Complex Coacervation in Polyelectrolytes from a Coarse-Grained Model

Abstract

Complex coacervation refers to the formation of distinct liquid phases that arise when polyelectrolytes are mixed under appropriate polymer and salt concentrations. Molecular-level studies of coacervation have been limited. In this work, a coarse-grained model of the polymers and the corresponding counterions is proposed and used to simulate coacervation as a function of polymer length and overall salt concentration. Several sampling methods are used to determine the phase behavior of the underlying polymers. In particular, the results of simulations in different ensembles are shown to be consistent and to reproduce a number of phenomena observed in experiments, including the disruption of complexation by increasing ionic strength or by decreasing molecular weight. The coacervate concentrations determined from phase behavior calculations are then used to examine the rheology of the corresponding materials. By relying on long dynamic simulations, we are able to generate the dynamic response of the material in the form of dynamic moduli as a function of frequency, which are also found to compare favorably with experimental measurements.

Figure 1.

Modification of Coulomb force and comparison to inclusion of pairwise forces. “Soft Coulomb & Repulsion” are set to capture the interplay of long-range Coulomb and short-range LJ interactions “Coulomb+LJ”. The attractive Coulomb force is shown.

Figure 2.

Prediction of composition of the supernatant and the coacervate and comparison with experimental data by Spruijt et al. Here c_AA is monomer concentration of polyanion (poly(acrylic acid)), and c_salt is concentration of added salt ions. Filled color symbols are coacervate predictions of the model, filled black symbols correspond to experimental data for coacervate, and empty color symbols are supernatant predictions of the model; experimental data for supernatant is not shown. For all predictions of supernatant the polyelectrolyte concentration is 0. Predictions are obtained with Gibbs ensemble calculations. Dashed lines show corresponding supernatant and coacervate phases. See Spruijit et al. for a discussion of the determination of the uncertainty in the measurements.

Figure 3.

Prediction by the Voorn–Overbeek model and comparison with experimental data as presented by Spruijt et al. Model parameters: α = 0.9, σ = 0.95; N_p is equal to the number of monomers.

Figure 4.

Soft-core model prediction for polymer center-of-mass mean-square displacement. Also shown is the mean-square displacement for the neutral polymer at the same concentration as coacervate. Insets highlight the small effect of salt concentration on MSD.

Figure 5.

Prediction for dynamic modulus superimposed on experimental data. Filled symbols show the G′ elastic component of the modulus, and empty symbols show the G′ viscous component of the modulus. Predictions are scaled by 500 kPa vertically and by {0.0006 s, 0.012 s, and 0.12 s} for N₂₀, N₅₀, and N₁₄₀ horizontally. Also shown is the dynamic modulus of the neutral N50 polymer at the same concentration as coacervate.