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The adsorbed species may also be transported from solutions to a solid phase through intra-particle diffusion or transport process. Intra-particular diffusion is the limiting step for the sorption–desorption phenomenon. The Weber Morris mode is the formula used to describe the mechanism by which intra-particles can diffuse (Weber & Morris 1963; Mckay et al. 1980; Mckay 1983):
formula
9
where C is a constant and kdif is the rate constant for intra-particle diffusion. The kdif values for the tested adsorbent are obtained as slopes of the graphs (Figure 10) and reported in Table 5. The uptake of cadmium and nickel ions at the surface of the magnetic particles may be governed by the intra-particle diffusion kinetics, since the qt values are linear correlation with t1/2. The regression coefficient values are ≈1.0, indicating the applicability of this model. The intra-particle diffusion plots are shown in Figure 10, where the main parameters of this model are determined and gathered in Table 5. The values of C, obtained from the intercept of the graph, are the measure of the boundary layer effects or the extent of resistance to external mass diffusion. A greater value of C indicates larger thickness of the boundary layer.
Table 5

Intra-particle diffusion model parameters for Cd(II) and Ni(II) ions adsorption

Metal ionskdif1, mg/g·min1/2Cr2kdif2, mg/g·min1/2Cr2
Cd(II) 5.199 39.33 0.989 1.38 60.22 0.9714 
Ni(II) 5.621 6.585 0.9492 0.8434 23.952 0.9802 
Metal ionskdif1, mg/g·min1/2Cr2kdif2, mg/g·min1/2Cr2
Cd(II) 5.199 39.33 0.989 1.38 60.22 0.9714 
Ni(II) 5.621 6.585 0.9492 0.8434 23.952 0.9802 
Figure 10

qt versus t1/2 plot for the intraparticle diffusion.

Figure 10

qt versus t1/2 plot for the intraparticle diffusion.

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