Anomalous Size Effect Research Articles

Anomalous size effect of impact resistance in carbon nanotube film

Dynamic mechanical behavior and size-related impact resistance of CNT films are studied by employing laser-induced projectile impact test (LIPIT) and coarse-grained molecular dynamics (CGMD) simulation. The energy dissipation mechanisms of the CNT films are investigated via CGMD simulations. An evident anomalous thickness-dependent effect is directly observed in the experiment, consistent with simulation phenomena. The mechanisms underlying this anomalous thickness-dependent effect are investigated at the atomic scale. The disparities between experiments and simulations are discussed. Our analysis of energy dissipation modes, deformation behaviors during impact, and impact area reveals that kinetic energy change predominantly governs the deformation mode. Meanwhile, a plugging failure mode near the exit face of CNT film is identified at high impact velocity (∼160 m/s), leading to a deterioration in impact resistance and a corresponding reduction in SEA with increasing CNT film thickness. These findings provide a feasible strategy for the protection design of CNT film in broaden protective application scenarios.

Anomalous size effects of ultra-small graphene sheets on the thermal properties of macroscopic films

Graphene films assembled from graphene nanosheets have achieved a wide range of applications in thermal management due to their ultra-high thermal conductivity. Although it is well established in the micron range that increasing the lateral size of graphene sheets enhances the thermal conductivity of graphene films. However, the preparation of large-size graphene sheets and their assembly into ordered film structures remain challenging, which impedes the development of high-performance thermally conductive graphene films. Herein, by unifying the properties of graphene sheets and preparation processes, we correlate the thermal conductivity of graphene films and the lateral size of starting sheets ranging from 0.32 to 20.32 μm and probe the underlying mechanism from the perspectives of macroscopic and microscopic structural defects. Surprisingly, decreasing lateral size to 0.32 μm achieved as high in-plane thermal conductivity (K//, 1550.06 ± 12.99 W/mK) and significantly higher through-plane thermal conductivity (K⊥, 8.11 ± 0.08 W/mK) of graphene films as the case of 20.32 μm. Besides, the commonly overlooked size effect of K⊥ shows an unexpected negative correlation, and the size effect of K// is also not monotonically increasing. These phenomena are correlated with micro-structure defects and lattice defects. Mechanism analysis reveals that thermally induced gas generation and the complex gas-sheet interactions during micro-structure evolution play a critical role in the size effect and may explain the unexpected negative size effect in the sub-micro range. These findings in size effects provide theoretical guidance for the selection of raw materials in fabricating highly thermally conductive graphene films.

Anomalous size effect of thermal conductivity of two-dimensional dielectric materials

In this work, we find that two-dimensional characteristics of hydrodynamic phonon transports in two-dimensional dielectric materials lead to the anomalous length dependency and even divergence of thermal conductivities. For suspended monolayer graphene the analytical solution of the two-dimensional Guyer-Krumhansl equations shows that the thermal conductivity increases with the increase of its length from 1 micron to 9 micron. When a specific temperature distribution at the inlet boundary is given, and the positive partial derivative of the heat flux along the length direction at the inlet and outlet boundaries is prescribed, analytical results show that the thermal conductivity of suspended monolayer graphene at the room temperature tends to infinity with the increase of its length. This result can be used to artificially regulate the thermal conductivity of suspended single-layer graphene.

A general theory for the bending of multilayer van der Waals materials

Multilayer van der Waals (vdW) materials exhibit nontrivial out-of-plane responses and deformability due to their inherent atomic scale thickness coupled with weak interlayer vdW interactions, which call for a general mechanical framework to quantify such extraordinary characteristics given the structure and material properties. Here, we demonstrate that by considering the competing mechanisms between intralayer stretching, interlayer shearing, and monolayer bending, a general centerline-based theory for multilayered structures is developed to portray the bending landscape of multilayer vdW materials. Combined with large-scale molecular dynamics simulations of three-point bending, we find that when the slenderness ratio or the interlayer shear rigidity is smaller or the intralayer elasticity is higher, the multilayered structures exhibit pronounced nonplanar section deformation due to the interlayer shear capacity. To elucidate quantitative correlations between deformation distribution and structural dimensions and material properties, a critical criterion is proposed to depict the transformation from planar to nonplanar section deformation through a dimensionless characteristic parameter. The effective bending stiffness is then systematically explored in the space of characteristic geometries and material properties to reveal the underlying mechanism of the anomalous size effect. We identify that the effective bending stiffness follows a unified scaling law regarding the dimensionless characteristic parameter. More importantly, a series of deformation-mode phase diagrams are constructed using two universal characteristic lengths, intuitively illustrating the transition of dominated deformation modes and the synergism of geometries and inherent material properties on the bending responses. Validated by several typical vdW materials and novel semiconducting two-dimensional materials, the proposed diagrams not only deepen the understanding of bending in multilayer vdW materials but also provide guidelines for the design and optimization of vdW material-based devices.

Unusual Size Effect in Ion and Charge Transport in Micron‐Sized Particulate Aluminum Anodes of Lithium‐Ion Batteries

Aluminum is a promising anode material for lithium-ion batteries owing to its high theoretical capacity, excellent conductivity, and natural abundance. An anomalous size effect was observed for micron-sized aluminum powder electrodes in this work. Experimental and theoretical investigations reveal that the insulating oxide surface layer is the underlying cause, which leads to poor electrical conductivity and limited capacity utilization when the particle is too small. Additionally, poor electrolyte wettability also accounts for the hindered reaction kinetics due to the weak polarity feature of the oxide layer. Surface grafting of polar amino groups was demonstrated to be an effective strategy to improve electrolyte wettability. The present work revealed the critical limitations and underlying mechanisms for the aluminum anode, which is crucial for its practical application. Our results are also valuable for other metallic anodes with similar issues.

Unusual Size Effect in Ion and Charge Transport in Micron‐Sized Particulate Aluminum Anodes of Lithium‐Ion Batteries

AbstractAluminum is a promising anode material for lithium‐ion batteries owing to its high theoretical capacity, excellent conductivity, and natural abundance. An anomalous size effect was observed for micron‐sized aluminum powder electrodes in this work. Experimental and theoretical investigations reveal that the insulating oxide surface layer is the underlying cause, which leads to poor electrical conductivity and limited capacity utilization when the particle is too small. Additionally, poor electrolyte wettability also accounts for the hindered reaction kinetics due to the weak polarity feature of the oxide layer. Surface grafting of polar amino groups was demonstrated to be an effective strategy to improve electrolyte wettability. The present work revealed the critical limitations and underlying mechanisms for the aluminum anode, which is crucial for its practical application. Our results are also valuable for other metallic anodes with similar issues.

Anomalous size effect on yield strength enabled by compositional heterogeneity in high-entropy alloy nanoparticles

High-entropy alloys (HEAs), although often presumed to be random solid solutions, have recently been shown to display nanometer-scale variations in the arrangements of their multiple chemical elements. Here, we study the effects of this compositional heterogeneity in HEAs on their mechanical properties using in situ compression testing in the transmission electron microscope (TEM), combined with molecular dynamics simulations. We report an anomalous size effect on the yield strength in HEAs, arising from such compositional heterogeneity. By progressively reducing the sample size, HEAs initially display the classical “smaller-is-stronger” phenomenon, similar to pure metals and conventional alloys. However, as the sample size is decreased below a critical characteristic length (~180 nm), influenced by the size-scale of compositional heterogeneity, a transition from homogeneous deformation to a heterogeneous distribution of planar slip is observed, coupled with an anomalous “smaller-is-weaker” size effect. Atomic-scale computational modeling shows these observations arise due to compositional fluctuations over a few nanometers. These results demonstrate the efficacy of influencing mechanical properties in HEAs through control of local compositional variations at the nanoscale.

Anomalous Size Effect of Pt Ultrathin Nanowires on Oxygen Reduction Reaction.

The classical size effect of Pt particles on oxygen reduction reaction (ORR) suggests that the activity and durability would decrease with reducing the particle size, self-limiting the effectiveness in maximizing the Pt utilization efficiency with the particle-size-reduction strategy. Herein, we discover an anomalous size effect based on Pt nanowires (NWs) with tunable diameters, where the monotonically increasing activity and durability for ORR were observed with decreasing the diameter from 2.4 to 1.1 nm. Our results reveal that the dominant role of increased compressive strain induced by decreasing the diameter of NWs in weakening the adsorption and suppressing the Pt dissolution accounts for this anomalous size effect, where the reduced low-coordinated sites on NWs, the intrinsic structural advantage, is the root. Our findings not only expand the knowledge to the classical size effect but also provide new implications to break through the size limit in the design of Pt-based ORR catalysts.

Anomalous size effect in micron-scale CoCrNi medium-entropy alloy wire

Micron-sized CoCrNi medium-entropy alloy (MEA) wires are successfully fabricated by Taylor-Ulitovsky method for the first time. The wires of two different sizes, with diameters of 40 and 100 microns, exhibit an excellent combination of tensile strength and ductility. In-depth microstructure characterization indicates the superior mechanical properties stem from the synergy of Lomer-Cottrell locks, mechanical nano-twinning and HCP stacking. Surprisingly, an anomalous size effect is presented in the tension of these microwires, i.e., the much higher tension strength and ductility are observed in the 40 micron-wire, in sharp contrast to conventional single-principal element alloys only showing negligibly minor tension size effect. Much higher density of geometrically necessary dislocation accompanying heterogeneous deformation is observed in 40 micron-wire, leading to a high strain gradient, which is in turn joined with multiple deformation twins giving rise to high strength and ductility in 40 micron-wire.

Anomalous size effect in thermal residual stresses in pressure sintered alumina-chromium composites

This paper explores an anomalous size effect in thermal residual stresses occurring in the alumina matrix of Al2O3/Cr sintered composite upon varying the particle size of the chromium reinforcement. When a coarse chromium powder (45 μm mean particle size) is used the average residual stress in the alumina phase after cooling is compressive in accordance with the classical Eshelby solution. However, in the case of a fine chromium (5 μm mean particle size) it switches to tension. This effect, detected by photoluminescence piezospectroscopy, is also confirmed by X-ray and neutron diffraction experiments. As the classical micromechanics models are incapable to capture it, a finite element model is developed with the actual composite microstructure being reconstructed from the microtomography images. It is shown by numerical simulations that the anomalous size effect is associated with the complex microstructure of the composite fabricated with the fine chromium powder. It is also pointed out that the temperature dependence of the coefficients of thermal expansion of the matrix and the reinforcement affects the residual stress levels.

Anomalous size effects in nanoporous materials induced by high surface energies

Abstract

A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape-changers or topological insulators: a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations---relevant for small systems---and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials in the thermodynamic limit.

On the domain size effect of thermal conductivities from equilibrium and nonequilibrium molecular dynamics simulations

Equilibrium molecular dynamics (EMD) simulations with the Green-Kubo formula and nonequilibrium molecular dynamics (NEMD) simulations with the Fourier's Law are two widely used methods for calculating thermal conductivities of materials. It is well known that both methods suffer from domain size effects, especially for NEMD. But the underlying mechanisms and their comparison have not been much quantitatively studied before. In this paper, we investigate their domain size effects by using crystalline silicon at 1000 K, graphene at 300 K, and silicene at 300 K as model material systems. The thermal conductivity of silicon from EMD simulations increases normally with the increasing domain size and converges at a size of around 4×4×4 nm3. The converging trend agrees well with the wavelength-accumulated thermal conductivity. The thermal conductivities of graphene and silicene from EMD simulations decrease abnormally with the increasing domain size and converge at a size of around 10×10 nm2. We ascribe the anomalous size effect to the fact that as the domain size increases, the effect of more phonon scattering processes (particularly the flexural phonons) dominates over the effect of more phonon modes contributing to the thermal conductivity. The thermal conductivities of the three material systems from NEMD simulations all show normal domain size effects, although their dependences on the domain size differ. The converging trends agree with the mean free path accumulation of thermal conductivity. This study provides new insights that other than some exceptions, the domain size effects of EMD and NEMD are generally associated with wavelength and mean free path accumulations of thermal conductivity, respectively. Since phonon wavelength spans over a much narrower range than mean free path, EMD usually has less significant domain size effect than NEMD.

Creep rupture due to thermally induced cracking

ABSTRACTWe study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization.

Size Scaling and Bursting Activity in Thermally Activated Breakdown of Fiber Bundles

We study subcritical fracture driven by thermally activated damage accumulation in the framework of fiber bundle models. We show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect; i.e., the average lifetime t{f} decreases as a power law of the system size t{f} approximately L{-z}, where the exponent z depends on the external load sigma and on the temperature T in the form z approximately f(sigma/T{3/2}). We propose a modified form of the Arrhenius law which provides a comprehensive description of thermally activated breakdown. Thermal fluctuations trigger bursts of breakings which have a power law size distribution.

Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a nonplanar way at $T=0$. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}{P}^{3}$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations, and ${\mathbb{Z}}_{2}$ vortices. Extensive Monte Carlo simulations show that the $T=0$ chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and ${\mathbb{Z}}_{2}$ vortices proliferate near the chiral domain walls, explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized ${\mathbb{Z}}_{2}$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size effects suggest the proximity of the present model to a tricritical point. A body of results is presented, which all support this claim: (i) first-order transitions obtained by Monte Carlo simulations on several related models, (ii) approximate mapping between the Ising-$\mathbb{R}{P}^{3}$ model and a dilute Ising model (exhibiting a tricritical point), and, finally, (iii) mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}{P}^{3}$ model.

Thermal conductivity of 4He I from near T lambda to 3.6 K and vapor pressure to 30 bars.

We present new data for the thermal conductivity of liquid $^{4}\mathrm{He}$ along isotherms from 2.1 to 3.6 K, covering the pressure range from vapor pressure to 30 bars, and along isobars from vapor pressure to 28 bars, covering the reduced-temperature range 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$\ensuremath{\lesssim}t [=(T-${T}_{\ensuremath{\lambda}}$)/${T}_{\ensuremath{\lambda}}$]\ensuremath{\lesssim}0.1. Measurements in several cells with spacings from 0.0025 to 0.453 cm revealed no anomalous size effect. For t\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}3}$, the accuracy of the data is 0.2% to 0.3%. Closer to ${T}_{\ensuremath{\lambda}}$ systematic errors due to uncertainties in boundary-resistance corrections gradually increase with decreasing t, and reach about 2% near t=2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$. With decreasing t\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}4}$ random errors due to finite temperature resolution increase also, and reach about 2% near t=2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$.

Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. II. Application to simple liquids

The theory of the previous paper is used to predict anomalous size effects observed for computer simulated liquid Ar. The theoretical results for the boundary condition induced anisotropy of two-particle correlations are found to be large, and in excellent agreement with the computer experimental data of Mandell for densities near the Ar triple point density. The agreement is less good at higher densities.

Kinetic properties of electrons in bismuth thin films

The resistivity ϱ of bismuth films in the absence of a magnetic field exhibits the following features: it decreases with increasing temperature T; the temperature dependence of the resistance has a maximum at low temperatures for very thin films and a minimum at higher temperatures for films of larger thickness; below 1000 Å the conductivity increases with decreasing film thickness L (anomalous size effect); the classical size effect appears as the film thickness increases. For very thin films the magnetoresistance coefficient (in the region ωτ < 1) changes non-monotonically with rising T: at a certain temperature determined by the film thickness a minimum appears and then an anomalous rise in magnetoresistance. From an analysis of the magnetic field dependence of σ xx and σ yx , calculated from our data on ϱ, Δϱ/ϱ and the Hall e.m.f., and using the formula of the two-band model for strong and weak magnetic fields, we obtained the change in concentration ( n,p) and mobility (μ, ν) of the charge carriers with varying T and L, and hence we were able to explain the observed features of their kinetic properties. The appearance of anomalies results both from the resonance scattering of carriers under size quantization and from the non-uniformity of the distribution through the film thickness of carriers of different sign due to potential bending near the surface. This leads to a shift in the electron spectrum characteristics with decreasing Bi film thickness.

Negative Transverse Magnetoresistance in Dilute Polycrystalline Alloys ofAuFe

The field dependence of the negative transverse magnetoresistance has been evaluated from the total effect measured in polycrystalline wires of the $\mathrm{Au}\mathrm{Fe}$ system at 2 and 4.2\ifmmode^\circ\else\textdegree\fi{}K. The solute concentration ranged from 10-400 atomic ppm, and the applied field strengths ranged up to 26 kOe. In making this evaluation, consideration was given to the high-field-low-field transition, the anomalous size effects, the field dependence of the electron's relaxation time, and possible changes in the anisotropy of the solute scattering---considerations which will be relevant to similar measurements carried out on dilute alloys of analogous Kondo systems. For sufficiently concentrated samples, the negative component is shown to vary linearly with the square of the effective magnetization obtained from other work.