Giant charge inversion of a macroion due to multivalent counterions
and monovalent coions: Molecular dynamics study

Two conditions for charge inversion in the electrolyte:
Counterions must be multivalently charged, Z= 2 or 3
Coulomb interactions must be strong compared to thermal energy

in

M. Tanaka and A. Grosberg, J.Chem.Phys., 115, 567 (2001).

We report molecular dynamics simulation of the (overall neutral) system consisting of
an immobile macroion surrounded by the electrolyte of multivalent counterions and
monovalent coions. In a short time (< a few nanoseconds), counterions adsorb on the
macroion surface in the amount much exceeding neutralization requirement, thus
effectively inverting the sign of the macroion charge. We find two conditions necessary
for charge inversion, namely, counterions must be multivalently charged and Coulomb
interactions must be strong enough compared to thermal energy. On the other hand,
coion condensation on the multivalent counterions similar to Bjerrum pairing is the
major factor restricting the amount of charge inversion. Depending on parameters,
we observe inverted charge up to about 200% the original charge of the macroion in
absolute value. The inverted charge scales as ζ^(1/2) when ζ<1 and crosses over to
ζ for ζ>1, where ζ= (A_0/r_s)^2, r_s is the Debye screening length in the electrolyte
and A_0 is the distance between adsorbed counterions under neutralizing conditions.
These findings are consistent with the theory of “giant charge inversion” [Phys. Rev. Lett.
85, 1568 (2000)].

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