Electrokinetic ion transport in an asymmetric double-gated nanochannel with a pH-tunable zwitterionic surface.

Bioinspired, artificial functional nanochannels for intelligent molecular and ionic transport control have versatile potential applications in nanofluidics, energy conversion, and controlled drug release. To simulate the gating and rectification functions of biological ion channels, we model the electrokinetic ion transport phenomenon in an asymmetric double-gated nanochannel having a pH-regulated, zwitterionic surface. Taking account of the effect of electroosmotic flow (EOF), the conductance of the nanochannel and its ion current rectification (ICR) behavior are investigated and the associated mechanisms interpreted. In particular, the influences of the solution pH, the bulk salt concentration, and the base opening radius and the surface curvature of the nanochannel on these behaviors are examined. We show that through adjusting the base opening radius and the surface curvature of a nanochannel, its ICR behavior can be tuned effectively. In addition to proposing underlying mechanisms for the phenomena observed, the results gathered in this study also provide necessary information for designing relevant devices.

Ion Current Rectification Behavior of Bioinspired Nanopores Having a pH-Tunable Zwitterionic Surface.

The ion current rectification behavior of bioinspired nanopores is modeled by adopting a bullet-shaped nanopore having a pH-tunable zwitterionic surface, focusing on discussing the underlying mechanisms. We show that with its specific geometry, such nanopore is capable of exhibiting several interesting behaviors, including ion concentration polarization and ion current rectification. The influences of the nanopore shape, solution pH, and bulk salt concentration on the associated ion current rectification behavior are examined. We found that if pH exceeds the isoelectric point, the rectification factor has a local maximum as the curvature of the nanopore surface varies, and if it is lower than the isoelectric point, that factor increases (rectification effect decreases) monotonically with increasing surface curvature. In addition to capable of interpreting relevant electrokinetic phenomena, the results gathered also provide necessary information for a sophisticated design of relevant devices.

Importance of polyelectrolyte modification for rectifying the ionic current in conically shaped nanochannels.

Due to their specific geometry, conical nanochannels/nanopores are capable of exhibiting several interesting electrokinetic phenomena including, for example, ion concentration polarization (ICP) and ion current rectification (ICR). Extending previous analyses, we consider two types of nanochannels: only the inner surface of a nanochannel is functionalized by a polyelectrolyte (PE) layer in a type I nanochannel, and both its outer and inner surfaces are functionalized in a type II nanochannel. The influences of the thickness of a double layer and that of the PE layer on ICR are examined through numerical simulation. We show that the ICP of a type I nanochannel is more significant than that of the corresponding type II nanochannel. The behavior of the rectification factor of the former as the bulk salt concentration varies also differs significantly from that of the latter. In particular, the rectification factor of a type I nanochannel at a low bulk salt concentration shows an inversion.

Separation of charge-regulated polyelectrolytes by pH-assisted diffusiophoresis.

The potential of separating colloidal particles through simultaneous application of a salt gradient and a pH gradient, or pH-assisted diffusiophoresis, is evaluated by considering the case of spherical polyelectrolytes (PEs) having different equilibrium dissociation constants in an aqueous solution with KCl as the background salt. The simulation results gathered reveal that the dependence of the particle velocity on pH is more sensitive than that in pH-assisted electrophoresis, where an electric field and a pH gradient are applied simultaneously. This implies that the separation efficiency of pH-assisted diffusiophoresis can be better than that of pH-assisted electrophoresis. In particular, two types of PE having different equilibrium dissociation constants can be separated effectively by applying the former by enhancing/reducing their diffusiophoretic velocities.

Ionic Current Rectification in a pH-Tunable Polyelectrolyte Brushes Functionalized Conical Nanopore: Effect of Salt Gradient.

The behavior of ionic current rectification (ICR) in a conical nanopore with its surface modified by pH-tunable polyelectrolyte (PE) brushes connecting two large reservoirs subject to an applied electric field and a salt gradient is investigated. Parameters including the solution pH, types of ionic species, strength of applied salt gradient, and applied potential bias are examined for their influences on the ionic current and rectification factor, and the mechanisms involved are investigated comprehensively. The ICR behavior depends highly on the charged conditions of the PE layer, the level of pH, the geometry of nanopore, and the thickness of the double layer. In particular, the distribution of ionic species and the local electric field near the nanopore openings play a key role, yielding profound and interesting results that are informative to device design as well as experimental data interpretation.

Regulating Current Rectification and Nanoparticle Transport Through a Salt Gradient in Bipolar Nanopores.

Tuning of ion and nanoparticle transport is validated through applying a salt gradient in two types of nanopores: the inner wall of a nanopore has bipolar charges and its outer wall neutral (type I), and both the inner and outer walls of a nanopore have bipolar charges (type II). The ion current rectification (ICR) behavior of these nanopores can be regulated by an applied salt gradient: if it is small, the degree of ICR in type II nanopore is more significant than that in type I nanopore; a reversed trend is observed at a sufficiently large salt gradient. If the applied salt gradient and electric field have the same direction, type I nanopore exhibits two significant features that are not observed in type II nanopore: (i) a cation-rich concentration polarization field and an enhanced funneling electric field are present near the cathode side of the nanopore, and (ii) the magnitude of the axial electric field inside the nanopore is reduced. These features imply that applying a salt gradient to type I nanopore is capable of simultaneously enhancing the nanoparticle capture into the nanopore and reducing its translocation velocity inside, so that high sensing performance and resolution can be achieved.

Simulation of polyelectrolyte electrophoresis: effects of the aspect ratio, double-layer polarization, effective charge, and electroosmotic flow.

The electrophoresis of a deformable polyelectrolyte (PE) is studied theoretically by considering a Poisson-Nernst-Planck model coupled with modified Navier-Stokes equations, taking account of the effects of double-layer polarization, counterion condensation, and electroosmotic flow. The influences of the local electric field and the effective PE charge on the PE mobility are discussed, thereby providing a complete picture for the phenomenon under consideration. Our model explains successfully the presence of a local minimum in the mobility of a highly charged PE as the bulk salt concentration varies, as observed experimentally. Numerical simulation also reveals several interesting and important results. For example, the more a PE is stretched in the direction of electrophoresis, the larger is its mobility. As the double layer becomes thin, the local electric field becomes independent of the PE shape, and its behavior mainly depends upon its effective charge. We show that the force that stretches a PE is maximal when it is spherical and decreases with an increasing aspect ratio, which has not been reported previously.

Influence of polyelectrolyte shape on its sedimentation behavior: effect of relaxation electric field.

The sedimentation of an isolated, charged polyelectrolyte (PE) subjected to an applied field is modeled theoretically, taking into account the variation of its shape. In particular, the effects of double-layer relaxation, effective charge density, and strength of the induced relaxation electric field are examined. We show that the interaction of these effects yields complex and interesting sedimentation behaviors. For example, the behavior of the electric force acting on a loosely structured PE can be different from that on a compactly structured one; the former is dominated mainly by the convective fluid flow. For thick double layers, electric force has a local maximum as the Reynolds number varies, but tends to increase monotonically with increasing Reynolds number if the layer is thin. The drag factor is found to behave differently from literature results. The shape of a PE significantly influences its sedimentation behavior by affecting the amount of counterions attracted to its interior and the associated local electric field. Interestingly, a more stretched PE has a higher effective charge density but experiences a weaker electric force.

Gel electrophoresis of a charge-regulated, bi-functional particle.

Adopting a Brinkman fluid model, we analyzed the electrophoresis of a charged-regulated, bi-functional particle containing both acidic and basic functional groups in a gel solution. Both the long-range hydrodynamic effect arising from the liquid drag and the short-range steric effect from particle-polymer interaction are considered. The type of particle considered is capable of simulating both biocolloids such as microorganisms and cells, and particles with adsorbed polyelectrolyte or membrane layer. Our model describes successfully the experimental data in the literature. The presence of gel has the effect of reducing the particle mobility and alleviating double-layer polarization so that the particle behavior is less complicated than that in the case where gel is absent. On the other hand, both the quantitative and qualitative behaviors of a particle depend highly on solution pH and background salt concentration, yielding interesting and significant results. These results provide valuable information for both experimental data interpretation and electrophoresis devices design.

Capillary osmosis in a charged nanopore connecting two large reservoirs.

Experimental evidence revealed that the performance of nanopore-based biosensing devices can be improved by applying a salt concentration gradient. To provide a theoretical explanation for this observation and explore the mechanisms involved, we model the capillary osmosis (or diffusioosmosis) in a charged solid-state nanopore connecting two large reservoirs. The effects of nanopore geometry and the reservoir salt concentrations are examined. We show that the capillary osmotic flow is from the high salt concentration reservoir to the low salt concentration one, and its magnitude has a maximum as the reservoir salt concentrations vary. In general, the shorter the nanopore and/or the smaller its radius, the faster the osmotic flow. This flow enhances the current recognition, and the ion concentration polarization across nanopore openings raises the entity capture rate, thereby being capable of improving the performance of electrophoresis-based biosensors. The results gathered provide necessary information for designing nanopore-based biosensor devices.

Electrophoresis of deformable polyelectrolytes in a nanofluidic channel.

The influence of the shape of a polyelectrolyte (PE) on its electrophoretic behavior in a nanofluidic channel is investigated by considering the translocation of a deformable ellipsoidal PE along the axis of a cylindrical nanochannel. A continuum model comprising a Poisson equation for the electric potential, Nernst-Planck equations for the ionic concentrations, and modified Stokes equations for the flow field is adopted. The effects of the PE shape, boundary, bulk ionic concentration, counterion condensation, electroosmotic retardation flow, and electroosmotic flow (EOF) on the PE mobility are discussed. Several interesting behaviors are observed. For example, if the nanochannel is uncharged and the double layer is thick, then the PE mobility increases (decreases) with increasing double-layer thickness for a smaller (larger) boundary, which has not been reported previously. If the nanochannel is negatively charged and the double layer is thick, then a negatively charged PE moves in the direction of the applied electric field. The results gathered provide necessary information for both the interpretation of experimental data and the design of nanochannel-based sensing devices.

Electrophoresis of a pH-regulated zwitterionic nanoparticle in a pH-regulated zwitterionic capillary.

We consider the electrophoresis of a rigid sphere along the axis of a narrow cylindrical capillary; both are pH-regulated and zwitterionic. This extends available analyses in the literature to a more general and realistic case. Adopting a titanium oxide (TiO2) particle in a silicon dioxide (SiO2) capillary as an example, we examine the capillary radius, the solution pH, and the electrolyte concentration (or double-layer thickness) for their influences on the electrophoretic behavior of a particle. Because the pH solution is adjusted by HCl and NaOH, the presence of four kinds of ionic species, namely, H(+), OH(-), Na(+), and Cl(-), should be considered if NaCl is the background electrolyte. This also extends conventional electrophoresis analyses to the case of multiple ionic species. The interactions of the electroosmotic flow, the properties of the particle and the solution, and the capillary wall yield complicated electrophoretic behavior that can be regulated by the solution pH and the background electrolyte concentration. The results gathered are necessary for the future design of nanopore-based electrophoresis devices.

Electrophoresis of a soft sphere in a necked cylindrical nanopore.

The influence of boundary shape on electrophoresis is modeled by considering a soft spherical particle comprising a positively charged rigid core and an uncharged membrane layer on the axis of a necked cylindrical pore with its throat positively charged. The presence of the throat makes the associated flow and electric fields nonuniform, yielding several interesting behaviors. In general, the reduction in the cross-section area of the pore intensifies the local electric field and, therefore, accelerates the particle. It also makes the ionic distribution nonuniform, and the electric field induced accelerates the particle. The maximum mobility occurs at the center of a throat, and the higher the charge density of the throat the larger the ratio of maximum mobility/mobility far away from the throat. This result is informative for the design of separation devices having variable cross sectional area.

Importance of temperature on the diffusiophoretic behavior of a charge-regulated zwitterionic particle.

Previous theoretical diffusiophoresis analyses were usually based on a fixed temperature, and its influence on the diffusiophoresis behavior of a particle was seldom discussed. Because both the physicochemical properties of the liquid phase and the charged conditions of a particle can be influenced appreciably by the temperature, so is diffusiophoresis behavior. This effect is taken into account in the present study for the first time, along with the possible presence of multiple ionic species in the liquid phase, a factor of practical significance if reactions occur on the particle surface and/or the solution pH is adjusted. Taking an aqueous dispersion of SiO2 particles as an example, a thorough numerical simulation is conducted to examine the behavior of a charge-regulated, zwitterionic particle subject to an applied salt concentration gradient under various conditions. Considering the potential applications of diffusiophoresis, the results gathered provide necessary information for the design of diffusiophoresis devices, and empirical relationships that correlate the scaled particle mobility with key parameters are developed for that purpose.

Diffusiophoresis of a polyelectrolyte in a salt concentration gradient.

The diffusiophoresis of a polyelectrolyte subject to an applied salt concentration gradient is modeled theoretically. The entirely porous type of particle is capable of simulating entities such as DNA, protein, and synthetic polymeric particles. The dependence of the diffusiophoretic behavior of the polyelectrolyte on its physical properties, and the types of ionic species and their bulk concentrations are discussed in detail. We show that in addition to the effects coming from the polarization of double layer and the difference in the ionic diffusivities, the polarization of the condensed counterions inside the polyelectrolyte might also be significant. The last effect, which has not been reported previously, reduces both the electric force and the hydrodynamic force acting on the polyelectrolyte. Both the direction and the magnitude of the diffusiophoretic velocity of the polyelectrolyte are found to highly depend upon its physical properties. These results provide valuable references for applications such as DNA sequencing and catalytic nano- or micromotors.

Importance of temperature effect on the electrophoretic behavior of charge-regulated particles.

The Joule heating effect is inevitable in electrophoresis operations. To assess its influence on the performance of electrophoresis, we consider the case of a charge-regulated particle in a solution containing multiple ionic species at temperatures ranging from 298 to 308 K. Using an aqueous SiO(2) dispersion as an example, we show that an increase in the temperature leads to a decrease in both the dielectric constant and the viscosity of the liquid phase, and an increase in both the diffusivity of ions and the particle surface potential. For a particle having a constant surface potential, its electrophoretic mobility is most influenced by the variation in the liquid viscosity as the temperature varies, but for a charged-regulated particle both the liquid viscosity and the surface potential can play an important role. Depending upon the level of pH, the degree of increase in the mobility can be on the order of 40% for a 5 K increase in the temperature. The presence of double-layer polarization, which is significant when the surface potential is sufficiently high, has the effect of inhibiting that increase in the mobility. This implies that the influence of the temperature on the mobility of the particle is most significant when the pH is close to the point of zero charge.

Electrophoresis of a particle at an arbitrary surface potential and double layer thickness: importance of nonuniformly charged conditions.

Recent advances in material science and technology yield not only various kinds of nano- and sub-micro-scaled particles but also particles of various charged conditions such as Janus particles. The characterization of these particles can be challenging because conventional electrophoresis theory is usually based on drastic assumptions that are unable to realistically describe the actual situation. In this study, the influence of the nonuniform charged conditions on the surface of a particle at an arbitrary level of surface potential and double layer thickness on its electrophoretic behavior is investigated for the first time in the literature taking account of the effect of double-layer polarization. Several important results are observed. For instance, for the same averaged surface potential, the mobility of a nonuniformly charged particle is generally smaller than that of a uniformly charged particle, and the difference between the two depends upon the thickness of double layer. This implies that using the conventional electrophoresis theory may result in appreciable deviation, which can be on the order of ca. 20%. In addition, the nonuniform surface charge can yield double vortex in the vicinity of a particle by breaking the symmetric of the flow field, which has potential applications in mixing and/or regulating the medium confined in a submicrometer-sized space, where conventional mixing devices are inapplicable.

Influence of membrane layer properties on the electrophoretic behavior of a soft particle.

The influence of the physical properties of the membrane layer of a soft particle, which comprises a rigid core and a porous membrane layer, on its electrophoretic behavior, is investigated. Because that influence was almost always neglected in the previous studies, the corresponding results can be unrealistic. The applicability of the model proposed is verified by the available theoretical and experimental results. The electrophoretic mobility of the particle under various conditions is simulated through varying the dielectric constant, the thickness, and the drag coefficient of the membrane layer, and the bulk ionic concentration. We show that under typical conditions, the deviation in the electrophoretic mobility arising from assuming that the dielectric constant of the membrane layer is the same as that of the bulk liquid phase can be in the order of 50%. In addition, the thicker the membrane layer and/or the higher the bulk ionic concentration, the larger the deviation. If the surface of the core of the particle is charged, as in the case of inorganic particles covered by an artificial membrane layer, the deviation at constant core surface potential is larger than that under other types of charged conditions. However, if the surface of the core is uncharged, as in the case of biocolloids, then that deviation becomes negligible. These findings are of fundamental significance to theoreticians in their analysis on the electrokinetic behaviors of soft particles, and to experimentalists in the interpretation of their data.

Diffusiophoresis of a nonuniformly charged sphere in an electrolyte solution.

The diffusiophoresis of a rigid, nonuniformly charged spherical particle in an electrolyte solution is analyzed theoretically focusing on the influences of the thickness of double layer, the surface charge distribution, the effect of electrophoresis, and the effect of double-layer polarization. We show that the nonuniform charge distribution on the particle surface yields complicated effect of double-layer polarization, leading to interesting diffusiophoretic behaviors. For example, if the sign of the middle part of the particle is different from that of its left- and right-hand parts, then depending upon the charge density and the fraction of the middle part, the particle can move either to the high-concentration side or to the low-concentration side. Both the diffusiophoretic velocity and its direction can be manipulated by the distribution of the surface charge density. In particular, if the electrophoresis effect is significant, then those properties are governed by the averaged surface charge density of the particle. A dipolelike particle, where its left- (right-) hand half is negatively (positively) charged, always migrates toward the low-concentration (left-hand) side, that is, it has a negative diffusiophoretic velocity. In addition, that diffusiophoretic velocity has a negative local minimum as the thickness of double layer varies.

Diffusiophoresis of a soft sphere normal to two parallel disks.

The diffusiophoresis of a soft spherical particle normal to two parallel disks subject to an applied ionic concentration gradient is modeled theoretically. The soft particle, which comprises a rigid core and a porous membrane layer, is capable of simulating a wide class of particles such as biocolloids and particles covered by an artificial membrane layer; a rigid particle can also be recovered as the limiting case where the membrane layer is infinitely thin. The problem considered simulates, for example, the chemotaxis of cells or microorganisms. We show that the presence of the membrane layer is capable of yielding complicated diffusiophoretic behavior when the sign of the charge carried by that layer is different from that on the surface of the rigid core of the particle. Both the sign and the magnitude of the diffusiophoretic velocity of a particle can be adjusted through varying the friction coefficient of its membrane layer. These results are of practical significance, for example, in the case where diffusiophoresis is adopted as a separation operation or as a tool to carry and/or control the rate of drug release.