# Effective Adsorption of Phenoxyacetic Herbicides by Tomato Stem-Derived Activated Carbons
## 3 Results and Discussion
### Adsorption Study
#### 3.2.1 Adsorption Kinetics
Kinetic modeling data for the adsorption of the herbicides on AC produced from tomato stems are listed in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**2,4-D**} & \multicolumn{4}{c}{**MCPA**} \\ \cline{2-7}
**TS-AC** & \multicolumn{4}{c}{**Pseudo-First-Order (PFO) Kinetic Model**} \\ \cline{2-7}  & \(k_{1}\) & \(R^{2}\) & \(\chi^{2}\) & \(k_{1}\) & (l/min) & \(R^{2}\) & \(\chi^{2}\) \\ \hline AC-KOH-550 & 0.0299 & 0.991 & 0.185 & 0.0356 & 0.981 & 0.045 \\ AC-KOH-650 & 0.0368 & 0.958 & 0.522 & 0.0396 & 0.971 & 0.089 \\ AC-KOH-750 & 0.0342 & 0.911 & 0.711 & 0.0472 & 0.941 & 0.258 \\ AC-NaOH-550 & 0.0502 & 0.955 & 0.369 & 0.0391 & 0.990 & 0.029 \\ AC-NaOH-650 & 0.0472 & 0.927 & 0.412 & 0.0386 & 0.953 & 0.337 \\ AC-NaOH-750 & 0.0504 & 0.978 & 0.089 & 0.0327 & 0.901 & 0.679 \\ \hline  & \multicolumn{4}{c}{**Pseudo-second-order (PSO) kinetic model**} \\ \cline{2-7}  & \(k_{2}\) & \(\chi^{2}\) & \(k_{2}\) & (g/mmol-min) & \(R^{2}\) & \(\chi^{2}\) \\ \hline AC-KOH-550 & 0.130 & 0.997 & 0.023 & 0.128 & 0.998 & 0.029 \\ AC-KOH-650 & 0.187 & 0.999 & 0.011 & 0.181 & 0.999 & 0.017 \\ AC-KOH-750 & 0.235 & 0.999 & 0.019 & 0.259 & 0.999 & 0.014 \\ AC-NaOH-550 & 0.145 & 0.998 & 0.038 & 0.151 & 0.999 & 0.015 \\ AC-NaOH-650 & 0.208 & 0.999 & 0.018 & 0.193 & 0.998 & 0.027 \\ AC-NaOH-750 & 0.218 & 0.999 & 0.028 & 0.211 & 0 The \(q_{\rm e}\) (\(q_{\rm e(cal)}\)) values from the PSO model were closer to \(q_{\rm e(exp)}\) than those from the PFO model, which also exhibited higher \(R^{2}\) and lower \(\chi^{2}\) values, showing a better fit. This is illustrated in Figure 4.  
Based on these findings, the PSO kinetic model accurately describes the adsorption of 2_4_-D and MCPA on TS-AC. This aligns with previous research, as reviews [3; 7; 8; 28] indicate that the PSO model is commonly the most suitable for phenoxyacetic herbicide adsorption onto various adsorbents. As shown by the very similar \(k_{2}\) values, both herbicides were adsorbed on individual AC at more or less the same rate. However, the disparities become more apparent when adsorbents are compared against each other rather than the adsorbates. The \(k_{2}\) values obtained for both herbicides increase in order: AC-KOH-550 < AC-NaOH-550 < AC-KOH-650 < AC-NaOH-650 < AC-NaOH-750 < AC-KOH-750. Thus, 2,4-D and MCPA adsorbed rapidly on AC-KOH-750 and most slowly on AC-KOH-550. This observed sequence seems closely related to the porous structure of these activated carbons, as shown in Table 4. While the adsorption capacity of adsorbents is primarily determined by micropore volume and BET surface area, the adsorption rate is influenced mainly by mesopore volume. Mesopores (2-50 nm diameter) serve as transport pathways, facilitating adsorbate molecule diffusion into the adsorbent particle and ultimately to the micropores, where adsorption occurs via surface interaction. Consequently, a greater mesopore volume generally correlates with a faster rate of adsorbate uptake from the solution. Both 2,4-D and MCPA adsorbed most slowly on AC-KOH-550, which has the smallest mesoporous structure (\(V_{\rm me}=0.055\) cm\({}^{3}\)/g). On the other hand, adsorption occurred most rapidly on AC-KOH-750, the adsorbent with the largest mesopore volume (\(V_{\rm me}=0.337\) cm\({}^{3}\)/g). Thus, individual ACs' observed adsorption rate characteristic is closely correlated with their mesoporous structure (mesopore volume). Although the PSO kinetic model describes the adsorption kinetics well, it does not explain the adsorption mechanism. Therefore, a diffusion model was also used to describe the kinetics [29]. This is the Weber-Morris model [30], also known as the intra-particle diffusion model [31], which is expressed by the following formula:  
\[q_{t}=k_{\rm i}t^{0.5}+C_{\rm i} \tag{12}\]  
where \(k_{\rm i}\) is the intra-particle diffusion rate constant (mmol/g\(\cdot\)min\({}^{-0.5}\)) and \(C_{\rm i}\) is the thickness of the boundary layer.