One of the exciting topics in electrolyte solutions concerns
the distribution of ions around other charged objects.66 In the
present case with counterions, the proper theoretical context is
given by the (mean-field) Debye−Hückel (DH) theory, where
for counterions around a charged particle, one combines the
Poisson equation to specify the electrostatic potential of an ion
with the Boltzmann equation for charge distribution. In radial
symmetry, the Debye−Hückel description for the counterion
distribution around a charged NP reads as Ae−Br/r + C, where
A, B, and C are (positive) constants. Here, the constant C is
included due to finite system size. However, the most relevant
parameter for our purposes is 1/B = κ, known as the Debye
screening length.