Effect of finite ion sizes in an electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution

Ionic-size dependent electroosmotic flow in ion-selective biomimetic nanochannels

Electrokinetic phenomena, especially electroosmosis in ion-selective environments, play a key role in many systems, from ion-selective nanopores to cellular processes. In this paper, the impact of ionic size on the electroosmotic flow through an ion-selective soft slit nanochannel is analytically studied. Meanwhile, the modified Poisson-Boltzmann and the modified Navier-Stokes equations were used for modeling the electrostatics and the electrohydrodynamics of the problem, respectively, and the derived equations were solved by linearizing method. The results reveal the importance of considering the effect of ionic size in the calculation, as the steric effects, especially at high charge densities of polyelectrolytes (PELs), dramatically alter both the ions arrangement and the electric potential; and amplify the electroosmotic flow. Considering Debye-Huckel parameters of 4 and 10 for the electrolyte layer and the PEL, respectively, we demonstrate that the dimensionless electroosmotic velocity in a soft nanochannel having a dimensionless soft layer thickness of 0.2, from 3.2 by ignoring the steric effect, can reach the value of 6 by considering the steric effect of ν=0.3.

Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Soft interface design for electrokinetic energy conversion

The exploitation and utilization of renewable clean energy is of great significance to the sustainable development of society. Electrokinetic energy conversion (EKEC) based on micro/nanochannels is expected to provide immense potential for ocean energy harvesting, self-powered micro/nanodevices, and small portable power supplies through converting environmental energy into electrical energy. Herein, aiming to get a deeper understanding of EKEC based on micro/nanochannels, several classic theoretical models and corresponding calculation equations are introduced briefly. For high efficiency energy conversion, it is essential to clearly discuss the interface properties between the inner surface of the channel and the bulk electrolyte solution. Therefore, we put forward soft interface designs of solid-liquid and liquid-liquid interfaces, and summarize their recent progress. In addition, the different applications of EKEC, harvesting from environmental energy, are further discussed. We hope that this review will attract more scientists' attention to transform the experimental results of EKEC systems in the lab into available products on shelves.

Revisiting the strong stretching theory for pH-responsive polyelectrolyte brushes: effects of consideration of excluded volume interactions and an expanded form of the mass action law

In this paper, we develop a theory to account for the effect of excluded volume (EV) interactions in the strong stretching theory (SST) based description of pH-responsive polyelectrolyte (PE) brushes. The existing studies have considered the PE brushes to be present in a θ-solvent and hence have neglected the EV interactions; however, such a consideration cannot describe the situations where the pH-responsive brushes are in a "good" solvent. Secondly, we consider a more expanded form of the mass action law, governing the pH-dependent ionization of the PE molecules, in the SST description of the PE brushes. This expanded form of the mass action law considers different values of γa³ (γ is the density of chargeable sites on the PE molecule and a is the PE Kuhn length) and therefore is an improvement over the existing SST models of PE brushes as well as other theories involving pH-responsive PE molecules that always consider γa³ = 1. Our results demonstrate that the EV effects enhance the brush height by inducing additional PE inter-segmental repulsion. Similarly, the consideration of the expanded form of the mass action law would lead to a reduced (enhanced) brush height for γa³ < 1 (γa³ > 1). We also quantify variables such as the monomer density distribution, the distribution of the ends of the PE brush, and the EDL electrostatic potential and explain their differences with respect to those obtained with no EV interactions or γa³ = 1.

Softness Induced Enhancement in Net Throughput of Non-Linear Bio-Fluids in Nanofluidic Channel under EDL Phenomenon

In this article, we describe the electro-hydrodynamics of non-Newtonian fluid in narrow fluidic channel with solvent permeable and ion-penetrable polyelectrolyte layer (PEL) grafted on channel surface with an interaction of non-overlapping electric double layer (EDL) phenomenon. In this analysis, we integrate power-law model in the momentum equation for describing the non-Newtonian rheology. The complex interplay between the non-Newtonian rheology and interfacial electrochemistry in presence of PEL on the walls leads to non-intuitive variations in the underlying flow dynamics in the channels. As such, we bring out the variations in flow dynamics and their implications on the net throughput in the channel in terms of different parameters like power-law index (n), drag parameter (α), PEL thickness (d) and Debye length ratio (κ/κ_PEL) are discussed. We show, in this analysis, a relative enhancement in the net throughput through a soft nanofluidic channel for both the shear-thinning and shear-thickening fluids, attributed to the stronger electrical body forces stemming from ionic interactions between polyelectrolyte layer and electrolyte layer. Also, we illustrate that higher apparent viscosity inherent with the class of shear-thickening fluid weakens the softness induced enhancement in the volumetric flow rate for the shear-thickening fluids, since the viscous drag offered to the f low f ield becomes higher for the transport of shear-thickening fluid.

Ion size effect on electrostatic and electroosmotic properties in soft nanochannels with pH-dependent charge density

We report a theoretical study of the ion size effect on various properties in a soft nanochannel with pH-dependent charge density.

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.

Polyelectrolyte brushes: theory, modelling, synthesis and applications

Polyelectrolyte (PE) brushes are a special class of polymer brushes (PBs) containing charges. Polymer chains attain "brush"-like configuration when they are grafted or get localized at an interface (solid-fluid or liquid-fluid) with sufficiently close proximity between two-adjacent grafted polymer chains - such a proximity triggers a particular nature of interaction between the adjacent polymer molecules forcing them to stretch orthogonally to the grafting interface, instead of random-coil arrangement. In this review, we discuss the theory, synthesis, and applications of PE brushes. The theoretical discussion starts with the standard scaling concepts for polymer and PE brushes; following that, we shed light on the state of the art in continuum modelling approaches for polymer and PE brushes directed towards analysis beyond the scaling calculations. A special emphasis is laid in pinpointing the cases for which the PE electrostatic effects can be de-coupled from the PE entropic and excluded volume effects; such de-coupling is necessary to appropriately probe the complicated electrostatic effects arising from pH-dependent charging of the PE brushes and the use of these effects for driving liquid and ion transport at the interfaces covered with PE brushes. We also discuss the atomistic simulation approaches for polymer and PE brushes. Next we provide a detailed review of the existing approaches for the synthesis of polymer and PE brushes on interfaces, nanoparticles, and nanochannels, including mixed brushes and patterned brushes. Finally, we discuss some of the possible applications and future developments of polymer and PE brushes grafted on a variety of interfaces.

Electrostatics of soft charged interfaces with pH-dependent charge density: effect of consideration of appropriate hydrogen ion concentration distribution

Explicit consideration of hydrogen ion concentration for describing the electrostatics of grafted polyelectrolyte layers with pH-dependent charge density exhibits the necessity of considering a non-uniform depth dependent monomer distribution.

Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates

A new theory quantifies the effect of finite ion size in osmotic pressure (Πosm) between two soft charged plates.

Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters

In this paper we provide analytical solutions for the streaming potential and electroviscous effects in soft nanochannels. The analysis is based on the solution of the linearized Poisson-Boltzmann equation, valid for small electrostatic potentials. We identify the important dimensionless parameters that dictate these two effects. Results are provided for a large range of electric double layer (EDL) thickness values, spanning from the case of very thin to very large overlapped EDL thicknesses. We compare the results with those of a rigid nanochannel, having zeta potential equal to the electrostatic potential at the solid-polyelectrolyte interface of the soft nanochannels. For the soft nanochannel, the streaming potential varies very weakly with the EDL thickness and can be substantially larger than that corresponding to the rigid nanochannel. The electroviscous effects for the soft nanochannel, unlike the rigid nanochannel, virtually always exhibit a monotonic decrease with the EDL thickness, and for certain parameter ranges can be several times larger than that for a rigid nanochannel. Most importantly, for the soft nanochannels the electrochemomechanical energy conversion, associated with the generation of streaming potential, is found to be highly efficient, with the efficiency being several times higher than that of a rigid nanochannel.

Filling of charged cylindrical capillaries

We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because of decreased velocity gradients at the wall. Both these effects essentially stem from the spontaneous formation of an electric double layer (EDL) and the resulting streaming potential caused by the net capillary-flow-driven advection of ionic species within the EDL. Our results demonstrate that filling of charged capillaries also exhibits the well-known linear and Washburn regimes witnessed for uncharged capillaries, although the filling rate is always lower than that of the uncharged capillary. We attribute this to a competitive success of the lowering of the driving forces (because of electroviscous effects), in comparison to the effect of weaker drag forces. We further reveal that the time at which the transition between the linear and the Washburn regime occurs may become significantly altered with the introduction of surface charges, thereby altering the resultant capillary dynamics in a rather intricate manner.