Measuring biomaterials mechanics with atomic force microscopy. 1. Influence of the loading rate and applied force (pyramidal tips)

Atomic force microscopy (AFM) is today an established tool in imaging and determination of mechanical properties of biomaterials. Due to their complex organization, those materials show intricate properties such as viscoelasticity. Therefore, one has to consider that the loading rate at which the sample is probed will lead to different mechanical response (properties). In this work, we studied the dependence of the mechanical properties of endothelial cells on the loading rate using AFM in force spectroscopy mode. We employed a sharp, four‐sided pyramidal indenter and loading rates ranging from 0.5 to 20 μm/s. In addition, by variation of the load (applied forces from 100 to 10,000 pN), the dependence of the cell properties on indentation depth could be determined. We then showed that the mechanical response of endothelial cells depends nonlinearly on the loading rate and follows a weak power‐law. In addition, regions of different viscous response at varying indentation depth could be determined. Based on the results we obtained, a general route map for AFM users for design of cell mechanics experiments was described.     

Atomic force microscopy and cells: Indentation profiles around the AFM tip,cell shape changes,and other examples of experimental factors affecting modeling

We use atomic force microscopy in conjunction with a fluorescence microscope capable of optical sectioning to acquire images of white blood cells while force is applied with the AFM tip. The indentation profile within the cell is compared to the profile of the AFM tip: examples are shown for indentations at the center of the cell which are reasonable matches to the tip profile, and an additional example is shown for an indentation that is on the tilted side of a highly rounded cell and that differs from the tip shape. We also demonstrate that the AFM tip can interact with internal cell structures, we show that the contact area between the cell and the substrate can increase under applied pressure, that the main body of the cell can fuse with the extended lamellipodium, and that the cell can be displaced laterally by the AFM tip. The features illustrated here are relevant to the interpretation of indentation experiments that measure cell elasticity properties, as is discussed briefly. Microsc. Res. Tech. 78:626–632, 2015. © 2015 Wiley Periodicals, Inc.     

Lateral force microscopy of multiwalled carbon nanotubes

Carbon nanotubes are usually imaged with the atomic force microscope (AFM) in non-contact mode. However, in many applications, such as mechanical manipulation or elasticity measurements, contact mode is used. The forces affecting the nanotube are then considerable and not fully understood. In this work lateral forces were measured during contact mode imaging with an AFM across a carbon nanotube. We found that, qualitatively, both magnitude and sign of the lateral forces to the AFM tip were independent of scan direction and can be concluded to arise from the tip slipping on the round edges of the nanotube. The dependence on the normal force applied to the tip and on the ratio between nanotube diameter and tip radius was studied. We show that for small values of this ratio, the lateral force signal can be explained with a simple geometrical model.     

Quantitative measurement of indentation hardness and modulus of compliant materials by atomic force microscopy

An atomic force microscopy (AFM) based technique is proposed for the characterization of both indentation modulus and hardness of compliant materials. A standard AFM tip is used as an indenter to record force versus indentation curves analogous to those obtained in standard indentation tests. In order to overcome the lack of information about the apex geometry, the proposed technique requires calibration using a set of reference samples whose mechanical properties have been previously characterized by means of an independent technique, such as standard indentation. Due to the selected reference samples, the technique has been demonstrated to allow reliable measurements of indentation modulus and hardness in the range of 0.3-4.0 GPa and 15-250 MPa, respectively.     

压痕标定法中弹塑性边界位置影响因素的研究

在压痕标定法中，实验所得应变量应避免局部接触区域塑性变形的影响，因此利用理论分析方法和有限元分析的方法研究在局部载荷下影响弹塑性边界位置的各种因素。结果表明：在弹塑性变形过程中，弹塑性边界大小与压痕大小、载荷、试件材料特性等内在的关系可由数学公式来描述；弹塑性．边界大小与试件内应力之间的关系可由有限元分析得到的曲线来描述。     

AFM studies of environmental effects on nanomechanical properties and cellular structure of human hair

Characterization of cellular structure and physical and mechanical properties of hair are essential to develop better cosmetic products and advance biological and cosmetic science. Although the morphology of the cellular structure of human hair has been traditionally investigated using scanning electron microscopy and transmission electron microscopy, these techniques provide limited capability to in situ study of the physical and mechanical properties of human hair in various environments. Atomic force microscopy (AFM) overcomes these problems and can be used for characterization in ambient conditions without requiring specific sample preparations and surface treatment. In this study, film thickness, adhesive forces and effective Young's modulus of various hair surfaces were measured at different environments (humidity and temperature) using force calibration plot technique with an AFM. Torsional resonance mode phase contrast images were also taken in order to characterize the morphology and cellular structure changes of human hair at different humidity. The correlation between the nanomechanical properties and the cellular structure of hair is discussed.     

A high-resolution and large force-range load cell by means of nonlinear cantilever beams

In the present work, we describe a nonlinear stiffening load cell with high resolution (the ability to detect 1% changes in the force) that can function over a large force range (5 orders of magnitude), and exhibit minimal hysteresis and intrinsic geometric protection from force overload. The stiffening nature of the load cell causes its deflection and strain to be very sensitive to small forces and less sensitive to large forces. High stiffness at high forces prevents the load cell from over-straining. We physically implement the nonlinear springs with cantilever beams that increasingly contact rigid surfaces with carefully chosen curvatures as more force is applied. We analytically describe the performance of the load cell as a function of its geometric and material parameters. We also describe a method for manufacturing the mechanical component of the load cell out of one monolithic part, which decreases hysteresis and assembly costs. We experimentally verify the theory for two load cells with two different sets of parameters.     

Plane punch indentation of a ductile honeycomb

The stresses and deformations in an anisotropic half-space indented by a flat punch are calculated for material parameters that characterize a transversely crushed ductile honeycomb. After a small range of elastic deformations, the honeycomb crushes in localized bands that extend in characteristic directions within the half-space. Large geometric changes in the crushed cells modify their mechanical properties and constrain the deformation of adjacent cells. A lower estimate of the indentation force is obtained by comparing the peak stress beneath the indenter with the yield strength of the honeycomb. An upper estimate of the indentation force is calculated by equating the work-rate of indentation with the dissipation-rate of a flow-field that is compatible with the crushing bands.     

Mechanical properties of plasma membrane and nuclear envelope measured by scanning probe microscope

Atomic force microscopy has been used to visualize nano‐scale structures of various cellular components and to characterize mechanical properties of biomolecules. In spite of its ability to measure non‐fixed samples in liquid, the application of AFM for living cell manipulation has been hampered by the lack of knowledge of the mechanical properties of living cells. In this study, we successfully combine AFM imaging and force measurement to characterize the mechanical properties of the plasma membrane and the nuclear envelope of living HeLa cells in a culture medium. We examine cantilevers with different physical properties (spring constant, tip angle and length) to find out the one suitable for living cell imaging and manipulation. Our results of elasticity measurement revealed that both the plasma membrane and the nuclear envelope are soft enough to absorb a large deformation by the AFM probe. The penetrations of the plasma membrane and the nuclear envelope were possible when the probe indents the cell membranes far down close to a hard glass surface. These results provide useful information to the development of single‐cell manipulation techniques.     

Indentation modulus and hardness of viscoelastic thin films by atomic force microscopy: A case study

We propose a nanoindentation technique based on atomic force microscopy (AFM) that allows one to deduce both indentation modulus and hardness of viscoelastic materials from the force versus penetration depth dependence, obtained by recording the AFM cantilever deflection as a function of the sample vertical displacement when the tip is pressed against (loading phase) and then removed from (unloading phase) the surface of the sample. Reliable quantitative measurements of both indentation modulus and hardness of the investigated sample are obtained by calibrating the technique through a set of different polymeric samples, used as reference materials, whose mechanical properties have been previously determined by standard indentation tests. By analyzing the dependence of the cantilever deflection versus time, the proposed technique allows one to evaluate and correct the effect of viscoelastic properties of the investigated materials, by adapting a post-experiment data processing procedure well-established for standard depth sensing indentation tests. The technique is described in the case of the measurement of indentation modulus and hardness of a thin film of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate), deposited by chronoamperometry on an indium tin oxide (ITO) substrate.     

Non-optical tip–sample distance control method for scanning near-field optical microscopy using a piezoresistive micro cantilever

A piezoresistive micro cantilever is applied to monitor the displacement of an optical fibre probe and to control tip–sample distance. The piezoresistive cantilever was originally made for a self-sensitive atomic force microscopy (AFM) probe and has dimensions of 400 µm length, 50 µm width and 5 µm thickness with a resistive strain sensor at the bottom of the cantilever. We attach the piezoresistive cantilever tip to the upper side of a vibrating bent optical fibre probe and monitor the resistance change amplitude of the strain sensor caused by the optical fibre displacement. By using this resistance change to control the tip–sample distance, the two-cantilever system successfully provides topographic and near-field optical images of standard samples in a scanning near-field optical microscopy (SNOM)/AFM system. A resonant characteristic of the two-cantilever system is also simulated using a mechanical model, and the results of simulation correspond to the experimental results of resonance characteristics.     

Evaluation of a nonlinear Hertzian‐based model reveals prostate cancer cells respond differently to force than normal prostate cells

Understanding how the mechanical properties of cells alter with disease may help with the development of novel diagnostics and treatment regimes. The emergence of tools such as the atomic force microscope (AFM) has enabled us to physically measure the mechanical properties of cells. However, suitable models for the analysis of real experimental data are either absent, or fail to provide a simple analysis tool in which experimental data can be analyzed quickly and reliably. The Hertz model has been widely used to study AFM data on living cells, however it makes assumptions that are untrue for cells, namely that cells behave as linear elastic bodies. This article presents and evaluates an alternative nonlinear Hertz model, which allows the Young's modulus to vary according to a second order polynomial function of indentation depth. Evaluation of the model revealed that prostate cancer cells (PC3) responded more uniformly to force compared to the normal PNT2 cells. Also, more energy (J) was needed to deform the normal prostate cells compared to the prostate cancer cells. Finally, the model described here suggests that overall the normal prostate cells behave in a more linear fashion to applied force compared to the prostate cancer cells. Microsc. Res. Tech., 2013. © 2012 Wiley Periodicals, Inc.     

Anisotropic strain transfer through the aortic valve and its relevance to the cellular mechanical environment

Aortic valve interstitial cells are responsible for maintaining the valve in response to their local mechanical environment. However, the complex organization of the extracellular matrix means cell strains cannot be directly derived from gross strains, and knowledge of tissue structure-function correlations is fundamental towards understanding mechanotransduction. This study investigates strain transfer through the valve, hypothesizing that organization of the valve matrix leads to non-homogenous local strains. Radial and circumferential samples were cut from aortic valve leaflets and subjected to quasi-static mechanical characterization. Further samples were imaged using confocal microscopy, to determine local strains in the matrix. Mechanical data demonstrated that the valve was significantly stronger and stiffer when loaded circumferentially, comparable with previous studies. Micromechanical studies demonstrated that strain transfer through the matrix is anisotropic and indirect, with local strains consistently smaller than applied strains in both orientations. Under radial loading, strains were transferred linearly to cells. However, under circumferential loading, strains were only one-third of applied values, with a less direct relationship between applied and local strains. This may result from matrix reorganization, and be important for preventing cellular damage during normal valve function. These findings should be taken into account when investigating interstitial cell behaviours, such as cell metabolism and mechanotransduction.     

Artesunate induced morphological and mechanical changes of Jurkat cell studied by AFM

In this study, we have used atomic force microscopy (AFM) to study the morphology and mechanical property changes of Jurkat cells exposed to different concentrations of Artesunate (ART) for 24 h at single cellular level. Cell viability and proliferation assays were performed by using the Cell Counting Kit‐8. The concentration of ART, which resulted in the inhibition rate >50% was selected. The AFM images revealed that the cell membrane changed and the ultrastructure also became complex. Mechanical properties of individual cell were tracked with AFM‐based force spectroscopy. The force curves revealed that when a cell was exposed to the ART, the mechanical properties changed obviously. Treated cells had a lower adhesion force of 416.8±37.9 pN, whereas control group had a higher adhesion force of 1064.2±97.0 pN. The Young's modulus decreased to nearly one‐third, from control group of 0.648±0.037 kPa to treated group of 0.254±0.035 kPa and the stiffness increased to nearly 1.5 times, from control group of 1.231±0.084 mN/m to treated group of 1.917±0.137 mN/m. These results suggest that ART can inhibit the proliferation of Jurkat and induce changes in the morphological structure and mechanical properties of Jurkat cells. The high resolution and high sensitivity of AFM can be used to detect morphological and mechanical properties of cells exposed to ART. The AFM may be developed to be a useful tool for detecting the cell death and evaluating the anti‐carcinogen efficacy against tumor cell. SCANNING 31: 83–89, 2009. © 2009 Wiley Periodicals, Inc.     

利用原子力显微镜探测化学基团间的单键力

原子力显微镜(AFM)不仅可用于形貌测量,而且还可在纳米尺度上测量微观组分间的相互作用力。本文简要介绍了AFM的一种令人非常感兴趣的用途——测量和推算单个化学基团对之间的作用力(单键力)。单键力的测量和推算涉及AFM针尖的自组装单分子膜的化学修饰和Poisson统计方法的利用,文中概述了测量和推算的步骤和原理。AFM应用范围的拓宽必将促进它的进一步改进和发展。     

An atomic force microscope operating at hypergravity for in situ measurement of cellular mechano-response

We present a novel atomic force microscope (AFM) system, operational in liquid at variable gravity, dedicated to image cell shape changes of cells in vitro under hypergravity conditions. The hypergravity AFM is realized by mounting a stand-alone AFM into a large-diameter centrifuge. The balance between mechanical forces, both intra- and extracellular, determines both cell shape and integrity. Gravity seems to be an insignificant force at the level of a single cell, in contrast to the effect of gravity on a complete (multicellular) organism, where for instance bones and muscles are highly unloaded under near weightless (microgravity) conditions. However, past space flights and ground based cell biological studies, under both hypogravity and hypergravity conditions have shown changes in cell behaviour (signal transduction), cell architecture (cytoskeleton) and proliferation. Thus the role of direct or indirect gravity effects at the level of cells has remained unclear. Here we aim to address the role of gravity on cell shape. We concentrate on the validation of the novel AFM for use under hypergravity conditions. We find indications that a single cell exposed to 2 to 3 ×  g reduces some 30–50% in average height, as monitored with AFM. Indeed, in situ measurements of the effects of changing gravitational load on cell shape are well feasible by means of AFM in liquid. The combination provides a promising technique to measure, online, the temporal characteristics of the cellular mechano-response during exposure to inertial forces.     

Mapping the 3D-surface strain field of patterned tensile stainless steels using atomic force microscopy

The quantification of microstructural strains at the surface of materials is of major importance for understanding the reactivity of solids. The present paper aims at demonstrating the potentialities of the atomic force microscopy (AFM) for mapping the three-dimensional surface strain field on patterned tensile specimens. Electron beam (e-beam) lithography has been used to deposit 16 x 16 arrays of gold-squared pads. Monitoring the evolution of such a pattern under applied strain allows to quantify the triaxial strains both at the micro-(plastic) domain and nanoscale (elastic) domain vs. applied strain. The proposed method was applied to stainless steels after 4.5% plastic strain.     

基于应变梯度塑性理论的微塑性成形力学性能

不同厚度的T2紫铜试样的单向拉伸、微硬度和微弯曲试验表明,材料的力学行为与内禀的材料特征参数相关：厚度为30μm的板材,其拉伸强度比厚度为150μm的板材提高了28%,平均晶粒尺寸D为50μm的细晶,其拉伸强度比平均晶粒尺寸D为120μm的粗晶拉伸强度提高了33%,拉伸时呈现出“越小越强”的特征;当压痕深度与板材厚度的比值大于0.2时,压入深度越大,压痕硬度越大,呈现出“越大越硬”的现象;回弹角随板料厚度的减小而增大,当材料厚度小于一定值（0.06mm）时,材料的应变梯度硬化效应使得回弹角随板料厚度的变化更为剧烈,这种变化与采用应变梯度塑性理论预测的结果基本一致。     

Energy, Adhesion, and the Elastic Foundation

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linear-elastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of $ F_{\text{adh}} \cong 7\pi R\Updelta \gamma . $      

Fabrication and analysis of cylindrical resin AFM microcantilevers

In this paper a new method of fabricating cylindrical resin microcantilevers using the Direct Digital Manufacturing (DDM) technique of Micro-stereolithography (MSL) is described. The method is rapid and commercially viable, allowing the fabrication of atomic force microscope (AFM) cantilevers which exhibit much larger spring constants than those currently commercial available. This allows for experimentation in a force regime orders of magnitude higher than currently possible using the AFM. This makes these cantilevers ideally suited for AFM-based depth sensing indentation. Due to their geometry, the assumptions used in the standard Euler-Bernoulli beam theory usually used to analyse AFM cantilevers may no longer be valid. Therefore approximate analytical solutions based on Timoshenko beam theory have been derived for the stiffness and resonant frequency of these cantilevers. Prototypes of the cantilevers have been fabricated and tested. Results show good agreement between experiment and theory.