Relaxation dynamics of salt-free polyelectrolyte solutions using flow birefringence and rheometry

Abstract

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η0 was found to scale with molecular weight and concentration as η0 ∼ c0.5Mw over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η0 ∼ c1.5M 2.9w, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c−0.42M −0.9w and τ ∼ c0M 0w for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999

Solvent Properties Influence the Rheology and Pinching Dynamics of Polyelectrolyte Solutions: Thickening the Pot with Glycerol and Cellulose Gum

“…In contrast, our measurements reflect the concentration by weight of the as-received NaCMC, leading to a slight shift in the plotted values. Even though we label our polymers with the supplier-reported M w , we expect that the macromolecular parameters such as the number of Kuhn segments, dispersity, charge fraction, and DS are also similar to those reported by Lopez et al The exponent of 0.68 or η sp ∝ c 0.68 is stronger than η sp ∝ c 1/2 , associated with the Fuoss law, observed experimentally and anticipated by scaling theories for semi-dilute, unentangled polyelectrolyte solutions. ,,− ,− ,− Likewise, the exponent of 1.6 or η sp ∝ c 1.6 has slightly stronger dependence than 3/2 predicted by Dobrynin, Colby, and Rubinstein ,,, and somewhat weaker than 1.7 expected by Muthukumar. ,, The exponent of 3/2 is reported for entangled solutions of poly­(methyl-2-vinyl pyridinium chloride) PMVP-Cl random copolymer in ethylene glycol, , aqueous NaCMC solutions, and aqueous xanthan gum solutions …”

Extensional Relaxation Time, Pinch-Off Dynamics, and Printability of Semidilute Polyelectrolyte Solutions

“…The influence of polydispersity in molecular weight, variation in charge fraction and chain hydrophobicity, amount of dissolved carbon dioxide, and flaws in rheometric measurements (see detailed discussion in Boris and Colby) can all contribute to the measured concentration-dependent response. However, the data sets obtained by Boris and Colby ( M w = 1200 kDa) as well as Chen and Archer ( M w = 262, 585, 801, and 1188 kDa) exhibit a 3/2 power law for salt-free aqueous NaPSS solutions. The power law of 3/2 is also observed for solutions of poly­(methyl-2-vinylpyridinium chloride) (PMVP-Cl) random copolymer in ethylene glycol, , sodium carboxymethyl cellulose aqueous solutions, and xanthan gum aqueous solutions .…”

“…Furthermore, the PAA solutions data show that λ E exhibits a concentration-dependent scaling of λ E ∝ c 1/2 for the unentangled, semidilute regime and λ E ∝ c 3/2 for the entangled regime. The concentration-dependent scaling behavior shown by λ E data for aqueous PAA solutions in both regimes is strikingly different from the shear relaxation time values predicted by scaling theory and measured experimentally in both the semidilute, unentangled regime ,,− ,,, with λ ∝ c –1/2 and the entangled regime with λ ∝ c 0 (independent of concentration). ,, Using the intrinsic viscosity of the polyelectrolyte, the Zimm time for the polyelectrolyte chain (in single chain limit) can be estimated using the formula λ = Λ­[η]­η s M w / RT (here pre-factor Λ depends on solvent quality and has an O(1) value) which gives λ Z ≈ 0.82 ms as the estimate for NaPSS and λ Z ≈ 0.15 ms for PAA solutions. The Zimm time represents a lower bound for relaxation time, and even though the estimated value for PAA solutions is lower, the elastocapillary regime is observed for semidilute, unentangled PAA solutions, and λ E is measurable for c > c *.…”

Determining the Molecular Weight of Polyelectrolytes Using the Rouse Scaling Theory for Salt-Free Semidilute Unentangled Solutions

“…The scaling model predicts η sp ∼ N w (weight-average degree of polymerization) based on Rouse dynamics in the semidilute unentangled regime. , To test the N dependence of η sp for aqueous polyelectrolyte solutions, η sp is first normalized by N w and plotted as a function of concentration as shown in Figure A, which includes CsPSS from this study and NaPSS from the literature that studied NaPSS with no added salt. ,− It is worth noting that all polystyrene sulfonate samples plotted in Figure A are from sulfonation of polystyrene with less than 100% degree of sulfonation. The molecular weight of the repeat unit from each source is calculated according to its respective degree of sulfonation.…”