Ions and dipoles in electric field: nonlinear polarization and field-dependent chemical reaction.

We investigate electric-field effects in dilute electrolytes with nonlinear polarization. As a first example of such systems, we add a dipolar component with a relatively large dipole moment [Formula: see text] to an aqueous electrolyte. As a second example, the solvent itself exhibits nonlinear polarization near charged objects. For such systems, we present a Ginzburg-Landau free energy and introduce field-dependent chemical potentials, entropy density, and stress tensor, which satisfy general thermodynamic relations. In the first example, the dipoles accumulate in high-field regions, as predicted by Abrashikin et al.[Phys.Rev.Lett. 99, 077801 (2007)]. Finally, we consider the case, where Bjerrum ion pairs form a dipolar component with nonlinear polarization. The Bjerrum dipoles accumulate in high-field regions, while field-induced dissociation was predicted by Onsager [J. Chem. Phys.2, 599 (1934)]. We present an expression for the field-dependent association constant K(E), which depends on the field strength nonmonotonically.

Long-range correlations of polarization and number densities in dilute electrolytes.

In dilute electrolytes, we calculate the pair correlation functions among the solvent polarization p, the solvent density n1, the cation density n2, and the anion density n3. We set up a simple Ginzburg-Landau free energy for these variables, so our results are valid at distances longer than the molecular size σ. In particular, we reproduce the Høye-Stell result for the polarization correlation ⟨pα(r)pß(0)⟩ (α, ß = x, y, z) [J. S. Høye and G. Stell, J. Chem. Phys. 68, 4145 (1978)], which is proportional to the second derivative ∂2(e-κr/r)/∂xα∂xß for r ≫ σ with κ being the Debye wave number. We also show that size asymmetry between the cations and the anions gives rise to similar long-range correlations in ⟨pα(r)δn1(0)⟩ and ⟨δni(r)δn1(0)⟩ (i = 1, 2, 3). Moreover, we calculate the polarization time-correlation function. As a unique feature in dynamics, the longitudinal polarization fluctuations (∝∇ · p) consist of rapidly decaying and slowly decaying components, where the latter relax with the charge density ρ. As a result, the long-range part of the equal-time polarization correlation changes into a different long-ranged and long-lived form after the shorter polarization relaxation.

Acoustic resonance in periodically sheared glass: damping due to plastic events.

Using molecular dynamics simulation, we study acoustic resonance in a low-temperature model glass by applying a small periodic shear at a boundary wall. Shear wave resonance occurs as the frequency ω approaches ωl = πc⊥l/L (l = 1, 2…). Here, c⊥ is the transverse sound speed and L is the cell width. At resonance, large-amplitude sound waves appear after many cycles even if the applied strain γ0 is very small. They then induce plastic events, which are heterogeneous on the mesoscopic scale and intermittent on timescales longer than the oscillation period tp = 2π/ω. We visualize them together with the extended elastic strains around them. These plastic events serve to damp sounds. We obtain the nonlinear damping Q-1 = tan δ due to the plastic events near the first resonance at ω ≅ ω1, which is linear in γ0 and independent of ω. After many resonant cycles, we observe an increase in the shear modulus (measured after switching-off the oscillation). We also observe catastrophic plastic events after a very long time (∼103tp), which induce system-size elastic strains and cause a transition from resonant to off-resonant states. At resonance, stroboscopic diffusion becomes detectable.

Theory of electrolytes including steric, attractive, and hydration interactions.

We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional F for the coarse-grained solvent, cation, and anion densities, including the Debye-Hückel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution ∝exp(-F/kBT). Eliminating the solvent density deviation in F, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density ns. Second, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model [J. Chem. Phys. 54, 1523 (1971)] for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule [Biophys. J. 72, 65 (1997)]. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.

Theory of applying heat flow from thermostatted boundary walls: Dissipative and local-equilibrium responses and fluctuation theorems.

We construct a microscopic theory of applying a heat flow from thermostatted boundary walls in the film geometry. We treat a classical one-component fluid, but our method is applicable to any fluids and solids. We express linear response of any variable B in terms of the time-correlation functions between B and the heat flows JK from the thermostats to the particles. Furthermore, the surface variables JK can be written in the form of space integrals of bulk quantities from the equations of motion. Owing to this surface-to-bulk relation, the steady-state response functions consist of dissipative and local-equilibrium parts, where the former gives rise to Fourier's law with Green's expression for the thermal conductivity. In the nonlinear regime, we derive the steady-state distribution in the phase space in the McLennan-Zubarev form from the first principles. Some fluctuation theorems are also presented.

Theory of applying shear strains from boundary walls: Linear response in glasses.

We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linear-response expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expressed in terms of the inter-particle correlations, as has been shown in the previous literature. Our stress relaxation function includes the effect of the boundary walls and can be used for inhomogeneous flow response. We show the presence of long-ranged, long-lived correlations among the fluctuations of the forces from the walls and the displacements of all the particles in the cell. We confirm these theoretical results numerically in a two-dimensional model glass. As an application, we describe emission and propagation of transverse sounds after boundary wall motions using these time-correlation functions. We also find resonant sound amplification when the frequency of an oscillatory shear approaches that of the first transverse sound mode.

Theory of nonionic hydrophobic solutes in mixture solvent: Solvent-mediated interaction and solute-induced phase separation.

We present a theory of nonionic solutes in a mixture solvent composed of water-like and alcohol-like species. First, we show the relationship among the solvation chemical potential, the partial volumes vi, the Kirkwood-Buff integrals, the second osmotic virial coefficient, and the Gibbs transfer free energy. We examine how the solute density n3 is coupled to the solvent densities n1 and n2 in thermodynamics. In the limit of small compressibility, we show that the space-filling condition ∑i vini = 1 nearly holds for inhomogeneous densities ni, where the concentration fluctuations of the solvent can give rise to a large solute-solute attractive interaction. We also derive a solute spinodal density n3spi for solute-induced instability. Next, we examine gas-liquid and liquid-liquid phase transitions induced by a small amount of a solute using the Mansoori, Carnahan, Starling, and Leland model for hard-sphere mixtures [J. Chem. Phys. 54, 1523-1525 (1971)]. Here, we assume that the solvent is close to its gas-liquid coexistence and the solute interacts repulsively with the water-like species but attractively with the alcohol-like one. We calculate the binodal and spinodal curves in the phase diagrams and examine nucleation for these two phase transitions.

Electric Double Layer Composed of an Antagonistic Salt in an Aqueous Mixture: Local Charge Separation and Surface Phase Transition.

We examine an electric double layer containing an antagonistic salt in an aqueous mixture, where the cations are small and hydrophilic but the anions are large and hydrophobic. In this situation, a strong coupling arises between the charge density and the solvent composition. As a result, the anions are trapped in an oil-rich adsorption layer on a hydrophobic wall. We then vary the surface charge density σ on the wall. For σ>0 the anions remain accumulated, but for σ<0 the cations are attracted to the wall with increasing |σ|. Furthermore, the electric potential drop Ψ(σ) is nonmonotonic when the solvent interaction parameter χ(T) exceeds a critical value χ_{c} determined by the composition and the ion density in the bulk. This leads to a first-order phase transition between two kinds of electric double layers with different σ and common Ψ. In equilibrium such two-layer regions can coexist. The steric effect due to finite ion sizes is crucial in these phenomena.

Erratum: Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes [Phys. Rev. E 86, 041504 (2012)].

This corrects the article DOI: 10.1103/PhysRevE.86.041504.

Ferroelectric glass of spheroidal dipoles with impurities: polar nanoregions, response to applied electric field, and ergodicity breakdown.

Using molecular dynamics simulation, we study dipolar glass in crystals composed of slightly spheroidal, polar particles and spherical, apolar impurities between metal walls. We present physical pictures of ferroelectric glass, which have been observed in relaxors, mixed crystals (such as KCN x KBr1-x ), and polymers. Our systems undergo a diffuse transition in a wide temperature range, where we visualize polar nanoregions (PNRs) surrounded by impurities. In our simulation, the impurities form clusters and their space distribution is heterogeneous. The polarization fluctuations are enhanced at relatively high T depending on the size of the dipole moment. They then form frozen PNRs as T is further lowered into the nonergodic regime. As a result, the dielectric permittivity exhibits the characteristic features of relaxor ferroelectrics. We also examine nonlinear response to cyclic applied electric field and nonergodic response to cyclic temperature changes (ZFC/FC), where the polarization and the strain change collectively and heterogeneously. We also study antiferroelectric glass arising from molecular shape asymmetry. We use an Ewald scheme of calculating the dipolar interaction in applied electric field.

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory.

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980)PHYADX0378-437110.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ(r), where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ(r) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h_{1}, where the surface order parameter ψ(a) is determined by h_{1} and is independent of the radius a. If r considerably exceeds a, ψ(r) decays as r^{-(1+η)} for a sphere and r^{-(1+η)/2} for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.

Ionization at a solid-water interface in an applied electric field: Charge regulation.

We investigate ionization at a solid-water interface in an applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density Γ0, where the degree of dissociation α is determined by the proton density in water close to the film. We show how α depends on the density n0 of NaOH in water and the surface charge density σm on the electrode. For σm > 0, the protons are expelled away from the film, leading to an increase in α. In particular, in the range 0 < σm < eΓ0, self-regulation occurs to realize α ≅ σm/eΓ0 for n0 ≪ nc, where nc is 0.01 mol/L for silica surfaces and is 2 × 10-5 mol/L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness H below the Debye length κ-1, where a crossover occurs at the Gouy-Chapman length. In particular, when σm ∼ eΓ0 and H ≪ κ-1, the surface charges remain only partially screened by ions, leading to a nonvanishing electric field in the interior.

Density functional theory of gas-liquid phase separation in dilute binary mixtures.

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas [Formula: see text] (the Gibbs energy of transfer) is considerably larger than the thermal energy [Formula: see text] for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by [Formula: see text], where [Formula: see text] is the solute density added in liquid. For [Formula: see text], phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Fluctuations of local electric field and dipole moments in water between metal walls.

We examine the thermal fluctuations of the local electric field Ek (loc) and the dipole moment µk in liquid water at T = 298 K between metal walls in electric field applied in the perpendicular direction. We use analytic theory and molecular dynamics simulation. In this situation, there is a global electrostatic coupling between the surface charges on the walls and the polarization in the bulk. Then, the correlation function of the polarization density pz(r) along the applied field contains a homogeneous part inversely proportional to the cell volume V. Accounting for the long-range dipolar interaction, we derive the Kirkwood-Fröhlich formula for the polarization fluctuations when the specimen volume v is much smaller than V. However, for not small v/V, the homogeneous part comes into play in dielectric relations. We also calculate the distribution of Ek (loc) in applied field. As a unique feature of water, its magnitude |Ek (loc)| obeys a Gaussian distribution with a large mean value E0 ≅ 17 V/nm, which arises mainly from the surrounding hydrogen-bonded molecules. Since |µk|E0 ∼ 30kBT, µk becomes mostly parallel to Ek (loc). As a result, the orientation distributions of these two vectors nearly coincide, assuming the classical exponential form. In dynamics, the component of µk(t) parallel to Ek (loc)(t) changes on the time scale of the hydrogen bonds ∼5 ps, while its smaller perpendicular component undergoes librational motions on time scales of 0.01 ps.

Bubble formation in water with addition of a hydrophobic solute.

We show that phase separation can occur in a one-component liquid outside its coexistence curve (CX) with addition of a small amount of a solute. The solute concentration at the transition decreases with increasing the difference of the solvation chemical potential between liquid and gas. As a typical bubble-forming solute, we consider O2 in ambient liquid water, which exhibits mild hydrophobicity and its critical temperature is lower than that of water. Such a solute can be expelled from the liquid to form gaseous domains while the surrounding liquid pressure is higher than the saturated vapor pressure p cx. This solute-induced bubble formation is a first-order transition in bulk and on a partially dried wall, while a gas film grows continuously on a completely dried wall. We set up a bubble free energy ΔG for bulk and surface bubbles with a small volume fraction ϕ. It becomes a function of the bubble radius R under the Laplace pressure balance. Then, for sufficiently large solute densities above a threshold, ΔG exhibits a local maximum at a critical radius and a minimum at an equilibrium radius. We also examine solute-induced nucleation taking place outside CX, where bubbles larger than the critical radius grow until attainment of equilibrium.

Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture.

We investigate bridging and aggregation of two colloidal particles in a near-critical binary mixture when the fluid far from the particles is outside the coexistence (CX) curve and is rich in the component disfavored by the colloid surfaces. In such situations, the adsorption-induced interaction is enhanced, leading to bridging and aggregation of the particles. We realize bridging firstly by changing the temperature with a fixed interparticle separation and secondly by letting the two particles aggregate. The interparticle attractive force dramatically increases upon bridging. The dynamics is governed by hydrodynamic flow around the colloid surfaces. In aggregation, the adsorption layers move with the particles and squeezing occurs at narrow separation. These results suggest relevance of bridging in the reversible colloid aggregation observed so far. We use the local functional theory [J. Chem. Phys., 2012, 136, 114704] to take into account the renormalization effect and the simulation method [Phys. Rev. Lett., 2000, 85, 1338] to calculate the hydrodynamic flow around the colloidal particles.

Molecular Dynamics Simulation of Water between Metal Walls under an Electric Field: Dielectric Response and Dynamics after Field Reversal.

We study water between parallel metal walls under an applied electric field accounting for the image effect at T = 298 K. The electric field due to the surface charges serves to attract and orient nearby water molecules, whereas it tends to a constant determined by the mean surface charge density away from the walls. We find Stern boundary layers with thicknesses of about 5 Å and a homogeneously polarized bulk region. The molecules in the layers respond more sensitively to the applied field than the molecules in the bulk. As a result, the potential drop in the layers is larger than that in the bulk unless the cell length exceeds 10 nm. We also examine the hydrogen bonds, which tend to make small angles with respect to the walls in the layers even without an applied field. The average local field considerably deviates from the classical Lorentz field and the local field fluctuations are very large in the bulk. If we suppose a nanometer-sized sphere around each molecule, the local field contribution from its exterior is nearly equal to that from the continuum electrostatics and that from its interior yields the deviation from the classical Lorentz field. As a nonequilibrium problem, we investigate the dynamics after a reversal of applied field, where the relaxation is mostly caused by large-angle rotational jumps after 1 ps due to the presence of the hydrogen bond network. The molecules undergoing these jumps themselves form hydrogen-bonded clusters heterogeneously distributed in space.

Nematic caps on colloidal particles in a nematogenic liquid under an electric field.

We examine the localized nematic regions (caps) on spherical colloidal particles suspended in a nematogenic liquid in the isotropic phase in the bulk by solving the Poisson equation with an orientation-dependent dielectric tensor. These caps appear and grow with an increasing applied electric field. We assume positive dielectric anisotropy of the nematogenic liquid and a high dielectric constant of the particles. Then, the electric field becomes the strongest near the poles of each particle along the field direction, leading to nematic caps. This cap formation occurs continuously for homeotropic anchoring, but is a discontinuous transition otherwise. We also discuss how the nematic caps can be observed in dielectric response, birefringence, and depolarized light scattering.

Orientational glass in mixtures of elliptic and circular particles: structural heterogeneities, rotational dynamics, and rheology.

Using molecular dynamics simulation with an angle-dependent Lennard-Jones potential, we study orientational glass with quadrupolar symmetry in mixtures of elliptic particles and circular impurities in two dimensions. With a mild aspect ratio (= 1.23) and a mild size ratio (= 1.2), we realize a plastic crystal at relatively high temperature T. With further lowering T, we find a structural phase transition for very small impurity concentration c and pinned disordered orientations for not small c. The ellipses are anchored by the impurities in the planar alignment. With increasing c, the orientation domains composed of isosceles triangles gradually become smaller, resulting in orientational glass with crystal order. In our simulation, the impurity distribution becomes heterogeneous during quenching from liquid, which then produces rotational dynamic heterogeneities. We also examine rheology in orientational glass to predict a shape memory effect and a superelasticity effect, where a large fraction of the strain is due to collective orientation changes.

Dynamics in a tetrahedral network glassformer: vibrations, network rearrangements, and diffusion.

We perform molecular dynamics simulation on a tetrahedral network glassformer using a model for viscous SiO2 by Coslovich and Pastore [J. Phys.: Condens. Matter 21, 285107 (2009)]. In this system, Si and O particles form a random network at low temperature T. We attach an ellipsoid to each particle to represent its time-averaged vibration tensor. We then examine the anisotropic vibrations of Si and O, where the ellipsoid orientations are correlated with the network. The ellipsoids exhibit marked vibrational heterogeneity. The configuration changes occur as breakage and reorganization of the network, where only one or two particles undergo large jumps at each rearrangement leading to diffusion. To the time-correlation functions, however, the particles surrounding these largely displaced ones yield significantly T-dependent contributions, resulting in a weak violation of the Stokes-Einstein relation. This crossover is mild in silica due to the small Si-O bond numbers per particle, while it is strong in fragile glassformers with large coordination numbers. On long timescales, jump events tend to occur in the same regions forming marked dynamic heterogeneity. We also calculate the diffusion constants and the viscosity. The diffusion obeys activation dynamics and may be studied by short-time analysis of irreversible jumps.