Size-dependent Energy Research Articles

Some metallic nanoparticles’ ignition temperature by thermodynamic consideration

Self-propagating high-temperature synthesis (SHS) provides an attractive alternative route for the preparation of various compounds. Considering the diffusion reaction at the solid interface, the size-dependent activation energy and ignition temperature of the compounds synthesized by SHS can be used to help in modeling. Therefore, a quantitative model for size-dependent ignition temperature is established by considering energetic and physical characteristics. To the author’s knowledge, this is the first theoretical model to explore the effects of size on ignition temperature for SHS applications, with size ranging from nano- to microscale. An assumption of ideal SHS is made in the deduction of the model. As the size of reactants decreases, the ignition temperature decreases. This is because increasing the contact area and reducing the diffusion barrier between the reactants must be used specifically to calculate the reactants at the nanometer scale. The model predictions are still in good agreement with the experimental and theoretical observations for metallic aluminides and titanium carbide systems.

Size-dependent vibration analysis of an axially moving sandwich beam with MR core and axially FGM faces layers in yawed supersonic airflow

The aim of this article is to study the influences of aerodynamic pressure and axially moving behavior on the size-dependent vibration of a sandwich structure. Here, the core of sandwich structure is a magnetorheological (MR) fluid and face layers are made of functionally graded material (FGM). In order to obtain the aerodynamic pressure due to supersonic flow over upper face of structure, the linear piston theory is considered. The displacement field of sandwich structure is written according to layerwise theory and the size-dependent strain energy is obtained based on modified first strain gradient theory (MFSGT). The Hamilton's principle is applied to derive the governing equations of motion. In order to solve the partial differential equations, the Galerkin method is applied. To validate the presented formulation and solution method, the obtained results are compared with the available results in the literature, which shows a good agreement. The first set of results investigate the first five natural frequencies of MR sandwich beam based on the different MR materials. The variations of frequency and corresponding loss factor are plotted against aerodynamic pressure, length scale parameters, axially speed, intensity of external magnetic field, yaw angle, and power-law index, and the resulting trends in the plots are discussed in detail. Also, the parameters of critical aerodynamic pressure and critical axially speed in different conditions are tabulated.

Temperature and size dependent surface energy of metallic nano-materials

In this study, we report a theoretical model for the temperature and size dependent surface energy of metallic nanomaterials. The model is verified by making a comparison with the available simulation and experimental data. Reasonable agreement has been observed between these results. This study reveals that the decrease of surface energy at high temperatures is caused by cohesive energy weakening and bond expansion. With the same nanomaterial size, the sequence of size effects on the surface energy from weak to strong is thin films, nanowires, and nanoparticles. In particular, this work can provide a theoretical basis for the prediction of size dependent surface energy of metallic nanomaterials at different temperatures, which can help in the understanding of the mechanical and thermodynamic properties of metal surfaces.

Effect of electrophoresis time deposition of colloidal gold nanoparticles on inducing the crystallization of amorphous Si thin films

This work investigates the metal induced crystallization of hydrogenated amorphous Silicon (a-Si:H) thin films, processed by plasma enhanced chemical vapor deposition, using Au nanoparticles (AuNPs) as crystallizing mediator metal. Electrophoresis deposition (EPD) of colloidal AuNPs was used to coat the Si substrates before the a-Si:H processing. Then, the crystallization was conducted by isothermal annealing for temperatures above the eutectic (500 and 600 °C). Raman spectroscopy analysis showed that the crystalline volume fraction doubled as the EPD time increases. Scanning electronic microscopy and energy-dispersive X-ray microanalysis revealed that AuNPs induced crystallization at 600 °C was achieved through eutectic reaction with mixing layers. Structural characterizations showed that the low amounts of AuNPs exhibited a metal mediating effect more pronounced than that of continuous Au thin film deposited by dry physical methods. The enhancing effect of AuNPs was assigned to their size dependent high surface energy. Herein, we discuss as well, the effect of the EPD time on the development of Si crystallites on the basis of thermodynamic and kinetic considerations.

Structural optimization and quantum size effect of Si-nanocrystals in SiC interlayer fabricated with bio-template

Amorphous SiC/Si multilayers were fabricated using alternately magnetron sputtering of SiC and electron beam evaporation of Si targets. The as-deposited films were annealed at different temperatures from 800 till 1000 °C to form Si-nanocrystals (Si-NCs) and study the layered structural stability by different analytical techniques, including x-ray reflectivity (XRR), x-ray diffraction (XRD), secondary ion mass spectroscopy (SIMS), transmission electron microscopy (TEM), and surface morphology by atomic force microscopy (AFM). XRR demonstrated that SiC/Si multilayers annealed at temperatures up to 1000 °C retain their layered structure. XRD and TEM confirmed the formation of Si-NCs after annealing at ≥800 °C. The Si-NCs size estimated from the TEM images is ∼4 nm for the multilayered sample with alternating 2 nm SiC and 4 nm Si layers. SIMS revealed that SiC/Si multilayers annealed at 800 °C possess the best periodic structure possibly due to the lowest carbon interdiffusion as compared to the samples annealed at higher temperatures. AFM micrograph confirmed that SiC/Si multilayers annealed at 800 °C characterized by the lowest surface roughness having RMS value of 0.123 nm as compared to the samples annealed at 900 °C and 1000 °C having RMS values of 0.207 and 0.530 nm, respectively. Size-controlled 3D array of Si-NCs separated by SiC barriers was fabricated by neutral beam etching of annealed SiC/Si multilayers with different Si layers thickness from 2 to 6 nm using a bio-template consisting of ferritin molecules. The size-dependent band gap energy of Si-NCs was estimated by optical spectroscopy to vary from 1.61 till 1.92 eV owing to the quantum confinement effect as the Si-NCs size decreases, which is appropriate for application in Si-based tandem solar cells.

A combined study of thermodynamic and first-principle calculation for single bond energy of Cu clusters

In the past, single bond energy of nanomaterials did not attract much attention, since many of their properties show a direct relation to cohesive energy. However, it is the single bond energy that determines the interaction between two atoms and even their bond lengths. Through introducing the bond number and the size-dependent cohesive energy model, the size-related single bond energy ɛ(N) of Cu clusters is resolved in this work, with the support of a thermodynamic method combined with first-principle calculation. It is found that the single bond is gradually strengthened as the size drops when compared with the bulk. Moreover, this enhanced bond strength is greatly important, especially in analyzing the Raman shift of semiconductor nanoparticles.

Size dependent stability and surface energy of amorphous FePt nanoalloy

The effects of particle size (2–6 nm) and temperature (300–2700 K) on the stability and local structural evolutions of amorphous equiatomic FePt bulk/nanoalloys have been investigated by combining Embedded Atom Model (EAM) with classical molecular dynamics (MD) simulation method. The three dimensional (3D) atomic configuration of amorphous FePt NPs by means of Voronoi analysis reveals that, deformed bcc (d-bcc) and icosahedron (d-ico) type structures are most probable local atomic configurations for 2–6 nm sized Fe50Pt50 NPs both in liquid (1700 K) and glassy (300 K) states. It was shown that nano-scale phase separation takes place around 300 K for 2 nm sized FePt NPs that leads to formation of spherical core-shell segregated structure having Pt-Fe-rich core and Fe-rich surface. Compared to core region, more ordered and high dense configuration of atoms at the surface gives rise to decrease in surface entropy of NPs and hence bringing about surface energy anomaly with positive temperature coefficient above the glass transition temperatures. Below glass transition temperatures of the FePt nanoalloy particles, the thermodynamically stable amorphous phase (TSA) would appear. Glass transition temperature of amorphous Fe50Pt50 NPs increases with increasing particle size and eventually approaches to the glass temperature of bulk system for NPs diameters ≥ ∼16 nm. Results of current predictions are in good qualitative and semi-quantitative agreement with other theoretical and experimental findings reported in the literature.

Direct Measurement of Length Scale Dependence of the Hydrophobic Free Energy of a Single Collapsed Polymer Nanosphere.

The physics underlying hydrophobicity at macroscopic and microscopic levels is fundamentally distinct. However, experimentally quantifying the length scale dependence of hydrophobicity is challenging. Here we show that the size-dependent hydrophobic free energy of a collapsed polymer nanosphere can be continuously monitored from its single-molecule force-extension curve using a novel theoretical framework. The hydrophobic free energy shows a change from cubic to square dependence of the radius of the polymer nanosphere at a radius of ∼1 nm-this is consistent with Lum-Chandler-Weeks theory and simulations. We can also observe a large variation of the hydrophobic free energy of each polymer nanosphere implying the heterogeneity of the self-assembled structures and/or the fluctuation of the water-polymer interface. We expect that our approach can be used to address many fundamental questions about hydrophobic hydration, which are otherwise inaccessible by ensemble measurements.

Body size-dependent energy storage causes Kleiber's law scaling of the metabolic rate in planarians.

Kleiber's law, or the 3/4 -power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber's law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body mass over 3 orders of magnitude reveal that Kleiber's law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber's law in planarians and have general implications for understanding a fundamental scaling law in biology.

Non-stationary vibration and super-harmonic resonances of nonlinear viscoelastic nano-resonators

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nanoresonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton\'s principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge–Kutta technique. The Hilbert–Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

Влияние дисперсии магнитной анизотропии кластеров Ge-=SUB=-3-=/SUB=-Mn-=SUB=-5-=/SUB=- на температурные зависимости намагниченности тонких пленок Ge:Mn

AbstractThe temperature dependences of magnetization M ( T ) of thin ion-implanted Ge:Mn (4 at % Mn) films containing Ge_3Mn_5 clusters were measured on samples cooled in the absence of magnetic field (zero field cooled, ZFC) and in a magnetic field of 10 kOe (field-cooled, FC). It has been established that the shape of ZFC–FC differential M ( T ) curves is determined by lognormal distribution of the size-dependent magnetic anisotropy energy of Ge_3Mn_5 clusters. Analysis of the observed ZFC–FC magnetization curves allowed the magnetic anisotropy dispersion (variance) and magnetic anisotropy constant to be estimated.

Influence of the Magnetic Anisotropy Dispersion in Ge3Mn5 Clusters on the Temperature Dependences of Magnetization in Thin Ge:Mn Films

The temperature dependences of magnetization M(T) of thin ion-implanted Ge:Mn (4 at % Mn) films containing Ge3Mn5 clusters were measured on samples cooled in the absence of magnetic field (zero field cooled, ZFC) and in a magnetic field of 10 kOe (field-cooled, FC). It has been established that the shape of ZFC–FC differential M(T) curves is determined by lognormal distribution of the size-dependent magnetic anisotropy energy of Ge3Mn5 clusters. Analysis of the observed ZFC–FC magnetization curves allowed the magnetic anisotropy dispersion (variance) and magnetic anisotropy constant to be estimated.

Size-dependent surface energy of Ar and Si nanovoids

A simple model for the size dependence of liquid–vapor surface energy of a liquid drop, free of any adjustable parameter, has been extended for the size dependence of the surface energy of nanovoids in this work. Considering nanovoids, there is a negative curvature on the void surface, which is completely different from nanoparticles or liquid drops, which have positive curvature surfaces. Thus curvature has an important effect on material properties. Moreover, by introducing negative curvature into the model for deduction of liquid–vapor surface energy, a successful prediction for the behaviour of argon (Ar) and silicon (Si) surface energy on the surface of nanovoids are obtained, which further confirms the role of curvature. Furthermore, it is shown that the surface energy of nanovoids increases as void size is reduced, suggesting a greater difference in energy between surface atoms and interior atoms, especially when void size is smaller than 4 nm. This is owing to the fact that the surface energy gradually approaches that of the bulk when the void size is larger than 4 nm. Thus, the effect of size on the surface energy of voids is significant when the voids are of small dimensions.

Primary and Secondary Resonance Analyses of Viscoelastic Nanoplates Based on Strain Gradient Theory

In this study, the nonstationary oscillation, secondary resonance and nonlinear dynamic behavior of viscoelastic nanoplates with linear damping are investigated based on the modified strain gradient theory extended for viscoelastic materials. The viscous component of the nonclassical and classical stress tensors are evaluated on the basis of the Leaderman viscoelastic model. Then, incorporating the size-dependent potential energy, kinetic energy and an external excitation force work, the governing equations of the oscillations are obtained based on the Hamilton’s principle. The governing formula is obtained as a nonlinear second-order integro-differential partial equation. This size-dependent viscoelastic formula is solved using analytical Harmonic balance method (HBM) and the fourth-order Runge–Kutta technique after applying the expansion theory. Additionally, the stability of the steady-state response is examined by means of HBM. Then, the secondary resonance conditions due to the super-harmonic motion are determined by performing frequency response, force response, Poincare map and phase portrait analyses. In addition, the nonstationary transient vibration of viscoelastic nanosystem is analyzed by performing Hilbert–Huang transform.

Modeling size-dependent thermoelastic energy dissipation of graphene nanoresonators using nonlocal elasticity theory

Recent developments in nanostructured materials have led to the use of graphene sheets as resonators in advanced micro- and nanoelectromechanical systems. An important feature of micro- and nanoresonators is their ability to function with low power dissipation. The main intrinsic mechanism of energy loss in these advanced devices is thermoelastic damping (TED). In this article, we study TED effects in orthotropic graphene sheets of varied lengths operating at different temperatures using nonlocal elasticity theory. For this purpose, the fundamental thermoelastic relations are used to develop a system of coupled partial differential equations to describe the behavior of graphene nanoresonators. The orthotropic mechanical and thermal properties of graphene were taken into account in our model for zigzag and armchair chiralities operating at different temperatures. The free in-plane vibration of the graphene nanoresonator is analyzed using Galerkin method. Decidedly, we show that the developed system of equations is capable of describing the TED behavior of graphene nanoresonators along the two considered chiralities during thermoelastic vibration. Specifically, we examined the influence of size, chirality, and temperature upon thermoelastic damping, as measured by the so-called quality factor, of the graphene nanoresonator. Our results reveal that the nanoresonator experiences higher energy dissipation with increased temperature. They also reveal the dependence of the energy dissipation upon the size and chirality of the graphene sheet.

Simultaneous probing of nanocrystal (NC)-ligand interaction-induced charge transfer/transport properties at the electron donor (lead selenide NC)/acceptor (zinc oxide) functional interface

Understanding correlation between interfacial charge transfer and transport at the electron donor/acceptor functional interface has remained elusive despite its impact on the optoelectronic devices because the conventional vertically stacked diode structure as well as energetic and morphological disorder at the interface complicates analysis of the interfacial region. We fabricated a test platform to enable simultaneous probing of charge transfer and transport at the nanocrystal (NC)/metal oxide interface. Using the transmission line method (TLM) in a ZnO/PbSe/ZnO test structure, we measured the ZnO/PbSe contact resistance from which interfacial charge transfer and transport properties can be correlated in relation to interfacial energetics depending on the size of PbSe NC. The interfacial transfer-transport test probe was validated by comparing size dependent energy level offset derived from the contact resistance value with the established trend. Importantly, by altering the chemical nature of the molecules attached to the NC surface, we discovered that charge transport properties including mobility in the PbSe channel away from the interface are extended into the interfacial region, enabling correlation between carrier diffusion and the electrical mobility at the electron donor/acceptor interface. With a very low mobility in the interface region, charge transfer associated with carrier diffusion is suggested to reflect the nature of energetic disordered interfacial region rather than the electrical mobility.

Nonlinear mechanics of nanotubes conveying fluid

A nonlocal strain gradient elasticity approach is proposed for the mechanical behaviour of fluid-conveying nanotubes; a nonlinear analysis, incorporating stretching, is conducted for a model based on both a nonlocal theory along with a strain gradient one. A clamped–clamped nanotube conveying fluid, as a conservative gyroscopic nanosystem, is considered and the motion energy and size-dependent potential energy are developed via use of constitutive and strain–displacement relations. An energy minimisation is conducted via Hamilton's method for an oscillating nanotube subject to external forces. This gives the nonlinear equation of the motion which is reduced to a high DOF system via Galerkin's technique. As many nanodevices operate near resonance, the resonant motions are obtained using a frequency-continuation method. The effect of different nanosystem/fluid parameters, including fluid/solid interface and the flow speed, on the nonlinear resonance is analysed.

Investigation of the Size Effect on the Nano-beam Type Piezoelectric Low Power Energy Harvesting

In this paper, size dependent beam type peizoelectric energy hardvester is investigated. For this goal, first nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on the size-dependent piezoelectricity theory then special beam type piezoelectric energy hardvester is probed for different parameters. Basic nonlinear equations of piezoelectric nano-beam are derived using principle of minimum of potential energy and variational method. To evaluate the formulation derived, static deformation and free vibration of the clamped-clamped piezoelectric nano-beam is investigated in the special case. The results of the formulation derived are investigated under different parameters, and particularly, the ability and performance of the beam type piezoelectric low power energy harvesting was evaluated in nanoscale.

Nonlinear free vibration of viscoelastic nanoplates based on modified couple stress theory

In this paper, a new viscoelastic size-depended model developed based on a modified couple stress theory and the for nonlinear viscoelastic material in order to vibration analysis of a viscoelastic nanoplate. The material of the nanoplate is assumed to obey the Leaderman nonlinear constitutive relation and the von Karman plate theory is employed to model the system. The viscous parts of the classical and nonclassical stress tensors are obtained based on the Leaderman integral and the corresponding work terms are calculated. The viscous work equations are balanced by the terms of size-dependent potential energy, kinetic energy. Then the equations of motion are derived from Hamilton’s principle. The governing nonlinear integro-differential equations with coupled terms are solved by using the fourth-order Runge-Kutta method and Galerkin approach. The results are validated by carrying out the comparison with existing results in the literature when our model is reduced into an elastic case. In order to explore the vibrational characteristics, the influences of the thickness ratio, relaxation coefficient, and aspect ratio on the frequency and damping ratio were also examined. The results revealed that the frequency, vibration amplitude and damping ratio of viscoelastic nanoplate were significantly influenced by the relaxation coefficient of nanoplate material, and length scale parameter. Also, it was found that with increasing (h/l) the vibration frequency decreases and its amplitude and damping ratio increase.

Structural Evolution and Superatoms in Molybdenum Atom Stabilized Boron Clusters: MoBn (n = 10–24)

Doping transition metal atom is known as an effective approach to stabilize an atomic cluster and modify its structure and electronic properties. We herein report the effect of molybdenum doping on the structural evolution of medium-sized boron clusters. The lowest-energy structures of MoBn (n = 10, 12, 14, 16, 18, 20, 22, 24) clusters are globally searched using genetic algorithm combined with density functional theory calculations. We found that Mo doping has significantly affected the grow behaviors of Bn clusters, leading to a structural evolution from bowl-like to tubular and finally endohedral cage. The size-dependent binding energy, HOMO–LUMO gap, vertical ionization potential and vertical electron affinity show that MoB12, MoB22 and MoB24 clusters have relatively higher stability and enhanced chemical inertness. More interestingly, the endohedral MoB22 cage is identified as an elegant superatom, which satisfies 18-electron closed shell configuration well.