Correlation of data on preferential sorption using the modified flory‐huggins equation

Abstract

An equation derived from the Flory-Huggins relation with the concentration-dependent interaction parameters gij and the ternary parameter gT was used in the correlation of reported data on the preferential sorption in macromolecular coils. A linear plot was suggested, assuming that the dependence of gT on the composition of the mixed solvent resembles that of g,,, i. e. gT(ul) = ugglz(ul). Linear correlation could be carried out in 19 ternary systems out of 22, and the correlation constants were used to calculate the difference of interaction parameters g,, -(V, / V2) gz3 and the proportionality constant ug. For most systems, ug is positive and smaller than unity; for systems containing chloroform it approaches zero. The difference between the interaction parameters gij and the interaction parameters xij is discussed.A comparison between the difference g,, -(V, / V,) g,, obtained by a linear correlation of data on preferential sorption with the values calculated using data on the respective binary systems was possible only for the system benzene/cyclohexane/polystyrene; the fit was very good. It is shown how the individual parameters of the Flory-Huggins equation affect the occurrence, position and type of inversion in preferential sorption. 0025-1 16X/82/12 301 9-22/$03.O0

Thermodynamic Interpretation of the SEC Behavior of Polymers in a Polystyrene Gel Matrix

“…where v i (i = 1, 2, 3) is the volume fraction of component i in the mixture (v 1 + v 2 + v 3 = 1); g 1i (i = 2, 3) is the interaction function between a molecule of solvent 1 and a chain segment of polymer 2 or 3; g 23 is the interaction function between a segment of polymer 2 and a segment of polymer 3; and V i is the molar volume of the component i. g T is the ternary interaction function, the physical meaning of which is still unclear, but includes interac- tions that are ternary in nature [12,13,24,25] and it has been tested that its inclusion in the expression for DG is a better description of the phase separation equilibrium. [13,16] Therefore, DG depends on the interaction functions that are independent of the chain length of the polymer (molar mass) since they represent interaction energy between lattice sites.…”

“…Instead of these, the Flory-Huggins parameters, v ij , are usually reported [19] since they can be easily evaluated from the solvent activity in a binary solvent(1)-polymer(2) system (v 3 = 0). In these systems, both parameters are related by the following relationship: [27] Therefore, for the sake of comparison, Table 4 compiles v 12 values from literature, [19] the corresponding g 12 functions calculated with Equation (3) and the g 12 expressions evaluated from Table 3 by assuming that g 12 is independent of v 3 [12,28] and making v 1 = 1 -v 2 . As can be seen, the agreement between the functions evaluated in this paper and the literature ones is rather acceptable, at least in the tendency, and can be used to test the validity of the proposed procedure.…”

Association Equilibria Theory for Polymers in Mixed Solvents with Specific Interactions

“…[42] Likewise, Molineux and Vekavakayanondha, when studying interactions between PVP and diverse phenols, [35] observe a decrease in the relative amount of active sites occupied by phenols with decreasing M of the polymers. On the other hand, however, the later authors, as well as most others, [14,15,43,44] recognize the negligible influence of M on l values. It also happens in the systems studied here, as shown later.…”

“…[11][12][13] In this contribution, we focus our attention on a quantitative interpretation of sorption equilibrium in ternary polymeric systems (TPS), which has been undertaken in light of the Flory-Huggins formalism, as generalized by Pouchlý (FHP), and of Flory-Prigogine-Patterson (FPP) theory. Experimental dependences on solvent-mixture composition of preferential, l, and total, Y, sorption coefficients are smaller than those expected from FH formalism, [14,15] but the deviations could be explained by introducing ternary interaction parameters, as done in FHP formalism. Although the found relationships between ternary and the corresponding binary parameters has been ascertained both phenomenologically and semiempirically for polymer-mixed-solvent [16][17][18][19] and polymer blends in solution, [20][21][22] the physical origin of the above deviations could be explained by more advanced theories such as the FPP one.…”

Theoretical evaluation ofKp in size-exclusion chromatography from a thermodynamic viewpoint

“…In this context, a thermodynamic study of the phase equilibria of ternary polymer systems solvent(1)-polymer(2)-polymer (3) can be accomplished by means of the Flory-Huggins theory modified by Pouchly for ternary systems. [33,34] In previous work, [19,[23][24][25] the compatibility of the following blends has been studied: polystyrene(PS)/poly(vinylidene fluoride)(PVDF), PS/polyethersulfone (PES), PS/poly(methylmethacrylate)(PMMA) and PS/polybutadiene (PBD). By varying the concentration different interaction parameters have been obtained and herein the values of the parameters at infinite dilution were determined.…”