Related papers: Group theoretical methods to construct the graphen…
Sets of three types of convex pentagons that are aperiodic with no matching conditions on the edges are created from a chiral aperiodic monotile Tile(1, 1). This method divides the interior of Tile(1,1) into five convex polygons with five…
Odd electrons of benzenoid units and correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that…
The paper presents the first computational experiment on the transformation of a graphene sheet (graphene molecule Cn) into graphane (CH)n of regular chairlike structure. The transformation is considered as stepwise hydrogenation of the…
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions. Their topological properties are fully encoded within a…
A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…
Applying to graphene oxides, molecular theory of graphene is based on the oxide molecular origin when it is considered as a final product in the succession of a graphene molecule polyderivatives related to a particular oxidation reaction.…
Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization…
The chapter is devoted to chemical uniqueness of graphene. In view of molecular theory, the latter is a consequence of benzenoid packing of carbon atoms, based on three neighbors to each carbon atom leaving the atom fourth valence electron…
Driven by the growing demand in the energy, medical, and industrial sectors, we investigate a hydrogen isotope separation technique that offers both a high separation factor and economic feasibility. Our findings reveal that filtering…
Single layers of carbon dubbed "graphenes", from which graphite is built, have attracted broad interest in the scientific community because of recent exciting experimental results. Graphene is interesting from a fundamental research…
Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of 'degroupoidification': a…
The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional…
A polycrystalline graphene consists of perfect domains tilted at angle {\alpha} to each other and separated by the grain boundaries (GB). These nearly one-dimensional regions consist in turn of elementary topological defects, 5-pentagons…
Thermal decomposition of silicon carbide is a promising approach for the fabrication of graphene. However, the atomistic growth mechanism of graphene remains unclear. This paper describes the development of a new charge-transfer interatomic…
A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings…
Atomically thin crystals have recently been the focus of attention in particular after the synthesis of graphene, a monolayer hexagonal crystal structure of carbon. In this novel material class the chemically derived graphenes have…
Let $\Gamma$ be an Abelian group and let $G$ be a simple graph. We say that $G$ is $\Gamma$-colorable if for some fixed orientation of $G$ and every edge labeling $\ell:E(G)\rightarrow \Gamma$, there exists a vertex coloring $c$ by the…
The morphology of graphene on SiC {0001} surfaces formed in various environments including ultra-high vacuum, 1 atm of argon, and 10^-6 to 10^-4 Torr of disilane is studied by atomic force microscopy, low-energy electron microscopy, and…
We produce multilayer graphene by the Chemical Vapor Deposition (CVD) method at atmospheric pressure and 1000 {\deg}C, using flexible copper substrates as catalyst and liquid hexane as the source of carbon. We designed an optical device to…
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…