Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution
The transient elongational viscosity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">η</mi><mi mathvariant="normal">e</mi&g...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-04-01
|
| Series: | Polymers |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-4360/15/9/2067 |
| _version_ | 1797601867091410944 |
|---|---|
| author | Ming-Chang Hsieh Yu-Hao Tsao Yu-Jane Sheng Heng-Kwong Tsao |
| author_facet | Ming-Chang Hsieh Yu-Hao Tsao Yu-Jane Sheng Heng-Kwong Tsao |
| author_sort | Ming-Chang Hsieh |
| collection | DOAJ |
| description | The transient elongational viscosity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">η</mi><mi mathvariant="normal">e</mi></msub><mrow><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the polymer melt is known to exhibit strain hardening, which depends on the strain rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="sans-serif">ε</mi><mo>˙</mo></mover></mrow></semantics></math></inline-formula>. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions <i>P</i>(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">R</mi><mi mathvariant="normal">g</mi></msub><mrow><mo>,</mo><mi mathvariant="normal">t</mi></mrow></mrow></semantics></math></inline-formula>) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="normal">R</mi><mo>¯</mo></mover></mrow><mi mathvariant="normal">g</mi></msub><mrow><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and standard deviation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="sans-serif">σ</mi><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="normal">R</mi><mo>¯</mo></mover></mrow><mi mathvariant="normal">g</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">σ</mi></semantics></math></inline-formula> rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="sans-serif">ε</mi><mo>˙</mo></mover></mrow><mi mathvariant="normal">H</mi></msub><mi mathvariant="normal">t</mi></mrow></semantics></math></inline-formula>) and chain length (N). |
| first_indexed | 2024-03-11T04:09:38Z |
| format | Article |
| id | doaj.art-f63c55716a1e44fe891e30218a51dd06 |
| institution | Directory Open Access Journal |
| issn | 2073-4360 |
| language | English |
| last_indexed | 2024-03-11T04:09:38Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Polymers |
| spelling | doaj.art-f63c55716a1e44fe891e30218a51dd062023-11-17T23:34:47ZengMDPI AGPolymers2073-43602023-04-01159206710.3390/polym15092067Microstructural Dynamics of Polymer Melts during Stretching: Radial Size DistributionMing-Chang Hsieh0Yu-Hao Tsao1Yu-Jane Sheng2Heng-Kwong Tsao3Department of Chemical Engineering, National Taiwan University, Taipei 106, TaiwanDepartment of Chemical Engineering, National Taiwan University, Taipei 106, TaiwanDepartment of Chemical Engineering, National Taiwan University, Taipei 106, TaiwanDepartment of Chemical and Materials Engineering, National Central University, Jhongli 320, TaiwanThe transient elongational viscosity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="sans-serif">η</mi><mi mathvariant="normal">e</mi></msub><mrow><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the polymer melt is known to exhibit strain hardening, which depends on the strain rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="sans-serif">ε</mi><mo>˙</mo></mover></mrow></semantics></math></inline-formula>. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions <i>P</i>(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">R</mi><mi mathvariant="normal">g</mi></msub><mrow><mo>,</mo><mi mathvariant="normal">t</mi></mrow></mrow></semantics></math></inline-formula>) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="normal">R</mi><mo>¯</mo></mover></mrow><mi mathvariant="normal">g</mi></msub><mrow><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and standard deviation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="sans-serif">σ</mi><mo>(</mo><mi mathvariant="normal">t</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="normal">R</mi><mo>¯</mo></mover></mrow><mi mathvariant="normal">g</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">σ</mi></semantics></math></inline-formula> rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover><mi mathvariant="sans-serif">ε</mi><mo>˙</mo></mover></mrow><mi mathvariant="normal">H</mi></msub><mi mathvariant="normal">t</mi></mrow></semantics></math></inline-formula>) and chain length (N).https://www.mdpi.com/2073-4360/15/9/2067microstructural dynamicselongational viscositystrain hardeningradial size distributiondissipative particle dynamics |
| spellingShingle | Ming-Chang Hsieh Yu-Hao Tsao Yu-Jane Sheng Heng-Kwong Tsao Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution Polymers microstructural dynamics elongational viscosity strain hardening radial size distribution dissipative particle dynamics |
| title | Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution |
| title_full | Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution |
| title_fullStr | Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution |
| title_full_unstemmed | Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution |
| title_short | Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution |
| title_sort | microstructural dynamics of polymer melts during stretching radial size distribution |
| topic | microstructural dynamics elongational viscosity strain hardening radial size distribution dissipative particle dynamics |
| url | https://www.mdpi.com/2073-4360/15/9/2067 |
| work_keys_str_mv | AT mingchanghsieh microstructuraldynamicsofpolymermeltsduringstretchingradialsizedistribution AT yuhaotsao microstructuraldynamicsofpolymermeltsduringstretchingradialsizedistribution AT yujanesheng microstructuraldynamicsofpolymermeltsduringstretchingradialsizedistribution AT hengkwongtsao microstructuraldynamicsofpolymermeltsduringstretchingradialsizedistribution |