Gradient energy parameters for polymer–polymer–solvent systems and their application to spinodal decomposition in true ternary systems

Abstract

SynopsisThe entropic gradient contributions to the free energy of nonuniform polymer-solvent systems and polymer-polymer-solvent systems have been obtained using a mean field approach. The results for a polymer-polymer-solvent system reduce to those of de Gennes for a polymer-polymer system a t the appropriate limit. The binary results for a polymer-solvent system predict interfacial tensions that are systematically high but closer to experiment than those predicted by the earlier model of Balsara and Nauman. The ternary results have been applied to spinodal decomposition in polymerpolymer-solvent systems. The linear theory predicts a decrease in the domain size with increasing quench depth. Also, it predicts an increasing domain size with an increase in compatibility between the two polymers for any given quench depth.Hence the free energy of a nonuniform system consisting of M components may be written in a more general form as',

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

“…Equations (4)- (6) ignore the entropic contribution 28 to the gradient energy parameters 11 since simulations in a binary polymer solution where this assumption has been employed yielded results in very good agreement with experimental observations. 21 The ternary mobilities, M ij , are given in terms of the binary friction coefficients, ij , by 29,25 M 11…”

Phase Separation of Partially Miscible Solvent Systems: Flow Phenomena and Heat and Mass Transfer Applications

“…( 3.30) Other models for the parameter a, which considers also the relative sizes of the components (e.g., in polymer solutions) were suggested in the literature (see Debye, 1959;deGennes, 1971;McMaster, 1975;Enders andQuitzsch, 1998 anddiscussions in Ariyapadi andNauman, 1990;Kotnis and Muthukumar, 1992).…”

Continuum modelling of structure formation of biosilica patterns in diatoms

“…where φ( r) is the volume fraction of the phase separating component and g(φ) is the Gibbs energy density of mixing. The gradient energy coefficient κ will be assumed to be constant [27]. Together with the constraint…”