Understanding stress relaxation behavior of amorphous polystyrene based on microstructural heterogeneity

Zhang Jing-Qi; Hao Qi; Lyu Guo-Jian; Xiong Bi-Jin; Qiao Ji-Chao

doi:10.7498/aps.73.20231240

Abstract

The relationship between stress relaxation behavior and inherent microstructural heterogeneity in amorphous polystyrene materials is studied in this work. Starting from the basic Maxwell viscoelastic model and extending to the three-parameter stretched exponential equation, the nature of the distribution of characteristic timescales and the segmental effects during polymer stress relaxation are discussed. The results indicate that the stress relaxation behavior of amorphous polymers exhibits non-exponential characteristics. Neither a single characteristic time with exponential decay nor a finite spectrum method with finite characteristic time can adequately describe the stress relaxation behavior of polystyrene due to the continuous distribution of characteristic timescales resulting from microstructural heterogeneity in amorphous polymers. In addition, the changes in stress relaxation behavior caused by physical aging are explored. Aging leads to a transition of the system towards a more stable energy state, making it difficult to activate the relaxation of the individual units, thus slowing down the stress relaxation process and increasing the characteristic time.

Keywords:

Authors and contacts

1.
Queen Mary University of London Engineering School, Northwestern Polytechnical University, Xi’an 710072, China
2.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
3.
School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Corresponding author: Qiao Ji-Chao, qjczy@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51971178, 52271153), the Outstanding Youth Found of Shaanxi Province, China (Grant No. 2021JC-12), and National College Student Innovation and Entrepreneurship Training Program, China (Grant No. 202310699002).

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References

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[36]	Wagner H, Bedorf D, Küchemann S, Schwabe M, Zhang B, Arnold W, Samwer K 2011 Nat. Mater 10 439 Google Scholar
[37]	黄蓓蓓, 郝奇, 吕国建, 乔吉超 2023 物理学报 72 136101 Google Scholar Huang B B, Hao Q, Lyu G J, Qiao J C 2023 Acta Phys. Sin. 72 136101 Google Scholar
[38]	Gibbs M R J, Evetts J E, Leake J A 1983 J. Mater. Sci. 18 278 Google Scholar
[39]	Jiao W, Wen P, Peng H L, Bai H Y, Sun B A, Wang W H 2013 Appl. Phys. Lett. 102 101903 Google Scholar
[40]	Lu Z, Shang B, Sun Y, Zhu Z, Guan P, Wang W, Bai H 2016 J. Chem. Phys. 144 144501 Google Scholar
[41]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[42]	王峥, 汪卫华 2017 物理学报 66 176103 Google Scholar Wang Z, Wang W H 2017 Acta Phys. Sin. 66 176103 Google Scholar
[43]	Zhao Y, Shang B, Zhang B, Tong X, Ke H, Bai H, Wang W H 2022 Sci. Adv. 8 eabn3623 Google Scholar
[44]	Casalini R, Roland C M 2009 Phys. Rev. Lett. 102 035701 Google Scholar

Cited By

图 1 聚苯乙烯在给定应变0.4%条件下的应力松弛响应. 测试温度为355 K, 加载前保温30 min以使测试环境温度稳定; 红色实线为Maxwell模型 ((1)式)拟合曲线

Figure 1. Stress response of PS at a given strain of 0.4%. The test temperature is 355 K, and the temperature is kept for 30 min before loading to stabilize the ambient temperature in an equilibrium state. The red solid curve is the least fitting using the Maxwell model (Eq. (1)).

DownLoad: Full-Size Img PowerPoint

图 2 采用(2)式对聚苯乙烯应力松弛响应拟合结果, 其中(a)和(b)中红色实线分别对应于n = 2和n = 4

Figure 2. Fitting results of stress relaxation response of polystyrene using Eq. (2): (a), (b) The fitting curves of the finite spectrum approach when n = 2 and n = 4, respectively.

DownLoad: Full-Size Img PowerPoint

图 3 应力松弛实验曲线及KWW方程((3)式)最小二乘拟合结果

Figure 3. Comparison between fitting curve (Eq. (3)) and experiments (symbols) for stress relaxation behavior.

DownLoad: Full-Size Img PowerPoint

图 4 扩展指数方程计算所得应力松弛过程中特征时间分布谱图(绿色区域), 为便于对比, 图3中拟合结果亦被给出

Figure 4. Characteristic time distribution spectrum of the stress relaxation process calculated by the KWW equation (green area). For comparison, the fitting results in Fig. 3 are also given.

DownLoad: Full-Size Img PowerPoint

图 5 聚苯乙烯在340 K和355 K温度条件下所得(a)应力松弛数据及计算所得(b)激活能谱分布

Figure 5. (a) Stress relaxation data and (b) calculated activation energy spectrum distribution of polystyrene at temperatures of 340 K and 355 K.

DownLoad: Full-Size Img PowerPoint

图 6 不同温度条件下(340, 345, 350, 355 K)聚苯乙烯应力松弛曲线, 红色实线为扩展指数方程((3)式)拟合结果

Figure 6. Stress relaxation curves of polystyrene under different temperature conditions (340, 345, 350, 355 K). The red solid curves represent the fitting results of the extended exponential equation (Eq. (3)).

DownLoad: Full-Size Img PowerPoint

图 7 不同温度条件下(340, 345, 350, 355)聚苯乙烯应力松弛曲线, 红色实线为三参数扩展指数方程((6)式)拟合结果

Figure 7. Stress relaxation curves of polystyrene under different temperature conditions (340, 345, 350, 355 K). The red solid curves represent the fitting results of the three-parameter extended exponential equation (Eq. (6)).

DownLoad: Full-Size Img PowerPoint

图 8 不同老化时间条件下(15, 30, 60, 90, 120 min)聚苯乙烯应力松弛曲线, 测试温度为350 K, 红色实线为三参数扩展指数方程((6)式)拟合结果

Figure 8. Stress relaxation curves of polystyrene after annealing for different time (15, 30, 60, 90, 120 min). The red solid curves represent the fitting results of the three-parameter extended exponential equation (Eq. (6)).

DownLoad: Full-Size Img PowerPoint

图 9 不同老化时间条件下(15, 30, 60, 90, 120 min)根据(5)式所得聚苯乙烯应力松弛过程中激活能谱分布

Figure 9. Activation energy spectrum distribution of polystyrene calculated by Eq. (5) after annealing for different time (15, 30, 60, 90, 120 min).

DownLoad: Full-Size Img PowerPoint

[1]	Ozerin A N, Golubev E K, Ivanchev S S, Aulov V A, Kechek’yan A S, Kurkin T S, Ivan’kova E M, Adonin N Y 2022 Polym. Sci. Ser. A 64 73 Google Scholar
[2]	Müller M, Abetz V 2021 Chem. Rev. 121 14189 Google Scholar
[3]	Li Y, Tang S, Abberton B C, Kröger M, Burkhart C, Jiang B, Papakonstantopoulos G J, Poldneff M, Liu W K 2012 Polymer 53 5935 Google Scholar
[4]	Boland C S, Khan U, Ryan G, Barwich S, Charifou R, Harvey A, Backes C, Li Z, Ferreira M S, Möbius M E, Young R J, Coleman J N 2016 Science 354 1257 Google Scholar
[5]	金日光, 华幼卿 2000 高分子物理 (第二版) (北京: 化学工业出版社) Jin R G, Hua Y Q 2000 Polymer Physics (2nd Ed.) (Beijing: Chemical Industry Press
[6]	Hou J X, Svaneborg C, Everaers R, Grest G S 2010 Phys. Rev. Lett. 105 068301 Google Scholar
[7]	Spathis G, Kontou E 2012 Compos. Sci. Technol. 72 959 Google Scholar
[8]	Huang J S, Gibson L J 1991 J. Mater. Sci. 26 637 Google Scholar
[9]	Papanicolaou G C, Zaoutsos S P 2019 Creep and Fatigue in Polymer Matrix Composites (Woodhead Publishing) pp3–59
[10]	Di Marzio E A, Kasianowicz J J 2003 J. Chem. Phys. 119 6378 Google Scholar
[11]	Auhl R, Everaers R, Grest G S, Kremer K, Plimpton S J 2003 J. Chem. Phys. 119 12718 Google Scholar
[12]	Kreer T, Metzger S, Müller M, Binder K, Baschnagel J 2004 J. Chem. Phys. 120 4012 Google Scholar
[13]	Chui C, Boyce M C 1999 Macromolecules 32 3795 Google Scholar
[14]	Perez J 1998 Physics and Mechanics of Amorphous Polymers (CRC Press
[15]	Ediger M D 2000 Annu. Rev. Phys. Chem. 51 99 Google Scholar
[16]	Wang X Y, Xu W S, Zhang H, Douglas J F 2019 J. Chem. Phys. 151 184503 Google Scholar
[17]	Dmowski W, Iwashita T, Chuang C P, Almer J, Egami T 2010 Phys. Rev. Lett. 105 205502 Google Scholar
[18]	Hu Y, Guan P, Li M, Liu C, Yang Y, Bai H, Wang W 2016 Phys. Rev. B 93 214202 Google Scholar
[19]	Smith G D, Borodin O, Paul W 2002 J. Chem. Phys. 117 10350 Google Scholar
[20]	Jin W, Boyd R H 2002 Polymer 43 503 Google Scholar
[21]	Borodin O, Smith G D, Bandyopadhyaya R, Byutner O 2003 Macromolecules 36 7873 Google Scholar
[22]	Smith G D, Paul W, Monkenbusch M, Richter D 2001 J. Chem. Phys. 114 4285 Google Scholar
[23]	Gebremichael Y, Schrøder T B, Starr F W, Glotzer S C 2001 Phys. Rev. E 64 051503 Google Scholar
[24]	Bennemann C, Donati C, Baschnagel J, Glotzer S C 1999 Nature 399 246 Google Scholar
[25]	Etienne S, David L 2007 Philos. Mag. 87 417 Google Scholar
[26]	Lunkenheimer P, Wehn R, Schneider U, Loidl A 2005 Phys. Rev. Lett. 95 055702 Google Scholar
[27]	Bruns M, Hassani M, Varnik F, Hassanpour A, Divinski S, Wilde G 2021 Phys. Rev. Res. 3 013234 Google Scholar
[28]	Pan J, Ivanov Y P, Zhou W H, Li Y, Greer A L 2020 Nature 578 559 Google Scholar
[29]	Pan J, Wang Y X, Guo Q, Zhang D, Greer A L, Li Y 2018 Nat. Commun. 9 560 Google Scholar
[30]	Wunsch J R 2014 Polystyrene-Synthesis, Production and Applications (New York: Nova Science Publishers, Inc.
[31]	张智枢, 顾欣, 杨云云, 蔡绪福 2017 工程科学与技术 49 232 Google Scholar Zhang Z S, Gu X, Yang Y Y, Cai X F 2017 Adv. Eng. Sci. 49 232 Google Scholar
[32]	郝奇, 乔吉超 2022 力学学报 54 3058 Google Scholar Hao Q, Qiao J C 2022 Chin. J. Theo. Appl. Mech. 54 3058 Google Scholar
[33]	Taub A, Spaepen F 1981 J. Mater. Sci. 16 3087 Google Scholar
[34]	Qiao J C, Wang Y J, Zhao L Z, et al. 2016 Phys. Rev. B 94 104203 Google Scholar
[35]	Duan Y J, Zhang L T, Qiao J C, et al. 2022 Phys. Rev. Lett. 129 175501 Google Scholar
[36]	Wagner H, Bedorf D, Küchemann S, Schwabe M, Zhang B, Arnold W, Samwer K 2011 Nat. Mater 10 439 Google Scholar
[37]	黄蓓蓓, 郝奇, 吕国建, 乔吉超 2023 物理学报 72 136101 Google Scholar Huang B B, Hao Q, Lyu G J, Qiao J C 2023 Acta Phys. Sin. 72 136101 Google Scholar
[38]	Gibbs M R J, Evetts J E, Leake J A 1983 J. Mater. Sci. 18 278 Google Scholar
[39]	Jiao W, Wen P, Peng H L, Bai H Y, Sun B A, Wang W H 2013 Appl. Phys. Lett. 102 101903 Google Scholar
[40]	Lu Z, Shang B, Sun Y, Zhu Z, Guan P, Wang W, Bai H 2016 J. Chem. Phys. 144 144501 Google Scholar
[41]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[42]	王峥, 汪卫华 2017 物理学报 66 176103 Google Scholar Wang Z, Wang W H 2017 Acta Phys. Sin. 66 176103 Google Scholar
[43]	Zhao Y, Shang B, Zhang B, Tong X, Ke H, Bai H, Wang W H 2022 Sci. Adv. 8 eabn3623 Google Scholar
[44]	Casalini R, Roland C M 2009 Phys. Rev. Lett. 102 035701 Google Scholar

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