Study on the Adsorption Kinetics of Acid Red 3 B on Expanded Graphite

Expanded graphite (EG) is a kind of important adsorbent for organic compound such as oil and dyes. We have investigated the adsorption kinetics characteristics of this adsorbent for dye. EG was prepared with 50 mesh crude graphite through chemical oxidation intercalation of potassium permanganate and vitriol, and dye of acid red 3B was used as model sorbate. We have studied the adsorption kinetic models and rate-limiting step of the process. Adsorption rate and activation energy of the adsorption process were calculated. Kinetic studies show that the kinetic data are well described by the pseudo second-order kinetic model. The equilibrium adsorbance increases with the increase of the initial acid red 3B concentration. Initial adsorption rate increases with the increase of the initial dye concentration and temperature. Adsorption process of acid red 3B on EG has small activation energy. Internal diffusion appears to be the rate-limiting step for the adsorption process.


Introduction
Most of the industries such as textiles, paper, plastics, leather, food, cosmetic, etc. use dyes or pigments to color their final products.Such extensive uses of color often possess problems in the form of colored wastewaters.Most of the commercially used dyes are resistant to biodegradation, photo degradation and oxidizing agent.Biological methods have not been very successful for dye removal, due to the essential non-biodegradable nature of most of the dyes.
Adsorption is a kind of effective measure, active carbon [1][2][3][4] , anion exchange resin 5 , active sludge 6,7 , peat, steel plant slag and fly ash 8 have been reported to be employed for the treatment of dyes.Expanded graphite (EG) is a kind of eco-material and it has attracted attentions of scientists and engineers as an absorbent with a high sorption capacity for heavy oil and biomedical molecules 9 .Pores in EG are described using a 4-level model 10 , and the pore size ranges from several nm to hundreds µm, which makes it have the adsorption capability for dyes.But it has been reported not so much in this aspect.Wang studied the sorption capacity of EG low-density plate, and a decreasing rate of chemical oxygen demanded of 40% was obtained 11 .Yang studied the sorption capacity of dyes on EG 12 , and the decolored rate of medium yellow GG can arrived 13 to 97%.However, little work has been done to study the adsorption kinetics of dye on EG.In this work, a porous EG was prepared through chemical oxidation and intercalation.An organic dye of acid red 3B with azobenzene structure was used as model adsorbate to study the adsorption kinetics under various experimental conditions.

Experimental Preparation and characteristics of EG
Expandable graphite was prepared with 50 mesh crude graphite (C), and KMnO 4 as oxidant, vitriol as intercalation compound.The mass ratio of C to vitriol and KMnO 4 was controlled as 1.0:5.0:0.15.The mass concentration of vitriol was 50% and the reaction lasted 30 min at room temperature.After washing to a pH of 6.0-7.0 and drying below 80°C, expandable graphite was obtained.Expandable graphite was expanded in KSW heating oven at 900°C and EG was obtained.Structural parameters of EG were characterized by expanded volume, specific surface area and total pore volume.The porosity characteristics of EG were listed in Table 1.

Adsorption of dye
A series of desired dye concentration and of fixed volume 100.0 mL were placed in vessels, where they were brought into contact with EG at 5°C, 25°C and 45°C respectively.The mass of adsorbent to volume of solution was standardized at M/V=0.200 g/0.l l=2.00 g/L.
The dye solution corresponding to different adsorption time was then analysed using spectrophotometry technique.The amount of Acid red3B captured by EG was calculated as following: q= V(C 0 -C)/M (1) where: q = adsorption amount of acid red 3B on EG, mg/g V = the volume of the solution, mL C 0 = initial concentration of acid red 3B in solution; mg/L C = concentration of acid red 3B in solution corresponding to a definite adsorption time; mg/L M = mass of EG; g

Equilibrium time
The amount of dye adsorbed is showed as a function of time in Figure 1.As showed in this figure, adsorption occurs more rapidly at higher temperature: it takes about 2.5h to reach the adsorption equilibrium at 45°C, while it takes about 24.0h at 5°C.Initial dyes concentrations do not have a significant effect on the equilibrium time.

Adsorption kinetic models
Both pseudo first-and second-order adsorption models were used to describe the adsorption kinetics data 14,15 .In both models, all the steps of adsorption such as external diffusion, internal diffusion, and adsorption are lumped together, and the overall adsorption rate is proportional to either the driving force (as in the pseudo first-order equation) or the square of the driving force (as in the pseudo second-order equation).
First-order model：ln(q e −q)=lnq e −kt (2) Second-order model：t/q=1/(k q e 2 )+t/q e (3)   where: k=adsorption rate constant (min -1 for first-order adsorption, g•mg -1 •min -1 for second-order adsorption) t=adsorption time (min) Since q reaches a plateau (q e ) at equilibrium, q values smaller than the 0.9qe were used for analysis.The plots of ln(qe−q) versus t and t/q versus t were used to test the first-and secondorder models, and the fitting results are given in Table 3.According to the correlation coefficients, second-order model gives satisfactory fits, and at the same time, the q e,cal corresponding to second-order model agrees more well with the experimental data than the first-order model.Thus, second-order model is more suitable to describe the adsorption kinetics data.Similar results were observed in biosorption of dye Remazol Black B, RB2, PY2 on biomass, BBF on xerogel [16][17][18] , anionic dye adsorption on cross-linked chitosan beads 15,19 , and polyethylene glycol (PEG) adsorption on zeolite 20 .Table 3

First-order
Second-order C 0 mg/L T, 0 C q e,exp mg/g q e,cal mg/g k/10 (5) where: u = initial adsorption rate mg/(g•min) t 1/2 = half-adsorption time min As showed in Table 4, the initial adsorption rate is found to increase with the increase of the initial acid red 3B concentration and temperature, and the half-adsorption time t 1/2 decrease with the increase of temperature.

a:"--"the value of Ea is unavailable
Second-order rate constants listed in Table 3 is used to estimate the activation energy of acid red 3B adsorption on EG using Arrhenius equation: Lnk=LnA-Ea/(RT) (6) where: A = pre-exponential factor (g•mg -1 •min -1 ) E a = activation energy of adsorption (kJ/mol) The slope of plot of lnk versus 1/T is used to evaluate Ea, which was found to be about 0.407 kJ•mol −1 corresponding to an initial dye concentration of 600 mg/L (listed in Table 4).Values of Ea corresponding to other concentration were ignored for the reason of veracity (with the correlation coefficients less than 0.9000).

Internal diffusion analysis
The adsorption process on a porous adsorbent generally involves three stages: (i) external diffusion; (ii) internal diffusion (or intra-particle diffusion); (iii) actual adsorption 20 .The adsorption step is usually very fast for the adsorption of organic compounds on porous adsorbents compared to the external or internal diffusion step 21 , and it is known that the adsorption equilibrium is reached within several minutes in the absence of internal diffusion 22 .Thus, the long adsorption equilibrium time in experiments (2.5~24.0hcorresponding to adsorption temperature of 5~45°C) suggests that the internal diffusion may dominate the overall adsorption kinetics.
To provide definite information on the rate-limiting step, an internal diffusion model based on Fick's second law is used to test if the internal diffusion step is the rate-limiting step 23 : q =k id t 1/2 (7) where: k id = internal diffusion constant, mg/(g•min 1/2 ) According to the internal diffusion model, a plot of q versus t 1/2 should give a straight line with a slope k id and an intercept of zero if the adsorption is limited by the internal diffusion process 23 .The relationships between q and t 1/2 at different temperature are shown in Figure 2. Initially in all the cases studied, a linear relationship between q versus t 1/2 with a zero intercept is found, suggesting that the internal diffusion step dominates the adsorption process before the equilibrium is reached.To see this more clearly, two dimensionless variables are defined, ξ and θ: ξ=q/q e ； θ=t/t 1/2 (8)   Equation ( 8) can be rewrite as following： ξ=k' θ 1/2 (9) where: k' = dimensionless internal diffusion rate constant ξ = dimensionless adsorption amount θ = dimensionless time Figure 3 shows the plot of ξ versus θ 1/2 , which clearly show that all the data follow the same kinetics.This confirms that the adsorption process can be described by a simple internal diffusion model.For the adsorption of reactive dyes by activated carbon 24 , the adsorption of methylene blue by perlite 25 , and the adsorption of BBF by xerogel 17 , internal diffusion were found to be the rate limiting step.

Conclusions
The adsorption kinetics characteristics of EG for dye of acid red 3B have been investigated.The results are summarized as follows: • The adsorption kinetics of EG for acid red 3B can be well described by the pseudo second-order kinetic model.Initial adsorption rate increases with the increase in initial dye concentration and temperature.Equilibrium time and half-adsorption time t 1/2 decreases with the increase of temperature, while the initial dye concentration does not have an obvious effect.
• The equilibrium adsorption amount is found to increase with the increase in initial Acid red3B concentration.The internal diffusion of acid red 3B into the EG is the rate-limiting step of the overall adsorption process.
• Adsorption of acid red 3B on EG has small adsorption activation energy; the result might be caused by the macroporous characteristics of EG.

Figure 3 .
Figure 3. Plot of ξ vs. θ 1/2 in internal diffusion model.concentration refers to the initial acid red 3B concentration.

.
Structural parameter of EG a

Table 4 .
Kinetic parameters for the second-order adsorption model of acid red 3B adsorption on EG a