Liquid-liquid phase separation in solutions of ionic liquids: phase diagrams, corresponding state analysis and comparison with simulations of the primitive model

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Solid–liquid–liquid phase envelopes from temperature-scanned refractive index data

A novel method for estimating the upper critical solution temperature (UCST) of N,N-diethyl-m-toluamide (DEET)-polyethylene systems was developed. It was validated using data for the dimethylacetamide (DMA)-alkane systems which showed that refractive index mixing rules, linear in volume fraction, can accurately predict mixture composition for amide-alkane systems. Furthermore, rescaling the composition descriptor with a single adjustable parameter proved adequate to address any asymmetry when modeling the DMA-alkane phase envelopes. This allowed the translation of measured refractive index cooling trajectories of DEET-alkane systems into phase diagrams and facilitated the estimation of the UCST values by fitting the data with an adjusted composition descriptor model. For both the DEET- and DMA-alkane systems, linear behavior of UCST values in either the Flory–Huggins critical interaction parameter, or the alkane critical temperature, with increasing alkane molar mass is evident. The UCST values for polymer diluent systems were estimated by extrapolation using these two complimentary approaches. For the DEET-polyethylene system, values of 183.4 and 180.1 °C respectively were obtained. Both estimates are significantly higher than the melting temperature range of polyethylene. Initial liquid–liquid phase separation is therefore likely to be responsible for the previously reported microporous microstructure of materials formed from this binary system.

Wettability of ultra-small pores of carbon electrodes by size-asymmetric ionic fluids

Recently, we studied the phase behavior of ionic fluids under confinement using the classical density functional theory within the framework of the restricted primitive model. The theoretical results indicate that narrowing the pore size may lead to a drastic reduction in the electric double layer capacitance, while increasing the surface electrical potential would improve the ionic accessibility of micropores. In this work, we extend the theoretical investigation to systems containing size-asymmetric electrolytes that may exhibit a vapor-liquid like phase transition in the bulk phase. The effects of pore size and surface electric potential on the phase diagram and microscopic structures of the confined electrolytes were studied over a broad range of parameters. We found that decreasing the pore size or increasing the surface potential could destabilize the liquid phase in micropores, and capillary evaporation could occur regardless of the size asymmetry between cations and anions. Compared to that in a symmetric ionic system, the vapor-liquid phase separation is more likely to take place as the size asymmetry becomes more pronounced. The phase transition would alter the "accessibility" of ions to micropores and lead to coexisting micropores with different surface charge densities as identified by Monte Carlo simulation.

Revisiting the Liquid-Liquid Phase Behavior of n-Alkanes and Ethanol

Mixtures of alkanes and ethanol are important in many areas, for example, as fuel blends. This paper describes new experimental data obtained for the liquid-liquid equilibrium phase behavior of normal alkanes (n-alkanes; C_nH_2n+2; 9 ≤ n ≤ 24) with ethanol. The results were obtained by applying the cloud point method in a temperature range of T = 230-423 K at ambient pressure. All systems are partially miscible with an upper critical solution point. The two phase regions of the phase diagrams show no indication of any obvious optical irregularities, like birefringence, coloring, formation of schlieren, or remarkable turbidity, except critical opalescence. With increasing length of the molecular chain of the n-alkanes, the (liquid-liquid) critical point is shifted to higher temperatures and higher ethanol content. The data are analyzed numerically implying Ising criticality. The nonsymmetric shape of the phase body is considered in different approaches for describing the diameter by presuming (a) the validity of the rectilinear diameter rule, (b) a nonlinear diameter predicted in the theory of complete scaling, and (c) combining both concepts. The numerical analysis yields the critical temperature, the critical composition, the width, and the diameter of the phase diagrams. The results are compared with literature data sets from similar mixtures; these data are also evaluated in terms of the models applied here. Phase diagrams of 13 different sets of mixtures are measured and analyzed to extract general aspects of the behavior of the normal alkane-ethanol mixtures. A simple Flory-Huggins-like approach allows a semiquantitative description of the experimental results of the critical temperatures. Therefore, it confirms the picture of molecular ordering within the solutions.

Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom's particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by "diffusion" of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln(L), where L is the pore length.

Does capillary evaporation limit the accessibility of nonaqueous electrolytes to the ultrasmall pores of carbon electrodes?

Porous carbons have been widely utilized as electrode materials for capacitive energy storage. Whereas the importance of pore size and geometry on the device performance has been well recognized, little guidance is available for identification of carbon materials with ideal porous structures. In this work, we study the phase behavior of ionic fluids in slit pores using the classical density functional theory. Within the framework of the restricted primitive model for nonaqueous electrolytes, we demonstrate that the accessibility of micropores depends not only on the ionic diameters (or desolvation) but also on their wetting behavior intrinsically related to the vapor-liquid or liquid-liquid phase separation of the bulk ionic systems. Narrowing the pore size from several tens of nanometers to subnanometers may lead to a drastic reduction in the capacitance due to capillary evaporation. The wettability of micropores deteriorates as the pore size is reduced but can be noticeably improved by raising the surface electrical potential. The theoretical results provide fresh insights into the properties of confined ionic systems beyond electric double layer models commonly employed for rational design/selection of electrolytes and electrode materials.

Vapor Liquid Equilibria of Binary Mixtures of 1-Butyl-3-methylimidazolium Triflate (C4mimTfO) and Molecular Solvents: n-Alkyl Alcohols and Water

Isobaric vapor liquid equilibria (VLE) of binary mixtures of the ionic liquid (IL) 1-butyl-3-methylimidazolium trifluoromethanesulfonate (C₄mimTfO) with either water or short chained n-alkyl alcohols (methanol, ethanol, propan-1-ol, and butan-1-ol) are described in this study. Two different microebulliometers and a classical VLE apparatus were compared and the VLEs were determined in the composition range 0.4 ≤ x(solvent) ≤ 1 at three different pressure levels ( p = 500 mbar, 700 mbar, and 1000 mbar). The experimental data were modeled using the soft-SAFT equation of state, which was able to accurately describe the nonideal behavior of these mixtures. The combined experimental-modeling results obtained contribute to establish the structure-property relationship between the C₄mimTfO and n-alkyl alcohol molecules and to infer about its influence on the phase behavior of these solvents.

Determination of liquid-liquid critical point composition using 90^{∘} laser light scattering

Despite over a century of characterization efforts, liquid-liquid critical point compositions are difficult to identify with good accuracy. Reported values vary up to 10% for even well-studied systems. Here, a technique is presented for high-precision determination of the critical composition of a partially miscible binary liquid system. Ninety-degree laser light-scattering intensities from single-phase samples are analyzed using an equation derived from nonclassical power laws and the pseudospinodal approximation. Results are reported for four liquid-liquid systems (aniline + hexane, isobutyric acid + water, methanol + cyclohexane, and methanol + carbon disulfide). Compared to other methods, the 90^{∘} light-scattering approach has a strong dependence on composition near the critical point, is less affected by temperature fluctuations, and is insensitive to the presence of trace impurities in the samples. Critical compositions found with 90^{∘} light scattering are precise to the parts-per-thousand level and show long-term reproducibility.

Ginzburg criterion for ionic fluids: the effect of Coulomb interactions

The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.

Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: phase diagram and clustering

We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.