Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales.

The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.

The role of counterions in ionic liquid crystals.

Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid-crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension that accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation-anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogens (i.e., liquid-crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and hexagonal crystal phases. We find that in the ordinary smectic-A phase, the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase, the small counterions accumulate in between the smectic layers. Due to this phenomenology, the wide smectic-A phase could be interesting for applications, which hinge on the presence of conductivity channels for mobile ions.

Heterogeneous surface charge confining an electrolyte solution.

The structure of dilute electrolyte solutions close to a surface carrying a spatially inhomogeneous surface charge distribution is investigated by means of classical density functional theory within the approach of fundamental measure theory. For electrolyte solutions, the influence of these inhomogeneities is particularly strong because the corresponding characteristic length scale is the Debye length, which is large compared to molecular sizes. Here, a fully three-dimensional investigation is performed, which accounts explicitly for the solvent particles, and thus provides insight into effects caused by ion-solvent coupling. The present study introduces a versatile framework to analyze a broad range of types of surface charge heterogeneities even beyond the linear response regime. This reveals a sensitive dependence of the number density profiles of the fluid components and of the electrostatic potential on the magnitude of the charge as well as on the details of the surface charge patterns at small scales.

Charge regulation radically modifies electrostatics in membrane stacks.

Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.

Transient response of an electrolyte to a thermal quench.

We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage V_{T} for early (t≪τ_{T}) and late (t≫τ_{T}) times as compared to the relaxation time τ_{T} of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and V_{T}) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τ_{T} regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, V_{T} exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)JCPSA60021-960610.1063/1.4923199].

Interface structures in ionic liquid crystals.

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which additionally carry charges. This combination gives rise to a complex interplay of the underlying (anisotropic) contributions to the pair interactions. It promises interesting and distinctive structural and orientational properties to arise in systems of ILCs, combining properties of liquid crystals and ionic liquids. While previous theoretical studies have focused on the phase behavior of ILCs and the structure of the respective bulk phases, in the present study we provide new results, obtained within density functional theory, concerning (planar) free interfaces between an isotropic liquid L and two types of smectic-A phases (SA or SAW). We discuss the structural and orientational properties of these interfaces in terms of the packing fraction profile η(r) and the orientational order parameter profile S2(r) concerning the tilt angle α between the (bulk) smectic layer normal and the interface normal. The asymptotic decay of η(r) and of S2(r) towards their values in the isotropic bulk is discussed, too.

Interfacial premelting of ice in nano composite materials.

The interfacial premelting in ice/clay nano composites was studied by high energy X-ray diffraction. Below the melting point of bulk water, the formation of liquid water was observed for the ice/vermiculite and ice/kaolin systems. The liquid fraction is gradually increasing with temperature. For both minerals, similar effective premelting layer thicknesses of 2-3 nm are reached 3 K below the bulk melting point. For the quantitative description of the molten water fraction in wet clay minerals we developed a continuum model for short range interactions and arbitrary pore size distributions. This model quantitatively describes the experimental data over the entire temperature range. Model parameters were obtained by fitting using a maximum entropy (MaxEnt) approach. Pronounced differences in the deviation from Antonow's rule relating interfacial free energy between ice, water, and clay are observed for the charged vermiculite and uncharged kaolin minerals. The resultant parameters are discussed in terms of their ice nucleation efficiency. Using well defined and characterized ice/clay nano composite samples, this work bridges the gap between studies on single crystalline ice/solid model interfaces and naturally occurring soils and permafrost.

Electrostatic interaction of particles trapped at fluid interfaces: effects of geometry and wetting properties.

The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson-Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle θ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with θ only within an interval around 90°. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle.

A ferronematic slab in external magnetic fields.

The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off.

Microphase separation and the formation of ion conductivity channels in poly(ionic liquid)s: A coarse-grained molecular dynamics study.

We study generic properties of poly(ionic liquid)s (PILs) via coarse-grained molecular dynamics simulations in bulk solution and under confinement. The influence of different side chain lengths on the spatial properties of the PIL systems and on the ionic transport mechanism is investigated in detail. Our results reveal the formation of apolar and polar nanodomains with increasing side chain length in good agreement with previous results for molecular ionic liquids. The ion transport numbers are unaffected by the occurrence of these domains, and the corresponding values highlight the potential role of PILs as single-ion conductors in electrochemical devices. In contrast to bulk behavior, a pronounced formation of ion conductivity channels in confined systems is initiated in close vicinity to the boundaries. We observe higher ion conductivities in these channels for increasing PIL side chain lengths in comparison with bulk values and provide an explanation for this effect. The appearance of these domains points to an improved application of PILs in modern polymer electrolyte batteries.

Correction: Surface induced smectic order in ionic liquids - an X-ray reflectivity study of [C22C1im]+[NTf2].

Correction for 'Surface induced smectic order in ionic liquids - an X-ray reflectivity study of [C22C1im]+[NTf2]-' by Julian Mars et al., Phys. Chem. Chem. Phys., 2017, 19, 26651-26661.

Effective Landau theory of ferronematics.

An effective Landau-like description of ferronematics, i.e., suspensions of magnetic colloidal particles in a nematic liquid crystal (NLC), is developed in terms of the corresponding magnetization and nematic director fields. The study is based on a microscopic model and on classical density functional theory. Ferronematics are susceptible to weak magnetic fields and they can exhibit a ferromagnetic phase, which has been predicted several decades ago and has recently been found experimentally. Within the proposed effective Landau theory of ferronematics, one has quantitative access, e.g., to the coupling between the magnetization of the magnetic colloids and the nematic director of the NLC. On mesoscopic length scales, this generates complex response patterns.

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation.

We revisit a classical problem of theoretical electrochemistry: the response of an electric double-layer capacitor (EDLC) subject to a small, suddenly applied external potential. We solve the Debye-Falkenhagen equation to obtain exact expressions for key EDLC quantities: the ionic charge density, the ionic current density, and the electric field. In contrast to earlier works, our results are not restricted to the long-time asymptotics of those quantities. The solutions take the form of infinite sums whose successive terms all decay exponentially with increasingly short relaxation times. Importantly, this set of relaxation times is the same among all aforementioned EDLC quantities; this property is demanded on physical grounds but not generally achieved within approximation schemes. The scaling of the largest relaxation timescale τ_{1}, that determines the long-time decay, is in accordance with earlier results: Depending on the Debye length, λ_{D}, and the electrode separation, 2L, it amounts to τ_{1}≃λ_{D}L/D for L≫λ_{D} and τ_{1}≃4L^{2}/(π^{2}D) for L≪λ_{D}, respectively (with D being the ionic diffusivity).

Electrostatic interaction between dissimilar colloids at fluid interfaces.

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.

Electrolyte solutions at heterogeneously charged substrates.

The influence of a chemically or electrically heterogeneous distribution of interaction sites at a planar substrate on the number density of an adjacent fluid is studied by means of classical density functional theory (DFT). In the case of electrolyte solutions the effect of this heterogeneity is particularly long ranged, because the corresponding relevant length scale is set by the Debye length which is large compared to molecular sizes. The DFT used here takes the solvent particles explicitly into account and thus captures phenomena, inter alia, due to ion-solvent coupling. The present approach provides closed analytic expressions describing the influence of chemically and electrically nonuniform walls. The analysis of isolated δ-like interactions, isolated interaction patches, and hexagonal periodic distributions of interaction sites reveals a sensitive dependence of the fluid density profiles on the type of the interaction, as well as on the size and the lateral distribution of the interaction sites.

Local pressure for confined systems.

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium, the local pressure is a functional of the shape of the walls. It is shown that, due to the intrinsic nonlocal character of the interactions among the particles forming the fluid, the applicability of approximate schemes such as the concept of a surface of tension or morphometric thermodynamics is limited to wall curvatures that are small compared to the range of particle-particle interactions.

Spontaneous symmetry breaking of charge-regulated surfaces.

The interaction between two chemically identical charge-regulated surfaces is studied using the classical density functional theory. In contrast to common expectations and assumptions, under certain realistic conditions we find a spontaneous emergence of disparate charge densities on the two surfaces. The surface charge densities can differ not only in their magnitude, but quite unexpectedly, even in their sign, implying that the electrostatic interaction between the two chemically identical surfaces can be attractive instead of repulsive. Moreover, an initial symmetry with equal charge densities on both surfaces can also be broken spontaneously upon decreasing the separation between the two surfaces. The origin of this phenomenon is a competition between the adsorption of ions from the solution to the surface and the interaction between the adsorbed ions already on the surface. These findings are fundamental for the understanding of the forces between colloidal objects and, in particular, they are bound to strongly influence the present picture of protein interaction.

Smectic phases in ionic liquid crystals.

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which carry charges and therefore combine properties of liquid crystals, e.g. the formation of mesophases, and of ionic liquids, such as low melting temperatures and tiny triple-point pressures. Previous density functional calculations have revealed that the phase behavior of ILCs is strongly affected by their molecular properties, i.e. their aspect ratio, the loci of the charges, and their interaction strengths. Here, we report new findings concerning the phase behavior of ILCs as obtained by density functional theory and Monte Carlo simulations. The most important result is the occurrence of a novel, wide smectic-A phase [Formula: see text], at low temperature, the layer spacing of which is larger than that of the ordinary high-temperature smectic-A phase [Formula: see text]. Unlike the ordinary smectic S A phase, the structure of the [Formula: see text] phase consists of alternating layers of particles oriented parallel to the layer normal and oriented perpendicular to it.

Surface induced smectic order in ionic liquids - an X-ray reflectivity study of [C22C1im]+[NTf2].

Surface induced smectic order was found for the ionic liquid 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide by X-ray reflectivity and grazing incidence scattering experiments. Near the free liquid surface, an ordered structure of alternating layers composed of polar and non-polar moieties is observed. This leads to an oscillatory interfacial profile perpendicular to the liquid surface with a periodicity of 3.7 nm. Small angle X-ray scattering and polarized light microscopy measurements suggest that the observed surface structure is related to fluctuations into a metastable liquid crystalline SmA2 phase that was found by supercooling the bulk liquid. The observed surface ordering persists up to 157 °C, i.e. more than 88 K above the bulk melting temperature of 68.1 °C. Close to the bulk melting point, we find a thickness of the ordered layer of L = 30 nm. The dependency of L(τ) = Λ ln(τ/τ1) vs. reduced temperature τ follows a logarithmic growth law. In agreement with theory, the pre-factor Λ is governed by the correlation length of the isotropic bulk phase.

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.