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Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
iii. Intra-particle Diffusion:
Since rate of adsorption is usually measured by determining the change in concentration of
adsorbate with the adsorbent as a function of time, linearization of the data is obtained by plotting the
amount adsorbed per unit weight of adsorbent q versus t 1/2 as given by ref. (18) and Eq. (4): The intraparticle
diffusion model, Morris and Weber model, is presented as the following (19) .
q = kad t 1/2 + C (4)
where kad is the rate constant of intra-particle transport (mmol/g min 1/2 ).
The value C (mmol/g) in this equation is a constant which indicates that there exist a boundary layer
diffusion effects, and is proportional to the extent of boundary layer thickness (20) larger the value the
greater is the boundary effect (21) . If the plot of q versus t 1/2 gives a straight line, the adsorption process
is controlled by intra-particle diffusion only. However, if the data exhibit multi-linear plots, then two
or more steps influence the sorption process (22) .
The plots of q versus t 1/2 are given in Figs. (13-1) : (13-6) for the adsorption of Eu 3+ , Nd +3 ,
Sr +2 , Co +2 , Cd +2 , and Zn +2, ions on poly-acrylic acid/Acrylonitrile (P-AAc/AN) at different
temperatures. It can be seen from the figures that the adsorption data gives a straight lines, therefore
the intra-particle diffusion model is applicable for the adsorption process and the adsorption is
controlled by intra-particle diffusion.. The kinetic parameters are given in Table (5).
Table (5) The kinetic parameters of intra-particle diffusion model for sorption of Zn 2+ , Cd 2+
Co 2+ , Sr 2+ , Nd 3+ and Eu 3+ onto P-AAc/HEMA at different temperatures.
Temp
,
o K
Cd
Zn
Co
Sr
Nd
Eu
kad,
mmol
/g h 1/2
0.34
0.39
0.40
0.52
0.82
1.11
298 o K
C,
mmol
/g
0.000
4
0.002
9
0.000
8
0.000
1
0.000
2
0.000
1
R 2
0.99
0.99
0.98
0.97
0.98
0.98
kad ,
mm
ol/g
h 1/2
0.25
0.28
0.22
0.42
0.50
0.80
303 o K
C,
mmol/
g
0.0077
0.007
0.0054
0.0028
0.005
0.0049
R 2
0.97
0.97
0.99
0.98
0.96
0.97
14
kad,
mmol/
g h 1/2
0.20
0.24
0.13
0.24
0.28
0.57
313 o K
C,
mm
ol/g
0.00
93
0.00
9
0.00
94
0.00
91
0.00
95
0.00
86
R 2
0.98
0.99
0.99
0.96
0.98
0.98
kad,
mmol/
g h 1/2
0.16
0.17
0.07
0.17
0.25
0.44
323 o K
C,
mm
ol/g
0.01
1
0.01
1
0.01
2
0.01
1
0.01
1
0.01
2
R 2
0.9
8
0.9
8
0.9
8
0.9
6
0.9
9
0.9
7