# [lammps-users] The calculationof prefactor A

Dear lammps users,

I have a problem understanding the colloid radius in the calculation of ‘The prefactor A’. For pair yukuwa/colloid, the prefactor A is calculated as the equation below. (A = 2 \pi R\varepsilon\varepsilon_0 \kappa \psi^2)

I am confused here. For the same colloid type, it is easy to calculate. But what if f I have two types of colloids? For colloid i and j, what’s the value of R and surface potential here if I need to set pair_coeff i j ?

Best regards
Ting

I think you would be fine just using the ave radius (r1 + r2)/2 for cross-type interactions
between 2 different sized particles. Similar to the energy formula for yukawa/colloid.

I’m CCing Dan Bolintineanu in case he has other thoughts.

Steve

Thank you for the clarification.

Steve Plimpton <[email protected]>于2021年8月18日 周三上午12:26写道：

Ting,

It may be more accurate to use an effective radius, where R = 2*(R1*R2) /(R1+R2) in this case.

Note the ‘restrictions’ in the doc page:

Per-particle polydispersity is not yet supported by this pair style; per-type polydispersity is allowed. This means all particles of the same type must have the same diameter. Each type can have a different diameter.

Dan