# Biochars as a Solution for Silver Removal and Antimicrobial Activity in Aqueous Systems
## 3 Results and Discussion
### Adsorption Studies
#### 3.4.3 Adsorption Isotherms  
Adsorption isotherms describe the relationship between the amount of solute adsorbed onto a sorbent surface at equilibrium and the concentration of the solute in the solution (Figure 8). They provide insights into the adsorption capacity and mechanism of the sorbent. In this research, the adsorption equilibrium data for silver ions were evaluated using three commonly utilized isotherm models: Langmuir, Freundlich, and Dubinin-Radushkevich. The linear equations for these models are the follows:  
\[\text{Langmuir isotherm: }\text{C}_{\text{e}}/\text{Q}_{\text{e}}=1/\text{K} _{\text{L}}\text{Q}_{0}+\text{C}_{\text{e}}/\text{Q}_{0} \tag{5}\]  
\[\text{Freundlich isotherm: ln}\text{Q}_{\text{e}}=\text{ln}\text{K}_{\text{F}}+(1/ \text{n})\text{ln}\text{C}_{\text{e}} \tag{6}\]  
\[\text{Dubinin-Radushkevich isotherm: ln}\text{Q}_{\text{e}}=\text{ln}\text{Q}_{ \text{m}}-\beta\epsilon^{2} \tag{7}\]  
where Ce is the concentration of metal ions in the equilibrium solution (mg L\({}^{-1}\)); Q\({}_{\text{e}}\) is the amount of Ag\({}^{+}\) adsorbed (mg) per unit mass of adsorbent (g); Q\({}_{0}\) and Q\({}_{\text{m}}\) are the maximum adsorption capacity (mg g\({}^{-1}\)); K\({}_{\text{L}}\) and k\({}_{\text{F}}\) are the Langmuir and Freundlich constants; \(\beta\) is the adsorption energy constant (mol\({}^{2}\) J\({}^{-2}\)); and \(\varepsilon\) is the Polanyi potential, calculated by Equation (8):  
\[\varepsilon=\text{RTln}(1+1/\text{C}_{\text{e}}) \tag{8}\]  
R is the universal gas constant (J mol\({}^{-1}\) K\({}^{-1}\)) and T is the temperature in K.  
The mean adsorption energy E (KJ mol\({}^{-1}\)) can be calculated using the parameter \(\beta\) by Equation (9):  
\[\text{E}=1/(-2\beta)^{1/2} \tag{9}\]  
On the other hand, the Langmuir model assumes monolayer adsorption onto a surface with uniform adsorption sites, where adsorption is limited once the surface is fully covered. It predicts a linear relationship between the adsorbed amount and the equilibrium concentration of the solute. The Freundlich model is an empirical equation describing adsorption onto heterogeneous surfaces, suggesting multilayer adsorption with non-uniform energies on the surface. It describes a non-linear relationship between the adsorbed amount and the equilibrium concentration, reflecting the heterogeneous nature of the adsorbent surface. The Dubinin-Radushkevich model is used to characterize physical adsorption onto porous materials. It relates the logarithm of the equilibrium adsorption capacity to the square of  
Figure 8: Adsorption isotherms. the equilibrium concentration, indicating that the adsorption occurs due to the filling of micropores within the sorbent material. The calculated isotherm constants and correlation coefficients for the Langmuir, Freundlich, and Dubinin-Radushkevich models are presented in Table 3. The data reveal that both the Langmuir and Freundlich models provide good correlations for the adsorption of silver ions on the three biochars. However, based on the correlation coefficient (r2) values, it is evident that the Freundlich model most accurately describes the adsorption process for materials CB (r2 = 0.9992) and ARHB (r2 = 0.9894), indicating multilayer adsorption on heterogeneous surfaces. In contrast, the Langmuir model shows the best fit for material RHB (r2 = 0.9949), which suggests monolayer adsorption on a homogenous surface. The values of \"n\" derived from the Freundlich isotherm model for the investigated biochars range from 1.16 to 2.09, indicating that the adsorption process is favourable for all three materials. The Dubinin-Radushkevich (D-R) isotherm model provides further insights into the adsorption mechanisms through the calculated adsorption energy (E) values. For biochars CB (E = 0.86 kJ/mol) and RHB (E = 0.35 kJ/mol), the low energy values confirm that physical adsorption, driven by Van der Waals forces, is the predominant mechanism.