Asymmetric Rectified Electric Fields for Symmetric Electrolytes.

In this paper, building upon the numerical discovery of asymmetric rectified electric fields (AREFs), we explore the generation of AREF by applying a sawtooth-like voltage to 1:1 electrolytes with equal diffusion coefficients confined between two planar blocking electrodes. This differs from an earlier approach based on a sinusoidal AC voltage applied to 1:1 electrolytes with unequal diffusion coefficients. By numerically solving the full Poisson-Nernst-Planck equations, we demonstrate that AREF can be generated by a slow rise and a fast drop of the potential (or vice versa), even for electrolytes with equal diffusion coefficients of the cations and anions. We employ an analytically constructed equivalent electric circuit to explain the underlying physical mechanism. Importantly, we find that the strength of AREF can be effectively tuned from zero to its maximal value by only manipulating the time dependence of the driving voltage, eliminating the necessity to modify the electrolyte composition between experiments. This provides valuable insights to control the manipulation of AREF, which facilitates enhanced applications in diverse electrochemical systems.

Asymmetric rectified electric fields: nonlinearities and equivalent circuits.

Recent experiments [S. H. Hashemi et al., Phys. Rev. Lett., 2018, 121, 185504] have shown that a long-ranged steady electric field emerges when applying an oscillating voltage over an electrolyte with unequal mobilities of cations and anions confined between two planar blocking electrodes. To explain this effect we analyse full numerical calculations based on the Poisson-Nernst-Planck equations by means of analytically constructed equivalent electric circuits. Surprisingly, the resulting equivalent circuit has two capacitive elements, rather than one, which introduces a new timescale for electrolyte dynamics. We find a good qualitative agreement between the numerical results and our simple analytic model, which shows that the long-range steady electric field emerges from the different charging rates of cations and anions in the electric double layers.

Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors.

Experiments have shown that the conductance of conical channels, filled with an aqueous electrolyte, can strongly depend on the history of the applied voltage. These channels hence have a memory and are promising elements in brain-inspired (iontronic) circuits. We show here that the memory of such channels stems from transient concentration polarization over the ionic diffusion time. We derive an analytic approximation for these dynamics which shows good agreement with full finite-element calculations. Using our analytic approximation, we propose an experimentally realizable Hodgkin-Huxley iontronic circuit where micrometer cones take on the role of sodium and potassium channels. Our proposed circuit exhibits key features of neuronal communication such as all-or-none action potentials upon a pulse stimulus and a spike train upon a sustained stimulus.

Unveiling the capabilities of bipolar conical channels in neuromorphic iontronics.

Conical channels filled with an aqueous electrolyte have been proposed as promising candidates for iontronic neuromorphic circuits. This is facilitated by a novel analytical model for the internal channel dynamics [T. M. Kamsma, W. Q. Boon, T. ter Rele, C. Spitoni and R. van Roij, Phys. Rev. Lett., 2023, 130(26), 268401], the relative ease of fabrication of conical channels, and the wide range of achievable memory retention times by varying the channel lengths. In this work, we demonstrate that the analytical model for conical channels can be generalized to channels with an inhomogeneous surface charge distribution, which we predict to exhibit significantly stronger current rectification and more pronounced memristive properties in the case of bipolar channels, i.e. channels where the tip and base carry a surface charge of opposite sign. Additionally, we show that the use of bipolar conical channels in a previously proposed iontronic circuit features hallmarks of neuronal communication, such as all-or-none action potentials and spike train generation. Bipolar channels allow, however, for circuit parameters in the range of their biological analogues, and exhibit membrane potentials that match well with biological mammalian action potentials, further supporting their potential biocompatibility.

Coulombic Surface-Ion Interactions Induce Nonlinear and Chemistry-Specific Charging Kinetics.

While important for many industrial applications, chemical reactions responsible for the charging of solids in water are often poorly understood. We theoretically investigate the charging kinetics of solid-liquid interfaces and find that the time-dependent equilibration of surface charge contains key information not only on the reaction mechanism, but also on the valency of the reacting ions. We construct a nonlinear differential equation describing surface charging by combining chemical Langmuir kinetics and electrostatic Poisson-Boltzmann theory. Our results reveal a clear distinction between late-time (near-equilibrium) and short-time (far-from-equilibrium) relaxation rates, the ratio of which contains information on the charge valency and ad- or desorption mechanism of the charging process. Similarly, we find that single-ion reactions can be distinguished from two-ion reactions, as the latter show an inflection point during equilibration. Interestingly, such inflection points are characteristic of autocatalytic reactions, and we conclude that the Coulombic ion-surface interaction is an autocatalytic feedback mechanism.

Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations.

Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT) and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one is based on the simplest mean-field treatment of Coulomb interactions (MFC), while the other two employ the Mean Spherical Approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function, whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that are in excellent agreement with MD simulations in the near field, in the far field, we observe that the decay lengths are consistent between IET, MSAc, and MD simulations, whereas those from MFC and MSAu deviate significantly. Using DFT, we calculated the solvation force, which relates directly to surface force experiments. We find that its decay length is neither qualitatively nor quantitatively close to the large decay lengths measured in experiments and conclude that the latter cannot be accounted for by the primitive model. The anomalously large decay lengths found in surface force measurements require an explanation that lies beyond primitive models.

Flow-Induced Surface Charge Heterogeneity in Electrokinetics due to Stern-Layer Conductance Coupled to Reaction Kinetics.

We theoretically study the electrokinetic problem of a pressure-induced liquid flow through a narrow long channel with charged walls, going beyond the classical Helmholtz-Schmolukowski picture by considering the surprisingly strong combined effect of (i) Stern-layer conductance and (ii) dynamic charge-regulating rather than fixed surface charges. We find that the water flow induces, apart from the well-known streaming potential, also a strongly heterogeneous surface charge and zeta potential on chemically homogeneous channel walls. Moreover, we identify a novel steady state with a nontrivial 3D electric flux with 2D surface charges acting as sources and sinks. For a pulsed pressure drop our findings also provide a first-principles explanation for ill-understood experiments on the effect of flow on interfacial chemistry [D. Lis et al., Science 344, 1138 (2014)SCIEAS0036-807510.1126/science.1253793].

Colloid-oil-water-interface interactions in the presence of multiple salts: charge regulation and dynamics.

We theoretically and experimentally investigate colloid-oil-water-interface interactions of charged, sterically stabilized, poly(methyl-methacrylate) colloidal particles dispersed in a low-polar oil (dielectric constant ε = 5-10) that is in contact with an adjacent water phase. In this model system, the colloidal particles cannot penetrate the oil-water interface due to repulsive van der Waals forces with the interface whereas the multiple salts that are dissolved in the oil are free to partition into the water phase. The sign and magnitude of the Donnan potential and/or the particle charge is affected by these salt concentrations such that the effective interaction potential can be highly tuned. Both the equilibrium effective colloid-interface interactions and the ion dynamics are explored within a Poisson-Nernst-Planck theory, and compared to experimental observations.

Tuning Colloid-Interface Interactions by Salt Partitioning.

We show that the interaction of an oil-dispersed colloidal particle with an oil-water interface is highly tunable from attractive to repulsive, either by varying the sign of the colloidal charge via charge regulation or by varying the difference in hydrophilicity between the dissolved cations and anions. In addition, we investigate the yet unexplored interplay between the self-regulated colloidal surface charge distribution with the planar double layer across the oil-water interface and the spherical one around the colloid. Our findings explain recent experiments and have direct relevance for tunable Pickering emulsions.

Alternating strings and clusters in suspensions of charged colloids.

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

Analysis of electrolyte transport through charged nanopores.

We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)JCPSA60021-960610.1063/1.1669814]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

A Landau-de Gennes theory for hard colloidal rods: Defects and tactoids.

We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory, we are not only able to describe the isotropic-nematic phase transition as function of density, including the well-known density jump, but also the isotropic-nematic planar interface. The resulting theory is applied in calculations of the isotropic core size in a radial hedgehog defect, the density dependence of linear defects of hard rods in square confinement, and the formation of a nematic droplet in an isotropic background.

Density-induced reentrant melting of colloidal Wigner crystals.

Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloidal systems, the phase boundaries as well as crystal structure are highly tunable by experimental parameters such as salt concentration and pH. By using projections of the colloid-ion mixture to a system of (soft) repulsive spheres and the one-component plasma (OCP), we study the hitherto unexplained experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density. Our study shows that the surface chemistry should involve a competition between adsorption of cations and anions to explain the observed density-induced reentrant melting.

Density functional theory for chiral nematic liquid crystals.

Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Rapid Communication we address the problem by means of a density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropy-driven cholesteric phase, which can be either right or left handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an interplay between local nematic alignment and excluded-volume differences between left- and right-handed particle pairs.

Free minimization of the fundamental measure theory functional: Freezing of parallel hard squares and cubes.

Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy functional, we apply fundamental measure theory to analyze the phase behavior of parallel hard squares and hard cubes. We compare our results with those obtained by the traditional approach based on the Gaussian parameterization, finding small deviations and good overall agreement between the two methods. For hard squares, our predictions feature at intermediate packing fraction a smectic phase, which is however expected to be unstable due to thermal fluctuations. Due to this inconsistency, we cannot determine unambiguously the prediction of the theory for the expected fluid-to-crystal transition of parallel hard squares, but we deduce two alternative scenarios: (i) a second-order transition with a coexisting vacancy-rich crystal or (ii) a higher-density first-order transition with a coexisting crystal characterized by a lower vacancy concentration. In accordance with previous studies, a second-order transition with a high vacancy concentration is predicted for hard cubes.

Depletion-induced biaxial nematic states of boardlike particles.

With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid-crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.

Polydispersity stabilizes biaxial nematic liquid crystals.

Inspired by the observations of a remarkably stable biaxial nematic phase [van den Pol et al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality regime in between uniaxial nematic and smectic states.

The effects of shape and flexibility on bio-engineered fd-virus suspensions.

We present a theoretical model to describe binary mixtures of semi-flexible rods, applied here to fd-virus suspensions. We investigate the effects of rod stiffness on both monodisperse and binary systems, studying thick-thin and long-short mixtures. For monodisperse systems, we find that fd-virus particles have to be made extremely stiff to even approach the behavior of rigid rods. For thick-thin mixtures, we find increasingly rich phase behavior as the rods are either made more flexible or if their diameter ratio is increased. For long-short rod mixtures we find that the phase behavior is controlled by the relative stiffness of the rods, with increasing the stiffness of the long rods or decreasing that of the short rods resulting in richer phase behavior. We also calculate the state point dependent effective shape of the rods. The flexible rods studied here always behave as shorter, thicker rigid rods, but with an effective shape that varies widely throughout the phase diagrams, and plays a key role in determining phase behavior.

Phase diagram and effective shape of semiflexible colloidal rods and biopolymers.

We study suspensions of semiflexible colloidal rods and biopolymers using an Onsager-type second-virial functional for a segmented-chain model. For mixtures of thin and thick fd virus particles, we calculate full phase diagrams, finding quantitative agreement with experimental observations. We show that flexibility, which renders the rods effectively shorter and thicker depending on the state point, is crucial to understanding the topologies of the phase diagrams. We also calculate the stretching of wormlike micelles in a host fd virus suspension, finding agreement with experiments.

Charge regulation and ionic screening of patchy surfaces.

The properties of surfaces with charge-regulated patches are studied using nonlinear Poisson-Boltzmann theory. Using a mode expansion to solve the nonlinear problem efficiently, we reveal the charging behavior of Debye-length sized patches. We find that the patches charge up to higher charge densities if their size is relatively small and if they are well separated. The numerical results are used to construct a basic analytical model which predicts the average surface charge density on surfaces with patchy chargeable groups.