Contemporary Materials I−1 (2010)
Contemporary Materials, I–1 (2010) Page 94 - 97
REGULARITY-CHAOS TRANSITION TEMPERATURE AND GUISBIERS-BUCHAILLOT EQUATION
D. Malivuk, S. Nježić, S. Lekić, Z. Rajilić
University of Banja Luka, Faculty of Science and Mathematics, Mladena Stojanovića 2, 78000 Banja Luka, Bosnia and Herzegovina
Abstract
A focus of frontline interdisciplinary research today is the development of the conceptual framework and the experimental background of the science of nanostructured materials and the perspectives of its technological applications. G. Guisbiers and L. Buchaillot found out the general equation (GBE) which was based only on the surface area to volume ratio of nanostructures and statistics (Fermi–Dirac or Bose–Einstein) followed by the particles involved in the considered phenomena (melting, ferromagnetism, vibration and superconductivity). In this paper, we consider another phenomenon, the regularity-chaos transition, and find its connection with GBE. We have performed the computational experiments with one hydrogen molecule and one graphene sheet. H2-C interactions are described by Lennard-Jones potential. The main goal of our experiments is find out the critical temperatures of regularity-chaos transition. The results of computation derived using Runge-Kutta-Fehlberg method show approximate agreement with GBE.
Keywords: Hydrogen molecule, critical temperature, regularity-chaos transition, Guisbiers-Buchaillot equation.
References
[1] J. Jortner, C. N. R. Rao, Nanostructured advanced materials. Perspectives and directions, Pure Appl. Chem. Vol. 74 (2002)1491–1506.
[2] W. H. Qi, B.Y.Huang, M.P.Wang, Z.Li, Z.M.Yu, Generalized bond-energy model for cohesive energy of small metallic particles, Phys. Lett. A Vol. 370 (2007) 494–498.
[3] T. Enoki, Physics and Chemistry of Graphene, (2009) (Hackensack: Pan Stanford Publishing).
[4] G. K. Dimitrakakis, E. Tylianakis, G. E. Froudakis, Pillared Graphene: A New 3-D Network Nanostructure for Enhanced Hydrogen Storage, Nano Lett. Vol. 8 (2008) 3166-3170. PMid:18800853
[5] T. Heine, L. Zhechkov, S. Patchkovskii, G. Seifert, Novel Carbon Materials can Store and Sieve Hydrogen, SPIE Newsroom (2007) 10.1117/ 2.1200704.0714.
[6] G. Guisbiers, Size-Dependent Materials Properties Toward a Universal Equation, Nanoscale Res. Lett. Vol. 5 (2010) 1132-1136. PMid:20596422 PMCid:2894066
[7] G. Guisbiers, L. Buchaillot, Universal Size/Shape-Dependent Law for Characteristic Tempe-ratures, Phys. Lett. A Vol. 374 (2009) 305-308.