A Study of Temperature Dependence of Thermodynamic Interactions in Polymer Solutions of Infinite Dilution by Equation-of-State Theory

Abstract

ABSTRACT:On the basis of Flory"s equation-of-state theory, an expression is developed to characterize the thermodynamic interactions in polymer solutions of infinite dilution. It has been successfully applied to deal with the variations of Flory-Huggins interaction parameter with temperature for polystyrene and polyisobutylene in both good and poor solvents. The shortcomings of the model are discussed. The lattice model of polymeric systems originally proposed by Flory and Huggins indeed plays a major role in understanding the thermodynamic properties of polymer solutions as well as the thermodynamic miscibility of polymer and copolymer blends. 1 • 2 This classical theory adopts a binary interaction parameter, which, in the present context, is designated by the polymer-solvent interaction parameter, X, to characterize the exchange interaction energy. Traditionally, x is treated as an empirical quantity. As a result, the Flory-Huggins solution thermodynamics fails to elucidate the underlying causes of lower and upper critical solution temperatures (LCST and UCST) and volume change of mixing. However, the recent advances of equation-ofstate theroy which expresses x as a function of polymer concentration and temperature, T, explicitly, provide the theoretical basis for the foregoing phenomena. 3 -6 In this work, the x-T relationships for a number of polymer solutions are examined by the equation-of-state theory. More important, it offers an alternative route to extract the characteristic parameters of this contemporary model as described later. KEY WORDSAccording to the Flory-Huggins theory, the thermodynamic interactions in polymer solutions are given by x=µ~/RTV~ (1) where R is the gas constant, V2 andµ~ are the volume fraction and residual chemical potential respectively. Hereafter, the subscripts I and 2 respectively refer to the solvent and polymer in the mixture. By considering the importance of the free volume constribution and the exchange interaction enthalpy and entropy to the free energy of mixing, Flory has derived where M;, i\, i5;, T;, and P;* (i = 1, 2) are the molecular weight, specific volume (ml g-1 ), 321

Concentration-Dependent Thermodynamic Interaction Parameters for Polymer Solutions: Quick and Reliable Determination via Normal Gas Chromatography

“…The relation reported by Koningsveld and Kleintjens4 (KK), who evaluated critical data, deviates close to the pure polymer only. The agreement of the data of Scholte7 (Sch), which stem from equilibrium Figure 6. Dependence of the Flory-Huggins interaction parameter on ipps.…”

“…where is the ratio of the molar volumes of solute and solvent (proportional to the degree of polymerization) and the differential interaction parameter for the solvent (usually the only one experimentally accessible); is defined in terms of the partial molar residual Gibbs energy of mixing of this component as = AG^/RT = g-{l-2) dg/d<p2 (5) Since Gibbs energy and vapor pressures are interrelated by AGJRT = In QVP!0) (6) if one neglects the small corrections for the nonideality of the vapor, the Flory-Huggins interaction parameter is experimentally accessible from the ratio of pi and pi0, the vapor pressures above the solution and above the pure solvent, respectively, according to…”

Effect of the extent and morphology of phase separation on the thermal behavior of co-blending systems based on soy protein isolate/alginate

“…The first method involves the use of the tested viscosity of dilute solutions with different composition of co-blending to evaluate the solutions, the classic theory of which includes the criterion curve regarding the viscosity of diluted solution and the composition of polymer co-blending proposed by Klushreslhstha along with the m criterion proposed by Chee based on FloryeHuggins theory (Chee, 1991). The second method involves the use of the viscosity of polymer 2 in dilute solution of polymer 3 to evaluate the solutions.…”