Quantifying the Effect of Multivalent Ions in Polyelectrolyte Solutions

Abstract

We implemented a scaling approach, based on the relationship between the solution correlation length ξ = lg ν /B and the number of repeat units per correlation blob g for polymers with repeat unit projection length l, to quantify properties of solutions of carboxymethylcellulose and polystyrene sulfonate with monovalent and divalent counterions. The parameter B is equal to B pe , B g , B th , and 1, and the exponent v = 1, 0.588, 0.5, and 1 in semidilute polyelectrolyte solutions, solutions of overlapping electrostatic and thermal blobs, and concentrated polymer solutions, which are separated by crossover concentrations c D , c th , and c**, respectively. The values of the B-parameters are obtained using the linear relationship between the specific viscosity η sp (c) in the unentangled solution regime and the number of correlation blobs N w /g per chain, with the weight-average degree of polymerization, N w , and g = B 3/(3ν−1) (cl 3 ) 1/(1−3ν) as a function of the repeat unit concentration, c, and the B-parameters in different solution regimes. This analysis shows that (i) there is only a small fraction of free counterions, f * < 12%; (ii) divalent ions have a strong effect on the renormalization of the excluded volume, reducing it by a factor of 2; and (iii) the effect of divalent counterions is much weaker on the renormalization of the Kuhn length, accounting for an increase of up to 10%. In combination, these effects significantly reduce chain stretching, increase the number of repeat units per solution correlation length, and promote chain disentanglement in polyelectrolyte solutions with divalent ions in comparison with that in solutions with monovalent counterions. There is an indication of chain bridging by Ca 2+ ions in concentrated solutions of carboxymethylcellulose, manifested as an increase in solution viscosity. The concentration dependence of the solution correlation length ξ calculated using the set of B-parameters is in good agreement with that obtained from the peak position of the scattering function for concentrations c < c D .

Solution Properties of Polyelectrolytes with Divalent Counterions

“…The two limits in eq 7 can be interpolated by the following expression where A is a parameter related to the electrostatic blob size and β = 1 – 3ν. An updated model by Dobrynin et al , introduces an additional length scale, the thermal blob size, which marks the onset of excluded volume interactions for distances smaller than the electrostatic blob length.…”

“…where A is a parameter related to the electrostatic blob size and β = 1 − 3ν. An updated model by Dobrynin et al 77,78 introduces an additional length scale, the thermal blob size, which marks the onset of excluded volume interactions for distances smaller than the electrostatic blob length. We determine the overlap concentration of MgPSS using Colby's method, 31,38,98,100 that is, η sp (c*) ≃ 1.…”

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

“…Biologically sourced polysaccharides and cellulose derivatives are in increasing demand as rheology and processability modifiers for creating sustainable, water-based formulations with minimal or no VOCs (volatile organic compounds) and reduced carbon footprint and pollution. − The consumer, environmental, and market-driven impetus to increase the use of polysaccharides due to their non-toxicity, biocompatibility, and biodegradability has driven extensive shear rheological characterization of the influence of polymer type, molecular weight ( M w ), concentration ( c ), polydispersity ( Đ ), degree of substitution (DS), and branching. − Polysaccharides, such as cellulose gum and xanthan gum, that contain ionizable groups behave as polyelectrolytes, − acquiring an expanded conformation in solution due to the electrostatic interaction among dissociated ionic groups surrounded by a cloud of counterions along the polymer backbone. Consequently, a significant enhancement in solution shear viscosity, η, occurs at a relatively low concentration of polyelectrolytes compared with neutral polymers. − Theoretical and experimental studies show that dynamics, shear rheological response, and processability are influenced significantly by variation in polyelectrolyte concentration, charge fraction, added salt, and pH. − However, surprisingly, little effort is dedicated to the influence of solvent properties on the rheology of charged polysaccharide (and polyelectrolyte) solutions, primarily motivating this study.…”

Quantifying Properties of Polysaccharide Solutions

“…At higher polymer concentrations, c > c th , the solution properties are similar to those in a θ solvent for the polymer backbone, and the statistics of a chain is qualitatively different from that near c ≈ c * . To address this issue, we have recently developed a generalized scaling approach − which provides a means to obtain crossover concentrations into different solution regimes and system parameters describing chain statistics at different length scales by using the concentration dependence of the solution viscosity. Here, we adapt this approach to describe solution properties of chitosan, sodium hyaluronate, ,, sodium alginate, sodium κ-carrageenan, , xanthan, , galactomannan, ,, and various cellulose derivatives. ,,, Specifically, for these solutions of polysaccharides, we calculate the interaction parameters, crossover concentrations, and chain packing parameter describing chain entanglements in solutions of overlapping chains.…”