Gelation theory for solutions of polymers with loci of strong interaction

This paper presents a statistical mechanical analysis of gelation in certain solutions ofA/B copolymers. Repeat unitsA, the major units, must constitute about 90 mole% or more of the copolymer, and are compatible with the solvent. Repeat unitsB, the minor units, must be totally incompatible with the solvent and represent loci of strong interaction between the macromolecular chains. If these interactions are sufficiently strong they can lead to gelation of the mixture. The following simplifications of the model afford results that can be expressed in simple, closed form: (1) TheB units are uniformly distributed along the chain backbone. (2) Polymer concentration must be greater then that for chain overlap. (3)B–B interactions lead to dimerization ofB units only. Examples include: (1) Any aqueous polymer solution where theA repeat units are hydrophilic and theB repeat units are hydrophobic;B–B interactions are thus by hydrophobic bonding. (2) Neutralized acrylic acid/acrylamide copolymers where theB are acrylamide repeat units which associate by hydrogen bonds. (3) Ionomer solutions whereB–B bonding is by dipole-dipole interaction. The results show that there is a critical copolymer concentration for gel formation, C _c . It turns out that C _c decreases withB content for low dimerization energies and increases withB content for higher dimerization energies. At intermediate dimerization energies, C _c is insensitive to theB content. The two extreme regimes of behavior are similar to contradictory predictions of previously published theories. Received: 18 September 2000 / Reviewed and accepted: 20 September 2000