## 3 Results and Discussion
### Influence of Soil Characteristics on Plant Uptake
It is important to underline that no thermodynamic value can be attributed to the parameters of the Freundlich-like equation, which can be used exclusively as an operational tool to relate plant uptake and tungsten soil concentration. In broad terms, similarly to the Freundlich equation, \(K\) can be considered as the uptake capacity (a larger \(K\) indicates a greater uptake). The Freundlich parameters (Table 4) can be estimated from the linearized form of the equation (2):  
\[\log q=logK_{f}+\frac{1}{n}\log C \tag{2}\]  
By operationally using the Freundlich model parameters, we can infer that the uptake capacity increased when the value of K was increased. As expected, the results from this model confirm that the uptake always increased with increasing soil pH due to the alkaline pH of soil influencing the desorption of tungsten from soil surfaces, and its release in soil solution. The coefficient 1/n has been interpreted as an index of a plant's ability to control metal accumulation [47]. A value of less than 1 of the coefficient 1/n is considered an index of active tungsten uptake, whereas higher values of this index suggest the reduced ability of the plant to control the tungsten uptake. The obtained data show a different behavior of this index among soils and between the roots and shoot uptake of the plants. The correlation between the concentrations calculated by the model and measured in the shoots was high, with R\({}^{2}\) values ranging from 0.922 (soil A) to 0.942 (soil C). Similar results were obtained for the root portion with R\({}^{2}\) values ranging from 0.896 (soil A) to 0.944 (soil C). The same Freundlich-like model was also applied by correlating the amount absorbed by the plants with tungsten concentration in soil solution. This amount is determined by the retention/release processes, which influence the distribution of tungsten between the solid and liquid phases, and thus regulate the amount of tungsten in the soil solution from which the plants absorb the element. The results are reported in Table 5 for shoots and roots, respectively. Also in this case, a Freundlich-like equation can be used to describe the pattern of plant uptake from soil solution with correlation coefficients higher than those of uptake vs. total content (see Table 4) \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Soil**} & \multicolumn{3}{c}{**Shoots**} & \multicolumn{3}{c}{**Roots**} \\ \cline{2-7}  & **Log K** & **1/n** & **R\({}^{2}\)** & **Log K** & **1/n** & **R\({}^{2}\)** \\ \hline A & \(-2.17\) & \(1.26\) & \(0.922\) & \(-0.718\) & \(0.791\) & \(0.896\) \\ B & \(-1.48\) & \(1.15\) & \(0.932\) & \(-0.5357\) & \(0.933\) & \(0.937\) \\ C & \(-0.522\) & \(0.936\) & \(0.942\) & \(-0.4886\) & \(1.24\) & \(0.944\) \\ \hline \end{tabular}
\end{table} 
Table 4: Relationship between tungsten concentration in shoots and roots and tungsten concentration in soil. Parameters of the Freundlich-like model. with R\({}^{2}\) values ranging from 0.961 (soil B) to 0.973 (soil C); whereas, for the root portion, R\({}^{2}\) values range from 0.959 (soil B) to 0.988 (soil A). The K and 1/n coefficients changed, but the trend was similar to the uptake vs. total concentration, with the highest K value in soil C, and the lowest in soil A. We have to consider that soil pH exerts a great influence on W solubility due to increased sorption under acidic conditions [57], and this parameter appears to mainly determine plant uptake. Although speciation of tungsten in soil is of great importance [9; 58], especially for the polymerization phenomena [59; 60], we decided to evaluate the trend of the tungsten uptake using a model as simple as possible. This approach of course can only be considered as a preliminary step in developing mechanistic models. More experiments need to be performed by varying plant species and using soils with different characteristics to improve the modeling of tungsten uptake by plants, or to develop more complex models.