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Polyelectrolytes in solution

The central aim of our group's research is to understand the physics of polyelectrolyte conformation and dynamics in solution, a problem which we primarily tackle using scattering and rheological techniques. We applying scaling concepts to complex, multicomponent systems (e.g. polyelectrolytes in the presence of salts, surfactants or non-solvents) and extract structural and hydrodynamic properties.


Polyelectrolytes (PEs) are polymers with ionic groups along their backbone. In solution, counterions dissociate leaving the polymer with net charge, which makes them strongly correlated systems. Polyelectrolytes are present in the synovial fluid, where they provide lubrication between joints, in food products and pharmaceutical creams, where they act as texture modifiers. In wines, they can be added to prevent tartaric acid crystallisation, in laundry detergents they act as anti-soil redeposition agents and as water-softeners. Recently, mRRA (a polyelectrolyte) vaccines have transformed immunisation against COVID-19 on a global scale. Despite their enormous prominence in biological phenomena and industrial products, polyelectrolytes were once described by PG de Gennes as ‘the least understood form of condensed matter’, a designation which still holds true. Some of our research areas on polyelectrolyte solutions are outlined below. For overviews of some of the problems in polyelectrolyte physics, also check these reviews:

Phase behaviour, ion solvation and counterion condensation in polyelectrolyte solutions

Polyelectrolytes in salt-free solution are unusual among polymer systems in that their phase behaviour is independent of their molar mass. The reason for this is that the osmotic pressure of the dissociated counterions (≈ \(k_BT\) per free counterion): \[\Pi \simeq k_BTfc\] is much larger than that of the chains (≈ \(k_BT\) per chain): \[\Pi \simeq k_BTc/N\] Polyelectrolyte solubility should then depend primarily on the fraction of free counterions (f). According to the Manning theory of counterion condensation, the fraction of free counterions is given by the ratio of the charge spacing to the Bjerrum length of the solvent media: \[l_B=\frac{e^2}{4\pi\epsilon k_BT}\] here \(\epsilon\) is the dielectric constant of the solvent. According to the above picture, the dielectric constant should be the main parameter indicating whether a polyelectrolyte is soluble in a given solvent. Experimentally, this is found to not be the case for polyelectrolyte solutions and gels.[1] An example is shown in the figure to the right, where the solubility of two polyelectrolyte is plotted in the Hansen representation. Here \(\delta_H\) is the Hansen hydrogen bonding parameter and \(\delta_P\) is the Hansen polarity parameter. The results suggest that polymer-solvent interactions and/or counterion-solvent interactions are the primary factor influencing polyelectrolyte solubility. This contrast with the classical models of polyelectrolyte solutions, which expect solubility is set by counterion entropy.

Our current research on this topic tries to elucidate the phase behaviour of polyelectrolytes in salt-free and salt-containing solutions, probing the influence of counterion and solvent type. We also use osmometric, potentiometric methods to understand the influence of dielectric constant and solvent quality on the fraction of dissociated counterions.

Image description
Phase behaviour of poly(ionic liquid) poly(1-butyl-3-vinylimidazolium bis(trifluoromethanesulfonyl)imide) (PC4-TFSI) and of polysaccharide tetra butyl ammonium carboxymethyl cellulose (TBACMC). Red: insoluble, Yellow: partially soluble, Green: soluble

Polyelectrolyte rheology

Understanding the influence of charges on the dynamics of ion-containing polymers remains a formidable challenge. Polyelectrolytes find extensive applications in solutions as flow modifiers for as stabilizers in colloidal suspensions, and structuring agents in pharmaceutical creams and food products. We study the rheology of polyelectrolyte solutions in aqueous and organic media and resolve the influence of different parameters (molar mass, backbone solvohilicity, counterion type, solvent ionic strength and dielectric constant...) on their flow behavior.

Image description
Rheology of polystyrene sulfonate solutions
Selected publications


Reinforcing gels with colloidal nano-particles

Ionic liquids are salts with melting points usually below 100oC which display good electrical conductivity, thermal stability and low vapour pressure. In recent years, they have attracted great interest due to their applications as lubricants, as solvents for cellulose, in bio-catalysis, or as electrolytes in fuel cells. The polymerisation and cross-linking of ionic liquids produces elastomeric gels with excellent conductive properties. Compared to hydrogels, which are affected by ambient moisture and degrade at moderate temperatures, cross-linked hydrophobic polyionic liquids (CL-PIL) display high durability and are stable over a broad temperature range. The composition of CL-PILs can be tuned by ion exchange reactions, which allows for fine modulation of their properties with minimal synthesis work. For example, high resistance to moisture can be achieved with hydrophobic counterions. The good permeability and selectivity for CO2/N2 gas mixtures of CL-PILs makes them useful as membranes in CO2 capture.

As with many polymeric gel systems, iongels display limited mechanical strength, which hinders their practical applications. One strategy to overcome this limitation is to reinforce polymer gels by constructing a second network, the so-called double network principle. In this context, it was recently shown that the addition of fumed silica nanoparticles (SNPs) or cellulose nanofibers (CN) can be used to improve the mechanical properties of cross-linked polyionic liquids (Watanabe et al, 2020. Soft Matter, 16(6), 1572-1581, Watanabe, et al 2023. Soft Matter, 19(15), pp.2745-2754.). The formation particle clusters lead to a substantial increase in the Young’s modulus and fracture strain of the gels without influencing their thermal stability or moisture resistance. The objective of this research theme is to understand the mechanism underpinning the network reinforcement in cross-linked PILs. Results indicate the improved mechanical properties are not the result of a ‘filler’ effect, as observed in nanoparticle-loaded polymer melts and rubbers. The surface properties of the particles, and not their volume fraction determine the degree to which mechanical properties are enhanced. We use oscillatory shear rheology and DMA to quantify the mechanical strength of the networks. Small angle neutron and x-ray scattering techniques are used to determine the aggregation state of the nanoparticles. Ionic liquids supercool easily and thus their dynamics are well-suited to be studied by time-temperature superposition rheology: varying the sample temperature between ≈ -80°C and +40°C, some 10 orders of magnitude in frequency can be obtained, extending from the rubbery plateau to the glassy region.

Selected publications

Polysaccharides in solution

Polysaccharides are a major class of biopolymers which find many uses as thickners as strucring agents in formulated products such as pharmaceutical creams, foods or drilling fluids. Our group studies their solution rheology, and their interactions with other soft matter systems such as, simple electrolytes, nano-ions and surfactants.

Interaction of polysaccharides with nano-ions

Nanonometer sized ions exhibit properties which are intermediate between those of classical ions (e.g. Na+, K+, F-) and those of charged colloids. Polyoxometalates or boron clusters exhibit so-called super-chaotropic behavior, and bind strongly to hydrated non-ionic matter in aqueous media. For polysaccharides such as hydroxypropyl cellulose, these ions bind to the backbone, turning the neutral polymers into a strongly charged polyelectrolyte. Nano-ions can also promote inter-chain crosslinking and lead to gelation. Hydrophobic nanions such as tetraphenyl borate lead to similar effects, however, the strength of ion binding to the backbone increases with temperature.

Our research seeks to understand the structure and dynamics of polysaccharides in the presence of nanoions. X-ray and neutron scattering techniques are used to quantify polymer conformation and the structure of the polymer mesh in solution. Rheology allows us to measure inter-molecular cross-linking. Dielectric spectroscopy yields information on the dynamic processes of nano-ions, which allows us to quantify ion-binding to the polymer backbone.

Selected publications
Superchaotropic Nano‐ion Binding as a Gelation Motif in Cellulose Ether Solutions

Polysaccharide Entanglement

The dynamics of polymer chains in non-dilute solutions and melts are hindered by topological constrains known as entanglements. While their the effects of entanglements are well-known, a detailed microscopic picture of what constitutes an entanglement remains elusive. In 1981, Graessley and Edwards derived a simple scaling law for the plateau modulus of a polymer solution \(G_P\), which is proportional to the entanglement density:

\[ \frac{G_Pl_K^3}{k_BT} = K (l_K^2\rho L)^\alpha \]

here \(l_K\) is the Kuhn length of the polymer, L is the contour length, \(\rho\) is the number density of chains and K is a constant that is dependent on the polymer−solvent pair. The exponent α is a free parameter in the Graessley-Edwards model, and experiments on flexible polymers show it to be in the range of ≈ 2−2.3. A different scaling regime applies for stiff polymers. The situation is less clear for polysaccharides, which display intermediate behaviour between flexible and rigid polymers. An additional complication arises from the presence of hyperentanglements, a term used to describe the combined effect of topological constraints and associative inter-chain interactions. Our group studies the flow properties of entangled polysaccharides using rheological and micro-rheological techniques. We seek to understand the correlation between the polymer's structure, polymer-solvent interactions and entanglement interactions.

Selected publications