TY - JOUR A1 - Li, Hailong A1 - Bier, Markus A1 - Mars, Julian A1 - Weiss, Henning A1 - Dippel, Ann-Christin A1 - Gutowski, Olof A1 - Honkimäki, Veijo A1 - Mezger, Markus T1 - Interfacial premelting of ice in nano composite materials JF - Physical Chemistry Chemical Physics N2 - 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. Y1 - 2019 UR - https://doi.org/10.1039/C8CP05604H VL - 21 SP - 3734 EP - 3741 ER - TY - JOUR A1 - Bartsch, Hendrik A1 - Bier, Markus A1 - Dietrich, S. T1 - The role of counterions in ionic liquid crystals JF - The Journal of Chemical Physics N2 - 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. KW - Liquid crystals, Phase transitions, Electrostatics, Ions and properties, Crystal structure, Intermolecular forces, Monte Carlo methods, Classical statistical mechanics Y1 - 2021 UR - https://doi.org/10.1063/5.0034314 VL - 154 IS - 1 SP - 014901 ER - TY - JOUR A1 - Bier, Markus A1 - Mußotter, Maximilian A1 - Dietrich, S. T1 - Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales JF - Physical Review E N2 - 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. KW - Classical statistical mechanics, Electrostatic interactions, Interface & surface thermodynamics, Complex fluids, Ionic fluids, Liquid-solid interfaces, Polymers & Soft Matter, Statistical Physics Y1 - 2022 UR - https://doi.org/10.1103/PhysRevE.106.054801 VL - 106 IS - 5 SP - 054801 ER - TY - JOUR A1 - Janssen, Mathijs A1 - Bier, Markus T1 - Transient response of an electrolyte to a thermal quench JF - Physical Review E N2 - 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 VT for early (t≪τT) and late (t≫τT) times as compared to the relaxation time τT 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 VT) 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≪τT 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, VT exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)]. KW - Electrochemistry, Electrokinetic flows, Ionic transport, Nonequilibrium & irreversible thermodynamics, Thermoelectrics, Thermophoresis, Ionic fluids, Condensed Matter, Materials & Applied Physics, Statistical Physics, General Physics Y1 - 2019 UR - https://doi.org/10.1103/PhysRevE.99.042136 VL - 99 IS - 4 SP - 042136 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Blossey, Ralf A1 - Podgornik, Rudolf T1 - Charge symmetry broken complex coacervation JF - Physical Review Research N2 - Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve as a proxy for simple coacervation. First, a low-density density functional calculation reveals the dominance of two-particle configurations coupled by ion adsorption on neighboring macroions. Then a binary cell model, solved on the Debye-Hückel as well as the full nonlinear Poisson-Boltzmann level, unveils the charge symmetry breaking as inducing the phase separation between low- and high-density phases as a function of pH. These results can be identified as a charge symmetry broken complex coacervation between chemically identical macroions. KW - Aggregation, Biomolecular self-assembly, Electrostatic interactions, Charged colloids, Colloids, Proteins, Density functional calculations, Polymers & Soft Matter, Biological Physics, Statistical Physics Y1 - 2020 UR - https://doi.org/10.1103/PhysRevResearch.2.043417 VL - 2 IS - 4 ER - TY - JOUR A1 - Mußotter, Maximilian A1 - Bier, Markus A1 - Dietrich, S. T1 - Heterogeneous surface charge confining an electrolyte solution JF - The Journal of Chemical Physics N2 - 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. KW - Density functional theory, Fundamental measure theory, Electrostatics, Partial differential equations, Elementary particle interactions, Electrochemistry, Electrolytes, Interfaces Y1 - 2020 UR - https://doi.org/10.1063/5.0006208 VL - 152 IS - 23 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Dietrich, Siegfried T1 - Electrostatic interaction of particles trapped at fluid interfaces: effects of geometry and wetting properties JF - Soft Matter N2 - 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. Y1 - 2018 UR - https://doi.org/10.1039/C8SM01765D VL - 14 SP - 9436 EP - 9444 ER - TY - JOUR A1 - Bartsch, Hendrik A1 - Bier, Markus A1 - Dietrich, Siegfried T1 - Interface structures in ionic liquid crystals JF - Soft Matter N2 - 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. Y1 - 2019 UR - https://doi.org/10.1039/C9SM00062C VL - 15 SP - 4109 EP - 4126 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Blossey, Ralf A1 - Podgornik, Rudolf T1 - Charge regulation radically modifies electrostatics in membrane stacks JF - Physical Review E N2 - 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. KW - Applications of soft matter, Classical statistical mechanics, Electrostatic double layer forces, Electrostatic interactions, Charged colloids, Complex fluids, Interfaces, Polymers & Soft Matter, Statistical Physics Y1 - 2019 UR - https://doi.org/10.1103/PhysRevE.100.050601 VL - 100 IS - 5 SP - 050601 ER - TY - JOUR A1 - Zarubin, Grigorii A1 - Bier, Markus A1 - Dietrich, S. T1 - A ferronematic slab in external magnetic fields JF - Soft Matter N2 - 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. Y1 - 2018 UR - https://doi.org/10.1039/C8SM01813H VL - 14 SP - 9806 EP - 9818 ER - TY - JOUR A1 - Bier, Markus T1 - Non-equilibrium steady states of electrolyte interfaces JF - New Journal of Physics N2 - The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions. KW - Poisson-Nernst-Planck theory, non-equilibrium steady state, electrolyte interface, Gouy-Chapman model Y1 - 2024 UR - https://doi.org/10.1088/1367-2630/ad19a9 VL - 26 IS - 1 SP - 013008 ER -