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 L as a power law L(-η(u)) with η(u)≃0.325, in agreement with the membrane theory. We provide explicit expressions for the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Our results explain the recently experimentally observed increase of the Young modulus by more than a factor of 2 for a tensile strain of only a few per mill. The difference of a factor of 2 between the measured asymptotic value of the Young modulus for tensilely strained systems and the value from ab initio calculations remains, however, unsolved. We also discuss the asymptotic behavior of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.

Melting of graphene: from two to one dimension.

The high temperature behaviour of graphene is studied by atomistic simulations based on an accurate interatomic potential for carbon. We find that clustering of Stone-Wales defects and formation of octagons are the first steps in the process of melting which proceeds via the formation of carbon chains. The molten state forms a three-dimensional network of entangled chains rather than a simple liquid. The melting temperature estimated from the two-dimensional Lindemann criterion and from extrapolation of our simulation for different heating rates is about 4900 K.

Theoretical study of the nucleation/growth process of carbon clusters under pressure.

We used molecular dynamics and the empirical potential for carbon LCBOPII to simulate the nucleation/growth process of carbon clusters both in vacuum and under pressure. In vacuum, our results show that the growth process is homogeneous and yields mainly sp(2) structures such as fullerenes. We used an argon gas and Lennard-Jones potentials to mimic the high pressures and temperatures reached during the detonation of carbon-rich explosives. We found that these extreme thermodynamic conditions do not affect substantially the topologies of the clusters formed in the process. However, our estimation of the growth rates under pressure are in much better agreement with the values estimated experimentally than our vacuum simulations. The formation of sp(3) carbon was negligible both in vacuum and under pressure which suggests that larger simulation times and cluster sizes are needed to allow the nucleation of nanodiamonds.

Solubility of molecular crystals: polymorphism in the light of solubility theory.

The thermodynamic theory of solubility of molecular crystals in solvents is reviewed with an emphasis on solutes showing polymorphism as in case of many pharmaceuticals. The relation between solubility and binary phase diagrams of the solute solvent system is treated. The astonishing variety of possible solubility curves as a function of temperature is explained using simple models for the solution thermodynamics assuming no mixing between the solvent and solute in the solid phase, though including the case of solvates or pseudo polymorphs. In passing a new method is introduced that allows to estimate the transition temperature of enantiotropically related polymorphs from melting temperatures and enthalpies of the polymorphs.

Intrinsic ripples in graphene.

The stability of two-dimensional (2D) layers and membranes is the subject of a long-standing theoretical debate. According to the so-called Mermin-Wagner theorem, long-wavelength fluctuations destroy the long-range order of 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes meaning that a 2D membrane can exist but will exhibit strong height fluctuations. The discovery of graphene, the first truly 2D crystal, and the recent experimental observation of ripples in suspended graphene make these issues especially important. Besides the academic interest, understanding the mechanisms of the stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest owing to its unusual Dirac spectrum and electronic properties. We address the nature of these height fluctuations by means of atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear owing to thermal fluctuations with a size distribution peaked around 80 A which is compatible with experimental findings (50-100 A). This unexpected result might be due to the multiplicity of chemical bonding in carbon.

On the definition of a Monte Carlo model for binary crystal growth.

We show that consistency of the transition probabilities in a lattice Monte Carlo (MC) model for binary crystal growth with the thermodynamic properties of a system does not guarantee the MC simulations near equilibrium to be in agreement with the thermodynamic equilibrium phase diagram for that system. The deviations remain small for systems with small bond energies, but they can increase significantly for systems with large melting entropy, typical for molecular systems. These deviations are attributed to the surface kinetics, which is responsible for a metastable zone below the liquidus line where no growth occurs, even in the absence of a 2D nucleation barrier. Here we propose an extension of the MC model that introduces a freedom of choice in the transition probabilities while staying within the thermodynamic constraints. This freedom can be used to eliminate the discrepancy between the MC simulations and the thermodynamic equilibrium phase diagram. Agreement is achieved for that choice of the transition probabilities yielding the fastest decrease of the free energy (i.e., largest growth rate) of the system at a temperature slightly below the equilibrium temperature. An analytical model is developed, which reproduces quite well the MC results, enabling a straightforward determination of the optimal set of transition probabilities. Application of both the MC and analytical model to conditions well away from equilibrium, giving rise to kinetic phase diagrams, shows that the effect of kinetics on segregation is even stronger than that predicted by previous models.