Environmental Engineering Reference
In-Depth Information
The exponential summand in the expression for the potential describing the
repulsion of the molecules at small distances, often approximated as
Ae
r
−s
r
C
≈
12
12
r
In this case we obtain the Lennard-Jones potential:
C
C
( )
Vr
=−
12
12
6
(2.1)
6
r
r
The interaction between carbon atoms is described by the potential
( )
(
)
2
C
V
r
=−
,
Kr b
b
=
1
4
A
where,
- constant tension (compression) connection;
-
the equilibrium length of connection;
r
- current length of the connection.
The interaction between the carbon atom and hydrogen molecule is described
by the Lennard-Jones
12
6
s
s
�
�
�
�
( )
V
r
=
4
e
−
ƒ
„
ƒ
„
-
r
r
For all particles
(Fig. 2.2),
the equations of motion are written:
dr
m
2
( )
(
)
∑
,
i
=
F
r
+
F
rr
−
THi
−
HHi
−
j
dt
2
2
2
2
ji
≠
where,
- Force, acting by the CNT.
F
(
r
)
T
−
H
2
The resulting system of equations is solved numerically. However, the mo-
lecular dynamics method has limitations of applicability:
1) the de Broglie wavelength
h/mv
(where,
h
- Planck's constant;
m
- the mass
of the particle;
v
-velocity);
2) Classical molecular dynamics cannot be applied for modeling systems
consisting of light atoms such as helium or hydrogen;
3)
At low temperatures, quantum effects become decisive for the consider-
ation of such systems must use quantum chemical methods;
4)
The time at which we consider the behavior of the system were more than
the relaxation time of the physical quantities.
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