ENERGY DISSIPATION IN TAPPING MODE ATOMIC FORCE MICROSCOPY

原子力显微镜有多种成像模式,其中轻敲模式是最为常用的扫描方式.轻敲模式能获取样品表面形貌的高度信息和相位信息,其中相位信息具有更多的价值,如能反映样品的表面能、弹性、亲疏水性等.依据振动力学理论,相位与振动系统的能量耗散有关.探针样品间的能量耗散对于理解轻敲模式下原子力显微镜的成像机理至关重要,样品特性和测量环境会影响能量耗散.本文在不考虑毛细力影响下,基于JKR接触模型,给出了探针样品相互作用下的加卸载曲线,结合原子力显微镜力曲线实验,给出了探针-样品分离失稳点的位置,从而计算一个完整接触分离过程的能量耗散,进而讨论考虑表面粗糙度对能量耗散的影响.在轻敲模式下考虑毛细力影响,通过特征时间对比,证明挤出效应是液桥生成的主导因素,在等容条件下,用数值方法计算了不同相对湿度对能量耗散的影响.通过一维振子模型,简要说明原子力显微镜相位像与样品表面能、杨氏模量、表面粗糙度、相对湿度之间的关系.分析表明,表面粗糙度和环境湿度均会引起相位的变化,进而认为它们是引起赝像的因素.     

A new type of atomic force microscope based on chaotic motions

Local flow variation (LFV) method of non-linear time series analysis is applied to develop a chaotic motion-based atomic force microscope (AFM). The method is validated by analyzing time series from a simple numerical model of a tapping mode AFM. For both calibration and measurement procedures the simulated motions of the AFM are nominally chaotic. However, the distance between a tip of the AFM and a sample surface is still measured accurately. The LFV approach is independent of any particular model of the system and is expected to be applicable to other micro-electro-mechanical system sensors where chaotic motions are observed or can be introduced.     

轻敲模式下 AFM 动力学模型及能量耗散机理研究

轻敲模式下探针从远离到间歇性接触样品表面,是一个连续的能量耗散过程.针对该连续过程的能量耗散机理研究仅零星存在于各个文献之中,对于连续过程中各个阶段的能量耗散机理也没有一个系统的解释和实验验证.本文提出了新的位移激励下原子力显微镜探针-样品系统简化模型并得到了一维振子系统等效阻尼的计算方法,并通过该方法计算了探针在远离样品表面时的空气黏性阻尼和靠近样品时的空气压膜阻尼,分析了探针从远离样品到间歇性接触样品表面这一过程中的环境耗散机理变化,得到了原子力显微镜系统理论品质因数与探针工作位置的关系曲线;在此基础上设计了轻敲模式下的微悬臂梁扫频实验,得到了系统实验品质因数与探针工作位置的关系曲线,进而验证了理论模型的准确性. 本文通过对轻敲模式下AFM环境耗散机理进行理论分析和实验验证,希望可以对轻敲模式下AFM动力学特性及其阻尼作用机理有更近一步的认识,同时对微纳米机电系统 (MEMS/NEMS) 能量耗散机理的研究提供理论参考和实验方法.      

STUDY ON A DYNAMICS MODEL OF TAPPING MODE AFM AND ENERGY DISSIPATION MECHANISM$^{\bf 1)}$

轻敲模式下探针从远离到间歇性接触样品表面,是一个连续的能量耗散过程.针对该连续过程的能量耗散机理研究仅零星存在于各个文献之中,对于连续过程中各个阶段的能量耗散机理也没有一个系统的解释和实验验证.本文提出了新的位移激励下原子力显微镜探针-样品系统简化模型并得到了一维振子系统等效阻尼的计算方法,并通过该方法计算了探针在远离样品表面时的空气黏性阻尼和靠近样品时的空气压膜阻尼,分析了探针从远离样品到间歇性接触样品表面这一过程中的环境耗散机理变化,得到了原子力显微镜系统理论品质因数与探针工作位置的关系曲线;在此基础上设计了轻敲模式下的微悬臂梁扫频实验,得到了系统实验品质因数与探针工作位置的关系曲线,进而验证了理论模型的准确性. 本文通过对轻敲模式下AFM环境耗散机理进行理论分析和实验验证,希望可以对轻敲模式下AFM动力学特性及其阻尼作用机理有更近一步的认识,同时对微纳米机电系统 (MEMS/NEMS) 能量耗散机理的研究提供理论参考和实验方法.     

原子力显微镜探针振动的简化模型分析

为对原子力显微镜(atomic force microscope,AFM)的微悬臂梁进行定性动力学特性分析,建立AFM微悬臂梁的简化模型,探讨AFM探针的受迫振动.通过理论计算得出AFM探针简化模型的运动方程,并得到振动波形,证明了AFM实际应用中的对称问题和"频漂"问题,并发现AFM简化模型的间歇式碰撞现象.用负弹簧模拟探针针尖与样品之间的长程引力,并通过理论计算探讨长程引力对AFM测量的影响.     

On the dynamics of tapping mode atomic force microscope probes

A?mathematical model is developed to investigate the grazing dynamics of tapping mode atomic force microscopes (AFM) subjected to a base harmonic excitation. A?multimode Galerkin approximation is utilized to discretize the nonlinear partial differential equation of motion governing the cantilever response and associated boundary conditions and obtain a set of nonlinearly coupled ordinary differential equations governing the time evolution of the system dynamics. A?comprehensive numerical analysis is performed for a wide range of the excitation amplitude and frequency. The tip oscillations are examined using nonlinear dynamic tools through several examples. The non-smoothness in the tip/sample interaction model is treated rigorously. A?higher-mode Galerkin analysis indicates that period doubling bifurcations and chaotic vibrations are possible in tapping mode microscopy for certain operating parameters. It is also found that a single-mode Galerkin approximation, which accurately predicts the tip nonlinear responses far from the sample, is not adequate for predicting all of the nonlinear phenomena exhibited by an AFM, such as grazing bifurcations, and leads to both quantitative and qualitative errors.     

Theory of amplitude modulation atomic force microscopy with and without Q-Control

The present text reviews the fundamentals of amplitude-modulation atomic force microscopy (AM-AFM), which is frequently also referred to as dynamic force microscopy, non-contact atomic force microscopy, or “tapping mode” AFM. It is intended to address two different kinds of readerships. First, due to a thorough coverage of the theory necessary to explain the basic features observed in AM-AFM, it serves theoreticians that would like to gain overview on how nanoscale cantilevers interacting with the surrounding environment can be used to characterize nanoscale features and properties of suitable sample surfaces. On the other hand, it is designed to introduce experimentalists to the physics underlying AM-AFM measurements to a degree that is not too specialized, but sufficient to allow them measuring the quantities they need with optimized imaging parameters.More specifically, this article first covers the basics of the various driving mechanisms that are used in AFM imaging modes relying on oscillating cantilevers. From this starting point, an analytical theory of AM-AFM is developed, which also includes the effects of external resonance enhancement (“Q-Control”). This theory is then applied in conjunction with numerical simulations to various situations occurring while imaging in air or liquids. In particular, benefits and drawbacks of driving exactly at resonance frequency are examined as opposed to detuned driving. Finally, a new method for the continuous measurement of the tip-sample interaction force is discussed.     

微观摩擦学研究进展

早在十九世纪中叶就有人试图从原子、分子水平上揭示摩擦过程的本质，然而直到原子力显微镜和摩擦力显微镜问世之后的本世纪八十年代，学术界才明确提出了微观摩擦学这个概念。为了推动微观摩擦学的发展，对微观摩擦学的研究方法及其最新研究进展作了综合介绍与评述。微观摩擦学在基础研究方面首先是从边界润滑之研究提出的，而在应用方面则是从磁头－盘之润滑提出的；在研究方法上主要是原子力显微镜、ＬＢ膜技术、表面力装置、石英晶体微量天平、红外、电子能谱和计算机分子动力学模拟等。目前，微观摩擦学主要应用于高密度磁纪录介质的摩擦学研究，同时还应用于微型机械和大规模集成电路的制造，以及微观摩擦、粘着与磨损行为的基础研究等方面，除此以外，还简明地指出了今后微观摩擦学研究应当重视的若干问题。     

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.     

原子力显微镜在纳米摩擦学中应用的进展

近年来，原子力显微镜在纳米摩擦学研究中获得了越来越广泛的应用，已经成为进行纳米摩擦学研究的重要工具之一，有力地促进了纳米摩擦学的发展．因此，对应用原子力显微镜研究纳米摩擦、纳米磨损、纳米润滑、纳米摩擦化学反应和微型机电系统的纳米表面工程等方面所取得的主要进展作了系统的综合归纳与阐述，并且提出了原子力显微镜在纳米摩擦学应用中亟待解决的几个主要问题．     

Simulations of nanowire bend tests for extracting mechanical properties

Mechanical properties of nickel nanowires are characterized based on the numerical simulations of bend tests performed with a customized atomic force microscope (AFM) and scanning electron microscope (SEM). Nickel nanowire specimens are subjected to bending loads by the tip of the AFM cantilever. The experimental force versus bending displacement curves are compared against simulations from finite element analysis and peridynamic theory, and the mechanical properties are extracted based on their best correlations. Similarly, SEM images of fractured nanowires are compared against peridynamic failure simulations. The results of this study reveal that nickel nanowires have significantly higher strengths than their bulk counterparts, although their elastic modulus values are comparable to bulk nickel modulus values.     

石英岩表面分子沉积膜的微观摩擦性能的试验研究

利用原子力显微镜对石英岩表面单层分子沉积膜的微观摩擦特性进行了研究,发现该分子沉积膜具有一定的减摩性.通过对其表面力-位移曲线、表面形貌像、调制力像和摩擦力像的进一步分析表明,石英岩表面分子沉积膜具有减摩作用的原因在于它能够降低表面的粘着力并对表面具有微观修饰作用.     

Experimental study of evaporation of sessile water droplet on PDMS surfaces

Evaporation of sessile water droplet on polydimethylsiloxane （PDMS） surfaces with three different curing ratios （5：1, 10：1, and 20：1） was experimentally investigated in this paper. We show that the constant contact radius （CCR） evaporation on surface with high curing ratio lasts longer than that with low curing ratio. We also measured Young＇s moduli of PDMS films by using atomic force microscopy （AFM） and simulated surface deformation of PDMS films induced by sessile water droplet. With increasing curing ratio of PDMS film, Young＇s modulus of PDMS film is getting lower, and then there will be larger surface deformation and more elastic stored energy. Since such energy acts as a barrier to keep the three-phase contact line pinned, thus it will result in longer CCR evaporation on PDMS surface with higher curing ratio.     

Asymptotical Correction to Bottom Substrate Effect Arising in AFM Indentation of Thin Samples and Adherent Cells Using Conical Tips

The bottom substrate effect is one of the major sources of error in force map studies of adherent cells and thin soft samples in an atomic force microscope (AFM)-based force spectroscopy. Because of this, samples appear stiffer than the natural. The popular Sneddon’s contact model, which assumes the sample as infinitely thick, fails to correct this error. In the present work, a simple asymptotically correct analytical correction to the bottom substrate effect is derived through contact mechanics approach and later the model is experimentally validated on a wide range of thickness of soft polyacrylamide gel and on adherent cells.     

Near-grazing dynamics of base excited cantilevers with nonlinear tip interactions

In this article, nonsmooth dynamics of impacting cantilevers at different scales is explored through a combination of analytical, numerical, and experimental efforts. For off-resonance and harmonic base excitations, period-doubling events close to grazing impacts are experimentally studied in a macroscale system and a microscale system. The macroscale test apparatus consists of a base excited aluminum cantilever with attractive and repulsive tip interactions. The attractive force is generated through a combination of magnets, one located at the cantilever structure??s tip and another attached to a high-resolution translatory stage. The repulsive forces are generated through impacts of the cantilever tip with the compliant material that covers the magnet on the translatory stage. The microscale system is an atomic force microscope cantilever operated in tapping mode. In this mode, this microcantilever experiences a long-range attractive van der Waals force and a repulsive force as the cantilever tip comes close to the sample. The qualitative changes observed in the experiments are further explored through numerical studies, assuming that the system response is dominated by the fundamental cantilever vibratory mode. In both the microscale and macroscale cases, contact is modeled by using a quadratic repulsive force. A reduced-order model, which is developed on the basis of a single mode approximation, is employed to understand the period-doubling phenomenon experimentally observed close to grazing in both the macroscale and microscale systems. The associated near-grazing dynamics is examined by carrying out local analyses with Poincaré map constructions to show that the observed period-doubling events are possible for the considered nonlinear tip interactions. In the corresponding experiments, the stability of the observed grazing periodic orbits has been assessed by constructing the Jacobian matrix from the experimentally obtained Poincaré map. The present study also sheds light on the use of macroscale systems to understand near-grazing dynamics in microscale systems.     

Influence of Scanning Rotation on Nanoscale Artificial Strain in Open-Loop Atomic Force Microscopy

For nanoscale metrology using atomic force microscopy (AFM), it is essential to know the baseline error induced by the AFM scanning process. A systematic study has been performed using digital image correlation (DIC) to quantify the influence of scanning rotation angle on the artificial strain (error) in an open loop AFM. It is found that significant artificial strain has been induced by the scanning rotation angle, demonstrating that highly accurate metrology can only be performed in an open loop AFM when the scan angle is held constant during imaging.     

Novel Method for Analyzing Crack Growth in Polymeric Microtensile Specimens by <Emphasis Type="Italic">In Situ</Emphasis> Atomic Force Microscopy

In this paper a micro tensile test which allows the determination and observation of the crack growth behaviour in thin polymer layers is presented. The setup consists of micromanipulators and piezo actuators for straining the sample while an atomic force microscope (AFM) is used for scanning the crack tip area with high lateral resolution. The stress in the specimen is determined by an optical microscope for observation of the deflection of a force sensing beam. The material under investigation is an amorphous and strongly entangled thermoplastic polyimide which can be patterned photolithographically and is spin cast to form layers of 3 μm thickness. The results show the potential of the setup to measure crack length, crack tip opening and nominal stress. The stress-crack length-diagram then allows to determine different stages during crack growth.     

Bifurcations and chaos in vibrating microcantilevers of tapping mode atomic force microscopy

We study the dynamics of a microcantilever in tapping mode atomic force microscopy when it is close to the sample surface and the van der Waals force has an important influence. Utilizing the averaging method, the extended version of the subharmonic Melnikov method and the homoclinic Melnikov method, we show that abundant bifurcation behavior and chaotic motions occur in vibrations of the microcantilever. In particular, in the subharmonic Melnikov analyses, a degenerate resonance is treated appropriately. Necessary computations for the subharmonic and homoclinic Melnikov methods are performed numerically. Numerical bifurcation analyses and numerical simulations are also given to demonstrate the theoretical results.     

片状颗粒间液桥力变化规律的计算研究

研究颗粒间液桥力有助于揭示非饱和土持水特性的内在机理. 为探究片状颗粒间液桥力演化规律, 从细观尺度研究非饱和土的水力特性机理, 使用Surface Evolver软件在两平行的片状颗粒间构建出三维液桥模型, 分析了液桥拉伸过程中接触角、液桥体积、分离距离以及固液接触线钉扎效应等对液桥力变化规律的影响. 基于圆弧假定, 计算相应条件下液桥力以及接触半径的大小, 并与上述模拟结果进行对比分析. 结果表明: 片状颗粒间液桥力随液桥体积增大而递增, 随分离距离的增大而递减, 随固液接触角的增大先增后减或一直递减; 液桥体积一定时, 在钉扎状态下, 其液桥力随着分离距离的增大迅速递增达到峰值, 而后逐渐降低; Surface Evolver模拟与液桥界面环形近似的计算结果相对比, 当固液接触角较大时(θ = 60°和θ = 80°), 二者相对误差在6%以内, 而当固液接触角减小到30°及以下时, 相对误差随之增大, 且颗粒间分离距离越大, 相对误差越大.      

Planning and control of 3-D nano-manipulation

The use of atomic force microscope (AFM) as a nanomanipulator has been evolving for various kinds of nano-manipulation tasks. Due to the bow effect of the piezo scanner of the AFM, the AFM space is different from the Cartesian space. Traditional nanomanipulation based on AFM is only a 2-D operation and does not consider the bow effect of the piezotube. In this paper, different 3-D nanomanipulation tasks using AFM such as nanolithography, pushing and cutting have been discussed. 3-D path planning is performed directly in the AFM space and the 3-D paths are generated based on the 3-D topography information of the surface represented in the AFM space. This approach can avoid the mappings between the AFM space and Cartesian space in planning. By following the generated motion paths, the tip can either follow the topography of the surface or move across the surface by avoiding collision with bumps. Nanomanipulation using this method can be considered as the “true“ 3-D operations since the cantilever tip can be controlled to follow any desired 3-D trajectory within the range of AFM space. The experimental study shows the effectiveness of the planning and control scheme.