Quantifying the Effect of Multivalent Ions in Polyelectrolyte Solutions

Extreme dependence of dynamics on concentration in highly crowded polyelectrolyte solutions

Charge-carrying species, such as polyelectrolytes, are vital to natural and synthetic processes that rely on their dynamic behavior. Through single-particle tracking techniques, the diffusivity of individual polyelectrolyte chains and overall system viscosity are determined for concentrated polylysine solutions. These studies show scaling dependences of D ~ c-6.1 and η ~ c7.2, much stronger than theoretical predictions, drawing the applicability of power law fits into question. Similar trends are observed in concentrated solutions prepared at various pH and counterion conditions. These hindered system dynamics appear universal to polyelectrolyte systems and are attributed to the large effective excluded volumes of polyelectrolyte chains inducing glassy dynamics. The framework of the Vrentas-Duda free-volume theory is used to compare polyelectrolyte and neutral systems. Supported by this theory, excluding counterion mass from total polymer mass results in all environmental conditions collapsing onto a common trendline. These results are applicable to crowded biological systems, such as intracellular environments where protein mobility is strongly inhibited.

Rheological and dielectric behavior of sodium carboxymethyl cellulose (NaCMC)/Ca2+ and esterified NaCMC/Ca2+ hydrogels: Correlating microstructure and dynamics with properties

Polyelectrolyte-based conductive hydrogels are being extensively explored for applications in energy storage and as electrode materials for batteries. We synthesized ionically crosslinked sodium carboxymethyl cellulose (NaCMC), esterified NaCMC, and Ca2+ doped esterified NaCMC hydrogels. This work aims to understand the effect of Ca2+ ions on the NaCMC and esterified NaCMC. FTIR, SEM, Rheology and EIS studies were performed to understand the structure and dynamics of hydrogels. Results confirmed that Ca2+ ions have an important role in determining the rheological and dielectric response of hydrogels. Power law behavior was observed in their rheological response with exponent (n) of 0.81 for G' and 0.76 for G″ of ionically crosslinked NaCMC, 5.38 for G' and 4.70 for G″ of esterified NaCMC, whereas, negative exponents -1.44 for G' and -1.10 for G″ of Ca2+ ion doped esterified NaCMC. Ionically crosslinked NaCMC hydrogels have relaxation times (τ) in the range of 8.9 × 10-5 s-2.8 × 10-5 s may be due to the formation of temporary dipoles by electrostatic bridge formations with dc conductivity of (0.1 S/cm-5 S/cm), whereas, esterified NaCMC showed relaxation times (10-3 s-8.9 × 10-5 s) with increasing ester crosslinks and dc conductivity of (0.05 S/cm-0.8 S/cm). Interestingly, Ca2+ ion doped esterified hydrogels showed multiple dielectric relaxations on Ca2+ ion addition with different relaxation times may be due to change in ionic environment. The understanding obtained from this work may be useful for designing tuneable hydrogels with optimum electrical and mechanical properties.

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Interchain Hydrodynamic Interaction and Internal Friction of Polyelectrolytes

Polyelectrolytes (PE) are polymeric macromolecules in aqueous solutions characterized by their chain topology and intrinsic charge in a neutralizing fluid. Structure and dynamics are related to several characteristic screening length scales determined by electrostatic, excluded volume, and hydrodynamic interactions. We examine PE dynamics in dilute to semidilute conditions using dynamic light scattering, neutron spinecho spectroscopy, and pulse field gradient NMR spectroscopy. We connect macroscopic diffusion to segmental chain dynamics, revealing a decoupling of local chain dynamics from interchain interactions. Collective diffusion is described within a colloidal picture, including electrostatic and hydrodynamic interactions. Chain dynamics is characterized by the classical Zimm model of a neutral chain retarded by internal friction. We observe that hydrodynamic interactions are not fully screened between chains and that the internal friction within the chain increases with an increase in ion condensation on the chain.

A Sulfonated All-Aromatic Polyamide for Heavy Metal Capture: A Model Study with Pb(II)

Polyelectrolytes are widely used in heavy metal removal, finding applications as coagulants and flocculants. We compare the heavy metal removal capability of a water-soluble sulfonated semirigid polyamide, poly(2,2'-disulfonyl-4,4'-benzidine isophthalamide) (PBDI), with that of a well-known random-coil polymer, poly(sodium 4-styrenesulfonate) (PSS). Using lead (Pb(II)) as a model contaminant, both polymers precipitate out from solution at ~500 mg/L Pb(II) in water. The ability to remove Pb(II) from water was quantified using adsorption isotherms and fitted with Langmuir and Freundlich adsorption models. The sorption of Pb(II) by PSS fit the Langmuir model with a high degree of correlation (0.976 R2), but the sorption of Pb(II) by PBDI could not be accurately predicted using the Langmuir or Freundlich model. The sorption of Pb(II) by PBDI and PSS was compared by normalizing sorption by the number of sulfonate groups of each polymer and the ion exchange capacity (IEC), found by titration. We find that PBDI removes a greater amount of Pb(II) per gram of sorbent compared to PSS, 410 mg/g vs 260 mg/g, respectively, which cannot be accounted for by differences in IEC or number of sulfonate groups. Our findings confirm that the positioning of the sulfonate groups and the rigidity of the polymer backbone play an important role in how Pb(II) coordinates to the polymer prior to precipitating out from solution.

Rheological Properties of Sodium Carboxymethylcellulose Solutions in Dihydroxy Alcohol/Water Mixtures

The aim of the research presented in this paper was to determine the effect of dihydroxy alcohols on the rheological properties of sodium carboxymethylcellulose (Na-CMC) solutions with different degrees of substitution and different average molecular masses. Rheological measurements were carried out with a rotational rheometer in continuous and oscillatory flows. Two dihydroxy alcohols were used in the study: butane-1,3-diol and propane-1,2-diol. The concentration of Na-CMC in the solutions was 1.6% and 2.2%, while the concentration of the dihydroxy alcohols ranged from 10% to 60%. The measurements show that the viscoelastic properties of Na-CMC solutions are strongly linked to the type of solvent used. The application of low-substituted high-molecular-mass Na-CMC makes it possible to obtain fluids with the properties of weak physical gels. On the other hand, the dissolution of Na-CMC with a high degree of substitution (>1) and low molecular mass in dihydroxy alcohol/water mixtures yields a viscoelastic fluid. Based on oscillatory measurements, increasing concentrations of polyhydroxy alcohols in Na-CMC solutions were found to induce an increase in the strength of the network structure. At the same concentrations of polyhydroxy alcohols in solutions containing butane-1,3-diol, a stronger network structure is formed compared to solutions containing propane-1,2-diol. The rheological measurement results presented in this paper may be useful in the formulation of drug carriers and cosmetics in which rheological properties are a significant factor.

Electrostatic Repulsion Slows Relaxations of Polyelectrolytes in Semidilute Solutions

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

Quantifying Properties of Polysaccharide Solutions

We apply a scaling theory of semidilute polymer solutions to quantify solution properties of polysaccharides such as galactomannan, chitosan, sodium carboxymethyl cellulose, hydroxypropyl methyl cellulose, methyl cellulose, xanthan, apple pectin, cellulose tris(phenyl carbamate), hydroxyethyl cellulose, hydroxypropyl cellulose, sodium hyaluronate, sodium alginate, and sodium κ-carrageenan. In particular, we obtain the molar mass of the chain segment inside a correlation blob M _g = B̂ ^3/(3ν-1) c ^1/(1-3ν) as a function of concentration c, interaction parameter B̂, and exponent ν. Parameter B̂ assumes values B̂ _g, B̂ _th and M ₀/N _A ^1/3 l for exponents v = 0.588, 0.5 and 1, respectively, where M ₀ is the molar mass of a repeat unit, l is the projection length of a repeat unit, and N _A is the Avogadro number. In the different solution regimes, the values of the B̂-parameters are extracted from the plateaus of the normalized specific viscosity η_sp (c)/M _w c ^1/(3ν-1), where M _w is the weight-average molecular weight of the polymer chain. The values of the B̂-parameters are used in calculations of the excluded volume v, Kuhn length b, and crossover concentrations c*, c _th, and c** into a semidilute polymer solution, a solution of overlapping thermal blobs and a concentrated polymer solution, respectively. This information is summarized as a diagram of states of different polysaccharide solution regimes by implementing a v/bl ² and c/c** representation. The scaling approach is extended to the entangled solution regime, allowing us to obtain the chain packing number, P̃ _e. This completes the set of parameters {B̂ _g, B̂ _th, P̃ _e} which uniquely describes the static and dynamic properties of a polysaccharide solution.