pubs.acs.org/Langmuir © 2010 American Chemical Society
Relating Interactions of Dye Molecules with Chitosan to Adsorption Kinetic Data George Z. Kyzas, Margaritis Kostoglou, and Nikolaos K. Lazaridis* Laboratory of General & Inorganic Chemical Technology, Division of Chemical Technology, School of Chemistry, Aristotle University of Thessaloniki, GR-541 24 Thessaloniki, Greece Received January 15, 2010. Revised Manuscript Received March 12, 2010 The scope of the present work is the study of the adsorption behavior of two dyes of different nature/class on several chitosan derivatives. The adsorbents used were grafted with different functional groups (carboxyl, amido, sulfonate, N-vinylimidazole) to increase their adsorption capacity and cross-linked to improve their mechanical resistance. This complete kinetic analysis was realized at 25, 45, and 65 C to observe the effect of temperature on adsorption rates for each adsorbent-adsorbate system. Activated carbon was also used as an adsorbent for reference/comparison. The experimental equilibrium data were successfully fitted to the Langmuir-Freundlich (L-F) isotherms, presenting high correlation coefficients (R2 ∼ 0.998). A detailed pore-surface diffusion with local adsorption-desorption model has been developed to describe the adsorption kinetics in chitosan adsorbents. The existence of kinetic data in several temperatures assists in recognizing the diffusion mechanism in the adsorbent particles. The findings on diffusion mechanisms and the corresponding coefficients, from using the model to match the experimental data, are compatible with the expected adsorbent-dye interactions based on their chemical structure.
1. Introduction Chitosan (poly-β-(1f4)-2-amino-2-deoxy-D-glucose) is an aminopolysaccharide, a cationic polymer produced by the N-deacetylation of chitin, and presents high affinity for most classes of dyes.1 Moreover, it is characterized as an excellent adsorbent presenting abundance, nontoxicity, hydrophilicity, biocompatibility, biodegradability, antibacterial property, inexpensiveness, and effective sorptive ability.2,3 Therefore, chitosan has much potential as dye adsorbent and it is interesting to study its interactions in aqueous solutions (diffusion of dye molecules) during adsorption process. Many studies were realized to reveal the effect of temperature on the equilibrium of the dye adsorption onto chitosan derivatives.3,4 Different studies have been employed with the kinetic analysis of adsorption by the aforementioned adsorbents.5 In spite of the fact that the main kinetic models used are the pseudo first-order model (Lagergren),6 the pseudo second-order model (Ho and McKay),7 and the intraparticle diffusion model (Webber and Morris),8 these models are generalized and can be easily fitted to the majority of the sorption processes, without any adjustment to the particular behavior of each material (the adsorption behavior of carbon-based materials is far away from the respective of chitosan-based). The main disadvantage of the above models is that they are not used as physical tools, but just as advanced fitting procedures leaving without any physical meaning the fitting parameters. For example, it is usual in literature to *To whom correspondence should be addressed. E-mail: nlazarid@chem. auth.gr. Telephone: þ30 2310 997807. Fax: þ30 2310 997859.
(1) Blackburn, S. R. Environ. Sci. Technol. 2004, 38, 4905–4909. (2) Rinaudo, M. Prog. Polym. Sci. 2006, 31, 603–632. (3) Crini, G.; Badot, P.-M. Prog. Polym. Sci. 2008, 33, 399–447. (4) Guibal, E.; McCarrick, P.; Tobin, J. M. Sep. Sci. Technol. 2003, 38, 3049– 3073. (5) Chiou, M. S.; Li, H. Y. J. Hazard. Mater. 2002, 93, 233–248. (6) Lagergren, S. Handlingar 1898, 24, 1–39. (7) Ho, Y. S.; McKay, G. Trans. Chem. Eng. 1998, 76, 183–191. (8) Webber, W. J.; Morris, J. C. J. Sanitary End. Div. Am. Soc. Civ. Eng. 1963, 89, 31–59.
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accept values of pore diffusivity larger than the solute diffusivity in water.9 So, the novelty of our present work is the detailed derivation of a diffusion-adsorption-desorption model in a dye-chitosan system with the corresponding assumptions and relation to other models used in literature. The model is derived for porous solid (since activated carbon is used in this work for reference), but then it is shown how it can be adjusted to be used for gel-like materials like chitosan. It will be shown that the mathematical model of the adsorption process can be used as probe (through the values of diffusivity constants that fit the experimental data) that identifies the nature of interaction between dye molecules and adsorbents. So, it is crucial for this purpose to have adsorption kinetic data for several temperatures. There is a lack of studies regarding the effect of temperature on the kinetic rate of the dye adsorption. Limited attempts have been carried out to investigate the above behavior with contradictory results, due to the different adsorbates used (reactive-dye or basicdye solutions).5,10 In our current study, the adsorption behavior of the prepared materials has been studied through equilibrium and kinetic experiments. A kinetic analysis was realized at 25, 45, and 65 C to examine the effect of temperature on the adsorption rate and the diffusion coefficients of each adsorbent-adsorbate system. The structure of the present work is the following: First, the experimental part of the work is presented from the preparation of the several types of adsorbents to the adsorption equilibrium and kinetics experiments. Then the mathematical model is described in detail and it is related with the simplified model used in the literature. The derivation is presented for the case of porous solid adsorbents and then the modification needed for the case of gel-structure adsorbents is discussed. In the next section, the experimental results are presented and an extensive discussion of the findings from fitting the model to the kinetics data follows. (9) Papegeorgiou, S. K.; Kouvelos, E. P.; Katsaros, F. K. Desalination 2008, 224, 293–306. (10) Cestari, A. R.; Vieira, E. F. S.; Dos Santos, A. G. P.; Mota, G. A.; De Almeida, V. P. J. Colloid Interface Sci. 2004, 280, 380–386.
Published on Web 03/19/2010
DOI: 10.1021/la100206y
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2. Materials and Methods 2.1. Materials. High molecular weight chitosan (the highMW form of chitosan was selected, because it has more in number repeated glucosamine units and consequently more adsorption sites (amino, hydroxyl groups etc.) compared to those of low- and medium-MW forms2) was obtained from Sigma-Aldrich and purified by extraction with acetone in a Soxhlet apparatus for 24 h, followed by drying under vacuum at room temperature. Its average molecular weight (MW) was given (from the supplier) 3.55 105 g/mol, while its degree of deacetylation (DDA) was estimated to be 82 wt %, according to the FT-IR method described in the literature.2,11,12 Acrylamide (97% p.a.) and cerium(IV) ammonium nitrate (initiator) were purchased from Sigma-Aldrich and used without further purification. Acrylic acid, potassium persulfate (initiator), N-vinylimidazole, and dimethylformamide were obtained from Merck. Glutaraldehyde (cross-linker), 50 wt % in water, was purchased from SigmaAldrich, as well as formamide (g99.5%), chlorosulfonic acid (g99%), and sodium carbonate (g99%). In final, dichloroacetic acid (g98.5%) was obtained from Fluka. 2.2. Adsorbents. Five derivatives of chitosan (Figure 1) (75-125 μm) and one sample of commercial activated carbon were used for adsorption experiments, whose preparation was based on already published works: (i) nongrafted cross-linked chitosan (Ch);13 (ii) cross-linked and grafted with acrylamide chitosan (Ch-g-Aam);13,14 (iii) cross-linked and grafted with acrylic acid chitosan (Ch-g-Aa);13,15 (iv) cross-linked and grafted with N-Vinylimidazole chitosan (Ch-g-VID);16 (v) cross-linked and grafted with sulfonate groups chitosan (Ch-g-Sulf);17 (vi) commercial activated carbon named SAE-2 (AC), which is supplied by Norit (used as adsorbent of reference/comparison). The characteristic parameters of the chitosan adsorbents prepared were taken from the already published studies.13-17 It is a great of interest the formation of the open chain ether linkage of the amido- and carboxyl- chitosan derivatives after the grafting reactions (Ch-g-Aam, Ch-g-Aa). Explaining the above mention, in previously published works has been extensively reported the formation of the imine (CdNH) and the open chain ether linkage presented after the grafting reactions of the acrylamide and acrylic acid.13,18 The above mentions have been confirmed through FTIR spectra of the prepared adsorbents, where the open chain ether linkage (Figures 1b, 1c) presented new bands in ∼1070 cm-1.13,18 Moreover, the imine moiety was confirmed with the appearance of a strong peak at 1660 cm-1, as a result of the grafting reaction on the chitosan backbone.13,18 However, the Schiff base formed is stable in acidic conditions, but become weaker (unstable) in alkaline pH values. This mention is mainly for the liquid molecules.19 In the case of the adsorbent materials and especially for the chitosan, after the grafting reactions (where a Schiff base was formed), cross-linking reactions were realized to render the molecule of modified chitosan extremely stable in both alkaline and acidic conditions.2,14,15,18 Furthermore, the final grafting percentages, determined on the basis of the percentage weight increase of the final product relative to the initial weight of chitosan GP % = 100% (W2 - W1)/W1 (where W1 and W2 denote the weight of chitosan before and after grafting reaction, (11) Brugnerotto, J.; Lizardi, J.; Goycoolea, F. M.; Arg€uelles-Monal, W.; Desbrieres, J.; Rinaudo, M. Polymer 2001, 42, 3569–3580. (12) Miya, M.; Iwamoto, R.; Ycshikawa, S.; Mima, S. Int. J. Biol. Macromol. 1980, 2, 323–324. (13) Lazaridis, N. K.; Kyzas, G. Z.; Vassiliou, A. A.; Bikiaris, D. N. Langmuir 2007, 23, 7634–7643. (14) Yasdani-Pedram, M.; Lagos, A.; Retuert, P. J. Polym. Bull. 2002, 48, 93–98. (15) Yasdani-Pedram, M.; Retuert, P. J.; Quijada, R. Macromol. Chem. Phys. 2000, 201, 923–930. (16) Caner, H.; Yilmaz, E.; Yilmaz, O. Carbohyd. Polym. 2007, 69, 318–325. (17) Miao, J.; Chen, G.-H.; Gao, C.-J. Desalination 2005, 181, 173–183. (18) Kyzas, G. Z.; Bikiaris, D. N.; Lazaridis, N. K. Langmuir 2008, 24, 4791– 4799. (19) Smith, M. B.; March, J. March’s Advanced Organic Chemistry, 5th ed.; John Wiley & Sons Inc: New York, 2001.
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Figure 1. Structure of chitosan adsorbents used: (a) Ch; (b) Ch-gAa; (c) Ch-g-Aam; (d) Ch-g-VID; (e) Ch-g-Sulf. respectively). So, the GP % was found as follows: Ch-g-Aam, 300%; Ch-g-Aa, 230%; Ch-g-Sulf, 210%; Ch-g-VID, 140%. 2.3. Adsorbates. Two dyes from different classes (reactive and basic) were used in single-component aqueous solutions. The reactive dye, namely Remazol Brilliant Blue RN, was supplied by DyStar (C22H162Na2O11S3, MW = 626.54 g/mol, λmax = 541 nm, purity=56% w/w) and the basic one namely Basic Blue 3G, was supplied by Hochest (C20H26ClN3O, MW = 359.18 g/mol, λmax = 607 nm, purity=53% w/w). These dyes are denoted hereafter as RB and BB, respectively and their dye content (purity) was taken into account for all calculations. The chemical structures of the dyes used are presented in Figure 2. 2.4. Analysis. Samples were extracted from suspensions using a syringe, filtered through 50 μm pore size membrane and then analyzed spectrophotometrically by monitoring the absorbance of the dyes using a UV-vis spectrophotometer (model U-2000, Hitachi). Prior to the adsorption experiments, the effect Langmuir 2010, 26(12), 9617–9626
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Figure 2. Chemical structure of dyes used: (a) Remazol Brilliant Blue RN, (RB); (b) Basic Blue 3G, (BB). of pH over the calibration curves of each dye was studied, but no significant deviation was observed (data non shown). 2.5. Experimental Procedure. Kinetics. Kinetic experiments were performed by mixing 1 g/L of adsorbent with 50 mL of dye solution (500 mg/L). The suspensions were shaken for 24 h at constant pH 2 (microadditions of 1 M HNO3) for the removal of RB and at constant pH 10 (microadditions of 1 M NaOH) for the removal of BB in water bath (Julabo SW-21C). Samples were collected at fixed intervals (5, 10, 20, 30 min; 1, 2, 3, 4, 5, 6, 9, 12, 15, 18, 21, 24 h). To study the effect of temperature on the rate of adsorption, the kinetic experiments were carried out at 25, 45, and 65 C. Preliminary experiments for the effect of pH were realized (data non shown) and confirmed the results of the already published works, in which the optimum pH value was found to be 2 for the adsorption of reactive dyes onto chitosan and 10 for the basic ones.3,13,18 Equilibrium - Isotherms. The effect of initial dye concentration was realized by mixing 1 g/L of adsorbent with 50 mL of dye solutions of different initial concentrations (0 - 1000 mg/L). The suspensions were shaken for 24 h at pH 2 for RB and at pH 10 for BB in water bath at 25, 45, and 65 C. The experimental equilibrium data were best fitted to the Langmuir-Freundlich isotherm (L-F, eq 1), which is essentially a Freundlich isotherm and approaches a maximum at high concentrations:20 Qe ¼
Qmax KLF Ce 1=n 1 þ KLF Ce 1=n
ð1Þ
Here Qe (adsorbed dye weight/adsorbent weight) is the equilibrium concentration in the solid phase, Qmax is the maximum amount of adsorption (adsorbed dye weight/adsorbent weight), KLF is the Langmuir-Freundlich constant, and n (-) is the Langmuir-Freundlich heterogeneity constant. This isotherm corresponds to a generalized equilibrium condition for the particular case of electrostatic attraction dominated adsorption. The equilibrium concentration in the solid phase Qe, was calculated using the following mass balance equation: Qe ¼
ðCbo - Ce ÞV m
ð2Þ
Here m is the mass of adsorbent, V is the volume of solution, and (20) Ho, Y. S.; Ng, J. C. Y.; McKay, G. Sep. Purif. Method 2000, 29, 189–232.
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Cbo and Ce (dye weight/liquid volume) are the initial and equilibrium dye concentrations in the liquid phase, respectively. 2.6. Kinetic Modeling: Theory. The most usual approach to model the batch adsorption process is the empirical fitting based on a single functional dependence between the global adsorption rate and the difference between the actual and the equilibrium adsorbed adsorbate concentration. This dependence is usually quadratic.21 The parameters resulted from the above procedure may be appropriate to fit the experimental data, but they do not have any physical meaning (although some researchers relate them to an hypothetical diffusion coefficient). In addition, this type of empirical modeling cannot be extended to describe more complicated geometries of processes than the simple batch experiments. Therefore, a more phenomenological (based on fundamental principles) approach must be followed, in order to develop models with parameters having physical meaning. On the one hand, this type of model can be extended to be used for the design of processes of engineering interest (e.g., fixed bed adsorption) and on the other hand, they can help to better understanding of the adsorbent structure and its interaction with the adsorbate. Although the phenomenological approach to the batch adsorption is well-known in the literature,22 it will be attempted here a description of the derivation of the models, of the inherent assumptions and of how several simplified models used in literature are hooked to the general approach. The actual difficulty to the modeling of the adsorption process in porous adsorbents is not its physics (see refs 23 and 24, for an extensive discussion on the physics of adsorption process) but its geometry in microscale. The physics is well-understood in terms of the occurring processes: diffusion of the adsorbate in the liquid, adsorptiondesorption between the liquid and solid phase, and surface diffusion of the adsorbate. 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.25 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 adsorption applications) and time-consuming, and its use is restricted to porous media development applications. A more effective approach is needed for the purpose of adsorption process design. So, the classical approach of “homogenizing” the corresponding partial differential equations and transferring the lack of knowledge of the geometry to the values of the physical parameters of the problem is followed. The adsorbate can be found in the adsorbent particle phase as solute in the liquid filling the pores of the particle (concentration C in kg/m3) and adsorbed on the solid phase (concentration q in kg of adsorbate/kg of adsorbent). The “homogeneous” equations for the evolution of C and q inside a spherical adsorbent particle of radius R, are the following: εp
∂C 1 ∂ ∂C ¼ 2 r2 Dp - Fp GðC, qÞ ∂t r ∂r ∂r ∂q 1 ∂ ∂q ¼ 2 r2 Ds - GðC, qÞ ∂t r ∂r ∂r
ð3Þ
ð4Þ
Here t is the time, r is the radial direction, εp the porosity of the particle, Fp 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 (21) Ho, Y. S.; McKay, G. Process Biochem. 1999, 34, 451–465. (22) Tien, C. Adsorption Calculation and Modeling; Butterworth-Heinemann: Boston, MA, 1994. (23) Rudzinski, W.; Plazinski, W. Langmuir 2008, 24, 5393–5399. (24) Liu, Y.; Shen, L. Langmuir 2008, 24, 11625–11630. (25) Konstandopoulos, A. G.; Vlachos, N.; Kostoglou, M.; Patrianakos, G. Proceedings of the 6th International Conference of Multiphase Flow; Leipzig, Germany, 2007.
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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, and Fp 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 as follows. (i) Mass transfer from the solution to particle ∂C , at r ¼ R ð5Þ km ðCb - CÞ ¼ - Dp ∂r r ¼R where Cb is the concentration of the adsorbate in the bulk solution and km is the mass transfer coefficient from the bulk solution to the particle. (ii) Spherical symmetry ∂C ∂q ¼ ¼ 0, ∂r ∂r
at r ¼ 0
ð6Þ
Having values for the initial concentrations of adsorbate in the particle and for the bulk concentration 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 nonequilibrium 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.26 In the case of adsorption 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 adsorption isotherm is directly related to the global adsorption isotherm (eq 1), leading to q ¼ qm bC1=n =ð1 þ bc1=n Þ
ð7Þ
where qm and b corresponds to Qmax and KLF, respectively, of the L-F model. In the limit of very fast adsorption-desorption kinetics, it can be shown by a rigorous derivation that the mathematical problem can be transformed to the following: ∂q 1 ∂ ∂q ¼ 2 r2 DðCÞ ∂t r ∂r ∂r
ð8Þ
∂q ¼0 ∂r r ¼0
ð9Þ
km ðCb - CÞ ¼ Fp Dp
∂q ∂r r ¼R
ð10Þ
An additional assumption considered in the above derivation is that the amount of the adsorbate found in the liquid phase in the pores of the particle is insignificant compared with the respective amount adsorbed on the solid phase (i.e., εpC , Fpq). This assumption always holds, as it can be easily checked by recalling the definition of the adsorption process. The concentration C in eqs 8, and 10 can be found by inverting the relation q = f(C). The diffusivity D is an overall diffusivity, which combines the bulk and surface diffusivities and is given by the relation: Dp D ¼ Ds þ Fp f 0 ðCÞ (26) Hitchcock, P. W.; Smith, D. W. Geoderma 1998, 84, 109–120.
9620 DOI: 10.1021/la100206y
ð11Þ
where the prime denotes the differentiation of a function with respect to its argument. The average concentration of the adsorbed species can be computed by the relation qave ¼
3 R3
Z
R
qr2 dr
ð12Þ
0
In the 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 Cb ¼ Cbo -
m qave V
ð13Þ
where Cbo is the initial value of Cb, m is the total mass of the adsorbent particles, and V is the volume of the tank. It is noted that the dependence of the effective diffusivity on the concentration (given by eq 11) does not require an intrinsic dependence of the pore or surface diffusivity on the concentration, but results from the inclusion of the adsorption-desorption isotherm into the diffusion equation. Let now refer to the several analytical or simple numerical techniques used in literature for the above problem and to 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 isotherm, 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.27 The complete solution is given by Tien,22 but their simplified versions,28 which ignore external mass transfer and/or the solute concentration reduction through eq 13 (i.e., assuming an infinite liquid volume), are extensively used in the adsorption literature.29 If the diffusivity is constant, but the adsorption isotherm is not linear (which implies no pore diffusion and it is usually used in adsorption from liquid phase studies), several techniques based on the fundamental solutions of the diffusion equation can be used. 27,30 In general, the partial differential equation is transformed to an integro-differential equation for the average concentration qave (dimensionality reduction). Another class of approximate methods, which can be used in any case (but with a questionable success for nonlinear problems), is the so-called linear driving force model (LDF model).31 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 appropriate for use in batch adsorption studies, but in cases like fixed bed adsorption. In these cases, where the solution of eq 8 in several positions along the bed is required, LDF approximation is very useful. In cases, 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 rapidly (or even discontinuous) changes of the parameters inside the particle. In order to be able to extend our approach to nonuniform particles, a typical finite difference discretization (permitting arbitrarily dense grid) is performed in (27) McKay, G. AIChE J. 1985, 31, 335–339. (28) Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford University Press: London, 1975. (29) Lazaridis, N. K.; Karapantsios, T. D.; Georgantas, G. Water Res. 2003, 37, 3023–3033. (30) Larson, A. C.; Tien, C. Chem. Eng. Commun. 1984, 27, 339–379. (31) Coates, J. I.; Glueckauf, E. J. Chem. Soc. 1947, 5, 1308–1314.
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the spatial dimension. The term “high accuracy” used above refers to the accuracy of the solution of the specific mathematical model and it is not related to the experimental results. Here a highly accurate numerical solution technique is employed. The approximate solutions for nonlinear diffusion coefficient proposed in the literature22 cannot be used for the specific geometry and conditions employed here (whereas the proposed numerical approach is very general). In order to proceed, the following nondimensionalization of the problem is introduced: q q ¼ , qm
C Cb ¼ , Cbo
r r ¼ , R Sh ¼
DðCÞ D ðCÞ ¼ , DðCbo Þ
km R DðCbo Þ
ð14Þ
scheme to the eq 22, the equation is led to the following system of ordinary differential equations (i = 1 to N - 1): q þ qi þ 1 qi þ 1 - qi dqi 1 ri þ ri þ 1 ¼ 2 Dq i dτ 2 2 h2 ri ! ri þ ri - 1 qi þ qi - 1 qi - qi - 1 Dq 2 2 h2
This system is not closed, since the values of qo, qN are unknown. The problem can be overcome by discretizing the two boundary conditions (eqs 18, and 23) and using one-sided second-order finite differences for the derivative term, aiming to keep secondorder accuracy for the complete code. The final equations are: qo ¼
1=n b ¼ bCbo ,
Cbo Z ¼ , Fp qm
mqm E ¼ , V
DðCbo Þt τ ¼ R2
ð15Þ
q ¼
∂q ∂r
ð16Þ
1=n 1=n
ð17Þ
¼0
ð18Þ
1 þ bC r ¼0
∂q ZBiðC b - C Þ ¼ D ðCÞ , ∂r r ¼R Z qave ¼ 3
at r ¼ 1
1
qr2 dr
ð19Þ
ð20Þ
0
Cb ¼ 1 - Eqave
ð21Þ
After some algebra, the pore liquid concentration can be eliminated completely, giving a more compact form to the mathematical problem: ∂q 1 ∂ ∂q ¼ 2 r2 D q ðqÞ ∂τ ∂r r ∂r
ð22Þ
with the boundary condition at r = 1: n ! 1 q ∂q ¼ D q ðqÞ ZSh 1 - E qave - n 1 q ∂r b
ð23Þ
The diffusivity, as a function of the adsorbed amount q, is denoted as Dq and is given from the relation: D q ðqÞ ¼
Dp Ds n qn - 1 þ Z n DðCbo Þ DðCbo Þ b ð1 - qÞnþ1
ð24Þ
The radial direction is discretized to N þ 1 equidistant points with radial coordinates ri = ih for i = 0 to N. The discretization step is h = 1/N. Applying a second-order finite difference discretization Langmuir 2010, 26(12), 9617–9626
"
N -1 X i ¼1
∂q 1 ∂ ∂q ¼ 2 r2 D ðCÞ ∂τ ∂r r ∂r
bC
0 ZSh@1 - 3E
The nondimensional problem takes the form
ð25Þ
4q1 - q2 3
hq r2i qi h þ N 2
#
ð26Þ
1 n 1 q A - n b 1-q
3q - 4qN - 1 þ qN - 2 ¼ D q ðqN Þ N 3
ð27Þ
The usual approach to the solution of the system is through an implicit finite difference scheme for time discretization (e.g., Crank-Nicolson discretization).21,28 Here, the method of lines will be employed i.e. the system of equation will be integrated by using an ODEs integrator with specified accuracy and automatic step adjustment during the integration. Since the system (eq 25) is not stiff, it is more efficient to use an explicit integrator,32 but it is not straightforward, because the eq 27 is transcendental with respect to qN. This problem is overcome by implementing a Newton-Raphson algorithm for the solution of eq 27 at each step of time integration of the system (eq 25). Above, it is described in detail the derivation and the solution procedure for the case of adsorption by activated carbon. The model for adsorption by chitosan derivatives will be discussed now. The chitosan particles are homogeneous consisting by swollen polymeric material. The basic (cationic) dyes are diffused in the swollen polymer phase and are incorporated (adsorbed) on the polymer by interaction with the amino and hydroxyl groups.33 In the case of reactive (anionic) dyes, the incorporation step is due to strong electrostatic attraction.21 The kinetics of the whole process have been modeled in two distinct ways: based on diffusion34 or based on the global chelation (or in general immobilization) reaction.35 In our 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 adsorption site to another). The system of equation for the above model is exactly the same as this of eqs 3 and 4, 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 diffusivity associated with 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 electrostatic attraction). The rest of the model development is exactly the same with that of the activated carbon, assuming that the form of the adsorption-desorption equilibrium isotherm is this of extended Langmuir. (32) Press, W. Flannery, B.; Teukolski, S.; Vetterling, W. Numerical recipes. The art of scientific computing, 2nd ed.; Cambridge University Press: New York, 1992. (33) Guibal, E. Sep. Purif. Technol. 2004, 38, 43–74. (34) Guibal, E.; Milot, C.; Tobin, J. M. Ind. Eng. Chem. Res. 1998, 37, 1454– 1463. (35) Chu, K. H. J. Hazard. Mater. 2002, 90, 77–95.
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Figure 3. Equilibrium data of reactive dye fitted to the L-F isotherm model: (a) Ch, Ch-g-Aa, and Ch-g-Aam; (b) AC, Ch-gVID, and Ch-g-Sulf.
Figure 4. Equilibrium data of basic dye fitted to the L-F isotherm model: (a) Ch, Ch-g-Aa, and Ch-g-Aam; (b) AC, Ch-g-VID, and Ch-g-Sulf.
3. Results and Discussion 3.1. Effect of Initial Dye Concentration. Figures 3 and 4 present the isotherms resulted from the adsorption of the two dyes (RB, BB) onto chitosan (four derivatives) and commercial activated carbon. Tables SI1 and SI2 (Supporting Information) report the maximum adsorption capacities and the other isothermal parameters resulted from the fitting to the L-F model. For all the studied adsorbents the equilibrium dye uptake was affected by the initial dye concentration using constant dosage of adsorbent (1 g/L). At low initial concentrations, the adsorption of dyes (reactive and basic) is very intense and reaches equilibrium rapidly. This phenomenon indicates the possibility of the formation of monolayer coverage of dye molecules at the outer interface of chitosan. Furthermore, for the low concentrations (0-30 mg/L) the ratio of initial number of dye molecules to the available adsorption sites is low and subsequently the fractional adsorption becomes independent of initial concentration.36,37 Brunauer et al. divided the isotherms of physical adsorption into five types.38 Type I isotherms represents unimolecular adsorption and applies to nonporous, microporous and adsorbents with small pore sizes (not significantly greater than the molecular diameter of the adsorbate). So, the shapes of curves (Figures 3 and 4) indicate that the isotherms for all the adsorbent-dye systems are I-Type, according to the BET classification,38 and characterized by a (36) Chatterjee, S.; Chatterjee, S.; Chatterjee, B. P.; Das, A. R.; Guha, A. K. J. Colloid Interface Sci. 2005, 288, 30–35. (37) Chiou, M. S.; Chuang, G. S. Chemosphere 2006, 62, 731–740. (38) Brunauer, S.; Deming, L. S.; Deming, W. E.; Teller, E. J. Am. Chem. Soc. 1940, 62, 1723–1732.
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high degree of adsorption at low concentrations. At higher concentrations, the available adsorption sites become lower and subsequently the adsorption depends on the initial concentration of dye. As a matter of fact, the diffusion of exchanging molecules within chitosan particles may govern the adsorption rate at higher initial concentrations. The activated carbon illustrated similar qualitatively isothermal curves as those of chitosan adsorbents, presenting however lower adsorption capacities than those of grafted chitosan. The calculated maximum adsorption capacities (Qmax) for RB removal at 25 C were (Supporting Information, Table SI1): Ch-g-VID, 1329 mg/g > Ch-g-Aam, 1160 mg/g > Ch-g-Aa, 552 mg/g > AC, 475 mg/g > Ch, 398 mg/g > Ch-g-Sulf, 204 mg/g. The respective values for BB removal were (Supporting Information, Table SI2): Ch-g-Sulf, 1022 mg/g > Ch-g-Aa, 595 mg/g> Ch-g-VID, 456 mg/g > Ch-g-Aam, 390 mg/g > AC, 295 mg/g> Ch, 254 mg/g. The fitting of the experimental data to the L-F model was successfully realized, presenting high correlation coefficients (R2=0.997-0.999). The above experimental data confirmed the recent published literature, according to which the grafting of different groups on chitosan backbone is able to increase drastically the adsorption ability of chitosan derivatives, rendering them more adsorptive than activated carbon.4 However, the adsorption of the dye onto chitosan adsorbents is dependent on the pH of the solution. As reported in literature,39,40 (39) Kyzas, G. Z.; Lazaridis, N. K. J. Colloid Interface Sci. 2009, 331, 32–39. (40) Sakkayawong, N.; Thiravetyan, P.; Nakbanpote, W. J. Colloid Interface Sci. 2005, 286, 36–42.
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for the reactive dye, in acidic solutions, the amino groups of chitosan are protonated under acidic conditions according and simultaneously, the reactive dye molecule is dissociated to sulfonate groups. As a result, the adsorption process mainly proceeds through electrostatic interaction between the two counterions R-NH3þ and D-SO3-. Increasing the pH of the solution, electrostatic interactions decrease due to the deprotonation of amino groups. However, chitosan still sorbs dye molecules at pH 6-8, but in lower percentages. This fact occurs through a combination of other interactions, as van der Waals forces and hydrogen bonding. In the highly alkaline region deprotonation of the hydroxyl groups of chitosan occurs and the resulting dissociated groups can substitute the chloride atom from the dye molecule in a similar manner as in the dyeing process of textiles, by covalent bonding. In each case, the pH dependence in the adsorption mechanism for the reactive dyes is the aforementioned. In the case of basic dye,7,39 the amino groups of chitosan are protonated in acidic pH values which render the adsorbent positively charged. Because of the positively charge of the basic dye, strong Coulombic repulsions are developed between them. Increasing the pH of the solution the repulsive forces weaken since the amino groups of adsorbent are deprotonated and dye uptake increases. At alkaline pH values, some other bonds occur, as van der Waals forces and hydrogen bonds or/and π-π interactions.7,39 All the chitosan adsorbents behave in the same manner as described above, but the phenomena occurred are more intense or weaker according to the charge of the adsorbent (positively charged adsorbents, Ch-g-Aam and Ch-g-VID, or negatively charged, Ch-g-Sulf and Ch-g-Aa). 3.2. Effect of Temperature on Equilibrium. The effect of temperature on equilibrium is presented through isotherms curves (Figures 3 and 4) .The adsorption behavior is similar for all the studied adsorbents: increasing the temperature of process from 25 to 65 C, an increase of the adsorption capacity (dye uptake) is observed. This may be attributed to the fact that a great number of active sites is generated on the adsorbent because of an enhanced rate of protonation/deprotonation of the functional groups on the adsorbent.41 It is a great of interest the fact that the adsorbents with the highest capacity at 25 C for BB removal (Chg-Sulf, 1022 mg/g; Ch-g-Aa, 595 mg/g) increased in low level their capacity to 1044 mg/g and 630 mg/g (at 65 C), respectively. In contrast, the adsorbents with the lowest capacity at 25 C (Ch, 254 mg/g; AC, 295 mg/g) improved it in higher percentages at 65 C (Ch, 320 mg/g; AC, 347 mg/g). The same qualitative behavior was observed for the RB removal but in larger amounts due to the great number of active groups occurred in reactive-dye molecules. Many researchers studied the removal of reactive dyes by various chitosan derivatives, which presented adsorption capacities in the range of 50-2400 mg/g.42-44 In contrast, a limited number of references mention the removal of basic dyes by chitosan, presenting capacities between 30 and 600 mg/g.45-47 In the current study, the adsorption capacities presented are between 200 and 1400 mg/g for the reactive dyes and 250-1050 mg/g (41) McKay, G.; Otterburn, M. S.; Sweeney, A. G. Water Res. 1980, 14, 21–27. (42) Juang, R. S.; Tseng, R. L.; Wu, F. C.; Lee, S. H. J. Chem. Technol. Biot. 1997, 70, 391–399. (43) Wang, L.; Wang, A. Bioresour. Technol. 2008, 99, 1403–1408. (44) Wu, F. C.; Tseng, R. L.; Juang, R. S. Water Res. 2001, 35, 613–618. (45) Chao, A. C.; Shyu, S. S.; Lin, Y. C.; Mi, F. L. Bioresour. Technol. 2004, 91, 157–162. (46) Crini, G.; Robert, C.; Gimbert, F.; Martel, B.; Adam, O.; De Giorgi, F.; Badot, P.-M. J. Hazard. Mater. 2008, 153, 96–106. (47) Uzun, I.; Guzel, F. J. Colloid Interface Sci. 2004, 274, 398–412.
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Figure 5. (a) Kinetic data of adsorbents at 25 C fitted to the proposed kinetic model for reactive dye. (b) Kinetic data of Ch-gSulf at 25, 45, 65 C fitted to the proposed kinetic model both for reactive and basic dye.
for the basic ones. This differentiation is due to the different class of grafted functional groups. The typical dye concentration in the dyeing process is 2-3 g/L,48 and no aggregation/precipitation phenomena are taking place.48,49 This is in accordance with the aggregation/precipitation value of dyes which is approximately 10 g/L.49 Given that the initial dye concentrations used in the current study was in the range of 0.01-0.7 g/L, there is no any possibility of aggregation/precipitation phenomena, and therefore, the high adsorption capacities presented were only due to the adsorption process. 3.3. Kinetics. First, it is clear from Figure 5a that the kinetic rate of the adsorption depends on the material used. The kinetic behavior of Ch (an adsorbent without grafted groups) is sensibly different than the respective of grafted chitosan (Ch-g-Sulf, Ch-gAa, Ch-g-Aam, Ch-g-VID). The adsorbents, which presented greater capacity, illustrated a sharp decrease of the residual dye concentration approximately 120 min after the beginning of the adsorption/reaction. Then, a period of milder dye removal was determined which however varies, depending on the material used and effecting the final plateau (equilibrium period, in which no dye removal occurred) of the kinetic curve. Thus, the kinetic data of RB revealed that the “slowest” chitosan adsorbent is Ch-g-Sulf reaching the plateau after 15 h, while the “faster” is Ch-g-VID (equilibrium after approximately 180 min). In the case of AC, the (48) O’Neill, C.; Hawkes, F. R.; Hawkes, D. L.; Lourenc-o, N. D.; Pinheiro, H. M.; Delee, W. J. Chem. Technol. Biot. 1999, 74, 1009–1018. (49) Zollinger, H. Color Chemistry. Syntheses, Properties, and Applications of Organic Dyes and Pigments; VCH: Weinheim, Germany, and New York, 1987; pp 117-136.
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Table 1. Diffusion Coefficients of Chitosan Derivatives for the Basic Dye Adsorption, Calculated by the Proposed Kinetic Model, Suggesting Only Pore Diffusion (R2 > 0.993)a
Table 2. Diffusion Coefficients of Chitosan Derivatives for the Basic Dye Adsorption, Calculated by the Proposed Kinetic Model, Suggesting both Pore and Surface Diffusion (R2 > 0.993)a
basic dye
basic dye
Dp 10-10 (m2/s) adsorbent
25 C
45 C
Ch 0.342 0.491 Ch-g-Aa 1.539 1.582 Ch-g-Aam 0.869 0.930 Ch-g-VID 1.140 1.222 Ch-g-Sulf 1.978 2.059 a Dp¥ 10-10 = 4.181, 5.812, and 7.621 m2/s at 25, 45, and respectively. Ds = 0 m2/s at 25, 45, and 65 C, respectively.
Dp 10-10 (m2/s) 65 C
adsorbent
0.650 1.621 0.991 1.310 2.140 65 C,
Ch 0.342 0.491 Ch-g-Aa 0.342 0.491 Ch-g-Aam 0.342 0.491 Ch-g-VID 0.342 0.491 Ch-g-Sulf 0.342 0.491 a Dp¥ 10-10 = 4.181, 5.812, respectively.
kinetic differentiation can be easily observed even visually, where the adsorption is ended in 60 min. In the same manner, for BB adsorption (kinetic data were non presented for the saving of space), the “slowest” chitosan adsorbent is Ch, which reaches the plateau after 4 h, while the “faster” is Ch-g-Sulf (equilibrium after approximately 60 min). The commercial activated carbon (AC) complete the removal of dye after 30 min of adsorption’s beginning. The best fitting of the model proposed could be observed even visually in Figure 5b, where the time scaling of the horizontal axis is up to 120 min. In this figure is presented the kinetic behavior of one of the prepared adsorbents (Ch-g-Sulf) for both RB and BB adsorption. 3.4. Modeling-Diffusion. 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.33 The dye molecules (it was estimated, by employing the BioMedCAChe 5.02 program of Fujitsu, to have 2.1 nm (RB) and 1.1 nm (BB) diameters), 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 developed in this study. First, there are two unknown parameters, namely pore and surface diffusivities (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, keeping fixed the value of the one parameter, and calculating the value of the other one that fits the experimental kinetic data. At the first stage of employing the model, the surface diffusion is ignored (setting Ds = 0) and the pore diffusivity is calculated and fitted to the experimental data of all the adsorbents used (Ch; Ch-g-Aa; Ch-g-Aam; Ch-g-VID; Ch-g-Sulf; AC) for the two dyes (RB; BB) at the three temperatures (25, 45, 65 C). The results for Dp are reported in Tables 1, 3, and 4. However, to make the coefficients comparative, it was necessary to estimate the diffusivity of each dye in the water (Dp¥) at three temperatures (25, 45, 65 C). These coefficients were calculated according to the Wilke-Chang correlation:50 Dp¥ ¼ ð7:4 10 - 12 Þ
Tð2:6MÞ0:5 ηV 0:6
ð28Þ
V (cm3/mol) is the molar volume of dye as it was estimated by employing the BioMedCAChe 5.02 program by Fujitsu; M (g/ mol) is the molecular weight of the solvent (water); T (K) is (50) Wilke, C. R.; Chang, P. AIChE J. 1955, 1, 264–270.
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25 C
45 C
Ds 10-10 (m2/s)
65 C
25 C
0.650 0.650 0.650 0.650 0.650 and 7.621
45 C
0.743 0.479 0.621 0.629 0.701 0.708 0.876 0.887 m2/s at 25, 45, and
65 C 0.755 0.630 0.714 0.898 65 C,
Table 3. Diffusion Coefficients of Chitosan Derivatives for the Reactive Dye Adsorption, Calculated by the Proposed Kinetic Model, Suggesting Pore Diffusion (R2 > 0.993)a reactive dye Dp 10-10 (m2/s) adsorbent
25 C
45 C
65 C
Ch 0.172 0.180 Ch-g-Aa 0.178 0.184 Ch-g-Aam 0.441 0.492 Ch-g-VID 0.654 0.713 Ch-g-Sulf 0.058 0.062 a Dp¥ 10-10 = 3.092, 4.210, and 5.623 m2/s at 25, 45, and respectively.Ds = 0 m2/s at 25, 45, and 65 C, respectively.
0.188 0.191 0.541 0.771 0.066 65 C,
Table 4. Diffusion Coefficients of Activated Carbon (AC) for the Dyes (BB, RB) Adsorption, Calculated by the Proposed Kinetic Model, Suggesting Only Pore Diffusion (R2 > 0.993)a Dp 10-10 (m2/s) adsorbent
T (C)
basic dye
reactive dye
5.251 4.151 5.972 4.542 6.331 4.839 a Basic dye: Dp¥ x 10-10 = 4.181, 5.812, and 7.621 m2/s at 25, 45, and 65 C, respectively. Reactive dye: Dp¥ 10-10 = 3.092, 4.210, and 5.623 m2/s at 25, 45, and 65 C, respectively. Ds = 0 m2/s at 25, 45, and 65 C, respectively. AC
25 45 65
temperature; η (cP) represents the dynamic viscosity of the solvent and in our case for water was found (0.893 at 298 K, 0.595 at 318 K, 0.431 at 338 K) to be as follows:51 η ¼ A 10B=ðT - LÞ
ð29Þ
-2
Here A = 2.414 10 cP; B = 247.8 K; L = 140 K. The key point of the study is to compare the effective pore diffusivity (Dp) of the dye with its diffusivity in the water (Dp¥). This relation has the well-known form:52 Dp ¼ Dp¥
ε τ
ð30Þ
where ε is the porosity (water volume fraction), and τ is the tortuosity of the adsorbent particle. Given that the structure of the (51) Daugherty, R. L.; Franzini, J. B.; Finnemore, E. J. Fluid Mechanics with Engineering Applications, 10th ed.; McGraw-Hill: New York, 1985. (52) Smith, J. M. Chemical Engineering Kinetics; McGraw-Hill: New York, 1981.
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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 calculated, the only one in which Dp follows the temperature’s dependence of Dp¥ is the combination of BB-Ch (adsorption of basic dye onto nongrafted chitosan) (Table 1). The value Dp/ Dp¥ = τ/ε is computed as 12.294, 11.854, and 11.723 for the three temperatures of 25, 45, and 65 C, respectively, suggesting that the actual transport mechanism is the pore diffusion with no specific interactions between adsorbent and solute (τ/ε≈12). Indeed, 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, π-π interactions, chelation)11,19 do not affect drastically the transportation/diffusion of dye. Taking into account that ε for chitosan derivatives ranges between 0.4 and 0.6, it is observed that τ is about 6; this is a reasonable value located between the generally proposed value (τ = 3) and those values that hold for microporous solids as activated carbon (τ > 10).53 On the contrary, the higher values of the Dp, which were found in the case of grafted chitosan derivatives, indicate that the surface diffusion mechanism takes part. So, the fitting procedure must be repeated using the Dp values calculated (as an approximation assuming similar geometric structures) for the nongrafted chitosan (Ch) at 25, 45, and 65 C and searching for the Ds values that fits these data (Table 2). Of course, the 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 diffusion coefficients calculated for the basic dye in all the chitosan derivatives are shown in Table 2. It is noted that surface diffusivities exhibit a much smaller temperature dependence than the pore diffusivities do. In the 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 the pore diffusivity is related to the decrease of the water viscosity. The surface diffusivity also increases with grafting as the density of the adsorption sites increases (Tables 2 and SI2). 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 dye (RB). First, it would be helpful to observe the structure of this type of dye (Figure 2a) and the respective structure of the adsorbents used (Figure 1). The dye is composed of sulfonate groups,49 and the adsorbents contain amino groups (the higher basicity/alkalinity of adsorbent, the stronger protonation occurs at acidic conditions).19 So, the main adsorption mechanism of reactive dyes onto chitosan is based on the strong electrostatic interactions between the dissociated sulfonate groups of the dye and the protonated amino groups of the chitosan. Many studies confirm 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).40,54
Proposing our diffusion concept, it is obvious from the experimental data that (i) the temperature dependence of the coefficients Dp (Table 3) suggests that the transport mechanism is not simply a pure diffusion through the pores and (ii) the small values of Dp versus Dp¥ set questions 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 nongrafted chitosan (Ch), the existence of charges of opposite sign at the pore walls creates 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 diffusivities. 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 dependence of this electrostatically facilitated diffusion process is weaker than that of the pure diffusion process. However, the opposite phenomenon is occurred in the case of sulfonate-chitosan derivative (Ch-gSulf), where the surface charge is of the same sign as that of the dye molecule, inhibiting the diffusion process. The above concept of the adsorption process of reactive dyes on chitosan derivatives suggests the need for the development of models taking into account explicitly the electrostatic interaction between dye and adsorbent, instead of considering them only by the modification which they create to the effective pore diffusivity Dp. Activated Carbon. First, the material exhibited a mixed type between I and IV (the classification of types is based on IUPAC) of nitrogen adsorption-desorption isotherms, indicating a presence of both microporous and meso-/macroporous domains.55 Its specific surface area (determined by multipoint BET analysis) is 878 m2/g, while its zeta potential was observed at pH 2.4 (pHzpc).55 Furthermore, the analysis/modeling for the activated carbon was made just to confirm that our methodology is compatible with the well established fact in the literature, suggesting that the adsorbate transport in activated carbon is made by surface diffusion.56 So, at the first stage, the values of Dp were found to be larger than the corresponding Dp¥ (Table 4), suggesting the existence of surface diffusion. The pore diffusion contribution can be completely ignored, considering that the tortuosity for activated carbon is τ>10,52 which means that the real value of Dp is at least 20 times smaller than the value found from the fitting of experimental data (assuming Ds = 0). Therefore, the whole fitting procedure was repeated to find the Ds values, setting Dp=0 (Table 5). All the results from this procedure are presented in Tables 4, 5. The activated carbon is used in this work just to validate that the proposed procedure will indicate the surface diffusion mechanism as the dominant one as it is wellknown in the literature.
(53) Yang, R. T. Gas separation by adsorption processes; Butterworths: Boston, MA, 1987. (54) Wang, L.; Wang, A. Bioresour. Technol. 2008, 99, 1403–1408.
(55) Asouhidou, D. D.; Triantafyllidis, K. S.; Lazaridis, N. K.; Matis, K. A.; Kim, S.-S.; Pinnavaia, T. J. Micropor. Mesopor. Mater. 2009, 117, 257–267. (56) Fritz, W.; Merk, W.; Schlunder, E. U. Chem. Eng. Sci. 1981, 36, 731–741.
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4. Conclusions In the present study, the behavior of the adsorption of two dyes (different types: reactive and basic) on several chitosan derivatives, combined with a typical diffusion-adsorption desorption mathematical model using the Langmuir-Freundlich (L-F)
DOI: 10.1021/la100206y
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Table 5. Diffusion Coefficients of Activated Carbon (AC) for the Dyes (BB, RB) Adsorption, Calculated by the Proposed Kinetic Model, Suggesting Only Surface Diffusion (R2 > 0.993)a Ds 10-10 (m2/s) adsorbent
T (C)
basic dye
25 0.904 45 0.962 65 0.993 a Dp = 0 m2/s at 25, 45, and 65 C, respectively. AC
reactive dye 0.711 0.743 0.795
isotherm, is used as probe to analyze the interaction between adsorbents and dyes. By matching the experimental data to the mathematical model for several temperatures, using as fitting parameters the pore or surface diffusivities, and exploring the knowledge of the temperature dependence should be exhibited by the pore diffusivity several, while results regarding the mechanism
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of the motion of the dye in the adsorbent particle were derived. The analysis revealed that in the case of the basic dye the relatively weak interaction forces (chelation reaction) permits the appearance of surface diffusion, having an increasing contribution as the density of adsorption sites increases. In the case of the reactive dye, the stronger electrostatic interactions prevents the surface diffusion, but their longer range creates electrostatic fields in the pores and correspondingly charge gradients in the particle, which inhibits or facilitates the pore diffusion depending of the dominant charge sign in the adsorbent particle. The findings of the present work set the basis for more complex and detailed models for the adsorption kinetics of the particular system. Supporting Information Available: Tables of equilibrium constants for the adsorption of reactive and basic dye onto chitosan adsorbents and activated carbon. This material is available free of charge via the Internet at http://pubs.acs.org.
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