The concentrations of Cr, Cu, Zn, and As were quantified in the digested samples using an ICP-MS. The results were expressed in mg/kg of dry matter. Concentrations were calculated according to the following equation:
Cmesured=(Vfinal×Csolurion)/msample (1)
Where, Csolurion is the concentration measured by ICPMS (mg/l), Vfinal is the final volume after digestion (L), and msample is the mass of the dry digested sample (kg).
Calculation of bio concentration factors: Bio concentration factors were calculated for each metal using the following formula:
BCF=CMP/CMS (2)
Where, CMP is the concentration of the metal in plant tissues (mg/kg dry weight), and CMS is the total concentration of the metal in the soil (mg/kg dry weight).
Kinetic modelling: First-order model fitting: This model assumes that the adsorption rate is proportional to the residual concentration of available sites. Using the experimental data and the linearized kinetic equation:
Log (qe-qt)=log (qe)-k1/2.303-t (3)
Pseudo-second-order model fitting: The pseudo-second-order model is based on the assumption that adsorption is governed by chemical interactions (covalent or surface bonding). The linear form of the equation is:
t/qt =1/(k2qc2 )+t/qe (4)
Adsorption isotherm modelling: Langmuir model: This model assumes monomolecular adsorption on a homogeneous surface with a defined maximum capacity:
Ce/qe=1/(KLqmax )+Ce/qmax (5)
Where qe is the amount adsorbed at equilibrium (mg/g), Ce is the equilibrium concentration in solution (mg/g), qmax is the maximum adsorption capacity (mg/g), and KL is the Langmuir constant (l/mg). Freundlich model: This empirical model assumes multilayer adsorption on a heterogeneous surface:
log(qe)=log(KF+1/n log(Ce) (6)
Where KF is the adsorption capacity constant (l/mg), and n is the adsorption intensity (adsorption is favourable when 1<n<10).
Temkin model: This model accounts for the linear decrease in adsorption heat as surface coverage increases:
qe=BlnA+BlnCe avec B=RT/b (7)
Where A is the Temkin constant related to adsorption capacity, b is the constant related to adsorption heat, R is the universal gas constant (8.314 J/mol·K), and T is the absolute temperature (K).
Thermodynamic modelling: Thermodynamic parameters were calculated from the equilibrium constant Kc, determined at different temperatures (298, 308, and 318 K), using the following relationships:
Equilibrium constant: Ke=qe/Ce (8)
Where qe is the amount adsorbed at equilibrium (mg/g), Ce is the residual concentration in solution (mg/l).
Van’t Hoff equation: lnKC=-(ΔH°)/RT+(ΔS°)/R (9) (Linear equation of the form y=ax+b)
Where R is the universal gas constant (8.314 J/mol·K) and T is the absolute temperature (K).
Gibbs free energy: ΔG°=ΔH°-TΔS°=-RTlnKc (10)