Topological changes at the gel transition of a reversible polymeric network

We investigate how the network topology of an ensemble of telechelic polymers changes with temperature. The telechelic polymers serve as “links" between “nodes", which consist of aggregates of their associating end groups. Our analysis shows that the degree distribution of the system is bimodal and consists of two Poissonian distributions with different average degrees. The number of nodes in each of them as well as the distribution of links depend on temperature. By comparing the eigenvalue spectra of the simulated gel networks with those of reconstructed networks, the most likely topology at each temperature is determined. Topological changes occur at the transition temperatures reported in our previous study (Baljon A. R. C. et al., J. Chem. Phys., 126 (2007) 044907). Below the micelle transition the topology can be described by a robust bimodal network in which superpeer nodes are linked among themselves and all peer nodes are linked only to superpeers. At even lower temperatures the peers completely disappear leaving a structure of interconnected superpeers.