Environmental Engineering Reference
In-Depth Information
Table 1.1
Parameters in Lennard-Jones
potential for different systems
σ
(A)
ε
(meV)
a
He
3.25
1.72
a
Ne
2.93
1.12
a
Ar
3.37
10.34
a
Kr
3.66
15.51
a
Xe
4.05
21.80
b
Graphene
3.41
2.39
b
C
60
3.47
2.86
b
Graphene-C
60
3.44
2.62
c
C-Si
3.63
8.91
c
C-O
3.27
3.44
c
C-B
3.53
5.96
c
C-N
3.35
3.69
a
From Ref. [18a].
b
From Ref. [18b].
c
FromRef.[19]basedonmixingrule(seeSection1.2.3).
used,whichtakesintoaccountthemany-bodyinteraction.However,
regardless of how well it is able to model actual materials, the
importanceofLJpotentialcannotbeunderestimatedasitrepresents
an important model to describe the vdW interaction. LJ potential
is the standard potential to use when the investigation is focused
on the fundamental physics, rather than studying the properties
of a specific material. For instance, LJ potential is widely used in
literatures to model graphene-substrate interaction and inter-layer
interaction in multi-layer graphene [17]. Table 1.1 summarizes the
LJpotentialparametersfordifferentsystemsrecordedinliteratures.
1.2.2
Many-Body Potential
The Stillinger-Weber (SW) potential [20] is a popular many-body
potential to model the crystalline silicon. It consists of both two-
bodyand three-body terms defined as
v
2
(
r
i
,
r
j
)
=
ε
f
2
(
r
ij
/σ
), (1.6)
v
3
(
r
i
,
r
j
,
r
k
)
=
ε
f
3
(
r
i
/σ
,
r
j
/σ
,
r
k
/σ
), (1.7)
where
r
i
is the position of atom
i
,
r
ij
is the distance between atom
i
and
j
,and
ε
σ
and
denote the energy and length unit, respectively.
