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The kinetic parameter of the phosphazene reaction was influenced by the particle diffusion of the reactant.
If the plot of Bt versus time (having slope B) is a straight line passing through the origin, then the adsorption rate is governed by the particle diffusion mechanism; otherwise, it is governed by film diffusion (Singh et al. 2003).
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Alternatively, in scenarios of high molecular concentrations, delay distributions of simple translocation processes can also be obtained by solving the more general advection-diffusion equation, subject to appropriate boundary and initial conditions and characterized by the particles' diffusion constant D and the geometry of the spatial domain.
The optical and electrical characterizations connected with the changes in surface morphology induced by the particle surface diffusion bring important new information to this field of research.
The results of the aforementioned models (not reported) showed that adsorption kinetic was not wholly controlled by the intra-particle diffusion or by the liquid film mass transfer diffusion.
The rate of adsorption was controlled by the intra-particle diffusion and mass transfer through the liquid film, and the relative importance of these limiting steps depended on the operating conditions.
The three stages can be determined by the intra-particle diffusion rate as referred to k p. The increase in q t versus t 1/2 profiles of MR dye adsorption by DSAC adsorbents was non-linear (Fig. 8).
According to this model, the plot of B t against t (Figure not shown) will yield a straight line passing through the origin if the adsorption is governed by particle diffusion and if not, the process is controlled by film diffusion.
The experimental data were also analyzed by the intra-particle diffusion kinetic model.
If the plot of Qt against t1/2 were linear, the adsorption process was deemed to have been determined by the intra-particle diffusion step.
Similarly at concentrations 25 and 50 mg/l the adsorption was governed by particle diffusion in most of the cases while at >50 mg/l it was film diffusion controlled.
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