Molecular Dynamics - Molecular Modelling - page 139

Radial distribution functions can be deduced experimentally from diffraction studies.
In the case of a liquid (Figure 10.4), the curve resembles that expected for a solid at low
temperatures, and at high temperatures it resembles the quadratic expected for an ideal gas.
At intermediate temperatures, the two features can be clearly seen; essentially a solid pattern
is superimposed on the gas pattern. This gives the experimental basis for the well-known
remark about liquid structure quoted above.

Distance r

Figure 10.4 Radial distribution function for a liquid superimposed on an ideal gas

10.2 Pair Correlation Functions

The radial distribution function for a gas varies as 4π r 2 and so tends to infinity as r tends to
infinity. It is usual to remove the 4π r 2 dependence by defining a related quantity called the
pair correlation function g AB ( r ), which gives information about the probability of finding
two particlesAand B separated by distance r . If the volume of a system is V and it contains
N A species of type A and N B species of type B, then the number densities are N A / V and
N B / V . The fraction of time that the differential volume elements dτ 1 and dτ 2 , which are
separated by distance r , simultaneously contain species of type A and B is given by
N A
V

N B
V g AB ( r ) dτ 1 dτ 2
In a mixture of A and B we would be interested in the three distinct pair correlation
functions g AA ( r ), g BB ( r ) and g AB ( r ). These pair correlation functions have a limiting value
of 1 for a fluid.