Influence of atomic force microscope (AFM) probe shape on adhesion force measured in humidity environment

In micro-manipulation, the adhesion force has very important influence on behaviors of micro-objects. Here, a theoretical study on the effects of humidity on the adhesion force is presented between atomic force microscope （AFM） tips and substrate. The analysis shows that the precise tip geometry plays a critical role on humidity depen- dence of the adhesion force, which is the dominant factor in manipulating micro-objects in AFM experiments. For a blunt （paraboloid） tip, the adhesion force versus humidity curves tends to the apparent contrast （peak-to-valley corrugation） with a broad range. This paper demonstrates that the abrupt change of the adhesion force has high correla- tion with probe curvatures, which is mediated by coordinates of solid-liquid-vapor contact lines （triple point） on the probe profiles. The study provides insights for further under- standing nanoscale adhesion forces and the way to choose probe shapes in manipulating micro-objects in AFM experiments.     

Surface instability of a semi-infinite anisotropic elastic body under surface van der Waals forces

We investigate the surface instability of an anisotropic elastic half-plane subjected to surface van der Waals forces due to the influence of another rigid contactor by means of the Stroh formalism. It is observed that the surface of a generally anisotropic elastic half-plane subjected to van der Waals forces from another rigid flat is always unstable. The wave number of the surface wrinkling is only reliant on the positive M₂₂ component of the 3 × 3 surface admittance tensor M, the van der Waals interaction coefficient β and the surface energy γ of the elastic half-plane. The decay rate of surface perturbation along the direction normal to the surface of the anisotropic half-plane is different from the wave number, a phenomenon different from that observed for an isotropic half-plane.     

相对湿度对材料表面粘附力影响的研究

利用自制微摩擦及粘附力测试装置考察了在微载荷条件下,相对湿度对Si(100)材料表面粘附力的影响,分析了在大气环境中水分子的毛细作用力和范德华力对粘附力的贡献,并以BET吸附模型为基础推导出考虑湿度影响的粘附力计算公式.结果表明:在微载荷条件下,相对湿度对材料表面的粘附力影响十分显著,随着相对湿度升高粘附力增加,特别是相对湿度RH在40%～80%之间时,粘附力变化最为显著;当相对湿度RH小于20%时,范德华力大于水的毛细作用力且占主导地位;当相对湿度RH大于20%后,水分子的毛细作用力不断增加,同时范德华力因水膜的存在而降低,水的毛细作用力占主导地位.     

Chaotic flexural oscillations of a spinning nanoresonator

The paper investigates the chaotic flexural oscillations of the spinning nanoresonator. The influence of cubic nonlinearity arising from the van der Waals interactions between two neighboring layers of carbon nanotubes on the structural oscillations of the system is considered. The integral–differential equations describing the flexural displacements of the nanoresonator are discretized into two coupled Duffing-type equations using the Galerkin–Ritz procedures. The linear stiffness can be either positive or negative, depending on the amplitudes of the linear trap rigidity arising from both the van der Waals interactions and the axial tensile loads. The chaotic flexural oscillations of the appropriately excited spinning nanoresonator are predicted theoretically. Using the Nayfeh–Mook multiscale perturbation algorithms, the coupled Duffing-type equations with linear positive stiffness may be transformed into autonomous equations of slowly modulated amplitudes whose equilibrium points and chaotic dynamics are investigated numerically. The potential chaotic oscillations of the elastic nanoresonator can be determined by the Melnikov–Holmes–Marsden (MHM) integral associated with the homoclinic/heteroclinic solutions of the disturbed Hamiltonian systems with linear negative stiffness. The findings are validated through the Poincare sections and Lyapunov exponents.     

Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction

The linear bifurcation theory is used to investigate the stability of soft thin films bonded to curved substrates. It is found that such a film can spontaneously lose its stability due to van der Waals or electrostatic interaction when its thickness reduces to the order of microns or nanometers. We first present the generic method for analyzing the surface stability of a thin film interacting with the substrate and then discuss several important geometric configurations with either a positive or negative mean curvature. The critical conditions for the onset of spontaneous instability in these representative examples are established analytically. Besides the surface energy and Poisson's ratio of the thin film, the curvature of the substrate is demonstrated to have a significant influence on the wrinkling behavior of the film. The results suggest that one may fabricate nanopatterns or enhance the surface stability of soft thin films on curved solid surfaces by modulating the mechanical properties of the films and/or such geometrical properties as film thickness and substrate curvature. This study can also help to understand various phenomena associated with surface instability.     

A diffuse-interface approach to two-phase isothermal flow of a Van der Waals fluid near the critical point

A novel numerical method for simulations of isothermal, compressible two-phase flows of one fluid component near the critical point is presented on the basis of a diffuse-interface model and a Van der Waals equation of state. Because of the non-convexity of the latter, the nature of the set of governing equations is mixed hyperbolic–elliptic. This prevents the application of standard numerical methods for compressible flow. Moreover, the Korteweg capillary stress tensor, characteristic for the diffuse-interface approach, introduces third-order spatial derivatives of mass density in the Navier–Stokes equation, resulting in a dispersive behavior of the solution. Our computational method relies on a transformation of the conserved variables, which controls dispersion, stabilizes the numerical simulation and enables the use of coarser grids. A one-dimensional simulation shows that this method provides better stability and accuracy than without transformation of variables. Two- and three-dimensional simulations for isothermal liquid–vapor flows, in particular the retraction of a liquid non-spherical drop in vapor and the binary droplet collision in vapor, show the applicability of the method. The surface tension calculated from the numerical results is in good agreement with its theoretical value if the computational grid is sufficiently fine.     

Spinodal surface instability of soft elastic thin films

When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.     

Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium

The torsional buckling of a double-walled carbon nanotube embedded in an elastic medium is studied in this paper. The effects of surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model is presented for the torsional buckling of a double-walled carbon nanotube. Based on the model, a condition is derived in terms of the buckling modes of the shell and the parameters describing the effect of van der Waals interaction and surrounding elastic medium. A simplified analysis is also carried out estimate the critical torque for torsional buckling of the double-walled carbon nanotube.     

范德华力对计算机磁头/磁盘超薄气膜承载性能的影响

在纳米间隙条件下,以楔型滑块和双轨式磁头为例,推导出楔型及双轨式磁头范德华力的计算公式,考察了范德华力对计算机磁头/磁盘超薄气膜承载性能的影响.结果表明,范德华力对计算机磁头/磁盘的承载性能影响很大,范德华力可以降低磁头的承载能力,尤其在最小空气间隙小于6 nm时;在相同尺寸的磁头中,双轨式磁头的范德华力小于楔型滑块的范德华力,而前者的承载力大于后者,双轨式磁头的范德华力对其承载性能影响较小.范德华力可以使飞行高度降低,为磁头设计和磁头/磁盘装配的重要依据.     

DEM simulation of soil-tool interaction under extraterrestrial environmental effects

In contrast to terrestrial environment, the harsh lunar environment conditions include lower gravity acceleration, ultra-high vacuum and high (low) temperature in the daytime (night-time). This paper focuses on the effects of those mentioned features on soil cutting tests, a simplified excavation test, to reduce the risk of lunar excavation missions. Soil behavior and blade performance were analyzed under different environmental conditions. The results show that: (1) the cutting resistance and the energy consumption increase linearly with the gravity. The bending moment has a bigger increasing rate in low gravity fields due to a decreasing moment arm; (2) the cutting resistance, energy consumption and bending moment increase significantly because of the raised soil strength on the lunar environment, especially in low gravity fields. Under the lunar environment, the proportions of cutting resistance, bending moment and energy consumption due to the effect of the van der Waals forces are significant. Thus, they should be taken into consideration when planning excavations on the Moon. Therefore, considering that the maximum frictional force between the excavator and the lunar surface is proportional to the gravity acceleration, the same excavator that works efficiently on the Earth may not be able to work properly on the Moon.     

Microbuckling of a doublewalled carbon nanotube embedded in an elastic matrix

Microbuckling of a doublewalled carbon nanotube (DWCNT) in an elastic (polymer) matrix is studied. The investigations are made within the scope of the piecewise homogeneous body model by utilizing the three-dimensional linearized theory of stability of deformable bodies. Flexural and axisymmetric microbuckling modes are considered. The DWCNT is modeled as concentrically-nested two circular hollow cylinders between which there is free space. It is assumed that on the inner surface of the outer tube (cylinder) and on the outer surface of the inner tube (cylinder) of the DWCNT full slipping conditions occur. At the same time, it is assumed that the difference between the radial displacements of the adjacent surfaces of the tubes resists with the van der Waals forces. On the interface between the matrix and DWCNT complete contact conditions are satisfied. Numerical results on the influence of the problem parameters on the critical deformation are presented and discussed. Also, numerical results related to the cases where the interlayer space is ignored and where full contact between the tubes is assumed are presented and compared with the mentioned results. In particular, it is established that full slipping between the tubes causes the values of the critical deformation to decrease significantly with respect to those obtained in the case where complete contact conditions occur between the tubes. Moreover, it is established that an increase in the values of the van der Waals forces also causes a decrease in the values of the critical compressing strain and the magnitude of this decrease depends on the thicknesses of the tubes of the DWCNT.     

Effects of camberwise varying tip injection on loss and wake characteristics of a low pressure turbine blade

This paper presents the results of an experimental study that investigates the effects of camberwise varying tip injection on the total pressure loss and wake flow characteristics downstream of a row of Low Pressure Turbine (LPT) blades. This injection technique involves spanwise jets at the tip that are issued from a series of holes distributed along the camber line. The injection from each hole is individually and separately controlled using a computer driven solenoid valve and therefore the flow injection geometrical pattern at the tip can be adjusted to any desired variation. Three different injection cases are investigated including triangular, reversed triangular and uniform injection patterns. Here, triangular and reversed triangular cases refer to discrete blowing from the blade tip in which the blowing velocity increases (triangular) or decreases (reverse triangular) linearly from the leading to trailing edge along the camber. For uniform injection, the injection velocity is kept constant for all injection holes. The total mass injection from the tip is kept the same for all injection cases. The experiments are conducted in a continuous-flow wind tunnel with a linear cascade test section and measurements involve Kiel probe traverses 0.5 axial chords downstream of the blades covering a region between 85% and 100% span as well as two-dimensional Particle Image Velocimetry (PIV) measurements on 50%, 85% and 95% spanwise planes. For all injection cases, results show that tip injection reduces the total pressure loss levels in general. Highest measured overall loss reduction occurs in the case of reversed-triangular injection. The least effective waveform is observed to be triangular injection. There is significant reduction in the extent of the low momentum zone of the leakage vortex with injection. This effect is much less pronounced for the passage vortex. On the other hand, complex flow patterns are observed within the passage vortex, especially in the case of reversed-triangular injection, such as a possible embedded vortical structure along the passage vortex core, which creates double peaks in the velocity and turbulent kinetic energy fields.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates. Three different systems have been considered. In the first system the interaction between particles has been simulated using the JKR （Johnson, Kendall and Roberts） contact theory, while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively. In order to compare the mechanical behaviour of the three systems, the magnitude of the maximum attractive force between particles has been kept the same in all cases. However, the relationship between force and separation distance differs from case to case and thus, the range of the interparticle force. The results clearly indicate that as the range of the interparticle force increases, the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates.Three different systems have been considered.In the first system the interaction between particles has been simulated using the JKR (Johnson,Kendall and Roberts) contact theory,while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively.In order to compare the mechanical behaviour of the three systems,the magnitude of the maximum attractive force between particles has been kept the same in all cases.However,the relationship between force and separation distance differs from case to case and thus,the range of the interparticle force.The results clearly indicate that as the range of the interparticle force increases,the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

Evolution of planar and cylindrically symmetric magneto-acoustic waves in a van der Waals fluid

We consider a quasilinear system of partial differential equations (PDEs) governing the one-dimensional unsteady planar and cylindrically symmetric motion of an electrically conducting van der Waals fluid permeated with a transverse magnetic field. An asymptotic method is used to derive an evolution equation that governs the wave amplitude in the far field. Our main objective is to study the evolution equation, and to investigate as to how the presence of magnetic field and geometrical spreading (in cylindrical case) along with the cubic nonlinearity, inherently present in the system, influence the wave structure that finally develops.     

Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf (1970) and Molerus (1975). The flow properties of fluid cracking catalyst (FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500 °C. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.     

On the relationship between the work of adhesion and the critical shear stress for the onset of flow instabilities

The relationship between the critical shear stress for the onset of flow instabilities and the work of adhesion at the interface has been evaluated experimentally for a series of polyolefins on several steels, brasses, and coated steels. The critical shear stress was considerably affected by the chemical nature of the die. Low-surface-energy materials were found to produce smooth extrudates presumably by inducing slippage at the wall. Steel, tungsten carbide, and brass surfaces promoted sharkskin defect at shear stresses above the first critical shear stress. A linear relationship between the critical shear stress and the work of adhesion was found to be valid for values of work of adhesion smaller than approximately 30 mN/m. This indicates that slippage occurs due to a breakdown of the adhesion at the interface. For values of work of adhesion greater than approximately 30 mN/m a stronger interaction at the interface may induce a cohesive failure at the interface and subsequently, extrudate distortions.     

两种不同形状压头与单晶铜基体间接触力和摩擦力的纳观分析

在考虑单晶铜基体弹塑性形变和晶体各向异性情况下,基于原子尺度,采用混合势函数(EAM和Morse)和Verlet算法动态模拟了半球形和圆锥形两种不同形状压头与单晶铜基体的黏着接触和滑动摩擦过程,分析了接触力和摩擦力对单晶铜基体内失效原子变化情况.研究表明:当压头下压位移为0.9 nm时,由于半球形压头比圆锥形压头底部表面积大,导致半球形压头与基体之间的引力更大而更易产生黏着接触现象.在下压接触过程中,与半球形压头相接触的基体内出现位错原子长大成位错环,而与圆锥形压头相接触的基体未出现此位错环现象,但位错原子数均随压深的增加而增多;在滑动过程中,因半球形压头对基体的摩擦力和法向力比圆锥形压头对基体的摩擦力和法向力大,使得半球形压头比圆锥形压头正前方堆积的位错原子数多,但均随滑动距离的增加而增多.     

The relation between a microscopic threshold-force model and macroscopic models of adhesion

This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale(Hulikal et al., J. Mech. Phys. Solids 76,144–161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally,while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study roughsurface adhesion.