Hou Wang a, b , Xingzhong Yuan a, b * , Guangming Zeng a, b Lijian Leng a, b , Xin Peng a, b
, Lingli Liaokai,
a, b
Lijuan Peng
a, b
, Zhihua Xiao
a, b a
College of Environmental Science and Engineering, Hunan University, Changsha
410082, P.R. China b Key Laboratory of Environment Biology and Pollution Control, Hunan University,
Ministry of Education, Changsha 410082, P.R. China
1. Theory
The amount of malachite green adsorbed onto different adsorbents at equilibrium
( q e
) and time t , q t
(mg/g) was calculated by means of the following equations: q e
=
(
C
0
m
C e
)
× V (1) q t
=
(
C
0
C t
)
× V m
(2) where C
0
and C e
are the initial and equilibrium concentrations of MG in solution
*
Corresponding author at: College of Environmental Science and Engineering, Hunan University,
Changsha 410082, P.R. China. Tel.: +86 731 88821413; fax: +86 731 88823701.
E-mail address: yxz@hnu.edu.cn
(X.Z. Yuan)

(mg/L) respectively, C t
is concentrations of MG at time t ; V is the volume of solution
(L) , m is the adsorbent mass (g).
And dye removal efficiency i.e. % of adsorption was obtained as
% Adsorption =
(
C
0
C e
)
× 100
C
0
(3)
Adsorption dynamics can describe the solute uptake rate and evidently this rate controls the residence time of adsorbate uptake at the solid-solution interface. Four well-known, commonly used models to analyze the adsorption behavior and mechanism of MG on solid surfaces are pseudo-first-order, pseudo-second-order, elovich kinetic model and intra-particle diffusion model. Linearized-integral forms of kinetic models are expressed as follows (Wang et al. 2013 ): ln ( q e
q t
) = ln q e
k
1
2 .
303 t
(4) t q t
=
1 k
2 q e
2
+ t q e
(5) q t
= k si t 1 2 + C i
(6) where q e
and q t
(mg/g) are the values of amount adsorbed per unit mass at equilibrium and at instant of time t (min). k
1
(1/min) is the pseudo-first-order adsorption rate coefficient. k
2
(g/(mg
· min)) is the pseudo-second-order rate coefficient. The elovich coefficients, a represents the initial adsorption rate (mg/g
· min) and b (g/mg) is related to the extent of surface coverage and activation energy for chemisorption. The value of (1/b) is indicative of the available number of sites for adsorption. k si
(mg/(g
· min
0.5
)) is the diffusion rate coefficient. C i
is the idea about thickness of the boundary layer.

Adsorption isotherm can provide an essential parameter for understanding the properties of adsorbents and designing a desired adsorption system. In this study, the adsorption equilibrium isotherm was investigated at different temperatures. Different isotherms model, such as Langmuir, Freundlich, and Temkin isotherm were employed to describe the equilibrium data and the non-linear forms were expressed as follows
(Sun et al. 2008 ): q e
= q max k
L
C e
1 + k
L
C e
(9) q e
= k f
C
1 e n
(10) q e
= B ln ( AC e
)
(11) where q max
is the maximum adsorption capacity (mg/g); k
L is the Langmuir constant related to the affinity of the binding sites and energy of adsorption (L/g); k f is
Freundlich constant (L/mg)
1/ n
, which indicates the relative adsorption capacity of the adsorbent; 1/ n is a measure of adsorption intensity; B and A (L/g) are the Temkin constant and the Temkin equilibrium binding constant (L/g).
Thermodynamic parameters involving Gibbs free energy (∆
G
0 ), enthalpy change (∆
H
0
) and change in entropy (∆
S
0
) were obtained according to the following formulas: q e log (
C e
)=
Δ S
0
2 .
303 R
Δ H
0
-
2 .
303 RT
(7)
ΔG 0
=
ΔH 0
T
Δ
S
0
(8) where R is ideal gas constant (8.314 J/mol K); T (K) is the absolute solution

temperature. The values of Δ H and Δ S were calculated from the slope and intercept of the linear plot of log( q e
/ C e
) versus 1/T.
Reference
Sun XF, Wang SG, Liu XW, Gong WX, Bao N, Gao BY, Zhang HY (2008)
Biosorption of malachite green from aqueous solutions onto aerobic granules: kinetic and equilibrium studies, Bioresour Technol 99:3475–3483.
Wang H, Yuan X, Wu Y, Huang H, Zeng G, Liu Y, Wang X, Lin N, Qi Y (2013)
Adsorption characteristics and behaviors of graphene oxide for Zn(II) removal from aqueous solution, App Surf Sci 279: 432–440.