Wall Potential Research Articles

Adsorption of Chain Molecules in Slit-Shaped Pores: Development of a SAFT-FMT-DFT Approach

Density functional theory (DFT) is commonly used to treat the adsorption of molecules in carbon and silica pores of various geometries. In this work, we develop a DFT with an accurate molecular-based equation of state to calculate thermodynamic properties using fundamental measure theory (FMT), which is a rigorous approach for the treatment of homogeneous and nonhomogeneous hard-sphere fluids. A theoretical framework results with adsorbing molecules treated as hard-sphere chains with square-well attractive interactions. The Mansoori–Carnahan–Starling–Leland and Carnahan–Starling–Boublik equations of state are used for the hard-sphere interactions, and a version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to describe the square-well fluid. First- and second-order perturbative attractive terms are included in the theory. Theoretical predictions are in good agreement with published results for Monte Carlo simulations of the adsorption of chain molecules. In an extension to published studies, the impact of potentials of increasing complexity are compared using square-well and Lennard–Jones wall potentials. For more realistic adsorption of molecules of varying chain length, full slit-shaped pores are modeled using a 10–4 wall potential. The new approach provides accurate predictions of adsorption of chain molecules in model systems. It should be useful for predicting adsorption on flat surfaces and in slit-shaped pores as well as for analyzing experimental data.

An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles

Abstract The electric potential in an electro-osmotic flow is governed by the Poisson-Boltzmann (P-B) equation. A new solution is obtained by solving the fully nonlinear P-B model in a rectangular channel using the Hirota bilinear method, without invoking the Debye-Hückel (D-H) (linearization) approximation. This new solution is anti-symmetric about the centerline of two parallel plates, representing the case of opposite charges on two walls of a microchannel. The electric potentials and velocity fields derived from both the complete and linearized P-B equations are compared. Significant deviations are revealed, in particular for cases with high zeta potential. If a boundary slip on the wall is permitted, the electro-osmotic flow corresponding to this anti-symmetric wall potential can still induce a net fluid flow. These results will have important applications in characterizing bi-directional flows within microchannels, capillary tubes, membranes and porous materials.

Measurements of SiH4/H2 VHF Plasma Parameters with Heated Langmuir Probe

AbstractThe parameters of a SiH4/H2 VHF plasma were measured as a function of silane gas concentration with a heated Langmuir probe. It was found that when the sailane gas concentration is increased, the nagative ion density increases. Here the negative ion density was estimated from the reduction of the electron saturation current. In addition, the dependence of the wall potential on the silane gas concentration agreed with the theoretical values derived from the Bohm sheath equation including negative ions. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

3D MHD lead–lithium liquid metal flow analysis and experiments in a Test-Section of multiple rectangular bends at moderate to high Hartmann numbers

Experiments with liquid lead–lithium (Pb–Li) were carried out in a stainless steel (SS) Test Section (TS) consisting of multiple 90° bends for various flow rates and applied magnetic fields of up to 4T. Characteristic MHD flow parameter Hartmann number, Ha (=B0aσ/μ, Ha2 is the ratio of electromagnetic force to viscous force) and interaction parameter, N (=σaB02/ρU,N is the ratio of electromagnetic force to inertial force) of these experiments were varied from Ha=515 to 2060 and N=25 to 270 by changing the applied magnetic field and flow rates respectively. Three dimensional numerical simulations have been carried out using MHD module of FLUENT code. The measured Hartmann and side wall electric potential distribution at various locations of the Test Section have been compared with the numerical simulation results for different Hartmann numbers and interaction parameters (Ha=1030, N=25, 40, 67 for B=2T and Ha=2060, N=129, 161, 270 for B=4T). The numerical predictions based on laminar flow model are matching well with the measured values at all locations including bend regions for high magnetic field and low flow rates. However, at higher flow rates and lower magnetic fields (smaller Ha/Re values), the agreement was not good near the bend regions. This may be attributed to the significant presence of turbulence that was not accounted in the present simulation. The core velocity, estimated from the measured Hartmann wall potential at the locations far away from the bends, matched well with the numerical results. The analysis indicates that the flow distribution becomes rapidly symmetric when it turns at the bend where both the legs are perpendicular to the applied magnetic field. In contrast, flow distribution remains asymmetric for a longer distance when it turns from parallel to perpendicular direction of the applied field. The code is predicting reasonably well for MHD parameters relevant to Blanket Modules for single channel flows with bends.

Multiscale Study of Gas Slip Flows in Nanochannels

A multiscale modeling of the anisotropic slip phenomenon for gas flows is presented in a tree-step approach: determination of the gas–wall potential, simulation and modeling of the gas–wall collisions, simulation and modeling of the anisotropic slip effects. The density functional theory (DFT) is used to examine the interaction between the Pt–Ar gas–wall couple. This potential is then passed into molecular dynamics (MD) simulations of beam scattering experiments in order to calculate accommodation coefficients. These coefficients enter in an effective gas–wall interaction model, which is the base of efficient MD simulations of gas flows between anisotropic surfaces. The slip effects are quantified numerically and compared with simplified theoretical models derived in this paper. The paper demonstrates that the DFT potential is in good agreement with empirical potentials and that an extension of the Maxwell model can describe anisotropic slip effects due to surface roughness, provided that two tangential accommodation parameters are introduced. MD data show excellent agreement with the tensorial slip theory, except at large Kundsen numbers (for example, Kn ≃0.2) and with an analytical expression which predicts the ratio between transverse and longitudinal slip velocity components.

Effect of confining wall potential on charged collimated dust beam in low-pressure plasma

The effect of confining wall potential on charged collimated dust beam in low-pressure plasma has been studied in a dusty plasma experimental setup by applying electrostatic field to each channel of a multicusp magnetic cage. Argon plasma is produced by hot cathode discharge method at a pressure of 5×10−4 millibars and is confined by a full line cusped magnetic field confinement system. Silver dust grains are produced by gas-evaporation technique and move upward in the form of a collimated dust beam due to differential pressure maintained between the dust and plasma chambers. The charged grains in the beam after coming out from the plasma column enter into the diagnostic chamber and are deflected by a dc field applied across a pair of deflector plates at different confining potentials. Both from the amount of deflection and the floating potential, the number of charges collected by the dust grains is calculated. Furthermore, the collimated dust beam strikes the Faraday cup, which is placed above the deflector plates, and the current (∼pA) so produced is measured by an electrometer at different confining potentials. The experimental results demonstrate the significant effect of confining wall potential on charging of dust grains.

Oscillatory electro-osmotic flow through a slit channel with slipping stripes on walls

A theoretical model is presented in this paper for time-oscillating electro-osmotic flow through a plane channel bounded by two parallel plates, which are patterned with periodic stripes of distinct hydrodynamic slippage and wall potential. The flow is driven by oscillatory pressure gradient and electric field of the same frequency in the axial direction. Flows that are longitudinal or transverse to the stripes are investigated. Based on the Debye–Hückel approximation, and assuming Stokes flow, the electric potential and the velocity fields are found by the methods of eigenfunction expansion and point collocation. The phenomenological coefficients of the Onsager relations for the fluid and current fluxes are deduced as functions of the channel height, the area fraction of wall with slippage, the intrinsic slip length, the Debye parameter, the zeta potentials and the oscillation parameter. Considering several kinds of wall patterns, we extend the theoretical limits in the steady-flow regime to the oscillatory-flow regime. For a uniformly charged wall, the effective slip length obtained from the hydrodynamic problem can still be used directly in the electro-osmotic flow as if the wall were uniformly slipping. When the slipping stripes are perfectly slipping but uncharged, the presence of such stripes will always have a decreasing effect on the streaming conductance, unlike the steady case in which it gives no net effect on the flow in the limit of a very thin double layer. Furthermore, we confirm the presence of a threshold frequency, beyond which the flow will diminish significantly. The slipping fraction of the wall will always introduce a phase lag to the response and lower the threshold frequency. Increasing the wall potential in the presence of slippage can appreciably increase the streaming conductance and the phase lag.

Phase transitions and phase equilibria in spherical confinement

Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interplay between preferential adsorption of one species to the confining surface and bulk unmixing leads to very special shapes of the loops observed for the chemical potential of the colloids as a function of their packing fraction. We also discuss the extent to which concepts used for phase transitions in macroscopic systems, such as critical exponents of the order parameter distinguishing the phases, or the Kelvin equation describing the shift of the chemical potential at phase coexistence with the radius $R$, are applicable.

Nonlinear Electroosmosis Pressure-Driven Flow in a Wide Microchannel With Patchwise Surface Heterogeneity

In this paper, we have studied the electrokinetics and mixing driven by an imposed pressure gradient and electric field in a charged modulated microchannel. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discussed electrokinetic transport and other hydrodynamic effects under the application of combined pressure and dc electric fields for different values of electric double layer thickness and channel patch potential. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. Since electroosmotic flow depends on the magnitude and sign of wall potential, a vortex can be generated through adjusting the patch potential. The dependence of the vortical flow on imposed pressure gradient is investigated. Formation of vortex in electroosmotic flow has importance in producing solute dispersion. The circulation of vortex grows with the rise of patch potential, whereas the pressure-assisted electroosmotic flow produces a reduction in vortex size. However, the flow rate is substantially increased in pressure-assisted electroosmotic flow. Flow reversal and suppression of fluid transport is possible through an adverse pressure gradient. The ion distribution and electric field above the potential patch are distorted by the imposed pressure gradient. At higher values of the pressure gradient, the combined pressure electroosmotic-driven flow resembles the fully developed Poiseuille flow. Current density is found to increase with the rise of imposed pressure gradient.

Dispersion due to electroosmotic flow in a circular microchannel with slowly varying wall potential and hydrodynamic slippage

An analysis using the lubrication approximation is performed for the dispersion of a neutral non-reacting solute due to electro-osmotic flow through a circular channel under the combined effects of longitudinal non-uniformity of potential and hydrodynamic slippage on the channel wall. The wall is periodically patterned for the charge and slip distributions, with a wavelength much longer than the channel radius. It is shown that the presence of slip can greatly amplify the increased dispersion caused by induced pressure gradient brought about by the non-uniformity of wall potential. Non-uniform wall potential interacting with non-uniform slip can give rise to effects much different from those when the potential and slip are both uniformly distributed and equal to the averages of the non-uniform distributions. Mobility and dispersion associated with recirculating flow resulting from oppositely charged slipping region is also examined.

Crystalline multilayers of charged colloids in soft confinement: experiment versus theory

We combine real-space experiments and lattice sum calculations to investigate the phase diagram of charged colloidal particles under soft confinement. In the experiments we explore the equilibrium phase diagram of charged colloidal spheres in aqueous suspensions confined between two parallel charged walls at low background salt concentrations. Motivated by the experiments, we perform lattice sum minimizations to predict the crystalline ground state of point-like Yukawa particles which are exposed to a soft confining wall potential. In the multilayered crystalline regime, we obtain good agreement between the experimental and numerical findings: upon increasing the density we recover the sequence 2□ → 2△ → 2hcp⊥ → 3□ → 3△ → 3hcp⊥ → 4□.

Controlling the wetting properties of the Asakura–Oosawa model and applications to spherical confinement

We demonstrate for the Asakura–Oosawa model and an extension of this model that uses continuous rather than hard potentials, how wetting properties at walls can be easily controlled. By increasing the interaction range of the repulsive wall potential acting on the colloids (while keeping the polymer–wall interactions constant) polymers begin to substitute colloids at walls and the system can be driven from complete wetting of colloids via partial wetting to complete wetting of polymers. As an application, we discuss the morphology and wetting behavior of colloid–polymer mixtures in spherical confinement. We apply the recently developed ‘ensemble switch method’ where the Hamiltonian is extended to a combination of a system with walls and of a system without walls to calculate the surface excess free energies of colloid-rich and polymer-rich phases. The contact angle then is inferred from Young’s equation.

Wall Charge and Potential from a Microscopic Point of View

AbstractMacroscopic objects floating in an ionized gas (plasma walls) accumulate electrons more efficiently than ions because the influx of electrons outruns the influx of ions. The floating potential acquired by plasma walls is thus negative with respect to the plasma potential. Until now plasma walls are typically treated as perfect absorbers for electrons and ions, irrespective of the microphysics at the surface responsible for charge deposition and extraction. This crude description, sufficient for present day technological plasmas, will run into problems in solid‐state based gas discharges where, with continuing miniaturization, the wall becomes an integral part of the plasma device and the charge transfer across it has to be modelled more precisely. The purpose of this paper is to review our work, where we questioned the perfect absorber model and initiated a microscopic description of the charge transfer across plasma walls, put it into perspective, and indicate directions for future research (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electro-osmotic flow through a thin channel with gradually varying wall potential and hydrodynamic slippage

The lubrication approximation is applied to electro-osmotic flow through a thin parallel-plate channel under the combined effect of charge and hydrodynamic slippage modulation on the walls. The walls are periodically patterned for the charge and slip distributions, with a wavelength much longer than the channel height. It is shown that the phase of the wall patterns will play a significant role in determining the section-averaged velocity as well as the local convection pattern, both quantitatively and qualitatively. The effect of the phase on the flow will be dramatically different, depending on whether the electric field is applied along or perpendicular to the varying direction of the patterns. The possibility of generating a net flow in a direction perpendicular to the applied field is demonstrated.

Capillary wave spectrum at adsorbed liquid films

Capillary wave fluctuations at the edges of liquid wetting layers are analyzed in Monte Carlo simulations of a Lennard-Jones fluid adsorbed on a planar wall substrate. The analysis is based on the Fourier modes of the liquid surface, constructed via the intrinsic sampling method. For films thinner than four molecular layers we can quantify the damping of the capillary waves due to the wall potential. Our results are presented in the theoretical framework of the effective surface Hamiltonians, to establish a quantitative link between the molecular structure and the mesoscopic descriptions used for renormalization-group analysis. We observe the predicted exponential decay of the wall damping, with the correlation length of the liquid bulk. However, associated with the molecular layering of the density profiles, we observe a strong oscillatory dependence with respect to the mean film thickness, not included in any theoretical prediction. We discuss the possibility of finite-size effects in this respect. Three different definitions of the intrinsic surface at molecular level are tested, to show that the square gradient terms of the Hamiltonian are robust, while the surface bending (or nonlocal) terms are tied to each specific definition.

Wall-liquid and wall-crystal interfacial free energies via thermodynamic integration: A molecular dynamics simulation study

A method is proposed to compute the interfacial free energy of a Lennard-Jones system in contact with a structured wall by molecular dynamics simulation. Both the bulk liquid and bulk face-centered-cubic crystal phase along the (111) orientation are considered. Our approach is based on a thermodynamic integration scheme where first the bulk Lennard-Jones system is reversibly transformed to a state where it interacts with a structureless flat wall. In a second step, the flat structureless wall is reversibly transformed into an atomistic wall with crystalline structure. The dependence of the interfacial free energy on various parameters such as the wall potential, the density and orientation of the wall is investigated. The conditions are indicated under which a Lennard-Jones crystal partially wets a flat wall.

Strong stretching theory for diblock copolymers in thin films under application of electric fields

We investigate the microphases of asymmetric AB diblock copolymers confined to thin films in the strong segregation limit under the application of electric fields. We evaluate the free energy of a given set of possible phases and present phase diagrams for diblock copolymers with a cylindrical bulk phase in dependence of the film thickness and the attraction between the confining walls and the A or B monomers. This is done for different field strengths and volume fractions. We find that with increasing field strength structures show a preference for alignment with the field. The alignment is stronger when the permittivity of the minority monomer is larger than that of the majority monomer. Depending on the strength of the wall potential and the film thickness, the walls can become completely wetted by the minority monomer.

Electric Field at a Plasma‐Facing Wall for a Two‐Temperature Electron Distribution

AbstractThe floating potential drop and the electric field at a plasma‐facing wall are studied in the case of double electron temperature, where electrons have a double‐Maxwellian velocity distribution and the ion distribution function is modeled by a Maxwellian distribution shifted by the ion sound speed at the sheath entrance. It was quantitatively clarified that the effects between the hot electron component and the ion temperature to the floating wall potential drop, where the higher hot electron component increases the potential drop and the finite ion temperature decreases it. The electric field is almost proportional to the density of the hot component for the case of lower hot component. On the other hand, at the higher hot electron component the electric field has its maximum with respect to the density of the hot component (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of Molecular Dynamics with Classical Density Functional and Poisson-Boltzmann Theories of the Electric Double Layer in Nanochannels.

Comparisons are made among Molecular Dynamics (MD), Classical Density Functional Theory (c-DFT), and Poisson–Boltzmann (PB) modeling of the electric double layer (EDL) for the nonprimitive three component model (3CM) in which the two ion species and solvent molecules are all of finite size. Unlike previous comparisons between c-DFT and Monte Carlo (MC), the present 3CM incorporates Lennard-Jones interactions rather than hard-sphere and hard-wall repulsions. c-DFT and MD results are compared over normalized surface charges ranging from 0.2 to 1.75 and bulk ion concentrations from 10 mM to 1 M. Agreement between the two, assessed by electric surface potential and ion density profiles, is found to be quite good. Wall potentials predicted by PB begin to depart significantly from c-DFT and MD for charge densities exceeding 0.3. Successive layers are observed to charge in a sequential manner such that the solvent becomes fully excluded from each layer before the onset of the next layer. Ultimately, this layer filling phenomenon results in fluid structures, Debye lengths, and electric surface potentials vastly different from the classical PB predictions.

Electric-double-layer potential distribution in multiple-layer immiscible electrolytes: Effect of finite ion sizes

In a recent study [S. Das and S. Hardt, Phys. Rev. E 84, 022502 (2011).], we provided analytical results for the electric-double-layer (EDL) electrostatic potential distribution in a system of immiscible electrolyte layers confined between plates with gap dimensions comparable to the EDL thickness. We demonstrated that the intrinsic jumps in the ion-solvent interactions across the interface of the immiscible electrolytes lead to nontrivial electrostatic potential distributions that may completely defy or substantially augment the effect of the boundary wall potential. In this Brief Report, I extend this calculation to obtain analytical and numerical results for the case with finite ion sizes (or a finite ionic steric effect). It is found that the finite steric effect substantially enhances the contributions of jump in the ion-solvent interactions in the overall electrostatic potential distribution. More importantly, I demonstrate that such jumps in the ion-solvent interactions, owing to the immiscibility of the electrolytes, ensure that even for very weak wall zeta potentials, the steric effect can significantly affect the electrostatic potential distribution.