Harold S. Park

Negative poisson’s ratio in single-layer black phosphorus

The Poissons ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. Although this value can theoretically be negative, it is positive for nearly all materials, though negative values have been observed in so-called auxetic structures. However, nearly all auxetic materials are bulk materials whose microstructure has been specifically engineered to generate a negative Poissons ratio. Here we report using first-principles calculations the existence of a negative Poissons ratio in a single-layer, two-dimensional material, black phosphorus. In contrast to engineered bulk auxetics, this behaviour is intrinsic for single-layer black phosphorus, and originates from its puckered structure, where the pucker can be regarded as a re-entrant structure that is comprised of two coupled orthogonal hinges. As a result of this atomic structure, a negative Poissons ratio is observed in the out-of-plane direction under uniaxial deformation in the direction parallel to the pucker.

Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles

Abstract Recent advances in nanotechnology have led to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators, which have recently received significant attention from the scientific community. This is not only due to their capability of label-free detection of bio/chemical molecules at single-molecule (or atomic) resolution for future applications such as the early diagnosis of diseases like cancer, but also due to their unprecedented ability to detect physical quantities such as molecular weight, elastic stiffness, surface stress, and surface elastic stiffness for adsorbed molecules on the surface. Most experimental works on resonator-based molecular detection have been based on the principle that molecular adsorption onto a resonator surface increases the effective mass, and consequently decreases the resonant frequencies of the nanomechanical resonator. However, this principle is insufficient to provide fundamental insights into resonator-based molecular detection at the nanoscale; this is due to recently proposed novel nanoscale detection principles including various effects such as surface effects, nonlinear oscillations, coupled resonance, and stiffness effects. Furthermore, these effects have only recently been incorporated into existing physical models for resonators, and therefore the universal physical principles governing nanoresonator-based detection have not been completely described. Therefore, our objective in this review is to overview the current attempts to understand the underlying mechanisms in nanoresonator-based detection using physical models coupled to computational simulations and/or experiments. Specifically, we will focus on issues of special relevance to the dynamic behavior of nanoresonators and their applications in biological/chemical detection: the resonance behavior of micro/nanoresonators; resonator-based chemical/biological detection; physical models of various nanoresonators such as nanowires, carbon nanotubes, and graphene. We pay particular attention to experimental and computational approaches that have been useful in elucidating the mechanisms underlying the dynamic behavior of resonators across multiple and disparate spatial/length scales, and the resulting insight into resonator-based detection that has been obtained. We additionally provide extensive discussion regarding potentially fruitful future research directions coupling experiments and simulations in order to develop a fundamental understanding of the basic physical principles that govern NEMS and NEMS-based sensing and detection applications.

Nano Mechanics and Materials: Theory, Multiscale Methods and Applications

Preface. 1. Introduction. 1.1 Potential of Nanoscale Engineering. 1.2 Motivation for Multiple Scale Modeling. 1.3 Educational Approach. 2. Classical Molecular Dynamics. 2.1 Mechanics of a System of Particles. 2.2 Molecular Forces. 2.3 Molecular Dynamics Applications. 3. Lattice Mechanics. 3.1 Elements of Lattice Symmetries. 3.2 Equation of Motion of a Regular Lattice. 3.3 Transforms. 3.4 Standing Waves in Lattices. 3.5 Greens Function Methods. 3.6 Quasistatic Approximation. 4. Methods of Thermodynamics and Statistical Mechanics. 4.1 Basic Results of the Thermodynamic Method. 4.2 Statistics of Multiparticle Systems in Thermodynamic Equilibrium. 4.3 Numerical Heat Bath Techniques. 5. Introduction to Multiple Scale Modeling. 5.1 MAAD. 5.2 Coarse Grained Molecular Dynamics. 5.3 Quasicontinuum Method. 5.4 CADD. 5.5 Bridging Domain. 6. Introduction to Bridging Scale. 6.1 Bridging Scale Fundamentals. 6.2 Removing Fine Scale Degrees of Freedom in Coarse Scale Region. 3D Generalization. 6.3 Discussion on the Damping Kernel Technique. 6.4 Cauchy-Born Rule. 6.5 Virtual Atom Cluster Method. 6.6 Staggered Time Integration Algorithm. 6.7 Summary of Bridging Scale Equations. 6.8 Discussion on the Bridging Scale Method. 7. Bridging Scale Numerical Examples. 7.1 Comments On Time History Kernel. 7.4 Two-Dimensional Wave Propagation. 7.5 Dynamic Crack Propagation in Two Dimensions. 7.6 Dynamic Crack Propagation in Three Dimensions. 7.7 Virtual Atom Cluster Numerical Examples. 8. Non-Nearest Neighbor MD Boundary Condition. 8.1 Introduction. 8.2 Theoretical Formulation in 3D. 8.3 Numerical Examples - 1D Wave Propagation. 8.4 Time History Kernels for FCC Gold. 8.5 Conclusion on the Bridging Scale Method. 9. Multiscale Methods for Material Design. 9.1 Multiresolution Continuum Analysis. 9.2 Multiscale Constitutive Modeling of Steels. 9.3 Bio-Inspired Materials. 9.4 Summary and Future Research Directions. 10. Bio-Nano Interface. 10.3 Vascular Flow and Blood Rheology. 10.4 Electrohydrodynamic Coupling. 10.5 CNT/DNA Assembly Simulation. 10.6 Cell Migration and Cell-Substrate Adhesion. 10.7 Conclusions. Appendix A: Kernel Matrices for EAM Potential. Bibliography. Index.

Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-Weber parametrization, mechanical properties, and thermal conductivity

We present a parameterization of the Stillinger-Weber potential to describe the interatomic interactions within single-layer MoS2 (SLMoS2). The potential parameters are fitted to an experimentally obtained phonon spectrum, and the resulting empirical potential provides a good description for the energy gap and the crossover in the phonon spectrum. Using this potential, we perform classical molecular dynamics simulations to study chirality, size, and strain effects on the Youngs modulus and the thermal conductivity of SLMoS2. We demonstrate the importance of the free edges on the mechanical and thermal properties of SLMoS2 nanoribbons. Specifically, while edge effects are found to reduce the Youngs modulus of SLMoS2 nanoribbons, the free edges also reduce the thermal stability of SLMoS2 nanoribbons, which may induce melting well below the bulk melt temperature. Finally, uniaxial strain is found to efficiently manipulate the thermal conductivity of infinite, periodic SLMoS2.

The bridging scale for two-dimensional atomistic/continuum coupling

In this paper, we present all necessary generalisations to extend the bridging scale, a finite-temperature multiple scale method which couples molecular dynamics (MD) and finite element (FE) simulations, to two dimensions. The crucial development is a numerical treatment of the boundary condition acting upon the reduced atomistic system, as such boundary conditions are analytically intractable beyond simple one-dimension systems. The approach presented in this paper offers distinct advantages compared to previous works, specifically the compact size of the resulting time history kernel, and the fact that the time history kernel can be calculated using an automated numerical procedure for arbitrary multi-dimensional lattice structures and interatomic potentials. We demonstrate the truly two-way nature of the coupled FE and reduced MD equations of motion via two example problems, wave propagation and dynamic crack propagation. Finally, we compare both problems to benchmark full MD simulations to validate the accuracy and efficiency of the proposed method.

Superplastic Deformation of Defect-Free Au Nanowires via Coherent Twin Propagation

We report that defect-free Au nanowires show superplasticity on tensile deformation. Evidences from high-resolution electron microscopes indicated that the plastic deformation proceeds layer-by-layer in an atomically coherent fashion to a long distance. Furthermore, the stress-strain curve provides full interpretation of the deformation. After initial superelastic deformation, the nanowire shows superplastic deformation induced by coherent twin propagation, completely reorientating the crystal from <110> to <100>. Uniquely well-disciplined and long-propagating atomic movements deduced here are ascribed to the superb crystallinity as well as the radial confinement of the Au nanowires.

Mechanical properties of single-layer black phosphorus

The mechanical properties of single-layer black phosphrous under uniaxial deformation are investigated using first-principles calculations. Both Youngs modulus and the ultimate strain are found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure. Specifically, the in-plane Youngs modulus is 44.0 GPa in the direction perpendicular to the pucker, and 92.7 GPa in the parallel direction. The ultimate strain is 0.48 and 0.20 in the perpendicular and parallel directions, respectively.

Surface piezoelectricity: Size effects in nanostructures and the emergence of piezoelectricity in non-piezoelectric materials

In this work, using a combination of a theoretical framework and atomistic calculations, we highlight the concept of “surface piezoelectricity,” which can be used to interpret the piezoelectricity of nanostructures. Focusing on three specific material systems (ZnO, SrTiO3, and BaTiO3), we discuss the renormalization of apparent piezoelectric behavior at small scales. In a rather interesting interplay of symmetry and surface effects, we show that nanostructures of certain non-piezoelectric materials may also exhibit piezoelectric behavior. Finally, for the case of ZnO, using a comparison with first principles calculations, we also comment on the fidelity of the widely used core–shell interatomic potentials to capture non-bulk electro-mechanical response.

Elastic bending modulus of single-layer molybdenum disulfide (MoS2): finite thickness effect.

We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2.

The importance of edge effects on the intrinsic loss mechanisms of graphene nanoresonators.

We utilize classical molecular dynamics simulations to investigate the intrinsic loss mechanisms of monolayer graphene nanoresonators undergoing flexural oscillations. We find that spurious edge modes of vibration, which arise not due to externally applied stresses but intrinsically due to the different vibrational properties of edge atoms, are the dominant intrinsic loss mechanism that reduces the quality (Q) factors. We additionally find that while hydrogen passivation of the free edges is ineffective in reducing the spurious edge modes, fixing the free edges is critical to removing the spurious edge-induced vibrational states. Our atomistic simulations also show that the Q factor degrades inversely proportional to temperature; furthermore, we also demonstrate that the intrinsic losses can be reduced significantly across a range of operating temperatures through the application of tensile mechanical strain.