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Abstract
This paper presents a statistical mechanical analysis of gelation in certain solutions of A/B copolymers. Repeat units A, the major units, must constitute about 90 mole% or more of the copolymer, and are compatible with the solvent. Repeat units B, 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) The B 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 of B units only.
Examples include: (1) Any aqueous polymer solution where the A repeat units are hydrophilic and the B repeat units are hydrophobic; B-B interactions are thus by hydrophobic bonding. (2) Neutralized acrylic acid/acryl- amide copolymers where the B are acrylamide repeat units which associate by hydrogen bonds. (3) Ionomer solutions where B-B bonding is by dipole-dipole interaction.
The results show that there is a critical copolymer concentration for gel formation, Cc. It turns out that Cc decreases with B content for low dimerization energies and increases with B content for higher dimerization energies. At intermediate dimerization energies, Cc is insensitive to the B content. The two extreme regimes of behavior are similar to contradictory predictions of previously published theories.