Biomedical Engineering Reference
In-Depth Information
10.5 Molten Salts
Molten salts (such as the alkali halides) are of great technological interest in the field of
metal extraction. The first simulations were done in byWoodcock (1971). Molten salts bring
a new problem because the potential energy terms are long range. Consider a (hypothetical)
one-dimensional infinite crystal, part of which is shown in Figure 10.6.
+
Q
-
Q
a
Figure 10.6
Part of a one-dimensional crystal; separation between ions is
a
Q
and the spacing
between the ions is
a
. Suppose we start with the central (grey) ion at infinity, and all the
other ions at their lattice positions as shown. The work done
W
in bringing the grey ion
from infinity to its place in the lattice is
The unshaded ions have charge
−
Q
, the shaded ions have charge
+
1
2
Q
2
4πε
0
a
1
2
+
1
3
−
1
4
+···
W
=−
−
and the term in brackets converges very slowly to its limiting value of ln(2):
No. of terms
Sum
1
1.0000
2
0.5000
3
0.8333
4
0.5833
100
0.6882
Such series have to be summed when calculating the force on a given ion in a periodic
box; in the case of neutral species, the sum is very quickly convergent because of the short-
range nature of the forces. For neutral systems, a cut-off radius is usually taken beyond
which the interactions are set to zero.
10.6 Liquid Water
Water plays a prominent place amongst solvents for obvious reasons. Two-thirds of our
planet is covered in water, chemical reactions tend to be done in aqueous solution, and
so on. The relatively strong hydrogen bonding in liquid water causes many of its physical
properties to be 'anomalous', and the structure of ice has long interested both theoreticians
and experimentalists.
Neutron diffraction studies on heavy ice, solid D
2
O, have shown that water molecules
retain their identity in condensed phases with very little distortion of their molecular geo-
metry. This means that water molecules may be treated as rigid asymmetric rotors (with six
