Theory of relaxation properties of two-dimensional polymer networks, 1 - Normal modes and relaxation times

The local relaxation properties of polymer networks with a two-dimensional connectivity are considered. We use the mesh-like network model in which th e average positions of junctions form the regular spatial structure consist ing of square repeating units (network cells). The two-dimensional polymer network consisting of "head and spring" Rouse chains and the simplified coa rse-grained network model describing only the large-scale collective relaxa tion of a network are studied. For both dynamic network models the set of r elaxation times and the transformation from Cartesian coordinates of networ k elements to normal modes are obtained. Using the normal mode transformati on obtained, in Part 2 of this series the exact analytical expressions for various local dynamic characteristics of the polymer network having a two-d imensional connectivity will be calculated.