Adsorption of Basic Magenta II onto H₂SO₄ activated immature Gossypium hirsutum seeds: Kinetics, isotherms, mass transfer, thermodynamics and process design

2.1 Chemicals

Basic Magenta II (also called Basic red 9, molecular weight = 337.86, chemical formula C₂₀H₂₀ClN₃ and λ_max = 550 nm) was obtained from Hi Media Laboratories Ltd, Mumbai. All other chemicals used were obtained from Merck India Ltd, Mumbai. The structure of BM2 is shown in Fig. 1.

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Figure 1

Structure of BM2.

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2.2 Preparation of dye solution

The stock solution of BM2 was prepared by dissolving 1 g of dye in 1 l of doubly distilled water. All working solutions were prepared by diluting the stock solution with doubly distilled water to the desirable concentration. The initial pH of working solution was adjusted to the required value by adding 0.1 N HCl or 0.1 N NaOH solutions before mixing the adsorbent with the dye solution. The concentration of dye in the sample was analysed using a double beam UV–Vis spectrophotometer (ELICO-SL244, India) at a maximum wavelength of 550 nm.

2.3 Activated carbon preparation

Immature G. hirsutum seeds were collected from G. hirsutum seed producers near Attur, Tamil Nadu, India. The collected seeds were washed thoroughly with distilled water to remove dirt and dried at 40 °C in a temperature controlled oven for 3 days. The dried biomass was soaked with 98% concentrated sulphuric acid in the weight ratio of 1:4 (1 g G. hirsutum seed: 4 g H₂SO₄). In order to achieve effective activation the acid soaked biomass was stirred periodically and kept for 12 h. The resultant slurry was carefully washed with doubly distilled water. Further, the traces of acid were removed by washing the material twice with 0.1 N sodium bicarbonate solution. The resultant material, immature G. hirsutum seed activated carbon (IGHSAC) was dried, finely ground sieved with 170 mesh and stored in an air tight container to subsequently use it in the batch adsorption experiments.

2.4 The characterization of IGHSAC

The iodine number and methylene blue number of IGHSAC was calculated based on the ASTM 4607-86 standards at 298 K (Moreno-Castillaa et al., 2001). To measure iodine number, 0.1 g of carbon was washed initially by 5% HCl solution and agitated with 100 ml of 0.1 N iodine solution until equilibrium reached. The residual iodine concentration in the aqueous phase was determined by titrating with 0.1 N sodium thiosulphate solution taking starch as an indicator. Methylene blue number was determined by agitating 0.1 g of carbon with 10 ml of 150 mg l⁻¹ methylene blue solution. The concentration of methylene blue was analysed using a double beam UV–Vis spectrophotometer (ELICO-SL244, India) at 665 nm. The specific surface area of IGHSAC was determined from the adsorption–desorption isotherm of nitrogen 77 K using a surface analyser (Micromeritics ASAP 2020). 1 g of carbon was added to 100 ml of deionized water and agitated for 2 h and the pH of the slurry was noted subsequently as the pH of carbon. The bulk density of the carbon was measured using a pycnometer.

2.5 Batch adsorption

Batch adsorption studies were conducted for the selected concentration range (50–250 mg l⁻¹), at the pH of 12, IGHSAC dosage of 5 g and contact time of 3 h. The thermodynamic studies were carried at four different temperatures (20–40 °C). Each experiment were carried out by agitating 5 g of adsorbent with 200 ml of dye solution taken in Erlenmeyer flasks and agitating them using a thermo-regulated shaker (GeNei SLM-IN-OS-16, India) operating at 100 rpm. The samples were withdrawn from the flasks at predetermined time intervals for kinetic studies and at equilibrium time for isotherm studies. Obtained samples were centrifuged for 2 min (Remi R-24 Centrifuge, India) to remove the suspended solids. The clear supernatants were analysed for the residual dye concentration using double beam UV–Vis spectrophotometer (ELICO-SL244, India). The dye adsorption capacity q_t (mg g⁻¹) was determined as

2.6 Nonlinear error analysis

Frequently, by linear regression magnitude of the coefficient of determination (R²) is the index to measure the quality of the fit to the batch adsorption data. However, transformation of non-linear equations into linear ones utterly upset their error structure and may defy the error variance of normality assumptions of standard least squares (Myers, 1990; Ratkowski, 1990). Additionally linear regression is not always a good choice to apply for equations with more than two parameters and therefore the non-linear regression analysis is preferable to determine isotherm and kinetic parameters (Ho, 2006; Kumar and Sivanesan, 2007; Ncibi, 2008). Generally, the optimization procedure required an error function to be able to evaluate the fit of the equation to the experimental data and the parameters derived can be affected by the choice of the error function (Hanna and Sandall, 1995; Ho, 2004; Sivarajasekar and Baskar, 2013). Various error functions employed are:

These error functions and statistical comparison values can be evaluated using the tools like solver add-in with Microsoft’s spread sheet, Excel (Microsoft™, 1995) through any of the iteration methods. The application of these five different error methods will produce different parameter sets; therefore, it is hard to recognize an overall optimum parameter set. In order to facilitate a meaningful comparison between the isotherms parameter sets, the procedure of ‘sum of the normalized errors’ (SNE) is usually adopted (Ho et al., 2002; Foo and Hameed, 2010). This approach allows a direct comparison of the scaled errors and thus identifies the parameter set that would provide the closest fit to the measured data. The parameter set derived based on the smallest SNE will be an optimal one providing that there is no bias in the data sampling and type of error functions selected.

3.1 Characterization of IGHSAC

Iodine number is an index of pores with diameter ranging from 10 to 28 Å usually falls in the microporous range (<20 Å) which is 510 mg g⁻¹ in our case. The development of micro pores on the IGHSAC was depicted by methylene blue number since the molecular diameters of its molecules were 15 Å (Kasaoka et al., 1981; Rajgopal et al., 2006) and was measured to be 42 mg g⁻¹. These results demonstrated that good amount of meso and micro-pores were developed on the surface of IGHSAC. The larger BET surface area (496.5 m² g⁻¹) also indicated the suitability of the carbon for dye adsorption. The pH and bulk density of IGHSAC were found to be 6.5 and 0.56 g ml⁻¹ respectively.

3.2 Kinetics

The kinetics of solute sorption is required for selecting optimum operating conditions for the full-scale batch process. The kinetic parameter, which is supportive for the prediction of adsorption rate and equilibrium time, gives important information for designing and modelling the processes (Sivarajasekar and Baskar, 2014). Therefore various kinetic equations including two-parameter kinetic models: Ho, modified Freundlich, and Sobkowsk–Czerwi, and three-parameter kinetic models: Blanchard, Elovich, Avrami and modified Ritchie were employed for testing the experimental batch data.

The pseudo-second order model proposed by Ho and McKay Ho (1995) describes that adsorption process is controlled by chemisorption which involve valence forces through sharing or exchange of electron between the solute and the adsorbent. The Ho pseudo-second order model can be represented in the following form:

The modified Freundlich equation was authored by Kuo and Lotse (Yeddou et al., 2010):

Blanchard et al. (1984) postulated a second order kinetic model assuming that the solute adsorption on the adsorbent follows ion exchange mechanism. Blanchard model is given as

Elovich equation is also used successfully to describe second-order kinetic assuming that the actual solid surfaces are energetically heterogeneous (Sparks, 1989). It can be expressed in the following form:

The Avrami kinetic equation determines some kinetic parameters as possible changes of the adsorption rates in terms of the initial concentration and the adsorption time in addition to the determination of fractional kinetic orders (Ho and McKay, 2003). Avrami kinetic equation can be written as follows:

Ritchie Cheung et al. (2000) proposed a method for the second-order kinetic adsorption of gases on solids. He assumed that the rate of adsorption of solute onto adsorbent depends solely on the fraction of surface sites (θ), which are occupied by adsorbed gas. It is in the following form:

A second order kinetic model proposed by Sobkowsk and Czerwi (1974) similar to Ritchie model based on the maximum adsorption capacity of adsorbents. Modified form of this model is expressed as:

Batch experiments were carried out for differential concentrations (50–250 mg l⁻¹) with pH 12, temperature 40 °C, and contact time 3 h. The resulting experimental data was analysed on the basis of the nonlinear curve fitting SNE procedure by minimizing one error function and calculating all other error values. The determined SNE values for the two-parameter and three parameter kinetic models are displayed in Tables 1 and 2 respectively. Error functions which contribute minimum SNE value were selected to calculate the optimum parameter set for that kinetic model. From Table 1, it was inferred that the HYBRID error function produced the best fit giving the lowest SNE value for the 14 cases out of the 35 cases studied followed by the MPSD error function for 9 cases and EABS error function for 7 cases. Additionally, the ERRSQ error function selected to measure optimum parameter set for 4 cases and ARE error function provided optimum parameter set for only one case. The values of optimum parameter sets calculated based on minimum SNE procedure and their coefficient of determination (R²) and root mean square error (RMSE) values are presented in Tables 3 and 4 in order to assess the fitness of the kinetic models.

Among the two-parameter kinetic models, the Sobkowsk–Czerwi model provided a better fit to the experimental data with high R² (0.9996–0.95596) and low RMSE (0.9313–6.51135) values than Ho and modified Freundlich models at studied concentration range. This conveyed an idea that the adsorption may be followed first order kinetics at low concentrations and second order kinetics at high concentrations (Ho, 2006). As for as three-parameter kinetic models concerned, the Avrami kinetic model followed by modified Ritchie kinetic model had a good agreement with the experimental batch data which was known from their high R² and low RMSE values (Table 4). The applicability of Avrami kinetic model (R²: 0.9997–0.9789, RMSE: 0.7388–4.5028) indicated that the mechanism of adsorption certainly followed multiple kinetic orders which may change during the contact of the dye with IGHSAC (Lopes et al., 2003). The modified Ritchie kinetic model also reasonably explained the experimental data (R²: 0.9996–0.9537, RMSE: 0.9299–6.6785) which conveyed the idea that dye molecules were adsorbed onto two different surface sites. The higher initial dye uptake at small time duration (<30 min) was most likely due to certain active surface sites on IGHSAC; and quickly adsorption becoming dependent on the diffusion controlling process which had good agreement with the conclusion arrived by Sobkowsk–Czerwi kinetic model. The poor R² and high RMSE values of Elovich and modified Freundlich kinetic models were shown that these models failed to explain the experimental data. According to the R² and RMSE values the best-fitted kinetic models were found in the order: Avrami > Sobkowsk–Czerwi > modified Ritchie > Blanchard > Elovich > modified Freundlich > Ho. Therefore the q_e values predicted by the Avrami kinetic model were considered for the isotherm calculations.

3.3 Isotherms

To optimize the design of an adsorption system for the removal of solutes by adsorbents, it is important to establish the most appropriate correlation for the equilibrium curves. Adsorption isotherm provides valuable information such as equilibrium sorption capacity and certain constants whose values express the surface properties and affinity of the adsorbent (Sivarajasekar and Baskar, 2013). In many cases, the equilibrium sorption capacity is unknown, chemisorption tends to become immeasurably slow, and the amount sorbed is still significantly smaller than the equilibrium amount (Ungarish and Aharoni, 1981). This problem can be easily rectified if the equilibrium adsorption capacity (q_e) and equilibrium concentration (C_e) values owing to the well-fitting kinetic models are adopted for isotherm fitting (Ho, 2004; Ho and Wang, 2004). Therefore the amount of dye adsorbed at equilibrium predicted from the Avrami kinetic model was considered for isotherm studies. The equilibrium solute phase concentration in liquid can be calculated from the Eq. (1) as follows:

The predicted equilibrium data from Avrami kinetics were fitted to the five isotherm models to understand the nature of adsorption process. The most widely used two-parameter isotherm models (Langmuir, Freundlich and Temkin) and three-parameter isotherm models (Sips and Hill) isotherms were used to describe the equilibrium nature of adsorption.

According to the Langmuir isotherm, the monolayer adsorption is taking place on a structurally homogeneous adsorbent where all the adsorption sites are identical and energetically equivalent (Langmuir, 1918). Langmuir Isotherm is:

The empirical Freundlich isotherm model describes the non-ideal and reversible nature of adsorption. The multilayer adsorption with non-uniform distribution of adsorption heat and affinities over the heterogeneous surface explained by its relationship (Adamson and Gast, 1997):

The isotherm postulated by Temkin and Pyzhev (1940) relates the effects of heat of adsorption that decreases linearly with the coverage of the solute and the adsorbent interactions on the surface at moderate values of solute concentrations. It is represented by:

Sips (1948) proposed a combined form of Langmuir and Freundlich isotherms deduced for predicting the heterogeneous adsorption systems. At low solute concentrations it effectively reduces to Freundlich isotherm and at high solute concentrations, it predicts characteristics of monolayer sorption capacity of the Langmuir isotherm. Sips isotherm is given by

Hill (1910) postulated an isotherm to describe the binding of different solutes onto a homogeneous adsorbent. The model assumes that adsorption is a cooperative occurrence, owing to the ligand binding ability at one site on the macromolecule, tends to influence different binding sites on the same macromolecule. The Hill equation is:

Nonlinear SNE procedure was adopted to evaluate the optimum parameters for the five types of isotherms. The error functions, SNE values and optimum parameters are presented in Tables 5 and 6. The HYBRID error function produced optimum parameter set for all the selected isotherms due to their small SNE values. By analysing the R² and RMSE values of the isotherm models, the best fitting was observed using Sips (R²: 0.9945, RMSE: 0.5492) and Hill (R²: 0.9945, RMSE: 0.5494) isotherms. The Langmuir isotherm (R²: 0.9918, RMSE: 0.6731) reasonably fitted the data followed by Freundlich isotherm (R²: 0.9183, RMSE: 2.1254) but Temkin isotherm failed to define the equilibrium data well. The adequacy of Sips and Hill isotherms confirmed that the homogeneous adsorption on the heterogeneous surface of IMSAC and the co-operative manifestations of the adsorptive BM2 molecules. The maximum adsorption capacity predicted by the Sips (77.76 mg g⁻¹) and Hill (77.78 mg g⁻¹) isotherms were lower than Langmuir (86.24 mg g⁻¹) isotherm. The value of Sips exponent (0.95 ≈ 1) conveyed the idea that the sorption data was more of a Langmuir form rather than that of Freundlich isotherm. In turn, Freundlich isotherm almost fitted to the equilibrium data supporting the assumptions of heterogeneous mode of adsorption to certain extend. The Hill exponent n_H was greater than unity (1.05) depicted that the binding interaction between BM2 molecule and IGHSAC was in the form of positive cooperativity. The separation factor (R_L) value determined from the Langmuir isotherm indicated that dye adsorption onto IMSAC was in favourable region (R_L < 1). Fig. 2 collectively represents all the isotherm models.

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Figure 2

Comparison of isotherms.

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3.4 Sorption mechanisms

The knowledge of the rate-limiting step is an important one to be considered in the adsorption process. It is governed by the adsorption mechanism which depends on the physical and chemical characteristics of the adsorbent as well as on the mass transfer process (Metcalf and Eddy, 2003). For a solid–liquid sorption process, the solute transfer is usually characterized by external mass transfer or intraparticle diffusion, or both. The three steps involved in the mechanism of adsorption as follows:

• Transport of the solute from bulk solution through boundary layer to the adsorbent exterior surface (film diffusion);

• Transport of the solute within the pores of the adsorbent (particle diffusion);

• Adsorption of the solute on the exterior surface of the adsorbent (equilibrium reaction).

Usually, the last step is very rapid; the resistance is therefore assumed to be negligible. The slowest step determines the rate-controlling parameter in the adsorption process. Yet, the rate-controlling parameter may be distributed between intraparticle and film diffusion mechanisms. Irrespective of the case external diffusion will be involved in the sorption process. In general, external diffusion or external mass transfer is characterized by the initial solute uptake (McKay et al., 1981) which can be calculated from the slope of Furusawa and Smith plot assuming a linear relation between C_t/C_i and time for the first initial rapid phase (Vadivelan and Kumar, 2005). That is,

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Figure 3

(a) Furusawa and Smith Plot; (b) Weber and Morris Plot; (c) Reichenberg and Helfferich plot and (d) Boyd plot.

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The common technique used for identifying the mechanism involved in the adsorption process is described by Weber and Morris (1963) via fitting a plot for the following equation:

To understand the diffusion mechanism quantitatively and to estimate the rate determining step (pore diffusion or film diffusion), it is prerequisite to calculate their coefficients. By assuming the adsorbent particle to be a sphere of radius ‘r’ and the diffusion follows Fick’s law, the adsorption kinetic data was further analysed using the relationship between fractional attainment of equilibrium and time according to Reichenberg and Helfferich (Reichenberg, 1953; Vadivelan and Kumar, 2005):

At smaller times (t tends to 0) D is substituted by D_f and Eq. (18) reduces to:

The calculated Bt values were plotted against time and presented in Fig. 3(d). As seen these plots were linear at all concentrations but does not pass through the origin, conforming the film diffusion was the rate controlling one (Reichenberg, 1953). The pore diffusion coefficients D_p (cm² s⁻¹) were obtained from the calculated Biot number values using Eq. (21) and presented in Table 7. Pore diffusion coefficient values are to be in the range of 10⁻¹¹–10⁻¹³ cm² s⁻¹ for pore diffusion controlled adsorption mechanism (McKay and Poots, 1980) and the film diffusion coefficient values are to be in the range of 10⁻⁶–10⁻⁸ cm² s⁻¹ for film diffusion controlled adsorption mechanism (Michelson et al., 1975). Diffusion coefficients data (Table 7) revealed that the values of film coefficients are in the order of 10⁻⁸ and 10⁻⁶ cm² s⁻¹, respectively which indicated that the adsorption of BM2 onto IGHSAC was controlled purely by film diffusion at the studied concentration range which was supported by the results derived from Boyd plot.

3.5 Sorption thermodynamics

Thermodynamic parameters including the changes in Gibbs free energy ΔG⁰ (J mol⁻¹) enthalpy ΔH⁰ (J mol⁻¹) and entropy ΔS⁰ (J mol⁻¹ K⁻¹) can be calculated in order to illustrate the thermodynamic behaviour of adsorption process. The adsorption equilibrium constant (K_ad) can be correlated to the Gibbs free energy change ΔG⁰ as (Smith and Van Ness, 1987):

The change in entropy ΔS⁰ (J mol⁻¹ K⁻¹) and Gibbs free energy ΔG⁰ (kJ mol⁻¹) can be related at constant temperature as follows:

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Figure 4

(a) Vant’s Hoff plot and (b). Isoster plot.

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The apparent isosteric heat of adsorption ΔH_is (kJ kg⁻¹) can be calculated from the Clausius–Clapeyron equation:

At constant q_e values the above equation becomes

ΔH_is was calculated from slope of the plot ln(C_e) versus 1/T (Fig. 4(b)). The positive values of ΔH_is confirmed the endothermic nature of the adsorption process (Lataye et al., 2009).

3.6 Process design

Single stage batch adsorber can be designed using empirical design procedures based on adsorption isotherms for predicting the adsorber size and performance (McKay et al., 1981; Vadivelan and Kumar, 2005). The schematic single stage batch adsorber is shown in Fig. 5(a). With the design objective as BM2 solution with initial concentration of C₀ (mg l⁻¹) and effective volume of V (l) to be reduced to C_t (mg l⁻¹) with the IGHSAC loading of M (g), mass balance equation can be written as follows

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Figure 5

(a) Single stage batch adsorber and (b) adsorbent mass (g) against the volume of dye solution treated (l).

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Since the equilibrium data for BM2 onto IGHSAC was explained well by Sips isotherm, q_t values at equilibrium (q_e) can be evaluated from Sips isotherm, therefore at equilibrium the Eq. (35) turned to

Fig. 5(b) shows the plots obtained from Eq. (25) indicating the predicted amount of IGHSAC required for removing dye solution of initial concentration 150 mg l⁻¹ to the extent of 75–90% colour removal at different solution volumes (1–5 l). For instance, the amount of IGHSAC required to reduce the colour of 150 mg l⁻¹ to the degree of 90% was 6.3, 12.7, 19.1, and 25.4, 31.7 g for dye solution volumes of 1, 2, 3, 4 and 5 l respectively. Therefore Fig. 5(b) can be utilized to predict the amount of IGHSAC required for desired purification to the fixed concentration of 150 mg l⁻¹.