Comments on the scaling behavior of flexible polyelectrolytes within the Debye-Huckel approximation

Over the years, there has been much debate regarding the conformational behavior of flexible polyelectrolytes with electrostatic interactions described by the Debye-Huckel approximation. In particular, the electrostatic persistence length has been reported to depend both quadratically and linearly on the screening length as well as having no consistent power-law dependence at all. On the basis of simulation results together with a careful analysis of analytical approaches, including Odijk-Skolnick-Fixman (OSF) theory, variational calculations, and renormalization group results, it is possible to present a consistent picture, which contains a better understanding of the true behavior as well as an explanation for the diverse results. The projection length of long chains can be described by power laws in three regimes, and an expression by Odijk is qualitatively correct in two of these regimes. Scaling arguments based on OSF theory and excluded volume considerations give good agreement with the third power law, but the underlying assumptions are not entirely correct. More than one parameter is required to describe the internal chain behavior, which is characterized by short-range flexibility and long-range stiffness. Still, most analytical approaches end up in one of two one-parameter approximations, either an OSF-like perturbation expansion around a rigid-rod state or a Flory-type variational calculation based on an unperturbed chain. The latter describes at best the short-range behavior. A field-theoretic renormalization group treatment, which has suggested that there should be no power law behavior, is not valid in three dimensions. Previous support from simulation results were obtained through an unfortunate mistake.