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\DOI{10.5802/crchim.285}
\datereceived{2023-09-08}
\daterevised{2023-12-29}
\dateaccepted{2024-01-18}
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\dateposted{2024-06-19}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Removal and adsorption kinetics of copper(II) ions from aqueous
media on activated carbon in dynamic adsorption on a fixed-bed column}

\alttitle{Elimination et cin\'{e}tiques d'adsorption des ions
cuivre(II) issus de milieux aqueux sur charbon actif en adsorption
dynamique sur colonne \`{a} lit fixe}

\author{\firstname{Charly} \lastname{Mve Mfoumou}\CDRorcid{0000-0001-8393-9985}\IsCorresp}
\address{Laboratoire de Chimie des Milieux et des Mat\'{e}riaux
Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences et Techniques
de Masuku (USTM), BP~: 943 Franceville, Gabon}
\address{D\'{e}partement de Chimie, Facult\'{e} des
Sciences/Universit\'{e} des Sciences et Techniques de Masuku (USTM),
BP~: 943 Franceville, Gabon}
\email[C. Mve Mfoumou]{charly.mvemfoumou@univ-masuku.org}

\author{\firstname{Pradel} \lastname{Tonda-Miki\'ela}\CDRorcid{0009-0009-6133-8703}}
\addressSameAs{1}{Laboratoire de Chimie des Milieux et des
Mat\'{e}riaux Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences
et Techniques de Masuku (USTM), BP~: 943 Franceville, Gabon}
\addressSameAs{2}{D\'{e}partement de Chimie, Facult\'{e} des
Sciences/Universit\'{e} des Sciences et Techniques de Masuku (USTM),
BP~: 943 Franceville, Gabon}
%\email{pradel.tonda.mikiela@gmail.com}

\author{\firstname{Francis} \lastname{Ngoye}}
\addressSameAs{1}{Laboratoire de Chimie des Milieux et des
Mat\'{e}riaux Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences
et Techniques de Masuku (USTM), BP~: 943 Franceville, Gabon}
%\email{ngoyefrancis@yahoo.fr}
                                    
\author{\firstname{Spenseur} \lastname{Bouassa Mougnala}\CDRorcid{0009-0002-4562-8902}}
\addressSameAs{1}{Laboratoire de Chimie des Milieux et des
Mat\'{e}riaux Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences
et Techniques de Masuku (USTM), BP~: 943 Franceville, Gabon}
\addressSameAs{2}{D\'{e}partement de Chimie, Facult\'{e} des
Sciences/Universit\'{e} des Sciences et Techniques de Masuku (USTM),
BP~: 943 Franceville, Gabon}
%\email{spenseurm@gmail.com}

\author{\firstname{Berthy Lionel} \lastname{Mbouiti}\CDRorcid{0009-0007-1210-6549}}
\addressSameAs{1}{Laboratoire de Chimie des Milieux et des
Mat\'{e}riaux Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences
et Techniques de Masuku (USTM), BP~: 943 Franceville, Gabon}
\addressSameAs{2}{D\'{e}partement de Chimie, Facult\'{e} des
Sciences/Universit\'{e} des Sciences et Techniques de Masuku (USTM),
BP~: 943 Franceville, Gabon}
%\email{lionelberthy@gmail.com}

\author{\firstname{Guy~Raymond} \lastname{Feuya~Tchouya}\CDRorcid{0000-0002-9264-086X}}
\addressSameAs{1}{Laboratoire de Chimie des Milieux et des
Mat\'{e}riaux Inorganiques (LC2MI), URCHI/Universit\'{e} des Sciences
et Techniques de Masuku (USTM), BP~: 943 Franceville, Gabon}
\addressSameAs{2}{D\'{e}partement de Chimie, Facult\'{e} des
Sciences/Universit\'{e} des Sciences et Techniques de Masuku (USTM),
BP~: 943 Franceville, Gabon}
%\email{gfeuya@yahoo.fr}

\shortrunauthors

\keywords{\kwd{Cu\textsuperscript{2+}}\kwd{Removal}\kwd{Activated
carbon}\kwd{Coconut shells}\kwd{Dynamic adsorption}\kwd{Adsorption
\mbox{kinetics}}}

\altkeywords{\kwd{Cu\textsuperscript{2+}}\kwd{\'{E}limination}\kwd{Charbon
actif}\kwd{Coques de noix de coco}\kwd{Adsorption
dynamique}\kwd{Cin\'{e}tique d'adsorption}}

\begin{abstract}
Dynamic adsorption experiments on fixed-bed columns and adsorption
kinetics studies of Cu\textsuperscript{2+} in aqueous media, under various
experimental conditions, were carried out on activated carbon (AC)
prepared using coconut shells from Franceville (Gabon). Results of
dynamic adsorption experiments showed that particle size (\textit{x}) of the
column bed, flow rate (\textit{D}) and bed height (\textit{h}) influence adsorption
capacities at saturation (\textit{Q}\textsubscript{sat}) and removal percentages
(\textit{E}) of Cu\textsuperscript{2+} on the prepared AC. The best \textit{Q}\textsubscript{sat} and
\textit{E} (52.52~mg/g and 55.02\%, respectively) were obtained with 0.01 < \textit{x}
< 0.04~mm, \textit{D} = 2~mL/min, and \textit{h} = 3~cm, with Cu\textsuperscript{2+}
concentration and pH constant at 250~mg/L and 6.5, respectively. The
adsorption kinetic studies indicated that the Thomas model and
pseudo-first-order kinetic model best describe the adsorption
mechanisms of Cu\textsuperscript{2+} in our experimental conditions.\ On the other
hand, in addition to reversible interactions \mbox{(physisorption)}, it
appeared that irreversible reactions (chemisorption) also took place on
the surface of the adsorbent.\ Results obtained from the intraparticle
kinetics model study indicated that intraparticle diffusion is not the
limiting step in Cu\textsuperscript{2+} adsorption and that surface adsorption
plays a{\break} predominant role.
\end{abstract}

\begin{altabstract}
Les exp\'{e}riences d'adsorption dynamique sur colonne \`{a} lit fixe
et des \'{e}tudes de cin\'{e}tique d'adsorption de Cu\textsuperscript{2+} en milieux
aqueux, dans des conditions exp\'{e}rimentales vari\'{e}es, ont
\'{e}t\'{e} r\'{e}alis\'{e}es sur un charbon actif (AC) pr\'{e}par\'{e}
\`{a} partir des coques de noix de coco de Franceville (Gabon).

Dans les exp\'{e}riences d'adsorption dynamique, il ressort que la
granulom\'{e}trie (\textit{x}) des particules composant le lit de la colonne,
le d\'{e}bit (\textit{D}) et la hauteur du lit (\textit{h}) influencent les
capacit\'{e}s d'adsorption \`{a} saturation (\textit{Q}\textsubscript{sat}) et les
pourcentages d'\'{e}limination (\textit{E}) de Cu\textsuperscript{2+} sur le AC
pr\'{e}par\'{e}. Les meilleurs \textit{Q}\textsubscript{sat} et \textit{E} (52.52~mg/g et
55.02~\% respectivement) ont \'{e}t\'{e} obtenus pour 0.01 < \textit{x} <
0.04~mm, \textit{D} = 2~mL/min et \textit{h} = 3~cm, avec une concentration en
Cu\textsuperscript{2+} et un pH constants (250~mg/L et 6.5 respectivement). 

Les \'{e}tudes de la cin\'{e}tique d'adsorption ont indiqu\'{e} que le
mod\`{e}le de Thomas et de cin\'{e}tique de pseudo-premier ordre sont
les mod\`{e}les qui d\'{e}crivent le mieux les m\'{e}canismes
d'adsorption de Cu\textsuperscript{2+} dans nos conditions exp\'{e}rimentales. En
revanche, en plus des interactions r\'{e}versibles (physisorption), des
r\'{e}actions irr\'{e}versibles (chimisorption) ont aussi eu lieu \`{a}
la surface de l'adsorbant. Les r\'{e}sultats du mod\`{e}le de
cin\'{e}tique intraparticulaire ont indiqu\'{e} que la diffusion
intraparticulaire n'est pas l'\'{e}tape limitante dans l'adsorption de
Cu\textsuperscript{2+} et que l'adsorption en surface joue un r\^{o}le
pr\'{e}dominant.
\end{altabstract}

\maketitle

\vspace*{1.7pc}

\twocolumngrid

\end{noXML}

\section{Introduction} \label{sec1}

The development of chemical, metallurgical and mining industries in the
Congo Basin subregion and Gabon in particular, contributes to
environmental pollution by heavy metals (Cu, Fe, Mn,
Cr,\,{\ldots})~\cite{1,2}. The huge exploitation of these materials is
the main cause of the pollution of water resources and soil.

Copper (Cu) for example, in its ionic form, is toxic to species in
aqueous media and can cause major health problems in humans. The
presence of copper(II) ions (Cu$^{2+}$) at high concentrations in
waters, can cause, during repeated exposure or by ingestion, several
health problems: anemia, weight loss, breathing difficulties, kidney
and liver damages that can lead to death~\cite{3}.\ The World Health
Organization (WHO) recommends a limit value for Cu$^{2+}$ of 2~mg/L in
drinking water due to its toxicity~\cite{4}. Thus, the treatment of
industrial and drinking water is important before discharge
into the environment and before distribution in the drinking water
systems, \mbox{respectively}.

In fact, in industrial environments, wastewater treatment techniques
exist. Thus, decantation, flocculation or chemical
coagulation~\cite{5,6}, chemical precipitation~\cite{7} and reverse
osmosis~\cite{8} are among the methods used. These water treatment
methods are very expensive and very effective for the removal of
organic matter but require additional treatments. In addition, they
have limited effectiveness for ionic species, due mainly to the high
water solubility and non-biodegradability of these ionic
species~\cite{9}.

On the other hand, adsorption techniques which use porous solids, such
as activated carbons (AC), appear to be the least expensive and have
fewer disadvantages~\cite{10}.\ These methods have been extensively
studied to compensate the shortcomings of other methods used in the
treatment of industrial or drinking water~\cite{10}.\ According to the
literature, adsorption studies in static (batch) or dynamic conditions
have shown that AC-type adsorbents prepared from agricultural waste or
biomass with a high carbon content~\cite{3,8,11,12,13} can be used to
trap metal ions in aqueous solution.\ In the case of copper(II) ions,
studies under static conditions showed that pH and concentration of the
initial solution, mass of adsorbent and contact time, influenced the
adsorption capacities at saturation of
ACs~\cite{3,14,15,16,17,18,19,20,21}.\ In addition, the kinetic studies
have shown that the pseudo-second-order kinetic model appears most
suitable to describe the adsorption kinetics of copper(II) ions on ACs
in static adsorption mode~\cite{18,20,21,22}. However, very few studies
on the elimination and in particular on the adsorption kinetics of
copper(II) ions, in dynamic conditions on fixed-bed columns, have been
carried out.

Thus, the goal of this work was to valorize waste from coconuts
(shells) of the Haut-Ogoou\'{e} region (Franceville) in Gabon, in the
preparation of AC-type adsorbents, thus to carry out dynamic Cu$^{2+}$
adsorption studies in aqueous media on a fixed-bed column under
different experimental conditions and subsequently, to study the
Cu$^{2+}$ adsorption kinetics on the prepared AC.

\section{Experimental}\label{sec2}
\subsection{Preparation of\, $\mathrm{Cu}^{2+}$ solution} \label{sec2.1}

A solution of 500~mg/L of Cu$^{2+}$ was prepared by dissolving 1.965~g
of copper sulphate pentahydrate salt
($\text{CuSO}_4{\cdot}5\text{H}_2\text{O}$) from LABOSI in a 500~mL
volumetric flask. The mixture was stirred for 20~min and thereafter
water was added to obtain a solution of concentration 250~mg/L. The
latter solution was then used as initial solution for all dynamic
adsorption \mbox{experiments}.

\subsection{Preparation of activated carbon} \label{sec2.2}

The AC preparation method from coconut shells is the same as that used
in a recent study~\cite{23}. The coconut shells were cleaned, washed
several times with distilled water, and then dried at room temperature
for 7 days. The dried solids were then crushed, washed with distilled
water, dried in an oven for 24~hours (h) at 110~{\textdegree}C and kept
in a borosilicate glass crucible. Then, 50~g of the dry material were
soaked in a solution of zinc chloride at 1~M (ZnCl$_2$: dry material
$=$ 1:1~\% by weight) for 72~h. The impregnated solid was dried in the
oven for 24~h at 110~{\textdegree}C, then heated to 600~{\textdegree}C
under air, in a NABERTHEN brand oven, for 1~h and 30 minutes (min) with
a rise in temperature of 5~{\textdegree}C/min. The AC obtained was left
to cool, rinsed with a solution of HCl (0.1~M), and washed with
distilled water until pH of the residual water became neutral. The AC
was then dried for 48~h at 110~{\textdegree}C and sieved using a
TAMISAR sieve (Standard: AFNOR\_NF-X11-501) to obtain different sizes
of AC particles.

\subsection{Characterizations} \label{sec2.3}

Measurements of surface areas and pore volumes were carried out with a
Micromeritics TRISTAR 3000 instrument~\cite{24}. 100~mg of adsorbent
were pretreated for 1~h at 90~{\textdegree}C and 10~h at
350~{\textdegree}C, successively. The nitrogen (N$_2$) isotherm was
acquired at ${-}$196~{\textdegree}C. The specific surface area of the AC
prepared was determined by means of the Brunauer, Emmett and Teller
(BET) theory~\cite{25}. Mesoporous and microporous volumes were
obtained by the $t$-plot method of De Boer and Dubinin-Radushkevich
equations, respectively~\cite{26,27,28}.

The pH at the point of zero charge (pH$_{\mathrm{pzc}}$) of the
adsorbent prepared was evaluated based on the acid--base titration
method~\cite{29} and described in a recent study~\cite{2}.
pH$_{\mathrm{pzc}}$ was determined by the point of intersection between
the experimental curve and the theoretical curve of pHf $=$ f(pHi).

Assessments of surface functional groups of the adsorbent were
performed using the modified Boehm method~\cite{30}. The concentrations
(mmol/g) of acid or basic groups were calculated using the following
equation: 
{\[
n\ (\text{mmol/g})=\frac{C \times (V_{b}-V_{s})\times 1000}{m_{A}}
\]}\unskip
where $C$ is the concentration of NaOH or HCl (mol/L); $V_b$ and $V_s$
are the equivalent volumes of the blank and sample (L) respectively;
$m_A$ is the mass of adsorbent (g) and 1000 is the conversion factor to
mmol.{\vspace*{-.8pc}}

\subsection{Experiments of dynamic adsorption{\hfill\break} on column}
\label{sec2.4}

For dynamic adsorption experiments of Cu$^{2+}$ on the prepared AC, we
used a Pyrex brand glass column of length 55~cm and diameter 1.4~cm.
The protocol and scheme of the experimental set-up were reported in a
recent study~\cite{2}.

During the experiments, various parameters were kept constant:
concentration ($C_0 = 250$~mg/g), pH of the solution (pH $=$ 6.5) and
temperature ($T = 25 \pm 2$~{\textdegree}C). In contrast, particle
sizes, heights of adsorbent bed and flow rates were modified according
to experiments.

The experiments were stopped when the residual concentrations ($C$)
were equal to the concentrations at the inlet of the column ($C/C_0 =
1$). 

The breakthrough curves were established by varying the ratio $C/C_0$
versus time ($t$). Exploitation of curve data ($C/C_{0}=f(t)$) gives an
area ($A$) in minutes obtained by integration according to the trapeze
method~\cite{31,32}:
{\[
A\ (\min)=\sum_{n}\frac{\left(1-\frac{C_{{t_{n}}}}{C_{0}}\right)+
\left(1-\frac{C_{{t_{n+1}}}}{C_{0}}\right)}{2}\times(t_{n+1}-t_{n})
\]}\unskip
where $C_0$ and $C$ are the inlet and outlet concentrations (mg/L) at
times $t_n$ and $t_{n+1}$, respectively.

The Cu$^{2+}$ amounts ($q_{\mathrm{ads}}$) and saturation adsorption
capacities ($Q_{\mathrm{sat}}$) were calculated with the following
relations~\cite{23}:
{\begin{eqnarray*}
& q_{\mathrm{ads}}\;(\text{mg})=D \cdot C_{0} \cdot A\\
& \displaystyle Q_{\mathrm{sat}}\;(\text{mg/g})=\frac{D\cdot C_{0}
\cdot A} {m_{A}}
\end{eqnarray*}}\unskip
with $D$, $C_0$, $A$, and $m_A$ corresponding to the flow rate
(mL/min), the concentration at the inlet of the column (mg/L), the
surface area (min) corresponding to the amount of Cu$^{2+}$ adsorbed,
and the adsorbent mass used (g), respectively.

Removal percentages ($E$) of copper(II) ions on the prepared adsorbent were
determined by the relation \mbox{below}~\cite{23}: 
{\[
E\;(\%)=\frac{A}{t_{\mathrm{sat}}}\times 100
\]}\unskip
where $t_{\mathrm{sat}}$ is the saturation time (min).

\subsection{Adsorption kinetics studies} \label{sec2.5}

In order to describe the dynamic behavior and to evaluate the
adsorption kinetics of copper(II) ions in adsorption experiments on a
fixed-bed column, four mathematical models were applied to the
experimental data: the Thomas model, the pseudo-first-order,
pseudo-second-order, and intraparticle kinetic models.

\subsubsection{Thomas model} \label{sec2.5.1}

The Thomas model~\cite{33}, described by Sarkar et~al.~and in a recent
work~\cite{23,34}, assumes the Langmuir kinetic model is valid with no
mass transfer and axial dispersion during the fixed-bed column
adsorption process. It is expressed as:
{\[
\frac{C}{C_{0}}=\frac{1}{1+\exp\left[\left(\frac{k_{Th}\cdot q_{e}\cdot
m_{A}}{D}\right)-k_{Th}\cdot C_{0}\cdot t\right]}.
\]}\unskip
The linear form is as below~\cite{23,34}:
{\[
\ln\left(\frac{C}{C_{0}}-1\right)=\frac{k_{Th}\cdot q_{e}\cdot m_{A}}
{D}-k_{Th} \cdot C_{0}\cdot t
\]}\unskip
where $k_{Th}$ (mL/(min${\cdot}$mg)) is the Thomas model constant,
$q_e$ (mg/g) is the theoretical adsorption capacity, $m_A$ is the
adsorbent mass (g), $D$ is the flow rate (mL/min), $C_0$ is the initial
solution concentration (mg/L), and $C$ represents residual (or
equilibrium) concentrations at the column outlet (mg/L).

\subsubsection{Pseudo-first-, pseudo-second-order, and{\hfill\break}
intraparticle kinetic models} \label{sec2.5.2}

The pseudo-first-order model is described by the following
relation~\cite{23,35}:
{\[
\frac{\mathrm{d}q_{t}}{\mathrm{d}t}=k(q_{e}-q_{t}).
\]}\unskip
By integration between $t = 0$ ($q_t = 0$) and $t$, the following
linear form is obtained:
{\[
\log(q_{e}-q_{t})=\log (q_{e})-\frac{k_{1}}{2.3}\cdot t
\]}\unskip
where $q_t$ and $q_e$ correspond to maximum adsorption capacities at
time $t$ and equilibrium (mg/g), respectively, and $k_1$ is the
adsorption rate constant of the pseudo-first-order kinetic model
(min$^{-1}$).

The pseudo-second-order model is described by the following
relation~\cite{23,36}: 
{\[
\frac{\mathrm{d}q}{\mathrm{d}t}=k_{2}(q_{e}-{q_{t}})^{2}.
\]}\unskip
After integration between $t = 0$ and $t$, the following linear form is
obtained: 
{\[
\frac{t}{q}=\frac{1}{k_{2}\cdot q_{e}^{2}}+\frac{1}{q_{e}}\cdot t
\]}\unskip
where $q_{t}$ and $q_{e}$ correspond to maximum adsorption capacities
at time $t$ and equilibrium (mg/g), respectively, and $k_{2}$ is the
adsorption rate constant of the pseudo-second-order kinetic model
(g/(mg${\cdot}$min)).

According to Webber and Morris~\cite{35}, the kinetic expression of
intraparticle diffusion is described by:
{\[
q_{t}=k_{d}\cdot t^{1/2}+C_{d}
\]}\unskip
with $k_{d}$ the intraparticle diffusion rate constant
(mg/(g${\cdot}$min$^{1/2}$)) and $C_{d}$ the intercept of the curve.
$C_{d}$~gives an indication of the boundary layer thickness 
and/or adhesion to the surface~\cite{35}.

\section{Results and discussion} \label{sec3}
\subsection{AC chemical and textural properties} \label{sec3.1}

Textural and chemical properties of the prepared adsorbent were
evaluated jointly by $N_{2}$ physisorption, quantification of the
surface functional groups and determination of pH at zero charge point
(pH$_{\mathrm{pzc}}$).

Figure~\ref{fig1}a presents the $N_{2}$ physisorption isotherm.
Textural and chemical properties are listed in Table~\ref{tab1}.
According to IUPAC classification~\cite{37}, the isotherm obtained is
of type~I, indicating a microporous material with a hysteresis loop of
type~H4 which reveals the presence of slit-shaped pores. Results in
Table~\ref{tab1} confirm these observations. In fact, the total pore
volume (0.087~cm$^3$/g) is very close to the microporous volume
(0.082~cm$^3$/g). The average pore size and specific surface area
obtained are 1.68~nm and 208.2~m$^2$/g, respectively.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}$N_2$ adsorption--desorption isotherm (a) and pore
sizes distribution (b) of prepared activated carbon (AC).}
\end{figure}

\begin{table*}[t!] %tab1
\fontsize{9}{11}\selectfont
\tabcolsep4.6pt
\caption{\label{tab1}Structural and chemical characteristics of
prepared activated carbon (AC)}
\begin{tabular}{ccccccccccc}
\thead
\xmorerows{1}{Sample} & 
\morerows{1}{\parbox[t]{.9cm}{\centering$S_{\mathrm{BET}}$ (m$^2$/g)}} & 
\morerows{1}{\parbox[t]{1.1cm}{\centering$V_{\mathrm{micro.}}$ (cm$^3$/g)}} & 
\morerows{1}{\parbox[t]{1.1cm}{\centering$V_{\mathrm{meso.}}$ (cm$^3$/g)}} &
\morerows{1}{\parbox[t]{1.7cm}{\centering Average pore size (nm)}} &
\xmorerows{1}{pH$_{\mathrm{pzc}}$} & 
\morerows{1}{\parbox[t]{2.05cm}{\centering Basic functions (mmol/g)}}\vspace*{2pt} 
& \multicolumn{4}{c}{Acidic functions (mmol/g)}\\
\cline{8-11} 
&&&&&&& Total & Carboxyl & Lactone & Phenol\\
\endthead
AC & 208.2 & 0.082 & 0.003 & 1.68 & 6.3 & 0.12 & 3.39 & 1.45 & 1.08 & 0.86
\botline
\end{tabular}
\tabnote{$S_{\mathrm{BET}}$: specific surface area BET.
$V_{\mathrm{micro}}$: microporous volume. $V_{\mathrm{meso}}$:
mesoporous volume.}
\end{table*}

Based on the results of $N_{2}$ physisorption, the prepared AC shows
predominantly a microporous \mbox{structure}.

Results of the chemical properties study from the surface functional
group quantification by the Boehm titration method~\cite{30} revealed
the presence of basic functional groups and phenolic (--OH), lactonic
(--COO--), and carboxylic acids (--COOH). Basic functional groups are
less abundant than acidic functional groups (Table~\ref{tab1}).\ 
Moreover, carboxylic acid functional groups (1.45~mmol/g) are more
abundant than lactone (1.08~mmol/g) and phenol (0.85~mmol/g) functional
groups.\ Benmahdi \mbox{et~al.}~\cite{38} observed similar results in
their work on the synthesis and characterization of microporous
\mbox{granular} AC using ZnCl$_{2}$ activation. It appears that the
activating agent ZnCl$_{2}$ promotes the formation of acidic functional
groups and microporous structure in the AC preparation.

The evaluated pH$_{\mathrm{pzc}}$ of the
prepared AC is 6.3 (\mbox{Figure}~\ref{fig2}). This acidic value
confirms the results obtained on surface functional groups where the
acidic functional groups are in majority. In addition, it reveals that
the surface of the prepared adsorbent will be positively charged when
pH $<$ pH$_{\mathrm{pzc}}$, and vice versa~\cite{2,38}.

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}pH$_{\mathrm{pzc}}$ determination of prepared
activated carbon (AC) using Boehm titration method~\cite{30}.}
\end{figure}

Therefore, to increase the number of adsorption sites on the surface of
the prepared AC (--COO$^{-}$, --O$^{-}$, etc.) favorable to
Cu$^{2+}$--AC interactions, the pH of the solution must be greater than
pH$_{\mathrm{pzc}}$.

\subsection{Dynamic adsorption experiments} \label{sec3.2}

The adsorption capacities at saturation and removal percentage of
Cu$^{2+}$ were evaluated. Moreover, effects of various parameters on
the bed efficiency were studied, including the size ($x$) of the
particles composing the adsorbent bed of the column, flow~rate~($D$),
and bed height ($h$); and Cu$^{2+}$ adsorption kinetics studies were
performed.

\subsubsection{Effect of particle size, flow rate and bed height}
\label{sec3.2.1}

Two sizes were studied: $0.1 < x < 0.25$~mm and $0.01 < x < 0.04$~mm. 
Figure~\ref{fig3} shows breakthrough curves (Figure~\ref{fig3}a) and
the evolution of Cu$^{2+}$ removal efficiency (Figure~\ref{fig3}b)
\mbox{obtained}.

\begin{figure}
\includegraphics{fig03}
{\vspace*{-.25pc}}
\caption{\label{fig3}Breakthrough curves~(a) and evolution of Cu$^{2+}$
removal efficiency~(b) obtained at 25~{\textdegree}C on the prepared AC
with various particle sizes ($h = 1$~cm, $D = 2$~mL/min, $C_0 =
250$~mg/L and pH $=$ 6.5).}
{\vspace*{-.55pc}}
\end{figure}

The breakthrough curves show a multistep adsorption kinetics of
Cu$^{2+}$ on the prepared AC \mbox{according} to the time intervals
(adsorption zones). The profiles obtained seem to show comparable
adsorption kinetics, diffusion and Cu$^{2+}$--AC interaction energies
on beds of $0.1 < x < 0.25$~mm and $0.01 < x < 0.04$~mm in the first
adsorption domain (5--10~min and 10--30~min respectively) and the third
zone (35--55~min and 65--95~min respectively).\ Indeed, the slopes
obtained in these zones (Figure~\ref{fig3}) are almost
similar~\cite{39}.

However in the second adsorption zone (10--30~min and 30--60~min,
respectively), the adsorption kinetics, the diffusions and the
adsorption sites strengths are different.\ The particle bed of $0.01 <
x < 0.04$~mm shows slower adsorption kinetics and diffusion of the
aqueous phase between grains or in the microporosity with stronger
Cu$^{2+}$--AC interactions on the material surface or in the pores. The
slope for $0.01 < x < 0.04$~mm (Figures~\ref{fig3}a and~\ref{fig3}b)
tends more towards the horizontal compared to that for $0.1 < x <
0.25$~mm in the second adsorption zone~\cite{25}.

In addition, Figures~\ref{fig3}a and~\ref{fig3}b reveal that the bed
with $0.01 < x < 0.04$~mm is more efficient in removing Cu$^{2+}$.
Indeed, the breakthrough ($t_{p}$) and saturation ($t_{\mathrm{sat}}$)
times obtained (Table~\ref{tab2}) on the bed with $0.01 < x < 0.04$~mm
(12 and 84~min respectively) are higher than those obtained on the bed
with $0.1 < x < 0.25$~mm (4 and 50~min respectively). Also, the results
shown in Table~\ref{tab2} indicate that the amounts of Cu$^{2+}$
adsorbed ($q_{\mathrm{ads}}$), the adsorption capacities at saturation
($Q_{\mathrm{sat}}$) and the elimination percentage ($E$) obtained on
the finer particles bed (20~mg; 40.44~mg/g and 48.14\%, respectively)
are higher than those of the larger particles bed (8.99~mg; 12.85~mg/g
and 35.97\% respectively). Based on Weber's work~\cite{35}, this can be
explained by the fact that smaller particles have greater flow
resistance and a shorter diffusion path in pores or between grains,
allowing Cu$^{2+}$ to easily access the surface of AC particles and
providing a larger accessible surface area or adsorption sites.

\begin{table*} %tab2
\caption{\label{tab2}Experimental results of Cu$^{2+}$ removal in
aqueous media on the prepared AC at 25~{\textdegree}C and under
different experimental conditions}
\tabcolsep=4pt
\begin{tabular}{ccccccc}
\thead
Parameters & Experimental conditions & $t_c$ (s) & 
$t_p/t_{\mathrm{sat}}$ (min) & $q_{\mathrm{ads}}$ (mg) &
$Q_{\mathrm{sat}}$ (mg/g) & $E$ (\%)\\
\endthead
\morerows{1}{Particle sizes (mm)} & $0.01 < x < 0.04$ & \morerows{1}{\046.18} & 12/84 & 20.22 & 40.44 & 48.14\\
& $0.1 < x < 0.25$ && 4/50 & \08.99 & 12.85 & 35.97{\vspace*{7pt}}\\
\morerows{2}{Bed heights $h$ (cm)} & 1 & \046.18 & 12/84 & 20.22 & 40.44 & 48.14\\
& 2 & \092.36 & 18/120 & 30.74 & 46.23 & 51.23\\
& 3 & 135.54 & 24/134 & 36.87 & 52.52 & 55.02{\vspace*{7pt}}\\
\morerows{2}{Flow rates $D$ (mL/min)} & 2 & \046.18 & 12/84 & 20.22 & 40.44 & 48.14\\
& 4 & \023.09 & 8/68 & 24.44 & 30.55 & 47.92\\
& 6 & \015.39 & 4/52 & 27.23 & 19.79 & 35.49
\botline
\end{tabular}
\end{table*}

In general, breakthrough curves showed slow adsorption kinetics and
diffusion of the aqueous phase between grains, with stronger
Cu$^{2+}$--adsorbent interactions as the adsorbent bed particle size 
decreases. This allows a better affinity (adsorption)
between Cu$^{2+}$ and the prepared AC. In our experimental conditions,
the bed composed of the lowest particle sizes ($0.01 < x < 0.04$~mm)
appears more efficient in the elimination of Cu$^{2+}$.

In the study of bed height ($h$) influence, three bed heights
(1; 2 and 3~cm) were studied. \mbox{Figure}~\ref{fig4}a shows the
breakthrough curves obtained. Regardless of bed height, the multistep
adsorption process is always visible on the adsorption profiles
obtained. The adsorption kinetics and diffusion of the
Cu$^{2+}$-containing aqueous phase on the surface of the materials or
between the grains are comparable for heights 2 and 3~cm
(Figures~\ref{fig4}a and~\ref{fig4}b). On the other hand, in the third
adsorption zone for $h = 1$~cm (65--95~min), the Cu$^{2+}$ adsorption
kinetics and the diffusion of the aqueous phase are faster compared to
those with $h = 2$ and 3~cm (80--105~min and 95--120~min,
respectively). Indeed, the slope for $h = 1$~cm tends to be much more
vertical compared to that for $h = 2$ and 3~cm (Figure~\ref{fig4}a).

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Breakthrough curves~(a) and evolution of bed
removal efficiency~(b) of Cu$^{2+}$ obtained at 25~{\textdegree}C on
the prepared AC at various bed heights ($D = 2$~mL/min, $C_0 =
250$~mg/L and pH $=$ 6.5).}
\end{figure}

Figures~\ref{fig4}a and~\ref{fig4}b indicate that the bed $h = 3$~cm is
more efficient in removing Cu$^{2+}$. Indeed $t_p$ (24~min) and
$t_{\mathrm{sat}}$ (134~min) obtained are higher than those obtained
with beds $h = 2$ and 1~cm (Table~\ref{tab2}). In addition,
$q_{\mathrm{ads}}$, $Q_{\mathrm{sat}}$ and $E$ obtained with $h = 3$~cm
(36.87~mg; 52.52 and 55.02\%) are higher than those with $h = 2$ and
1~cm as summarized in Table~\ref{tab2}. This could be explained by the
fact that an increase in $h$ leads to an increase in the accessible
surface area of the adsorbent and a greater dispersion of adsorption
sites favorable to Cu$^{2+}$--AC interactions. Similar results were
observed in the work of Hasfalina {et~al.}~\cite{39} and Kavianinia
{et~al.}~\cite{40}. Thus, the higher the adsorbent bed, the more
efficient the bed becomes in removing Cu$^{2+}$ under our operating\break
conditions.

Regarding the influence of flow rate ($D$), 2; 4 and 6~mL/min were flow
rates studied. Based on Figure~\ref{fig5}a, the multistep adsorption
mode disappears when $D$ increases. With 6~mL/min, a single-step
adsorption is visible. It seems that the diffusion of the
Cu$^{2}$-containing aqueous phase is rapid between grains and therefore
limits the Cu$^{2+}$--AC interactions.

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5}Breakthrough curves~(a) and evolution of Cu$^{2+}$
removal efficiency~(b) obtained at 25~{\textdegree}C on the prepared AC
at various flow rates ($h = 1$~cm, $C_{0} = 250$~mg/L and pH $=$ 6.5).}
\end{figure}

The results in Table~\ref{tab2} show that when $D$ increases,
$q_{\mathrm{ads}}$, $Q_{\mathrm{sat}}$ and $E$ decrease. These results
also indicate that the prepared AC is more effective in removing
Cu$^{2+}$ when the applied flow rate is 2~mL/min. Indeed,
$Q_{\mathrm{sat}}$ and $E$ obtained with 2~mL/min (40.44~mg/g and
48.14\%, respectively) are higher than those obtained with 4~mL/min
(30.55~mg/g and 47.92\%, respectively) and 6~mL/min (19.79~mg/g and
35.49\%, respectively). The decrease in $E$ at higher flow rates is due
to the decrease in contact time (Table~\ref{tab2}) between the
Cu$^{2+}$-containing aqueous phase and the adsorbent. This resulted in
low diffusion of adsorbate into the surface or rapid diffusion between
the grains of the adsorbent bed~\cite{41}. Chen {et~al.}~\cite{21}
observed similar results in their studies concerning the effect of
contact time on the removal of copper ions in an aqueous solution on
ACs.

Based on results of the influence of flow rates, it appears that
increasing the flow rate decreases the efficiency of the prepared AC in
Cu$^{2+}$ removal. In our experimental conditions, 2~mL/min is the
optimal flow rate.

\subsubsection{Adsorption kinetics studies} \label{sec3.2.2}

Adsorption kinetics studies were carried out on experiments performed
on the influence of flow rates. Several kinetics models (Thomas,
\mbox{pseudo-first-,}
pseudo-second-order and intraparticle) were applied to
experimental data in this study.

Figure~\ref{fig7} shows the linear plots after application of the
Thomas linear model. According to these profiles, the experimental
points are in agreement with the model. Indeed, the linear regression
coefficients $R^{2}$ of each curve are very close to~1
(Table~\ref{tab3}).

\begin{sidewaystable*}[p!] %tab3
\vspone
\caption{\label{tab3}Parameters of the Thomas, pseudo-first-order,
pseudo-second-order, and intraparticle kinetic models of Cu$^{2+}$
adsorption ions on the prepared AC}
\fontsize{9}{11}\selectfont
\tabcolsep3.6pt
\begin{tabular}{cccccccccccccccccc}
\thead
\multicolumn{2}{c}{Experimental data} && \multicolumn{3}{c}{Thomas
model} && \multicolumn{3}{c}{Pseudo-first-order} &&
\multicolumn{3}{c}{Pseudo-second-order} &&
\multicolumn{3}{c}{Intraparticle}\\
\cline{1-2}\cline{4-6}\cline{8-10}\cline{12-14}\cline{16-18}
\parbox[t]{1.2cm}{\centering$D$ (ml/min)} &
\parbox[t]{1.2cm}{\centering$Q_{e\;\mathrm{exp}}$ (mg/g)} &&
\parbox[t]{1.1cm}{\centering$Q_{e\;\mathrm{cal}}$ (mg/g)} & 
\parbox[t]{2cm}{\centering$k_{Th}\times 10^{-3}$ mL/(mg${\cdot}$min)} &
$R^2$ && \parbox[t]{1.2cm}{\centering$Q_{e\;\mathrm{cal}}$ (mg/g)} &
\parbox[t]{1.5cm}{\centering$k_1 \times 10^{-4}$ (1/min)} & $R^2$ &&
\parbox[t]{1.2cm}{\centering$Q_{e\;\mathrm{cal}}$ (mg/g)} &
\parbox[t]{1.6cm}{\centering$k_2 \times 10^{-6}$ (g/(mg${\cdot}$min))}
& $R^2$ && \parbox[t]{2cm}{\centering$K_d$ (mg/($\text{min}^{1/2}{\cdot}
\text{g}$))} & $C_d$ & $R^2$\\
\endthead
2 & 40.44 && 40.27 & 147 & 0.976 && 43.86 & 359 & 0.989 && 95.24 & \0121 & 0.979 && 6.05 & 8.54 & 0.998\\
4 & 30.55 && 31.76 & 257 & 0.989 && 40.50 & 467 & 0.986 && 78.74 & \0200 & 0.986 && 5.93 & 7.32 & 0.997\\
6 & 19.79 && 15.79 & 346 & 0.989 && 21.76 & 708 & 0.992 && 31.25 & 1364 & 0.992 && 3.67 & 2.83 & 0.992
\botline
\end{tabular}
\end{sidewaystable*}

\begin{figure}
\includegraphics{fig06}
{\vspace*{-.35pc}}
\caption{\label{fig7}Linear plots of the Thomas kinetic model applied
to experimental data of Cu$^{2+}$ removal on the prepared AC at various
flow rates.}
{\vspace*{-.4pc}}
\end{figure}

In addition, the calculated capacities at saturation
($Q_{e,\mathrm{Cal}}$) are close to the experimental capacities
($Q_{e,\mathrm{exp}}$) as summarized in Table~\ref{tab3}. In particular
for the linear plot obtained with 2~mL/min, $Q_{e,\mathrm{exp}}$ and
$Q_{e,\mathrm{cal}}$ are 40.44 and 40.27~mg/g, respectively. Based on
these results and according to the Thomas model, external and internal
diffusion limitations are non-existent in the Cu$^{2+}$ adsorption
experiments performed, the driving force follows the Langmuir isotherm
and the reaction kinetics is reversible. Thus, Cu$^{2+}$ adsorption on
the prepared AC is limited by physical interactions or physisorption,
but it is controlled by mass transfer at the\break interface.

Figure~\ref{fig8} shows the linearization of the pseudo-first-
(Figure~\ref{fig8}a) and pseudo-second-order kinetic models
(Figure~\ref{fig8}b) applied to experimental data for Cu$^{2+}$
adsorption. According to the results of linearization, both kinetic
models are in good agreement with the experimental points. The linear
regression coefficients $R^{2}$ obtained in both cases are all close
to~1 (Table~\ref{tab3}). The results indicate that we have two types of
interactions on the surface of the \mbox{prepared} AC: chemisorption
and physisorption. These results differ from those of Chen
{et~al.}~\cite{21} obtained during their work on kinetic adsorption
studies of copper(II) ions on ACs in an aqueous media by batch
adsorption.

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig07}
{\vspace*{2pt}}
\caption{\label{fig8}Linear plots of pseudo-first-order~(a) and
pseudo-second-order~(b) kinetic models applied to experimental data of
Cu$^{2+}$ removal on the prepared AC at various flow rates.}
{\vspace*{2pt}}
\end{figure}

However, the calculated capacities at saturation ($Q_{e,\mathrm{cal}}$)
according to the pseudo-second-order kinetic model are very high
compared to the experimental values ($Q_{e,\mathrm{exp}}$). In
contrast, $Q_{e,\mathrm{cal}}$ obtained with the pseudo-first-order
kinetic model is close to the values of $Q_{e,\mathrm{exp}}$
(Table~\ref{tab3}).

It therefore seems that the pseudo-first-order kinetic model is the
model that best describes the adsorption kinetics of copper(II) ions on
the prepared AC in our experimental conditions.\ On the other hand, in
addition to reversible \mbox{interactions} (physisorption), it seems that
irreversible reactions (chemisorption) also take place on the surface
of the adsorbent.\ Chemisorption, also known as chemical adsorption,
involves the formation of chemical bonds.\ In other words, it is
mainly based on {interactions} of a covalent nature, i.e.,
involving the formation of a bond between the adsorbate and the
adsorbent, the effects of which are often irreversible~\cite{42}.\ In
our experimental conditions (pH~$=$~6.5), the products of chemical
reactions at the surface of the adsorbent appear to be the CuO copper
oxide~\mbox{\cite{43,44}.}\looseness=1

Figure~\ref{fig9} shows the linear plots obtained after application of
the intraparticle model to the Cu$^{2+}$ adsorption data on the
prepared adsorbent. Results show that regardless of the flow rate
applied, the linear plots do not pass through the origin ($C_d \neq
0$). According to this model~\cite{35,45}, in our experimental
conditions, intraparticle diffusion is involved in the Cu$^{2+}$
adsorption mechanism on the prepared AC. Thus, it is not the limiting
step and the only process controlling Cu$^{2+}$ adsorption.

\begin{figure}
{\vspace*{3pt}}
\includegraphics{fig08}
\caption{\label{fig9}Intraparticle kinetic model applied to
experimental data of Cu$^{2+}$ removal on the prepared AC at various
flow rates.}
\end{figure}

On the other hand, the linear regression coefficients $R^{2}$ obtained
for each plot are close to~1 (\mbox{Table}~\ref{tab2}). Therefore,
intraparticle diffusion plays an important role in the process
(mechanism) of Cu$^{2+}$ adsorption on the prepared AC in our
experimental conditions~\cite{23}. Also, the intercept curve ($C_d$)
informs on the boundary layer thickness. The higher the $C_d$ values,
the greater the contribution to surface grip in the speed-limiting
step~\cite{45}. The results in \mbox{Table}~\ref{tab3} indicate that
the lower the flow rate, the greater the adhesion of Cu$^{2+}$ to the
surface of the prepared adsorbent. However, regardless of the flow rate
applied, the $C_d$ values obtained are very high. This confirms that
intraparticle diffusion is not the limiting step in Cu$^{2+}$
adsorption on the prepared AC and that surface adsorption plays a
predominant role in our experimental conditions.

\section{Conclusion} \label{sec4}

This work aimed to prepare an activated carbon (AC) from coconut shells
collected in Franceville in the Haut-Ogoou\'{e} region (Gabon) with the
activating agent ZnCl$_2$. Then we carried out dynamic adsorption
experiments of copper(II) ions (Cu$^{2+}$) on fixed-bed columns in
aqueous media at different experimental conditions, in order to
determine optimal conditions for Cu$^{2+}$ removal. Studies of
Cu$^{2+}$ adsorption kinetics were also performed.

Textural and chemical characterizations of the prepared AC revealed a
predominantly microporous structure with a microporous volume of
0.082~cm$^3$/g, an average pore size of 1.68~nm, a specific surface
area ($S_{\mathrm{BET}}$) of 208.4~m$^2$/g and a pH at the point of
zero charge (pH$_{\mathrm{pzc}}$) of~6.3. Here, acid functional groups
(carboxylic acid, phenol and lactone) are in majority on the surface of
the prepared AC.

In dynamic adsorption experiments, it appears that the particle size
($x$) of the column bed, flow rate ($D$) and bed height ($h$) influence
adsorption capacities at saturation ($Q_{\mathrm{sat}}$) and Cu$^{2+}$
removal percentages on the prepared AC. The best $Q_{\mathrm{sat}}$ and
$E$ (52.52~mg/g and 55.02\% respectively) were obtained with $0.01 < x
< 0.04$~mm, $D = 2$~mL/min and $h = 3$~cm with Cu$^{2+}$ concentration
and pH constant (250~mg/L and 6.5, respectively).

Kinetic studies indicated that the Thomas and pseudo-first-order
kinetics model best describe the mechanisms of Cu$^{2+}$ adsorption in
our experimental conditions. On the other hand, in addition to
reversible interactions (physisorption), it appeared that irreversible
reactions (chemisorption) also took place on the surface of the
prepared adsorbent. Results from the intraparticle kinetic model
indicate that intraparticle diffusion is not the limiting step in
Cu$^{2+}$ adsorption and that Cu$^{2+}$ surface adsorption on the
prepared AC plays a predominant role. Based on the results, the
prepared AC could be used as adsorbent in depollution of aqueous media
with low concentrations of copper(II) ions.

\section*{Declaration of interests}

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

\section*{Acknowledgments}

The authors are grateful to Professor Samuel Mignard and the CNRS
Research Fellow Alexander Sachse of the Institute of Media and
Materials Chemistry of Poitiers (IC2MP) for their help in the surface
characterization of activated carbon.

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