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<p>Strain hardening of polymer melts in extensional flows is considered a desirable rheological feature because it stabilizes the homogeneity of free surface flows which is of importance, e.g., in film blowing, blow molding, and fiber spinning. Relating strain hardening to molecular characteristics, specifically topology in homopolymer melts, has been a long-standing challenge in rheology. While long-chain branching is known to be a decisive feature to enhance strain hardening, a general, quantitative relation between strain hardening and molecular topology is still missing. We propose a novel Strain Hardening Index (SHI) that can be used to assess the strain hardening behavior and to compare strain hardening of polymer melts with different topology and different chemistry, and we&#xa0;discuss its correlation with the steady-state compliance <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="397_2025_1509_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_s^0\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>J</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math></EquationSource> </InlineEquation>. We consider the strain hardening characteristics of model polystyrene comb and pom-pom systems as well as of model poly(( ±)-lactide) graft copolymers and several polydisperse low-density polyethylene melts. We show that the proposed SHI of typical low-density polyethylene melts is equivalent to that of polystyrene pom-poms and combs with specific topologies. This finding might pave the way to rheologically informed topological tailoring of the strain hardening of industrially important polymers such as, e.g., polyethylene.</p> Graphical Abstract <p></p>

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A novel generalized strain hardening index (SHI) for long-chain branched polymer melts and its correlation to the steady-state compliance

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  • 发表日期：

    2025年8月4日

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  • Manfred H. Wagner,
  • Max G. Schußmann,
  • Manfred Wilhelm,
  • Valerian Hirschberg

摘要

Strain hardening of polymer melts in extensional flows is considered a desirable rheological feature because it stabilizes the homogeneity of free surface flows which is of importance, e.g., in film blowing, blow molding, and fiber spinning. Relating strain hardening to molecular characteristics, specifically topology in homopolymer melts, has been a long-standing challenge in rheology. While long-chain branching is known to be a decisive feature to enhance strain hardening, a general, quantitative relation between strain hardening and molecular topology is still missing. We propose a novel Strain Hardening Index (SHI) that can be used to assess the strain hardening behavior and to compare strain hardening of polymer melts with different topology and different chemistry, and we discuss its correlation with the steady-state compliance \(J_s^0\) J s 0 . We consider the strain hardening characteristics of model polystyrene comb and pom-pom systems as well as of model poly(( ±)-lactide) graft copolymers and several polydisperse low-density polyethylene melts. We show that the proposed SHI of typical low-density polyethylene melts is equivalent to that of polystyrene pom-poms and combs with specific topologies. This finding might pave the way to rheologically informed topological tailoring of the strain hardening of industrially important polymers such as, e.g., polyethylene.

Graphical Abstract