# How should I think of a liquid in terms of interatomic potential and molecular speed?

A rather simple question for liquids specialists I guess but I have hard time finding information about this.

Here is my problem. I understand the ideal gas theory and the Maxwell's speed distribution. I see an ideal gas as small balls (mostly surrounded by void) moving around very fast and colliding elasticly with each others. If you want to be more precise, you use an interatomic potential such as the Lennard Jones potential that takes into account Van der Waals attractive interactions as well as the repulsive ones. You can define a kinetic (positive) pressure, kinetic temperature and molecular (negative) pressure with such a simple model. I think I understand that pretty well for now.

On the other side, I think I understand cristals fine as well. I see them as atoms bounded together by springs in which waves can flow and each atom oscillates around an minimal potential energy position. I have seen how you can calculate cristal's thermal capacity using Debye's model. So for now I think I have an idea of how a solid behaves at the molecular scale.

But what about liquids? I have read very interesting posts here about molecules velocity in liquids and I would be glad to have a more general view of what a liquid is from a molecular perspective.

As I understood it, molecules in liquids also oscillate around a minimal potential energy position but they can also swap positions with each other. Is that correct? Are there any tabulated values of molecules swapping speed in liquids ?

Concerning pressure. Should I represent pressure in liquids as a sum of a (positive) kinetic pressure due to molecules collision and a (negative) molecular pressure due to attractive interactions between molecules? Is this a good way of representing myself a liquid at a molecular scale?

Is there a model explaining the relation between viscosity and molecules attractive interactions ?

-----------EDIT---------

I got the answer about swapping molecules. Now this brings me to my question about pressure in liquids from a molecular perspective. Concerning ideal gases, pressure is due to molecules collisions. Does this still stand for liquids or is it more a question of "weight" exerted by molecules on each others? Does any one know a molecular pressure model for liquids?

Thank you

• You are correct about swaps; in the case of water these take on the order of tens of picoseconds to occur. Regarding pressure, look at the atomic virial stress which is used in MD codes to compute the pressure. (Sorry I don't have time to write a more detailed answer) – lemon Mar 16 '16 at 18:18

It is indeed correct that in a liquid atoms/molecules swap position. You can think of this as a vibrating atom caged by other atoms. In order to escape from this "cage" (which is higher in energy) the atom wants to make a jump to a lower energy. The time associated with this process depends on the random motions due to the intermolecular forces. Now, with some elementary physics you can estimate the characteristic time $t$ to make this jump.
Assume the atom vibrates with a certain frequency $f$ and has to cross an energy barrier $E$. Using the Boltzmann factor from statistical physics we can write $$t^{-1} \backsim f e^{-E/kT},$$
which is dimensionally consistent. I'm not aware of tabulated values for the speed but $t$ will be very small for simple liquids.