Communication: Cosolvency and cononsolvency explained in terms of a Flory-Huggins type theory

Abstract

Standard Flory-Huggins (FH) theory is utilized to describe the enigmatic cosolvency and cononsolvency phenomena for systems of polymers dissolved in mixed solvents. In particular, phase boundaries (specifically upper critical solution temperature spinodals) are calculated for solutions of homopolymers B in pure solvents and in binary mixtures of small molecule liquids A and C. The miscibility (or immiscibility) patterns for the ternary systems are classified in terms of the FH binary interaction parameters { χ α β } and the ratio r = φ A /φ C of the concentrations φ A and φ C of the two solvents. The trends in miscibility are compared to those observed for blends of random copolymers (A x C 1−x ) with homopolymers (B) and to those deduced for A/B/C solutions of polymers B in liquid mixtures of small molecules A and C that associate into polymeric clustersAlthough the classic FH theory is able to explain cosolvency and cononsolvency phenomena, the theory does not include a consideration of the mutual association of the solvent molecules and the competitive association between the solvent molecules and the polymer. These interactions can be incorporated in refinements of the FH theory, and the present paper provides a foundation for such extensions for modeling the rich thermodynamics of polymers in mixed solvents. C 2015 AIP Publishing LLC.[http://dx

Solution properties of star polyelectrolytes having a moderate number of arms

“…42,43 Moreover, simulation of the competitive binding of the solvent and counter-ions to the polyelectrolyte backbone, an essential feature of these molecules, requires an explicit solvent. Competitive binding of molecular species to macromolecules is known to greatly alter the phase behavior of polymer solutions, 45,46 leading to often counter-intuitive phase behavior. Even greater complexity can be expected when associated species have long range interactions.…”

On the Schroeder paradox for nonionogenic polymers

“…It should, however, be noted that the action of mixed solvents is not purely additive even at the qualitative level. For example, the use of two thermodynamically poor solvents may, in some cases, induce swelling of macromolecules (see, e.g., [13,14]). We shall not consider such situations, but rather assume that solvent components mixed in a certain proportion act on a polymer in accordance with their thermodynamic characteristics.…”

“…The density of this force (per unit volume) may be represented as follows [18,19] (we have confined ourselves to allowance for only one term, because this work is mainly devoted to the estimation of corresponding values): (14) where the "frequencies" are the prime symbol at the sum denotes that the term comprising l = 0 is taken with a weight of 1/2, and repeated index k indicates the summation over the indices; after the implementation each of them, the following may be obtained from (13): …”

“…Moreover, expression (13) may approximately be applied to slightly nonuniform media [19], if we take the dielectric permittivity to be dependent on the spatial coordinates. In the case of highly nonuniform media, a corresponding solution must, naturally, be found for the Green function.…”

“…The contribution of the fluctuation electromagnetic field (the energy of the fluctuation electromagnetic field) to the thermodynamic characteristics is expressed via the so-called "Green function" [18] with the component (which we are interested in) of this function for a uniform medium with complex dielectric permittivity where ω is the electromagnetic-field frequency, may be presented as follows [18,19]: (13) where is the Planck constant, c is the speed of light, is the Kronecker symbol, are the vectors of spatial coordinates, and x i denotes the spatial coordinates. Moreover, expression (13) may approximately be applied to slightly nonuniform media [19], if we take the dielectric permittivity to be dependent on the spatial coordinates.…”