Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density

Nanochannels, functionalized by grafting with a layer of charged polyelectrolyte (PE), have been employed for a large number of applications such as flow control, ion sensing, ion manipulation, current rectification and nanoionic diode fabrication. Recently, we established that such PE-grafted nanochannels, often denoted as “soft” nanochannels, can be employed for highly efficient, streaming-current-induced electrochemomechanical energy conversion in the presence of a background pressure-driven transport. In this paper, we extend our calculation for the practically realizable situation when the PE layer demonstrates a pH-dependent charge density. Consideration of such pH dependence necessitates consideration of hydrogen and hydroxyl ions in the electric double layer charge distribution, cubic distribution of the monomer profile, and a PE layer-induced drag force that accounts for this given distribution of the monomer profile. Our results express a hitherto unknown dependence of the streaming electric field (or the streaming potential) and the efficiency of the resultant energy conversion on parameters such as the pH of the surrounding electrolyte and the \(\hbox {pK}_{\mathrm{a}}\) of the ionizable group that ionizes to produce the PE charge—we demonstrate that increase in the pH and the PE layer thickness and decrease in the \(\hbox {pK}_{\mathrm{a}}\) and the ion concentration substantially enhance the energy conversion efficiency.     

Cleaning a network with brushes

Following the decontamination metaphor for searching a graph, we introduce a cleaning process, which is related to both the chip-firing game and edge searching. Brushes (instead of chips) are placed on some vertices and, initially, all the edges are dirty. When a vertex is ‘fired’, each dirty incident edge is traversed by only one brush, cleaning it, but a brush is not allowed to traverse an already cleaned edge; consequently, a vertex may not need degree-many brushes to fire. The model presented is one where the edges are continually recontaminated, say by algae, so that cleaning is regarded as an on-going process. Ideally, the final configuration of the brushes, after all the edges have been cleaned, should be a viable starting configuration to clean the graph again. We show that this is possible with the least number of brushes if the vertices are fired sequentially but not if fired in parallel. We also present bounds for the least number of brushes required to clean graphs in general and some specific families of graphs.     

Analysis of capillary filling in nanochannels with electroviscous effects

Capillary filling is the key phenomenon in planar chromatography techniques such as paper chromatography and thin layer chromatography. Recent advances in micro/nanotechnologies allow the fabrication of nanoscale structures that can replace the traditional stationary phases such as paper, silica gel, alumina, or cellulose. Thus, understanding capillary filling in a nanochannel helps to advance the development of planar chromatography based on fabricated nanochannels. This paper reports an analysis of the capillary filling process in a nanochannel with consideration of electroviscous effect. In larger scale channels, where the thickness of electrical double layer (EDL) is much smaller than the characteristic length, the formation of the EDL plays an insignificant role in fluid flow. However, in nanochannels, where the EDL thickness is comparable to the characteristic length, its formation contributes to the increase in apparent viscosity of the flow. The results show that the filling process follows the Washburn’s equation, where the filled column is proportional to the square root of time, but with a higher apparent viscosity. It is shown that the electroviscous effect is most significant if the ratio between the channel height (h) and the Debye length (κ ⁻¹) reaches an optimum value (i.e. κh ≈ 4). The apparent viscosity is higher with higher zeta potential and lower ion mobility.     

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.     

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.     

Two-dimensional molecular dynamic simulations on accommodation coefficients in nanochannels with various wall configurations

The accommodation coefficients are often utilized in slip boundary conditions to characterize gas-wall interactions. Due to the insufficient transport of momentum and energy in nanochannels, the accommodation coefficients are always less than unity and greatly influenced by temperature and surface structures. In the present paper, a statistical algorithm of the accommodation coefficients was described in molecular dynamic method. The accommodation coefficients were calculated for various wall configurations in two-dimensional nanochannels. The channels were constituted by several layers of platinum atoms, which vibrated and attached to face centered cubic (FCC) lattice sites. The results revealed that the NMAC and EAC are sensitive with the spring constant and wall atom layers. Subtle distinctions in FCC lattice and nanoscale roughness had strong effects. On FCC (1 1 1) lattice plane, the TMAC in isothermal flows was larger, while the NMAC and EAC in thermal conductions are smaller, than those on FCC (1 1 0) lattice plane. Moreover, larger roughness induced more normal momentum transferred into tangential momentum so that the NMAC decreases while the TMAC and EAC increases for larger roughness. In addition, the accommodation coefficients are also affected by rarefaction that the TMAC and EAC decrease as the Knudsen number increases.     

Surface wettability effects on flow in rough wall nanochannels

The effect of rough-wall/fluid interaction on flow in nanochannels is investigated by NEMD. Hydrophobic and hydrophilic surfaces are studied for walls with nearly atomic-size rectangular protrusions and cavities. Our NEMD simulations reveal that the number of liquid atoms temporarily trapped in the cavities is affected by the strength of the potential energy inside the cavities. Regions of low potential energy are possible trapping locations. Fluid atom localization is also affected by the hydrophilicity/hydrophobicity of the surface. Potential energy is greater between two successive hydrophilic protrusions, compared to hydrophobic ones. Moreover, groove size and wall wettability are factors that control effective slip length. Surface roughness and wall wettability have to be taken into account in the design of nanofluidic devices.     

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.     

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.     

Solutal transport in rectangular nanochannels under pressure-driven flow conditions

In this article, we investigate the effect of channel sidewalls on the transport of neutral samples through rectangular conduits under pressure-driven flow and small zeta potential conditions. Our analyses show that while these structures can significantly reduce the streaming potential in small aspect ratio rectangular channels, they introduce a very minor variation in the sample velocity with the extent of Debye layer overlap in the system. Moreover, the increase in sample dispersion due to the channel side-regions has been shown to be nearly independent of the Debye layer thickness and very comparable to that reported under simple pressure-driven flow conditions. Interestingly however, a simple one-dimensional (1D) model that decouples band broadening arising due to diffusional limitations across the depth and width of the rectangular conduit has been shown to capture the predicted dependence of the Taylor–Aris dispersion coefficient on the channel aspect ratio under all operating conditions with less than 3% error.     

Mesoscopic simulations of electroosmotic flow and electrophoresis in nanochannels

We review recent dissipative particle dynamics (DPD) simulations of electrolyte flow in nanochannels. A method is presented by which the slip length δB at the channel boundaries can be tuned systematically from negative to infinity by introducing suitably adjusted wall-fluid friction forces. Using this method, we study electroosmotic flow (EOF) in nanochannels for varying surface slip conditions and fluids of different ionic strength. Analytic expressions for the flow profiles are derived from the Stokes equation, which are in good agreement with the numerical results. Finally, we investigate the influence of EOF on the effective mobility of polyelectrolytes in nanochannels. The relevant quantity characterizing the effect of slippage is found to be the dimensionless quantity κδB, where 1/κ is an effective electrostatic screening length at the channel boundaries.     

Research on forming and application of U-form glass micro-nanofluidic chip with long nanochannels

The forming process of U-form glass micro-nanofluidic chip with long nanochannels is presented in this paper, in which the fabrication of channels and the assembly of plates are included. The micro-nanofluidic chip is composed of two glass plates in which there are microchannels and nanochannels, respectively. This chip can be used for trace sample enrichment, molecule filtration, and sample separation, etc. In fabrication process, the two-step photolithograph on one wafer is often required in early papers, as nano and micro structure designed in one plate have different depths. In this paper, the channels in micro-nanofluidic chip are designed in two glass plates instead of in one wafer. The nanochannels and microchannels are, respectively, formed on plates using wet etching and two-step photolithograph on one wafer is not required. Since the channels are formed, the upper plate and the bottom plate are assembled together by alignment, preconnection and thermal bonding orderly. Firstly these plates are aligned with the cross-marks on an inverted microscope. The aqueous film between plates is controlled to decrease the static friction force for accurate adjustment. Then the adhesion strength of connection is enhanced with semi-dry status for limiting movement from slight inclining and shaking. At last, the bottom plate and the upper one are irreversibly linked together with thermal bonding. The heating period and max temperature of thermal bonding are optimized to eliminate thermal stress gradient and the size shrinking. With the micro-nanofluidic chip, the 1 μM fluorescein isothiocyanate in 10 mM PBS buffer is concentrated successfully. The sample concentrating factor of light intensity varies from 2.2 to 8.4 with applied voltages between 300 and 2,000 V. The switch effect and the instability effect in concentrating process are described and analyzed too.     

Hot embossing of polymer nanochannels using PMMA moulds

A novel hot embossing method is developed to fabricate polymer nanochannels. The pattern on the silicon nanomould is transferred to polymethylmethacrylate (PMMA) plates, and then polyethylene terephthalate (PET) nanochannels are embossed by using the PMMA mould. The use of the PMMA intermediate mould can extremely increase the device yield of the expensive silicon nanomould. To avoid the use of nanolithography, a method based on UV-lithography techniques for fabricating silicon nanomoulds with sub-micrometer width was put forward. 1 PMMA mould can be used to repeatedly emboss at least 30 PET substrates without damage and obvious deformation. Good pattern fidelity of PET nanochannels was obtained at the optimized embossing temperature of 90 °C. For an 808 nm-wide and 195 nm-deep nanochannel, the variations in width and depth between PET nanochannels and PMMA moulds were 1.8 and 2.5 %, respectively. The reproducibility was also evaluated, and the relative standard deviations in width and depth of 5 PET nanochannels were 5.1 and 7.3 %, respectively.     

Capillary filling speed of ferrofluid in hydrophilic microscope slide nanochannels

The capillary filling speed of ferrofluid in hydrophilic nanofluidic channels is investigated under various temperature and constant magnetic field conditions. Nanochannels with depths ranging from 50 to 150 nm and widths of 30 to 200 μm are fabricated on borosilicate glass substrates using buffered oxide wet etching and glass–glass fusion bonding techniques. The capillary filling speed of the ferrofluid is measured experimentally and compared with the theoretical results predicted by the classical Washburn equation. It is found that the experimental filling speed is significantly slower than the theoretical filling speed due to the erroneous assumption in the Washburn model of a constant contact angle irrespective of the flow rate and the presence of flow obstructions. The experimental results show that the filling speed reduces with a reducing channel depth, an increasing ferrofluid concentration, a lower operating temperature and an increased filling length. However, the filling speed is enhanced in the presence of an external magnetic field.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.     

Power generation from concentration gradient by reverse electrodialysis in ion-selective nanochannels

In an aqueous solution, the surface of inorganic nanochannels acquires charges from ionization, ion adsorption, and ion dissolution. These surface charges draw counter-ions toward the surface and repel co-ions. In the presence of a concentration gradient, counter-ions are transported through nanochannels much more easily than co-ions, which results in a net charge migration of one type of ions. The Gibbs free energy of mixing, which forces ion diffusion, thus can be converted into electrical energy by using inorganic ion-selective nanochannels. Silica nanochannels with heights of 4, 26, and 80 nm were used in this study. We experimentally investigated the power generation from these nanochannels placed between two potassium chloride solutions with various combinations of concentrations. The power generation per unit channel volume increases when the concentration gradient increases, and also increases as channel height decreases. The highest power density measured was 7.7 W/m². Our data also indicate that the energy conversion efficiency and the ion selectivity increase with a decrease of concentrations and channel height. The best efficiency obtained was 31%. Power generation from concentration gradients in inorganic ion-selective nanochannels could be used in a variety of applications, including micro batteries and micro power generators.     

Fully explicit dissipative particle dynamics simulation of electroosmotic flow in nanochannels

A fully explicit mesoscale simulation of electroosmotic flow (EOF) in nanochannels is presented by an extended dissipative particle dynamics (DPD) method. To avoid formation of ionic pairs through interacting soft-core charges, a Slater-type smearing distribution borrowed from quantum mechanics is utilized to surround each soft DPD ion with a charge cloud. To account for reduced periodicity normal to the walls direction, a corrected version of 3D Ewald sum is implemented in which a dipole moment term is deducted from energy and force terms of non-frozen charges. Simulation box is then elongated normal to walls to dampen spurious interslab interactions by adding vacuum gaps between periodic images. These measures together with the established unit conversions guarantee perfect match to molecular dynamics results. The transition of EOF velocity profile from parabolic (equivalent to overlap of electric double layers) to plug-like shapes is studied across the changing electric field between 0.06 and 0.41 [V/nm], and varying salt concentration from 0.26 to 2.0 [M]. It is found that 1.25 [V] increase in the driving voltage can potentially enhance the electroosmotic flow rate by 8–11 times in the range of ionic concentrations studied. The range of surface zeta potential calculated as \( 27 < \zeta < 52 \) [mV] in the linear response regime, as identified to occur for 0.24 ≤ E [V/nm], agrees reasonably with numerical and experimental studies.