kinetic modeling of methylene blue adsorption onto acid-activated spent tea: a comparison between linear and non-linear regression analysis

the kinetic study of methylene blue (mb) adsorption using acid-activated spent tea (aast) as an adsorbent from aqueous solution with the aim of comparing linear and non-linear regression analysis methods was performed at varying initial mb concentrations (10-100 mg/l). hence, spent tea leaves, which were activated using concentrated sulfuric acid, were prepared. the physicochemical characteristics of the prepared adsorbent were also measured. in addition, a scanning electron microscope (sem) and fourier transform infrared spectroscopy (ftir) instruments were employed to determine the size, morphology, and functional groups of aast. furthermore, the influence of different particle sizes of adsorbent on the adsorptive removal efficiency of mb was evaluated. the obtained data on mb adsorption were fitted using 4 kinetic models, namely pseudo first-order, pseudo second-order, elovich, and intraparticle diffusion (i-d). the results of kinetic investigations showed that pseudo second-order kinetic model compared to the other applied models, with significant coefficient of determination (r2 > 0.98), could best fit the experimental data of mb adsorption. in addition, among all linear forms of the pseudo second-order model, form 1 could better fit the mb adsorption data. additionally, by comparing the performance of both linear and non-linear forms of the pseudo second-order kinetic model, it can be postulated that non-linear regression analysis could be more appropriate than the linear approach for kinetic study of mb adsorption onto the aast adsorbent. ultimately, based on the results of particle size experiments, the smaller the size of the adsorbent particles, the higher the adsorption efficiency of mb will be.