An upper bound for the equitable chromatic number of complete n-partite graphs

A proper vertex coloring of a graph $G$ is equitable if the size of color classes differ by at most one. The equitable chromatic number of $G$ is the smallest integer $m$ such that $G$ is equitable m-colorable. In this paper, we derive an upper bound for the equitable chromatic number of complete n-partite graph $K_{p_{1},p_{2}, ... ,p_{n}}$

Stability, Adsorption and Diffusion of CH4, CO2 and H2 in Clathrate Hydrates

We present a study of the adsorption and diffusion of CH4, CO2 and H2 molecules in clathrate hydrates using ab initio van der Waals density functional formalism [Dion et al. Phys. Rev. Lett. 92, 246401 (2004)]. We find that the adsorption energy is dominated by van der Waals interactions and that, without them, gas hydrates would not be stable. We calculate the maximum adsorption capacity as well as the maximum hydrocarbon size that can be adsorbed.The relaxation of the host lattice is essential for a good description of the diffusion activation energies, which are estimated to be of the order of 0.2, 0.4, and 1.0 eV for H2, CO2, and CH4, respectively.Comment: 4 pages, 4 figures, 3 table

Theoretical study of the dynamics of atomic hydrogen adsorbed on graphene multilayers

We present a theoretical study of the dynamics of H atoms adsorbed on graphene bilayers with Bernal stacking. First, through extensive density functional theory calculations, including van der Waals Interactions, we obtain the activation barriers involved in the desorption and migration processes of a single H atom. These barriers, along with attempt rates and the energetics of H pairs, are used as input parameters in kinetic Monte Carlo simulations to study the time evolution of an initial random distribution of adsorbed H atoms. The simulations reveal that, at room temperature, H atoms occupy only one sublattice before they completely desorb or form clusters. This sublattice selectivity in the distribution of H atoms may last for sufficiently long periods of time upon lowering the temperature down to 0 ◦C. The final fate of the H atoms, namely, desorption or cluster formation, depends on the actual relative values of the activation barriers which can be tuned by doping. In some cases, a sublattice selectivity can be obtained for periods of time experimentally relevant even at room temperature. This result shows the possibility for observation and applications of the ferromagnetic state associated with such distributionThis work was supported by MINECO under Grant Nos. FIS2013-47328 and FIS2012-37549, by CAM under Grant Nos. S2013/MIT-3007, P2013/MIT-2850, and by Generalitat Valenciana under Grant PROMETEO/2012/01

Local electroexfoliation of graphene with a STM tip

Graphite surfaces can be manipulated by several methods to create graphene structures of different shapes and sizes. Scanning tunneling microscopy (STM) can be used to create these structures either through mechanical contact between the tip and the surface or through electro-exfoliation. In the latter, the mechanisms involved in the process of exfoliation with an applied voltage are not fully understood. Here we show how a graphite surface can be locally exfoliated in a systematic manner by applying an electrostatic force with a STM tip at the edge of a terrace, forming triangular flakes several nanometers in length. We demonstrate, through experiments and simulations, how these flakes are created by a two-step process: first a voltage ramp must be applied at the edge of the terrace, and then the tip must be scanned perpendicularly to the edge. Ab-initio electrostatic calculations reveal that the presence of charges on the graphite surface weakens the interaction between layers allowing for exfoliation at voltages in the same range as those used experimentally. Molecular dynamics simulations show that a force applied locally on the edge of a step produces triangular flakes such as those observed under STM. Our results provide new insights towards surface modification that can be extended to other layered materials

Graphene flakes obtained by local electro-exfoliation of graphite with a STM tip

Graphite surfaces can be manipulated by several methods to create graphene structures of different shapes and sizes. Scanning tunneling microscopy (STM) can be used to create these structures either through mechanical contact between the tip and the surface or through electro-exfoliation. In the latter, the mechanisms involved in the process of exfoliation at an applied voltage are not fully understood. Here, we show how a graphite surface can be locally exfoliated in a systematic manner by applying an electrostatic force with a STM tip at the edge of a terrace, forming triangular flakes several nanometers in length. We demonstrate, through experiments and simulations, how these flakes are created by a two-step process: first a voltage ramp must be applied at the edge of the terrace, and then the tip must be scanned perpendicular to the edge. Ab initio electrostatic calculations reveal that the presence of charges on the graphite surface weakens the interaction between layers allowing for exfoliation at voltages in the same range as those used experimentally. Molecular dynamics simulations show that a force applied locally on the edge of a step produces triangular flakes such as those observed under STM. Our results provide new insights into surface modification that can be extended to other layered materials.Las superficies de grafito se pueden manipular mediante varios métodos para crear estructuras de grafeno de diferentes formas y tamaños. La microscopía de túnel de barrido (STM) se puede utilizar para crear estas estructuras ya sea a través del contacto mecánico entre la punta y la superficie o mediante electroexfoliación. En este último, los mecanismos involucrados en el proceso de exfoliación a un voltaje aplicado no se comprenden completamente. Aquí, mostramos cómo una superficie de grafito puede exfoliarse localmente de manera sistemática aplicando una fuerza electrostática con una punta STM en el borde de una terraza, formando escamas triangulares de varios nanómetros de longitud. Demostramos, a través de experimentos y simulaciones, cómo se crean estos copos mediante un proceso de dos pasos: primero se debe aplicar una rampa de voltaje en el borde de la terraza, y luego se debe escanear la punta perpendicular al borde. Los cálculos electrostáticos Ab initio revelan que la presencia de cargas en la superficie de grafito debilita la interacción entre capas, lo que permite la exfoliación a voltajes en el mismo rango que los utilizados experimentalmente. Las simulaciones de dinámica molecular muestran que una fuerza aplicada localmente en el borde de un escalón produce escamas triangulares como las observadas en STM. Nuestros resultados proporcionan nuevos conocimientos sobre la modificación de la superficie que pueden extenderse a otros materiales en capas.Universidad Nacional, Costa RicaDepartamento de Físic