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This study presents a molecular tube theory explaining how long-chain branching in polymer melts creates a characteristic peak in their nonlinear oscillatory response, measured by the Nonlinearity Index (NLI). The theory demonstrates that branched polymers exhibit a competition between backbone orientation and arm retraction processes: the backbone initially behaves like a linear polymer, but delayed retraction of long arms subsequently relaxes tension at branch points and erases orientational memory. This mechanism produces a distinct NLI maximum followed by decay, with the peak's characteristics depending on branching architecture (sparse versus dense).
Why it matters
Understanding and predicting the nonlinear rheological behavior of branched polymers is crucial for industrial processing of plastics, as these materials are widely used in manufacturing applications where flow properties determine processability and final product quality. This theoretical framework enables direct prediction of material behavior from molecular structure, potentially accelerating polymer design for specific applications.
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arXiv:2607.09561v1 Announce Type: cross
Abstract: Long-chain branching profoundly modifies the nonlinear oscillatory response of entangled polymer melts by introducing arm-retraction pathways absent in linear polymers. We present a molecular tube theory that explains the characteristic maximum of the Nonlinearity Index (NLI) observed experimentally in long-chain-branched polymers. The theory extends the recently developed nonlinear tube-orientation description of linear polymers by incorporating branch-point force transmission and delayed arm retraction. The backbone initially develops nonlinear orientation as in the corresponding linear polymer, whereas long-arm retraction subsequently relaxes the stored branch-point tension and progressively erases backbone orientational memory. This competition produces a characteristic NLI maximum followed by a post-peak decay. The theory predicts two distinct nonlinear regimes corresponding to sparse and dense long-chain branching and introduces an architecture parameter governing the height and width of the nonlinear peak. The resulting framework provides a molecular interpretation of nonlinear Fourier rheology and directly links the nonlinear harmonic response to polymer architecture.