Dynamic Coupling in Unentangled Liquid Coacervates Formed by Oppositely Charged Polyelectrolytes

Abstract

We develop a scaling theory that predicts the dynamics of symmetric and asymmetric unentangled liquid coacervates formed by solutions of oppositely charged polyelectrolytes. Symmetric coacervates made from oppositely charged polyelectrolytes consist of polycations and polyanions with equal and opposite charge densities along their backbones. These symmetric coacervates can be described as mixtures of polyelectrolytes in the quasi-neutral regime with a single correlation length. Asymmetric coacervates are made from polycations and polyanions with unequal charge densities. The difference in charge densities results in a double semidilute structure of asymmetric coacervates with two correlation lengths, one for the high-charge-density and the other for the low-charge-density polyelectrolytes. We predict that the double semidilute structure in asymmetric coacervates results in a dynamic coupling, which increases the friction of the high-charge-density polyelectrolyte. This dynamic coupling increases the contribution to the zero-shear viscosity of the high-charge-density polyelectrolyte. The diffusion coefficient of the high-charge-density polyelectrolyte is predicted to depend on the concentration and degree of polymerization of the low-charge-density polyelectrolyte in the coacervate if the size of the low-charge-density polymer is smaller than the correlation length of the high-charge-density polymer. We also predict a non-monotonic salt concentration dependence of the zero-shear viscosity of asymmetric coacervates.

Crossover from Rouse to Reptation Dynamics in Salt-Free Polyelectrolyte Complex Coacervates

“…The natural question is whether chain dynamics within PECCs can be described by classical Rouse and reptation models. , Aponte-Rivera and Rubinstein have argued that salt-free PECCs consisting of PEs, where only a small fraction of the monomers are charged, f ≪ 1, can be treated as a melt of oppositely charged electrostatic blobs and are, therefore, similar to neutral semidilute solutions. − This view suggests that the Rouse and reptation models should be valid. , Consider salt-free symmetric PECC of flexible PEs containing N statistical segments, each of length a , in athermal solvent (Flory exponent ν = 0.588). Each polyion is represented as a chain of N / g electrostatic blobs, and each blob contains g ≃ ( l B f 2 / a ) −1/(2−ν) monomers, − where l B = e 2 /ε k B T is the solvent Bjerrum length.…”

“…The blob size, that is, the correlation length within the PECC, is written as ξ ≃ ag ν ≃ a ( l B f 2 / a ) −ν/(2−ν) . At f ≪ 1, the Coulomb attraction between PEs is weak and ion pairing is negligible, , suggesting that the use of classical (nonsticky) models of polymer dynamics is appropriate. , For short and long PEs, N / g < N e 0 and N / g > N e 0 , chain dynamics can be described by the Rouse and reptation models, , respectively. Here N e 0 is the number of monomers between adjacent entanglements in a melt, N e 0 ≈ 30–50. , The chain relaxation time τ within the PECC then scales as , where τ ξ ≃ η s ξ 3 / k B T is the Zimm relaxation time of the blob, τ 0 ≃ η s a 3 / k B T is the monomer relaxation time, and η s is the solvent viscosity.…”

“…At f ≪ 1, the Coulomb attraction between PEs is weak and ion pairing is negligible, , suggesting that the use of classical (nonsticky) models of polymer dynamics is appropriate. , For short and long PEs, N / g < N e 0 and N / g > N e 0 , chain dynamics can be described by the Rouse and reptation models, , respectively. Here N e 0 is the number of monomers between adjacent entanglements in a melt, N e 0 ≈ 30–50. , The chain relaxation time τ within the PECC then scales as , where τ ξ ≃ η s ξ 3 / k B T is the Zimm relaxation time of the blob, τ 0 ≃ η s a 3 / k B T is the monomer relaxation time, and η s is the solvent viscosity. For highly charged PEs, l B f 2 / a ≥ 1, ionic pairs are formed between oppositely charged monomers, indicating that sticky Rouse and reptation models , should be applicable. ,, In this case, τ ξ and τ 0 in eq should be modified to account for ion pairing, which slows down the local dynamics. ,, …”

DNA dynamics in complex coacervate droplets and micelles

“…These other effects have not been discussed earlier for strongly charged polyelectrolyte complexes, but in a scaling model for weakly charged complexes a more complex length dependence has already been predicted for certain cases. 44 Yet, we can also not exclude that the observed large difference between the density change and diffusion coefficient change is caused by experimental uncertainty. For example, there is a quite large variation in the donor fluorescence lifetime measured in the same complex coacervate ( Fig.…”

Rheology of Polyelectrolyte Solutions: Current Understanding and Perspectives

“…On the other hand, when two opossitely charged polyelectrolytes are mixed in a solution, coacervates can be formed to make the solution viscoelastic, and their properties are one of the hot topics in the field of the molecular rheology although not discussed in this review. [4][5][6] The unique conformation and resulting rheological properties for polyelectrolyte solutions have been recognized since † Corresponding author.…”