用有限元法计算飞秒激光双光子成型点弹性模量

采用有限元法对材料为SCR500的飞秒激光双光子成型点力学性能进行建模及仿真计算，得出了不同弹性模量下成型点与探针之间的作用力．进而利用原子力显微镜接触模式，选用无针尖探针，测量了成型点的力学性能，得出了相同位移载荷下成型点与探针之间的作用力．将测量结果和仿真结果进行比较，推算出成型点的弹性模量．分析结果表明。双光子固化成型点的弹性模量大约为宏观材料弹性模量的1／7．这为进一步研究双光子飞秒激光加工微器件的力学性能提供了基础．     

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10?GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10?nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75?GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.     

Combination of normal and lateral force-displacement measurements as a new technique for the mechanical characterization of surfaces and coatings

Nanoindentation with Vickers or Berkovich tips has become an established technique for the measurement of hardness and Young's modulus. Also the use of spherical indenters has attracted more and more attention for the determination of the Young's modulus and yield strength. However, these techniques are still far away from the conditions in a real applications where usually normal forces are combined with lateral forces in a tribological system. Therefore, often scratch and wear tests are used additionally to characterize the mechanical behavior. However, conventional techniques, which apply lateral forces, have the disadvantage that they often do not deliver characteristic and comparable material parameters which are independent of the measurement conditions and which can serve as input parameters for the modeling with analytical or finite element methods. This shall be overcome by a new technique, which will allow the measurement of lateral force-displacement curves with the same accuracy like conventional nanoindentation can do in normal direction. The realization of two independent measurements with the same tip at the same sample position will allow the calculation of more unknown material parameters than before. The use of spherical indenters with forces at which elastic or beginning plastic deformation takes place makes it easier to combine the measurements with analytical stress calculations and to derive critical material parameters. As a first step towards the abovementioned characterization method, a new nanomechanical tester with a high-resolution measurement of force and displacement in normal and lateral direction was developed and tested.     

Uncertainty quantification in nanomechanical measurements using the atomic force microscope

Quantifying uncertainty in measured properties of nanomaterials is a prerequisite for the manufacture of reliable nanoengineered materials and products. Yet, rigorous uncertainty quantification (UQ) is rarely applied for material property measurements with the atomic force microscope (AFM), a widely used instrument that can measure properties at nanometer scale resolution of both inorganic and biological surfaces and nanomaterials. We present a framework to ascribe uncertainty to local nanomechanical properties of any nanoparticle or surface measured with the AFM by taking into account the main uncertainty sources inherent in such measurements. We demonstrate the framework by quantifying uncertainty in AFM-based measurements of the transverse elastic modulus of cellulose nanocrystals (CNCs), an abundant, plant-derived nanomaterial whose mechanical properties are comparable to Kevlar fibers. For a single, isolated CNC the transverse elastic modulus was found to have a mean of 8.1?GPa and a 95% confidence interval of 2.7-20?GPa. A key result is that multiple replicates of force-distance curves do not sample the important sources of uncertainty, which are systematic in nature. The dominant source of uncertainty is the nondimensional photodiode sensitivity calibration rather than the cantilever stiffness or Z-piezo calibrations. The results underscore the great need for, and open a path towards, quantifying and minimizing uncertainty in AFM-based material property measurements of nanoparticles, nanostructured surfaces, thin films, polymers and biomaterials.     

Quantitative mechanical characterization of materials at the nanoscale through direct measurement of time-resolved tip-sample interaction forces

We introduce a new method for material characterization at the nanoscale using a recently developed atomic force microscope (AFM) probe. The FIRAT (force sensing integrated readout and active tip) probe is integrated into a commercial AFM system to obtain time-resolved interaction forces (TRIFs) between the probe tip and sample at speeds suitable for nondestructive and fast imaging of material properties. We present a basic interaction model to extract the material elasticity and surface energy. Numerical simulations are performed and compared to the experimental results for three different polymers and a silicon sample. We find that our interaction model does not completely explain the observed long-range surface forces, but it agrees fairly well with the measurements during the tip-sample contact.     

Nanoscale mapping of contact stiffness and damping by contact resonance atomic force microscopy

In this work, a new procedure is demonstrated to retrieve the conservative and dissipative contributions to contact resonance atomic force microscopy (CR-AFM) measurements from the contact resonance frequency and resonance amplitude. By simultaneously tracking the CR-AFM frequency and amplitude during contact AFM scanning, the contact stiffness and damping were mapped with nanoscale resolution on copper (Cu) interconnects and low-k dielectric materials. A detailed surface mechanical characterization of the two materials and their interfaces was performed in terms of elastic moduli and contact damping coefficients by considering the system dynamics and included contact mechanics. Using Cu as a reference material, the CR-AFM measurements on the patterned structures showed a significant increase in the elastic modulus of the low-k dielectric material compared with that of a blanket pristine film. Such an increase in the elastic modulus suggests an enhancement in the densification of low-k dielectric films during patterning. In addition, the subsurface response of the materials was investigated in load-dependent CR-AFM point measurements and in this way a depth dimension was added to the common CR-AFM surface characterization. With the new proposed measurement procedure and analysis, the present investigation provides new insights into characterization of surface and subsurface mechanical responses of nanoscale structures and the integrity of their interfaces.     

A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscopy

A method is proposed for quantitatively measuring the elastic modulus of materials using atomic force microscopy (AFM) nanoindentation. In this method, the cantilever deformation and the tip-sample interaction during the early loading portion are treated as two springs in series, and based on Sneddon's elastic contact solution, a new cantilever-tip property α is proposed which, together with the cantilever sensitivity A, can be measured from AFM tests on two reference materials with known elastic moduli. The measured α and A values specific to the tip and machine used can then be employed to accurately measure the elastic modulus of a third sample, assuming that the tip does not get significantly plastically deformed during the calibration procedure. AFM nanoindentation tests were performed on polypropylene (PP), fused quartz and acrylic samples to verify the validity of the proposed method. The cantilever-tip property and the cantilever sensitivity measured on PP and fused quartz were 0.514?GPa and 51.99?nm?nA(-1), respectively. Using these measured quantities, the elastic modulus of acrylic was measured to be 3.24?GPa, which agrees well with the value measured using conventional depth-sensing indentation in a commercial nanoindenter.     

Surface deflection of a microtubule loaded by a concentrated radial force

Microtubules are hollow cylindrical filaments of a eukaryotic cytoskeleton which are sensitive to externally applied radial forces due to their low circumferential elastic modulus. In this work, an orthotropic elastic shell model for microtubules is used to study the surface radial deflection of a microtubule loaded by a concentrated radial force generated by either a single molecular motor or a radial indentation tip. Our results show that the maximum surface radial deflection of a microtubule generated by a concentrated radial force of a few pN can be as large as a few nanometers (a significant fraction of the radius of microtubules), which could cause significant surface morphological non-uniformity of the microtubule. In contrast, radial indentation under a much larger compressive force, which can be as large as a few hundreds of pN, will cause hardening of the circumferential elastic modulus almost equal to the longitudinal modulus of microtubules. In this case, our results show that a microtubule can withstand a concentrated radial compressive force as large as a few hundreds of pN, with a maximum radial deflection not more than a few nanometers, in good agreement with recent experiments on radial indentation of microtubules. These results offer useful data and new insights into the basic understanding of elastic interaction between microtubules and molecular motors and radial indentation of microtubules.     

Determination of the young modulus from elastic section of the Berkovich indenter loading curve

A new procedure for the determination of a local elastic modulus is suggested, which is based on the comparison between the nanoindentation data and the results of a numerical modelling of the contact interaction in the indenter-sample system. An image of an indent of the Berkovich indenter in a material with a low elastic recovery have been obtained by atomic force microscopy and the geometry of an equivalent indenter in the form of a body of revolution required for the adequate setting of a model contact problem have been defined. A procedure for the determination of the Young modulus by solving the inverse problem of the theory of elasticity from the condition of the best correlation between the experimental and calculated loading curves has been suggested. The data reported in the paper show that the taking into account of the real tip shape of the Berkovich indenter allows more precision measurements of the elastic modulus in nanoindentation as compared with other methods.     

Parameters of tip–sample interactions in shear mode using a quartz tuning fork AFM with controllable Q-factor

A quartz tuning fork-based atomic force microscopy for investigating the tip–sample interactions at the nanoscale in the shear-force mode is described. Results of force interactions (damping and elastic forces) can be obtained from the amplitude-phase-distance spectroscopy measurements made with a tuning fork with a tungsten tip and a sample surface. The influence of the interaction between tip and sample using the quality factor as an indicator is investigated. Furthermore, a simple model shows that the extension of a tuning fork-based AFM can be applied to quantitative analysis of the properties of the sample surface. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 141–149, January–February, 2009.     

Mechanics and contraction dynamics of single platelets and implications for clot stiffening

Platelets interact with fibrin polymers to form blood clots at sites of vascular injury. Bulk studies have shown clots to be active materials, with platelet contraction driving the retraction and stiffening of clots. However, neither the dynamics of single-platelet contraction nor the strength and elasticity of individual platelets, both of which are important for understanding clot material properties, have been directly measured. Here we use atomic force microscopy to measure the mechanics and dynamics of single platelets. We find that platelets contract nearly instantaneously when activated by contact with fibrinogen and complete contraction within 15?min. Individual platelets can generate an average maximum contractile force of 29?nN and form adhesions stronger than 70?nN. Our measurements show that when exposed to stiffer microenvironments, platelets generated higher stall forces, which indicates that platelets may be able to contract heterogeneous clots more uniformly. The high elasticity of individual platelets, measured to be 10?kPa after contraction, combined with their high contractile forces, indicates that clots may be stiffened through direct reinforcement by platelets as well as by strain stiffening of fibrin under tension due to platelet contraction. These results show how the mechanosensitivity and mechanics of single cells can be used to dynamically alter the material properties of physiologic systems.     

An atomic force microscope tip designed to measure time-varying nanomechanical forces

Tapping-mode atomic force microscopy (AFM), in which the vibrating tip periodically approaches, interacts and retracts from the sample surface, is the most common AFM imaging method. The tip experiences attractive and repulsive forces that depend on the chemical and mechanical properties of the sample, yet conventional AFM tips are limited in their ability to resolve these time-varying forces. We have created a specially designed cantilever tip that allows these interaction forces to be measured with good (sub-microsecond) temporal resolution and material properties to be determined and mapped in detail with nanoscale spatial resolution. Mechanical measurements based on these force waveforms are provided at a rate of 4 kHz. The forces and contact areas encountered in these measurements are orders of magnitude smaller than conventional indentation and AFM-based indentation techniques that typically provide data rates around 1 Hz. We use this tool to quantify and map nanomechanical changes in a binary polymer blend in the vicinity of its glass transition.     

Finite element study of the effect of material properties on reaction forces produced by solitary wave propagation in granular chains

The response of a granular chain to impulse loading was investigated as a function of material properties. Using COMSOL Multiphysics, the elastic modulus and density of the grains were varied while the piston and force sensor properties remained fixed. The result of solitary wave propagation through the granular chain was recorded at the force sensor as a series of reaction force waves. It was found that wave velocity and amplitude increased with elastic modulus. Increasing density caused a decrease in wave velocity and an increase in amplitude. In addition, higher density granular chains exhibited a decrease in the number of waves in their respective reaction force wave trains. LS-DYNA was then used to explore the response of a variety of ceramic and metallic granular chains. Density, elastic modulus, and Poisson’s ratio were all set to representative values for the respective material. It was found that solitary wave development and decay occurred at different rates for different materials. In addition, the kinetic energy decay of the impactor was slower for glass compared with tungsten. Finally, it was shown that a single reaction force wave with no train could be produced by impacting a high density, high modulus chain such as tungsten with a glass piston, which has relatively low density and elastic modulus. Increasing impact velocity for this case resulted in a single high-amplitude wave with no train.     

Extracellular-matrix tethering regulates stem-cell fate

To investigate how substrate properties influence stem-cell fate, we cultured single human epidermal stem cells on polydimethylsiloxane (PDMS) and polyacrylamide (PAAm) hydrogel surfaces, 0.1?kPa-2.3?MPa in stiffness, with a covalently attached collagen coating. Cell spreading and differentiation were unaffected by polydimethylsiloxane stiffness. However, cells on polyacrylamide of low elastic modulus (0.5?kPa) could not form stable focal adhesions and differentiated as a result of decreased activation of the extracellular-signal-related kinase (ERK)/mitogen-activated protein kinase (MAPK) signalling pathway. The differentiation of human mesenchymal stem cells was also unaffected by PDMS stiffness but regulated by the elastic modulus of PAAm. Dextran penetration measurements indicated that polyacrylamide substrates of low elastic modulus were more porous than stiff substrates, suggesting that the collagen anchoring points would be further apart. We then changed collagen crosslink concentration and used hydrogel-nanoparticle substrates to vary anchoring distance at constant substrate stiffness. Lower collagen anchoring density resulted in increased differentiation. We conclude that stem cells exert a mechanical force on collagen fibres and gauge the feedback to make cell-fate decisions.     

AFM indentation method used for elastic modulus characterization of interfaces and thin layers

Atomic force microscopy (AFM) is increasingly being used as a nanoindentation tool to measure local elastic properties of surfaces. In this article, a method based on AFM in force volume (force curve mapping) mode is employed to measure the elastic modulus distribution at the interface of a glass flake-reinforced polypropylene sample and at a lead-free Cu–solder joint. Indentation arrays are performed using a diamond AFM tip. The processing of experimental AFM indentation data is automated by customized software that can analyse and calibrate multiple force curves. The analysis algorithm corrects the obtained force curves by selecting the contact point, discarding the non-contact region and subtracting the cantilever deflection from the measured force curve in order to obtain true indentation curves. A Hertzian model is then applied to the resulting AFM indentation data. Reference materials are used to estimate the tip radius needed to extract the elastic modulus values. With the proposed AFM measurement method, we are able to obtain high-resolution maps showing elastic modulus variations around a composite interface and a Cu–solder joint. No distinct interphase region is detected in the composite case, whereas a separate intermetallic layer (1–2 μm thick) of much higher Young’s modulus (~131 GPa) than Cu and solder material is identified in the Cu–solder joint. Elastic modulus results obtained for the Cu (~72 GPa), solder (~50 GPa) and glass (~65 GPa) materials are comparable to the results obtained by instrumented indentation [~73, ~46 and ~61 GPa], which accentuates the potential of this method for applications requiring high lateral resolution.     

Mapping the elastic properties of granular Au films by contact resonance atomic force microscopy

Endowed with nanoscale spatial resolution, contact resonance atomic force microscopy (CR-AFM) provides extremely localized elastic property measurements. We advance here the applicability of CR-AFM on surfaces with nanosize features by considering the topography contribution to the CR-AFM signal. On nanosize granular Au films, the elastic modulus at the grain scale has been mapped out by considering a self-consistent deconvolution of the contact geometry effect in the CR-AFM image. Significant variation in the contact area over granular topography arises as the probe is either in single-?or multiple-asperity contact with the surface. Consequently, in extracting the elastic modulus from CR-AFM measurements on granular surfaces we considered both the normal and lateral couplings established through multiple-asperity contacts between the tip and the surface. Thus, by appropriately considering the change in the contact mechanics during CR-AFM imaging, variations in the elastic modulus have been revealed in the intergrain regions as well as across individual grains.     

Elastic property of vertically aligned nanowires

An atomic force microscopy (AFM) based technique is demonstrated for measuring the elastic modulus of individual nanowires/nanotubes aligned on a solid substrate without destructing or manipulating the sample. By simultaneously acquiring the topography and lateral force image of the aligned nanowires in the AFM contacting mode, the elastic modulus of the individual nanowires in the image has been derived. The measurement is based on quantifying the lateral force required to induce the maximal deflection of the nanowire where the AFM tip was scanning over the surface in contact mode. For the [0001] ZnO nanowires/nanorods grown on a sapphire surface with an average diameter of 45 nm, the elastic modulus is measured to be 29 +/- 8 GPa.     

Direct measurements of non-linear stress-strain curves and elastic properties of metal matrix composite sandwich beams with any core material

A theory for measuring non-linear stress-strain curves and elastic properties of metal matrix composite (MMC) sandwich beams subjected to pure bending loads is discussed. The beam is made from any core material sandwiched between an upper facing of unreinforced metal and a lower facing of MMC with unidirectional fibre reinforcement or vice versa. The model developed shows that the determination of the position of the neutral axis is critical to the measurements discussed in this paper. The analysis removes the restriction of the effects of the core. With the aid of this model, we show that the position of the neutral axis can be determined directly from surface strain measurements. Measurements of neutral axis position lead directly to the determination of the beam elastic properties and, thus, directly obtained from surface strain measurements. It is shown that the model predicts longitudinal stresses and strains within any layer of the beam. The analysis includes the limiting case of a very weak core material. A consequence of this model is the determination of the MMC facing fibre volume fraction. A detailed error analysis predicts that the longitudinal elastic modulus of an MMC material facing can be obtained with an uncertainty between 4 and 6% if the surface strain measurements and beam dimensions can be obtained with an uncertainty of 1%. The volume fraction can be obtained within 10% uncertainty, although better methods are available for that measurement.     

Mechanical elasticity of vapour-liquid-solid grown GaN nanowires

Mechanical elasticity of hexagonal wurtzite GaN nanowires with hexagonal cross sections grown through a vapour-liquid-solid (VLS) method was investigated using a three-point bending method with a digital-pulsed force mode (DPFM) atomic force microscope (AFM). In a diameter range of 57-135?nm, bending deflection and effective stiffness, or spring constant, profiles were recorded over the entire length of end-supported GaN nanowires and compared to the classic elastic beam models. Profiles reveal that the bending behaviour of the smallest nanowire (57.0?nm in diameter) is as a fixed beam, while larger nanowires (89.3-135.0?nm in diameter) all show simple-beam boundary conditions. Diameter dependence on the stiffness and elastic modulus are observed for these GaN nanowires. The GaN nanowire of 57.0?nm diameter displays the lowest stiffness (0.98?N?m(-1)) and the highest elastic modulus (400 ± 15?GPa). But with increasing diameter, elastic modulus decreases, while stiffness increases. Elastic moduli for most tested nanowires range from 218 to 317?GPa, which approaches or meets the literature values for bulk single crystal and GaN nanowires with triangular cross sections from other investigators. The present results together with further tests on plastic and fracture processes will provide fundamental information for the development of GaN nanowire devices.     

Quantitative Elastic‐Property Measurements at the Nanoscale with Atomic Force Acoustic Microscopy

We are developing metrology for rapid, quantitative assessment of elastic properties with nanoscale spatial resolution. Atomic force acoustic microscopy (AFAM) methods enable measurements of modulus at either a single point or as a map of local property variations. The information obtained furthers our understanding of nanopatterned surfaces, thin films, and nanoscale structures.