Aspect Ratio Dependence Research Articles

Directional change of magnetic easy axis of arrays of cobalt nanowires: Role of non-dipolar magnetostatic interaction

Abstract Room temperature magnetization of two dimensional (2D) arrays of cobalt nanowires (NWs) having diameter 50 and 150 nm prepared by electrodeposition are studied in details. Diffraction patterns of the NWs reveal that the crystallites of the NWs become more textured on decreasing their diameter. Magnetic hysteresis loop measurements show the magnetic easy axis changes its direction from axial to perpendicular direction of NWs on increasing the length of the NWs. The magnetostatic interaction among the NWs, known as the key factor in defining the easy direction is found not to be dipolar at all the circumstances. An aspect ratio (length/diameter of NWs) dependence of the non-dipolar interaction in 150 nm NWs is evident from the static magnetization as well as from ferromagnetic resonance (FMR) measurements.

Two-Stage Hydrothermal Growth of Long ZnO Nanowires for Efficient TiO2 Nanotube-Based Dye-Sensitized Solar Cells

Vertically aligned TiO2 1-D nanostructures synthesized directly on transparent conducting oxide (TCO) have shown great promise to overcome the limitation of the random network of TiO2 nanoparticles currently used in dye-sensitized solar cells (DSCs). A promising process for synthesis of such structures is to first grow aligned ZnO nanowire arrays and then convert them to TiO2 nanotubes. Growth of ZnO nanowires with a sufficient length and density but without fusion of their roots, however, remains challenging. In this paper, we investigate the dependence of wire density and aspect ratio on the temperature, concentrations of reagents, and seeding crystals used in a liquid-phase ZnO nanowire synthesis process. On the basis of the results of the investigation, we introduce a two-step hydrothermal process for synthesis of long and vertically aligned ZnO nanowire arrays, and demonstrate that, by dividing the wire growth process into two steps at two different temperatures and reducing Zn2+ concentration, ZnO nanowires up to 20 μm long can be obtained without fusing their roots. The resulting ZnO nanowires can be converted into TiO2 nanotubes, and DSCs fabricated using such TiO2 nanotubes yield power conversion efficiencies up to 6.1%.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple-layer integral approach for Pr>1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

Effect of aspect-ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

Numerical and experimental data for the heat transfer as function of the Rossby number Ro in rotating Rayleigh-Benard are presented for Pr = 4.38 and up to Ra = 4.52 × 109 . The aspect ratio is varied between Γ = 0.5 and Γ = 2.0. Without rotation, where the aspect ratio influences the global flow structure, we see a small aspect-ratio dependence in the Nusselt number. For stronger rotation, i.e. 1/Ro ≫ 1/Roc, the heat transport becomes independent of the aspect-ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically-aligned vortices. Since these vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, an analysis of the vortex statistics shows that the fraction of the horizontal area that is covered by vortices is aspect-ratio independent when 1/Ro ≫ 1/Roc. In agreement with the results of Weiss & Ahlers (2011) we find a vortex-depleted area close to the sidewall. Here, we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio. This proceeding is a summary of Stevens et al. (2011).

Transition to oscillatory flow in a differentially heated cavity with a conducting partition

AbstractNumerical evidence is presented for previously unreported flow behaviour in a two-dimensional rectangular side-heated cavity partitioned in the centre by vertical wall with an infinite conductivity. In this flow heat is transferred between both sides of the cavity through the conducting wall with natural convection boundary layers forming on all vertical surfaces. Simulations have been conducted over the range of Rayleigh numbers $\mathit{Ra}= 0. 6\text{{\ndash}} 1. 6\ensuremath{\times} 1{0}^{10} $ at Prandtl number $\mathit{Pr}= 7. 5$ and at aspect ratios of $H/ W= 1\text{{\ndash}} 2$ where $H$ and $W$ are the height and width of the cavity. It was found that the thermal coupling of the boundary layers on either side of the conducting partition causes the cavity flow to become absolutely unstable for a Rayleigh number at which otherwise similar non-partitioned cavity flow is steady but convectively unstable. Additionally, unlike the non-partitioned cavity, which eventually bifurcates to a multi-modal oscillatory regime, this bifurcation is manifested as a single mode oscillation with ${f}^{+ } = f{\nu }^{1/ 3} / \mathop{ (g\ensuremath{\beta} \mrm{\Delta} \theta )}\nolimits ^{2/ 3} \approx 0. 0145$, where $ \mrm{\Delta} \theta $ is the temperature difference between the hot and cold walls, $g$ is the gravitational acceleration, $f$ is the oscillation frequency and $\nu $ and $\ensuremath{\beta} $ are the fluid viscosity and coefficient of thermal expansion respectively. The critical Rayleigh number for this transition occurs between $\mathit{Ra}= 1. 0\text{{\ndash}} 1. 2\ensuremath{\times} 1{0}^{10} $ for $H/ W= 2$ and $\mathit{Ra}= 1. 2\text{{\ndash}} 1. 4\ensuremath{\times} 1{0}^{10} $ for $H/ W= 1$, indicating that the instability has an aspect ratio dependence.

Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×10(8) up to Ra=4.52×10(9). The aspect ratio Γ≡D/L, where L is the height and D the diameter of the cylindrical sample, is varied between Γ=0.5 and 2.0. Without rotation, where the aspect ratio influences the global large-scale circulation, we see a small-aspect-ratio dependence in the Nusselt number for Ra=2.91×10(8). However, for stronger rotation, i.e., 1/Ro>>1/Ro(c), the heat transport becomes independent of the aspect ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically aligned vortices. Since the vertically aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when 1/Ro>>1/Ro(c). In agreement with the results of Weiss et al. [Phys. Rev. Lett. 105, 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.

Connecting flow structures and heat flux in turbulent Rayleigh-Bénard convection

The aspect ratio (Γ) dependence of the heat transfer (Nusselt number Nu in dimensionless form) in turbulent (two-dimensional) Rayleigh-Bénard convection is numerically studied in the regime 0.4≤Γ≤1.25 for Rayleigh numbers 10(7)≤Ra≤Ra(9) and Prandtl numbers Pr=0.7 (gas) and 4.3 (water). Nu(Γ) shows a very rich structure with sudden jumps and sharp transitions. We connect these structures to the way the flow organizes itself in the sample and explain why the aspect ratio dependence of Nu is more pronounced for small Pr. Even for fixed Γ different turbulent states (with different resulting Nu) can exist, between which the flow can or cannot switch. In the latter case the heat transfer thus depends on the initial conditions.

Polyol Synthesis of Silver Nanowires: An Extensive Parametric Study

Silver nanowires have been synthesized by a polyol process. A detailed parametric study determining the relationship between final morphology of the products and temperature, injection rate, molar ratio of poly(vinylpyrrolidone) to silver nitrate, sodium chloride amount, and stirring rate is presented. The as-synthesized silver nanowires are analyzed by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD). The dependency of nanowire morphology and aspect ratio on synthesis parameters is shown via SEM images. Furthermore, the nanowire diameter is found to decrease with stirring rate, poly(vinylpyrrolidone) to silver nitrate molar ratio, and temperature and to increase with injection rate. The lack of sodium chloride and its presence in excess amounts resulted in the formation of particles with different sizes in addition to nanowires. In addition, poly(vinylpyrrolidone) to silver nitrate molar ratio is found to affect the morphology of the resulting nanostr...

Aspect-ratio dependence of thermodynamic Casimir forces

We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature T(c). Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary ρ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for ρ=1 and becomes repulsive in periodic systems for ρ>1.

Interrelations Between Microstructure and Piezoelectric Sensitivity in Novel 0–3–0 Composites Based on 0.67Pb(Mg1/3Nb2/3)O3 − 0.33PbTiO3 Single Crystal

This paper reports results on effective piezoelectric properties of advanced composites based on polydomain relaxor-ferroelectric single crystals of 0.67Pb(Mg1/3Nb2/3)O3 − 0.33PbTiO3. Two variants of the single crystal/porous polymer composite with 0–3–0 connectivity are proposed to study the role of microstructural factors in forming high piezoelectric sensitivity. The effective properties of the related 0–3 single crystal/polymer composite are predicted and considered to show ways of increasing the piezoelectric anisotropy and sensitivity. Examples of the volume-fraction and aspect-ratio dependences of the effective piezoelectric coefficients d 3j *, g 3j *, the hydrostatic piezoelectric coefficient gh *, and squared figures of merit d 33* g 33* and dh * gh * of composites are analysed to show in which ranges high piezoelectric sensitivity is attained. The presence of single-crystal polydomain inclusions in the porous 3–0 matrix promotes the large effective parameters (g 33* ∼ 103 mV · m/N, gh * ∼ 103 mV · m/N, d 33* g 33* ∼ 10−10 Pa−1, and dh * gh * ∼ 10−10 Pa−1), and the obvious high-performance advantage of the 0–3–0 composites is discussed taking into account features of their microstructure.

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Γ of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is Pr = 0.7 throughout the study. The aspect ratio Γ is varied between 0.5 and 12 for a Rayleigh number range between 107 and 109. The Nusselt number Nu is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law Nu = A × Raβ shows a power law dependence of both fit coefficients A and β on the aspect ratio. A minimum of Nu(Γ) is found at Γ ≈ 2.5 and Γ ≈ 2.25 for Ra = 107 and Ra = 108, respectively. This is the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Γ ≳ 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Γ is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen–Loève or proper orthogonal decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Γ ≥ 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale – the Kolmogorov scale ηK – and the largest scale – the cell height H – are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Γ ≳ 8).

Aspect-Ratio Dependence on Formation Process of Gold Nanorods Studied by Time-Resolved Distance Distribution Functions

Gold nanorods with aspect ratios of 2, 4, and 6 were generated by a seed-mediated growth method developed by Jana et al. and improved by Nikoobakht and El-Sayed. Nanorod formation during synthesis was investigated by time-resolved measurements of small-angle X-ray scattering (SAXS) and in situ UV−vis−NIR absorption. A sample holder made entirely of titanium was newly constructed for the simultaneous measurements. Distance distribution functions were calculated from the SAXS profiles, and the growth in nanorod length as a function of reaction time was determined without having to approximate or simplify the actual nanorod shape. Structural anisotropy, which corresponds to aspect ratio of nanorods, was also evaluated from the functions. For formed nanorods with aspect ratios in the range of 2−4, the time dependence of anisotropy shows maxima. In contrast, for formed aspect-ratio 6 nanorods, a maximum is not observed, and anisotropy continuously increases until an early reaction-equilibrium is reached. Growt...

Microstructural regimes of colloidal rod suspensions, gels, and glasses

We review the diverse range of materials made up of rod-shaped colloids. A common feature of such suspensions is the strong and efficient contribution of rods to the material's solid-like rheological properties such as elastic modulus and yield stress. Colloidal rod suspensions span from biomaterials such as f-actin and fd virus to inorganic materials such as boehmite and hematite, and to commercial fibers such as cellulose. We argue that, depending on the strength of pair potential interactions, such rod suspensions form microstructures that vary between the two limits of heterogeneous fractal clusters and homogeneous fiber networks. The volume fraction range for transition between these two limiting cases is strongly aspect ratio dependent. The two limiting microstructures can be distinguished by differences in the scattering vector dependence of their structure factors, as long as the range of scattering vector probed is sufficient to span regimes both above and below qL ≈ 1. Here q is the scattering vector and L is the rod length. Theories of the Brownian dynamics of fractal clusters and fiber networks show that the two types of microstructure can lead to the arrested dynamics of gelation and the glass transition, respectively. The volume fraction and aspect ratio dependences of the dynamical slowing down of these two cases differ significantly; we suggest that probing these differences is a convenient way to distinguish between gels and glasses of colloidal rods. This distinction is important to clarify because these microstructures are determinants of rheological properties such as elasticity and yielding. By combining these structural and dynamical ideas about rods, we classify a set of literature measurements on more than fifteen different colloidal materials and thereby distinguish between regimes of gelation and vitrification. We conclude by suggesting directions for future research in the arrested dynamics, the non-linear rheology, and the absolute lower limit of gelation in colloidal rod suspensions.

Influence of Ice Crystal Aspect Ratio on the Evolution of Ice Size Spectra during Vapor Depositional Growth

Abstract The relationship among aspect ratio, initial size, and the evolution of the size spectrum is explored for ice crystals growing by vapor deposition. Ice crystal evolution is modeled based on the growth of spheroids, and the ice size spectrum is predicted using a model that is Lagrangian in crystal size and aspect ratio. A dependence of crystal aspect ratio on initial size is discerned: more exaggerated shapes are shown to result when the initial crystals are small, whereas more isometric shapes are found to result from initially large crystals. This result is due to the nature of the vapor gradients in the vicinity of the crystal surface. The more rapid growth of the smaller crystals is shown to produce a period during which the size distribution narrows, followed by a broadening led by the initially smallest crystals. The degree of broadening is shown to depend strongly on the primary habit and hence temperature.

Accurate modeling of buckling of single- and double-walled carbon nanotubes based on shelltheories

The accuracy of widely employed classical shell-theory-based formulae to calculate thebuckling strain of single- and double-walled carbon nanotubes is assessed here. It is notedthat some simplifications have been made in deriving these widely employed formulae. As aresult critical buckling strains calculated from these formulae are independent of aspectratio (length/diameter). However, molecular dynamics simulation results in the literatureshow an aspect ratio dependence of buckling strain. Therefore, analytical expressions arederived in this paper to calculate buckling strains of single- and double-walled carbonnanotubes based on classical shell theory without simplifications. Applicability of theseexpressions is further verified through molecular dynamics simulations based on theCOMPASS force field. In addition, improvement in results achieved through arefinement of classical shell theory is assessed by calculating buckling strainsbased on first-order shell theory. Results show that simplified formulae introducea significant error at higher aspect ratios and smaller diameters. The formulaederived here show reasonable agreement with the molecular dynamics results at allaspect ratios and diameters. First-order shell theory is found to produce a slightimprovement in results for CNTs with smaller diameters and lower aspect ratios.

Growth kinetics of three-dimensional ZnO islands on various substrates

Growth kinetics of three-dimensional (3D) ZnO islands on silicon, sapphire, quartz glass and lime glass substrates, fabricated by radio-frequency magnetron sputtering, were investigated through physical–statistical analysis and the scaling behaviour method. These results show that the 3D islands nucleate with only one atom, and the scattered island size distribution indicates that the strain effect is significant for disturbing the atomic diffusion kinetic process. Gradual strain relaxation through dislocation is confirmed by the decreasing trend in the aspect ratio dependence on the lateral sizes for 3D islands. Additionally, surface roughening also works during strain relaxation.

Study of the island morphology at the early stages of Fe/Mo(110) MBE growth

Abstract We present theoretical study of morphology of Fe islands grown at Mo(110) surface in submonolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500 K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluate qualitatively morphological changes, we measured average aspect ratio of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.

On contact numbers in random rod packings

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards $${\langle \gamma \rangle = 9}$$ at high aspect ratio, strikingly close to the experimental contact number $${\langle C \rangle \approx 9.8}$$ for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod–rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.

Frequencies of Radially Symmetric Excitations in Vortex State Disks

Submicron ferromagnetic disks with a vortex ground state exhibit interesting and potentially useful dynamic properties arising from excitations on the ground state. In particular, a magnetic pulse applied perpendicular to the vortex plane will excite radially symmetric modes. Previous calculations of the frequencies of these modes based on the linearized Landau-Lifschitz equation and the magnetostatic Green's function give eigenfrequencies proportional to the square root of the aspect ratio radic( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L/R)</i> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> is the disk thickness and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> is the disk radius. However, experimental frequency data show significant deviation from the square root dependence. An improved calculation of the frequency is done through a collective variable approach by exploiting the high symmetry of these modes. In the linear approximation, this approach gives the main contribution to the frequency proportional to radic(( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L/R</i> )ln( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R/L</i> )), which is closer to the observed aspect ratio dependence.

Diffusion-Limited Reactions and Mortal Random Walkers in Confined Geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.