16 Topological Mechanochemistry of Graphene
287
external mechanical loading is extremely sensitive to the state of the edge atoms
and makes it possible to disclose a topological nature of this sensitivity.
Oppositely to real physical experiments, when changing the object shape under
loading is usually monitored, computational experiments deal with the total energy
response to the object shape deformation that simulates either tension and contraction or bending, screwing, shift, and so forth. As for graphene, whose mechanical
properties are amenable to experimental study with difficulty, the computational experiments take on great significance.
A lot of works are devoted to the calculation of mechanical properties of
graphene due to which two approaches, namely, continuum and atomistic ones have
been formulated. The continuum approach is based on the well developed theory
of elasticity of continuous solid media applied to shells, plates, beams, rods, and
trusses. The latter are the structure elements used for the continuum description.
When applying to graphene, its lattice structure is presented in terms of the above
continuum structure elements and the main task of the calculations is the reformulation of the total energy of the studied atomic-molecular system subjected to
changing in shape in terms of the continuum structure elements. This procedure
actually involves the adaptation of the theory of elasticity of continuous media to
nanosize objects which makes allowance for introducing macroscopic basic mechanical parameters such as Young’s modulus (E), the Poisson ratio (ν), the potential energy of the elastic deformation, etc into the description of mechanical
properties of graphene. Since the energy of graphene is mainly calculated in the
framework of quantum chemistry, which takes the object atom structure into account, the main problem of the continuum approach is a linkage between molecular configuration and continuum structure elements. Nanoscale continuum methods
(see Refs. [13–17] and references therein), among which those based on the structural mechanics concept [18] are the most developed, have shown the best ability to
simulate nanostructure materials. In view of this concept, graphene is a geometrical frame-like structure where the primary bonds between two nearest-neighboring
atoms act like the load-bearing beam members, whereas an individual atom acts as
the joint of the related beams [19–22].
The basic concept of the atomistic approach consists in obtaining mechanical
parameters of the object from results of the direct solutions of either Newton motion
laws [22, 23] or Schrödinger equations [24, 25] under changing the object shape
following a particular algorithm of simulation of the wished type of deformation. It
should be necessary to issue a general comment concerning calculations based on
the application of the DFT computational schemes. All the latter, except the recent
one [26], were performed in the framework of restricted versions of the programs
that do not take into account spins of the graphene odd electrons and thus ignore the
correlation interaction between the latter. Peculiarities of the graphene odd electron
behavior is connected with a considerable enlarging of its C–C bonds, which, in its
turn, causes a noticeable weakening of the odd electron interaction and thus requires
taking into account these electrons correlation [27, 28].
In the case of atomistic approach, not energy itself, but forces applied to atoms
become the main goal of calculations. These forces are inputted later into the rela-
287
external mechanical loading is extremely sensitive to the state of the edge atoms
and makes it possible to disclose a topological nature of this sensitivity.
Oppositely to real physical experiments, when changing the object shape under
loading is usually monitored, computational experiments deal with the total energy
response to the object shape deformation that simulates either tension and contraction or bending, screwing, shift, and so forth. As for graphene, whose mechanical
properties are amenable to experimental study with difficulty, the computational experiments take on great significance.
A lot of works are devoted to the calculation of mechanical properties of
graphene due to which two approaches, namely, continuum and atomistic ones have
been formulated. The continuum approach is based on the well developed theory
of elasticity of continuous solid media applied to shells, plates, beams, rods, and
trusses. The latter are the structure elements used for the continuum description.
When applying to graphene, its lattice structure is presented in terms of the above
continuum structure elements and the main task of the calculations is the reformulation of the total energy of the studied atomic-molecular system subjected to
changing in shape in terms of the continuum structure elements. This procedure
actually involves the adaptation of the theory of elasticity of continuous media to
nanosize objects which makes allowance for introducing macroscopic basic mechanical parameters such as Young’s modulus (E), the Poisson ratio (ν), the potential energy of the elastic deformation, etc into the description of mechanical
properties of graphene. Since the energy of graphene is mainly calculated in the
framework of quantum chemistry, which takes the object atom structure into account, the main problem of the continuum approach is a linkage between molecular configuration and continuum structure elements. Nanoscale continuum methods
(see Refs. [13–17] and references therein), among which those based on the structural mechanics concept [18] are the most developed, have shown the best ability to
simulate nanostructure materials. In view of this concept, graphene is a geometrical frame-like structure where the primary bonds between two nearest-neighboring
atoms act like the load-bearing beam members, whereas an individual atom acts as
the joint of the related beams [19–22].
The basic concept of the atomistic approach consists in obtaining mechanical
parameters of the object from results of the direct solutions of either Newton motion
laws [22, 23] or Schrödinger equations [24, 25] under changing the object shape
following a particular algorithm of simulation of the wished type of deformation. It
should be necessary to issue a general comment concerning calculations based on
the application of the DFT computational schemes. All the latter, except the recent
one [26], were performed in the framework of restricted versions of the programs
that do not take into account spins of the graphene odd electrons and thus ignore the
correlation interaction between the latter. Peculiarities of the graphene odd electron
behavior is connected with a considerable enlarging of its C–C bonds, which, in its
turn, causes a noticeable weakening of the odd electron interaction and thus requires
taking into account these electrons correlation [27, 28].
In the case of atomistic approach, not energy itself, but forces applied to atoms
become the main goal of calculations. These forces are inputted later into the rela-