Elasticity of Phantom Model Networks with Cyclic Defects

TL;DR

This paper provides an exact calculation of how finite cycles in phantom network models affect the network's modulus, revealing that cycles reduce the modulus and cause chain stretching, with implications for understanding network elasticity.

Contribution

It offers a precise analysis of the influence of cyclic defects on the phantom modulus, including the effects of both pending and nonpending cycles, and discusses chain stretching due to loop formation.

Findings

Pending cycles reduce the phantom modulus by kT/V.

Nonpending cycles have a larger correction than previously estimated.

Loop formation leads to chain stretching observable in simulations.

Abstract

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.