Accepted Manuscript Molecular mechanism of anionic dyes adsorption on cationized

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19 
Table 3 Kinetics parameters on the adsorption of Diamine Green B (DG-B), Acid 
Black 24 (AB-24) and Congo red (CR) onto CRHC. 
Dyes 
Pseudo-first-order 
Pseudo-second-order 
Elovich 
q
e.exp
k
1
 
q
e.cal

R
2
 
K
2
 
q
e.cal
 
R
2
 
 
α 
β 
R
2
DG-B 
303.15 K  
0.054 
162.30 
0.6471 
0.0014 
172.00 
0.9636 
21.01 0.074 0.9076 
185.22 
313.15 K  
0.049 
149.13 
0.8463 
0.0013 
158.25 
0.9939 
10.51 0.076 0.8522 
157.32 
323.15 K  
0.019 
141.12 
0.9192 
0.00037 
157.87 
0.9852 
36.83 0.038 0.9396 
151.03 
AB-24 
303.15 K  
0.079 
146.69 
0.4897 
0.0027 
152.71 
0.9114 
72.80 
0.12 
0.9311 
162.76 
313.15 K  
0.052 
139.44 
0.8038 
0.0015 
147.67 
0.9880 
16.02 0.085 0.8792 
153.20 
323.15 K  
0.054 
131.98 
0.6556 
0.0017 
139.87 
0.9566 
15.75 0.090 0.9155 
145.54 
CR 
303.15 K  
0.12 
230.97 
0.4913 
0.0036 
236.07 
0.9283 
50.79 
0.15 
0.9136 
248.10 
313.15 K  
0.11 
234.86 
0.4898 
0.0034 
240.24 
0.9263 
16.62 
0.14 
0.9071 
249.34 
323.15 K  
0.10 
238.06 
0.5170 
0.0033 
243.52 
0.9385 
19.39 
0.13 
0.8898 
252.11 
Adsorption is a complex process that usually involves three stages. The first 
stage mainly reflects the external diffusion, the second and the third stages mainly 
reflect the internal diffusion. Therefore, the adsorption behavior cannot be completely 
analyzed with only one or two kind of kinetic models. The intra-particle diffusion 
model is mainly applicable to describe the kinetics of the diffusion process. It is 
necessary to analyze the kinetic data by using an intra-particle diffusion model. The 
expression of the intra-particle diffusion model is shown as below. 
c
t
k
q
id
t


2
/
1
Where c is the intercept (mg g
-1
) and k
id
is the intraparticle diffusion rate constant 
(mg g
–1
min
–1/2
). The values can be obtained by plotting q
t
vs t. 
The intra-particle diffusion kinetics of Diamine Green B (DG-B), Acid Black 24 
(AB-24) and Congo Red (CR) onto CRHC at different temperatures are shown in Fig. 
6. The first fitting line does not pass through the origin of the coordinates, indicating 
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that the adsorption process includes not only intra-particle diffusion, but in fact its key 
rate limiting step should have other reasons, and the entire purification process should 
be subject to a variety of adsorption stages. The fitted curve is divided into three 
straight lines. The first is the instantaneous adsorption process in which the dye 
adsorbent is adsorbed on the surface of the adsorbent. This stage is the step where the 
adsorption process occurs fastest and the adsorption rate is the highest; followed by 
the gradual adsorption process, the adsorption rate decreases at this stage; the 
adsorption reaches a state of equilibrium in the last process, in which the dye 
concentration in the solution is reduced and the adsorption rate is lowest. 
Fig. 7. The intra-particle diffusion kinetics of DG-B, AB-24 and CR onto CRHC. 

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