Thickness Of Polyelectrolyte Layer Research Articles

Impact of charged soft layers on electroosmosis of Maxwell fluids in soft nanochannels

In the present paper, we theoretically study the transient electroosmotic flow of general Maxwell fluids through the polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain the transient electroosmotic flow from the Cauchy momentum equation and the Maxwell constitutive equation. For the nanochannels grafted with polyelectrolyte layers having different layered distributions of charges, we consider the influence of the dimensionless relaxation time, the dimensionless polyelectrolyte layer thickness, and the dimensionless drag coefficient on the transient electroosmotic flow. We present the results for some particular cases. First, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, the total electroosmotic flow is non-zero. In particular, depending on charge distribution within the end part of polyelectrolyte layers, the direction of the electroosmotic flow can be reversed critically. Second, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between the layered charge densities of two polyelectrolyte layers. Increasing ks allows the electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can intentionally control the direction of the flows as well as the strength of electroosmotic flow.

Effect of ion partitioning on an oscillatory electro-osmotic flow on solute transport process of fractional Jeffrey fluid through polyelectrolyte-coated nanopore with reversible wall reaction

The ion-partitioning effects on solute transport phenomena of time-periodic electro-osmotic flow in fractional Jeffrey fluid are investigated through a polyelectrolyte layer (PEL)-coated conical nanopore within a reactive wall whose ends are connected with two large reservoirs. By considering the ion-partitioning effects, analytical solutions for the induced potential and the axial velocity are presented, respectively, from the modified Poisson–Boltzmann equation and the Cauchy momentum equation with the proper constitutive equation of the fractional Jeffrey fluid model in the exterior and interior of the PEL. The analytic solution of the convection–diffusion for solute transport is established in the entire domain. The influence of the oscillating Reynolds number Rew, permittivity ratio εr between two mediums, relaxation time λ1ω, retardation time λ2ω, phase partitioning coefficient σp, PEL fixed charge density qfix, Debye–Hückel parameter κa, and softness parameter λs are investigated in this study. Asymptotic solution for the axial velocity was also presented for low-oscillating Reynolds numbers and validated. The maximum axial velocity occurs when the permittivity between the PEL and electrolyte is the same for all models. The volumetric flow rate decreases with the increase in the PEL thickness, positive PEL charge density, and softness parameter in our study. The volume flow rate of the Newtonian fluid increased 24.07% for Maxwell fluid (λ1ω=5, α = 1) and 11.56% for Jeffrey fluid (λ1ω=5, λ1ω=1, α = 1, and β=0.5), when κa=25, Rew = 10, qfix = 5, d = 0.2, εr=0.6, and λs=1.0. The mass transport rate increases with relaxation time, tidal displacement, and permittivity ratio between these layers.

Ion partitioning effect on the electrostatic interaction between two charged soft surfaces

We theoretically investigate electrostatic properties between two charged surfaces with a grafted polyelectrolyte layer in an aqueous electrolyte solution by using the Poisson-Boltzmann approach accounting for ion partitioning. In order to consider the ion partitioning effect, we focus on changes of electrostatic properties due to the difference in dielectric permittivity of the polyelectrolyte layer and the aqueous electrolyte solution. We find that ion partitioning enhances electrostatic potential in the region between two charged soft surfaces and hence increases the electrostatic interaction between two charged soft surfaces. Ion partitioning effect on osmotic pressure is enhanced not only by an increase in the thickness of polyelectrolyte layer and Debye length but also by a decrease in ion radius.

Space charge modulation and ion current rectification of a cylindrical nanopore functionalized with polyelectrolyte brushes subject to an applied pH-gradient

Considering versatile potential applications of bioinspired membranes, we simulate the electrokinetic behavior of a cylindrical nanopore, surface modified by a polyelectrolyte (PE) layer. Taking account of the effect of electroosmotic flow and an additionally applied pH gradient, the influences of the strength of the pH gradient, the PE layer thickness, the length of the nanopore and its radius on its conductance and ion current rectification (ICR) performance are assessed. We show that if pHU (the pH at the higher pH end of the nanopore) is fixed at 11 and pHL (the pH at the lower pH end of the nanopore) varies from 3 to 11, the rectification factor Rf has a local maximum occurring in 6 < pHL <8; the greater the magnitude of the applied potential bias |V| the smaller the pHL at which the local maximum occurs. The influence of the PE layer thickness on the nanopore rectification performance is important only if 5 < pHL <8, and the optimum performance is reached at a medium thick PE layer (ca. 3 nm). Possible mechanisms associated with the ion transport phenomenon under consideration are proposed and discussed in detail.

Electroosmotic thrusters in soft nanochannels for space propulsion

Space propulsion of electroosmotic thrusters (EOTs) with a soft charged nanochannel is investigated considering the Navier slip boundary and constant surface charge density on the walls of slit channels. The soft nanochannel is characterized by a wall-grafted ion-penetrable charged polyelectrolyte layer (PEL). The Poisson–Boltzmann equation is solved to give the electric potential distribution based on the assumption of the Debye–Hückel linearization for the low electric potential. An analytical solution of the electroosmotic velocity through the soft channel is obtained. The thrust, specific impulse, and total input power of EOTs produced by the electroosmotic flow are presented, and then, two significant physical quantities, thruster efficiency and thrust-to-power ratio, are described. It is found that these performance curves strongly depend on the slip length, surface charge density on the walls, drag coefficient, equivalent electric double layer thickness, PEL thickness, and density ratio of the PEL to the electrolyte solution layer. By analyzing and optimizing these design parameters, the simulated EOTs can deliver the thrust from 0 μN to 10 µN as well as the specific impulse from 40 s to 100 s, and the thruster efficiency up to 87.22% is realized. If more thrust control and kinetic energy are needed for different space missions, an array composed of thousands of single EOT emitters is constructed and maintains high thruster efficiency. Moreover, during mission operation, the total potential can be simply varied to optimize the performances of thrusters at any moment.

Rheology modulated high electrochemomechanical energy conversion in soft narrow-fluidic channel

We study the influence of viscoelastic fluid on the enhancement of the electrochemomechanical energy conversion efficiency in the polyelectrolyte layer grafted narrow-fluidic channels. We obtain the velocity distribution using the simplified Phan-Thien-Tanner model and calculate the conversion efficiency in the purview of both with and without Debye-Hückel approximations. The analysis unveils that an increment in the fluid velocity obtained with an increment in the shear-thinning nature of the viscoelastic fluid increases the streaming of the counter-ions, which, in turn, increases the conversion efficiency. Also, it is shown that the increased electroviscous effect due to higher rate of streaming potential being developed results in a reduction in the predicted enhancement of the conversion efficiency. This phenomenon is observed for a window of parameters viz. higher polyelectrolyte layer thickness, higher viscoelastic parameter, and lower Debye-Hückel parameter of the electrolyte. We also report that the relatively higher electrostatic potential stemming from the overlapping electrical double layers and the higher wall potential (greater than 25 mV), lead to non-intuitive variation in the conversion efficiency following the pronounced influence of the electroviscous effect. While targeting an increment in the conversion efficiency using viscoelastic fluid and grafted polyelectrolyte layer, we also examine the influence of slip at the walls of the channel and the spatial variation of electrical conductance between the stern layer conductance and that of the walls of the channel. However, the rheology modulated enhancement in the efficiency is found to be effective in case of variation in the stern layer conductance and interfacial slip at the walls of the channel.

Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption

The dispersion of a neutral solute band by electrokinetic flow in polyelectrolyte layer (PEL)-grafted rectangular/slit microchannels is theoretically studied. The flow is assumed to be both steady and fully developed and a first-order irreversible reaction is considered at the wall to account for probable surface adsorption of solutes. Considering low electric potentials, analytical solutions are obtained for electric potential, fluid velocity and solute concentration. Special solutions are also obtained for the case without wall adsorption. To track the dispersion properties of the solute band, the generalized dispersion model is adopted by considering the exchange, the convection and the dispersion coefficients. The solutions developed are validated by comparing the results with the predictions of finite-element-based numerical simulations. Even though the solutions can take any form of initial solute concentration into account, the results are presented by considering a solute band of rectangular shape. The results reveal that, while the short-term transport coefficients are strongly affected by the initial concentration profile, the long-term values are not dependent upon the initial conditions. In addition, it is shown that the mass transport coefficients are strong functions of the channel aspect ratio; hence, approximating a rectangular geometry by the space between two parallel plates may lead to considerable errors in the estimation of mass transport characteristics. This is particularly important for the dispersion coefficient for which the long-term values for a slit microchannel are quite different from those for a rectangular channel of very high aspect ratio. It is also illustrated that the exchange and convection coefficients increase on increasing the Damkohler number, whereas the opposite is true for the dispersion coefficient. The convection and dispersion coefficients are generally increasing functions of the PEL fixed charge density and the PEL thickness and decreasing functions of the PEL friction coefficient. Last but not least, a thicker electric double layer is found to provide a larger degree of solute dispersion, which is the opposite of that observed in a microchannel with bare walls.

Mass transfer of a neutral solute in polyelectrolyte grafted soft nanochannel with porous wall

A soft nanochannel involves a soft interface that contains a polyelectrolyte layer (PEL) sandwiched between a rigid surface and a bulk electrolyte solution. Mass transfer of a neutral solute in a combined electroosmotic and pressure driven flow through a polyelectrolyte grafted charged nanochannel with porous wall is presented in this work. Assuming the PEL as fixed charged layer and PEL-electrolyte interface as a semi-penetrable membrane, analytical solutions were obtained for potential distributions (for small wall potential). Velocity profiles were also derived in the same domains, for both inside and outside the PEL. Convective-diffusive species balance equation was semi-analytically solved inside the PEL. Expression of length averaged Sherwood number was also obtained and effects of different parameters, namely, drag parameter (α), Debye parameter , and PEL thickness were studied in detail. The variation of permeate concentration and permeation flux across the porous wall was obtained.

The Effects of Finite Ionic Sizes and Wall Slip on Entropy Generation in Electroosmotic Flows in a Soft Nanochannel

Abstract The combined effects of finite ionic sizes and boundary slip on the entropy generation in mixed pressure driven and electroosmotic flows (EOFs) in a soft nanochannel are investigated in this study. The soft nanochannel is represented by a rigid nanochannel covered by a charged polyelectrolyte layer (PEL) on its surface. The entropy generation analysis of EOFs in such a soft nanochannel is addressed for the first time. Under the assumption of high zeta potentials, the electric potential, velocity, and temperature distributions are obtained numerically by using the finite difference method. Subsequently, the thermal transport characteristic and the corresponding entropy generation analysis are discussed based on the obtained velocity and temperature distributions. Our results show that the soft nanochannel in the present model is not appropriate for cooling purposes. We also demonstrate that the steric factor v and the PEL thickness d can enhance the entropy generation rate. However, the slip boundary coefficient γ, the drag parameter α, and the equivalent electric double-layer (EDL) thickness λFCL can restrain this entropy generation rate. In addition, the contributions of Joule heating and viscous friction in the entropy generation rate are more prominent than the contribution due to heat transfer. The present theoretical research can be used to design the efficient thermofluidic devices.

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/κPEL) 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.

Theoretical modeling of electroosmotic flow in soft microchannels: A variational approach applied to the rectangular geometry

Modeling of fluid flow in polyelectrolyte layer (PEL)-grafted microchannels is challenging due to their two-layer nature. Hence, the pertinent studies are limited only to circular and slit geometries for which matching the solutions for inside and outside the PEL is simple. In this paper, a simple variational-based approach is presented for the modeling of fully developed electroosmotic flow in PEL-grafted microchannels by which the whole fluidic area is considered as a single porous medium of variable properties. The model is capable of being applied to microchannels of a complex cross-sectional area. As an application of the method, it is applied to a rectangular microchannel of uniform PEL properties. It is shown that modeling a rectangular channel as a slit may lead to considerable overestimation of the mean velocity especially when both the PEL and electric double layer (EDL) are thick. It is also demonstrated that the mean velocity is an increasing function of the fixed charge density and PEL thickness and a decreasing function of the EDL thickness and PEL friction coefficient. The influence of the PEL thickness on the mean velocity, however, vanishes when both the PEL thickness and friction coefficient are sufficiently high.

Alternating current electroosmotic flow in polyelectrolyte-grafted nanochannel

In this work, we investigate the time periodic electroosmotic flow (EOF) of an electrolyte solution through a slit polyelectrolyte-grafted (PE-grafted) nanochannel under applied alternating current (AC) electrical field. The PE-grafted nanochannel is represented by a rigid surface covered by a polyelectrolyte layer (PEL) in a brush-like configuration. Under Debye-Hückel approximation, we obtain analytical solutions of electrical potential in decoupled regime of PE-grafted nanochannel, where the thickness of PEL is independent of the electrostatic effects triggered by polyelectrolyte charges. Based upon the electrical potential obtained above, we calculate EOF velocities with uniform and non-uniform drag coefficients for PE-grafted nanochannel and compare their results. The effects of pertinent dimensionless parameters on EOF velocity amplitude are discussed in detail. Moreover, the amplitude of EOF velocity in a PE-grafted nanochannel is compared with that in a rigid one. It is shown that larger EOF velocity and volume flow rate are found for a PE-grafted nanochannel. In addition, AC EOF velocity is further investigated. The oscillation of velocity reduces and is restricted within the region near the PEL-electrolyte interface for higher oscillating Reynolds number Re.

Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density

Nanochannels, functionalized by grafting with a layer of charged polyelectrolyte (PE), have been employed for a large number of applications such as flow control, ion sensing, ion manipulation, current rectification and nanoionic diode fabrication. Recently, we established that such PE-grafted nanochannels, often denoted as “soft” nanochannels, can be employed for highly efficient, streaming-current-induced electrochemomechanical energy conversion in the presence of a background pressure-driven transport. In this paper, we extend our calculation for the practically realizable situation when the PE layer demonstrates a pH-dependent charge density. Consideration of such pH dependence necessitates consideration of hydrogen and hydroxyl ions in the electric double layer charge distribution, cubic distribution of the monomer profile, and a PE layer-induced drag force that accounts for this given distribution of the monomer profile. Our results express a hitherto unknown dependence of the streaming electric field (or the streaming potential) and the efficiency of the resultant energy conversion on parameters such as the pH of the surrounding electrolyte and the $$\hbox {pK}_{\mathrm{a}}$$ of the ionizable group that ionizes to produce the PE charge—we demonstrate that increase in the pH and the PE layer thickness and decrease in the $$\hbox {pK}_{\mathrm{a}}$$ and the ion concentration substantially enhance the energy conversion efficiency.

Electrostatics and Charge Regulation in Polyelectrolyte Multilayered Assembly

We examine the implications of electrostatic interactions on formation of polyelectrolyte multilayers, in application to field-effect based biosensors for label-free detection of charged macromolecules. We present a quantitative model to describe the experimental potentiometric observations and discuss its possibilities and limitations for detection of polyelectrolyte adsorption. We examine the influence of the ionic strength and pH on the sensor response upon polyelectrolyte layer-by-layer formation. The magnitude of potential oscillations on the sensor-electrolyte interface predicted upon repetitive adsorption charge-alternating polymers agrees satisfactorily with experimental results. The model accounts for different screening by mobile ions in electrolyte and inside tightly interdigitated multilayered structure. In particular, we show that sensors' potential oscillations are larger and more persistent at lower salt conditions, while they decay faster with the number of layers at higher salt conditions, in agreement with experiments. The effects of polyelectrolyte layer thickness, substrate potential, and charge regulation on the sensor surface triggered by layer-by-layer deposition are also analyzed.

Empirical correlations to estimate agglomerate size and deposition during injection of a polyelectrolyte-modified Fe 0 nanoparticle at high particle concentration in saturated sand

Controlled emplacement of polyelectrolyte-modified nanoscale zerovalent iron (NZVI) particles at high particle concentration (1–10 g/L) is needed for effective in situ subsurface remediation using NZVI. Deep bed filtration theory cannot be used to estimate the transport and deposition of concentrated polyelectrolyte-modified NZVI dispersions (> 0.03 g/L) because particles agglomerate during transport which violates a fundamental assumption of the theory. Here we develop two empirical correlations for estimating the deposition and transport of concentrated polyelectrolyte-modified NZVI dispersions in saturated porous media when NZVI agglomeration in porous media is assumed to reach steady state quickly. The first correlation determines the apparent stable agglomerate size formed during NZVI transport in porous media for a fixed hydrogeochemical condition. The second correlation estimates the attachment efficiency (sticking coefficient) of the stable agglomerates. Both correlations are described using dimensionless numbers derived from parameters affecting deposition and agglomeration in porous media. The exponents for the dimensionless numbers are determined from statistical analysis of breakthrough data for polyelectrolyte-modified NZVI dispersions collected in laboratory scale column experiments for a range of ionic strength (1, 10, and 50 mM Na + and 0.25, 1, and 1.25 mM Ca 2+), approach velocity (0.8 to 55 × 10 −4 m/s), average collector sizes (d 50 = 99 μm, 300 μm, and 880 μm), and polyelectrolyte surface modifier properties. Attachment efficiency depended on approach velocity and was inversely related to collector size, which is contrary to that predicted from classic filtration models. High ionic strength, the presence of divalent cations, lower extended adsorbed polyelectrolyte layer thickness, decreased approach velocity, and a larger collector size promoted NZVI agglomeration and deposition and thus limited its mobility in porous media. These effects are captured quantitatively in the two correlations developed. The application and limitations of using the correlations for preliminary design of in situ NZVI emplacement strategies is discussed.

Effect of Layer-by-Layer Electrostatic Assemblies on the Surface Potential and Current Voltage Characteristic of Metal−Insulator−Semiconductor Structures

In the present Article, the Kelvin probe method for surface potential measurement is introduced to study polyelectrolyte multilayer coatings deposited on silicon plates. Metal-insulator-semiconductor (MIS) structures with polyelectrolyte layers as insulator were fabricated. The polyelectrolyte layer deposition on the surface of silicon plates led to a change of the current-voltage characteristics connected with resistance changes of the MIS structures. Poly(ethylenimine) (PEI) monolayer formation resulted in resistance decrease, and the following increase of the polyelectrolyte layer number led to MIS structure resistance increase. The results are interpreted as an interplay between accumulation of majority carriers (electrons) near the semiconductor surface and resistance increase due to insulating polyelectrolyte adsorption, and both effects can be discriminated by varying the polyelectrolyte layer thickness.

Electrophoretic mobility of a particle covered with a partially ion-penetrable polyelectrolyte layer

A theory of electrophoresis of a colloidal particle coated with a polyelectrolyte layer [H. Ohshima, J. Colloid Interface Sci., 163 (1994) 474] is extended to cover the case where a polyelectrolyte layer is not fully ion-penetrable. Partition coefficients b of the electrolyte ions into the polyelectrolyte layer are introduced. For the extreme case of b = 0, where the polyelectrolyte layer is not ion-penetrable at all so that the ionic shielding effects in the polyelectrolyte layer disappears, the mobility exhibits a significant dependence on the polyelectrolyte layer thickness. This is in contrast to the opposite extreme case of fully ion-penetrable polyelectrolyte layers (b = 1), where the dependence of the mobility on the polyelectrolyte layer thickness is quite small for most cases.

Variation of ellipsometric adsorbed polyelectrolyte layer thickness with potential

The ellipsometric thickness of sodium poly (styrene sulfonate) (NaPSS) layers adsorbed from aqueous NaCl solution onto a platinum plate was measured as a function of molecular weight and applied potential. A cathodic potential with respect to the rest potential was applied. At rest potential the ellipsometric thickness scales as M. 0.5 and M. 0.4 in theta and good solvents, respectively, and increases with increasing solvent power (decreasing ionic strength). The variation of the ellipsometric thickness with the molecular weight at applied potentials differs markedly from that without applied potential and becomes weaker with increasing applied potential. Small NaPSS chains extended more readily than large NaPSS chains by the applied potential. In particular, high applied potentials induce a stretched conformation of adsorbed small NaPSS molecules.