Electrostatic Contributions to Chain Stiffness and Excluded-Volume Effects in Sodium Poly(styrenesulfonate) Solutions

Abstract

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...

Chain Stiffness and Excluded-Volume Effects in Polyelectrolyte Solutions: Characterization of Sodium Poly(2-acrylamido-2-methylpropanesulfonate) in Aqueous Sodium Chloride

“…Thus, we may conclude that the estimation of q for Na PAMPS in the aqueous salts is hardly affected by the diminution of the electrostatic interaction energy on the chain accompanying a decrease in L. This is similar to the earlier conclusion drawn for Na PSS. 7 …”

“…[5][6][7][8] The major problem in the estimation of q el is that excluded-volume and stiffness effects can hardly be separated for those polymers without resort to a relevant excluded-volume theory. In previous studies, [5][6][7][8][9][10][11] we utilized the quasi-two-parameter (QTP) theory (the Yamakawa-Stockmayer-Shimada theory) [12][13][14] for the wormlike chain 15 or, more generally, the helical wormlike chain 14 to estimate these effects in aqueous NaCl solutions of sodium hyaluronate and sodium poly(styrenesulfonate) (Na PSS).…”

“…[5][6][7][8] The major problem in the estimation of q el is that excluded-volume and stiffness effects can hardly be separated for those polymers without resort to a relevant excluded-volume theory. In previous studies, [5][6][7][8][9][10][11] we utilized the quasi-two-parameter (QTP) theory (the Yamakawa-Stockmayer-Shimada theory) [12][13][14] for the wormlike chain 15 or, more generally, the helical wormlike chain 14 to estimate these effects in aqueous NaCl solutions of sodium hyaluronate and sodium poly(styrenesulfonate) (Na PSS). Except for some details, the QTP scheme satisfactorily explained the molecular weight dependence of intrinsic viscosity [] and mean-square radius of gyration hS 2 i for the two polyelectrolytes at fixed salt concentrations C s higher than 10 À2 M. On the other hand, the available polyelectrolyte theories [1][2][3][4]16 failed to describe the C s dependence of the estimated q el and excluded-volume strength, though the degree of disagreement appeared to depend on the intrinsic chain stiffness.…”

Electrostatic Contributions to Chain Stiffness and Excluded-Volume Effects in Sodium Poly(2-acrylamido-2-methylpropanesulfonate) Solutions

“…This behavior of [], due to enhanced electrostatic repulsion between charged groups of the polyelectrolyte chain, is similar to the previously observed C s -dependence for Na hyaluronate in aqueous NaCl. 12 Interestingly, however, it is partly contrasted to that for Na PSS, 16 for which the increases in [] (with lowering C s ) were more pronounced in the higher C s region owing probably to a greater reduction in the attractive contribution to excluded-volume effects. Note that Na PSS attains the theta state in aqueous NaCl of C s ¼ 4:17 M at 16.4 C. and those for C s !…”

“…It is an extension of our previous studies on Na hyaluronte 11-14 (a weakly stiff polysaccharide) and Na poly(styrenesulfonate), [15][16][17] for which the ionic strength dependence of q and B was determined from measured [] with the aid of the QTP theory. In the work reported below, these parameters for Na PAMPS are estimated as functions of C s in the range from 0.005 to 1 M and compared with predictions from polyeletrolyte theories.…”