Negative Poisson's Ratio in Single-Layer Black Phosphorus

J-W Jiang and H.S. Park
Accepted for publication in Nature Communications 2014

Abstract

The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. While 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 Poisson's ratio. Here, we report using first principles calculations the existence of a negative Poisson's ratio in a single-layer, two-dimensional material, black phosphorus. In contrast to engineered bulk auxetics, this behavior 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 Poisson's ratio is observed in the out-of-plane direction under uniaxial deformation in the direction parallel to the pucker.

Mechanical Properties of MoS2/Graphene Heterostructures

J-W Jiang and H.S. Park
Applied Physics Letters 2014; 105:033108

Abstract

We perform classical molecular dynamics simulations to comparatively investigate the mechanical properties of single-layer MoS2 and a graphene/MoS2/graphene heterostructure under uniaxial tension. We show that the lattice mismatch between MoS2 and graphene will lead to a spontaneous strain energy in the interface. The Young's modulus of the heterostructure is significantly larger than that of MoS2. While its stiffness is enhanced, the yield strain of the heterostructure is considerably smaller than MoS2 due to lateral buckling of the outer graphene layers resulting from the applied mechanical tension.

This paper is available in PDF form .


Fermi-Pasta-Ulam Physics With Nanomechanical Graphene Resonators: Intrinsic Relaxation and Thermalization from Flexural Mode Coupling

D. Midtvedt, A. Croy, A. Isacsson, Z.N. Qi and H.S. Park
Physical Review Letters 2014; 112:145503

Abstract

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate Γ to be independent of radius and scaling as , where and are effective resonator temperature and prestrain.

This paper is available in PDF form .


MoS2 Nanoresonators: Intrinsically Better Than Graphene?

J-W Jiang, H.S. Park and T. Rabczuk
Nanoscale 2014; 6:3618-3625

Abstract

We perform classical molecular dynamics simulations to examine the intrinsic energy dissipation in single-layer MoS2 nanoresonators, where a point of emphasis is to compare its dissipation characteristics with those of single-layer graphene. Our key finding is that MoS2 nanoresonators exhibit significantly lower energy dissipation, and thus higher quality (Q)-factors by at least a factor of four below room temperature, than graphene. Furthermore, this high Q-factor endows MoS2 nanoresonators with a higher figure of merit, defined as frequency times Q-factor, despite a resonant frequency that is 50% smaller than graphene for the same size. By utilizing arguments from phonon-phonon scattering theory, we show that this reduced energy dissipation is enabled by the large energy gap in the phonon dispersion of MoS2, which separates the acoustic phonon branches from the optical phonon branches, leading to a preserving mechanism for the resonant oscillation of MoS2 nanoresonators. We further investigate the effects of tensile mechanical strain and nonlinear actuation on the Q-factors, where the tensile strain is found to counteract the reductions in Q-factor that occur with higher actuation amplitudes. Overall, our simulations illustrate the potential utility of MoS2 for high frequency sensing and actuation applications.

This paper is available in PDF form .


Adsorbate Migration Effects on Continuous and Discontinuous Temperature-Dependent Transitions in the Quality Factors of Graphene Nanoresonators

J-W Jiang, B-S Wang, H.S. Park and T. Rabczuk
Nanotechnology 2014; 25:025501

Abstract

We perform classical molecular dynamics simulation to investigate the mechanisms underpinning the unresolved, experimentally-observed temperature-dependent scaling transition in the quality factors of graphene nanomechanical resonators (GNMR). Our simulations reveal that the mechanism underlying this temperature scaling phenomenon is the out-of-plane migration of adsorbates on GNMRs. Specifically, the migrating adsorbate undergoes frequent collisions with the GNMR, which strongly influences the resulting mechanical oscillation, and thus the quality factors. We also predict a discontinuous transition in the quality factor at a lower critical temperature, which results from the in-plane migration of the adsorbate. Overall, our work clearly demonstrates the strong effect of adsorbate migration on the quality factors of GNMRs.

This paper is available in PDF form .


Density Functional Theory Calculation of Edge Stresses in Monolayer MoS2

Z.N. Qi, P. Cao and H.S. Park
Journal of Applied Physics 2013; 114:163508

Abstract

We utilize density functional theory to calculate the edge energy and edge stress for monolayer MoS2 nanoribbons. In contrast to previous reports for graphene, for both armchair and zigzag chiralities, the edge stresses for MoS2 nanoribbons are found to be tensile, indicating that their lowest energy configuration is one of compression in which Mo-S bond lengths are shorter than those in a bulk, periodic MoS2 monolayer. The edge energy and edge stress is found to converge for both chiralities for nanoribbon widths larger than about 1 nm.

This paper is available in PDF form .


Elastic Bending Modulus of Single-Layer Molybdenum Disulphide (MoS2): Finite Thickness Effect

J-W Jiang, Z.N. Qi, H.S. Park and T. Rabczuk
Nanotechnology 2013; 24:435705

Abstract

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.

This paper is available in PDF form .


Molecular Dynamics Simulations of Single-Layer Molybdenum Disulphide (MoS2): Stillinger-Weber Parametrization, Mechanical Properties, and Thermal Conductivity

J-W Jiang, H.S. Park and T. Rabczuk
Journal of Applied Physics 2013; 114:064307

Abstract

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 Young's 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 Young's 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.

This paper is available in PDF form .


Defecting controllability of bombarding graphene with different energetic atoms via reactive force field model

X.Y. Liu, F.C. Wang, H.S. Park and H.A. Wu
Journal of Applied Physics 2013; 114:054313

Abstract

We study the bombardment of a suspended monolayer graphene sheet via different energetic atoms via classical molecular dynamics based on the reactive force field (ReaxFF). We find that the probability, quality and controllability of defects are mainly determined by the impact site, the properties of the incident atom and the incident energy. Through comparison with density functional theory calculations, we demonstrate that defects and vacancies in graphene form only in regions of sufficiently high electron density. Furthermore, the quality of defects is influenced by the bond order of the incident atom-carbon bonds, where a higher bond order leads to lower probability of pristine defects (vacancies) but a higher probability of direct-substitution. Finally, the incident energy plays an important role on the evolution and final pattern of defects in graphene. Based on the probability, quality and controllability analysis performed, we depict a full-range energy spectrum for atomic bombardment, where we demonstrate that desirable defects such as single vacancies and direct-substitution can be created with the appropriate incident energy.

This paper is available in PDF form .


Resonant Tunneling in Graphene Pseudomagnetic Quantum Dots

Z.N. Qi, D.A. Bahamon, V.M. Pereira, H.S. Park, D.K. Campbell and A.H. Castro Neto
Nano Letters 2013; 13:2692-2697

Abstract

Realistic relaxed configurations of triaxially strained graphene quantum dots are obtained from unbiased atomistic mechanical simulations. The local electronic structure and quantum transport characteristics of y-junctions based on such dots are studied, revealing that the quasi-uniform pseudomagnetic field induced by strain restricts transport to Landau level- and edge state-assisted resonant tunneling. Valley degeneracy is broken in the presence of an external field, allowing the selective filtering of the valley and chirality of the states assisting in the resonant tunneling. Asymmetric strain conditions can be explored to select the exit channel of the y-junction.

This paper is available in PDF form .


How graphene slides: Measurement and theory of strain-dependent frictional forces between graphene and SiO2

A.L. Kitt, Z.N. Qi, S. Remi, H.S. Park, A.K. Swan and B.B. Goldberg
Nano Letters 2013; 13:2605-2610

Abstract

Strain, bending rigidity, and adhesion are interwoven in determining how graphene responds when pulled across a substrate. Using Raman spectroscopy of circular, graphene-sealed microchambers under variable external pressure, we demonstrate that graphene is not firmly anchored to the substrate when pulled. Instead, as the suspended graphene is pushed into the chamber under pressure, the supported graphene outside the microchamber is stretched and slides, pulling in an annulus. Analyzing Raman G band line scans with a continuum model extended to include sliding, we extract the pressure dependent sliding friction between the SiO2 substrate and mono-, bi-, and tri-layer graphene. The sliding friction for trilayer graphene is directly proportional to the applied load, but the friction for monolayer and bilayer graphene is inversely proportional to the strain in the graphene, in violation of Amontons' law. We attribute this behavior to the high surface conformation enabled by the low bending rigidity and strong adhesion of few layer graphene.

This paper is available in PDF form .


Enhancing the Mass Sensitivity of Graphene Nanoresonators Via Nonlinear Oscillations: The Effective Strain Mechanism

J-W Jiang, H.S. Park and T. Rabczuk
Nanotechnology 2012; 23:475501

Abstract

We perform classical molecular dynamics simulations to investigate the enhancement of the mass sensitivity and resonant frequency of graphene nanomechanical resonators that is achieved by driving them into the nonlinear oscillation regime. The mass sensitivity as measured by the resonant frequency shift is found to triple if the actuation energy is about 2.5 times the initial kinetic energy of the nanoresonator. The mechanism underlying the enhanced mass sensitivity is found to be the effective strain that is induced in the nanoresonator due to the nonlinear oscillations, where we obtain an analytic relationship between the induced effective strain and the actuation energy that is applied to the graphene nanoresonator. An important implication of this work is that there is no need for experimentalists to apply tensile strain to the resonators before actuation in order to enhance the mass sensitivity. Instead, enhanced mass sensitivity can be obtained by the far simpler technique of actuating nonlinear oscillations of an existing graphene nanoresonator.

This paper is available in PDF form .


Intrinsic Energy Dissipation in CVD-Grown Graphene Nanoresonators

Z.N. Qi and H.S. Park
Nanoscale 2012; 4:3460-3465

Abstract

We utilize classical molecular dynamics to study the the quality (Q)-factors of monolayer CVD-grown graphene nanoresonators. In particular, we focus on the effects of intrinsic grain boundaries of different orientations, which result from the CVD growth process, on the Q-factors. For a range of misorientations orientation angles that are consistent with those seen experimentally in CVD-grown graphene, i.e. 0 to 20 degrees, we find that the Q-factors for graphene with intrinsic grain boundaries are 1-2 orders of magnitude smaller than that of pristine monolayer graphene. We find that the Q-factor degradation is strongly influenced by both the symmetry and structure of the 5-7 defect pairs that occur at the grain boundary. Because of this, we also demonstrate that find the Q-factors CVD-grown graphene can be significantly elevated, and approach that of pristine graphene, through application of modest (1%) tensile strain.

This paper is available in PDF form .


On The Effective Plate Thickness of Monolayer Graphene from Flexural Wave Propagation

S.Y. Kim and H.S. Park
Journal of Applied Physics 2011; 110:054324

Abstract

We utilize classical molecular dynamics to study flexural, or transverse wave propagation in monolayer graphene sheets, and compare the resulting dispersion relationships to those expected from continuum thin plate theory. In doing so, we determine that regardless of the chirality for monolayer graphene, transverse waves exhibit a dispersion relationship that corresponds to the lowest order antisymmetric (A0) mode of wave propagation in a thin plate with plate thickness of h=0.104 nm. Finally, we find that the achievable wave speeds in monolayer graphene are found to exceed those reported previously for single walled carbon nanotubes, while the frequency of wave propagation in the graphene monolayer is found to reach the terahertz range, similar to that of carbon nanotubes.

This paper is available in PDF form .


Size-Dependence of the Nonlinear Elastic Softening of Nanoscale Graphene Monolayers Under Plane-Strain Bulge Tests: A Molecular Dynamics Study

S. Jun, T. Tashi and H.S. Park
Journal of Nanomaterials 2011; 380286.
(Invited paper: Special issue on Low-Dimensional Carbon Nanomaterials: Synthesis, Properties, and Applications)

Abstract

The pressure bulge test is an experimental technique to characterize the mechanical properties of microscale thin films. Here we perform constant-temperature molecular dynamics simulations of the plane-strain cylindrical bulge test of nano-sized monolayer graphene subjected to high gas pressure induced by hydrogen molecules. We observe a nonlinear elastic softening of the graphene with an increase in hydrogen pressure due to the stretching and weakening of the carbon-carbon bonds; we further observe that this softening behavior depends upon the size of the graphene monolayers. Our simulation results suggest that the traditional microscale bulge formulas, which assume constant elastic moduli, should be modified to incorporate the size dependence and elastic softening that occur in nano-sized graphene bulge tests.

This paper is available in PDF form .


Boundary Condition and Strain Effects on the Quality Factors of Single Walled Carbon Nanotubes

S.Y. Kim and H.S. Park
Journal of Computational and Theoretical Nanoscience 2011; 8:814-819.
(Invited paper: Special Issue on Multiscale and Multiphysics Simulations for Energy Applications)

Abstract

We utilize classical molecular dynamics to study energy dissipation (the Q-factors) of carbon nanotube-based nanoresonators undergoing flexural oscillations. Specifically, we have studied the difference in Q-factors of nanotubes with fixed/fixed and fixed/free boundary conditions. In doing so, we have found that fixed/fixed nanotubes have significantly higher Q-factors, particularly at low temperatures. Furthermore, we have found that mechanical strain can be utilized to enhance the Q-factors of fixed/fixed nanotubes by factors of 2-4 across a range of temperatures for tensile strains ranging from 0 to 6%. The results collectively indicate that fixed/fixed carbon nanotubes should be preferable for NEMS applications at low temperature due to a combination of inherently higher Q-factors, and the fact that the Q-factors can be further improved through the application of tensile strain.

This paper is available in PDF form .


A Molecular Simulation Analysis of Producing Monatomic Carbon Chains by Stretching Ultranarrow Graphene Nanoribbons

Z.N. Qi, F.P. Zhao, X.Z. Zhou, H.S. Park and H.A. Wu
Nanotechnology 2010; 21:265702.

Abstract

Atomistic simulations were utilized to develop fundamental insights regarding the elongation process starting from ultranarrow graphene nanoribbons (GNRs) and resulting in monatomic carbon chains (MACCs). There are three key findings. First, we demonstrate that complete, elongated, and stable MACCs with fracture strains exceeding 100% can be formed from both ultranarrow armchair and zigzag GNRs. Second, we demonstrate that the deformation processes leading to the MACCs have strong chirality dependence. Specifically, armchair GNRs first form DNA-like chains, then develop into monatomic chains by passing through an intermediate configuration in which monatomic chain sections are separated by two-atom attachments. In contrast, zigzag GNRs form rope-ladder-like chains through a process in which the carbon hexagons are first elongated into rectangles; these rectangles eventually coalesce into monatomic chains through a novel triangle-pentagon deformation structure under further tensile deformation. Finally, we show that the width of GNRs plays an important role in the formation of MACCs, and that the ultranarrow GNRs facilitate the formation of full MACCs. The present work should be of considerable interest due to the experimentally demonstrated feasibility of using narrow GNRs to fabricate novel nanoelectronic components based upon monatomic chains of carbon atoms.

This paper is available in PDF form .


On the Utility of Vacancies and Tensile Strain-Induced Quality Factor Enhancement for Mass Sensing Using Graphene Monolayers

S. Y. Kim and H. S. Park
Nanotechnology 2010; 21:105710.

Abstract

We have utilized classical molecular dynamics to investigate the mass sensing potential of graphene monolayers, using gold as the model adsorbed atom. In doing so, we report two key findings. First, we find that while perfect graphene monolayers are effective mass sensors at very low (T<10K) temperatures, their mass sensing capability is lost at higher temperatures due to diffusion of the adsorbed atom at elevated temperatures. We demonstrate that even if the quality (Q) factors are significantly elevated through the application of tensile mechanical strain, the mass sensing resolution is still lost at elevated temperatures, which demonstrates that high Q-factors alone are insufficient to ensure the mass sensing capability of graphene. Second, we find that while the introduction of single vacancies into the graphene monolayer prevents the diffusion of the adsorbed atom, the mass sensing resolution is still lost at higher temperatures, again due to Q-factor degradation. We finally demonstrate that if the Q-factors of the graphene monolayers with single vacancies are kept acceptably high through the application of tensile strain, that the high Q-factors, in conjunction with the single atom vacancies to stop the diffusion of the adsorbed atom, enables graphene to maintain its mass sensing capability across a range of technologically relevant operating temperatures.

This paper is available in PDF form .


Multilayer Friction and Attachment Effects on Energy Dissipation in Graphene Nanoresonators

S. Y. Kim and H. S. Park
Applied Physics Letters 2009; 94:101918.
(Also selected for publication in the Virtual Journal of Nanoscale Science and Technology, March 30, 2009).

Abstract

We utilize classical molecular dynamics to study the effects of intrinsic, interlayer friction between graphene monolayers, as well as extrinsic attachment or clamping strength between graphene and a model silicon substrate on the energy dissipation (Q-factors) of oscillating graphene nanoresonators. Both interlayer friction and attachment effects are found to significantly degrade the graphene Q-factors, with an increase in energy dissipation with increasing temperature, while both effects are found to be strongly dependent on the strength of the van der Waal's interactions, either between adjacent layers of graphene or between graphene and the underlying substrate.

This paper is available in PDF form .


The Importance of Edge Effects on the Intrinsic Loss Mechanisms of Graphene Nanoresonators

S. Y. Kim and H. S. Park
Nano Letters 2009; 9(3):969-974.

Abstract

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 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; however, we also demonstrate that the intrinsic losses can be reduced significantly across a range of operating temperatures through the application of tensile mechanical strain.

This paper is available in PDF form .


Action-Derived Ab Initio Molecular Dynamics

S. Jun, S. Pendurti, I.-H. Lee, S. Y. Kim, H. S. Park and Y.-H. Kim
International Journal of Applied Mechanics 2009; 1:469-482.

Abstract

Action-derived molecular dynamics (ADMD) is a numerical method to search for minimum-energy dynamic pathways on potential-energy surface. The method is based on the Hamilton's least action principle and has been developed for problems of activated processes, rare events, and long-time simulations. In this paper, ADMD is further extended to incorporate ab initio total-energy calculations, which enables the detailed electronic analysis of transition states as well as the exploration of energy landscapes. Three numerical examples are solved to demonstrate the capability of this action-derived ab initio molecular dynamics. The proposed approach is expected to circumvent the severe time-scale limitation of conventional ab intio molecular dynamics simulations.

This paper is available in PDF form .