Structure and Dynamics of Polyelectrolyte Solutions and Coacervates

The shear rate dependence of viscosity is used to evaluate the concentration dependences of specific viscosity, relaxation time and terminal modulus for several polyelectrolytes in three solvents: deionized water, ethylene glycol and glycerol. Small-angle X-ray scattering determines the correlation length of these polyelectrolyte solutions from a peak in their scattering function, which changes as expected with solvent dielectric constant. In semidilute unentangled solutions, dynamics are described by the Rouse model and combined with the correlation length in different ways to determine the number density of chains, which allows calculation of the number-average molecular weight using a robust method that is insensitive to the presence of salt.
The high viscosity glycerol solvent allows characterization of the viscoelastic response of high molecular weight polyelectrolytes over a wide range of frequency, showing Rouse character in unentangled solutions and a clear rubbery plateau in strongly entangled solutions. The linear viscoelastic response is identical to that of neutral polymer solutions, suggesting that entanglements are unaffected by the configuration of the chain inside the correlation length.
A simple way to make a polyampholyte gel is to mix oppositely charged polyelectrolytes, which precipitate to form a sediment that is termed a coacervate. Hydrophilic coacervates (with roughly 70 % water in them) are reversible gels with labile ionic interactions and their dynamics are described by a sticky Rouse model. In both examples, while not everything is understood for these complicated forms of condensed matter, polymer physics can be used to gain important insights.