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\DOI{10.5802/crchim.419}
\datereceived{2025-06-10}
\daterevised{2025-08-28}
\dateaccepted{2025-09-04}
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\dateposted{2026-02-16}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Efficient adsorption of the antidiabetic drug metformin from an
aqueous medium using a graphene oxide membrane}

\alttitle{Adsorption efficace du m\'{e}dicament antidiab\'{e}tique
metformine  en milieu aqueux \`{a} l'aide d'une membrane en oxyde de
graph\`{e}ne}

\author{\firstname{Mourad} \lastname{Makhlouf}\CDRorcid{0000-0002-6157-5073}\IsCorresp}
\address{Energy Processes and Nanotechnology Laboratory 
EPNL, University of Blida, Algeria}
\address{Combustion, Detonation and Ballistics Research 
Laboratory, M A C, D P HB, Tipaza, Algeria}
\email[M. Makhlouf]{makhlouf\_mourad@univ-blida.dz}

\author{\firstname{Sabrina} \lastname{Bouriche}\CDRorcid{0009-0000-0037-1168}}
\addressSameAs{1}{Energy Processes and Nanotechnology Laboratory 
EPNL, University of Blida, Algeria}

\author{\firstname{Zoubir} \lastname{Benmaamar}\CDRorcid{0000-0001-9469-7301}}
\addressSameAs{1}{Energy Processes and Nanotechnology Laboratory 
EPNL, University of Blida, Algeria}

\shortrunauthors

%\thanks{}

\keywords{\kwd{Metformin (Met)}
\kwd{Adsorption}
\kwd{Graphene oxide (GO)}
\kwd{Polyvinyl chloride (PVC)}
\kwd{Composite membrane}
\kwd{Micropollutants}
\kwd{Wastewater treatment}}

\altkeywords{\kwd{Metformine (Met)}
\kwd{Adsorption}
\kwd{Oxyde de graph\`{e}ne (GO)}
\kwd{Polychlorure de vinyle (PVC)}
\kwd{Membrane composite}
\kwd{Micropolluants}
\kwd{Traitement des eaux us\'{e}es}}

\begin{abstract}
The presence of micropollutants, such as pharmaceuticals, in aquatic 
environments is a major concern due to the risks they pose to living 
organisms. Given the often inadequate management of wastewater, it is 
crucial to develop reliable and effective methods to eliminate these 
contaminants, thus ensuring our safety and protecting the ecosystem.
This  study aims to test the ability of a polyvinyl chloride/graphene
oxide  (PVC/GO) composite membrane to adsorb metformin (Met) in an
aqueous  solution. The graphene oxide was synthesized using the Hummers
method from  recycled graphite obtained from drilling molds, thereby
adding an ecological  dimension to this research. This graphene oxide
was then used to prepare  PVC/GO. The resulting materials were
characterized using Fourier-transform  infrared spectroscopy,
thermogravimetric analysis and  Brunauer--Emmett--Teller analysis. The
following adsorption parameters were  investigated: pH (2--8),
temperature (25--\mbox{40 \textdegree C}), time (5--30 min), GO content
in PVC/GO (0--15{\%}) and initial concentration (4, 6, 8,  and
\mbox{10 mg/L).} Adsorption experiments revealed that 75{\%} removal of Met
was  achieved within 15 min at an optimum concentration of 4 mg/L.
Maximum  adsorption efficiency of Met was obtained at 40 \textdegree C
in an acidic  medium (pH 2); however, adsorption decreased as the pH
increased.  Thermodynamic studies indicated that Met adsorption was
spontaneous (\tralicstex{∆\textit{G}\text{\textdegree} < 0}{$\Delta  G\text{\textdegree} < 0$}) and exothermic (\tralicstex{∆\textit{H}\text{\textdegree} < 0}{$\Delta  H\text{\textdegree} < 0$})  at 25, 30, and 35 \textdegree C. However, the
process was endothermic and  non-spontaneous at 40 \textdegree C. Based
on the obtained results, PVC/GO  5{\%} was found to be an efficient and
promising adsorbent for Met.
\vspace*{2pt}
\end{abstract}

\begin{altabstract}
La pr\'{e}sence de micropolluants, tels que les produits
pharmaceutiques,  dans les milieux aquatiques est une pr\'{e}occupation
majeure en raison des  risques qu'ils repr\'{e}sentent pour les
organismes vivants. Compte tenu de  la gestion souvent inad\'{e}quate
des eaux us\'{e}es, il est crucial de  d\'{e}velopper des m\'{e}thodes
fiables et efficaces pour \'{e}liminer ces  contaminants, assurant
ainsi notre s\'{e}curit\'{e} et prot\'{e}geant  l'\'{e}cosyst\`{e}me.
Cette \'{e}tude vise \`{a} tester la capacit\'{e}  d'une membrane
composite polychlorure de vinyle/oxyde de graph\`{e}ne  (PVC/GO) \`{a}
adsorber la metformine (Met) dans une solution aqueuse.  L'oxyde de
graph\`{e}ne a \'{e}t\'{e} synth\'{e}tis\'{e} selon la  m\'{e}thode
Hummers \`{a} partir de graphite recycl\'{e} provenant de moules  de
forage, ajoutant ainsi une dimension \'{e}cologique \`{a} cette 
recherche. Cet oxyde de graph\`{e}ne a ensuite \'{e}t\'{e} utilis\'{e}
pour  pr\'{e}parer le PVC/GO. Les mat\'{e}riaux obtenus ont \'{e}t\'{e}
caract\'{e}ris\'{e}s par spectroscopie infrarouge \`{a} transform\'{e}e
de  Fourier, analyse thermogravim\'{e}trique et analyse
Brunauer--Emmett--Teller.  Les param\`{e}tres d'adsorption suivants ont
\'{e}t\'{e} \'{e}tudi\'{e}s :  pH (2--8), temp\'{e}rature (25--40
\textdegree C), dur\'{e}e (5--30 min),  teneur en GO dans le PVC/GO
(0--15{\%}) et concentration initiale (4, 6, 8 et  10 mg/L). Les
exp\'{e}riences d'adsorption ont r\'{e}v\'{e}l\'{e} que 75{\%} de
l'\'{e}limination de la Met \'{e}tait r\'{e}alis\'{e}e en 15 min  \`{a}
une concentration optimale de 4 mg/L. L'efficacit\'{e} d'adsorption 
maximale de la Met a \'{e}t\'{e} obtenue \`{a} 40 \textdegree C dans un
milieu acide (pH 2) ; cependant, l'adsorption a diminu\'{e} \`{a}
mesure que  le pH augmentait. Les \'{e}tudes thermodynamiques ont
indiqu\'{e} que  l'adsorption de la Met \'{e}tait spontan\'{e}e
(\tralicstex{∆\textit{G}\text{\textdegree} < 0}{$\Delta  G\text{\textdegree} < 0$}) et exothermique (\tralicstex{∆\textit{H}\text{\textdegree} < 0}{$\Delta  H\text{\textdegree} < 0$}) \`{a} 25,  30, et 35 \textdegree C.
Cependant, le processus \'{e}tait endothermique et  non spontan\'{e}
\`{a} 40 \textdegree C. Sur la base des r\'{e}sultats  obtenus, le
PVC/GO 5{\%} s'est av\'{e}r\'{e} \^{e}tre un adsorbant efficace  et
prometteur pour la Met.
\end{altabstract}

%\input{CR-pagedemetas}

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\section{Introduction}\label{sec1}
\vspace*{-5pt}

Water pollution is the biggest problem around the world. This is due to
the  presence of micropollutants in wastewater, rivers, and seas.
Pharmaceutical  and personal care products are considered recalcitrant
micropollutants~\cite{1}.  Their increased consumption threatens the
environment, humans, and other  organisms~\cite{2,3,4}. Metformin (Met)
is the most commonly prescribed  antihyperglycemic agent for the
treatment of type 2 diabetes mellitus and  other diseases, such as
endocrine disorders and cancers. 

As this drug is incompletely metabolized by the human body, it is
discharged  into the environment and becomes an emerging
micropollutant~\cite{5}. Some  studies have reported that its presence
in soil affects the growth of fruits  and vegetables (tomatoes, squash,
carrots, etc.). It has also been  demonstrated that exposure of fathead
minnows (\textit{Pimephales promelas}) to metformin (40~mg/L)  induces
\mbox{intersex} gonads and reduces the size and fecundity of male
fish~\cite{2}.  Demarco et~al.\ studied the effects of sublethal
concentrations of Met on the  antioxidant system. Their results
demonstrated mutagenicity, oxidative  stress, and activation of the
antioxidant system in metformin therapy for up  to 30 days, as well as
severe tissue damage and apoptotic cells after 60  days. This affects
the survival of non-target animals~\cite{6}. For these  reasons, Met is
harmful to animals and the aquatic environment, even at low 
concentrations~\cite{7}. Therefore, an efficient method of removing
this  micropollutant is required. The literature reports on different
strategies  for removing Met, such as advanced oxidation processes
(AOPs), flocculation,  phytoremediation, and adsorption. The incomplete
removal of micropollutants  from water and the high cost of some
methods are considered inconvenient.  Due to its affordability and ease
of use, adsorption is a promising process  that is widely used to
remove Met~\cite{8}. Many adsorbents have been studied and  applied for
the removal of antidiabetics, including modified biochar~\cite{9}, 
magnetic--carbon composites~\cite{10,10a}, 
hydrogels~\cite{11}, and
activated  carbons~\cite{12,13,14,15}. Carbon nanomaterials, namely
graphene and graphene oxide (GO), can  adsorb Met. A graphene
derivative, GO is a two-dimensional material with  functional groups,
including hydroxyl, epoxy, and carboxyl, on its surface  and
edges~\cite{16,17}. Its fascinating physicochemical properties and
large  surface area mean that it has a wide range of applications,
particularly in  adsorption as an adsorbent~\cite{18,19}. The
adsorption of Met was tested using  GO. Zhu et~al.~\cite{19} carried
out a study under different conditions of  temperature, pH, ionic
strength, and background electrolyte conditions.  These parameters
influenced the adsorption capacity. On GO at pH 6 and 15  \textdegree
C, 80{\%} of Met was adsorbed within 20~min. A thermodynamic  study
confirmed that the adsorption process was exothermic and spontaneous. 
Even after numerous adsorption--desorption cycles, GO exhibited
excellent  adsorption capacity due to $\uppi $--$\uppi$ and hydrogen
bonding interactions  between GO and Met. Thus, GO could be an
efficient and effective adsorbent  for metformin removal~\cite{19}.
Balasubramani et~al.~\cite{1} conducted a study to  optimize the Met
adsorption parameters, including pH, contact time, initial 
concentration, and GO dose. In their study, GO was prepared from
graphite  using Hummer's method and examined for Met adsorption. 

A thermodynamic study confirmed that metformin adsorption onto graphene
oxide (GO) is spontaneous and exothermic~\cite{20}. Reusability studies
showed  that a 1 N sodium hydroxide solution could regenerate the GO
for up to six  cycles. The synthesized GO was found to have a better
adsorption capacity  than most other reported GOs~\cite{1}. Although
these materials effectively  eliminate pollutants from various water
sources, it is sensible to seek more  cost-effective, high-performance
materials. To our knowledge, no literature  exists on the adsorption of
Met on a membrane-based polymer/GO composite.  Thus, this study aims to
investigate Met adsorption on a polyvinyl  chloride/graphene oxide
(PVC/GO) composite membrane. We characterized the  synthesized
materials using thermogravimetric analysis (TGA), Fourier  transform
infrared spectroscopy (FTIR), and Brunauer--Emmett--Teller (BET) 
analysis. The membrane composite was then used as an adsorbent in Met 
adsorption experiments. These experiments examined the impact on the
Met  adsorption process of various parameters, including temperature,
pH, contact  time, and GO content in PVC/GO. Additionally, we examined
the adsorption  data using different isotherms and investigated
thermodynamics.

\section{Materials and methods}\label{sec2}
\subsection{Synthesis of graphene oxide}\label{sec21}

Graphene oxide was synthesized using Hummer's method, in which graphite
is  oxidized and exfoliated using a mixture of oxidants, sodium nitrate
(NaNO$_3$),  and concentrated sulfuric acid (H$_2$SO$_4$).  The
reaction mixture was kept in an  ice bath at 0 \textdegree C with
continuous stirring for 60 min. Then, over  a period of 2 h, 15 g of
KMnO$_4$ was slowly added to the mixture while keeping  it below
15~\textdegree C. After removing the mixture from the ice bath, it  was
stirred at 35 \textdegree C for two days until a brownish paste formed.
Slowly diluting the resulting mixture with 100 mL of distilled water 
produced an exothermic reaction, raising the temperature to
98~\textdegree C  and changing the color to brown. To complete the
reaction, the solution was  stirred for 30~min at 98 \textdegree C.
Then, the solution was diluted with  200 mL of distilled water and
neutralized with a 30{\%} hydrogen peroxide  solution. This converted
the residual permanganate and MnO$_2$ formed during  the reaction into
soluble manganese ions until outgassing ceased. The  solution was
diluted with a 5{\%} HCl solution. To remove impurities, the  mixture
was washed with deionized water. The product was subjected to 
ultrasonic treatment for 30 min to exfoliate the GO sheets. The
resulting GO  was dried for 24 h at 60 \textdegree C. Advanced
characterization techniques  such as Raman spectroscopy, scanning
electron microscopy (SEM), X-ray  diffraction (XRD),
Brunauer--Emmett--Teller (BET) surface area analysis, 
Fourier-transform infrared spectroscopy (FTIR), and X-ray fluorescence 
analysis (XRF) confirmed the presence of GO in the synthesized 
material~\cite{21}.

\subsection{Preparation of the PVC/GO composite membrane}\label{sec22}
Membranes with a polymer matrix of PVC were prepared using the solution
casting method described in~\cite{22}. A GO mass ranging from 0 to
15{\%} was  dispersed in a dibutyl sebacate (DBS) emulsion under
ultrasonic vibration at  room temperature for 15 min. Once fully
dissolved, the required amount of  PVC was added to the mixture while
stirring. After stirring for an  additional period of time, the
resulting solution was poured into a mold.  The resulting membrane was
removed from the mold with forceps after being  placed in an oven at
150 \textdegree C for 1.5 h. 

\section{Characterization}\label{sec3}

Thermogravimetric analysis (TGA) of GO and PVC/GO was performed using
SDT  Q600 V20.9 Build 20 from TA Instruments to determine the samples'
thermal  stability. Fourier transform infrared (FTIR) spectroscopy was
carried out  using a JASCO V-770 FTIR spectrometer, with spectra
recorded from 4000 to  400~cm$^{-1}$. The Brunauer--Emmett--Teller
(BET) method was used  to determine the specific surface area, pore
size, and pore volume of the  GO. Measurements were taken via N$_2$
adsorption and desorption, and the data  were collected and processed
using Gemini VII 4.00.

Adsorption of Met was carried out in a batch process. First, PVC/GO's 
efficiency toward Met adsorption was investigated to determine the
optimal  removal conditions. A predetermined amount of adsorbent was
mixed with 80 mL  of Met solution at various concentrations. The
temperature was 25  \textdegree C, and the pH of the solution was
neutral. Based on preliminary  experiments, a reaction time of 30 min
was selected. After determining the  optimal concentration, equilibrium
time values were established for the  prepared adsorbent. After
adsorption by PVC/GO, the residual Met  concentration was measured
using a UV spectrophotometer at a wavelength of  232 nm. The percentage
removal of Met was calculated using the following  equation: 
{$$
\mbox{\% Removal }=\frac{(C_0-C_{\mathrm{e}})} {C_{0}}\times 100
$$}\unskip
with  $C_{{0}}$ and $C_{{\mathrm{e}}}$ the Met concentrations at the
start and  equilibrium, respectively. 

\subsection{Thermal gravimetric analysis (TGA)}\label{sec31}
Thermal stability of GO and the GO-reinforced PVC composite membrane
was  studied using TGA. As evidenced by two peaks observed in the
differential  thermal analysis (DTG) curves in Figure~\ref{fig1}, GO
exhibited a two-step  degradation. 

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Thermogravimetric analysis (TGA) and differential
thermal  analysis (DTG) curves of graphene oxide (GO) and the polyvinyl
chloride (PVC)/GO composite.}
\end{figure*}

The first step occurred between 50 and 150 \textdegree C and is
attributed  to the evaporation of adsorbed water molecules. The second
step occurred  between 180 and 250 \textdegree C due to the
decomposition of GO's  oxygenated functional groups. The PVC/GO
composite is thermally stable up to  200 \textdegree C. Thermal
degradation occurred in two steps. The first step  occurred between 200
and 250 \textdegree C and is characterized by the  elimination of the
oxygenated functional groups of the membrane component.  The second
step occurred between 318 and 440 \textdegree C, due to the 
decomposition of conjugated polyene chains. This leads to the formation
of  volatile aromatic compounds and a stable carbon residue~\cite{23}.

\subsection{Fourier-transform infrared spectroscopy (FTIR)}\label{sec32}
Figure~\ref{fig2} shows the FTIR spectrum of PVC/GO. The spectrum exhibits 
characteristic bands at 2958, 2940, and 2858 cm$^{{-1}}$, which are 
associated with symmetrical and asymmetrical C--H stretching vibrations, 
respectively. 

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}FTIR spectrum of PVC/GO.}
\end{figure}

Bands around 2450~cm$^{-1}$ are due to the absorption of CO$_2$ from 
the air~\cite{24}. Intense bands at 1732, 1071, and 
1025~cm$^{-1}$ are  due to C--O elongation. The bands at 1461 and 
963~cm$^{-1}$  correspond to in-plane and out-of-plane C--H deformation,
respectively. The  bands at 1246 and 1071~cm$^{-1}$ correspond to
C--C elongation. The  C--Cl elongation band was found at 692~cm$^{-1}$.

\subsection{Determination of specific surface area}\label{sec33}

Figure~\ref{fig3} shows the nitrogen adsorption--desorption isotherm of
GO. The  material exhibits a IUPAC type IV isotherm with a type H3
hysteresis loop  between 0.2 and 0.99 P/P$^{0}$. This confirms that
the material is  mesoporous.

\begin{figure}
\includegraphics{fig03}
\caption{\label{fig3}Adsorption--desorption of N$_{2}$ by graphene oxide.}
\vspace*{3pt}
\end{figure}

The values obtained with GO for the BET and BJH parameters (specific
surface  area, pore size, and pore volume) are presented in
Table~\ref{tab1}.

%tab1
\begin{table}
\caption{\label{tab1}Different parameters of graphene oxide}
\begin{tabular}{cccc}
\thead
\xmorerows{1}{Parameters}  &  $S_{\mathrm{BET}}$& 
\multicolumn{2}{c}{$S_{\mathrm{BJH}}$} \\\cline{3-4} 
&  &  Adsorption&  Desorption \\
\endthead
\parbox[t]{2.3cm}{\centering Specific surface (m$^{2}$/g)}&  
625& 673.24& 2490.45 \\
\parbox[t]{2cm}{\centering Pore volume (cm$^{{3}}$/g)}&  -& 
\0\00.80& \0\0\02.99 \\
Pore size (nm)&  -& \0\04.79& \0\0\04.81
\botline
\end{tabular}
\end{table}

\begin{figure*}
\includegraphics{fig04}
\caption{\label{fig4}Effect of contact time on metformin adsorption.}
\end{figure*}

The results show that the BET surface area of GO is 625~m$^2$/g, which
is lower than GO's theoretical surface area (2418~m$^2$/g). This
discrepancy is likely due to incomplete  exfoliation and aggregation
during synthesis~\cite{25}. Our previous study~\cite{21}  reported a
detailed analysis of the characterization results (SEM, XRF, Raman
spectroscopy, XRD, and optical absorption properties) for the 
synthesized GO.

\section{Study of the adsorption of met on PVC/GO composite
membranes}\label{sec4}

\subsection{Effect of contact time on Met adsorption}\label{sec41}

The equilibrium time of Met adsorption by PVC/GO was determined.  Tests
were performed using an aqueous Met solution at various concentrations 
(4, 6, 8, and 10~mg/L) brought into contact with 1 g of PVC/GO for 5 to
30  min. The results are presented in Figure~\ref{fig4}.

As can be seen from the histograms, the adsorption phenomenon occurs in
two  stages. In the first stage, adsorption of Met is low for the first
5 min,  then increases rapidly until equilibrium is reached for the
different  concentrations. This can be explained by Met molecules
binding to vacant  sites on PVC/GO's surface until they are fully
occupied. The second stage  corresponds to the desorption of Met after
equilibrium is reached. This  process involves adsorption followed by
desorption under the influence of  agitation~\cite{26,27}. According to
the results shown in Figure~\ref{fig4}, the  equilibrium for Met
adsorption is achieved after 15 min, with an adsorption  rate of 75{\%}
and an optimum concentration of 4~mg/L. We therefore chose  these
conditions for further testing.

\subsection{Effect of pH}\label{sec42}
The pH of the solution is an essential parameter that affects
adsorption. It  considerably impacts the \mbox{surface} charge of the
adsorbent, the extent of  ionization, the speciation of the aqueous
adsorbate species, and the  adsorption rate. The pH effect was
evaluated by mixing 1 g of adsorbent with  80 mL of a 4~mg/L Met
solution at various pH levels (2, 4, 6, and 8). The  results of the pH
effect on Met adsorption are presented in Figure~\ref{fig5}.

\begin{figure*}
\includegraphics{fig05}
\vspace*{-3pt}
\caption{\label{fig5}Effect of pH on the adsorption of metformin.}
\vspace*{-3pt}
\end{figure*}

At low pH, the adsorbent surface becomes highly protonated, which
enhances  the electrostatic attraction between the positively charged
Met molecules  and the active adsorption sites. In addition, the high
availability of H$^+$  ions promotes favorable interactions, leading to
maximum adsorption  efficiency. As the pH increases to neutral and
alkaline conditions (pH  6--8), the adsorption efficiency decreases.
This reduction can be attributed  to changes in surface charge of the
adsorbent, increased competition between  hydroxyl ions (OH$^-$) and Met
molecules for active sites, and possible  electrostatic repulsion,
which collectively hinder the adsorption process.  Overall, the results
indicate that acidic pH is optimal for Met adsorption,  and pH ${=}$ 2
provides the most favorable conditions for maximum removal.  This
behavior confirms that electrostatic interactions play a dominant role 
in the adsorption mechanism.

According to the results, the adsorption efficiency is highest in an
acidic  medium (pH ${=}$ 2), at 91{\%}. This can be explained by Met
molecules binding  to PVC/GO's surface due to strong interaction forces
between the positively  charged adsorbate and the \mbox{adsorbent} surface at
this pH value. Based on these  results, it can be deduced that PVC/GO's
surface is negatively charged.  However, increasing the pH value to 4,
6, or 8 reveals a decrease in Met  adsorption efficiency. This decrease
can be attributed to repulsive  interactions between the surface charge
of PVC/GO and the negative part of  the Met. Therefore, Met adsorption
is favored in an acidic medium,  consistent with the results obtained
by \c{C}avu\c{s}o\u{g}lu  et~al.~\cite{10a}.

\vspace*{-3pt}
\subsection{Effect on Met adsorption of GO content in the PVC/GO
composite membrane}\label{sec43}

To investigate this, we conducted a
series of adsorption experiments at various levels of GO content
(0--15{\%}). One gram of adsorbent was brought  into contact with a Met
solution under the following conditions: 4~mg/L, pH  2, and $T  =
40$~\textdegree C. The mixtures were stirred at 250 rpm.
Figure~\ref{fig6}  shows the effect on adsorption of GO content in
PVC/GO.

\begin{figure}
\includegraphics{fig06}
\caption{\label{fig6}Effect on metformin adsorption of graphene oxide
content in  PVC/GO.}
\vspace*{3pt}
\end{figure}

The results show that adsorption efficiency varied according to the GO 
content in PVC/GO. The highest adsorption rate, 91{\%}, was obtained
for  PVC/GO 5{\%}. A decrease in adsorption efficiency was observed as
the GO  content increased. Maximum adsorption of Met was 79, 76, and
46{\%} for  PVC/GO 0, 10, and 15{\%}, respectively. This can be
explained by GO  agglomeration in PVC/GO and overlap of the adsorption
sites. Based on these  results, PVC/GO 5{\%} was selected as the most
effective adsorbent for Met.

\vspace*{-3pt}

\subsection{Effect of temperature}\label{sec44}

One gram of the adsorbent was mixed with a 4~mg/L Met solution under
250 rpm  agitation at pH 2 and temperatures ranging from 25 to 40
\textdegree C in 5  \textdegree C increments.

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Effect of temperature on metformin adsorption.}
\vspace*{3pt}
\end{figure}

As shown Figure~\ref{fig7}, adsorption efficiency increased with
temperature. The  maximum adsorption percentages were 75 and 91{\%} at
25 and 40 \textdegree  C, respectively. These results suggest that the
Met adsorption process is  favored at higher temperatures and that the
diffusion rate of Met molecules  into PVC/GO's pores increases with
temperature.

\subsection{Adsorption isotherms}\label{sec45}

We processed the experimental data on the adsorption of Met onto PVC/GO
using the linearized equations of the Freundlich and Langmuir models.
This  allowed us to determine the maximum adsorption capacity and
establish which  model the adsorption conforms to. The validity of the
results depends on the  value of the correlation coefficient $R^2$;
the closer  $R^2$ is to 1, the better the results agree with the
considered  model. Figure~\ref{fig8} shows the Langmuir isotherm, which
is used for monomolecular  adsorption of the adsorbate on the adsorbent
surface at a constant  temperature. The quantity adsorbed at
equilibrium is given by the following  equation:
{$$
\frac{C_{{\mathrm{e}}}}{Q_{{\mathrm{e}}}}= \frac{1}{Q_{\mathrm{m}}\times 
K_{\mathrm{L}}}+\frac{C_{{\mathrm{e}}}}{Q_{\mathrm{m}}}
$$}\unskip
with  $C_{{\mathrm{e}}}$ the equilibrium concentration of the adsorbate
in the  solution (mg/L), $Q_{{\mathrm{e}}}$ the amount adsorbed at
equilibrium (mg/g),  $Q_{\mathrm{m}}$ the maximum adsorption capacity
(mg/g), and  $K_{\mathrm{L}}$ the Langmuir constant (L/mg).

\begin{figure}
\includegraphics{fig08}
\vspace*{3pt}
\caption{\label{fig8}Adsorption of metformin using Langmuir's model.}
\vspace*{6pt}
\end{figure}

Plotting $1/Q_{{\mathrm{e}}}$ against $1/C_{{\mathrm{e}}}$ produces a straight  line with
a slope of $1/Q_{\mathrm{m}}$. This is used to determine the values  of the
characteristic parameters $Q_{\mathrm{m}}$ and $K_{\mathrm{L}}$. The  linear
transform plot of the Langmuir model is shown in Figure~\ref{fig8}, and
the  isotherm parameters are summarized in Table~\ref{tab2}.

%tab2
\begin{table}
\caption{\label{tab2}Langmuir isotherm parameters for metformin adsorption on
PVC/GO}
\begin{tabular}{cccc}
\thead
\xmorerows{1}{Adsorbate}& \multicolumn{3}{c}{Parameters}\\\cline{2-4} 
 & $Q_{\mathrm{m}}$ (mg/g)& $K_{\mathrm{L}}$ (L/mg)& $R^{{2}}$ \\
\endthead
{Met}&  1.75& 1.16& 0.97
\botline
\end{tabular}
\end{table}

The results show a satisfactory correlation coefficient $R^2$ of  0.97.
The Langmuir model parameter $K_{\mathrm{L}}$ above 1 indicates that 
$Q_{\mathrm{m}}$ is only reached at low solution concentrations.
Therefore,  the \mbox{Langmuir} model is well suited to describing the
adsorption of Met onto  the material under study. The Freundlich
isotherm (Figure~\ref{fig9}) describes  adsorption on heterogeneous
surfaces using a multilayer adsorption model.  The quantity adsorbed
increases with concentration according to the  following equation: 
{$$
\ln Q_{\mathrm{e}}=\ln  K_{\mathrm{F}}+\left(
\frac{1}{n}\right) \ln C_{\mathrm{e}}
$$}\unskip
with  $Q_{\mathrm{e}}$ and $Q_{\mathrm{m}}$ as previously defined, 
$K_{\mathrm{F}}$ the \mbox{Freundlich} constant (mg/g) and $n$ the Freundlich
exponent. 

Plotting ln $Q_{\mathrm{e}}$ against ln $C_{\mathrm{e}}$
yields a straight  line. The parameters $K_{\mathrm{F}}$ and $1/n$ are
deduced from the y-intercept  and slope of the line, respectively.
Figure~\ref{fig9} shows the results of  linearizing Met adsorption on
PVC/GO according to this model. Table~\ref{tab3}  summarizes the
isotherm parameters.

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}Metformin adsorption isotherm using the Freundlich model.}
\vspace*{6pt}
\end{figure}

%tab3
\begin{table}
\caption{\label{tab3}Freundlich model parameters for metformin adsorption}
\begin{tabular}{cccc}
\thead
\xmorerows{1}{Adsorbate}&  \multicolumn{3}{c}{Parameters} \\\cline{2-4} 
 & $1/n$& $K_{\mathrm{F}}$ (L/mg)& $R^{\mathrm{2}}$ \\
\endthead
{Met}& 0.58& 0.77& 0.96
\botline
\end{tabular}
\vspace*{3pt}
\end{table}

\begin{figure}
\includegraphics{fig10}
\caption{\label{fig10}Pseudo-first-order kinetic model of metformin
adsorption on  PVC/GO.}
\end{figure}

The results show that the correlation coefficient was satisfactory 
($R^2=0.96$). The corresponding $K_{\mathrm{F}}$ value (0.77~L/mg) is
lower than the value obtained for the Langmuir model. From
Table~\ref{tab3},  $n$ equals 1.72, indicating that adsorption is
favorable. The linearity  coefficients in previous tables show that the
Langmuir model better  describes adsorption than the Freundlich model.

\subsection{Kinetic study}\label{sec46}

Modeling experimental kinetic data allows us to determine the Met
adsorption  mechanism on PVC/GO. In this work, both pseudo-first-order
and  \mbox{pseudo-second-order} models were tested. In the pseudo-first-order
model,  plotting $\mathrm{ln}( Q_{\mathrm{e}}{-}Q_{t})$ as a  function of time
$t$ yields a straight line with a slope of  $K_{{1}}$ and an
intercept of $\mathrm{ln} (Q_{\mathrm{e}})$ (Figure~\ref{fig10}).


In the pseudo-second-order model, plotting $t/Q_{t}$ as a function of
time $t$  yields a straight line with a slope of $1/Q_{\mathrm{e}}$ and an
intercept of  $1/(K_{2}Q_{\mathrm{e}}^2)$ (Figure~\ref{fig11}).

\begin{figure}
\includegraphics{fig11}
\caption{\label{fig11}Pseudo-second-order kinetic model of metformin
adsorption on  PVC/GO.}
\end{figure}

Table~\ref{tab4} summarizes the kinetic parameters obtained by applying
the  pseudo-first-order and pseudo-second-order kinetic models to the
adsorption  kinetics.

%tab4
\begin{table}
\caption{\label{tab4}Kinetic parameters for the adsorption of 
metformin on PVC/GO}
\begin{tabular}{cc}
\tbody
\multicolumn{2}{c}{Pseudo-first-order}\vspace*{4pt} \\
$K_{1}$ (min$^{-1}$)& $1.28 \times 10^{{-2}}$ \\
$Q_{\mathrm{e}}$ (mg/g)&  $2.28 \times 10^{{-2}}$ \\
$R^{2}$& 0.14 \vspace*{4pt}\\
\multicolumn{2}{c}{Pseudo-second-order} \vspace*{4pt}\\
$K_{2}$ (mg/g$\cdot$min)& 1.458 \\
$Q_{\mathrm{e}}$ (mg/g)& $5.24 \times 10^{{-2}}$ \\
$R^{2}$&  0.98
\botline
\end{tabular}
\end{table}

Based on the results in Table~\ref{tab4}, the pseudo-second-order
kinetic model had  the highest correlation coefficient ($R^2=0.98$) and
the  value of $Q_{\mathrm{e}}$ was $5.24 \times 10^{-2}$~(mg/g). These results
suggest that the \mbox{adsorption} of Met by PVC/GO is better  described by
the pseudo-second-order kinetic model. \mbox{Previous} studies on the 
adsorption of Met have found that the pseudo-second-order model is the
most  reliable for determining adsorption kinetics. These \mbox{studies}
include those on  GO~\cite{1,19}, \textit{Zea mays} tassel activated carbon
(ZMTAC)~\cite{14},  chich\'{a}-do-cerrado (Sterculia striata) fruit
shells~\cite{10,10a}, activated  carbon-based magnetic
composites~\cite{11}, Fe$_3$O$_4$/GO composites~\cite{18}, chemically 
treated peach kernels~\cite{28}, and
carboxymethylcellulose-g-poly(acrylic  acid-co-acrylamide)
hydrogels~\cite{12}.

\subsection{Thermodynamic study}\label{sec47}
In order to determine the nature of the Met adsorption process, it is 
necessary to calculate the thermodynamic parameters  ($\Delta
G$\textdegree,  $\Delta H$\textdegree,  and $\Delta S$\textdegree).
These parameters were  calculated using the following expressions:
$\Delta G{\text{\textdegree}}=-RT\mathrm{ln}{(K}_{\mathrm{d}})$ and
$\Delta G{\text{\textdegree}}=\Delta H{\text{\textdegree}}-T\Delta
S{\text{\textdegree}}$. Combining these two equations yields the 
linear form of the van 't Hoff equation: 
${-}RT\mathrm{ln}(K_{\mathrm{d}})=\Delta
H{\text{\textdegree}}-T\mathrm{\Delta }S{\text{\textdegree}}$ dividing
by ${-}RT$: $\mathrm{ln}(K_{\mathrm{d}})=- \Delta
H{\text{\textdegree}}/RT+\Delta S{\text{\textdegree}}/R$.

The thermodynamic parameters ($\Delta H\text{\textdegree}$, $\Delta
S\text{\textdegree}$)  were calculated from the slope $({-}\Delta
H\text{\textdegree}/R)$  and ordinate  $(\Delta S\text{\textdegree}/R)$
of the straight line shown in Figure~\ref{fig12}. The  results obtained
are presented in Table~\ref{tab5}.

\begin{figure}
\vspace*{4pt}
\includegraphics{fig12}
\vspace*{2pt}
\caption{\label{fig12}Natural logarithm of $K_{\mathrm{d}}$ as a
function of $1/T$ for metformin adsorption.}
\end{figure}

%tab5
\begin{table}
\caption{\label{tab5}Thermodynamic parameter values for metformin adsorption}
\begin{tabular}{ccccc}
\thead
Adsorbent&  $T$ (\textdegree  C) & 
\parbox[t]{1.2cm}{\centering$\Delta G{\text{\textdegree}}$ (kJ/mol)}& 
\parbox[t]{1.1cm}{\centering $\Delta H{\text{\textdegree}}$ (J/mol)}& 
\parbox[t]{1.1cm}{\centering$\Delta S{\text{\textdegree}}$ (J/mol)}\vspace*{2pt} \\
\endthead
\morerows{3}{Met}&  25 &  ${-}$1.18\0& \morerows{3}{${-}36.13$}& \morerows{3}{${-}0.11$} \\
 & 30& ${-}0.373$&  &  \\
 & 35& ${-}0.380$&  &  \\
 & 40& \mn0.778&  & 
\botline
\end{tabular}
\end{table}


As shown in Table~\ref{tab5}, the free energy ($\Delta G$\textdegree)
is negative at  25, 30, and 35 \textdegree C (i.e., ${-}$1.18, ${-}$0.37,
and ${-}$0.38 kJ/mol,  respectively), indicating spontaneous adsorption.
The positive value of  $\Delta G$\textdegree~at 40 \textdegree C shows
that adsorption is not  spontaneous at this temperature. The negative
enthalpy (${-}$36.13 J/mol)  indicates that the adsorption reaction is
exothermic. The values of $\Delta  H$\textdegree~and $\Delta
G$\textdegree~(between 1 and ${-}$20~kJ/mol) suggest  that the adsorption
process is physisorption at 25, 30, and 35 \textdegree  C, which is
consistent with the \mbox{findings} of Zhu et~al.\ and Balasubramani 
et~al.~\cite{1, 19}. Entropy ($\Delta S$\textdegree), related to the
system's order  after adsorption, showed a negative value of --0.11
J/mol. This indicates a  decrease in randomness at the solid--solution
interface, meaning adsorption  occurs in more ordered layers on the
surface.

\section{Conclusion}

This study investigated the potential of using a PVC/GO composite
membrane  as an adsorbent for Met. The adsorbent's surface was
characterized using TGA  and FTIR analysis. Adsorption studies were
performed on the composite to  determine the effects of temperature,
pH, contact time, and GO content in  PVC/GO. Langmuir and Freundlich
isotherm models were applied to the  experimental results. A
concentration of 4~mg/L was shown to be optimal. The  equilibrium time
for the PVC/GO composite membrane was 15 min, after which  desorption
phenomena occurred. Within the investigated range, maximum Met 
adsorption effectiveness was observed at 40 \textdegree C and in an
acidic  medium (pH 2). The isotherm parameters were well explained by
the Langmuir  isotherm. At low temperatures, the adsorption process was
exothermic and  spontaneous. Thermodynamic analysis confirmed that the
process was  endothermic and non-spontaneous at 40 \textdegree C. This
means that Met was  first adsorbed via physisorption, followed by
chemisorption. Based on the  results obtained, PVC/GO 5{\%} was
identified as an efficient and promising  adsorbent for Met.

\section*{Acknowledgments}
The authors thank Dr Bouriche Sihem from Environmental Engineering 
Department of Houari Boumadiene University, for providing metformin.

\section*{Declaration of interests}
\vspace*{-3pt}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could \mbox{benefit} from this article, and
have declared no affiliations other than their research organizations.

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