15 Molecular Theory of Graphene
267
according to the attached scale. The absolute N DA values are shown in panel c according to the atom numbering in the output file. As seen in the figure, 22 edge
atoms involving 2 × 5 zg and 2 × 6 ach ones have the highest N DA thus marking the perimeter as the most active chemical space of the molecule. The molecule
hydrogenation will start on atom 14 (star-marked in Fig. 15.5c) according to the
highest N DA in the output file. The next step of the reaction involves the atom from
the edge set as well, and this is continuing until all the edge atoms are saturated by a
pair of hydrogen atoms each since all 44 steps are accompanied with the high-rank
N DA list where edge atoms take the first place [60]. Thus obtained hydrogen-framed
graphene molecule is shown in Fig. 15.6 alongside with the corresponding N DA image map. Two equilibrium structures are presented. The structure in panel a corresponds to the optimization of the molecule structure without any restriction. In the
second case, positions of the edge carbon atoms and framing hydrogen atoms under
optimization were fixed. In what follows, we shall refer to the two structures as a
free standing and fixed membrane, respectively. Blue atoms in Fig. 15.6c alongside
with the framing hydrogens are excluded from the forthcoming optimization under
all steps of the further hydrogenation.
The chemical portraits of the structures shown in Figs. 15.6b and 15.6d are quite
similar and reveal the transformation of brightly shining edge atoms in Fig. 15.5b
into dark spots. The addition of two hydrogen atoms to each of the edge ones saturates the valence of the latter completely, which results in zeroing N DA values, as
is clearly seen in Fig. 15.6e. The chemical activity is shifted to the neighbouring inner atoms and retains higher in the vicinity of zg edges, however, differently in the
two cases. The difference is caused by the redistribution of the C–C bond lengths of
the free standing membrane when it is fixed over perimeter, thus providing different
starting conditions for the hydrogenation of the two membranes.
Besides the two types of initial membranes, the hydrogenation will obviously depend on other factors, such as (1) the hydrogen species in use and (2) the accessibility of the membranes sides to the hydrogen. Even these circumstances evidence the
hydrogenation of graphene to be a complicated chemical event that strongly depends
on the initial conditions, once divided into 8 adsorption modes in regard to atomic
or molecular adsorption; one- or two-side accessibility of membranes; and free or
fixed state of the membranes perimeter. Only two ones of the latter correspond to
the experimental observation of hydrogenated specimens discussed in [61], namely:
two-side and one-side atomic hydrogen adsorption on the fixed membrane. Stepwise
hydrogenation of the (5, 5) NGr molecule was considered in details in [60]. Here,
we restrict ourselves with a brief description of the main results.
Two-Side Atomic Adsorption of Hydrogen on Fixed Membrane The hydrogenation concerns the basal plane of the fixed hydrogen-framed membrane shown
in Fig. 15.6c that is accessible to hydrogen atoms from both sides. As seen in
Fig. 15.6e, the first hydrogenation step should occur on basal atom 13 marked by a
star. Since the membrane is accessible to hydrogen from both sides, one has to check
which deposition of the hydrogen atom, namely, above the carbon plane (‘up’) or
below it (‘down’) satisfies the LTE criterion.
267
according to the attached scale. The absolute N DA values are shown in panel c according to the atom numbering in the output file. As seen in the figure, 22 edge
atoms involving 2 × 5 zg and 2 × 6 ach ones have the highest N DA thus marking the perimeter as the most active chemical space of the molecule. The molecule
hydrogenation will start on atom 14 (star-marked in Fig. 15.5c) according to the
highest N DA in the output file. The next step of the reaction involves the atom from
the edge set as well, and this is continuing until all the edge atoms are saturated by a
pair of hydrogen atoms each since all 44 steps are accompanied with the high-rank
N DA list where edge atoms take the first place [60]. Thus obtained hydrogen-framed
graphene molecule is shown in Fig. 15.6 alongside with the corresponding N DA image map. Two equilibrium structures are presented. The structure in panel a corresponds to the optimization of the molecule structure without any restriction. In the
second case, positions of the edge carbon atoms and framing hydrogen atoms under
optimization were fixed. In what follows, we shall refer to the two structures as a
free standing and fixed membrane, respectively. Blue atoms in Fig. 15.6c alongside
with the framing hydrogens are excluded from the forthcoming optimization under
all steps of the further hydrogenation.
The chemical portraits of the structures shown in Figs. 15.6b and 15.6d are quite
similar and reveal the transformation of brightly shining edge atoms in Fig. 15.5b
into dark spots. The addition of two hydrogen atoms to each of the edge ones saturates the valence of the latter completely, which results in zeroing N DA values, as
is clearly seen in Fig. 15.6e. The chemical activity is shifted to the neighbouring inner atoms and retains higher in the vicinity of zg edges, however, differently in the
two cases. The difference is caused by the redistribution of the C–C bond lengths of
the free standing membrane when it is fixed over perimeter, thus providing different
starting conditions for the hydrogenation of the two membranes.
Besides the two types of initial membranes, the hydrogenation will obviously depend on other factors, such as (1) the hydrogen species in use and (2) the accessibility of the membranes sides to the hydrogen. Even these circumstances evidence the
hydrogenation of graphene to be a complicated chemical event that strongly depends
on the initial conditions, once divided into 8 adsorption modes in regard to atomic
or molecular adsorption; one- or two-side accessibility of membranes; and free or
fixed state of the membranes perimeter. Only two ones of the latter correspond to
the experimental observation of hydrogenated specimens discussed in [61], namely:
two-side and one-side atomic hydrogen adsorption on the fixed membrane. Stepwise
hydrogenation of the (5, 5) NGr molecule was considered in details in [60]. Here,
we restrict ourselves with a brief description of the main results.
Two-Side Atomic Adsorption of Hydrogen on Fixed Membrane The hydrogenation concerns the basal plane of the fixed hydrogen-framed membrane shown
in Fig. 15.6c that is accessible to hydrogen atoms from both sides. As seen in
Fig. 15.6e, the first hydrogenation step should occur on basal atom 13 marked by a
star. Since the membrane is accessible to hydrogen from both sides, one has to check
which deposition of the hydrogen atom, namely, above the carbon plane (‘up’) or
below it (‘down’) satisfies the LTE criterion.