Orientational correlation functions have been obtained from Monte Carlo simulations of long, freely jointed chains (1000 monomers and more) with screened Coulomb interactions truncated after a certain number of bonds. This makes it possible to study chain-length dependence without “end effects” and to display excluded-volume effects. These correlation functions form the basis for a discussion of the conformational response to electrostatic interactions. In particular, they are related to the concept of electrostatic persistence length and the correlation functions illustrate the differences between different definitions of persistence length. To facilitate future discussions, we have identified four types of definitions and given them separate names:  (1) projection length, which involves integration of the orientational correlation function; (2) orientational correlation length, which is the decay length of an exponential function; (3) bending coefficient, which is a length representing a bending force constant; and (4) crossover distance, which is the monomer−monomer distance at the boundary between a rodlike and a swollen behavior. Previous conclusions that the projection length obeys a power law at high salt concentrations, while the orientational correlation length does not, are confirmed. Furthermore, a power law is also found in the salt-free limit for the projection length corresponding to an infinite chain with a finite range of interactions. The two power laws make it possible to construct a universal curve that gives an almost quantitative description of the chain behavior.

Over the years, there has been much debate regarding the conformational behavior of flexible polyelectrolytes with electrostatic interactions described by the Debye−Hückel 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.

Monte Carlo simulations have been performed for two simple models of a titrating polyelectrolyte:  (i) a rigid rod and (ii) a freely jointed chain. Both models have fixed bond lengths, and the polyelectrolyte charges interact through a screened Coulomb potential. Chains consisting of 80−1000 monomeric units have been studied at three salt concentrations:  0.001, 0.01, and 0.1 M. Conformational properties and the apparent dissociation constant are reported as functions of chain length, chain ionization, monomer−monomer bond length, and salt concentration. Mean field expressions are compared to the simulation results and are, in general, found to be excellent approximations for the rigid rod, but they are also able to provide semiquantitative descriptions of the apparent dissociation constant for the freely jointed chain. Comparisons with experimental data show that the conformational properties of the flexible model can reproduce features of the titration curves, although the use of a screened Coulomb potential overestimates the response to changes in salt concentration.