Electrokinetic transport of nanoparticles in functional group modified nanopores

Nanopore detection is a hot issue in current research. One of the challenges is how to slow down the transport velocity of nanoparticles in nanopores. In this paper, we propose a functional group modified nanopore. That means a polyelectrolyte brush layer is grafted on the surface of the nanopore to change the surface charge properties. The existing studies generally set the charge density of the brush layer to a fixed value. On the contrary, in this paper, we consider an essential property of the brush layer: the volume charge density is adjustable with pH. Thus, the charge property of the brush layer will change with the local H⁺ concentration. Based on this, we established a mathematical model to study the transport of nanoparticles in polyelectrolyte brush layer modified nanopores. We found that pH can effectively adjust the charge density and even the polarity of the brush layer. A larger pH can reduce the transport velocity of nanoparticles and improve the blockade degree of ion current. The grafting density does not change the polarity of the brush charge. The larger the grafting density, the greater the charge density of the brush layer, and the blockade degree of ion current is also more obvious. The polyelectrolyte brush layer modified nanopores in this paper can effectively reduce the nanoparticle transport velocity and retain the essential ion current characteristics, such as ion current blockade and enhancement.     

Electrokinetic transport through nanochannels

This article presents a numerical study of the electrokinetic transport phenomena (electroosmosis and electrophoresis) in a three-dimensional nanochannel with a circular cross-section. Due to the nanometer dimensions, the Boltzmann distribution of the ions is not valid in the nanochannels. Therefore, the conventional theories of electrokinetic flow through the microchannels such as Poisson-Boltzmann equation and Helmholtz-Smoluchowski slip velocity approach are no longer applicable. In the current study, a set of coupled partial differential equations including Poisson-Nernst-Plank equation, Navier-Stokes, and continuity equations is solved to find the electric potential field, ionic concentration field, and the velocity field in the three-dimensional nanochannel. The effects of surface electric charge and the radius of nanochannel on the electric potential, liquid flow, and ionic transport are investigated. Unlike the microchannels, the electric potential field, ionic concentration field, and velocity field are strongly size-dependent in nanochannels. The electric potential gradient along the nanochannel also depends on the surface electric charge of the nanochannel. More counter ions than the coions are transported through the nanochannel. The ionic concentration enrichment at the entrance and the exit of the nanochannel is completely evident from the simulation results. The study also shows that the flow velocity in the nanochannel is higher when the surface electric charge is stronger or the radius of the nanochannel is larger.     

Size-selective molecular transport through silica colloidal nanopores

Diffusion rate of dye-labelled PAMAM dendrimers through free-standing silica colloidal crystals was studied as a function of the dendrimer generation and nanopore size to determine the transport selectivity.     

Control of ionic transport through gated single conical nanopores

Control of ionic transport through nanoporous systems is a topic of scientific interest for the ability to create new devices that are applicable for ions and molecules in water solutions. We show the preparation of an ionic transistor based on single conical nanopores in polymer films with an insulated gold thin film “gate.” By changing the electric potential applied to the “gate,” the current through the device can be changed from the rectifying behavior of a typical conical nanopore to the almost linear behavior seen in cylindrical nanopores. The mechanism for this change in transport behavior is thought to be the enhancement of concentration polarization induced by the gate. Figure   Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Membrane-Potential-induced electroporation as a physical mechanism for metal nanoparticle penetration through a cell membrane

A mechanism of the penetration of nanosized metal particles from an ambient solution into the cytoplasm of a living cell, has been proposed. The driving force of this new mechanism is membrane potential, i.e., the potential difference between the cellular cytoplasm and the ambient solution. The essence of the mechanism consists in the fact that a metal particle occurring at a cell membrane shunts the potential drop in the diffuse part of the electrical double layer of the membrane. As a result, almost the entire membrane potential, which, at a normal state of the cell, is distributed between its electrical double layer and the lipid bilayer of the cell membrane, appears to be completely applied to the latter. As a consequence, the field strength in the lipid bilayer rises, thereby increasing the probability of the formation of a pore in it, through which a metal particle with a diameter lying in a certain range (in the case under consideration, from two to three tens of nanometers) can penetrate into the cytoplasm without inflicting any damage on the cell.     

A model for methanol transport through Nafion membrane in diffusion cell

The transport of methanol through Nafion^® membrane in diffusion cell is investigated using the open circuit potential method at different initial methanol concentration solutions. A simple mathematical model based on quasi-steady-state diffusion for the transport of methanol across the membrane in a diffusion cell is developed to simulate the experimental data in order to measure the methanol permeability. The influence of the diffusion cell parameters and thickness of the membrane on the methanol permeability measurement has been evaluated and analyzed. By means of Maclaurin expansion technique, this model can be used to predict the deviation of methanol permeability determined by steady-state diffusion model.     

Water transport coefficient distribution through the membrane in a polymer electrolyte fuel cell

The net water transport coefficient through the membrane, defined as the ratio of the net water flux from the anode to cathode to the protonic flux, is used as a quantitative measure of water management in a polymer electrolyte fuel cell (PEFC). In this paper we report on experimental measurements of the net water transport coefficient distribution for the first time. This is accomplished by making simultaneous current and species distribution measurements along the flow channel of an instrumented PEFC via a multi-channel potentiostat and two micro gas chromatographs. The net water transport coefficient profile along the flow channels is then determined by a control-volume analysis under various anode and cathode inlet relative humidity (RH) at 80 °C and 2 atm. It is found that the local current density is dominated by the membrane hydration and that the gas RH has a large effect on water transport through the membrane. Very small or negative water transport coefficients are obtained, indicating strong water back diffusion through the 30 μm Gore-Select^® membrane used in this study.     

Effects of radially dependent parameters on proton transport in polymer electrolyte membrane nanopores

A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and water in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst-Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is located inside the pore, a few Angstroms from the pore wall. To solve the system numerically, the steady-state solution for the transport of protons and water is considered to be a perturbation around the equilibrium solution. Our results indicate that a radial variation of relative permittivity has the greatest influence on pore conductivity, reducing it by about 50% when compared to that of constant permittivity. On the other hand, viscosity plays the dominant role when the effective water drag within such pores is considered. We conclude that a continuum approach, including constant viscosity, is applicable in nanoscale models provided that the location of the no-slip surface is properly specified and the radial variation of the relative permittivity is taken into consideration.     

Electrokinetic translocation of a deformable nanoparticle controlled by field effect in nanopores

Nanopores have become a popular single-molecule manipulation and detection technology. In this paper, we have constructed a continuum model of the nanopore; the arbitrary Lagrangian-Eulerian (ALE) method is used to describe the motion of particles and fluid. The mathematical model couples the stress-strain equation for the dynamics of a deformable particle, the Poisson equation for the electric field, the Navier-Stokes equations for the flow field, and the Nernst-Planck equations for ionic transport. Based on the model, the mechanism of field-effect regulation of particles passing through a nanopore is investigated. The results show that the transport of particles which is controlled by the field effect depends on the electroosmotic flow (EOF) generated by the gate electrode in the nanopore and the electrostatic interaction between the nanopore and particles. That also explains the asymmetry of particle transport velocity in the nanopore with a gate electrode. When the gate potential is negative, or the gate electrode length is small, the maximum deformation of the particles is increased. The field-effect regulation in the nanopore provides an active and compatible method for nanopore detection, and provides a convenient method for the active control of the particle deformation in the nanopore.     

Temperature dependence of fluid transport in nanopores

Understanding the temperature-dependent nanofluidic transport behavior is critical for developing thermomechanical nanodevices. By using non-equilibrium molecular dynamics simulations, the thermally responsive transport resistance of liquids in model carbon nanotubes is explored as a function of the nanopore size, the transport rate, and the liquid properties. Both the effective shear stress and the nominal viscosity decrease with the increase of temperature, and the temperature effect is coupled with other non-thermal factors. The molecular-level mechanisms are revealed through the study of the radial density profile and hydrogen bonding of confined liquid molecules. The findings are verified qualitatively with an experiment on nanoporous carbon.     

Quantitative imaging of ion transport through single nanopores by high-resolution scanning electrochemical microscopy

Here we report on the unprecedentedly high resolution imaging of ion transport through single nanopores by scanning electrochemical microscopy (SECM). The quantitative SECM image of single nanopores allows for the determination of their structural properties, including their density, shape, and size, which are essential for understanding the permeability of the entire nanoporous membrane. Nanoscale spatial resolution was achieved by scanning a 17 nm radius pipet tip at a distance as low as 1.3 nm from a highly porous nanocrystalline silicon membrane in order to obtain the peak current response controlled by the nanopore-mediated diffusional transport of tetrabutylammonium ions to the nanopipet-supported liquid-liquid interface. A 280 nm × 500 nm image resolved 13 nanopores, which corresponds to a high density of 93 nanopores/μm(2). A finite element simulation of the SECM image was performed to assess quantitatively the spatial resolution limited by the tip diameter in resolving two adjacent pores and to determine the actual size of a nanopore, which was approximated as an elliptical cylinder with a depth of 30 nm and major and minor axes of 53 and 41 nm, respectively. These structural parameters were consistent with those determined by transmission electron microscopy, thereby confirming the reliability of quantitative SECM imaging at the nanoscale level.     

Electrokinetic DNA transport in 20 nm-high nanoslits: evidence for movement through a wall-adsorbed

The electrokinetic transport behavior of λ-DNA (48 kbp) in 20 nm-high fused-silica nanoslits in the presence of short-chain PVP is investigated. Mobility and video data show a number of phenomena that are typical of DNA transport through gels or polymer solutions, thus indicative of rigid migration obstacles in the DNA pathway. Calculations show that a several nanometer thin layer of wall-adsorbed PVP ('nano-gel') can provide such a rigid obstacle matrix to the DNA. Such ultrathin wall-adsorbed polymer layers represent a new type of matrix for electrokinetic DNA separation.     

Interfacial transport of evaporating water confined in nanopores

A semianalytical, continuum analysis of evaporation of water confined in a cylindrical nanopore is presented, wherein the combined effect of electrostatic interaction and van der Waals forces is taken into account. The equations governing fluid flow and heat transfer between liquid and vapor phases are partially integrated analytically, to yield a set of ordinary differential equations, which are solved numerically to determine the flow characteristics and effect on the resulting shape and rate of evaporation from the liquid-vapor interface. The analysis identifies three important parameters that significantly affect the overall performance of the system, namely, the capillary radius, pore-wall temperature, and the degree of saturation of vapor phase. The extension of meniscus is found to be prominent for smaller nanoscale capillaries, in turn yielding a greater net rate of evaporation per unit pore area. The effects of temperature and ambient vapor pressure on net rate of evaporation are shown to be analogous. An increase in pore-wall temperature, which enhances saturation pressure, or a decrease in the ambient vapor pressure result in enhancing the net potential for evaporation and increasing the curvature of the interface.     

Electrokinetic transport and separations in fluidic nanochannels

This article presents a summary of theory, experimental studies, and results for the electrokinetic transport in small fluidic nanochannels. The main focus is on the effect of the electric double layer on the EOF, electric current, and electrophoresis of charged analytes. The double layer thickness can be of the same order as the width of the nanochannels, which has an impact on the transport by shaping the fluid velocity profile, local distributions of the electrolytes, and charged analytes. Our theoretical consideration is limited to continuum analysis where the equations of classical hydrodynamics and electrodynamics still apply. We show that small channels may lead to qualitatively new effects like selective ionic transport based on charge number as well as different modes for molecular separation. These new possibilities together with the rapid development of nanofabrication capabilities lead to an extensive experimental effort to utilize nanochannels for a variety of applications, which are also discussed and analyzed in this review.     

Electrokinetic characterization of a microporous non-commercial polysulfone membrane: phenomenological coefficients and transport parameters

Electrical and electrokinetic phenomena (electrical resistance, streaming potential and membrane potential) in a porous polysulfone membrane was studied in the framework of the linear thermodynamics of irreversible processes and the phenomenological coefficients were determined for different concentrations of NaCl and MgCl₂ solutions (10⁻³M<5×10⁻²M). From experimental values, other characteristic membrane parameters such as the concentration of fixed charge in the membrane (=−3×10⁻³M), the ionic transport numbers and permeabilities through the membrane (t(Na⁺)=0.392 and t(Mg⁺²)=0.363; P(Na⁺)=3.5×l0⁻⁸m/sec and P(Mg⁺²)=2.9×10⁻⁸m/sec) were also obtained. Membrane surface-electrolyte solution interface was characterized by zeta potential values. The effect of both salt concentration and pH on zeta potential results was also studied.     

Total mass transport through a nonhomogeneous membrane

A recent analysis of total mass transport through a homogeneous membrane is generalized to the case of membrane nonuniformity as well as the presence of irreversible, firstorder degradation or hydrolysis. The results show that for initial conditions where none of the transported mass is present in the membrane, the total mass transported is just the ratio of the time integral of the mass concentration on the donor side of the membrane to the effective steady-state resistance of the membrane. Four specific cases are considered which can be applied to the transport analysis of biological membranes such as the skin and the cornea.     

Molecular transport in nanopores: a theoretical perspective

Molecular transport in nanopores plays a central role in many emerging nanotechnologies for gas separation and storage, as well as in nanofluidics. Theories of the transport provide an understanding of the mechanisms that influence the transport and their interplay, and can lead to tractable models that can be used to advance these nanotechnologies through process analysis and optimisation. We review some of the most influential theories of fluid transport in small pores and confined spaces. Starting from the century old Knudsen formulation, the dusty gas model and several other related approaches that share a common point of departure in the Maxwell-Stefan diffusion equations are discussed. In particular, the conceptual basis of the models and the validity of the assumptions and simplifications necessary to obtain their final results are analysed. It is shown that the effect of adsorption is frequently either neglected, or treated on an ad hoc basis, such as through the division of the pore flux into gas-phase and surface diffusion contributions. Furthermore, while it is commonplace to assume that cross-sectional pressure is uniform, it is demonstrated that this violates the Gibbs-Duhem relation and that it is the chemical potential that essentially remains constant in the cross-section, as near-equilibrium density profiles are preserved even during transport. The Dusty Gas model and Maxwell-Stefan model for surface diffusion are analysed, and their strengths and weaknesses discussed, illustrating the use of conflicting choices of frames of reference in the former case, and the importance of assigning appropriate values for the binary diffusivity in the latter case. The oscillator model, developed in this laboratory, which is exact in the low density limit under diffuse reflection conditions, is shown to represent an advance on the classical Knudsen formula, although the latter frequently appears as a fundamental part of many transport models. The distributed friction model, also developed in this laboratory for the study of multi-component transport at any Knudsen number is discussed and compared with previous approaches. Finally, the outlook for theory and future research needs are discussed.     

Ion transport through track etched polypropylene membrane

The transport properties through track etched polypropylene (PP) of 25 μm have been examined. The asymmetric pores in PP have been prepared by track etching technique. The PP membrane was exposed by α-source (₉₅Am²⁴¹). Irradiated PP membrane placed into an electrolyte cell and etched from one side while stopping medium protected other side. The etching is controlled by monitoring the electric current and to be stopped shortly after the breakthrough, which, is observed as a sudden increase in current, indicating that the two chambers of cell are connected through the pores. Asymmetric etching condition allows the preparation of charged pores of conical shape. The resulting conical pores rectify ion current. The voltage current characteristics is strongly non-linear, comparable to that of an electrical diode.     

Electrokinetic transport of aqueous solutions of electrolytes through fibrous systems. Non-linear phenomenological relations

An experimental investigation on streaming potentials of porous plugs of cellulose and glass fibre in the non-linear range is described. The variation of the second order electrokinetic coefficients, L₂₁₁ and L₂₂₁, as a function of fibre concentration in the porous pad has been studied. The electroviscous effect accounts for the decrease of these coefficients as packing density increases. The dependence of L₂₁₁ and L₂₂₁ on the concentration of the various electrolytes used is somewhat similar to that of the first order coefficients L₂₁ and L₂₂ (s), respectively. The explanation for this effect might be found in the influence exerted by the hydrodynamic conditions prevailing in the capillaries on the structure of the electric double layer and on the surface conductance.     

Electrokinetic transport of red blood cells in microcapillaries

Electrokinetic flow of a suspension of erythrocytes (red blood cells, RBCs) in 20 num cylindrical fused-silica capillaries is examined in the present work. Flow direction anomalies are observed experimentally and tentatively explained by the development of a pH gradient between the cathode well and the anode well due to electrolysis reactions at the electrodes. This pH gradient alters the local zeta potentials of both the capillary and the RBC and thus the local electroendosmotic liquid flow (EOF) velocities and RBC electrophoretic (EP) velocities. The two velocities are opposite in direction but with EOF dominating such that the RBC moves toward the cathode, opposite to the anode migration observed in bulk conditions. The opposing zeta potentials also lead to RBC aggregation at the anode end for low fields less than 25 V/cm. As the electroendosmotic velocity decreases at the anode end due to decreasing pH, pressure-driven back flow develops to oppose the original EOF at the remaining portions of the capillary ensuring constant fluid flux. When the anode EOF velocity is smaller in magnitude than the EP velocity, reversal of blood cell transport is observed after a short transient time in which a pH gradient forms. RBC velocities and pH dependencies on electric field and MgCl(2) concentration are presented along with data showing the accumulation of charge separation across the capillary. Also, a short-term solution to the pH gradient formation is presented that could help thwart development of pH gradients in micro-devices at lower voltages.