Constraint-Limited Tube Orientation of Entangled Polymers in Oscillatory Shear Deformation
Abstract
We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by Sxy≤ 1/2. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value NLImax=3 asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain γs, defined by NLI(γs)=3/2, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain γc for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.
Versions
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BibTeX
@misc{nichetti2026constraintlimited,
title = {{Constraint-Limited Tube Orientation of Entangled Polymers in Oscillatory Shear Deformation}},
author = {Dario Nichetti and Alessio Zaccone},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.20049},
eprint = {2606.20049},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20049},
}
RIS
TY - UNPB
TI - Constraint-Limited Tube Orientation of Entangled Polymers in Oscillatory Shear Deformation
AU - Dario Nichetti
AU - Alessio Zaccone
PY - 2026
DA - 2026/06/18
PB - arXiv
DO - 10.48550/arxiv.2606.20049
UR - https://arxiv.org/abs/2606.20049
AB - We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by S_xy≤ 1/2. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value NLI_max=3 asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain γ_s, defined by NLI(γ_s)=3/2, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain γ_c for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.
ER -