The conformation of conducting polymer chains: Hubbard polymers

The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic degrees of freedom extend the size of the chain. The end-to-end distance behaves as $R\propto L^{\nu}$ with $\nu=(d+1)/(d+2)$, where $d$ is the spatial dimension.Comment: 11 pages of Latex + uuencoded postscript figur

Self- generated disorder and structural glass formation in homopolymer globules

We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected molecules on nano scales. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self - generated (in contrast to spin glasses) and can be related with competitive interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.Comment: 22 pages, 4 figures, submitted to Phys. Rev.

MOBILITY IN A ONE-DIMENSIONAL DISORDER POTENTIAL

In this article the one-dimensional, overdamped motion of a classical particle is considered, which is coupled to a thermal bath and is drifting in a quenched disorder potential. The mobility of the particle is examined as a function of temperature and driving force acting on the particle. A framework is presented, which reveals the dependence of mobility on spatial correlations of the disorder potential. Mobility is then calculated explicitly for new models of disorder, in particular with spatial correlations. It exhibits interesting dynamical phenomena. Most markedly, the temperature dependence of mobility may deviate qualitatively from Arrhenius formula and a localization transition from zero to finite mobility may occur at finite temperature. Examples show a suppression of this transition by disorder correlations.Comment: 10 pages, latex, with 3 figures, to be published in Z. Phys.

Reversible stretching of homopolymers and random heteropolymers

We have analyzed the equilibrium response of chain molecules to stretching. For a homogeneous sequence of monomers, the induced transition from compact globule to extended coil below the $\theta$-temperature is predicted to be sharp. For random sequences, however, the transition may be smoothed by a prevalence of necklace-like structures, in which globular regions and coil regions coexist in a single chain. As we show in the context of a random copolymer, preferential solvation of one monomer type lends stability to such structures. The range of stretching forces over which necklaces are stable is sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure

Scattering from random-sequenced-copolymers: RPA and replicas

This paper discusses the scattering from a melt of randomly sequenced copolymers. Since the distribution of random sequences are quenched new collective variables have to be introduced which carry two replica indices. The disorder has a strong influence as the resulting scattering function. Moreover a microphase separation is speculated

Polymeric fractals and the unique treatment of polymers

It has been suggested that r-fractals allow a uniform description of arbitrarily connected polymers. r is the exponent of the maximal possible radius of gyration, i.e. R ∼ Nr. We conjecture that 1/r is identical with the spectral dimension of the polymeric fractal.Il est suggéré que les r-fractals permettent une description unifiée des polymères connectés arbitrairement. r est l'exposant du rayon de giration maximum possible, R ∼ Nr. Nous conjecturons que 1/r est identique à la dimension spectrale du fractal polymère

Mean field dynamics of random manifolds

The mean field dynamics of manifolds in a quenched random potential is discussed by means of the Martin-Siggia-Rose (MSR) method. In a self-consistent way we obtain for the dynamic exponent $z$ the value $z=({4-D})/[{4(1+\gamma)}]$ where $D$ is the dimension of the manifold and $\gamma$ the noise characteristics of the potential. This implies immediately for the wandering exponent $\zeta=({4-D})/[{2(1+\gamma)}]$, i.e. that obtained by hierarchical replica symmetry breaking. The general scaling law $z={1}/{2} \zeta$ is suggested. Moreover, we find as the replica theory two, different regimes for the wandering exponent as a function of the noise correlation function

Concentrated polymer solutions in the presence of fixed obstacles

We consider a dense concentrated polymer solution in the presence of fixed obstacles, which represent the quenched disorder. It is shown that the fluctuations are reduced and that the effective Edwards screening length becomes infinite at a certain obstacle concentration. The osmotic pressure and the size of a chain are calculated for such a system. We expect a disorder transition, where the chains are collapsed and localised. The results are compared with the case of annealed disorder (troubled solvent and troubled concentrated solution).On considère une solution concentrée et dense de polymères en présence d'obstacles fixes qui représentent le désordre après trempe. On montre que les fluctuations diminuent et que la longueur d'écran d'Edwards devient infinie pour une certaine concentration d'obstacles. On calcule la pression osmotique et la taille d'une chaîne dans ce système. On s'attend à une transition de désordre, quand les chaînes s'effondrent et se localisent. Les résultats sont comparés au cas du désordre après recuit

Are polymer chains in blends "localized" before their phase separation? Variational treatment and prediction of anomalous scattering results

In this communication we suggest, using the droplet picture in phase transitions, that polymer chains are localized before the phase separation in polymer mixtures. The effect is expected to be significant when the correlation length is of the order of the size of the polymer chain, i.e. usually for conventional polymers well above the phase separation. Several influences on experimental results are suggested. The first concerns the dynamic scattering function. This quantity does not relax to zero, but remains constant for longer times, as already indicated in first experiments. The static structure factor should show a hump in the Kratky plot