Linear Viscoelasticity of Polyelectrolyte Complex Coacervates

Abstract

Two flexible, oppositely charged polymers can form liquid-like complex coacervate phases with rich but poorly understood viscoelastic properties. They serve as an experimental model system for many biological and man-made materials made from oppositely charged macromolecules. We use rheology to systematically study the viscoelastic properties as a function of salt concentration, chain length, chain length matching, and mixing stoichiometry of model complex coacervates of poly(N,N-dimethylaminoethyl methacrylate), PDMAEMA, and poly(acrylic acid), PAA. The dynamics of making and breaking ionic bonds between the oppositely charged chains underlie all linear viscoelastic properties of the complex coacervates. We treat (clusters of) ionic bonds as sticky points and find that there is a remarkable resemblance between the relaxation spectra of these complex coacervates and the classical sticky Rouse model for single polymer systems. Salt affects all relaxation processes in the same way, giving rise to a widely applicable time–salt superposition principle. The viscoelastic properties of the complexes are very different from those of the individual components. In the complexes with a chain length mismatch, the effect of the mismatch on the viscoelastic properties is not trivial: changing the length of the polycation affects the relaxation behavior differently from changing the length of the polyanion.

Linear viscoelasticity of complex coacervates

“…Rheological characterization demonstrated that these trends correlate with decreasing coacervate viscosity with increasing salt concentration ( Figure 5a) [71,79,157]. Furthermore, the viscosity was seen to increase as a function of degree of polymerization ( Figure 5b) [79], as would be expected for polymeric materials. Inspection of the data in Figure 5 suggests that viscosity varies exponentially with salt concentration, and follows a power-law behavior as a function of polymer chain length.…”

“…In general, the trends observed in frequency sweep data parallel those for viscosity, due to the relationship between dynamic viscosity and modulus. In general, increasing salt concentration leads to a decrease in both the storage and loss modulus (Figure 7a) [71,75,79]. Similarly, changes in pH that weaken the electrostatic interactions between polymer chains also decrease the moduli (Figure 7b) [75].…”

“…Inspection of the data in Figure 5 suggests that viscosity varies exponentially with salt concentration, and follows a power-law behavior as a function of polymer chain length. Interestingly, no change in viscosity was observed as a function of PDMAEMA/PAA stoichiometry, suggesting that the coacervate may undergo disproportionation to maintain a charge-neutral ratio of the two polymers [79].…”

“…Spruijt et al proposed a model for these rheological observations based on "sticky" Rouse (or Zimm) polymer dynamics, where ionic bonds between polyelectrolyte chains act as "sticky" points that enhance the effective friction of polymer chains and decrease their mobility, thus slowing down stress relaxation [79,111]. This model provides a platform for developing and testing our understanding of molecular-level interactions within the material, and reasonable agreement was obtained between the model and the data.…”

“…In numerous examples, the elastic behavior dominates (i.e., the storage modulus (G') dominates) [8,61,137,138,171,175,[177][178][179][180], while in other coacervates the viscous or liquid-like behavior (i.e., the loss modulus (G") dominates) [95,103,171]. Meanwhile, there are other systems where a crossover is observed between the two regimes, with G" dominating at low frequencies, and G' dominating at higher frequencies [61,71,72,79,111,130,162,171]. Considering these observations in the context of the expected characteristic responses for polymeric materials suggests that the differences in the observed material properties are the result of experimental limitations and thermodynamic factors that limit experimental access to the full range of frequency behavior, rather than an inherent characteristic of the material itself.…”