doi:10.11777/j.issn1000-3304.2020.20230

引用本文: 刘双, 曹晓, 张嘉琪, 韩迎春, 赵欣悦, 陈全. 流变技术在高分子表征中的应用：如何正确地进行剪切流变测试[J]. 高分子学报, 2021, 52(4): 406-422. doi: 10.11777/j.issn1000-3304.2020.20230 shu

Citation: Shuang Liu, Xiao Cao, Jia-qi Zhang, Ying-chun Han, Xin-yue Zhao and Quan Chen. Toward Correct Measurements of Shear Rheometry[J]. Acta Polymerica Sinica, 2021, 52(4): 406-422. doi: 10.11777/j.issn1000-3304.2020.20230 shu

流变技术在高分子表征中的应用：如何正确地进行剪切流变测试

1.
中国科学院长春应用化学研究所高分子物理与化学国家重点实验室　长春 130022
2.
中国科学技术大学应用化学与工程学院　合肥 230026

作者简介: 陈全，男，1981年生. 中国科学院长春应用化学研究所研究员. 本科和硕士毕业于上海交通大学，2011年在日本京都大学取得工学博士学位，之后赴美国宾州州立大学继续博士后深造. 于2015年回国成立独立课题组，同年当选中国流变学学会专业委员会委员；于2016年获美国TA公司授予的Distinguished Young Rheologist Award (2~3人/年)，同年入选2016年中组部QR计划青年项目；于2017年获基金委优青项目资助；于2019年入选中国化学会高分子学科委员会委员，同年获得日本流变学会奖励赏(1~2人/年)，目前担任《Nihon Reoroji Gakkaishi》(日本流变学会志)和《高分子学报》编委;

通讯作者: 陈全, E-mail: qchen@ciac.ac.cn

摘要: 流变学是高分子加工和应用的重要基础，流变学表征对于深入理解高分子流动行为非常重要，获取的流变参数可用于指导高分子加工. 本文首先总结了剪切流变测试中的基本假设：(1)设置的应变施加在样品上，(2)应力来源于样品自身的响应和(3)施加的流场为纯粹的剪切流场；之后具体阐述了这些假设失效的情形和所导致的常见的实验错误；最后，通过结合一些实验实例具体说明如何培养良好的测试习惯和获得可靠的测试结果.

关键词:

English

Toward Correct Measurements of Shear Rheometry

1.
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, State Key Laboratory of Polymer Physics and Chemistry, Changchun 130022
2.
School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026

Corresponding author: Quan Chen, E-mail: qchen@ciac.ac.cn

Received Date: 2020-10-14
Accepted Date: 2020-12-03
Available Online: 2021-04-03

Abstract: Rheology is an important tool for characterizing polymeric materials. The knowledge of polymer dynamics obtained from rheological measurements can guide the processing of polymeric materials. Nevertheless, it is a challenging task to conduct precise measurements on shear rheometers. First, we summarize the basic assumptions of rheological measurements: (1) the applied strain is on the sample, (2) the stress reflects sample’s own stress response, and (3) the flow field is purely the shear flow. Second, we highlight the conditions under which the above assumptions become invalid, which leads to incorrect measurements. For example, the first assumption is violated when compliance of the equipment or the wall-slip becomes non-negligible, the second assumption is violated when either inertia of the equipment, that of the sample, or the interfacial tension contributes non-negligibly to the overall torque, and the third assumption is violated when there is the secondary flow, shear-banding, or edge fracture. We show some examples of the incorrect measurements owing to these violations of the assumptions. Finally, we stress the importance of good experimental practice in rheological experiments.

Key words:

1. [1]
  Tadmor Z, Gogos C G. Principles of Polymer Processing. 2^nd ed. Hoboken, New Jersey: John Wiley & Sons, 2013
2. [2]
  Ptaszek P. Large Amplitude Oscillatory Shear (LAOS) measurement and fourier-transform rheology: application to food. In: Ahmed J, Ptaszek P, Basu S, eds. Advances in Food Rheology and Its Applications. London: Woodhead Publishing, 2017. 87−123
3. [3]
  Kaneda I. Rheology Control Agents for Cosmetics. Rheology of Biological Soft Matter. Tokyo: Springer, 2017, 295−321
4. [4]
  Eley R R. J Coat Technol Res, 2019, 16(2): 263−305 doi: 10.1007/s11998-019-00187-5
5. [5]
  Ahmed J, Ptaszek P, Basu S. Advances in Food Rheology and Its Applications. London: Woodhead Publishing, 2016
6. [6]
  Zhang Z, Liu C, Cao X, Gao L, Chen Q. Macromolecules, 2016, 49(23): 9192−9202 doi: 10.1021/acs.macromol.6b02017
7. [7]
  Chen Q, Tudryn G J, Colby R H. J Rheol, 2013, 57(5): 1441−1462 doi: 10.1122/1.4818868
8. [8]
  Liu S, Wu S, Chen Q. ACS Macro Lett, 2020, 9: 917−923 doi: 10.1021/acsmacrolett.0c00256
9. [9]
  Larson R G. The Structure and Rheology of Complex Fluids. New York: Oxford University Press, 1999
10. [10]
  Mihai M, Huneault M A, Favis B D. Polym Eng Sci, 2010, 50(3): 629−642 doi: 10.1002/pen.21561
11. [11]
  Ariawan A B, Hatzikiriakos S G, Goyal S K, Hay H. Adv Polym Technol: J Polym Process Inst, 2001, 20(1): 1−13
12. [12]
  Lundahl M J, Berta M, Ago M, Stading M, Rojas O J. Eur Polym J, 2018, 109: 367−378 doi: 10.1016/j.eurpolymj.2018.10.006
13. [13]
  Li B, Yu W, Cao X, Chen Q. J Rheol, 2020, 64(1): 177−190 doi: 10.1122/1.5134532
14. [14]
  Watanabe H, Matsumiya Y, Chen Q, Yu W. Rheological characterization of polymeric liquids. In: Matyjaszewski K, Möller M, eds. Polymer Science: A Comprehensive Reference. Amsterdam: Elsevier, 2012. 683−722
15. [15]
  Marín J M R, Huusom J K, Alvarez N J, Huang Q, Rasmussen H K, Bach A, Skov A L, Hassager O. J Non-Newton Fluid, 2013, 194: 14−22 doi: 10.1016/j.jnnfm.2012.10.007
16. [16]
  Watanabe H, Matsumiya Y, Inoue T. Macromolecules, 2002, 35(6): 2339−2357 doi: 10.1021/ma011782z
17. [17]
  Yoshida H, Adachi K, Watanabe H, Kotaka T. Polym J, 1989, 21(11): 863−872 doi: 10.1295/polymj.21.863
18. [18]
  Trouton F T. Proc R Soc London, Ser A, 1906, 77(519): 426−440 doi: 10.1098/rspa.1906.0038
19. [19]
  Liu C, Zhang J, Zhang Z, Huang S, Chen Q, Colby R H. Macromolecules, 2020, 53(8): 3071−3081 doi: 10.1021/acs.macromol.9b02431
20. [20]
  Zhang J, Liu C, Zhao X, Zhang Z, Chen Q. Soft Matter, 2020, 16(21): 4955−4960 doi: 10.1039/D0SM00572J
21. [21]
  Buscall R, McGowan J I, Morton-Jones A J. J Rheol, 1993, 37(4): 621−641 doi: 10.1122/1.550387
22. [22]
  Buscall R. J Rheol, 2010, 54(6): 1177−1183 doi: 10.1122/1.3495981
23. [23]
  Ballesta P, Petekidis G, Isa L, Poon W, Besseling R. J Rheol, 2012, 56(5): 1005−1037 doi: 10.1122/1.4719775
24. [24]
  Magda J, Larson R. J Non-Newton Fluid, 1988, 30(1): 1−19 doi: 10.1016/0377-0257(88)80014-4
25. [25]
  Costanzo S, Huang Q, Ianniruberto G, Marrucci G, Hassager O, Vlassopoulos D. Macromolecules, 2016, 49(10): 3925−3935 doi: 10.1021/acs.macromol.6b00409
26. [26]
  Liu C Y, Yao M, Garritano R G, Franck A J, Bailly C. Rheol Acta, 2011, 50(5−6): 537 doi: 10.1007/s00397-011-0560-3
27. [27]
  Pogodina N, Nowak M, Läuger J, Klein C, Wilhelm M, Friedrich C. J Rheol, 2011, 55(2): 241−256 doi: 10.1122/1.3528651
28. [28]
  Gottlieb M, Macosko C. Rheol Acta, 1982, 21(1): 90−94 doi: 10.1007/BF01520709
29. [29]
  Hutcheson S, McKenna G. J Chem Phys, 2008, 129(7): 074502 doi: 10.1063/1.2965528
30. [30]
  Krieger I M. J Rheol, 1990, 34(4): 471−483 doi: 10.1122/1.550138
31. [31]
  Läuger J, Stettin H. J Rheol, 2016, 60(3): 393−406 doi: 10.1122/1.4944512
32. [32]
  Ewoldt R H, Johnston M T, Caretta L M. Experimental challenges of shear rheology: how to avoid bad data. Complex Fluids In Biological Systems. In: Spagnolie S E, ed. Complex Fluids in Biological Systems. New York: Springer, 2015. 207−241
33. [33]
  Yosick J A, Giacomin J A, Stewart W E, Ding F. Rheol Acta, 1998, 37(4): 365−373 doi: 10.1007/s003970050123
34. [34]
  Schrag J L. Transactions of the Society of Rheology, 1977, 21(3): 399−413 doi: 10.1122/1.549445
35. [35]
  Shaqfeh E S. Annu Rev Fluid Mech, 1996, 28(1): 129−185 doi: 10.1146/annurev.fl.28.010196.001021
36. [36]
  McKinley G H, Pakdel P, Öztekin A. J Non-Newton Fluid, 1996, 67: 19−47 doi: 10.1016/S0377-0257(96)01453-X
37. [37]
  Pakdel P, McKinley G H. Phys Rev Lett, 1996, 77(12): 2459 doi: 10.1103/PhysRevLett.77.2459
38. [38]
  Chandrasekhar S. Hydromagnets and Hydrodynamics Stability. New York: Dover Publishing, 1981
39. [39]
  Larson R G. Rheol Acta, 1992, 31(3): 213−263 doi: 10.1007/BF00366504
40. [40]
  Taylor G I. Philos Trans R Soc London, Ser A, 1923, 223(605-615): 289−343 doi: 10.1098/rsta.1923.0008
41. [41]
  Turian R M. Ind Eng Chem Fundam, 1972, 11(3): 361−368 doi: 10.1021/i160043a014
42. [42]
  Andablo-Reyes E, Vicente J d, Hidalgo-Alvarez R. J Rheol, 2011, 55(5): 981−986 doi: 10.1122/1.3606633
43. [43]
  Griffiths D, Walters K. J Fluid Mech, 1970, 42(2): 379−399 doi: 10.1017/S0022112070001337
44. [44]
  Johnston M T, Ewoldt R H. J Rheol, 2013, 57(6): 1515−1532 doi: 10.1122/1.4819914
45. [45]
  Shipman R W, Denn M M, Keunings R. Ind Eng Chem Res, 1991, 30(5): 918−922 doi: 10.1021/ie00053a014
46. [46]
  Sharma V, Jaishankar A, Wang Y C, McKinley G H. Soft Matter, 2011, 7(11): 5150−5160 doi: 10.1039/c0sm01312a
47. [47]
  Castellanos M M, Pathak J A, Colby R H. Soft Matter, 2014, 10(1): 122−131 doi: 10.1039/C3SM51994E
48. [48]
  Wolff F, Münstedt H. Rheol Acta, 2013, 52(4): 287−289 doi: 10.1007/s00397-013-0687-5
49. [49]
  Shabbir A, Huang Q, Baeza G P, Vlassopoulos D, Chen Q, Colby R H, Alvarez N J, Hassager O. J Rheol, 2017, 61(6): 1279−1289 doi: 10.1122/1.4998158
50. [50]
  Stadler F J. Korea-Aust Rheol J, 2014, 26(3): 277−291 doi: 10.1007/s13367-014-0032-2
51. [51]
  Hawke L G D, Romano D, Rastogi S. Macromolecules, 2019, 52(22): 8849−8866 doi: 10.1021/acs.macromol.9b01152
52. [52]
  Wang X, Tao F, Sun P, Zhou D, Wang Z, Gu Q, Hu J, Xue G. Macromolecules, 2007, 40(14): 4736−4739 doi: 10.1021/ma0700025
53. [53]
  Teng C, Gao Y, Wang X, Jiang W, Zhang C, Wang R, Zhou D, Xue G. Macromolecules, 2012, 45(16): 6648−6651 doi: 10.1021/ma300885w
54. [54]
  Lippits D R, Rastogi S, Talebi S, Bailly C. Macromolecules, 2006, 39(26): 8882−8885 doi: 10.1021/ma062284z
55. [55]
  Stadler F J, Still T, Fytas G, Bailly C. Macromolecules, 2010, 43(18): 7771−7778 doi: 10.1021/ma101028b
56. [56]
  Ling G H, Wang Y, Weiss R. Macromolecules, 2012, 45(1): 481−490 doi: 10.1021/ma201854w
57. [57]
  Scherz L F, Costanzo S, Huang Q, Schlüter A D, Vlassopoulos D. Macromolecules, 2017, 50(13): 5176−5187 doi: 10.1021/acs.macromol.7b00747
1. [1]
  于逢源 , 张洪斌 . 非线性大应变振荡剪切流场中PP结晶行为的傅立叶转变流变学研究. 高分子学报, 2010, (3): 372-376. doi: 10.3724/SP.J.1105.2010.00372
2. [2]
  李文林 , 牛艳华 , 王志刚 , 张军 . 网络结构对多层聚乙烯共混物界面扩散行为的影响. 高分子学报, 2012, (9): 1007-1014. doi: 10.3724/SP.J.1105.2012.12037
3. [3]
  阳京京 , 方华高 , 章亚琼 , 施文涛 , 陈鹏 , 王志刚 . 黏弹性对聚丙烯/碳纳米管复合材料熔体挤出特性影响研究. 高分子学报, 2013, (10): 1325-1333. doi: 10.3724/SP.J.1105.2013.13080
4. [4]
  李文林 , 牛艳华 , 王志刚 . 聚合物熔体界面扩散理论与研究方法. 高分子学报, 2013, (7): 817-826. doi: 10.3724/SP.J.1105.2013.13032
5. [5]
  申伟 , 何鹏 , 俞炜 , 周持兴 . 介观相分离对等规聚丙烯/烯烃嵌段共聚物共混体系相容性的影响. 高分子学报, 2014, (8): 1116-1123. doi: 10.11777/j.issn1000-3304.2014.13463
6. [6]
  罗锦添 , 欧阳希凯 , 刘庚鑫 . 巨型分子的黏弹性研究进展. 高分子学报, 2020, 51(7): 687-697. doi: 10.11777/j.issn1000-3304.2020.20056
7. [7]
  陈青 , 范毓润 , 郑强 . 剪切流场诱导iPP等温结晶行为的研究. 高分子学报, 2007, (5): 467-471.
8. [8]
  王伟 , 徐德时 . 壳聚糖浓溶液流变性质研究──零剪切粘度的测定和外推. 高分子学报, 1995, (3): 291-295.
9. [9]
  刘冬梅 , 刘茗竹 , 卢宇源 , 安立佳 , 张汉壮 . 近平衡态与快速启动剪切下缠结高分子流体流变行为研究. 高分子学报, 2015, (7): 858-866. doi: 10.11777/j.issn1000-3304.2015.15055
10. [10]
  许少锋 , 汪久根 . 高分子链在微通道剪切流中的迁移机制及浓度的影响. 高分子学报, 2015, (3): 346-355. doi: 10.11777/j.issn1000-3304.2015.14290
11. [11]
  李润明 , 俞炜 , 周持兴 . 流变学方法测定共混物相图及其分辨尺度探讨. 高分子学报, 2008, (5): 481-486. doi: 10.3724/SP.J.1105.2008.00481
12. [12]
  杨红梅 , 杨永柱 , 张小虎 , 郑强 ,  . 聚乙烯交联过程结构演化的流变学研究. 高分子学报, 2009, (8): 741-747. doi: 10.3724/SP.J.1105.2009.00741
13. [13]
  杜雪 , 许元泽 , 钱人元 . 顺丁生胶加工行为的流变学表征. 高分子学报, 1986, (6): 458-462.
14. [14]
  许元泽 , 杜雪 . 聚丙烯熔体流动中结构化的流变学研究. 高分子学报, 1986, (4): 304-307.
15. [15]
  杜宇 , 杨凯 , 俞炜 , 周持兴 . 触变/非触变水凝胶的傅里叶变换流变学研究. 高分子学报, 2012, (12): 1376-1382. doi: 10.3724/SP.J.1105.2012.12197
16. [16]
  杨敖霜 , 王宇 , 刘正英 , 杨伟 , 谢邦互 , 杨鸣波 . 聚合物熔体界面分子链扩散的流变学研究. 高分子学报, 2013, (3): 361-366. doi: 10.3724/SP.J.1105.2013.12261
17. [17]
  陆佳俊 , 白绘宇 , 王玮 , 刘静 , 马丕明 , 东为富 , 刘晓亚 . 动态流变学对PVDF/PTW共混物流体相容性研究. 高分子学报, 2016, (3): 315-323. doi: 10.11777/j.issn1000-3304.2016.15206
18. [18]
  罗贤光 . 橡胶中简单剪切与纯剪切的关系. 高分子学报, 1994, (4): 385-391.
19. [19]
  谢严莉 , 上官勇刚 , 郑强 . 抗冲聚丙烯共聚物熔体结构演化的动态流变学表征. 高分子学报, 2008, (1): 93-96. doi: 10.3724/SP.J.1105.2008.00093
20. [20]
  谢瑞 , 杨秉新 , 姜炳政 , 章其忠 , 许元泽 . 高聚物两相体系相行为的流变学研究──Ⅱ．嵌段高聚物微相溶合的研究. 高分子学报, 1994, (2): 134-140.
Figure 1. Illustration of two representative modes of deformation: the simple shear for which the direction of velocity gradient is perpendicular to that of velocity, and the uniaxial elongation for which the direction of velocity gradient is parallel to that of velocity. (Reprinted with permission from Ref.[14]; Copyright (2012) Elsevier)

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Figure 2. Geometry and parameters K_γ and K_σ of parallel-plate, cone-and-plate and Couette fixtures

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Figure 3. The different responses of Newtonian fluid, Hookean solid, and viscoelastic materials to the imposed steady flow (stress growth, transient or steady mode that depends on the focus), step strain (stress relaxation, transient mode), step stress (creep and recovery, transient mode) and small amplitude oscillatory shear (SAOS, dynamic mode).

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Figure 4. The secondary flow occurs when sample under rotary geometry moves radially outward and sample on the static geometry moves radially inward.

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Figure 5. Schematic view of the CPP fixture. Green: cone; red: sample; blue: outer partition (section); yellow: translation stages (section); orange: bridge (section); grey: inner tool (Drawing not in scale). The sample disk should have size sufficiently larger than the inner plate. (Reprinted with permission from Ref.[25]; Copyright (2016) American Chemical Society)

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Figure 6. (a) The effect of geometry compliance on linear viscoelasticity; (b) Comparison of commanded strain (as 100%), measured strain (with force rebalance torque transducers (FRT) compliance correction), and corrected strain (with tool correction) obtained for a polyisobutylene sample at −20 °C using 25 mm parallel plates (Reprinted with permission from Ref.[26]; Copyright (2011) Society of Rheology)

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Figure 7. A simple schematic showing the geometry of the solid rod and the disposable platens (Reprinted with permission from Ref.[29]; Copyright (2008) American Institute of Physics).

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Figure 8. Vector diagram of torques, including acceleration torque T_a, total or electrical torque T₀, and sample torque T_s, where $ \delta $ and $ \alpha $ are phase angle of T₀ and T_s, respectively. The sample torque can be decomposed into viscous part T_v and elastic part T_e (Reprinted with permission from Ref.[31]; Copyright (2016) Society of Rheology).

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Figure 9. Frequency sweep measurement on the S4 oil sample with viscosity of 4 mPa·s (CP60-0.5 geometry). In addition to the complex viscosity, the measured total torque T₀ and the sample torque T_s obtained after the inertia correction are plotted against angular frequency $\omega $. Arrows point to data points at 25 rad·s⁻¹ (see text), above which the inertia correction fails. (Reprinted with permission from Ref.[31]; Copyright (2016) Society of Rheology)

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Figure 10. Phase angle (circles) and storage G' (triangles) and loss modulus G" (squares) for the S4 oil measured in SMT mode with three cone angles, 0.5° (red), 1° (green), 2° (blue). The arrow indicates the direction of increasing the cone angle. (Reprinted with permission from Ref.[31]; Copyright (2016) Society of Rheology)

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Figure 11. Steady shear flow measurements of H₂O using cone-and-plate with diameter of 50 mm, the scattered plots in the blue regime are obtained from torque below the low-torque limit, the thickening behavior in the red regime is due to secondary flow effect.

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Figure 12. (a) Contact line and interface angle: ideal versus non-ideal cases. In the non-ideal case, asymmetries are exaggerated compared to typical loading and can also occur as a result of overfilling; (b) Contact line in z=0 plane represented by an arbitrary parametric curve, $ \underline r $(s). (Reprinted with permission from Ref.[44]; Copyright (2013) Society of Rheology).

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Figure 13. Evaporation-induced contact line migration, which causes surface tension torque. The geometry is parallel plate (diameter 40 mm) with constant velocity $ {\Omega } $=0.01 rad·s⁻¹. Inset images (views from below) illustrate the contact lines of the overfilled and underfilled cases (Reprinted with permission from Ref.[44]; Copyright (2013) Society of Rheology).

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Figure 14. Steady shear flow with different surface tension (water and n-Decane) using the concentric double gap (DG) geometry (Reprinted with permission from Ref.[44]; Copyright (2013) Society of Rheology)

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Figure 15. (a) Increase of apparent viscosity of surfactant-free BSA solutions during the protein aggregation. (b) Increase of viscosity with time, owing to the protein aggregation in the mAb solutions even after introduction of the surfactant. (Reprinted with permission from Ref.[47]; Copyright (2014) The Royal Society of Chemistry)

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Figure 16. The storage and loss moduli as functions of the angular frequency for a PDMS silicone oil with and without bubbles (Reprinted with permission from Ref.[48]; Copyright (2013) Spring)

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Figure 17. The storage and loss moduli as functions of the angular frequency for PTMO-Li in dried and undried states. (Reprinted with permission from Ref.[49]; Copyright (2017) Society of Rheology)

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Figure 18. Thermal instability of sample mLLDPE F18F. The sample without stabilizer exceeds the ±5% criterion after 4300 s owing to the crosslinking, while the sample with stabilizer stays within this criterion for 8.24×10⁵ s (≈9.5 days). (Reprinted with permission from Ref.[50]; Copyright (2014) Springer).

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Figure 19. Buildup of modulus in disentangled polymer melts with time of ultra-high-molecular-weight polyethylene. The top scheme shows the mechanism and the bottom figure shows the measured storage modulus G'(t) against time (symbols), where G'(t) has been normalized by the equilibrium plateau modulus G_N⁰. Curves are the predictions based on tube theory. (Reprinted with permission from Ref.[51]; Copyright (2019) American Chemical Society)

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