Dyes are synthetic aromatic water-soluble dispersible organic colorants, having potential applications in various industries. They are widely used in textile, paper, plastic, food and cosmetic industries in order to give the certain coloration to the desired product and also consume substantial volumes of water. It is reported that, over 100,000 dyes are commercially available and more than 700,000 ton/year are produced in the world   . Most of the dyes are highly toxic, mutagenic, carcinogenic and recognized pollutants    . It is for this reason that, some dyes discharged from the effluents of these industries into receiving streams are sources of water pollution. Water effluents containing dyes have a very hazardous impact on environment, thus causing chronic and acute diseases  . Dyes can significantly affect visibility, photosynthesis and also aquatic life due to the presence of aromatics, metals and chlorides  . Hence the elimination of dyes from waste water is essential to prevent continuous environmental pollution. The commonly used procedures for removing organic dyes from aqueous solution include flocculation, electroflotation, chemical precipitation, electrokinetic coagulation, ion exchange, membrane filtration, electrochemical destruction, irradiation, ozonation and microbial biodegradation    . However, these methods are ineffective, non-economical and have many disadvantages such as high reagent and energy requirements, generation of toxic sludge or other waste products that require disposal or treatment  . There is thus a need to search for new processes that could remove organic dyes. The adsorption technique is one of the preferred methods of advanced wastewater treatment which industries employ to reduce hazardous organic dyes present in the effluent because it is efficient, simple to design and does not produce any sludge     . At first, the adsorbent used in adsorption was commercial activated carbon. However, the high cost of activated carbon used in adsorption and problems of regeneration of adsorbent after adsorption  led to the search for new adsorbents that are lower in cost, locally available and efficient  . Several researchers were led to the use of agricultural solid wastes. Ever since, many agricultural solid wastes were used to adsorb organic dyes in aqueous solutions. Examples are: rice husk, tea leaves, orange peel, corncobs, coconut husk, barley husks, peanut hull, coir pith, wheat bran, eggshell, cocoa shell  , hazelnut shells  , olive stone  , sugarcane bagasse  and wood sawdust  . All of these are excellent for organic dyes removal. The aim of this study was to investigate about a natural and abundant lignocellulosic material, palm tree trunk, for the adsorption of organic dyes which are mostly toxic nowadays. 2,6-DCPIP was chosen as an example of an organic dye. The effects of some important parameters such as treatment of biosorbent, initial dye concentration, pH of solution, adsorbent dosage, ionic strength, contact time and interfering ions on the adsorption of 2,6-DCPIP onto both natural and treated PTT were compared. The possibility to reuse the materials was also examined.
2. Materials and Methods
2.1. Materials, Preparation and Characterization of Biomass
All chemical reagents used in this experiment were of analytical grade, purchased and used without further purification. NaCl, CaCl2 and NaOH were purchased from Fisher, CH3COOH and BaCl2 were purchased from BDH, HNO3 and 2,6-DCPIP were purchased from Riedel-de-Häen and HCl was purchased from Phillip Harris. The structure of 2,6-DCPIP is illustrated in Figure 1.
The palm tree trunk used in this work was collected from a local agricultural field of the Littoral region in Cameroon. The biomass was cut into small pieces, washed several times with tap water to remove dust and soil particles, and then dried in sun for 8 days. The dried biomass was ground into fine powder and sieved to obtain sizes ranging from 0 - 100 µm. The powder was washed several times with distilled water, air-dried for 2 days and then in an oven at 110˚C for 24 h before being kept in a bottle for further use.
In view of studying the effect of chemical pretreatment of biomass on 2,6-DCPIP uptake capacity, the biomass was submitted to pretreatment with acetic acid, according to the following procedure: 5 g of the natural biomass was put into contact with 100 mL of 2 mol∙L−1 acetic acid solution. The mixture was stirred in a mechanical platform shaker (EDMUND BÜHLER GmbH) for 2 h at a speed of 200 rpm. The resultant biomass was washed several times with distilled water in order to remove the excess of acetic acid until the pH (6.3) of washed water was stable. After washing thoroughly, the biosorbent was air-dried for 2 days and then in an oven at 110°C for 24 h before being kept in a bottle for further use.
The determination of the pzc of natural PTT and treated PTT was performed according to the method previously described by  . The pzc was measured by adding 0.1 g of biomass to 50 mL of 0.1 mol∙L−1 NaCl solution whose initial pH (
) was measured and adjusted between 1 and 12 with NaOH or HCl solutions. The containers were sealed and placed on a mechanical platform shaker for 48 h at a speed of 150 rpm after which the final pH (
The natural and treated PTT were also characterized by using Fourier transform infrared spectroscopy (FT-IR) which allowed to identify different chemical
Figure 1. Chemical formula of 2,6-dichlorophenolindophenol  .
functional groups present in natural and treated PTT powder. FT-IR spectra were obtained by means of the ATR technique with a Bruker α-P FT-IR spectrophotometer within a range of 4000 - 400 cm−1 with a resolution of 4 cm−1; 200 scans were collected for each spectrum.
2.2. Batch Biosorption and Desorption Studies
The stock solution of 2,6-DCPIP was prepared at 10−3 mol∙L−1 by dissolving 0.327 g of the hydrated sodium salt of 2,6-dichlorophenolindophenol in 1 L of distilled water. Solutions of different concentrations (2 × 10−5 - 10−4 mol∙L−1) were prepared by dilution of the stock solution with distilled water. The pH of each solution of 2,6-DCPIP was adjusted to the required value using HCl or NaOH solutions.
The biosorption studies were achieved in aqueous solution, in a shake flask, at room temperature. In this study, the batch biosorption experiments were carried out by mixing pre-weighted amounts (5 - 60 mg) of biosorbent with 10 mL of 2,6-DCPIP of various initial concentrations (2 × 10−5 - 10−4 mol∙L−1) into a flask. The mixture was stirred at constant agitation speed of 150 rpm for an interval time between 5 - 70 min on a mechanical platform shaker. After agitation, the suspensions were filtered using whatman filter paper. The filtrates were analyzed by measuring the absorbance using UV-Vis Spectrophotometer (JENWAY) at a maximum adsorption wavelength of 600 nm  . The obtained absorbance was converted to the corresponding concentration Ce by using the equation of calibration curve. The amount of 2,6-DCPIP adsorbed at equilibrium qe (mol∙g−1) (Equation (1)), at time t qt (mol∙g−1) (Equation (2)) and the percentage of adsorption ( ) (Equation (3)) were calculated as follows    :
where , and (mol∙L−1) are the initial concentration, the final concentration at equilibrium and the final concentration at time t of 2,6-DCPIP, respectively. (L) is the volume of 2,6-DCPIP solution and m (g) is the weight of the biosorbent.
The desorption studies were achieved by mixing 300 mg of biosorbents with 100 mL of 2,6-DCPIP of initial concentrations 10−4 mol∙L−1 into a flask. The mixtures were stirred at constant agitation speed of 150 rpm for 40 min. After agitation, the suspensions were filtered using whatman filter paper. The filtrates were analyzed by measuring the absorbance using UV-Vis Spectrophotometer. The 2,6-DCPIP loaded biosorbents were recovered and dried in an oven. After drying, 30 mg of 2,6-DCPIP loaded biosorbents were mixed with 10 mL of the desorption solutions of H2O, 10−2 mol∙L−1 of NaOH or HNO3. The mixtures were stirred at constant agitation speed of 150 rpm for 40 min on a mechanical platform shaker. After agitation, the suspensions were filtered. The filtrates were also analyzed by measuring the absorbance using UV-Vis Spectrophotometer. The desorption percentages ( ) were calculated as follows (Equation (4))  :
where; and (mol∙L−1) are the initial concentration and the final concentration of 2,6-DCPIP loaded biosorbents, respectively.
3. Results and Discussion
3.1. Characterization of Biomass
3.1.1. Fourier Transform Infrared (FT-IR) Spectroscopy
The FT-IR spectra of PTT were recorded in order to explore the surface functional groups as shown in Figure 2(a). The spectra showed the presence of a broad peak, characteristic of OH group in the region 3400 - 3200 cm−1, this peak shows the presence of alcohol, phenol or carboxylic acids   . Another major peak detected at 2915.89 cm−1 was attributed to asymmetric and symmetric C - H stretching of aliphatic methyl and methylene. The peaks localized at 1725.38 cm−1 and 1628.20 cm−1 are characteristic of carbonyl (C = O) of carboxylic acids and carboxylate, respectively. The peak at 1510.65 cm−1 is a constant value for all the lignin esters. The IR peak at 1422.53 cm−1 may be due to the symmetrical bending vibration of alkane bonds (-CH2). The absorption peak at 1238.72 cm−1 could be due to C - O, C - H or C - C stretching vibrations of carboxyl groups (-COOH). The band localized at 1031.92 cm−1 is attributed to C - O stretching vibrations of lignin   . The region below 1000 cm−1 is the fingerprint zone and the absorption cannot clearly be assigned to any particular vibration because they correspond to complex interacting vibration systems  . The FT-IR spectrum of natural and treated PTT had similar bands with distinctive peak intensities (Figure 2).
Figure 2. FT-IR spectra of (a) natural PTT and (b) treated PTT.
3.1.2. Point of Zero Charge (pzc)
The pzc of a material in a solution is the pH value at which the net surface charge of the material is equal to zero  . The PZC value of PTT was 4.8 (Figure 3), indicating that when the pH < 4.8, the surface of the material behaves as bases, fix protons contained in solution and become positively charged. This can be explained by the fact that the protons in solution migrate into PTT and settle on the carboxylate and hydroxyl function with which they interact to form a protonated material that is positively charge. This protonation increases the pH of the solution after equilibrium. On the other hand, when the pH > 4.8, the surface of material behaves as acids, releasing protons into the medium and become negatively charged. This can be explained by the dissociation of acidic functional groups of materials such as carboxylic acids involving the decreasing of the pH of the solution after equilibrium   .
The pzc value of the pretreated PTT with acetic acid (3.8) is lower than the pzc value of PTT (Figure 3). This decrease in pzc values can be explained by the fact that the treatment with acetic acid involves the reduction of basic functions and an increase in acidic functions that result to the action of this acid on the biosorbent.
3.2. Effect of Pretreatment of Biomass
The biosorbent was treated with acetic acid. The treatment affected the functional groups contained at the surface of the material. Figure 4 shows the effect of chemical treatment on the biosorption of 2,6-DCPIP. It can be observed from this figure that the amount of 2,6-DCPIP adsorbed at equilibrium is 20.303 µmol∙g−1 for natural PTT and 26.007 µmol∙g−1 for treated PTT. As can be seen, the amount of 2,6-DCPIP adsorbed at equilibrium is higher with treated PTT than natural PTT. This result can be explained by the fact that the treatment with acetic acid like all the acid treatments, lead to the protonation of the surface functional groups of the material  , which increased the electrostatic interaction between the positively charged surface of the material and the negatively charged molecules of 2,6-DCPIP.
Figure 3. Graph of point of zero charge.
3.3. Effect of Biosorbents Dosage
The effect of biosorbents dosage on the removal of 2,6-DCPIP was studied and the results of this study are shown in Figure 5. The removal percentage of 2,6-DCPIP increased from 8.251% to 81.169% and from 22.789% to 89.755% for natural and treated PTT, respectively. As can be seen, the removal percentage of 2,6-DCPIP increased considerably with increasing adsorbent dosage. This is because of the greater surface area, the availability of more adsorption sites (carboxyl groups) for 2,6-DCPIP adsorption during the adsorption reaction  . A further increase in adsorbent dosage for treated PTT (>4.0 g/L) did not cause significant improvement in 2,6-DCPIP adsorption. This may be due to the adsorption of almost all the 2,6-DCPIP onto the biosorbent and the establishment of equilibrium. This situation can also be attributed to overlapping of adsorption sites as a result of overcrowding of biomass  . A quite similar tendency was reported by  for the adsorption of malachite green by sea shell powder.
Figure 4. Effect of pretreatment of PTT on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; m = 3 g∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
Figure 5. Effect of biosorbents dose on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
3.4. Effect of Contact Time
The effect of contact time on biosorption of 2,6-DCPIP is presented in Figure 6. It can be observed from this figure that, rapid adsorption of 2,6-DCPIP takes place in the first 5 minutes for the two materials, thereafter, the rate of adsorption decreases gradually with the progress of adsorption and reaches equilibrium in about 20 minutes for natural PTT and 40 minutes for treated PTT. No significant change in 2,6-DCPIP removal is obtained after the equilibrium time. The initial rapid phase may be due to rapid attachment of 2,6-DCPIP to the biosorbent surface or to the availability of more adsorption vacant sites at the initial stage  . But after some of the easily available active sites are used up, the dye needs some time to find out more active sites for binding until the equilibrium time is reached   .
3.5. Effect of Initial Concentration
The effect of initial concentration on the biosorption of 2,6-DCPIP was investigated and the results are shown in Figure 7. It can be observed from this figure that, the amount of 2,6-DCPIP adsorbed at equilibrium increases from 3.690 to 18.395 µmol∙g−1 and from 4.644 to 23.451 µmol∙g−1 for natural and treated PTT, respectively. As can be seen, the amount adsorbed at equilibrium for both biosorbents increases as the 2,6-DCPIP concentration increases. This result can be explained by the fact that increasing the initial 2,6-DCPIP concentration would increase the mass transfer driving force, and hence, the rate at which 2,6-DCPIP molecules pass from solution to the particle surface    . This behaviour suggests that available sites on the biosorbent are the limiting factor for the 2,6-DCPIP removal  .
3.6. Effect of Solution pH
The pH is an important factor that affects biosorption processes. It is used in
Figure 6. Effect of contact time on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; m = 3 g∙L−1; G = 0 - 100 µm; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
Figure 7. Effect of initial concentration on the biosorption of 2,6-DCPIP. Experimental conditions: m = 3 g∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
Figure 8. Effect of pH of solution on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; m = 3 g∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; at room temperature.
industry to increase the adsorption of dyes. The effect of initial pH on biosorption of 2,6-DCPIP on natural and treated PTT is shown in Figure 8 and the results indicate that, the maximum capacity of adsorption is obtained at pH = 2. When the pH increases, the capacity of adsorption decreases from 36.955 to 0.706 µmol∙g−1 and from 36.993 to 3.529 µmol∙g−1 for natural and treated PTT, respectively. This can be explained by the fact that, the PZC of natural PTT is 4.8 and treated PTT is 3.8. Thus, at low pH (pH < PZC) more protons will be available for the protonation of the biosorbent surface which increases the electrostatic attraction between the positively charged biosorbent sites and the negatively charged 2,6-DCPIP. There is nearly no electrostatic repulsion between the biosorbent and the 2,6-DCPIP at pH = 2 and hence, the amount adsorbed is at its maximum. Increasing the pH (pH > PZC) leads to an increase in 2,6-DCPIP anions in the solution as well as the number of negatively charged sites on the adsorbent due to the increase in hydroxyl ions. This results in electrostatic repulsion between the 2,6-DCPIP and the adsorbent, which is the reason for the decrease in the amount of adsorption. A similar trend was observed for the adsorption of azo dyes by glutaraldehyde-crosslinked chitosans  .
3.7. Effect of Ionic Strength
The ionic strength of the solution is one of the factors that control both electrostatic and non-electrostatic interactions between the adsorbate and the adsorbent surface  . The effect of ionic strength on biosorption of 2,6-DCPIP was carried out using the initial concentration of NaCl. The results illustrated in Figure 9 reveal that an increase of ionic strength causes an increase in the adsorption capacity of the 2,6-DCPIP. This result can be explained by the fact that the addition of salt increases the aggregation of dye molecules and decreases the solubility. An increase in aggregation promotes the adsorption of dye molecules   . Another possibility is that an increase in ionic strength increases the positive charge of the biosorbent surface, thus increasing the electrostatic attraction between dye (2,6-DCPIP) and biosorbent  . Additionally, an increase in ionic strength of aqueous solution may result in the compression of the diffuse double layer on the biosorbent. This eases the electrostatic attraction and consequently participates in adsorption  .
3.8. Effect of Interfering Ions
The effect of interfering ions on biosorption of 2,6-DCPIP was carried out using different salts; BaCl2, CaCl2 and NaCl. The results show that the capacity of adsorption increases with the presence of salts in the order NaCl < CaCl2 < BaCl2 (Figure 10). The capacity of adsorption is higher with divalent ions. This is because the doubly charged ions increase the surface charges of biosorbents, which increases the electrostatic interaction and/or anionic exchange between the
Figure 9. Effect of ionic strength on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; m = 3 g∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
Figure 10. Effect of interfering ions on the biosorption of 2,6-DCPIP. Experimental conditions: [2,6-DCPIP] = 10−4 mol∙L−1; m = 3 g∙L−1; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V = 10 mL; pH = 6.7; at room temperature.
2,6-DCPIP and the biosorbents. This can also be explained by the fact that the divalent ions favour more aggregation of dye molecules and decreases the solubility than the monovalent ions. The higher capacity of adsorption of BaCl2 than CaCl2 can be explained by the fact that, the higher molecular weight of BaCl2 favours more aggregation of dye molecules and decreases the solubility than the lower molecular weight of CaCl2.
3.9. Adsorption Isotherms
In order to understand the mechanism of biosorption, it is important to perform the adsorption isotherms. In this study, four adsorption isotherms were used to describe the obtained equilibrium data: Langmuir, Freundlich, Dubinin-Radushkevich and Temkin isotherms.
3.9.1. Langmuir Isotherm
The general equation of Langmuir isotherm is described as follows (Equation (5))   :
where; and are the equilibrium and maximum biosorption capacities of biosorbent, respectively. is the equilibrium concentration of solution. is the Langmuir biosorption constant. The constants and were calculated from the slopes and intercepts of
linear plots of versus . The essential characteristic of Langmuir isotherm
can be expressed in terms of a dimensionless constant called separation factor ( ), which is defined as follows (Equation (6))  :
The value of indicates whether the type of adsorption isotherm will be favorable , unfavorable , linear or irreversible .
3.9.2. Freundlich Isotherm
The general equation of Freundlich isotherm is described as follows (Equation (7))   :
where is the Freundlich constant related to the biosorption capacity and is an empirical parameter related to the biosorption intensity of the adsorbent. The Freundlich isotherm constants and were calculated from the slopes and intercepts of linear plots of versus .
3.9.3. Dubinin-Radushkevich Isotherm
The general formula of Dubinin-Radushkevich isotherm is given by the following Equation (8)   :
where; (mol2∙kJ−2) is the activity coefficient related to the mean free energy (E (kJ∙mol−1)) obtained from Equation (10) and is polanyi potential which is determined from Equation (9):
where, R is the universal gas constant (8.314 × 10−3 kJ∙mol−1∙K−1) and T is the absolute temperature in kelvin in our case (298 K). The constants and were calculated from the slopes and the intercepts of linear plot of versus .
3.9.4. Temkin Isotherm
The general formula of Temkin isotherm is given by the following Equation (11)    :
where; (kJ∙mol−1) is the heat of adsorption, (L.µmol−1) is the Temkin isotherm constant. The constants and were calculated from the slopes and the intercepts of linear plot of versus .
The values of correlation coefficients of Dubinin-Radushkevich and Temkin isotherms are closest to unity, implying that Dubinin-Radushkevich and Temkin isotherms are most appropriate to describe the biosorption of 2,6-DCPIP on natural and treated PTT, respectively. The values of 1/n determined by the Freundlich isotherm (Table 1) are less than unity, implying that biosorption is favorable for both biosorbents    .
Figure 11. Adsorption isotherms of Langmuir (a), Freundlich (b), Dubinin-Radushkevich (c) and Temkin (d).
Table 1. Langmuir, Freundlich, Dubinin-Radushkevich and Temkin constants of adsorption.
The adsorption energies obtained from Dubinin-Radushkevich isotherm (Table 1) are between 8 and 16 kJ∙mol−1, implying that chemisorption (anionic exchange) is the mechanism which controls the biosorption process  . The positive values of the heat of adsorption from Temkin isotherm (Table 1) indicate that the adsorption process is exothermic   . Moreover, the heat of adsorption of treated PTT is greater than the heat of adsorption of natural PTT. This implies that interactions between 2,6-DCPIP ions and treated PTT are more energetic than interactions between 2,6-DCPIP ions and natural PTT  .
The values of the separation factor determined by the Langmuir isotherm (Figure 12) are found between 0 - 1 (0.612 - 0.888 for treated PTT and 0.691 - 0.918 for natural PTT), meaning that biosorption is favorable for both biosorbents. This result is in agreement with what was already noted with the Freundlich isotherm. The lower values at higher initial 2,6-DCPIP concentrations showed that the adsorption was more favorable at higher concentrations  . The values of of treated PTT are lower than the values of natural PTT, implying that the adsorption of 2,6-DCPIP is more favorable with treated PTT rather than natural PTT  .
3.10. Adsorption Kinetics
The controlling mechanisms of adsorption process such as chemical reaction, diffusion control or mass transfer coefficient are used to determine kinetic models. Thus, the kinetics of dye onto various adsorbent materials was analyzed using different kinetic models which are presented below.
3.10.1. Pseudo-First Order Model
The pseudo-first order equation of Lagergren is generally expressed as follows (Equation (12))    :
where; and (µmol∙g−1) are the amounts of 2,6-DCPIP adsorbed at
Figure 12. Evolution of separation factor against the initial concentration of 2,6-DCPIP.
equilibrium and at time t, respectively. (min−1) is the rate constant of pseudo-first order. The values of and were calculated from the slopes and intercepts of the linear plots of versus t.
3.10.2. Pseudo-Second Order Model
The pseudo-second order equation is generally expressed as follows (Equation (13))    :
where (g.µmol−1.min−1) is the rate constant of pseudo-second order. The values of and were calculated from the slopes and intercepts of the
linear plots of versus t. This model allows determining the initial rate of
reaction h (µmol∙g−1∙min−1) (Equation (14)) and the half time of the reaction t1⁄2 (min) (Equation (15)).
3.10.3. Elovich Model
The Elovich model is represented by the following Equation (16)  :
where; (mmol∙g−1∙min−1) is the initial adsorption rate and (g∙µmol−1) is related to the extent of surface coverage and activation energy for chemisorption. The values of and were calculated from the slopes and intercepts of the linear plots of versus .
3.10.4. Intraparticle Diffusion Model
Weber and Morris demonstrated that in intraparticle diffusion studies, rate processes are usually expressed in terms of square root of time    . The intraparticle diffusion model is deﬁned by Equation (17).
where; (µmol∙g−1.min−1/2) is the intraparticle diffusion rate constant and C (µmol∙g−1) is the thickness of boundary layer. The values of and C were calculated from the slopes and intercepts of the linear plots of versus .
3.10.5. External Mass Transfer Resistance Model
This model assumes that the surface solute concentration , on the sorbent is negligible at t = 0, and that intraparticle diffusion is also negligible; it is used to calculate the initial rate of solute sorption. The initial rate of sorption can be determined using the classical mass transfer equation, which describes the evolution of solute concentration in solution (Equation (18))   :
where; is the external mass transfer coefficient, is the liquid phase solute concentration at time t, is the liquid phase solute concentration at the particle surface and S is the specific surface area for mass transfer. This equation can be simplified by substituting the following boundary conditions: and when ; C0 = initial solute concentration, to Equation (19)   :
So the external mass transfer rate , was approximated by the initial slope of the versus time graph.
3.10.6. Boyd Model
In order to interpret the rate-controlling step during the adsorption process, the experimental data were further analyzed by the model given by Boyd (Equation (20))    :
Since , Bt could be represented as follows (Equation (21)):
where; F is the fraction of solute sorbed at different times t and Bt is a mathematical function of F. The calculated B values are used to calculate the effective diffusion coefficient, using Equation (22)   :
where, r represents the mean radius of the particle calculated by sieve analysis and by assuming them as spherical particles.
Table 2 indicate that the pseudo-second order model adequately describes the adsorption kinetics of 2,6-DCPIP on the biosorbents with a high correlation coefficient. Moreover, it can be observed that the values of the calculated of pseudo-second order model are in good agreement with experimental values. This means that the biosorption of 2,6-DCPIP on biosorbents is a process that is controlled by chemisorption    . On the other hand, the low reaction half time and the high initial rate of reaction (Table 2) of treated PTT compared to natural PTT conﬁrm that the biosorption of 2,6-DCPIP is very fast with treated PTT than natural PTT   .
Figure 13. Kinetic adsorptions of pseudo-first order (a), pseudo-second order (b), intraparticle diffusion (c), Elovich (d), Boyd (e) and external mass transfer (f).
From Figure 13(c), the curves of intraparticle diffusion present two linear portions. The first portion located at the beginning of the process is attributed to the film diffusion, where the 2,6-DCPIP diffuses through the solution to the external surface of adsorbent or boundary layer diffusion. The second portion located at the end of the process describes the pore diffusion  . It is also clear from Figure 13(c) and Table 2 that the first stage is faster than the second one, which may be ascribed to the very slow diffusion of the 2,6-DCPIP from the surface film into the micropores which represent the least accessible sites for
Table 2. Pseudo-first order, Pseudo-second order, Elovich, Intraparticle diffusion, External mass transfer and Boyd constants of adsorption.
adsorption. Also, the intraparticle diffusion model curve does not pass through the origin, which is an indication that 2,6-DCPIP diffusion in the bulk of natural and treated PTT is not the only process that governs the biosorption   . Moreover, the values of the thickness of boundary layer C for each linear portion are not zero, indicating that intraparticle diffusion is present as a part of diffusion process, but it is not the sole rate-controlling step in all the stages  .
Figure 13(e) shows that the straight line obtained by the Boyd model does not pass through the origin of the graph, implying that external mass transfer is the main rate controlling step at the initial stages   . The values of presented in Table 2 lie in the range 10−13 to 10−5 cm2⁄s, indicating that chemisorption occurs during the biosorption process  . This result is in agreement with the pseudo-second order model and Dubinin-Radushkevich isotherm. Thus, the biosorption of 2,6-DCPIP on the natural and treated PTT is best described by external mass transfer diffusion rather than internal diffusion.
The repeated availability of the adsorbents after adsorption-desorption cycles is crucial to illustrate the stability and potential recovery of the adsorbents. In this study, NaOH, HNO3 and H2O were used as desorbing agents to regenerate the biosorbents. The results show that the maximum desorption percentage, 67.371% for natural PTT and 54.260% for treated PTT is obtained in NaOH medium (Figure 14). This can be explained by the phenomenon of anionic exchange between the hydroxyl ions (OH−) of NaOH solution and 2,6-DCPIP loaded biosorbent. However, the low percentage of desorption obtained with treated PTT compared to natural PTT is due to the strong bond formed between the 2,6-DCPIP and the treated PTT  .
From this study, the capacity of using natural and treated PTT for the removal of
Figure 14. Effect of desorption solution on the recovery of adsorbed 2,6-DCPIP. Experimental conditions: 30 mg of 2,6-DCPIP loaded biosorbents; G = 0 - 100 µm; t = 40 min; v = 150 rpm; V =10 mL; at room temperature.
2,6-DCPIP from aqueous solution has been proven. Both materials are efficient biosorbents, but the treated PTT showed better performance than natural PTT. The adsorption was highly dependent on various operating parameters such as; treatment of biosorbent, contact time, pH of solution, biosorbents dosage, initial concentration of 2,6-DCPIP, ionic strength and interfering ions. The adsorption isotherms indicate that the equilibrium data are the best described by the Dubinin-Radushkevich and Temkin isotherms for natural and treated PTT, respectively. Results of adsorption kinetics demonstrated that the adsorption processes were controlled by pseudo-second order kinetics. The mechanism of diffusion was studied and the results showed that external mass transfer was the main rate controlling step. Desorption using NaOH as desorbing agent recovers a maximum quantity of 2,6-DCPIP. From the results obtained, the utilization of PTT for the removal of 2,6-DCPIP from aqueous solution is promising.
The authors acknowledge the support of the International Foundation for Science (Grant n˚ W/5859-1 awarded to Evangeline NJANJA). Financial support from The World Academy of Sciences for the Advancement of Science in Developing Countries (TWAS grant no. 12-117 RG/CHE/AF/AC-G) is gratefully acknowledged.