Direct measurement of electric double layer in a nanochannel by electrical impedance spectroscopy

The ion distribution and physical behavior induced by applying an electric field to a nano-interfacial space are very important for investigating electric double layers (EDLs) in very confined spaces. We perform direct measurements of an EDL in a nanochannel by electrical impedance spectroscopy to experimentally evaluate the EDL thickness dependence on the ion density and the channel width. To this end, we developed a nanofluidic device consisting of a pair of sensing electrodes with a nanochannel between them. The measurement electrodes are completely embedded in a substrate to generate a uniform electric field and to provide a flat surface that can easily be used to seal the nanochannel. Using this device, we found that the EDL on one electrode expands with decreasing ion concentration and eventually merges with the EDL on the opposite electrode so that the nanochannel becomes completely filled with the EDL. The trend observed for the EDL width agrees well with that predicted by theory for the Debye length. These results provide valuable insight into the physical ionic structure in nanochannels, which will improve impedance-based electrical sensing and electrokinetic applications.     

Electrokinetic energy conversion in micrometer-length nanofluidic channels

In this study, we present a theoretical and numerical investigation of electrokinetic energy conversion in short-length nanofluidic channels, taking into account reservoir resistance and concentration polarization effects. The concentration polarization effect was demonstrated through numerical modeling using the Poisson–Nernst–Planck (PNP) model. In the absence of concentration polarization, the modified Onsager reciprocal relation for the electrokinetic flow through a one-dimensional (1D) nanochannel is derived from both Ohm’s law and Kirchhoff’s current law while considering the reservoir resistance. Based on this modified Onsager reciprocal relation and the Poisson–Boltzmann (PB) model, a theoretical model for electrokinetic energy conversion is proposed to address the importance of the reservoir resistance effect on electrokinetic energy conversion. The applicability of our proposed model is also verified through numerical modeling of the PNP model. The results calculated from our proposed model are shown to be in good agreement with those from the PNP model when the concentration polarization effect does not occur significantly at the reservoirs. The conversion efficiency and generation power are decreased when the channel resistance is not much larger than the reservoir resistance, especially for a shorter-length nanochannel (e.g., a channel several micrometers in length) with a lower electrolyte concentration and a higher surface charge density. After the concentration polarization effect becomes increased as a larger pressure gradient is applied through an ideal ion-selective nanochannel, the conversion efficiency/generation power is further decreased due to the ion depletion at the inlet reservoir, which increases the electrical resistance of the inlet reservoir or the equivalent electrical resistance of the electrokinetic energy conversion system. The onset pressure difference (or gradient) for a significant concentration polarization is identified both theoretically and numerically. In order to avoid decreases in the conversion efficiency/generation power mentioned above, some key factors such as the length of the nanochannel, the position of electrodes at the reservoirs, and the applied pressure gradient were noticed in this study.     

Numerical investigation of micro- and nanochannel deformation due to discontinuous electroosmotic flow

Large pressures can induce detrimental deformation in micro- and nanofluidic channels. Although this has been extensively studied for systems driven by pressure and/or capillary forces, deflection in electrokinetic systems due to internal pressure gradients caused by non-uniform electric fields has not been widely explored. For example, applying an axial electric field in a channel with a step change in conductivity and/or surface charge can lead to internally generated pressures large enough to cause cavitation, debonding, and/or channel collapse. Finite electric double layers within nanofluidic channels can further complicate the physics involved in the deformation process. In order to design devices and experimental procedures that avoid issues resulting from such deformation, it is imperative to be able to predict deformation for given system parameters. In this work, we numerically investigate pressures resulting from a step change in conductivity and/or surface charge in micro- and nanofluidic channels with both thin and thick double layers. We show an explicit relation of pressure dependence on concentration ratio and electric double layer thickness. Furthermore, we develop a numerical model to predict deformation in such systems and use the model to unearth trends in deformation for various electric double layer thicknesses and both glass and PDMS on glass channels. Our work is particularly impactful for the development and design of micro- and nanofluidic-based devices with gradients in surface charge and/or conductivity, fundamental study of electrokinetic-based cavitation, and other systems that exploit non-uniform electric fields.     

Application of continuum mechanics to fluid flow in nanochannels

A fundamental understanding of the transport phenomena in nanofluidic channels is critical for systematic design and precise control of such miniaturized devices towards the integration and automation of Lab-on-a-chip devices. The goal of this study is to develop a theoretical model of electroosmotic flow in nano channels to gain a better understanding of transport phenomena in nanofluidic channels. Instead of using the Boltzmann distribution, the conservation condition of ion number and the Nernst equation are used in this new model to find the ionic concentration field of an electrolyte solution in nano channels. Correct boundary conditions for the potential field at the center of the nanochannel and the concentration field at the wall of the channel are developed and applied to this model. It is found that the traditional plug-like velocity profile is distorted in the center of the channel due to the presence of net charges in this region opposite to that in the electrical double layer region. The developed model predicted a trend similar to that observed in experiments reported in the literature for the area-average velocity versus the ratio of Debye length to the channel height.     

Gated transport in nanofluidic devices

The surface property of the nanochannel plays an important role in controlling the ion transport through the nanochannel. Embedding electrodes outside the nanochannel (referred to as gated nanochannels) is a simple way to control the surface charge density of the nanochannel. Based on the numerical simulations using coupled Poisson–Nernst–Planck and Stokes equations, we show that a relative difference between the applied voltage and the gate voltage would alter the space charge density along the nanochannel. Thus, the gate voltage can tune the nanochannel into a p- or n-type field effect transistor, enabling the control of fluid flow in the nanochannel. The ionic currents reveal that the ionic flux can be controlled by the gate voltage. Analytical expressions are derived to estimate the effective space charge density and the fluid flow in the nanochannels for a fixed gate voltage. We also suggest potential applications of the gated nanochannels.     

Electrokinetic motion of single nanoparticles in single PDMS nanochannels

Electrokinetic motion of single nanoparticles in single nanochannels was studied systematically by image tracking method. A novel method to fabricate PDMS-glass micro/nanochannel chips with single nanochannels was presented. The effects of ionic concentration of the buffer solution, particle-to-channel size ratio and electric field on the electrokinetic velocity of fluorescent nanoparticles were studied. The experimental results show that the apparent velocity of nanoparticles in single nanochannels increases with the ionic concentration when the ionic concentration is low and decreases with the ionic concentration when the concentration is high. The apparent velocity decreases with the particle-to-channel size ratio (a/b). Under the condition of low electric fields, nanoparticles can hardly move in single nanochannels with a large particle-to-channel size ratio. Generally, the apparent velocity increases with the applied electric field linearly. The experimental study presented in this article is valuable for future research and applications of transport and manipulation of nanoparticles in nanofluidic devices, such as separation of charged nanoparticles and DNA molecules.     

Entrance effect on ion transport in nanochannels

We investigate the effect of the surface charge at channel entrances upon ion conductance, which has been overlooked in the study of nanofluidics. Nonlinear ion transport behaviors were observed in 20-nm thick nanochannels having opposite surface charge polarity on the entrance side-walls with respect to that in the nanochannel. The heterogeneous distribution of surface charge at the channel entrance functions as a parasitic diode, which can cause ion current saturation under high voltage biases. Such effect becomes crucial at low bath concentration at which the electric double layers originated from the bath sidewalls pinch off the channel entrance. The experimental results are clarified by theoretical calculations based on 2D Poisson–Nernst–Planck equations. With such strong effect on ionic conductance of nanochannels, the change of surface charge polarity at the entrance sidewalls may find applications in chemical and biological sensing.     

Electrokinetic microslit experiments to analyse the charge formation at solid/liquid interfaces

Electrokinetic effects play an important role in microfluidics and nanofluidics. Although the related phenomena are often utilized to control fluid flow and sample transport in lab-on-a-chip devices, their dependency on the surface charges on the channel walls often remain enigmatic. This is mainly due to the lack of adequate experimental methods to analyse the electrical charging of solid/liquid interfaces of interest. To address this need, an experimental set-up—designated as microslit electrokinetic set-up (MES)—has been recently developed and applied for the investigation of charge formation processes at planar solid/liquid interfaces. The device permits to perform streaming potential and streaming current measurements across a rectangular streaming channel formed by two parallel sample carriers (20×10×3 mm³) at variable distance allowing for the determination of the surface conductivity. Utilizing the MES, charge characteristics can be determined for a wide variety of materials prepared as thin films on top of planar glass substrates. Streaming potential and streaming current data permit to investigate the mechanisms of charge formation while surface conductivity data provide information about mobile charge carriers located in different zones at the interface. The applicability of this advanced experimental approach is demonstrated with examples obtained for surfaces with different levels of complexity:

1. Preferential ion adsorption onto unpolar fluoropolymer (Teflon^® AF) films was characterized in simple electrolyte solutions; the results were quantitatively evaluated with respect to interfacial ion concentrations.
2. Interrelation of charge density and conformation of grafted poly(L-glutamic acid layers) were unravelled from the determination of pH-depended variations of surface conductivity and layer thickness.
3. The impact of spatial confinements of surface functional groups on their acid–base behaviour was studied with self-assembled monomolecular films of alkanethiols chemisorbed on gold.
4. Charging of and ion mobility within poly(acrylic acid) (PAA) brushes prepared by a Langmuir–Blodgett technique were analysed at varied pH and ionic strength.
5. Interfacial modes of adsorbed proteins were distinguished at two polymer surfaces with varied hydrophobicity/charge density.

     

Development of a nanofluidic preconcentrator with precise sample positioning and multi-channel preconcentration

A nanofluidic preconcentrator with the capability of rapidly preconcentrating and precisely positioning protein bands in multiple microchannels has been developed for highly sensitive detection of biomolecules. A novel electrical resistive network model is developed to guide the design of the nanofluidic preconcentrator which consists of a PDMS slab bonded with a glass slide. In the prototype design, two microchannels (23 mm long, 25–50 μm wide, and 5–15 μm deep), one preconcentration microchannel and one ground microchannel are connected in the middle via 16 nanochannels (25–50 μm long, 25 μm wide, and 50–80 nm deep). With two sets of optimal voltage settings applied on the opposite ends of the nanofluidic chip, the ion depletion region and electrokinetic trapping were generated to carry out the preconcentration. With the optimal voltage settings (30–30 V) predicted by the model, the ionic current of the nanochannel in our optimized preconcentrator was adjusted to be greater than the threshold value (3.9 nA) needed for the occurrence of the preconcentration, and a preconcentration factor >10⁵ was achieved in 5 min. The sample positioning capability of the preconcentrator was demonstrated by adjusting the applied voltages and moving the preconcentrated protein bands to multiple sites by a distance from several micrometers to several millimeters in the preconcentration channel. The multi-channel preconcentration capability was also demonstrated by preconcentrating two protein bands in two separate microchannels. In this work, the resistive network model was developed and validated to optimize nanofluidic preconcentrators for rapid, high throughput and highly sensitive sensing of low abundance analytes.     

Electrokinetics in nanochannels grafted with poly-zwitterionic brushes

In this paper, we compute the electrokinetic transport in soft nanochannels grafted with poly-zwitterionic (PZI) brushes. The transport is induced by an external pressure gradient, which drives the ionic cloud (in the form of an electric double layer or EDL) at the brush surfaces to induce an electric field that drives an induced electroosmotic transport. We characterize the overall transport by quantifying this electric field, overall flow velocity, and the energy conversion associated with the development of the electric field and a streaming current. We specially focus on how the ability of the PZI to ionize and demonstrate a significant charge at both large and small pH can be efficiently maneuvered to develop a liquid transport, an electric field, and an electrokinetically induced power across a wide range of pH values.     

Theoretical investigation of enzymatic hydrolysis of polypeptides in nanofluidic channels

Label-free detection of enzymes using nanofluidic channels requires enzymes to diffuse into a nanochannel and react with substrates already immobilized on the nanochannel surfaces. A theoretical model is necessary to predict the reaction progress in the confined space and translate it to the electrical readouts of the nanochannel. In this paper, enzymatic hydrolysis of polypeptides in nanofluidic channels is considered and a 1-D model is developed that accounts for various reaction kinetics, enzyme diffusion and non-specific adsorption. The polypeptides have multiple cleavage sites which can be cleaved in different orders depending on the type of enzyme. Here it is shown that this process creates two types of reaction fronts inside the nanochannel which advance linearly with time once they are fully developed. Such constant reaction rates can be predicted by an analytical model. The numerical simulations are validated against the experimental results of trypsin–polylysine reaction in nanochannels, and a good agreement between the two is observed. This study deepens our understandings of enzymatic reactions in nanoscale-confined spaces and can guide the development of a fast-response, label-free enzyme sensor based on nanochannels.     

Simple and cost-effective fabrication of two-dimensional plastic nanochannels from silica nanowire templates

Nanofluidic systems are attracting a great deal of interest due to their fundamental significance and potential applications in chemistry, biology and physics. However, high fabrication cost, expensive equipments and complicated fabrication process of most current fabrication techniques prevent lots of researchers from entering the nanofluidic field. Here we present a quick, simple and cost-effective method for fabricating two-dimensional (2D) nanochannel in polycarbonate (PC) substrates. Silica nanowires, taper-drawn from commercially available single-mode fiber were used as templates and embedded in the PC substrate by hot embossing. The nanochannels were created after removing the nanowires by hydrofluoric acid (HF) etching. Poly(dimethylsiloxane) (PDMS) was used to seal the nanochannel reversibly. Nanochannels with widths range from 100 to 900 nm and lengths up to several millimeters were obtained. Various nanostructures including integrated micro and nanochannels, nanochannel array, bent nanochannel and cross-shaped nanochannel were fabricated and characterized by fluorescent microscope, scanning electron microscope (SEM) and atomic force microscope (AFM).     

Electrokinetic characterization of individual nanoparticles in nanofluidic channels

We electrokinetically characterize properties of single 42-nm polystyrene nanoparticles (NP) in nanofluidic channels imaged with frustrated total internal reflection fluorescence microscopy (fTIRFM). Specifically, we demonstrate fTIRFM of individual NPs in nanofluidic channels shallower than the evanescent field and use the resultant illumination field to gain insight into the behavior and electrokinetic properties of individual NP transport in channels. We find that the electrophoretic mobility of nanoparticles in 100-nm channels is lower than in larger channels or in bulk, presumably due to hindrance effects. Furthermore, we notice a non-intuitive increase in mobility with buffer concentration, which we attribute to electric double layer interactions. Finally, since the evanescent field intensity decreases with distance from the channel wall, we use the measured fluorescence intensity to report probable transverse distributions of free-solution 42-nm polystyrene fluorescent particles. Our method promises to be useful for characterizing nanoscale molecules for many applications in drug discovery, bioanalytics, nanoparticle synthesis, viral targeting, and the basic science of understanding nanoparticle behavior.     

Monolithic fabrication of nanochannels using core–sheath nanofibers as sacrificial mold

A simple and reliable approach for fabricating circular nanofluidic channels in polydimethylsiloxane (PDMS) microfluidic systems is described, which uses core–sheath nanofibers as sacrificial molds. The core–sheath structures consist of an electrospun polyvinylpyrrolidone (PVP) core and a sputtered aluminum sheath. The rupture of the sheath during master template releasing allows easy removal of the nanofibers to form the nanochannels. Straight nanochannels with the diameter as small as 390 nm are demonstrated. This technology is advantageous over existing nanochannel fabrication approaches in reduced risks of fluidic leakage and channel blocking, simpler fabrication process, lower cost and easier dimension control. This work provides a solid technical basis that enables development of various on-chip analytical devices for investigation of the unique transport phenomena at nanoscale.     

Solid-like heat transfer in confined liquids

The aim of this research is to identify possible mechanisms that govern heat transport at a solid–liquid interface using molecular dynamics. The study reveals that, unlike its bulk analogue, a liquid in a nanochannel sustains long-lived collective vibrations, phonons, which propagate over longer timescales and distances. The larger phonon mean free path in nanochannels is attributed to the greater structural order of the liquid atoms and to the larger liquid relaxation time—the time in which the liquid structure remains unchanged and solid-like. For channels of height less than \(10\sigma\), long-range phonons are the dominant means of heat transfer in the directions parallel to the channel walls. The present findings are in agreement with experiments, which have observed significantly increased liquid relaxation times for the same range of channel heights. Finally, it is argued that confinement introduces additional transverse modes of vibration that also contribute to the thermal conductivity enhancement.     

A design method for nanofluidic circuits

A design method is proposed for nanofluidic circuits, based on the flow equation for a nanoscale fluid flow. This method incorporates the use of the concepts of the flow resistance, the flow rate, the pressure drop and the power loss, as like in electric circuits. The equations for calculating the flow resistance and the power loss in exemplary nanofluidic circuits including in a nanotube tree are presented. It was found that the nanotube size and the fluid-tube wall interaction both have great influences on the flow resistance and the power loss in nanochannel flow. Exemplary design analysis is given for some nanofluidic circuits, based on the proposed method.

     

Modulation of electroosmotic flow by electric field-responsive polyelectrolyte brushes: a molecular dynamics study

Molecular dynamics simulations were done to study the electroosmotic flow (EOF) transport in a nanochannel grafted with polyelectrolytes under the control of an electric field normal to the channel wall. This study first addresses some problems on the interplay between complex EOF and non-equilibrium conformational behavior of polyelectrolyte brushes at a molecular level. We demonstrated that changing the normal electric field has a significant impact on the conformational transition of polyelectrolytes and ion distributions, further leading to some new flow phenomena. The coupling mechanisms of polyelectrolyte chain dynamics and electrohydrodynamics were discussed. A remarkable result obtained is that fluid flux depends nonmonotonically on the normal electric field. Our work provides fundamental understanding of the EOF modulation using polyelectrolyte brushes and guidance for the design of smart nanofluidic channels.     

Ionic current in a pH-regulated nanochannel filled with multiple ionic species

Considering recent widespread applications in nanofluidics, we analyze the ionic current in a pH-regulated nanochannel, using an aqueous NaCl solution in an SiO₂ nanochannel with pH adjusted by HCl and NaOH as an example. The model assumed is closer to reality than that in previous analyses, where the channel surface is maintained either at constant potential or constant charge, and only ionic species coming from background salt are considered. The electrical potential, velocity distribution, and ionic current under various conditions are examined by varying the pH, the density of surface functional groups, and the background salt concentration. We show that neglecting ionic species other than those from back ground salt might yield appreciable deviation in ionic current. The mechanisms involved in ionic transport are discussed, and we show that the effects of double-layer thickness and surface potential yield complicated and interesting behaviors in ionic current.     

Ion bridges in microfluidic systems

Recently many microfluidic systems are increasingly equipped with functional units for ionic controls for various applications. In this review article, we define an ion bridge as a structure that controls current or distribution of ions in a microfluidic system, and summarize the ion bridges in the literature in terms of characteristics, fabrication methods, advantages and disadvantages. The ion bridges play two basic roles, namely to ensure electrical contact in a microfluidic network and mechanically separate a liquid phase from another. More interestingly, the charged surfaces of ion bridges, which can be chemically modified, create new characteristics such as permselectivity and concentration polarization. Asymmetric ion transport as well as ionic conductivity through the ion bridges suggests a variety of applications including sample preconcentration, electroosmotic pump, electrospray ionization, electrically driven valve and many others. This review categorizes the ion bridges into several classes and describes the structures, materials, fundamental functions and applications. In Perspectives, new opportunities of microfluidics and nanofluidics provided by the ion bridges are discussed.     

Electrochemomechanical energy conversion efficiency in silica nanochannels

The electrochemomechanical energy conversion efficiency has been investigated using a new theoretical and numerical framework for modeling the multiphysiochemical transport in long silica nanochannels. Both the chemical dissociation effects on surface charge boundary conditions and the bulk concentration enrichment caused by double layer interactions are considered in the framework. The results show that the energy conversion efficiency decreases monotonically with the increasing ionic concentration at pH = 8. For a given ionic concentration, there is an optimal channel height for the highest efficiency. The efficiency does not increase with the pH value monotonically, and there is an optimal pH value for the maximum energy conversion efficiency as the other conditions are given. The energy conversion efficiency increases with the environmental temperature. The present results may guide the design and optimization of nanofluidic devices for energy conversion.