arXiv subjects
Publications and source records attributed to B. I. Shklovskii.
We comment on the huge enhancement of Coulomb drag in double layers two dimensional hole system observed in the experiment by Pillarisetty R., et al, PRL 86 (2002) 016805.
Charge inversion of a DNA double helix by an oppositely charged flexible polyelectrolyte (PE) is widely used for gene delivery. It is considered here in terms of discrete charges of DNA. We concentrate on the worst scenario case when in the neutral state of the DNA-PE complex, each of the DNA charges is locally compensated by a PE charge and show that charge inversion exists even in this case. When an additional PE molecule is adsorbed by DNA, its charge gets fractionalized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized DNA. These charges spread all over the DNA eliminating the self-energy of PE. Fractionalization leads to a substantial charge inversion of DNA. We show that fractionalization mechanism charge inversion works also for nonlinear polymers such as dendrimers. Remarkably, such fractionalization happens for adsorption of both PE or dendrimers on a two-dimensional charged lattice, as well. Relation of fractionalization to other mechanisms of charge inversion is discussed.
We suggest to augment standard isoelectronic focusing for separation of proteins in a gradient of pH by a similar focusing in the presence of a strongly charged polyelectrolyte (PE). Proteins which have the same isoelectric point but different "hidden" charge of both signs in pI point make complexes with PE, which focus in different pH. This is a result of charge inversion of such proteins by adsorbed PE molecules, which is sensitive to the hidden charge. Hence the hidden charge is a new separation parameter.
We address the long standing problem of the dependence of the electrostatic persistence length $l_e$ of a flexible polyelectrolyte (PE) on the screening length $r_s$ of the solution within the linear Debye-Huckel theory. The standard Odijk, Skolnick and Fixman (OSF) theory suggests $l_e \propto r_s^2$, while some variational theories and computer simulations suggest $l_e \propto r_s$. In this paper, we use Monte-Carlo simulations to study the conformation of a simple polyelectrolyte. Using four times longer PEs than in previous simulations and refined methods for the treatment of the simulation data, we show that the results are consistent with the OSF dependence $l_e \propto r_s^2$. The linear charge density of the PE which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.
We review recent advances in the physics of strongly interacting charged systems functioning in water at room temperature. We concentrate on the phenomena which go beyond the framework of mean field theories, whether linear Debye-Huckel or non-linear Poisson-Boltzmann. We place major emphasis on charge inversion - a counterintuitive phenomenon in which a strongly charged particle, called macroion, binds so many counterions that its net charge changes sign. We discuss the universal theory of charge inversion based on the idea of a strongly correlated liquid of adsorbed counterions, similar to a Wigner crystal. This theory has a vast array of applications, particularly in biology and chemistry; for example, the DNA double helix in the presence of positive multivalent ions (e.g., polycations) acquires a net positive charge and drifts as a positive particle in electric field. This simplifies DNA uptake by the cell as needed for gene therapy, because the cell membrane is negatively charged. We discuss also the analogies of charge inversion in other fields of physics.
It is shown that the voltage dependence of the tunneling conductance between two lightly doped semiconductors, which are separated by an large area tunneling barrier, can reveal the high energy part of the Coulomb gap if the barrier is thick enough. At the barrier thickness smaller than average distance between impurities no Coulomb gap feature can be found. This happens because such tunneling is sensitive to very rare shortest pairs of occupied and empty states localized at opposite sides of the barrier, whose density of states in this limit has no Coulomb gap. Small area tunneling contacts are also discussed. It is shown that the tunneling conductance of a point-like contact exponentialy grows with the applied voltage. This dependence does not permit a direct measurement of the Coulomb gap, but indirectly has information about it.
Due to the strong correlations between multivalent counterions condensed on a macroion, the net macroion charge changes sign at some critical counterion concentration. This effect is known as the charge inversion. Near this critical concentration the macroion net charge is small. Therefore, short range attractive forces between macroions dominate Coulomb repulsion and lead to their coagulation. The kinetics of macroion coagulation in this range of counterion concentrations is studied. We calculate the Coulomb barrier between two approaching like charged macroions at a given counterion concentration. Two different macroion shapes (spherical and rod-like) are considered. A new "self-regulated" regime of coagulation is found. As the size of aggregates increases, their charge and Coulomb barrier also grow and diminish the sticking probability of aggregates. This leads to a slow, logarithmic increase of the aggregate size with time.
Charge inversion of a DNA double helix by an oppositely charged flexible polyelectrolyte (PE) is considered. We assume that, in the neutral state of the DNA-PE complex, each of the DNA charges is locally compensated by a PE charge. When an additional PE molecule is adsorbed by DNA, its charge gets fractionized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized DNA. These charges spread all over the DNA eliminating the self-energy of PE. This fractionization mechanism leads to a substantial inversion of the DNA charge, a phenomenon which is widely used for gene delivery.
We review works on screening of a macroion, such as colloidal particle or double helix DNA, by multivalent counterions. Multivalent metal ions, charged micelles, short or long polyelectrolytes can play the role of multivalent counterions. Due to the strong Coulomb repulsion such multivalent counterions form a strongly correlated liquid resembling a Wigner crystal at the surface of the macroion. Even if the macroion is neutralized by this liquid, a newly arriving counterion creates in the liquid a correlation hole or image which attracts the ion to the surface. As a result, total charge of adsorbed counterions can substantially exceed the bare macroion charge, so that the macroion net charge inverts its sign. We discuss two previously suggested explanations of charge inversion and show that physics underlying both of them is intrinsically that of correlations, so that correlation is the universal force driving charge inversion.
The complexation of a polyelectrolyte with an oppositely charged spherical macroion is studied for both salt free and salty solutions. When a polyelectrolyte winds around the macroion, its turns repel each other and form an almost equidistant coil. It is shown that this repulsive correlations of turns lead to the charge inversion: more polyelectrolyte winds around the macroion than it is necessary to neutralize it. The charge inversion becomes stronger with increasing concentration of salt and can exceed 100%. This paper confirms that correlations are the universal mechanism of charge inversion.
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 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 $k_BT$. As a result even for a moderate concentration of multivalent counterions in the solution, their total charge at the surface of 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 giant inversion of charge can be observed by electrophoresis or by direct counting of multivalent counterions.
Screening of a strongly charged macroion by oppositely charged colloidal particles, micelles, or short polyelectrolytes is considered. Due to strong lateral repulsion such multivalent counterions form a strongly correlated liquid at the surface of the macroion. This liquid provides correlation induced attraction of multivalent counterions to the macroion surface. As a result even a moderate concentration of multivalent counterions in the solution inverts the sign of the net macroion charge. We show that at high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This giant inversion of charge can be observed in electrophoresis.
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 N_0. DNA condensation takes place in the vicinity of N_0, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N > N_0 positive DNA should move in the oppisite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe$^{4+}$, we obtain that N_0 = 3.2 mM and that the energy of DNA condensation per nucleotide is $0.07 k_B T$.
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 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. 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 the net macroion charge. Absolute value of the inverted charge density can be as large as 20% of that 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 sign with growing concentration of counterions. Moreover the condensation looses its universality and the net charge linear density depends on the bare one.
Screening of a macroion by multivalent counterions is considered. It is shown that ions form strongly correlated liquid at the macroion surface. Cohesive energy of this liquid leads to strong additional attraction of counterions to the surface. Away from the surface this attraction is taken into account by a new boundary condition for the Poisson-Boltzmann equation. This equation is solved with the new boundary condition for a charged flat surface and a long cylinder. For a cylinder Onsager-Manning theory looses its universality so that apparent charge of the cylinder is smaller than their theory predicts and depends on its bare charge. It can also vanish or change sign.
Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the other so that thermodynamic properties of SCL contribute to the bending rigidity. Thermodynamic properties of SCL are similar to those of Wigner crystal and are anomalous in the sense that the pressure, compressibility and screening radius of SCL are negative. This brings about substantial negative correction to the bending rigidity. For the case of DNA this effect qualitatively agrees with experiment.
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.
Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the disorder is decreased. This transition occurs at a similar strength of disorder as the one-electron delocalization crossover in a finite 2d system and develops almost simultaneously at all energies. We interpret this crossover in terms of delocalization in the space of occupation numbers of strongly bound and compact electron-hole pairs (excitons).