Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck

Influence of the Dielectric Constant on the Ionic Current Rectification of Bipolar Nanopores

In this paper, we investigate how the dielectric constant, ϵ, of an electrolyte solvent influences the current rectification characteristics of bipolar nanopores. It is well recognized that bipolar nanopores with two oppositely charged regions rectify current when exposed to an alternating electric potential difference. Here, we consider dilute electrolytes with NaCl only and with a mixture of NaCl and charged nanoparticles. These systems are studied using two levels of description, all-atom explicit water molecular dynamics (MD) simulations and coarse-grained implicit solvent MD simulations. The charge density and electric potential profiles and current-voltage relationship predicted by the implicit solvent simulations with ϵ = 11.3 show good agreement with the predictions from the explicit water simulations. Under nonequilibrium conditions, the predictions of the implicit solvent simulations with a dielectric constant closer to the one of bulk water are significantly different from the predictions obtained with the explicit water model. These findings are closely aligned with experimental data on the dielectric constant of water when confined to nanometric spaces, which suggests that ϵ decreases significantly compared to its value in the bulk. Moreover, the largest electric current rectification is observed in systems containing nanoparticles when ϵ = 78.8. Using enhanced sampling, we have shown that this larger rectification arises from the presence of a significantly deeper minimum in the free energy of the system with a larger ϵ, and when a negative voltage bias is applied. Since implicit solvent models and mean-field continuum theories are often used to design Janus membranes based on bipolar nanopores, this work highlights the importance of properly accounting for the effects of confinement on the dielectric constant of the electrolyte solvent. The results presented here indicate that the dielectric constant in implicit solvent simulations may be used as an adjustable parameter to approximately account for the effects of nanometric confinement on aqueous electrolyte solvents.

Designing Nanofluidic Diode from a Hybrid-Bilayer Covalent Organic Framework: Molecular Simulation Investigation

Nanofluidic diodes are potentially useful in many important applications such as sensing, electronics, and energy conversion. However, the manufacturing of controllable nanopores for nanofluidic diodes is technically challenging. Herein, a nanofluidic diode is designed from a highly programmatic covalent organic framework (COF). Through molecular simulation, remarkable diode behavior is observed in a hybrid-bilayer COF but not in its constituent single-layer COFs. The rectification effect of ion current in the hybrid-bilayer COF is attributed to an asymmetric electrostatic potential across the COF nanopore. Furthermore, a synergistic effect of counterion is unraveled in the hybrid-bilayer COF, and the presence of counterion is found to reduce the entry barrier and facilitate ion transport. The performance of the hybrid-bilayer COF as a nanofluidic diode is comprehensively investigated by varying salt concentration, layer number, interlayer spacing, and slipping. This proof-of-concept simulation study demonstrates the feasibility of the hybrid-bilayer COF as a nanofluidic diode and the finding may stimulate the development of new nanofluidic platforms.

Pushing the limits of nanopore transport performance by polymer functionalization

Inspired by the design and performance of biological pores, polymer functionalization of nanopores has emerged as an evolving field to advance transport performance within the last few years. This feature article outlines developments in nanopore functionalization and the resulting transport performance including gating based on electrostatic interaction, wettability and ligand binding, gradual transport controlled by polymerization as well as functionalization-based asymmetric nanopore and nanoporous material design going towards the transport direction. Pushing the limits of nanopore transport performance and thus reducing the performance gap between biological and technological pores is strongly related to advances in polymerization chemistry and their translation into nanopore functionalization. Thereby, the effect of the spatial confinement has to be considered for polymer functionalization as well as for transport regulation, and mechanistic understanding is strongly increased by combining experiment and theory. A full mechanistic understanding together with highly precise nanopore structure design and polymer functionalization is not only expected to improve existing application of nanoporous materials but also opens the door to new technologies. The latter might include out of equilibrium devices, ionic circuits, or machine learning based sensors.

Ultrafast rectifying counter-directional transport of proton and metal ions in metal-organic framework-based nanochannels

Bioinspired control of ion transport at the subnanoscale has become a major focus in the fields of nanofluidics and membrane separation. It is fundamentally important to achieve rectifying ion-specific transport in artificial ion channels, but it remains a challenge. Here, we report a previously unidentified metal-organic framework nanochannel (MOF NC) nanofluidic system to achieve unidirectional ultrafast counter-directional transport of alkaline metal ions and proton. This highly effective ion-specific rectifying transport behavior is attributed to two distinct mechanisms for metal ions and proton, elucidated by theoretical simulations. Notably, the MOF NC exhibits ultrafast proton conduction stemming from ultrahigh proton mobility, i.e., 11.3 × 10^-7 m² /V·s, and low energy barrier of 0.075 eV in MIL-53-COOH subnanochannels. Furthermore, the MOF NC shows excellent osmotic power-harvesting performance in reverse electrodialysis. This work expects to inspire further research into multifunctional biomimetic ion channels for advanced nanofluidics, biomimetics, and separation applications.

Conditions for electroneutrality breakdown in nanopores

It has recently been suggested that a breakdown of electroneutrality occurs in highly confined nanopores that are encompassed by a dielectric material. This work elucidates the conditions for this breakdown. We show that the breakdown within the pore results from the response of the electric field within the dielectric. Namely, we show that this response is highly sensitive to the boundary condition at the dielectric edge. The standard Neumann boundary condition of no-flux predicts that the breakdown does not occur. However, a Dirichlet boundary condition for a zero-potential predicts a breakdown. Within this latter scenario, the breakdown exhibits a dependence on the thickness of the dielectric material. Specifically, infinite thickness dielectrics do not exhibit a breakdown, while dielectrics of finite thickness do exhibit a breakdown. Numerical simulations confirm theoretical predictions. The breakdown outcomes are discussed with regard to single pore systems and multiple pore systems.

Bipolar Nanochannels: A Systematic Approach to Asymmetric Problems

Nanofluidic diodes are capable of rectifying the electrical current by several orders of magnitude. In the current state of affairs, determining the rectification factor is not possible as it depends on many system parameters. In this work, we systematically scan the effects of geometry and excess counterion concentrations (i.e., surface charge effects). We show that the current-voltage response varies between the two extreme behaviors of unipolar and bipolar responses. The exact behavior depends on the geometry and surface charge properties of the system. Here, we have gone beyond the typical setup that only considers the dynamics within the nanochannel itself and we have included the effects of the adjoining microchannels. Systems that include both nanochannels and microchannels exhibit the classical signatures of concentration polarization, such as ionic depletion and enrichment. Here, where we have scanned a wide range of parameters, we show that bipolar and semi-bipolar systems exhibit a wider range of phenomena that are intrinsically more complicated. Our system characterization is for both, the much more investigated case of steady state and the less investigated, but equally interesting, time-transient case. For example, it is common to characterize the system by its steady-state result (current-voltage response, rectification factor, and transport number). Here, we demonstrate that the time-transient behavior of the fluxes can also be used to characterize the system, and that the time-dependent rectification factors and transport numbers are meaningful. The systematic approach taken in this work, and the results presented herein, can be used to further elucidate the complicated behavior of the current-voltage response of nanofluidic diodes and to rationalize experimental results. The insights of this work can be used to enhance and improve the design of all nanofluidic diodes.

Ion transport in nanopores with highly overlapping electric double layers

Investigation of ion transport through nanopores with highly overlapping electric double layers is extremely challenging. This can be attributed to the non-linear Poisson-Boltzmann equation that governs the behavior of the electrical potential distribution as well as other characteristics of ion transport. In this work, we leverage the approach of Schnitzer and Yariv [Phys. Rev. E 87, 054301 (2013)] to reduce the complexity of the governing equation. An asymptotic solution is derived, which shows remarkable correspondence to simulations of the non-approximated equations. This new solution is leveraged to address a number of highly debated issues. We derive the equivalent of the Gouy-Chapman equation for systems with highly overlapping electric double layers. This new relationship between the surface charge density and the surface potential is then utilized to determine the power-law scaling of nanopore conductances as a function of the bulk concentrations. We derive the coefficients of transport for the case of overlapping electric double layers and compare it to the renowned uniform potential model. We show that the uniform potential model is only an approximation for the exact solution for small surface charges. The findings of this work can be leveraged to uncover additional hidden attributes of ion transport through nanopores.

Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models

Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.

Rectification of bipolar nanopores in multivalent electrolytes: effect of charge inversion and strong ionic correlations

Bipolar nanopores have powerful rectification properties due to the asymmetry in the charge pattern on the wall of the nanopore. In particular, bipolar nanopores have positive and negative surface charges along the pore axis. Rectification is strong if the radius of the nanopore is small compared to the screening length of the electrolyte so that both cations and anions have depletion zones in the respective regions. The depths of these depletion zones is sensitive to sign of the external voltage. In this work, we are interested in the effect of the presence of strong ionic correlations (both between ions and between ions and surface charge) due to the presence of multivalent ions and large surface charges. We show that strong ionic correlations cause leakage of the coions, a phenomenon that is absent in mean field theories. In this modeling study, we use both the mean-field Poisson-Nernst-Planck (PNP) theory and a particle simulation method, Local Equilibrium Monte Carlo (LEMC), to show that phenomena such as overcharging and charge inversion cannot be reproduced with PNP, while LEMC is able to produce nonmonotonic dependence of currents and rectification as a function of surface charge strength.

Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations

We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel with three ion species, two positively charged with the same valence and one negatively charged. Bikerman's local hard-sphere potential is included in the model to account for ion sizes. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations due to the nonlinear interplay between finite ion sizes, diffusion coefficients and boundary conditions, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between these physical parameters. Numerical simulations are performed to identify some critical potentials which play critical roles in examining properties of ionic flows in our analysis.

Ionic circuitry with nanofluidic diodes

Ionic circuits composed of nanopores functionalized with polyelectrolyte chains can operate in aqueous solutions, thus allowing the control of electrical signals and information processing in physiological environments. We demonstrate experimentally and theoretically that different orientations of single-pore membranes with the same and opposite surface charges can operate reliably in series, parallel, and mixed series-parallel arrangements of two, three, and four nanofluidic diodes using schemes similar to those of solid-state electronics. We consider also different experimental procedures to externally tune the fixed charges of the molecular chains functionalized on the pore surface, showing that single-pore membranes can be used efficiently in ionic circuitry with distinct ionic environments.

Application of a bipolar nanopore as a sensor: rectification as an additional device function

We model and simulate a nanopore sensor that selectively binds analyte ions. This binding leads to the modulation of the local concentrations of the ions of the background electrolyte (KCl), and, thus, to the modulation of the ionic current flowing through the pore. The nanopore's wall has a bipolar charge pattern with a larger positive buffer region determining the anions as the main charge carriers and a smaller negative binding region containing binding sites. This charge pattern proved to be an appropriate one as shown by a previous comparative study of varying charge patterns (Mádai et al. J. Mol. Liq., 2019, 283, 391-398.). Binding of the positive analyte ions attracts more anions in the pore thus increasing the current. The asymmetric nature of the pore results in an additional device function, rectification. Our model, therefore, is a dual response device. Using a reduced model of the nanopore studied by a hybrid computer simulation method (Local Equilibrium Monte Carlo coupled with the Nernst-Planck equation) we show that we can create a sensor whose underlying mechanisms are based on the changes in the local electric field as a response to changing thermodynamic conditions. The change in the electric field results in changes in the local ionic concentrations (depletion zones), and, thus, changes in ionic currents.