The recycling of rare earth elements and nuclear waste management based on solvent extraction is important for the success of present and future carbon-free technologies. It is crucial to identify and to investigate the motors of selectivity and efficiency of the related two-phasic hydrometallurgical approaches [1,2]. The activity in both phases is one of the decisive factors for the cation extraction. Understanding and quantifying this activity is therefore a key point for predicting the behavior of the extraction systems. Herein, a new theoretical method emulating osmotic equilibria and activities for concentrated solutions is presented, where a bulk liquid and its corresponding vapor phase are simulated with molecular dynamics with polarizable force fields[3,4].
Time-averaged number density profiles based on the resulting trajectories provide the amount of evaporated molecules present in the vapor phase and consequently the vapor phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at a certain solute concentration with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient and the corresponding Gibbs-Duhem relation the activity coefficient of the solute is calculated by fitting the osmotic coefficient of the solvent. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This allows a precise control of the error of this method.
This method was applied on a variety of different systems such as aqueous electrolyte solutions of different compositions like nitrate salts of rare earth elements and other metallic elements, organic solvent phases, and alcohol-water mixtures. The densities of the liquid, the solvent activitiy, and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions [5]. Density profiles of the liquid-vapor interface at different concentrations provide a detailed insight on the spatial distribution of all compounds. Radial distribution functions and the corresponding coordination numbers yield the hydration properties of the compounds involved at different solute-solvent ratios. Future research will cover mixtures of different cations of nitrate salts in aqueous solution and the activities of organic solvents for understanding the driving forces of hydrometallurgical separation processes.
Figure 1: Schematic representation of a production box representing an aqueous Dysprosium nitrate solution (1.0 mol kg-1) in equilibrium with water vapor.
[1] J.-F. Dufrêche, and Th. Zemb., Chem. Phys. Lett. 622, 45 – 49 (2015).
[2] M. Bley, B. Siboulet, A. Karmakar, Th. Zemb, and J.-F. Dufrêche., J. Colloid Interface Sci. 479, 106 – 114 (2016).
[3] L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991)
[4] M. Duvail, P. Guilbaud, Phys. Chem. Chem. Phys., 13, 5840-5847 (2011)
[5] J. A. Rard, F. H. Spedding, J. Chem. Eng. Data, 26, 391-395 (1981)
