Macroscopic theory for equilibrium properties of ionic-dipolar mixtures and application to an ionic model fluid

Response to "Comment on 'Binding Debye-Hückel theory for associative electrolyte solutions'" [J. Chem. Phys. 159, 154503 (2023)]

This Response addresses critiques raised about the Binding Debye-Hückel (BiDH) theory [Naseri Boroujeni et al., J. Chem. Phys. 159, 154503 (2023)] by Simonin and Bernard [J.-P. Simonin and O. Bernard, J. Chem. Phys. (2024)]. The critiques questioned the foundational framework of the Debye-Hückel (DH) theory, the relevance of ion pairing in primitive model fluids, and the accuracy of the BiDH model compared to mean spherical approximation model. Through a systematic rebuttal, supported by extensive literature review and comparison with Monte Carlo simulation data, this Response addresses these concerns. It demonstrates the efficacy of DH theory in describing real electrolyte solutions, validates the relevance of ion pairing in primitive model fluids, and establishes the BiDH model's accuracy in describing electrolyte properties.

Binding Debye-Hückel theory for associative electrolyte solutions

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard-Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson-Boltzmann-Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Are Room-Temperature Ionic Liquids Dilute Electrolytes?

An important question in understanding the structure of ionic liquids is whether ions are truly "free" and mobile, which would correspond to a concentrated ionic melt, or are rather "bound" in ion pairs, that is, a liquid of ion pairs with a small concentration of free ions. Recent surface force balance experiments from different groups have given conflicting answers to this question. We propose a simple model for the thermodynamics and kinetics of ion pairing in ionic liquids. Our model takes into account screened ion-ion, dipole-dipole, and dipole-ion interactions in the mean-field limit. The results of this model suggest that almost two-thirds of the ions are free at any instant, and ion pairs have a short lifetime comparable to the characteristic time scale for diffusion. These results suggest that there is no particular thermodynamic or kinetic preference for ions to reside in pairs. We therefore conclude that ionic liquids are concentrated, rather than dilute, electrolytes.

A simulation assessment of the thermodynamics of dense ion-dipole mixtures with polarization

Molecular dynamics (MD) simulations are employed to ascertain the relative importance of various electrostatic interaction contributions, including induction interactions, to the thermodynamics of dense, hot ion-dipole mixtures. In the absence of polarization, we find that an MD-constrained free energy term accounting for the ion-dipole interactions, combined with well tested ionic and dipolar contributions, yields a simple, fairly accurate free energy form that may be a better option for describing the thermodynamics of such mixtures than the mean spherical approximation (MSA). Polarization contributions induced by the presence of permanent dipoles and ions are found to be additive to a good approximation, simplifying the thermodynamic modeling. We suggest simple free energy corrections that account for these two effects, based in part on standard perturbative treatments and partly on comparisons with MD simulation. Even though the proposed approximations likely need further study, they provide a first quantitative assessment of polarization contributions at high densities and temperatures and may serve as a guide for future modeling efforts.

The ion speciation of ionic liquids in molecular solvents of low and medium polarity

The ion speciation of ionic liquids dissolved in molecular liquids of low and medium polarity is studied experimentally and theoretically. The ion speciation in some representative systems is characterized by dielectric relaxation spectroscopy and electrical conductance measurements. A corresponding-states approach is used to compare the experimental results with predictions for a reference system of charged hard spheres in a dielectric continuum. Topics of special interest are the formation of ion pairs and larger ion clusters in dilute solutions and their fate at high concentrations, where they have to redissociate in the excess ionic liquid to form the charge-ordered structure of the fused salt. In solvents of low polarity this transition leads to electrical conductance minima and liquid-liquid immiscibilities.

Inflation of the screening length induced by Bjerrum pairs

Within a modified Poisson-Boltzmann theory we study the effect of Bjerrum pairs on the typical length scale [Formula: see text] over which electric fields are screened in electrolyte solutions, taking into account a simple association-dissociation equilibrium between free ions and Bjerrum pairs. At low densities of Bjerrum pairs, this length scale is well approximated by the Debye length [Formula: see text], with ρ(s) the free-ion density. At high densities of Bjerrum pairs, however, we find [Formula: see text], which is significantly larger than 1/κ due to the enhanced effective permittivity of the electrolyte, caused by the polarization of Bjerrum pairs. We argue that this mechanism may explain the recently observed anomalously large colloid-free zones between an oil-dispersed colloidal crystal and a colloidal monolayer at the oil-water interface.

Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model

In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.

Critical concentration fluctuations of the ionic binary mixture ethylammonium nitrate-n-octanol: an ultrasonic spectrometry study

Between 200 kHz and 130 MHz, the ultrasonic attenuation spectrum of the ionic ethylammonium nitrate--n-octanol mixture of critical composition has been measured at various reduced temperatures (1.5 x 10(-4)<or= t <or=5.7 x 10(-2)). Using static and dynamic light scattering data as well as viscosity and heat capacity data from the literature, the experimental spectra have been evaluated to yield the scaling function, with the background contribution to the spectra as the only adjustable parameter. Agreement, within the limits of experimental error, of the measured scaling function with that of the nonionic binary system ethanol--dodecane and with the theoretical predictions of the Bhattacharjee-Ferrell dynamic scaling model is found. The amplitude of the fluctuation correlation length xi(o) (=0.47 nm) and the amount of the coupling constant /g/ (=1.3) are rather high as compared to nonionic binary critical mixtures. The amplitude of the relaxation rate of order parameter fluctuations Gamma(o)(=2.6 x 10(8) s(-1)) exhibits an unusual small value, likely to the most part a reflection of the high viscosity and thus small diffusion coefficient of the ionic liquid.