Conformation of polyelectrolytes in poor solvents: variational approach and quantitative comparison with scaling...

We present the results of variational calculations of a polyelectrolyte solution with low salt in poor solvent conditions for a polymer backbone. By employing the variation method, we quantitatively determined the diagram of the state of the polyelectrolyte in poor solvents as a function of the charge density and the molecular weight. The exact structure and diagram of the polyelectrolyte were compared to the scaling predictions of the necklace model developed by Dobrynin and Rubinstein [Prog. Polym. Sci. 30, 1049-1118 (2005); Dobrynin and Rubinstein, Macromolecules 32, 915-922 (1999); Dobrynin and Rubinstein, Macromolecules 34, 1964-1972 (2001)]. We find that the scaling necklace model may be used as a rather good estimation and analytical approximation of the exact variational model. It is also pointed out that the molecular connection of polymer is crucial for ellipsoid and necklace conformation.