Adsorption of Reactive Dyes by Palm Kernel Shell Activated Carbon : Application of Film Surface and Film Pore Diffusion Models

The rate of adsorption of two reactive dyes, Reactive Black 5 and Reactive Red E onto palm kernel shell-based activated carbon was studied. The experiment was carried out to investigate three models: film diffusion model, filmsurface and film-pore diffusion models. The results showed that the external coefficients of mass transfer decreased with increasing of initial adsorbate concentration. In addition, it was found that the adsorption process was better described by using the two resistance models, i.e. film-surface diffusion.


Introduction
Industries, such as textile, ceramic, paper, printing and plastic, use dye as their raw material, thus generating a large amount of colored wastewater.Adsorption methods are promising in decolorizing textile effluents, but this application is limited by the high cost of adsorbents.The activated carbon derived from agricultural wastes is important due to the fact that it is inexpensive, adequate to remove organic and inorganic contaminants from wastewater and locally available 1 .Malaysia is a major producer of palm oil.In 2002 alone, the amount of palm kernel shell generated in Malaysia was approximately 4.3 million tons which can cause serious disposal problem 2 .Considering the volume of this waste, several studies were initiated to utilize Palm Kernel Shell as the crude material for activated carbon and it is reported that a good quality product can be obtained, such as its granular structure, insolubility in water, chemical stability and high mechanical strength 2,3 .
It is important to be able to predict the rate at which pollutant is removed from aqueous solutions in order to design appropriate sorption treatment plants.Therefore, the kinetics that describes the dye uptake rate needs to be determined.The adsorption mechanism can be described by three essential steps 4 : 1. External mass transfer from bulk solution to adsorbent surface across the boundary layer surrounding the adsorbent surface particle.2. Intraparticle diffusion within the internal structure of particle.Internal diffusion is diffusion of molecule inside the pores and surface diffusion is diffusion of the molecules on surface phase.3. Adsorption at an interior site.Generally, the total rate of the kinetic process is controlled by the rate of the slowest process.The transport of the adsorbate from the bulk of fluid phase to the external surface of adsorbent forms an important step in the uptake process.
Single resistance models involve only a liquid film resistance, pore diffusion resistance or surface diffusion resistance 5 .In most cases, single resistance models are not adequate to explain the adsorption process for porous adsorbents.Therefore, two resistance mass transfer models which incorporate both external and intraparticle diffusion effects is applied 6 .Two resistance models can be divided into: 1. Film-pore diffusion model.

Film-surface diffusion model.
A model which incorporated film, pore diffusion and concentration dependent surface diffusion was introduced 7 and later on a three-resistance model based on external mass transfer, pore and concentration dependent surface diffusion for removal of methylene blue by PKS based-AC was presented 8 .They expressed that the film-pore-concentrationdependent surface diffusion (FPCDSD) model was able to fit the experimental data using a single set of mass transfer parameters for a wide range of initial dye concentrations.However, a two resistance model may be easier for implementation.

Experimental
PKS-based activated carbon supplied from KD Technology Sdn.Bhd was used without any chemical or physical treatment.Two reactive dyes were used for this investigation, namely, Reactive Black 5 (RB 5) and Reactive Red E (RR E) supplied from Texchem-Pack Bhd.The chemical structure of these dyes is given in Table 1.According to data obtained from pH meter, for single solution pH of the solution of RB 5 and RRE was 6.5 and 6.4, respectively.For binary solution, treating both dyes RB 5 and RR E in one solution, pH was 6.4.To prepare the stock solution, 1.000 g (+0.0005) of each dye was dissolved in 1 L distilled water.In order to maintain homogenous condition, the solution was shaken for 5 hours using orbital incubator shaker (Sepilau Saintifik, Malaysia) at 28 o C. Then the solution was kept in dark place for avoiding any off-color due to sunlight.The stock solution would then be diluted into desired concentration.

Batch kinetic study
Batch kinetic studies were performed to investigate the dynamic behavior of PKS -based activated carbon for removal of reactive dyes.The experiments were accomplished in shaking conical flasks with 1000 mL dye solution at a constant temperature of 28 °C (+ 2 °C), using an incubator.The pH of the solutions was without any modification.Sample of 1 mL was carefully withdrawn at every 3 minutes for the first 30 minutes and at every 5 minutes for the next 30 minutes of adsorption process.For the next 60 minutes, sampling was done every 10 minutes and eventually every 60 minutes for the next 20 hours and every 6 hours until equilibrium point.The same procedure was applied for kinetic study for binary mixture at concentration of 20 mg/L (for each dye) and activated carbon mass of 2 g/L.

Theoretical model External mass transfer
The mass transfer rate at the external surface layer of the adsorbent particle 10 is: Where N t is adsorption rate at time t, k f is the interphase mass transfer coefficient, S A is surface area, c b and c s are adsorbate concentration in the bulk of fluid and that at the fluidparticle interface, respectively.The differential mass balance is given by: where q is average adsorbed-phased concentration, M is mass of adsorbent, V is volume of solution, a p is particle radius and ρ p is pellet density.The concentration of adsorbate, q , with respect to time is related to the mass transfer coefficient k f by: Equation 4 can be solved with appropriate initial condition:

Intraparticle mass transfer Film-surface diffusion
Fick's second law of diffusion suggested that the adsorbate molecule is transferred through the adsorbent particles by creeping from one adsorption site to another on the solid surface.The surface diffusivity D s of adsorbed molecules is assumed here to be concentration independent.The mass transport in the spherical particle is described by following equation.
Equation 6 was solved with appropriate initial and boundary conditions: The second-boundary condition for external mass transfer is 10 : The external mass transfer coefficient, k f, is estimated from the single-resistance model.To calculate the value of the solid phase diffusivity, D s , equation 6 was solved numerically, considering the value of k f obtained from single-resistance model.

Film-pore diffusion
Pore diffusion equations are described as follow: (13)   where D p is pore diffusivity.
Both the two resistance models were solved by using finite-difference method, as approximating the spatial derivation by central difference expression.

Results and Discussion
To evaluate the external mass diffusion, the values of external mass transfer coefficient k f were calculated for different initial concentrations.Table 2 presents the values of k f for adsorption of RR5 and RR E onto PKS based-AC.It can be noted that these values, ranging between 3.7×10 -3 to 3.7×10 -4 cm/s, decrease with an increase in initial dye concentration.The value of k f in a single resistance mass transport model is normally expected to be constant, variation of external mass coefficient shows that intraparticle diffusion is playing a significant role in the mass transport process 6 .It is expressed that the values of k f decreased with increasing of initial adsorbate concentration 11 .The same results were shown for adsorption of dye onto bagasse pith 12 .It can be noted from the Table 2 that it agrees with finding of this work.It is possible that increasing the concentration of dyes, considering the large molecule of dye, causes the reduction of mobility of transferring adsorbates into the boundary layer 4 .

Table 2. External mass transfer coefficient k f for adsorption of RB 5 and RR E onto PKSbased AC (single system).
Isotherm model Interphase Mass Transfer Coefficient, cm/s 100, mg/L 20, mg/L RB 5 / PKS Pellet 5.5×10 -4 3.7×10 -3 RR E / PKS Pellet 3.7×10 -4 7.4×10 -4 By changing the values of k f and D s it is possible to obtain the best fit to the experimental curves for batch adsorption.Table 3 presents the values of D s for adsorption of RB 5 and RR E with dye concentration 20 mg/L onto PKS-based AC with dosage 2 g/L.It can be seen that the values of D s ranges between 1.5×10 -9 to 1.5×10 -10 cm 2 /s.From Table 3, it can be noted that the values of D s for RB 5 and RR E are different from values of other literatures.The difference shows specificity of adsorption.In other word interaction between adsorbate and adsorbent is characteristic for each system and it is not common for all systems 13 .This work.
Figures 1(a) and 1(b) show the comparisons of results of both adsorptions of RB 5 and RR E onto PKS-based activated carbon with predictions based on the film-surface diffusion and film-pore diffusion models.It is obvious from these figures that prediction based on the film-surface diffusion model fits better with experiment data than the film-pore diffusion model, and it agrees with both dyes.The values of SSE for film-surface diffusion are significantly less than values of SSE for film-pore diffusion, as shown in Table 5.As a result, it indicated that the adsorption process was governed by the resistance models, i.e. film-surface diffusion mechanism.The values of D p are as listed in Table 4.

Conclusion
The rate of the kinetic process for both dyes was better described by two resistance models.Based on SSE, the film-surface diffusion model was able to fit experimental better than the film-pore diffusion model for both RB 5 and RR E on palm kernel based activated carbon.

Figure 1 (Figure 1 (
Figure 1(a).Comparison between prediction of film-surface diffusion (S.D) and film-pore diffusion (P.D) models with experiments data from adsorption of RB 5 onto PKS-based activated carbon at dye concentration of 20 mg/L and dosage of adsorbent 2 g/L (single system).

Table 1 .
Properties of RB 5 and RR E 9 .
Adsorption of Reactive Dyes by Palm Kernel Shell Activated Carbon 953Some values of the surface diffusivity, reported in other literature are listed in Table3, as well.

Table 3 .
Values of D s , reported in the literature on adsorption of different dyes using different adsorbents and this work.

Table 4 .
Values of D p for adsorption of RB 5 and RR E onto PKS based-AC.

Table 5 .
Comparison of SSE of film-surface diffusion and film-pore diffusion models for adsorption of RB 5and RR E onto PKS based-AC.