Sixteen narrow-distribution samples of sodium poly(styrenesulfonate) (NaPSS) ranging in weight-average molecular weight M w from 2.6 × 103 to 6.5 × 105 were prepared by the radical polymerization of sodium-p-styrenesulfonate, followed by repeated fractional precipitation, and were studied by static light scattering, sedimentation equilibrium, and viscometry in 0.5 M aqueous NaCl at 25 °C and in 4.17 M aqueous NaCl at 16.4 °C, the ϑ point, where the light scattering second virial coefficient vanished for high M w. The characteristic ratio (i.e., the mean-square radius of gyration at the ϑ point divided by the degree of polymerization) for high-molecular-weight NaPSS was found to be considerably smaller than that for polystyrene in cyclohexane. Data for the intrinsic viscosity [η] in 4.17 M aqueous NaCl at ϑ were analyzed by the theory of Yoshizaki et al. (Macromolecules 1988, 21, 165) for the wormlike chain, a special limit of the helical wormlike chain, to obtain 0.23 (± 0.03), 0.69 (± 0.07), and 1.2 (± 0.1) nm for the monomeric contour length, the persistence length q, and the chain diameter, respectively. This q value is much smaller than the intrinsic persistence length of 1.2 nm widely used in the literature for experimental tests of available theories for the electrostatic persistence length. At the lower NaCl concentration of 0.5 M where intramolecular excluded-volume effects were significant, the molecular weight dependence of [η] was explained quantitatively by a combination of Yoshizaki et al.'s theory and the quasi-two-parameter theory with a larger q of 1.5 nm and an excluded-volume strength parameter of 1.6 nm.

ABSTRACT:Intrinsic viscosities for sodium poly(styrenesulfonate) in aqueous sodium chloride at 25°C have been determined for 15 samples ranging in weight-average molecular weight from 3.8 X 10 3 to 6.5 X 10 5 at five salt concentrations C, between 0.05 and 2 M. Their molecular weight dependence at each C, is fairly satisfactorily explained by the theory ofYoshizaki et al. for unperturbed wormlike chains combined with the quasi-two-parameter theory for excludedvolume effects. The estimated persistence length q and excluded-volume strength B both increase with decreasing C,. This increase in q is not quantitatively described by the known theories for the electrostatic persistence length when the previously determined q of 0.69 nm in 4.17 M aqueous NaCl at the theta point is used for the intrinsic persistence length. It is also shown that the values of B computed on the conventional bead model and the rodlike segment model in the Debye-Htickel approximation with the ion condensation hypothesis are too large compared to the experimental estimates at lower C, of0.05 and 0.1 M though the latter model gives considerably smaller B than does the former one.KEY WORDS Polyelectrolyte I Poly(styrenesulfonate) / Wormlike Chain/ Chain Stiffness/ Electrostatic Persistence Length/ Excluded-Volume Effect/ According to the current polyelectrolyte theory, 1 -4 the persistence length q of a charged linear polymer, modeled by the Kratky-Porod wormlike chain,5 in aqueous salt increases with lowering salt concentration Cs. Although much experimental work on this electrostatic stiffening effect has been reported in the past two decades, our understanding of it still leaves much to be desired, at least, for intrinsically flexible or weakly stiff polyelectrolytes. 6 The problem 7 • 8 is that the effects of chain stiffness and volume exclusion in those polymers can hardly be separated without resort to a relevant excluded-volume theory, but no such theory is, of course, as yet known. In this situation, it is intriguing and probably significant to estimate q and the excluded-volume strength B (or the binary cluster integral) from data for the intrinsic viscosity [1]] or the radius of gyration with the aid of the quasi-two-parameter (QTP) theory 9 -11 for uncharged wormlike or helical wormlike chains,9 since the theory is capable of almost quantitatively explaining the radius and viscosity expansion factors for nonionic polymers, both flexible 9 and stiff. 12In a series of previous studies, 7 • 13 -15 we made such attempts for aqueous NaCl solutions of sodium hyaluronate, a charged polysaccharide with a q of about 4 nm at high ionic strength and a linear charge density of 1 nm-1 , and drew the following conclusions. 1. The QTP scheme is applicable to this polysaccharide down to Cs = 0.01 M. 2. The electrostatic contribution to q obtained as a function of Cs is considerably larger than predicted by the known theories.1 -4 3. The dependence of estimated B on Cs is in moderate agreement with the FixmanSkolnick theory 16 for the excluded volum...

Seven narrow-distribution samples of six-arm star polystyrene ranging in weight-average molecular weight Mw from 6.1 x 10 4 to 3.4 x 10 6 in benzene at 25°C have been studied by light scattering and viscometry to determine their z-average radii of gyration, second and third virial coefficients, and intrinsic viscosities. The ratios of the respective properties to those of linear polystyrene in the same solvent are established for high Mw. Data analysis shows that the relation between the radius expansion factor and the conventional excluded-volume parameter z comes close to the known relations for four-arm star and linear polystyrenes of high molecular weight and is described fairly satisfactorily by the previously proposed interpolation formula. On the other hand, the viscosity expansion factor vs. z curve appears slightly below that for linear polystyrene though almost superimposed on that for the four-arm star polymer. Thus the difference in this expansion factor between the linear and star chains remains to be explained theoretically. The experimental interpenetration function for the six-arm star polymer gradually decreases to about 0.6, a value close to recent Monte Carlo data, with increasing Mw. Its comparison with the previously constructed interpolation expression suggests that, as was the case for linear flexible polymers, the effect of chain stiffness on the second virial coefficient needs to be considered for Mw below 10 6 •