Structure of Salt-free Linear Polyelectrolytes in the Debye-Hückel Approximation

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Abstract
We examine the effects of the common Debye-Hiickel approximation used in the- ories of polyelectrolytes. Molecular dynamics simulations using the Debye-Hiickel pair potential of salt-free polyelectrolytes have been performed. The results of these simulations are compared to earlier "Coulomb" simulations which explicitly treated the counterions. We report here the comparisons of the osmotic pressure, the end-to-end distance and the single chain structure factor. In the dilute regime the Debye-Hiickel chains are more elongated than the Coulomb chains implying that the counterion screening is stronger than the Debye-Hiickel prediction. Like the Coulomb chains the Debye-Hiickel chains contract significantly below the overlap den- sity in contradiction to all theories. Entropy thus plays an important and sorely neglected role in theory. The understanding of polyelectrolytes is one of the important unresolved problems in poly- mer physics (1-3). The presence of charges on the polymer chains presents difficult problems both theoretically and experimentally. Recent application of computer simulations to poly- electrolytes has revealed many interesting results and illuminated various problems with the theoretical approaches (4-7). References (4-6) treated the complete Coulomb interactions for salt-free polyelectrolytes in solutions. That is, the counterions in the solutions were explicitly simulated, and the full I/r potential was treated including long-range effects. In contrast, all theoretical approaches use a screened Coulomb or Yukawa pair potential to treat the effective charged monomer interactions (8-12). In this paper, we report results of simulations of poly- electrolytes in solution with the Coulomb interactions treated at the Debye-Hfickel (DH) level. In this way we can determine the utility of the DH approximation in theory. The DH approximation is the linearization of the Poisson-Boltzmann equations which are the mean-field equations. Because the DH equation is linear there is an analytic form for the DH pair potential, u~j jr) = q~kBTlB exp(-t~r)/r, (I) where lB " e~lekBT is the Bjerrum length, t~ = A~~ = (4~lBP)~/~ is the inverse Debye length in a salt-free solution, p is the monomer density and q is the monomer charge which is always one electron charge in this work. Theoretical works use the DH potential, since the full

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