Determination of intermolecular forces using surface tension

[Telemachus]

Hi there. I have found the surface tension for liquid etanol on a given problem. Then the problem says: supposing that the coordination number for etanol is 12, what value does the intermolecular interaction energy has?
I have $\gamma=21,26355\frac{dyna}{cm}$, gamma is the surface tension that I've found.

The coordination number gives the number of molecules around one molecule in the liquid. I think that because the surface tension happens in the interface, the coordination number in there is 12/2=6.

I also know that $\gamma=F/2l$, I have this in my notes from class. This is what you get by analysing the virtual work by pushing a thin film a $\Delta x$ distance.

$F\Delta x=2l\Delta x \gamma$

PS: I made a mistake in the title, it's not the determination of intermolecular forces, but intermolecular energy.

 

[haruspex]

The coordination number gives the number of molecules around one molecule in the liquid. I think that because the surface tension happens in the interface, the coordination number in there is 12/2=6.

A quick Google on the subject suggests it will be more than half. I see a couple of places where a bulk number of 6 is presumed to correspond to a surface number of 5. But I couldn't find a general rule or any theoretical basis for the assumption. With optimally stacked spheres, each interior sphere has 12 neighbours, while each on a flat surface would have 9.

 

[Telemachus]

Thanks for your answer. Do you have any idea on how to determine the interaction energy using the surface tension and the coordination number?

 

[haruspex]

Do you have any idea on how to determine the interaction energy using the surface tension and the coordination number?

It's a field I know nothing about, but see if this helps: http://mail.vssd.nl/hlf/d007ch02.pdf

 

[Telemachus]

Thank you very much. I think it will help.

I would need to know how to determinate systematically the coordination number for molecules in the surface. And I would like to know also how to derive the equations (2.4) to (2.8).