Correlated fluctuations in polymer networks

Polymer micronetworks with Cayley tree and random topologies are compared. The fluctuations of junctions in random networks exhibit significant departures from the mean value corresponding to those in Cayley tree topology. Correlations among the fluctuations are examined for the two types of networks. Correlations are stronger, and cover longer distances along the chain contours in random networks, compared to those observed in Cayley trees. This is a consequence of the non-uniform spatial distribution of connected vertices in a random network, as opposed to Cayley trees in which chains extend between junctions located in successive tiers only. The relaxation spectra of the two types of networks are compared. The cumulative distribution of frequencies obeys a power law dependence on frequency, with exponents of 1.4 and 1.1 for trifunctional Cayley tree and random networks, respectively. These exponents are significantly smaller than the Debye value of 3 for regular three dimensional crystals.