Intra-Particle Diffusion Kinetic Model and Mechanism of Solute Adsorption

The mechanism of adsorption techniques involve four steps: migration of dye molecules from bulk solution to the surface of the sorbent, diffusion through the boundary layer to the surface of the sorbent, adsorption at a site, and intra-particle diffusion into the interior of the sorbent [126]. According to Weber and Morris [127], the amount of adsorption varies proportional with t¹² for most adsorption processes and can be expressed as:

where q_t is the adsorption capacity at time t, t⁰'⁵ is the half-life time in second, K_id (mg/g min^{0 5}) is the rate constant of intraparticle diffusion. A plot q_t versus t ' will give a linear

relationship where Kid can be determined from the slope of the plot.

Usually the kinetic adsorption data is better represented by pseudo-second-order model for most of dye adsorption systems. Zolgharnein et al. [128] studied the adsorption of Methyl Violet by Platanus Carpinifolia tree leaves and they found that the linear correlation coefficient R² values of the Pseudo-second-order model was higher (0.99) fitted than the Pseudo-first-order kinetic (0.79). Dursun et al. [129] evaluated the adsorption of Remazol Black B dye using sugar beet pulp and they found that the applicability of Pseudo-second over Pseudo-first order models. Rebitanim et al. [130] studied the use of raw empty fruit bunch biomass for adsorption of Methylene blue and they found that the values of the regression correlation coefficient R² for Pseudo-first-order model were between 0.83 and 0.86, while the values of R² for the second order model were between 0.992 and 0.999 indicating applicability of second order model was more accurate. Table 9 presented compilation results of the applicability of Pseudo-second-order Kinetic models for dye adsorption using several agricultural solid waste adsorbents.

Table 9. Various Kinetic studies for dye adsorption by various agricultural

solid waste adsorbents