CURRENT TRENDS OF MICRO- AND NANOMECHANICS

Introduction Scaling down to the micro- and nanoscale is a strong current trend in the development of science and technology. ‘Small is energy efficient and cost effective’ has long been for the motto of the semiconductor industry, including micro- and nanoelectronics, micro-electro-mechanical systems (MEMS) and nano- electro-mechanical systems (NEMS). But shrinking to small scales brings big challenges to traditional disciplines, including mechanics. Entering the micro- and especially nanoscale, matter shows distinctly different behavior from the bulk, macroscopic case, ranging from mechanical to functional properties, and from elastic deformation to yielding and failure behaviors. This special issue is organized by the Micro- and Nanomechanics Workgroup of the Chinese Society of Theoretical and Applied Mechanics, which was founded in 2008, to promote the multidisciplinary research at micro- and nano-scale on mechanics of materials and devices. All the research papers and two review articles included in this issue are invited contributions by the workgroup, from fifteen independent research groups in China and related regions, reflecting the current research activities in the field.

Review Articles As reviewed by Zheng and Qiao (page 511), the size dependence of the mechanical properties of nanowires is coupled with applied electric field effects. In fact, external fields induce mechanical defor- mation and even phase transitions in functional materials, such as piezoelectric, pyroelectric, electro- and magnetostrictive, ferroelectric, ferromagnetic as well as the recently extensively studied multifer- roic materials. The review article by Zheng et al. (page 524) provides a comprehensive understanding of thermodynamic modeling of one class of nanomaterial: nanoscale ferroelectric systems. Based on a Spontaneous-Polarization-Order-Parameter approach, some important properties of the nanoscale ferroelectrics are calculated and analyzed. They also provide instructive discussions about the results.

Size effect A fundamental challenge to applying solid mechanics to atomic systems is the definition of stress, which is essentially a concept of continuum mechanics. For example, the Cauchy stress at a point of matter is defined through average traction per unit area on area elements surrounding the point, as the area becomes infinitesimally small. However, before reaching zero sizes, the systems become discrete at the atomic level. Although several statistical methods have been proposed to extract the Cauchy stress from the atomistic mechanics simulations, how to define the equivalent stress in both continuum and discrete frames still remains controversial. Xu and Liu (page 644) checked the effectiveness of three widely used stress concepts for atomic systems against selected atomistic simulation examples, leading us to deeper thinking about this challenge, especially in multiscale modeling. Size effects on elastic moduli and Poisson’s ratio become significant when the sample size decreases to the nanoscale, but the elastic modulus can either decrease or increase with decreasing sample size. Tang et al. (page 605) provide a unified understanding of the two opposite trends by a one-dimensional model with intermolecular potentials that simulate the relative density of the atomic lattice near the surface in comparison with the bulk lattice: a looser surface atomic lattice leads to a decrease in elastic moduli with decreasing sample size, while a tighter surface lattice leads to the reverse trend. Wang and Zhao (page 630) probed this issue by a residual stress concept. A looser surface lattice can be modeled by tensile surface stress, which will induce a compressive residual stress field in the interior of a nano-plate, thus changing the size-dependent bending and self-buckling behaviors of the plate. Surface roughness, as shown by Duan et al. on page 550, can also influence the elastic behavior of a micro-cantilever. In fact, the roughness can be an equivalent expression of surface lattice change or surface stress. It is demonstrated that surface roughness can enhance, reduce or even annul the effect of surface stress on the resonance frequency of micro-cantilevers, depending on surface stress states, geometry of the rough surface and Poisson’s ratio of the material. Based on molecular mechanics and the embedded-atom potential, Zheng et al. (page 657) showed that the torsion coefficient of metallic copper nanospring

I increases with the increase of the wire radius as well as helix radius, and that the classic spring theory is invalid to torsional nanosprings. Nanoporous materials are an intriguing new member of the nanomaterial family, which used to consist of zero-, one-, two-dimensional nanomaterials and nanograined bulk materials, or three-dimensional nanomaterials. By molecular dynamics simulations, Zhao et al. (page 650) investigated not only the stress-strain behavior, but also the incipient yielding of nanoporous single crystal copper under multiaxial loading conditions. The yielding mechanism and surface are found to be stress-state and loading-path dependent. When the material parameters are properly determined, powerful numerical methods, such as the finite element method can be used for nanostructural analysis or optimization design. Zhu et al. (page 665) performed design optimization on the process condition for grating fabrication of nanostructures with hot embossing lithography, and the effectiveness of the design was checked against experiments. In comparison with modeling and simulating, mechanics tests at the nanoscale are much greater challenges. In comparing with nanoindentation techniques, tensile experiment can provide direct mea- surement of mechanical parameters of nanostructures, especially one-dimensional ones. But how to realize strong clamping or gripping in nano-tensile-tests is always a tough task. Liu et al. (page 584) studied two important kinds of clamping, based on electron-beam-induced deposition (EBID) and van der Waals interaction respectively, in micro- and nanoscale experiments through combining theoretical and experimental efforts. The influence of environment, material properties and sample size on the clamping strengths was carefully discussed. Standardization of nanomechanics tests still has a long way to go. In situ manipulating of one-dimensional nanostructures on substrates within SEM or high resolution TEM by probe-tips and bending or vibrating suspended nanowires or nanotubes over micro or nanoholes or grooves by probe-tips or applied external fields provide diversified routes to study the mechanical properties and physical mechanical coupling effects. The root of the size effect or surface effects should go beyond the stress, strain and geometry factors, and should go down to the electron, even spin state levels. Nanostructures have much large surface ratio over volume or weight, and atoms at free surfaces have dangling bonds which are chemically active and have significant different density of states than in the interior of the structure. These surface states will not only change the mechanical properties as shown by the mentioned articles, but also cause ex- ceptional physical, chemical and biological properties of nanostructures, so that nanostructures can be ultrasensitive chemical and biosensors, actuators, and ideal building blocks for functional nanodevices. Even common materials can become highly ‘intelligent’ at nanoscale, such as carbon nanotubes and graphene nanoribbons which will be introduced in the following. Therefore, to jointly and efficiently use the continuum mechanics, molecular dynamics as well as quantum mechanics tools is necessary for deeper understanding of the intriguing size effects of nanostructures and devices.

Mechanics of Carbon Nanotubes and Systems In the past two decades, the most studied nanomaterials are undoubtedly the carbon nanostructures. From the finding of fullerene balls at the middle of 1980s, high-resolution characterization of carbon nanotubes at the beginning of 1990s, and successful manipulation of single carbon atomic layers or graphene since 2004, the sp2 carbon nanostructures have brought us continuous surprises and created important trends in nanoresearch , In addition, the fascinating, there has been much interest in nano- diamonds (particles and films) and diamond-like-carbon structures which consist of both sp3 and sp2 (at least on surfaces) C-C bonding structures. These carbon nanostructures are mechanically exceptional and have fantastic functional properties: they can be metallic or semiconducting, spin magnetic even half-metallic. Even the simplest hollow geometry of carbon nanotubes can provide plenty of potential applications. For example, they can transport water very efficiently, producing electricity when fluid is flowing through, outside or inside of them. Wang et al. (page 623) contributed a work on the dynamics of carbon nanotubes containing water. The most attractive aspect of carbon nanotubes may be their potential application in new generation nanoelectronics. Nearly all the functions of silicon devices have been realized or demonstrated in laboratory after more than a decade of great joint efforts from both academic and industry communities, but how to control their chirality, which determines their device properties, still remains as a hard challenge. Raman modes, from radial breathing, to D- and G-bands, have been shown theoretically and experimentally to be capable to determine the chirality of a carbon nanotube. Although large amount of theoretical studies on the Raman modes of carbon nanotubes have been conducted, analytical solutions

II for D- and G-bands are still lacking. Here, Li and Chang provide for the first time an explicit solution for the G-band frequency of single walled carbon nanotubes (page 571). In comparison, the single atomic layer of graphene has many intriguing properties due to its intrinsic instable two-dimensional geometry and rich edge states, in addition to the Dirac point very near to its Fermi level. It can be expected that this nanomaterial will bring our mechanics community another exciting interdisciplinary field, although we have no invited article along this line in this issue.

Biomechanics and Molecular Bionics Nature is always our best teacher. Particularly in the micro and nanoscale, biological systems are full of secrets which provide us endless inspiration for creation. With fast developments in both nanotechnol- ogy and molecular biology, our ability to probe the natural secrets and learn to mimic biosystems from cell to functional proteins, from flying to walking on different surfaces by insects, and from seashells to our bones, to produce bionic composites and create spider webs. Here, three articles are contributed to understand the adhesion mechanism between gecko paws and wet surfaces (Su et al. on page 593), the interaction of cardiac myocytes and elastic substrate (Huang et al. on page 563), and bionic principle for fabricating nano-CaCO3 incorporated polystyrene composites (Gao et al. on page 555), respectively. Su and colleagues start from a careful observing the tine tip of fiber of some insect paws and observed concave tip morphology of the tine fiber to analyze how the concave tip can change the adhesion to a wet surface and find in wonder that concave surface can effectively enhance the wet adhesion by reducing the effective contact angle of the fiber. Huang et al. developed an experimental method to characterize the spatial-temporal traction dynamics of single cardiac myocyte by high-resolution displacement field of the elastic substrate on which the cardiac myocyte exposing to different microenvironments. Gao et al. show experimentally that improvement in tensile modulus and creep resistance can be achieved by adding nano-CaCO3 particles to the polystyrene matrix, but tensile strength and toughness are decreased by adding the nanoparticles. In fact, to simutaneusly enhance the modulus, tensile strength and fracture toughness of nanocomposites still remain an attractive and challenging topic.

Perspectives Mechanics has been the fundamental of engineering technology for hundreds of years and traditional mechanics is so well developed that it seems there the number of essential tasks left to professional mechanics scientists at the macroscale are dwindling. However, the developing field of nanotechnology brings plenty of new challenges and responsibilities to mechanics scientists, especially with the frontier engineering technology shifting from mechanical engineering to intelligent nanosystems, from micro- electronic engineering to nano and spin electronics and photonics, and the increasing pressure to find alternative energy sources. Also, the life science and biological technology have developed to such a depth, for example in the study of the dynamic functions of proteins with known atomic structures, that mechanics scientist are being called on to join in the effort to achieve a more comprehensive understand- ing of the secrets of bio and neural systems at an atomistic level. Entering the nano or molecular level, strong coupling between the local fields of matter consisting of charge, electronic structures, orbital and spin states and external applied fields such as mechanical strain and stress, electric and magnetic fields and optical and phonon excitation, plays a dominant role and leads to great opportunities and also challenges to our narrow knowledge basis provided by a specific discipline. Such nanoscale multifield coupling softens the boundary between traditional disciplines, and interdisciplinary research become essential. To our mechanics community, the developing nanotechnology call for a ‘big mechanics’or ‘multimechanics’ formed by uniting traditional mechanics with quantum mechanics and raising the discipline to a new level.

Guest Editors: Wanlin Guo (Institute of Nanoscience, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. Email: [email protected])

Huiming Xie (AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China. Email: [email protected])

Quanshui Zheng (Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China. Email: [email protected])

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