Biomedical Engineering Reference
In-Depth Information
40
20
3
.
10
-10
4.5
.
10
-10
6
.
10
-10
7.5
.
10
-10
-20
-40
Interatom distance /m
Figure 2.6
Lennard-Jones 12-6 potential for Ar-Ar. The plot is of
ε/
k
B
against R.
2.9 Combination Rules
A large number of L-J parameters have been deduced over the years, but they relate to pairs
of like atoms. Rather than try to deduce corresponding parameters for unlike pairs, it is usual
to use so-called
combination rules
, which enable us to relate the
C
12
and
C
6
parameters
for an unlike-atom pair A-B to those of A-A and B-B. The use of such combination rules
is common in subjects like chemical engineering, and is widely applied to many physical
properties.
There are three common combination rules in the literature. The first is
R
i
2
+
12
R
j
2
√
ε
i
ε
j
C
12,
ij
=
2
R
i
6
R
j
2
√
ε
i
ε
j
C
6,
ij
=
2
+
(2.22)
where
R
i
is the minimum energy separation for two atoms of type
i
and ε
i
the well depth.
The second is
