Constant Surface Charge Research Articles

Transient electrophoresis of a conducting spherical particle embedded in an electrolyte-saturated Brinkman medium.

In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.

Estimation of calcite wettability using surface forces

The shift in the wetting conditions during injection of modified salinity water (MSW) in carbonate reservoirs has been interpreted in several recent works through the DLVO extended theory. Two simplifications are usually adopted when applying the DLVO extended theory: (i) the electrostatic energy interaction is quantified by an analytical solution developed for systems containing only monovalent ions and (ii) the structural forces are independent of the type of brine. We address those by prioritizing the brine chemistry. We initially calculate the potential at the mineral and oil surfaces using two different surface complexation models implemented in Phreeqc and then we quantify the electrostatic forces by solving numerically the Poisson Boltzmann (PB) equations for non/symmetrical electrolytes. We observe that not only the identity of the ions, but also, more importantly, the boundary conditions (constant surface charge or constant surface potential) considered for the solution of PB can drastically modify the calculated electrostatic energy profile. We then calculate the total interaction energy and estimate a microscopic contact angle that is consistent with measured values. Our calculations show that increasing the concentration of salts such as MgCl2, CaCl2, and MgSO4 leads to more water-wet conditions, whereas salts like NaCl, KCl, and Na2SO4 show the opposite effect.

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers.

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.

Electrospun PVDF-TrFE/MXene Nanofiber Mat-Based Triboelectric Nanogenerator for Smart Home Appliances.

Understanding of the triboelectric charge accumulation from the view of microcapacitor formation plays a critical role in boosting the output performance of the triboelectric nanogenerator (TENG). Here, an electrospun nanofiber-based TENG (EN-TENG) using a poly(vinylidene fluoride-trifluoroethylene) (PVDF-TrFE)/MXene nanocomposite material with superior dielectric constant and high surface charge density is reported. The influence of dielectric properties on the output performance of the EN-TENG is investigated theoretically and experimentally. The fabricated EN-TENG exhibited a maximum power density of 4.02 W/m2 at a matching external load resistance of 4 MΩ. The PVDF-TrFE/MXene nanocomposite improved the output performance of the EN-TENG fourfold. The EN-TENG successfully powered an electronic stopwatch and thermo-hygrometer by harvesting energy from human finger tapping. Moreover, it was utilized in smart home applications as a self-powered switch for controlling electrical home appliances, including fire alarms, fans, and smart doors. This work presents an effective and innovative approach toward self-powered systems, human-machine interfaces, and smart home applications.

Interaction between Charge-Regulated Metal Nanoparticles in an Electrolyte Solution

We present a theory which allows us to calculate the interaction potential between charge-regulated metal nanoparticles inside an acid-electrolyte solution. The approach is based on the recently introduced model of charge regulation which permits us to explicitly-within a specific microscopic model-relate the bulk association constant of a weak acid to the surface association constant for the same weak acid adsorption sites. When considering metal nanoparticles we explicitly account for the effect of the induced surface charge in the conducting core. To explore the accuracy of the approximations, we compare the ionic density profiles of an isolated charge-regulated metal nanoparticle with explicit Monte Carlo simulations of the same model. Once the accuracy of the theoretical approach is established, we proceed to calculate the interaction force between two charge-regulated metal nanoparticles by numerically solving the Poisson-Boltzmann equation with charge regulation boundary condition. The force is then calculated by integrating the electroosmotic stress tensor. We find that for metal nanoparticles the charge regulation boundary condition can be well approximated by the constant surface charge boundary condition, for which a very accurate Derjaguin-like approximation was recently introduced. On the other hand, a constant surface potential boundary condition often used in colloidal literature, shows a significant deviation from the charge regulation boundary condition for particles with large charge asymmetry.

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.

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.

Modified 3D Ewald Summation for Slab Geometry at Constant Potential

We present a new Monte Carlo method to simulate ionic liquids in slab geometry at constant potential. The algorithm is built upon two previous methods while retaining the advantages of each of them. The method is tested against a Poisson-Boltzmann theory and the constant surface charge ensemble, achieving consistency among all of them. We then analyze the computational time of the developed algorithm, showing substantial speedup in relation to the method of Kiyohara and Asaka [J. Chem. Phys., 2007, 126, 214704]. As an application of our method, we investigate crowding and overscreening in confined room-temperature ionic liquids. We show that we can switch between two behaviors of the double layer by changing the Bjerrum length alone.

Ion Transport in Electrically Imperfect Nanopores.

Ionic transport through a charged nanopore at low ion concentration is governed by the surface conductance. Several experiments have reported various power-law relations between the surface conductance and ion concentration, i.e., Gsurf ∝ c0α. However, the physical origin of the varying exponent, α, is not yet clearly understood. By performing extensive coarse-grained Molecular Dynamics simulations for various pore diameters, lengths, and surface charge densities, we observe varying power-law exponents even with a constant surface charge and show that α depends on how electrically "perfect" the nanopore is. Specifically, when the net charge of the solution in the pore is insufficient to ensure electroneutrality, the pore is electrically "imperfect" and such nanopores can exhibit varying α depending on the degree of "imperfectness". We present an ionic conductance theory for electrically "imperfect" nanopores that not only explains the various power-law relationships but also describes most of the experimental data available in the literature.

Features of Electrical Double Layers Formed Around Strongly Charged Nanoparticles Immersed in an Electrolyte Solution. The Effect of Ion Sizes

Using the modified Poisson–Boltzmann (PB) theory, which includes restrictions on the maximum attainable concentration of ionic species in a solution Cmax determined by their effective sizes, the distributions of electrostatic potential φ(r) and ion concentration near a spherical nanoparticle with radius a immersed in a 1 : 1 electrolyte solution have been studied under the conditions of constant surface charge density σs. For weakly charged particles, the φ(r) profiles are almost independent of Cmax and coincide with the profile obtained in terms of the classical PB model. Surface potential |φs| gradually increases with a rise in |σs|. Far from the particle, when the potential becomes lower than its thermal value $${{\varphi }_{{\text{T}}}} = \frac{{kT}}{e}$$ (k is the Boltzmann constant, T is the temperature, and e is the elementary charge), the potential decreases exponentially irrespective of the counterion sizes: $$\psi \left( r \right) = \frac{{\varphi \left( r \right)}}{{{{\varphi }_{{\text{T}}}}}} = {{\psi }_{{{\text{eff}}}}}\frac{a}{r}\exp \left( { - \kappa \left( {r - a} \right)} \right),$$ where r is the distance from the particle center and κ is the reciprocal Debye radius. According to the classical PB theory, the growth of the surface charge leads to the saturation of $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|~\left( { \to 4} \right),$$ with the value of $$\left| {{{\psi }_{{\text{s}}}}} \right|$$ obtained by solving the nonlinear PB equation being higher than $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|.$$ In the modified PB theory, which takes into account the size of electrolyte ions in the simplest form, this effect of saturation is absent. Now, $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|$$ depends on both the value of the surface charge and the sizes of counterions. Moreover, at a large size of counterions, $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|$$ substantially exceeds the corresponding value obtained by solving the nonlinear modified PB equation. The difference between the electrical double layer properties obtained by solving the classical and modified PB equations directly follows from the fact that the modified theory predicts the appearance of a condensed layer at a particle surface, with the concentration of counterions in this layer being equal to Cmax. Therewith, the thickness of the layer grows with increasing |σs| (at a constant size of the ions) and the size of the ions (at constant σs).

Analysis and spline approximation of surface charge and potential at planar electrochemical interfaces

In this paper, we consider the Poisson‐Boltzmann theory to model the electrostatic potential of a bulk electrolyte containing a single planar charged surface. In the case of a constant surface charge density, we address the problem as a ODE system by using the stability theory for autonomous dynamical systems. By stating that the surface charge density and the surface potential are non‐linearly related through the Grahame equation, we give a description of the stable manifold of the system. To solve the Grahame equation and obtain an approximation for the stable manifold, we propose a smoothing collocation method based on cubic splines, including implementation details and numerical results.

Steady-state voltage distribution in three-dimensional cusp-shaped funnels modeled by PNP.

We study here the bulk electro-diffusion properties of micro- and nanodomains containing a cusp-shaped structure in three-dimensions when the cation concentration dominates over the anions. To determine the consequences on the voltage distribution, we use the steady-state Poisson-Nernst-Planck equation with an integral constraint for the number of charges. A non-homogeneous Neumann boundary condition is imposed on the boundary. We construct an asymptotic approximation for certain surface charge distribution that agree with numerical simulations. Finally, we analyze the consequences of several piecewise constant non-homogeneous surface charge densities, motivated by designing new nanopipettes. To conclude, when electro-neutrality is broken at the scale of hundreds of nanometers, the geometry of cusp-shaped domains influences the voltage profile, specifically inside the cusp structure. The main results are summarized in the form of new three-dimensional electrostatic laws for non-electroneutral electrolytes. These formula provide a refined characterization of voltage distribution at steady-state in neuronal microdomains such as dendritic spines, but can also be used to design nanometric patch-pipettes.

Dynamic Stern layers in charge-regulating electrokinetic systems: three regimes from an analytical approach

We present analytical solutions for the electrokinetic equations at a charged surface with both non-zero Stern-layer conductance and finite chemical reaction rates. We have recently studied the same system numerically [B.L. Werkhoven et al., Phys. Rev. Lett. 120, 264502 (2018)], and have shown that an applied pressure drop across the surface leads to a non-trivial, laterally heterogeneous surface charge distribution at steady state. In this work, we linearise the governing electrokinetic equations to find closed expressions for the surface charge profile and the generated streaming electric field. The main results of our calculations are the identification of three important length and time scales that govern the charge distribution, and consequently the classification of electrokinetic systems into three distinct regimes. The three governing time scales can be associated to (i) the chemical reaction, (ii) diffusion in the Stern layer, and (iii) conduction in the Stern layer, where the dominating (smallest) time scale characterises the regime. In the reaction-dominated regime, we find a constant surface charge with an edge effect and recover the Helmholtz–Smoluchowski equation. In the other two regimes, we find that the surface charge heterogeneity extends over the entire surface, either linearly (diffusion-dominated regime) or nonlinearly (conduction-dominated regime).

Upper limits for output performance of contact-mode triboelectric nanogenerator systems

Intensive research efforts have been devoted to increasing output performance of triboelectric nanogenerators (TENGs) by selecting or modifying materials, increasing effective area, optimizing device structures and harvesting circuits. Considering field emission and gas-ionization for electric breakdown, this paper proposes new theoretical models to predict the upper limits for output performance of contact-mode TENG harvesting system. It reveals that a constant surface charge density exists on the dielectric layer with an effective thickness below a critical value. The resultant TENG exhibits a high output power. The working efficiency of the TENG harvesting system quantitatively highlights the scope and focus of improvement for high output power. The findings would provide a powerful tool to guide the experimental design in selection of materials, structure of TENG, harvesting circuits and storage device for intended applications.

Finite ion size effect on the force and energy of the double-layer interaction between two parallel similar plates at arbitrary separations in an electrolyte solution

Expressions are derived for the force and energy of the double-layer interaction between two parallel similar plates with arbitrary surface charge densities or surface potentials at arbitrary separations in an electrolyte solution, by taking into account the finite ion size effect on the basis of the full expression of the activity coefficients of electrolyte ions derived by Carnahan and Starling. The results for two models of the double-layer interaction, that is, the constant surface potential and constant surface charge density models, are given. It is shown that in the constant surface potential model, at large plate separations, the magnitudes of the double-layer interaction force and energy increase as the total ion volume fraction increases but this tendency reverses at small plate separations, while in the constant surface charge density model, they always increase as the total ion volume fraction increases.

Electroviscous effect on pressure driven flow and related heat transfer in microchannels with surface chemical reaction

This study investigates the fluidic flow and related heat transfer in a microchannel formed by two parallel plates. Uniform heat flux is applied at the walls with considering the surface chemical reaction, which determines the surface charge on the wall of the microchannel. Our results show that the pH and ionic concentration apparently affect the surface chemical reaction and the subsequent fluidic behavior and heat transfer in the microchannel, especially with the boundary slip. The dimensionless velocity and temperature increase with the ionic concentration. The difference of the dimensionless flow rate and the Nusselt number is obvious under three different electrical boundary conditions: constant surface charge density, constant zeta potential and MI model. Under the boundary slip, the dimensionless flow rate and Nusselt number decrease by 50% and 12%, respectively, with increasing pH under the MI model, but keep unchanged under constant zeta potential or surface charge model. The dimensionless flow rate and Nusselt number also increase with the ionic concentration due to weakened electroviscous effect. Meanwhile, the slip increases the influence of ionic concentration on the dimensionless flow rate and Nusselt number. The results of this work may guide the design and optimization of microfluidic devices.

Effects of fibre dimension and charge density on nanocellulose gels

HypothesisCarboxylated cellulose nanofibres can produce gels at low concentrations. The effect of pulp source on the nanocellulose fibre dimension and gel rheology are studied. It is hypothesised that fibre length and surface charge influence aspects of the gel rheological properties. ExperimentsTEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl)- mediated oxidised cellulose nanofibres from never-dried hardwood and softwood pulp and containing different charge levels were produced and characterized. Steady-state and dynamic rheological studies were performed to ascertain the effects of pulp type on gel behavior and properties. FindingsNanocellulose fibres extracted from softwood (SW-TOCN) and hardwood (HW-TOCN) pulp exhibit similar widths but different length dimensions as shown via AFM analysis. Rheological measurements show that the dynamic moduli (G′ and G′′) of nanocellulose gels are independent of pulp source and are mostly influenced by fibre concentration. Differences in the steady-state behavior (i.e. viscosity) at constant surface charge can be attributed to differences in fibre length. Increasing the surface charge density influences the critical strain and the viscosity at the percolation concentration (0.1 wt%) due to higher electrostatic interactions.

Adsorption of charged macromolecules upon multicomponent responsive surfaces.

Adsorption of polyions onto charged surfaces has long been recognized as a crucial phenomenon in biological and technological applications. An intuitive model relating polyelectrolyte adsorption with the imposed features of polarizable surfaces of different compositions and charges is proposed based on Monte Carlo simulations using a coarse-grained approach. The excellent performance of the equation allows simultaneously describing a wide range of adsorption regimes and accounting for specific non-monotonic trends. For a constant surface charge density, the surface composition governs adsorption, promoting variations exceeding 100%. Adsorption increases with the number of attractive charges in the surface until reaching a maximum, decreasing thereafter due to the presence of polyanion-like charged particles. The presence of crowders hampers adsorption. These results can be used to efficiently predict and modulate the interaction between charged macromolecules and different substrates with direct implications in de novo designs of vehicles and biomedical devices.

Enhanced electroosmotic flow in a nano-channel patterned with curved hydrophobic strips

We consider the electroosmotic flow (EOF) in a nano-channel in which the channel walls are modulated with a periodic array of curved hydrophobic patches. The objective is to achieve an enhanced flow compared to a slit nano-channel. The shape of the hydrophobic strips are considered to be of sinusoidal form, which resembles the situation in which the channel indentations are filled with immiscible nonconducting fluid over which the electrolyte is considered to be in metastable Cassie state. The homogeneous no-slip portions of the channel walls are considered to posses a constant surface-potential (zeta-potential) or constant surface charge density, while the hydrophobic regions are uncharged. A mathematical model based on the Nernst–Planck–Navier-Stokes equations are considered to analyze the present EOF. A coordinate transformation is adopted to map the irregular physical domain to a regular computational domain. A pressure-correction based control volume approach is adopted to solve the governing equations. We have studied the EOF by varying the amplitude of the hydrophobic region. Our results show that an enhancement in EOF compared to a slit-channel is possible when the Debye length is in the order of the channel height. The EOF in the patterned channel varies with the planform length of the hydrophobic region as well as the relative span of the slip and no-slip regions. A comparison with the pressure-driven flow is also presented to analyze the hindrance created by the electric body force of the unbalanced ions.

Steady/unsteady electroosmotic flow through nanochannel filled with electrolyte solution surrounded by an immiscible liquid

This article deals with the electroosmotic flow through nanochannel filled with electrolyte solution surrounded by an immiscible oil layer where the fluid is driven by either DC or AC electric field. The walls of the nanochannel are considered to bear a constant negative surface charge. Additional mobile ions with positive polarity are present in the surface oil layer. The electrostatic potential can be obtained from the nonlinear Poisson-Boltzmann equation. With the known electric potential, we calculate the axial velocity distribution from the unsteady Stokes equation. The effects of intrinsic parameters on the overall electrostatic behavior as well as velocity distribution are discussed in a great detail. We identify several interesting key features of the flow distributions under externally applied DC or AC electric field. For lower range of Debye-Huckel parameter, the overlap of adjacent electric double layers significantly affects the flow profile. In addition for externally applied sinusoidal AC electric field, a finite settling time is required to diffuse the momentum of the fluid from the adjacent region of the channel wall to the bulk fluid. As a result, a phase shift between the applied electric field and velocity field may occur. Under AC electric field, the oscillatory behavior of the axial velocity is further investigated.