# How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling the units according to the potential well. But I assume the potential well is not the same for a case with particles of different sizes. Neither the sigma parameter should remain the same in my opinion. How can I propose the units or incorporate such feature to my code?

The question can be answered theoretically, but it would be nice to have examples with real code (in Fortran, Matlab, C, or whatever language you have experience with).

• This isn't really a site for code, though. As a theoretical question, it's perfectly fine here, but you may or may not get actual code samples. – David Z Feb 17 '14 at 2:32
• Yes, I know, it was just a suggestion. Thanks for the comment anyways. – adpala Feb 18 '14 at 3:14

when you say "sizes of the particles" you need to be more specific. do you mean you have hard core repulsion? if so than each particle will have it's potential with it's radius $r_c$:
$$u(r) = 4\cdot\epsilon[(\frac{\sigma}{r})^{12}-(\frac{\sigma}{r})^{6}] \ for :r>r_c$$ $$u(r) = \infty for :r<r_c$$