The Structure of Graphene on Graphene/C60/Cu Interfaces: A Molecular Dynamics Study

Two experimental studies reported the spontaneous formation of amorphous and crystalline structures of C60 intercalated between graphene and a substrate. They observed interesting phenomena ranging from reaction between C60 molecules under graphene to graphene sagging between the molecules and control of strain in graphene. Motivated by these works, we performed fully atomistic reactive molecular dynamics simulations to study the formation and thermal stability of graphene wrinkles as well as graphene attachment to and detachment from the substrate when graphene is laid over a previously distributed array of C60 molecules on a copper substrate at different values of temperature. As graphene compresses the C60 molecules against the substrate, and graphene attachment to the substrate between C60s ("C60s" stands for plural of C60) depends on the height of graphene wrinkles, configurations with both frozen and non-frozen C60s structures were investigated in order to verify the experimental result of stable sagged graphene when the distance between C60s is about 4 nm and height of graphene wrinkles is about 0.8 nm. Below the distance of 4 nm between C60s, graphene becomes locally suspended and less strained. We show that this happens when C60s are allowed to deform under the compressive action of graphene. If we keep the C60s frozen, spontaneous "blanketing" of graphene happens only when the distance between them are equal or above 7 nm. Both above results for the existence of stable sagged graphene for C60 distances of 4 or 7 nm are shown to agree with a mechanical model relating the rigidity of graphene to the energy of graphene-substrate adhesion. In particular, this study might help the development of 2D confined nanoreactors that are considered in literature to be the next advanced step on chemical reactions.Comment: 7 pages, 4 figure

Isospin Constraints on the Parametric Coupling Model for Nuclear Matter

We make use of isospin constraints to study the parametric coupling model and the properties of asymmetric nuclear matter. Besides the usual constraints for nuclear matter - effective nucleon mass and the incompressibility at saturation density - and the neutron star constraints - maximum mass and radius - we have studied the properties related with the symmetry energy. These properties have constrained to a small range the parameters of the model. We have applied our results to study the thermodynamic instabilities in the liquid-gas phase transition as well as the neutron star configurations.Comment: 11 pages, 10 figure

Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding \mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial non-periodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parameterized by the normalized incomplete beta function I_d = I_{1/4}[1/2,(d+1)/2]. The joint distribution S_{\mu,d}^{(N)}(t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is: S_{1,d}^{(\infty)}(t,p) = [\Gamma(1+I_d^{-1}) (t+I_d^{-1})/\Gamma(t+p+I_d^{-1})] \delta_{p,2}, where t=0,1,2,...,\infty, \Gamma(z) is the gamma function and \delta_{i,j} is the Kronecker's delta. The mean field models are random link model, which corresponds to d \to \infty, and random map model which, even for \mu = 0, presents non-trivial cycle distribution [S_{0,rm}^{(N)}(p) \propto p^{-1}]: S_{0,rm}^{(N)}(t,p) = \Gamma(N)/\{\Gamma[N+1-(t+p)]N^{t+p}\}. The fundamental quantities are the number of explored points n_e=t+p and I_d. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.Comment: 9 pages and 4 figure

A control on quantum fluctuations in 2+1 dimensions

A functional method is discussed, where the quantum fluctuations of a theory are controlled by a mass parameter and the evolution of the theory with this parameter is connected to its renormalization. It is found, in the framework of the gradient expansion, that the coupling constant of a N=1 Wess-Zumino theory in 2+1 dimensions does not get quantum corrections.Comment: Comments adde