Titrating polyelectrolytes with up to 2000 monomers are studied by Monte Carlo simulations. The polyelectrolyte, regarded to be a polyacid in a salt-free solution, is modelled with harmonic bonds between monomers that can be either neutral or negatively charged. The charges are allowed to fluctuate in a grand canonical ensemble and charged monomers interact via a Coulomb potential. Scaling laws expressing the root-mean-square end-to-end distance and the apparent dissociation constant as functions of the number of monomers and degree of ionization are obtained from a simple Flory approach. Comparisons with the simulation results show that these scaling laws describe a universal behavior for long and highly charged chains.
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Ullner et al. (1994) studied this question.