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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 [lowercase_phi_synonym]1 and [lowercase_phi_synonym]2, such that one end of each network chain has functionality [lowercase_phi_synonym]1, while the opposite end has functionality [lowercase_phi_synonym]2. Quantities calculated include fluctuations of [lowercase_phi_synonym]1-functional and [lowercase_phi_synonym]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. [ABSTRACT FROM AUTHOR]

An analytical solution to the master equation governing the conformational dynamics of linear polymer chains is formulated. Symmetric chains with N bonds subject to independent rotational potentials are considered. The eigenvalues of the transition rate matrix, which characterize the frequencies of the various relaxation modes, and the corresponding eigenvectors and eigenrows are obtained in closed form. A simple recurrence equation permits one to express the eigenvalues of the N-bond motion in terms of the nonzero eigenvalues associated with the isomeric transitions of single bonds. This leads to a clear understanding of the increase in conformational mobility with N. [ABSTRACT FROM AUTHOR]