Monte Carlo test of electrostatic persistence length for short polymers

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Abstract
A Metropolis Monte Carlo program with reptation is used to generate sample configurations of short electrically charged polymers with thermally distributed Debye–Hückel electrostatic energies. The polymer is a three fold rotational isomeric state model with bond angle θ between 5° and 90° and number of units N between 10 and 225. To compare the resulting root‐mean‐square (rms) values for radius of gyration S, and end‐to‐end length R, to theory, we use a wormlike chain with contour length L equal to the stretched out length of the polymer, the same total charge, and an intrinsic persistence length set so that, for large N, for specified θ and L, S agrees with the rotational isomeric state model. The results are compared with the predictions for S, with correction for finite L, of Odijk [J. Polymer Sci., Polymer Phys. Ed. 1 5, 477 (1977)]. They are then compared with three attempted corrections for excluded volume: (1) Odijk and Houwaart [J. Polymer Sci., Polymer Phys. Ed. 1 6, 627 (1978)]; (2) correction (1) modified by using the electrostatic excluded volume of Fixman and Skolnick [Macromolecules1 1, 863 (1978)]; (3) correction (2) modified by replacing the Yamakawa–Tanaka formula by an approximation due to Gupta and Forsman [Macromolecules5, 779 (1972)]. Odijk’s prediction with correction for finite length works fairly well under conditions of small excluded volume. The excluded volume corrections are often but not always of about the right size; the latter two work better.