Effect of long-range interactions on ion equilibria in liquid–liquid extraction

Molecular Forces in Liquid-Liquid Extraction

The phase transfer of ions is driven by gradients of chemical potentials rather than concentrations alone (i.e., by both the molecular forces and entropy). Extraction is a combination of high-energy interactions that correspond to short-range forces in the first solvation shell such as ion pairing or complexation forces, with supramolecular and nanoscale organization. While the latter are similar to the long-range solvent-averaged interactions in the colloidal world, in solvent extraction they are associated with lower characteristic lengths of the nanometric domain. Modeling of such complex systems is especially complicated because the two domains are coupled, whereas the resulting free energy of extraction is around k_BT to guarantee the reversibility of the practical process. Nevertheless, quantification is possible by considering a partitioning of space among the polar cores, interfacial film, and solvent. The resulting free energy of transfer can be rationalized by utilizing a combination of terms which represent strong complexation energies, counterbalanced by various entropic effects and the confinement of polar solutes in nanodomains dispersed in the diluent, together with interfacial extractant terms. We describe here this ienaics approach in the context of solvent extraction systems; it can also be applied to further complex ionic systems, such as membranes and biological interfaces.

Impact of Water Extraction on Malonamide Aggregation: A Molecular Dynamics and Graph Theoretic Approach

Solution structure in liquid-liquid extraction affects the efficacy of separation; however, even for simplified organic phases, structural characterization and attribution of aggregation to intermolecular interactions are fundamental challenges. We investigate water uptake into organic phases for two malonamides commonly applied to actinide and lanthanide separations. Extracted water induces reorganization of the amphiphilic extractant molecules, although we find this rearrangement is not strongly manifested in small-angle X-ray scattering making it challenging to probe without methods such as atomistic simulation. Using a graph theoretic approach to define hydrogen bonded water/malonamide aggregates from molecular dynamics simulations, we find evidence of a characteristic aggregate size by water number that results from geometric accommodation of the surrounding malonamide molecules. This implies a degree of size selectivity inherent to these water-in-oil aggregates. Conversely, we find no evidence of a characteristic size of the aggregates with respect to their malonamide number. By defining a separate graphical representation of self-association of the amphiphilic malonamides, we quantify how water affects the local and nonlocal topology of the malonamide network, providing a basis for characterization of the structure and impact of polar solutes in increasingly complex organic phases.

Origins of Clustering of Metalate-Extractant Complexes in Liquid-Liquid Extraction

Effective and energy-efficient separation of precious and rare metals is very important for a variety of advanced technologies. Liquid-liquid extraction (LLE) is a relatively less energy intensive separation technique, widely used in separation of lanthanides, actinides, and platinum group metals (PGMs). In LLE, the distribution of an ion between an aqueous phase and an organic phase is determined by enthalpic (coordination interactions) and entropic (fluid reorganization) contributions. The molecular scale details of these contributions are not well understood. Preferential extraction of an ion from the aqueous phase is usually correlated with the resulting fluid organization in the organic phase, as the longer-range organization increases with metal loading. However, it is difficult to determine the extent to which organic phase fluid organization causes, or is caused by, metal loading. In this study, we demonstrate that two systems with the same metal loading may impart very different organic phase organizations and investigate the underlying molecular scale mechanism. Small-angle X-ray scattering shows that the structure of a quaternary ammonium extractant solution in toluene is affected differently by the extraction of two metalates (octahedral PtCl₆^2- and square-planar PdCl₄^2-), although both are completely transferred into the organic phase. The aggregates formed by the metalate-extractant complexes (approximated as reverse micelles) exhibit a more long-range order (clustering) with PtCl₆^2- compared to that with PdCl₄^2-. Vibrational sum frequency generation spectroscopy and complementary atomistic molecular dynamics simulations on model Langmuir monolayers indicate that the two metalates affect the interfacial hydration structures differently. Furthermore, the interfacial hydration is correlated with water extraction into the organic phase. These results support a strong relationship between the organic phase organizational structure and the different local hydration present within the aggregates of metalate-extractant complexes, which is independent of metalate concentration.

Ion-specific clustering of metal-amphiphile complexes in rare earth separations

The nanoscale structure of a complex fluid can play a major role in the selective adsorption of ions at the nanometric interfaces, which is crucial in industrial and technological applications. Here we study the effect of anions and lanthanide ions on the nanoscale structure of a complex fluid formed by metal-amphiphile complexes, using small angle X-ray scattering. The nano- and mesoscale structures we observed can be directly connected to the preferential transfer of light (La and Nd) or heavy (Er and Lu) lanthanides into the complex fluid from an aqueous solution. While toluene-based complex fluids containing trioctylmethylammonium-nitrate (TOMA-nitrate) always show the same mesoscale hierarchical structure regardless of lanthanide loading and prefer light lanthanides, those containing TOMA-thiocyanate show an evolution of the mesoscale structure as a function of the lanthanide loading and prefer heavy lanthanides. The hierarchical structure indicates the presence of attractive interactions between ion-amphiphile aggregates, causing them to form clusters. A clustering model that accounts for the hard sphere repulsions and short-range attractions between the aggregates has been adapted to model the X-ray scattering results. The new model successfully describes the nanoscale structure and helps in understanding the mechanisms responsible for amphiphile assisted ion transport between immiscible liquids. Accordingly, our results imply different mechanisms of lanthanide transport depending on the anion present in the complex fluid and correspond with anion-dependent trends in rare earth separations.

Synergistic Solvent Extraction Is Driven by Entropy

In solvent extraction, the self-assembly of amphiphilic molecules into an organized structure is the phenomenon responsible for the transfer of the metal ion from the aqueous phase to the organic solvent. Despite their significance for chemical engineering and separation science, the forces driving the solute transfer are not fully understood. Instead of assuming the simple complexation reaction with predefined stoichiometry, we model synergistic extraction systems by a colloidal approach that explicitly takes into account the self-assembly resulting from the amphiphilic nature of the extractants. Contrary to the current paradigm of simple stoichiometry behind liquid-liquid extraction, there is a severe polydispersity of aggregates completely different in compositions, but similar in the free energy. This variety of structures on the nanoscale is responsible for the synergistic transfer of ions to the organic phase. Synergy can be understood as a reciprocal effect of chelation: it enhances extraction because it increases the configurational entropy of an extracted ion. The global overview of the complex nature of a synergistic mixture shows different regimes in self-assembly, and thus in the extraction efficiency, which can be tuned with respect to the green chemistry aspect.

Colloidal Model for the Prediction of the Extraction of Rare Earths Assisted by the Acidic Extractant

We propose the statistical thermodynamic model for the prediction of the liquid-liquid extraction efficiency in the case of rare-earth metal cations using the common bis(2-ethyl-hexyl)phosphoric acid (HDEHP) extractant. In this soft matter-based approach, the solutes are modeled as colloids. The leading terms in free-energy representation account for: the complexation, the formation of a highly curved extractant film, lateral interactions between the different extractant head groups in the film, configurational entropy of ions and water molecules, the dimerization, and the acidity of the HDEHP extractant. We provided a full framework for the multicomponent study of extraction systems. By taking into account these different contributions, we are able to establish the relation between the extraction and general complexation at any pH in the system. This further allowed us to rationalize the well-defined optimum in the extraction engineering design. Calculations show that there are multiple extraction regimes even in the case of lanthanide/acid system only. Each of these regimes is controlled by the formation of different species in the solvent phase, ranging from multiple metal cation-filled aggregates (at the low acid concentrations in the aqueous phase), to the pure acid-filled aggregates (at the high acid concentrations in the aqueous phase). These results are contrary to a long-standing opinion that liquid-liquid extraction can be modeled with only a few species. Therefore, a traditional multiple equilibria approach is abandoned in favor of polydisperse spherical aggregate formations, which are in dynamic equilibrium.

Multicomponent Model for the Prediction of Nuclear Waste/Rare-Earth Extraction Processes

We develop a minimal model for the prediction of solvent extraction. We consider a rare earth extraction system for which the solvent phase is similar to water-poor microemulsions. All physical molecular quantities used in the calculation can be measured separately. The model takes into account competition complexation, mixing entropy of complexed species, differences of salt concentrations between the two phases, and the surfactant nature of extractant molecules. We consider the practical case where rare earths are extracted from iron nitrates in the presence of acids with a common neutral complexing extractant. The solvent wetting of the reverse aggregates is taken into account via the spontaneous packing. All the water-in-oil reverse aggregates are supposed to be spherical on average. The minimal model captures several features observed in practice: reverse aggregates with different water and extractant content coexist dynamically with monomeric extractant molecules at and above a critical aggregate concentration (CAC). The CAC decreases upon the addition of electrolytes in the aqueous phase. The free energy of transfer of an ion to the organic phase is lower than the driving complexation. The commonly observed log-log relation used to determine the apparent stoichiometry of complexation is valid as a guideline but should be used with care. The results point to the fact that stoichiometry, as well as the probabilities of a particular aggregate, is dependent on the composition of the entire system, namely the extractant and the target solutes' concentrations. Moreover, the experimentally observed dependence of the extraction efficiency on branching of the extractant chains in a given solvent can be quantified. The evolution of the distribution coefficient of particular rare earth, acid, or other different metallic cations can be studied as a function of initial extractant concentration through the whole region that is typically used by chemical engineers. For every chemical species involved in the calculation, the model is able to predict the exact equilibrium concentration in both the aqueous and the solvent phases at a given thermodynamic temperature.

Nanometric Surface Oscillation Spectroscopy of Water-Poor Microemulsions

Selectively exchanging metal complexes between emulsified water-poor microemulsions and concentrated solutions of mixed electrolytes is the core technology for strategic metal recycling. Nanostructuration triggered by solutes present in the organic phase is understood, but little is known about fluctuations of the microemulsion-water interface. We use here a modified version of an optoelectric device initially designed for air bubbles, in order to evidence resonant electrically induced surface waves of an oily droplet suspended in an aqueous phase. Resonant waves of nanometer amplitude of a millimeter-sized microemulsion droplet containing a common ion-specific extractant diluted by dodecane and suspended in a solution of rare earth nitrate are evidenced for the first time with low excitation fields (5 V/cm). From variation of the surface wave spectrum with rare earth concentration, we evidence uptake of rare-earth ions at the interface and at higher concentration the formation of a thin "crust" of liquid crystal forming at unusually low concentration, indicative of a surface induced phase transition. The effect of the liquid crystal structure on the resonance spectrum is backed up by a model, which is used to estimate crust thickness.

Outer-Sphere Water Clusters Tune the Lanthanide Selectivity of Diglycolamides

Fundamental understanding of the selective recognition and separation of f-block metal ions by chelating agents is of crucial importance for advancing sustainable energy systems. Current investigations in this area are mostly focused on the study of inner-sphere interactions between metal ions and donor groups of ligands, while the effects on the selectivity resulting from molecular interactions in the outer-sphere region have been largely overlooked. Herein, we explore the fundamental origins of the selectivity of the solvating extractant N,N,N',N'-tetraoctyl diglycolamide (TODGA) for adjacent lanthanides in a liquid-liquid extraction system, which is of relevance to nuclear fuel reprocessing and rare-earth refining technologies. Complementary investigations integrating distribution studies, quantum mechanical calculations, and classical molecular dynamics simulations establish a relationship between coextracted water and lanthanide extraction by TODGA across the series, pointing to the importance of the hydrogen-bonding interactions between outer-sphere nitrate ions and water clusters in a nonpolar environment. Our findings have significant implications for the design of novel efficient separation systems and processes, emphasizing the importance of tuning both inner- and outer-sphere interactions to obtain total control over selectivity in the biphasic extraction of lanthanides.

Thermodynamic Description of Synergy in Solvent Extraction: II Thermodynamic Balance of Driving Forces Implied in Synergistic Extraction

In the second part of this study, we analyze the free energy of transfer in the case of synergistic solvent extraction. This free energy of the transfer of an ion in dynamic equilibrium between two coexisting phases is decomposed into four driving forces combining long-range interactions with the classical complexation free energy associated with the nearest neighbors. We demonstrate how the organometallic complexation is counterbalanced by the cost in free energy related to structural change on the colloidal scale in the solvent phase. These molecular forces of synergistic extraction are driven not only by the entropic term associated with the tight packing of electrolytes in the solvent and by the free energy cost of coextracting water toward the hydrophilic core of the reverse aggregates present but also by the entropic costs in the formation of the reverse aggregate and by the interfacial bending energy of the extractant molecules packed around the extracted species. Considering the sum of the terms, we can rationalize the synergy observed, which cannot be explained by classical extraction modeling. We show an industrial synergistic mixture combining an amide and a phosphate complexing site, where the most efficient/selective mixture is observed for a minimal bending energy and maximal complexation energy.

Thermodynamic Description of Synergy in Solvent Extraction: I. Enthalpy of Mixing at the Origin of Synergistic Aggregation

Revisiting aggregation of extractant molecules into water-poor mixed reverse micelles, we propose in this paper to identify the thermodynamic origins of synergy in solvent extraction. Considering that synergistic extraction properties of a mixture of extractants is related to synergistic aggregation of this mixture, we identify here the elements at the origin of synergy by independently investigating the effect of water, acid, and extracted cations. Thermodynamic equations are proposed to describe synergistic aggregation in the peculiar case of synergistic solvent extraction by evaluating critical aggregation concentration (CAC) as well as specific interactions between extractants due to the presence of water, acid and cations. Distribution of two extractant molecules in the free extractants and in reverse micelles was assessed, leading to an estimation of the in-plane interaction parameter between extractants in the aggregates as introduced by Bergström and Eriksson ( Bergström, M.; Eriksson, J. C. A Theoretical Analysis of Synergistic Effects in Mixed Surfactant Systems . Langmuir 2000 , 16 , 7173 - 7181 ). Based on this model, we study the N,N'-dimethyl-N,N'-dioctylhexylethoxymalonamide (DMDOHEMA) and di(2-ethylexyl) phosphoric acid (HDEHP) mixture and show that adding nitric acid enhances synergistic aggregation at the equimolar ratio of the two extractants and that this configuration can be related to a favored enthalpy of mixing.

Solvent Extraction: Structure of the Liquid-Liquid Interface Containing a Diamide Ligand

Knowledge of the (supra)molecular structure of an interface that contains amphiphilic ligand molecules is necessary for a full understanding of ion transfer during solvent extraction. Even if molecular dynamics already yield some insight in the molecular configurations in solution, hardly any experimental data giving access to distributions of both extractant molecules and ions at the liquid-liquid interface exist. Here, the combined application of X-ray and neutron reflectivity measurements represents a key milestone in the deduction of the interfacial structure and potential with respect to two different lipophilic ligands. Indeed, we show for the first time that hard trivalent cations can be repelled or attracted by the extractant-enriched interface according to the nature of the ligand.

Synergy in Extraction System Chemistry: Combining Configurational Entropy, Film Bending, and Perturbation of Complexation

Iron-uranium selectivity in liquid-liquid extraction depends not only on the mole fraction of extractants, but also on the nature of the diluent used, even if the diluent has no complexation interaction with the extracted ions. Modeling strong nonlinearity is difficult to parametrize without a large number of parameters, interpreted as "apparent constants". We determine in this paper the synergy curve versus mole fraction of HDEHP-TOPO (di(2-ethylexyl) phosphoric acid/tri-n-octyl phosphine oxide) and compare the free energy of aggregation to the free energy of extraction in various diluents. There is always a concomitant maximum of the two quantities, but with a gradual influence on intensity. The diluent is wetting the chains of the reverse aggregates responsible of the extraction. We show here that the intensity of the unexplained synergy peak is strongly dependent on the "penetrating" or "nonpenetrating" nature of the diluent. This experimental determination allows us to attribute the synergy to a combination of entropic effects favoring extraction, opposed to perturbation of the first coordination sphere by penetration as well as surfactant film bending energy.