Theory of Surface Forces in Multivalent Electrolytes

Surfactant-Aided Stabilization of Individual Carbon Nanotubes in Water around the Critical Micelle Concentration

Surfactants are widely used to disperse single-walled carbon nanotubes (SWCNTs) and other nanomaterials for liquid-phase processing and characterization. Traditional techniques, however, demand high surfactant concentrations, often in the range of 1-2 wt/v% of the solution. Here, we show that optimal dispersion efficiency can be attained at substantially lower surfactant concentrations of approximately 0.08 wt/v%, near the critical micelle concentration. This unexpected observation is achieved by introducing "bare" nanotubes into water containing the anionic surfactant sodium deoxycholate (DOC) through a superacid-surfactant exchange process that eliminates the need for ultrasonication. Among the diverse ionic surfactants and charged biopolymers explored, DOC exhibits the highest dispersion efficiency, outperforming sodium cholate, a structurally similar bile salt surfactant containing just one additional oxygen atom compared to DOC. Employing all-atomistic molecular dynamics simulations, we unravel that the greater stabilization by DOC arises from its higher binding affinity to nanotubes and a substantially larger free energy barrier that resists nanotube rebundling. Further, we find that this barrier is nonelectrostatic in nature and does not obey the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability, underscoring the important role of nonelectrostatic dispersion and hydration interactions at the nanoscale, even in the case of ionic surfactants like DOC. These molecular insights advance our understanding of surfactant chemistry at the bare nanotube limit and suggest low-energy, surfactant-efficient solution processing of SWCNTs and potentially other nanomaterials.

Ion correlation-driven like-charge attraction in multivalent salt solutions

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations.

Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.

Orientational Ordering in Nano-confined Polar Liquids

Water and other polar liquids exhibit nanoscale structuring near charged interfaces. When a polar liquid is confined between two charged surfaces, the interfacial solvent layers begin to overlap, resulting in solvation forces. Here, we perform molecular dynamics simulations of polar liquids with different dielectric constants and molecular shapes and sizes confined between charged surfaces, demonstrating strong orientational ordering in the nanoconfined liquids. To rationalize the observed structures, we apply a coarse-grained continuum theory that captures the orientational ordering and solvation forces of those liquids. Our findings reveal the subtle behavior of different nanoconfined polar liquids and establish a simple law for the decay length of the interfacial orientations of the solvents, which depends on their molecular size and polarity. These insights shed light on the nature of solvation forces, which are important in colloid and membrane science, scanning probe microscopy, and nano-electrochemistry.

Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow

HYPOTHESIS

The classical Schulze-Hardy rule states that the critical coagulation concentration (CCC) of colloidal particles is inversely proportional to the counter-ionic valence at powers ranging from 2 to 6. However, the inverse Schulze-Hardy rule has recently been proposed, suggesting that the CCC can also be inversely proportional to the co-ionic valence. Previous studies on these rules did not consider the effect of flow on aggregation kinetics and the CCC. This study aims to investigate the effect of multivalent counter-ions and co-ions on aggregation kinetics and the CCCs in systems with and without a mixing flow.

EXPERIMENTS

We measured the aggregation rate coefficients of polystyrene sulfate latex particles as a function of the salt concentration with different ionic species. Furthermore, we analyzed these measurements using theoretical models based on hydrodynamic pair-diffusion in a random flow and trajectory analysis in two steady flows. The analysis was conducted using zeta potentials determined through electrophoretic measurements.

FINDINGS

Although the trajectory analysis underestimates the CCCs, the hydrodynamic pair-diffusion model can capture the shift of critical coagulation concentrations in the mixing flow to higher values than those in Brownian aggregation and also shows a better agreement with the experimental results. This result suggests that combining random flow and Brownian diffusion is crucial for developing a consistent framework for predicting both Brownian aggregation and aggregation in a mixing flow.

Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids

In this paper, we present a covariant approach that utilizes Noether's second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach is applied to several models of inhomogeneous ionic liquids that consider electrostatic correlations of ions or short-range correlations related to packing effects. Specifically, we derive analytical expressions for the symmetric stress tensors of the Cahn-Hilliard-like model, Bazant-Storey-Kornyshev model, and Maggs-Podgornik-Blossey model. All of these expressions are found to be consistent with respective self-consistent field equations.

Elucidating Trivalent Ion Adsorption at Floating Carboxylic Acid Monolayers: Charge Reversal or Water Reorganization?

We study the adsorption of trivalent neodymium on floating arachidic acid films at the air-water interface by two complementary surface specific probes, sum frequency generation spectroscopy and X-ray fluorescence near total reflection. In the absence of background ions, neodymium ions compensate for the surface charge of the arachidic acid film at a bulk concentration of 50 μM without any charge reversal. Increasing the bulk concentration to 1 mM does not change the neodymium surface coverage but affects the interfacial water structure significantly. In the presence of a high concentration of NaCl, there is overcharging at 1 mM Nd³⁺, i.e., 30% more Nd³⁺ than needed to compensate for the surface charge. These results show that the total coverage of neodymium ions is not enough to describe the complete picture at the interface, and interfacial water and ion coverage needs to be considered together to understand more complex ion adsorption and transport processes.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Macroscopic forces in inhomogeneous polyelectrolyte solutions

In this paper, we present a self-consistent field theory of macroscopic forces in spatially inhomogeneous flexible chain polyelectrolyte solutions. We derive an analytical expression for a stress tensor which consists of three terms: isotropic hydrostatic stress, electrostatic (Maxwell) stress, and stress rising from conformational entropy of polymer chains-conformational stress. We apply our theory to the description of polyelectrolyte solutions confined in a conductive slit nanopore and observe anomalous behavior of disjoining pressure and electric differential capacitance.

Probing Silica-Kaolinite Interactions with Sum Frequency Generation Spectroscopy

Treating the oil sands tailings ponds is a major challenge because of the vast amounts of tailings and the need for a reliable treatment technique for releasing water and generating the highly consolidated material required for land reclamation. Treatment with chemicals such as lime (calcium (hydr)oxide) is a promising technology for tailings dewatering and consolidation, particularly at higher pH. Given that kaolinite and silica minerals are the main constituents of many oil sands, we have investigated the influence of lime and NaOH addition on the silica/aqueous kaolinite interface over the pH range 7.4-12.4 using vibrational sum frequency generation spectroscopy (SFG). With lime addition, at pH 12.0 and above we observe a complete disappearance of the vibrational features of the interfacial water molecules for planar silica in contact with an aqueous dispersion of kaolinite particles. A concurrent increase in the amount of adsorbed kaolinite on the silica surface at pH 12.0 and above is observed, shown in the increased intensity of the kaolinite SFG peak at 3694 cm^-1. This suggests that the absence of water features in the SFG spectra is associated with conditions that facilitate dewatering. With NaOH addition, however, the interfacial water SF intensity is still significant even under highly alkaline conditions despite the increase in adsorbed kaolinite at high pH. To better understand the SFG observations and get a deeper insight into the chemistry of the silica/aqueous kaolinite interface, we measure the ζ-potential on the planar silica/aqueous interface and kaolinite aqueous dispersions under the same pH conditions with NaOH and lime addition.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Relation of EDL Forces between Clay Particles Calculated by Different Methods

Calculation of the electrostatic double layer force (EDL force) between clay particles is relevant as it is closely related to important macroscopic mechanical behaviors of clays. The popular method to calculate the EDL force is to integrate the electric potential and Maxwell stress along the boundary enclosing a simply connected domain within which a clay particle resides. The EDL force has also been calculated by the integration of the electrostatic force density over the preceding domain. However, the subtle relation of the EDL forces calculated by the different existing methods has not yet been investigated. By means of theoretical analysis and finite element simulation, it was shown that the force calculated by the integration of Maxwell stress along the complete boundary enclosing a multiply connected domain in which the clay particle is excluded, and that along the partial boundary enclosing the preceding simply connected domain represents the electrical attractive force and osmotic repulsive force, respectively, while the integration of the potential along both the same complete and partial boundary denotes the osmotic force. Numerical results showed that the calculated EDL force deviates from its actual value significantly with the decrease in distance between the chosen integral boundary and particle surface, and the deviation varies with surface potential and angle between particles. Moreover, the recommended minimum distance was proposed to be 10 times the thickness of the particle based on the present simulation results.

Applicability of the linearized Poisson-Boltzmann theory to contact angle problems and application to the carbon dioxide-brine-solid systems

In colloidal science and bioelectrostatics, the linear Poisson Boltzmann equation (LPBE) has been used extensively for the calculation of potential and surface charge density. Its fundamental assumption rests on the premises of low surface potential. In the geological sequestration of carbon dioxide in saline aquifers, very low pH conditions coupled with adsorption induced reduction of surface charge density result in low pH conditions that fit into the LPB theory. In this work, the Gouy–Chapman model of the electrical double layer has been employed in addition to the LPBE theory to develop a contact angle model that is a second-degree polynomial in pH. Our model contains the point of zero charge pH of solid surface. To render the model applicable to heterogeneous surfaces, we have further developed a model for the effective value of the point of zero charge pH. The point of zero charge pH model when integrated into our model enabled us to determine the point of zero charge pH of sandstone, quartz and mica using literature based experimental data. In this regard, a literature based thermodynamic model was used to calculate carbon dioxide solubility and pH of aqueous solution. Values of point of zero charge pH determined in this paper agree with reported ones. The novelty of our work stems from the fact that we have used the LPB theory in the context of interfacial science completely different from the classical approach, where the focus is on interparticle electrostatics involving colloidal stabilization.

Zeta potential of CO2-rich aqueous solutions in contact with intact sandstone sample at temperatures of 23 °C and 40 °C and pressures up to 10.0 MPa

Despite the broad range of interest and applications, controls on the electric surface charge and the zeta potential of silica in contact with aqueous solutions saturated with dissolved CO₂ at conditions relevant to natural systems, remains unreported. There have been no published zeta potential measurements conducted in such systems at equilibrium, hence the effect of composition, pH, temperature and pressure remains unknown. We describe a novel methodology developed for the streaming potential measurements under these conditions, and report zeta potential values for the first time obtained with Fontainebleau sandstone core sample saturated with carbonated NaCl, Na₂SO₄, CaCl₂ and MgCl₂ solutions under equilibrium conditions at pressures up to 10 MPa and temperatures up to 40 °C. The results demonstrate that pH of solutions is the only control on the zeta potential, while temperature, CO₂ pressure and salt type affect pH values. We report three empirical relationships that describe the pH dependence of the zeta potential for: i) dead (partial CO₂ pressure of 10^-3.44 atm) NaCl/Na₂SO₄, ii) dead CaCl₂/MgCl₂ solutions, and iii) for all live (fully saturated with dissolved CO₂) solutions. The proposed new relationships provide essential insights into interfacial electrochemical properties of silica-water systems at conditions relevant to CO₂ geological storage.

Biomolecular interactions of ultrasmall metallic nanoparticles and nanoclusters

The use of nanoparticles (NPs) in biomedicine has made a gradual transition from proof-of-concept to clinical applications, with several NP types meeting regulatory approval or undergoing clinical trials. A new type of metallic nanostructures called ultrasmall nanoparticles (usNPs) and nanoclusters (NCs), while retaining essential properties of the larger (classical) NPs, have features common to bioactive proteins. This combination expands the potential use of usNPs and NCs to areas of diagnosis and therapy traditionally reserved for small-molecule medicine. Their distinctive physicochemical properties can lead to unique in vivo behaviors, including improved renal clearance and tumor distribution. Both the beneficial and potentially deleterious outcomes (cytotoxicity, inflammation) can, in principle, be controlled through a judicious choice of the nanocore shape and size, as well as the chemical ligands attached to the surface. At present, the ability to control the behavior of usNPs is limited, partly because advances are still needed in nanoengineering and chemical synthesis to manufacture and characterize ultrasmall nanostructures and partly because our understanding of their interactions in biological environments is incomplete. This review addresses the second limitation. We review experimental and computational methods currently available to understand molecular mechanisms, with particular attention to usNP-protein complexation, and highlight areas where further progress is needed. We discuss approaches that we find most promising to provide relevant molecular-level insight for designing usNPs with specific behaviors and pave the way to translational applications.

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a "critical" value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the "critical" particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the "critical" particle charge based on the Lindemann melting law.

A grahame triple-layer model unifies mica monovalent ion exchange, zeta potential, and surface forces

A triple-layer model of the mica/water electrical double layer (EDL) unifies prediction of zeta potential, ion-exchange, and surface-force isotherms. The theory treats cations as partially dehydrated and complexed specifically to the anionic exchange sites of mica. A diffuse layer commencing at the outer Helmholtz plane (OHP) balances the surface charge not neutralized by adsorbed cations in the inner Helmholtz plane (IHP). Ion-binding equilibrium constants are assessed from zeta-potential measurements and used thereafter to predict ion-exchange isotherms and surface forces. Basal-plane mica surface charge is almost completely neutralized by specific binding of cations, including hydronium ions. The charge in the diffuse layer is only a few percent of the mica crystallographic charge density but leads to long-range electrostatic interactions between charged surfaces. The Grahame triple-layer model of the aqueous EDL provides a robust, quantitative, and unified description of the mica/water interface.

Mathematical model of electromigration allowing the deviation from electroneutrality

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

Imaging Arrangements of Discrete Ions at Liquid-Solid Interfaces

The individual and collective behavior of ions near electrically charged interfaces is foundational to a variety of electrochemical phenomena encountered in biology, energy, and the environment. While many theories have been developed to predict the interfacial arrangements of counterions, direct experimental observations and validations have remained elusive. Utilizing cryo-electron microscopy, here we directly visualize individual counterions and reveal their discrete interfacial layering. Comparison with simulations suggests the strong effects of finite ionic size and electrostatic interactions. We also uncover correlated ionic structures under extreme confinement, with the channel widths approaching the ionic diameter (∼1 nm). Our work reveals the roles of ionic size, valency, and confinement in determining the structures of liquid-solid interfaces and opens up new opportunities to study such systems at the single-ion level.

Anomaly of the dielectric function of water under confinement and its role in van der Waals interactions

We present a theoretical calculation of the changes in the Hamaker constant due to the anomalous reduction of the static dielectric function of water. Under confinement, the dielectric function of water decreases from a bulk value of 80 down to 2. If the confining walls are made of a dielectric material, the Hamaker constant reduces by almost 90%. However, if the confinement is realized with metallic plates, there is little change in the Hamaker constant. Additionally, we show that confinement can be used to decreases the Debye screening length without changing the salt concentration. This in turn is used to change the Hamaker constant in the presence of electrolytes.

Temperature-Induced Aggregation in Portlandite Suspensions

Temperature is well known to affect the aggregation behavior of colloidal suspensions. This paper elucidates the temperature dependence of the rheology of portlandite (calcium hydroxide: Ca(OH)₂) suspensions that feature a high ionic strength and a pH close to the particle's isoelectric point. In contrast to the viscosity of the suspending medium (saturated solution of Ca(OH)₂ in water), the viscosity of Ca(OH)₂ suspensions is found to increase with elevating temperature. This behavior is shown to arise from the temperature-induced aggregation of polydisperse Ca(OH)₂ particulates because of the diminution of electrostatic repulsive forces with increasing temperature. The temperature dependence of the suspension viscosity is further shown to diminish with increasing particle volume fraction as a result of volumetric crowding and the formation of denser fractal structures in the suspension. Significantly, the temperature-dependent rheological response of suspensions is shown to be strongly affected by the suspending medium's properties, including ionic strength and ion valence, which affect aggregation kinetics. These outcomes provide new insights into aggregation processes that affect the temperature-dependent rheology of portlandite-based and similar suspensions that feature strong charge screening behavior.

Interfacial Layering in the Electric Double Layer of Ionic Liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Learning the Physics of Pattern Formation from Images

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.