# wall/colloid coefficients?

Hi all,

Would you please provide a reference where derivation of wall/colloid potential is in? I want to understand the how to deal with the constants, I read a thread where Steve had mentioned that phi^2 is typo. I don’t know how 144 is showing up there and also shouldn’t a rho (density) be there?

Is the derivation like the derivation of LJ93 except that using colloid-solvent potential (http://lammps.sandia.gov/doc/pair_colloid.html) instead of LJ126 and integrate over the 3d half lattice of the wall (think that wall is composed of the same material as the solvent)?

For the case of wall/lj93 it’s said that the user has to incorporate (2pirho/3) (http://lammps.sandia.gov/threads/msg14396.html )into epsilon as it’s not in the code. I wanna know what are the terms that should be incorporated into wall/colloid by the user?

Thanks,

Kasra.

I derived the equation and I get everything inside the brackets correct except that Sigma^6 is outside the bracket. but what I get for the constants outside the bracket I get: 4pi^2epsilonrho_wallrho_colloidsigma^6, so I assume the code just incorporate epsilon and I have to apply 4pi^2rho_wallrho_colloid*sigma^6 myself, however, I still don’t know what 144 is there?

Kasra.

I don’t think there is any paper besides the Everaers PRE 2003, and
Accurate and Efficient Methods for Modeling Colloidal Mixtures in an Explicit Solvent using Molecular Dynamics, P. J. in 't Veld, S. J. Plimpton, G. S. Grest, Comp Phys Comm, 179, 320-329 (2008).
neither of which discuss the wall/colloid case.

I think Pieter did the derivation for this, so I’ve CCd him.

Pieter - the formula for the wall/colloid potential on this doc page:
http://lammps.sandia.gov/doc/fix_wall.html
seems incompletely documented, particulary the phi^2 term
in the pre-factor.

Also, the derivation of this is the colloid/solvent formula
from the pair colloid doc page
http://lammps.sandia.gov/doc/pair_colloid.html
integrated over a half-plane of solvent?

Do you have any old notes or details on your derivation?

Thanks,
Steve

Well what I get from the derivation I did and the source code of wall/colloid it seems that 144*phi^2 is a typo in the manual and shouldn’t be there, right?

Kasra.

@Kasra: Indeed. According to the code there should not be a phi^2. All other terms agree between manual formula and code interpretation. Additionally, phi is not a parameter in the Hamaker force field definition.

@Steve: I think Jeremy did the derivation. It looks like a Derjaguin-type derivation for the interaction of a spherical particle with a plane.

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Forwarding this on to Jeremy as well …

Jeremy - if you worked on the fix wall/colloid
in LAMMPS, can you take a look at the Qs
below. I will delete the phi^2 term in
the doc page, which apparently is there by mistake.

Steve

Pieter & Jeremy - like Kasra said, I think
there are a couple other issues (besides deleting the phi^2),
that are a mis-match between the code and the doc page.
I’m presuming the code is correct, although see my
sigma comment below.

The 144 pre-factor on the doc page does not appear in
the code. E.g. in the def of coeff[3], which is the
leading term in the energy expression. Also, as Kasra
said, why is the sigma^6 not applied to both terms
on the doc page? It is also not in both terms in the
code I believe. That seems odd.

We should also probably define what epsilon means
if it includes some other pre-factors (e.g. pi, etc) and is
not simply the true small-particle epsilon.

Steve

Steve,

The term “sigma^6” does not apply to both terms because this is an integration of the colloid potential with an LJ wall (analogous to the LJ-wall93 potential). I think the doc page for of the equation has made some assumptions about the colloid particle being made up of individual LJ atoms (analogous to Pieter’s derivation in paper with Mark Horsch et al.). I will look at it more closely and try to find my notes on it.

Sorry for the confusion,

Jeremy

Steve,

The term “sigma^6” does not apply to both terms because this is an integration of the colloid potential with an LJ wall (analogous to the LJ-wall93 potential). I think the doc page for of the equation has made some assumptions about the colloid particle being made up of individual LJ atoms (analogous to Pieter’s derivation in paper with Mark Horsch et al.). I will look at it more closely and try to find my notes on it.

Sorry for the confusion,

Jeremy

So the answer is just set the two factors equal to each other and note that the volume fraction of LJ atoms , phi_c = rho_c*(pi/6)sigma^3. Let phi_c = phi_w = phi. Then, rho_crho_w = (36phi^2)/(pi^2sigma^6), and voila! 144 = 4*36. And the factors of pi^2 and sigma^6 drop out.

Regards,

Jeremy

Shouldn’t the wall/colloid fix get the phi as an input in this case? How does the density appear in the inputs of the fix? is it through the epsilon?

Kasra.

Must be. Epsilon in the code is the entire 144phi^2epsilon_LJ from the doc page, no?

Jeremy

I don’t think so, I checked the code but it doesn’t seem like that. what I did is that I absorbed all the constants into epsilon and use that in the input. Basically I use 4pi^2rho^2*sigma^6 (if rho_c=rho_w) as the value of epsilon.

Kasra.