Reversible ion binding for polyelectrolytes with adaptive conformations

Abstract

Polyelectrolytes may adopt rod-or coil-like conformations depending on the strength of intrachain repulsion and the effective charge density. The charge density of polyelectrolytes is influenced not only by the binding of small ions, but also by the binding with oppositely charged chains. We introduce a coupled variational approach that treats reversible ion binding, adaptive chain structure, and electrostatic correlations simultaneously. This approach captures the swelling and deswelling of single polyelectrolyte chains, and the competition between interchain cross-linking and ion binding in mixtures of polyelectrolytes. Applying our theory to study polyelectrolyte coacervation, we identify two distinct regimes. In the weak binding regime, the charge density is high and the solution properties are dependent on the conformations of polyelectrolytes. In the strong binding regime, this dependence is weakened and the solution thermodynamics are dominated by the short-range ion-binding equilibrium.

Driving force and pathway in polyelectrolyte complex coacervation

“…This electrostatically induced LLPS underpins a number of important biological phenomena such as membraneless organelles in cells ( 3 – 6 ) and ocean life adhesion ( 7 – 11 ) and is also being exploited in novel biomedical and biomimetic applications such as drug delivery ( 12 – 14 ) and underwater adhesion ( 10 , 15 – 19 ). In the 6 decades since the pioneering theoretical work by Overbeek and Voorn ( 20 ), significant progress has been made on both the theory/simulation and experiment fronts in understanding the many effects on this LLPS, such as chain connectivity ( 21 – 30 ), excluded volume ( 22 , 25 , 31 – 35 ), charge sequence ( 36 – 40 ), ion pairing ( 22 , 41 , 42 ), charge asymmetry ( 43 – 47 ), temperature ( 48 – 53 ), pH ( 54 – 57 ), and solvent quality ( 58 – 60 ). We refer readers to several excellent recent reviews ( 61 – 65 ).…”

Bridging Field Theory and Ion Pairing in the Modeling of Polyelectrolytes and Complex Coacervation

“…Larson, Qin, and co-workers modified the RPA model of polyelectrolyte coacervation by accounting for effective chemical reactions between the charged species ,,− ,, that form ion pairs between polycation/polyanion monomers, cation/polyanion monomers, and anion/polycation monomers. While all pair combinations are typically explicitly included, ,, we start with the simpler case that does not include polycation/polyanion pairs β f normalL normalQ ν 0 = φ P + N P + ln nobreak0em.25em⁡ φ P + + φ P − N P − ln nobreak0em.25em⁡ φ P − + φ + ′ ln nobreak0em.25em⁡ φ + ′ + φ − ′ ln nobreak0em.25em⁡ φ − ′ + φ normalW ln nobreak0em.25em⁡ φ normalW + prefix+ φ normalP + [ ζ + ln ⁡ ζ + + false( 1 −...…”

Bridging Field Theory and Ion Pairing in the Theory of Polymer Complex Coacervation

“…Larson, Qin, and co-workers modified the RPA model of polyelectrolyte coacervation by accounting for effective chemical reactions between the charged species, 36,39,[99][100][101]109,127 that form ion pairs between polycation/polyanion monomers, cation/polyanion monomers, and anion/polycation monomers:…”

“…is the version from Olvera de la Cruz 76 that modifies the interaction potential to account for the finite size of the ion (related to the length scale b). Similarly, we can choose what we consider for g D (k), and for this work we choose an approximate form for the wormlike chain that interpolates between the rigid rod and random walk limits: 127,133,134…”

“…[99][100][101]109 This version of the model neglects polyanion-polycation pairing, which is a straightforward extension of this model that the authors used in some of their papers. 127 This approach was originally developed to account for chemical bonding between the polyelectrolytes and their counterions, such that the free energy of binding ∆G P ±,∓ is interpreted as a free energy of reaction and careful accounting of the number of counterions is included in the mixing entropy terms. 100 However, this model could alternatively be interpreted as reflecting concepts such as ion pairing and counterion condensation that are expected to emerge for polymers with high linear charge density, 112,128,129 and are challenging to include explicitly in polymer field theory calculations.…”