B. I. Shklovskii

Screening of a macroion by multivalent ions: Correlation-induced inversion of charge

Screening of a strongly charged macroion by multivalent counterions is considered. It is shown that counterions form a strongly correlated liquid at the surface of the macroion. Cohesive energy of this liquid leads to additional attraction of counterions to the surface, which is absent in conventional solutions of the Poisson-Boltzmann equation. Away from the surface this attraction can be taken into account by a new boundary condition for the concentration of counterions near the surface. The Poisson-Boltzmann equation is solved with this boundary condition for a charged flat surface, a cylinder, and a sphere. In all three cases, screening is much stronger than in the conventional approach. At some critical exponentially small concentration of multivalent counterions in the solution, they totally neutralize the surface charge at small distances from the surface. At larger concentrations they invert the sign of the net macroion charge. The absolute value of the inverted charge density can be as large as 20% of the bare one. In particular, for a cylindrical macroion it is shown that for screening by multivalent counterions, predictions of the Onsager-Manning theory are quantitatively incorrect. The net charge density of the cylinder is smaller than their theory predicts and inverts the sign with a growing concentration of counterions. Moreover, the condensation loses its universality and the net charge linear density depends on the bare one.

Wigner Crystal Model of Counterion Induced Bundle Formation of Rodlike Polyelectrolytes

A simple electrostatic theory of condensation of rod-like polyelectrolytes under influence of polyvalent ions is proposed. It is based on the idea that Manning condensation of ions results in formation of the Wigner crystal on a background of a bundle of rods. It is shown that, depending on a single dimensionless parameter, this can be the densely packed three-dimensional Wigner crystal or the two-dimensional crystal on the rod surfaces. For DNA the location of charge on the spiral results in a model of the one-dimensional Wigner crystal. It is also argued that the Wigner crystal idea can be applied to self-assembly of other polyelectrolytes, for example, colloids and DNA-lipid complexes.

Reentrant condensation of DNA induced by multivalent counterions

A theory of condensation and resolubilization of a dilute DNA solution with growing concentration of multivalent cations, N, is suggested. It is based on a new theory of screening of a macroion by multivalent cations, which shows that due to strong cation correlations at the surface of DNA the net charge of DNA changes sign at some small concentration of cations N0. DNA condensation takes place in the vicinity of N0, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N>N0 positive DNA should move in the opposite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe4+, we obtain that N0=3.2 mM and that the energy of DNA condensation per nucleotide is 0.07 kBT.

Charge density wave in two-dimensional electron liquid in weak magnetic field.

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where

Screening of a charged particle by multivalent counterions in salty water: Strong charge inversion

N\ensuremath{\gg}1

Complexation of a polyelectrolyte with oppositely charged spherical macroions: Giant inversion of charge

lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factors equal to 1 and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a gap linearly dependent on the magnetic field in the limit of large

Overcharging of a macroion by an oppositely charged polyelectrolyte

N

Complexation of DNA with positive spheres: Phase diagram of charge inversion and reentrant condensation

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Phase diagram of solution of oppositely charged polyelectrolytes

Screening of a macroion such as a charged solid particle, a charged membrane, double helix DNA, or actin by multivalent counterions is considered. Small colloidal particles, charged micelles, short or long polyelectrolytes can play the role of multivalent counterions. Due to strong lateral repulsion at the surface of the macroion such multivalent counterions form a strongly-correlated liquid, with the short-range order resembling that of a Wigner crystal. These correlations create additional binding of multivalent counterions to the macroion surface with binding energy larger than kBT. As a result even for a moderate concentration of multivalent counterions in the solution, their total charge at the surface of the macroion exceeds the bare macroion charge in absolute value. Therefore, the net charge of the macroion inverts its sign. In the presence of a high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This strong inversion of charge can be observ...

Density of states and conductivity of a granular metal or an array of quantum dots

Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE in the solution is larger than total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case when the total charge of spheres is larger, we predict another correlation effect; spheres bind to the PE in such a great number that they invert the charge of the PE. The inverted charge by absolute value can be larger than the bare charge of PE even when screening by monovalent salt is weak. At larger concentrations of monovalent salt, the inverted charge can reach giant proportions. Near the isoelectric point where total charges of spheres and PE are equal, necklaces condense into macroscopic bundles. Our theory ...