Phase Separation and Gelation in Solutions and Blends of Hetero-Associative Polymers

Abstract

An equilibrium statistical mechanical theory for the formation of reversible networks in two-component solutions of associative polymers is presented to account for the phase behavior due to hydrogen bonding, metal–ligand, electrostatic, or other pairwise heterotypic associative interactions. We derive explicit analytical expressions for the binding statistics, gelation condition, and free energy, in which we consider polymers of types A and B with many associating groups per chain and consider only A–B association between the groups. The free energy is approximated at the mean-field level, considering overlapping polymer chains with an ideal gas of "stickers" capable of intermolecular association. It is shown that the number of associations is maximized at stoichiometric conditions between A and B associative groups. Accordingly, homogeneous networks are most easily formed near stoichiometric conditions between A and B associative groups, resulting in a re-entrant sol–gel–sol transition as the overall composition is altered. Association and reversible network formation are found to be accompanied by a tendency for phase separation. These results demonstrate that reversibly associating polymers have a large parameter space in terms of molecular design, binding energy, and mixture compositions. Our predictions are expected to be useful in the rational design of interacting polymer mixtures and the formation of reversible networks.

Chemical Compatibilization, Macro-, and Microphase Separation of Hetero-Associative Polymers

“…We consider a mixture of multifunctional polymers consisting of linear chains with associating groups of type i = A, B (Figure 1). 47 The polymers have N i segments of size a and have ideal chain statistics described by the continuous Gaussian chain model. Each chain contains f i stickers separated by spacers with s i = N i /(f i − 1) segments.…”

“…Finally, the last term in eq. 2 is responsible for the enthalpy of sticker bonds and combinatorial entropy of stickers, 47,56,57…”

“…The vast potential of the property space and the complexity of the design space motivate a theoretical foundation for robust design principles that link the thermodynamics, gelation, and resulting properties of these materials. [29][30][31]35,[43][44][45][46][47][48][49][50][51][52][53][54][55] In a companion work, we developed a mean-field theory for the thermodynamics and gelation of two-component solutions of heterotypic or A − B-type associative polymers. 47 Reversible binding between hetero-complementary associating groups were found to result in branched copolymers and macroscopic percolation.…”

“…[29][30][31]35,[43][44][45][46][47][48][49][50][51][52][53][54][55] In a companion work, we developed a mean-field theory for the thermodynamics and gelation of two-component solutions of heterotypic or A − B-type associative polymers. 47 Reversible binding between hetero-complementary associating groups were found to result in branched copolymers and macroscopic percolation. Homogeneous networks are most easily stabilized near stoichiometric sticker conditions, enabling sol-gel-sol transitions as the overall composition of the mixture is altered.…”

“…Gelation proceeds when the reversible network achieves percolation across the sample, with an average of two cross-links per chain. 47 By extension of an equilibrium mean-field theory to account for spatial concentration fluctuations, we can furthermore describe the competition between chemical incompatibility and reversible binding that leads to macro-and microphase separation. The described polymer alloys have the advantage of thermal tuning of connectivity and segregation strength, leading to controllable phase behavior and network formation, with implications for biological condensates and polymer reprocessing.…”