# Oxidized Renewable Materials for the Removal of Cobalt(II) and Copper(II) from Aqueous Solution Using in Batch and Fixed-Bed Column Adsorption

Authors: Josilene Aparecida Vieira Rodrigues; Luide Rodrigo Martins; Laís Milagres Furtado; Amália Luísa Pedrosa Xavier; Francine Tatiane Rezende de Almeida; Ana Luísa da Silva Lage Moreira; Tânia Márcia Sacramento Melo; Laurent Frédéric Gil; Leandro Vinícius Alves Gurgel
Journal: Advances in Polymer Technology
 (2020)

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## Abstract

Batch and continuous adsorption of Co2+ and Cu2+ from aqueous solutions by oxidized sugarcane bagasse (SBox) and oxidized cellulose (Cox) were investigated. The oxidation reaction of sugarcane bagasse and cellulose was made with a mixture of H3PO4‒NaNO2 to obtain SBox and Cox, with the introduction of high number of carboxylic acid functions, 4.5 and 4.8 mmol/g, respectively. The adsorption kinetics of Co2+ and Cu2+ on SBox and Cox were modeled using two models (pseudo-first-order and pseudo-second-order) and the rate-limiting step controlling the adsorption was evaluated by Boyd and intraparticle diffusion models. The Sips and Langmuir models better fitted the isotherms with values of maximum adsorption capacity Q
max of 0.68 and 0.37 mmol/g for Co2+ and 1.20 and 0.57 mmol/g for Cu2+ adsorption on Cox and SBox, respectively. The reuse of both spent adsorbents was evaluated. Adsorption of Cu2+ and Co2+ on SBox in continuous was evaluated using a 22 factorial design with spatial time and initial metal concentration as independent variables and Q
max and effective use of the bed as responses. The breakthrough curves were very well described by the Bohart–Adams original model and the Q
max values for Co2+ and Cu2+ were 0.22 and 0.55 mmol/g. SBox confirmed to be a promising biomaterial for application on a large scale.


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## Body

## 1. Introduction

The pollution of water resources by toxic metal species is one of the main environmental problems in the world. These inorganic pollutants can cause serious negative effects on the ecosystem, because they have high toxicity to living organisms and are persistent in the environment due to their nonbiodegradability. Metal ions such as Cu2+and Co2+ are essential, but become toxic by excess exposure. Cobalt is an essential element of vitamin B12, which is necessary for the red blood cell production, but becomes toxic [1] when a high amount is ingested by humans, producing an erythropoietic effect, cardiomyopathy, hypothyroidism, and polycythemia. On the other band, the immoderate accumulation of copper in the human body can produce hepatic necrosis and Wilson’s disease, resulting in abnormalities of the nervous system, liver, kidneys, and cornea [2, 3].Nowadays, several processes have been used to remove inorganic pollutants of different sources from water. These processes are mostly conventional processes based on physicochemical treatments (in combination or not) such as coagulation, flocculation, precipitation, and nano- and ultra-filtration [4, 5]. However, these processes have a high cost and/or a low efficiency in removing metal ions at low concentrations and, in addition, some of them can generate a large amount of waste that requires to be further disposed of [6]. Therefore, these problems have increased the number of studies in this area, aimed at the development of original processes with a higher efficiency and lower cost [7]. In this context, adsorption has been highlighted with the development of new adsorbent materials of lower cost and can be efficiently reused; these materials were obtained from designed syntheses using agroindustrial residues as natural materials [8]. During the two last decades, low-cost bioadsorbents such as lignocellulose biomass [9, 10] from agricultural crop waste or chitosan [11–13] from fishing industry waste have been studied as potential materials to be used in the treatment of effluents containing organic pollutants or toxic metal species.The reuse of agroindustrial residues adds a greater economic value and mitigates a series of environmental problems caused by them. Agroindustrial residues mainly consist of lignocellulose biomass (LB), which can be applied in the adsorption of toxic metal species as an alternative to conventional adsorbents as activated carbons and styrene-divinylbenzene ion-exchange resins, since agroindustrial residues are cheap and efficient metal ion accumulators [14]. However, LB can be chemically modified to increase their attraction towards specific pollutants or to be applied to specific processes, enhancing their physicochemical properties, such as adsorption capacity, chemical resistance to acidic and basic media, and selectivity [15, 16].Oxidation process is an interesting strategy to modify chemically LB. In addition, the type of oxidizing mixture used will determine the changes in the chemical groups, physical structure, and crystallinity of the LB, producing oxidized materials with different physicochemical properties [17]. Thus, materials with new interesting properties for many purposes can be obtained [18].Most previous studies using agroindustrial residues for adsorption of toxic metal species are based on batch equilibrium and kinetic studies. Batch adsorption is useful to provide information about the efficiency of an adsorbent and its physicochemical properties; however, batch adsorption may not be the most convenient process to be applied to an industrial scale that requires the treatment of high flow rates. In this way, for a full-scale adsorption process, continuous adsorption is often preferred [19].In this study, sugarcane bagasse (SB) and cellulose (Cel) were chemically modified by oxidation with a mixture of sodium nitrite (NaNO2) and orthophosphoric acid (H3PO4) to obtain oxidized sugarcane bagasse (SBox) and oxidized cellulose (Cox). Adsorption capacity of SBox and Cox for Co2+ and Cu2+ ions from spiked aqueous solutions was investigated. The batch adsorption was carried out as a function of the contact time, solution pH and initial Co2+ or Cu2+ concentration. The reuse of SBox and Cox was also evaluated. The adsorption of Co2+ and Cu2+ in continuous using a fixed-bed column filled with SBox was evaluated with a 22 experimental design.


## 2. Material and Methods

### 2.1. Material

Cellulose grade chromatography paper (3MM, Cat. No. 3030–861) was acquired from Whatman, England. Sugarcane bagasse was collected from the Jatiboca Ethanol and Sugar Plant, Urucânia, Minas Gerais, Brazil. HCl (37 wt.% in water), NaOH, HNO3, H3PO4 (85 wt.%), and CuSO4·5H2O were acquired from Synth (Brazil). CoCl2·6H2O and NaNO2 were acquired from Vetec (Brazil).


### 2.2. Cellulose and Sugarcane Bagasse Preparation

An analytical mill (Model A11, IKA) was used to mill 50 mm2 paper sheets of Cel before oxidation reaction. For oxidation reaction, sugarcane bagasse (SB) was treated using the methodology described by Ramos et al. [20]. The SB fraction utilized in this study was that retained on the 0.150 mm (100 mesh) sieve.


### 2.3. Oxidation of Sugarcane Bagasse and Cellulose

The oxidation reaction of SB and Cel was performed using the procedure previously described by Martins et al. [21]. In a typical methodology, 5.000 g of Cel or SB was weighed into a 250 mL Erlenmeyer flask and then 80.0 mL of H3PO4 (85% wt.%) was added to the flask under agitation at 25°C. Afterward, it was added in this flask 4.000 g of NaNO2 under vigorous agitation for about 10 min and the mixture was allowed to stand for 5 h with the flask opened. Then, a vacuum filtration on a sintered glass funnel (porosity 2) was used to separate the reaction mixture from the oxidized material (SBox or Cox), which was washed with distilled water until pH reached neutrality (pH ~ 7). The drying of the oxidized material was performed in an oven at 65°C for 4 h. The oxidized material was kept in a desiccator prior to use.


### 2.4. FTIR Spectroscopy

To prepare the FTIR KBr pellets of 13 mm, 100 mg of KBr (spectroscopy grade) and 1 mg of sample (dried powder) were mixed and pressed using a hydraulic press (Model 181-1110, Pike Technologies, Canada) at 6 ton for 30 s. The spectrum was obtained from an FTIR spectrometer (Model MB3000, ABB Bomen, Canada) from 500 to 4000 cm−1 with a resolution of 4 cm−1 and 32 scans per sample.


### 2.5. Adsorption Experiments

The adsorption of Cu2+ and Co2+ on SBox or Cox was studied as a function of the contact time, solution pH, and initial Cu2+ or Co2+ concentration. The following typical methodology was used in all adsorption experiments, which were carried out in duplicate. Samples of 20 mg of SBox or Cox and 100.0 mL of aqueous Cu2+ or Co2+ solution were added to 250 mL Erlenmeyer flasks. Then, drops of aqueous 0.1 mol/L NaOH or HCl solutions were added to adjust the pH. The flasks were placed in an orbital incubator shaker (Model TE-424, Tecnal, Brazil) at 150 rpm and 25°C. At the end of the adsorption experiments, a single filtration (filter paper JP-41) was carried out to separate the liquid and solid fractions. A flame atomic absorption spectrophotometer (FAAS) (Model SpectrAA 50B, Varian) was used to determine the concentration of Cu2+ or Co2+ in the liquid fraction (λ
Cu = 324.8 nm [22], λ
Co = 240.7 nm [22]). The adsorption capacity, q, was calculated utilizing Equation (1):(1)
q
/
mmol
/
g
=
C
i
−
C
V
w
,whereq
mmol
/
g is the amount of Cu2+ or Co2+ adsorbed per unit weight of SBox or Cox at time t or equilibrium, V
L is the volume of Cu2+ or Co2+ solution, C
i
mmol
/
L is the initial Cu2+ or Co2+ concentration, C
mmol
/
L is the Cu2+ or Co2+ concentration at time t or equilibrium and w
g is the weight of SBox or Cox.


#### 2.5.1. Adsorption of Cu2+ and Co2+ on SBox or Cox as a Function of Solution pH

The following conditions were employed to evaluate the effect of solution pH on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: pH from 2.0 to 5.5, contact time of 4 h and initial Cu2+ or Co2+ concentration of 50 mg/L.


#### 2.5.2. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Contact Time

The following conditions were employed to evaluate the effect of contact time on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: time interval from 5 to 600 min, pH 5.5 and initial Cu2+ or Co2+ concentration of 50 mg/L.


#### 2.5.3. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Cu2+ or Co2+ Concentration

The adsorption isotherms were obtained to evaluate the influence of initial Cu2+ or Co2+ concentration on metal ion uptake by SBox and Cox by varying the initial Cu2+ or Co2+ concentration. The following conditions were employed to obtain the adsorption isotherms: initial Cu2+ or Co2+ concentration range from 8 to 100 mg/L, equilibrium time of 3 h and pH 5.5.


### 2.6. Desorption and Reuse of SBox and Cox

Desorption of SBox and Cox was made to evaluate the possible reuse of these adsorbent materials. The loading of SBox or Cox (50 mg) with Cu2+ or Co2+ was performed at pH 5.5 using 100.0 mL of 125 mg/L of Cu2+ or Co2+ solution and a time of 3 h. At the end of adsorption experiments, a single filtration was made to recover the loaded adsorbent, which was washed with distilled water to eliminate any nonadsorbed Cu2+ or Co2+. The loaded adsorbent was dried at 80°C in an oven for 1 h. Then, 20 mg of Cox or SBox loaded with Cu2+ or Co2+ was weighed into Erlenmeyer flasks (125 mL) and then 20.0 mL of aqueous 0.5 mol/L HNO3 solution was added. Desorption experiments were performed in an orbital incubator shaker (Model TE‒424, Tecnal, Brazil) at 150 rpm and 25°C for time intervals of 10 and 15 min for SBox and Cox, respectively. The concentration of Cu2+ or Co2+ in the desorption solution was determined by FAAS (Section 2.5). The desorption efficiency, E
des, was calculated utilizing Equation (2), [17]:(2)
E
des
/
%
=
C
e
V
Q
T
,
max
w
ads
′
×
100
,whereC
e
mg
/
L is the equilibrium Cu2+ or Co2+ concentration in aqueous HNO3 solution, V
L is the volume of the aqueous HNO3 solution, Q
T
,
max
mg
/
g is the maximum adsorption capacity obtained from loading adsorbent with Cu2+ or Co2+ before the desorption experiment and w
ads
′
g is the weight of SBox or Cox adsorbent contained in SBox or Cox loaded with Cu2+ or Co2+
w
ads
,
M
2
+ [22]. The calculation of w
ads
′ is given in Equation (3):(3)
w
ads
′
/
g
=
w
ads
,
M
2
+
Q
T
,
max
/
1000
+
1
.All reuse studies were made using the following procedure: 20 mg of SBox or Cox recovered from Cu2+ or Co2+ desorption was added to Erlenmeyer flasks (250 mL) with 100.0 mL of an aqueous 50 mg/L Cu2+ or Co2+ solution (pH 5.5). The Erlenmeyer flasks were placed in an orbital incubator shaker (Model TE‒424, Tecnal) at 150 rpm and 25°C for 3 h. Then, a single filtration (filter paper JP-41) was used to separate the liquid and solid fractions and the equilibrium concentration of Cu2+ or Co2+ in the liquid fraction was determined by FAAS (Section 2.5). The re-adsorption efficiency, E
re
-
ads, for one adsorption/desorption/re-adsorption cycle was calculated utilizing Equation (4).(4)
E
re
-
ads
/
%
=
Q
re
-
ads
,
max
Q
T
,
max
×
100
,whereQ
re
-
ads
,
max
mg
/
g is the maximum re-adsorption capacity obtained after one adsorption/desorption/adsorption cycle [22]. Q
re
-
ads
,
max is calculated utilizing Equation (5).(5)
Q
re
-
ads
,
max
/
mg
/
g
=
w
ads
,
M
2
+
−
w
a
d
s
′
1
−
E
des
/
100
−
C
i
−
C
e
V
w
ads
′
.


### 2.7. Fixed-Bed Column Adsorption Experiments

The adsorption experiments in continuous were carried out in a jacket glass column (10.0 cm height × 1.0 cm inner diameter) filled with 0.400 g of SBox adsorbent (dry-weight basis). The SBox adsorbent was packed between two layers containing glass beads (10 mm of diameter) and glass wool to give a uniform upflow of the Cu2+ or Co2+ solution into the column. For all experiments, the bed height was fixed at 3.80 cm. The inlet upflow rate was controlled by a peristaltic pump (Model BP600/2, Milan, Brazil). The temperature of the inlet metal solution and the column was kept at 25 ± 1°C by a thermostatic bath with forced water circulation (Model MA470, Marconi, Brazil). The Cu2+ or Co2+ solutions were prepared using a buffer of pH 5.5 (CH3COOH/CH3COONa). Effluent samples were sampled at the top of the column at predetermined time intervals to obtain the breakthrough curve. Metal concentration in the effluent samples was determined by FAAS (Section 2.5). To ensure that metal concentration was in the range of the calibration curve, appropriate dilutions were made. The saturation time and breakthrough point were fixed at 95% and 5% of influent metal concentration, respectively [23].


#### 2.7.1. Design of Experiments

The continuous monocomponent adsorption of Cu2+ and Co2+ on SBox was optimized employing a 22 experimental design to evaluate the influence of the initial Cu2+ or Co2+ concentration (C
0, mmol/L) and spatial time (τ, min) on the responses. The value of τ was calculated using the empty volume of the column (mL) and the flow rate (mL/min). The dependent variables (responses) evaluated were the maximum adsorption capacity (Q
max, mmol/g) of the bed and the effective use of the bed (H, cm).Table1 presents the independent variables (IVs) and their levels used in the continuous adsorption of Cu2+ and Co2+ on SBox adsorbent. They were defined considering the batch adsorption studies and the lowest flow rate (1.4 mL/min) of the pump. Then, 1 min was defined as the center point of spatial time; and the center point of initial Cu2+ and Co2+ concentration was calculated based on the values of C
e obtained from the batch adsorption isotherms.Table 1
Independent variables evaluated in the 22 experimental design and their levels for Cu2+ and Co2+ adsorption in a fixed-bed column using SBox as adsorbent.
Independent variable
Level
−1
0
+1
C
0
mmol
Cu
2
+
/
L
0.47
0.86
1.26
C
0
mmol
Co
2
+
/
L
0.17
0.42
0.68
τ
min
0.70
1.05
1.40Statistica 10.0 (StatSoft, Inc.) routines were used to evaluate the obtained results for analyses of variance (ANOVA), regression coefficients and graphical analysis. To analyze the experimental error, pure error was used and a confidence level equal to 95% was used in the statistical analyses. AnIV was statistically significant when its p-value <0.05.


### 2.8. Modeling the Experimental Data

#### 2.8.1. Batch Kinetic Data

Pseudo-first-order (PFO) and pseudo-second-order (PSO) models were used to investigate the adsorption kinetics of Cu2+ and Co2+ on SBox and Cox.The PFO kinetic model of Lagergren [24] is expressed by Equation (6).(6)
q
t
/
mmol
/
g
=
q
e
1
−
exp
−
k
1
t
,wherek
1
min
−
1 is the pseudo-first-order rate constant.The PSO kinetic model of Ho and McKay [25] is expressed by Equation (7).(7)
q
t
/
mmol
/
g
=
k
2
q
e
2
t
1
+
k
2
q
e
t
,wherek
2
g
/
mmol
min is the pseudo-second-order rate constant.In addition, to elucidate the adsorption mechanism of Cu2+ and Co2+ on Cox and SBox, two models were used: intraparticle diffusion (IPD) and Boyd.The IPD model of Weber and Morris [26] is expressed by Equation (8).(8)
q
t
/
mmol
/
g
=
k
i
t
1
/
2
+
C
,whereC
mmol
/
g is the intercept and k
i
mmol
/
g
min
1
/
2 is the intraparticle diffusion rate constant. The constant C may be correlated to the thickness of the boundary layer.The model of Boyd et al. [27] is expressed by Equation (9):(9)
f
=
1
−
6
π
2
∑
n
=
1
∞
1
n
2
exp
−
n
2
B
t
,wheref
f
=
q
t
/
q
e is the fractional surface coverage as a function of time and B
t is a function of f. Reichenberg [28] provided solutions for Equation (9) using Fourier transform, which are expressed by Equations (10) and (11), as follows:(10)
B
t
=
−
0.4977
−
ln
1
−
f
,
(11)
B
t
=
π
−
π
−
π
2
f
3
2
.Forf
>
0.85, Equation (10) was utilized, whereas for f
<
0.85, Equation (11) was utilized to obtain the values of B
t.The effective diffusion coefficient,D
i, was determined by Equation (12), as follows:(12)
D
i
/
m
2
/
min
=
B
r
2
π
2
,wherer is the radius of the Cox (r = 0.250 × 10−3 m) or SBox (r = 0.150 × 10−3 m) particles, assuming a spherical shape.


#### 2.8.2. Batch Equilibrium Data

Adsorption isotherms were fitted by the Freundlich, Langmuir, and Sips isotherm models.The Langmuir [29] isotherm model is expressed by Equation (13).(13)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
+
b
C
e
,whereQ
max
mmol
/
g is the maximum adsorption capacity of SBox or Cox for a metal ion and b
L
/
mmol is the Langmuir binding constant.The Freundlich [30] isotherm model is expressed by Equation (14).(14)
q
e
/
mmol
/
g
=
K
F
C
e
1
/
n
,whereK
F
mmol
/
g
L
/
mmol
1
/
n and n are the Freundlich model constants. The parameter n is associated to the adsorption intensity.The Langmuir–Freundlich isotherm model, developed by Sips [31], is a hybrid model of the Freundlich and Langmuir isotherm models, which is expressed by Equation (15).(15)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
/
n
1
+
b
C
e
1
/
n
,wheren is a parameter describing the heterogeneity of the system.


#### 2.8.3. Analysis of the Breakthrough Curve

The area under the breakthrough curves gives the amount of Cu2+ or Co2+ adsorbed in the bed [32]. Then, the value of Q
max of the bed can be obtained from Equation (16), until the saturation time t
s is reached, as follows:(16)
Q
max
/
mmol
/
g
=
C
0
V
̇
1000
w
SBox
∫
0
t
1
−
C
t
C
0
d
t
,whereV
̇ is the inlet flow rate (mL/min), t is the time, C
0 and C
t are the influent and effluent Cu2+ or Co2+ concentrations (mmol/L) and w
SBox is the weight of SBox (g).The value ofH is defined as the height of the bed that was effectively utilized in the continuous adsorption process [33]. The value of H was obtained from Equation (17), as follows:(17)
H
/
cm
=
q
M
2
+
,
t
b
q
M
2
+
,
t
s
Z
,whereZ is the bed height (cm), q
M
2
+
,
t
b is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the breakthrough time t
b (mmol) and q
M
2
+
,
t
s is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the saturation time t
s (mmol). The values of q
M
2
+
,
t
b and q
M
2
+
,
t
s were determined by the integration of the area under the breakthrough curves until t
b and t
s, respectively.(i) Modeling the Breakthrough Curves.The development of mathematical models to predict the breakthrough curve, the mechanism involved in the process and even the evaluation of the effect of different variables on adsorption process is an important demand. However, this is a difficult task for such systems since the concentration profiles in both solid and liquid phases vary with both Z and t [32]. Thus, analytical models based on modeling the experimental data by means of nonlinear or linear regression analyses with physical meaning are available [34–38]. The original model of Bohart and Adams [38] is successfully employed when the adsorption isotherm is favorable. This model supposes that the rate of adsorption is proportional to the remaining adsorption capacity of the adsorbent and the concentration of the solute, neglecting axial dispersion. Equations (18)–(20) describe the relationship between C
t
/
C
0 and t for this model.(18)
C
t
C
0
=
exp
α
exp
α
+
exp
β
−
1
,(19)
α
=
k
B
-
A
C
0
t
−
Z
ν
,(20)
β
=
k
B
-
A
ρ
b
Q
max
Z
ν
ε
,whereν (cm/min) is the interstitial velocity, C (mmol/L) is the liquid phase Cu2+ or Co2+ concentration initially C
0 and at time t
C
t, Z (cm) is the column height, t (min) is the time, ε is the column void fraction, ρ
b (g/mL) is the bulk density and k
B
-
A (L/mmol min) is the Bohart–Adams kinetic rate constant.The relation between the adsorbent densityρ
p and bulk density ρ
b was used to determine the porosity of the bed, as given in Equation (21).(21)
ε
=
1
−
ρ
b
ρ
p
.


#### 2.8.4. Calculation of Variation in Standard Free Energy of Adsorption

The variation in standard free energy of adsorptionΔ
ads
G
° for batch adsorption was determined by Equation (22) [39].(22)
Δ
ads
G
°
/
kJ/mol
=
−
R
T
ln
K
a
,whereT
K is the absolute temperature, K
a is the thermodynamic equilibrium constant (dimensionless) and R is the gas constant (8.3144 J/K mol).Liu [39] suggested that b (Langmuir constant) can be used to calculate the value of K
a, as given in Equation (23).(23)
K
a
=
b
γ
e
1
mol/L
,whereγ
e is the activity coefficient (dimensionless) at equilibrium at 25°C.The value ofγ
e can be calculated utilizing the extended Debye Hückel law (Equation (24)), which is applied to ionic strengths up to 0.1 mol/L.(24)
log
γ
e
=
−
0.509
z
2
I
e
1
+
α
I
e
/
305
,whereI
e (mol/L) is the ionic strength, z is the charge of the Cu2+ or Co2+ and α (pm) is the hydrated ion size of Cu2+ or Co2+ (600 pm) [40]. The values of I
e were calculated as described by Ramos et al. [20].


#### 2.8.5. Regression Analysis and Error Evaluation

(i) Batch Adsorption Data. The experimental batch equilibrium and kinetic data were modeled with the PFO and PSO and Freundlich, Langmuir, and Sips models by nonlinear regression (NLR) analysis using Microcal OriginPro®2015. The modeling of the kinetic data with IPD and Boyd models was made by linear regression (LR) analysis of the experimental data. The software was set to use the weight method named “statistical” and the Levenberg–Marquardt algorithm. The reduced chi‒square χ
red
2 was employed to determine which model best described the experimental adsorption data [41].(ii) Continuous Adsorption Data. The breakthrough curves obtained were fitted using the set of Equations (18)–(20). The algorithm genetic function (ga) of the MATLAB®2010a software (Mathworks Inc.) was used for adjusting the parameters of the Bohart-Adams model to the continuous experimental data by minimization of the objective function. The objective function used was the root-mean-square error (RMSE) [18], as given in Equation (25).(25)
RMSE
=
∑
i
=
1
n
y
i
−
y
̂
i
2
n
,wheren is the number of experimental points and y
i is the value of experimental point i
,
y
̂
i is the predicted value by the model for the experimental point i.


## 2.1. Material

Cellulose grade chromatography paper (3MM, Cat. No. 3030–861) was acquired from Whatman, England. Sugarcane bagasse was collected from the Jatiboca Ethanol and Sugar Plant, Urucânia, Minas Gerais, Brazil. HCl (37 wt.% in water), NaOH, HNO3, H3PO4 (85 wt.%), and CuSO4·5H2O were acquired from Synth (Brazil). CoCl2·6H2O and NaNO2 were acquired from Vetec (Brazil).


## 2.2. Cellulose and Sugarcane Bagasse Preparation

An analytical mill (Model A11, IKA) was used to mill 50 mm2 paper sheets of Cel before oxidation reaction. For oxidation reaction, sugarcane bagasse (SB) was treated using the methodology described by Ramos et al. [20]. The SB fraction utilized in this study was that retained on the 0.150 mm (100 mesh) sieve.


## 2.3. Oxidation of Sugarcane Bagasse and Cellulose

The oxidation reaction of SB and Cel was performed using the procedure previously described by Martins et al. [21]. In a typical methodology, 5.000 g of Cel or SB was weighed into a 250 mL Erlenmeyer flask and then 80.0 mL of H3PO4 (85% wt.%) was added to the flask under agitation at 25°C. Afterward, it was added in this flask 4.000 g of NaNO2 under vigorous agitation for about 10 min and the mixture was allowed to stand for 5 h with the flask opened. Then, a vacuum filtration on a sintered glass funnel (porosity 2) was used to separate the reaction mixture from the oxidized material (SBox or Cox), which was washed with distilled water until pH reached neutrality (pH ~ 7). The drying of the oxidized material was performed in an oven at 65°C for 4 h. The oxidized material was kept in a desiccator prior to use.


## 2.4. FTIR Spectroscopy

To prepare the FTIR KBr pellets of 13 mm, 100 mg of KBr (spectroscopy grade) and 1 mg of sample (dried powder) were mixed and pressed using a hydraulic press (Model 181-1110, Pike Technologies, Canada) at 6 ton for 30 s. The spectrum was obtained from an FTIR spectrometer (Model MB3000, ABB Bomen, Canada) from 500 to 4000 cm−1 with a resolution of 4 cm−1 and 32 scans per sample.


## 2.5. Adsorption Experiments

The adsorption of Cu2+ and Co2+ on SBox or Cox was studied as a function of the contact time, solution pH, and initial Cu2+ or Co2+ concentration. The following typical methodology was used in all adsorption experiments, which were carried out in duplicate. Samples of 20 mg of SBox or Cox and 100.0 mL of aqueous Cu2+ or Co2+ solution were added to 250 mL Erlenmeyer flasks. Then, drops of aqueous 0.1 mol/L NaOH or HCl solutions were added to adjust the pH. The flasks were placed in an orbital incubator shaker (Model TE-424, Tecnal, Brazil) at 150 rpm and 25°C. At the end of the adsorption experiments, a single filtration (filter paper JP-41) was carried out to separate the liquid and solid fractions. A flame atomic absorption spectrophotometer (FAAS) (Model SpectrAA 50B, Varian) was used to determine the concentration of Cu2+ or Co2+ in the liquid fraction (λ
Cu = 324.8 nm [22], λ
Co = 240.7 nm [22]). The adsorption capacity, q, was calculated utilizing Equation (1):(1)
q
/
mmol
/
g
=
C
i
−
C
V
w
,whereq
mmol
/
g is the amount of Cu2+ or Co2+ adsorbed per unit weight of SBox or Cox at time t or equilibrium, V
L is the volume of Cu2+ or Co2+ solution, C
i
mmol
/
L is the initial Cu2+ or Co2+ concentration, C
mmol
/
L is the Cu2+ or Co2+ concentration at time t or equilibrium and w
g is the weight of SBox or Cox.


### 2.5.1. Adsorption of Cu2+ and Co2+ on SBox or Cox as a Function of Solution pH

The following conditions were employed to evaluate the effect of solution pH on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: pH from 2.0 to 5.5, contact time of 4 h and initial Cu2+ or Co2+ concentration of 50 mg/L.


### 2.5.2. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Contact Time

The following conditions were employed to evaluate the effect of contact time on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: time interval from 5 to 600 min, pH 5.5 and initial Cu2+ or Co2+ concentration of 50 mg/L.


### 2.5.3. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Cu2+ or Co2+ Concentration

The adsorption isotherms were obtained to evaluate the influence of initial Cu2+ or Co2+ concentration on metal ion uptake by SBox and Cox by varying the initial Cu2+ or Co2+ concentration. The following conditions were employed to obtain the adsorption isotherms: initial Cu2+ or Co2+ concentration range from 8 to 100 mg/L, equilibrium time of 3 h and pH 5.5.


## 2.5.1. Adsorption of Cu2+ and Co2+ on SBox or Cox as a Function of Solution pH

The following conditions were employed to evaluate the effect of solution pH on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: pH from 2.0 to 5.5, contact time of 4 h and initial Cu2+ or Co2+ concentration of 50 mg/L.


## 2.5.2. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Contact Time

The following conditions were employed to evaluate the effect of contact time on the adsorption capacity of Cu2+ and Co2+ on SBox or Cox: time interval from 5 to 600 min, pH 5.5 and initial Cu2+ or Co2+ concentration of 50 mg/L.


## 2.5.3. Adsorption of Cu2+ or Co2+ on SBox or Cox as a Function of Cu2+ or Co2+ Concentration

The adsorption isotherms were obtained to evaluate the influence of initial Cu2+ or Co2+ concentration on metal ion uptake by SBox and Cox by varying the initial Cu2+ or Co2+ concentration. The following conditions were employed to obtain the adsorption isotherms: initial Cu2+ or Co2+ concentration range from 8 to 100 mg/L, equilibrium time of 3 h and pH 5.5.


## 2.6. Desorption and Reuse of SBox and Cox

Desorption of SBox and Cox was made to evaluate the possible reuse of these adsorbent materials. The loading of SBox or Cox (50 mg) with Cu2+ or Co2+ was performed at pH 5.5 using 100.0 mL of 125 mg/L of Cu2+ or Co2+ solution and a time of 3 h. At the end of adsorption experiments, a single filtration was made to recover the loaded adsorbent, which was washed with distilled water to eliminate any nonadsorbed Cu2+ or Co2+. The loaded adsorbent was dried at 80°C in an oven for 1 h. Then, 20 mg of Cox or SBox loaded with Cu2+ or Co2+ was weighed into Erlenmeyer flasks (125 mL) and then 20.0 mL of aqueous 0.5 mol/L HNO3 solution was added. Desorption experiments were performed in an orbital incubator shaker (Model TE‒424, Tecnal, Brazil) at 150 rpm and 25°C for time intervals of 10 and 15 min for SBox and Cox, respectively. The concentration of Cu2+ or Co2+ in the desorption solution was determined by FAAS (Section 2.5). The desorption efficiency, E
des, was calculated utilizing Equation (2), [17]:(2)
E
des
/
%
=
C
e
V
Q
T
,
max
w
ads
′
×
100
,whereC
e
mg
/
L is the equilibrium Cu2+ or Co2+ concentration in aqueous HNO3 solution, V
L is the volume of the aqueous HNO3 solution, Q
T
,
max
mg
/
g is the maximum adsorption capacity obtained from loading adsorbent with Cu2+ or Co2+ before the desorption experiment and w
ads
′
g is the weight of SBox or Cox adsorbent contained in SBox or Cox loaded with Cu2+ or Co2+
w
ads
,
M
2
+ [22]. The calculation of w
ads
′ is given in Equation (3):(3)
w
ads
′
/
g
=
w
ads
,
M
2
+
Q
T
,
max
/
1000
+
1
.All reuse studies were made using the following procedure: 20 mg of SBox or Cox recovered from Cu2+ or Co2+ desorption was added to Erlenmeyer flasks (250 mL) with 100.0 mL of an aqueous 50 mg/L Cu2+ or Co2+ solution (pH 5.5). The Erlenmeyer flasks were placed in an orbital incubator shaker (Model TE‒424, Tecnal) at 150 rpm and 25°C for 3 h. Then, a single filtration (filter paper JP-41) was used to separate the liquid and solid fractions and the equilibrium concentration of Cu2+ or Co2+ in the liquid fraction was determined by FAAS (Section 2.5). The re-adsorption efficiency, E
re
-
ads, for one adsorption/desorption/re-adsorption cycle was calculated utilizing Equation (4).(4)
E
re
-
ads
/
%
=
Q
re
-
ads
,
max
Q
T
,
max
×
100
,whereQ
re
-
ads
,
max
mg
/
g is the maximum re-adsorption capacity obtained after one adsorption/desorption/adsorption cycle [22]. Q
re
-
ads
,
max is calculated utilizing Equation (5).(5)
Q
re
-
ads
,
max
/
mg
/
g
=
w
ads
,
M
2
+
−
w
a
d
s
′
1
−
E
des
/
100
−
C
i
−
C
e
V
w
ads
′
.


## 2.7. Fixed-Bed Column Adsorption Experiments

The adsorption experiments in continuous were carried out in a jacket glass column (10.0 cm height × 1.0 cm inner diameter) filled with 0.400 g of SBox adsorbent (dry-weight basis). The SBox adsorbent was packed between two layers containing glass beads (10 mm of diameter) and glass wool to give a uniform upflow of the Cu2+ or Co2+ solution into the column. For all experiments, the bed height was fixed at 3.80 cm. The inlet upflow rate was controlled by a peristaltic pump (Model BP600/2, Milan, Brazil). The temperature of the inlet metal solution and the column was kept at 25 ± 1°C by a thermostatic bath with forced water circulation (Model MA470, Marconi, Brazil). The Cu2+ or Co2+ solutions were prepared using a buffer of pH 5.5 (CH3COOH/CH3COONa). Effluent samples were sampled at the top of the column at predetermined time intervals to obtain the breakthrough curve. Metal concentration in the effluent samples was determined by FAAS (Section 2.5). To ensure that metal concentration was in the range of the calibration curve, appropriate dilutions were made. The saturation time and breakthrough point were fixed at 95% and 5% of influent metal concentration, respectively [23].


### 2.7.1. Design of Experiments

The continuous monocomponent adsorption of Cu2+ and Co2+ on SBox was optimized employing a 22 experimental design to evaluate the influence of the initial Cu2+ or Co2+ concentration (C
0, mmol/L) and spatial time (τ, min) on the responses. The value of τ was calculated using the empty volume of the column (mL) and the flow rate (mL/min). The dependent variables (responses) evaluated were the maximum adsorption capacity (Q
max, mmol/g) of the bed and the effective use of the bed (H, cm).Table1 presents the independent variables (IVs) and their levels used in the continuous adsorption of Cu2+ and Co2+ on SBox adsorbent. They were defined considering the batch adsorption studies and the lowest flow rate (1.4 mL/min) of the pump. Then, 1 min was defined as the center point of spatial time; and the center point of initial Cu2+ and Co2+ concentration was calculated based on the values of C
e obtained from the batch adsorption isotherms.Table 1
Independent variables evaluated in the 22 experimental design and their levels for Cu2+ and Co2+ adsorption in a fixed-bed column using SBox as adsorbent.
Independent variable
Level
−1
0
+1
C
0
mmol
Cu
2
+
/
L
0.47
0.86
1.26
C
0
mmol
Co
2
+
/
L
0.17
0.42
0.68
τ
min
0.70
1.05
1.40Statistica 10.0 (StatSoft, Inc.) routines were used to evaluate the obtained results for analyses of variance (ANOVA), regression coefficients and graphical analysis. To analyze the experimental error, pure error was used and a confidence level equal to 95% was used in the statistical analyses. AnIV was statistically significant when its p-value <0.05.


## 2.7.1. Design of Experiments

The continuous monocomponent adsorption of Cu2+ and Co2+ on SBox was optimized employing a 22 experimental design to evaluate the influence of the initial Cu2+ or Co2+ concentration (C
0, mmol/L) and spatial time (τ, min) on the responses. The value of τ was calculated using the empty volume of the column (mL) and the flow rate (mL/min). The dependent variables (responses) evaluated were the maximum adsorption capacity (Q
max, mmol/g) of the bed and the effective use of the bed (H, cm).Table1 presents the independent variables (IVs) and their levels used in the continuous adsorption of Cu2+ and Co2+ on SBox adsorbent. They were defined considering the batch adsorption studies and the lowest flow rate (1.4 mL/min) of the pump. Then, 1 min was defined as the center point of spatial time; and the center point of initial Cu2+ and Co2+ concentration was calculated based on the values of C
e obtained from the batch adsorption isotherms.Table 1
Independent variables evaluated in the 22 experimental design and their levels for Cu2+ and Co2+ adsorption in a fixed-bed column using SBox as adsorbent.
Independent variable
Level
−1
0
+1
C
0
mmol
Cu
2
+
/
L
0.47
0.86
1.26
C
0
mmol
Co
2
+
/
L
0.17
0.42
0.68
τ
min
0.70
1.05
1.40Statistica 10.0 (StatSoft, Inc.) routines were used to evaluate the obtained results for analyses of variance (ANOVA), regression coefficients and graphical analysis. To analyze the experimental error, pure error was used and a confidence level equal to 95% was used in the statistical analyses. AnIV was statistically significant when its p-value <0.05.


## 2.8. Modeling the Experimental Data

### 2.8.1. Batch Kinetic Data

Pseudo-first-order (PFO) and pseudo-second-order (PSO) models were used to investigate the adsorption kinetics of Cu2+ and Co2+ on SBox and Cox.The PFO kinetic model of Lagergren [24] is expressed by Equation (6).(6)
q
t
/
mmol
/
g
=
q
e
1
−
exp
−
k
1
t
,wherek
1
min
−
1 is the pseudo-first-order rate constant.The PSO kinetic model of Ho and McKay [25] is expressed by Equation (7).(7)
q
t
/
mmol
/
g
=
k
2
q
e
2
t
1
+
k
2
q
e
t
,wherek
2
g
/
mmol
min is the pseudo-second-order rate constant.In addition, to elucidate the adsorption mechanism of Cu2+ and Co2+ on Cox and SBox, two models were used: intraparticle diffusion (IPD) and Boyd.The IPD model of Weber and Morris [26] is expressed by Equation (8).(8)
q
t
/
mmol
/
g
=
k
i
t
1
/
2
+
C
,whereC
mmol
/
g is the intercept and k
i
mmol
/
g
min
1
/
2 is the intraparticle diffusion rate constant. The constant C may be correlated to the thickness of the boundary layer.The model of Boyd et al. [27] is expressed by Equation (9):(9)
f
=
1
−
6
π
2
∑
n
=
1
∞
1
n
2
exp
−
n
2
B
t
,wheref
f
=
q
t
/
q
e is the fractional surface coverage as a function of time and B
t is a function of f. Reichenberg [28] provided solutions for Equation (9) using Fourier transform, which are expressed by Equations (10) and (11), as follows:(10)
B
t
=
−
0.4977
−
ln
1
−
f
,
(11)
B
t
=
π
−
π
−
π
2
f
3
2
.Forf
>
0.85, Equation (10) was utilized, whereas for f
<
0.85, Equation (11) was utilized to obtain the values of B
t.The effective diffusion coefficient,D
i, was determined by Equation (12), as follows:(12)
D
i
/
m
2
/
min
=
B
r
2
π
2
,wherer is the radius of the Cox (r = 0.250 × 10−3 m) or SBox (r = 0.150 × 10−3 m) particles, assuming a spherical shape.


### 2.8.2. Batch Equilibrium Data

Adsorption isotherms were fitted by the Freundlich, Langmuir, and Sips isotherm models.The Langmuir [29] isotherm model is expressed by Equation (13).(13)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
+
b
C
e
,whereQ
max
mmol
/
g is the maximum adsorption capacity of SBox or Cox for a metal ion and b
L
/
mmol is the Langmuir binding constant.The Freundlich [30] isotherm model is expressed by Equation (14).(14)
q
e
/
mmol
/
g
=
K
F
C
e
1
/
n
,whereK
F
mmol
/
g
L
/
mmol
1
/
n and n are the Freundlich model constants. The parameter n is associated to the adsorption intensity.The Langmuir–Freundlich isotherm model, developed by Sips [31], is a hybrid model of the Freundlich and Langmuir isotherm models, which is expressed by Equation (15).(15)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
/
n
1
+
b
C
e
1
/
n
,wheren is a parameter describing the heterogeneity of the system.


### 2.8.3. Analysis of the Breakthrough Curve

The area under the breakthrough curves gives the amount of Cu2+ or Co2+ adsorbed in the bed [32]. Then, the value of Q
max of the bed can be obtained from Equation (16), until the saturation time t
s is reached, as follows:(16)
Q
max
/
mmol
/
g
=
C
0
V
̇
1000
w
SBox
∫
0
t
1
−
C
t
C
0
d
t
,whereV
̇ is the inlet flow rate (mL/min), t is the time, C
0 and C
t are the influent and effluent Cu2+ or Co2+ concentrations (mmol/L) and w
SBox is the weight of SBox (g).The value ofH is defined as the height of the bed that was effectively utilized in the continuous adsorption process [33]. The value of H was obtained from Equation (17), as follows:(17)
H
/
cm
=
q
M
2
+
,
t
b
q
M
2
+
,
t
s
Z
,whereZ is the bed height (cm), q
M
2
+
,
t
b is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the breakthrough time t
b (mmol) and q
M
2
+
,
t
s is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the saturation time t
s (mmol). The values of q
M
2
+
,
t
b and q
M
2
+
,
t
s were determined by the integration of the area under the breakthrough curves until t
b and t
s, respectively.(i) Modeling the Breakthrough Curves.The development of mathematical models to predict the breakthrough curve, the mechanism involved in the process and even the evaluation of the effect of different variables on adsorption process is an important demand. However, this is a difficult task for such systems since the concentration profiles in both solid and liquid phases vary with both Z and t [32]. Thus, analytical models based on modeling the experimental data by means of nonlinear or linear regression analyses with physical meaning are available [34–38]. The original model of Bohart and Adams [38] is successfully employed when the adsorption isotherm is favorable. This model supposes that the rate of adsorption is proportional to the remaining adsorption capacity of the adsorbent and the concentration of the solute, neglecting axial dispersion. Equations (18)–(20) describe the relationship between C
t
/
C
0 and t for this model.(18)
C
t
C
0
=
exp
α
exp
α
+
exp
β
−
1
,(19)
α
=
k
B
-
A
C
0
t
−
Z
ν
,(20)
β
=
k
B
-
A
ρ
b
Q
max
Z
ν
ε
,whereν (cm/min) is the interstitial velocity, C (mmol/L) is the liquid phase Cu2+ or Co2+ concentration initially C
0 and at time t
C
t, Z (cm) is the column height, t (min) is the time, ε is the column void fraction, ρ
b (g/mL) is the bulk density and k
B
-
A (L/mmol min) is the Bohart–Adams kinetic rate constant.The relation between the adsorbent densityρ
p and bulk density ρ
b was used to determine the porosity of the bed, as given in Equation (21).(21)
ε
=
1
−
ρ
b
ρ
p
.


### 2.8.4. Calculation of Variation in Standard Free Energy of Adsorption

The variation in standard free energy of adsorptionΔ
ads
G
° for batch adsorption was determined by Equation (22) [39].(22)
Δ
ads
G
°
/
kJ/mol
=
−
R
T
ln
K
a
,whereT
K is the absolute temperature, K
a is the thermodynamic equilibrium constant (dimensionless) and R is the gas constant (8.3144 J/K mol).Liu [39] suggested that b (Langmuir constant) can be used to calculate the value of K
a, as given in Equation (23).(23)
K
a
=
b
γ
e
1
mol/L
,whereγ
e is the activity coefficient (dimensionless) at equilibrium at 25°C.The value ofγ
e can be calculated utilizing the extended Debye Hückel law (Equation (24)), which is applied to ionic strengths up to 0.1 mol/L.(24)
log
γ
e
=
−
0.509
z
2
I
e
1
+
α
I
e
/
305
,whereI
e (mol/L) is the ionic strength, z is the charge of the Cu2+ or Co2+ and α (pm) is the hydrated ion size of Cu2+ or Co2+ (600 pm) [40]. The values of I
e were calculated as described by Ramos et al. [20].


### 2.8.5. Regression Analysis and Error Evaluation

(i) Batch Adsorption Data. The experimental batch equilibrium and kinetic data were modeled with the PFO and PSO and Freundlich, Langmuir, and Sips models by nonlinear regression (NLR) analysis using Microcal OriginPro®2015. The modeling of the kinetic data with IPD and Boyd models was made by linear regression (LR) analysis of the experimental data. The software was set to use the weight method named “statistical” and the Levenberg–Marquardt algorithm. The reduced chi‒square χ
red
2 was employed to determine which model best described the experimental adsorption data [41].(ii) Continuous Adsorption Data. The breakthrough curves obtained were fitted using the set of Equations (18)–(20). The algorithm genetic function (ga) of the MATLAB®2010a software (Mathworks Inc.) was used for adjusting the parameters of the Bohart-Adams model to the continuous experimental data by minimization of the objective function. The objective function used was the root-mean-square error (RMSE) [18], as given in Equation (25).(25)
RMSE
=
∑
i
=
1
n
y
i
−
y
̂
i
2
n
,wheren is the number of experimental points and y
i is the value of experimental point i
,
y
̂
i is the predicted value by the model for the experimental point i.


## 2.8.1. Batch Kinetic Data

Pseudo-first-order (PFO) and pseudo-second-order (PSO) models were used to investigate the adsorption kinetics of Cu2+ and Co2+ on SBox and Cox.The PFO kinetic model of Lagergren [24] is expressed by Equation (6).(6)
q
t
/
mmol
/
g
=
q
e
1
−
exp
−
k
1
t
,wherek
1
min
−
1 is the pseudo-first-order rate constant.The PSO kinetic model of Ho and McKay [25] is expressed by Equation (7).(7)
q
t
/
mmol
/
g
=
k
2
q
e
2
t
1
+
k
2
q
e
t
,wherek
2
g
/
mmol
min is the pseudo-second-order rate constant.In addition, to elucidate the adsorption mechanism of Cu2+ and Co2+ on Cox and SBox, two models were used: intraparticle diffusion (IPD) and Boyd.The IPD model of Weber and Morris [26] is expressed by Equation (8).(8)
q
t
/
mmol
/
g
=
k
i
t
1
/
2
+
C
,whereC
mmol
/
g is the intercept and k
i
mmol
/
g
min
1
/
2 is the intraparticle diffusion rate constant. The constant C may be correlated to the thickness of the boundary layer.The model of Boyd et al. [27] is expressed by Equation (9):(9)
f
=
1
−
6
π
2
∑
n
=
1
∞
1
n
2
exp
−
n
2
B
t
,wheref
f
=
q
t
/
q
e is the fractional surface coverage as a function of time and B
t is a function of f. Reichenberg [28] provided solutions for Equation (9) using Fourier transform, which are expressed by Equations (10) and (11), as follows:(10)
B
t
=
−
0.4977
−
ln
1
−
f
,
(11)
B
t
=
π
−
π
−
π
2
f
3
2
.Forf
>
0.85, Equation (10) was utilized, whereas for f
<
0.85, Equation (11) was utilized to obtain the values of B
t.The effective diffusion coefficient,D
i, was determined by Equation (12), as follows:(12)
D
i
/
m
2
/
min
=
B
r
2
π
2
,wherer is the radius of the Cox (r = 0.250 × 10−3 m) or SBox (r = 0.150 × 10−3 m) particles, assuming a spherical shape.


## 2.8.2. Batch Equilibrium Data

Adsorption isotherms were fitted by the Freundlich, Langmuir, and Sips isotherm models.The Langmuir [29] isotherm model is expressed by Equation (13).(13)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
+
b
C
e
,whereQ
max
mmol
/
g is the maximum adsorption capacity of SBox or Cox for a metal ion and b
L
/
mmol is the Langmuir binding constant.The Freundlich [30] isotherm model is expressed by Equation (14).(14)
q
e
/
mmol
/
g
=
K
F
C
e
1
/
n
,whereK
F
mmol
/
g
L
/
mmol
1
/
n and n are the Freundlich model constants. The parameter n is associated to the adsorption intensity.The Langmuir–Freundlich isotherm model, developed by Sips [31], is a hybrid model of the Freundlich and Langmuir isotherm models, which is expressed by Equation (15).(15)
q
e
/
mmol
/
g
=
Q
max
b
C
e
1
/
n
1
+
b
C
e
1
/
n
,wheren is a parameter describing the heterogeneity of the system.


## 2.8.3. Analysis of the Breakthrough Curve

The area under the breakthrough curves gives the amount of Cu2+ or Co2+ adsorbed in the bed [32]. Then, the value of Q
max of the bed can be obtained from Equation (16), until the saturation time t
s is reached, as follows:(16)
Q
max
/
mmol
/
g
=
C
0
V
̇
1000
w
SBox
∫
0
t
1
−
C
t
C
0
d
t
,whereV
̇ is the inlet flow rate (mL/min), t is the time, C
0 and C
t are the influent and effluent Cu2+ or Co2+ concentrations (mmol/L) and w
SBox is the weight of SBox (g).The value ofH is defined as the height of the bed that was effectively utilized in the continuous adsorption process [33]. The value of H was obtained from Equation (17), as follows:(17)
H
/
cm
=
q
M
2
+
,
t
b
q
M
2
+
,
t
s
Z
,whereZ is the bed height (cm), q
M
2
+
,
t
b is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the breakthrough time t
b (mmol) and q
M
2
+
,
t
s is the amount of Cu2+ or Co2+ adsorbed on the adsorbent until the saturation time t
s (mmol). The values of q
M
2
+
,
t
b and q
M
2
+
,
t
s were determined by the integration of the area under the breakthrough curves until t
b and t
s, respectively.(i) Modeling the Breakthrough Curves.The development of mathematical models to predict the breakthrough curve, the mechanism involved in the process and even the evaluation of the effect of different variables on adsorption process is an important demand. However, this is a difficult task for such systems since the concentration profiles in both solid and liquid phases vary with both Z and t [32]. Thus, analytical models based on modeling the experimental data by means of nonlinear or linear regression analyses with physical meaning are available [34–38]. The original model of Bohart and Adams [38] is successfully employed when the adsorption isotherm is favorable. This model supposes that the rate of adsorption is proportional to the remaining adsorption capacity of the adsorbent and the concentration of the solute, neglecting axial dispersion. Equations (18)–(20) describe the relationship between C
t
/
C
0 and t for this model.(18)
C
t
C
0
=
exp
α
exp
α
+
exp
β
−
1
,(19)
α
=
k
B
-
A
C
0
t
−
Z
ν
,(20)
β
=
k
B
-
A
ρ
b
Q
max
Z
ν
ε
,whereν (cm/min) is the interstitial velocity, C (mmol/L) is the liquid phase Cu2+ or Co2+ concentration initially C
0 and at time t
C
t, Z (cm) is the column height, t (min) is the time, ε is the column void fraction, ρ
b (g/mL) is the bulk density and k
B
-
A (L/mmol min) is the Bohart–Adams kinetic rate constant.The relation between the adsorbent densityρ
p and bulk density ρ
b was used to determine the porosity of the bed, as given in Equation (21).(21)
ε
=
1
−
ρ
b
ρ
p
.


## 2.8.4. Calculation of Variation in Standard Free Energy of Adsorption

The variation in standard free energy of adsorptionΔ
ads
G
° for batch adsorption was determined by Equation (22) [39].(22)
Δ
ads
G
°
/
kJ/mol
=
−
R
T
ln
K
a
,whereT
K is the absolute temperature, K
a is the thermodynamic equilibrium constant (dimensionless) and R is the gas constant (8.3144 J/K mol).Liu [39] suggested that b (Langmuir constant) can be used to calculate the value of K
a, as given in Equation (23).(23)
K
a
=
b
γ
e
1
mol/L
,whereγ
e is the activity coefficient (dimensionless) at equilibrium at 25°C.The value ofγ
e can be calculated utilizing the extended Debye Hückel law (Equation (24)), which is applied to ionic strengths up to 0.1 mol/L.(24)
log
γ
e
=
−
0.509
z
2
I
e
1
+
α
I
e
/
305
,whereI
e (mol/L) is the ionic strength, z is the charge of the Cu2+ or Co2+ and α (pm) is the hydrated ion size of Cu2+ or Co2+ (600 pm) [40]. The values of I
e were calculated as described by Ramos et al. [20].


## 2.8.5. Regression Analysis and Error Evaluation

(i) Batch Adsorption Data. The experimental batch equilibrium and kinetic data were modeled with the PFO and PSO and Freundlich, Langmuir, and Sips models by nonlinear regression (NLR) analysis using Microcal OriginPro®2015. The modeling of the kinetic data with IPD and Boyd models was made by linear regression (LR) analysis of the experimental data. The software was set to use the weight method named “statistical” and the Levenberg–Marquardt algorithm. The reduced chi‒square χ
red
2 was employed to determine which model best described the experimental adsorption data [41].(ii) Continuous Adsorption Data. The breakthrough curves obtained were fitted using the set of Equations (18)–(20). The algorithm genetic function (ga) of the MATLAB®2010a software (Mathworks Inc.) was used for adjusting the parameters of the Bohart-Adams model to the continuous experimental data by minimization of the objective function. The objective function used was the root-mean-square error (RMSE) [18], as given in Equation (25).(25)
RMSE
=
∑
i
=
1
n
y
i
−
y
̂
i
2
n
,wheren is the number of experimental points and y
i is the value of experimental point i
,
y
̂
i is the predicted value by the model for the experimental point i.


## 3. Results and Discussion

### 3.1. Synthesis and Characterization of the Oxidized Materials

The oxidation reaction of SB and Cel was performed using a mixture of NaNO2 and H3PO4 to obtain the adsorbent materials SBox and Cox with high amounts of carboxylic acid groups according to the optimized procedure reported in a previous study by our research group [21]. The use of this oxidation system (H3PO4‒NaNO2) provides a cheaper methodology to prepare materials containing carboxyl functionality, thus adding value to these materials. The reaction mainly produced the oxidation of the primary R-CH2OH groups of SB and Cel into R-COOH groups. The reaction conditions were optimized by response surface methodology (RSM) and design of experiments (DOE). Through the optimization of the synthesis conditions, SBox and Cox were obtained with a number of R-COOH functions (n
COOH) of 4.5 and 4.8 mmol/g, respectively, which were determined as described by Martins et al. [21]. Cel oxidation was accomplished with a weight gain equal to 7.7%. This can be explained by the fact that the primary alcohol groups were converted into carboxylic acid groups, increasing the molar mass of the biopolymer. A weight loss equal to 18.4% was reported for SB oxidation, because of the presence of oxidant species and the acidic conditions, which degraded lignin and hemicelluloses fractions, increasing the solubility of these fractions in an aqueous medium.SBox and Cox were characterized by FTIR spectroscopy and solid‒state13C NMR spectroscopy, as described in our previous study by Martins et al. [21]. The 13C NMR spectrum of Cox indicated that the main product has carboxylic acid groups but that starting material (nonoxidized cellulose) is also still present in much smaller amounts.The main advantage of these oxidized materials (SBox and Cox) comparing to other carboxylated materials prepared by our research group [14, 15, 20, 22, 42–45] is that carboxylic acid functions in SBox and Cox are mainly from the oxidation of primary hydroxyl groups (R-CH2OH) of cellulose (in SB or Cel). On the contrary, when carboxylic acid groups are introduced in the Cel or SB through esterification reaction with cyclic carboxylic acid anhydrides, the application of esterified Cel or SB is limited to a pH range where the ester groups may not be easily hydrolyzed in the aqueous phase, e.g., 2–9 [46].


### 3.2. Adsorption Studies

#### 3.2.1. Effect of Solution pH on the Removal of Cu2+ and Co2+ by SBox and Cox

The batch removal of Cu2+ and Co2+ by adsorption on SBox and Cox from spiked aqueous solutions depends on the solution pH, since both adsorbent materials contain ionizable carboxylic acid groups. The net surface charge of the adsorbents in aqueous solution is directly related to pH of point of zero charge (pHPZC). The values of pHPZC for SBox and Cox are 2.72 and 2.70, respectively, as reported by Martins et al. [21]. Thus, at pH values greater than pHPZC both surfaces of SBox and Cox became predominantly negative due to conversion of carboxylic acid groups into carboxylate anion. Therefore, when pH values are higher than 2.7, SBox and Cox have a net negative surface charge, thereby promoting the adsorption of the cationic pollutants, such as Cu2+and Co2+.Graphs ofq
e against initial solution pH for adsorption of Cu2+ and Co2+ on Cox and SBox are shown in Figures 1(a) and 1(b), respectively. As expected, the adsorption of both metals increased when the solution pH was higher, reaching a maximum at pH value of 5.5 for all adsorption systems. Interestingly, Cox exhibited a higher q
e value than SBox for both metals studied, with both adsorbent materials even having a similar value for n
COOH. Then, the next studies of adsorption of Cu2+ and Co2+ on both materials as a function of the contact time (kinetics) and initial Cu2+and Co2+ concentration (isotherm) were carried out at a pH value of 5.5.Figure 1
Effect of initial solution pH on the adsorption of Co2+ and Cu2+ on (a) Cox and (b) SBox (contact time of 4 h, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 25°C, 150 rpm, 0.2 g/L Cox or SBox).
(a)
(b)A similar tendency was reported by Gurgel et al. [14, 43] and Ramos et al. [20] for the adsorption of Cu2+ on succinylated cellulose (Cell 6) [14], succinylated sugarcane bagasse (SCB 2) [43] and sugarcane bagasse modified with trimellitic anhydride (STA) [20]. SCB 2 has a higher amount of carboxylic acid groups (6.0 mmol/g), but a higher pHPZC value (5.26) [47] than SBox [21]. As a result, SCB 2 only exhibited an adsorptive capacity for Cu2+ ions from a pH value of 3.0. The pHPZC value of STA is 3.16 because this material possesses carboxylic acid groups bonded to an aromatic ring and showed more significant adsorptive capacity for Cu2+ and Co2+ ions from a pH value of 3.0. In the present study, because of the structural properties of SBox and Cox, i.e. a carboxyl group directly bonded to the glycosyl ring, both SBox and Cox are able to adsorb Cu2+ ions from a pH of 2.0 due to their lower pHPZC values. This represents a great advantage of SBox and Cox in comparison to other carboxylated materials prepared from lignocellulose biomass that have been reported in the literature.


#### 3.2.2. Effect of Contact Time on the Removal of Cu2+ and Co2+ by SBox and Cox

To design a wastewater treatment plant operating in batch or continuous mode, it is fundamental to study and understand the adsorption kinetics. Thus, experiments with each metal and SBox and Cox adsorbents were performed to define the values ofq
e and equilibrium time t
e as well as the adsorption rate constant. Other important factors to explain the adsorption mechanism are the physicochemical and textural properties of the Cox and SBox adsorbents as well as the mass transport processes.The curves generated from the NLR analyses of the experimental data with the PFO and PSO are presented in Figures2(a) and 2(b). Table 2 presents kinetic parameters estimated by modeling of the experimental data. Comparing the values of R
2 and χ
red
2 presented in Table 2, it was possible to confirm that the PSO model better described the Cu2+ adsorption by both adsorbent materials. When comparing the values of q
e
,
exp of Cu2+ with those of q
e
,
est, it can be observed for both adsorbent materials that the values of q
e
,
est estimated by the PSO model were closer to those of q
e
,
exp.Figure 2
Effect of contact time on the adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
(a)
(b)Table 2
Results of modeling the experimental kinetic data for the adsorption of Cu2+ and Co2+on Cox and SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
q
e
,
exp
mmol
/
g
1.16 ± 0.02
0.70 ± 0.01
0.56 ± 0.01
0.41 ± 0.02
q
e
,
exp
mg
/
g
73.53 ± 1.58
41.18 ± 0.41
35.30 ± 0.52
23.87 ± 1.17
t
e
min
120
120
45
180
Model
Pseudo-first-order (PFO)
q
e,est
mmol
/
g
1.12 ± 0.04
0.71 ± 0.01
0.54 ± 0.01
0.41 ± 0.01
q
e,est
mg
/
g
71.08 ± 2.28
41.88 ± 0.58
34.33 ± 0.63
24.25 ± 0.34
k
1
min
−
1
0.088 ± 0.010
0.028 ± 0.001
0.664 ± 0.064
0.020 ± 0.001
R
2
0.952
0.994
0.930
0.989
R
adj
2
0.947
0.993
0.923
0.988
χ
red
2
0.008
8.44×10−4
0.002
4.14×10−4
Model
Pseudo-second-order (PSO)
q
e,est
mmol
/
g
1.19 ± 0.02
0.80 ± 0.04
0.56 ± 0.00
0.47 ± 0.01
q
e,est
mg
/
g
75.42 ± 1.50
47.11 ± 2.12
35.37 ± 0.27
27.41 ± 0.65
k
2
g
/
mmol
min
0.109 ± 0.011
0.042 ± 0.008
1.865 ± 0.110
0.055 ± 0.006
R
2
0.984
0.955
0.988
0.981
R
adj
2
0.983
0.950
0.987
0.979
χ
red
2
0.003
0.006
2.87 × 10−4
7.42 × 10−4
Model
Intraparticle diffusion (IPD)
1st step
k
i
,
1 (mmol/g min1/2)
0.171 ± 0.001
0.114 ± 0.011
0.291 ± 0.000
0.036 ± 0.004
C (mmol/g)
0.061 ± 0.003
−0.210 ± 0.050
−0.015 ± 0.000
−0.006 ± 0.023
R
2
0.999
0.991
1.000
0.980
R
adj
2
0.999
0.981
—
0.969
2nd step
k
i
,
2 (mmol/g min1/2)
0.077 ± 0.007
0.040±
0.033 ± 0.000
0.019 ± 0.004
C (mmol/g)
0.512 ± 0.036
0.296±
0.385 ± 0.00
0.153 ± 0.035
R
2
0.985
0.983
1.000
0.967
R
adj
2
0.977
0.966
—
0.934
Model
Boyd
B
0.035 ± 0.003
0.031 ± 0.002
0.135 ± 0.034
0.016 ± 0.000
Intercept
0.030 ± 0.057
−0.403 ± 0.116
0.380 ± 0.193
−0.213 ± 0.060
Di (m2/min)
2.19 × 10−10
1.98 × 10−10
8.55 × 10−10
9.98 × 10−11
R
2
0.974
0.983
0.888
0.986
R
2
adj
0.969
0.978
0.832
0.983The values ofk
2 indicated a higher kinetic rate constant for Cu2+ adsorption on SBox than Cox. As can be seen in Figures 2(a) and 2(b), the equilibrium time for Cu2+ adsorption was achieved in 45 and 120 min for SBox and Cox, respectively.For Co2+ adsorption on both SBox and Cox, the model that better described the experimental data was the PFO model with the values of q
e
,
exp for this model being closer to those values of q
e
,
est. The values of k
1 showed a higher kinetic rate constant for Co2+ adsorption on Cox than SBox. As can be seen in Figures 2(a) and 2(b), the Co2+ adsorption equilibrium time was achieved in 180 and 120 min for SBox and Cox, respectively.The parameters of IPD and Boyd models estimated by LR analyses of the experimental data are presented in Table2. The adsorption process of Cu2+ and Co2+ on SBox and Cox exhibited three stages (Figures not shown). These plots suggest that the adsorption of Cu2+ and Co2+ on SBox and Cox was initially governed by the diffusion of Cu2+ or Co2+ through the thin solvent film surrounding both Cox and SBox particles and then changed to intraparticle diffusion. Afterward, equilibrium was reached. Boyd’s plots (Figures not shown) were only linear for the initial stage of Cu2+ or Co2+ adsorption and did not intersect the origin, suggesting that external mass transfer can be the rate-limiting step governing the initial stage of Cu2+ or Co2+ adsorption, which then changed to intraparticle diffusion, corroborating the IPD plots [48]. In addition, for both adsorbent materials, the values of D
i were higher for Cu2+ adsorption than Co2+ adsorption, which will have a great influence in the behavior of Cu2+ and Co2+ adsorption on SBox in a fixed-bed column, as presented in Section 3.4.


#### 3.2.3. Adsorption Isotherms of Cu2+ and Co2+ on SBox and Cox

Adsorption isotherms can be employed to describe the different affinities of various solutes for the adsorption sites of an adsorbent. To evaluate the equilibrium data, Freundlich, Langmuir, and Sips models, three of various isotherm models available in the literature, were chosen. The isotherm model parameters estimated by fitting the models to the experimental data are presented in Table3. The curves fitted to the experimental data of Cu2+ and Co2+ adsorption on SBox and Cox are presented in Figures 3(a) and 3(b).Figure 3
Isotherms for adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (pH 5.5, 25°C, 150 rpm, and 0.2 g/L Cox or SBox).
(a)
(b)Table 3
Isotherm model parameters estimated for the adsorption of Cu2+ and Co2+ on Cox and SBox (pH 5.5, 25°C, 150 rpm and 0.2 g/L Cox or SBox).
Isotherm model
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
Experimental data
Q
max
,
exp
mmol
/
g
1.20 ± 0.01
0.68 ± 0.01
0.57 ± 0.00
0.37 ± 0.00
Q
max
,
exp
mg
/
g
76.14 ± 0.92
39.82 ± 0.33
36.23 ± 0.10
22.05 ± 0.25
I
e
mol
/
L
3.145 × 10−3
3.365 × 10−3
3.148 × 10−3
3.407 × 10−3
γ
e
0.789
0.783
0.789
0.782
CN
4.01
7.10
7.89
12.03
Langmuir
Q
max
,
est
mmol
/
g
1.17 ± 0.03
0.70 ± 0.01
0.60 ± 0.01
0.40 ± 0.00
Q
max
,
est
mg
/
g
74.36 ± 2.11
41.24 ± 0.35
38.07 ± 0.57
23.64 ± 0.22
b
L
/
mmol
30.47 ± 0.068
23.04 ± 1.09
17.93 ± 1.24
11.67 ± 0.53
R
2
0.914
0.988
0.977
0.989
R
adj
2
0.908
0.987
0.974
0.988
χ
red
2
0.006
2.08 × 10−4
4.40 × 10−4
1.03 × 10−4
K
a
38616.6
29430.3
22728.9
14944.3
Δ
G
°
kJ
/
mol
‒26.18
‒25.51
‒24.87
‒23.83
Freundlich
K
F
mmol
/
g
L
/
mmol
1
/
n
1.22 ± 0.02
0.68 ± 0.01
0.57 ± 0.01
0.37 ± 0.01
n
5.43 ± 0.26
7.25 ± 0.78
6.01 ± 0.52
5.39 ± 0.43
1
/
n
0.184
0.138
0.167
0.185
R
2
0.975
0.900
0.933
0.939
R
adj
2
0.974
0.890
0.926
0.933
χ
red
2
0.002
0.002
0.001
5.89 × 10−4
Sips
Q
max
,
est
mmol
/
g
1.62 ± 0.08
0.72 ± 0.01
0.64 ± 0.03
0.42 ± 0.01
Q
max
,
est
mg
/
g
102.83 ± 5.01
42.52 ± 0.77
40.68 ± 1.59
25.01 ± 0.62
b
L
/
mmol
10.71 ± 2.54
23.88 ± 1.17
17.20 ± 1.53
11.26 ± 0.58
n
2.26 ± 0.15
1.19 ± 0.10
1.37 ± 0.18
1.24 ± 0.10
R
2
0.997
0.992
0.988
0.995
R
adj
2
0.996
0.991
0.986
0.993
χ
red
2
2.27 × 10−4
1.45 × 10−4
2.47 × 10−4
5.73 × 10−5The isotherm curves obtained presented a downward-concave profile, characterizing a favorable adsorption [35]. The steepest initial slopes of adsorption isotherms of Cu2+ on SBox and Cox in comparison to Co2+ adsorption isotherms on SBox and Cox indicate that Cu2+ ions had more affinity for the adsorption sites of SBox and Cox than Co2+ ions. This is corroborated by the higher values of b for Cu2+ adsorption than for Co2+ adsorption (Table 3). In addition, for both Cu2+ and Co2+, even at low metal concentrations, the adsorbed amount was relatively high until reaching a plateau at which the adsorbed amount remained constant. In agreement with the classification of isotherms proposed by Giles et al. [49], the profiles of the isotherm curves for all adsorption systems studied corresponded to group L, subgroup 2.The adsorption isotherms (Figures3(a) and 3(b)) with initial curvature (type L) suggest that the available active sites are more difficult to find when the surface coverage increases, indicating that the Cu2+ and Co2+ may have been adsorbed onto a monolayer.The evaluation of the values ofχ
red
2 and the comparison between the values of Q
max
,
exp and Q
max
,
est were used to select the best isotherm model in order to characterize the adsorption systems. Analyzing the values of χ
red
2
,
Q
max
,
exp and Q
max
,
est presented in Table 3, it can be seen that for Cu2+ or Co2+ adsorption on both adsorbents, both the Sips and Langmuir isotherm models can describe very well the experimental data. The Sips model is a hybrid of the Freundlich and Langmuir isotherms. The parameter n of the Sips model can be employed to evaluate the degree of heterogeneity of an adsorption system. Thus, if the value of n is closer to unity, this suggests a more homogeneous adsorption; and if the value of n is equal to unity, the Sips isotherm is reduced to the Langmuir isotherm. Contrarily, if the value of n is far from unity, this indicates a more heterogeneous adsorption system, approaching to the Freundlich model.From the values ofn reported in Table 3 for the Sips model, it is concluded that the adsorption systems involving the adsorption of Co2+ on SBox and Cox are more homogeneous than the adsorption systems involving the adsorption of Cu2+ on SBox and Cox. It is also noted that the adsorption of Cu2+ on Cox is significantly more heterogeneous than other adsorption systems studied.Parameterb of the Langmuir model is associated to the solute affinity for the adsorbent sites [50]. Comparing the values of b of the Langmuir model (Table 3), it is concluded that Cu2+ has a greater affinity for both Cox and SBox adsorption sites than Co2+, as was previously concluded by the initial slopes of Cu2+ adsorption isotherms in comparison to Co2+ adsorption isotherms. The solute affinity for the adsorbent sites of the materials increased in the order: Co2+-SBox < Cu2+-SBox < Co2+-Cox < Cu2+-Cox.The values of variation in standard free energy of adsorptionΔ
ads
G
° were negative for all adsorption systems studied, indicating the spontaneous character of the adsorption in the standard conditions. Adsorption experiments of Cu2+ on raw cellulose (Cel) and raw sugarcane bagasse (SB) were only performed for comparison purposes. The values of Q
max for Cu2+ adsorption on SB and Cel were 0.23 mmol/g (13.3 mg/g) and 0.21 mmol/g (13.2 mg/g), respectively, which showed that SBox and Cox presented a much higher Q
max than SB and Cel. For, example, the values of Q
max
,
exp for Cu2+ adsorption on SBox and Cox were 2.7 times and 5.8 times higher than SB and Cel, respectively, which shows the efficiency of the functionalization process of SB and Cel to obtain SBox and Cox.The values of the coordination numbers (CN) (Table 3) [14] for Cu2+ and Co2+ adsorption on SBox and Cox suggested that not all carboxylic acid groups were available to adsorb metals. The values of CN for adsorption of Cu2+ and Co2+ on Cox were lower than those for adsorption on SBox, indicating that the n
COOH taking part on the adsorption of Cu2+ and Co2+ by SBox and Cox was different. Probably, this was responsible for a decrease in the value of Q
max for SBox in comparison to Cox, as both Cox (4.8 mmol/g) and SBox (4.5 mmol/g) have similar values for n
COOH.


### 3.3. Desorption and Reuse of SBox and Cox

Desorption and re-adsorption were evaluated for both SBox and Cox adsorbents with Cu2+ and Co2+, respectively. The desorption efficiencies E
des and re-adsorption efficiencies E
re
-
ads obtained for both SBox and Cox are presented in Table 4.Table 4
Desorption efficiencyE
des and re-adsorption efficiency E
re
-
ads for Cu2+ and Co2+ for Cox and SBox adsorbents.
Material
Metal ion
E
des
%
E
re
-
ads
%
Cox
Cu2+
87.7
99.4
Co2+
72.3
98.4
SBox
Cu2+
98.1
104.1
Co2+
85.3
92.9It was observed that the desorption of the metals was fast, with a maximum value ofE
des achieved in a short time, i.e., 10 min for SBox and 15 min for Cox. The best result for E
des was obtained for the SBox-Cu system; however, the other systems showed values of E
des between 72.3% and 87.7%. Even though SBox and Cox were not completely desorbed, this should not impair their reuse as they still present a large amount of free adsorption sites.The desorption experiments performed at acidic aqueous medium showed that both metals were fast desorbed, which indicated the ion-exchange was the mechanism controlling both adsorption and desorption of both metals. Xavier et al. [23], who investigated the adsorption/desorption/re-adsorption of Co2+, Cu2+ and Ni2+ on trimellitated sugarcane bagasse reported a similar behavior in comparison to that observed in the present study.The infrared spectra of Cox and SBox before and after desorption of Cu2+ (Cox-D-Cu2+, SBox-D-Cu2+) and Co2+ (Cox-D-Co2+, SBox-D-Co2+), respectively, are presented in Figures 4(a) and 4(b). As can be seen in Figures 4(a) and 4(b), the band at 1730 cm−1 related to C=O stretching in carboxylic acid groups is still present in both spectra of Cox and SBox after desorption of Cu2+ and Co2+, showing that both adsorbent materials were not degraded after desorption.Figure 4
FTIR spectra of (a) Cox, Cox-D-Cu2+ and Cox-D-Co2+ and (b) SBox, SBox-D-Cu2+ and SBox-D-Co2+.
(a)
(b)Re-adsorption was performed to evaluate the alternative of reusing both adsorbents. The desorbed SBox and Cox were used in a new adsorption cycle to evaluate their performances as they were not completely desorbed. The obtained results are shown in Table4. The lower value of E
re
-
ads was for Co2+-SBox system; however, the other systems showed values of E
re
-
ads higher than >98%. Therefore, SBox and Cox still exhibited excellent values of E
re
-
ads in comparison to their values of Q
T
,
max showing that these materials are interesting adsorbents from both point of view of chemical resistance to degradation and reuse.


### 3.4. Monocomponent Adsorption of Cu2+and Co2+ on SBox Adsorbent in a Fixed-Bed Column

The choice of SBox to investigate continuous adsorption of Cu2+ and Co2+ in a fixed-bed column is due to its lower cost in comparison to Cox, although Cox had higher values of Q
max
,
exp in comparison to SBox.The breakthrough curves plotted as effluent concentration-time profiles provide information about the dynamic behavior of a determined fixed-bed column adsorption from the mass transfer zone (MTZ). MTZ is the area of the bed where the adsorption of Cu2+ and Co2+ occurs. MTZ varies with t
b, which is the time when the value of C in the effluent reaches 5% of C
0, to t
s, which is the time when the value of C in the effluent reaches 95% of C
0. Figures 5(a) and 5(b) present the breakthrough curves obtained for adsorption of Cu2+ and Co2+ on SBox in a fixed-bed column. Table 5 presents the values of H and Q
max.Figure 5
Breakthrough curves for adsorption of (a) Cu2+and (b) Co2+ on SBox adsorbent in a fixed-bed column at 25°C (experiments from 1 to 7 refers to the 22 experimental design matrices for Cu2+ and Co2+ presented in Tables 1 and 5).
(a)
(b)Table 5
Results of 22 experimental design for adsorption of Cu2+ and Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
Number of experiment
Independent variable
Cu2+
Co2+
C
0
mmol
/
L
τ
min
Q
max
mmol
/
g
H
cm
Q
max
mmol
/
g
H
cm
1
−1
−1
0.261
0.40
0.091
0.23
2
−1
1
0.237
0.73
0.088
0.82
3
1
−1
0.554
1.50
0.224
0.68
4
1
1
0.428
1.41
0.220
1.58
5
0
0
0.316
1.61
0.203
2.12
6
0
0
0.345
1.54
0.195
1.39
7
0
0
0.347
1.67
0.192
1.71The results presented in Table5 show that the higher value of Q
max (0.554 mmol/g) for Cu2+ adsorption was obtained in experiment 3, while the lower value of Q
max (0.237 mmol/g) was obtained in experiment 2. For Co2+ adsorption, the higher and lower values of Q
max (0.224 and 0.088 mmol/g) were obtained in experiments 3 and 2, respectively. These results suggest that higher levels of initial metal concentration and lower levels of spatial time favored higher values of Q
max. Furthermore, lower levels of initial metal concentration and higher levels of spatial time disfavored higher values of Q
max. In addition, the value of Q
max for Cu2+ in continuous adsorption was 2.9% lower than in batch adsorption, while the value of Q
max for Co2+ in continuous adsorption was 65.2% lower than in batch adsorption.The rate-limiting steps of an adsorption process are: (1) the mass transfer of the Cu2+ or Co2+ from the bulk phase to the SBox surface; (2) the diffusion of the Cu2+ or Co2+ into the SBox porous structure; and (3) the adsorption of Cu2+ or Co2+ onto the SBox surface [51]. In a mass transfer process, the mass flow is proportional to the concentration gradient difference. This is the driving force for the adsorption process. Moreover, the resistance at the liquid film interface (step 1) decreases with increasing flow rate. Therefore, it is expected that higher levels of inlet Cu2+ or Co2+ concentration and lower levels of spatial time provide a higher concentration gradient difference between the adsorbed Cu2+ or Co2+ at the interface and the Cu2+ or Co2+ in the bulk solution, as well as a smaller resistance at the liquid film, thereby increasing the value of Q
max of the adsorbent.Higher values ofH for adsorption of Cu2+ and Co2+ on SBox were obtained at the center point for both metal ions, with 1.67 (experiment 7) and 2.12 cm (experiment 5), respectively. The lower values of H, 0.40 cm for Cu2+ and 0.23 cm for Co2+, were obtained in experiment 1. The characteristics of the breakthrough curve are related with the equilibrium adsorption, mass transfer of Cu2+ or Co2+ from the bulk solution to the SBox surface and porous structure of the SBox as well as with fluid flow properties during continuous adsorption into the column [52]. The instantaneous equilibrium produces, under ideal conditions, a shock-like wave which moves as a sharp concentration step through the bed [53], where the entire length of bed is utilized. This suggests that, at the center point, the overall resistance to the adsorption of Cu2+ or Co2+ on SBox is reduced, favoring the adsorption. As a consequence, the application of lower levels of C
0 and lower levels of τ increased the overall resistance to the adsorption.The 22 experimental design was employed to evaluate the effect of C
0 and τ on the adsorption of Cu2+ and Co2+ on SBox in continuous. The analysis of variance (ANOVA) of the experimental data was carried out. The results are shown in Table 6. It is necessary to have a significant regression for a well-adjusted model, i.e., F
>
F
tab and p
<
0.05 together with a non-significant lack of fit, i.e., F
<
F
tab and p
>
0.05. The linear model used to fit the response Q
max yielded coefficients of determination R
2 of 0.963 for Cu2+ and 0.857 for Co2+. However, the values of R
2 for H for adsorption of Cu2+ (0.579) and Co2+ (0.358) were not high as for Q
max. In addition, the models used to fit the DVs Q
max for Co2+and H for Cu2+ exhibited a lack of fit, indicating that these models cannot predict the behavior of these dependent variables very well.Table 6
ANOVA for 22 experimental design for adsorption of Cu2+ and Co2+ on SBox in a fixed-bed column adsorption at 25°C.
Response
Q
max
Cu
2
+
R
2
=
0.963
H
Cu
2
+
R
2
=
0.579
Factor
Effect
SS
dF
MS
F
p
Effect
SS
dF
MS
F
p
(1)τ
min
−0.075
0.006
1
0.006
18.536
0.050
0.12
0.014
1
0.014
3.402
0.206
(2)C
0
mmol
/
L
0.242
0.058
1
0.058
192.608
0.005
0.890
0.792
1
0.792
187.110
0.005
1 by 2
−0.051
0.003
1
0.003
8.622
0.099
−0.210
0.044
1
0.044
10.417
0.084
Lack of fit
0.002
1
0.002
6.528
0.125
0.610
1
0.610
144.166
0.007
Pure error
0.001
2
0.000
0.008
2
0.004
Total SS
0.069
6
1.469
6
Response
Q
max
Co
2
+
R
2
=
0.857
H
Co
2
+
R
2
=
0.358
Factor
Effect
SS
dF
MS
F
p
Effect
SS
dF
MS
F
p
(1)τ
/
min
−0.004
0.000
1
0.000
0.387
0.597
0.745
0.555
1
0.555
4.145
0.179
(2)C
0
/
mmol
/
L
0.132
0.017
1
0.017
465.534
0.002
0.605
0.366
1
0.366
2.734
0.240
1 by 2
−0.001
0.000
1
0.000
0.011
0.927
0.155
0.024
1
0.024
0.179
0.713
Lack of fit
0.003
1
0.003
75.858
0.013
1.427
1
1.427
10.660
0.082
Pure error
0.000
2
0.000
0.268
2
0.134
Total SS
0.020
6
2.640
6As can be seen in Table6, both independent variables were statistically significant for response Q
max for Cu2+ with τ presenting a negative effect and C
0 a positive effect on Cu2+ adsorption. This means that the use of C
0 in a higher level and τ in a lower level favored a higher value of Q
max. The DV
Q
max for Co2+ adsorption was only influenced by C
0 with this variable presenting a statistically significant positive effect. For the DV H, both variables were not statistically significant for Co2+ adsorption, and only C
0 was statistically significant, presenting a positive effect on Cu2+ adsorption. The interactions between the independent variables C
0
×
τ had no statistically significant effects on any DVs (Q
max or H) evaluated for the adsorption of both metals on SBox.When comparing these results of adsorption in continuous with the profiles of the kinetic curves obtained for batch adsorption of Cu2+ and Co2+ on SBox (Figures 2(a) and 2(b)), it can be seen that the spatial time only influenced Cu2+ adsorption, which presented kinetic curves with steeper initial slopes than those for Co2+ adsorption. This suggests that the mass transfer of Cu2+ or Co2+ from the bulk phase to the SBox surface may have contributed more to the rate-limiting step for Cu2+ adsorption on SBox while Co2+ adsorption on SBox may be influenced by both diffusional and adsorption rates.Table7 presents the results when Bohart-Adams original model was used to model the experimental breakthrough curves. The Bohart-Adams original model better fitted the experimental breakthrough curves for Co2+ adsorption than those for Cu2+ adsorption, presenting higher R
2 values and smaller RMSE values. The values of Q
max estimated by the Bohart-Adams original model and those obtained experimentally presented low values of mean absolute error (MAE), between 4.2% and 1.9% for Cu2+ and Co2+ adsorption, respectively, showing that this model can predict the experimental data very well.Table 7
Results of the modeling the experimental breakthrough curves with the Bohart–Adams model for adsorption of Cu2+ and Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
Metal ion
Cu2+
Number of experiment
1
2
3
4
5
6
7
Q
max
,
exp
mmol
/
g
0.261
0.237
0.554
0.428
0.316
0.345
0.347
k
B
-
A
L
/
mmol
min
0.101
0.075
0.061
0.042
0.092
0.068
0.100
Q
max
mmol
/
g
0.249
0.215
0.480
0.377
0.294
0.291
0.288
RMSE
0.053
0.047
0.085
0.066
0.056
0.062
0.065
R
2
0.979
0.979
0.944
0.964
0.980
0.967
0.973
Metal ion
Co2+
Number of experiment
1
2
3
4
5
6
7
Q
max
,
exp
mmol
/
g
0.091
0.088
0.224
0.220
0.203
0.195
0.192
k
B
-
A
L
/
mmol
min
0.322
0.253
0.213
0.118
0.158
0.162
0.164
Q
max
mmol
/
g
0.081
0.080
0.165
0.204
0.201
0.176
0.171
RMSE
0.043
0.022
0.059
0.019
0.047
0.034
0.032
R
2
0.985
0.997
0.967
0.997
0.986
0.992
0.994Figures6(a) and 6(b) show the breakthrough curves obtained for the experiment 7 for adsorption of Cu2+ and Co2+ on SBox in continuous modeled by the Bohart-Adams original model. The values of Bohart-Adams rate constants k
B
-
A for the metals studied were smaller for higher levels of C
0 and/or τ, whereas higher values of k
B
-
A were observed for lower levels of C
0 and/or τ. The k
B
-
A is a lumped parameter [51], which includes all effects of internal and external diffusion, adsorption kinetics as well as any dispersion in the bed. Then, the adsorption in continuous at the conditions evaluated in this study is influenced by all of these effects. However, for Cu2+ adsorption, the k
B
-
A value at center point was closer to experiment 1, while for Co2+ adsorption in the experiment 4 had a value of k
B
-
A closer to that obtained at the center point. As the levels of C
0 and τ in experiments 1 and 4 were opposite (Table 5), this indicates that the adsorption of these metals on SBox, in fact, presented different rate-limiting steps.Figure 6
Breakthrough curves for experiment 7 of the 22 experimental design modeled by the Bohart-Adams original model for adsorption of (a) Cu2+ and (b) Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
(a)
(b)


### 3.5. Comparison with Literature Adsorption Data for Cu2 and Co2+ on Different Adsorbents

Table8 presents some adsorbents reported in the literature for the removal of Co2+ and Cu2+ from spiked aqueous solutions in continuous. It is possible to compare the performance of different adsorbent materials in continuous from the values of Q
max, C
0, and τ. Both the values of C
0 and τ affect the value of Q
max of an adsorbent material. It is possible to have a high value of Q
max using a high value of C
0 combined with a low value of τ or a low value of C
0 combined with a high value of τ. Comparing the performance of SBox adsorbent in continuous with those reported in the literature data, it should be noted that SBox showed a very good performance, mainly for Cu2+ removal, because it presented a medium value of Q
max, which was obtained from a lower value of τ combined with a medium value of C
0. However, SBox presented a lower value of Q
max for Co2+ removal.Table 8
Comparison of adsorbent materials reported in the literature for removal of Cu2+ and Co2+ from aqueous solutions in a fixed-bed column adsorption.
Adsorbent
Fixed-bed column adsorption parameter
Q
max
mmol
/
g
Fixed-bed model
Reference
pH
T (°C)
C
0
mmol
/
L
τ
min
Cu2+
Co2+
SBox
5.5
25
1.26 (Cu), 0.68 (Co)
0.7
0.55
0.22
B
-
A
b
This study
Tetraethylenepentamine modified sugarcane bagasse
5.0
30-35
0.31
-
0.26
-
-
[54]
Sugarcane bagasse modified with trimellitic anhydride (STA)
5.5
25
0.94 (Cu), 1.61 (Co)
1.05 (Cu); 1.4 (Co)
1.06
0.80
Thomasa and B
-
A
a
[23]
Citrus maxima peel
5.4–5.7
25
4.72
1.2
1.54
-
Thomasa
[55]
Passion fruit shell
0.57
-
Sugarcane bagasse
0.35
-
Multi-metal binding biosorbent (MMBB)
5.5
23
0.47
8
0.75
-
Thomasa
[56]
Bagasse fly ash (BFA)
5.0
30
3.14
4.3
0.42
-
-
[57]
Conventional zeolitic BFA (CZBFA)
0.83
-
Electrolyte treated CZBFA
0.84
-
Magnetized sawdust (Fe3O4-SD)
5.0
25
0.16
0.67
0.50
-
Thomasa and B
-
A
a
[58]
Sargassum wightii biomass
4.5
-
1.70
3.9
0.83
BDST
[59]
Biomass beads of immobilizedSaccharomyces cerevisiae (PTCC 5010)
8.0
25
1.70
19.6
0.04
Thomasa
[60]
Polyamine chelating resin (NDC-984)
5.0
30
5.00
12.0
0.96
-
[61]
Native teak leaves power
-
30
0.85
3.14
-
0.35
Thomasa and B
-
A
a
[62]
Biochar of teak leaves
-
0.39
Free seaweedSargassum sp.
5.0
30
0.77
31.4
1.51
-
Thomasb
[63]
Immobilized seaweedSargassum sp.
0.78
1.69
-
SeaweedSargassum sp.
3.5
30
2.08
31.4
0.12
-
Thomasb and B
-
A
b
[64]
aSimplified model; bOriginal model. Thomas: Thomas model; B–A: Bohart–Adams model; BDST: Bed depth service time.


## 3.1. Synthesis and Characterization of the Oxidized Materials

The oxidation reaction of SB and Cel was performed using a mixture of NaNO2 and H3PO4 to obtain the adsorbent materials SBox and Cox with high amounts of carboxylic acid groups according to the optimized procedure reported in a previous study by our research group [21]. The use of this oxidation system (H3PO4‒NaNO2) provides a cheaper methodology to prepare materials containing carboxyl functionality, thus adding value to these materials. The reaction mainly produced the oxidation of the primary R-CH2OH groups of SB and Cel into R-COOH groups. The reaction conditions were optimized by response surface methodology (RSM) and design of experiments (DOE). Through the optimization of the synthesis conditions, SBox and Cox were obtained with a number of R-COOH functions (n
COOH) of 4.5 and 4.8 mmol/g, respectively, which were determined as described by Martins et al. [21]. Cel oxidation was accomplished with a weight gain equal to 7.7%. This can be explained by the fact that the primary alcohol groups were converted into carboxylic acid groups, increasing the molar mass of the biopolymer. A weight loss equal to 18.4% was reported for SB oxidation, because of the presence of oxidant species and the acidic conditions, which degraded lignin and hemicelluloses fractions, increasing the solubility of these fractions in an aqueous medium.SBox and Cox were characterized by FTIR spectroscopy and solid‒state13C NMR spectroscopy, as described in our previous study by Martins et al. [21]. The 13C NMR spectrum of Cox indicated that the main product has carboxylic acid groups but that starting material (nonoxidized cellulose) is also still present in much smaller amounts.The main advantage of these oxidized materials (SBox and Cox) comparing to other carboxylated materials prepared by our research group [14, 15, 20, 22, 42–45] is that carboxylic acid functions in SBox and Cox are mainly from the oxidation of primary hydroxyl groups (R-CH2OH) of cellulose (in SB or Cel). On the contrary, when carboxylic acid groups are introduced in the Cel or SB through esterification reaction with cyclic carboxylic acid anhydrides, the application of esterified Cel or SB is limited to a pH range where the ester groups may not be easily hydrolyzed in the aqueous phase, e.g., 2–9 [46].


## 3.2. Adsorption Studies

### 3.2.1. Effect of Solution pH on the Removal of Cu2+ and Co2+ by SBox and Cox

The batch removal of Cu2+ and Co2+ by adsorption on SBox and Cox from spiked aqueous solutions depends on the solution pH, since both adsorbent materials contain ionizable carboxylic acid groups. The net surface charge of the adsorbents in aqueous solution is directly related to pH of point of zero charge (pHPZC). The values of pHPZC for SBox and Cox are 2.72 and 2.70, respectively, as reported by Martins et al. [21]. Thus, at pH values greater than pHPZC both surfaces of SBox and Cox became predominantly negative due to conversion of carboxylic acid groups into carboxylate anion. Therefore, when pH values are higher than 2.7, SBox and Cox have a net negative surface charge, thereby promoting the adsorption of the cationic pollutants, such as Cu2+and Co2+.Graphs ofq
e against initial solution pH for adsorption of Cu2+ and Co2+ on Cox and SBox are shown in Figures 1(a) and 1(b), respectively. As expected, the adsorption of both metals increased when the solution pH was higher, reaching a maximum at pH value of 5.5 for all adsorption systems. Interestingly, Cox exhibited a higher q
e value than SBox for both metals studied, with both adsorbent materials even having a similar value for n
COOH. Then, the next studies of adsorption of Cu2+ and Co2+ on both materials as a function of the contact time (kinetics) and initial Cu2+and Co2+ concentration (isotherm) were carried out at a pH value of 5.5.Figure 1
Effect of initial solution pH on the adsorption of Co2+ and Cu2+ on (a) Cox and (b) SBox (contact time of 4 h, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 25°C, 150 rpm, 0.2 g/L Cox or SBox).
(a)
(b)A similar tendency was reported by Gurgel et al. [14, 43] and Ramos et al. [20] for the adsorption of Cu2+ on succinylated cellulose (Cell 6) [14], succinylated sugarcane bagasse (SCB 2) [43] and sugarcane bagasse modified with trimellitic anhydride (STA) [20]. SCB 2 has a higher amount of carboxylic acid groups (6.0 mmol/g), but a higher pHPZC value (5.26) [47] than SBox [21]. As a result, SCB 2 only exhibited an adsorptive capacity for Cu2+ ions from a pH value of 3.0. The pHPZC value of STA is 3.16 because this material possesses carboxylic acid groups bonded to an aromatic ring and showed more significant adsorptive capacity for Cu2+ and Co2+ ions from a pH value of 3.0. In the present study, because of the structural properties of SBox and Cox, i.e. a carboxyl group directly bonded to the glycosyl ring, both SBox and Cox are able to adsorb Cu2+ ions from a pH of 2.0 due to their lower pHPZC values. This represents a great advantage of SBox and Cox in comparison to other carboxylated materials prepared from lignocellulose biomass that have been reported in the literature.


### 3.2.2. Effect of Contact Time on the Removal of Cu2+ and Co2+ by SBox and Cox

To design a wastewater treatment plant operating in batch or continuous mode, it is fundamental to study and understand the adsorption kinetics. Thus, experiments with each metal and SBox and Cox adsorbents were performed to define the values ofq
e and equilibrium time t
e as well as the adsorption rate constant. Other important factors to explain the adsorption mechanism are the physicochemical and textural properties of the Cox and SBox adsorbents as well as the mass transport processes.The curves generated from the NLR analyses of the experimental data with the PFO and PSO are presented in Figures2(a) and 2(b). Table 2 presents kinetic parameters estimated by modeling of the experimental data. Comparing the values of R
2 and χ
red
2 presented in Table 2, it was possible to confirm that the PSO model better described the Cu2+ adsorption by both adsorbent materials. When comparing the values of q
e
,
exp of Cu2+ with those of q
e
,
est, it can be observed for both adsorbent materials that the values of q
e
,
est estimated by the PSO model were closer to those of q
e
,
exp.Figure 2
Effect of contact time on the adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
(a)
(b)Table 2
Results of modeling the experimental kinetic data for the adsorption of Cu2+ and Co2+on Cox and SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
q
e
,
exp
mmol
/
g
1.16 ± 0.02
0.70 ± 0.01
0.56 ± 0.01
0.41 ± 0.02
q
e
,
exp
mg
/
g
73.53 ± 1.58
41.18 ± 0.41
35.30 ± 0.52
23.87 ± 1.17
t
e
min
120
120
45
180
Model
Pseudo-first-order (PFO)
q
e,est
mmol
/
g
1.12 ± 0.04
0.71 ± 0.01
0.54 ± 0.01
0.41 ± 0.01
q
e,est
mg
/
g
71.08 ± 2.28
41.88 ± 0.58
34.33 ± 0.63
24.25 ± 0.34
k
1
min
−
1
0.088 ± 0.010
0.028 ± 0.001
0.664 ± 0.064
0.020 ± 0.001
R
2
0.952
0.994
0.930
0.989
R
adj
2
0.947
0.993
0.923
0.988
χ
red
2
0.008
8.44×10−4
0.002
4.14×10−4
Model
Pseudo-second-order (PSO)
q
e,est
mmol
/
g
1.19 ± 0.02
0.80 ± 0.04
0.56 ± 0.00
0.47 ± 0.01
q
e,est
mg
/
g
75.42 ± 1.50
47.11 ± 2.12
35.37 ± 0.27
27.41 ± 0.65
k
2
g
/
mmol
min
0.109 ± 0.011
0.042 ± 0.008
1.865 ± 0.110
0.055 ± 0.006
R
2
0.984
0.955
0.988
0.981
R
adj
2
0.983
0.950
0.987
0.979
χ
red
2
0.003
0.006
2.87 × 10−4
7.42 × 10−4
Model
Intraparticle diffusion (IPD)
1st step
k
i
,
1 (mmol/g min1/2)
0.171 ± 0.001
0.114 ± 0.011
0.291 ± 0.000
0.036 ± 0.004
C (mmol/g)
0.061 ± 0.003
−0.210 ± 0.050
−0.015 ± 0.000
−0.006 ± 0.023
R
2
0.999
0.991
1.000
0.980
R
adj
2
0.999
0.981
—
0.969
2nd step
k
i
,
2 (mmol/g min1/2)
0.077 ± 0.007
0.040±
0.033 ± 0.000
0.019 ± 0.004
C (mmol/g)
0.512 ± 0.036
0.296±
0.385 ± 0.00
0.153 ± 0.035
R
2
0.985
0.983
1.000
0.967
R
adj
2
0.977
0.966
—
0.934
Model
Boyd
B
0.035 ± 0.003
0.031 ± 0.002
0.135 ± 0.034
0.016 ± 0.000
Intercept
0.030 ± 0.057
−0.403 ± 0.116
0.380 ± 0.193
−0.213 ± 0.060
Di (m2/min)
2.19 × 10−10
1.98 × 10−10
8.55 × 10−10
9.98 × 10−11
R
2
0.974
0.983
0.888
0.986
R
2
adj
0.969
0.978
0.832
0.983The values ofk
2 indicated a higher kinetic rate constant for Cu2+ adsorption on SBox than Cox. As can be seen in Figures 2(a) and 2(b), the equilibrium time for Cu2+ adsorption was achieved in 45 and 120 min for SBox and Cox, respectively.For Co2+ adsorption on both SBox and Cox, the model that better described the experimental data was the PFO model with the values of q
e
,
exp for this model being closer to those values of q
e
,
est. The values of k
1 showed a higher kinetic rate constant for Co2+ adsorption on Cox than SBox. As can be seen in Figures 2(a) and 2(b), the Co2+ adsorption equilibrium time was achieved in 180 and 120 min for SBox and Cox, respectively.The parameters of IPD and Boyd models estimated by LR analyses of the experimental data are presented in Table2. The adsorption process of Cu2+ and Co2+ on SBox and Cox exhibited three stages (Figures not shown). These plots suggest that the adsorption of Cu2+ and Co2+ on SBox and Cox was initially governed by the diffusion of Cu2+ or Co2+ through the thin solvent film surrounding both Cox and SBox particles and then changed to intraparticle diffusion. Afterward, equilibrium was reached. Boyd’s plots (Figures not shown) were only linear for the initial stage of Cu2+ or Co2+ adsorption and did not intersect the origin, suggesting that external mass transfer can be the rate-limiting step governing the initial stage of Cu2+ or Co2+ adsorption, which then changed to intraparticle diffusion, corroborating the IPD plots [48]. In addition, for both adsorbent materials, the values of D
i were higher for Cu2+ adsorption than Co2+ adsorption, which will have a great influence in the behavior of Cu2+ and Co2+ adsorption on SBox in a fixed-bed column, as presented in Section 3.4.


### 3.2.3. Adsorption Isotherms of Cu2+ and Co2+ on SBox and Cox

Adsorption isotherms can be employed to describe the different affinities of various solutes for the adsorption sites of an adsorbent. To evaluate the equilibrium data, Freundlich, Langmuir, and Sips models, three of various isotherm models available in the literature, were chosen. The isotherm model parameters estimated by fitting the models to the experimental data are presented in Table3. The curves fitted to the experimental data of Cu2+ and Co2+ adsorption on SBox and Cox are presented in Figures 3(a) and 3(b).Figure 3
Isotherms for adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (pH 5.5, 25°C, 150 rpm, and 0.2 g/L Cox or SBox).
(a)
(b)Table 3
Isotherm model parameters estimated for the adsorption of Cu2+ and Co2+ on Cox and SBox (pH 5.5, 25°C, 150 rpm and 0.2 g/L Cox or SBox).
Isotherm model
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
Experimental data
Q
max
,
exp
mmol
/
g
1.20 ± 0.01
0.68 ± 0.01
0.57 ± 0.00
0.37 ± 0.00
Q
max
,
exp
mg
/
g
76.14 ± 0.92
39.82 ± 0.33
36.23 ± 0.10
22.05 ± 0.25
I
e
mol
/
L
3.145 × 10−3
3.365 × 10−3
3.148 × 10−3
3.407 × 10−3
γ
e
0.789
0.783
0.789
0.782
CN
4.01
7.10
7.89
12.03
Langmuir
Q
max
,
est
mmol
/
g
1.17 ± 0.03
0.70 ± 0.01
0.60 ± 0.01
0.40 ± 0.00
Q
max
,
est
mg
/
g
74.36 ± 2.11
41.24 ± 0.35
38.07 ± 0.57
23.64 ± 0.22
b
L
/
mmol
30.47 ± 0.068
23.04 ± 1.09
17.93 ± 1.24
11.67 ± 0.53
R
2
0.914
0.988
0.977
0.989
R
adj
2
0.908
0.987
0.974
0.988
χ
red
2
0.006
2.08 × 10−4
4.40 × 10−4
1.03 × 10−4
K
a
38616.6
29430.3
22728.9
14944.3
Δ
G
°
kJ
/
mol
‒26.18
‒25.51
‒24.87
‒23.83
Freundlich
K
F
mmol
/
g
L
/
mmol
1
/
n
1.22 ± 0.02
0.68 ± 0.01
0.57 ± 0.01
0.37 ± 0.01
n
5.43 ± 0.26
7.25 ± 0.78
6.01 ± 0.52
5.39 ± 0.43
1
/
n
0.184
0.138
0.167
0.185
R
2
0.975
0.900
0.933
0.939
R
adj
2
0.974
0.890
0.926
0.933
χ
red
2
0.002
0.002
0.001
5.89 × 10−4
Sips
Q
max
,
est
mmol
/
g
1.62 ± 0.08
0.72 ± 0.01
0.64 ± 0.03
0.42 ± 0.01
Q
max
,
est
mg
/
g
102.83 ± 5.01
42.52 ± 0.77
40.68 ± 1.59
25.01 ± 0.62
b
L
/
mmol
10.71 ± 2.54
23.88 ± 1.17
17.20 ± 1.53
11.26 ± 0.58
n
2.26 ± 0.15
1.19 ± 0.10
1.37 ± 0.18
1.24 ± 0.10
R
2
0.997
0.992
0.988
0.995
R
adj
2
0.996
0.991
0.986
0.993
χ
red
2
2.27 × 10−4
1.45 × 10−4
2.47 × 10−4
5.73 × 10−5The isotherm curves obtained presented a downward-concave profile, characterizing a favorable adsorption [35]. The steepest initial slopes of adsorption isotherms of Cu2+ on SBox and Cox in comparison to Co2+ adsorption isotherms on SBox and Cox indicate that Cu2+ ions had more affinity for the adsorption sites of SBox and Cox than Co2+ ions. This is corroborated by the higher values of b for Cu2+ adsorption than for Co2+ adsorption (Table 3). In addition, for both Cu2+ and Co2+, even at low metal concentrations, the adsorbed amount was relatively high until reaching a plateau at which the adsorbed amount remained constant. In agreement with the classification of isotherms proposed by Giles et al. [49], the profiles of the isotherm curves for all adsorption systems studied corresponded to group L, subgroup 2.The adsorption isotherms (Figures3(a) and 3(b)) with initial curvature (type L) suggest that the available active sites are more difficult to find when the surface coverage increases, indicating that the Cu2+ and Co2+ may have been adsorbed onto a monolayer.The evaluation of the values ofχ
red
2 and the comparison between the values of Q
max
,
exp and Q
max
,
est were used to select the best isotherm model in order to characterize the adsorption systems. Analyzing the values of χ
red
2
,
Q
max
,
exp and Q
max
,
est presented in Table 3, it can be seen that for Cu2+ or Co2+ adsorption on both adsorbents, both the Sips and Langmuir isotherm models can describe very well the experimental data. The Sips model is a hybrid of the Freundlich and Langmuir isotherms. The parameter n of the Sips model can be employed to evaluate the degree of heterogeneity of an adsorption system. Thus, if the value of n is closer to unity, this suggests a more homogeneous adsorption; and if the value of n is equal to unity, the Sips isotherm is reduced to the Langmuir isotherm. Contrarily, if the value of n is far from unity, this indicates a more heterogeneous adsorption system, approaching to the Freundlich model.From the values ofn reported in Table 3 for the Sips model, it is concluded that the adsorption systems involving the adsorption of Co2+ on SBox and Cox are more homogeneous than the adsorption systems involving the adsorption of Cu2+ on SBox and Cox. It is also noted that the adsorption of Cu2+ on Cox is significantly more heterogeneous than other adsorption systems studied.Parameterb of the Langmuir model is associated to the solute affinity for the adsorbent sites [50]. Comparing the values of b of the Langmuir model (Table 3), it is concluded that Cu2+ has a greater affinity for both Cox and SBox adsorption sites than Co2+, as was previously concluded by the initial slopes of Cu2+ adsorption isotherms in comparison to Co2+ adsorption isotherms. The solute affinity for the adsorbent sites of the materials increased in the order: Co2+-SBox < Cu2+-SBox < Co2+-Cox < Cu2+-Cox.The values of variation in standard free energy of adsorptionΔ
ads
G
° were negative for all adsorption systems studied, indicating the spontaneous character of the adsorption in the standard conditions. Adsorption experiments of Cu2+ on raw cellulose (Cel) and raw sugarcane bagasse (SB) were only performed for comparison purposes. The values of Q
max for Cu2+ adsorption on SB and Cel were 0.23 mmol/g (13.3 mg/g) and 0.21 mmol/g (13.2 mg/g), respectively, which showed that SBox and Cox presented a much higher Q
max than SB and Cel. For, example, the values of Q
max
,
exp for Cu2+ adsorption on SBox and Cox were 2.7 times and 5.8 times higher than SB and Cel, respectively, which shows the efficiency of the functionalization process of SB and Cel to obtain SBox and Cox.The values of the coordination numbers (CN) (Table 3) [14] for Cu2+ and Co2+ adsorption on SBox and Cox suggested that not all carboxylic acid groups were available to adsorb metals. The values of CN for adsorption of Cu2+ and Co2+ on Cox were lower than those for adsorption on SBox, indicating that the n
COOH taking part on the adsorption of Cu2+ and Co2+ by SBox and Cox was different. Probably, this was responsible for a decrease in the value of Q
max for SBox in comparison to Cox, as both Cox (4.8 mmol/g) and SBox (4.5 mmol/g) have similar values for n
COOH.


## 3.2.1. Effect of Solution pH on the Removal of Cu2+ and Co2+ by SBox and Cox

The batch removal of Cu2+ and Co2+ by adsorption on SBox and Cox from spiked aqueous solutions depends on the solution pH, since both adsorbent materials contain ionizable carboxylic acid groups. The net surface charge of the adsorbents in aqueous solution is directly related to pH of point of zero charge (pHPZC). The values of pHPZC for SBox and Cox are 2.72 and 2.70, respectively, as reported by Martins et al. [21]. Thus, at pH values greater than pHPZC both surfaces of SBox and Cox became predominantly negative due to conversion of carboxylic acid groups into carboxylate anion. Therefore, when pH values are higher than 2.7, SBox and Cox have a net negative surface charge, thereby promoting the adsorption of the cationic pollutants, such as Cu2+and Co2+.Graphs ofq
e against initial solution pH for adsorption of Cu2+ and Co2+ on Cox and SBox are shown in Figures 1(a) and 1(b), respectively. As expected, the adsorption of both metals increased when the solution pH was higher, reaching a maximum at pH value of 5.5 for all adsorption systems. Interestingly, Cox exhibited a higher q
e value than SBox for both metals studied, with both adsorbent materials even having a similar value for n
COOH. Then, the next studies of adsorption of Cu2+ and Co2+ on both materials as a function of the contact time (kinetics) and initial Cu2+and Co2+ concentration (isotherm) were carried out at a pH value of 5.5.Figure 1
Effect of initial solution pH on the adsorption of Co2+ and Cu2+ on (a) Cox and (b) SBox (contact time of 4 h, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 25°C, 150 rpm, 0.2 g/L Cox or SBox).
(a)
(b)A similar tendency was reported by Gurgel et al. [14, 43] and Ramos et al. [20] for the adsorption of Cu2+ on succinylated cellulose (Cell 6) [14], succinylated sugarcane bagasse (SCB 2) [43] and sugarcane bagasse modified with trimellitic anhydride (STA) [20]. SCB 2 has a higher amount of carboxylic acid groups (6.0 mmol/g), but a higher pHPZC value (5.26) [47] than SBox [21]. As a result, SCB 2 only exhibited an adsorptive capacity for Cu2+ ions from a pH value of 3.0. The pHPZC value of STA is 3.16 because this material possesses carboxylic acid groups bonded to an aromatic ring and showed more significant adsorptive capacity for Cu2+ and Co2+ ions from a pH value of 3.0. In the present study, because of the structural properties of SBox and Cox, i.e. a carboxyl group directly bonded to the glycosyl ring, both SBox and Cox are able to adsorb Cu2+ ions from a pH of 2.0 due to their lower pHPZC values. This represents a great advantage of SBox and Cox in comparison to other carboxylated materials prepared from lignocellulose biomass that have been reported in the literature.


## 3.2.2. Effect of Contact Time on the Removal of Cu2+ and Co2+ by SBox and Cox

To design a wastewater treatment plant operating in batch or continuous mode, it is fundamental to study and understand the adsorption kinetics. Thus, experiments with each metal and SBox and Cox adsorbents were performed to define the values ofq
e and equilibrium time t
e as well as the adsorption rate constant. Other important factors to explain the adsorption mechanism are the physicochemical and textural properties of the Cox and SBox adsorbents as well as the mass transport processes.The curves generated from the NLR analyses of the experimental data with the PFO and PSO are presented in Figures2(a) and 2(b). Table 2 presents kinetic parameters estimated by modeling of the experimental data. Comparing the values of R
2 and χ
red
2 presented in Table 2, it was possible to confirm that the PSO model better described the Cu2+ adsorption by both adsorbent materials. When comparing the values of q
e
,
exp of Cu2+ with those of q
e
,
est, it can be observed for both adsorbent materials that the values of q
e
,
est estimated by the PSO model were closer to those of q
e
,
exp.Figure 2
Effect of contact time on the adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
(a)
(b)Table 2
Results of modeling the experimental kinetic data for the adsorption of Cu2+ and Co2+on Cox and SBox (25°C, 150 rpm, pH 5.5, 0.79 mmol/L Cu2+, 0.85 mmol/L Co2+, 0.2 g/L Cox or SBox).
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
q
e
,
exp
mmol
/
g
1.16 ± 0.02
0.70 ± 0.01
0.56 ± 0.01
0.41 ± 0.02
q
e
,
exp
mg
/
g
73.53 ± 1.58
41.18 ± 0.41
35.30 ± 0.52
23.87 ± 1.17
t
e
min
120
120
45
180
Model
Pseudo-first-order (PFO)
q
e,est
mmol
/
g
1.12 ± 0.04
0.71 ± 0.01
0.54 ± 0.01
0.41 ± 0.01
q
e,est
mg
/
g
71.08 ± 2.28
41.88 ± 0.58
34.33 ± 0.63
24.25 ± 0.34
k
1
min
−
1
0.088 ± 0.010
0.028 ± 0.001
0.664 ± 0.064
0.020 ± 0.001
R
2
0.952
0.994
0.930
0.989
R
adj
2
0.947
0.993
0.923
0.988
χ
red
2
0.008
8.44×10−4
0.002
4.14×10−4
Model
Pseudo-second-order (PSO)
q
e,est
mmol
/
g
1.19 ± 0.02
0.80 ± 0.04
0.56 ± 0.00
0.47 ± 0.01
q
e,est
mg
/
g
75.42 ± 1.50
47.11 ± 2.12
35.37 ± 0.27
27.41 ± 0.65
k
2
g
/
mmol
min
0.109 ± 0.011
0.042 ± 0.008
1.865 ± 0.110
0.055 ± 0.006
R
2
0.984
0.955
0.988
0.981
R
adj
2
0.983
0.950
0.987
0.979
χ
red
2
0.003
0.006
2.87 × 10−4
7.42 × 10−4
Model
Intraparticle diffusion (IPD)
1st step
k
i
,
1 (mmol/g min1/2)
0.171 ± 0.001
0.114 ± 0.011
0.291 ± 0.000
0.036 ± 0.004
C (mmol/g)
0.061 ± 0.003
−0.210 ± 0.050
−0.015 ± 0.000
−0.006 ± 0.023
R
2
0.999
0.991
1.000
0.980
R
adj
2
0.999
0.981
—
0.969
2nd step
k
i
,
2 (mmol/g min1/2)
0.077 ± 0.007
0.040±
0.033 ± 0.000
0.019 ± 0.004
C (mmol/g)
0.512 ± 0.036
0.296±
0.385 ± 0.00
0.153 ± 0.035
R
2
0.985
0.983
1.000
0.967
R
adj
2
0.977
0.966
—
0.934
Model
Boyd
B
0.035 ± 0.003
0.031 ± 0.002
0.135 ± 0.034
0.016 ± 0.000
Intercept
0.030 ± 0.057
−0.403 ± 0.116
0.380 ± 0.193
−0.213 ± 0.060
Di (m2/min)
2.19 × 10−10
1.98 × 10−10
8.55 × 10−10
9.98 × 10−11
R
2
0.974
0.983
0.888
0.986
R
2
adj
0.969
0.978
0.832
0.983The values ofk
2 indicated a higher kinetic rate constant for Cu2+ adsorption on SBox than Cox. As can be seen in Figures 2(a) and 2(b), the equilibrium time for Cu2+ adsorption was achieved in 45 and 120 min for SBox and Cox, respectively.For Co2+ adsorption on both SBox and Cox, the model that better described the experimental data was the PFO model with the values of q
e
,
exp for this model being closer to those values of q
e
,
est. The values of k
1 showed a higher kinetic rate constant for Co2+ adsorption on Cox than SBox. As can be seen in Figures 2(a) and 2(b), the Co2+ adsorption equilibrium time was achieved in 180 and 120 min for SBox and Cox, respectively.The parameters of IPD and Boyd models estimated by LR analyses of the experimental data are presented in Table2. The adsorption process of Cu2+ and Co2+ on SBox and Cox exhibited three stages (Figures not shown). These plots suggest that the adsorption of Cu2+ and Co2+ on SBox and Cox was initially governed by the diffusion of Cu2+ or Co2+ through the thin solvent film surrounding both Cox and SBox particles and then changed to intraparticle diffusion. Afterward, equilibrium was reached. Boyd’s plots (Figures not shown) were only linear for the initial stage of Cu2+ or Co2+ adsorption and did not intersect the origin, suggesting that external mass transfer can be the rate-limiting step governing the initial stage of Cu2+ or Co2+ adsorption, which then changed to intraparticle diffusion, corroborating the IPD plots [48]. In addition, for both adsorbent materials, the values of D
i were higher for Cu2+ adsorption than Co2+ adsorption, which will have a great influence in the behavior of Cu2+ and Co2+ adsorption on SBox in a fixed-bed column, as presented in Section 3.4.


## 3.2.3. Adsorption Isotherms of Cu2+ and Co2+ on SBox and Cox

Adsorption isotherms can be employed to describe the different affinities of various solutes for the adsorption sites of an adsorbent. To evaluate the equilibrium data, Freundlich, Langmuir, and Sips models, three of various isotherm models available in the literature, were chosen. The isotherm model parameters estimated by fitting the models to the experimental data are presented in Table3. The curves fitted to the experimental data of Cu2+ and Co2+ adsorption on SBox and Cox are presented in Figures 3(a) and 3(b).Figure 3
Isotherms for adsorption of Cu2+ and Co2+ on (a) Cox and (b) SBox (pH 5.5, 25°C, 150 rpm, and 0.2 g/L Cox or SBox).
(a)
(b)Table 3
Isotherm model parameters estimated for the adsorption of Cu2+ and Co2+ on Cox and SBox (pH 5.5, 25°C, 150 rpm and 0.2 g/L Cox or SBox).
Isotherm model
Parameter
Cox-Cu2+
Cox-Co2+
SBox-Cu2+
SBox-Co2+
Experimental data
Q
max
,
exp
mmol
/
g
1.20 ± 0.01
0.68 ± 0.01
0.57 ± 0.00
0.37 ± 0.00
Q
max
,
exp
mg
/
g
76.14 ± 0.92
39.82 ± 0.33
36.23 ± 0.10
22.05 ± 0.25
I
e
mol
/
L
3.145 × 10−3
3.365 × 10−3
3.148 × 10−3
3.407 × 10−3
γ
e
0.789
0.783
0.789
0.782
CN
4.01
7.10
7.89
12.03
Langmuir
Q
max
,
est
mmol
/
g
1.17 ± 0.03
0.70 ± 0.01
0.60 ± 0.01
0.40 ± 0.00
Q
max
,
est
mg
/
g
74.36 ± 2.11
41.24 ± 0.35
38.07 ± 0.57
23.64 ± 0.22
b
L
/
mmol
30.47 ± 0.068
23.04 ± 1.09
17.93 ± 1.24
11.67 ± 0.53
R
2
0.914
0.988
0.977
0.989
R
adj
2
0.908
0.987
0.974
0.988
χ
red
2
0.006
2.08 × 10−4
4.40 × 10−4
1.03 × 10−4
K
a
38616.6
29430.3
22728.9
14944.3
Δ
G
°
kJ
/
mol
‒26.18
‒25.51
‒24.87
‒23.83
Freundlich
K
F
mmol
/
g
L
/
mmol
1
/
n
1.22 ± 0.02
0.68 ± 0.01
0.57 ± 0.01
0.37 ± 0.01
n
5.43 ± 0.26
7.25 ± 0.78
6.01 ± 0.52
5.39 ± 0.43
1
/
n
0.184
0.138
0.167
0.185
R
2
0.975
0.900
0.933
0.939
R
adj
2
0.974
0.890
0.926
0.933
χ
red
2
0.002
0.002
0.001
5.89 × 10−4
Sips
Q
max
,
est
mmol
/
g
1.62 ± 0.08
0.72 ± 0.01
0.64 ± 0.03
0.42 ± 0.01
Q
max
,
est
mg
/
g
102.83 ± 5.01
42.52 ± 0.77
40.68 ± 1.59
25.01 ± 0.62
b
L
/
mmol
10.71 ± 2.54
23.88 ± 1.17
17.20 ± 1.53
11.26 ± 0.58
n
2.26 ± 0.15
1.19 ± 0.10
1.37 ± 0.18
1.24 ± 0.10
R
2
0.997
0.992
0.988
0.995
R
adj
2
0.996
0.991
0.986
0.993
χ
red
2
2.27 × 10−4
1.45 × 10−4
2.47 × 10−4
5.73 × 10−5The isotherm curves obtained presented a downward-concave profile, characterizing a favorable adsorption [35]. The steepest initial slopes of adsorption isotherms of Cu2+ on SBox and Cox in comparison to Co2+ adsorption isotherms on SBox and Cox indicate that Cu2+ ions had more affinity for the adsorption sites of SBox and Cox than Co2+ ions. This is corroborated by the higher values of b for Cu2+ adsorption than for Co2+ adsorption (Table 3). In addition, for both Cu2+ and Co2+, even at low metal concentrations, the adsorbed amount was relatively high until reaching a plateau at which the adsorbed amount remained constant. In agreement with the classification of isotherms proposed by Giles et al. [49], the profiles of the isotherm curves for all adsorption systems studied corresponded to group L, subgroup 2.The adsorption isotherms (Figures3(a) and 3(b)) with initial curvature (type L) suggest that the available active sites are more difficult to find when the surface coverage increases, indicating that the Cu2+ and Co2+ may have been adsorbed onto a monolayer.The evaluation of the values ofχ
red
2 and the comparison between the values of Q
max
,
exp and Q
max
,
est were used to select the best isotherm model in order to characterize the adsorption systems. Analyzing the values of χ
red
2
,
Q
max
,
exp and Q
max
,
est presented in Table 3, it can be seen that for Cu2+ or Co2+ adsorption on both adsorbents, both the Sips and Langmuir isotherm models can describe very well the experimental data. The Sips model is a hybrid of the Freundlich and Langmuir isotherms. The parameter n of the Sips model can be employed to evaluate the degree of heterogeneity of an adsorption system. Thus, if the value of n is closer to unity, this suggests a more homogeneous adsorption; and if the value of n is equal to unity, the Sips isotherm is reduced to the Langmuir isotherm. Contrarily, if the value of n is far from unity, this indicates a more heterogeneous adsorption system, approaching to the Freundlich model.From the values ofn reported in Table 3 for the Sips model, it is concluded that the adsorption systems involving the adsorption of Co2+ on SBox and Cox are more homogeneous than the adsorption systems involving the adsorption of Cu2+ on SBox and Cox. It is also noted that the adsorption of Cu2+ on Cox is significantly more heterogeneous than other adsorption systems studied.Parameterb of the Langmuir model is associated to the solute affinity for the adsorbent sites [50]. Comparing the values of b of the Langmuir model (Table 3), it is concluded that Cu2+ has a greater affinity for both Cox and SBox adsorption sites than Co2+, as was previously concluded by the initial slopes of Cu2+ adsorption isotherms in comparison to Co2+ adsorption isotherms. The solute affinity for the adsorbent sites of the materials increased in the order: Co2+-SBox < Cu2+-SBox < Co2+-Cox < Cu2+-Cox.The values of variation in standard free energy of adsorptionΔ
ads
G
° were negative for all adsorption systems studied, indicating the spontaneous character of the adsorption in the standard conditions. Adsorption experiments of Cu2+ on raw cellulose (Cel) and raw sugarcane bagasse (SB) were only performed for comparison purposes. The values of Q
max for Cu2+ adsorption on SB and Cel were 0.23 mmol/g (13.3 mg/g) and 0.21 mmol/g (13.2 mg/g), respectively, which showed that SBox and Cox presented a much higher Q
max than SB and Cel. For, example, the values of Q
max
,
exp for Cu2+ adsorption on SBox and Cox were 2.7 times and 5.8 times higher than SB and Cel, respectively, which shows the efficiency of the functionalization process of SB and Cel to obtain SBox and Cox.The values of the coordination numbers (CN) (Table 3) [14] for Cu2+ and Co2+ adsorption on SBox and Cox suggested that not all carboxylic acid groups were available to adsorb metals. The values of CN for adsorption of Cu2+ and Co2+ on Cox were lower than those for adsorption on SBox, indicating that the n
COOH taking part on the adsorption of Cu2+ and Co2+ by SBox and Cox was different. Probably, this was responsible for a decrease in the value of Q
max for SBox in comparison to Cox, as both Cox (4.8 mmol/g) and SBox (4.5 mmol/g) have similar values for n
COOH.


## 3.3. Desorption and Reuse of SBox and Cox

Desorption and re-adsorption were evaluated for both SBox and Cox adsorbents with Cu2+ and Co2+, respectively. The desorption efficiencies E
des and re-adsorption efficiencies E
re
-
ads obtained for both SBox and Cox are presented in Table 4.Table 4
Desorption efficiencyE
des and re-adsorption efficiency E
re
-
ads for Cu2+ and Co2+ for Cox and SBox adsorbents.
Material
Metal ion
E
des
%
E
re
-
ads
%
Cox
Cu2+
87.7
99.4
Co2+
72.3
98.4
SBox
Cu2+
98.1
104.1
Co2+
85.3
92.9It was observed that the desorption of the metals was fast, with a maximum value ofE
des achieved in a short time, i.e., 10 min for SBox and 15 min for Cox. The best result for E
des was obtained for the SBox-Cu system; however, the other systems showed values of E
des between 72.3% and 87.7%. Even though SBox and Cox were not completely desorbed, this should not impair their reuse as they still present a large amount of free adsorption sites.The desorption experiments performed at acidic aqueous medium showed that both metals were fast desorbed, which indicated the ion-exchange was the mechanism controlling both adsorption and desorption of both metals. Xavier et al. [23], who investigated the adsorption/desorption/re-adsorption of Co2+, Cu2+ and Ni2+ on trimellitated sugarcane bagasse reported a similar behavior in comparison to that observed in the present study.The infrared spectra of Cox and SBox before and after desorption of Cu2+ (Cox-D-Cu2+, SBox-D-Cu2+) and Co2+ (Cox-D-Co2+, SBox-D-Co2+), respectively, are presented in Figures 4(a) and 4(b). As can be seen in Figures 4(a) and 4(b), the band at 1730 cm−1 related to C=O stretching in carboxylic acid groups is still present in both spectra of Cox and SBox after desorption of Cu2+ and Co2+, showing that both adsorbent materials were not degraded after desorption.Figure 4
FTIR spectra of (a) Cox, Cox-D-Cu2+ and Cox-D-Co2+ and (b) SBox, SBox-D-Cu2+ and SBox-D-Co2+.
(a)
(b)Re-adsorption was performed to evaluate the alternative of reusing both adsorbents. The desorbed SBox and Cox were used in a new adsorption cycle to evaluate their performances as they were not completely desorbed. The obtained results are shown in Table4. The lower value of E
re
-
ads was for Co2+-SBox system; however, the other systems showed values of E
re
-
ads higher than >98%. Therefore, SBox and Cox still exhibited excellent values of E
re
-
ads in comparison to their values of Q
T
,
max showing that these materials are interesting adsorbents from both point of view of chemical resistance to degradation and reuse.


## 3.4. Monocomponent Adsorption of Cu2+and Co2+ on SBox Adsorbent in a Fixed-Bed Column

The choice of SBox to investigate continuous adsorption of Cu2+ and Co2+ in a fixed-bed column is due to its lower cost in comparison to Cox, although Cox had higher values of Q
max
,
exp in comparison to SBox.The breakthrough curves plotted as effluent concentration-time profiles provide information about the dynamic behavior of a determined fixed-bed column adsorption from the mass transfer zone (MTZ). MTZ is the area of the bed where the adsorption of Cu2+ and Co2+ occurs. MTZ varies with t
b, which is the time when the value of C in the effluent reaches 5% of C
0, to t
s, which is the time when the value of C in the effluent reaches 95% of C
0. Figures 5(a) and 5(b) present the breakthrough curves obtained for adsorption of Cu2+ and Co2+ on SBox in a fixed-bed column. Table 5 presents the values of H and Q
max.Figure 5
Breakthrough curves for adsorption of (a) Cu2+and (b) Co2+ on SBox adsorbent in a fixed-bed column at 25°C (experiments from 1 to 7 refers to the 22 experimental design matrices for Cu2+ and Co2+ presented in Tables 1 and 5).
(a)
(b)Table 5
Results of 22 experimental design for adsorption of Cu2+ and Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
Number of experiment
Independent variable
Cu2+
Co2+
C
0
mmol
/
L
τ
min
Q
max
mmol
/
g
H
cm
Q
max
mmol
/
g
H
cm
1
−1
−1
0.261
0.40
0.091
0.23
2
−1
1
0.237
0.73
0.088
0.82
3
1
−1
0.554
1.50
0.224
0.68
4
1
1
0.428
1.41
0.220
1.58
5
0
0
0.316
1.61
0.203
2.12
6
0
0
0.345
1.54
0.195
1.39
7
0
0
0.347
1.67
0.192
1.71The results presented in Table5 show that the higher value of Q
max (0.554 mmol/g) for Cu2+ adsorption was obtained in experiment 3, while the lower value of Q
max (0.237 mmol/g) was obtained in experiment 2. For Co2+ adsorption, the higher and lower values of Q
max (0.224 and 0.088 mmol/g) were obtained in experiments 3 and 2, respectively. These results suggest that higher levels of initial metal concentration and lower levels of spatial time favored higher values of Q
max. Furthermore, lower levels of initial metal concentration and higher levels of spatial time disfavored higher values of Q
max. In addition, the value of Q
max for Cu2+ in continuous adsorption was 2.9% lower than in batch adsorption, while the value of Q
max for Co2+ in continuous adsorption was 65.2% lower than in batch adsorption.The rate-limiting steps of an adsorption process are: (1) the mass transfer of the Cu2+ or Co2+ from the bulk phase to the SBox surface; (2) the diffusion of the Cu2+ or Co2+ into the SBox porous structure; and (3) the adsorption of Cu2+ or Co2+ onto the SBox surface [51]. In a mass transfer process, the mass flow is proportional to the concentration gradient difference. This is the driving force for the adsorption process. Moreover, the resistance at the liquid film interface (step 1) decreases with increasing flow rate. Therefore, it is expected that higher levels of inlet Cu2+ or Co2+ concentration and lower levels of spatial time provide a higher concentration gradient difference between the adsorbed Cu2+ or Co2+ at the interface and the Cu2+ or Co2+ in the bulk solution, as well as a smaller resistance at the liquid film, thereby increasing the value of Q
max of the adsorbent.Higher values ofH for adsorption of Cu2+ and Co2+ on SBox were obtained at the center point for both metal ions, with 1.67 (experiment 7) and 2.12 cm (experiment 5), respectively. The lower values of H, 0.40 cm for Cu2+ and 0.23 cm for Co2+, were obtained in experiment 1. The characteristics of the breakthrough curve are related with the equilibrium adsorption, mass transfer of Cu2+ or Co2+ from the bulk solution to the SBox surface and porous structure of the SBox as well as with fluid flow properties during continuous adsorption into the column [52]. The instantaneous equilibrium produces, under ideal conditions, a shock-like wave which moves as a sharp concentration step through the bed [53], where the entire length of bed is utilized. This suggests that, at the center point, the overall resistance to the adsorption of Cu2+ or Co2+ on SBox is reduced, favoring the adsorption. As a consequence, the application of lower levels of C
0 and lower levels of τ increased the overall resistance to the adsorption.The 22 experimental design was employed to evaluate the effect of C
0 and τ on the adsorption of Cu2+ and Co2+ on SBox in continuous. The analysis of variance (ANOVA) of the experimental data was carried out. The results are shown in Table 6. It is necessary to have a significant regression for a well-adjusted model, i.e., F
>
F
tab and p
<
0.05 together with a non-significant lack of fit, i.e., F
<
F
tab and p
>
0.05. The linear model used to fit the response Q
max yielded coefficients of determination R
2 of 0.963 for Cu2+ and 0.857 for Co2+. However, the values of R
2 for H for adsorption of Cu2+ (0.579) and Co2+ (0.358) were not high as for Q
max. In addition, the models used to fit the DVs Q
max for Co2+and H for Cu2+ exhibited a lack of fit, indicating that these models cannot predict the behavior of these dependent variables very well.Table 6
ANOVA for 22 experimental design for adsorption of Cu2+ and Co2+ on SBox in a fixed-bed column adsorption at 25°C.
Response
Q
max
Cu
2
+
R
2
=
0.963
H
Cu
2
+
R
2
=
0.579
Factor
Effect
SS
dF
MS
F
p
Effect
SS
dF
MS
F
p
(1)τ
min
−0.075
0.006
1
0.006
18.536
0.050
0.12
0.014
1
0.014
3.402
0.206
(2)C
0
mmol
/
L
0.242
0.058
1
0.058
192.608
0.005
0.890
0.792
1
0.792
187.110
0.005
1 by 2
−0.051
0.003
1
0.003
8.622
0.099
−0.210
0.044
1
0.044
10.417
0.084
Lack of fit
0.002
1
0.002
6.528
0.125
0.610
1
0.610
144.166
0.007
Pure error
0.001
2
0.000
0.008
2
0.004
Total SS
0.069
6
1.469
6
Response
Q
max
Co
2
+
R
2
=
0.857
H
Co
2
+
R
2
=
0.358
Factor
Effect
SS
dF
MS
F
p
Effect
SS
dF
MS
F
p
(1)τ
/
min
−0.004
0.000
1
0.000
0.387
0.597
0.745
0.555
1
0.555
4.145
0.179
(2)C
0
/
mmol
/
L
0.132
0.017
1
0.017
465.534
0.002
0.605
0.366
1
0.366
2.734
0.240
1 by 2
−0.001
0.000
1
0.000
0.011
0.927
0.155
0.024
1
0.024
0.179
0.713
Lack of fit
0.003
1
0.003
75.858
0.013
1.427
1
1.427
10.660
0.082
Pure error
0.000
2
0.000
0.268
2
0.134
Total SS
0.020
6
2.640
6As can be seen in Table6, both independent variables were statistically significant for response Q
max for Cu2+ with τ presenting a negative effect and C
0 a positive effect on Cu2+ adsorption. This means that the use of C
0 in a higher level and τ in a lower level favored a higher value of Q
max. The DV
Q
max for Co2+ adsorption was only influenced by C
0 with this variable presenting a statistically significant positive effect. For the DV H, both variables were not statistically significant for Co2+ adsorption, and only C
0 was statistically significant, presenting a positive effect on Cu2+ adsorption. The interactions between the independent variables C
0
×
τ had no statistically significant effects on any DVs (Q
max or H) evaluated for the adsorption of both metals on SBox.When comparing these results of adsorption in continuous with the profiles of the kinetic curves obtained for batch adsorption of Cu2+ and Co2+ on SBox (Figures 2(a) and 2(b)), it can be seen that the spatial time only influenced Cu2+ adsorption, which presented kinetic curves with steeper initial slopes than those for Co2+ adsorption. This suggests that the mass transfer of Cu2+ or Co2+ from the bulk phase to the SBox surface may have contributed more to the rate-limiting step for Cu2+ adsorption on SBox while Co2+ adsorption on SBox may be influenced by both diffusional and adsorption rates.Table7 presents the results when Bohart-Adams original model was used to model the experimental breakthrough curves. The Bohart-Adams original model better fitted the experimental breakthrough curves for Co2+ adsorption than those for Cu2+ adsorption, presenting higher R
2 values and smaller RMSE values. The values of Q
max estimated by the Bohart-Adams original model and those obtained experimentally presented low values of mean absolute error (MAE), between 4.2% and 1.9% for Cu2+ and Co2+ adsorption, respectively, showing that this model can predict the experimental data very well.Table 7
Results of the modeling the experimental breakthrough curves with the Bohart–Adams model for adsorption of Cu2+ and Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
Metal ion
Cu2+
Number of experiment
1
2
3
4
5
6
7
Q
max
,
exp
mmol
/
g
0.261
0.237
0.554
0.428
0.316
0.345
0.347
k
B
-
A
L
/
mmol
min
0.101
0.075
0.061
0.042
0.092
0.068
0.100
Q
max
mmol
/
g
0.249
0.215
0.480
0.377
0.294
0.291
0.288
RMSE
0.053
0.047
0.085
0.066
0.056
0.062
0.065
R
2
0.979
0.979
0.944
0.964
0.980
0.967
0.973
Metal ion
Co2+
Number of experiment
1
2
3
4
5
6
7
Q
max
,
exp
mmol
/
g
0.091
0.088
0.224
0.220
0.203
0.195
0.192
k
B
-
A
L
/
mmol
min
0.322
0.253
0.213
0.118
0.158
0.162
0.164
Q
max
mmol
/
g
0.081
0.080
0.165
0.204
0.201
0.176
0.171
RMSE
0.043
0.022
0.059
0.019
0.047
0.034
0.032
R
2
0.985
0.997
0.967
0.997
0.986
0.992
0.994Figures6(a) and 6(b) show the breakthrough curves obtained for the experiment 7 for adsorption of Cu2+ and Co2+ on SBox in continuous modeled by the Bohart-Adams original model. The values of Bohart-Adams rate constants k
B
-
A for the metals studied were smaller for higher levels of C
0 and/or τ, whereas higher values of k
B
-
A were observed for lower levels of C
0 and/or τ. The k
B
-
A is a lumped parameter [51], which includes all effects of internal and external diffusion, adsorption kinetics as well as any dispersion in the bed. Then, the adsorption in continuous at the conditions evaluated in this study is influenced by all of these effects. However, for Cu2+ adsorption, the k
B
-
A value at center point was closer to experiment 1, while for Co2+ adsorption in the experiment 4 had a value of k
B
-
A closer to that obtained at the center point. As the levels of C
0 and τ in experiments 1 and 4 were opposite (Table 5), this indicates that the adsorption of these metals on SBox, in fact, presented different rate-limiting steps.Figure 6
Breakthrough curves for experiment 7 of the 22 experimental design modeled by the Bohart-Adams original model for adsorption of (a) Cu2+ and (b) Co2+ on SBox adsorbent in a fixed-bed column at 25°C.
(a)
(b)


## 3.5. Comparison with Literature Adsorption Data for Cu2 and Co2+ on Different Adsorbents

Table8 presents some adsorbents reported in the literature for the removal of Co2+ and Cu2+ from spiked aqueous solutions in continuous. It is possible to compare the performance of different adsorbent materials in continuous from the values of Q
max, C
0, and τ. Both the values of C
0 and τ affect the value of Q
max of an adsorbent material. It is possible to have a high value of Q
max using a high value of C
0 combined with a low value of τ or a low value of C
0 combined with a high value of τ. Comparing the performance of SBox adsorbent in continuous with those reported in the literature data, it should be noted that SBox showed a very good performance, mainly for Cu2+ removal, because it presented a medium value of Q
max, which was obtained from a lower value of τ combined with a medium value of C
0. However, SBox presented a lower value of Q
max for Co2+ removal.Table 8
Comparison of adsorbent materials reported in the literature for removal of Cu2+ and Co2+ from aqueous solutions in a fixed-bed column adsorption.
Adsorbent
Fixed-bed column adsorption parameter
Q
max
mmol
/
g
Fixed-bed model
Reference
pH
T (°C)
C
0
mmol
/
L
τ
min
Cu2+
Co2+
SBox
5.5
25
1.26 (Cu), 0.68 (Co)
0.7
0.55
0.22
B
-
A
b
This study
Tetraethylenepentamine modified sugarcane bagasse
5.0
30-35
0.31
-
0.26
-
-
[54]
Sugarcane bagasse modified with trimellitic anhydride (STA)
5.5
25
0.94 (Cu), 1.61 (Co)
1.05 (Cu); 1.4 (Co)
1.06
0.80
Thomasa and B
-
A
a
[23]
Citrus maxima peel
5.4–5.7
25
4.72
1.2
1.54
-
Thomasa
[55]
Passion fruit shell
0.57
-
Sugarcane bagasse
0.35
-
Multi-metal binding biosorbent (MMBB)
5.5
23
0.47
8
0.75
-
Thomasa
[56]
Bagasse fly ash (BFA)
5.0
30
3.14
4.3
0.42
-
-
[57]
Conventional zeolitic BFA (CZBFA)
0.83
-
Electrolyte treated CZBFA
0.84
-
Magnetized sawdust (Fe3O4-SD)
5.0
25
0.16
0.67
0.50
-
Thomasa and B
-
A
a
[58]
Sargassum wightii biomass
4.5
-
1.70
3.9
0.83
BDST
[59]
Biomass beads of immobilizedSaccharomyces cerevisiae (PTCC 5010)
8.0
25
1.70
19.6
0.04
Thomasa
[60]
Polyamine chelating resin (NDC-984)
5.0
30
5.00
12.0
0.96
-
[61]
Native teak leaves power
-
30
0.85
3.14
-
0.35
Thomasa and B
-
A
a
[62]
Biochar of teak leaves
-
0.39
Free seaweedSargassum sp.
5.0
30
0.77
31.4
1.51
-
Thomasb
[63]
Immobilized seaweedSargassum sp.
0.78
1.69
-
SeaweedSargassum sp.
3.5
30
2.08
31.4
0.12
-
Thomasb and B
-
A
b
[64]
aSimplified model; bOriginal model. Thomas: Thomas model; B–A: Bohart–Adams model; BDST: Bed depth service time.


## 4. Conclusions

The oxidized sugarcane bagasse (SBox) and cellulose (Cox) were successfully synthesized by a cheap chemical modification method and shown to be efficient for the removal of Cu2+ and Co2+ from spiked single aqueous solutions in both batch and continuous. The adsorption of Cu2+ on SBox and Cox was better modeled by the pseudo-second-order kinetic model, while the adsorption of Co2+ on SBox and Cox was better modeled by the pseudo-first-order kinetic model. The results of equilibrium adsorption were modeled by three isotherm models and the Sips and Langmuir models closely fitted the experimental data with maximum adsorption capacities Q
max of 1.20 and 0.57 mmol/g for Cu2+ and 0.68 and 0.37 mmol/g for Co2+ adsorption on Cox and SBox, respectively. In addition, Cox and SBox exhibited excellent desorption efficiencies E
des and re-adsorption efficiencies E
re
-
ads, allowing their reuse in further adsorption cycles. SBox was further used in fixed-bed column adsorption experiments. The Bohart–Adams original model fitted continuous adsorption data very well. The value of Q
max for Cu2+ (0.55 mmol/g) was closer to batch adsorption, while Q
max for Co2+ (0.22 mmol/g) was lower than that obtained in batch adsorption. Thus, the main results obtained in this study show that both adsorbents are interesting materials for a real application in a wastewater treatment plant, mainly SBox, which is a cheaper adsorbent in comparison to Cox.



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*Source: 8620431-2020-01-10.xml*