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Charge Inversion of a Macroion in Solvents

   A macroion with large charges can be significantly reverse charged in
electrolyte (salt) solution at room temperature.
 This is called charge inversion
phenomenon. Here, the "macroion" stands for an ion that is larger in radius
and charge content than ordinary ions like sodium Na or calcium Ca. People
who are familiar with the Debye screening theory in electrolyte liquid may have
difficulty in accepting this fact. Namely, the screening theory insists that the test
charge of positive sign be monotonically shielded by cloud of positive charges.

 However, this strange phenomenon occurs Charge inverted macroion and ionic atmosphere
when
the electrostatic energy, the source
of structuralization,
is larger than thermal
energy
that cause diffusion, and also simul-
taneously when the gathering
counterions
are multivalently charged
like calcium Ca+2
or aluminum Al+3 ions.

  The above condition corresponds to
the strongly Coulomb coupled state where
ions are highly correlated, recognizing each
others positions. This means that the particle distribution is deviated from
the Boltzman distribution which holds in ordinary thermal conditions. As
previously mentioned, this correlation causes the attraction force to exceed
the repulsive force, leading to structure formation in electrically neutral
solvent (and plasma). In fact, we get a Coulomb crystal at very low
temperatures

  
The figure above depicts a charge inverted macroion (red sphere), on
which trivalent counterions (light blue sphere) are electrostatically adsorbed. 
The dark blue spheres are coions of monovalent charges which are some
distance apart from the macroion due to repulsion and condensed on the
topside of the counterions. As easily understood, the counterions must
have larger valence than the coions so that the counterion charges are not
cancelled by the coions. 
  
  Further we have shown that the polymer counterions (polyelectrolyte) and
the rod (cylindrical) macroions are more favorable for charge inversion, especially
for a weakly charged macroion around the threshold surface charge density,
including
the DNA (the figure and reference below).



References: 
  
Review of ionic soft condensed matters  Solid State Physics (in
                                Japanese, April 2002).


  
Static profile of a charge inverted macroion  J.Chem.Phys. 115 (2001)

  Electrophoresis study of charge inversion Euro.Phys.J., E7 (2002).

  Weakly charged rod macroion (DNA) with charged polymers
                     Phys.Rev. E68 (2003).

 
Is DNA subject to charge inversion? Cond-mat/0311009 (2003)

      
      
Charge inversion by polymer counterions consisting of
            (a) trivalent(red) and (b) monovalent(yellow) monomers


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