Time-dependent ion transport in heterogeneous permselective systems

Advances in Two-Dimensional Ion-Selective Membranes: Bridging Nanoscale Insights to Industrial-Scale Salinity Gradient Energy Harvesting

Salinity gradient energy, often referred to as the Gibbs free energy difference between saltwater and freshwater, is recognized as "blue energy" due to its inherent cleanliness, renewability, and continuous availability. Reverse electrodialysis (RED), relying on ion-selective membranes, stands as one of the most prevalent and promising methods for harnessing salinity gradient energy to generate electricity. Nevertheless, conventional RED membranes face challenges such as insufficient ion selectivity and transport rates and the difficulty of achieving the minimum commercial energy density threshold of 5 W/m2. In contrast, two-dimensional nanostructured materials, featuring nanoscale channels and abundant functional groups, offer a breakthrough by facilitating rapid ion transport and heightened selectivity. This comprehensive review delves into the mechanisms of osmotic power generation within a single nanopore and nanochannel, exploring optimal nanopore dimensions and nanochannel lengths. We subsequently examine the current landscape of power generation using two-dimensional nanostructured materials in laboratory-scale settings across various test areas. Furthermore, we address the notable decline in power density observed as test areas expand and propose essential criteria for the industrialization of two-dimensional ion-selective membranes. The review concludes with a forward-looking perspective, outlining future research directions, including scalable membrane fabrication, enhanced environmental adaptability, and integration into multiple industries. This review aims to bridge the gap between previous laboratory-scale investigations of two-dimensional ion-selective membranes in salinity gradient energy conversion and their potential large-scale industrial applications.

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.

Approximate time-dependent current-voltage relations for currents exceeding the diffusion limit

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro- and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, “solution-diffusion” and “pore-flow” models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.

Transient response of nonideal ion-selective microchannel-nanochannel devices

We report evidence of variation in ion selectivity of a fabricated microchannel-nanochannel device resulting in the appearance of a distinct local maximum in the overlimiting chronopotentiometric response. In this system consisting of shallow microchannels joined by a nanochannel, viscous shear at the microchannel walls suppresses the electro-osmotic instability and prevents any associated contribution to the nonmonotonic response. Thus, this response is primarily electrodiffusive. Numerical simulations indicate that concentration polarization develops not only within the microchannel but also within the nanochannel itself, with a local voltage maximum in the chronopotentiometric response correlated with interfacial depletion and having the classic i^{-2} Sands time dependence. Furthermore, the occurrence of the local maxima is correlated with the change in selectivity due to internal concentration polarization. Understanding the transient nonideal permselective response is essential for obtaining fundamental insight and for optimizing efficient operation of practical fabricated nanofluidic and membrane devices.

Interplay between Nanochannel and Microchannel Resistances

Current nanochannel system paradigm commonly neglects the role of the interfacing microchannels and assumes that the ohmic electrical response of a microchannel-nanochannel system is solely determined by the geometric properties of the nanochannel. In this work, we demonstrate that the overall response is determined by the interplay between the nanochannel resistance and various microchannel attributed resistances. Our experiments confirm a recent theoretical prediction that in contrast to what was previously assumed at very low concentrations the role of the interfacing microchannels on the overall resistance becomes increasingly important. We argue that the current nanochannel-dominated conductance paradigm can be replaced with a more correct and intuitive microchannel-nanochannel-resistance-model-based paradigm.

Asymmetry-induced electric current rectification in permselective systems

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order 10^{2}-10^{3}.