Pair dynamics of active force dipoles in an odd-viscous fluid.

We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible fluid with an odd viscosity, while the force dipole (representing an active protein or enzyme) induces a dipolar flow. Taking into account the momentum decay in the 2D fluid, we obtain analytically the mobility tensor that depends on the odd viscosity and includes nonreciprocal hydrodynamic interactions. We find that the particle pair shows spiral behavior due to the transverse flow induced by the odd viscosity. When the magnitude of the odd viscosity is large as compared with the shear viscosity, two types of oscillatory behaviors are seen. One of them can be understood as arising from closed orbits in dynamical systems, and its circular trajectories are determined by the ratio between the magnitude of the odd viscosity and the force dipole. In addition, the phase diagrams of the particle dipolar angles are obtained numerically. Our findings reveal that the nonreciprocal response leads to complex dynamics of active particles embedded in an active fluid with odd viscosity.

The Process-Directed Self-Assembly of Block Copolymer Particles.

The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, χAB ) and the selectivity of solvent toward one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, it is identified that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. The findings lead to an effective way of tailoring nanostructure of BCP particles for various industrial applications.

Conductivity of Concentrated Electrolytes.

The conductivity of ionic solutions is arguably their most important trait, being widely used in electrochemical, biochemical, and environmental applications. The Debye-Hückel-Onsager theory successfully predicts the conductivity at very low ionic concentrations of up to a few millimolars, but there is no well-established theory applicable at higher concentrations. We study the conductivity of ionic solutions using a stochastic density functional theory, paired with a modified Coulomb interaction that accounts for the hard-core repulsion between the ions. The modified potential suppresses unphysical, short-range electrostatic interactions, which are present in the Debye-Hückel-Onsager theory. Our results for the conductivity show very good agreement with experimental data up to 3 molars, without any fit parameters. We provide a compact expression for the conductivity, accompanied by a simple analytical approximation.

Conductance of concentrated electrolytes: Multivalency and the Wien effect.

The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.

Critical behavior of charge-regulated macro-ions.

Based on a collective description of electrolytes composed of charge-regulated macro-ions and simple salt ions, we analyze their equilibrium charge state in the bulk and their behavior in the vicinity of an external electrified surface. The mean-field formulation of mobile macro-ions in an electrolyte bathing solution is extended to include interactions between association and dissociation sites. We demonstrate that above a critical concentration of salt, similar to the critical micelle concentration, a non-trivial distribution of charge states sets in. Such a charge state can eventually lead to a liquid-liquid phase separation based on charge regulation.

Surface Pressure of Charged Colloids at the Air/Water Interface.

Charged colloidal monolayers at the interface between water and air (or oil) are used in a large number of chemical, physical, and biological applications. Although considerable experimental and theoretical effort has been devoted in the past few decades to the investigation of such monolayers, some of their fundamental properties are not yet fully understood. In this article, we model charged colloidal monolayers as a continuum layer of finite thickness, with a separate charge distribution on the water and air sides. The electrostatic surface free energy and surface pressure are calculated via the charging method and within the Debye-Hückel approximation. We obtain the dependence of surface pressure on several system parameters: the monolayer thickness, its distinct dielectric permittivity, and the ionic strength of the aqueous subphase. The surface pressure scaling with the area per particle, a, is found to be between a-2 in the close-packing limit and a-5/2 in the loose-packing limit. In general, it is found that the surface pressure is strongly influenced by charges on the air side of the colloids. However, when the larger charge resides on the water side, a more subtle dependence on salt concentration emerges. This corrects a common assumption that the charges on the water side can always be neglected due to screening. Finally, using a single fit parameter, our theory is found to fit the experimental data well for strong- to intermediate-strength electrolytes. We postulate that an anomalous scaling of a-3/2, recently observed in low ionic concentrations, cannot be accounted for within a linear theory, and its explanation requires a fully nonlinear analysis.

Charge regulating macro-ions in salt solutions: screening properties and electrostatic interactions.

We revisit the charge-regulation mechanism of macro-ions and apply it to mobile macro-ions in a bathing salt solution. In particular, we examine the effects of correlation between various adsorption/desorption sites and analyze the collective behavior in terms of the solution effective screening properties. We show that such a behavior can be quantified in terms of the charge asymmetry of the macro-ions, defined by their preference for a non-zero effective charge, and their donor/acceptor propensity for exchanging salt ions with the bathing solution. Asymmetric macro-ions tend to increase the screening, while symmetric macro-ions can in some cases decrease it. Macro-ions that are classified as donors display a rather regular behavior, while those that behave as acceptors exhibit an anomalous non-monotonic Debye length. The screening properties, in their turn, engender important modifications to the disjoining pressure between two charged surfaces. Our findings are in particular relevant for solutions of proteins, whose exposed amino acids can undergo charge dissociation/association processes to/from the bathing solution, and can be considered as a solution of charged regulated macro-ions, as analyzed here.

Osmotic pressure between arbitrarily charged planar surfaces: A revisited approach.

The properties of ionic solutions between charged surfaces are often studied within the Poisson-Boltzmann framework, by finding the electrostatic potential profile. For example, the osmotic pressure between two charged planar surfaces can be evaluated by solving coupled equations for the electrostatic potential and osmotic pressure. Such a solution relies on symmetry arguments and is restricted to either equally or oppositely charged surfaces. Here, we provide a different and more efficient scheme to derive the osmotic pressure straightforwardly, without the need to find the electrostatic potential profile. We derive analytical expressions for the osmotic pressure in terms of the inter-surface separation, salt concentration, and arbitrary boundary conditions. Such results should be useful in force measurement setups, where the force is measured between two differently prepared surfaces, or between two surfaces held at a fixed potential difference. The proposed method can be systematically used for generalized Poisson-Boltzmann theories in planar geometries, as is demonstrated for the sterically modified Poisson-Boltzmann theory.

Dielectric constant of ionic solutions: Combined effects of correlations and excluded volume.

The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper, we study two such possible sources: long-range Coulombic correlations and solvent excluded-volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as a function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to the correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.

Surface Tension of Acid Solutions: Fluctuations beyond the Nonlinear Poisson-Boltzmann Theory.

We extend our previous study of surface tension of ionic solutions and apply it to acids (and salts) with strong ion-surface interactions, as described by a single adhesivity parameter for the ionic species interacting with the interface. We derive the appropriate nonlinear boundary condition with an effective surface charge due to the adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero loop (mean field) corresponds of the full nonlinear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension and the one-loop contribution gives a generalization of the Onsager-Samaras result. Adhesivity significantly affects both contributions to the surface tension, as can be seen from the dependence of surface tension on salt concentration for strongly absorbing ions. Comparison with available experimental data on a wide range of different acids and salts allows the fitting of the adhesivity parameter. In addition, it identifies the regime(s) where the hypotheses on which the theory is based are outside their range of validity.

Bjerrum pairs in ionic solutions: A Poisson-Boltzmann approach.

Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the Debye screening length and relate our results to recent surface-force experiments. Furthermore, we show that Bjerrum pairs reduce the ionic concentration in bulk electrolyte and at the proximity of charged surfaces, while they enhance the attraction between oppositely charged surfaces.

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions.

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show that how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm as well as the ionic profiles is used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.

Differential capacitance of the electric double layer: the interplay between ion finite size and dielectric decrement.

We study the electric double layer by combining the effects of ion finite size and dielectric decrement. At high surface potential, both mechanisms can cause saturation of the counter-ion concentration near a charged surface. The modified Grahame equation and differential capacitance are derived analytically for a general expression of a permittivity ε(n) that depends on the local ion concentration, n, and under the assumption that the co-ions are fully depleted from the surface. The concentration at counter-ion saturation is found for any ε(n), and a criterion predicting which of the two mechanisms (steric vs. dielectric decrement) is the dominant one is obtained. At low salinity, the differential capacitance as function of surface potential has two peaks (so-called camel-shape). Each of these two peaks is connected to a saturation of counter-ion concentration caused either by dielectric decrement or by their finite size. Because these effects depend mainly on the counter-ion concentration at the surface proximity, for opposite surface-potential polarity either the cations or anions play the role of counter-ions, resulting in an asymmetric camel-shape. At high salinity, we obtain and analyze the crossover in the differential capacitance from a double-peak shape to a uni-modal one. Finally, several nonlinear models of the permittivity decrement are considered, and we predict that the concentration at dielectrophoretic saturation shifts to higher concentration than those obtained by the linear decrement model.

Surface tension of electrolyte interfaces: ionic specificity within a field-theory approach.

We study the surface tension of ionic solutions at air/water and oil/water interfaces by using field-theoretical methods and including a finite proximal surface-region with ionic-specific interactions. The free energy is expanded to first-order in a loop expansion beyond the mean-field result. We calculate the excess surface tension and obtain analytical predictions that reunite the Onsager-Samaras pioneering result (which does not agree with experimental data), with the ionic specificity of the Hofmeister series. We derive analytically the surface-tension dependence on the ionic strength, ionic size, and ion-surface interaction, and show consequently that the Onsager-Samaras result is consistent with the one-loop correction beyond the mean-field result. Our theory fits well a wide range of salt concentrations for different monovalent ions using one fit parameter per electrolyte and reproduces the reverse Hofmeister series for anions at the air/water and oil/water interfaces.

Correlated lateral phase separations in stacks of lipid membranes.

Motivated by the experimental study of Tayebi et al. [Nat. Mater. 11, 1074 (2012)] on phase separation of stacked multi-component lipid bilayers, we propose a model composed of stacked two-dimensional Ising spins. We study both its static and dynamical features using Monte Carlo simulations with Kawasaki spin exchange dynamics that conserves the order parameter. We show that at thermodynamical equilibrium, due to strong inter-layer correlations, the system forms a continuous columnar structure for any finite interaction across adjacent layers. Furthermore, the phase separation shows a faster dynamics as the inter-layer interaction is increased. This temporal behavior is mainly due to an effective deeper temperature quench because of the larger value of the critical temperature, Tc, for larger inter-layer interaction. When the temperature ratio, T/Tc, is kept fixed, the temporal growth exponent does not increase and even slightly decreases as a function of the increased inter-layer interaction.

Charge-induced phase separation in lipid membranes.

Phase separation in lipid bilayers that include negatively charged lipids is examined experimentally. We observed phase-separated structures and determined the membrane miscibility temperatures in several binary and ternary lipid mixtures of unsaturated neutral lipid, dioleoylphosphatidylcholine (DOPC), saturated neutral lipid, dipalmitoylphosphatidylcholine (DPPC), unsaturated charged lipid, dioleoylphosphatidylglycerol (DOPG((-))), saturated charged lipid, dipalmitoylphosphatidylglycerol (DPPG((-))), and cholesterol. In binary mixtures of saturated and unsaturated charged lipids, the combination of the charged head with the saturation of the hydrocarbon tail is a dominant factor in the stability of membrane phase separation. DPPG((-)) enhances phase separation, while DOPG((-)) suppresses it. Furthermore, the addition of DPPG((-)) to a binary mixture of DPPC/cholesterol induces phase separation between DPPG((-))-rich and cholesterol-rich phases. This indicates that cholesterol localization depends strongly on the electric charge on the hydrophilic head group rather than on the ordering of the hydrocarbon tails. Finally, when DPPG((-)) was added to a neutral ternary system of DOPC/DPPC/cholesterol (a conventional model of membrane rafts), a three-phase coexistence was produced. We conclude by discussing some qualitative features of the phase behaviour in charged membranes using a free energy approach.

Dipolar Poisson-Boltzmann approach to ionic solutions: a mean field and loop expansion analysis.

We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a mean-field level, we account for any internal charge distribution of particles. The dipolar degrees of freedom are added to the ionic ones and result in a generalization of the Poisson-Boltzmann (PB) equation called the Dipolar PB (DPB). By looking at the DPB equation around a fixed point-like ion, a closed-form formula for the dielectric constant is obtained. We express the dielectric constant using the "hydration length" that characterizes the hydration shell of dipoles around ions, and thus the strength of the dielectric decrement. The DPB equation is then examined for three additional cases: mixture of solvents, polarizable medium, and ions of finite size. Employing field-theoretical methods, we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. For pure water, the dipolar fluctuations represent an important correction to the mean-field value and good agreement with the water dielectric constant is obtained. For ionic solutions we predict analytically the dielectric decrement that depends on the ionic strength in a nonlinear way. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. A linear dependence of the dielectric constant on the salt concentration is observed at low salinity, and a noticeable deviation from linearity can be seen for ionic strength above 1 M, in agreement with experiments.