On the elasticity of a single polyelectrolyte chain

This paper discusses the elastic behavior of a single polyelectrolyte chain. A simple scaling analysis as in self avoiding walk chains are not possible, because three interplaying relevant length scales are involved, i.e., the Debye screening length and the Pincus blob size. Therefore a selfconsistent computation of an effective variational propagator is employed. It is shown that the elastic force f is proportional to the end to end distance R for small f. For larger forces we find a new regime, characterized by deformations larger than a computed electrostatic "blob size". These results are supported by simulations and intuitive physical arguments.Comment: to be published in J. de Phys. I

Replica field theory for a polymer in random media

In this paper we revisit the problem of a (non self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM). As noticed by Cates and Ball (CB) there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ``localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the radius of gyration, g is the strength of the disorder, \mu is the spring constant associated with the confining potential and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln(V) as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d<2 and for large V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The 1-step replica symmetry breaking solution is crucial for obtaining the above results.Comment: Revtex, 32 page

Elasticity of entangled polymer loops: Olympic gels

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto \lambda^{5/2}$ where $\lambda$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio

Monte Carlo results for the hydrogen Hugoniot

We propose a theoretical Hugoniot obtained by combining results for the equation of state (EOS) from the Direct Path Integral Monte Carlo technique (DPIMC) and those from Reaction Ensemble Monte Carlo (REMC) simulations. The main idea of such proposal is based on the fact that DPMIC provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level using a binding potential calculated by Kolos and Wolniewicz. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson {\textit{et al.}} \cite{1} and Collins {\textit{et al.}} \cite{2}.Comment: 10 pges, 2 figures, 2 table

Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas

Extending our previous work \cite{filinov-etal.jpa03ik} we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: i) the diagonal Kelbg potential, ii) the off-diagonal Kelbg potential iii) the {\em improved} diagonal Kelbg potential, iv) an effective potential obtained with the Feynman-Kleinert variational principle v) the ``exact'' quantum pair potential derived from the two-particle density matrix. For the {\em improved} diagonal Kelbg potential a simple temperature dependent fit is derived which accurately reproduces the ``exact'' pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo (PIMC) and molecular dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about $60 000$ K. Finally, we point out an interesting relation between the quantum potentials and effective potentials used in density functional theory.Comment: 18 pages, 11 figure

Geometrical properties of chemically adsorbed copolymers at surfaces

In this paper we calculate the mean-square end-to-end distance and the mean-square perpendicular distance of chemically adsorbed copolymers of type A-B. The adsorbed monomers are assumed to be a quenched system. The calculation of the mean-square end-to-end distance shows that this distance is fully determined by the frozen-in disorder of the adsorbed monomers. The result obtained for mean-square perpendicular distance predicts a dependence of the fraction of adsorbed monomers. In comparison with homopolymers there is a difference within the power law behaviour, but no difference occurs for the physical adsorption of copolymers

Functional integral approach to the dissolution of polyelectrolyte complexes

A functional integral approach to the dissolution of fully symmetric polyelectrolyte complexes is presented. The dissolution itself may be caused by adding of low molecular salt or by varying the temperature. The zero-component Landau-Ginzburg-Wilson Hamiltonian, which is used for describing the system under consideration, is transformed to a pair field representation exactly via functional integrals. The pair field has many features reminding of the gap-parameter in superconductivity. The transformed Hamiltonian allows the Helmholtz free energy and the specific heat in the critical region to be calculated. The specific heat shows a discontinuity at the critical point.Nous présentons une étude basée sur l'intégrale fonctionnelle de la dissolution des complexes polyélectrolytes complètement symétriques. La dissolution elle-même peut être causée par l'addition de sel ou par une variation de la température. Nous utilisons l'intégrale fonctionnelle pour transformer le hamiltonien de Landau-Ginzburg-Wilson qui décrit le système en une représentation à deux champs. La paire de champs a plusieurs propriétés qui font penser au paramètre d'ordre en supraconductivité. Le hamiltonien transformé nous permet de calculer l'énergie libre de Helmholtz et la chaleur spécifique dans la région critique. La chaleur spécifique a une discontinuité au point critique