Elasticity of Phantom Model Networks with Cyclic Defects

The
impact of finite cycles on the phantom modulus in an otherwise
perfect network is computed exactly. It is shown that pending cycles
reduce the phantom modulus of the network by kT/V independent of junction functionality. The correction
for nonpending cycles is larger than estimated previously within this
particular approximation of the surrounding network structure. It
is discussed that loop formation inevitably leads to streched chain
conformations, if the loops are built step by step as part of the
network structure. All network loops tend to contract simultaneously
to optimize conformations, which leads to an increasing stretch of
chains in larger loops that can be observed in computer simulations.
Possible other corrections to the phantom modulus that were left aside
in previous work are discussed briefly.