Biomedical Engineering Reference
In-Depth Information
with a large number of
identical
copies. In this case the boxes are truly identical at the atomic
level rather than in the usual thermodynamic sense of having
N
,
V
and
T
in common.
Figure 9.5 shows a two-dimensional slice through a small portion of the system (the
central box where the atoms are shown grey) and the copies (where the atoms are shown
black). Each copy is identical at the atomic level, and each corresponding atom undergoes
the same MC change as its image in every other copy.
If a MC move causes the dark grey atom (top left, central cell) to leave the central cell,
its image enters from an adjoining copy, shown by the vector displacements in the figure.
This keeps the density constant.
There are no effects due to the walls because each atom in the central cell is under the
influence of every other atom in the central cell and in all other cells.
9.5 Cut-Offs
This means we have to be able to calculate the mutual potential energy of (for example) the
dark grey atom with all the others shown in Figure 9.5. This would give an infinite sum.
In the case of a short-range potential such as the Lennard-Jones, we simply decide on
a cut-off distance
R
C
beyond which the pair potential will be negligible; this defines a
sphere of radius
R
C
centred on each atom. In order to treat the dark grey atom, we just
include contributions from all other atoms in the sphere as shown in two dimensions in
Figure 9.6.
Figure 9.6
The cut-off distance
