From bulk self-assembly to electrical diffuse layer in a continuum approach for ionic liquids: The impact of anion and cation size asymmetry

Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

The Role of Energy Scales for the Structure of Ionic Liquids at Electrified Interfaces: A Theory-Based Approach

Ionic liquids offer unique bulk and interfacial characteristics as battery electrolytes. Our continuum approach naturally describes the electrolyte on a macroscale. An integral formulation for the molecular repulsion, which can be quantitatively determined by both experimental and theoretical methods, models the electrolyte on the nanoscale. In this article, we perform a systematic series expansion of this integral formulation, derive a description of chemical potentials in terms of higher-order concentration gradients, and rationalize the appearance of fourth-order derivative operators in modified Poisson equations, as recently proposed in this context. In this way, we formulate a rigorous multiscale methodology from atomistic quantum chemistry calculations to phenomenological continuum models. We apply our generalized framework to ionic liquids near electrified interfaces and perform analytical asymptotic analysis. Three energy scales describing electrostatic forces between ions, molecular repulsion, and thermal motion determine the shape and width of the long-ranging charged double layer. We classify the charge screening mechanisms dependent on the system parameters as dielectricity, ion size, interaction strength, and temperature. We find that the charge density of electrochemical double layers in ionic liquids either decays exponentially, for negligible molecular repulsion, or oscillates continuously. Charge ordering across several ion diameters occurs if the repulsion between molecules is comparable with thermal energy and Coulomb interactions. Eventually, phase separation of the bulk electrolyte into ionic layers emerges once the molecular repulsion becomes dominant. Our framework predicts the exact phase boundaries among these three phases as a function of temperature, dielectricity, and ion size.

Localized X-Ray Photoelectron Impedance Spectroscopy (LoXPIS) for Tapping into Charge-Dynamics of Ionic-Liquid Electrolytes within Energy Storage Devices

Many electrochemical devices are based on the fundamental process of ion migration and accumulation on surfaces. Complex interplay of molecular properties of ions and device dimensions control the entire process...

Stripes on finite domains: Why the zigzag instability is only a partial story

Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical, and biological media and to macro-scale vegetation and cloud patterns. Their formation is usually due to a primary symmetry breaking of a uniform state to stripes, often followed by secondary instabilities to form zigzag and labyrinthine patterns. These secondary instabilities are well studied under idealized conditions of an infinite domain; however, on finite domains, the situation is more subtle since the unstable modes depend also on boundary conditions. Using two prototypical models, the Swift-Hohenberg equation and the forced complex Ginzburg-Landau equation, we consider finite size domains with no flux boundary conditions transversal to the stripes and reveal a distinct mixed-mode instability that lies in between the classical zigzag and the Eckhaus lines. This explains the stability of stripes in the mildly zigzag unstable regime and, after crossing the mixed-mode line, the evolution of zigzag stripes in the bulk of the domain and the formation of defects near the boundaries. The results are of particular importance for problems with large timescale separation, such as bulk-heterojunction deformations in organic photovoltaic and vegetation in semi-arid regions, where early temporal transients may play an important role.

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsager's relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.

Salt-induced microheterogeneities in binary liquid mixtures

The salt-induced microheterogeneity (MH) formation in binary liquid mixtures is studied by small-angle x-ray scattering (SAXS) and liquid state theory. Previous experiments have shown that this phenomenon occurs for antagonistic salts, whose cations and anions prefer different components of the solvent mixture. However, so far the precise mechanism leading to the characteristic length scale of MHs has remained unclear. Here, it is shown that MHs can be generated by the competition of short-ranged interactions and long-ranged monopole-dipole interactions. The experimental SAXS patterns can be reproduced quantitatively by fitting to the derived correlation functions without assuming any specific model. The dependency of the MH structure with respect to ionic strength and temperature is analyzed. Close to the demixing phase transition, critical-like behavior occurs with respect to the spinodal line in the phase diagram.