**3. Adsorption conditions**

#### **3.1. Equilibrium**

#### *3.1.1. pH*

The pH of the dye solution plays an important role in the whole adsorption process and par‐ ticularly on the adsorption capacity; influences the surface charge of the adsorbent, the de‐ gree of ionization of the material present in the solution, the dissociation of functional groups on the active sites of the adsorbent, and the chemistry of dye solution. It is important to indicate that while the adsorption on activated carbon was largely independent of the pH, the adsorption of dyes on chitosan was controlled by the acidity of the solution. pH affects the surface charge of the adsorbent. Chitosan is a weak base and is insoluble in water and organic solvents, however, it is soluble in dilute aqueous acidic solution (pH~6.5), which can convert the glucosamine units into a soluble form R-NH3 <sup>+</sup> . Chitosan is precipitated in alka‐ line solution or in the presence of polyanions and forms gels at lower pH. Its pKa depends on the deacetylation degree, the ionic strength and the neutralization of amine groups. In practice pKa lies within 6.5-6.7 for fully neutralized amine functions [50]. So, chitosan is pol‐ ycationic in acidic medium: the free amino groups are protonated and the polymer becomes fully soluble and this facilitates electrostatic interaction between chitosan and the negatively charged anionic dyes. This cationic property, especially in the case of anionic dyes, depend‐ ing on the charge and functions of the dye under the corresponding experimental conditions will influence the adsorption procedure [51]. In the literature, the ability of the anionic dyes to adsorb onto chitosan beads is often attributed to the surface charge which depends on the pH of the operating batch system, as mentioned. Dye adsorption occurred through electro‐ stactic attraction on protonated amine groups and numerous researchers concluded that the influence of the pH confirmed the essential role of electrostatic interactions between the chi‐ tosan and the target dye. For example, chitosan had a positively charged surface below pH=6.5 (point of zero potential) [52], and reducing the pH increased the positivity of the sur‐ face, thus making the adsorption process pH sensitive. Decreasing the pH makes more pro‐ tons available to protonate the amine group of chitosan with the formation of a large number of cationic amines. This results in increased dye adsorption by chitosan due to in‐ creased electrostatic interactions. Differences in pH of the solution have also been reported to influence the dye adsorption capacity of chitosan and its mechanism [44,45]. They noted that, at low pH, chitosan's free amino groups are protonated, causing them to attract anionic dyes, demonstrating that pH is one of the most important parameters controlling the ad‐ sorption process. Some researchers [32,33,53] also found that the adsorption capacity of cati‐ onic dyes on chitosan-grafted materials was strongly affected by the pH of solution and was generally significantly decreased by increasing the pH. pH is also known to affect the struc‐ tural stability of dye molecules (in particular the dissociation of their ionizable sites), and therefore their colour intensity. As a result, the dye molecule has high positive charge densi‐ ty at a low pH. This indicates that the deprotonation (or protonation) of a dye must be taken into consideration. If the dyes to be removed are either weakly acidic or weakly basic, then the pH of the medium affects their structure and adsorption. Initial pH also influences the solution chemistry of the dyes: hydrolysis, complexation by organic and/or inorganic li‐ gands, redox reactions, and precipitation are strongly influenced by pH, and on the other side strongly influence speciation and the adsorption capacity of the dyes. Some useful structural characteristics must be pointed out, as given below:

The free amine groups in chitosan are much more reactive and effective for chelating pollu‐ tants than the acetyl groups in chitin. There is no doubt that amine sites are the main reac‐ tive groups for (anionic) dye adsorption, though hydroxyl groups (especially in the C-3 position) may contribute to adsorption. Almost all functional properties of chitosan depend on the chain length, charge density and charge distribution and much of its potential as ad‐ sorbent is effected by its cationic nature and solution behaviour. However, at neutral pH, about 50% of total amine groups remain protonated and theoretically available for the ad‐ sorption of dyes. The existence of free amine groups may cause direct complexation of dyes co-existing with anionic species, depending on the charge of the dye. As the pH decreases, the protonation of amine groups increases together with the efficiency. The optimum pH is frequently reported in the literature to be around pH 2-4. Below this range, usually a large excess of competitor anions limits adsorption efficiency. This competitor effect is the subject of many studies aiming to develop materials that are less sensitive to the presence of com‐ petitor anions and to the pH of the solution, as described in the next two paragraphs.

It is not really the total number of free amine groups that must be taken into account but the number of accessible free amine groups. There are several explanations for this. The availa‐ bility of amine groups is controlled by two important parameters: (i) the crystallinity of pol‐ ymer, and (ii) the diffusion properties of dyes. It is known that some of the amine sites on chitosan are included in both the crystalline area and in inter or intramolecular hydrogen bonds. Moreover the residual crystallinity of the polymer may control the accessibility to ad‐ sorption sites. The deacetylation degree also controls the fraction of free amine groups avail‐ able for interactions with dyes. Indeed, the total number of free amine groups is not necessarily accessible for dye uptake. Actually, rather than the fraction or number of free amine groups available for dye uptake, it would be better to consider the number of accessi‐ ble free amine groups. It is also concluded that the hydrogen bonds linked between mono‐ mer units of the same chain (intramolecular bonds) and/or between monomer units of different chains (intermolecular bonds) decrease their reactivity. The weakly porous struc‐ ture of the polymer and its residual crystallinity are critical parameters for the hydratation and the accessibility to adsorption sites.

#### *3.1.2. Isotherms*

change the crystalline nature of chitosan, as suggested by the XRD diffractograms. After the cross-linking reaction, there was a small increase in the crytallinity of the chitosan beads and

The pH of the dye solution plays an important role in the whole adsorption process and par‐ ticularly on the adsorption capacity; influences the surface charge of the adsorbent, the de‐ gree of ionization of the material present in the solution, the dissociation of functional groups on the active sites of the adsorbent, and the chemistry of dye solution. It is important to indicate that while the adsorption on activated carbon was largely independent of the pH, the adsorption of dyes on chitosan was controlled by the acidity of the solution. pH affects the surface charge of the adsorbent. Chitosan is a weak base and is insoluble in water and organic solvents, however, it is soluble in dilute aqueous acidic solution (pH~6.5), which can

line solution or in the presence of polyanions and forms gels at lower pH. Its pKa depends on the deacetylation degree, the ionic strength and the neutralization of amine groups. In practice pKa lies within 6.5-6.7 for fully neutralized amine functions [50]. So, chitosan is pol‐ ycationic in acidic medium: the free amino groups are protonated and the polymer becomes fully soluble and this facilitates electrostatic interaction between chitosan and the negatively charged anionic dyes. This cationic property, especially in the case of anionic dyes, depend‐ ing on the charge and functions of the dye under the corresponding experimental conditions will influence the adsorption procedure [51]. In the literature, the ability of the anionic dyes to adsorb onto chitosan beads is often attributed to the surface charge which depends on the pH of the operating batch system, as mentioned. Dye adsorption occurred through electro‐ stactic attraction on protonated amine groups and numerous researchers concluded that the influence of the pH confirmed the essential role of electrostatic interactions between the chi‐ tosan and the target dye. For example, chitosan had a positively charged surface below pH=6.5 (point of zero potential) [52], and reducing the pH increased the positivity of the sur‐ face, thus making the adsorption process pH sensitive. Decreasing the pH makes more pro‐ tons available to protonate the amine group of chitosan with the formation of a large number of cationic amines. This results in increased dye adsorption by chitosan due to in‐ creased electrostatic interactions. Differences in pH of the solution have also been reported to influence the dye adsorption capacity of chitosan and its mechanism [44,45]. They noted that, at low pH, chitosan's free amino groups are protonated, causing them to attract anionic dyes, demonstrating that pH is one of the most important parameters controlling the ad‐ sorption process. Some researchers [32,33,53] also found that the adsorption capacity of cati‐ onic dyes on chitosan-grafted materials was strongly affected by the pH of solution and was generally significantly decreased by increasing the pH. pH is also known to affect the struc‐

. Chitosan is precipitated in alka‐

also increased accessibility to the small pores of the material.

convert the glucosamine units into a soluble form R-NH3 <sup>+</sup>

**3. Adsorption conditions**

188 Eco-Friendly Textile Dyeing and Finishing

**3.1. Equilibrium**

*3.1.1. pH*

Adsorption properties and equilibrium data, commonly known as adsorption isotherms, de‐ scribe how pollutants interact with adsorbent materials and so, are critical in optimizing the use of adsorbents [31]. In order to optimize the design of an adsorption system to remove dye from solutions, it is important to establish the most appropriate correlation for the equi‐ librium curve. An accurate mathematical description of equilibrium adsorption capacity is indispensable for reliable prediction of adsorption parameters and quantitative comparison of adsorption behaviour for different adsorbent systems (or for varied experimental condi‐ tions) within any given system. Adsorption equilibrium is established when the amount of dye being adsorbed onto the adsorbent is equal to the amount being desorbed. It is possible to depict the equilibrium adsorption isotherms by plotting the concentration of the dye in the solid phase versus that in the liquid phase. The distribution of dye molecule between the liquid phase and the adsorbent is a measure of the position of equilibrium in the adsorption process and can generally be expressed by one or more of a series of isotherm models [54-58]. The shape of an isotherm may be considered with a view to predicting if a sorption system is "favourable" or "unfavourable". The isotherm shape can also provide qualitative information on the nature of the solute–surface interaction. In addition, adsorption iso‐ therms have been developed to evaluate the capacity of chitosan materials for the adsorp‐ tion of a particular dye molecule. They constitute the first experimental information, which is generally used as a convenient tool to discriminate among different materials and thereby choose the most appropriate one for a particular application in standard conditions. The most popular classification of adsorption isotherms of solutes from aqueous solutions has been proposed by Giles et al. [57,58]. Four characteristic classes are identified, based on the configuration of the initial part of the isotherm (i.e., class S, L, H, C). The Langmuir class (L) is the most widespread in the case of adsorption of dye compounds from water, and it is characterized by an initial region, which is concave to the concentration axis. Type L also suggests that no strong competition exists between the adsorbate and the solvent to occupy the adsorption sites. However, the H class (high affinity) results from extremely strong ad‐ sorption at very low concentrations giving rise to an apparent intercept on the ordinate. The H-type isotherms suggest the uptake of pollutants by materials through chemical forces rather than physical attraction. There are several isotherm models available for analyzing experimental data and for describing the equilibrium of adsorption, including Langmuir, Freundlich, Langmuir-Freunldich, BET, Toth, Temkin, Redlich-Peterson, Sips, Frumkin, Harkins-Jura, Halsey, Henderson and Dubinin-Radushkevich isotherms. These equilibrium isotherm equations are used to describe experimental adsorption data. The different equa‐ tion parameters and the underlying thermodynamic assumptions of these models often pro‐ vide insight into both the adsorption mechanism, and the surface properties and affinity of the adsorbent. Therefore, it is important to establish the most appropriate correlation of equilibrium curves to optimize the condition for designing adsorption systems. Various re‐ searchers have used these isotherms to examine the importance of different factors on dye molecule sorption by chitosan. However, the two most frequently used equations applied in solid/liquid systems for describing sorption isotherms are the Langmuir [55] and the Freundlich [56] models and the most popular isotherm theory is the Langmuir one which is commonly used for the sorption of dyes onto chitosan.

amount of the dye adsorbed onto chitosan increased with an increase in the initial concen‐ tration of dye solution if the amount of adsorbent was kept unchanged. This is due to the increase in the driving force of the concentration gradient with the higher initial dye concen‐ tration. In most cases, at low initial concentration the adsorption of dyes by chitosan is very intense and reaches equilibrium very quickly. This indicates the possibility of the formation of monolayer coverage of the dye molecules at the outer interface of the chitosan. At a fixed adsorbent dose, the amount of dye adsorbed increases with the increase of dye concentra‐ tion in solution, but the percentage of adsorption decreased. In other words, the residual concentration of dye molecules will be higher for higher initial dye concentrations. In the case of lower concentrations, the ratio of initial number of dye moles to the available adsorp‐ tion sites is low and subsequently the fractional adsorption becomes independent of initial concentration [3,41,46,47,49,52,53]. At higher concentrations, however, the number of availa‐ ble adsorption sites becomes lower and subsequently the removal of dyes depends on the initial concentration. At the high concentrations, it is not likely that dyes are only adsorbed in a monolayer at the outer interface of chitosan. As a matter of fact, the diffusion of ex‐ changing molecules within chitosan particles may govern the adsorption rate at higher ini‐ tial concentrations. In another theory, it is claimed that adsorption rate may diminish with an increase in dye concentration [34].This could be ascribed to the accompanying increase in

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dye aggregation and/or depletion of accessible active sites on the material.

Generally speaking, the adsorption of pollutants increases with the increase in temperature, because high temperatures provide a faster rate of diffusion of adsorbate molecules from the solution to the adsorbent [31,41]. However, it is well known that temperature plays an im‐ portant role in adsorption onto activated carbon, generally having a negative influence on the amount adsorbed. The adsorption of organic compounds (including dyes) is an exother‐ mic process and the physical bonding between the organic compounds and the active sites of the carbon will weaken with increasing temperature. Also with the increase of tempera‐ ture, the dye solubility also increases, the interaction forces between the solute and the sol‐ vent become stronger than those between solute and adsorbent, consequently the solute is more difficult to adsorb. Both of these features are consistent with the order of Langmuir ad‐ sorption capacity. The adsorption of dyes by chitosan is also usually exothermic: an increase in the temperature leads to an increase in the dye adsorption rate, but diminishes total ad‐ sorption capacity [3,41,53]. However, these effects are small and normal wastewater temper‐ ature variations do not significantly affect the overall decolorization performance [59]. In addition, the adsorption process is not usually operated at high temperature, because this would increase operation costs. The increase in temperature affects not only the solubility of the dye molecule (its solubility increases), but also the adsorptive potential of the material (its adsorption capacity increases). Both effects work in the same direction causing an in‐ crease of cost operation in the batch system. In general, this could be confirmed by the ther‐ modynamic parameters. An increase in temperature is also followed by an increase in the diffusivity of the dye molecule, and consequently by an increase in the adsorption rate if dif‐ fusion is the rate-limiting step. Temperature could also influence the desorption step and consequently the reversibility of the adsorption equilibrium. So, the temperature (and its variation) is an important factor affecting chitosan adsorption and investigations of this pa‐

The majority of researchers found significant correlations between dye concentration and the dye-binding capacity of polymeric adsorbents and particularly chitosan [3,41,53]. The amount of the dye adsorbed onto chitosan increased with an increase in the initial concen‐ tration of dye solution if the amount of adsorbent was kept unchanged. This is due to the increase in the driving force of the concentration gradient with the higher initial dye concen‐ tration. In most cases, at low initial concentration the adsorption of dyes by chitosan is very intense and reaches equilibrium very quickly. This indicates the possibility of the formation of monolayer coverage of the dye molecules at the outer interface of the chitosan. At a fixed adsorbent dose, the amount of dye adsorbed increases with the increase of dye concentra‐ tion in solution, but the percentage of adsorption decreased. In other words, the residual concentration of dye molecules will be higher for higher initial dye concentrations. In the case of lower concentrations, the ratio of initial number of dye moles to the available adsorp‐ tion sites is low and subsequently the fractional adsorption becomes independent of initial concentration [3,41,46,47,49,52,53]. At higher concentrations, however, the number of availa‐ ble adsorption sites becomes lower and subsequently the removal of dyes depends on the initial concentration. At the high concentrations, it is not likely that dyes are only adsorbed in a monolayer at the outer interface of chitosan. As a matter of fact, the diffusion of ex‐ changing molecules within chitosan particles may govern the adsorption rate at higher ini‐ tial concentrations. In another theory, it is claimed that adsorption rate may diminish with an increase in dye concentration [34].This could be ascribed to the accompanying increase in dye aggregation and/or depletion of accessible active sites on the material.

use of adsorbents [31]. In order to optimize the design of an adsorption system to remove dye from solutions, it is important to establish the most appropriate correlation for the equi‐ librium curve. An accurate mathematical description of equilibrium adsorption capacity is indispensable for reliable prediction of adsorption parameters and quantitative comparison of adsorption behaviour for different adsorbent systems (or for varied experimental condi‐ tions) within any given system. Adsorption equilibrium is established when the amount of dye being adsorbed onto the adsorbent is equal to the amount being desorbed. It is possible to depict the equilibrium adsorption isotherms by plotting the concentration of the dye in the solid phase versus that in the liquid phase. The distribution of dye molecule between the liquid phase and the adsorbent is a measure of the position of equilibrium in the adsorption process and can generally be expressed by one or more of a series of isotherm models [54-58]. The shape of an isotherm may be considered with a view to predicting if a sorption system is "favourable" or "unfavourable". The isotherm shape can also provide qualitative information on the nature of the solute–surface interaction. In addition, adsorption iso‐ therms have been developed to evaluate the capacity of chitosan materials for the adsorp‐ tion of a particular dye molecule. They constitute the first experimental information, which is generally used as a convenient tool to discriminate among different materials and thereby choose the most appropriate one for a particular application in standard conditions. The most popular classification of adsorption isotherms of solutes from aqueous solutions has been proposed by Giles et al. [57,58]. Four characteristic classes are identified, based on the configuration of the initial part of the isotherm (i.e., class S, L, H, C). The Langmuir class (L) is the most widespread in the case of adsorption of dye compounds from water, and it is characterized by an initial region, which is concave to the concentration axis. Type L also suggests that no strong competition exists between the adsorbate and the solvent to occupy the adsorption sites. However, the H class (high affinity) results from extremely strong ad‐ sorption at very low concentrations giving rise to an apparent intercept on the ordinate. The H-type isotherms suggest the uptake of pollutants by materials through chemical forces rather than physical attraction. There are several isotherm models available for analyzing experimental data and for describing the equilibrium of adsorption, including Langmuir, Freundlich, Langmuir-Freunldich, BET, Toth, Temkin, Redlich-Peterson, Sips, Frumkin, Harkins-Jura, Halsey, Henderson and Dubinin-Radushkevich isotherms. These equilibrium isotherm equations are used to describe experimental adsorption data. The different equa‐ tion parameters and the underlying thermodynamic assumptions of these models often pro‐ vide insight into both the adsorption mechanism, and the surface properties and affinity of the adsorbent. Therefore, it is important to establish the most appropriate correlation of equilibrium curves to optimize the condition for designing adsorption systems. Various re‐ searchers have used these isotherms to examine the importance of different factors on dye molecule sorption by chitosan. However, the two most frequently used equations applied in solid/liquid systems for describing sorption isotherms are the Langmuir [55] and the Freundlich [56] models and the most popular isotherm theory is the Langmuir one which is

190 Eco-Friendly Textile Dyeing and Finishing

commonly used for the sorption of dyes onto chitosan.

The majority of researchers found significant correlations between dye concentration and the dye-binding capacity of polymeric adsorbents and particularly chitosan [3,41,53]. The

Generally speaking, the adsorption of pollutants increases with the increase in temperature, because high temperatures provide a faster rate of diffusion of adsorbate molecules from the solution to the adsorbent [31,41]. However, it is well known that temperature plays an im‐ portant role in adsorption onto activated carbon, generally having a negative influence on the amount adsorbed. The adsorption of organic compounds (including dyes) is an exother‐ mic process and the physical bonding between the organic compounds and the active sites of the carbon will weaken with increasing temperature. Also with the increase of tempera‐ ture, the dye solubility also increases, the interaction forces between the solute and the sol‐ vent become stronger than those between solute and adsorbent, consequently the solute is more difficult to adsorb. Both of these features are consistent with the order of Langmuir ad‐ sorption capacity. The adsorption of dyes by chitosan is also usually exothermic: an increase in the temperature leads to an increase in the dye adsorption rate, but diminishes total ad‐ sorption capacity [3,41,53]. However, these effects are small and normal wastewater temper‐ ature variations do not significantly affect the overall decolorization performance [59]. In addition, the adsorption process is not usually operated at high temperature, because this would increase operation costs. The increase in temperature affects not only the solubility of the dye molecule (its solubility increases), but also the adsorptive potential of the material (its adsorption capacity increases). Both effects work in the same direction causing an in‐ crease of cost operation in the batch system. In general, this could be confirmed by the ther‐ modynamic parameters. An increase in temperature is also followed by an increase in the diffusivity of the dye molecule, and consequently by an increase in the adsorption rate if dif‐ fusion is the rate-limiting step. Temperature could also influence the desorption step and consequently the reversibility of the adsorption equilibrium. So, the temperature (and its variation) is an important factor affecting chitosan adsorption and investigations of this pa‐ rameter offer interesting results, albeit often contradictory. The usual increase in adsorption may be attributed to the fact that on increasing temperature, a greater number of active sites is generated on the polymer beads because of an enhanced rate of protonation/deprotona‐ tion of the functional groups on the beads. The fact that adsorption of dyes on chitosan in‐ creases with higher temperature can be surprising. Other authors concluded that an increase in temperature leads to a decrease in the amount of adsorbed dye at equilibrium since ad‐ sorption on chitosan is exothermic [60,61].

On the other hand, the actual shape of the geometry, in which the above phenomena occur, is completely unknown. Recently, several reconstructions or tomographic techniques have been developed for the 3-D digitization of the internal structure of porous media [64]. This digitized structure can be used to solve the equations describing the prevailing phenomena. The above approach is extremely difficult (still inapplicable for the size of pores met in ad‐ sorption applications), time consuming and its use is restricted to porous media develop‐ ment applications. A more effective approach is needed for the purpose of adsorption process design. So, the classical approach of "homogenizing" the corresponding partial dif‐ ferential equations and transferring the lack of knowledge of the geometry to the values of the physical parameters of the problem is given below. In the adsorbent particle phase, the adsorbate can be found both as solute in the liquid, filling the pores of the particle (concen‐

sorbent). The "homogeneous" equations for the evolution of C and q inside a spherical

( ) <sup>2</sup>

 ∂

> ∂

where t is the time, r is the radial direction, εp the porosity of the particle, ρ<sup>p</sup> the density of

the corresponding surface diffusivity. The diffusivity Dp for a given pair of adsorbate-fluid depends only on the temperature, whereas the diffusivity Ds depends both on the type of adsorbent and on q also (apart from their dependence on geometry). For particles with nonuniform structure the parameters Dp, Ds, εp, ρp are functions of r but this case will not be considered here. The function G(C,q) denotes the rate of the adsorption-desorption process.

r=R

r r R æ ö - - ç ÷ <sup>è</sup> <sup>=</sup> <sup>ø</sup> ∂

where *C <sup>b</sup>* is the concentration of the adsorbate in the bulk solution, and *k <sup>m</sup>* is the mass trans‐

∂

at

2 s q1 q = r D G C,q trr r -

 ∂

 ∂

) and adsorbed on the solid phase (concentration q in kg adsorbate/kg ad‐

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<sup>∂</sup>*<sup>r</sup>* <sup>−</sup>*ρpG*(*C*, *<sup>q</sup>*) (1)

(2)

(3)

(4)

), Dp is the liquid phase diffusivity of the adsorbate and Ds is

tration C in kg/m3

the particle (kg adsorbent/m3

ii) spherical symmetry:

adsorbent particle of radius R, are the following:

*εp* ∂*C* <sup>∂</sup>*<sup>t</sup>* <sup>=</sup> <sup>1</sup> *r* 2 ∂ ∂*r r* 2 *Dp* ∂*C*

∂

∂

The boundary conditions for the above set of equations are:

m b ( ) <sup>p</sup>

<sup>C</sup> k C C= D

C q = =0 r r

 ∂

 ∂

at r R æ öæ ö ç ÷ç ÷ è øè <sup>=</sup> <sup>ø</sup>

i) mass transfer from the solution to particle:

fer coefficient from the bulk solution to the particle.

∂

∂

## **3.3. Kinetics – Modelling**

The conventional approach to quantify the batch adsorption process is the empirical fit‐ ting based on the dependence between the global adsorption rate and the driving force for adsorption i.e. the difference between the actual and the equilibrium adsorbate concentra‐ tion. This dependence can be a linear one but in most cases is taken as quadratic. The parameters extracted from the fitting procedure may be appropriate to represent the exper‐ imental data, but they do not have any direct physical meaning (although some research‐ ers relate them to an hypothetical diffusion coefficient). In addition, this type of empirical modelling cannot be extended to describe more complicated process geometries than the simple batch one. A phenomenological approach based on fundamental principles) is need‐ ed, in order to develop models with parameters with physical meaning. This type of mod‐ els can be extended to be used for the design of processes of engineering interest (like fixed bed adsorption) and improve the understanding of the adsorbent structure in line with its interaction with the adsorbate.

The phenomenological approach to the batch adsorption is well-known. Kyzas et al [41] made an attempt for the description of the derivation of the models, of the inherent assump‐ tions and of how several simplified models used in literature are hooked to the general ap‐ proach. The description of the approach will be made for a general porous solid and then the adjustment to the particular structure of the chitosan derivatives will be presented. The actual difficulty in the modeling of the adsorption process for porous adsorbents is not its physics but its geometry in micro-scale. For extensive discussion on the physics of adsorp‐ tion process please see other works [62,63]. The physics is well-understood in terms of the occurring processes: (i) diffusion of the adsorbate in the liquid, (ii) adsorption-desorption between the liquid and solid phase, and (iii) surface diffusion of the adsorbate. See a simple schematic on the phenomena occurring in a pore in Figure 4.

**Figure 4.** Phenomena occurring in pore scale

On the other hand, the actual shape of the geometry, in which the above phenomena occur, is completely unknown. Recently, several reconstructions or tomographic techniques have been developed for the 3-D digitization of the internal structure of porous media [64]. This digitized structure can be used to solve the equations describing the prevailing phenomena. The above approach is extremely difficult (still inapplicable for the size of pores met in ad‐ sorption applications), time consuming and its use is restricted to porous media develop‐ ment applications. A more effective approach is needed for the purpose of adsorption process design. So, the classical approach of "homogenizing" the corresponding partial dif‐ ferential equations and transferring the lack of knowledge of the geometry to the values of the physical parameters of the problem is given below. In the adsorbent particle phase, the adsorbate can be found both as solute in the liquid, filling the pores of the particle (concen‐ tration C in kg/m3 ) and adsorbed on the solid phase (concentration q in kg adsorbate/kg ad‐ sorbent). The "homogeneous" equations for the evolution of C and q inside a spherical adsorbent particle of radius R, are the following:

$$
\varepsilon\_p \frac{\partial \mathcal{C}}{\partial t} = \frac{1}{r^2} \frac{\partial}{\partial r} r^2 D\_p \frac{\partial \mathcal{C}}{\partial r} - \rho\_p G(\mathcal{C}, q) \tag{1}
$$

$$\frac{\partial \mathbf{q}}{\partial \mathbf{t}} = \frac{1}{\mathbf{r}^2} \frac{\partial}{\partial \mathbf{r}} \mathbf{r}^2 \mathbf{D}\_s \frac{\partial \mathbf{q}}{\partial \mathbf{r}} - \mathbf{G} \left( \mathbf{C}, \mathbf{q} \right) \tag{2}$$

where t is the time, r is the radial direction, εp the porosity of the particle, ρ<sup>p</sup> the density of the particle (kg adsorbent/m3 ), Dp is the liquid phase diffusivity of the adsorbate and Ds is the corresponding surface diffusivity. The diffusivity Dp for a given pair of adsorbate-fluid depends only on the temperature, whereas the diffusivity Ds depends both on the type of adsorbent and on q also (apart from their dependence on geometry). For particles with nonuniform structure the parameters Dp, Ds, εp, ρp are functions of r but this case will not be considered here. The function G(C,q) denotes the rate of the adsorption-desorption process. The boundary conditions for the above set of equations are:

i) mass transfer from the solution to particle:

$$\mathbf{k}\_m \left( \mathbf{C}\_b - \mathbf{C} \right) = -\mathbf{D}\_p \left( \frac{\partial \mathbf{C}}{\partial \mathbf{r}} \right)\_{\mathbf{r} = \mathbf{R}} \quad \text{at } \mathbf{r} = \mathbf{R} \tag{3}$$

where *C <sup>b</sup>* is the concentration of the adsorbate in the bulk solution, and *k <sup>m</sup>* is the mass trans‐ fer coefficient from the bulk solution to the particle.

ii) spherical symmetry:

rameter offer interesting results, albeit often contradictory. The usual increase in adsorption may be attributed to the fact that on increasing temperature, a greater number of active sites is generated on the polymer beads because of an enhanced rate of protonation/deprotona‐ tion of the functional groups on the beads. The fact that adsorption of dyes on chitosan in‐ creases with higher temperature can be surprising. Other authors concluded that an increase in temperature leads to a decrease in the amount of adsorbed dye at equilibrium since ad‐

The conventional approach to quantify the batch adsorption process is the empirical fit‐ ting based on the dependence between the global adsorption rate and the driving force for adsorption i.e. the difference between the actual and the equilibrium adsorbate concentra‐ tion. This dependence can be a linear one but in most cases is taken as quadratic. The parameters extracted from the fitting procedure may be appropriate to represent the exper‐ imental data, but they do not have any direct physical meaning (although some research‐ ers relate them to an hypothetical diffusion coefficient). In addition, this type of empirical modelling cannot be extended to describe more complicated process geometries than the simple batch one. A phenomenological approach based on fundamental principles) is need‐ ed, in order to develop models with parameters with physical meaning. This type of mod‐ els can be extended to be used for the design of processes of engineering interest (like fixed bed adsorption) and improve the understanding of the adsorbent structure in line with its

The phenomenological approach to the batch adsorption is well-known. Kyzas et al [41] made an attempt for the description of the derivation of the models, of the inherent assump‐ tions and of how several simplified models used in literature are hooked to the general ap‐ proach. The description of the approach will be made for a general porous solid and then the adjustment to the particular structure of the chitosan derivatives will be presented. The actual difficulty in the modeling of the adsorption process for porous adsorbents is not its physics but its geometry in micro-scale. For extensive discussion on the physics of adsorp‐ tion process please see other works [62,63]. The physics is well-understood in terms of the occurring processes: (i) diffusion of the adsorbate in the liquid, (ii) adsorption-desorption between the liquid and solid phase, and (iii) surface diffusion of the adsorbate. See a simple

sorption on chitosan is exothermic [60,61].

**3.3. Kinetics – Modelling**

192 Eco-Friendly Textile Dyeing and Finishing

interaction with the adsorbate.

**Figure 4.** Phenomena occurring in pore scale

schematic on the phenomena occurring in a pore in Figure 4.

$$
\left(\frac{\partial \mathbf{C}}{\partial \mathbf{r}}\right) = \left(\frac{\partial \mathbf{q}}{\partial \mathbf{r}}\right) = \mathbf{0} \qquad \text{at } \mathbf{r} = \mathbf{R} \tag{4}
$$

Having values for the initial concentrations of adsorbate in the particle and for the bulk con‐ centration Cb, the above mathematical problem can be solved for the functions C(r,t) and q(r,t). The above model is the so-called non-equilibrium adsorption model. Models of this structure are used in large scale solute transport applications (e.g. soil remediation), where the phenomena are of different scale from the present application [65]. In the case of adsorp‐ tion by small particles, the adsorption-desorption process is much faster than the diffusion, leading to an establishment of a local equilibrium (which can be found by setting G(C,q)=0 and corresponds to the adsorption isotherm q=f(C)). In the present case, the local

$$\mathbf{q} = \frac{\mathbf{q}\_m \mathbf{b} \mathbf{C}^{l/n}}{1 + \mathbf{b} \mathbf{C}^{l/n}} \tag{5}$$

2

<sup>R</sup> ò (10)

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195

Decolorization of Dyeing Wastewater Using Polymeric Absorbents - An Overview

<sup>m</sup> C =C q <sup>V</sup>- (11)

R

0 <sup>3</sup> q = qr dr

<sup>0</sup> b b ave

where Cbo is the initial value of Cb; m is the total mass of the adsorbent particles; V is the

Let us now refer to the several analytical or simple numerical techniques used in literature for the above problem and explain under which conditions they can be employed. In the case of an overall diffusion coefficient D with no concentration dependence (which implies (i) constant Ds, and (ii) zero Dp or linear adsorption isotherm) and a linear adsorption iso‐ therm, the complete problem is linear and it can be solved analytically. The mathematical problem for the case of surface diffusion is equivalent to the homogeneous diffusion or solid diffusion model used by several authors [66]. The complete solution is given by Tien [54], but their simplified versions [67], which ignore external mass transfer and/or the solute con‐ centration reduction through equation 13 (i.e. assuming an infinite liquid volume), are ex‐ tensively used in the literature with topic of dye adsorption [68]. In case of constant diffusivity, and non-linear adsorption isotherm (which implies no pore diffusion and it is usually used in adsorption from liquid phase studies), several techniques based on the fun‐ damental solutions of the diffusion equation can be used [66,69]. In general, the partial dif‐ ferential equation is transformed to an integro-differential equation for the average

Another class of approximation methods, which can be used in any case (but with a ques‐ tionable success for non-linear problems), is the so-called Linear Driving Force model (LDF model) [70]. The concentration profile in the particle is approximated by a simple function (usually polynomial with two or three terms) and using this, the partial differential equation problem can be replaced by an expression for the evolution of qave. This method is not ap‐ propriate for use in batch adsorption studies, but it has been proven to be successful in cases like fixed bed adsorption. In these cases, where the solution of equation 8 in several posi‐ tions along the case of adsorption bed is required, LDF approximation is very useful. In cas‐ es, where no simplifications are possible and high accuracy is required, one has to resort to numerical techniques. A widely used approach is the collocation discretization of the spatial dimension, which is very efficient due to the use of higher order approximation. However, its advantage can be completely lost for the case of very rapid (or even discontinuous) changes of the parameters inside the particle. In order to be able to extend our approach to

In case of batch experiments the concentration of the solute in bulk liquid Cb decreases due to its adsorption; so, the evolution of the Cb must be taken into account by the model. The

<sup>3</sup> ave

easier way to do this is to consider a global mass balance of the adsorbate:

volume of the tank.

concentration qave (dimensionality reduction).

where qm and b corresponds to Qmax and KLF, respectively of L-F model.

In the limit of very fast adsorption-desorption kinetics it can be shown by a rigorous deriva‐ tion that the mathematical problem can be transformed to the following:

$$\mathbf{r}\frac{\partial\mathbf{q}}{\partial\mathbf{t}} = \frac{1}{\mathbf{r}^2}\frac{\partial}{\partial\mathbf{r}}\mathbf{r}^2\mathbf{D}(\mathbf{C})\frac{\partial\mathbf{q}}{\partial\mathbf{r}}\tag{6}$$

$$\left(\frac{\partial \mathbf{q}}{\partial \mathbf{r}}\right)\_{\mathbf{r}=\mathbf{0}} = \mathbf{0} \tag{7}$$

$$k\_m(C\_b - C) = \rho\_p D\_p \left(\frac{\partial q}{\partial r}\right)\_{r=R} \tag{8}$$

An additional assumption considered in the above derivation is that the amount of the ad‐ sorbate found in the liquid phase in the pores of the particle is insignificant compared to the respective amount adsorbed on the solid phase (i.e. εpC<<ρpq). This assumption always holds, as it can be easily checked by recalling the definition of the adsorption process.

The concentration C in eqs 6, 8 can be found by inverting the relation q=f(C). The diffusivity D is an overall diffusivity, which combines the bulk and surface diffusivity and is given by the relation:

$$\mathbf{D} = \mathbf{D}\_s + \frac{\mathbf{D}\_p}{\rho\_p \mathbf{f}'(\mathbf{C})} \tag{9}$$

where the prime denotes the differentiation of a function with respect to its argument. The average concentration of the adsorbed species (dye molecules) can be computed by the relation: Decolorization of Dyeing Wastewater Using Polymeric Absorbents - An Overview http://dx.doi.org/10.5772/52817 195

$$\mathbf{q}\_{\text{ }u} = \frac{\mathbf{3}}{\mathbf{R}} \stackrel{\text{R}}{\underset{\text{0}}{\text{ }}} \stackrel{\text{R}}{\text{ }} \text{qr}^{\text{ }} \text{dr} \tag{10}$$

In case of batch experiments the concentration of the solute in bulk liquid Cb decreases due to its adsorption; so, the evolution of the Cb must be taken into account by the model. The easier way to do this is to consider a global mass balance of the adsorbate:

Having values for the initial concentrations of adsorbate in the particle and for the bulk con‐ centration Cb, the above mathematical problem can be solved for the functions C(r,t) and q(r,t). The above model is the so-called non-equilibrium adsorption model. Models of this structure are used in large scale solute transport applications (e.g. soil remediation), where the phenomena are of different scale from the present application [65]. In the case of adsorp‐ tion by small particles, the adsorption-desorption process is much faster than the diffusion, leading to an establishment of a local equilibrium (which can be found by setting G(C,q)=0

> 1/n m

> > 1/n

In the limit of very fast adsorption-desorption kinetics it can be shown by a rigorous deriva‐

( ) <sup>2</sup>

 ∂

> ∂

q bC q = 1+ bC (5)

(6)

<sup>∂</sup>*<sup>r</sup>* )*r*=*<sup>R</sup>* (8)

ρf C¢ (9)

(7)

and corresponds to the adsorption isotherm q=f(C)). In the present case, the local

where qm and b corresponds to Qmax and KLF, respectively of L-F model.

tion that the mathematical problem can be transformed to the following:

∂

∂

the relation:

194 Eco-Friendly Textile Dyeing and Finishing

2 q1 q = rDC trr r

∂

*km*(*Cb* <sup>−</sup>*C*) <sup>=</sup>*ρpDp*( <sup>∂</sup>*<sup>q</sup>*

 ∂

 ∂

r=0 <sup>q</sup> = 0 r æ ö ç ÷ è ø ∂

An additional assumption considered in the above derivation is that the amount of the ad‐ sorbate found in the liquid phase in the pores of the particle is insignificant compared to the respective amount adsorbed on the solid phase (i.e. εpC<<ρpq). This assumption always

The concentration C in eqs 6, 8 can be found by inverting the relation q=f(C). The diffusivity D is an overall diffusivity, which combines the bulk and surface diffusivity and is given by

> ( ) p

p

where the prime denotes the differentiation of a function with respect to its argument. The average concentration of the adsorbed species (dye molecules) can be computed by the relation:

D

holds, as it can be easily checked by recalling the definition of the adsorption process.

s

D=D +

$$\mathbf{C}\_{b} = \mathbf{C}\_{b\_{0}} - \frac{\mathbf{m}}{\mathbf{V}} \mathbf{q}\_{\text{ave}} \tag{11}$$

where Cbo is the initial value of Cb; m is the total mass of the adsorbent particles; V is the volume of the tank.

Let us now refer to the several analytical or simple numerical techniques used in literature for the above problem and explain under which conditions they can be employed. In the case of an overall diffusion coefficient D with no concentration dependence (which implies (i) constant Ds, and (ii) zero Dp or linear adsorption isotherm) and a linear adsorption iso‐ therm, the complete problem is linear and it can be solved analytically. The mathematical problem for the case of surface diffusion is equivalent to the homogeneous diffusion or solid diffusion model used by several authors [66]. The complete solution is given by Tien [54], but their simplified versions [67], which ignore external mass transfer and/or the solute con‐ centration reduction through equation 13 (i.e. assuming an infinite liquid volume), are ex‐ tensively used in the literature with topic of dye adsorption [68]. In case of constant diffusivity, and non-linear adsorption isotherm (which implies no pore diffusion and it is usually used in adsorption from liquid phase studies), several techniques based on the fun‐ damental solutions of the diffusion equation can be used [66,69]. In general, the partial dif‐ ferential equation is transformed to an integro-differential equation for the average concentration qave (dimensionality reduction).

Another class of approximation methods, which can be used in any case (but with a ques‐ tionable success for non-linear problems), is the so-called Linear Driving Force model (LDF model) [70]. The concentration profile in the particle is approximated by a simple function (usually polynomial with two or three terms) and using this, the partial differential equation problem can be replaced by an expression for the evolution of qave. This method is not ap‐ propriate for use in batch adsorption studies, but it has been proven to be successful in cases like fixed bed adsorption. In these cases, where the solution of equation 8 in several posi‐ tions along the case of adsorption bed is required, LDF approximation is very useful. In cas‐ es, where no simplifications are possible and high accuracy is required, one has to resort to numerical techniques. A widely used approach is the collocation discretization of the spatial dimension, which is very efficient due to the use of higher order approximation. However, its advantage can be completely lost for the case of very rapid (or even discontinuous) changes of the parameters inside the particle. In order to be able to extend our approach to non-uniform particles, a typical finite difference discretization (permitting arbitrarily dense grid) is performed in the spatial dimension.

The key point of the procedure developed here is to compare the effective pore diffusivity (Dp) of the dye with its diffusivity in the water (Dw). This relation has the well known form [75]:

Decolorization of Dyeing Wastewater Using Polymeric Absorbents - An Overview

τ

where ε is the porosity (water volume fraction), and τ is the tortuosity of the adsorbent par‐ ticle. Given that the structure of the particle (ε,τ) does not depend on the temperature, and assuming that the pure pore diffusion with no any other type of interactions is responsible for the solute transfer in the adsorbent particle, the temperature's dependence of Dp must

*Basic dye*. From all the combinations of dye-adsorbent examined up to now, the only one in which Dp follows the temperature dependence of Dw is the combination of basic dye-Ch (ad‐ sorption of basic dye onto non-grafted chitosan). The value Dp/Dw = τ/ε is found to be tem‐ perature independent, suggesting that the actual transport mechanism is the pore diffusion with no specific interactions between adsorbent and solute (τ/ε is found to be about 12). In‐ deed, Ch has amino and hydroxyl groups in its molecule, but smaller in number compared to that of grafted chitosan. So, the relatively weak interactions between dye and adsorbent (hydrogen bonding, van der Waals forces, pi-pi interactions, chelation) [72,76] do not drasti‐ cally affect the transportation/diffusion of dye. Taking into account that ε for chitosan deriv‐ atives ranges between 0.4 and 0.6, τ is calculated to be about 6; this is a reasonable value located between the generally proposed value (τ=3) and the values that holds for micropo‐ rous solids as activated carbon (τ>10) [77]. On the contrary, the higher values of the Dp, which were found in the case of grafted chitosan derivatives, indicate that the surface diffu‐ sion mechanism takes part. So, the fitting procedure must be repeated using the Dp values calculated (as an approximation assuming similar geometric structures) for the non-grafted chitosan (Ch) and searching for the Ds values that fits these data. Of course, a slight decrease of τ/ε versus temperature, which was found for Ch, suggests that some surface diffusion is still presented, but given the approximate nature of analysis, it is reasonable to ignore it. The surface diffusivity extracted from the experimental data appears to exhibit smaller tempera‐ ture dependence than pore diffusivity. In surface diffusivity, the increase with temperature is related to the enhancement of the thermal motion of the adsorbed molecules (proportional to the absolute temperature), whereas in pore diffusivity the latter is related to the decrease of the water viscosity. The surface diffusivity also increases with grafting as the density of the adsorption sites increases. It is due to the fact that the larger density of adsorption sites corresponds to the smaller site-to-site distance in the chitosan backbone, and consequently

(11)

197

http://dx.doi.org/10.5772/52817

p w <sup>ε</sup> D = D

follow the temperature's dependence of Dp.

to the higher probability of transition from one site to another.

*Reactive dye*. The situation (mechanism of diffusion) is different in the case of the reactive dyes. It would be helpful to observe the relation of the structure of this type of dye and the respective structure of the adsorbents used. The dye is composed of sulfonate groups [8], and the adsorbents contain amino groups (the higher basicity of adsorbent, the stronger pro‐ tonation occurs at acidic conditions) [75]. So, the main adsorption mechanism of reactive

The model for adsorption by chitosan derivatives and how it fits to the above general ad‐ sorption model will be discussed next. The chitosan particles are homogeneous consisting of swollen polymeric material. The basic (cationic) dyes are diffused in the swollen polymer phase and are incorporated (adsorbed) on the polymer with the interaction of the amino and hydroxyl groups [71]. In the case of reactive (anionic) dyes, the incorporation step is due to strong electrostatic attraction [72]. The kinetics of the whole process have been modeled in two distinct ways: based on diffusion [73] or based on the global chelation (or in general im‐ mobilization) reaction [75]. In the present study, the two modeling approaches are unified by assuming a composite mechanism of diffusion in the water phase, adsorption-desorption on the polymeric structure and diffusion on the polymeric structure (transition from one ad‐ sorption site to another). The system of equations for the above model is exactly the same, but with different meaning for some symbols. In particular, εp is the liquid volume fraction of the particle, Dp is again the liquid phase diffusivity of the adsorbate, and Ds is the diffu‐ sivity associated to the transition rate from one adsorption site to another. The function G(C,q) denotes the rate of the reversible adsorption process (chelation reaction or electro‐ static attraction). The rest of the model development is exactly the same with that of the gen‐ eral porous solid, assuming that the form of the adsorption-desorption equilibrium isotherm is that of extended Langmuir.

A very useful application to experimental data of the model described above is developed by our research team [41]. The dye adsorbents were grafted chitosan beads with sulfonate groups (abbreviated as Ch-g-Sulf), N-vinylimido groups (abbreviated as Ch-g-VID), and non-graft‐ ed beads (abbreviated as Ch). The tests were carried out both for reactive and basic dyes.

Although chitosan has a gel-like structure, the water molecules can be found in relatively large regions, which can be characterized as pores with diameters of 30-50 nm for the pure chitosan. The dye molecules which are diffused through these pores, are adsorbed-desorbed on the pore walls and finally are diffused (transferred) from one adsorption site to the other. All these phenomena are included to the kinetic model described in this study. There are two unknown parameters, namely pore and surface diffusivity (Dp and Ds), which must be found from the kinetic data. The simultaneous determination of both parameters requires experimental data of intraparticle adsorbate concentration, which are not easily available. Thus, the kinetic data can be fitted to the infinite pairs of Dp and Ds by keeping the value of the one parameter fixed and calculating the value of the other one that fits the experimental kinetic data.

At the first stage of model employment, the surface diffusion is ignored (setting Ds=0) and the pore diffusivity is calculated and fitted to the experimental kinetic data. In order to make the diffusion coefficients comparative, it is necessary to estimate the diffusivity of each dye in the water (Dw) at the corresponding temperatures. The diffusivity in water are calculated according to the Wilke-Chang correlation (molecular radius can be found by employing co‐ des like the BioMedCAChe 5.02 program by Fujitsu).

The key point of the procedure developed here is to compare the effective pore diffusivity (Dp) of the dye with its diffusivity in the water (Dw). This relation has the well known form [75]:

non-uniform particles, a typical finite difference discretization (permitting arbitrarily dense

The model for adsorption by chitosan derivatives and how it fits to the above general ad‐ sorption model will be discussed next. The chitosan particles are homogeneous consisting of swollen polymeric material. The basic (cationic) dyes are diffused in the swollen polymer phase and are incorporated (adsorbed) on the polymer with the interaction of the amino and hydroxyl groups [71]. In the case of reactive (anionic) dyes, the incorporation step is due to strong electrostatic attraction [72]. The kinetics of the whole process have been modeled in two distinct ways: based on diffusion [73] or based on the global chelation (or in general im‐ mobilization) reaction [75]. In the present study, the two modeling approaches are unified by assuming a composite mechanism of diffusion in the water phase, adsorption-desorption on the polymeric structure and diffusion on the polymeric structure (transition from one ad‐ sorption site to another). The system of equations for the above model is exactly the same, but with different meaning for some symbols. In particular, εp is the liquid volume fraction of the particle, Dp is again the liquid phase diffusivity of the adsorbate, and Ds is the diffu‐ sivity associated to the transition rate from one adsorption site to another. The function G(C,q) denotes the rate of the reversible adsorption process (chelation reaction or electro‐ static attraction). The rest of the model development is exactly the same with that of the gen‐ eral porous solid, assuming that the form of the adsorption-desorption equilibrium isotherm

A very useful application to experimental data of the model described above is developed by our research team [41]. The dye adsorbents were grafted chitosan beads with sulfonate groups (abbreviated as Ch-g-Sulf), N-vinylimido groups (abbreviated as Ch-g-VID), and non-graft‐ ed beads (abbreviated as Ch). The tests were carried out both for reactive and basic dyes.

Although chitosan has a gel-like structure, the water molecules can be found in relatively large regions, which can be characterized as pores with diameters of 30-50 nm for the pure chitosan. The dye molecules which are diffused through these pores, are adsorbed-desorbed on the pore walls and finally are diffused (transferred) from one adsorption site to the other. All these phenomena are included to the kinetic model described in this study. There are two unknown parameters, namely pore and surface diffusivity (Dp and Ds), which must be found from the kinetic data. The simultaneous determination of both parameters requires experimental data of intraparticle adsorbate concentration, which are not easily available. Thus, the kinetic data can be fitted to the infinite pairs of Dp and Ds by keeping the value of the one parameter fixed and calculating the value of the other one that fits the experimental

At the first stage of model employment, the surface diffusion is ignored (setting Ds=0) and the pore diffusivity is calculated and fitted to the experimental kinetic data. In order to make the diffusion coefficients comparative, it is necessary to estimate the diffusivity of each dye in the water (Dw) at the corresponding temperatures. The diffusivity in water are calculated according to the Wilke-Chang correlation (molecular radius can be found by employing co‐

des like the BioMedCAChe 5.02 program by Fujitsu).

grid) is performed in the spatial dimension.

196 Eco-Friendly Textile Dyeing and Finishing

is that of extended Langmuir.

kinetic data.

$$\mathbf{D}\_{\mathfrak{p}} = \mathbf{D}\_{\mathfrak{w}} \frac{\mathfrak{c}}{\mathfrak{r}} \tag{11}$$

where ε is the porosity (water volume fraction), and τ is the tortuosity of the adsorbent par‐ ticle. Given that the structure of the particle (ε,τ) does not depend on the temperature, and assuming that the pure pore diffusion with no any other type of interactions is responsible for the solute transfer in the adsorbent particle, the temperature's dependence of Dp must follow the temperature's dependence of Dp.

*Basic dye*. From all the combinations of dye-adsorbent examined up to now, the only one in which Dp follows the temperature dependence of Dw is the combination of basic dye-Ch (ad‐ sorption of basic dye onto non-grafted chitosan). The value Dp/Dw = τ/ε is found to be tem‐ perature independent, suggesting that the actual transport mechanism is the pore diffusion with no specific interactions between adsorbent and solute (τ/ε is found to be about 12). In‐ deed, Ch has amino and hydroxyl groups in its molecule, but smaller in number compared to that of grafted chitosan. So, the relatively weak interactions between dye and adsorbent (hydrogen bonding, van der Waals forces, pi-pi interactions, chelation) [72,76] do not drasti‐ cally affect the transportation/diffusion of dye. Taking into account that ε for chitosan deriv‐ atives ranges between 0.4 and 0.6, τ is calculated to be about 6; this is a reasonable value located between the generally proposed value (τ=3) and the values that holds for micropo‐ rous solids as activated carbon (τ>10) [77]. On the contrary, the higher values of the Dp, which were found in the case of grafted chitosan derivatives, indicate that the surface diffu‐ sion mechanism takes part. So, the fitting procedure must be repeated using the Dp values calculated (as an approximation assuming similar geometric structures) for the non-grafted chitosan (Ch) and searching for the Ds values that fits these data. Of course, a slight decrease of τ/ε versus temperature, which was found for Ch, suggests that some surface diffusion is still presented, but given the approximate nature of analysis, it is reasonable to ignore it. The surface diffusivity extracted from the experimental data appears to exhibit smaller tempera‐ ture dependence than pore diffusivity. In surface diffusivity, the increase with temperature is related to the enhancement of the thermal motion of the adsorbed molecules (proportional to the absolute temperature), whereas in pore diffusivity the latter is related to the decrease of the water viscosity. The surface diffusivity also increases with grafting as the density of the adsorption sites increases. It is due to the fact that the larger density of adsorption sites corresponds to the smaller site-to-site distance in the chitosan backbone, and consequently to the higher probability of transition from one site to another.

*Reactive dye*. The situation (mechanism of diffusion) is different in the case of the reactive dyes. It would be helpful to observe the relation of the structure of this type of dye and the respective structure of the adsorbents used. The dye is composed of sulfonate groups [8], and the adsorbents contain amino groups (the higher basicity of adsorbent, the stronger pro‐ tonation occurs at acidic conditions) [75]. So, the main adsorption mechanism of reactive dyes onto chitosan is based on the strong electrostatic interactions between dissociated sul‐ fonate groups of the dye and protonated amino groups of the chitosan. Many studies con‐ firm that the above process is favored under acidic conditions, where the total "charge" of chitosan adsorbent is more positive (due to the stronger protonation of amino groups at acidic pH values) [78,79].

optimum pH of desorption was determined to be the contrast of the optimum of adsorption [53]. Another study has shown the desorption capability of chitosan even at the same pH conditions as those of adsorption [3]. In the same study, 10 cycles were achieved with no

Decolorization of Dyeing Wastewater Using Polymeric Absorbents - An Overview

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199

The treatment of industrial dyeing effluent that contains the large number of organic dyes by adsorption process, using easily available low-cost adsorbents, is an interesting alterna‐ tive to the traditionally available aqueous waste processing techniques (chemical coagula‐ tion/flocculation, ozonation, oxidation, photodegradation, etc.). Undoubtedly, low-cost adsorbents offer a lot of promising benefits for commercial purposes in the future. The dis‐ tribution of size, shape, and volume of voids species in the porous materials is directly relat‐ ed to the ability to perform the adsorption application. The comparison of adsorption performance of different adsorbents depend not only on the experimental conditions and analytical methods (column, reactor, and batch techniques) but also the surface morphology of the adsorbent, surface area, particle size and shape, micropore and mesopore volume, etc. Many researchers have made comparison between the adsorption capacities of the adsorb‐ ents, but they have nowhere discussed anything about the role of morphology of the adsorb‐ ent, even in case of the inorganic material where it plays a major role in the adsorption process. The pH value of the solution is an important factor which must be considered dur‐ ing the designing of the adsorption process. The pH has two kinds of influences on dye: (i) an effect on the solubility, and (ii) speciation of dye in the solution (it depends on dye class). It is well known that surface charge of adsorbent can be modified by changing the pH of the solution. The high adsorption of cationic or acidic dyes at higher pH may be due to the sur‐ face of adsorbent becomes negative, which enhances the positively charged dyes through electrostatic force of attraction and vice versa in case of anionic or basic dyes. In case of chi‐ tosan-based materials, the literature reveals that maximum removal of dyes from aqueous waste can be achieved in the pH range of 2-4. However, physical and chemical processes such as drying, autoclaving, cross-linking reactions, or contacting with organic or inorganic chemicals proposed for improving the sorption capacity and the selectivity. The production of chitosan also involves a chemical deacetylation process. Chitosan is characterized by its easy dissolution in many dilute mineral acids, with the remarkable exception of sulfuric acid. It is thus necessary to stabilize it chemically for the recovery of dyes in acidic solutions. Several methods have been developed to reinforce chitosan stability. The advantage of chi‐ tosan over other polysaccharides is that its polymeric structure allows specific modifications without too many difficulties. The chemical derivatization of the polymer by grafting new functional groups onto the chitosan backbone may be used to increase the adsorption effi‐ ciency, to improve adsorption selectivity, and also to decrease the sensitivity of adsorption environmental conditions. It is interesting to note the relationships between physicochemi‐ cal properties and/or sources of chitosan and the dye-binding properties. Most of the prop‐ erties and potential of chitosan as adsorbent can be related to its cationic nature, which is

significant loss of re-adsorption capacity (~5% loss between 1st and last cycle).

**5. Conclusions**

Proposing our diffusion concept, it is obvious from the experimental data that: (i) the tem‐ perature's dependence of the coefficients Dp suggests that the transport mechanism is not simply a pure diffusion through the pores, and (ii) the small values of Dp versus Dw set ques‐ tions about the existence of surface diffusivity. The above observations are compatible to the nature of interactions between the reactive dye and the adsorbent, which is described above. The strong electrostatic interaction in the adsorption sites inhibits the surface diffusion. Moreover, the electrostatic forces have a relatively large region of action. Using as reference the non-grafted chitosan (Ch), the existence of charges of opposite sign at the pore walls cre‐ ates a surface charge gradient in addition to the adsorbate gradient in the adsorbent particle. This charge gradient drags the oppositely charged dye molecules inside the particle and leads to enhanced effective pore diffusivity. This fact could completely explain the increase of diffusivity related with the grafting groups (the more positively charged grafted groups, the stronger attraction of negatively charged dye molecule). As the density of the adsorption sites increases, the charge density in the particle increases, leading to higher effective pore diffusivity values. The temperature's dependence of this electrostatically facilitated diffu‐ sion process is weaker than that of the pure diffusion process. However, the opposite phe‐ nomenon is occurred in the case of sulfonate-chitosan derivative (Ch-g-Sulf), where the surface charge is of the same sign as that of the dye molecule, inhibiting the diffusion proc‐ ess. The above concept of the adsorption process of reactive dyes on chitosan derivatives suggests the development of models that take into account explicitly the electrostatic inter‐ action between dye and adsorbent, instead of considering them only by the modification, which they create to the effective pore diffusivity Dp. Conclusively, by employing the phe‐ nomenological model based on the pair pore-surface diffusion for the transport of the dye in the adsorbent particle information about the actual mechanism of adsorption and on interac‐ tion between adsorbent and adsorbate can be extracted.
