6,879 research outputs found
Mechanics of thermally fluctuating membranes
Besides having unique electronic properties, graphene is claimed to be the
strongest material in nature. In the press release of the Nobel committee it is
claimed that a hammock made of a squared meter of one-atom thick graphene could
sustain the wight of a 4 kg cat. More practically important are applications of
graphene like scaffolds and sensors which are crucially dependent on the
mechanical strength. Meter-sized graphene is even being considered for the
lightsails in the starshot project to reach the star alpha centaury. The
predicted strength of graphene is based on its very large Young modulus which
is, per atomic layer, much larger than that of steel. This reasoning however
would apply to conventional thin plates but does not take into account the
peculiar properties of graphene as a thermally fluctuating crystalline
membrane. It was shown recently both experimentally and theoretically that
thermal fluctuations lead to a dramatic reduction of the Young modulus and
increase of the bending rigidity for micron-sized graphene samples in
comparison with atomic scale values. This makes the use of the standard
F\"oppl-von Karman elasticity (FvK) theory for thin plates not directly
applicable to graphene and other single atomic layer membranes. This fact is
important because the current interpretation of experimental results is based
on the FvK theory. In particular, we show that the FvK-derived Schwerin
equation, routinely used to derive the Young modulus from indentation
experiments has to be essentially modified for graphene at room temperature and
for micron sized samples. Based on scaling analysis and atomistic simulation we
investigate the mechanics of graphene under transverse load up to breaking. We
determine the limits of applicability of the FvK theory and provide
quantitative estimates for the different regimes.Comment: to appear in npj 2D Materials and Application
Scaling behavior and strain dependence of in-plane elastic properties of graphene
We show by atomistic simulations that, in the thermodynamic limit, the
in-plane elastic moduli of graphene at finite temperature vanish with system
size as a power law with , in
agreement with the membrane theory. Our simulations clearly reveal the size and
strain dependence of graphene's elastic moduli, allowing comparison to
experimental data. Although the recently measured difference of a factor 2
between the asymptotic value of the Young modulus for tensilely strained
systems and the value from {\it ab initio} calculations remains unsolved, our
results do explain the experimentally observed increase of more than a factor 2
for a tensile strain of only a few permille. We also discuss the scaling of the
Poisson ratio, for which our simulations disagree with the predictions of the
self-consistent screening approximation.Comment: 5 figure
Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure
Computer simulations are used to generate two-dimensional diffusion-limited
deposits of dipoles. The structure of these deposits is analyzed by measuring
some global quantities: the density of the deposit and the lateral correlation
function at a given height, the mean height of the upper surface for a given
number of deposited particles and the interfacial width at a given height.
Evidences are given that the fractal dimension of the deposits remains constant
as the deposition proceeds, independently of the dipolar strength. These same
deposits are used to obtain the growth probability measure through Monte Carlo
techniques. It is found that the distribution of growth probabilities obeys
multifractal scaling, i.e. it can be analyzed in terms of its
multifractal spectrum. For low dipolar strengths, the spectrum is
similar to that of diffusion-limited aggregation. Our results suggest that for
increasing dipolar strength both the minimal local growth exponent
and the information dimension decrease, while the fractal
dimension remains the same.Comment: 10 pages, 7 figure
Diffusion-limited deposition of dipolar particles
Deposits of dipolar particles are investigated by means of extensive Monte
Carlo simulations. We found that the effect of the interactions is described by
an initial, non-universal, scaling regime characterized by orientationally
ordered deposits. In the dipolar regime, the order and geometry of the clusters
depend on the strength of the interactions and the magnetic properties are
tunable by controlling the growth conditions. At later stages, the growth is
dominated by thermal effects and the diffusion-limited universal regime
obtains, at finite temperatures. At low temperatures the crossover size
increases exponentially as T decreases and at T=0 only the dipolar regime is
observed.Comment: 5 pages, 4 figure
Melting temperature of graphene
We present an approach to the melting of graphene based on nucleation theory
for a first order phase transition from the 2D solid to the 3D liquid via an
intermediate quasi-2D liquid.
The applicability of nucleation theory, supported by the results of
systematic atomistic Monte Carlo simulations, provides an intrinsic definition
of the melting temperature of graphene, , and allows us to determine it.
We find K, about 250 K higher than that of graphite using the
same interatomic interaction model. The found melting temperature is shown to
be in good agreement with the asymptotic results of melting simulations for
finite disks and ribbons of graphene. Our results strongly suggest that
graphene is the most refractory of all known materials
Spiral graphone and one sided fluorographene nano-ribbons
The instability of a free-standing one sided hydrogenated/fluorinated
graphene nano-ribbon, i.e. graphone/fluorographene, is studied using ab-initio,
semiempirical and large scale molecular dynamics simulations. Free standing
semi-infinite arm-chair like hydrogenated/fluorinated graphene (AC-GO/AC-GF)
and boat like hydrogenated/fluorinated graphene (B-GO/B-GF) (nano-ribbons which
are periodic along the zig-zag direction) are unstable and spontaneously
transform into spiral structures. We find that rolled, spiral B-GO and B-GF are
energetically more favorable than spiral AC-GO and AC-GF which is opposite to
the double sided flat hydrogenated/fluorinated graphene, i.e.
graphane/fluorographene. We found that the packed, spiral structures exhibit
unexpected localized HOMO-LUMO at the edges with increasing energy gap during
rolling. These rolled hydrocarbon structures are stable beyond room temperature
up to at least =1000\,K.Comment: Phys. Rev. B 87, 075448 (2013
Levy-Nearest-Neighbors Bak-Sneppen Model
We study a random neighbor version of the Bak-Sneppen model, where "nearest
neighbors" are chosen according to a probability distribution decaying as a
power-law of the distance from the active site, P(x) \sim |x-x_{ac
}|^{-\omega}. All the exponents characterizing the self-organized critical
state of this model depend on the exponent \omega. As \omega tends to 1 we
recover the usual random nearest neighbor version of the model. The pattern of
results obtained for a range of values of \omega is also compatible with the
results of simulations of the original BS model in high dimensions. Moreover,
our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in
contrast with previous claims.Comment: To appear on Phys. Rev. E, Rapid Communication
Atomistic simulations of structural and thermodynamic properties of bilayer graphene
We study the structural and thermodynamic properties of bilayer graphene, a
prototype two-layer membrane, by means of Monte Carlo simulations based on the
empirical bond order potential LCBOPII. We present the temperature dependence
of lattice parameter, bending rigidity and high temperature heat capacity as
well as the correlation function of out-of-plane atomic displacements. The
thermal expansion coefficient changes sign from negative to positive above
K, which is lower than previously found for single layer graphene
and close to the experimental value of bulk graphite. The bending rigidity is
twice as large than for single layer graphene, making the out-of-plane
fluctuations smaller. The crossover from correlated to uncorrelated
out-of-plane fluctuations of the two carbon planes occurs for wavevectors
shorter than nmComment: 6 pages, 7 figures
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