Citation: Dong-Lei Liu, Feng Zhou, Kun Fang. A Theoretical Study on Transitional Shear Flow Behavior of the Compressible and Isothermal Thermoplastic Polymer[J]. Chinese Journal of Polymer Science, ;2019, 37(5): 518-526. doi: 10.1007/s10118-019-2214-3 shu

A Theoretical Study on Transitional Shear Flow Behavior of the Compressible and Isothermal Thermoplastic Polymer

Dong-Lei Liu ^1,2,, ,
Feng Zhou ^1,2 ,
Kun Fang ^1,2

a.
College of Mechanical and Electrical Engineering, Nanchang University, Jiangxi 330031, China
b.
Key Laboratory of Lightweight and High Strength Structural Materials of Jiangxi Province, Nanchang University, Jiangxi 330031, China

Corresponding author: Dong-Lei Liu,
Received Date: 29 September 2018
Revised Date: 16 December 2018
Available Online: 29 January 2019

By extending the virtual conformational element of the polymer chain, a dynamic end-to-end (ETE) vector was presented to describe the chain’s instantaneous morphology based on the spring-bead theory. A feasible viscoelastic model was proposed to describe the rheological behavior of the isothermal thermoplastic polymer materials, based on the molecular kinetics, thermodynamics, and continuum mechanics method. The model is simplified as the generalized Newton’s law. Its integral formula with similar form to the K-BKZ model was also derived. Rheological experiments were carried out with the isotactic polypropylene material. The experimental results reveal that the viscoelastic model exhibits a three-stage rheological characteristic. There is a distinct high-elastic rheological region in the middle stage, reflecting the pseudoplastic fluids properties. Compared with the Ostwald-de Waele power law model, the viscoelastic model shows a better agreement with the rheological practices.
- Shear flow,
- Theoretical model,
- Thermoplastic polymer,
- Rheological experiments
1. [1]
  Wang, S. Q.; Ravindranath, S.; Wang, Y.; Boukany, P. New theoretical considerations in polymer rheology: Elastic breakdown of chain entanglement network. J. Chem. Phys. 2007, 127, 064903. DOI: 10.1063/1.2753156. doi: 10.1063/1.2753156
2. [2]
  Lu, Z. L.; Pan, Y. M.; Liu, X. H.; Zheng, G. Q.; Schubert, D. W.; Liu, C. T. Molar mass and temperature dependence of rheological properties of polymethylmethacrylate melt. Mater. Lett. 2018, 221, 62-65. DOI: 10.1016/j.matlet.2018.03.077. doi: 10.1016/j.matlet.2018.03.077
3. [3]
  Luo, F.; Liu, X. H.; Shao C. G.; Zhang, J. X.; Shen, C. Y.; Guo, Z. H. Micromechanical analysis of molecular orientation in high-temperature creep of polycarbonate. Mater. Des. 2018, 144, 25-31. DOI: 10.1016/j.matdes.2018.02.025. doi: 10.1016/j.matdes.2018.02.025
4. [4]
  Liu, X. H.; Pan, Y. M.; Zheng, G. Q.; Schubert, D. W. Rheological and electrical behavior of poly(methyl methacrylate)/carbon black composites as investigated by creep recovery in shear. Compos. Sci. Technol. 2016, 128, 1-7. DOI: 10.1016/j.compscitech.2016.03.011. doi: 10.1016/j.compscitech.2016.03.011
5. [5]
  Isayev, A. I.; Shyu, G. D.; Li, C. T. Residual stresses and birefringence in injection molding of amorphous polymers: simulation and comparison with experiment. J. Polym. Sci., Part B: Polym. Phys. 2006, 44: 622-639. DOI: 10.1002/polb.20724. doi: 10.1002/polb.20724
6. [6]
  Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 1. Brownian motion in the equilibrium state. J. Chem. Soc. Faraday Trans. 1978, 74: 1789-1801. DOI: 10.1039/F29787401789. doi: 10.1039/F29787401789
7. [7]
  Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 2. Molecular motion under flow. J. Chem. Soc. Faraday. Trans. 1978, 74: 1802-1817. DOI: 10.1039/F29787401802. doi: 10.1039/F29787401802
8. [8]
  Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 3. The constitutive equation. J. Chem. Soc. Faraday Trans. 1978, 74: 1818-1832. DOI: 10.1039/F29787401818. doi: 10.1039/F29787401818
9. [9]
  Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 4. Rheological properties. J. Chem. Soc. Faraday. Trans. 1978, 75: 38-54. DOI: 10.1039/F29797500038. doi: 10.1039/F29797500038
10. [10]
  Doi, M.; Edwards, S. F., in Theory of polymer dynamics, Oxford University Press, New York, 1986.
11. [11]
  Larson, R. G. in The structure and rheology of complex fluid, Oxford University Press, New York, 1999.
12. [12]
  Bird, R. B.; Wiest, J. M. Constitutive equation for polymeric liquids. Annu. Rev. Fluid Mech. 1995, 27: 169-193. DOI: 10.1146/annurev.fl.27.010195.001125. doi: 10.1146/annurev.fl.27.010195.001125
13. [13]
  White, J. L.; Mertzner, A. B. Development of constitutive equation for polymeric melts and solution. J. Appl. Polym. Sci. 1963, 7: 1867-1889. DOI: 10.1002/app.1963.070070524 doi: 10.1002/app.1963.070070524
14. [14]
  Larson R. G., in Constitutive equation for polymer melts and solutions, Butterworks, Boston, 1988.
15. [15]
  Bird, R. B.; Armstrong, R. C.; Hassager, O. in Dynamics of polymer liquids, Vol.1, Fluid Mechanics, Wiley Interscience, New York, 1987.
16. [16]
  Kiriakidis, D. G.; Park, H. J.; Mitsoulis, E.; Mitsoulis, E.; Agassant, J. F. A Study of Stress Distribution in Contraction Flows of and LLDPE Melt. J. Non-Newtonian Fluid. Mech. 1993, 47: 339-356. DOI: 10.1016/0377-0257(93)80057-I. doi: 10.1016/0377-0257(93)80057-I
17. [17]
  Maders, H.; Vergnes, B.; Demay, Y.; Agassant, J. F. Steady flow of a white-metzner fluid in a 2-D abrupt contraction: Computation and experiments. J. Non-Newtonian Fluid. Mech. 1992, 45: 63-80. DOI:10.1016/0377-0257(92)80061-2. doi: 10.1016/0377-0257(92)80061-2
18. [18]
  Phan-Thien, N.; Tanner, R. I. A new constitutive equation derived from network theory. J. Non-Newtonian Fluid. Mech. 1977, 2: 353-365. DOI: 10.1016/0377-0257(77)80021-9. doi: 10.1016/0377-0257(77)80021-9
19. [19]
  Johnson, M. W.; Segalman, D. A model for viscoelastic fluid behavior which allows non-affine deformation. J. Non-Newtonian Fluid. Mech. 1977, 2: 255-270. DOI: 10.1016/0377-0257(77)80003-7. doi: 10.1016/0377-0257(77)80003-7
20. [20]
  Giesekus, H. A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid. Mech. 1982, 11: 69-109. DOI: 10.1016/0377-0257(82)85016-7. doi: 10.1016/0377-0257(82)85016-7
21. [21]
  Oliveira, P. J. Alternative derivation of differential constitutive equations of the oldroyd-b type. J. Non-Newtonian Fluid. Mech. 2009, 160: 40-46. DOI: 10.1016/j.jnnfm.2008.11.013. doi: 10.1016/j.jnnfm.2008.11.013
22. [22]
  Bernstein, B.; Kearsley, E. A.; Zapas, L. J. A study of stress relaxation with finite strain. J. Rheol. 1963, 7: 391-410. DOI: 10.1122/1.548963. doi: 10.1122/1.548963
23. [23]
  Christainsen, R. L; Bird, R. B. Dilute solution rheology: Experimental results and finitely extensible nonlinear elastic dumbbell theory. J. Non-Newton. Fluid. Mech. 1977, 3: 161-177. DOI: 10.1016/0377-0257(77)80047-5. doi: 10.1016/0377-0257(77)80047-5
24. [24]
  Doi, M. A constitutive equation derived from the model of doiand edwards for concentrated polymer solutions and polymer melts. J. Polym. Sci., Part B: Polym. Phys. 1980, 18: 2055-2067. DOI: 10.1002/pol.1980.180181005. doi: 10.1002/pol.1980.180181005
25. [25]
  Laso, M.; Öttinger, H. C. Calculation of viscoelastic flow using molecular models: The connffessit approach. J. Non-Newton. Fluid. Mech. 1993, 47: 1-20. DOI: 10.1016/0377-0257(93)80042-A. doi: 10.1016/0377-0257(93)80042-A
26. [26]
  Liu, D. L.; Cao, W.-H.; Xin, Y.; Sun, L. Relationship model theory of polymer o-rientation stress-morphology for incompressible and isothermal melts in injection molding. Polym. Mater. Sci. Eng. 2014, 30: 109-118. DOI: 10.16865/j.cnki.1000-7555.2014.08.022. doi: 10.16865/j.cnki.1000-7555.2014.08.022
27. [27]
  Liu, D.-L.; Cao, W.-H.; Xin, Y. Study on the polymer melt flow-induced orientation stress model in injection molding: with the isothermal compressible hypothesis. J. Mech. Eng. 2014, 50: 75-82. DOI: 10.3901/JME.2014.12.075. doi: 10.3901/JME.2014.12.075
28. [28]
  Therkelsen S. V., in Constitutive modeling of active polymers, B.S. Mechanical Engineering, University of Iowa, 2002.
29. [29]
  Doi, M., in Introduce of polymer physics, Clarendon Press, Oxford, 1996.
30. [30]
  Reddy, J. N., in Introduction to continuum mechanics: With applications, Cambridge University Press, Cambridge, 2008.
31. [31]
  Tanner, R. I. From A to (BK)Z in constitutive relations. J. Rheol. 1988, 32: 673-702. DOI: 10.1122/1.549986. doi: 10.1122/1.549986
1. [1]
  Bingwei Wang , Yihong Ding , Xiao Tian . Benchmarking model chemistry composite calculations for vertical ionization potential of molecular systems. Chinese Chemical Letters, 2025, 36(2): 109721-. doi: 10.1016/j.cclet.2024.109721
2. [2]
  Chen Chen , Jinzhou Zheng , Chaoqin Chu , Qinkun Xiao , Chaozheng He , Xi Fu . An effective method for generating crystal structures based on the variational autoencoder and the diffusion model. Chinese Chemical Letters, 2025, 36(4): 109739-. doi: 10.1016/j.cclet.2024.109739
3. [3]
  Hui Jin , Qin Cai , Peiwen Liu , Yan Chen , Derong Wang , Weiping Zhu , Yufang Xu , Xuhong Qian . Multistep continuous flow synthesis of Erlotinib. Chinese Chemical Letters, 2024, 35(4): 108721-. doi: 10.1016/j.cclet.2023.108721
4. [4]
  Fangwen Peng , Zhen Luo , Yingjin Ma , Haibo Ma . Theoretical study of aromaticity reversal in dimethyldihydropyrene derivatives. Chinese Journal of Structural Chemistry, 2024, 43(5): 100273-100273. doi: 10.1016/j.cjsc.2024.100273
5. [5]
  Shaohua Zhang , Liyao Liu , Yingqiao Ma , Chong-an Di . Advances in theoretical calculations of organic thermoelectric materials. Chinese Chemical Letters, 2024, 35(8): 109749-. doi: 10.1016/j.cclet.2024.109749
6. [6]
  Quan Zhou , Xiao-Min Chen , Xujie Qin , Zhe-Ning Chen , Jun Chen , Wei Zhuang . The counterintuitive aromaticity of bent metallabenzenes: A theoretical exploration. Chinese Chemical Letters, 2025, 36(4): 109770-. doi: 10.1016/j.cclet.2024.109770
7. [7]
  Peiwen Liu , Fang Zhao , Jing Zhang , Yunpeng Bai , Jinxing Ye , Bo Bao , Xinggui Zhou , Li Zhang , Changlu Zhou , Xinhai Yu , Peng Zuo , Jianye Xia , Lian Cen , Yangyang Yang , Guoyue Shi , Lin Xu , Weiping Zhu , Yufang Xu , Xuhong Qian . Micro/nano flow chemistry by Beyond Limits Manufacturing. Chinese Chemical Letters, 2024, 35(5): 109020-. doi: 10.1016/j.cclet.2023.109020
8. [8]
  Tao Wei , Jiahao Lu , Pan Zhang , Qi Zhang , Guang Yang , Ruizhi Yang , Daifen Chen , Qian Wang , Yongfu Tang . An intermittent lithium deposition model based on bimetallic MOFs derivatives for dendrite-free lithium anode with ultrahigh areal capacity. Chinese Chemical Letters, 2024, 35(8): 109122-. doi: 10.1016/j.cclet.2023.109122
9. [9]
  Huashan Huang , Jingze Chen , Luyun Zhang , Hong Yan , Siqi Li , Fen-Er Chen . Oscillatory flow reactor facilitates fast photochemical Wolff rearrangement toward synthesis of α-substituted amides in flow. Chinese Chemical Letters, 2025, 36(2): 109992-. doi: 10.1016/j.cclet.2024.109992
10. [10]
  Lingling Su , Qunyan Wu , Congzhi Wang , Jianhui Lan , Weiqun Shi . Theoretical design of polyazole based ligands for the separation of Am(Ⅲ)/Eu(Ⅲ). Chinese Chemical Letters, 2024, 35(8): 109402-. doi: 10.1016/j.cclet.2023.109402
11. [11]
  Liliang Chu , Xiaoyan Zhang , Jianing Li , Xuelei Deng , Miao Wu , Ya Cheng , Weiping Zhu , Xuhong Qian , Yunpeng Bai . Continuous-flow synthesis of polysubstituted γ-butyrolactones via enzymatic cascade catalysis. Chinese Chemical Letters, 2024, 35(4): 108896-. doi: 10.1016/j.cclet.2023.108896
12. [12]
  Yuxin Xiao , Xiaowei Wang , Yutong Yin , Fangchao Yin , Jinchao Li , Zhiyuan Hou , Mashooq Khan , Rusong Zhao , Wenli Wu , Qiongzheng Hu . Distance-based lateral flow biosensor for the quantitative detection of bacterial endotoxin. Chinese Chemical Letters, 2024, 35(12): 109718-. doi: 10.1016/j.cclet.2024.109718
13. [13]
  Xiaoman Dang , Zhiying Wu , Tangxin Xiao , Zhouyu Wang , Leyong Wang . Highly robust supramolecular polymer networks crosslinked by metallacycles. Chinese Chemical Letters, 2024, 35(12): 110208-. doi: 10.1016/j.cclet.2024.110208
14. [14]
  Yaohua Li , Qi Cao , Xuanhua Li . Tailoring the configuration of polymer passivators in perovskite solar cells. Chinese Journal of Structural Chemistry, 2025, 44(2): 100413-100413. doi: 10.1016/j.cjsc.2024.100413
15. [15]
  Chaozheng He , Jia Wang , Ling Fu , Wei Wei . Nitric oxide assists nitrogen reduction reaction on 2D MBene: A theoretical study. Chinese Chemical Letters, 2024, 35(5): 109037-. doi: 10.1016/j.cclet.2023.109037
16. [16]
  Hongmei Yu , Baoxi Zhang , Meiju Liu , Cheng Xing , Guorong He , Li Zhang , Ningbo Gong , Yang Lu , Guanhua Du . Theoretical and experimental cocrystal screening of temozolomide with a series of phenolic acids, promising cocrystal coformers. Chinese Chemical Letters, 2024, 35(5): 109032-. doi: 10.1016/j.cclet.2023.109032
17. [17]
  Longlong Geng , Huiling Liu , Wenfeng Zhou , Yong-Zheng Zhang , Hongliang Huang , Da-Shuai Zhang , Hui Hu , Chao Lv , Xiuling Zhang , Suijun Liu . Construction of metal-organic frameworks with unsaturated Cu sites for efficient and fast reduction of nitroaromatics: A combined experimental and theoretical study. Chinese Chemical Letters, 2024, 35(8): 109120-. doi: 10.1016/j.cclet.2023.109120
18. [18]
  Xiaobo Li , Qunyan Wu , Congzhi Wang , Jianhui Lan , Meng Zhang , Weiqun Shi . Theoretical perspectives on the reduction of Pu(Ⅳ) and Np(Ⅵ) by methylhydrazine in HNO₃ solution: Implications for Np/Pu separation. Chinese Chemical Letters, 2024, 35(7): 109359-. doi: 10.1016/j.cclet.2023.109359
19. [19]
  Hongjie Guo , Qiang Wei , Yangyang Wu , Wei Qiu , Hongliang Li , Changyong Zhang . Enhanced nitrate removal from groundwater using a conductive spacer in flow-electrode capacitive deionization. Chinese Chemical Letters, 2024, 35(8): 109325-. doi: 10.1016/j.cclet.2023.109325
20. [20]
  Jinlong Li , Ruixin Li , Jiahui Liu , Ji-Quan Liu , Jia Xu , Xianglin Zhou , Yefan Zhang , Kairui Wang , Lin Lei , Gang Xie , Fengmei Wang , Ying Yang , Liping Cao . A TOC- and deposition-free electrochromic window driven by redox flow battery. Chinese Chemical Letters, 2024, 35(12): 110355-. doi: 10.1016/j.cclet.2024.110355

Get Citation

PDF

XML

Metrics

PDF Downloads(0)
Abstract views(728)
HTML views(4)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142