Chapter 16
Topological Mechanochemistry of Graphene
E.F. Sheka, V.A. Popova, and N.A. Popova
Abstract In view of the formal topology, two common terms, namely, the connectivity and adjacency, determine the ‘quality’ of the C–C bonds of sp 2 nanocarbons.
The feature is the most sensitive point of the inherent topology of the species so
that such external action as the mechanical deformation should obviously change
it and result in particular topological effects. The current chapter describes the
effects caused by uniaxial tension of a graphene molecule in due course of the
mechanochemical reaction. Basing on the molecular theory of graphene, the effects
are attributed to both mechanical loading and chemical modification of the edge
atoms of the molecule. The mechanical behavior is shown to be not only highly
anisotropic with respect to the direction of the load application, but greatly dependent on the chemical modification of the molecule edge atoms thus revealing the
topological character of the graphene deformation.
16.1 Introduction
The modern topology in chemistry covers two large valleys, namely, formal, mathematical and empirical, chemical. The former is concerned with the description of the
molecular structures on the basis of the finite topological spaces. The space shows
itself as a mathematical image or instrument of the theoretical study. A large collection of comprehensive reviews, related to the topological description of fullerenes
from this viewpoint, has recently been published [1]. The second field covers vastly
studied topochemical reactions. The space in this case is the physical reality defining the real place where the reactions occur. If the appearance of the mathematical topology in chemistry can be counted off the publication of the Merrifield and
Simmons monograph in 1989 [2], the topochemical reactions have been studying
from the nineteenth century (see [3] and references therein). The first stage of the
study was completed in the late nineteenth-twenties [4] and then obtained a new
pulse after appearing the Woodward and Hoffmann monograph, devoted to the conservation of orbital symmetry, in 1970 [5]. Since then, the topochemical reactions
E.F. Sheka (B)
Peoples’ Friendship University of Russia, Miklukho-Maklay, 6, Moscow, 117198, Russia
e-mail: sheka@icp.ac.ru
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_16,
© Springer International Publishing Switzerland 2013
285
Topological Mechanochemistry of Graphene
E.F. Sheka, V.A. Popova, and N.A. Popova
Abstract In view of the formal topology, two common terms, namely, the connectivity and adjacency, determine the ‘quality’ of the C–C bonds of sp 2 nanocarbons.
The feature is the most sensitive point of the inherent topology of the species so
that such external action as the mechanical deformation should obviously change
it and result in particular topological effects. The current chapter describes the
effects caused by uniaxial tension of a graphene molecule in due course of the
mechanochemical reaction. Basing on the molecular theory of graphene, the effects
are attributed to both mechanical loading and chemical modification of the edge
atoms of the molecule. The mechanical behavior is shown to be not only highly
anisotropic with respect to the direction of the load application, but greatly dependent on the chemical modification of the molecule edge atoms thus revealing the
topological character of the graphene deformation.
16.1 Introduction
The modern topology in chemistry covers two large valleys, namely, formal, mathematical and empirical, chemical. The former is concerned with the description of the
molecular structures on the basis of the finite topological spaces. The space shows
itself as a mathematical image or instrument of the theoretical study. A large collection of comprehensive reviews, related to the topological description of fullerenes
from this viewpoint, has recently been published [1]. The second field covers vastly
studied topochemical reactions. The space in this case is the physical reality defining the real place where the reactions occur. If the appearance of the mathematical topology in chemistry can be counted off the publication of the Merrifield and
Simmons monograph in 1989 [2], the topochemical reactions have been studying
from the nineteenth century (see [3] and references therein). The first stage of the
study was completed in the late nineteenth-twenties [4] and then obtained a new
pulse after appearing the Woodward and Hoffmann monograph, devoted to the conservation of orbital symmetry, in 1970 [5]. Since then, the topochemical reactions
E.F. Sheka (B)
Peoples’ Friendship University of Russia, Miklukho-Maklay, 6, Moscow, 117198, Russia
e-mail: sheka@icp.ac.ru
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_16,
© Springer International Publishing Switzerland 2013
285