Polyelectrolyte Persistence Length: Attractive Effect of Counterion Correlations and Fluctuations

The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mechanical instability (collapse) for highly charged polyelectrolytes with multivalent counterions. In addition, we calculate the amount of condensed counterions on a slightly bent polyelectrolyte. More counterions are found to be adsorbed as compared to the Manning condensation on a cylinder.Comment: 5 pages, 1 ps figur

The scaling behaviour of screened polyelectrolytes

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex

Structure of Polyelectrolytes in Poor Solvent

We present simulations on charged polymers in poor solvent. First we investigate in detail the dilute concentration range with and without imposed extension constraints. The resulting necklace polymer conformations are analyzed in detail. We find strong fluctuations in the number of pearls and their sizes leading only to small signatures in the form factor and the force-extension relation. The scaling of the peak in the structure factor with the monomer density shows a pertinent different behavior from good solvent chains.Comment: 7 pages, 5 figures. submitted to EP

Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study

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.Comment: 7 pages, 6 figures. Various corrections in text and reference

Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure

Dynamics of Collapse of flexible Polyelectrolytes and Polyampholytes

We provide a theory for the dynamics of collapse of strongly charged polyelectrolytes (PEs) and flexible polyampholytes (PAs) using Langevin equation. After the initial stage, in which counterions condense onto PE, the mechanism of approach to the globular state is similar for PE and PA. In both instances, metastable pearl-necklace structures form in characteristic time scale that is proportional to N^{4/5} where N is the number of monomers. The late stage of collapse occurs by merger of clusters with the largest one growing at the expense of smaller ones (Lifshitz- Slyozov mechanism). The time scale for this process T_{COLL} N. Simulations are used to support the proposed collapse mechanism for PA and PE.Comment: 14 pages, 2 figure

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure

Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.Comment: 4 pages, 3 figure

A Modified Random Phase Approximation of Polyelectrolyte Solutions

We compute the phase diagram of salt-free polyelectrolyte solutions using a modified Debye-Huckel Approach. We introduce the chain connectivity via the Random Phase Approximation with two important modifications. We modify the electrostatic potential at short distances to include a bound on the electrostatic attractions at the distance of closest approach between charges. This modification is shown to act as a hard core in the phase diagram of electrolyte solutions. We also introduce a cut-off on the integration of the modes of wave length smaller than the size over which the chains are strongly perturbed by the electrostatic interactions. This cut-off is shown to be essential to predict physical phase diagram in long chain solutions