Coalescence Initiation in Liquid-Liquid Systems: A Stochastic Model.

Coalescence is a complex phenomenon leading to the merging of deformable particles of fluid. The complexity stems largely from the simultaneous occurrence of phenomena of a different nature (hydrodynamic, electrostatic, physicochemical) acting at different scales. The stochastic effects controlling the formation of the liquid bridge between two droplets of the same liquid, immersed in another nonmiscible liquid, are studied through a series of molecular dynamics simulations. The case of heptane droplets in water, relevant to solvent extraction, a key process of the circular economy, is considered. From this series of simulations, we have confirmed that the probability function of coalescence of two identical droplets in contact follows a Poisson distribution. We moreover propose a criterion for the initiation of coalescence based on nucleation theory. A complete description of the stochastic initiation of coalescence is hence provided, opening many perspectives for the simulation of coalescence in continuous approaches used in fluid mechanics and chemical engineering. The methodology can be generalized to droplets of different size and composition, immersed in gas, or to bubbles, i.e., to other physical problems whose kinetics is influenced by the molecular scale.

Liquid-Liquid Flow at Nanoscale: Slip and Hydrodynamic Boundary Conditions.

Nonequilibrium molecular dynamics (NEMD) simulations have been performed to describe the flow of a fluid nanolayer confined by another fluid. The results show that the behavior of liquids can still be described by the Navier-Stokes equation at the nanoscale, i.e., when only few molecular layers are involved. NEMD furthermore gives additional knowledge on flow. Indeed, while a very small slip is evidenced for a solid-liquid interface as, e.g., in lubrication, the slip lengths are significantly larger at the liquid-liquid interface, as encountered, e.g., in droplet coalescence. The slip lengths of the two fluids are linked. The increase in hydrodynamic slip for liquid-liquid interfaces is attributed to the enhancement of fluid diffusion, which reduces friction.

Why local and non-local terms are essential for second harmonic generation simulation?

Second Harmonic Generation (SHG) today represents one of the most powerful techniques to selectively probe all types of interfaces. However, the origin of the SHG signal at a molecular level is still debated since the local dipole contribution, which is strongly correlated to the molecular orientation can be counterbalanced by non-local quadrupole contributions. Here, we propose a method to simulate the SHG signal of a model water/air interface from the molecular response of each contribution. This method includes both local and non-local terms, which are represented, respectively, by the dependency of the polarisability and hyperpolarisability upon the chemical environment of the molecule and by the bulk quadrupole response. The importance of both terms for the sound simulation of the SHG signals and their interpretation is assessed. We demonstrate that the sole dipole term is unable to simulate a SHG signal, even if the dependency of the hyperpolarisability on the local environment is considered. The inclusion of the bulk quadrupole contribution, which largely dominates the dipole contribution, is essential to predict the SHG response, although the accuracy of the prediction is increased when the dependency upon the local environment is considered.

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 kBT 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.

Liquid/liquid interface in periodic boundary condition.

We study how surface phenomena can change the interface geometry in liquid-liquid two-phase systems with periodic boundary conditions. Without any curvature effect on surface tension, planar (slab), cylindrical, and spherical structures are successively obtained as a function of the total composition and elongation of the box, in accordance with molecular dynamics simulations for a water/heptane system. The curvature effects described by Tolman relationship desymmetrize the phase diagram by stabilizing a concavity but it leads to inconsistencies with high curvature. Helfrich model partially resolves this and predicts the possible presence of shells reflecting a frustrated system.

Phase separation of binary mixtures induced by soft centrifugal fields.

We use the model system ethanol-dodecane to demonstrate that giant critical fluctuations induced by easily accessible weak centrifugal fields as low as 2000g can be observed above the miscibility gap of a binary liquid mixture. Moreover, several degrees above the phase transition, i.e. in the one-phase region, strong gradients of ethanol concentration occur upon centrifugation. In this case, the standard interpretation of sedimentation equilibrium in the analytical ultracentrifuge (AUC) yields an apparent molar mass of ethanol three orders of magnitude higher than the real value. Notably, these composition gradients have no influence on the distribution gradient of solutes such as dyes like Nile red. The thick opaque interphase formed upon centrifugation does not appear as the commonly observed sharp meniscus, but as a turbidity zone, similar to critical opalescence. This layer is a few millimeters thick and separates two fluids with low compositional gradients. All these effects can be qualitatively understood and explained using the Flory-Huggins solution model coupled to classical density functional theory (DFT). In this domain hetero-phase fluctuations can be triggered by gravity even far from the critical point. Taking into account Jean Perrin's approach to external fields in colloids, a self-consistent definition of the Flory effective volume and an explicit calculation of the total free energy per unit volume is possible.

Deformation of a Liquid Near an AFM Tip: Molecular Dynamics Approach.

The interaction between an atomic force microscopy (AFM) probe and a thin film of water deposited over a flat substrate is studied using molecular dynamics (MD). The effects of the film thickness and the probe radius on both the deformation height of the liquid interface and the distance of the jump to contact at which the liquid comes in direct contact with the probe are investigated. The dynamics of the surface deformation and the role of interface fluctuations are studied in detail. The systems considered belong to the thin-film regime described in a semianalytical model previously established by Ledesma-Alonso et al. (Langmuir 2013, 29, 7749-7757). MD simulations predict that for shallow films, both the distance at which the jump to contact occurs and the surface maximal deformation height increase steadily with the layer thickness regardless of the probe radius, which is in agreement with the previously proposed theoretical model. The deformation of the surface was shown to be unstable because of the strong effect of thermal fluctuations. For each of the considered systems, the film thickness was such that interface fluctuations induced the jump to contact. The comparison of the deformation obtained in MD with the profiles predicted by the continuous model points out the complementarity between the two approaches. The results of the molecular approach not only are consistent with those of the continuous model but also provide more information on the description of nanoscale phenomena. In particular, MD results point out the importance of fluctuations when it comes to the description of the particular dynamics of nanosystems involving soft interfaces. This shows the need to improve continuous models by complementing them with a molecular approach for a better accuracy.

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.

The role of curvature effects in liquid-liquid extraction: assessing organic phase mesoscopic properties from MD simulations.

The bending rigidity of small reverse aggregates involved in liquid-liquid extraction processes has been investigated by molecular dynamics simulations. Simulations of a common extractant (DMDOHEMA) with four hydrophobic chains in explicit solvent (n-heptane) and in vacuum have been performed to determine the effect of solvent penetration on film stiffness. Elastic film bending energy that is needed for mesoscopic modelling of transfer of species between complex fluids is harmonic in terms of curvature (Helfrich formalism) and the packing parameter only if the solvent is explicitly taken into account. In terms of the packing parameter of the real molecular film constituting the reverse water in oil aggregates and taking into account molecular volume, area and film thickness (that is in agreement with Tanford's model), the bending rigidity is calculated to be about 16 kBT per extractant molecule (about 40 kJ mol-1), which is smaller than the free energy of transfer from an isolated "monomer" molecule to a weak aggregate, but of the order of magnitude of the free energy of transfer used in liquid-liquid extraction processes.

Stability of reverse micelles in rare-earth separation: a chemical model based on a molecular approach.

Molecular complexes formed in the organic phase during solvent extraction may self-assemble as reverse micelles, and therefore induce a supramolecular organization of this phase. In most of the cases, water molecules play an essential role in the organization of this non polar medium. The aim of this work is to investigate the speciation of the aggregates formed in the organic phase during solvent extraction, and especially to assess their stability as a function of the number of water molecules included in their polar core. We have focused on malonamide extractants that have already been investigated experimentally. Different stoichiometries of reverse micelles in the organic phase have been studied by means of classical molecular dynamics simulations. Furthermore, umbrella-sampling molecular dynamics simulations have been used to calculate the equilibrium constant (K°) representing the association/dissociation pathways of water molecules in the aggregates and the corresponding reaction free energies (ΔrG°).

Analysis of the second harmonic generation signal from a liquid/air and liquid/liquid interface.

Three different liquid interfaces, water/air, thiophene/air, and water/thiophene, were probed using the second harmonic generation (SHG) technique. Thiophene and water have been chosen because the hyperpolarizability of these molecules has already been measured or calculated and the different values can be found in literature. We have studied the microscopic structure of these interfaces by comparing the components of the second order susceptibility tensor determined from the SHG polarization curve analysis with those determined via a molecular dynamics (MD) simulation of these interfaces. We have indeed computed the structure and orientation of water and thiophene molecules at the liquid/air and liquid/liquid (L/L) interfaces as a function of the distance from the interface. The integrated susceptibility values calculated by MD simulations agree well with SHG results and validate the choice of force fields that should permit to quantify more complex L/L interfaces.

Modeling and Speciation Study of Uranium(VI) and Technetium(VII) Coextraction with DEHiBA.

The N,N-dialkylamide DEHiBA (N,N-di-2-ethylhexyl-isobutyramide) is a promising alternative extractant to TBP (tri-n-butylphosphate) to selectively extract uranium(VI) from plutonium(IV) and spent nuclear fuel fission products. Extraction of technetium, present as pertechnetic acid (HTcO4) in the spent fuel solution, by DEHiBA was studied for different nitric acid and uranium concentrations. The uranium(VI) and technetium(VII) coextraction mechanism with DEHiBA was investigated to better understand the behavior of technetium in the solvent extraction process. Uranium and technetium distribution ratios were first determined from batch experiments. On the basis of these data, a thermodynamic model was developed. This model takes into account deviations from ideality in the aqueous phase using the simple solution concept. A good representation of uranium and technetium distribution data was obtained when considering the formation of (DEHiBA)i(HNO3)j(HTcO4)k complexes, as well as mixed (DEHiBA)2(UO2)(NO3)(TcO4) and (DEHiBA)3(UO2)(NO3)(TcO4)(HNO3) complexes, where one pertechnetate anion replaces one nitrate in the uranium coordination sphere in the two complexes (DEHiBA)2(UO2)(NO3)2 and (DEHiBA)3(UO2)(NO3)2(HNO3). Combination of complementary spectroscopic techniques (FT-IR and X-ray absorption) supported by theoretical calculations (density functional theory) enabled full characterization of the formation of mixed uranium-technetium species (DEHiBA)2(UO2)(NO3)(TcO4) in the organic phase for the first time. The structural parameters of this complex are reported in the paper and lead to the conclusion that the pertechnetate group coordinates the uranyl cation in a monodentate fashion in the inner coordination sphere. This study shows how combining a macroscopic approach (distribution data acquisition and modeling) with molecular-scale investigations (FT-IR and X-ray absorption analysis supported by theoretical calculations) can provide a new insight into the description of a solvent extraction mechanism.

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.

Ion-specific adsorption and electroosmosis in charged amorphous porous silica.

Monovalent and divalent aqueous electrolytes confined in negatively charged porous silica are studied by means of molecular simulations including free energy calculations. Owing to the strong cation adsorption at the surface, surface charge overcompensation (overscreening) occurs which leads to an effective positive surface next to the Stern layer, followed by a negatively charged diffuse layer. A simple Poisson-Boltzmann model in which the single-ion potential of mean force is introduced is shown to capture the most prominent features of ion density profiles near an amorphous silica surface. Nevertheless, due to its mean-field nature, which fails to account for correlations, this simple model does not predict overscreening corresponding to charge inversion at the surface. Such an overscreening drastically affects the transport of confined electrolytes as it leads to flow reversal when subjected to an electric field. A simple continuum theory is shown to capture how the electro-osmotic flow is affected by overscreening and by the apparent enhanced viscosity of the confined electrolytes. Comparison with available experimental data is discussed, as well as the implications of these phenomena for ζ-potential measurements.

Multi-scale modelling of uranyl chloride solutions.

Classical molecular dynamics simulations with explicit polarization have been successfully used to determine the structural and thermodynamic properties of binary aqueous solutions of uranyl chloride (UO2Cl2). Concentrated aqueous solutions of uranyl chloride have been studied to determine the hydration properties and the ion-ion interactions. The bond distances and the coordination number of the hydrated uranyl are in good agreement with available experimental data. Two stable positions of chloride in the second hydration shell of uranyl have been identified. The UO2(2+)-Cl(-) association constants have also been calculated using a multi-scale approach. First, the ion-ion potential averaged over the solvent configurations at infinite dilution (McMillan-Mayer potential) was calculated to establish the dissociation/association processes of UO2 (2+)-Cl(-) ion pairs in aqueous solution. Then, the association constant was calculated from this potential. The value we obtained for the association constant is in good agreement with the experimental result (KUO2Cl(+) = 1.48 l mol(-1)), but the resulting activity coefficient appears to be too low at molar concentration.

Reverse aggregate nucleation induced by acids in liquid-liquid extraction processes.

We show in the case of N,N'-dimethyl-N,N'-dioctyl-2-(2(hexyloxy)ethyl)-malonamide (DMDOHEMA) chosen as a typical oil-soluble extractant with surface activity that the free energy of formation of reverse micelles in the solvent phase strongly depends on the presence of polar solutes. Free energies per molecule vary typically from 0 to 2 kT per molecule (5 kJ mol(-1)), depending on the kosmotropic/chaotropic nature of the anion extracted. Variations of the reverse aggregation free energy introduced by acids and other co-extracted solutes as deduced from the critical aggregation concentrations cannot be neglected while modelling extraction. With typical aggregation numbers of 4-6, the free energy of formation of one reverse aggregate varies up to 20 kJ mol(-1), which is four times the typical difference in free energy of one single cation transfer between a "target" and a non-target ion in practical extraction and stripping industrial processes.

Predicting for thermodynamic instabilities in water/oil/surfactant microemulsions: a mesoscopic modelling approach.

The thermodynamics and structural properties of flexible and rigid nonionic water/oil/surfactant microemulsions have been investigated using a two level-cut Gaussian random field method based on the Helfrich formalism. Ternary stability diagrams and scattering spectra have been calculated for different surfactant rigidities and spontaneous curvatures. A more important contribution of the Gaussian elastic constants compared to the bending one is observed on the ternary stability diagrams. Furthermore, influence of the spontaneous curvature of the surfactant points out a displacement of the instability domains which corresponds to the difference between the spontaneous and effective curvatures. We enlighten that a continuous transition from a connected water in oil droplets to a frustrated locally lamellar (oil in water in oil droplets) microstructure is found to occur when increasing the temperature for an oil-rich microemulsion. This continuous transition translated in a shift in the scattering functions, points out that the phase inversion phenomenon occurs by a coalescence of the water droplets.

Modeling Lanthanide Ions in Solution: A Versatile Force Field in Aqueous and Organic Solvents.

In this paper, we propose a new nonpolarizable force field for describing the Ln3+ (Ln = lanthanide) series based on a 12-6-4 Lennard-Jones potential. The development of the force field was performed in pure water by adjusting both the ion-oxygen distance and the hydration free energy. This force field accurately reproduces the Ln3+ hydration properties through the series, especially the coordination number that is hardly accessible using a nonpolarizable force field. Then, the validity and the transferability of the current force field were evaluated for two different systems containing Ln3+ in various solvents, namely, 0.1 mol L-1 La(NO3)3 salts in methanol and Eu(NO3)3 salts in solvent organic phases composed of DMDOHEMA molecules in n-heptane. The good agreement between our simulations and the data available in the literature confirms the accuracy of the force field for describing the lanthanide cations in both aqueous and nonaqueous media.

Mesoscopic modelling of frustration in microemulsions.

The swelling behaviour of water-oil microemulsions - considering a surfactant layer between oil and water - has been studied using a two level-cuts Gaussian random field approach based on the Helfrich formalism. Microstructures and scattering properties of microemulsions have been calculated for different amounts of oil (and water) for flexible and rigid microemulsions. When the stiffness, the spontaneous curvature of the interfacial film, and the surface to volume ratio of the immiscible fluids are varied, the microemulsion topology and morphology change in order to minimize the microemulsion free energy. Our simulations point out a change in the microemulsion morphology as a function of the surfactant film rigidity and the composition of oil, water and the surfactant. Locally lamellar structures are found for rigid microemulsions, whereas for more flexible ones, the connected-droplet and/or bicontinuous structures are preferred. Furthermore, we show that the microemulsion swelling versus the volume fraction gives a specific signature of the microemulsion microstructure. This allows for discriminating between different types of microemulsions: flexible, frustrated and unfrustrated (close to bi-liquid foams), and connected structures as molten hexagonal and cubic phases. The universal swelling behaviour is compared to different analytic expressions of Disordered Open Connected (DOC) models for the microemulsion swelling versus the volume fraction.