A Generalized Mechanical Model for the Cycle Rank Dependence of Stretch at Break in Phantom Chain Star Polymer Networks

Abstract

A simple mechanical model was recently proposed to explain the universality of stretch at break (λ_b) as a function of cycle-rank density (ξ) in phantom-chain network simulations [J Non-Newtonian Fluid Mech., 349, 105620 (2026)]. Here, that model is reformulated as a series of the bottleneck strand and the surrounding network, yielding λ_b-1=(λ_bs-1)[1+ν_h/(1+cξ)]. In this formula, λ_bsis the stretch at break of the bottleneck strand, ν_h is the number of stiff units in series along the rupture path, and c is a geometric constant for the parallel redundancy of the medium. Since c and ν_hare difficult to separate over the examined range of ξ, c is fixed, and λ_bs and ν_hare treated as fitting parameters. The formula is applied to phantom-chain simulations of networks with various conditions. In all cases, it reasonably captures the data, and the two parameters represent network characteristics.