Find the equilibrium separation between two materials

[TheFerruccio]

Homework Statement

Find the equilibrium separation between Diamond and Copper materials.

Homework Equations

Lennard-Jones force/unit area:

$p_a(z)=\frac{8w}{3z_0}\left[\left(\frac{z}{z_0}\right)^{-9}-\left(\frac{z}{z_0}\right)^{-3}\right]$

I need to find $z_0$ which is the equilibrium separation.

w is the surface adhesion energy in Joules/m^2.

The Attempt at a Solution

I did not know where to post this question because I do not know if it even has a solution with the information that I have. It is a question I am asking myself because I am trying to predict some behavior to purchase some things. I know that equilibrium separation is where there is zero force/stress encountered. However, I do not know where actual data for equilibrium separation is obtained. Must it be done experimentally? Is it something non-trivial?

Is this the right board to post this in? Should this be in physics, or elsewhere?

 

[Borek]

LJ potential is mentioned in the GenChem curriculum, other than that I don't see much chemistry here. Moving it to General Physics for you.

 

[TheFerruccio]

Thanks for the info.