Brain-inspired computing with fluidic iontronic nanochannels.

The brain's remarkable and efficient information processing capability is driving research into brain-inspired (neuromorphic) computing paradigms. Artificial aqueous ion channels are emerging as an exciting platform for neuromorphic computing, representing a departure from conventional solid-state devices by directly mimicking the brain's fluidic ion transport. Supported by a quantitative theoretical model, we present easy-to-fabricate tapered microchannels that embed a conducting network of fluidic nanochannels between a colloidal structure. Due to transient salt concentration polarization, our devices are volatile memristors (memory resistors) that are remarkably stable. The voltage-driven net salt flux and accumulation, that underpin the concentration polarization, surprisingly combine into a diffusionlike quadratic dependence of the memory retention time on the channel length, allowing channel design for a specific timescale. We implement our device as a synaptic element for neuromorphic reservoir computing. Individual channels distinguish various time series, that together represent (handwritten) numbers, for subsequent in silico classification with a simple readout function. Our results represent a significant step toward realizing the promise of fluidic ion channels as a platform to emulate the rich aqueous dynamics of the brain.

Realization of the Brazil-nut effect in charged colloids without external driving.

Sedimentation is a ubiquitous phenomenon across many fields of science, such as geology, astrophysics, and soft matter. Sometimes, sedimentation leads to unusual phenomena, such as the Brazil-nut effect, where heavier (granular) particles reside on top of lighter particles after shaking. We show experimentally that a Brazil-nut effect can be realized in a binary colloidal system of long-range repulsive charged particles driven purely by Brownian motion and electrostatics without the need for activity. Using theory, we argue that not only the mass-per-charge for the heavier particles needs to be smaller than the mass-per-charge for the lighter particles but also that at high overall density, the system can be trapped in a long-lived metastable state, which prevents the occurrence of the equilibrium Brazil-nut effect. Therefore, we envision that our work provides valuable insights into the physics of strongly interacting systems, such as partially glassy and crystalline structures. Finally, our theory, which quantitatively agrees with the experimental data, predicts that the shapes of sedimentation density profiles of multicomponent charged colloids are greatly altered when the particles are charge-regulating with more than one ion species involved. Hence, we hypothesize that sedimentation experiments can aid in revealing the type of ion adsorption processes that determine the particle charge and possibly the value of the corresponding equilibrium constants.

The interplay between chemo-phoretic interactions and crowding in active colloids.

Many motile microorganisms communicate with each other and their environments via chemical signaling which leads to long-range interactions mediated by self-generated chemical gradients. However, consequences of the interplay between crowding and chemotactic interactions on their collective behavior remain poorly understood. In this work, we use Brownian dynamics simulations to investigate the effect of packing fraction on the formation of non-equilibrium structures in a monolayer of diffusiophoretic self-propelled colloids as a model for chemically active particles. Focusing on the case when a chemical field induces attractive positional and repulsive orientational interactions, we explore dynamical steady-states of active colloids of varying packing fractions and degrees of motility. In addition to collapsed, active gas, and dynamical clustering steady-states reported earlier for low packing fractions, a new phase-separated state emerges. The phase separation results from a competition between long-range diffusiophoretic interactions and motility and is observed at moderate activities and a wide range of packing fractions. Our analysis suggests that the fraction of particles in the largest cluster is a suitable order parameter for capturing the transition from an active gas and dynamical clustering states to a phase-separated state.

Universal motion of mirror-symmetric microparticles in confined Stokes flow.

Comprehensive understanding of particle motion in microfluidic devices is essential to unlock additional technologies for shape-based separation and sorting of microparticles like microplastics, cells, and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.

Microscopic Model for Cyclic Voltammetry of Porous Electrodes.

Cyclic voltammetry (CV) is a widespread experimental technique for characterizing electrochemical devices such as supercapacitors. Despite its wide use, a quantitative relation between CV and microscopic properties of supercapacitors is still lacking. In this Letter, we use both the microscopic "stack-electrode" model and its equivalent circuit for predicting the cyclic voltammetry of electric double-layer formation in porous electrodes. We find that the dimensionless combination ωτ_{n}, with ω the scan frequency of the time-dependent potential and τ_{n} the relaxation timescale of the stack-electrode model, governs the CV curves and capacitance: the capacitance is scan-rate independent for ωτ_{n}≪1 and scan-rate dependent for ωτ_{n}≫1. With a single fit parameter and all other model parameters dictated by experiments, our model reproduces experimental CV curves over a wide range of ω. Meanwhile, the influence of the pore size distribution on the charging dynamics is investigated to explain the experimental data.

Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations.

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference 2Φ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements. We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers. Next to the dimensionless applied potential Φ, we consider the ratio R/Rb of the pore's resistance R to the bulk reservoir resistance Rb and the ratio rp/λ of the pore radius rp to the Debye length λ. We compare our data to theoretical predictions by Aslyamov and Janssen (Φ), Posey and Morozumi (R/Rb), and Henrique, Zuk, and Gupta (rp/λ). Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.

Dynamic density functional theory for the charging of electric double layer capacitors.

We consider the charging of a model capacitor comprised of two planar electrodes and an electrolyte. Upon switching on a voltage difference, electric double layers build up in this setup, which we characterize with a classical dynamic density functional theory (DDFT) that accounts for electrostatic correlations and for molecular excluded volume of finite-sized ions and solvent molecules. Our DDFT predicts the electrode charge Q(t) to form exponentially with two timescales: at early times, the system relaxes on the RC time, namely, λDL/[D(2 + σ/λD)], with λD being the Debye length, L being the electrode separation, σ being the ion diameter, and D being the ionic diffusivity. Contrasting an earlier DDFT study, this early-time response does not depend on the applied potential. At late times, the capacitor relaxes with a relaxation time proportional to the diffusion time L2/D.

Chains of cubic colloids at fluid-fluid interfaces.

Inspired by recent experimental observations of spontaneous chain formation of cubic particles adsorbed at a fluid-fluid interface, we theoretically investigate whether capillary interactions can be responsible for this self-assembly process. We calculate adsorption energies, equilibrium particle orientations, and interfacial deformations, not only for a variety of contact angles but also for single cubes as well as an infinite 2D lattice of cubes at the interface. This allows us to construct a ground-state phase diagram as a function of areal density for several contact angles, and upon combining the capillary energy of a 2D lattice with a simple expression for the entropy of a 2D fluid we also construct temperature-density or size-density phase diagrams that exhibit large two-phase regions and triple points. We identify several regimes with stable chainlike structures, in line with the experimental observations.

The differential capacitance as a probe for the electric double layer structure and the electrolyte bulk composition.

In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.

Blessing and Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging.

The development of novel electrolytes and electrodes for supercapacitors is hindered by a gap of several orders of magnitude between experimentally measured and theoretically predicted charging time scales. Here, we propose an electrode model, containing many parallel stacked electrodes, that explains the slow charging dynamics of supercapacitors. At low applied potentials, the charging behavior of this model is described well by an equivalent circuit model. Conversely, at high potentials, charging dynamics slow down and evolve on two relaxation time scales: a generalized RC time and a diffusion time, which, interestingly, become similar for porous electrodes. The charging behavior of the stack-electrode model presented here helps to understand the charging dynamics of porous electrodes and qualitatively agrees with experimental time scales measured with porous electrodes.

Coupled water, charge and salt transport in heterogeneous nano-fluidic systems.

We theoretically study the electrokinetic transport properties of nano-fluidic devices under the influence of a pressure, voltage or salinity gradient. On a microscopic level the behaviour of the device is quantified by the Onsager matrix L, a generalised conductivity matrix relating the local driving forces and the induced volume, charge and salt flux. Extending L from a local to a global linear-response relation is trivial for homogeneous electrokinetic systems, but in this manuscript we derive a generalised conductivity matrix G from L that applies also to heterogeneous electrokinetic systems. This extension is especially important in the case of an imposed salinity gradient, which gives necessarily rise to heterogeneous devices. Within this formalism we can also incorporate a heterogeneous surface charge due to, for instance, a charge regulating boundary condition, which we show to have a significant impact on the resulting fluxes. The predictions of the Poisson-Nernst-Planck-Stokes theory show good agreement with exact solutions of the governing equations determined using the finite element method under a wide variety of parameters. Having established the validity of the theory, it provides an accessible method to analyse electrokinetic systems in general without the need of extensive numerical methods. As an example, we analyse a reverse electrodialysis "blue energy" system, and analyse how the many parameters that characterise such a system affect the generated electrical power and efficiency.

A Landau-de Gennes theory for twist-bend and splay-bend nematic phases of colloidal suspensions of bent rods.

We develop a phenomenological Landau-de Gennes (LdG) theory for lyotropic colloidal suspensions of bent rods using a Q-tensor expansion of the chemical-potential dependent grand potential. In addition, we introduce a bend flexoelectric term, coupling the polarization and the divergence of the Q-tensor, to study the stability of uniaxial (N), twist-bend (NTB), and splay-bend (NSB) nematic phases of colloidal bent rods. We first show that a mapping can be found between the LdG theory and the Oseen-Frank theory. By breaking the degeneracy between the splay and bend elastic constants, we find that the LdG theory predicts either an N-NTB-NSB or an N-NSB-NTB phase sequence upon increasing the particle concentration. Finally, we employ our theory to study the first-order N-NTB phase transition, for which we find that K33 as well as its renormalized version K33 eff remain positive at the transition, whereas K33 eff vanishes at the nematic spinodal. We connect these findings to recent simulation results.

Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the "Smectic Blanket".

We perform an extensive computational study on the phase behavior of hard banana-shaped particles, and show that biaxial, twist-bend, and splay-bend nematic phases are metastable with respect to a smectic phase for a system of hard bent spherocylinders. However, if the smectic phase is destabilized-either by polydispersity in the particle length or by curvature in the particle shape-stable biaxial, twist-bend, and splay-bend nematic phases are obtained. This provides a unified and consistent picture on the subtle role of particle shape on the phase behavior of bent rods.

Equilibrium configurations and capillary interactions of Janus dumbbells and spherocylinders at fluid-fluid interfaces.

We numerically investigate the adsorption of a variety of Janus particles (dumbbells, elongated dumbbells and spherocylinders) at a fluid-fluid interface by using a numerical method that takes into account the interfacial deformations. We first determine the equilibrium configuration of a single adsorbed particle, and we find that the overall shape of the induced deformation field has a strong hexapolar mode while non-Janus particles of the same shape do not induce any interfacial deformation. We then calculate the capillary interactions between two Janus spherocylinders adsorbed at an interface. The hexapolar deformation field induces capillary attractions for laterally aligned Janus spherocylinders and repulsions for laterally anti-aligned ones. We also experimentally synthesize micrometer-sized charged Janus dumbbells and let them adsorb at a water-decane interface. After several hours we observe the formation of aggregates of dumbbells predominantly induced by interactions that appear to be capillary in nature. Our Janus dumbbells attach laterally and are all aligned, as predicted by our numerical calculations.

Interparticle torques suppress motility-induced phase separation for rodlike particles.

To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of self-propelled particles whose shape varies smoothly from isotropic (disks/spheres) to weakly elongated (rods). We construct the phase diagrams of 2D active disks, 3D active spheres, and 2D/3D active rods of aspect ratio l/σ = 2. A stability analysis of the homogeneous isotropic phase allows us to predict the onset of MIPS based on the effective swimming speed and rotational diffusion of the particles. Both methods find suppression of MIPS as the particle shape is elongated. We propose a suppression mechanism based on the duration of collisions and argue that this mechanism can explain both the suppression of MIPS found here for rodlike particles and the enhancement of MIPS found for particles with Vicsek interactions.

Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths.

We use computer simulations to study the existence and stability of a biaxial nematic N_{b} phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long (L), medium (M), and short (S) particle axis. For all three shape families, we find stable N_{b} states provided the shape is not only close to the so-called dual shape with M=sqrt[LS] but also sufficiently anisotropic with L/S>9,11,14,23 for rhombi, (two types of) triangular prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-N_{b} transition does not occur in these systems due to a destabilization of N_{b} by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small L/S or by an intervening uniaxial nematic phase at large L/S. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.