Semidilute and Concentrated Solutions of a Solvophobic Polyelectrolyte in Nonaqueous Solvents Thomas A. Waigh, † Raymond Ober, and Claudine E. Williams* Laboratoire de Physique de Matie ` re de la Condense ´ e, CNRS URA 792, Colle ` ge de France, 11 Place Marcelin Berthelot, F75231, Paris Cedex 05, France Jean-Claude Galin Institut Charles Sadron, CNRS-ULP, 6 rue Boussingault, 67083 Strasbourg Cedex, France Received June 22, 2000; Revised Manuscript Received December 18, 2000 ABSTRACT: We study the behavior of a solvophobic polyelectrolyte in a series of polar organic solvents of various quality and polarity. Small-angle X-ray scattering is used to measure the semidilute correlation length  as a function of polymer concentration. In polar solvents of good quality  varies as c -1/2 in the whole concentration range, as expected. Contrastingly, in acetonitrile, a polar solvent of poor quality, the scaling exponent is found to change from - 1 /2 to - 1 /7, in qualitative agreement with the predictions of the pearl necklace model of Dobrynin and Rubinstein. This behavior is attributed to the crossover between “string” and “bead-colloid” controlled regimes of the isotropic transient network. At yet higher concentrations a gel-like phase is found attributed to bead interpenetration. It is thought to be driven by the small Debye-Huckel screening length at these concentrations, in agreement with recent molecular dynamics simulations of Micka et al. The crossover concentration for both string/bead-colloid and colloid/ gel regimes can be adjusted by mixing solvents of varying dielectric constant and quality. The effect of added of salt and temperature is also studied. 1. Introduction Flexible polyelectrolytes in good solvents have been well studied both experimentally and theoretically. Although a quantitative theory of their behavior in solution is still lacking, scaling approaches have been successful in providing a qualitative description of their solution-state features. 1-3 In these theories, a monomer- monomer correlation length  is introduced to describe the semidilute solution properties; it characterizes the average interchain mesh size of an assembly of overlap- ping chains above the overlap concentration c*.  is easily measured in reciprocal space as the inverse of the position of a broad correlation peak in small-angle scattering techniques.  has been shown to depend on concentration as c -1/2 by scaling theories, 1-3 experi- ments, 4-6 and molecular dynamics simulations. 7 Note that below c* a peak is also observed by scattering techniques, when the range of the interchain repulsive electrostatic interaction is larger than the distance between them. In this case, 1,5 the 3-d order peak position scales as c +1/3 . Flexible polyelectrolytes in poor solvents have expe- rienced comparatively fewer experimental or theoretical studies. Theoretical progress has been made recently for the structure of single globular chains motivating further work. 8,9 Single chain globular structures are predicted to break up into a series of “beads” on “strings” as their charge increases, due to the Rayleigh charge instability, i.e., the increase in surface energy is bal- anced by a decrease in electrostatic energy, because of the mutual repulsion between charged segments, and the metastability is realized through capillary wave fluctuations on the surface of the globule. It is the pearl necklace model where highly stretched segments alter- nate with collapsed globules along the chain. This model, first proposed by Kantor and Kardar 8 for polyam- pholytes (chains containing both positively and nega- tively charged monomers), was introduced by Dobrynin, Rubinstein, and Obukhov 9 for polyelectrolytes. Extend- ing their study into the semidilute regime, Dobrynin and Rubinstein 10 found two different regimes above c*, labeled “bead controlled” and “string controlled”, de- pending on whether the concentration is sufficient for the interbead repulsion to become important or not. This theory has received partial corroboration with the experiments of Essafi et al. 11,12 and Spitteri et al. 13 on partially charged poly(styrenesulfonate) (PSS) in water. Essafi 11 found a /c exponent which was a function of f; for instance, the exponent was -0.38 for 40% charged PSS (f ) 0.4) in the whole semidilute regime while totally charged PSS displayed the typical -0.5 behavior. Similar findings were also reported by Heitz et al. 14 for poly(methacrylic acid) in water as a function of its neutralization (R): the /c exponent was found to vary from -0.43 to -0.31 when R decreased from 0.95 to 0.09. Evidence for an intrachain bead correlation peak has also been seen in the single chain scattering function in semidilute solutions by small-angle neutron scatter- ing. 13 A very recent investigation by Heinrich and Rawiso 15 of a more complex system of star PSS con- firmed the general picture; the authors interpret the appearance of a peak whose position varies as c +1/3 as being due to a correlation between hydrophobic ag- gregates, possibly the beads of the model, along the star arms. Moreover, the important question of counterion condensation 16,17 in these systems has also been studied experimentally and provides a further layer of rich phenomena; there is a strong reduction of the number of osmotically active counterions (or effective charge of the chains), compared to the prediction of Manning † Present address: Polymers and Complex Fluids, Department of Physics, University of Leeds, Leeds, LS2 9JT, U.K. * To whom correspondence should be addressed. 1973 Macromolecules 2001, 34, 1973-1980 10.1021/ma001086j CCC: $20.00 © 2001 American Chemical Society Published on Web 02/10/2001