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 the average positions of junctions form the regular spatial structure consisting of square repeating units (network cells). The two‐dimensional polymer network consisting of “bead and spring” Rouse chains and the simplified coarse‐grained network model describing only the large‐scale collective relaxation of a network are studied. For both dynamic network models the set of relaxation times and the transformation from Cartesian coordinates of network elements to normal modes are obtained. Using the normal mode transformation obtained, in Part 2 of this series the exact analytical expressions for various local dynamic characteristics of the polymer network having a two‐dimensional connectivity will be calculated.