Effect of ion partitioning on the electrostatics of soft particles with a volumetrically charged core

Non-monotonic variation in the streaming potential in polyelectrolyte grafted nanochannels mediated by ion partitioning effects

BACKGROUND

Polyelectrolyte grafted 'soft' nanochannels are known to enhance electrokinetic energy conversion efficiency, paving the way for a sustainable energy harvesting mechanism. However, the true potential of their efficacy remains to be tapped, as attributed to a deficit in accounting for the interplay between solution pH and ion partitioning effect arising due to permittivity contrast between the coated layer and the bulk media, leading to predictions of an erroneous ionic distribution and a wrongly estimated electrokinetic response.

RESULTS

We unravel the electrokinetic behavior of a pH-regulated zwitterionic polyelectrolyte layer grafted nanofluidic system. To this end, we derive a detailed theoretical formulation that considers the nuanced interplay between solution pH and the ion partitioning effect through a thermodynamically consistent ionic distribution. Here, for the first time, we demonstrate a non-monotonic trend in the streaming potential with an increase in the ion partitioning effect, in contrast to a monotonic increase as reported previously. Additionally, we identify a critical permittivity ratio specific to the solution pH at which maximum streaming potential can be obtained.

SIGNIFICANCE

We shed light on the counterintuitive effect borne from the increased ion partitioning effect, unveiling a hitherto hidden facet of electrokinetics. By elucidating the delicate balance between solution pH, ion partitioning effect, and polyelectrolyte charge, our findings offer a comprehensive understanding of the multifaceted interplay shaping soft-electrokinetic systems, thereby paving the way for transformative advancements in energy conversion technologies.

Maximizing blue energy: the role of ion partitioning in nanochannel systems

This study describes a numerical analysis on blue energy generation using a charged nanochannel with an integrated pH-sensitive polyelectrolyte layer (PEL), considering ion partitioning effects due to permittivity differences. The mathematical model for ionic and fluidic transport is solved using the finite element method, and the model validation is performed against existing theoretical and experimental results. The study investigates the influence of electrolyte concentration, permittivity ratio, and salt types (KCl, BeCl2, AlCl3) on the energy conversion process. The findings illustrate the substantial role of ion partitioning in modulating ionic concentration and potential fields, thereby affecting current profiles and energy conversion efficiencies. Remarkably, overlooking ion partitioning leads to significant overestimations of power density, highlighting the necessity of this consideration for accurate device performance predictions. This work introduces a promising configuration that achieves higher power densities, paving the way for the next generation of efficient energy-harvesting devices. The findings offer valuable insights into the development of state-of-the-art blue energy harvesting nanofluidic devices, advancing sustainable energy production.

Layer-by-Layer Nanofluidic Membranes for Promoting Blue Energy Conversion

Access to and use of energy resources are now crucial components of modern human existence thanks to the exponential growth of technology. Traditional energy sources provide significant challenges, such as pollution, scarcity, and excessive prices. As a result, there is more need than ever before to replace depleting resources with brand-new, reliable, and environmentally friendly ones. With the aid of reverse electrodialysis, the salinity gradient between rivers and seawater as a clean supply with easy and infinite availability is a viable choice for energy generation. The development of nanofluidic-based reverse electrodialysis (NRED) as a novel high-efficiency technology is attributable to the progress of nanoscience. However, understanding the predominant mechanisms of this process at the nanoscale is necessary to develop and disseminate this technology. One viable option to gain insight into these systems while saving expenses is to employ simulation tools. In this study, we looked at how a layer-by-layer (LBL) soft layer influences ion transport and energy production in charged nanochannels. We solved the steady-state Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations for three different types of nanochannels with a trumpet geometry, where the narrow part is covered with a built-up LbL soft layer and the rest is a hard wall with a surface charge density of σ = -10, 0, or +10 mC/m2. The findings show that in type (I) nanochannels, at NPEL/NA = 100 mol/m3 and pH = 7, the maximum power output rises 675-fold as the concentration ratio rises from 10 to 1000. The results of this study can aid in a better understanding of energy harvesting processes using nanofluidic-based reverse electrodialysis in order to identify optimal conditions for the design of an intelligent route with great controllability and minimal pollution.

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through a polyelectrolyte layer (PEL) coated cylindrical annulus with reversible and irreversible wall reactions. The ion partitioning effect is observed due to the difference in permittivity of the PEL and the electrolyte solution, which is accounted for by the Born energy. Considering ion partitioning effects, analytical solutions for induced potential and axial velocity are presented, respectively in both the PEL and electrolyte region from the modified Poisson-Boltzmann equation and the Cauchy momentum equation with a proper constitutive equation, respectively. The Maxwell fluid and classical viscous Newtonian fluid models can be achieved separately by adjusting the relaxation and retardation time in the constitutive equation of this model. The analytical solution of the convection-diffusion equation for solute transport is established in the full domain. The separation of species is found to be dependent mainly on the Damköhler number, absorption parameter, phase partitioning coefficient, etc. It is observed that the osmotic pressure increases with the thickness and fixed charge density of the PEL. The velocity decreases with an increase in the permittivity difference of these layers. Our results suggest that the separation may be achieved through a difference in absorption kinetics.

Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer.In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

Effects of surface charge and environmental factors on the electrostatic interaction of fiber with virus-like particle: A case of coronavirus

We propose a theoretical model to elucidate intermolecular electrostatic interactions between a virus and a substrate. Our model treats the virus as a homogeneous particle having surface charge and the polymer fiber of the respirator as a charged plane. Electric potentials surrounding the virus and fiber are influenced by the surface charge distribution of the virus. We use Poisson-Boltzmann equations to calculate electric potentials. Then, Derjaguin's approximation and a linear superposition of the potential function are extended to determine the electrostatic force. In this work, we apply this model for coronavirus or SARS-CoV-2 case and numerical results quantitatively agree with prior simulation. We find that the influence of fiber's potential on the surface charge of the virus is important and is considered in interaction calculations to obtain better accuracy. The electrostatic interaction significantly decays with increasing separation distance, and this curve becomes steeper when adding more salt. Although the interaction force increases with heating, one can observe the repulsive-attractive transition when the environment is acidic.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH-regulated and highly charged polyelectrolyte layer

Electrophoresis of core-shell composite soft particles possessing hydrophobic inner core grafted with highly charged polyelectrolyte layer (PEL) has been studied analytically. The PEL bears pH-dependent charge properties due to the presence of zwitterionic functional groups. The dielectric permittivity of the PEL and bulk aqueous medium were taken to be different, which resulted in the ion-partitioning effect. Objective of this study was to provide a simple expression for the mobility of such core-shell soft particles under Donnan limit where the thickness of the PEL well exceeds the electric double layer thickness. Going beyond the widely used Debye-Hückel linearization, the nonlinear Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations was solved to determine the electrophoretic mobility. The derived expression further recovers all the existing results for the electrophoretic mobility under various simplified cases. The graphical presentation of the results illustrated the impact of pertinent parameters on the electrophoretic mobility of such a soft particle.

Space Electroosmotic Thrusters in Ion Partitioning Soft Nanochannels

Space electroosmotic thrusters (EOTs) are theoretically investigated in a soft charged nanochannel with a dense polyelectrolyte layer (PEL), which is considered to be more realistic than a low-density PEL. When the PEL is dense, its permittivity is smaller than the one of the electrolyte solution layer, leading to rearrangement of ions in the channel, which is denoted as the ion partitioning effect. It is noted that fluid viscosity becomes high within the PEL owing to the hydration effect. An analytical solution for electroosmotic velocity through the channel is obtained by utilizing the Debye-Hückel linearization assumption. Based on the fluid motion, thruster performances, including thrust, specific impulse, thrust-to-power ratio, and efficiency, are calculated. The ion partitioning effect leads to enhancement of the thruster velocity, while increase of the dynamic viscosity inside the PEL reduces the flow rate of the fluid. Therefore, these performances are further impacted by the dense soft material, which are discussed in detail. Moreover, changes or improvements of the thruster performances from the dense PEL to the weak PEL are presented and compared, and distributions of various energy items are also provided in this study. There is a good result whereby the increase in electric double layer thickness promotes the development of thruster performances. Ultimately, the simulated EOTs produce thrust of about 0 to 20 μN and achieve thruster efficiency of 90.40%, while maintaining an appropriate thrust-power ratio of about 1.53 mN/W by optimizing all design parameters.

Electrokinetics of Concentrated Suspension of Soft Particles with pH-Regulated Volumetric Charges

This article presents a theoretical study on the electrokinetics of concentrated suspension of charge-regulated soft particles under a weak electric field and low potential assumptions. The inner core of the undertaken particle is "semisoft" in nature, which allows ion penetration while the fluid cannot flow within it, and the outer soft polymeric shell allows the flow of the ionized fluid. In addition, the inner core and the outer polyelectrolyte layer (PEL) bear pH-regulated basic and acidic functional groups, respectively. The Poisson-Boltzmann equation-based mathematical model was adopted here for electric potential. The fluid flow across the electrolyte medium and PEL is governed by the Stokes equation and the Darcy-Brinkman equation, respectively. The Kuwabara's unit cell model (J. Phys. Soc. Japan, 1959, 14, 522-527) was invoked to observe the effect of the interaction between the neighboring particles in a concentrated suspension. A first order perturbation technique was used to determine the mean electrophoretic mobility of the undertaken soft particles in a concentrated suspension. The effect of pH and concentration of bulk electrolyte, electrohydrodynamic properties of both the inner core and PEL, on the mean electrophoretic mobility has been studied extensively. In addition, the results have been presented for the neutralization factor that measures the fraction of fixed charges neutralized by the mobile counterions.

Impact of ion-steric and ion-partitioning effects on electrophoresis of soft particles

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility

Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility.

Covering the conical nanochannels with dense polyelectrolyte layers significantly improves the ionic current rectification

Because of their asymmetry, conical nanochannels/nanopores exhibit various attractive electrokinetic features, including ion selectivity, ionic concentration polarization, and ionic current rectification. The polyelectrolyte layer (PEL)-covered (soft) conical nanochannels have recently attracted significant attention because of their unique rectification characteristics. In the modeling of soft nanochannels, it is usually assumed that the properties of the PEL and the electrolyte are the same, an assumption that is not true, especially for dense PELs. In the present work, the influence of the PEL-electrolyte property difference on the ionic current rectification in conical soft nanochannels is studied. To this end, adopting a finite-element approach, the Poisson-Nernst-Planck and Navier-Stokes equations are numerically solved for a steady-state by considering different values of permittivity, diffusivity, and dynamic viscosity for the PEL and the electrolyte. The model is validated by comparing the results with the available theoretical and experimental data. The results show that the PEL-electrolyte property difference leads to a significant improvement of the rectification behavior, especially at low and moderate salt concentrations. This not only highlights the importance of considering different properties for the PEL and the electrolyte but also implies that the rectification behavior of soft nanochannels/nanopores may be improved considerably by utilizing denser PELs.

Ion partitioning effect on the electrophoresis of a soft particle with hydrophobic core

A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

Effect of ion partitioning on electrostatics of soft particles with volumetrically charged inner core coated with pH-regulated polyelectrolyte layer

The effect of ion partitioning on the electrostatics of a soft particle with a volumetrically charged core and a pH-dependent polyelectrolyte layer (PEL) is numerically investigated. It is observed that, whenever the ion partitioning is noticeable, the soft layer can be fully charged in a broader range of pH. Besides, a higher number density of the PEL functional groups and a lower charge density of the core result in a sharper dependence of the electric potential on the electrolyte pH. Briefly, we conclude that, since the PEL charge is dependent upon the concentration of the hydroxide/hydrogen ions, for the pH-regulated soft particles, the ion partitioning effect, as a phenomenon influencing the ionic distribution, can be a determinant factor. So taking the effect of the ion partitioning into consideration is strongly recommended for a more realistic description of the electrostatics of the pH-regulated soft particles.