Elastic Activity of Imperfect Networks

The number of elastically effective chains in an elastomeric network is veff = 2ξ, where ξ is the number of independent circuits, or the cycle rank of the network. This universal measure of network connectivity applies regardless of the functionalities of the junctions, of their statistical distribution, and of the distribution of free ends of chains in an imperfect network. It is unambiguously related according to ξ = va − μa to the number μa of “active” junctions arbitrarily identified as those joined by three or more paths to the network and the number va of active chains attached at both ends to active junctions. The number va of active chains thus defined is not, however, a proper substitute for veff. © 1982, American Chemical Society. All rights reserved.