UNIFAC-FV Applied to Dendritic Macromolecules in Solution: Comment on “Vapor−Liquid Equilibria for Dendritic-Polymer Solutions” (Lieu, J. G.; Liu, M.; Fréchet, J. M. J.; Prausnitz, J. M. J. Chem. Eng. Data 1999, 44, 613−620)

Abstract

Dendrimers have been proposed as rheology modifiers for use as processing aids,1 as well as for other more specialized applications where predicting solubility in both small molecule solvents and polymer melts will be essential for tailoring the dendritic molecules for specific uses. The large number of end groups, core-shell structure, and constrained molecular conformations due to the high degree of branching make thermodynamic modeling of these macromolecules challenging. In a recent article, Lieu et al.2 report solvent activity coefficients measured in vapor-liquid equilibria experiments on dendritic polymer solutions. They further demonstrate that some but not all of their data can be correlated by a modified version of the Flory-Huggins lattice theory. The use of a model derived for linear polymer chains in semidilute solution to describe the more globular structure of dendrimers in solution is questionable, however, given the wealth of recent X-ray and small angle neutron scattering measurements as well as simulations3 of dendrimer structures in solution.4-10 Similarly, solution rheological properties strongly suggest a globular, unentangled structure for most dendrimers in solution and in the melt.9-13 Given this recent wealth of structural data, we propose that the solvent activity of dendrimer solutions may be predicted by group-contribution methods that have been modified to account for the free volume contributions of the molecular architecture. The free-volume modification14 of the UNIFAC15 model (UNIFAC-FV) is a predictive group-contribution method that accounts for the free volume of mixing of a structured macromolecule with a small molecule solvent. Flory’s polymer equation of state16 provides a correction for the effects of polymer architecture (as characterized by the molecular free volume) on raising the free energy of the solution. This correction involves a “reduced volume” (ratio of specific volume to the hard-core specific volume) for the solvent and the mixture (which is presumed to be additive). In calculating this reduced volume, an empirical dimensionless parameter (b) is introduced as an adjustable fit parameter. Oishi and Prausnitz14 successfully correlated VLE data for solutions of linear chains with the UNIFACFV theory with a single parameter value of b ) 1.28. As this parameter reflects the determination of the hard-core specific volume of the molecules, we might anticipate that it will be affected by a high degree of branching in the macromolecule, as this would be expected to affect the ability of the solvent to penetrate into the dendrimers. Further, this would be expected to manifest itself as an increasing value of the excluded hard-core volume as the solvent’s molecular size is increased for a fixed macro* Corresponding author. Figure 1. (a) Acetone activity in solution with the A4 dendrimer at 50 °C.2 (b) Chloroform activity in solution with the B4 dendrimer at 70 °C.2 376 J. Chem. Eng. Data 2002, 47, 376-377