Effect of Water on the Manifestation of the Reaction Selectivity of Nitrogen-Doped Graphene Nanoclusters toward Oxygen Reduction Reaction.

We investigated the selectivity of N-doped graphene nanoclusters (N-GNCs) toward the oxygen reduction reaction (ORR) using first-principles calculations within the density functional theory. The results show that the maximum electrode potentials (U Max) for the four-electron (4e-) pathway are higher than those for the two-electron (2e-) pathway at almost all of the reaction sites. Thus, the N-GNCs exhibit high selectivity for the 4e- pathway, that is, the 4e- reduction proceeds preferentially over the 2e- reduction. Such high selectivity results in high durability of the catalyst because H2O2, which corrodes the electrocatalyst, is not generated. For the doping sites near the edge of the cluster, the value of U Max greatly depends on the reaction sites. However, for the doping sites around the center of the cluster, the reaction-site dependence is hardly observed. The GNC with a nitrogen atom around the center of the cluster exhibits higher ORR catalytic capability compared with the GNC with a nitrogen atom in the vicinity of the edge. The results also reveal that the water molecule generated by the ORR enhances the selectivity toward the 4e- pathway because the reaction intermediates are significantly stabilized by water.

Hierarchical structure in sharply divided phase space for the piecewise linear map.

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ∼t^{-2}, the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Formation of Water Layers on Graphene Surfaces.

Although graphitic materials were thought to be hydrophobic, recent experimental results based on contact angle measurements show that the hydrophobicity of graphitic surfaces stems from airborne contamination of hydrocarbons. This leads us to question whether a pristine graphitic surface is indeed hydrophobic. To investigate the water wettability of graphitic surfaces, we use molecular dynamics simulations of water molecules on the surface of a single graphene layer at room temperature. The results indicate that a water droplet spreads over the entire surface and that a double-layer structure of water molecules forms on the surface, which means that wetting of graphitic surfaces is possible, but only by two layers of water molecules. No further water layers can cohere to the double-layer structure, but the formation of three-dimensional clusters of liquid water is confirmed. The surface of the double-layer structure acts as a hydrophobic surface. Such peculiar behavior of water molecules can be reasonably explained by the formation of hydrogen bonds: The hydrogen bonds of the interfacial water molecules form between the first two layers and also within each layer. This hydrogen-bond network is confined within the double layer, which means that no "dangling hydrogen bonds" appear on the surface of the double-layer structure. This formation of hydrogen bonds stabilizes the double-layer structure and makes its surface hydrophobic. Thus, the numerical simulations indicate that a graphene surface is perfectly wettable on the atomic scale and becomes hydrophobic once it is covered by this double layer of water molecules.

Weyl law for open systems with sharply divided mixed phase space.

A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions in phase space. For a piecewise linear map, we numerically check the validity of our hypothesis, and find good agreement not only for the case with a sharply divided phase space but also for the case where tiny island chains surround the main regular island. For the latter case, a nontrivial power law exponent appears in the survival probability of classical escaping orbits, which may provide a clue to develop the Weyl law for more generic mixed systems.