Driving force and pathway in polyelectrolyte complex coacervation

Abstract

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation–polyanion complexation and polyion pair–pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Structure and Dynamics of Hybrid Colloid–Polyelectrolyte Coacervates

“…Generally speaking, they are unequal, which can be demonstrated using a more refined analysis. The result similar to eq has been recently reported for the spinodal concentration in the case of conventional PE–PE complex coacervation, which is also preceded by the formation of finite-size neutral pairs (globules). − …”

“…Generally speaking, they are unequal, which can be demonstrated using a more refined analysis. The result similar to eq has been recently reported for the spinodal concentration in the case of conventional PE–PE complex coacervation, which is also preceded by the formation of finite-size neutral pairs (globules). − Similar reasoning applied to regimes II and III yields B n p I I ≃ R 3 ( 1 − ξ e R e R / ξ e ) ≃ prefix− ξ e R 2 normale R / ξ e B n p I I I ≃ R 3 ( 1 − H I I I R e false( Q / q q false) 4 / 3 false( ξ e / R false) 5 / 3 ) ≃ prefix− H I I I R 2…”

“…The threshold concentration for complex coacervation can be estimated from c ≃ c pair and corresponds to the situation when half of the colloids/PEs are involved in neutral pairs and half of them form the macroscopic coacervate phase: The scaling diagram of states shown in Figure is in accordance with the results for c ads and c coac . Similar to stoichiometric solutions of symmetric oppositely charged PEs, − the formation of electroneutral colloid–PE pairs takes place at much lower concentrations than macroscopic coacervation: c coac ≫ c ads in all scaling regimes. This is due to the different strengths of the driving forces behind these processes.…”

Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications

“…62,63 Complex coacervation was also studied theoretically. 64,65 The first model that was able to phenomenologically capture the phase behavior of complex coacervates is the Voorn-Overbeek theory. 66,67 Essentially, the Voorn-Overbeek theory describes the mixing free energy of the system as a combination of the translational entropy within the Flory-Huggins theory framework, and the electrostatic attraction using the Debye-Hu ¨ckel theory.…”

Applicability of the Generalized Stokes–Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions

“…For example, Muthukumar has recently discussed this type of charge-based mode-coupling effect in polyelectrolyte solutions where additional relaxation modes were predicted and observed experimentally. , It is currently not clear whether these charge fluctuation effects are generally suppressed by neutralization accompanying polymer complexation in our case, which gives added interest for the present observations. The formation of soluble ion pairs via interpolyelectrolyte neutralization in dilute solution was observed by isothermal titration calorimetry − and in the dilute phase after phase separation with vanishingly small free polyelectrolytes by simulation . Moreover, additional relaxation processes are conceivable from the presence of ion–dipole, dipole–dipole, and multipole interactions that can arise when oppositely charged chain segments form complexes. , The DLS study by Kostko et al found that the viscoelasticity of high molecular mass polymer solutions led to observed deviations from the KF theory in near-critical solutions of this kind.…”