Molecular dynamics of contact behavior of self-assembled monolayers on gold using nanoindentation

Molecular dynamics simulation is used to study nanoindentation of the self-assembled monolayers (SAMs) on an Au surface. The interaction of SAM atoms is described by a general universal force field (UFF), the tight-binding second-moment approximation (TB-SMA) is used for Au substrate, and the Lennard-Jones potential function is employed to describe interaction among the indenter, the SAMs, and the Au substrate atoms. The model consists of a planar Au substrate with n-hexadecanethiol SAM chemisorbed to the substrate. The simulation results show that the contact pressure increases as the SAMs temperature increases. In addition, the contact pressure also increases as the depth and velocity of indentation increase.     

Dynamic characteristics of nanoindentation in Ni:A molecular dynamics simulation study

In this work,three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni.The substrate indenter system is modelled using hybrid interatomic potentials including the manybody potential(embedded atom method) and two-body Morse potential.The spherical indenter is chosen,and the simulation is performed for different loading rates from 10 m/s to 200 m/s.Results show that the maximum indentation load and hardness of the system increase with the increase of velocity.The effect of indenter size on the nanoindentation response is also analysed.It is found that the maximum indentation load is higher for the large indenter whereas the hardness is higher for the smaller indenter.Dynamic nanoindentation is carried out to investigate the behaviour of Ni substrate to multiple loading-unloading cycles.It is observed from the results that the increase in the number of loading unloading cycles reduces the maximum load and hardness of the Ni substrate.This is attributed to the decrease in recovery force due to defects and dislocations produced after each indentation cycle.     

Domain shape relaxation and local viscosity in stratifying foam films

We studied the dynamics of two different types of domain shape relaxation in a stratifying foam film composed of an anionic polymer and cationic surfactant. Those films thin in stepwise fashion: circular domains of lower film thickness are formed, expand and coalesce until they cover the whole film surface. We found that the shape relaxation of coalescing domains is governed only by 2D dissipation, and the measurement of the time scales allows to determine the ratio between the driving force (line tension) and local film viscosity. Further, we analyzed the withdrawal of stripes and modeled it by a moving disc pulled by an external force. Here, 3D dissipation can not be neglected (Stokes paradox) and the equilibrium velocity depends logarithmically on the viscosity of the surrounding 3D air. The evaluation of both kinds of relaxation events yields the orders of magnitude of film viscosity and line tension. For the investigated system we found that the film viscosity is at least 30 times larger than the bulk viscosity, which can be explained by the local molecular ordering and strong interactions with film surfaces.     

Collective escape processes in many-particle systems

We study collective escape phenomena in nonlinear chain models. First we investigate the fragmentation of an overdamped polymer chain due to thermal fluctuations in the absence of an external force. We calculate the activation times of individual bonds in the coupled chain system and compare them with times obtained from Brownian dynamics simulations. We also consider a grafted chain exposed to an external force which monotonically grows as time goes on. In underdamped situations we show that collective localized excitations in a nonlinear force field with absorbing states can cause polymer fragmentation. In a similar fashion, localized modes assist a thermally activated escape of interacting particles in a metastable potential landscape which is additionally subjected to a periodic driving. The latter is necessary to obtain overcritical elongations which create localized modes even in case of stronger damping.     

Applying the method of dimensionality reduction to calculate the friction force between a rotationally symmetric indenter and a viscoelastic half-space

The method of dimensionality reduction is applied to the tangential contact between an elastomer and a rotationally symmetric indenter. The resulting equations are solved analytically, and numerical methods are discussed. The dependence of the normal and tangential force on the indentation depth and velocity is indicated.     

Deformation field in deep flat punch indentation and the persistence of dead-metal zones

The indentation of metal by a flat punch is a model system for forming processes and intimately linked with hardness testing. Here, we perform first-in-class, high-fidelity finite element (FE) simulations in an arbitrary Lagrangian–Eulerian (ALE) framework to study the deformation field in deep punch indentation of annealed copper. The use of ALE allows indentation depth to punch width ratios as high as 1.6, while the use of Lagrangian tracer particles reveals pathlines of material transport. Field quantities such as the plastic strain, strain rate and velocity are obtained at high resolution. A low-strain, dead-metal zone (DMZ) that is stationary with respect to the indenter forms immediately below the punch. Crucially, it is found that DMZs are unavoidable in deep punch indentation, forming at the outset and irrespective of the coefficient of friction. However, the area of this zone shrinks as the indentation progresses at a rate that is inversely related to the friction. The simulations thus explain why Prandtl’s view of punch indentation, which incorporates DMZs, is physically more accurate than Hill’s view. The computations successfully reproduce the strain field inhomogeneity seen in recent in situ imaging experiments. While DMZ formation is impervious to the hardening model used, Zerilli–Armstrong hardening provides more accurate indentation force estimates than Johnson–Cook hardening. Lastly, the residual impression and factors affecting its shape are studied. The sides of impressed metal are never vertical, but at an inclination to it. Methods to modify such features, of potential interest in metal forming, are discussed briefly.     

Effect of indenter-radius size on Au(001) nanoindentation

We address the question of whether results obtained for small indenters scale to indenter sizes in the experimental range. The quasicontinuum method is used in order to extend the computational cell size to 2x2x1 micro m(3), nominally containing of order 2.5x10(11) atoms, and in order to permit consideration of indenter radii in the range 70-700 A. The dislocation structures for the large indenter are found to be less sharp and to extend over a larger region than for the small indenter. In addition, the large-indenter force-displacement curve differs from that corresponding to the small indenter in one important respect, namely, the absence of force drops during indentation, despite profuse dislocation activity. Based on these observations, we conclude that the indenter force is not a reliable indicator of the onset of dislocation activity and plastic deformation for indenter sizes in the experimental range.     

Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation

The normalized relaxation modulus represents a salient feature of viscoelastic materials and its determination is of great significance for various applications. From the normalized relaxation modulus, for instance, one can derive the loss factor of a viscoelastic polymer and judge whether a material is suitable for damping applications or not. By using dimensional analysis and the elastic–viscoelastic correspondence principle, the normalized relaxation function of a linear viscoelastic material obtained from indentation relaxation tests is shown to depend only on the indentation load but not on the indenter geometry and the shape of the indented solid. The result could enable circumvention of the difficulties encountered in the calibration of the indenter geometry and the preparation of indented samples. Numerical simulations are performed on a number of cases of practical interest, including the spherical indentation test of a soft layer lying on a rigid substrate, a flat punch indenter indenting into a soft layer with a rough surface bonded to a rigid substrate, a rigid indenter with irregular shape indenting into a particle, inclined contact of a cylindrical indenter with a cylinder, and indentation of porous substrates. The numerical examples demonstrate that the conclusion from the theoretical analysis is valid for all these situations.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Molecular dynamics study of the mechanical characteristics of Ni/Cu bilayer using nanoindentation

<正>In the present work,a three-dimensional molecular dynamics simulation is carried out to perform the nanoindentation experiment on Ni single crystal.The substrate indenter system is modeled using hybrid interatomic potentials including the many-body potential embedded atom method(EAM),and two-body morse potential.To simulate the indentation process,a spherical indenter(diameter = 80 A,1 A=0.1 nm) is chosen.The results show that the mechanical behaviour of a monolithic Ni is not affected by crystalline orientation.To elucidate the effect of a heterogeneous interface, three bilayer interface systems are constructed,namely Ni(100)/Cu(111),Ni(110)/Cu(111),and Ni(111)/Cu(111).The simulations along these systems clearly describe that mechanical behaviour directly depends on the lattice mismatch. The interface with the smaller mismatch between the specified crystal planes is proved to be harder and vice versa.To describe the relationship between film thickness and interface effect,we choose various values of film thickness ranging from 20 A to 50 A to perform the nanoindentation experiment.It is observed that the interface is significant only for the relatively small thickness of film and the separation between interface and the indenter tip.It is shown that with the increase in film thickness,the mechanical behaviour of the film shifts more toward that of monolithic material.     

Radial elasticity of multiwalled carbon nanotubes

We report an experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius. We use atomic force microscopy and apply small indentation amplitudes in order to stay in the linear elasticity regime. The number of layers for a given tube radius is inferred from transmission electron microscopy, revealing constant ratios of external to internal radii. This enables a comparison with molecular dynamics results, which also shed some light onto the applicability of Hertz theory in this context. Using this theory, we find a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30+/-10 GPa.     

Possible manifestations of quantum effects in the boron microindentation kinetics

The kinetics of indentation of a solid (viz., the dependence of the indenter intrusion depth on the time, force, and temperature), is analyzed theoretically taking into account quantum effects in the atomic dynamics of solids. The experimental study of the temperature dependence of the boron microhardness reveals qualitative and quantitative agreement with calculated dependences. A possible manifestation of quantum (tunnel) effects in the boron microindentation kinetics is predicted.     

Reverse analysis in depth-sensing indentation for evaluation of the Young's modulus of thin films

This paper presents an approach to reverse analysis in depth-sensing indentation of composite film/substrate materials, which makes use of numerical simulation. This methodology allows the results of experimental hardness tests, acquired with pyramidal indenter geometry, to be used to determine the Young's modulus of thin film materials. Forward and reverse analyses were performing using three-dimensional numerical simulations of pyramidal and flat punch indentation tests to determine the Young's modulus of the thin films. The pyramidal indenter used in the numerical simulations takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses fictitious composite materials with different relationships between the values of the Young's modulus of the film and substrate. The proposed reverse analysis procedure provides a unique value for the film's Young's modulus. Depending on material properties, the value of the Young's modulus of the film can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment. The validity of the proposed reverse analysis method is checked using four real cases of composite materials.     

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.     

FeCrNiCoCu纳米压痕性能的分子动力学研究

纳米压痕是研究金属特性最广泛的方法之一.因此,本文采用分子动力学方法研究了晶粒数、压痕半径和压痕速度对FeCrNiCoCu压痕性能的影响.结果表明,晶粒数从4增加到16,杨氏模量和硬度值逐渐减小,呈现反Hall-Petch现象;随着压头半径的增加,杨氏模量增大,硬度受接触面积的影响较大而减小,较大的压头半径有利于模型内部位错的产生和扩展;压入速度对杨氏模量和硬度的影响微弱,压入速度越快,位错密度越低,位错传播速度越慢.本工作以期为FeCrNiCoCu的研究提供理论指导.     

Dynamical properties of magnetized two-dimensional one-component plasma

Molecular dynamics simulation are used to examine the effect of a uniform perpendicular magnetic field on a two-dimensional interacting electron system. In this simulation we include the effect of the magnetic field classically through the Lorentz force. Both the Coulomb and the magnetic forces are included directly in the electron dynamics to study their combined effect on the dynamical properties of the 2D system. Results are presented for the velocity autocorrelation function and the diffusion constants in the presence and absence of an external magnetic field. Our simulation results clearly show that the external magnetic field has an effect on the dynamical properties of the system.     

利用分子动力学方法铁素体-渗碳体相界面效应探究

珠光体是十分重要的组织结构,因此本文构建了含铁素体-渗碳体相界面的模型,并采用分子动力学模拟方法模拟纳米压入的过程。通过对模拟结果的力学性能和组织结构分析,探究了铁素体-渗碳体相界面效应。研究发现,距铁素体-渗碳体晶界不同距离（位置压入）,在压入最初阶段,压头载荷随着压头与晶界距离的增大而增大,当压入深度达到一定深度后,载荷随着距离的增大而减小。杨氏模量和最大剪切模量受压头尖端下方原子结构的直接影响,硬度受到结构完整性和类型的共同影响。铁素体-渗碳体相界面影响了纳米压入过程中位错形核、增殖和扩展,宏观表现为在相同压入深度下,不同压入位置压头载荷的差异。     

Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

Atomic-level simulations of nanoindentation-induced phase transformation in mono-crystalline silicon

Molecular dynamics (MD) simulations of nanoindentation are carried out to investigate the phase transformations in Si with a spherical indenter. Since the phase transformation induced by deformation in micro-scale is closely related to the carrier mobility of the material, it has become a key issue to be investigated for the chips especially with smaller feature size. Up to now, however, it is not possible to carry out the nanoindentation experimentally in such a small feature. Consequently, molecular dynamic simulation on nanoindentation is resorted to and becomes a powerful tool to understand the detailed mechanisms of stress-induced phase transformation in nano-scale. In this study, the inter-atomic interaction of Si atoms is modeled by Tersoff's potential, while the interaction between Si atoms and diamond indenter atoms is modeled by Morse potential. It is found that the diamond cubic structure of Si in the indentation zone transforms into a phase with body-centred tetragonal structure (β-Si) just underneath the indenter during loading stage and then changes to amorphous after unloading. By using the technique of coordinate number the results reveal that indentation on the (0 0 1) surface exhibits significant phase transformation along the <1 1 0> direction. In addition, indentation on the (1 1 0) surface shows more significant internal slipping and spreading of phase transformation than on the (0 0 1) surface. Furthermore, during the indentation process phase transformations of Si are somewhat reversible. Parts of transformed phases that are distributed over the region of elastic deformation can be gradually recovered to original mono-crystal structure after unloading.