Screened Coulomb pair potential ($U(R)\propto e^{-\kappa R}/R$)

A screened Coulomb pair potential models the effective electrostatic interaction of particles in an electrolyte. For identical weakly charged spheres of radius $a$, charge $Q$, and Debye–Hückel screening length ${\kappa }^{-1}$, a common pairwise approximation is $U(R)=Q^2{e}^{-\kappa (R-2a)}/[4\pi \epsilon (1+\kappa a{)}^{2}R]$ for $R\ge 2a$. The near-contact interaction can require more detailed boundary conditions or nonlinear screening. Charge, screening length and temperature all matter to a resulting phase diagram.