Monte Carlo test of electrostatic persistence length for short polymers

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 Sei., Polymer Phys. Ed. 15, 477 ( 1977) ]. They are then compared with three attempted corrections for excluded volume: ( 1 ) Odijk and Houwaart [J. Polymer Sei., Polymer Phys. Ed. 16, 627 ( 1978) ]; (2) correction ( 1 ) modified by using the electrostatic excluded volume of Fixman and Skolnick [Macromolecules 11, 863 ( 1978) ]; (3) correction (2) modified by replacing the YamakawaTanaka formula by an approximation due to Gupta and Forsman [Macromolecules 5, 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. © 1990 American Institute of Physics.