Hydrogen bonding in polymer blends. 2. Theory

Thermodynamics of Polymer Blends

“…The authors start by recasting Flory-Huggins Eq. 2.35 into the form : The novelty of the Coleman-Painter theory is the calculation of the hydrogenbonding contributions in the free energy of mixing (Painter et al , 1995(Painter et al , 2000. Previous attempts to describe blends with specific interactions, including hydrogen bonds, usually employed the FH theory and allowed the w parameter to become negative.…”

“…2.58). To compute the thermodynamic contribution of the strong interactions to the overall thermodynamic behavior of a blend, one must first determine the three principal constants: K A , K B , and K 2 ; these are defined as association equilibrium constants for the formation of hydrogen bond between B and A units (of polymer 2 and 1), respectively, the formation of self-association between sequences of multiple B units, and the formation of doublets of the hydrogen-bonded B units (Coleman and Painter 1995;Painter and Coleman 2000). The K A , K B , and K 2 can be quantified experimentally, e.g., by IR spectroscopy, they are interrelated (only two of the three Ks need to be determined independently) and are constrained by stoichiometry (the total number of i-type mers is the sum of the associated and non-associated mers); the fraction of hydrogen-bonded A groups, f A HB which can be determined experimentally, can yield…”

“…where h i is the enthalpy of formation of a hydrogen bond, which can be determined from experimental data (Painter and Coleman 2000). When the pressure influence on blend miscibility is of interest, the K i functions must be evaluated within the appropriate range of pressures as well: K A (T, P), K B (T, P), and K 2 (T, P).…”

“…The experimental data confirmed the theoretical prediction, thus corroborating the validity of the model. Since then, more blends, as well as polymer solutions, have been investigated experimentally and compared favorably against the theoretical predictions (Painter et al 2000).…”

Phase behavior of TPGS–PEG400/1450 systems and their application to liquid formulation: A formulation platform approach

“…29 Furthermore, for systems with known interactions such as hydrogen bonding, a free energy term accounting for this specific interaction was introduced into the F-H theory. 30,31 In this paper, PEG 400, TPGS, and water/or ethanol were chosen for their practical utilities in pharmaceutical formulations. Because PEG 400, water, and ethanol are either small molecules or oligomers, and the contribution of the entropy of mixing to the free energy is significant, the F-H theory has been chosen to evaluate this contribution.…”