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.

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.

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.

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 B T 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.

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The present research focuses on the comparative investigation of the acid-base surface properties (the isoelectric point, pH iep and point of zero charge, pH pzc ) of one-dimensional TiO 2 nanomaterials. Different one-dimensional TiO 2 nanomaterials, nanotubes (NTs) and nanowires (NWs) were prepared by an alkaline hydrothermal synthesis procedure. The structural properties of the synthesized TiO 2 nanomaterials were investigated with high-resolution scanning electron microscopy (HR-SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HR-TEM), atomic force microscopy (AFM), powder X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The NWs and NTs were characterized using Raman and Fourier transform infrared (FT-IR) spectroscopy as well as Brunauer-EmmettTeller (BET) measurements. Surface properties, i.e. pH iep and pH pzc of NWs and NTs were determined from electrokinetic measurements, potentiometric mass and electrolyte titrations. The relative acidity for the NWs is found to be in the interval 3 < pH iep < 4 in comparison with the NTs, with 4

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Charging of material surfaces in aqueous electrolyte solutions is one of the most important processes in the interactions between biomaterials and surrounding tissue. Other than a biomaterial, titania nanotubes (TiO NTs) represent a versatile material for numerous applications such as heavy metal adsorption or photocatalysis. In this article, the surface charge properties of titania NTs in NaNO solution were investigated through electrophoretic mobility and polyelectrolyte colloid titration measuring techniques. In addition, we used high-resolution transmission electron microscopy imaging to determine the morphology of TiO NTs. A theoretical model based on the classical density functional theory coupled with the charge regulation method in terms of mass action law was developed to understand the experimental data and to provide insights into charge properties at different physical conditions, namely, pH and NaNO concentration. Two intrinsic protonation constants and surface site density have been obtained. The electrostatic properties of the system in terms of electrostatic potentials and ion distributions were calculated and discussed for various pH values. The model can quantitatively describe the titration curve as a function of pH for higher bulk salt concentrations and the difference in the equilibrium amount of charges between the inner and outer surfaces of TiO NTs. Calculated counterion (NO) distributions show a pronounced decrease of NO ions for high bulk pH (both inside and outside TiO NT) because of the strong electric field. With the decrease of bulk pH or the increase of the salt concentration, NO is able to accumulate near the TiO NTs surfaces.