Multipoint contact modeling of nanoparticle manipulation on rough surface

In this paper, the atomic force microscopy (AFM)-based 2-D pushing of nano/microparticles investigated on rough substrate by assuming a multipoint contact model. First, a new contact model was extracted and presented based on the geometrical profiles of Rumpf, Rabinovich and George models and the contact mechanics theories of JKR and Schwartz, to model the adhesion forces and the deformations in the multipoint contact of rough surfaces. The geometry of a rough surface was defined by two main parameters of asperity height (size of roughness) and asperity wavelength (compactness of asperities distribution). Then, the dynamic behaviors of nano/microparticles with radiuses in range of 50–500 nm studied during their pushing on rough substrate with a hexagonal or square arrangement of asperities. Dynamic behavior of particles were simulated and compared by assuming multipoint and single-point contact schemes. The simulation results show that the assumption of multipoint contact has a considerable influence on determining the critical manipulation force. Additionally, the assumption of smooth surfaces or single-point contact leads to large error in the obtained results. According to the results of previous research, it anticipated that a particles with the radius less than about 550 nm start to slide on smooth substrate; but by using multipoint contact model, the predicted behavior changed, and particles with radii of smaller than 400 nm begin to slide on rough substrate for different height of asperities, at first.     

Dynamic modeling of manipulation of micro/nanoparticles on rough surfaces

In this paper, the dynamic behavior of spherical micro/nanoparticles, while being pushed on rough substrates, is studied by means of an Atomic Force Microscope (AFM). For this purpose, first, the contact adhesion force, and the areas and penetration depths of rough surfaces are derived based on the Johnson-Kendall-Roberts (JKR) theory, the Schwarz method, and the Rumpf/Rabinovich models. Then, the dynamic model of particle manipulation on rough substrates is revised using the specified contact theory for rough surfaces. And finally, the pushing of spherical particles with 50, 100, 200, 500, and 10000 nm radii is simulated. The results show that the critical force and the critical time of manipulation decrease when the particles are pushed on the rough surfaces as compared to the smooth ones. It is also observed that the critical force for a rough substrate containing asperities of low height and large radius approaches a comparable critical force magnitude to the smooth substrate, as is expected. Also, when the asperity radius in the substrate is within the range of 0.5 < r < 5 nm, the critical force of pushing decreases; however, as the asperity radius becomes larger than 5 nm, the critical force begins to increase again. Furthermore, the critical values are generally more sensitive to the changes of the asperity radius than the height. It is also found that the difference between the critical values based on the Rumpf and Rabinovich models is negligible. However, the estimation of particles’ dynamic behavior using the Rumpf model could be wrong for the rough substrates with small radius asperities, which is considerable in the manipulation and assembly practices. Moreover, the dynamic behavior of particles of small radius (r < 500 nm) change during the pushing process on rough surfaces, and the rolling behavior could be possible on the surfaces that have small radius asperities. The probability of this occurrence is increased in the pushing of larger particles on rougher substrates.     

纳米接触过程中黏着规律的变化

本文应用大规模分子动力学方法, 模拟了两种具有不同粗糙形貌的、刚性球形探头与弹性平面基体之间的纳米尺度接触, 计算了探头与基体之间的拉离力和黏着功, 研究了接触过程中界面黏着力随载荷的变化规律, 分析了接触界面原子的法向应力分布. 研究发现, 原子级光滑接触的黏着力随着载荷的增大而线性增大, 而原子级粗糙接触的黏着力-载荷曲线分为以不同斜率增长的两个阶段. 相比于原子级光滑探头, 原子级粗糙探头与基体之间具有较小的拉离力和黏着功, 却在接触过程中形成了较大的黏着力. 因此, 拉离力和黏着功不能表征出纳米接触过程中原子吸引作用对界面法向力的贡献大小.     

表面黏附导致的接触行为转变

应用大规模分子动力学方法, 模拟了具有不同原子级粗糙形貌的两种刚性球形探头与弹性平面基体的黏附接触行为. 研究了载荷与真实接触面积、接触界面排斥力与真实接触面积, 以及黏附力与真实接触面积之间的关系. 分子模拟得到的载荷与真实接触面积的关系, 与连续力学接触理论预测很好地定性一致. 无论是原子级光滑探头还是粗糙探头, 黏附接触下的排斥力与真实接触面积的关系, 都与无黏附接触时的规律相一致, 即黏附力对接触行为的影响作用, 可以等效为附加在真实外载荷基础上的虚拟载荷, 将对黏附接触行为的分析转变为无黏附接触分析. 两种探头的黏附力随真实接触面积都呈幂函数形式的增长, 但是, 原子级光滑探头的幂指数大于1, 而原子级粗糙探头的幂指数小于1. 关键词： 接触行为 表面黏附 分子动力学模拟     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

溶液液滴蒸发变干的环状沉积

液体蒸发驱动的颗粒自组装现象在许多的工业技术中有重要应用. 本文利用显微镜观测含有颗粒物质的液滴变干后留在固体表面的颗粒形成的环状沉积图案. 采用微米粒径的SiO₂小球水溶液液滴蒸发变干模拟咖啡环的形成过程, 结果发现液滴蒸发过程中接触线的钉扎是环状沉积的必要条件. 在液滴蒸发过程中颗粒随着补偿流不断的向液滴边缘移动, 聚集在接触线处形成环. 液滴蒸发变干后残留在液滴内部的颗粒数随颗粒质量分数的增加而增加, 可以达到单层的颗粒排列. 而玻璃衬底上的颗粒环在颗粒质量分数很小时, 形成单层排列, 且一排一排地生长. 蒸发过程中颗粒环由于液滴边缘的尺寸限制向液滴中心缓慢移动. 这会导致液滴中不同大小颗粒的分离. 关键词： 液滴 接触线 蒸发 颗粒     

Rolling resistance moment of microspheres on surfaces

In the current work, for the first time, the existence of a rolling moment of resistance of an adhesion bond between a microsphere and flat surface subjected to external dynamic force has been experimentally demonstrated. The rotational motion of spherical particles deposited on a wafer is excited in the 0–3.5?MHz range using a piezoelectric transducer. The approach is based on (i) the observation that the contribution of the rotational (rocking) motion to the axial displacement of the particle are few orders of magnitude higher than those of the purely axial motion and (ii) the existence of a relationship between the rotational natural frequency of the adhesion bond and the work of adhesion. The natural frequency of the rotational (rocking) motion is extracted from the low frequency components of the transient response of the particle in the axial direction, which is measured by a laser interferometer. The existing theoretical adhesion models for rolling resistance moment are evaluated using the experimental results. Good agreement between the theoretical predictions and experimental values is found.     

Rolling resistance moment of microspheres on surfaces: contact measurements

Using contact measurements, experimental evidence was obtained for the existence of the rolling resistance moment. The critical rolling distance prior to detachment is reported. Previously it has been argued that the critical rolling distance should be related to the lattice size and/or the molecular length of the particle and surface materials. However, there has been no theoretical prediction for the critical value and, currently, the reasons for its existence are not fully understood. For polystyrene latex (PSL) particles, measurements presented in the current study on silicon suggest much higher values for the critical rolling distance than previous anticipated levels. The current approach can also be employed to measure the work of adhesion between a spherical particle and a flat surface without the prior knowledge of the particle diameter since the rolling moment stiffness is directly proportional to the work of adhesion with no dependence on the diameter of the particle. Experimental results are compared with the available data and good agreement between the theoretical predictions and the experimental values is found.     

On the Sensitivity of Adhesion between Rough Surfaces to Asperity Height Distribution

There has been a long debate about the validity of asperity models in the contact between rough surfaces, much of it concentrated on relatively minor aspects of the solution for the special case of Gaussian random processes for roughness, like the exact value of the area-load slope or the extent of the linear regime. It is shown here that in the case of adhesion, the behavior is extremely sensitive to the shape of the height distribution. We show for example results for Weibull distributions, which has been suggested in a number of practical cases from macroscopic to nanoscopic roughness. Pull-off force is found to vary by several orders of magnitude both lower and higher than in the Gaussian case, whereas the "stickiness" criterion on the adhesion parameter changes by an order of magnitude. Additionally, in some operations like chemical-mechanical polishing, tails are almost completely removed and a sharp peak develops instead of a tail: modeling this with contact on the bounded side of the Weibull distribution, stickiness seems to occur for any level of roughness. Pome qualitative comparison with recent numerical experiments is attempted.     

Wetting property of smooth and textured hydrophobic surfaces under condensation condition

Static and dynamic wetting behaviors of sessile droplet on smooth, microstructured and micro/nanostructured surface under condensation condition are systematically studied. In contrast to the conventional droplet wetting on such natural materials by dropping, we demonstrate here that when dropwise condensation occurs, the sessile droplet will transit from the Cassie-Baxter wetting state to the Wenzel wetting state or partial Cassie-Baxter wetting state on the microstructured surface or the micro/nanostructured surface, which leads to a strong adhesion between the droplet and the substrate. In contrast, the apparent contact angle and the sliding angle on the smooth surface changes a little before and after the condensation because of small roughness. Theoretical analysis shows that the roughness factor controls the adhesion force of the droplet during condensation, and a theoretical model is constructed which will be helpful for us to understand the relationship between the adhesion force and the geometry of the surface.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

A multiscale molecular dynamics approach to contact mechanics

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.     

A Study of Resuspended Particles from a Line Bed at the Wall of a Fluid Flow. Statistical Aspects

A statistical analysis of the dynamic behaviour of a bed of particles on the wall of a fluid flow is presented. By applying the different forces acting on each particle, i.e. fluid forces, adhesion to the wall and autohesion forces, conditions needed to obtain possible motions are determined and motions of the last downstream particle are described. It is shown that, above a critical value, increasing flow rate will promote the re-entrainment process along the wall, whereas increasing adhesion and autohesion forces will maintain the line bed stationary. Moreover, in some circumstances, starting particles execute some small jumps before rolling and/or sliding along the wall, which reduces the residence time of the particle on the wall. These results confirms some published hypotheses.     

Effects of the ultrasonic flexural vibration on the interaction between the abrasive particles; pad and sapphire substrate during chemical mechanical polishing (CMP)

In this paper, the technique of ultrasonic flexural vibration assisted chemical mechanical polishing (UFV-CMP) was used for sapphire substrate CMP. The functions of the polishing pad, the silica abrasive particles, and the chemical additives of the slurry such as pH value regulator and dispersant during the sapphire's UFV-CMP were investigated. The results showed that the actions of the ultrasonic and silica abrasive particles were the main factors in the sapphire material removal rate (MMR) and the chemical additives were helpful to decrease the roughness of sapphire. Then the effects of the flexural vibration on the interaction between the silica abrasive particles, pad and sapphire substrate from the kinematics and dynamics were investigated to explain why the MRR of UFV-CMP was bigger than that of the traditional CMP. It indicated that such functions improved the sapphire's MRR: the increasing of the contact silica particles’ motion path lengths on the sapphire's surface, the enhancement of the contact force between the contact silica particles and the sapphire's surface, and the impaction of the suspending silica particles to the sapphire's surface.     

Ultraviolet laser removal of small metallic particles from silicon wafers

Laser removal of small 1 μm sized copper, gold and tungsten particles from silicon wafer surfaces was carried out using ultraviolet radiation at 266 nm generated by Nd:YAG harmonic generation. Successful removal of both copper and gold particles from the surface was achieved whereas tungsten particles proved to be difficult to remove. The cleaning efficiency was increased with an increase of laser fluence. The optimum processing window for safe cleaning of the surface without any substrate damage was determined by measuring the damage threshold laser fluence on the silicon substrate and the required fluence for complete removal of the particles. The different cleaning efficiencies with particle type are discussed by considering the adhesion force of the particle on the surface and the laser-induced cleaning force for the three different particles.     

Influence of surface roughness on adhesion between elastic bodies

We study the influence of surface roughness on the adhesion between elastic solids. We present experimental data for the force necessary to pull off rubber balls from hard rough substrates. We show that the effective adhesion (or the pull-off force) can be calculated accurately from the surface roughness power spectra obtained from the measured surface height profile.     

Experimental Study on Powder Flowability Using Vibration Shear Tube Method

The flowability of powders with different mass median diameters ranging from micrometers to nanometers was measured using the vibration shear tube method. In the measurement system used in this study, the powder was discharged through a narrow gap between a vibrating tube edge and a flat bottom surface, where each particle could experience high shear forces to overcome the adhesion and friction forces. The vibration amplitude was increased during the measurement, and the mass of particles discharged was measured at constant time intervals. From the relationship between the mass flow rate and the vibration acceleration, static and dynamic properties of the powders were evaluated using the critical vibration acceleration, characteristic mass flow rate, and gradient of mass flow rate. The correlation between the static and dynamic properties was studied in detail.     

基于超二次曲面的颗粒材料缓冲性能离散元分析

自然界或工业中普遍是由非球形颗粒组成的复杂体系,与球形颗粒相比,非球形颗粒间的高离散和咬合互锁可使冲击载荷引起的能量有效衰减实现缓冲作用.基于连续函数包络的超二次曲面单元能准确地描述非球形颗粒的几何形态,并可精确地计算单元间的接触碰撞作用.本文采用离散元方法对冲击载荷作用下非球形颗粒物质的缓冲性能进行数值分析,并与圆柱体冲击的理论结果和球体冲击的实验结果进行对比验证.在此基础之上,进一步研究了筒底作用力在不同颗粒层厚度和形状等因素影响下的变化规律.计算结果表明:不同颗粒形状都存在一个临界厚度H_c.当HH_c时,缓冲率随H的增加而增加;当HH_c时,缓冲率的变化不再显著并趋于稳定值.此外,减小颗粒表面尖锐度和增加或减小圆柱形和长方形颗粒的长宽比都会提高颗粒材料的缓冲效果.     

Effect of particle adhesion and interactions on motion by traveling waves on an electric curtain

A discrete-element/boundary-element method is developed for simulation of adhesive particle transport by traveling waves on an electric curtain. The study shows that both wall adhesion and particle–particle collisions have an important influence on particle transport on electric curtains at different wave frequencies. The most significant effect of particle collisions occurs for cases with medium frequencies in which particles with large negative-charge collect in high-concentration bands and move in a synchronous surfing mode, pushing forward particles with lower charge. Cases with higher and lower frequencies exhibited hopping motion, for which adhesion determines the range of non-transported particles.     

正癸烷纳米液滴润湿特性的分子动力学研究

流体液滴在固体表面的浸润性对其润滑性能至关重要.本文利用分子动力学方法研究了正癸烷纳米液滴在铜表面上的润湿特性.结果表明：在平坦光滑表面上,壁面的厚度和分子数目对润湿效果影响不大.随着壁面能量势阱参数εs 增大,接触角线性减小.随着温度升高,液滴的接触角减小.在沟槽粗糙表面上,随着粗糙度因子增大,对于疏液表面,接触角增大到一定值后基本保持不变,符合Cassie理论;中性和亲液表面接触角则会减小,为Wenzel润湿模式.当表面分数增大时,疏液与亲液表面接触角整体呈减小的趋势,对中性表面影响不大.当温度升高时,粗糙疏液表面接触角会增大,润湿效果更差,而粗糙中性和亲液表面液滴润湿性会更好.