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A matrix method is used to determine fluctuations of junctions and points along the polymer chains making up a phantom Gaussian network that has the topology of an infinite, symmetrically grown tree. The functionalities of the junctions alternates between phi(1) and phi(2), such that one end of each network chain has functionality phi(1), while the opposite end has functionality phi(2). Quantities calculated include fluctuations of phi(1)-functional and phi(2)-functional junctions, and fluctuations of points along network chains, as well as correlations of these fluctuations. This was done for points and junctions along any path in the network, where these points and junctions were separated by no junctions or several junctions, Fluctuations have also been calculated for the distances between points and junctions. The present results represent significant generalizations of earlier work in this area [Kloczkowski et al., Macromolecules 22, 1423 (1989)]. These generalizations and extensions should be very useful in a number of contexts, such as interpreting small-angle neutron scattering results on labeled paths in polymer networks, or fluctuations of loops in the Gaussian network model of proteins.

Chain dimensions and fluctuations in elastomeric networks in which the junctions alternate regularly in their functionality