UV convergence of the dimensionless pressure (a) and the excess chemical potential of the polycations (b) at C ± = 0.5, B = 1.0, and C s ± = 0; at these conditions, the system exists as a homogeneous phase. The x-axis in both cases is the grid spacing divided by the parameter a. Systems both with electrostatics (E = 1000 in red) and without electrostatic interactions (E = 0 in black) are shown. The solid horizontal lines show the RPA predictions for the model while the dashed lines show the results from the CL simulations that numerically sample the fully fluctuating fields. Each property was calculated in a cubic simulation box with periodic boundary conditions and L α = 3.0R g .
Density profiles of the polymer (left axis) and the small ions (right axis) for a system with E = 20000, B = 0.05, and C ± = 1.5. a) The density profile for a case with symmetric salt (Z s ± = ±1) and C s ± = 25. The curves for the polycations and polyanions lie directly on top of each other; similarly, the profiles for the small cations and anions overlap. b) The density profiles for a system with an asymmetric salt with Z s + = 2, Z s − = −1, C s + = 10, and C s − = 20. The density profile for the small cations has been scaled so that it lies on the same y-axis as the anions.
Polymer chain concentration profiles of the polycations (ρ+) and the polyanions (ρ−) at E = 20000 and B = 0.05 for two cases where the charge arising from the two polyelectrolytes is asymmetric. (a) C + = C − = 1.5, β+ = 1.0, and β− = 0.9. (b) β+ = β− = 1.0, C + = 1.5, and C − = 1.35. In both cases, overall charge neutrality is maintained by adding C s − = 15, and Z is fixed at ±1 for both species.
(a) Polycation concentration in the coacervate phase and (b) interfacial tension as a function of the dimensionless Bjerrum length E. In (a), the circular points are the results of our CL simulations, and the solid and dashed lines are the binodal and spinodal predictions of the RPA, respectively. In (b), red circles are calculated using the pressure tensor method and the blue diamonds are calculated using Bennett's method; the solid line represents the γ ∝ (E − E cr )0.52, with E cr ≈ 1490. All calculations represented in these figures were with B = 0.05, β+ = β− = 1, Z = ±1, C s ± = 0, and the total polymer concentration was adjusted so that the coacervate phase occupied approximately half of the simulation box.
Log-log plot of the polycation concentration in the coacervate phase (a) and the interfacial tension (b) as the excluded volume parameter B is increased. In (a), the solid and dashed lines represent the binodal and spinodal coexistence curves calculated using the RPA. The estimates of γ in (b) were obtained using Bennett's method. All calculations in these figures were performed with E = 20000, β+ = β− = 1, Z = ±1, C s ± = 0, and the total polymer concentration was adjusted so that the coacervate phase occupied approximately half of the simulation box.
(a) Changes in the polycation concentration in the coacervate phase and (b) the interfacial tension as the salt concentration is increased. In (a), the solid line is simply a guide to the eye, while in (b), the solid line represents the scaling γ ∝ (C s, crit − C s )3/2 with C s, crit ≈ 110. All calculations in these figures were performed with E = 20000, B = 0.05, C = 1.5, β± = 1 and Z = ±1.
Scaling of the interfacial tension in the absence of salt with the product CE, where C is the concentration of the polyelectrolytes in the coacervate phase. The solid line represents γ ∝ (CE)1/2. These data are taken from the simulations that are summarized in Fig. 4 where B was held constant and E was systematically varied.
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