# [lammps-users] yukawa/colloid -> reference needed

Hello,
Pair style yukawa/colloid uses the following formula for the energy: E = A/kappa exp(-kappa (r-(r1+r2))). This appears either in manual or in the source code pair_yukawa_colloid.cpp. I would like to know a reference paper where such formula is derived since I am afraid it is incorrect. From the literature I know this kind of pair potential should read E = A/r exp(-kappa(r-(r1+r2))). Seems that "r" is replaced by "kappa" - I wonder why. Could anybody explain that?
Regards
tomek

I'll let Randy explain this as he wrote the potential and give
a reference. The A/kappa pre-factor is correct..

Steve

Dear Steve,

I wanted to ask if Randall replied to this query. I have been looking that the literature and it seems like that A/kappa factor is incorrect. Instead it should be A/r.

Just a thought. The A is defined as (from the manual) = apiRepseps0kappapsi^2. Basically what is the point of multiplying kappa in the derivation of A and dividing it by kappa in the main equation.

Also, from physical interpretation, yukawa is a repulsive interaction. The energy should be infinite when the colloids are touching the each other (r=ri+rj). However, with the current definition, the enery is finite. Even the force will be finite.

Could you please look into it.

Best Regards,
Vikas

Below was the answer from Randy.
I will just add the following comment.
There are 2 issues here.

One is whether the yukawa/colloid potential
is implemented as advertised, i.e. whether
the code is consistent with the formula
on the doc page. We think it is. If
you have doubts, then please clarify.

The 2nd Q is whether this is the right
potential for the system you want to model.
That is up to you. We are simply arguing
this is a yukawa-like potential, suitable
for finite-size colloidal particles. There may
well be other models that are better for
your system, or the physics you have in mind.
Presumably they require different formulas
than the one the yukawa/colloid doc
page.

Steve