Application and evaluation of a modified intraparticle diffusion model for mono‑/multiadsorption of chlorobenzene pollutants on biochar

Purpose: With the developments of new materials and technologies for adsorption, it is necessary to develop new kinetic models to describe some more complex adsorption processes. This study aimed to evaluate the availability of a modified intraparticle diffusion model q_t = k₁t^1/2 (0 ≤ t ≤ t₁) and q_t-q_t=t1 = k₂ (t-t₁)^1/2 (t₁ < t ≤ t₂) for the adsorption of chlorobenzene pollutants (CBs) on biochar and to explore the corresponding mechanisms. Materials and methods: The adsorption kinetics of the four CBs with different numbers of Cl substituents were investigated in mono- or multi-CB adsorption experiments (equal or unequal initial concentration) with the corn straw-based biochar pyrolyzed at 500 °C. The kinetics process was fitted by the classical model (q_t = kt^1/2 + b) with linearization or nonlinearly regression, and by the modified intraparticle diffusion model q_t = kt^1/2 (0 ≤ t ≤ t₁) and q_t-q_t=t1 = k₂ (t-t₁)^1/2 (t₁ < t ≤ t₂). The optimal break point of t₁ separating the stages of 0 ≤ t ≤ t₁ and t₁ < t ≤ t₂ was obtained by comparing the parameters of adjR² and AICc calculated from different t₁ values. Combined with the characteristics of biochar morphology and structure, variation of initial concentrations and performances of competitive adsorption of CBs, the adsorption mechanisms were analyzed. Results and discussion: The modified model performed well the nonlinear fitting of the kinetic processes with R² values between 0.917 and 0.981, higher than that of the nonlinear and linear fitting of the classical model. The adsorption rate of k₁ was usually larger than k₂ regardless of the number of chlorine substitutions, or in the scenario of mono-/multi-CBs adsorption_. In the mono-adsorption, the k₁ and k₂ values of low-chlorinated CBs were mostly greater than those of the high-chlorinated CBs. In multi-adsorption, competitive adsorption decreased the intraparticle diffusion rates of each CBs. And the rates varied with the initial concentration of CBs, and with the numbers of chlorine substitutions which had an effect on the affinities of CBs to biochar and steric hindrance via hydrophobicity, electrophilicity and molecule sizes. Conclusions: The modified intraparticle diffusion model was suggested to be suitable to describe the diffusion processes of CBs with high aqueous phase concentrations on biochar. The modified model indicated the intraparticle diffusion and pore wall adsorption were two closely linked processes. The initial concentration, the number of chlorine substitutions and the morphology structure of biochar were suggested to be the key factors affecting the adsorption of CBs on the biochar.