Nanofluid flow and MHD mixed convection inside a vertical annulus with moving walls and transpiration considering the effect of Brownian motion and shape factor

In the present study, the exact solution of a nanofluid flow and mixed convection within a vertical cylindrical annulus with suction/injection, which is adjacent to the radial magnetic field, is presented with regard to the motion of cylinders’ walls. The impact of Brownian motion and shape factor on the thermal state of CuO–water nanofluid is also considered. The influence of such parameters as Hartmann number, mixed convection parameter, suction/injection, volume fraction of nanoparticles and motion of cylinders’ walls on flow and heat transfer is probed. The results show that the shape of the nanoparticles could change the thermal behavior of the nanofluid and when the nanoparticles are used in the shape of a platelet, the highest Nusselt number is obtained (about 2.5% increasement of Nusselt number on internal cylinders’ wall comparison to spherical shape). The results shed light on the fact that if, for example, the external cylinder is stationary and the internal cylinder moves in the direction of z axis, the maximum and minimum heat transfer take place on the walls of internal and external cylinders, respectively (for η?=?300, about 15% increasement of Nusselt number on internal cylinders’ wall). Furthermore, the enhancement of radius ratio between two cylinders increases the rate of heat transfer and decreases the shear stress on the internal cylinder’s wall.

     

Proper quantization rule approach to three‐dimensional quantum dots

In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius r_C by the proper quantization rule and the Wentzel‐Kramers‐Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius r_C in three dimensions. © 2013 Wiley Periodicals, Inc.     

Helium 4 dimer in nanotubes

The ground state of the helium 4 dimer is considered using the Monte Carlo technique. In a cylinder with a hard core wall, binding depends on its radius. For a small radius binding occurs as in the one-dimensional case. With an increase of the radius, the binding becomes stronger, reaches its maximum value, and then slowly diminishes. In conical geometry, that may be realized as a generalization of a cylindrical one, this dependence of the binding energy on the radius might lead to an effective force which tends to move the molecule toward the region of minimal energy. Thus, in channels, with nonhomogeneous cross-sections, the particles move easier in dimer form. In addition, the square of the momentum and of the particle separation along the cylinder axis and in the plane perpendicular to it are calculated as well.     

A scattering study on intermicellar interactions and structures of polymeric micelles

The micellar structure is usually considered to be composed of a hard sphere (liquid) core and a heavily solvated corona. Therefore, the correction for intermicellar interactions at finite concentrations can be relatively complicated. In this article, small-angle neutron scattering of a copolymer, known as Pluronic L64 (PEO₁₃PPO₃₀PEO₁₃), in o-xylene in the presence of D₂O is used to demonstrate that, based on the hard sphere approximation, intermicellar interactions can be corrected by representing the micellar size as having an equivalent hard sphere radius. The procedure remains valid even if the micellar shape becomes asymmetric, with axial ratios of 3 ? 4. For the present system, the equivalent hard sphere radius corresponds to the micellar core radius plus one-half of the micellar shell thickness. With the equivalent hard sphere approach, the scattering behavior of the micelle could be described by using a core-shell structure. © 1994 John Wiley & Sons, Inc.     

Surface Charge Density/Surface Potential Relationship for a Cylindrical Particle in an Electrolyte Solution

An accurate analytic expression of the surface charge density/surface potential relationship for an infinitely long cylindrical colloidal particle in a solution of general electrolytes is derived from an approximate solution to the nonlinear cylindrical Poisson– Boltzmann equation. The mathematical procedure is based on a method developed previously by Ohshima, Healy, and White for the case of a sphere (J. Colloid Interface Sci.90, 17 (1982)). Comparison is made with exact numerical results. Accurate expressions for the potential distribution around a cylinder and the effective surface potential of a cylinder are also derived. Finally, expressions for the double-layer interaction energy and force between two cylinders at large separations are derived on the basis of the method of Brenner and Parsegian (Biophys. J.14, 327 (1974)).     

Anisotropic swelling of hydrogel nanowires based on poly(vinylpyrrolidone) fabricated by single‐particle nanofabrication technique

We report a hydrogel nanowire based on poly(vinylpyrrolidone) (PVP) and N,N'‐methylenebis(acrylamide) (MBA), which have anisotropic swelling ratio for radius and length direction. The PVP/MBA nanowires were fabricated by single particle nanofabrication technique, which is a technique for the fabrication of polymeric nanowires using the single ion event, that cause the crosslinking reaction of polymer chains within the ion tracks along the ion paths; furthermore the size (length and radius) of the nanowires was controlled by changing the film thickness and amount of MBA crosslinker. The swelling behaviors in air and water were observed using atomic force microscopy. The PVP/MBA nanowires exhibited anisotropic swelling along the length and radius in aqueous environments, because the hydrogel nanowires consisted of crosslinked networks with inhomogeneous crosslinking points, which reflected the initial energy distribution from incident an ion within the ion track. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1950–1956     

Electrophoresis of two identical rigid spheres in a charged cylindrical pore

The electrophoresis of two identical spheres moving along the axis of a long cylindrical pore under the conditions of low surface potential and weak applied electric field is investigated. The geometry considered allows us to examine simultaneously the effects of boundary and the presence of a nearby entity on the behavior of a particle. The influences of the separation distance between two spheres, the thickness of a double layer, the ratio (radius of sphere/radius of pore), and the charged conditions on the surfaces of the spheres and the pore on the mobility of a particle are investigated. Several interesting results that are not reported in the literature are observed. For instance, although for the case of two positively charged spheres in an uncharged pore the qualitative behavior of a sphere depends largely on its size relative to that of a pore and the thickness of the double layer, this might not be the case when two uncharged spheres are in a positively charged pore. In addition, in the latter, the mobility of a sphere increases with the increases in the separation distance between two spheres, and this effect is pronounced when the ratio (radius of sphere/radius of pore) takes a medium value or the thickness of the double layer is either sufficiently thin or sufficiently thick.     

Association behavior of one-end hydrophobically modified poly[<Emphasis Type="Italic">N</Emphasis><Superscript>5</Superscript>-(2-hydroxyethyl) <Emphasis Type="SmallCaps">l</Emphasis>-glutamine] in water/ethylene glycol mixed solvent

Amphiphilic polymers Cn-PHEG consisting of water-soluble poly[N ⁵-2-(hydroxyethyl) l-glutamine] (PHEG) and hydrophobic alkyl chain (carbon number n = 12, 14, 16, or 18) attached at the PHEG terminal was prepared, and association behavior and structure of associate for Cn-PHEG in selective solvent (water/ethylene glycol mixed solvent) have been investigated. α-Helix content of PHEG block for all the polymers increased with weight fraction of ethylene glycol in the mixed solvent (W _EG). By light scattering measurements, formation of a small micelle was suggested for C14-, C16-, and C18-PHEG when W _EG = 0. With the increase in W _EG, appearance of a larger associate was revealed for C16- and C18-PHEG. Evaluated molecular weight and radius of gyration suggested that the micelle is star-like sphere when W _EG = 0 and worm-like cylinder when W _EG = 0.7. C12-PHEG did not demonstrate any distinct micellization behavior because of the weak hydrophobicity of C12 chain.     

Formation of kink bands by compression of the extrudate of solid linear polyethylene

Extrudates of solid linear polyethylene prepared under proper pressure and temperature conditions have a high c axis orientation along the extrusion direction, with lamellar crystals and amorphous layers stacked alternately along the extrusion direction. Kink bands were formed by compressing the oriented extrudate at room temperature along the extrusion direction. Inspection of the kink bands by wide-angle and small-angle x-ray diffraction and electron microscopy revealed that the fiber axis was rotated from the original axis direction by 70–75° and that the lamellar crystals were inclined to the fiber axis in the kink band by 55–60° and stacked nearly parallel to the kink boundary. The superstructural change during the formation of the kink band could not be interpreted in terms of uniform c axis shear alone. In addition to such a mechanism, it was necessary to take into account intermicrofibril and/or intercrystallite slip.     

Scattering of light by disordered spherulites

The scattering of light by a two-dimensional spherulite of radius R is calculated when there is disorder of optic axis orientation with respect to the radius. Special cases are considered when (1) the disorder occurs in the radial direction only, (2) the disorder occurs in the angular direction only, (3) there is combined radial and angular disorder, and (4) the optic axis makes a constant angle with the radius but there is disorder in the twist angle about the axis. In all of these calculations, a correlation function for disorder is defined and the scattering pattern depends on the ratio of the associated correlation distance to the size of the spherulite. With decreasing correlation distance, the azimuthal dependence of the scattering becomes less and there is a change in the variation of scattered intensity with scattering angles in a manner dependent upon the type of disorder.     

Boundary Effects on Diffusiophoresis of Cylindrical Particles in Nonelectrolyte Gradients

The diffusiophoretic motion of a long circular cylinder in a transversely imposed gradient of a nonionic solute near a large plane wall parallel to its axis is analyzed. The range of the interaction between the solute and the solid surfaces is assumed to be small relative to the particle radius and to the gap width between the particle and the wall, but the polarization effect of the mobile solute in the thin diffuse layers adjacent to the solid surfaces caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layers are used as the boundary conditions for the fluid domain outside the diffuse layers. Through the use of cylindrical bipolar coordinates along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and the wall effects on the diffusiophoresis of the cylinder are computed for various cases. For the diffusiophoretic motion of a cylinder normal to a plane, the particle mobility decreases monotonically with the decrease of the distance of the particle axis from the wall. The stronger the polarization effect in the diffuse layer, the weaker the wall effect on the diffusiophoresis. The effect of the normal plane on the diffusiophoresis of a cylinder is much more significant than that for a sphere at the same separation. For the diffusiophoresis of a cylinder parallel to a plane, the boundary effect is a complicated function of the relevant parameters (not necessarily varies monotonically with the extent of separation) mainly due to the existence of a diffusio-osmotic flow caused by the tangential fluid velocity at the plane wall. Copyright 2000 Academic Press.     

Oriented Electric Fields Accelerate Diels–Alder Reactions and Control the endo/exo Selectivity

Herein we demonstrate that an external electric field (EEF) acts as an accessory catalyst/inhibitor for Diels–Alder (DA) reactions. When the EEF is oriented along the “reaction axis” (the coordinate of approach of the reactants in the reaction path), the barrier of the DA reactions is lowered by a significant amount, equivalent to rate enhancements by 4–6 orders of magnitude. Simply flipping the EEF direction has the opposite effect, and the EEF acts as an inhibitor. Additionally, an EEF oriented perpendicular to the “reaction axis” in the direction of the individual molecule dipoles can change the endo/exo selectivity, favouring one or the other depending on the positive/negative directions of the EEF vis‐à‐vis the individual molecular dipole. At some critical value of the EEF along the “reaction axis”, there is a crossover to a stepwise mechanism that involves a zwitterionic intermediate. The valence bond diagram model is used to comprehend these trends and to derive a selection rule for EEF effects on chemical reactions: an EEF aligned in the direction of the electron flow between the reactants will lower the reaction barrier. It is shown that the exo/endo control by the EEF is not associated with changes in secondary orbital interactions.     

Structure and viscoelasticity of matched asymmetric diblock and triblock copolymers in the cylinder and sphere microstructures

A polystyrene–polyisoprene (PS–PI) diblock copolymer (10,000–50,000 g/mol) and a matched PS&ndashPI–PS triblock (10,000–100,000–10,000 g/mol) were employed to study the effect of chain architecture on the rheological response of ordered block copolymer melts. Both samples adopt hexagonal microstructures with PS cylinders embedded in a PI matrix; on further heating, an order–order transition (OOT) into a cubic array of spheres takes place prior to the order–disorder transition. Each morphology was verified by SAXS and TEM. Interestingly, at the OOT the low-frequency elastic modulus of the diblock increased abruptly, whereas that of the triblock decreased. In contrast, the modulus of the cubic phase was roughly independent of chain architecture. Chain relaxation parallel and perpendicular to the cylinders was probed by measuring the elastic modulus of a macroscopically aligned sample in directions parallel G and perpendicular (G) to the cylinder orientation. For both materials G < G < G where G is the elastic modulus of a randomly oriented sample. This result is attributed to the ability of the unentangled PS blocks to move along the direction of the cylinder axis, and thus relax the stress in the PI matrix in the parallel alignment. In each of the three cylindrical orientations the triblock had a larger modulus than the diblock, which is attributed to the presence of bridging PI blocks that connect distinct PS domains. About 20° below the OOT G showed a distinct change in its temperature dependence, which, coupled with SAXS measurements, is indicative of the onset of an undulation in the cylinder diameter that presages the pinching off of cylinders into spheres, as recently predicted by theory. The use of oriented samples also permitted SAXS confirmation of an approximate epitaxial relationship between the cylinder and the sphere unit cells, although a distinct change in the location of the structure factor maximum, q^*, is noted at the OOT. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2811–2823, 1997     

Iterative method for finding the low‐energy conformations based on the concept of molecular volumes

The recently proposed overlapping spheres (OS) method (Raos, N. Croat Chem Acta 1999, 72, 727) finds low‐energy conformations by minimizing the repulsion potential dependent on the free molecular volume inside the sphere with radius R_v. The sphere is situated at the geometrical center of the molecule or at the center of a molecular segment. The method was checked on branched alkanes and cyclic molecules (1,4‐diethylcyclohexane and copper(II) monochelates with N‐alkylated amino acids), yielding in all cases stable conformations with usually lower conformational energy than the “seed” conformations. The simple rules for segmentation of a molecule, based mostly on the topological considerations, were derived from the results of successfull optimizations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1353–1360, 2000     

Uniaxial drawing of polytetrafluoroethylene virgin powder by extrusion plus cold tensile draw

Polytetrafluoroethylene (PTFE) virgin powder was ultradrawn uniaxially by a two-stage draw. A film, compression molded from powder below the melting temperature (T_m), was initially solid-state coextruded to an extrudate draw ratio (EDR) of 6–20 at an established optimum extrusion temperature of 325°C, near the T_m of 335°C. These extrudates from first draw were found to exhibit the highest ductility at 45–100°C for the second-stage tensile draw, depending on the initial EDR and draw rate. The maximum achievable total draw ratio (DR_{t, max}) was 36–48. Such high ductility of PTFE, far below the T_g (125°C) and T_m, is in sharp contrast to other crystalline polymers that generally exhibit the highest ductility above their T_g and near T_m. The unusual draw characteristics of PTFE was ascribed to the existence of the reversible crystal/crystal transitions around room temperature and the low intermolecular force of this polymer, which leads to a rapid decrease in tensile strength with temperature. The structure and tensile properties of drawn products were sensitive to the initial EDR, although this had no significant influence on DR_t,max. The most efficient and highest draw was achieved by the second-stage tensile draw of an extrudate with the highest EDR 20 at 100°C, as evaluated by the morphological and tensile properties as a function of DR_t. The efficiency of draw for the cold tensile draw at 100°C was a little lower than that for solid-state coextrusion near the T_m. However, significantly higher tensile modulus and strength along the fiber axis at 24°C of 60 ± 2 GPa and 380 ± 20 MPa, respectively, were achieved by the two-stage draw, because the DR_t,max was remarkably higher for this technique than for solid-state coextrusion (DR_t,max = 48 vs. 25). The increase in the crystallite size along the fiber axis (D₀₀₁₅), determined by X-ray diffraction, is found to be a useful measure for the development of the morphological continuity along the fiber axis of drawn products.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2551–2562, 1998     

Exploring the ellipsoidal and core-shell geometries of copper-seamed C-alkylpyrogallol[4]arene nanocapsules in solution

Small-angle neutron scattering (SANS) studies were used to probe the stability and geometry of copper-seamed C-alkylpyrogallol[4]arene (PgC(n)Cu; n = 11, 13, 17) hexamers in solution. Novel structural features are observed at chain lengths greater than 10 in both solid and solution phase. Scattering data for the PgC(11)Cu and PgC(13)Cu in chloroform fitted as core-shell spheres with a total spherical radius of about 22.7 and 22.9 ? respectively. On the other hand, the scattering curve for the PgC(17)Cu hexamer at both 1% and 5% mass fractions in o-xylene did not fit as a discrete sphere but rather as a uniform ellipsoid. The geometric dimensions of the ellipsoid radii are 24 ? along the minor axis and 115 ? along the major axis. It is expected that an individual hexamer with heptadecyl chains would exhibit a uniform radius of ca. 24 ?. However, an approximate ratio of 1:5 between radii lengths for the minor axis and major axis is consistent with interpenetration of the heptadceyl chains of adjacent hexamers to form a single ellipsoidal assembly.     

Nanostructure reorganization in a thermotropic copolyester. A simultaneous WAXS and SAXS study

Thermally induced Angstrom and nanometer‐scale reorganization in thermotropic liquid crystalline polymer based on (1,4)‐hydroxybenzoic acid (B) and (2,6)‐hydroxynaphthoic acid (N) was investigated by simultaneous wide‐angle and small‐angle X‐ray scattering (SAXS, respectively). Extruded tapes 50 µm thick were annealed at 240°C under dry air conditions. The as‐received tape exhibited fiber‐like structure with crystalline order, whereas the SAXS patterns exhibited diamond‐shaped diffuse scattering elongated along the equatorial axis elucidating nanovoid morphology oriented along the extrusion axis. Guinier analyses showed that the radius of gyration R_g of nanovoids were ca. 17 nm along the extrusion axis. Heat treatment produced a sharpening of the 002 meridional reflection and the 110 equatorial reflection suggesting an improvement of molecular register and packing. The molecular alignment, as quantified by the order parameter , increased as well as the degree of crystallinity χ. On the other hand, SAXS intensity along the equatorial axis decreased evidencing reduction of R_g, i.e. lateral compression of the nanovoids and better molecular packing. Thermal treatment increased the thermal stability and the uniaxial tensile Young's modulus, E, along extrusion axis. However, the tapes exhibited microhardness anisotropy and the indentation anisotropy, ?H, gradually decreased suggesting reduction of elastic recovery in the molecular chain direction. Scanning electron microscopy evidenced an outer skin with an internal layered morphology that transformed into sheet‐like morphology with meandering fibrils. This investigation evidenced microstructure and morphology reorganization correlating with improved thermal and mechanical properties. Copyright © 2015 John Wiley & Sons, Ltd.     

Sphere‐Cap Mercury Microelectrodes for Scanning Electrochemical Microscopy Above an Insulating Substrate

Sphere‐cap mercury microelectrodes, fabricated onto platinum microdisks 1 and 10 μm radius, were employed as tips in scanning electrochemical microscopy (SECM). Experimental current vs distance curves were acquired above an insulating substrate with a series of sphere caps whose aspect ratio h/a (h is the height of mercury deposit, a is the disk basal radius) varied between 0.28 and 2.14. It was found that the hindered diffusion effect of the insulating surface was the less pronounced the higher was the h/a parameter of the sphere cap. Comparison of experimental and theoretical approach curves displayed a fairly good agreement for subhemisphere caps (h<a), and a less satisfactory agreement for hemispherical (h=a) and superhemispherical (h>a) caps. Preliminary coupled anodic stripping voltammetry and SECM measurements were also performed for the investigation on local chemical equilibria involving heavy metals at sediment/water interfaces.     

Polarized absorption and anomalous temperature dependence of fluorescence depolarization in cylindrical J-aggregates

We study chiral J-aggregates of the amphiphilic dye 1A that are spontaneously and asymmetrically generated from achiral dye monomers. These aggregates occur in two types. One type possesses a threefold split J-absorption band and forms micrometer-sized superhelices. The other type has a twofold split J-absorption band and forms smaller nanoparticles. We show that the analysis of optical experiments with polarized light in terms of an exciton model yields strong indications that the smaller aggregates have a cylindrical structure as well; the lower exciton band is polarized along the cylinder axis, while the higher band is polarized perpendicular to it. Our analysis allows for an estimate of the number of molecules around the circumference of the cylinder. Fluorescence–polarization excitation spectra at room temperature confirm the cylinder model. At low temperature, these spectra reveal a surprising loss of fluorescence polarization upon excitation in the higher exciton band. Possible explanations for this observation are discussed.