane. The primary peak indicates the presence of highly
organized crystalline cellulose, whereas the secondary peak corresponds
to a less organized polysaccharide structure. Based on X-ray line
broadening, the Debye--Scherer formula  $(D=K\lambda/\beta\cos\theta)$
was used to get the PP size. The formula takes into account the average
crystalline size $(D)$, the X-ray wavelength used  $(\lambda)$, the
angular width of the line at half maximum intensity  $(\beta)$, and the
Bragg  angle  $(\theta)$~\cite{59}. The estimated average size of the
PP for the (002) reflection is 7.83~nm. These findings are consistent
with those reported by other researchers like for instance Habibi 
et~al.~\cite{60} who observed comparable crystalline sizes in cellulose
derived from diverse sources, ranging from 5 to 8~nm, confirming the
consistency of crystalline structures in natural cellulose 
materials~\cite{60}.

The TGA profile of PP exhibits the characteristic behavior of
cellulosic material  (Figure~\ref{fig3}). It was intended to be a
lignocellulosic biomass consisting of cellulose, hemicellulose, and 
lignin~\cite{61}. The initial phase is ascribed to the evaporation of
water. The subsequent degradation phases might be elucidated by the
decomposition of organic  material~\cite{62}. The final step pertains
to carbonization, meaning the \mbox{completion} of organic material
decomposition.

\begin{figure}
\includegraphics{fig03}
\vspace*{-6pt}
\caption{\label{fig3}TGA analysis of PP.}
\vspace*{-2pt}
\end{figure}

The electrical charge on the surface is mainly dependent on the point
of zero charge (pH$_{\mathrm{pzc}}$). As seen in  Figure~\ref{fig4},
the pH$_{\mathrm{pzc}}$ was determined by the intersection point of the
pH$_{\mathrm{final}}$ versus pH$_{\mathrm{initial}}$ curve with the
bisector, which at 3.58 is not far from the value of 4.6 reported by
Ben-Ali et~al.~\cite{63}, while a different pH$_{\mathrm{pzc}}$ value
of 6.53 was obtained for Turkish pomegranate  peel~\cite{64}.
Consequently, the surface of PP had a positive charge when the solution
pH was less than 3.58 and a negative charge when the pH of the solution
was greater than 3.58. At lower pH values, the OH, COOH, and NH$_{2}$
groups became \mbox{protonated} whereas at higher pH values, they became
deprotonated. This resulted in the negative charge of PP at pH ${>}$
pH$_{\mathrm{pzc}}$, which increased the electrostatic attraction with
the SO  molecules~\cite{65,66}.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig04}
\caption{\label{fig4}pH$_{\mathrm{pzc}}$ of PP.}
\end{figure}

The pH of the adsorbent was found to be 4.52. This pH value gave an
idea about the acidic nature of the adsorbent. Moisture contents, ash
contents, and bulk density were 9\%, 11.98\%, and 0.47~g/cm$^{3}$,
respectively.

The Boehm titration of the surface functions, as shown in 
Table~\ref{tab1}, proves that the concentration of the acidic functions
is more important on the surface of the PP adsorbent (51.5~mmol/g), in
agreement with the obtained adsorbent value  $(\mathrm{pH} = 4.52)$.

\begin{table*}
\caption{\label{tab1}Physical and chemical properties of PP}
\begin{tabular}{cc}
\thead
Parameters & Experimental values \\
\endthead
$\mathrm{pH}_{\mathrm{pzc}}$ & 3.58\\ 
pH & 4.52\\ 
Bulk density (g/cm$^{3}$) & 0.47\\
Moisture content (\%) & 9\\
Ash contents (\%) & 11.98
\vspace*{6pt}\\
Textural properties & \\
Methylene blue number (mg/g) & 24.9\\
Iodine number (mg/g) & 589\\
Specific surface area (m$^{2}$/g) & 585.56\vspace*{6pt}\\
Surface functional groups (mmol/g) & \\ 
Carboxylic function & 7.57\\
Carbonyl function & 16.53\\
Phenol function & 27.4\\
Total acidic functions & 51.5\\
Total basic functions & 45  
\botline
\end{tabular}
\end{table*}

The surface area was determined using the iodine~number. The particle
size was 0.315~mm, and the iodine number~was 589~mg/g. The iodine
molecule is relatively small, with an area of 0.4~nm$^{2}$, and it
could enter the smaller  micropores~\cite{67,68}. Consequently, the
obtained value showed that PP had the highest adsorption capacities for
iodine molecules and that the pores were primarily micropores (diameter
${<}$ 2~nm). Furthermore, the specific surface area was calculated
using the iodine number as  follows~\cite{69,70}:
{\begin{equation}\label{eq32}
S=\frac{IN\times N\times A}{M_{w}}
\end{equation}}\unskip
where  $IN$ is the number of iodine molecules attached,  $N$ is the
Avogadro constant  $(6.02\times 10^{23}~\mathrm{mol}^{-1})$,  $A$ the
size of the iodine surface area $(0.2096\times10^{-18}~\mathrm{m}^{2})$, and
$M_w$ the molar mass of 
\mbox{iodine} (126.92~g/mol).  Consequently, the
specific surface area obtained was  585.56~m$^{2}$/g.  The surface area
and microporosity of active carbons were typically approximated using
the iodine number with a high  precision~\cite{70,71,72}.

The results of the physical and chemical characterization of PP from
this study are summarized in  Table~\ref{tab1}.

\subsection{Effect of physicochemical parameters on SO
adsorption}\label{sec2.2}

\subsubsection{Effect of initial dye concentration and contact
time}\label{sec2.2.1}
Figure~\ref{fig5} shows how the initial SO concentration (10--300~mg/L)
affected SO adsorption. During the first five minutes, the amount of
adsorbed SO increased quickly. After that, it increased more slowly
over the next five to thirty minutes until saturation was reached. When
SO concentration was increased from 10 to 300~mg/L, the equilibrium
adsorption rose from 0.99 to 25.01~mg/g. The results show that, when
the initial concentration was increased, a more significant mass
transfer driving force led to higher SO adsorption because the initial
concentration overcame all mass transfer resistances between the
aqueous and solid  phases~\cite{73}. To confirm that complete
equilibrium had been reached, the experimental data were measured after
120~min.

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5}Effect of initial SO concentration and contact
time on adsorption onto PP. Conditions: $\mathrm{pH}_{\mathrm{natural}}
= 5.85$, $\text{room temperature} = 20 \pm 2~\text{\textdegree}$C, 
$\text{adsorbent dosage} = 10$~g/L.}
\end{figure}

\subsubsection{Effect of adsorbent dosage}\label{sec2.2.2}
Adsorbent dosage is an important parameter that needs to be carefully
controlled during wastewater treatment. The effect of the PP adsorbent
dose on the removal of SO  (Figure~\ref{fig6}) was studied by varying
the adsorbent dosage (1--40~g/L); the initial concentration of SO was
50~mg/L in natural pH and room temperature. The SO removal efficiency
per gram of PP increased with the adsorbent dosage, reaching a plateau
of approximately 88\%. Because of the increased surface area caused by
the adsorbent dose, more active sites were created for SO adsorption,
increasing the removal efficiency. A plateau was observed beyond 10~g/L
of PP, indicating that the equilibrium between SO molecules in a bulk
aqueous solution and the SO adsorbed on the PP surface was established
at this dose with an initial SO concentration of 50~mg/L. However, the
amount of SO adsorbed per gram of PP decreased with the increase in
adsorbent dosage; this is probably because a stronger interaction
between the PP particles caused the conglomeration of exchanger
particles. As a result, the active sites overlapped, which prevented
the dosage from significantly increasing the effective surface 
area~\cite{74}. From  Figure~\ref{fig6}, the adsorption process was
insufficient to completely remove the SO dye. Additional treatments,
such as advanced oxidation processes (AOPs), photocatalysis,
electrochemical techniques, microbial or enzymatic biodegradation, and
membrane filtration, such as reverse osmosis, were then recommended.
The exploration of a combination of these methods might enhance dye
removal \mbox{efficiency.}

\begin{figure}
\vspace*{3pt}
\includegraphics{fig06}
\vspace*{4pt}
\caption{\label{fig6}Effect of adsorbent dosage on SO adsorption by PP.
Conditions:  $C_0=50$~mg/L, $\mathrm{pH}_{\mathrm{natural}}=5.85$, 
$\text{room temperature} = 20 \pm 2~\text{\textdegree}$C.}
\end{figure}

\subsubsection{Effect of initial pH on adsorption}\label{sec2.2.3}
The initial pH is a crucial factor affecting the process and the
adsorption capacity. The ionic species of the adsorbed molecule and the
surface charge of the adsorbent are both influenced by pH. SO
adsorption was investigated in the pH range 2--12. From 
Figure~\ref{fig7}, the results indicate that for  $\mathrm{pH} = 2$,
the only value lower than that of the pH$_{\mathrm{pzc}}$, the
adsorption capacity and the removal efficiency are equal to 4.65~mg/g
and 89.63\%, respectively. For an increased pH of 4, close to the
pH$_{\mathrm{pzc}}$ value of 3.58, the corresponding adsorption
capacity and removal efficiency reach their highest values at 5.03~mg/g
and 96.93\%, respectively. Generally, for pH values below
pH$_{\mathrm{pzc}}$, electrostatic repulsion happens between the
positively charged dye molecules and the positively charged adsorbent
surface. Furthermore, lower SO adsorption at acidic pH is caused by
excess H$^{+}$ ions competing with dye cations on the active sites. At
pH values greater than pH$_{\mathrm{pzc}}$, the electrostatic force of
attraction between the negatively charged surface of the PP and the
positively charged dye cations  increases~\cite{75}. The excess of
OH$^{-}$ ions interacts electrostatically with the dye cations to
prevent them from adhering to the anionic sites of the adsorbent, which
is why SO retention decreases at higher pH values.

\begin{figure}
\vspace*{-2pt}
\includegraphics{fig07}
\vspace*{-4pt}
\caption{\label{fig7}Effect of initial pH on SO adsorption capacity 
$(q_{e})$ and removal efficiency (RE) by PP. Conditions:  $C_0
= 50$~mg/L,  $\mathrm{temperature} = 20\pm2~\text{\textdegree}$C,
$\text{adsorbent dosage} = 10$~g/L.}
\vspace*{-5pt}
\end{figure}

\subsection{Kinetic study}\label{label2.3}
Determining the adsorbent adsorption efficiency requires an
understanding of adsorption kinetics. This supports researchers in the
design of the adsorption system and aids in the explanation of the
adsorption  mechanism~\cite{76}. Four models, pseudo-first-order (PFO),
pseudo-second-order (PSO), Elovich, and intraparticle diffusion (IPD),
were fitted to the experimental data to identify the step that controls
the adsorption of SO onto the PP surface. The plots of the non-linear
models are shown in  Figure~\ref{fig8}, whereas the linear fits of
these models are shown in  Figure~\ref{fig9}. 
\mbox{Table~\ref{tab2}}
summarizes the parameters and error values obtained through linear and
non-linear regression of each model.

\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}Non-linear kinetic models of SO adsorption by PP
at different dye concentrations; inset (a) and (b) represent the
non-linear kinetic models for  $C_0= 100$~mg/L and  $C_0= 300$~mg/L,
respectively. Conditions: $\mathrm{pH}_{\mathrm{natural}} = 5.85$,
$\text{room temperature} = 20 \pm 2~\text{\textdegree}$C, 
$\text{adsorbent dosage} = 10$~g/L.}
\vspace*{-6pt}
\end{figure*}

\begin{figure*}
\includegraphics{fig09}
\vspace*{4pt}
\caption{\label{fig9}Kinetic models of SO adsorption by PP at different
dye concentrations;  (a)~pseudo-first-order model, 
(b)~pseudo-second-order model,  (c)~Elovich model and 
(d)~Intraparticle diffusion model. Conditions: 
$\mathrm{pH}_{\mathrm{natural}} = 5.85$, 
$\text{room temperature} = 20\pm 2~\text{\textdegree}$C, 
$\text{adsorbent dosage} = 10$~g/L.}
\vspace*{4pt}
\end{figure*}

\begin{table*}
\fontsize{9}{10.2}\selectfont\tabcolsep3pt
\caption{\label{tab2}Kinetic parameters and error functions of the
linear and non-linear models for adsorption at three initial
concentrations of SO onto PP}
\begin{tabular}{cccccccc}
\thead
\xmorerows{1}{Kinetic model} & \xmorerows{1}{Coefficients}  &
\multicolumn{2}{c}{50~mg/L} & 
\multicolumn{2}{c}{100~mg/L} & 
\multicolumn{2}{c}{300~mg/L} \\
\cline{3-5}\cline{6-8}
 & & Non-linear & Linear & Non-linear & Linear & Non-linear & Linear\\
\endthead
\morerows{5}{{Pseudo-first-order}} 
 & $q_{e,\mathrm{exp}}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ &
4.5828 & 4.5828 & 9.2691 & 9.2691 & 25.018 & 25.018
\vspace*{4pt}\\ 
& $q_{e,\mathrm{cal}}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 
4.3159 & 0.5698 & 0.5305 & 9.0399 & 23.673 & 2.2304 \\
 & $k_{1}~(\mathrm{min}^{-1})$ &
 1.8897 & 0.0350 & 0.0339 & 3.5394 & 2.6739 & 0.0179 \\
 & ${R}^{{2}}$ & 0.9172 & 0.9342 & 0.8746 & 0.9037 & 0.1527 & 0.9416\\
 & SSE & 2.8795 & 1.2530 & 4.3047 & 0.4904 & 12.658 & 0.5219\\
 & RMSE & 0.3999 & 0.2503 & 0.4890 & 0.1566 & 0.8163 & 0.1702 
\vspace*{6pt}\\

\morerows{4}{{Pseudo-second-order}} & 
$q_{e,{\mathrm{cal}}}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 
4.4470 & 4.5943 & 9.1045 & 9.2652 & 24.095 & 24.801\\
 & $k_{2}~(\mathrm{g}{\cdot}\mathrm{mg}^{-1}{\cdot}\mathrm{min}^{-1})$ &
 0.7866 & 0.2911 & 1 & 0.3031 & 0.3119 & 0.0642 \\
 & $R^{2}$ & 0.6429 & 0.9999 & 0.0028 & 0.9999 & 0.5654 & 0.9998\\
 & SSE & 0.5652 & 0.0674 & 0.5518 & 0.0171 & 6.4932 & 0.0089\\
 & RMSE & 0.1724 & 0.0595 & 0.1704 & 0.0300 & 0.5845 & 0.0216
\vspace*{6pt}\\ 

\morerows{5}{{Elovich}} & 
$q_{e,\mathrm{cal}} =
1/\beta~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 
0.1842 & 0.3684 & 0.1098 & 0.2197 & 0.5705 & 1.1411 \\
 & $\alpha~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1})$ & 
$1.2\times10^8$ & 9632.8 & 
$2.9\times10^{33}$ & 
$3.6\times10^{16}$ & 
$3.1\times10^{16}$ &
$2.7\times10^{8}$\\
 & $\beta~(\mathrm{g}{\cdot}\mathrm{mg}^{-1})$ &
 5.4276 & 2.7138 & 9.1015 & 4.5508 & 1.7526 & 0.8763 \\
 & $R^{2}$ & 0.9383 & 0.9383 & 0.9544 & 0.9544 & 0.9509 & 0.9533\\
 & SSE & 0.0976 & 0.0976 & 0.0252 & 0.0252 & 0.6967 & 0.6967\\
 & RMSE & 0.0716 & 0.0716 & 0.0364 & 0.0364 & 0.1914 & 0.1914
\vspace*{6pt}\\

\morerows{19}{{Intraparticle diffusion}} & 
$K_{i1}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1/2})$ & 
0.0764 & 0.1703 & 0.2220 & 0.0586 & 0.2452 & 0.4667 \\
 & $C_{1}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 
3.8726 & 3.6272 & 7.4881 & 8.7396 & 22.340 & 21.7904 \\
 & $R_{1}^{2}$ & 0.8494 & 0.8785 & 0.1617 & 0.9197 & 0.2211 & 0.8299\\
 & SSE & 0.2383 & 0.0361 & 65.668 & 0.0027 & 427.34 & 0.4025\\
 & RMSE & 0.1119 & 0.0634 & 1.8120 & 0.0173 & 4.6224 & 0.2114 
\vspace*{4pt}\\
 & $K_{i2}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1/2})$ &
 - & 0.0094 & - & 0.0145 & - & 0.0591 \\
 & $C_{2}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ &
 - & 4.4514 & - & 9.0164 & - & 23.715 \\
 & $R_2^2$ & - & 0.8626 & - & 0.9507 & - & 0.8108\\
 & SSE & - & $1.1\times10^{-4}$ & - & $3.1\times10^{-5}$ & - & 0.0010\\
 & RMSE & - & 0.0054 & - & 0.0039 & - & 0.0322
\vspace*{4pt}\\
 & $K_{i3}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1/2})$ &
 - & 0.0241 & - & 0.031 & - & 0.1594 \\
 & $C_{3}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ &
 - & 4.3181 & - & 8.9240 & - & 23.050 \\
 & $R_3^2$ & - & 0.9736 & - & 0.9780 & - & 0.9511\\
 & SSE & - & $1.8\times10^{-5}$ & - & $1.3\times10^{-5}$ & - & 0.0041\\
 & RMSE & - & 0.0030 &  - & 0.0036 & - & 0.0371
\vspace*{4pt}\\
 & $K_{i4}~(\mathrm{mg}{\cdot}\mathrm{g}^{-1}{\cdot}\mathrm{min}^{-1/2})$ & 
 - & - & - & 0.0083 & - & 0.7686 \\
 & $C_4~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ &
 - & - & - & 9.1781 & - & 16.597 \\
 & $R_4^2$ & - & - & - & 0.9989 & - & 1\\
 & SSE & - & - & - & $3.3\times10^{-8}$ & - & -\\
 & RSME & - & - & - & $1.8\times10^{-4}$ &  - &  -\vspace*{6pt} \\
 & $D_{\mathrm{i}}~(\mathrm{cm}^{2}{\cdot}\mathrm{s}^{-1})$ & 
\multicolumn{2}{c}{$4.9\times10^{-7}$} &
\multicolumn{2}{c}{$2.4\times10^{-7}$} &
\multicolumn{2}{c}{$8.2\times10^{-8}$}
\botline
\end{tabular}
\end{table*}

From Table~\ref{tab2}, the error functions corresponding to the
minimized deviations between the experimental equilibrium data and
predicted kinetics suggest that PSO is the best fit followed by
Elovich. By comparing the error functions of SSE and RMSE obtained by
linear and non-linear regression methods, it can be observed that the
error functions of the non-linear method are reduced except that of the
Elovich model, where the error functions are not changed for the
non-linear regression method; this could be explained by the great
similitude between the linear and non-linear equation forms for this
model.  

The numerous paths to predict the applicable kinetic adsorption models
to the experimental data indicate that PSO is better at modeling the
adsorption process. On the other hand, comparing the statistical
parameters ($R^2$, SSE, and RMSE) and
$q_{e,\mathrm{exp}}$ versus $q_{e,\mathrm{cal}}$
for non-linear and linear PSO for the three different SO concentrations
(50, 200, and 300~mg/L) onto PP adsorbent show that linear PSO is more
appropriate with high $R^2$, small values of
SSE and RMSE, and relatively similar values for
$q_{e,\mathrm{cal}}$ and $q_{e,\mathrm{exp}}$ 
(Table~\ref{tab2}). For the Elovich model, it can be observed that the
error functions are not changed for linear and non-linear methods. The
lower $R^2$ values of the IPD kinetic model
indicate that this model is not applicable for predicting the SO
adsorption kinetics/dynamic behavior. This means that the adsorption
rate was not limited by mass transfer of SO from the solution to the
external surface of PP.

The results show that the determination coefficients of $R^2$ values
are higher for PSO models than for PFO. The higher $R^2$ values
indicate that PSO more closely modelled the adsorption process than
PFO. When SO was adsorbed onto PP, $R^2$ values ranged from 0.9998 to
0.9999 for PSO models, more significant than the PFO model range of
0.9037 to 0.9416. Moreover, there is a similarity between the
experimental adsorption capacities  $q_{e,\mathrm{exp}}$ and the
calculated adsorption capacities $q_{e,\mathrm{cal}}$  evaluated from
the PSO model; this implies that the adsorption process is
chemisorption, meaning that ion exchange between the adsorbent and the
adsorbate is the rate-limiting step in the adsorption of SO onto PP.

Equation~(\ref{eq15}) was used to fit the Elovich model to the
experimental data. The results are shown in  Figure~\ref{fig9}c and are
plotted as  $q_t$ versus  $\ln t$.  Table~\ref{tab2} lists the values
of  $\alpha$ and $\beta$ derived from the plots. According to the
viability of the Elovich equation, the adsorption process is controlled
by the chemisorption mechanism. Furthermore, a second-order model type
was described by an Elovich model with the 
\mbox{assumption} that the solid
surface was energetically heterogeneous. The Elovich model does not
match the experimental data for SO adsorption by PP in view of the
difference between $q_{e,\mathrm{exp}}$ and $q_{e,\mathrm{cal}}$\break
values.

The mechanism of dye diffusion could not be determined by using the PFO
and PSO models only. This is because they incorporate every stage of
the adsorption process, including intraparticle, external film, and
adsorption diffusion. As a result, the IPD model was applied~to provide
the required information regarding the rate-limiting 
mechanisms~\cite{77}. The adsorption capacity was proportional to the
square root of time. It indicates boundary layer resistance if the
straight line does not cross the origin. The parameters are listed in 
Table~\ref{tab2}, and $q_t$ versus the square root of time $t^{0.5}$ is
shown at various dye concentrations in  Figure~\ref{fig9}d. In the IPD
plots, boundary-layer diffusion is theoretically represented by up to
four linear regions. Following these regions, IPD occurred in macro,
meso, and micropores. The system at equilibrium should then be
represented by a \mbox{horizontal} line following these four 
regions~\cite{78}. For a dye concentration of 50~mg/L, the plots in 
Figure~\ref{fig9}d display three regions, suggesting that
boundary-layer diffusion was probably the rate-limiting step. Four
observable regions exist for more concentrated solutions with 
$C_0>50$~mg/L. The fact that the intercept did not cross the origin
$(C\neq0)$ suggests that other factors besides IPD also affected how
quickly SO adsorbed onto PP. Similar findings with the use of
pomegranate peels for removing dyes were reported by  Ahmed et~al. and
Ververi et~al.~\cite{79,80}. In  Table~\ref{tab2}, the pore diffusion
coefficient $D_{\mathrm{i}}$ varies from $10^{-6}$ to
$10^{-8}~\mathrm{cm}^{2}{\cdot}\mathrm{s}^{-1}$, which indicates that
film diffusion was the rate-limiting step. As a result, several steps
were involved in the dye adsorption onto PP with other processes
helping to regulate the adsorption  rate~\cite{81}.

Therefore, compared to the other models examined, the PSO kinetic model
can better explain the adsorption of SO on PP, followed by the IPD
model.

\subsection{Adsorption isotherm}\label{sec2.4}
The adsorption isotherm is critical for understanding the reactive
interactions between the solute and the adsorbent. It also aids in
describing various parameters, such as the adsorbent surface area, the
maximum capacity of adsorption, and the nature of the adsorbent,
whether multilayer or monolayer. Adsorption isotherms were investigated
using four models: the Langmuir isotherm, the \mbox{Freundlich} isotherm, the
Temkin isotherm, and the Dubinin--Radushkevich (D--R) isotherm,
as shown in Figure~\ref{fig10}. 
Figure~\ref{fig8} shows the non-linear plots of the various isotherms. 
Table~\ref{tab3} lists the equilibrium constants and the corresponding
fit of linear and non-linear isothermal constants, determination
coefficients $(R^2)$, and error functions for each model.

\begin{figure}
\includegraphics{fig10}
\caption{\label{fig10}Fitting of the Langmuir, Freundlich, Temkin, and
Dubinin--Radushkevich isotherm models to the 
experimental equilibrium data of SO adsorption by PP. Conditions: 
$C_0 =50\ndash300$~mg/L,~\text{$\mathrm{pH}_{\mathrm{natural}}=5.85$,}
$\text{room temperature} = 21
\pm 2~\text{\textdegree}$C, adsorbent dosage ${=}$ 10~g/L.}
\end{figure}

\begin{table*}
\caption{\label{tab3}Isotherm parameters calculated from linear and
non-linear models for SO adsorption onto PP\vspace*{-2pt}}
\begin{tabular}{cccc}
\thead
Isotherm model & Parameters & Linear & Non-linear\\
\endthead
\morerows{5}{Langmuir} & 
$q_m~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 152.67 & 44.008 \\
 & $b~(\mathrm{L}{\cdot}\mathrm{mg}^{-1})$ & 173.68 & 0.0270 \\
 & $R_{\mathrm{L}}$ & 1.15--1.91 & 0.1--0.42 \\
 & $R^2$ & 0.9420 & 0.9874 \\
 & SSE & 0.0011 & 3.0486 \\
 & RMSE & 0.0236 & 1.2346 \vspace*{6pt}\\
 
\morerows{4}{Freundlich} & $n$ & 1.3211 & 1.5756 \\
 & $K_f~((\mathrm{mg}{\cdot}\mathrm{g}^{-1}){\cdot}
 (\mathrm{L}{\cdot}\mathrm{mg}^{-1})1/n)$ & 
1.4516 & 2.1537 \\
 & $R^{2}$ & 0.9394 & 0.9671 \\
 & SSE & 0.1009 & 8.0021 \\
 & RMSE & 0.2246 & 2.0002\vspace*{6pt}\\
 
\morerows{5}{Temkin} & 
$a_{\mathrm{T}}~(\mathrm{L}{\cdot}\mathrm{g}^{-1})$ &
0.2828 & 0.2828 \\
 & $B$ & 9.4388 & 9.4388 \\
 & $b_{\mathrm{T}}~(\mathrm{J}{\cdot}\mathrm{mol}^{-1})$ & 
 258.08 & 258.08 \\
 & $R^{2}$ & 0.9985 & 0.9985 \\
 & SSE & 0.3539 & 0.3539 \\
 & RMSE & 0.4206 & 0.4206 
\vspace*{6pt}\\

\morerows{5}{D--R} &
$Q_m~(\mathrm{mg}{\cdot}\mathrm{g}^{-1})$ & 
3.0823 & 23.382 \\
 & $K_d~(\mathrm{mol}^2{\cdot}\mathrm{kJ}^{-2})$ & 
$1.1\times10^{-7}$ & 81.047 \\
 & $E~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ & 
 2132 & 0.0785 \\
 & $R^{2}$ & 0.9670 & 0.9376 \\
 & SSE & 0.054 & 15.202 \\
 & RMSE & 0.1655 & 2.7570 
\botline
\end{tabular}
\vspace*{-4pt}
\end{table*}

The Langmuir concept assumes that the adsorption occurs on the
individual homogeneous monolayer of the adsorbent. Parameters for
non-linear and linear isothermal models are summarized in 
Table~\ref{tab3}. The $q_m$ and  $b$ Langmuir constants were calculated
for the non-linear model by fitting the $q_e$ versus  $C_e$ plot curve
and for the linear model by fitting  $1/q_e$ versus  $1/C_e$. The value
of $q_m$ was 44 and 152.67 for the non-linear and linear Langmuir
models, respectively, while  $b$ was 0.027 for the non-linear model and
173.68 for the linear model. In comparison, the non-linear model $R^2$
(0.9874) was greater than the linear model $R^2$ (0.942). Based on the
Langmuir model, the $R_{\mathrm{L}}$ value for the non-linear model is in the
range of 0.1--0.42, implying that the SO \mbox{adsorption} process 
\mbox{using} PP was favorable $(0<R_{\mathrm{L}}<1)$, while 
$R_{\mathrm{L}}>1$ for the linear model
indicates that the adsorption process was  unfavorable~\cite{44}. As a
consequence, the non-linear model of Langmuir would match the
experimental adsorption data better than the linear model. According to
the results obtained from the non-linear model of Langmuir, the
adsorption process was carried out in a monolayer manner, demonstrating
that SO had a comparatively high adsorption rate. The maximum
adsorption amount of PP was confirmed by Langmuir  ($q_m = 44$~mg/g).
Additionally, because only one SO molecule was adsorbed by the active
site on the PP  surface~\cite{82}, the affinity of SO for the
adsorption sites on the surface was low  $(b = 0.0027)$, suggesting a
weak interaction between adsorbate and adsorbent. Comparable results
were found by Guzel  et~al.~\cite{64} for the removal of methylene blue
using raw PP with a $q_m$ value of 36.36~mg/g at 303~K. In another
study, Ahmed  et~al.~\cite{79} found that the Freundlich model best
fitted the experimental data for the removal of Remazol brilliant blue
reactive dye onto PP activated carbon with a maximum adsorption
capacity of 370.86~mg/g.

By comparing the error functions obtained by linear and non-linear
regression methods for Freundlich, Temkin, and D--R models, it can be
observed that the error functions of the non-linear method are reduced
except that of the Temkin isotherm model, where the error functions are
not changed for the non-linear regression method; this could be
explained by the great similitude between the linear and non-linear
forms for this model.

Two parameters were used to analyze the Freundlich model: the
linearized form's adsorption intensity  $(n)$ and adsorption capacity
$(K_f)$. In this investigation, the $K_f$ value was 1.45~L/g,
indicating a high SO adsorption amount  (Table~\ref{tab3}). The high
adsorption intensity of PP in this study  $(n=1.32)$, which suggests a
chemisorption process, shows that PP favorably adsorbed SO cations and
formed noticeably stronger bonds with the PP adsorbent. As a result,
multilayer adsorption on top of the already chemisorbed layer might be
used to continue the adsorption of SO cations on PP. Moreover, the high
$R^2$ value (0.9394) implies a role for multilayer adsorption in the
mechanism's process. 

The Temkin isotherm model confirmed the presence of heterogeneous sites
with varying binding energies, which is consistent with the
\mbox{experimental} findings. Based on the results in  Table~\ref{tab2}, the
Temkin model was found to be appropriate for SO adsorption on PP, as
evidenced by the highest $R^2$ value (0.9985). These findings prove
that chemisorption was involved in the SO adsorption process. The
higher  $b$ value (258.08~J/mol) indicates a strong ion exchange
mechanism and interaction between SO and the PP surface, which
decreased the dye adsorption heat in the layer. In another study, a
high value of  $b$ (139.52~KJ/mol) was found by  Ismi 
et~al.~\cite{83}; it demonstrated that the adsorption experiment
followed a chemical process, indicating strong chemical bonds between
adsorbate and  adsorbent~\cite{83}.\looseness=1

The D--R isotherm model determines whether the process of adsorption is
physical ($E < 8$~kJ/mol) or chemical  ($E> 16$~kJ/mol). The average
adsorption energy ($E$,~kJ/mol) is proportional to the energy 
\mbox{required} to transport dye~molecules~to the surface of the
adsorbent~\cite{84}. The mean free energy $(E)$ for PP in this
investigation was greater than 16~kJ/mol (2132~kJ/mol), indicating that
the SO adsorption process is  chemical~\cite{49}.

Since the $R^2$ values for the Temkin, Langmuir, Freundlich, and D--R
adsorption isotherms are all greater than 0.93, it can be concluded
that multilayer physisorption on top of the previously chemisorbed
layer played a significant role in the multi-mechanistic SO adsorption
by PP.

Table~\ref{tab4} displays a comparison of maximum adsorption capacity
($q_m$ value) with other researchers who used PP as an adsorbent and
the removal of SO with different adsorbents found in the literature.
Compared to other adsorbents, PP has a comparable adsorption capacity
for SO. Therefore, PP is suitable for SO elimination from aqueous
solutions as it has a relatively high adsorption capacity.

\begin{table*}
\fontsize{8.8}{12}\selectfont\tabcolsep3pt
\caption{\label{tab4}Comparison of Langmuir isotherm's maximum
adsorption capacity  $q_m$ for adsorption of SO on various adsorbents
and of other dyes on pomegranate peel}
\begin{tabular}{ccccccccc} 
\thead
\xmorerows{1}{Adsorbent} & \xmorerows{1}{Adsorbate} &
\multicolumn{5}{c}{Conditions} & 
\morerows{1}{\parbox[t]{.8cm}{\centering $q_m$ (mg/g)}}& 
\xmorerows{1}{Ref.} \vspace*{2pt}\\
\cline{3-7}
 & & pH & $T$~(\textdegree C) & $C_0$ (mg/L) & 
\parbox[t]{1.8cm}{\centering Adsorbent dosage (g/L)} & 
\parbox[t]{1.5cm}{\centering Contact time (min)}
& & \vspace*{2pt}\\
\endthead
{Peanut husks} & Safranin O & Natural & \parbox[t]{1.8cm}{\centering Room temperature} & - & 0.03 & \0180 & 86.1 & \cite{85}  \vspace*{2pt}\\
{Soybean hulls} & Safranin O & 8 & 50 & 20--100 & 0.04 & \0\090 & 29.49 & \cite{86} \\
{Mango seeds} & Safranin O & 10 & - & 50--300 & 1 & \0400 & 43.47 & \cite{87} \\
{Tea leaves} & Safranin O & 5 & 25 & 10--50 & 0.15 & \0\020 & 14.814 & \cite{88} \\
{Thuja orientalis} & Safranin O & 7 & 10 & 5--25 & 0.125 &\0\060 & 0.17 & \cite{89} \\
{PP} & Malachite green & 5 & 40 & 50 & 0.1 & \0\090 & 31.45 & \cite{29} \\
{PP} & Methylene blue & - & 30 & 25--300 & 1  & 1440 & 250 & \cite{32} \\
{PP} & Sulfasalazine & - & 25 & 50--200 & 0.5 & \0120 & 64.04 & \cite{90} \\
{PP} & \parbox[t]{1.8cm}{\centering Ciprofloxacin hydrochloride} & 4--5 & 25 & 5000--10,000 & 0.01 & \0120 & 999 & \cite{28} \vspace*{2pt}\\
{PP} & Safranin O & 5.8 & \parbox[t]{1.8cm}{\centering Room temperature} & 50--300 & 0.5 & \0120 & 44 & This work \vspace*{2pt}
\botline
\end{tabular}
\vspace*{2pt}
\end{table*}

\subsection{Thermodynamic properties}\label{sec2.5}
A thermodynamic investigation was carried out at different temperatures
(293 to 333~K) to examine the adsorption of SO by PP. The Van't Hoff
equation was used to study the various thermodynamic parameters for the
adsorption of SO onto PP, including the standard Gibbs free energy
change $(\Delta G{\text{\textdegree}}~\mathrm{kJ}
{\cdot}\mathrm{mol}^{-1})$, standard change in entropy  $(\Delta
S\text{\textdegree}~\mathrm{J}{\cdot}\mathrm{K}^{-1}{\cdot}
\mathrm{mol}^{-1})$, and standard change in enthalpy  $(\Delta
H\text{\textdegree}~\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$.  The plot of
ln $K_d$ versus  $1/T$ is shown in  Figure~\ref{fig11}, and
Table~\ref{tab5} summarizes the thermodynamic parameters.

\begin{figure}
\includegraphics{fig11}
\vspace*{-2pt}
\caption{\label{fig11}The plot of ln $K_d$ versus $1/T$ for the
adsorption of SO by PP, Conditions:  $C_0= 50$~mg/L,
$\mathrm{pH}_{\mathrm{natural}} = 5.85$, $\text{adsorbent dosage} =
10$~g/L.}
\vspace*{-2pt}
\end{figure}

\begin{table*}
\caption{\label{tab5}Thermodynamic parameters for SO adsorption by PP}
\begin{tabular}{cccc} 
\thead
Temperature (K) & 
$\Delta G{\text{\textdegree}}~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ & 
$\Delta H{\text{\textdegree}}~(\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ & 
$\Delta S{\text{\textdegree}}~(\mathrm{kJ}{\cdot}
\mathrm{mol}^{-1}{\cdot}\mathrm{K}^{-1})$\\
\endthead
{293} & \0${-}$1.416 & 77.987 & ${-}$0.271 \\
{303} & \0${-}$4.126 & &  \\
{313} & \0${-}$6.836 & & \\
{323} & \0${-}$9.546 & &  \\
{333} & ${-}$12.25\0 & &
\botline
\end{tabular}
\end{table*}

The negative $\Delta G\text{\textdegree}$ values indicate that SO
adsorption onto PP is thermodynamically favored. In addition, even more
negative values were found as the temperature increased gradually from
20 to 60~\textdegree C, indicating that the adsorption process became
more favorable and most feasible at high temperatures. In addition, the
negative values came from the increase in energy released when the dye
interacted with the adsorbent surface. The fact that the $\Delta
H\text{\textdegree}$ value of PP was positive 
$(77.987~\mathrm{kJ}{\cdot}\mathrm{mol}^{-1})$ indicates that the SO
adsorption process was  endothermic~\cite{91}. The negative value of
the entropy change $(\Delta S\text{\textdegree}=
-0.271~\mathrm{kJ}/\mathrm{mol})$ indicates a random decrease in
adsorption occurring at the solid--liquid interface. Similar results
were obtained by Penghi  Li et~al.~and Ben Ali  et~al.~\cite{54,92}.
Physisorption can be defined by  $\Delta G\text{\textdegree}$ values
over ${-}$20~kJ/mol, chemisorption from ${-}$80~kJ/mol  to~${-}$400~kJ/mol.
In this investigation, the values of Gibbs free energy varied from
${-}$1.416~kJ/mol to ${-}$12.25~kJ/mol. Consequently, the adsorption
occurred as physisorption.

\section{Conclusion}\label{sec3}
The recovery of agri-food waste and the effectiveness of pomegranate
peel (PP) as adsorbent for removing the organic pollutant Safranin O
(SO) in a synthetic medium has been highlighted in this study. Many
methods were used to characterize its structure, such as
pH$_{\mathrm{pzc}}$ analysis, XRD, FTIR, Boehm titration, and iodine
number. Its ability to adsorb the SO dye was investigated at various pH
values, temperatures, and initial~dye concentrations. The adsorption
process was rapid, achieving equilibrium after two hours of contact,
with maximum dye uptake occurring within the initial 30~min. The
adsorbent dose selected was 10~g/L. The dye removal percentage slightly
decreased beyond 10~mg/L of adsorbent due to overcrowding of the
sorbent. The PP adsorbent showed the highest SO removal efficiency,
with a removal rate of up to 96.93\%, under acidic conditions
$(\mathrm{pH} = 4)$. The adsorption of SO was shown to be chemisorption
when fitted to the pseudo-second-order kinetic model. The adsorption of
SO onto PP was confirmed to occur through different stages by the
multilinearity displayed by the intraparticle diffusion models. The
fact that the intercept did not pass through the origin suggests other
rate-determining steps besides intraparticle diffusion. The isotherms
of SO adsorption onto PP followed the Temkin and Langmuir isotherm
models. The obtained maximum monolayer adsorption capacity $(q_m)$ was
44~mg/g in a 50--300~mg/L range. The values of $\Delta
H{\text{\textdegree}}$ (77.987~kJ/mol) suggest that the adsorption
process of SO was  endothermic~\cite{92}. The negative values of
$\Delta G{\text{\textdegree}}$ indicate that the adsorption of SO was
favored. The adsorption mechanisms for SO onto PP were physisorption
and \mbox{chemisorption} based on the obtained data. As a result, inexpensive
PP appears as a promising adsorbent for the removal of cationic dyes
from wastewater, including SO.

\section*{Declaration of interests}
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 organizations.

\back{}

\printbibliography
\refinput{crchim20240510-reference.tex}

\end{document}
