Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴ < N < 2⁸ and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. Received 7 June 2001 and Received in final form 17 October 2001     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

Complexifications and real forms of Hamiltonian structures

We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms. Received 18 October 2001 / Received in final form 24 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Dynamical properties of the slithering-snake algorithm: A numerical test of the activated-reptation hypothesis

Correlations in the motion of reptating polymers in a melt are investigated by means of Monte Carlo simulations of the three-dimensional slithering-snake version of the bond-fluctuation model. Surprisingly, the slithering-snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction φ of occupied lattice sites), where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound (N) is set by the density of chain ends φ/N. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of “snakes” at t ≪ is identical to that of a benchmark system where all chains but one are frozen. We demonstrate that the subdiffusive dynamical regime is caused by the slow creeping of a chain out of its correlation hole. Our results are in good qualitative agreement with the activated-reptation scheme proposed recently by Semenov and Rubinstein (Eur. Phys. J. B, 1 (1998) 87). Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering-snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering-snake moves is crucial to equilibrate a melt of long chains efficiently. Received: 18 December 2002 / Accepted: 3 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: jwittmer@dpm.univ-lyon1.fr RID="b" ID="b"Current address: University of Illinois at Urbana-Champaign.     

Off equilibrium dynamics in disordered quantum spin chain

We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the x or z direction, we compute numerically the average quantities. They show similar behaviour to the homogeneous chain, that is an algebraic decay in time toward a stationary state. During the time evolution, the spatial correlations, measured from one end to the other of the chain, are building up and finally at long time they reach a size-dependent constant depending on the distance from criticality. Analytical arguments are given which support the numerical results. Received 11 July 2002 / Received in final form 9 September 2002 Published online 29 October 2002     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞). Received 24 September 2001 and Received in final form 28 January 2002     

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k _F charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological solitons carrying charge e/2 and spin zero. Relevance to the 4k _F charge density wave instability in (DI - DCNQI)₂ A g or recently discovered in (TMTTF)₂X ( X=PF ₆, AsF₆) is discussed. Received 30 March 2001 and Received in final form 11 May 2001     

Jamming, freezing and metastability in one-dimensional spin systems

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki dynamics. At zero temperature the dynamics of these models is fully irreversible, leading to an exponentially large number of blocked states. Using a mapping of these spin systems onto sequential adsorption models of, respectively, monomers, dimers, and hollow trimers, we present exact results on the statistics of blocked states. We determine the distribution of their energy or magnetization, and in particular the large-deviation function describing its exponentially small tails. The spin and energy correlation functions are also determined. The comparison with an approach based on a priori statistics reveals systematic discrepancies with the Edwards hypothesis, concerning in particular the fall-off of correlations. Received 26 February 2002 Published online 6 June 2002     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

The electrostatic persistence length of polymers beyond the OSF limit

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l _e of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length κ^-1 exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l _e∝κ^-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data. Received 12 February 2002     

Metastable states of the Ising chain with Kawasaki dynamics

We consider a ferromagnetic Ising chain evolving under Kawasaki dynamics at zero temperature. We investigate the statistics of the blocking time, as well as various characteristics of the metastable configurations reached by the system, including the statistics of the final energy, the spin correlations, and the distribution of domain sizes. Results of extensive numerical simulations are compared with analytical predictions made for the a priori ensemble of all blocked configurations with equal weights. Qualitative differences are found, e.g. in the domain sizes, which are found to be neither statistically independent nor exponentially distributed. Received 24 October 2002 / Received in final form 13 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: luck@spht.saclay.cea.fr RID="b" ID="b"URA 2306 of CNRS     

Self-averaging in complex brain neuron signals

Nonlinear statistical properties of Ventral Tegmental Area (VTA) of limbic brain are studied in vivo. VTA plays key role in generation of pleasure and in development of psychological drug addiction. It is shown that spiking time-series of the VTA dopaminergic neurons exhibit long-range correlations with self-averaging behavior. This specific VTA phenomenon has no relation to VTA rewarding function. Last result reveals complex role of VTA in limbic brain. Received 17 April 2002 / Received in final form 30 September 2002 Published online 31 December 2002     

Prompt dipole γ-ray emission in fusionlike heavy-ion reactions

The ³²S + ¹⁰⁰Mo and ³⁶S + ⁹⁶Mo fusionlike reactions were studied at incident energy of E _lab = 298 MeV and 320 MeV, respectively, with the aim of probing the influence of the entrance channel charge asymmetry on the dipole γ-ray emission. The excitation energy and spin distribution of the compound nucleus created in these reactions were identical, the only difference being associated with the unequal charge asymmetry of the two entrance channels. High-energy γ-rays were detected in an array of 9 seven-pack BaF₂ clusters. Coincidence with fusionlike residues detected in four PPAC ensured the selection of central reaction events. By studying the differential γ-ray multiplicity associated with the two reactions it was shown that the dipole strength excited in the compound nucleus increases with the entrance channel charge asymmetry. From the linearized spectra, the increase of the GDR γ-ray intensity was found to be ∼ 25% for the more charge asymmetric system. The results are discussed and compared with those of previous data obtained at different incident energies. Received: 21 October 2002 / Accepted: 23 December 2002 / Published online: 1 April 2003     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

Force-extension behavior of folding polymers

The elastic response of flexible polymers made of elements which can be either folded or unfolded, having different lengths in these two states, is discussed. These situations are common for biopolymers as a result of folding interactions intrinsic to the monomers, or as a result of binding of other smaller molecules along the polymer length. Using simple flexible-chain models, we show that even when the energy ε associated with maintaining the folded state is comparable to k _B T, the elastic response of such a chain can mimic usual polymer linear elasticity, but with a force scale enhanced above that expected from the flexibility of the chain backbone. We discuss recent experiments on single-stranded DNA, chromatin fiber and double-stranded DNA with proteins weakly absorbed along its length which show this effect. Effects of polymer semiflexiblity and torsional stiffness relevant to experiments on proteins binding to dsDNA are analyzed. We finally discuss the competition between electrostatic self-repulsion and folding interactions responsible for the complex elastic response of single-stranded DNA. Received 7 August 2002 and Received in final form 7 March 2003 / Published online: 15 April 2003 RID="a" ID="a"e-mail: jmarko@uic.edu     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001