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Abstract
We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length lB, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain Rg on lB characterized by Rg ∼ l. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.
Highlights
Charged polymers in solution, or polyelectrolytes (PEs), are ubiquitous in nature and play a significant role in our everyday life
We show that the new theory can describe the molecular dynamics (MD) results for both good and poor solvents
To develop a generalized theory for electrostatic-driven collapse of a PE in a poor solvent, we start with the modified counterionfluctuation theory for a good solvent and retain the electrostatic term
Summary
Polyelectrolytes (PEs), are ubiquitous in nature and play a significant role in our everyday life. The third theory, referred to as counterion fluctuation theory, proposes that attractive interactions driving the collapse transition is a result of the density fluctuations of the condensed counterions leading to a negative pressure This theory predicts γ = 1/2 for good solvent conditions. The counterion-fluctuation theory, originally developed for good solvent with a single exponent γ = 1/2, has been generalized by us 34 through the inclusion of higher order virial coefficients to reproduce both the collapsed regimes seen in our MD simulations It is more challenging, to study a collapsed state of a flexible PE in a poor solvent 35–41 since, unlike in a good solvent, there exist additional attractive interactions between monomers which compete with the repulsive part of electrostatic interactions.
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