Saddle selection, onset contours, and mixed-boundary heterogeneous nucleation in strain-induced crystallisation of polymer networks

Strain-induced crystallisation in polymer networks is an onset-selection problem: scattering detectscoherent crystallites only after nucleation and early growth. This analysis shows that postgrowthWAXD dimensions should not be imposed as critical-nucleus coordinates unless an independentpre-nucleation constraint is available. For a parallelepiped nucleus with lateral surfaceenergy σ, effective end-face energy σeffe , and mechanically generated driving force ΔGm(λ, ν, T),the unconstrained saddle gives x∗ = 4σ/ΔGm, c∗ = 4σeffe /ΔGm, and ΔΦ∗ = 32σ2σeffe /ΔG2m. TheWAXD-restricted branch c = L002 is therefore a different variational problem. It suppresses theend-face sensitivity needed to test heterogeneous nucleation. The NR/IR onset gap is treated asa mixed-boundary contour shift, σeffe /σe = 1 − fcov(1 − η)/2. With fcov = 0.745 and η = 0.10,the effective end-face ratio is Re ≃ 0.665. An IR-onset-calibrated effective detection contour givesλNRc = 4.003 and an NR/IR onset gap of 0.797. A three-parameter population model fitted to NRroom-temperature data with a weak low-temperature regularisation prior gives NR RMSE 0.66% andconditional IR post-onset RMSE 0.93%. The observed onset gap is quantitatively consistent witheffective end-face reduction. Terminal groups are one physically motivated route to that reduction,not a uniquely identified microscopic origin.