A self-consistent field (SCF) theory for the adsorption of polyelectrolyte chains onto oppositely charged spheres is considered. It is demonstrated that the criterion for critical adsorption shows a different behavior for small and large curvature of the surface. Experiments give indeed evidence for the power-law behavior as theoretically predicted for large curvature. a

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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 as a function f of the distance R behaves as f ∝ 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.

SUMMARY A self-consistent field (SCF) theory for the adsorption of polyelectrolyte chains onto oppositely charged spheres is considered. It is demonstrated that the criterion for critical adsorption shows a different behavior for small and large curvature of the surface. Experiments give indeed evidence for the power-law behavior as theoretically predicted for large curvature.

The case of polymers in strong quenched disorder is investigated. The disorder is modeled by a quenched random potential which is sampled by a flexible polymer chain. It is shown that the problem, originally formulated in terms of Edwards type path integrals, can be transformed into an effective field theory. Localized phases of the polymer, where the size of the chain is independent of its contour length, i.e. R2∝(1/Δ)2/(4−d), can be found by a weak breaking of the replica symmetry. Δ is a measure for the disorder. The same formalism predicts at d=4 an essential singularity R2 ∝exp(2π2/Δ) for vanishing disorder Δ→0.