The electrostatic persistence length of polymers beyond the OSF limit (original) (raw)
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Electrostatic contribution to the persistence length of a semiflexible dipolar chain
Physical Review E, 2004
We investigate the electrostatic contribution to the persistence length of a semiflexible polymer chain whose segments interact via a screened Debye-Hückel dipolar interaction potential. We derive the expressions for the renormalized persistence length on the level of a 1 / D-expansion method already successfully used in other contexts of polyelectrolye physics. We investigate different limiting forms of the renormalized persistence length of the dipolar chain and show that, in, general, it depends less strongly on the screening length than in the context of a monopolar chain. We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. This can be understood solely on the basis of a swifter decay of the dipolar interactions with separation compared to the monopolar electrostatic interactions. We comment also on the general contribution of higher multipoles to the electrostatic renormalization of the bending rigidity.
The Journal of Chemical Physics, 1997
Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. 1 fk2mul@dix.fkem2.lth.se 2 fk2boj@grosz.fkem2.lth.se 3 carsten@thep.lu.se 4 ola@thep.lu.se 5 bs@thep.lu.se
Computer Simulation Studies of a Single Polyelectrolyte Chain in Poor Solvent
Macromolecules, 1999
The conformational behavior of a single, intrinsically exible, weakly charged polyelectrolyte chain in poor solvent is analyzed by extensive computer simulations combining Monte Carlo and Molecular Dynamics techniques. After determining the point for the charge{free case, we focus on the weak screening limit, corresponding to low salt concentration in the solution. We study the dependence on both the solvent strength, characterized by the relative deviation from the point, , and the fraction of charged monomers in the chain, which is e ectively tuned by varying the Coulomb interaction parameter. The conformations are discussed in terms of global properties (like the end{to{end distance, the inertia tensor components, etc.), and functions revealing more detailed information, like the density distribution around the center of mass, and the structure factor. For chains in the regime our data con rm the picture of a string of electrostatic blobs. For poorer solvents (up to = 0:4) we observe, upon increasing the intra{chain Coulomb repulsion, a splitting of the spherical globule into a dumbbell{type structure, accompanied by a sharp increase in the chain's gyration radius. For su ciently large , a further splitting is observed as well. Such a \necklace globule" (a sequence of transitions) had been predicted by Dobrynin, Obukhov (Macromolecules 1996, v. 29, p. 2974), with a nontrivial scaling of the gyration radius with chain length and interaction parameters, which is con rmed by our data. By means of a scaling analysis we argue that the transitions can be interpreted as thermodynamic rst{ order phase transformations, when taking the appropriate thermodynamic limit, which implies a scaling of the electrostatic coupling with inverse chain length.
Electrostatic rigidity of polyelectrolytes from reparametrization invariance
Macromolecular Theory and Simulations, 1996
The persistence length I, of a polyelectrolyte chain can be represented as I, = I, + I, where I, is the bare persistence and I, is the electrostatic contribution coming from the effects of electrostatic chain self-interactions. Using a reparametrization-invariant path integral model of semiflexible polymers we find that I, depends on the ionic strength Z as I,-Z-"2. This result accords with experimental observations and recent Monte Carlo simulations. Reparametrization-invariance is apparently an essential constraint in selecting acceptable models of semiflexible polymers. The Kratky-Porod (K-P) model is widely utilized for the description of conformational properties of semiflexible chains ' 1. The basic feature of this model is that the tangent-tangent (t-t) correlator for the K-P chain is an exponential, exp (-I r I / l ,) , where T is the contour distance along the polymer chain and the "persistence length" I, is the rigidity correlation length. The second moment, i. e., the end-to-end distance (R2> of the K-P chain is determined by integrating the t-t to obtain the well known result, (R2> = 21: 01-1 + exp(-y)) wherey = N/Ip and N i s the total contour length of the chain. Not all conformational properties of semiflexible chains can be calculated using the K-P model however. For instance, there are no known closed form expressions for the moment generating function, the static scattering form factor S(k), etc. 2, Under these circumstances it is difficult to assess the adequacy of the K-P model for describing real polymers. Noticing that for y + 1 the limiting K-P result for (R2) = 21,Ncoincides with that known for fully flexible chains, it i s natural to assume that the K-P propagator describes simple random walk paths, at least in this limit. Following Polyakov's observation3) that "while in the bosonic case we have a Brownian path with its size R
Regimes of strong electrostatic collapse of a highly charged polyelectrolyte in a poor solvent
arXiv: Soft Condensed Matter, 2016
We perform extensive molecular dynamics simulations of a highly charged flexible polyelectrolyte (PE) chain in a poor solvent for the case when the chain is in a collapsed state and the electrostatic interactions, characterized by the reduced Bjerrum length ellB\ell_BellB, are strong. We detect the existence of several sub-regimes, RgsimellB−gammaR_g \sim \ell_B^{-\gamma}RgsimellB−gamma, in the dependence of the gyration radius of the chain RgR_gRg on ellB\ell_BellB. In contrast to a good solvent, the exponent gamma\gammagamma for a poor solvent crucially depends on the size and valency of counterions. To explain the different sub-regimes we generalize the existing counterion fluctuation theory by a more complete account of the volume interactions in the free energy of the chain. These include interactions between the chain monomers, between monomers and counterions and the counterions themselves. We also demonstrate that the presence of the condensed counterions can modify the effective attraction among the chain monomers and impa...
Persistence length of a polyelectrolyte in salty water: Monte Carlo study
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
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-Hückel theory. The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l(e) proportional, variant r(2)s, while some variational theories and some computer simulations suggest l(e) proportional, variant 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) proportional, variant r(2)s. The linear charge density of the PE, which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.
Scaling and scale breaking in polyelectrolytes
The Journal of Chemical Physics, 1996
We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain-length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest-neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems.
Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes
Physical Review Letters, 2016
We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius Rg on the reduced Bjerrum length ℓB and find two different regimes. In the first one, called as a weak electrostatic regime, Rg ∼ ℓ −1/2 B , which is consistent only with the predictions of the counterionfluctuation theory. In the second one, called a strong electrostatic regime, we find Rg ∼ ℓ −1/5 B. To explain the novel regime we modify the counterion-fluctuation theory.