# Biochars as a Solution for Silver Removal and Antimicrobial Activity in Aqueous Systems
## 3 Results and Discussion
### Adsorption Studies  
#### 3.4.1 Effect of Interaction Time on Adsorption  
The graphs in Figure 6 illustrate the adsorption capacity (Q\({}_{\text{L}}\), in mg/g) of three biochars (CB, RHB, and ARHB) over time (in minutes). Initially, all three samples show a rapid increase in adsorption capacity, eventually reaching a plateau. Biochar RHB demonstrates the fastest adsorption rate, achieving its maximum capacity within 10 min, while the ARHB sample attains the highest final adsorption capacity. Equilibrium is reached for all three materials within 30 min. The fast speed of the adsorption process is one of its most important advantages.  
Adsorption mechanisms can be described and understood through various kinetic models, including pseudo-first-order and pseudo-second-order kinetics, as well as diffusion mechanisms. These models help elucidate the rate and pathways by which adsorbates are removed from solutions by adsorbents. The linear equations of these models are the follows:  
\[\text{log}\left(\text{Q}_{\text{e}}-\text{Q}_{\text{L}}\right)=\text{log} \left(\text{Q}_{\text{e}}\right)-\left(\text{k}_{1}/2.303\right)\text{t} \tag{2}\]  
\[\left(\text{t}/\text{Q}_{\text{L}}\right)=\left(1/\text{k}_{2}\text{Q}_{\text{ e}}\right)+\left(1/\text{Q}_{\text{e}}\right)\text{t} \tag{3}\]  
\[\text{Q}_{\text{L}}=\text{k}_{\text{id}}\text{t}^{1/2}+\text{C} \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \begin{tabular}{c} **S\({}_{\text{BET}}\)** \\ **(m\({}^{2}\) g\({}^{-1}\))** \\ \end{tabular} & \begin{tabular}{c} **S\({}_{\text{MI}}\)** \\ **(m\({}^{2}\) g\({}^{-1}\))** \\ \end{tabular} & \begin{tabular}{c} **V\({}_{\text{r}}\)** \\ **(cm\({}^{3}\) g\({}^{-1}\))** \\ \end{tabular} & \
\begin{tabular}{c} **D\({}_{\text{av}}\)** \\ **(nm)** \\ \end{tabular} &
\begin{tabular}{c} **V\({}_{\text{mi}}\)** \\ **(cm\({}^{3}\) g\({}^{-1}\))** \\ \end{tabular} \\ \hline CB & 76 & 14 & 0.38 & 20 & 0.03 \\ \hline RHB & 17 & 6 & 0.08 & 7 & 0.05 \\ \hline ARHB & 844 & 770 & 0.42 & 2 & 0.38 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Texture characteristics.  
Figure 6: Kinetics of Ag\({}^{+}\) adsorption onto the biochars.  
where Q\({}_{t}\) represents the adsorbed amount of Ag\({}^{+}\) at a certain time t; Q\({}_{e}\) is the equilibrium adsorption capacity; and k\({}_{1}\), k\({}_{2}\), and k\({}_{id}\) is the rate constant for pseudo-first-order adsorption, pseudo-second-order adsorption, and the intraparticle diffusion, respectively. The kinetic parameters and their statistics are presented in Table 2. In comparison to other kinetic models, the pseudo-second-order model demonstrates exceptional fit with the experimental data, achieving values of 0.9996 or higher and calculated adsorption capacities close to those obtained experimentally. This strong correlation suggests that the adsorption of silver ions is predominantly governed by chemisorption mechanisms, facilitated by the reactive functional groups and minerals present on the biochar surface [17]. It should be noted that the diffusion model graphs do not pass through the origin of the coordinate system, indicating that intraparticle diffusion is not the sole mechanism controlling the adsorption process.