73 research outputs found

    Semiflexible polymers in a random environment

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    We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity.Comment: 10 pages, 3 figures, Revtex

    Polymer adsorption on heterogeneous surfaces

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    The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55 (1997), 226). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain.Comment: accepted in EPJB (the Journal formerly known as Journal de Physique

    Dynamics of a three-dimensional inextensible chain

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    In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the z−z-axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle.Comment: 15 pages, 3 figures, LaTeX, version accepted for publicatio

    Collective Dynamics of Random Polyampholytes

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    We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge qq and with a fluctuations in this charge of the size Q−1Q^{-1} and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite qq we then find that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy

    Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

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    The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/bd)N2−νd≥1(\Delta/b^d) N^{2 - \nu d} \ge 1, where Δ\Delta is a disorder strength, bb is a Kuhnian segment length, NN is a chain length and ν\nu is the Flory exponent. We have derived the general equation for the non - ergodicity function f(p)f(p) which characterizes the amplitude of frozen Rouse modes with an index p=2πj/Np = 2\pi j/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength Δc∼N−γ\Delta_c \sim N^{-\gamma} where the exponent γ≈0.25\gamma \approx 0.25 and does not depend from the solvent quality.Comment: 17 pages, 6 figures, submitted to EPJB (condensed matter

    Localization and freezing of a Gaussian chain in a quenched random potential

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    The Gaussian chain in a quenched random potential (which is characterized by the disorder strength Δ\Delta) is investigated in the dd - dimensional space by the replicated variational method. The general expression for the free energy within so called one - step - replica symmetry breaking (1 - RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center of mass localization and collapse. The critical disorder when the chain becomes localized scales as Δc≃bdN−2+d/2\Delta_c \simeq b^d N^{-2 + d/2} (where bb is the length of the Kuhn segment length and NN is the chain length) whereas the chain gyration radius Rg≃b(bd/Δ)1/(4−d)R_{\rm g} \simeq b (b^d/\Delta)^{1/(4 - d)}. The freezing of the internal degrees of freedom follows to the 1-RSB - scenario and is characterized by the beads localization length D2ˉ\bar{{\cal D}^2}. It was demonstrated that the solution for D2ˉ\bar{{\cal D}^2} appears as a metastable state at Δ=ΔA\Delta = \Delta_A and behaves similarly to the corresponding frozen states in heteropolymers or in pp - spin random spherical model.Comment: 18 pages, 6 figures, submitted to J. Chem. Phy

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

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    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 minimizing the free energy FNF_N, depending on N(N−1)/2N(N-1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 24<N<2162^4<N<2^{16} and for an open chain of length 24<N<292^4<N<2^9 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.Comment: submitted to EPJE (soft matter

    Constrained dynamics of a polymer ring enclosing a constant area

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    The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times. At long times, the time dependence is weak, and is mainly governed by the inverse of the first mode of the area. The presence of the constraint changes the nature of the relaxation of the internal modes. The time correlation of the position vectors of the ring is found to be dominated by the first Rouse mode which does not relax even at very long times. The mean square displacement of the radius vector is found to be diffusive, which is associated with the rotational diffusion of the ring.Comment: 6 page

    Description of the dynamics of a random chain with rigid constraints in the path integral framework

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    In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of a chain which can form only discrete angles with respect to the z−z-axis is also presented.Comment: 4 pages. To appear in the proceedings of `Path Integrals - New Trends and Perspectives`, 23-28 September 2007, Dresden, German
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