Atomistic molecular dynamics (MD) simulations are performed in order to derive thermodynamic properties important to understand the extraction of gadolinium (Gd) and uranium dioxide (UO) with dibenzo crown ether (DBCE) in nitrobenzene (NB) and octanol (OCT) solvents. The effect of polystyrene graft length, on DBCE, on the binding behavior of Gd and UO is investigated for the first time. Our simulation results demonstrate that the binding of Gd and UO onto the oxygens of crown ethers is favorable for polystyrene grafted crown ether in the organic solvents OCT and NB. The metal ion binding free energy (ΔG) in different solvent environments is calculated using the thermodynamic integration (TI) method. ΔG becomes more favorable in both solvents, NB and OCT, with an increase in the polystyrene monomer length. The metal ion transferability from an aqueous phase to an organic phase is estimated by calculating transfer free-energy calculations (ΔG). ΔG is significantly favorable for both Gd and UO for the transfer from the aqueous phase to the organic phase (i.e., NB and OCT) via ion-complexation to DBCE with an increase in polystyrene length. The partition coefficient (log P) values for Gd and UO show a 5-fold increase in separation capacity with polystyrene grafted DBCE. We corroborate the observed behavior by further analyzing the structural and dynamical properties of the ions in different phases.

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All atom molecular dynamics simulations and experiments were performed to understand the adsorption behavior of gadolinium (Gd 3+ ) ion on the crown ethers grafted polystyrene (PS) surface. Two different types of crown ethers, viz., dibenzo crown ether (DBCE) and dicyclo hexano crown ether (DCHCE), were grafted separately on the PS surface to understand the adsorption behavior. We investigate the roles of Gd 3+ ion concentration and grafting density (ρ s ) of the crown ether on the adsorption behavior of Gd 3+ ion on the PS surface. The adsorption of Gd 3+ shows an increasing trend with increasing salt concentration, for all cases of crown ether grafting densities. The adsorption behavior follows the Langmuir isotherm model. The maximum amount of Gd 3+ ion adsorption was observed to be 1.83 mg/g for DBCE and 2.02 mg/g for DCHCE at ρ s = 2.07 mol/nm 2 . The maximum amount of Gd 3+ ion adsorption on DBCE coated PS beads, in batch experiments, was found to be 1.76 mg/g, which is in good agreement with the theoretical results. The increase in ρ s from 0.25 to 2.07 mol/nm 2 shows an increase in the q max value by ∼422% and 329% for DBCE and DCHCE, respectively. The optimum value of the crown ether grafting density is found to be 1.25 mol/nm 2 , beyond which the q max saturates. We further investigate the dynamics of the Gd 3+ ion by evaluating the diffusion coefficient (D) and mean residence time (τ). It was found that D decreases with increasing salt concentration for both DBCE and DCHCE. On the contrary, as expected, the τ value of Gd 3+ increases with an increase in salt concentration. Overall, a 3-fold increase in τ was seen with increasing salt concentration. The potential of mean force analysis using umbrella sampling reveals favorable binding energy for higher grafting density of DCHCE compared to that of DBCE.

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