ABSTRACT
Abstract ..................................................................................................... 2 1.1 Introduction ...................................................................................... 3 1.2 Graphenic Topological Isomorphism ............................................... 5 1.2.1 Graphenic’s Type Ribbons and Their
Stone-Wales Defects ............................................................ 5 1.2.2 Stone-Wales Rearrangements’ Generation
and Propagation .................................................................. 15 1.3 Fourth Order Quantum Conditional Density and
Partition Function........................................................................... 19 1.3.1 Path Integral Semiclassical Time Evolution Amplitude ..... 19 1.3.2 Schrodinger’s Conditional Probability Density ................. 31 1.3.3 Partition Function Quantum Expansion ............................. 36 1.4 Topological-Bondonic Algorithm on Extended Nanostructures .... 39 1.4.1 Second Order Implementation ........................................... 42 1.4.2 Fourth Order Implementation ............................................ 45 1.5 Bondons on Nano-Ribbons with Stone-Wales Defects.................. 48 1.5.1 Second Order Effects of Bondons on
Graphenic Fragments ......................................................... 48 1.5.2 Fourth Order Effects of Bondons on
Honeycomb Fragments ...................................................... 52
1.6 Conclusion ..................................................................................... 69 Keywords ................................................................................................ 71 References ............................................................................................... 72 Author’s Main References ............................................................. 72 Specific References ........................................................................ 73
ABSTRACT
Recently introduced bosonic quasi-particle “bondon”, see Chapter 1 of the Volume III of the present five-volume set (Putz, 2016a) is shown in this chapter to account for the emergence of long-range interaction in onedimensional graphenic nanoribbons opening the door to possible phasetransitions effect. Current simulations also benefit from adopting pure topological potential (used as potential energy in the statistical treatment) that greatly simplify, as usual, the computational tasks without sacrificing the physical information stored in the connectivity of the chemical structures. This chapter advances the modeling of bondonic effects on graphenic and honeycomb structures, with an original two-fold generalization: (i) by employing the fourth order path integral bondonic formalism through considering the high order (second and fourth) derivatives of the given 1D potential for a certain network, here identified with the Wiener topological potential; and (ii) by modeling a class of honeycomb defective structures admitting graphenic as the carbon-based reference case and then generalizing the treatment to Si (Silicene), Ge (Germanene), Sn (Stannene) by using the fermionic two-degenerate statistical states function in terms of electronegativity, an useful parameterization easily extendable to related hetero-combinations C-Si, C-Ge, C-Sn, Si-Ge, Si-Sn, Ge-Sn. The honeycomb nanostructures present η-sized StoneWales topological defect, the isomeric dislocation dipole originally called by authors Stone-Wales wave or SWw. For these defective nanoribbons the bondonic formalism individuates a specific phase-transition whose critical behavior shows typical bondonic fast critical time and bonding energies. The quantum transition of the ideal-to-defect structural transformations is fully described by computing the caloric capacities for nanostructures triggered by η-sized topological isomerisations.
