Extending the Phantom Network Theory to Account for Cooperative Effect of Defects

Abstract

Recent developments in network theory have extended the classical phantom network theory to account for different types of defects. These theories are typically linear and adopt the ideal defect gas approximation, which is valid only in the infinite dilution limit of defects. In this study, the Virial expansion is used to determine the cooperative effects of multiple loops. It was found that in most cases, the Virial coefficients of all order vanish, and adjacent loops have no more negative impact than the individual isolated loops. Furthermore, a general nonlinear theory was developed to calculate the elasticity of phantom networks beyond the dilute limit. It was found that for a tree‐like complete network, the dispersity of network strands does not affect the elasticity of the network. However, for a tree‐like incomplete network, as conversion is lowered, a much slower decrease in the elasticity is predicted by the nonlinear theory. Finally, for loopy networks, the nonlinear theory gave predictions almost identical to that of the linear theory in small loop fraction regime. However, as loop fraction is increased, the nonlinear theory predicts a significant negative deviation from the linear theory. This behavior qualitatively matches with the behavior observed in experiments.