Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts
The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination...
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MDPI AG
2024
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| Online Access: | https://hdl.handle.net/1721.1/155798 |
| _version_ | 1824458323970228224 |
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| author | Ibar, Jean Pierre |
| author_facet | Ibar, Jean Pierre |
| author_sort | Ibar, Jean Pierre |
| collection | MIT |
| description | The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination of Mc by the break in the log viscosity curve against log M unequivocally differentiates un-entangled melts from entangled melts. We use reliable rheological data on monodispersed polystyrene samples from very low molecular weight (M/Mc = 0.015) to relatively high molecular weight (M/Mc = 34) to test the separation of M and T in the expression of the viscosity; we reveal that an overall illusion of the validity of the separation of T and M is mathematically comprehensible, especially at high temperature and for M > 2Mc, but that, strictly speaking, the separation of M and T is not valid, except for certain periodic values of M equal to Mc, 2Mc, 4Mc, 8Mc, 16Mc, etc. (period doubling) organized around a “pole reference” value MR = 4Mc. We also reveal, for M < Mc, the existence of a lower molecular weight limit, M’c = Mc/8 for the onset of the macromolecular behavior (macro-coil). The discrete and periodic values of M that validate the separation of the effect of M and T on the viscosity generate the fragmentation of the molecular range into three rheological ranges. Likewise, we show that the effect of temperature is also fragmented into three rheological ranges for T > Tg: Tg < T< (Tg + 23°), (Tg + 23°) < T < TLL and T > TLL’ where TLL is the liquid-liquid temperature. Our conclusion is that the classical formulation of the viscosity of polymer melts is so overly simplified that it is missing important experimental facts, such as period doubling for the separation of T and M, TLL, M’c, and Mc, resulting in its inability to understand the true nature of entanglements. We present in the discussion of the paper the alternative approach to the viscoelastic behavior, “the duality and cross-duality” of the Dual-conformers, showing how this model formalism was used to test mathematically and invalidate the separation of T and M in the classical formulation of viscosity. |
| first_indexed | 2024-09-23T14:54:07Z |
| format | Article |
| id | mit-1721.1/155798 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2025-02-19T04:24:04Z |
| publishDate | 2024 |
| publisher | MDPI AG |
| record_format | dspace |
| spelling | mit-1721.1/1557982025-01-08T04:27:46Z Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts Ibar, Jean Pierre The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination of Mc by the break in the log viscosity curve against log M unequivocally differentiates un-entangled melts from entangled melts. We use reliable rheological data on monodispersed polystyrene samples from very low molecular weight (M/Mc = 0.015) to relatively high molecular weight (M/Mc = 34) to test the separation of M and T in the expression of the viscosity; we reveal that an overall illusion of the validity of the separation of T and M is mathematically comprehensible, especially at high temperature and for M > 2Mc, but that, strictly speaking, the separation of M and T is not valid, except for certain periodic values of M equal to Mc, 2Mc, 4Mc, 8Mc, 16Mc, etc. (period doubling) organized around a “pole reference” value MR = 4Mc. We also reveal, for M < Mc, the existence of a lower molecular weight limit, M’c = Mc/8 for the onset of the macromolecular behavior (macro-coil). The discrete and periodic values of M that validate the separation of the effect of M and T on the viscosity generate the fragmentation of the molecular range into three rheological ranges. Likewise, we show that the effect of temperature is also fragmented into three rheological ranges for T > Tg: Tg < T< (Tg + 23°), (Tg + 23°) < T < TLL and T > TLL’ where TLL is the liquid-liquid temperature. Our conclusion is that the classical formulation of the viscosity of polymer melts is so overly simplified that it is missing important experimental facts, such as period doubling for the separation of T and M, TLL, M’c, and Mc, resulting in its inability to understand the true nature of entanglements. We present in the discussion of the paper the alternative approach to the viscoelastic behavior, “the duality and cross-duality” of the Dual-conformers, showing how this model formalism was used to test mathematically and invalidate the separation of T and M in the classical formulation of viscosity. 2024-07-26T18:46:33Z 2024-07-26T18:46:33Z 2024-07-17 2024-07-26T12:29:21Z Article http://purl.org/eprint/type/JournalArticle 2073-4360 https://hdl.handle.net/1721.1/155798 Ibar, J.P. Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts. Polymers 2024, 16, 2042. PUBLISHER_CC 10.3390/polym16142042 Polymers Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf MDPI AG Multidisciplinary Digital Publishing Institute |
| spellingShingle | Ibar, Jean Pierre Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title | Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title_full | Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title_fullStr | Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title_full_unstemmed | Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title_short | Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts |
| title_sort | raising two more fundamental questions regarding the classical views on the rheology of polymer melts |
| url | https://hdl.handle.net/1721.1/155798 |
| work_keys_str_mv | AT ibarjeanpierre raisingtwomorefundamentalquestionsregardingtheclassicalviewsontherheologyofpolymermelts |