Numerical Analysis of Circular Graphene Bubbles

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Peng Wang ◽  
Wei Gao ◽  
Zhiyi Cao ◽  
Kenneth M. Liechti ◽  
Rui Huang
Keyword(s):  
Large Scale ◽  
Plate Theory ◽  
Approximate Solutions ◽  
Van Der Waals Interactions ◽  
Monolayer Graphene ◽  
Graphene Monolayer ◽  
Lateral Loads ◽  
Adhesive Properties ◽  
Dynamics Simulations ◽  
Low Pressures

Pressurized graphene bubbles have been observed in experiments, which can be used to determine the mechanical and adhesive properties of graphene. A nonlinear plate theory is adapted to describe the deformation of a graphene monolayer subject to lateral loads, where the bending moduli of monolayer graphene are independent of the in-plane Young's modulus and Poisson's ratio. A numerical method is developed to solve the nonlinear equations for circular graphene bubbles, and the results are compared to approximate solutions by analytical methods. Molecular dynamics simulations of nanoscale graphene bubbles are performed, and it is found that the continuum plate theory is suitable only within the limit of linear elasticity. Moreover, the effect of van der Waals interactions between graphene and its underlying substrate is analyzed, including large-scale interaction for nanoscale graphene bubbles subject to relatively low pressures.

Snap Transitions of Pressurized Graphene Blisters

2016 ◽  
Vol 83 (7) ◽  
Author(s):  
Peng Wang ◽  
Kenneth M. Liechti ◽  
Rui Huang
Keyword(s):  
Plate Theory ◽  
Numerical Study ◽  
Van Der Waals ◽  
Approximate Solutions ◽  
Interfacial Properties ◽  
Pressure Control ◽  
Van Der Waals Interactions ◽  
Volume Control ◽  
Monolayer Graphene ◽  
Separation Relation

Blister tests are commonly used to determine the mechanical and interfacial properties of thin film materials with recent applications for graphene. This paper presents a numerical study on snap transitions of pressurized graphene blisters. A continuum model is adopted combining a nonlinear plate theory for monolayer graphene with a nonlinear traction–separation relation for van der Waals interactions. Three types of blister configurations are considered. For graphene bubble blisters, snap-through and snap-back transitions between pancake-like and dome-like shapes are predicted under pressure-controlled conditions. For center-island graphene blisters, snap transitions between donut-like and dome-like shapes are predicted under both pressure and volume control. Finally, for the center-hole graphene blisters, growth is stable under volume or N-control but unstable under pressure control. With a finite hole depth, the growth may start with a snap transition under N-control if the hole is relatively deep. The numerical results provide a systematic understanding on the mechanics of graphene blisters, consistent with previously reported experiments. Of particular interest is the relationship between the van der Waals interactions and measurable quantities in corresponding blister tests, with which both the adhesion energy of graphene and the equilibrium separation for the van der Waals interactions may be determined. In comparison with approximate solutions based on membrane analyses, the numerical method offers more accurate solutions that may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials.

Large Area Quasi-Free Standing Monolayer Graphene on 3C-SiC(111)

2012 ◽  
Vol 717-720 ◽  
pp. 617-620 ◽  
Author(s):  
Ulrich Starke ◽  
Camilla Coletti ◽  
Konstantin Emtsev ◽  
Alexei A. Zakharov ◽  
Thierry Ouisse ◽  
...  
Keyword(s):  
Graphene Layer ◽  
Large Scale ◽  
Bulk Crystal ◽  
Monolayer Graphene ◽  
Graphene Monolayer ◽  
Large Area ◽  
Free Standing ◽  
Hydrogen Intercalation

Large scale, homogeneous quasi-free standing monolayer graphene is obtained on a (111) oriented cubic SiC bulk crystal. The free standing monolayer was prepared on the 3C-SiC(111) surface by hydrogen intercalation of a -reconstructed carbon monolayer, so-called zerolayer graphene, which had been grown in Ar atmosphere. The regular morphology of the surface, the complete chemical and structural decoupling of the graphene layer from the SiC substrate as well as the development of sharp monolayer p-bands are demonstrated. On the resulting sample, homogeneous graphene monolayer domains extend over areas of hundreds of square-micrometers.

Nanoscale toughening of ultrathin graphene oxide-polymer composites: mechanochemical insights into hydrogen-bonding/van der Waals interactions, polymer chain alignment, and steric parameters

Nanoscale ◽  
2019 ◽  
Vol 11 (25) ◽  
pp. 12305-12316 ◽  
Author(s):  
Xu Zhang ◽  
Hoang Nguyen ◽  
Matthew Daly ◽  
SonBinh T. Nguyen ◽  
Horacio D. Espinosa
Keyword(s):  
Molecular Dynamics ◽  
Hydrogen Bonding ◽  
Graphene Oxide ◽  
Polymer Composites ◽  
Van Der Waals Interactions ◽  
Monolayer Graphene ◽  
Design Criteria ◽  
Thin Polymer ◽  
Dynamics Simulations ◽  
Polymer Chain Alignment

Systematic molecular dynamics simulations reveal design criteria for utilization of ultra-thin polymer adlayer to toughen monolayer graphene oxide through nanoscale crack-bridging.

scholarly journals On the Consistency of the Exfoliation Free Energy of Graphenes by Molecular Simulations

2021 ◽  
Vol 22 (15) ◽  
pp. 8291
Author(s):  
Anastasios Gotzias ◽  
Elena Tocci ◽  
Andreas Sapalidis
Keyword(s):  
Free Energy ◽  
Saline Water ◽  
Bilayer Graphene ◽  
Umbrella Sampling ◽  
Van Der Waals Interactions ◽  
Monolayer Graphene ◽  
Graphene Monolayer ◽  
Shear Direction ◽  
Liquid Environment ◽  
Before And After

Monolayer graphene is now produced at significant yields, by liquid phase exfoliation of graphites in solvents. This has increased the interest in molecular simulation studies to give new insights in the field. We use decoupling simulations to compute the exfoliation free energy of graphenes in a liquid environment. Starting from a bilayer graphene configuration, we decouple the Van der Waals interactions of a graphene monolayer in the presence of saline water. Then, we introduce the monolayer back into water by coupling its interactions with water molecules and ions. A different approach to compute the graphene exfoliation free energy is to use umbrella sampling. We apply umbrella sampling after pulling the graphene monolayer on the shear direction up to a distance from a bilayer. We show that the decoupling and umbrella methods give highly consistent free energy results for three bilayer graphene samples with different size. This strongly suggests that the systems in both methods remain closely in equilibrium as we move between the states before and after the exfoliation. Therefore, the amount of nonequilibrium work needed to peel the two layers apart is minimized efficiently.

scholarly journals Elucidating the Onset of Plasticity in Sliding Contacts Using Differential Computational Orientation Tomography

2021 ◽  
Vol 69 (3) ◽  
Author(s):  
S. J. Eder ◽  
P. G. Grützmacher ◽  
M. Rodríguez Ripoll ◽  
J. F. Belak
Keyword(s):  
Grain Boundary ◽  
Large Scale ◽  
Surface Deformation ◽  
Boundary Migration ◽  
Material Design ◽  
Lattice Rotation ◽  
Time Resolved ◽  
Near Surface ◽  
Color Saturation ◽  
Dynamics Simulations

Abstract Depending on the mechanical and thermal energy introduced to a dry sliding interface, the near-surface regions of the mated bodies may undergo plastic deformation. In this work, we use large-scale molecular dynamics simulations to generate “differential computational orientation tomographs” (dCOT) and thus highlight changes to the microstructure near tribological FCC alloy surfaces, allowing us to detect subtle differences in lattice orientation and small distances in grain boundary migration. The analysis approach compares computationally generated orientation tomographs with their undeformed counterparts via a simple image analysis filter. We use our visualization method to discuss the acting microstructural mechanisms in a load- and time-resolved fashion, focusing on sliding conditions that lead to twinning, partial lattice rotation, and grain boundary-dominated processes. Extracting and laterally averaging the color saturation value of the generated tomographs allows us to produce quantitative time- and depth-resolved maps that give a good overview of the progress and severity of near-surface deformation. Corresponding maps of the lateral standard deviation in the color saturation show evidence of homogenization processes occurring in the tribologically loaded microstructure, frequently leading to the formation of a well-defined separation between deformed and undeformed regions. When integrated into a computational materials engineering framework, our approach could help optimize material design for tribological and other deformation problems. Graphic Abstract .

scholarly journals Large-scale molecular dynamics simulations of TiN/TiN(001) epitaxial film growth

2016 ◽  
Vol 34 (4) ◽  
pp. 041509 ◽  
Author(s):  
Daniel Edström ◽  
Davide G. Sangiovanni ◽  
Lars Hultman ◽  
Ivan Petrov ◽  
J. E. Greene ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Large Scale ◽  
Epitaxial Film ◽  
Film Growth ◽  
Dynamics Simulations ◽  
Epitaxial Film Growth

scholarly journals Algebraic multigrid methods

Acta Numerica ◽  
2017 ◽  
Vol 26 ◽  
pp. 591-721 ◽  
Author(s):  
Jinchao Xu ◽  
Ludmil Zikatanov
Keyword(s):  
Minimization Problem ◽  
Large Scale ◽  
Multigrid Method ◽  
Approximate Solutions ◽  
Multigrid Methods ◽  
Algebraic Multigrid ◽  
Unified Framework ◽  
Smoothed Aggregation ◽  
Algebraic Multigrid Methods ◽  
Coarse Space

This paper provides an overview of AMG methods for solving large-scale systems of equations, such as those from discretizations of partial differential equations. AMG is often understood as the acronym of ‘algebraic multigrid’, but it can also be understood as ‘abstract multigrid’. Indeed, we demonstrate in this paper how and why an algebraic multigrid method can be better understood at a more abstract level. In the literature, there are many different algebraic multigrid methods that have been developed from different perspectives. In this paper we try to develop a unified framework and theory that can be used to derive and analyse different algebraic multigrid methods in a coherent manner. Given a smoother$R$for a matrix$A$, such as Gauss–Seidel or Jacobi, we prove that the optimal coarse space of dimension$n_{c}$is the span of the eigenvectors corresponding to the first$n_{c}$eigenvectors$\bar{R}A$(with$\bar{R}=R+R^{T}-R^{T}AR$). We also prove that this optimal coarse space can be obtained via a constrained trace-minimization problem for a matrix associated with$\bar{R}A$, and demonstrate that coarse spaces of most existing AMG methods can be viewed as approximate solutions of this trace-minimization problem. Furthermore, we provide a general approach to the construction of quasi-optimal coarse spaces, and we prove that under appropriate assumptions the resulting two-level AMG method for the underlying linear system converges uniformly with respect to the size of the problem, the coefficient variation and the anisotropy. Our theory applies to most existing multigrid methods, including the standard geometric multigrid method, classical AMG, energy-minimization AMG, unsmoothed and smoothed aggregation AMG and spectral AMGe.

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