## 3 Results
### Kinetics Studies  
The study of adsorption kinetics allows us to perceive how fast the process takes place and can indicate its limiting factor. Adsorption kinetics can be represented by a graph of adsorption versus time (Figure 10). This graph forms the basis of kinetic studies, as its shape represents the intrinsic kinetics of the process, which depends on factors such as the type of adsorbent and adsorbate, temperature and pH [36]. The steps for determining the adsorption rate include the diffusion process, chemical reactions and particle diffusion [37]. The most applied models in the study of adsorption kinetics are pseudo-first order and \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{2}{c}{**[PERSON]**} \\ \hline  & \(\mathbf{R^{2}}\) & \(\mathbf{q_{max}}\) & \(\mathbf{K_{L}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{N}\) & \(\mathbf{K_{F}}\) \\  & \(\mathbf{R^{2}}\) & \(\mathbf{(mg\ g^{-1})}\) & \(\mathbf{(L\ mg^{-1})}\) & & & \(\mathbf{(mg/g)/(mg/L)^{n}}\) \\ \hline Walnut shell & 0.996 & 4.82 & 0.121 & 0.942 & 2.11 & 0.781 \\ Chestnut shell & 0.998 & 2.50 & 0.278 & 0.859 & 4.72 & 0.946 \\ Pine wood & 0.994 & 3.45 & 0.063 & 0.936 & 2.41 & 0.449 \\ Burnt pine wood & 0.996 & 2.97 & 0.061 & 0.911 & 2.41 & 0.386 \\ \hline \end{tabular}
\end{table} 
Table 2: Isotherm parameters of nickel adsorption onto the lignocellulosic materials. Figure 8: Langmuir isotherm model for nickel adsorption with nickel concentrations from 5 to 200 mg L\({}^{-1}\) and 100 mg of adsorbent. Figure 9: Freundlich isotherm model for nickel adsorption with nickel concentrations from 5 to 200 mg L\({}^{-1}\) and 100 mg of adsorbent. pseudo-second order [36]. In this case study, the Elovich and intraparticle diffusion models were also tested. The most frequently used kinetics models are pseudo-first order (PFO) and pseudo-second order (PSO) equations [36] since they seem to work very well with the adsorption by lignocellulosic materials. Additionally, Elovich and intraparticle diffusion models were also tested. The results found by plotting pseudo-first order and pseudo-second order models are presented in Table 3 and results for Elovich and intraparticle diffusion models are presented in Table 4.  
The adsorption rate was higher in the beginning of the adsorption process, decreasing afterwards. This means that when all the adsorption sites are free, the adsorption process is faster but when the adsorption sites start to be occupied, the adsorption rate decreases. Nevertheless, the highest adsorption was reached for 1440 min. It was also observed that the removal rate promoted by chestnut shell and walnut shell was higher than the rate promoted by pine wood and burnt pine wood. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Biosorbent**} & \multicolumn{4}{c}{**Elovich Model**} & \multicolumn{4}{c}{**Intraparticle Diffusion Model**} \\ \cline{2-7}  & **A** & **B** & **R2** & **C** & **Kdiff** & **R2** \\  & **(mg-1.min-1)** & **(g-mg-1)** & **R2** & **C** & **(mg/g-min1/2)** & **R2** \\ \hline Walnut shell & \(9.94\times 10^{10}\) & 6.84 & 0.956 & 4.23 & 0.019 & 0.924 \\ Chestnut shell & \(1.05\times 10^{12}\) & 7.67 & 0.990 & 4.37 & 0.021 & 0.942 \\ Pine wood & \(1.00\times 10^{4}\) & 4.44 & 0.905 & 2.99 & 0.035 & 0.978 \\ Burnt pine wood & \(1.09\times 10^{5}\) & 5.59 & 0.908 & 2.84 & 0.027 & 0.970 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters for the kinetic data using Elovich and intraparticle diffusion models. Figure 10: Adsorption efficiency versus time, from 10 to 1440 min by the different adsorbent materials using 25 mg L\({}^{-1}\) nickel solutions and 100 mg of adsorbent.