Planar Slits Research Articles

Phase behavior of fluids in undulated nanopores

The geometry of walls forming a narrow pore may qualitatively affect the phase behavior of the confined fluid. Specifically, the nature of condensation in nanopores formed of sinusoidally shaped walls (with amplitude A and period P) is governed by the wall mean separation L as follows. For L>L_{t}, where L_{t} increases with A, the pores exhibit standard capillary condensation similar to planar slits. In contrast, for L<L_{t}, the condensation occurs in two steps, such that the fluid first condenses locally via bridging transition connecting adjacent crests of the walls, before it condenses globally. For the marginal value of L=L_{t}, all the three phases (gaslike, bridge, and liquidlike) may coexist. We show that the locations of the phase transitions can be described using geometric arguments leading to modified Kelvin equations. However, for completely wet walls, to which we focus on, the phase boundaries are shifted significantly due to the presence of wetting layers. In order to take this into account, mesoscopic corrections to the macroscopic theory are proposed. The resulting predictions are shown to be in a very good agreement with a density-functional theory even for molecularly narrow pores. The limits of stability of the bridge phase, controlled by the pore geometry, is also discussed in some detail.

A Configuration of Ultra-Wideband Planar Antenna Comprises Band Suppression at 5~6 and 3.3~3.7GHz

Two-slits in a UWB planar antenna in the means of suppressing the frequency bandwidths for 5~6 and 3.3~3.7GHz are studied. Frequency bandwidths for 5~6 and 3.3~3.7GHz are known as the Wireless Local Area Network (WLAN) and Worldwide Interoperable for Microwave Access (WIMAX), respectively. Both are coexisted with the UWB frequency bandwidth that is allocated between 3.1 and 10.6GHz. Coexistence between these frequency bandwidths have potentially caused interferences such as signal disruption and data lost in the respective systems. Two-slits are etched in the conductor elements in the means of generating the notched-band characteristics by producing impedance mismatched in the proposed antenna. Band notching are generated for the frequency bandwidths 5~6G and 3.3~3.7GHz, respectively. Band notch peaks are desired to achieve higher than -5dB. Slits are etched in the elliptical element and ground plane for band notching at the frequency 5~6 and 3.3~3.7GHz, and optimized proposed antenna’s peak of the reflection coefficient S11 are given -3 and -4dB, respectively. Slits parameters are studied in order to recognize the dominant parameters that affect the notched-band characteristics. It is shown that the two-slits have engendered the notched-band characteristics in the UWB planar antenna and slits parameters could be exploited in order to influence the notched-band characteristics accordingly.

Effect of Ground Pattern Size on FM‐Band Crosstalk Between Two Parallel Signal Traces of Printed Circuit Boards for Vehicles

SUMMARYIt is well known that electromagnetic disturbances in vehicle‐mounted radios are mainly caused by conducted noise currents flowing through wiring harnesses from vehicle‐mounted printed circuit boards (PCBs) with common ground patterns containing slits. To suppress the noise current outflow from these kinds of PCBs, we previously measured noise current outflow from simple two‐layer PCBs having two parallel signal traces and different ground patterns with and without slits to reveal that making slits with open ends on the ground patterns in parallel with the traces can reduce the conducted noise currents. In the present study, using FDTD simulation we investigated the reduction effects of ground pattern size on the FM‐band crosstalk noise levels between two parallel signal traces by using four types of simple PCB models having different ground patterns formed in different numbers but containing the same planar dimension slits parallel to the traces, in addition to two types of PCB models with different ground patterns divided into two parts parallel to the traces. It was found that the crosstalk noise currents for the above six types of PCBs decrease by 6.9 to 8.5 dB compared to the PCB which has a plain ground with no slits. We found that a contributing factor to the above‐mentioned crosstalk reduction is reduction of the mutual inductance between the two parallel traces. In addition, in this study it is interesting to note that noise current leakage from PCBs is more significantly reduced when the size of the return ground of each signal trace is small. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 186(1): 11–17, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22316

Asymmetric Profiles and Prewetting Lines in the Filling of Planar Slits with Ne

The filling of slits with identical planar walls is investigated in the frame of the density functional theory. For this kind of slit, the confining potential is symmetric with respect to its central plane. Closed and open systems are studied by applying, respectively, the canonical and grand canonical ensembles (CE and GCE). Results obtained for the confinement of fluid Ne by alkaline surfaces are reported. The behavior of these systems is analyzed by varying the strength of the Ne-substrate attraction, the temperature T, and the coverage Γ(l). It is assumed that the one-body density of the fluid, ρ(r), is uniform along the (x, y) planes parallel to the walls, becoming a function of the coordinate z perpendicular to those planes. Two sorts of solutions are found for the density profile: (i) symmetric ones that follow the left-right symmetry of the potential exerted by the walls and (ii) asymmetric ones that break the symmetry of the slit. The pores are wide enough for determining prewetting (PW) lines and wetting and critical PW temperatures, i.e., T(w) and T(cpw), from the analysis of symmetric solutions provided by both the CE and GCE schemes. Asymmetric species are examined in detail for T > T(w). It is shown that for a given Ne-substrate pair at a fixed T both the CE and GCE frames yield only one asymmetric 2-fold degenerate stable profile (formed by a "thin" wetting film at one wall and a "thick" wetting film at the other) coexisting with two symmetric profiles (formed by "thin" or "thick" wetting films at the two walls), while the remaining asymmetric states are at best metastable. This feature occurs along PW lines and disappears at T(cpw).

Self-Assembly of Lamellar- and Cylinder-Forming Diblock Copolymers in Planar Slits: Insight from Dissipative Particle Dynamics Simulations

We present a dissipative particle dynamics simulation study on nanostructure formation of symmetric and asymmetric diblock copolymers confined between planar surfaces. We consider symmetric and slightly asymmetric diblock copolymers that form lamellar nanostructures in the bulk, and highly asymmetric diblock copolymers that form cylindrical nanostructures in the bulk. The formation of the diblock copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. Both the slit width and the surface interaction strongly influence the phase diagram, especially for the asymmetric systems. For the symmetric and slightly asymmetric diblock copolymer systems, the confinement primarily affects the orientation of the lamellar domains and only marginally influences the domain morphologies. These systems form parallel lamellar phases with different number of lamellae, and perpendicular and mixed lamellar phases. In a narrow portion of the phase diagram, these systems exhibit a parallel perforated lamellar phase, where further insight into the appearance of this phase is provided through free-energy calculations. The confined highly asymmetric diblock copolymer system shows, in addition to nanostructures with parallel and perpendicular cylinders, noncylindrical structures such as parallel lamellae and parallel perforated lamellae. The formation of the various confined nanostructures is further analyzed by calculating structural characteristics such as the mean square end-to-end distance of the diblock copolymers and the nematic order parameter.

Phase behavior of the confined Lebwohl-Lasher model

The phase behavior of confined nematogens is studied using the Lebwohl-Lasher model. For three-dimensional systems the model is known to exhibit a discontinuous nematic-isotropic phase transition, whereas the corresponding two-dimensional systems apparently show a continuous Berezinskii-Kosterlitz-Thouless-like transition. In this paper, we study the phase transitions of the Lebwohl-Lasher model when confined between planar slits of different widths in order to establish the behavior of intermediate situations between the pure planar model and the three-dimensional system, and compare with previous estimates for the critical thickness, i.e., the slit width at which the transition switches from continuous to discontinuous.

Confinement of Ar between two identical parallel semi-infinite walls

The confinement of Ar in planar slits of two identical parallel semi-infinite walls of alkali metals, alkaline-earth metal Mg, and CO(2) is investigated within the framework of the density functional theory. It is assumed that (1) the fluid atoms interact via a recently proposed effective attractive pair potential with strength, epsilon(ff), which reproduces the experimental data of the surface tension of the liquid-vapor interface at the bulk coexistence curve, and (2) the adsorption on the walls is described by ab initio potentials characterized by a well depth, W(sf). In this way the systems were studied in the framework of a realistic approach. We found that for small coverages, the slit is always filled by forming two symmetric vapor films, one at each wall. For increasing coverage the behavior depends on the ratio W(sf)/epsilon(ff) and the temperature T. In the case of alkali metals, we found at the triple point, T(t), of the adsorbate a regime of average density rho(av) ( *) in which the ground state exhibits asymmetric density profiles, leading to the so-called spontaneous symmetry breaking (SSB) effect. The SSB appears at an average density rho(sb1) ( *) and disappears at a higher average density rho(sb2) ( *). When T is increased, the range of densities rho(sb1) ( *)<or=rho(av) ( *)<or=rho(sb2) ( *) diminishes and eventually the SSB disappears at a critical temperature, T(sb), which coincides with the critical prewetting temperature T(cpw) observed in the adsorption on a single wall. For T>T(cpw) the slit is filled symmetrically up to the phase transition to capillary condensation. All these features are examined as a function of the strength of the substrate and the width of the slit. Furthermore, no SSB effect was found for Mg and CO(2).

Self-Assembly of Symmetric Diblock Copolymers in Planar Slits with and without Nanopatterns: Insight from Dissipative Particle Dynamics Simulations

We present a dissipative particle dynamics simulation study on the formation of nanostructures of symmetric diblock copolymers confined between planar surfaces with and without nanopatterns. The nanopatterned surface is mimicked by alternating portions of the surface that interact differently with the diblock copolymers. The formation of the diblock-copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. For surfaces with nanopatterns, we also vary both the mutual area and location of the nanopatterns, where we consider nanopatterns on the opposing surfaces that are vertically (a) aligned, (b) staggered, and (c) partially staggered. In the case of planar slits without nanopatterns, we observe the formation of perpendicular and parallel lamellar phases with different numbers of lamellae. In addition, the symmetric diblock copolymers self-assemble into adsorbed layer and adsorbed layer-parallel lamellar phases and a mixed lamellar phase when the opposing surfaces of the planar slits are modeled by different types of wall beads. In the case of nanopatterned planar slits, we observe novel nanostructures and attempt to rationalize the diblock copolymer self-assembly on the basis of the behavior that we observed in the planar slits without nanopatterns. In particular, we investigate the applicability of predicting the structures formed in the nanopatterned slits by a superposition of the observed structures in slits without nanopatterns.

Density functional study of chemical reaction equilibrium for dimerization reactions in slit and cylindrical nanopores

We present a theoretical study of the effects of confinement on chemical reaction equilibrium in slit and cylindrical nanopores. We use a density functional theory (DFT) to investigate the effects of temperature, pore geometry, bulk pressure, transition layering, and capillary condensation on a dimerization reaction that mimics the nitric oxide dimerization reaction, 2NO <==> (NO)(2), in carbonlike slit and cylindrical nanopores in equilibrium with a vapor reservoir. In addition to the DFT calculations, we also utilize the reaction ensemble Monte Carlo method to supplement the DFT results for reaction conversion. This work is an extension of the previous DFT study by Tripathi and Chapman [J. Chem. Phys. 118, 7993 (2003)] on the dimerization reactions confined in the planar slits.

Fabrication of stationary micro-optical shutter based on semiconductor-to-metallic phase transition of W-doped VO2 active layer driven by an external voltage

The authors have successfully fabricated stationary micro-optical shutter arrays based on the well-known transmitting semiconductor (on) to the reflecting metallic (off) phase transition of thermochromic W-doped VO2 active layers operating at room temperature and driven by an external voltage. This shutter consists of 16 active planar micro-optical slits for which the optical switching (either transmittance or reflectance) can be controlled individually. This allows performing any desirable on-off switching combinations. The current-voltage characteristic of the micro-slit shows that the current jumps when the phase transition occurs. Transmittance switching as high as 25 dB and reflectance switching of about 6 dB were achieved with this device at λ=1.55 μm. Therefore, this electrically controllable VO2-array can be used as a stationary Hadamard shutter to increase the sensitivity of infrared spectrometers.

Depletion and Structural Forces in Confined Polyelectrolyte Solutions

Monte Carlo simulations and density functional calculations have been performed for charged macromolecules confined to planar slits. The force between the confining walls has been evaluated as a function of separation, while keeping the chemical potential of the macromolecules constant. Highly charged spherical particles and flexible polyelectrolyte chains in confinement give rise to depletion and structural oscillatory forces as a function of surface separation. The sign and magnitude of the surface charge of the confining walls have no dramatic effect on the qualitative behavior of the confined liquid. With neutral or oppositely charged surfaces, an accumulation of charged macroions is seen in the slit driven by the repulsive interaction between the macroions, while equally charged surfaces give rise to a pure depletion. The net charge, the range of interaction, and the particle density affect the details of the force curve. For spherical macroions, the period of the oscillations scales approximately as the bulk aggregate concentration, cbulk-1/3. Confined polyelectrolyte chains share some of these properties, but they partly display a different behavior. One clear difference is that the polyelectrolyte net charge, that is, the degree of polymerization, has no effect on the osmotic pressure. This is an indication that polyelectrolyte chains pack not as spheres but rather as cylindrical objects. Another difference is that the effective repulsive interaction between polyelectrolyte chains can be more long ranged and oscillatory forces can appear more readily than for a corresponding solution of equally charged spherical macroions.

Generalized slit flow of an ellis fluid

AbstractIsothermal, steady‐state and fully developed flows of Ellis fluids in planar and annular slits are discussed. The flow equations derived for Ellis fluids describe also the flows of Newtonian and power law fluids as specific cases. The most important flows resulting from thp general theory, i.e., the pressure flows in flat and annular slits for stationary channel walls and at transverse and longitudinal movements of a wall, are analyzed in detail. Numerical verification of the results leads to the conclusion that the planar and annular flows of Ellis and power law fluids are qualitatively similar The quantitative differences resulting from the slit curvature and the type of constitutive equation are relatively large only for flows of strongly non‐New‐tonian liquids.

Monte Carlo simulations of primitive water in planar slits with molecularly rough walls: surface self-organization

The behaviour of primitive water confined to molecularly rough slit-like pores is simulated by Metropolis MC in a NVT ensemble. Two models of molecular roughness are introduced covering the smooth pore walls by discrete surface molecules. One model called `hydrophobic', restricts the surface–surface and the surface–fluid potentials to hard-core interactions only. The other model called `hydrophilic', additionally takes into account associative surface–surface and water–surface interactions. The interplay between the self-organized molecular roughness of the pores and the network structure of primitive water in these confinements is studied in detail for several slit widths. Based on these results problems concerning the defining geometrical properties of molecularly rough pores are discussed on a molecular level in terms of the local densities and packing fractions of the surface and fluid particles as well as the topology of the formed molecular clusters and networks.

Depletion and bridging forces in polymer systems: Monte Carlo simulations at constant chemical potential

A new Monte Carlo simulation method designed for polymer solutions confined to planar slits is presented. The slit is in equilibrium with a surrounding bulk solution and the method allows a variation of the slit width while maintaining the polymer chemical potential constant. This is achieved by changing the tangential pressure as a function of slit width. An analysis of chain parameters and monomer distribution within the slit has been carried out. The model system used is supposed to mimick a macromolecular solution whose stability is manipulated by addition of adsorbing and/or nonadsorbing polymers. Generally, for the nonadsorbing polymer an attractive depletion force is found. At high volume fractions the attraction is reduced and a repulsive force appears at short separations. The depletion force can also be extinguished in the case of an adsorption potential of intermediate strength, while strong adsorption gives rise to a significant attraction due to polymer bridges.

Computer simulation studies of a square-well fluid in a slit pore. Spreading pressure and vapor–liquid phase equilibria using the virtual-parameter-variation method

We study model square-well fluids with well-width parameter λ=1.5 confined to hard planar slits. We derive a general computer simulation method for numerically calculating an arbitrary first derivative of the canonical ensemble partition function with respect to a simulation parameter, which we call the virtual-parameter-variation method. Two special cases of this approach are the Widom test-particle insertion method for calculating the excess chemical potential, and a method for calculating the pressure due to Eppenga and Frenkel [Mol. Phys. 52, 52, 1303 (1984)]. We use this approach to calculate the volume derivative parallel to the slit walls of the Helmholtz free energy in an (N,V,T) Monte Carlo simulation, and show that this spreading pressure is numerically consistent with the thermodynamic pressure obtained by integration of the Gibbs–Duhem equation using the simulated chemical potentials of the confined fluid as a function of density. We obtain new simulation results for the spreading pressure and the phase equilibrium properties of the confined square-well fluid, and we also estimate its critical point properties, observing a decrease of the critical temperature in comparison to the bulk fluid.

Simulations of coexistence between layered phases in planar slits

Layering transitions of a simple fluid in a planar pore with structureless attractive surfaces are investigated, using both simulations and density functional theory. The thermodynamic conditions for coexistence between three different layered phases, denoted 1, 2 and 3 in order of increasing average density, are determined, and coexistence curves are presented. The simulations are performed in the isotension ensemble at low temperatures, while the recently developed restricted isotension ensemble was used at elevated temperatures, in order to avoid phase transitions. According to the simulation results, 1–2 and 2–3 coexistences exist between stable phases at low temperatures, but the 2-phase is truncated by a triple point at which all three phases coexist. Above this triple point, 1–3 coexistence is the only stable one. These results are not confirmed by the density functional calculations, according to which 1–3 coexistence at low temperatures is replaced by a simple thin—thick coexistence at higher temperatures. With a slightly increased surface—fluid potential, the density functional calculations do predict the existence of a 1-2-3 triple point. However, in this case the relative stability of the layered phases above and below the triple point is reversed, as compared with the simulation results. Since the differences in the coexistence quantities are small, we have to consider the possibility that this unexpected behaviour is not a true effect, but rather a result of statistical fluctuations. At any rate, the occurrence of 1–3 coexistence together with a triple point is, to the best of our knowledge, a novel observation and is confirmed by density functional theory. Furthermore, the simulations show that the 1–2, 2–3 and 1–3 coexistence curves are very similar.

Simulations of coexistence between layered phases in planar slits

Simulations of coexistence between layered phases in planar slits

Highly charged colloidal suspensions in planar slits

A simple density functional approximation, which is based both on the density functional Taylor series expansion of the one-particle direct correlation function (DCF) and on the exact contact value theorem for a structureless hard wall with infinity wall distance, has been developed to study the structural properties of a highly charged colloidal suspension and compared with the computer simulation. Two kinds of two-particle DCFs, which are the rescaled mean spherical approximation (RMSA) and the Rogers-Young (RY) closure relation, have been used to calculate the local concentration profiles of a highly charged colloidal suspension confined in charged silt walls as input. The calculated results show that for a structureless hard wall the present approximation is better than the hypernetted chain (HNC) functional approximation and describes well the structural properties of a confined colloidal suspension compared with the computer simulation. However, the agreement between the computer simulation and the theory for the density profiles deteriorates with increasing the wall-particle interaction.

Monte Carlo simulation of hard sphere fluids in planar slits with molecularly rough surfaces

The structural and thermodynamic behaviour of hard-sphere fluids confined in planar slit-like pores with hard rough walls is investigated by canonical Monte Carlo simulations. The surfaces of the pores are modelled by means of parallel impenetrable walls. Additionally a molecular “roughness” of the pore surfaces is introduced using several models of randomly distributed hard spheres located (fixed or restricted in motion) at the walls. The density distribution of the hard spheres in the pore and the pressure normal to the walls are estimated and compared with the behaviour of fluids in slit-like pores with smooth hard walls. The results are discussed in the context of experimental studies of fluids confined in the polar interfaces of bilayers.

Thermodynamic perturbative approach for simple fluids: Structure of a confined square-well fluid

An approximation, which is based on both the weighted-density approximation (WDA) of Tarazona [Phys. Rev. A 31, 2672 (1985)] for the repulsive part of the model potential, and the density-functional approximation (CNPR) of Calleja et al. [Mol. Phys. 59, 973 (1991)] for the attractive part of the model potential, has been proposed to study the structural properties of simple fluids and is abbreviated as WDA-CNPR. The WDA-CNPR approximation can be considered as an extended Choudhury-Ghosh approximation, which is based on the density-functional expansion of a one-particle direct correlation function corresponding to the attractive part of the model potential. It has been applied to predict the density profiles of a confined square-well fluid, and compared with the computer simulation. The calculated results show that for the square-well fluid confined in planar slits the WDA-CNPR approximation is a significant improvement upon those of the Choudhury-Ghosh approximation, and compares well with the computer simulation. For the weak fluid-wall interaction a very good agreement between the results of theory and computer simulation are obtained, but the agreement deteriorates with the increase of the fluid-wall interaction.