Pressure-driven ionic transport through nanochannels with inhomogenous charge distributions

Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling

Artificial ion-exchange and other charged membranes, such as biomembranes, are self-organizing nanomaterials built from macromolecules. The interactions of fragments of macromolecules results in phase separation and the formation of ion-conducting channels. The properties conditioned by the structure of charged membranes determine their application in separation processes (water treatment, electrolyte concentration, food industry and others), energy (reverse electrodialysis, fuel cells and others), and chlore-alkali production and others. The purpose of this review is to provide guidelines for modeling the transport of ions and water in charged membranes, as well as to describe the latest advances in this field with a focus on power generation systems. We briefly describe the main structural elements of charged membranes which determine their ion and water transport characteristics. The main governing equations and the most commonly used theories and assumptions are presented and analyzed. The known models are classified and then described based on the information about the equations and the assumptions they are based on. Most attention is paid to the models which have the greatest impact and are most frequently used in the literature. Among them, we focus on recent models developed for proton-exchange membranes used in fuel cells and for membranes applied in reverse electrodialysis.

Dielectric Properties of Aqueous Electrolyte Solutions Confined in Silica Nanopore: Molecular Simulation vs. Continuum-Based Models

Dielectric behavior of electrolyte aqueous solutions with various concentrations in a cylindrical nanopore of MCM 41 silica has been investigated. The effect of confinement is investigated by using isothermal-isosurface-isobaric statistical ensemble, which has proved to be an effective alternative to the Grand Canonical Monte Carlo (GCMC) simulation method. Several single-salt solutions have been considered (e.g., NaCl, NaI, BaCl₂, MgCl₂) in order to investigate the effect of ion polarizability, ion size, and ion charge. The effect of salt concentration has also been addressed by considering NaCl solutions at different concentrations (i.e., 0.1 mol/L, 0.5 mol/L, and 1 mol/L). The motivation in performing this integrated set of simulations is to provide deep insight into the dielectric exclusion in NF theory that plays a significant role in separation processes. It was shown that the dielectric constant increased when ions were added to water inside the nanopore (with respect to the dielectric constant of confined pure water) unlike what was obtained in the bulk phase and this phenomenon was even more pronounced for electrolytes with divalent ions (MgCl₂ and BaCl₂). Therefore, our simulations indicate opposite effects of ions on the dielectric constant of free (bulk) and nanoconfined aqueous solutions.

Pressure-driven power generation and ion separation using a non-uniformly charged nanopore

Due to its versatile potential applications, nanofluidic devices have drawn much attention of researches in various fields. Among these, pressure-driven power generation is considered as a candidate for the next generation alternative green energy source, and pressure-driven ion separation (nanofiltration) for desalination. Aiming to achieve a better performance in these two representative cases, a cylindrical nanopore having different types of non-uniform surface charge profile is adopted, and its performance under various conditions assessed. We show that lower the surface charge density near the nanopore inlet region can suppress the effect of ion concentration polarization (ICP) and improve the selectivity, thereby enhancing appreciably its power generation performance. For a fixed averaged surface charge density, if the bulk salt concentration is low, the higher the surface charge density near the nanopore openings, the better its performance. The degree of ICP can be alleviated by applying a sufficiently large pressure difference. Although previous studies showed that salt rejection is influenced significantly by the profile of the electric field inside a nanopore, we find that the electric field at nanopore openings also plays a role. Through choosing appropriately the surface charge profile, it is possible to solve the trade-off between rejection and flow rate.

Influence of Pore-Size/Porosity on Ion Transport and Static BSA Fouling for TiO2-Covered Nanoporous Alumina Membranes

The influence of geometrical parameters (pore radii and porosity) on ion transport through two almost ideal nanoporous alumina membranes (NPAMs) coated with a thin TiO2 layer by the atomic layer deposition technique (Sf-NPAM/TiO2 and Ox-NPAM/TiO2 samples) was analyzed by membrane potential and electrochemical impedance spectroscopy measurements. The results showed the significant effect of pore radii (10 nm for Sf-NPAM/TiO2 and 13 nm for Ox-NPAM/TiO2) when compared with porosity (9% and 6%, respectively). Both electrochemical techniques were also used for estimation of protein (bovine serum albumin or BSA) static fouling, and the results seem to indicate deposition of a BSA layer on the Sf-NPAM/TiO2 fouled membrane surface but pore-wall deposition in the case of the fouled Ox-NPAM/TiO2 sample. Moreover, a typical and simple optical technique such as light transmission/reflection (wavelength ranging between 0 and 2000 nm) was also used for membrane analysis, showing only slight transmittance differences in the visible region when both clean membranes were compared. However, a rather significant transmittance reduction (~18%) was observed for the fouled Sf-NPAM/TiO2 sample compared to the fouled Ox-NPAM/TiO2 sample, and was associated with BSA deposition on the membrane surface, thus supporting the electrochemical analysis results.

Removal of Sulfadiazine by Polyamide Nanofiltration Membranes: Measurement, Modeling, and Mechanisms

In this study, a complete steric, electrostatic, and dielectric mass transfer model is applied to investigate the separation mechanism of typical antibiotic sulfadiazine by NF90, NF270, VNF-8040 and TMN20H-400 nanofiltration membranes. FTIR and XPS analysis clearly indicate that the membranes we used possess skin layers containing both amine and carboxylic acid groups that can be distributed in an inhomogeneous fashion, leading to a bipolar fixed charge distribution. We compare the theoretical and experimental rejection rate of the sulfadiazine as a function of the pressure difference across the nanopore for the four polyamide membranes of inhomogeneously charged nanopores. It is shown that the rejection rate of sulfadiazine obtained by the solute transport model has similar qualitative results with that of experiments and follows the sequence: RNF90>RVNF2−8040>RNF270>RTMN20H−400. The physical explanation can be attributed to the influence of the inhomogeneous charge distribution on the electric field that arises spontaneously so as to maintain the electroneutrality within the nanopore.

Direct Numerical Simulation of Seawater Desalination Based on Ion Concentration Polarization

The problem of water shortage needs to be solved urgently. The membrane-embedded microchannel structure based on the ion concentration polarization (ICP) desalination effect is a potential portable desalination device with low energy consumption and high efficiency. The electroosmotic flow in the microchannel of the cation exchange membrane and the desalination effect of the system are numerically analyzed. The results show that when the horizontal electric field intensity is 2 kV/m and the transmembrane voltage is 400 mV, the desalting efficiency reaches 97.3%. When the electric field strength increases to 20 kV/m, the desalination efficiency is reduced by 2%. In terms of fluid motion, under the action of the transmembrane voltage, two reverse eddy currents are formed on the surface of the membrane due to the opposite electric field and pressure difference on both sides of the membrane, forming a pumping effect. The electromotive force in the channel exhibits significant pressure-flow characteristics with a slip boundary at a speed approximately six times that of a non-membrane microchannel.

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.

Bioinspired smart asymmetric nanochannel membranes

Bioinspired smart asymmetric nanochannel membranes (BSANM) have been explored extensively to achieve the delicate ionic transport functions comparable to those of living organisms. The abiotic system exhibits superior stability and robustness, allowing for promising applications in many fields. In view of the abundance of research concerning BSANM in the past decade, herein, we present a systematic overview of the development of the state-of-the-art BSANM system. The discussion is focused on the construction methodologies based on raw materials with diverse dimensions (i.e. 0D, 1D, 2D, and bulk). A generic strategy for the design and construction of the BSANM system is proposed first and put into context with recent developments from homogeneous to heterogeneous nanochannel membranes. Then, the basic properties of the BSANM are introduced including selectivity, gating, and rectification, which are associated with the particular chemical and physical structures. Moreover, we summarized the practical applications of BSANM in energy conversion, biochemical sensing and other areas. In the end, some personal opinions on the future development of the BSANM are briefly illustrated. This review covers most of the related literature reported since 2010 and is intended to build up a broad and deep knowledge base that can provide a solid information source for the scientific community.

Influence of temperature gradients on charge transport in asymmetric nanochannels

Imposing a temperature gradient over a charge-selective asymmetric nanochannel enhances the selectivity, total current and rectification of the nanochannel.

Electro-osmosis in inhomogeneously charged microporous media by pore-scale modeling

Surface charge at solid-electrolyte interface is generally coupled with the local electrolyte properties (ionic concentration, pH, etc.), and therefore not as assumed homogeneous on the solid surfaces in the previous studies. The inhomogeneous charge brings huge challenges in predictions of electro-osmotic transport and has never been well studied. In this work, we first propose a classification of electro-osmosis based on a dimensionless number which is the ratio of the Debye length to the characteristic pore size. In the limit of thin electrical double layer, we establish a pore-scale numerical model for inhomogeneously charged electro-osmosis including four ions: Na⁺,Cl^-,H⁺ and OH^-. Based on reconstructed porous media, we simulate the electro-osmosis with inhomogeneous charge using lattice Boltzmann method. The nonlinear response of electro-osmotic velocity to applied electrical field and the reverse flow have been observed and analyzed.

Theoretical investigation of the ionic selectivity of polyelectrolyte multilayer membranes in nanofiltration

Polyelectrolyte multilayer membranes have proven to be promising materials for ion nanofiltration. In this work, we implement a continuum mesoscopic transport model developed in previous works (Szymczyk, A.; Zhu, H.; Balannec, B. Langmuir 2010, 26, 1214; Szymczyk, A.; Zhu, H.; Balannec, B. J. Phys. Chem. B 2010, 114, 10143) to investigate the pressure-driven transport of electrolyte mixtures through this kind of membrane. The model accounts for an inhomogeneous distribution of the fixed charge through an arbitrary number of polyelectrolyte bilayers. We show that accounting for the multiple bipolar charge distribution resulting from the layer-by-layer assembly of polyelectrolytes with opposite charge is responsible for the increase in the Na(+)/Mg(2+) selectivity reported experimentally with respect to conventional nanofiltration membranes. The model also allows the rationalizing of the seemingly contradictory experimental results reported in the literature (i.e., the increase or decrease in the selectivity with the number of bilayers or the existence of an optimum number of bilayers). It is shown, however, that the nonmonotonous variation of the ionic selectivity does not originate from the multibipolar distribution of the fixed charge through polyelectrolyte multilayer membranes but from the existence of an optimum skin layer thickness.

Overlimiting current in a microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.