Coexistence Curve of a Star-Shaped Polymer Solution. Comparison with the Hybrid Theory

Abstract

In a dilute polymer solution, polymer segments are not uniformly distributed in space because they are connected with chemical bonds. Such non-uniform distribution of local polymer segment density is of essential importance to thermodynamic properties of a dilute solution, while in a concentrated solution connectivity of segments reduces its influence on thermodynamic properties and the mean-field approximation is applicable to theoretical treatment of the solution. Phase equilibrium of a binary polymer solution is a phenomenon extending over these two concentration regimes and consequently the mean-field type theory such as the Flory-Huggins theory fails in quantitative description of phase diagram of a binary polymer solution. On the other hand, theories of dilute polymer solutions such as the virial expansions deteriorate their validity with increasing polymer concentration and cannot afford to give a phase diagram. To evade this difficulty, Koningsveld et a/. 1 proposed a theory in which the Flory-Huggins theory and the dilute polymer solution theory are combined so that the Flory-Huggins free energy crosses over to the free energy given by the virial expansion as concentration is decreased. Their theory, referred as the hybrid theory, was applied to linear polymer solutions and gave a good agreement with experimental results.Recent experimental studies on phase diagrams of star-shaped polymer solutions revealed that phase diagram of a star-shaped polymer solution differs from that of the homologous linear polymer of the same molecular weight. 2 -4 Such solubility difference caused by molecular architecture cannot be explained either by the Flory-Huggins theory. However, it is expected that the hybrid theory reproduces the observed difference of phase diagrams of these polymer solutions, if the difference in free energy of dilute phase is a principal origin of the difference in phase diagram. Since explicit expressions of the second virial coefficients of starshaped polymer solutions have been given by the perturbation theories, extension of the hybrid theory to star-shaped polymer solutions is straightforward.In this note, we calculated phase diagram of a binary star-shaped polymer solution based on the hybrid theory t To whom correspondence should be addressed.

Non-ionic Thermoresponsive Polymers in Water

“…On the basis of theoretical studies it is expected that, as a rule, branched macromolecules are more soluble than their linear analogues [563][564][565]. This prediction was confirmed experimentally in the case of a solution of star-like polystyrene in cyclohexane (an UCST-type phase separation) for which an increase in the degree of branching resulted in a decrease in the temperature of demixing [566,567]. On the basis of a review of water-soluble polymers of various shapes by Aoshima and Kanaoka [30], it appears that water-soluble polymers do not offer a uniform tendency in their LCST-type phase behaviour.…”

Osmotic Second Virial Coefficient, Intrinsic Viscosity and Molecular Simulation for Star and Linear Polystyrenes

“…For star-branched polymers of given molecular weight, deviations of the theta temperature from that for a linear polymer increase as the number of arms increases and as the arm molecular weight decreases [22], [23]. This and other experimental evidence [24]- [27] suggest that branching raises solubility.…”

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

“…Saeki12 focused on the effect on the entropy of fixing the arms of the star at its core, assumed no intramolecular interactions, and predicted an increase in the critical volume fraction (ϕ c ) for the star polymer over that of the linear polymer of the same total molecular mass; he did not address the shift in the critical temperature ( T c ). Shmakov13 expanded upon earlier work14 that treated the central part of the star as separate from the outer part of the star and included an interaction parameter dependent on the concentration and molecular weight. The Shmakov treatment predicts an increase in ϕ c and a decrease in the UCST for the star polymer with respect to that of the linear polymer of the same total molecular mass.…”