Charge transport in nanochannels: a molecular theory

Influence of nanopore coating patterns on the translocation dynamics of polyelectrolytes

Polyelectrolytes can electrophoretically be driven through nanopores in order to be detected. The respective translocation events are often very fast and the process needs to be controlled to promote efficient detection. To this end, we attempt to control the translocation dynamics by coating the inner surface of a nanopore. For this, different charge distributions are chosen that result in substantial variations of the pore-polymer interactions. In addition and in view of the existing detection modalities, experimental settings, and nanopore materials, different types of sensors inside the nanopore have been considered to probe the translocation process and its temporal spread. The respective transport of polyelectrolytes through the coated nanopores is modeled through a multi-physics computational scheme that incorporates a mesoscopic/electrokinetic description for the solvent and particle-based scheme for the polymer. This investigation could underline the interplay between sensing modality, nanopore material, and detection accuracy. The electro-osmotic flow and electrophoretic motion in a pore are analyzed together with the polymeric temporal and spatial fluctuations unraveling their correlations and pathways to optimize the translocation speed and dynamics. Accordingly, this work sketches pathways in order to tune the pore-polymer interactions in order to control the translocation dynamics and, in the long run, errors in their measurements.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Modelling lipid systems in fluid with Lattice Boltzmann Molecular Dynamics simulations and hydrodynamics

In this work we present the coupling between Dry Martini, an efficient implicit solvent coarse-grained model for lipids, and the Lattice Boltzmann Molecular Dynamics (LBMD) simulation technique in order to include naturally hydrodynamic interactions in implicit solvent simulations of lipid systems. After validating the implementation of the model, we explored several systems where the action of a perturbing fluid plays an important role. Namely, we investigated the role of an external shear flow on the dynamics of a vesicle, the dynamics of substrate release under shear, and inquired the dynamics of proteins and substrates confined inside the core of a vesicle. Our methodology enables future exploration of a large variety of biological entities and processes involving lipid systems at the mesoscopic scale where hydrodynamics plays an essential role, e.g. by modulating the migration of proteins in the proximity of membranes, the dynamics of vesicle-based drug delivery systems, or, more generally, the behaviour of proteins in cellular compartments.

Non-Negligible Roles of Pore Size Distribution on Electroosmotic Flow in Nanoporous Materials

Electroosmotic flow in nanoporous materials is of fundamental importance for the design and development of filtration membranes and electrochemical devices such as supercapacitors and batteries. Recent experiments suggest that ion transport in a porous network is substantially different from that in individual nanochannels due to the pore size distribution and pore connectivity. Herein, we report a theoretical framework for ion transport in nanoporous materials by combing the classical density functional theory to describe the electrical double layer (EDL) structure, the Navier-Stokes equation for the fluid flow, and the effective medium approximation to bridge the gap between individual nanopores and the network connectivity. We find that ion conductivity in nanoporous materials is extremely sensitive to the pore size distribution when the average size of micropores is comparable to the EDL thickness. The theoretical predictions provide an explanation of the giant gap between the conductivity of a single pore and that of a porous network and highlight the mechanism of ion transport through nanoporous materials important for numerous practical applications.

Electrokinetic droplet transport from electroosmosis to electrophoresis

Droplet transport in microfluidic channels by electrically induced flows often entails the simultaneous presence of electroosmosis and electrophoresis. Here we make use of coupled lattice-Boltzmann/molecular dynamics simulations to compute the mobility of a droplet in a microchannel under the effect of an external electric field. By varying the droplet solvation free energy of the counterions released at the channel walls, we observe the continuous transition between the electroosmotic and electrophoretic regime. We show that it is possible to describe the mobility of a droplet in a unified, consistent way, by combining the theoretical description of the electroosmotic flow with, in this case, the Hückel limit of electrophoresis, modified in order to take into account the Hadamard-Rybczynski droplet drag.

Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations

A coarse-grained model for simulating structural properties of double-stranded RNA is developed with parameters obtained from quantum-mechanical calculations. This model follows previous parametrization for double-stranded DNA, which is based on mapping the all-atom picture to a coarse-grained four-bead scheme. Chemical and structural differences between RNA and DNA have been taken into account for the model development. The parametrization is based on simulations using density functional theory (DFT) on separate units of the RNA molecule without implementing experimental data. The total energy is decomposed into four terms of physical significance: hydrogen bonding interaction, stacking interactions, backbone interactions, and electrostatic interactions. The first three interactions are treated within DFT, whereas the last one is included within a mean field approximation. Our double-stranded RNA coarse-grained model predicts stable helical structures for RNA. Other characteristics, such as structural or mechanical properties are reproduced with a very good accuracy. The development of the coarse-grained model for RNA allows extending the spatial and temporal length scales accessed by computer simulations and being able to model RNA-related biophysical processes, as well as novel RNA nanostructures.

Electrokinetic Lattice Boltzmann Solver Coupled to Molecular Dynamics: Application to Polymer Translocation

We have developed a theoretical and computational approach to deal with systems that involve a disparate range of spatiotemporal scales, such as those composed of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multicomponent Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multicomponent description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. Lastly, we discuss the advantages and complexities of the approach.

Shear-induced laning transition in a confined colloidal film

Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.

Electro-osmotic flow through nanopores in thin and ultrathin membranes

We theoretically study how the electro-osmotic fluid velocity in a charged cylindrical nanopore in a thin solid state membrane depends on the pore's geometry, membrane charge, and electrolyte concentration. We find that when the pore's length is comparable to its diameter, the velocity profile develops a concave shape with a minimum along the pore axis unlike the situation in very long nanopores with a maximum velocity along the central pore axis. This effect is attributed to the induced pressure along the nanopore axis due to the fluid flow expansion and contraction near the exit or entrance to the pore and to the reduction of electric field inside the nanopore. The induced pressure is maximal when the pore's length is about equal to its diameter while decreasing for both longer and shorter nanopores. A model for the fluid velocity incorporating these effects is developed and shown to be in a good agreement with numerically computed results.

Nanopore tweezers: voltage-controlled trapping and releasing of analytes

Several devices for single-molecule detection and analysis employ biological and artificial nanopores as core elements. The performance of such devises strongly depends on the amount of time the analytes spend into the pore. This residence time needs to be long enough to allow the recording of a high signal-to-noise ratio analyte-induced blockade. We propose a simple approach, dubbed nanopore tweezing, for enhancing the trapping time of molecules inside the pore via a proper tuning of the applied voltage. This method requires the creation of a strong dipole that can be generated by adding a positive and a negative tail at the two ends of the molecules to be analyzed. Capture rate is shown to increase with the applied voltage while escape rate decreases. In this paper we rationalize the essential ingredients needed to control the residence time and provide a proof of principle based on atomistic simulations.

Charge Relaxation Dynamics of an Electrolytic Nanocapacitor

Understanding ion relaxation dynamics in overlapping electric double layers (EDLs) is critical for the development of efficient nanotechnology-based electrochemical energy storage, electrochemomechanical energy conversion, and bioelectrochemical sensing devices as well as the controlled synthesis of nanostructured materials. Here, a lattice Boltzmann (LB) method is employed to simulate an electrolytic nanocapacitor subjected to a step potential at t = 0 for various degrees of EDL overlap, solvent viscosities, ratios of cation-to-anion diffusivity, and electrode separations. The use of a novel continuously varying and Galilean-invariant molecular-speed-dependent relaxation time (MSDRT) with the LB equation recovers a correct microscopic description of the molecular-collision phenomena and enhances the stability of the LB algorithm. Results for large EDL overlaps indicated oscillatory behavior for the ionic current density, in contrast to monotonic relaxation to equilibrium for low EDL overlaps. Further, at low solvent viscosities and large EDL overlaps, anomalous plasmalike spatial oscillations of the electric field were observed that appeared to be purely an effect of nanoscale confinement. Employing MSDRT in our simulations enabled modeling of the fundamental physics of the transient charge relaxation dynamics in electrochemical systems operating away from equilibrium wherein Nernst-Einstein relation is known to be violated.

Mechanosensitive channel activation by diffusio-osmotic force

For ion channel gating, the appearance of two distinct conformational states and the discrete transitions between them are essential, and therefore of crucial importance to all living organisms. We show that the physical interplay between two structural elements that are commonly present in bacterial mechanosensitive channels--namely, a charged vestibule and a hydrophobic constriction--creates two distinct conformational states, open and closed, as well as the gating between them. We solve the nonequilibrium Stokes-Poisson-Nernst-Planck equations, extended to include a molecular potential of mean force, and show that a first order transition between the closed and open states arises naturally from the diffusio-osmotic stress caused by the ions and the water inside the channel and the elastic restoring force from the membrane.

Time-dependent density functional theory for ion diffusion in electrochemical systems

We introduce a generic form of time-dependent density functional theory (TDDFT) to describe ion diffusion in electrochemical systems to account for steric effects and electrostatic correlations neglected in the Poisson-Nernst-Planck equations. An efficient numerical algorithm is proposed to analyze the charging kinetics of electric double layers in model electrochemical systems that consist of spherical ions in a dielectric continuum confined between two planar electrodes. By comparing the theoretical predictions from TDDFT and conventional electrokinetic methods for constant-voltage charging of the model electrochemical cells, we demonstrate that thermodynamic non-ideality plays a pivotal role in electrodiffusion even at relatively low electrolyte concentrations, and this effect cannot be captured by the lattice-gas model for the excluded volume effects. In particular, TDDFT predicts 'wave-like' variation of the ionic density profiles that has not been identified in previous investigations. At conditions where there are no significant correlations between electric double layers from opposite electrodes, the charging kinetics follows an exponential behavior with a linear dependence of the relaxation time on the cell thickness in excellent agreement with the equivalent circuit model. However, the conventional electrokinetic model breaks down when the electrodes are at small separation, in particular for systems with low ionic strength or high charging voltage. We also find that ionic screening retards the charging kinetics at low salt concentrations, but has the opposite effect at large salt concentrations.

Pore network model of electrokinetic transport through charged porous media

We introduce a method for the numerical determination of the steady-state response of complex charged porous media to pressure, salt concentration, and electric potential gradients. The macroscopic fluxes of solvent, salt, and charge are computed within the framework of the Pore Network Model (PNM), which describes the pore structure of the samples as networks of pores connected to each other by channels. The PNM approach is used to capture the couplings between solvent and ionic flows which arise from the charge of the solid surfaces. For the microscopic transport coefficients on the channel scale, we take a simple analytical form obtained previously by solving the Poisson-Nernst-Planck and Stokes equations in a cylindrical channel. These transport coefficients are upscaled for a given network by imposing conservation laws for each pores, in the presence of macroscopic gradients across the sample. The complex pore structure of the material is captured by the distribution of channel diameters. We investigate the combined effects of this complex geometry, the surface charge, and the salt concentration on the macroscopic transport coefficients. The upscaled numerical model preserves the Onsager relations between the latter, as expected. The calculated macroscopic coefficients behave qualitatively as their microscopic counterparts, except for the permeability and the electro-osmotic coupling coefficient when the electrokinetic effects are strong. Quantitatively, the electrokinetic couplings increase the difference between the macroscopic coefficients and the corresponding ones for a single channel of average diameter.

Numerical homogenization of electrokinetic equations in porous media using lattice-Boltzmann simulations

We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.

Nonlinear amplification in electrokinetic pumping in nanochannels in the presence of hydrophobic interactions

We discover a nonlinear coupling between the hydrophobicity of a charged substrate and electrokinetic pumping in narrow fluidic confinements. Our analyses demonstrate that the effective electrokinetic transport in nanochannels may get massively amplified over a regime of bare surface potentials and may subsequently get attenuated beyond a threshold surface charging condition because of a complex interplay between reduced hydrodynamic resistance on account of the spontaneous inception of a less dense interfacial phase and ionic transport within the electrical double layer. We also show that the essential physics delineated by our mesoscopic model, when expressed in terms of a simple mathematical formula, agrees remarkably with that portrayed by molecular dynamics simulations. The nontrivial characteristics of the initial increment followed by a decrement of the effective zeta potential with a bare surface potential may open up the realm of hitherto-unexplored operating regimes of electrohydrodynamically actuated nanofluidic devices.