Draw schematically the radial distribution function $g(r)$ for a Lennard-Jones fluid at low and high particle densities. Discuss in both cases the behavior at small $r$. At high densities $g(r)$ has some damped oscillations. Explain their origin and what would happen at long distances.
What I know:
The radial distribution function $g(r)$ describes how density varies as a function of distance from a reference particle (Wikipedia).
Specifically in Lennard-Jones case, we have (Pasteboard still does not work for me):
Here we can observe that if repulsion outweighs attraction, the curve will die out on the x axis. On the contrary, if it is the other way around, the curve will grow exponentially. For the sake of clarity, I would remark y = 0 as the Ideal Gas behaviour.
I have read that $g(r)$ vanishes at short distances, because the probability of finding two particles close to each other vanishes due to the repulsive part of the potential. At high densities $g(r)$ can show some damped oscillations: https://imgur.com/a/i32D39I.
These oscillations express the preference of the particles to be found at specific distances from a reference particle at the origin. For instance in the LJ case, a first layer of particles will be localized closed to the minimum of LJ's potential, which is the origin of the first peak in $g(r)$.
This layer prevents other particles from getting close to it, which is what causes the first
minimum in $g(r)$.
What I do not know.
1)The explanation: 'These oscillations express the preference of the particles to be found at specific distances from a reference particle at the origin'. How can particles have 'preference' to be at different distances? I think this is not a good physical explanation. I have been thinking about this and I would say that as there is a high density of particles at small distances, the repulsion force is exerted on these, which triggers such oscillations. Finally there is a point where they are so close to each other that the repulsion force provides them with an initial kinetic energy which will be equal to a final electrostatic potential energy of zero (selecting our zero of electrostatic potential energy at y=0) , and that is the moment when the curve dies out on the x axis. Do you agree with this explanation?
2)Are we dealing with underdamped oscillations at high densities? Could you give an insight into these kind of oscillations (if what I have just said is not enough or incorrect)?
3)When we are dealing with long distances, would $g(r)$ tend to be one? What would we observe, the Ideal Gas behaviour? Why? Is it because there is no interaction between the particles?
As always, I am interested in explaining such phenomena from a physical point of view.