Phase Separation and Gelation in Solutions and Blends of Heteroassociative 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 Heteroassociative Polymers

“…We consider a mixture of multifunctional polymers consisting of linear chains with associating groups of type i = A , B (Figure ). 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.…”

“…We assert in this analysis that v , w , and χ AB are not directly affected by the presence of cross-links and that the solvent is of equal quality for both A and B (i.e., v A = v B ≡ v and w A = w B ≡ w ). For simplicity and consistency with ref , we will set v = 0 and w = 1 to approximate Θ-solvent or nearly incompressible melt conditions. However, it should be noted that other choices for v and w are allowed in this framework and might be more suitable for compressible melts as in the Helfand description.…”

“…However, it should be noted that other choices for v and w are allowed in this framework and might be more suitable for compressible melts as in the Helfand description. Finally, the last term in eq is responsible for the enthalpy of sticker bonds and combinatorial entropy of stickers ,, F st k normalB T = prefix∫ normald 3 boldr [ ϕ A false( boldr false) s A false[ p A ( r ) + ln ( 1 − p A false( boldr false) ) false] + ϕ B false( boldr false) s B ln false( 1 − p B ( r ) false) ] where, importantly, the degrees of conversion of stickers p A ( r ) and p B ( r ) are also spatially dependent functions. The bond strength ϵ enters this sticker energy implicitly through the degrees of conversion of A and B .…”

“…Clearly, there is an immense parameter space possible in associating polymer mixtures: polymer architecture and molecular weight, solvent quality, chemical incompatibility between different species, sticker density and sequence, and binding strength of the associations. 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. − ,,− 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 . Reversible binding between heterocomplementary associating groups were found to result in branched copolymers and macroscopic percolation.…”

“…The reversible bonding of heteroassociating groups transforms the polymer blends into macroscopic copolymer networks. Gelation proceeds when the reversible network achieves percolation across the sample, with an average of two cross-links per chain . 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.…”