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 t^{12} for most adsorption processes and can be expressed as:
where q_{t} is the adsorption capacity at time t, t^{0}'^{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 R^{2} 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 R^{2} for Pseudo-first-order model were between 0.83 and 0.86, while the values of R^{2} 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
Adsorbents |
Dye |
Fitted Kinetic Model |
References |
Acer tree leaves |
Methylene blue |
P seudo-second-order |
[131] |
Reed |
Basic yellow 28 |
P seudo-second-order |
[132] |
Peach gum |
Methyl violet |
P seudo-second-order |
[133] |
Indian jujube seed powder |
Acid blue 25 |
P seudo-second-order |
[134] |
Modified Oil palm tree sawdust |
Malachite green |
P seudo-second-order |
[83] |
Modified phoenix tree leaves |
Crystal violet |
P seudo-second-order |
[114] |
Raw and modified pine cone |
Methylene blue |
P seudo-second-order |
[135] |
Raw and modified mango seed |
Methylene blue |
P seudo-second-order |
[82] |
Treated Onion Skins |
Methylene blue |
P seudo-second-order |
[136] |
Almond shell |
Methyl violet |
P seudo-second-order |
[137] |
Treated saw dust |
Brilliant green |
P seudo-second-order |
[109] |
Rice husk |
Direct orange 26 |
P seudo-second-order |
[105] |
Wood apple shell |
Crystal violet |
P seudo-second-order |
[67] |
Beech wood sawdust |
Basic blue 86 |
P seudo-second-order |
[138] |