Solvation and Dissociation in Weakly Ionized Polyelectrolytes

Abstract

We present a Ginzburg-Landau theory of inhomogeneous polyelectrolytes with a polar solvent. First, we take into account the molecular (solvation) interaction among the ions, the charged monomers, the uncharged monomers, and the solvent molecules, together with the electrostatic interaction with a composition-dependent dielectric constant. Second, we treat the degree of ionization as a fluctuating variable dependent on the local electric potential. With these two ingredients included, our results are as follows. (i) We derive a mass reaction law and a general expression for the surface tension. (ii) We calculate the structure factor of the composition fluctuations as a function of various parameters of the molecular interactions, which provides a general criterion of the formation of mesophases. (iii) We numerically examine some typical examples of interfaces and mesophase structures, which strongly depend on the molecular interaction parameters.

Colloquium: Phase transitions in polymers and liquids in electric fields

“…The Poisson-Boltzmann equation is obtained from the variation in f with respect to the potential and is coupled to δf /δφ. This formalism is similar to other formulations, but the crucial difference is the bistability of the mixture energy f m (Ben-Yaakov et al, 2009;Onuki and Kitamura, 2004).…”

“…It turns out that an interfacial instability does occur in BCPs in electric field, and the nature of the instability depends on the distance from the critical point. Onuki and Fukuda (1995) studied the strongsegregation regime by writing the copolymer composition as φ(x, z) = φ 0 + ϕ L cos[(2π/d)x + u(y)], with ϕ L as an amplitude and d as the lamellar period, and expanding the energy in small u. They found an interfacial instability with two characteristics: (i) two adjacent A/B polymer interfaces are parallel to each other and (ii) the most unstable wavelength is long, corresponding to the lateral film size [ Fig.…”

“…Ions have in general different solubilities in the different liquids. As an ion drifts toward the electrode, it might "drag" with it the preferred liquid component (Onuki and Kitamura, 2004). Usually the two ionic species are preferential in the same liquid, but it is also possible that they are preferentially soluble in different liquids.…”

“…A similar expression exists for the negative ions. The system free energy density including the interaction of ions and field is given on the mean-field level by (Onuki, 2006;Onuki and Okamoto, 2009) …”

Selective Solvation in Aqueous Mixtures: Interface Deformations and Instability

“…In this paper, we discuss the selective solvation effects in the range φ > φ i sol assuming the presence of well-defined hydration shells even in the water-poor region, where the variation of μ i sol (φ) is milder but g i is still large (being of order 10 for monovalent ions) [4]. Furthermore, for polyelectrolytes and colloids, dissociation of ions can occur at their ionizable groups and the degree of dissociation sensitively depends on the local composition [7][8][9]. Therefore, the ion densities and the solvent composition are strongly coupled ubiquitously in soft matter.…”