Explicit description of complexation between oppositely charged polyelectrolytes as an advantage of the random phase approximation over the scaling approach

Abstract

A polyelectrolyte complex (PEC) of oppositely charged linear chains is considered within the Random Phase Approximation (RPA). We study the salt-free case and use the continuous model assuming a homogeneous distribution of the charges throughout the polyions. The RPA correction to the PEC free energy is renormalized via subtraction of polyion self-energy in order to find the correlation free energy of the complex. An analogous procedure is usually carried out in the case of the Debye-Hückel (DH) plasma (a gas of point-like ions), where the infinite self-energy of point-like charges is subtracted from the diverging RPA correction. The only distinction is that in the PEC both the RPA correction and chain self-energy of connected like charges are convergent. This renormalization allows us to demonstrate that the correlation free energy of the PEC is negative, as could be expected, while the scaling approach postulates rather than proving the negative sign of the energy of interactions between the blobs. We also demonstrate that the increasing concentration of oppositely charged polyions in the solution first results in the formation of neutral globules of the PEC consisting of two polyions as soon as the concentration reaches a certain threshold value, c, whereas solution macroscopic phase separation (precipitation of globules) occurs at a much higher concentration, c, c ≫ c. Partitioning of polyions between different states is calculated and analytical dependencies of c and c on the polyion length, degree of ionization and solvent polarity are found.

Langevin Dynamics Simulations of the Exchange of Complex Coacervate Core Micelles: The Role of Nonelectrostatic Attraction and Polyelectrolyte Length

“…For low polyelectrolyte concentrations complex coacervation even does not occur, and instead only neutral globules are formed. 49,50 As already pointed out by Šindelka et al, 28 a stronger nonelectrostatic attraction introduces another enthalpic attraction that counteracts the entropy increase when the dimer is released. In this way, the dimer formation is diminished.…”

Modification of Polydiallyldimethylammonium Chloride with Sodium Polystyrenesulfonate Dramatically Changes the Resistance of Polymer-Based Coatings towards Wash-Off from Both Hydrophilic and Hydrophobic Surfaces

“…Water-soluble IPEC are affected by the presence of simple salts in solution. The IPEC structure should be considered as the dynamic system with areas of dense salt bonds between oppositive charged polyelectrolytes and areas with local excess to both cationic and anionic units [ 40 , 41 , 42 ]. So, the impact of the simple salts on the IPEC should be discussed from two general points of view.…”

Polyelectrolyte complex coacervation: Effects of concentration asymmetry

“…17 The VO theory is able to qualitatively capture phase behaviors of symmetric polycation and polyanion mixtures 15,16,[18][19][20][21] and is still used in recent studies. 22,23 However, since the DH correlation energy 17 is only valid for simple ionic solutions in the dilute limit, several advanced theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37] have been proposed to incorporate the effects of chain connectivity, ion-paring, and counterion release; we refer readers to two recent reviews on some of these developments. 12,13 In spite of the large number of theoretical studies, most previous publications focus on symmetric mixtures, 16,[25][26][27][30][31][32][33][34][35][36] in which polycations and polyanions are assumed to have the same chain length, flexibility, charge fraction, and concentration.…”