# Adsorption of Brilliant Green onto Luffa Cylindrical Sponge: Equilibrium, Kinetics, and Thermodynamic Studies

Authors: Olaseni Segun Esan; Oladoja Nurudeen Abiola; Olanrewaju Owoyomi; Christopher Olumuyiwa Aboluwoye; Medinat Olubunmi Osundiya
Journal: ISRN Physical Chemistry
 (2014)

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## Abstract

The sponge of Luffa cylindrical (LFC), a fibrous material, was employed as adsorbent for the removal of Brilliant Green (BGD) from aqueous effluent via batch studies. The optimum removal of BGD was found at pH 8.2 and the equilibrium was attained within 3 hours. The kinetic data are analyzed using several models including pseudo-first-order, pseudo-second-order, power function, simple elovich, intraparticle diffusion, and liquid film diffusion. The fitting of the different kinetics models to the experimental data, tested by error analysis, using the linear correlation coefficientr2 and chi-square analysis χ2, showed that the mechanism of adsorption process was better described by pseudo-second-order and power function kinetic models. The equilibrium isotherm data were analyzed using Langmuir, Freundlich, and Temkin models and the sorption process was described by the Langmuir isotherm with maximum monolayer adsorption capacity of 18.2 mg/g at 303 K. The thermodynamic properties ΔG0, ΔH0, and ΔS0 showed that adsorption of BGD onto LFC was spontaneous, endothermic, and feasible within the temperature range of 303–313 K.


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## Body

## 1. Introduction

Worldwide, over7×105 tons of dyes and pigments are produced annually [1] and an estimated 90% of this ends up on fabrics [2]. Due to the development of textile, printing, and tanning industries, large amounts of dye water waste are produced [3]. The textile industry alone accounts for two-third of the total dye stuff production and about 10 to 15% of the used dyes come out through the effluent [4]. Wastewater containing dyes is difficult to treat, since the dyes are recalcitrant organic molecules, resistant to aerobic digestion and are stable to light, heat, and oxidizing agents [5]. Efficient color removal from wastewaters is, therefore, of high importance, and so in recent years, it has attracted increased research and technological interest, involving physical and/or chemical methods (i.e., coagulation/flocculation) [6], adsorption [7], oxidation [8], and membrane based separation [9–11].Amongst all these treatment methods, adsorption is the most appropriate and efficient technique for the removal of nonbiodegradable pollutants (including dyes) from waste water [12, 13]. Although many adsorbents have been reported for removing some common dyes [14–19], such as methyl orange, methylene blue, Congo Red, and Brilliant Green (Figure 1), activated carbon has proven to be the most widely used adsorbent for the removal of dye but this has been restricted due to regeneration problem and high cost [20].Figure 1
Brilliant Green.Recently, researchers have focused on the development of cheaper, nonconventional, low-cost adsorbents as an alternative to activated carbon. Some of these include powdered peanut [21], bagasse fly ash [22], palm kernel coat [23], and raw pine cone [24].Brilliant Green (BGD) which appears as golden crystal is an organic dye that belongs to the family of triphenylmethane [25] and has been used for various purposes, for example, biological stain, dermatological agent, veterinary medicine, and an additive to poultry feed to inhibit propagation of mold, intestinal parasites, and fungus [19]. This dye is known to be toxic to humans and animals when injected. It causes irritation to the gastrointestinal tract and upon prolonged exposure resulted in organ damage [26]. Upon decomposition of this dye, carbon dioxide, sulphur oxides, and nitrogen oxides are produced [27].Luffa cylindrical (LFC) belongs to the Cucurbitaceae family [28] and is commonly grown in China, Japan, Nigeria, and countries in central and South America. LFC sponge is composed mainly of cellulose, hemicelluloses, and lignin [29]. On this note, LFC is called lignocelluloses material. Because it has a fibrous vascular system that can allow the removal of water pollutants. Various researchers utilized Luffa cylindrical in different forms to remove dyes from solution. Like Ola [30] used luffa activated carbon, Demir et al. [29] used NaOH treated luffa and Oladoja et al. [17] used untreated luffa to remove dyes from solution.Owing to the toxicity of BGD dye, it is essential to remove BGD from waste water. Early, Bhattacharyya and Sarma [31] have used finely ground neem leaf, Kismir and Aroguz [27] used saklikert mud, Mittal et al. [26] used bottom ash and deoiled soya, and Mane et al. [32] used rice husk ash as low-cost adsorbent for removing BGD from aqueous media. In the present study, Luffa cylindrical powder shall be studied as adsorbent for BGD removal.However, this study is detailed to investigate the possibility of utilizing LFC for the removal of BGD from aqueous solution by performing batch studies. The effect of different experimental conditions, such as contact time, initial pH, initial dye concentration, and temperature were investigated, and the adsorption mechanism was examined using kinetic and thermodynamic studies.


## 2. Materials and Methods

### 2.1. Sorbent Preparation

LFC was obtained locally from Akungba-Akoko, the University town, Nigeria. The LFC was dehusked and the intervening tissue was removed [17] while the LFC fibers were washed with water to remove all the water soluble contaminant, until the washing became clear, and dried in the oven at 70°C for 6 h [29]. The dried LFC fibers were ground with Laboratory blender and screened through a set of sieves to obtained particles of size 100 µm.


### 2.2. Dye Solution and Reagents

BGD [Sulfate of N,N-diethylaniline] is a cationic dye classified as C.I. basic green 1; (C.I. 42040; FW: 462.65 and 625 nmλmax⁡) was obtained from Fine Chemical, Mumbai, India and used without further purification. Stock solution, (500 mg/L), was prepared and working solutions were prepared from the stock by serial dilution. The pH of the solution was adjusted when required by adding drops of HCl (1.0 M or 0.1 M) or NaOH (1.0 M or 0.1 M) solutions. Changes were monitored with a pH meter (Jenway, model 710, USA).


### 2.3. Dye Quantification

The BGD concentration in aqueous solution was quantified by the determination of the optical density at the characteristic wavelength using a double beam UV/visible spectrophotometer. A standard solution of the dye was taken and the optical density was determined at different wavelength to obtain a plot of optical density versus wavelength. The wavelength corresponding to the maximum optical density(λmax⁡=625nm), as determined from this plot, was noted and the wavelength was used for the preparation of the calibration curve used in the present studies.


### 2.4. Characterization of Adsorbent (LFC)

#### 2.4.1. Point of Zero Charge (PZC) Determination and FTIR Study

The pHZPC shows considerable usage for the determination of surface electrical neutrality at a definite pH value. The determination of zero point charge (pHZPC) was done via the solid addition method [33]. Possible involvement of functional groups from LFC during the removal of BGD from aqueous solution was elucidated using the Fourier transform infrared (FTIR) analysis. FTIR spectra were obtained on a PerkinElmer FTIR-600 spectrometer. The analysis conditions used were 16 scans at a resolution of 4 cm−1 measured between 400 and 4000 cm−1.


### 2.5. Adsorption Experiments

Batch adsorption experiment studies were conducted by agitating 0.1 g of adsorbent with 50.0 mL of BGD solution of the desired initial dye concentration of 20–200 mg/L in a 250 mL stoppered conical flask. The mixture was agitated in a temperature controlled orbital shaker at a constant speed of 160 rpm at required temperature. Samples were withdrawn at regular interval and centrifuged and the residual BGD concentration was calculated from the calibration curve [34]. The kinetics of adsorption was conducted by analyzing adsorptive uptake of the dye from the aqueous solution at different time intervals (2, 5, 10, 30, 60, 90, 120, and 180 min). For studying the effect of solution pH on dye adsorption, experiment was conducted at different pH varying from 4.2 to 9.3 for initial dye concentration of 200 mg/L. To observe the effect of temperature on dye adsorption, sorption characteristic was investigated by determining the adsorption isotherms at 303, 313, 323, and 333 k. The amount of sorbate sorbed per unit mass of the LFC (qt in mg/g) and percentage dye removal efficiency, R, was calculated using the mass balance procedure as follows:
(1)qt=(C0-Ct)VM,R=(C0-CtC0)·100,
where C0 is the initial dye concentration (mg/L), Ct is the concentration of dye at any time t, V is the volume of solution in (L), and M is the mass of BGD (g).


### 2.6. Error Analysis

In the present study, each of the isotherm models was tested using the linear coefficient of determination,r2, and the chi-square statistical method, χ2. The coefficient of determination, r2, represents the percentage of variability in the dependents variable that has been explained by regression line. The value of the coefficient of determination may vary from zero to one. The linear coefficient of determination, r2, found from evaluation of data by linear model, was calculated with the aid of the following equation:
(2)r2=Sxy2SxxSyy,
where Sxx is the sum of squares of x, Syy is the sum of square of y, and Sxy is the sum of squares of x and y.In order to evaluate the best of the isotherm models that fit the experimental data, the sorption process was also examined using nonlinear chi-square statistical test. The chi-square statistic test is basically the sum of the squares of the differences between the experimental data and data obtained by calculating from models, with each squared difference divided by the corresponding data obtained by calculating from models. The equivalent mathematical statement is(3)χ2=∑(qe,exp⁡-qe)2qe.
If data from model are similar to the experimental data, then χ2 will be a small number, and if they are different, χ2 will be a bigger number.


## 2.1. Sorbent Preparation

LFC was obtained locally from Akungba-Akoko, the University town, Nigeria. The LFC was dehusked and the intervening tissue was removed [17] while the LFC fibers were washed with water to remove all the water soluble contaminant, until the washing became clear, and dried in the oven at 70°C for 6 h [29]. The dried LFC fibers were ground with Laboratory blender and screened through a set of sieves to obtained particles of size 100 µm.


## 2.2. Dye Solution and Reagents

BGD [Sulfate of N,N-diethylaniline] is a cationic dye classified as C.I. basic green 1; (C.I. 42040; FW: 462.65 and 625 nmλmax⁡) was obtained from Fine Chemical, Mumbai, India and used without further purification. Stock solution, (500 mg/L), was prepared and working solutions were prepared from the stock by serial dilution. The pH of the solution was adjusted when required by adding drops of HCl (1.0 M or 0.1 M) or NaOH (1.0 M or 0.1 M) solutions. Changes were monitored with a pH meter (Jenway, model 710, USA).


## 2.3. Dye Quantification

The BGD concentration in aqueous solution was quantified by the determination of the optical density at the characteristic wavelength using a double beam UV/visible spectrophotometer. A standard solution of the dye was taken and the optical density was determined at different wavelength to obtain a plot of optical density versus wavelength. The wavelength corresponding to the maximum optical density(λmax⁡=625nm), as determined from this plot, was noted and the wavelength was used for the preparation of the calibration curve used in the present studies.


## 2.4. Characterization of Adsorbent (LFC)

### 2.4.1. Point of Zero Charge (PZC) Determination and FTIR Study

The pHZPC shows considerable usage for the determination of surface electrical neutrality at a definite pH value. The determination of zero point charge (pHZPC) was done via the solid addition method [33]. Possible involvement of functional groups from LFC during the removal of BGD from aqueous solution was elucidated using the Fourier transform infrared (FTIR) analysis. FTIR spectra were obtained on a PerkinElmer FTIR-600 spectrometer. The analysis conditions used were 16 scans at a resolution of 4 cm−1 measured between 400 and 4000 cm−1.


## 2.4.1. Point of Zero Charge (PZC) Determination and FTIR Study

The pHZPC shows considerable usage for the determination of surface electrical neutrality at a definite pH value. The determination of zero point charge (pHZPC) was done via the solid addition method [33]. Possible involvement of functional groups from LFC during the removal of BGD from aqueous solution was elucidated using the Fourier transform infrared (FTIR) analysis. FTIR spectra were obtained on a PerkinElmer FTIR-600 spectrometer. The analysis conditions used were 16 scans at a resolution of 4 cm−1 measured between 400 and 4000 cm−1.


## 2.5. Adsorption Experiments

Batch adsorption experiment studies were conducted by agitating 0.1 g of adsorbent with 50.0 mL of BGD solution of the desired initial dye concentration of 20–200 mg/L in a 250 mL stoppered conical flask. The mixture was agitated in a temperature controlled orbital shaker at a constant speed of 160 rpm at required temperature. Samples were withdrawn at regular interval and centrifuged and the residual BGD concentration was calculated from the calibration curve [34]. The kinetics of adsorption was conducted by analyzing adsorptive uptake of the dye from the aqueous solution at different time intervals (2, 5, 10, 30, 60, 90, 120, and 180 min). For studying the effect of solution pH on dye adsorption, experiment was conducted at different pH varying from 4.2 to 9.3 for initial dye concentration of 200 mg/L. To observe the effect of temperature on dye adsorption, sorption characteristic was investigated by determining the adsorption isotherms at 303, 313, 323, and 333 k. The amount of sorbate sorbed per unit mass of the LFC (qt in mg/g) and percentage dye removal efficiency, R, was calculated using the mass balance procedure as follows:
(1)qt=(C0-Ct)VM,R=(C0-CtC0)·100,
where C0 is the initial dye concentration (mg/L), Ct is the concentration of dye at any time t, V is the volume of solution in (L), and M is the mass of BGD (g).


## 2.6. Error Analysis

In the present study, each of the isotherm models was tested using the linear coefficient of determination,r2, and the chi-square statistical method, χ2. The coefficient of determination, r2, represents the percentage of variability in the dependents variable that has been explained by regression line. The value of the coefficient of determination may vary from zero to one. The linear coefficient of determination, r2, found from evaluation of data by linear model, was calculated with the aid of the following equation:
(2)r2=Sxy2SxxSyy,
where Sxx is the sum of squares of x, Syy is the sum of square of y, and Sxy is the sum of squares of x and y.In order to evaluate the best of the isotherm models that fit the experimental data, the sorption process was also examined using nonlinear chi-square statistical test. The chi-square statistic test is basically the sum of the squares of the differences between the experimental data and data obtained by calculating from models, with each squared difference divided by the corresponding data obtained by calculating from models. The equivalent mathematical statement is(3)χ2=∑(qe,exp⁡-qe)2qe.
If data from model are similar to the experimental data, then χ2 will be a small number, and if they are different, χ2 will be a bigger number.


## 3. Result and Discussion

### 3.1. Results of Point of Zero Charge (pHPZC) Determination and FTIR Analysis

The point of intersection of ΔpH versus pH0 showed that the pHZPC of LFC occurred at pH 5.2 as shown in Figure 2. This showed that at pH less than 5.2 the surface of LFC is predominated by positive charges while at pH greater than 5.2, the surface is predominated by negative charges.Figure 2
Results of the determination of the pHZPC.It was clear from Figures3 to 4 that FTIR spectra of the LFC before and after adsorption of BGD displayed a number of absorption peaks, reflecting the complex nature of the material examined. They are carbonyl and hydroxyl groups, on the surface of LFC from FTIR analysis [35]. The broad absorption peaks around 3423 cm−1 were indicative of existence of bonded hydroxyl groups on the surface of LFC. The peaks at 2902 and 2360 cm−1 were assigned to the stretching vibration and bending vibration of C–H bond in methylene group, respectively. The broad band at 1735 cm−1 was assigned to the carbonyl and carbonyl moieties (C=O). The peaks associated with the stretching vibration in aromatic rings were verified at 1597 and 1425 cm−1. The peak at 1236 cm−1 was assigned to the bending vibration of carboxylic groups while deformation related to C–O bond was observed at 1057 cm−1 which also confirmed the lignin structure of the LFC. All of these surface functional groups of the LFC can interact with the BGD molecules. Thus, the adsorption of BGD on LFC may be attributed to (i) chemical interaction between surface functional groups and BGD molecules (ii) electrostatic interaction between the BGD molecules and electron-rich sites on the LFC surface, and (iii) week physical forces, mainly hydrogen bonding and van der Waals interactions between the BGD molecules and the LFC. Therefore, the adsorption of BGD onto LFC surface may emanate from the interaction between the carboxyl group of LFC and the electronegative groups in BGD, hydrogen bonding between the hydroxyl group of LFC and the nitrogen of the BGD molecules, and hydrogen bonding between the hydroxyl group of the LFC and the aromatic ring in the BGD molecule. This has confirmed that adsorption of BGD onto LFC follows a complicated pattern which involved both physical and chemical.Figure 3
FT-IR of Luffa cylindrical (LFC) before adsorption of BGD.Figure 4
FT-IR of Luffa cylindrical (LFC) after adsorption of BGD.


### 3.2. Effect of pH on the Adsorption Capacity

It is a known fact that solution pH is an important variable in sorption studies. The pH of the solution affects surface charge of the adsorbent, the degree of ionization of adsorbate molecule, and extent of dissociation of functional groups on the active sites of the adsorbent [19]. The dye uptake variations at different pH value and initial concentrations of 200 mg/L are shown in Figure 5. The adsorption rate changed at the beginning, from 11.5% at pH 2.0 to 89.9% at pH 6.97. With a further increase of pH from 6.97 to 10.0, the adsorption rate decreased. Consequently, pH 6.97 was selected as the operating pH for subsequent studies.Figure 5
Effects of initial solution pH on the sorption of BGD onto LFC.The possible explanations are as follows. (i) LFC has an estimated point of zero charge of pH 5.2, above which LFC surface is predominantly negatively charge, leading to a favorable electrostatic interaction between the cationic BGD molecule and the LFC, hence there is a linear increase in BGD uptake as shown in Figure5. (ii) In an acidic and at lesser alkaline medium, the Cl− and OH− from HCl and NaOH destroy the conjugated bond present in the aromatic rings of the dye molecule upon which the BGD structure changed and result in the formation of colorless compound [36], leading to increase in the uptake of BGD molecule from solution as shown in Figure 5. (iii) The presence of carboxyl groups on the surface of LFC, as confirmed by Figures 3 and 4 also, enhances sorption of BGD with increase in pH from 2 to 8 and later decrease at pH 10. This is because the pka value of carboxyl groups lies within the range of 3.8–5.0 [37]. Below pH 5.0, the carboxyl group on the surface of LFC gets protonated (H+) making the number of positive charge sites increase and the number of negative charge decrease resulting in electrostatic repulsion, hence decrease in BGD uptake by LFC. With an increase in pH of the solution, these functional groups became deprotonated (COO−), which resulted in an increase in the negative charge density on the LFC surface and facilitated the binding of BGD dyes [38]. Hence, the BGD ions binding to the adsorbent could be assumed to involve electrostatic interaction between cationic dyes and negatively charged COO− groups.The results of the equilibrium pH (i.e,pHf) at different initial solution pH (2–10) ranged between 2.39 and 9.3 for BGD/Luffa system as shown in Figure 5. The pHf values were higher than pH0 values for pH0<8.0 and this could be attributed to change in the structure of dye molecule.


### 3.3. Effect of Initial Dye Concentration and Adsorption Kinetics

The rates of sorption of BGD by LFC at different initial BGD concentrations are shown in Figure6. Uptake of BGD was rapid and equilibrium was attained within 180 min. It was found that the amount BGD sorbed increased from 9.2 to 92.9 mg/g with increasing initial concentration from 20–200mg/L. The adsorption was initially rapid and then slowed down over time. This observation was ascribed to a large number of available binding sites for adsorption during the initial stage, and then the remaining sites were difficult to occupy due to repulsive forces between the dye molecules on the LFC and the bulk phase [39]. The results showed that the time taken to attain equilibrium was independent of the initial dye concentration. Similar profile has been reported in the literature for the effect of time and initial concentration for the removal of BGD by adsorbents like kaolin [19], bottom ash and deoiled soya [26], neem leaf powder [31], and modified peat-resin [40].Figure 6
Effect of contact time on the removal of BDG onto LFC.In order to explore the kinetics involved in dye sorption, the experimental data were fitted into four kinetic models including the pseudo-first-order equation [41], pseudo-second-order equation [42], power function [43], and simple Elovich [44].The linear form of the pseudo-first-order kinetic is expressed as follows:(4)ln⁡(qe-qt)=ln⁡qe-kit,
where qe and qt are BGD adsorbed at equilibrium and time t, respectively (mg/g), and k1 is the rate constant for the pseudo-first-order model (min−1). The pseudo-first-order constant k1 and the correlation coefficient, r2, deduced from the kinetic data are presented in Table 1. The r2 value was poor and ranged between 0.747 and 0.966. A significant chi χ2 values were also obtained indicating the inapplicability of this model to the sorption process.Table 1
Kinetic parameters of sorption of BGD on LFC.
Initial conc.
Pseudo-first-order
Pseudo-second-order
Power function
Simple Elovich
mg/L
q
e
1
k
1
×
1
0
-
2
r
2
q
e
2
k
2
h
0
r
2
a
b
r
2
A
B
20
1.54
0.2303
0.820
9.621
0.132
12.20
0.999
8.79
0.016
0.920
8.80
0.799
40
1.86
0.2303
0.794
19.230
0.097
35.87
1.000
17.78
0.014
0.911
17.78
1.462
80
3.07
0.4606
0.747
40.000
0.057
91.20
1.000
35.73
0.015
0.916
35.70
3.001
150
7.50
1.1515
0.966
76.920
0.011
65.08
0.999
63.39
0.025
0.977
63.26
9.046
200
17.82
1.1612
0.916
100.000
0.004
40.00
0.999
70.15
0.051
0.967
69.51
22.48
k
1 = min−1, qe1 = mg/g, qe2 = mg/g, k2 =  g/mg/min, B = g/mg, A = mg/g min.The pseudo-second-order kinetic model is represented by the following linear equation:(5)tqt=1k2qe2+1qet,
where k2 is the rate constant for the pseudo-second-order model (g(mg min)−1), where qe, qt, and t have the same meaning as explained above.The initial sorption rate can be obtained from the pseudo-second-order linear plots asqt/t approaches zero:
(6)h0=k2qe2,
where h0 = initial sorption rate.Equation (3) can be rearranged to obtain [45] as follows:
(7)qt=11/h0+t/qe.
The r2 values for the pseudo-second-order kinetic model were close to 1.0 for all cases. Comparing r2 and chi χ2 value for pseudo-first- and second-kinetic model (Table 1), it is obvious that for the entire adsorption period, the pseudo-second-order model fits the experimental data better than the pseudo-first-order model. It thus shows that the system under study was more appropriately described by the pseudo-second-order model. This indicates that the adsorption mechanism for BGD is chemisorptions, involving covalent forces through sharing or exchange of electrons between sorbent and sorbate [46].The value ofh0, qe, and k2 along with r2 for the pseudo-second-order models are shown in Table 1. The value of qe increased with increase in the initial BGD concentration while h0 increase from 12.20 to 91.20 and later decreased drastically to 40.00 with the increases in initial concentration of BGD. According to Ho and Mckay [47] if the dye uptake is chemically rate controlled, the pseudo-second-rate constant will be independent of particle diameter and flow rate will depend on concentration of the ions in solution.Logarithm plots of pseudo-second-order constants,k2, and h0, versus C0 of BGD concentration were made, and the plots were found to be straight line whose linear regression values r2, in terms of C0, were given as 0.992 and 0.946, respectively [45].Mathematical expressions were therefore drawn relating the two pseudo-second-order constants and initial concentration as follows:(8)k2=-0.008C0-0.656,h0=-4.228C08.408.
Linear plots of qe2, k2, and h0 against initial concentration (C0) were regressed to obtain these values in terms of C0 with high concentration coefficient. Each of these parameters can be expressed as a function of C0 for BGD as reported by Ho and McKay [47];
(9)qe=C0EqC0+Fq,(10)k2=C0EkC0+Fk,(11)h0=C0EhC0+Fh,
where Eq, Fq, Ek, Fk, Eh0, and Fh0 are constants related to the respective equations. The values for these constants are listed in Table 2. Hence the generalized predictive model for BGD sorbed at any contact time and initial concentration within the given range with relationship of qe, C0, and t can be represented as follows by substituting the various values in  (10).Table 2
Empirical parameters for predictedqe, k, and h0 from C0 for BGD dye.
E
q (g/mg)
F
q (g min/L)
r
2
E
k (mg min/g)
F
k (mg2 min/gL)
r
2
E
h
0 (g min/mg)
F
h
0 (g min/L)
r
2
0.507
0.594
0.946
16.0
×
10
-
4
0.128
0.921
1.326
15.46
0.998For BGD-LFC system [47]:
(12)qt=t1/(1.326C0+15.46)+1/(0.507C0+0.594)t.
Equation (12) represents the generalized predictive model for BGD sorbed at any time and the initial BGD concentration within the given range.To further establish the appropriate kinetic for BGD uptake, the experimental data was fitted again to power function and simple Elovich models.The power function model is a modified form of the Freundlich equation and may be expressed as:(13)log⁡⁡q=log⁡⁡a+blog⁡⁡t
while the simple Elovich [45] is expressed as:
(14)q=A+2.303Blog⁡⁡t.
The results obtained for the fitting of the kinetic models to explained data are presented in Table 1 and the error functions are presented in Table 3. For the pseudo-first-order kinetic and simple Elovich models, the predicted qe values were at variance coincident with the experimental qe values. The predicted qe values derived from pseudo-second-order and power function model agreed with the experimental qe data. The values χ2 of the error function were negligible for pseudo-second-order and power function model. This result indicates that the pseudo-second-order and power function model provided a high degree of correlation with the experimental data for the sorption of BGD by LFC.Table 3
Error analysis for the kinetic data of the sorption of BGD on LFC.
Initial conc.
Pseudo-first
q
e
=
q
e
(
1
-
e
-
k
i
t
)
Pseudo-second
q
e
=
t
k
2
q
e
2
/
(
1
+
t
k
2
q
e
)
Power function
q
e
=
a
t
b
Simple Elovich
q
e
=
A
+
B
ln
⁡
⁡
t
(mg/L)
χ
2
r
2
χ
2
r
2
χ
2
r
2
χ
2
r
2
20
12.376
0.997
1.83
×
10
-
4
0.999
5.28
×
10
-
4
1.000
1.150
1.000
40
24.698
0.997
1.89
×
10
-
4
1.000
3.55
×
10
-
4
1.000
1.490
1.000
80
12.985
0.987
2.39
×
10
-
5
1.000
4.51
×
10
-
4
1.000
3.19
1.000
150
1.311
0.940
3.50
×
10
-
3
0.999
1.26
×
10
-
3
1.000
12.93
1.000
200
0.294
0.910
2.06
×
10
-
2
0.999
3.48
×
10
-
3
1.000
47.71
1.000


### 3.4. Intra-Particle Diffusion Model

Intraparticle diffusion model based on the theory proposed by Weber and Morris which has been widely applied for sorption studies was applied to investigate the mechanism of the adsorption of BGD onto LFC. The intraparticle diffusion model is typically given as follows [48]:
(15)qt=kidt0.5+Z,
where Z (mg g−1) is the intercept and kid (mg g−1 min0.5) is the intraparticle diffusion rate constant. Value of kid was obtained from the slope of the linear plot of qt versus t0.5 (Figure 7). Value of Z as shown in Table 3 gives an idea about the thickness of the boundary layer [49]. The deviation from this theory signifies the difference between the rate of mass transfer in the initial and final stage of adsorption [50].Figure 7
Plot ofqt versus t0.5 for the adsorption of BGD onto LFC.However, if the data exhibit multilinear plots, then two or more steps influence the sorption process. The first, sharper portion is attributed to the transport of the solute from bulk solution liquid film to the adsorbent exterior surface. The second linear portion is based on the diffusion across the liquid film surrounding the sorbent particle. The third portion is due to particle diffusion in the liquid contained in the pore and in the sorbate along the pore wall.Figure7 shows a representative qt versus t0.5 plot for BGD adsorption onto LFC for C0=20,40,80,150, and 200 mg/L at 30°C. Observation from the figure shows that the plots were not linear over the whole time range; an indication that more than one process controlled the sorption process which are: surface sorption and intraparticle diffusion. For C0=80,150, and 200 mg/L, there are two linear portions, the first straight portion depicting mesopore diffusion and the second represent micropore diffusion [51]. For C0=20 and 40 mg/L, there is only one linear portion depicting combined mesopore diffusion.There is every possibility that the intraparticle diffusion of BGD into pores is the rate controlling step in the adsorption process. The amount of adsorbate and the driving force for BGD adsorption is less forC0=20 and 40 mg/L as compared to that of C0=80,150, and 200 mg/L; hence, BGD adsorbed in mesopore only, and adsorption into mesopore is the rate-limiting step. For C0=80,150, and 200 mg/L, the driving force increases and overcomes the resistance for getting adsorbed into micropores; therefore, adsorption into micropores is the rate-limiting step for higher C0. An observation from Table 4 shows that Kid1 and Kid2 are higher for higher C0, which indicate enhanced diffusion of BGD through meso- and micropores at higher C0. This is a contribution from higher driving force at higher C0 [51]. Similar results have been reported for adsorption of BGD on saw dust [52], kaolin [19], and rice husk ash [32].Table 4
Macro- and micropores diffusion parameters for  the sorption of BGD by LFC at different initial BG concentration (mg/L).
Initial conc. (mg/L)
k
i
d
1
Intercept
r
2
k
i
d
2
Intercept
r
2
20
0.225
8.54
0.900
0.043
9.04
0.873
40
0.478
17.17
0.901
0.074
18.26
0.932
80
0.953
34.45
0.909
0.115
37.07
0.913
150
1.918
61.68
0.992
0.498
65.97
0.948
200
4.375
66.21
0.990
1.061
78.07
0.835


### 3.5. Liquid Film Diffusion Model

During sorption, the migration of dye molecules from bulk solution through liquid film to the exterior surface of adsorption may play an important role in determining the rate of the adsorption process. To predict the potential rate-controlling step, the adsorption dynamics of BGD onto LFC was investigated utilizing liquid film diffusion model (16) [53]:
(16)ln⁡⁡(1-F)=-kfdt,
where kfd (min−1) is the liquid film diffusion rate constants and F=qt/qe. The plot of -ln⁡(l-F) versus t, for the liquid film diffusion, was tested over all concentration of study. The first 30 mins of sorption process yielded linear plot (r2=0.465–0.943) while the overall yielded (r2=0.747–0.966). The rate constant for liquid film diffusion, kfd, is in the range 8.0×10-3 to 1.7×10-2 for the first 30 min and 2.0×10-3 to 1.6×10-2 for overall (Table 5). The inability of the plot to pass through the origin (i.e., zero intercept) shows that the prediction of this model will have only limited applicability in the adsorption of BGD by LFC.Table 5
Liquid film diffusion parameters for the sorption of BGD by LFC at different initial BGD concentration (mg/L).
Initial conc. (mg/L)
First 30 mins
Overall
k
i
d
1
Intercept
r
2
k
i
d
2
Intercept
r
2
20
0.008
1.85
0.650
0.002
1.93
0.820
40
0.011
2.28
0.465
0.004
2.38
0.794
80
0.017
2.39
0.581
0.005
2.57
0.747
150
0.017
2.19
0.718
0.011
2.28
0.966
200
0.031
1.54
0.943
0.016
1.65
0.916


### 3.6. Adsorption Equilibrium Isotherm Study

The distribution of BGD between the liquid phase and the solid adsorbent phase is a measure of the position of equilibrium in the adsorption process and can be expressed by different equilibrium isotherm models. In this study, the Langmuir, Freundlich, and Temkin isotherms models were used to describe the adsorption process and the isotherm parameters obtained using these models are presented in Table6.Table 6
Adsorption  isotherm constants for BGD on LFC.
Temperature (°C)
Langmuir
Freundlich
Temkin
Q
0
b
R
2
R
L
×
1
0
-
3
K
f
1
/
n
R
2
B
I
A
R
2
30
18.52
17.99
0.991
2.7
17.83
0.722
0.958
27.75
2.150
0.984
40
8.85
28.21
0.963
1.7
2.42
1.212
0.972
28.39
1.014
0.931
50
5.68
35.16
0.961
1.4
1.01
0.176
0.964
35.04
1.410
0.944
60
8.50
5.16
0.998
9.4
7.01
0.952
0.928
58.06
1.070
0.987The linear form of Langmuir’s isotherm model is represented by the following equation:(17)1qe=1Q0+1bQ0Ce.
The values of monolayer sorption capacities, Q0 (mg/g), obtained from Langmuir plot of sorption decreased with increasing temperature. The magnitude of Langmuir constant, b, which is the sorption equilibrium constant (dm3/mg), decreases as shown in Table 6. The decrease of b as temperature increases confirms the exothermic nature of the adsorption [54]. The essential characteristics of the Langmuir isotherm, used to predict the adsorption efficiency, was expressed in terms of a dimensionless equilibrium parameter RL, defined by the following equation [55]:
(18)RL=11+bC0,
where C0 (mg/L) is the highest initial concentration of the adsorbate. The value of RL indicates if the Langmuir isotherm is unfavorable (RL>1), linear (RL=1), favorable (0<RL<1), or irreversible (RL=0). The values of RL at C0 = 200 mg/L in the present study were found to be 2.7×10-3 at 303 K, 1.7×10-3 at 313 K, 1.4×10-3 at 323 K, and 9.4×10-3 at 333 K indicating that the adsorption of BGD on LFC is favorable.The experimental data obtained was also tested with Freundlich isotherm. Freundlich isotherm assumes heterogeneity of adsorption surfaces. The equation is commonly expressed as follows [56]:
(19)log⁡⁡qe=log⁡⁡Kf+1nlog⁡⁡Ce.
The values of the Freundlich constant, Kf and n, related to adsorption capacity and sorption intensity, respectively, obtained from the plot of log⁡⁡qe versus log⁡⁡Ce are presented in Table 6. Kf is the Freundlich affinity coefficient, and 1/n is the Freundlich linearity index. It can be found that the values of Kf and n decrease, indicating that adsorption is favorable at lower temperature predicting endothermic nature of the adsorption process. Experimental data was also fitted to Temkin isotherm.The Temkin isotherm assumes that a decrease in the adsorption heat is linear and that the adsorption is characterized by a uniform distribution of binding energies. The Temkin linear form of isotherm is given by equation [57, 58]:
(20)qe=BIln⁡⁡A+BIln⁡⁡Ce.BI=RT/b, T is the absolute temperature (K), and R is the universal gas constant (8.314 J/molK), A is the equilibrium binding constant (L/mg), and BI is related to the heat of adsorption. The Temkin constants were listed in Table 6. In order to assess the different isotherms and their ability to correlate the experimental results, the theoretical plots for each isotherm have been shown along with the experimental data for the sorption of BGD onto LFC (Figure 7). The r2 and χ2 values were shown in Table 7 and the different isotherms correlated with the experimental depicted in Figure 8 confirmed that the sorption of BGD onto LFC was best described by Langmuir isotherm model. The applicability of the Langmuir isotherm assumes that the entire adsorption sites are equivalent and there is no interaction between adsorbed species.Table 7
Error analysis for isotherm models for the sorption of BGD on LFC.
Initial conc. (mg/L)
Langmuir;qe=QLbce/(1+bce)
Freundlich;qe=kfcf1/n
Tempkin;qe=(RT/b)ln⁡(KTce)
χ
2
χ
2
χ
2
20
0.2664
0.3782
0.4525
40
0.0009
0.1016
0.2386
80
0.0008
1.0420
2.4264
150
0.1251
2.2042
16.5165
200
1.4370
4.1396
126.0713Figure 8
Comparison of experimental data with the theoretical data for equilibrium isotherm studies for the adsorption of BGD onto LFC.


### 3.7. Estimation of Thermodynamic Parameter

To characterize the thermodynamic parameter of adsorption study means to determine Gibb’s free energy, (ΔG0, KJ/mol), enthalpy change (ΔH0, KJ/mol), and entropy (ΔS0, KJ/mol/K) at a given reference temperature and to obtain ΔCp so as to be able to predict the change of the above three parameters with temperature.The Gibb’s free energy change,ΔG, of an association reaction is temperature dependent and best described by
(21)ΔG0=ΔH(TR)0+∫TRTΔCpdT-TΔS(TR)0-T∫TRTΔCpdln⁡⁡T.ΔH0 and ΔS0 are the change in enthalpy and entropy, ΔCp is the heat capacity change. TR is an appropriate reference temperature. In a simple term,
(22)ΔG0=ΔH0-TΔS0
which is related to sorption equilibrium constant b at different temperature
(23)ΔG0=-RTln⁡⁡b.
Combining (22) and (23) above, we obtained
(24)ln⁡⁡b=-ΔG0RT=ΔS0R-ΔH0R1T.T is the absolute temperature (K) and R is universal gas constant (8.314 J/molK). Thus, ΔH0 can be determined by the slope of the linear Van’t Hoff plot, that is, as ln⁡⁡K versus (1/T), (Figure 9) using equation:
(25)ΔH0=[Rdln⁡⁡Kd(1/T)].
This method is an indirect method but an accurate method to calculate thermodynamics parameters at solid/solution interfaces. Enthalpies of adsorption are assumed to be invariable in relation to temperature. However, difficulties arise from this assumption. Taking into account the curvatures of Van’t Hoff plots suggested in Figure 9, a second-order polynomial regression analysis of the Van’t Hoff plots was used. The general equation of this type of analysis is ln⁡⁡b=A+Bln⁡⁡(T)+C/T where A, B, and C are the regression coefficients. The -ΔH0/R values were found from individual regressive function.Figure 9
Van’t Hoff plot of BGD dye adsorption by LFC.The polynomial regression produced better fits (r2 value from 0.990 to 0.999) in relation to the traditional Van’t Hoff plot linear regression (less than 0.900). The curvatures indicate temperature dependence of ΔH0. Heat capacity, (ΔCp), which is influenced by the number of accessible energy state, was determined over the range temperature of studies. As an important parameter, it controls the magnitude of ΔH0 and ΔS0 [59].Considering temperature dependence ofΔH0, an equation can be written to represent nonzero temperature independent ΔCp:
(26)ln⁡⁡bd1bd2=ΔHi-TiΔCpR(1T1-1T2)+ΔCpRln⁡⁡T2T1.
The ΔCp value was calculated in a simple manner, as
(27)ΔCp=d(ΔH0)dT=Td(ΔS0)dT=ΔHT20-ΔHT10(T2-T1).
The thermodynamic parameters are shown in Table 8. ΔH0 is almost all positive and it decreases endothermically within the temperature range of 303 K to 333 K. Explanation for the ΔH0 obtained within the temperature range of study is based on the fact that BGD and LFC surfaces are both solvated in water. In order for BGD to be adsorbed, they have to lose part of their hydration shell. The dehydration processes of the BGD and LFC surfaces require energy. In general the dehydration processes of the BGD and LFC supersede the exothermicity of the adsorption processes. Overall, it may be assumed that the removal of water from BGD and LFC surfaces is essentially an endothermic processes; this process exceeds that of exothermicity provided by the heat of adsorption as observed in this study. Indication from Table 8 shows that the negative value of ΔCp couple with favorable positive entropy changes signifies hydrophobic interaction [59]. The negative value of ΔG0 over all temperature of studies indicates the spontaneous and feasible nature of the adsorption process and that binding of an adsorbate in solution is favored.Table 8
Thermodynamic parameters for adsorption of BGD on LFC.
Temperature (K)
ln
⁡
b
−ΔG0(KJmol-1)
Δ
H
0
(
KJ
mol
-
1
)
Δ
S
0
(
J
mol
-
1
k
-
1
)
Δ
C
p
(
KJ
k
-
1
mol
-
1
)
303
2.89
7.28
108.74
382.91
−8.91
313
3.34
8.69
19.62
90.46
323
3.56
9.56
−82.27
−225.09
333
1.64
4.53
−197.03
−578.08The positiveΔS0 values indicate an increase in disorderliness while negative ΔS0 value shows decrease in disorderliness. For the interaction of BGD with LFC, ΔS0 decrease positively; thus, from thermodynamic point of view entropy seems to be the driving force of adsorption [60].


### 3.8. Mechanism of Adsorption

BGD dye molecule can react with carbonyl and hydroxyl groups available on the surface of LFC. Comparing FTIR before and after adsorption, the peak at 3423 cm−1 from –OH remained unchanged but increased in intensity after adsorption suggesting that –OH group may bind with the immonium ion of the BGD molecule via hydrogen bonding which accounts for the emergence of the new peak at 3346 cm−1. The intensity of the peak at 1737 cm−1 assigned to carbonyl group of carboxylic acid decreased while the wavelength shifts to lower wave number after adsorption of BGD, indicating electrostatic interaction between the positively charged nitrogen moiety of the BGD dye molecule and the –COOH group of LFC.


## 3.1. Results of Point of Zero Charge (pHPZC) Determination and FTIR Analysis

The point of intersection of ΔpH versus pH0 showed that the pHZPC of LFC occurred at pH 5.2 as shown in Figure 2. This showed that at pH less than 5.2 the surface of LFC is predominated by positive charges while at pH greater than 5.2, the surface is predominated by negative charges.Figure 2
Results of the determination of the pHZPC.It was clear from Figures3 to 4 that FTIR spectra of the LFC before and after adsorption of BGD displayed a number of absorption peaks, reflecting the complex nature of the material examined. They are carbonyl and hydroxyl groups, on the surface of LFC from FTIR analysis [35]. The broad absorption peaks around 3423 cm−1 were indicative of existence of bonded hydroxyl groups on the surface of LFC. The peaks at 2902 and 2360 cm−1 were assigned to the stretching vibration and bending vibration of C–H bond in methylene group, respectively. The broad band at 1735 cm−1 was assigned to the carbonyl and carbonyl moieties (C=O). The peaks associated with the stretching vibration in aromatic rings were verified at 1597 and 1425 cm−1. The peak at 1236 cm−1 was assigned to the bending vibration of carboxylic groups while deformation related to C–O bond was observed at 1057 cm−1 which also confirmed the lignin structure of the LFC. All of these surface functional groups of the LFC can interact with the BGD molecules. Thus, the adsorption of BGD on LFC may be attributed to (i) chemical interaction between surface functional groups and BGD molecules (ii) electrostatic interaction between the BGD molecules and electron-rich sites on the LFC surface, and (iii) week physical forces, mainly hydrogen bonding and van der Waals interactions between the BGD molecules and the LFC. Therefore, the adsorption of BGD onto LFC surface may emanate from the interaction between the carboxyl group of LFC and the electronegative groups in BGD, hydrogen bonding between the hydroxyl group of LFC and the nitrogen of the BGD molecules, and hydrogen bonding between the hydroxyl group of the LFC and the aromatic ring in the BGD molecule. This has confirmed that adsorption of BGD onto LFC follows a complicated pattern which involved both physical and chemical.Figure 3
FT-IR of Luffa cylindrical (LFC) before adsorption of BGD.Figure 4
FT-IR of Luffa cylindrical (LFC) after adsorption of BGD.


## 3.2. Effect of pH on the Adsorption Capacity

It is a known fact that solution pH is an important variable in sorption studies. The pH of the solution affects surface charge of the adsorbent, the degree of ionization of adsorbate molecule, and extent of dissociation of functional groups on the active sites of the adsorbent [19]. The dye uptake variations at different pH value and initial concentrations of 200 mg/L are shown in Figure 5. The adsorption rate changed at the beginning, from 11.5% at pH 2.0 to 89.9% at pH 6.97. With a further increase of pH from 6.97 to 10.0, the adsorption rate decreased. Consequently, pH 6.97 was selected as the operating pH for subsequent studies.Figure 5
Effects of initial solution pH on the sorption of BGD onto LFC.The possible explanations are as follows. (i) LFC has an estimated point of zero charge of pH 5.2, above which LFC surface is predominantly negatively charge, leading to a favorable electrostatic interaction between the cationic BGD molecule and the LFC, hence there is a linear increase in BGD uptake as shown in Figure5. (ii) In an acidic and at lesser alkaline medium, the Cl− and OH− from HCl and NaOH destroy the conjugated bond present in the aromatic rings of the dye molecule upon which the BGD structure changed and result in the formation of colorless compound [36], leading to increase in the uptake of BGD molecule from solution as shown in Figure 5. (iii) The presence of carboxyl groups on the surface of LFC, as confirmed by Figures 3 and 4 also, enhances sorption of BGD with increase in pH from 2 to 8 and later decrease at pH 10. This is because the pka value of carboxyl groups lies within the range of 3.8–5.0 [37]. Below pH 5.0, the carboxyl group on the surface of LFC gets protonated (H+) making the number of positive charge sites increase and the number of negative charge decrease resulting in electrostatic repulsion, hence decrease in BGD uptake by LFC. With an increase in pH of the solution, these functional groups became deprotonated (COO−), which resulted in an increase in the negative charge density on the LFC surface and facilitated the binding of BGD dyes [38]. Hence, the BGD ions binding to the adsorbent could be assumed to involve electrostatic interaction between cationic dyes and negatively charged COO− groups.The results of the equilibrium pH (i.e,pHf) at different initial solution pH (2–10) ranged between 2.39 and 9.3 for BGD/Luffa system as shown in Figure 5. The pHf values were higher than pH0 values for pH0<8.0 and this could be attributed to change in the structure of dye molecule.


## 3.3. Effect of Initial Dye Concentration and Adsorption Kinetics

The rates of sorption of BGD by LFC at different initial BGD concentrations are shown in Figure6. Uptake of BGD was rapid and equilibrium was attained within 180 min. It was found that the amount BGD sorbed increased from 9.2 to 92.9 mg/g with increasing initial concentration from 20–200mg/L. The adsorption was initially rapid and then slowed down over time. This observation was ascribed to a large number of available binding sites for adsorption during the initial stage, and then the remaining sites were difficult to occupy due to repulsive forces between the dye molecules on the LFC and the bulk phase [39]. The results showed that the time taken to attain equilibrium was independent of the initial dye concentration. Similar profile has been reported in the literature for the effect of time and initial concentration for the removal of BGD by adsorbents like kaolin [19], bottom ash and deoiled soya [26], neem leaf powder [31], and modified peat-resin [40].Figure 6
Effect of contact time on the removal of BDG onto LFC.In order to explore the kinetics involved in dye sorption, the experimental data were fitted into four kinetic models including the pseudo-first-order equation [41], pseudo-second-order equation [42], power function [43], and simple Elovich [44].The linear form of the pseudo-first-order kinetic is expressed as follows:(4)ln⁡(qe-qt)=ln⁡qe-kit,
where qe and qt are BGD adsorbed at equilibrium and time t, respectively (mg/g), and k1 is the rate constant for the pseudo-first-order model (min−1). The pseudo-first-order constant k1 and the correlation coefficient, r2, deduced from the kinetic data are presented in Table 1. The r2 value was poor and ranged between 0.747 and 0.966. A significant chi χ2 values were also obtained indicating the inapplicability of this model to the sorption process.Table 1
Kinetic parameters of sorption of BGD on LFC.
Initial conc.
Pseudo-first-order
Pseudo-second-order
Power function
Simple Elovich
mg/L
q
e
1
k
1
×
1
0
-
2
r
2
q
e
2
k
2
h
0
r
2
a
b
r
2
A
B
20
1.54
0.2303
0.820
9.621
0.132
12.20
0.999
8.79
0.016
0.920
8.80
0.799
40
1.86
0.2303
0.794
19.230
0.097
35.87
1.000
17.78
0.014
0.911
17.78
1.462
80
3.07
0.4606
0.747
40.000
0.057
91.20
1.000
35.73
0.015
0.916
35.70
3.001
150
7.50
1.1515
0.966
76.920
0.011
65.08
0.999
63.39
0.025
0.977
63.26
9.046
200
17.82
1.1612
0.916
100.000
0.004
40.00
0.999
70.15
0.051
0.967
69.51
22.48
k
1 = min−1, qe1 = mg/g, qe2 = mg/g, k2 =  g/mg/min, B = g/mg, A = mg/g min.The pseudo-second-order kinetic model is represented by the following linear equation:(5)tqt=1k2qe2+1qet,
where k2 is the rate constant for the pseudo-second-order model (g(mg min)−1), where qe, qt, and t have the same meaning as explained above.The initial sorption rate can be obtained from the pseudo-second-order linear plots asqt/t approaches zero:
(6)h0=k2qe2,
where h0 = initial sorption rate.Equation (3) can be rearranged to obtain [45] as follows:
(7)qt=11/h0+t/qe.
The r2 values for the pseudo-second-order kinetic model were close to 1.0 for all cases. Comparing r2 and chi χ2 value for pseudo-first- and second-kinetic model (Table 1), it is obvious that for the entire adsorption period, the pseudo-second-order model fits the experimental data better than the pseudo-first-order model. It thus shows that the system under study was more appropriately described by the pseudo-second-order model. This indicates that the adsorption mechanism for BGD is chemisorptions, involving covalent forces through sharing or exchange of electrons between sorbent and sorbate [46].The value ofh0, qe, and k2 along with r2 for the pseudo-second-order models are shown in Table 1. The value of qe increased with increase in the initial BGD concentration while h0 increase from 12.20 to 91.20 and later decreased drastically to 40.00 with the increases in initial concentration of BGD. According to Ho and Mckay [47] if the dye uptake is chemically rate controlled, the pseudo-second-rate constant will be independent of particle diameter and flow rate will depend on concentration of the ions in solution.Logarithm plots of pseudo-second-order constants,k2, and h0, versus C0 of BGD concentration were made, and the plots were found to be straight line whose linear regression values r2, in terms of C0, were given as 0.992 and 0.946, respectively [45].Mathematical expressions were therefore drawn relating the two pseudo-second-order constants and initial concentration as follows:(8)k2=-0.008C0-0.656,h0=-4.228C08.408.
Linear plots of qe2, k2, and h0 against initial concentration (C0) were regressed to obtain these values in terms of C0 with high concentration coefficient. Each of these parameters can be expressed as a function of C0 for BGD as reported by Ho and McKay [47];
(9)qe=C0EqC0+Fq,(10)k2=C0EkC0+Fk,(11)h0=C0EhC0+Fh,
where Eq, Fq, Ek, Fk, Eh0, and Fh0 are constants related to the respective equations. The values for these constants are listed in Table 2. Hence the generalized predictive model for BGD sorbed at any contact time and initial concentration within the given range with relationship of qe, C0, and t can be represented as follows by substituting the various values in  (10).Table 2
Empirical parameters for predictedqe, k, and h0 from C0 for BGD dye.
E
q (g/mg)
F
q (g min/L)
r
2
E
k (mg min/g)
F
k (mg2 min/gL)
r
2
E
h
0 (g min/mg)
F
h
0 (g min/L)
r
2
0.507
0.594
0.946
16.0
×
10
-
4
0.128
0.921
1.326
15.46
0.998For BGD-LFC system [47]:
(12)qt=t1/(1.326C0+15.46)+1/(0.507C0+0.594)t.
Equation (12) represents the generalized predictive model for BGD sorbed at any time and the initial BGD concentration within the given range.To further establish the appropriate kinetic for BGD uptake, the experimental data was fitted again to power function and simple Elovich models.The power function model is a modified form of the Freundlich equation and may be expressed as:(13)log⁡⁡q=log⁡⁡a+blog⁡⁡t
while the simple Elovich [45] is expressed as:
(14)q=A+2.303Blog⁡⁡t.
The results obtained for the fitting of the kinetic models to explained data are presented in Table 1 and the error functions are presented in Table 3. For the pseudo-first-order kinetic and simple Elovich models, the predicted qe values were at variance coincident with the experimental qe values. The predicted qe values derived from pseudo-second-order and power function model agreed with the experimental qe data. The values χ2 of the error function were negligible for pseudo-second-order and power function model. This result indicates that the pseudo-second-order and power function model provided a high degree of correlation with the experimental data for the sorption of BGD by LFC.Table 3
Error analysis for the kinetic data of the sorption of BGD on LFC.
Initial conc.
Pseudo-first
q
e
=
q
e
(
1
-
e
-
k
i
t
)
Pseudo-second
q
e
=
t
k
2
q
e
2
/
(
1
+
t
k
2
q
e
)
Power function
q
e
=
a
t
b
Simple Elovich
q
e
=
A
+
B
ln
⁡
⁡
t
(mg/L)
χ
2
r
2
χ
2
r
2
χ
2
r
2
χ
2
r
2
20
12.376
0.997
1.83
×
10
-
4
0.999
5.28
×
10
-
4
1.000
1.150
1.000
40
24.698
0.997
1.89
×
10
-
4
1.000
3.55
×
10
-
4
1.000
1.490
1.000
80
12.985
0.987
2.39
×
10
-
5
1.000
4.51
×
10
-
4
1.000
3.19
1.000
150
1.311
0.940
3.50
×
10
-
3
0.999
1.26
×
10
-
3
1.000
12.93
1.000
200
0.294
0.910
2.06
×
10
-
2
0.999
3.48
×
10
-
3
1.000
47.71
1.000


## 3.4. Intra-Particle Diffusion Model

Intraparticle diffusion model based on the theory proposed by Weber and Morris which has been widely applied for sorption studies was applied to investigate the mechanism of the adsorption of BGD onto LFC. The intraparticle diffusion model is typically given as follows [48]:
(15)qt=kidt0.5+Z,
where Z (mg g−1) is the intercept and kid (mg g−1 min0.5) is the intraparticle diffusion rate constant. Value of kid was obtained from the slope of the linear plot of qt versus t0.5 (Figure 7). Value of Z as shown in Table 3 gives an idea about the thickness of the boundary layer [49]. The deviation from this theory signifies the difference between the rate of mass transfer in the initial and final stage of adsorption [50].Figure 7
Plot ofqt versus t0.5 for the adsorption of BGD onto LFC.However, if the data exhibit multilinear plots, then two or more steps influence the sorption process. The first, sharper portion is attributed to the transport of the solute from bulk solution liquid film to the adsorbent exterior surface. The second linear portion is based on the diffusion across the liquid film surrounding the sorbent particle. The third portion is due to particle diffusion in the liquid contained in the pore and in the sorbate along the pore wall.Figure7 shows a representative qt versus t0.5 plot for BGD adsorption onto LFC for C0=20,40,80,150, and 200 mg/L at 30°C. Observation from the figure shows that the plots were not linear over the whole time range; an indication that more than one process controlled the sorption process which are: surface sorption and intraparticle diffusion. For C0=80,150, and 200 mg/L, there are two linear portions, the first straight portion depicting mesopore diffusion and the second represent micropore diffusion [51]. For C0=20 and 40 mg/L, there is only one linear portion depicting combined mesopore diffusion.There is every possibility that the intraparticle diffusion of BGD into pores is the rate controlling step in the adsorption process. The amount of adsorbate and the driving force for BGD adsorption is less forC0=20 and 40 mg/L as compared to that of C0=80,150, and 200 mg/L; hence, BGD adsorbed in mesopore only, and adsorption into mesopore is the rate-limiting step. For C0=80,150, and 200 mg/L, the driving force increases and overcomes the resistance for getting adsorbed into micropores; therefore, adsorption into micropores is the rate-limiting step for higher C0. An observation from Table 4 shows that Kid1 and Kid2 are higher for higher C0, which indicate enhanced diffusion of BGD through meso- and micropores at higher C0. This is a contribution from higher driving force at higher C0 [51]. Similar results have been reported for adsorption of BGD on saw dust [52], kaolin [19], and rice husk ash [32].Table 4
Macro- and micropores diffusion parameters for  the sorption of BGD by LFC at different initial BG concentration (mg/L).
Initial conc. (mg/L)
k
i
d
1
Intercept
r
2
k
i
d
2
Intercept
r
2
20
0.225
8.54
0.900
0.043
9.04
0.873
40
0.478
17.17
0.901
0.074
18.26
0.932
80
0.953
34.45
0.909
0.115
37.07
0.913
150
1.918
61.68
0.992
0.498
65.97
0.948
200
4.375
66.21
0.990
1.061
78.07
0.835


## 3.5. Liquid Film Diffusion Model

During sorption, the migration of dye molecules from bulk solution through liquid film to the exterior surface of adsorption may play an important role in determining the rate of the adsorption process. To predict the potential rate-controlling step, the adsorption dynamics of BGD onto LFC was investigated utilizing liquid film diffusion model (16) [53]:
(16)ln⁡⁡(1-F)=-kfdt,
where kfd (min−1) is the liquid film diffusion rate constants and F=qt/qe. The plot of -ln⁡(l-F) versus t, for the liquid film diffusion, was tested over all concentration of study. The first 30 mins of sorption process yielded linear plot (r2=0.465–0.943) while the overall yielded (r2=0.747–0.966). The rate constant for liquid film diffusion, kfd, is in the range 8.0×10-3 to 1.7×10-2 for the first 30 min and 2.0×10-3 to 1.6×10-2 for overall (Table 5). The inability of the plot to pass through the origin (i.e., zero intercept) shows that the prediction of this model will have only limited applicability in the adsorption of BGD by LFC.Table 5
Liquid film diffusion parameters for the sorption of BGD by LFC at different initial BGD concentration (mg/L).
Initial conc. (mg/L)
First 30 mins
Overall
k
i
d
1
Intercept
r
2
k
i
d
2
Intercept
r
2
20
0.008
1.85
0.650
0.002
1.93
0.820
40
0.011
2.28
0.465
0.004
2.38
0.794
80
0.017
2.39
0.581
0.005
2.57
0.747
150
0.017
2.19
0.718
0.011
2.28
0.966
200
0.031
1.54
0.943
0.016
1.65
0.916


## 3.6. Adsorption Equilibrium Isotherm Study

The distribution of BGD between the liquid phase and the solid adsorbent phase is a measure of the position of equilibrium in the adsorption process and can be expressed by different equilibrium isotherm models. In this study, the Langmuir, Freundlich, and Temkin isotherms models were used to describe the adsorption process and the isotherm parameters obtained using these models are presented in Table6.Table 6
Adsorption  isotherm constants for BGD on LFC.
Temperature (°C)
Langmuir
Freundlich
Temkin
Q
0
b
R
2
R
L
×
1
0
-
3
K
f
1
/
n
R
2
B
I
A
R
2
30
18.52
17.99
0.991
2.7
17.83
0.722
0.958
27.75
2.150
0.984
40
8.85
28.21
0.963
1.7
2.42
1.212
0.972
28.39
1.014
0.931
50
5.68
35.16
0.961
1.4
1.01
0.176
0.964
35.04
1.410
0.944
60
8.50
5.16
0.998
9.4
7.01
0.952
0.928
58.06
1.070
0.987The linear form of Langmuir’s isotherm model is represented by the following equation:(17)1qe=1Q0+1bQ0Ce.
The values of monolayer sorption capacities, Q0 (mg/g), obtained from Langmuir plot of sorption decreased with increasing temperature. The magnitude of Langmuir constant, b, which is the sorption equilibrium constant (dm3/mg), decreases as shown in Table 6. The decrease of b as temperature increases confirms the exothermic nature of the adsorption [54]. The essential characteristics of the Langmuir isotherm, used to predict the adsorption efficiency, was expressed in terms of a dimensionless equilibrium parameter RL, defined by the following equation [55]:
(18)RL=11+bC0,
where C0 (mg/L) is the highest initial concentration of the adsorbate. The value of RL indicates if the Langmuir isotherm is unfavorable (RL>1), linear (RL=1), favorable (0<RL<1), or irreversible (RL=0). The values of RL at C0 = 200 mg/L in the present study were found to be 2.7×10-3 at 303 K, 1.7×10-3 at 313 K, 1.4×10-3 at 323 K, and 9.4×10-3 at 333 K indicating that the adsorption of BGD on LFC is favorable.The experimental data obtained was also tested with Freundlich isotherm. Freundlich isotherm assumes heterogeneity of adsorption surfaces. The equation is commonly expressed as follows [56]:
(19)log⁡⁡qe=log⁡⁡Kf+1nlog⁡⁡Ce.
The values of the Freundlich constant, Kf and n, related to adsorption capacity and sorption intensity, respectively, obtained from the plot of log⁡⁡qe versus log⁡⁡Ce are presented in Table 6. Kf is the Freundlich affinity coefficient, and 1/n is the Freundlich linearity index. It can be found that the values of Kf and n decrease, indicating that adsorption is favorable at lower temperature predicting endothermic nature of the adsorption process. Experimental data was also fitted to Temkin isotherm.The Temkin isotherm assumes that a decrease in the adsorption heat is linear and that the adsorption is characterized by a uniform distribution of binding energies. The Temkin linear form of isotherm is given by equation [57, 58]:
(20)qe=BIln⁡⁡A+BIln⁡⁡Ce.BI=RT/b, T is the absolute temperature (K), and R is the universal gas constant (8.314 J/molK), A is the equilibrium binding constant (L/mg), and BI is related to the heat of adsorption. The Temkin constants were listed in Table 6. In order to assess the different isotherms and their ability to correlate the experimental results, the theoretical plots for each isotherm have been shown along with the experimental data for the sorption of BGD onto LFC (Figure 7). The r2 and χ2 values were shown in Table 7 and the different isotherms correlated with the experimental depicted in Figure 8 confirmed that the sorption of BGD onto LFC was best described by Langmuir isotherm model. The applicability of the Langmuir isotherm assumes that the entire adsorption sites are equivalent and there is no interaction between adsorbed species.Table 7
Error analysis for isotherm models for the sorption of BGD on LFC.
Initial conc. (mg/L)
Langmuir;qe=QLbce/(1+bce)
Freundlich;qe=kfcf1/n
Tempkin;qe=(RT/b)ln⁡(KTce)
χ
2
χ
2
χ
2
20
0.2664
0.3782
0.4525
40
0.0009
0.1016
0.2386
80
0.0008
1.0420
2.4264
150
0.1251
2.2042
16.5165
200
1.4370
4.1396
126.0713Figure 8
Comparison of experimental data with the theoretical data for equilibrium isotherm studies for the adsorption of BGD onto LFC.


## 3.7. Estimation of Thermodynamic Parameter

To characterize the thermodynamic parameter of adsorption study means to determine Gibb’s free energy, (ΔG0, KJ/mol), enthalpy change (ΔH0, KJ/mol), and entropy (ΔS0, KJ/mol/K) at a given reference temperature and to obtain ΔCp so as to be able to predict the change of the above three parameters with temperature.The Gibb’s free energy change,ΔG, of an association reaction is temperature dependent and best described by
(21)ΔG0=ΔH(TR)0+∫TRTΔCpdT-TΔS(TR)0-T∫TRTΔCpdln⁡⁡T.ΔH0 and ΔS0 are the change in enthalpy and entropy, ΔCp is the heat capacity change. TR is an appropriate reference temperature. In a simple term,
(22)ΔG0=ΔH0-TΔS0
which is related to sorption equilibrium constant b at different temperature
(23)ΔG0=-RTln⁡⁡b.
Combining (22) and (23) above, we obtained
(24)ln⁡⁡b=-ΔG0RT=ΔS0R-ΔH0R1T.T is the absolute temperature (K) and R is universal gas constant (8.314 J/molK). Thus, ΔH0 can be determined by the slope of the linear Van’t Hoff plot, that is, as ln⁡⁡K versus (1/T), (Figure 9) using equation:
(25)ΔH0=[Rdln⁡⁡Kd(1/T)].
This method is an indirect method but an accurate method to calculate thermodynamics parameters at solid/solution interfaces. Enthalpies of adsorption are assumed to be invariable in relation to temperature. However, difficulties arise from this assumption. Taking into account the curvatures of Van’t Hoff plots suggested in Figure 9, a second-order polynomial regression analysis of the Van’t Hoff plots was used. The general equation of this type of analysis is ln⁡⁡b=A+Bln⁡⁡(T)+C/T where A, B, and C are the regression coefficients. The -ΔH0/R values were found from individual regressive function.Figure 9
Van’t Hoff plot of BGD dye adsorption by LFC.The polynomial regression produced better fits (r2 value from 0.990 to 0.999) in relation to the traditional Van’t Hoff plot linear regression (less than 0.900). The curvatures indicate temperature dependence of ΔH0. Heat capacity, (ΔCp), which is influenced by the number of accessible energy state, was determined over the range temperature of studies. As an important parameter, it controls the magnitude of ΔH0 and ΔS0 [59].Considering temperature dependence ofΔH0, an equation can be written to represent nonzero temperature independent ΔCp:
(26)ln⁡⁡bd1bd2=ΔHi-TiΔCpR(1T1-1T2)+ΔCpRln⁡⁡T2T1.
The ΔCp value was calculated in a simple manner, as
(27)ΔCp=d(ΔH0)dT=Td(ΔS0)dT=ΔHT20-ΔHT10(T2-T1).
The thermodynamic parameters are shown in Table 8. ΔH0 is almost all positive and it decreases endothermically within the temperature range of 303 K to 333 K. Explanation for the ΔH0 obtained within the temperature range of study is based on the fact that BGD and LFC surfaces are both solvated in water. In order for BGD to be adsorbed, they have to lose part of their hydration shell. The dehydration processes of the BGD and LFC surfaces require energy. In general the dehydration processes of the BGD and LFC supersede the exothermicity of the adsorption processes. Overall, it may be assumed that the removal of water from BGD and LFC surfaces is essentially an endothermic processes; this process exceeds that of exothermicity provided by the heat of adsorption as observed in this study. Indication from Table 8 shows that the negative value of ΔCp couple with favorable positive entropy changes signifies hydrophobic interaction [59]. The negative value of ΔG0 over all temperature of studies indicates the spontaneous and feasible nature of the adsorption process and that binding of an adsorbate in solution is favored.Table 8
Thermodynamic parameters for adsorption of BGD on LFC.
Temperature (K)
ln
⁡
b
−ΔG0(KJmol-1)
Δ
H
0
(
KJ
mol
-
1
)
Δ
S
0
(
J
mol
-
1
k
-
1
)
Δ
C
p
(
KJ
k
-
1
mol
-
1
)
303
2.89
7.28
108.74
382.91
−8.91
313
3.34
8.69
19.62
90.46
323
3.56
9.56
−82.27
−225.09
333
1.64
4.53
−197.03
−578.08The positiveΔS0 values indicate an increase in disorderliness while negative ΔS0 value shows decrease in disorderliness. For the interaction of BGD with LFC, ΔS0 decrease positively; thus, from thermodynamic point of view entropy seems to be the driving force of adsorption [60].


## 3.8. Mechanism of Adsorption

BGD dye molecule can react with carbonyl and hydroxyl groups available on the surface of LFC. Comparing FTIR before and after adsorption, the peak at 3423 cm−1 from –OH remained unchanged but increased in intensity after adsorption suggesting that –OH group may bind with the immonium ion of the BGD molecule via hydrogen bonding which accounts for the emergence of the new peak at 3346 cm−1. The intensity of the peak at 1737 cm−1 assigned to carbonyl group of carboxylic acid decreased while the wavelength shifts to lower wave number after adsorption of BGD, indicating electrostatic interaction between the positively charged nitrogen moiety of the BGD dye molecule and the –COOH group of LFC.


## 4. Conclusion

LFC, a lignocellulosic material, was used as adsorbent to remove BGD from aqueous solution via batch experimental method. The kinetic studies were performed and the result obtained was fitted to pseudo-first-order, pseudo-second order, power function, and simple Elovich models. Both the pseudo-second-order and power function kinetic models provided excellent data fitting based on the statistical coefficient and chi-square error analysis. The equilibrium data showed that the experimental data correlated reasonably with the Langmuir isotherm model. Nonzero heat capacities termΔCp was obtained with the emergence of the plot of ln⁡⁡b versus 1/T and the negative ΔCp shown in this study indicates absence of thermal dehydration, stable species in solution. Negative value of ΔG0 suggests spontaneity and feasibility of adsorption process while the positive ΔS0 predicted that entropy is the driving force adsorption of BGD onto LFC.



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*Source: 743532-2014-03-04.xml*