## 2 Results and Discussion
### Cd\({}^{2+}\) Adsorption with Biochar
#### 2.3.3 Cd\({}^{2+}\) Adsorption Kinetics for Both Types of Biochar Samples  
Figure 5 shows the results of the Cd\({}^{2+}\) adsorption kinetics for both types of biochar samples obtained at various pyrolysis temperatures. The Cd\({}^{2+}\) adsorption trends were consistent, regardless of the type of biochar, with initial rapid adsorption followed by decreased adsorption, whose equilibrium was reached after 6 h. This was due to the mass-transfer driving force induced by the Cd\({}^{2+}\) concentration gradient existing between the liquid and solid phase (i.e., the solution and the biochar), and also the adsorption sites available on the biochar surface [38]. At the start of adsorption, the Cd\({}^{2+}\) concentration gradient between the two phases was larger, resulting in a greater driving force for mass transfer and a greater adsorption rate. As the adsorption time increased, the Cd\({}^{2+}\) concentration gradient decreased, and the adsorption sites on the biochar surface became saturated, resulting in intragranular diffusion becoming dominant. This intragranular adsorption rate was relatively slower. Therefore, the adsorption rate decreased and tended towards the adsorption equilibrium [39]. The higher the pyrolysis temperature, the longer the saturation time became, and the larger the adsorbent amount became, shortening the time required to reach said equilibrium. As such, the system with sample RH700 reached the equilibrium in less than 1 h, while sample CS700 achieved 99.32% of Cd\({}^{2+}\) removal within 0.5 h. This was a direct consequence of the increased specific surface area of the biochar with increasing pyrolysis temperature, pH, and the number of surface charges [29]. Figure 4: Effects of the solution pH on Cd\({}^{2+}\) removal. Notes: RH300, RH400, RE500, RH600, and RH700 indicate that rice husk were pyrolyzed at 300, 400, 500, 600 and 700 \({}^{\circ}\)C, respectively; CS300, CS400, CS500, CS600, and CS700 indicate that cotton straw were pyrolyzed at 300, 400, 500, 600 and 700 \({}^{\circ}\)C, respectively. In order to better evaluate the rate-limiting step and mechanism during the adsorption process, we used pseudo-first-order kinetics (Figure 6) and pseudo-second-order kinetics (Figure 7) models to fit the data (Table 4). From the results, we can see that the pseudo-second-order kinetics model provided a better fit, with a coefficient of determination, \(R^{2}\geq 0.990\). This model, therefore, better reflected the Cd\({}^{2+}\) adsorption process for the rice-husk and cotton-straw biochar. In the reaction rate, the adsorption rate constant (\(K_{2}\)) indicates the speed of the adsorption process. The higher the \(K_{2}\) value gets, the faster the adsorption becomes, and the shorter the time required to reach the equilibrium. With increasing pyrolysis temperature, the adsorption rate for the rice-husk and cotton-straw biochar gradually increased. However, the \(K_{2}\) of biochar produced at 700 \({}^{\circ}\)C was smaller than expected. Biochar made from both materials at 600 \({}^{\circ}\)C afforded the maximum adsorption rate, with RH600 and CS600 values of 9.09 \(\times\) 10\({}^{-4}\) mg\(\cdot\)g\({}^{-1}\cdot\)h\({}^{-1}\) and 7.58 \(\times\) 10\({}^{-4}\) mg\(\cdot\)g\({}^{-1}\cdot\)h\({}^{-1}\), respectively. From Table 4, the amount of Cd\({}^{2+}\) (\(q_{\rm m}\)) adsorbed with rice husk biochar following the second-order kinetics model was highest for sample RH300 at 103.13 mg\(\cdot\)g\({}^{-1}\), although it was only 22.62 mg\(\cdot\)g\({}^{-1}\) for RH600. In contrast, the lowest amount of Cd\({}^{2+}\) adsorbed by the cotton-straw biochar was 110.29 mg\(\cdot\)g\({}^{-1}\) for sample CS700. Figure 5: Effect of various adsorption times on Cd\({}^{2+}\) removal by both sets of biochar samples. Notes: RH300, RH400, RE500, RH600, and RH700 indicate that rice husk were pyrolyzed at 300, 400, 500, 600 and 700 \({}^{\circ}\)C, respectively; CS300, CS400, CS500, CS600, and CS700 indicate that cotton straw were pyrolyzed at 300, 400, 500, 600 and 700 \({}^{\circ}\)C, respectively.