Solutions of highly charged polyelectrolyte chains are described by a model that introduces ion condensation as a random charge along the polymer. The degree of condensation is obtained by solving the Poisson-Boltzmann equation with cylindrical geometry. Short range electrostatic attractions between the monomers via the condensed counterions of high enough valency lead to reversible chain precipitation. The range of polymer concentration over which salt-free solutions are unstable is determined, as well as the miscibility of the chains when salt is added. Redissolution at high salt concentration is due to a screening of the short range electrostatic attractions. Precipitation of chains in mixtures of movalent and multivalent salts is also studied. We find the range of salt concentration where chains precipitate. The model explains the experimental results on the precipitation of sodium and lanthanum polystyrene sulfonate solutions in presence of multivalent salts ͓LaCl 3 and Th͑NO 3 ͒ 4 ͔.

We present experimental data on the dynamical behavior of polymer (polystyrene) solutions in good solvent. The technique used is intensity-fluctuation spectroscopy, which allows us to determine the characteristic time of the dynamical structure factor of the polymer. The dynamical response of the polymer is given as a function of wave vector K, concentration c, and molecular weight M. We determine three dynamical exponents a , d, and y:(1) In dilute solution, the hydrodynamical radius of the polymer increases with the molecular weight as M" where a = 0.55 f 0.02. We found experimentally that the geometrical radius scales as M u where u is the static exponent equal to 0.6. (2) At concentrations where polymer chains overlap the solutions behave like gels of finite lifetime. The cooperative diffusion coefficient depends on concentration only and increases with concentration as ci-i where d = 0.67 i 0.02. (3) In dilute solution, a t wave vector K greater than R-l, where R is the coil radius of gyration ( K R 2 4.4), the inverse characteristic time depends only on K and increases as KY where y = 2.85 f 0.05. These experimental data are compared to the exponent values and scaling laws proposed recently by de Gennes. The main assumption of de Gennes' calculation is that static and dynamical lengths are identical. This is not verified experimentally but the exponents a, @, and y measured are self-consistent and connected by the scaling laws: n = (31, -1)$, y = 2 + n/o.The conformation of macromolecules in good solvent has been studied both experimentally and theoretically1 in dilute and semidilute solutions. We shall first recall some of the concepts and methods used for the determination of spatial properties of polymers because they will be of importance in the derivation of dynamical properties.At very low monomer concentration e (dilute solution), the macromolecules behave like a collection of independent coils with a geometrical size R (radius of gyration) given by:a is the length and m the molecular weight associated with the statistical element, and M is the molecular weight of the macromolecule. The macromolecules begin to overlap at concentration e* such that the distance between the centers of two neighboring coils is equal to 2R:When the concentration is larger than c* (semidilute solution) the polymer chains have contact points and the spatial monomer distribution is homogeneous. Then the average distance between adjacent contact points, E, is independent of the polymer weight and varies with concentration as ~~' (~-3~) ( = C -O .~~) .This last point can be obtained by a scaling law.Assuming that the length E behaves like some power of the concentration and that E and R must have the same order of magnitude a t the transition between dilute and semidilute regime ( e * ) we derive:The important result obtained in recent studies of polymer configuration is that is also the distance beyond which excluded volume effects are screened out.These views have been extended recently to time-dependent properties by de Ge...

We report experiments performed with a heterodyne spectrometer at the temperature in the polystyrene-cyclohexane system. Two dynamical regimes are observed: a liquid regime and a gel regime. In the liquid regime, where the semidilute solution behaves like a viscous fluid, the time dependence of the dynamical structure factor is well described by a single-exponential function. The macroscopic mutual diffusion coefficient is related to the motion of the solvent through the polymer. In the gel regime, where the solution behaves like an elastic gel, the dynamical structure factor is multiexponential (>2). The two processes that control the relaxation of concentration fluctuations are the motion of the solvent through the transient gel and the structural relaxation of the transient gel. When the temperature is increased above the temperature, the nonexponentiality of the dynamical structure factor in the gel regime disappears and we recover an exponential function as in good solvent solutions (polystyrene-benzene). In a solvent, both liquid and gel regimes are observed because dynamical properties are governed by two different lengths as was shown previously by viscoelastic measurements.