Multiscale modelling of solvent phases for solvent extraction – MULTISEPAR

The strategy mainly combines three scales of description used for the extraction of lanthanides by malonamides: (1) Firstly, molecular dynamics simulations, which alone can deal with the elementary act and atomic phenomena such as metal complexation. However, given their computational cost, they can only be used to study systems of limited size over very short timescales, which do not cover all the phenomena involved. Other complementary methods on a larger scale have therefore been proposed (2) Brownian dynamics modelling in which the metal and its environment are considered in a similar way to inverted micelles, whether charged or not. In particular, this makes it possible to look at the dynamics and charging phenomena in these systems (3) Finally, an approach using random Gaussian fields and the theory of microemulsions. The organic phases are represented here as a sort of water/oil mixture made thermodynamically stable by the presence of extractants.

The important point is the link between the different scales: the molecular part not only allows us to parameterise but also to justify the other scales of description. This work is also validated by the experimental studies recently carried out on these reference systems, which allow a direct comparison of numerous quantities.

The molecular simulations carried out on the organic phases used a graph theory approach to study speciation, enabling us to determine the chemistry of the aggregates present. A thermodynamic model was proposed. The equilibrium constants obtained showed a progressive structuring of the solution with concentration. This structuring is more significant in the presence of salt, and the structure obtained indicates micellar behaviour typical of microemulsions. The curvature parameters could thus be calculated for biased simulations or using fluctuation theory. The idea is that the spontaneous shape of the extractants controls the nature of the chemical species present.

A Brownian dynamics code that calculates the structure of the solutions from a model potential has been developed. The thermodynamic properties of equilibrium have thus been evaluated. In particular, the osmotic coefficient, which allows comparison with experimental measurements of vapour pressure, was modelled. The study of transport phenomena showed that even if the species were neutral, they could exchange their ions, which explains the conductivity of the solvent phases. By generalising Born's approach for organic phases, we can describe the conductivity of the suspension by modelling both the diffusion of charged species and the exchange of ions between aggregates.

Since this Brownian model is not satisfactory at high concentrations, since larger structures (cylinders, tubes, etc.) appear and control the process, we have proposed another type of model based on the theory of microemulsions. Based on a random Gaussian field, it can be used to model much more complex structures. This microemulsion model has made it possible to describe behaviours that are known experimentally, such as the appearance of a critical aggregation concentration that enables ion transfer, and extraction in the form of a Langmuir isotherm linked to equilibrium experiments.

This project has made it possible, for the first time, to propose a consistent vision of liquid-liquid extraction on all scales, focusing on the case of rare earths with a malonamide extractant. Calculation codes have been proposed and implemented to represent this process in a more precise and general way than more traditional approaches based simply on simple chemical equilibria.

Two types of prospects are envisaged:

- In terms of methodology, some important phenomena could not be modelled. In particular, the appearance of the third phase needs to be predicted, as this phenomenon limits the process by destabilising the solvent phase at high concentration. This will require modelling the interactions between the mesostructures. It is therefore planned to use biased simulation to model these supramolecular forces in order to predict this demixing phenomenon. The microemulsion model has had very promising initial success in simple cases, and will need to be extended to more complex situations involving several metal ions, for example. Direct molecular calculation of extraction by simplifying large-scale structures is also desirable and is currently under development.

- Other prospects involve extending the processes described by this approach. Recycling can involve different solvents often described as green, such as DES (deep eutectic solvents) or ionic liquids. Work is in progress on this subject. A similar modelling strategy is also being studied to predict the other method used to separate metals, flotation. Although in this case the proposed strategy cannot be directly applied, since it involves a liquid/air interface and not a liquid/liquid one, the physico-chemistry remains the same and in particular the decomposition of the scales, which must also be taken into account.

5 published articles

[1]
«Liquid/liquid interface in periodic boundary condition«
M. Vatin, M. Duvail, Ph. Guilbaud, J.-F. Dufrêche
Phys. Chem. Chem. Phys. 23, 1178 – 1187 (2021)

[2]
«Thermodynamics of Malonamide Aggregation Deduced from Molecular Dynamics Simulations«
M. Vatin, M. Duvail, Ph. Guilbaud, J.-F. Dufrêche
J. Phys. Chem. B 125 (13), 3409 – 3418 (2021)

[3]
«Bending: from thin interfaces to molecular films in microemulsions«
J.-F. Dufrêche and Th. Zemb
Curr. Opin. Colloid Interface Sci. 49, 133 – 147 (2020)

[4]
«How Acidity Rules Synergism and Antagonism in Liquid–Liquid Extraction by Lipophilic Extractants — Part I: Determination of Nanostructures and Free Energies of Transfer«
S. Dourdain, M. Špadina, J. Rey, K. Bohinc, S. Pellet-Rostaing, Jean-François Dufrêche, T. Zemb
Solv. Ext. Ion Exch. ASAP (2021). DOI: 10.1080/07366299.2021.1899606

[5]
«How acidity rules synergism and antagonism in liquid–liquid extraction by lipophilic extractants — Part II: application of the ienaic modelling«
M. Špadina, S. Dourdain, J. Rey, K. Bohinc, S. Pellet-Rostaing, Jean-François Dufrêche, T. Zemb
Solv. Ext. Ion Exch. ASAP (2021). DOI: 10.1080/07366299.2021.1899614

The ANR MULTISEPAR project aims to model rare earth (lanthanide) separation processes used in hydrometallurgy and for recycling. More specifically, it will focus on the solvent phase of liquid-liquid extraction processes, the modelling of which being currently at a very early stage. The multi-scale approach will be based on three complementary levels of description. First, at the atomic level, molecular dynamics simulations will calculate the structure and speciation in these solvent phases. The molecular interaction potential that we will use here has recently been validated from ab initio simulations by comparison with spectroscopy experiments. An umbrella sampling methodology will calculate the forces between solutes. The purpose of this step will be both the determination of the physico-chemical ingredients required for solvent phase modelling and also the calculation of the mesoscopic properties used by the other more macroscopic description scales. In another level of descriptions, mesoscopic Brownian simulations will be performed to calculate the effects at greater distance. Based on molecular simulation data (effective interaction potential and mobilities), either Brownian dynamics simulations or Multiparticle Collision dynamics simulations will be used to access the largest scales. The solutes activity coefficients and the stability of the solvent phase can thus be calculated. At the dynamic level, solute transport (diffusion and electrical conductivity) as well as viscosity will also be studied because they drive many industrial processes. As both experiments and molecular simulations show that in some cases solutes decompose poorly into independent particles but rather form a continuous network of hydrophilic parts in the solvent phase, we will also propose a second mesoscopic model to describe these solvent phases, this time based on a microemulsion model. Using a Gaussian random field methodology, we will propose a code representing the Gibbs energy of the solvent phase, which will make it possible to predict both the structure and the extraction properties. The fundamental quantities of this level of description will be here the properties of curvature (spontaneous curvature and rigidity) due to the extractants which will be deduced from the molecular simulations. The study of extraction as a function of the concentrations in the aqueous phase and of the extractant concentration will validate this methodology. We believe that this calculation will be a success if this microemulsion model can represent extraction equilibria with a much smaller set of parameters than traditional models based on multiple chemical equilibria between species. Thus, this project on lanthanide extraction could lead to a model that will be implemented in chemical engineering codes describing this process. We hope that through this multiscale project and the extensive use of numerical computing resources a new image of extraction mechanism will emerge from molecular modelling and that it will be able to bridge the gap to the macroscopic descriptions of this method of separation chemistry.