Eur. Phys. J. E 6, 259-270 (2001)

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

G. Migliorini¹, N. Lee¹, V. Rostiashvili¹ and T.A. Vilgis<sup>1, 2

1</sup>  Max Planck Institute for Polymer Research, 10 Ackermannweg, 55128 Mainz, Germany
²  Laboratoire Européen Associé, Institute Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France

vilgis@mpip-mainz.mpg.de

(Received 7 June 2001 and Received in final form 17 October 2001)

Abstract
We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N-1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴< N< 2⁸ and for an open chain of length 50< N< 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented.

PACS
05.20.-y - Classical statistical mechanics.
36.20.-r - Macromolecules and polymer molecules.
82.35.Rs - Polyelectrolytes.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001