Topological constraints of network chains in telechelic associative polymer gels

We present an analysis of topological constraints of network chains, in particular entanglements, in ABA telechelic associative polymer gels generated by Brownian dynamics technique with a B selective solvent. We find two fundamental types of entanglements formed by bridge chains: first, two or more bridge chains linking different micelles impose topological constraints on each other because they cannot cross, denoted as type-I entanglement; second, two or more bridge chains linking a pair of micelles are twisted together, denoted as type-II entanglement. More complex constraints are composed of both types. There is no difference between type-I and type-II entanglements in polymer melts, but in gels, only type-I entanglement provides extra junctions that can significantly affect the modulus. The dependences of entanglement on chain length and concentration are investigated. The simulations reveal that even at low concentrations where only parts of long chains are entangled, they can provide a considerable number of junctions.