Wall Potential Research Articles

Molecular simulation of water vapor outgassing from silica nanopores.

The outgassing problem is solved numerically by molecular dynamics. A slit-shaped nanopore consisting of cavity and channel is built with an implicit tabulated wall potential that describes the water–silicon/silica interaction. A flexible three-point water model is used for the simulation. The effects of varying the system temperature, outlet pressure, geometry, and materials of the nanopore on the outgassing rate are investigated. The results show that the temperature plays an important role in the outgassing rate, while the effect of the outlet pressure is negligible as long as it is in the high to medium vacuum range. The geometry of the channel also has an influence on the outgassing rate, but not as much as the surface material. Three different types of silica materials are tested: silicon, silica-cristobalite (hydrophilic material), and silica-quartz (super hydrophilic material). The fastest outgassing rate is found for a silicon nanopore. It is also found that a thin water film is formed on the surface of the silica-quartz nanopore. This material shows hardly any outgassing of water.

On the calculation of the absolute grand potential of confined smectic-A phases

We determine the absolute grand potential Λ along a confined smectic-A branch of a calamitic liquid crystal system enclosed in a slit pore of transverse area A and width L, using the rod–rod Gay–Berne potential and a rod–wall potential favouring perpendicular orientation at the walls. For a confined phase with an integer number of smectic layers sandwiched between the opposite walls, we obtain the excess properties (excess grand potential Λexc, solvation force fs and adsorption Γ) with respect to the bulk phase at the same μ (chemical potential) and T (temperature) state point. While usual thermodynamic integration methods are used along the confined smectic branch to estimate the grand potential difference as μ is varied at fixed L, T, the absolute grand potential at one reference state point is obtained via the evaluation of the absolute Helmholtz free energy in the (N, L, A, T) canonical ensemble. It proceeds via a sequence of free energy difference estimations involving successively the cost of localising rods on layers and the switching on of a one-dimensional harmonic field to keep layers integrity coupled to the elimination of inter-layers and wall interactions. The absolute free energy of the resulting set of fully independent layers of interacting rods is finally estimated via the existing procedures. This work opens the way to the computer simulation study of phase transitions implying confined layered phases.

Electroosmotic flow of a power-law fluid in a slit microchannel with gradually varying channel height and wall potential

A mathematical model based on the lubrication theory is presented for quasi-one-dimensional electroosmotic flow of a power-law fluid through a slit microchannel with undulating and non-uniformly charged walls. The channel height and the wall potential may vary periodically with axial position, with a wavelength much longer than the average channel height. Owing to the nonlinear rheology, the pressure gradient that is internally induced to satisfy continuity of flow has to be found numerically. A trial-and-error method is adopted to search for a flow rate that will give rise to an axial pressure gradient distribution with a zero average over one wavelength of the channel. When the flow behavior index is equal to the reciprocal of an integer, polynomial equations relating the flow rate and the local pressure gradient can be deduced, which will greatly facilitate the seeking of the solution by trial and error. Numerical results are also presented to illustrate how the flow behavior index may qualitatively change the combined effect of the geometric and electrokinetic wall patterns on the flow rate.

Electroosmotic flow of a power-law fluid through an asymmetrical slit microchannel with gradually varying wall shape and wall potential

• Non-parallel electroosmotic flow of power-law fluid in a microchannel. • Lubrication theory for slowly varying channel height and wall potential. • Linear superposition of forces invalidated by asymmetry of channel. • Nonlinear interaction between wall undulation and wall charge modulation. • Flow-rate sensitive to phase shift of wall patterns and power-law index. This study aims to investigate electroosmotic flow of a power-law fluid through a slit channel with walls asymmetrically patterned with periodic variations in shape and zeta potential. On taking into account the near-wall depletion layer, the present problem is simplified on the basis of the lubrication approximation, and through the use of the Helmholtz–Smoluchowski slip boundary condition. Nonlinear equations are to be solved for two unknown functions of axial dependence, one being the induced pressure gradient, and another being an undetermined stress component. An efficient numerical scheme is devised in this work to solve the nonlinear problem. Results are generated to check whether the principle of linear superposition of forces, for electrokinetic flow of a non-Newtonian fluid in the presence of a Newtonian depletion layer, is still applicable to flow in an asymmetric channel. It is also found that phase shifts between the geometrical and electric potential patterns on the two walls may lead to qualitatively disparate effects, depending on the power-law behavior index of the fluid and the applied pressure gradient.

Critical wetting, first-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries.

Structure of the quantum spin Hall states in HgTe/CdTe and InAs/GaSb/AlSb quantum wells

A solution of the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model is presented for bulk and quantum spin hall (QSH) edge states in semiconductor topological insulator (TI) quantum wells (QWs), bounded at the edge by an infinite wall potential. The edge states are exponentially localized, with a nonzero amplitude at the QW edge, and obey standard boundary conditions for the wave function and its derivative. Single helical edge states with spin locked to the direction of motion are found in the TI band gap $({E}_{\mathrm{TI}})$ of QWs with both strong (HgTe/CdTe) and weak (InAs/GaSb/AlSb) $s\text{\ensuremath{-}}p$ hybridization, but in the second case only below a small critical band gap, ${E}_{\mathrm{crit}}\ensuremath{\sim}1.6\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. For ${E}_{\mathrm{TI}}>{E}_{\mathrm{crit}}$, there appear to be two degenerate states for each spin direction. It is suggested that ${Z}_{2}$-like topological properties can still be maintained if one of these states is spurious or suppressed by disorder. The effect of interface band mixing, and band mixing due to structural inversion asymmetry and bulk inversion asymmetry is also considered. Simple model Hamiltonians are developed for the bulk and edge states which are calibrated against a bulk eight-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ calculation close to the TI transition. At the transition, the zero gap bulk states exhibit a spin splitting, essentially changing the Dirac point to a circle. In the TI phase, there is a small change in the dispersion of the QSH edge states. These results confirm the robustness of the QSH edge states to spatial symmetry breaking interactions.

Wall charging of a helicon antenna wrapped plasma filled dielectric tube

Dielectric wall charging of a cylindrical glass wall surrounded by a helicon antenna of 18 cm length is measured in a linear helicon plasma device with a diverging magnetic field. The ions because of their lesser mobility do not respond to the high frequency electric field and the electrons charge the wall to a negative DC potential also known as the DC self-bias. The wall potential in this device is characterized for different neutral pressure, magnetic field, and radio frequency (RF) power. Axial variation of wall potential shows higher self-bias potentials near the antenna rings. Ion magnetization in the source chamber increases both wall charging and plasma potential of the source due to confinement.

Glassy dynamics in confinement: planar and bulk limits of the mode-coupling theory.

We demonstrate how the matrix-valued mode-coupling theory of the glass transition and glassy dynamics in planar confinement converges to the corresponding theory for two-dimensional (2D) planar and the three-dimensional bulk liquid, provided the wall potential satisfies certain conditions. Since the mode-coupling theory relies on the static properties as input, the emergence of a homogeneous limit for the matrix-valued intermediate scattering functions is directly connected to the convergence of the corresponding static quantities to their conventional counterparts. We show that the 2D limit is more subtle than the bulk limit, in particular, the in-planar dynamics decouples from the motion perpendicular to the walls. We investigate the frozen-in parts of the intermediate scattering function in the glass state and find that the limits time t→∞ and effective wall separation L→0 do not commute due to the mutual coupling of the residual transversal and lateral force kernels.

Effect of asymmetric secondary emission in bounded low-collisional E × B plasma on sheath and plasma properties

In a weakly-collisional bounded plasma, secondary electrons emitted from the walls can transit the plasma gap and reach the opposite wall. To accurately predict wall potentials and energy fluxes, one must account for this effect in the flux balance. We present 1D3V particle-in-cell simulations of a plasma slab in an E × B field where the emission yield is different at each wall and varied in a wide parameter range. Analytical formulas are derived to explain the dependence of wall potentials on the emission from both walls. When emission yields are asymmetric, the wall with a weaker emission charges more negatively to compensate the emission imbalance. We show that a small imbalance of emission can lead to relatively large wall potential changes. Moreover, details of secondary electron emission energy distribution are important to take into account for correct calculation of this effect; for example, a small fraction of energetic elastically backscattered secondary electrons can further enhance the wall potential difference. Both walls are usually negatively charged by plasma. But for certain magnitudes of the E × B field, a distinct state appears with a positive surface charge at one wall and a negative surface charge at the other, causing a drastic change in the plasma properties.

Inuence of Bias Voltage on the Associated Electrical Elements of an Ion Sheath

The effect of a wall potential on the sheath associated electrical elements, such as capacitance, resistance, and inductance, are estimated for real experimental parameters. The values of these elements are analyzed as a function of the applied wall potential. A parallel plate capacitor is supposed to be formed between the negatively biased grid and the positive ion space charge layer. The energy stored in such a capacitor is estimated. The capacitance of such a parallel plate capacitor is found to be almost equal to the sheath capacitance obtained from the LCR circuit model. Further, the theoretically estimated wall potential is found to be close to the potential applied in the experiment.

Combined electroosmotic and pressure driven flow in a microchannel at high zeta potential and overlapping electrical double layer

A mathematical model for combined electroosmotic and pressure driven flow in a rectangular microchannel at high zeta potential and overlapping electrical double-layer is presented. The potential distribution is solved numerically without Debye–Hückel approximation using site dissociation model. The corresponding hydrodynamic analysis along with the associated heat transfer problem was performed. For wall potential of 120 mv, the centerline potential could be 95% of wall potential at non-dimensional channel height κa = 0.3 and it was 90% for κa = 1.0, where κ−1 is Debye length and a is half height of the channel. Centerline potential was 84% of wall potential at pH 5.5 and beyond pH 6.5, centerline potential was close to zero, even at lower value of κa (=0.3). Centerline velocity decreases by 16% as κa decreases from 1 to 0.5, when both pressure driven flow and electroosmotic flow are equally dominant, for non-dimensional zeta potential α = 3 (77 mV). For ratio of Joule heating to surface cooling beyond 5, the non-dimensional temperature in the channel is always positive. In absence of Joule heating (G = 0), Nusselt number decreases by 28% as κa decreases from 1 to 0.5. Nusselt number also decreases by 34% with increase in non-dimensional wall zeta potential from 3 to 5.

A unified analysis of plasma-sheath transition in the Tonks–Langmuir model with warm ion source

The paper presents a comprehensive kinetic theory of the famous Tonks–Langmuir model of a plane symmetric discharge, taking into account the thermal motion of ion source particles. The ion kinetics is governed by the ionization of neutrals at electron impacts. The plasma consisting of Boltzmann distributed electrons and singly charged ions is in contact with the absorbing negative wall. The derivations are performed in the frame of the “asymptotic two-scale” approximation, when the ionization mean-free path Li is much larger than the electron Debye length λD. In the limit (λD/Li)→0, the plasma-wall transition (PWT) layer can be split into two sublayers: a quasineutral presheath (PS) (with the scale-length Li) and the Debye sheath (DS) (with the scale λD). Such a subdivision of the PWT layer allows to investigate these sublayers separately and simplify the analysis of the influence of the ion source thermal motion (this has been neglected in the major part of publications up to now). The uniform description of the PWT layer as a single unit is complicated by the singular presheath and sheath structure and by a coupling with the eigenvalue problem originating from the plasma balance in the bounded system. The issue is clarified both analytically and numerically by construction of a matched asymptotic expressions. The equation and the length-scale governing the transition between neighboring PS and DS sublayers are derived. The eigenvalue problem combining the wall potential, the wall location, and the ionization mean-free path is discussed.

Dispersion in oscillatory electro-osmotic flow through a parallel-plate channel with kinetic sorptive exchange at walls

Dispersion in time-oscillatory electro-osmotic flows in a slit micro-channel under the effect of kinetic sorptive exchange at walls is theoretically investigated using the homogenization method. The two walls of the channel are considered to be made up of different materials, and therefore have different zeta potentials and sorption coefficients. A general expression for the Taylor dispersion coefficient under different zeta potentials as well as various sorption conditions at the walls is derived analytically. The dispersion coefficient is found to be dependent on the oscillation frequency, the Debye parameter, the species partition coefficient, the reaction kinetics and the ratio of the wall potentials. The results demonstrate that the presence of wall sorption tends to enhance the dispersion when the oscillation frequency is low, but the effect is negligible in high-frequency oscillatory flows. Moreover, it is found that the dispersion coefficient could be significantly changed by adjusting the relative wall potentials for low-frequency flows.

Determination of the thermodynamic correction factor of fluids confined in nano-metric slit pores from molecular simulation.

The multi-component diffusive mass transport is generally quantified by means of the Maxwell-Stefan diffusion coefficients when using molecular simulations. These coefficients can be related to the Fick diffusion coefficients using the thermodynamic correction factor matrix, which requires to run several simulations to estimate all the elements of the matrix. In a recent work, Schnell et al. ["Thermodynamics of small systems embedded in a reservoir: A detailed analysis of finite size effects," Mol. Phys. 110, 1069-1079 (2012)] developed an approach to determine the full matrix of thermodynamic factors from a single simulation in bulk. This approach relies on finite size effects of small systems on the density fluctuations. We present here an extension of their work for inhomogeneous Lennard Jones fluids confined in slit pores. We first verified this extension by cross validating the results obtained from this approach with the results obtained from the simulated adsorption isotherms, which allows to determine the thermodynamic factor in porous medium. We then studied the effects of the pore width (from 1 to 15 molecular sizes), of the solid-fluid interaction potential (Lennard Jones 9-3, hard wall potential) and of the reduced fluid density (from 0.1 to 0.7 at a reduced temperature T* = 2) on the thermodynamic factor. The deviation of the thermodynamic factor compared to its equivalent bulk value decreases when increasing the pore width and becomes insignificant for reduced pore width above 15. We also found that the thermodynamic factor is sensitive to the magnitude of the fluid-fluid and solid-fluid interactions, which softens or exacerbates the density fluctuations.

Electroosmotic flow of a power-law fluid in a non-uniform microchannel

An analytical model is presented for electrokinetic flow of a power-law fluid through a slit channel with gradually varying channel height and wall potential. With the near-wall depletion effect taken into account, the present model is based on the lubrication approximation and the use of the Helmholtz–Smoluchowski slip boundary condition. It is found that interaction between the wall undulation and the wall potential modulation, under the combined action of hydrodynamic and electric forcings, may give rise to a rich set of nonlinear behaviors for flow of a non-Newtonian fluid in the channel. In particular, the linear superposition of flow components due separately to the two forcings is found to work only for a strictly uniform channel; non-uniformity in channel height or wall potential distribution will spoil such linearity.

Enhancement of flow mixing in micro and nano channels

The aim is to increase the mixing potential of ion species in micro and nano channels with heterogeneous surface potential. We discuss the generation of vortical flow, due to the presence of wall heterogeneity at different locations in the channel. The flow characteristics are obtained by numerical solution of the Poisson equation, the Nernst--Planck equation, and the Navier--Stokes equation, simultaneously. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. The strong recirculation vortices which appear above the heterogeneities generate a strong pressure gradient which increases mixing performance. References F. Tian, B. Li and D. Y. Kwok, Tradeoff between mixing and transport for EOF in hetero. microchannels with nonuniform surface potentials. Langmuir 21:1126–1131, 2005. doi:10.1021/la048203e R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref and D. J. Beebe, Passive mixing in a three dimensional serpentine microchannel. J. Microelectromech. S. 9:190–197, 2000. doi:10.1109/84.846699 Z. M. Wu, Z. J. Zhao, J. X. Yang, L. P. Liu and X. L. Yang, Freq.-modulation-type MI sensor with nanocrystalline ribbon core. Sensor. Actuat. A:Phys. 121:430–433, 2005. doi:10.1016/j.sna.2005.03.019 S. Bhattacharyya and A. K. Nayak, Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels. J. Fluids Eng. 132:041103, 2010. doi:10.1115/1.4001308 A. Ajdari, Electro-Osmosis on Inhomogeneously Charged Surfaces. Phy. Rev. Lett. 75:755–758, 1995. doi:10.1103/PhysRevLett.75.755 D. Erickson and D. Li Influence of surface heterogeneity on electrokinetically driven microfluidic mixing. Langmuir 18:1883–1892, 2002. doi:10.1021/la015646z L. M. Fu , J. Y. Lin and R. J. Yang, Analysis of electroosmtoic flow with step change in zeta potential. J. Colloid. Interf. Sci. 258:266–275, 2003. doi:10.1016/S0021-9797(02)00078-4 H. Watzig, S. Kaupp and M. Graf, Inner surface properties of capillaries for electrophoresis. Trac-Trend. Anal. Chem. 22:588–604, 2003. doi:10.1016/S0165-9936(03)01102-6 Z. Zheng and D. Hansford, and A. T. Conlisk, Effect of multivalent ions on EOF in micro- and nanochannels. Electrophoresis 24:3006–3017, 2003. doi:10.1002/elps.200305561 J. Wang, M. Wang and Z. Li, Lattice Poisson–Boltzmann Simulations of Electro-Osmotic Flows in Microchannels. J. Colloid. Interf. Sci. 296:729–736, 2006. doi:10.1016/j.jcis.2005.09.042 A. K. Nayak, An Analysis of Steady/Unsteady Electroosmotic flows Through Charged cylindrical nano channel. Theor. Comp. Fluid Dyn. 27:885–902, 2013. doi:10.1007/s00162-013-0295-0

Development of EEM based silicon–water and silica–water wall potentials for non-reactive molecular dynamics simulations

Molecular dynamics simulations of heat transfer in gases are computationally expensive when the wall molecules are explicitly modeled. To save computational time, an implicit boundary function is often used. Steele's potential has been used in studies of fluid–solid interface for a long time. In this work, the conceptual idea of Steele's potential was extended in order to simulate water–silicon and water–silica interfaces. A new wall potential model is developed by using the electronegativity-equalization method (EEM), a ReaxFF empirical force field and a non-reactive molecular dynamics package PumMa. Contact angle simulations were performed in order to validate the wall potential model. Contact angle simulations with the resulting tabulated wall potentials gave a silicon–water contact angle of 129°, a quartz–water contact angle of 0°, and a cristobalite–water contact angle of 40°, which are in reasonable agreement with experimental values.

Free energy analysis along the stalk mechanism of membrane fusion

The free energy profile of the stalk model of membrane fusion has been calculated using coarse-grained molecular dynamics simulations. The proposed method guides the lipid configuration using a guiding wall potential to make the transition from two apposed membranes to a stalk and a fusion pore. The free energy profile is obtained with a thermodynamic integration scheme using the mean force working on the guiding wall as a response of the system. We applied the method to two apposed flat bilayers composed of dioleoyl phosphatidylethanolamine/dioleoyl phosphatidylcholine expanding over the simulation box under the periodic boundary conditions. The two transition states are identified as pre-stalk and pre-pore states. The free energy barrier for the latter is confirmed to be in good agreement with that estimated by the pulling method. The present method provides a practical way to calculate the free energy profile along the stalk mechanism.

Secondary electron emission and the bifurcation of the heat flux to the targets in fusion plasmas

The presence of secondary electron emission (SEE) from plasma facing components in fusion devices can result in a strong localization of the heat flux from plasma to the wall and subsequent wall erosion. Usually, the impact of the SEE is considered assuming the Maxwellian distribution of the electrons coming to the surface. As a result, the SEE coefficient only depends on the temperature of primary electrons. However, the tail of primary electron distribution function in the scrape off layer (SOL) of fusion devices can be far from Maxwellian due to preferential loss of fast electrons. Consequently, it is shown that the SEE coefficient will depend on the wall potential and multiple solutions can be possible corresponding to different regimes of plasma flow to the wall: with and without SEE effects. This effect can cause two-slope electron temperature profiles in the SOL, which are often seen in experiments.

Plasma Wall Potentials with Secondary Electron Emissions up to the Stable Space-Charge-Limited Condition

Numerical solutions to floating plasma potentials for walls emitting secondary electrons are obtained for various surface materials. The calculations are made with plasma moment equations and the secondary electron emission coefficients, which were determined from recent laboratory experiments. The results estimate the wall potentials up to the physical conditions that allow stable plasma sheaths under the space-charge-limited condition. The materials often used in the laboratory, such as aluminum, silicon, boron, molybdenum, silicon dioxide, and alumina, are considered. The minimum wall potential before the onset of space-charge-limited emission is determined by the electron temperatures at which the effective secondary electron emission coefficient integrated over the velocity distributions is about 0.62. The corresponding potential is given by −eφ0 ∼ 1.87kBT. The condition for space-charge-limited emission is newly found by numerically searching for all the stable sheaths. The new condition is −eφ0 ∼ 0.95kBT, and this predicts a wall potential that is less negative than the previously found one. Calculation of the power dissipated to the wall for hydrogen plasmas shows that there is a large difference in terms of power dissipation among the considered materials in the temperature range 20∼50 eV.