Direct numerical simulation of electrokinetic translocation of a cylindrical particle through a nanopore using a Poisson-Boltzmann approach

Nanopore-based sensing of single molecules is based on a detectable change in the ionic current arising from the electrokinetic translocation of individual nanoparticles through a nanopore. In this study, we propose a continuum-based model to investigate the dynamic electrokinetic translocation of a cylindrical nanoparticle through a nanopore and the corresponding ionic current response. It is the first time to simultaneously solve the Poisson-Boltzmann equation for the ionic concentrations and the electric field contributed by the surface charges of the nanopore and the nanoparticle, the Laplace equation for the externally applied electric field, and the modified Stokes equations for the flow field using an arbitrary Lagrangian-Eulerian method. Current blockade due to the particle translocation is predicted when the electric double layers (EDLs) of the particle and the nanopore are not overlapped, which is in qualitative agreement with existing experimental observations. Effects due to the electric field intensity imposed, the EDL thickness, the nanopore's surface charge, the particle's initial orientation and lateral offset from the nanopore's centerline on the particle translocation including both translation and rotation, and the ionic current response are comprehensively investigated. Under a relatively low electric field imposed, the particle experiences a significant rotation and a lateral movement. However, the particle is aligned with its longest axis parallel to the local electric field very quickly due to the dielectrophoretic effect when the external electric field is relatively high.     

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.     

Electrokinetic particle translocation through a nanopore

Nanoparticle electrophoretic translocation through a single nanopore induces a detectable change in the ionic current, which enables the nanopore-based sensing for various bio-analytical applications. In this study, a transient continuum-based model is developed for the first time to investigate the electrokinetic particle translocation through a nanopore by solving the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential and the Navier-Stokes equations for the flow field using an arbitrary Lagrangian-Eulerian (ALE) method. When the applied electric field is relatively low, a current blockade is expected. In addition, the particle could be trapped at the entrance of the nanopore when the electrical double layer (EDL) adjacent to the charged particle is relatively thick. When the electric field imposed is relatively high, the particle can always pass through the nanopore by electrophoresis. However, a current enhancement is predicted if the EDL of the particle is relatively thick. The obtained numerical results qualitatively agree with the existing experimental results. It is also found that the initial orientation of the particle could significantly affect the particle translocation and the ionic current through a nanopore. Furthermore, a relatively high electric field tends to align the particle with its longest axis parallel to the local electric field. However, the particle's initial lateral offset from the centerline of the nanopore acts as a minor effect.     

On ion transport regulation with field-effect nonlinear electroosmosis control in microfluidics embedding an ion-selective medium

We study herein numerically the use of induced-charge electrokinetic phenomena to enable a flexible control of ion transport of dilute electrolyte in a straight ion concentration polarization system. The effect of three convection modes of induced-charge electrokinetic phenomena, including induced-charge electroosmosis, flow-field effect transistor, and alternating-current electroosmosis (ACEO), on convective arrestment of diffusive wave-front propagation is investigated by developing a cross-scale and fully coupled transient numerical simulation model, wherein multiple frequency electrochemical polarization and nonlinear diffuse charge dynamics in spatiotemporally varying solution conductivity are taken into account. We demonstrate by detailed comparative simulation studies that ACEO vortex flow field above a metal strip array arranged along the anodic chamber's bottom surface serves as the most efficient way for adjusting the salt density distribution at micrometer and even millimeter dimension, due to its high flexibility in controlling the stirring flow state with the introduction of two extra electrical parameters. The specific operating status is determined by whether the electrode array is floating in potential (induced-charge electroosmosis) or biased to ground (flow-field effect transistor) or forced to oscillate at another Fourier mode (ACEO). These results prove useful for on-chip electric current control with electroconvective stirring.     

Diffusiophoresis of an Elongated Cylindrical Nanoparticle along the Axis of a Nanopore

The translation of a charged, elongated cylindrical nanoparticle along the axis of a nanopore driven by an imposed axial salt concentration gradient is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the modified Stokes equations for the hydrodynamic field. The diffusiophoretic motion is driven by the induced electrophoresis and chemiphoresis. The former is driven by the generated overall electric field arising from the difference in the ionic diffusivities and the double layer polarization, while the latter is generated by the induced osmotic pressure gradient around the charged particle. The induced diffusiophoretic motion is investigated as functions of the imposed salt concentration gradient, the ratio of the particle’s radius to the double layer thickness, the cylinder’s aspect ratio (length/radius), the ratio of the nanopore size to the particle size, the surface charge densities of the nanoparticle and the nanopore, and the type of the salt used. The induced diffusiophoretic motion of a nanorod in an uncharged nanopore is mainly governed by the induced electrophoresis, driven by the induced electric field arising from the double layer polarization. The induced particle motion is driven by the induced electroosmotic flow, if the charges of the nanorod and nanopore wall have the same sign.     

Manipulating particles in microfluidics by floating electrodes

Various particle manipulations including enrichment, movement, trapping, separation, and focusing by floating electrodes attached to the bottom wall of a straight microchannel under an imposed DC electric field have been experimentally demonstrated. In contrast to a dielectric microchannel possessing a nearly uniform surface charge (or ζ potential), the metal strip (floating electrode) is polarized under the imposed electric field, resulting in a nonuniform distribution of the induced surface charge with a zero net surface charge along the floating electrode's surface, and accordingly induced-charge electroosmotic flow near the metal strip. The induced induced-charge electroosmotic flow can be regulated by controlling the strength of the imposed electric field and affects both the hydrodynamic field and the particle's motion. By using a single floating electrode, charged particles could be locally concentrated in a section of the channel or in an end-reservoir and move toward either the anode or the cathode by controlling the strength of the imposed electric field. By using double floating electrodes, negatively charged particles could be concentrated between the floating electrodes, subsequently squeezed to a stream flowing in the center region of the microchannel toward the cathodic reservoir, which can be used to focus particles.     

Electrophoretic motion of a soft spherical particle in a nanopore

Many biocolloids, biological cells and micro-organisms are soft particles, consisted with a rigid inner core covered by an ion-permeable porous membrane layer. The electrophoretic motion of a soft spherical nanoparticle in a nanopore filled with an electrolyte solution has been investigated using a continuum mathematical model. The model includes the Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes and Brinkman equations for the hydrodynamic fields outside and inside the porous membrane layer, respectively. The effects of the “softness” of the nanoparticle on its electrophoretic velocity along the axis of a nanopore are examined with changes in the ratio of the radius of the rigid core to the double layer thickness, the ratio of the thickness of the porous membrane layer to the radius of the rigid core, the friction coefficient of the porous membrane layer, the fixed charge inside the porous membrane layer of the particle and the ratio of the radius of the nanopore to that of the rigid core. The presence of the soft membrane layer significantly affects the particle electrophoretic mobility.     

Numerical investigation of field-effect control on hybrid electrokinetics for continuous and position-tunable nanoparticle concentration in microfluidics

We introduce herein an effective way for continuous delivery and position-switchable trapping of nanoparticles via field-effect control on hybrid electrokinetics (HEK). Flow field-effect transistor exploiting HEK delicately combines horizontal linear electroosmosis and transversal nonlinear electroosmosis of a shiftable flow stagnation line (FSL) on gate terminals under DC-biased AC forcing. The microfluidic nanoparticle concentrator proposed herein makes use of a simple device geometry, in which an individual or a series of planar metal strips serving as gate electrode (GE) are subjected to a hybrid gate voltage signal and arranged in parallel between a pair of 3D driving electrodes. On the application of a DC-biased AC electric field across channel length direction, all the GE are electrochemically polarized, and the action of imposed hybrid electric field on the multiple-frequency bipolar counterions within the composite-induced double layer generates two counter-rotating induced-charge electroosmotic (ICEO) micro-vortices on top of each GE. Symmetry breaking in ICEO flow profile occurs once the gate voltage deviates from natural floating potential of corresponding GE. The gate voltage offset not only results in an additional pump motion of working fluid for enhanced electroosmotic transport but also directly changes the location of FSL where nanoparticles are preferentially collected by field-effect HEK. Our results of field-effect control on HEK are supposed to guide an elaborate design of flexible electrokinetic frameworks embedding coplanar metal strips for a high degree of freedom analyte manipulation in modern micro-total-analytical systems.     

Modeling and simulation of nanoparticle separation through a solid-state nanopore

Recent experimental studies show that electrokinetic phenomena such as electroosmosis and electrophoresis can be used to separate nanoparticles on the basis of their size and charge using nanopore‐based devices. However, the efficient separation through a nanopore depends on a number of factors such as externally applied voltage, size and charge density of particle, size and charge density of membrane pore, and the concentration of bulk electrolyte. To design an efficient nanopore‐based separation platform, a continuum‐based mathematical model is used for fluid. The model is based on Poisson–Nernst–Planck equations along with Navier–Stokes equations for fluid flow and on the Langevin equation for particle translocation. Our numerical study reveals that membrane pore surface charge density is a vital parameter in the separation through a nanopore. In this study, we have simulated high‐density lipoprotein (HDL) and low‐density lipoprotein (LDL) as the sample nanoparticles to demonstrate the capability of such a platform. Numerical results suggest that efficient separation of HDL from LDL in a 0.2 M KCL solution (resembling blood buffer) through a 150 nm pore is possible if the pore surface charge density is ～ ?4.0 mC/m². Moreover, we observe that pore length and diameter are relatively less important in the nanoparticle separation process considered here.     

Efficient nanoparticle focusing utilizing cascade AC electroosmotic flow

This study presents on-chip continuous accumulation and concentration of nanoscale samples using a cascade alternating current electroosmosis (cACEO) flow. ACEO can generate flow motion caused by ion movement due to interactions between the AC electric field and the induced charge layer on the electrode surface, with the potential to accumulate particles, especially in low-conductive liquid. However, the intrinsic particle diffusive motion, which is sensitive to particle size, is an essential element influencing accumulation efficiency. In this study, an electrode combining chevron and double-gap geometry embedded in a microfluidic channel was developed to perform efficient three-dimensional (3D) nanoparticle focusing using ACEO. The chevron electrode pattern was introduced upstream of the focusing zone to overcome particle accumulation in scattering zones near the channel sidewall. To demonstrate the efficiency of the proposed device for particle accumulation, three nanoparticle types were used: latex, metal, and biomaterial. Continuous 3D concentration of 50-nm polystyrene particles was confirmed. The concentration factor, determined based on image processing, became quite high when 50-nm gold nanoparticles were used. Moreover, nanoparticles with a 20-nm diameter were accumulated using cACEO. Finally, we used the concentrator chip to accumulate 50-nm liposome particles, confirming that the device could also successfully concentrate biomaterials.     

The effects of electrostatic correlations on the ionic current rectification in conical nanopores

Ion‐ion electrostatic correlations are recognized to play a significant role in the presence of concentrated multivalent electrolytes. To account for their impact on ionic current rectification phenomenon in conical nanopores, we use the modified continuum Poisson‐Nernst‐Planck (PNP) equations by Bazant et al. Coupled with the Stokes equations, the effects of the EOF are also included. We thoroughly investigate the dependence of the ionic current rectification ratios as a function of the double layer thickness and the electrostatic correlation length. By considering the electrostatic correlations, the modified PNP model successfully captures the ionic current rectification reversal in nanopores filled with lanthanum chloride LaCl₃. This finding qualitatively agrees with the experimental observations that cannot be explained by the standard PNP model, suggesting that ion‐ion electrostatic correlations are responsible for this reversal behavior. The modified PNP model not only can be used to explain the experiments, but also go beyond to provide a design tool for nanopore applications involving multivalent electrolytes.     

Electrophoretic motion of a spherical particle with a symmetric nonuniform surface charge distribution in a nanotube

The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.     

Spatial blockage of ionic current for electrophoretic translocation of DNA through a graphene nanopore

Graphene nanopore has been promising the ultra‐high resolution for DNA sequencing due to the atomic thickness and excellent electronic properties of the graphene monolayer. The dynamical translocation phenomena and/or behaviors underneath the blocked ionic current, however, have not been well unveiled to date for the translocation of DNA electrophoretically through a graphene nanopore. In this report, the assessment on the sensitivity of ionic current to instantaneous statuses of DNA in a 2.4 nm graphene nanopore was carried out based on the all‐atom molecular dynamics simulations. By filtering out the thermal noise of ionic current, the instantaneous conformational variations of DNA in a graphene nanopore have been unveiled from the fluctuations of ionic current, because of the spatial blockage effect of DNA against ionic current. Interestingly, the neighborhood effect of DNA against ionic current was also observed within a distance of 1.5 nm nearby the graphene nanopore, suggesting the further precise control for DNA translocation through a graphene nanopore in gene sequencing. Moreover, the sensitivity of the blocked ionic current toward the instantaneous conformations of DNA in a graphene nanopore demonstrates the great potential of graphene nanopores in the dynamics analysis of single molecules.     

An Ohmic model for electrokinetic flows of binary asymmetric electrolytes

The transport of electrolytes in electric fields is a ubiquitous phenomenon commonly harnessed in microfluidics. A classic leaky dielectric model for flow generated by electric fields accurately predicts electrohydrodynamic transport phenomenon but is valid for millimeter-scale and larger flows and at relatively low ionic strength. Here, we derive and use a modified version of this model to sub-millimeter scales more relevant to microfluidics, where diffusive transport of charged species becomes non-negligible. We formulate a general equation set, the modified Ohmic model, applicable to the transport of binary, asymmetric electrolytes. We leverage this model to describe a variety of microfluidic electrokinetic systems, including DC electroosmosis, alternating current electrokinetics (ACEK) and induced-charge electroosmosis (ICEO), thus highlighting some unifying principles of these flows.     

Mechanism of electrostatic gating at conical glass nanopore electrodes

The mechanism of molecule-based electrostatic gating of redox fluxes at conical glass nanopore (GNP) electrodes has been investigated using finite-element simulations. The results demonstrate that the fluxes of cationic redox molecules through the nanopore orifice can be reduced to negligibly small values when the surface charge of the nanopore is switched from a negative to a positive value. Electrostatic charge reversal can be affected by ionization of surface-bound moieties in response to environmental stimuli (e.g., photoionization or acid protonation), but only if the negative charge of the glass is included in the analysis. Numerical simulations of the responses of GNP electrodes are based on a simultaneous solution of the Poisson and Nernst-Planck equations and are in excellent agreement with our previously reported experimental results for electrostatic gating of the fluxes of Ru(NH 3) 6 (3+) and Fe(bpy) 3 (2+) at GNP electrodes with orifice radii between 15 and 100 nm. The gating mechanism is discussed in terms of three components: (1) migration of ionic redox species in the depletion layer adjacent to the electrode surface; (2) migrational transport along the charged pore walls; (3) electrostatic rejection of charged molecules at the pore orifice. The numerical results indicate that all three components are operative, but that ion migration along the pore walls is dominant.     

基于石英纳米孔道的单颗粒尺寸分布分析

发展了一种基于石英纳米孔道的单颗粒电化学动态分析方法, 用于单个CdSe/ZnS量子点纳米颗粒的尺寸分布分析. 其机制是向石英纳米孔道两端施加电压, 表面带有正电荷的单个CdSe/ZnS量子点纳米颗粒在电场力驱动下由管内向管外运动, 当量子点纳米颗粒穿过纳米孔道尖端狭小的限域空间时, 其表面正电荷使石英纳米孔道内电荷密度增加, 孔道内的电化学限域效应进一步将电荷密度增加的信息放大并转变为可读的离子流增强信号. 通过对动态离子流信号解析可实时获取具有2种不同尺寸的量子点纳米颗粒所导致的2类过孔事件信息, 从而对在限域空间内运动的纳米颗粒进行尺寸分布分析.     

Processive replication of single DNA molecules in a nanopore catalyzed by phi29 DNA polymerase

Coupling nucleic acid processing enzymes to nanoscale pores allows controlled movement of individual DNA or RNA strands that is reported as an ionic current/time series. Hundreds of individual enzyme complexes can be examined in single-file order at high bandwidth and spatial resolution. The bacteriophage phi29 DNA polymerase (phi29 DNAP) is an attractive candidate for this technology, due to its remarkable processivity and high affinity for DNA substrates. Here we show that phi29 DNAP-DNA complexes are stable when captured in an electric field across the α-hemolysin nanopore. DNA substrates were activated for replication at the nanopore orifice by exploiting the 3'-5' exonuclease activity of wild-type phi29 DNAP to excise a 3'-H terminal residue, yielding a primer strand 3'-OH. In the presence of deoxynucleoside triphosphates, DNA synthesis was initiated, allowing real-time detection of numerous sequential nucleotide additions that was limited only by DNA template length. Translocation of phi29 DNAP along DNA substrates was observed in real time at ?ngstrom-scale precision as the template strand was drawn through the nanopore lumen during replication.     

On hybrid electroosmotic kinetics for field‐effect‐reconfigurable nanoparticle trapping in a four‐terminal spiral microelectrode array

Induced‐charge electroosmosis (ICEO) has attracted tremendous popularity for driving fluid motion from the microfluidic community since the last decade, while less attention has been paid to ICEO‐based nanoparticle manipulation. We propose herein a unique concept of hybrid electroosmotic kinetics (HEK) in terms of bi‐phase ICEO (BICEO) actuated in a four‐terminal spiral electrode array, for effective electrokinetic enrichment of fluorescent polystyrene nanoparticles on ideally polarizable metal strips. First, by alternating the applied AC voltage waves between consecutive discrete terminals, the flow stagnation lines where the sample nanoparticles aggregate can be switched in time between two different distribution modes. Second, we innovatively introduce the idea of AC field‐effect flow control on BICEO; by altering the combination of gating voltage sequence, not only the number of circulative particle trapping lines is doubled, but the collecting locations can be flexibly reconfigured as well. Third, hydrodynamic streaming of DC‐biased BICEO is tested in our device design, wherein the global linear electroosmosis dominates BICEO contributed from both AC and DC components, resulting in a reduction of particle enrichment area, while with a sharp increase in sample transport speed inside the bulk phase. The flow field associated with HEK is predicted using a linear asymptotic analysis under Debye–Huckel limit, with the simulation results in qualitative agreement with in‐lab observations of nanoparticle trapping by exploiting a series of improved ICEO techniques. This work provides an affordable and field‐deployable platform for real‐time nanoparticle trapping in the context of dilute electrolyte.     

Investigating the translocation of λ-DNA molecules through PDMS nanopores

We investigate the translocation of λ-DNA molecules through resistive-pulse polydimethylsiloxane (PDMS) nanopore sensors. Single molecules of λ-DNA were detected as a transient current increase due to the effect of DNA charge on ionic current through the pore. DNA translocation was found to deviate from a Poisson process when the interval between translocations was comparable to the duration of translocation events, suggesting that translocation was impeded during the presence of another translocating molecule in the nanopore. Characterization of translocation at different voltage biases revealed that a critical voltage was necessary to drive DNA molecules through the nanopore. Above this critical voltage, frequency of translocation events was directly proportional to DNA concentration and voltage bias, suggesting that transport of DNA from the solution to the nanopore was the rate limiting step. These observations are consistent with experimental results on transport of DNA through nanopores and nanoslits and the theory of hydrodynamically driven polymer flow in pores.     

Analysis of self-electrophoretic motion of a spherical particle in a nanotube: effect of nonuniform surface charge density

Autonomous motions of a spherical nanoparticle in a nanotube filled with an electrolyte solution were investigated using a continuum theory, which consisted of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. Contrary to the usual electrophoresis, in which an external electric field is imposed to direct the motion of charged particles, the autonomous motion originates from the self-generated electric field due to the ionic concentration polarization of the liquid medium surrounding an asymmetrically charged particle. In addition to the particle motion, the interaction between the electric field generated and the free charges of the polarized solution induces electroosmotic flows. These autonomous motions of the fluid as well as the particle were examined with focus on the effects of the surface-charge distribution of the particle, the size of the nanotube, and the thickness of the electric double layer, which affected the direction and the speed of the particle significantly.