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Regimes of strong electrostatic collapse of a highly charged polyelectrolyte in a poor solvent

We perform extensive molecular dynamics simulations of a highly charged flexible polyelectrolyte (PE) chain in a poor solvent for the case when the chain is in a collapsed state and the electrostatic interactions, characterized by the reduced Bjerrum length $\ell_B$, are strong. We detect the existence of several sub-regimes, $R_g \sim \ell_B^{-γ}$, in the dependence of the gyration radius of the chain $R_g$ on $\ell_B$. In contrast to a good solvent, the exponent $γ$ for a poor solvent crucially depends on the size and valency of counterions. To explain the different sub-regimes we generalize the existing counterion fluctuation theory by a more complete account of the volume interactions in the free energy of the chain. These include interactions between the chain monomers, between monomers and counterions and the counterions themselves. We also demonstrate that the presence of the condensed counterions can modify the effective attraction among the chain monomers and impact the sign of the second virial coefficient.