Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

A complete equation of state for polyethylene based on Helmholtz free energy

Zhang Xu-Ping Wang Gui-Ji Luo Bin-Qiang Tan Fu-Li Zhao Jian-Heng Sun Cheng-Wei Liu Cang-Li

Citation:

A complete equation of state for polyethylene based on Helmholtz free energy

Zhang Xu-Ping, Wang Gui-Ji, Luo Bin-Qiang, Tan Fu-Li, Zhao Jian-Heng, Sun Cheng-Wei, Liu Cang-Li
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Polyethylene (PE) is an important kind of plastic, which plays a significant role as the shell material of the fuel capsule, light weight structural element subjected to intense mechanical impact and explosion load. And it is well accepted that semi-empirical three-term equation of state (EOS) is one of the most widely used EOSs in practical work. Therefore, studies of semi-empirical three-term EOS of PE are significant for accurately predicting and analyzing the physical processes and experimental results under high pressure compression. A semi-empirical three-term complete EOS of PE based on the model of Helmholtz free energy is established in this work. According to the EOS model, the Helmholtz free energy is composed of cold energy, thermal contribution of atoms and thermal excitation of electrons. The cold energy is calculated by using the Mie potential. The optical frequency branch of atomic vibration and the thermal contribution of electrons are neglected in the calculation at temperatures below 104 K. The parameters of Helmholtz free energy are calculated by using the shock Hugoniot data and thermal parameters at ambient state. And then, the application pressure range and reliability of the semi-empirical three-term EOS of PE are evaluated. Shock Hugoniot, shock wave temperature and Grneisen coefficient of PE are deduced from the EOS. The results show that shock Hugoniot and shock wave temperature are consistent well with the experimental data and the first-principle calculation in a pressure range of 150 GPa. Because the specific volume of PE does not change obviously in the melting and chain dissociation process, the assumption of linear Hugoniot relation of PE is valid for calculating the cold energy parameters. The calculation results deviate from the experimental results at about 150 GPa while the compression lasts up to the chemical bond dissociation pressure of PE. In addition, the value of buck modulus and its derivative with respect to pressure at zero pressure and temperature depend strongly on Hugoniot parameters. Therefore, the parameter of Helmholtz free energy in this work is only valid for compression. In conclusion, the Helmholtz free energy model and parameters can well reproduce the experimental data and reasonably describe the thermodynamic state of PE at its dissociation pressure. Moreover, it should be pointed out that a more refined model of phase transition and thermal contribution of atoms and electrons should be considered when extrapolated to higher pressure.
      Corresponding author: Zhao Jian-Heng, jianh_zhao@caep.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11327803, 11272295, 11502252, 11302203).
    [1]

    Millett J C F, Bourne N K 2004J.Phys.D:Appl.Phys. 37 2901

    [2]

    Bourne N K, Millett J C F, Goveas S G 2007J.Phys.D:Appl.Phys. 40 5714

    [3]

    Barrios M A, Hicks D G, Boehly T R, Fratanduono D E, Eggert J H, Celliers P M, Collins G W, Meyerhofer D D 2010Phys.Plasmas 17 056307

    [4]

    Barrios M A, Boehly T R, Hicks D G, Fratanduono D E, Eggert J H, Collins G W, Meyerhofer D D 2012J.Appl.Phys. 111 093515

    [5]

    Marsh S P 1980LASL Shock Hugoniot Data(California:University of California Press) pp439-442

    [6]

    Nellis W J, Ree F H, Traintor R J, Mitchell A C, Boslough M B 1984J.Chem.Phys. 80 2789

    [7]

    Huang X G, Fu S Z, Shu H, Ye J J, Wu J, Xie Z Y, Fang Z H, Jia G, Luo P Q, Long T, He J H, Gu Y, Wang S J 2010Acta Phys.Sin. 59 6394(in Chinese)[黄秀光, 傅思祖, 舒桦, 叶君建, 吴江, 谢志勇, 方智恒, 贾果, 罗平庆, 龙滔, 何钜华, 顾援, 王世绩2010物理学报59 6394]

    [8]

    Gu Y J, Chen Q F, Cai L C, Chen Z Y, Zhen J 2009Chin.Phys.Lett. 26 085101

    [9]

    Fortov V E, Lomonosov I V 2010Shock Waves 20 53

    [10]

    Pastine D J 1968J.Chem.Phys. 49 3012

    [11]

    Dowell F 1982LANL Tech.Rep. 9564 11

    [12]

    Mattsson T R, Lane J M D, Cochrane K R, Desjarlais M P, Thompson A P, Pierce F, Grest G S 2010Phys.Rev.B 81 054103

    [13]

    Chantawansri T L, Sirk T W, Byrd E F C, Andzelm J W, Rice B M 2012J.Chem.Phys. 137 204901

    [14]

    Root S, Haill T A, Lane J M D, Thompson A P, Grest G S, Schroen D G, Mattsson T R 2013J.Appl.Phys. 114 103502

    [15]

    Yu J D, Li P, Wang W Q, Wu Q 2014Acta Phys.Sin. 63 116401(in Chinese)[于继东, 李平, 王文强, 吴强2014物理学报63 116401]

    [16]

    Li Y H, Chang J Z, Li X M, Yu Y Y, Dai C D, Zhang L 2012Acta Phys.Sin. 61 206203(in Chinese)[李英华, 常敬臻, 李雪梅, 俞宇颖, 戴程达, 张林2012物理学报61 206203]

    [17]

    Xu S X, Zhang W X 1986Introduction to Practical Equation of State(Beijing:Higher Education Press) p249(in Chinese)[徐锡申, 张万箱1986实用物态方程理论导引(北京:高等教育出版社)第249页]

    [18]

    Zhang L, Li Y H, Yu Y Y, Li X M, Ma Y, Gu C G, Dai C D, Cai L C 2011Physica B 406 4163

    [19]

    Khishchenko K V, Lomonosov I V, Fortov V E 1998High Temperatures-High Pressure 30 373

    [20]

    Bushman A V, Lomonosov I V, Fortov V E, Khishchenko K V, Zhernokletov M V, Sutulov Y N 1996Sov.Phys.JETP 82 895

    [21]

    Tang W H, Zhang R Q 2008Introduction of Theory and Computation of Equations of State(Beijing:Higher Education Press) p224(in Chinese)[汤文辉, 张若棋2008物态方程理论及计算概述(北京:高等教育出版社)第224页]

    [22]

    Wu Q, Jing F Q, Li X Z 2005Chin.J.High Pressure Phys. 19 97(in Chinese)[吴强, 经福谦, 李欣竹2005高压物理学报19 97]

    [23]

    Wunderlich B 1962J.Chem.Phys. 37 1207

    [24]

    Jing F Q 1999Introduction to Experimental Equation of State(Beijing:Science Press) p372(in Chinese)[经福谦1999实验物态方程导引(北京:科学出版社)第372页]

  • [1]

    Millett J C F, Bourne N K 2004J.Phys.D:Appl.Phys. 37 2901

    [2]

    Bourne N K, Millett J C F, Goveas S G 2007J.Phys.D:Appl.Phys. 40 5714

    [3]

    Barrios M A, Hicks D G, Boehly T R, Fratanduono D E, Eggert J H, Celliers P M, Collins G W, Meyerhofer D D 2010Phys.Plasmas 17 056307

    [4]

    Barrios M A, Boehly T R, Hicks D G, Fratanduono D E, Eggert J H, Collins G W, Meyerhofer D D 2012J.Appl.Phys. 111 093515

    [5]

    Marsh S P 1980LASL Shock Hugoniot Data(California:University of California Press) pp439-442

    [6]

    Nellis W J, Ree F H, Traintor R J, Mitchell A C, Boslough M B 1984J.Chem.Phys. 80 2789

    [7]

    Huang X G, Fu S Z, Shu H, Ye J J, Wu J, Xie Z Y, Fang Z H, Jia G, Luo P Q, Long T, He J H, Gu Y, Wang S J 2010Acta Phys.Sin. 59 6394(in Chinese)[黄秀光, 傅思祖, 舒桦, 叶君建, 吴江, 谢志勇, 方智恒, 贾果, 罗平庆, 龙滔, 何钜华, 顾援, 王世绩2010物理学报59 6394]

    [8]

    Gu Y J, Chen Q F, Cai L C, Chen Z Y, Zhen J 2009Chin.Phys.Lett. 26 085101

    [9]

    Fortov V E, Lomonosov I V 2010Shock Waves 20 53

    [10]

    Pastine D J 1968J.Chem.Phys. 49 3012

    [11]

    Dowell F 1982LANL Tech.Rep. 9564 11

    [12]

    Mattsson T R, Lane J M D, Cochrane K R, Desjarlais M P, Thompson A P, Pierce F, Grest G S 2010Phys.Rev.B 81 054103

    [13]

    Chantawansri T L, Sirk T W, Byrd E F C, Andzelm J W, Rice B M 2012J.Chem.Phys. 137 204901

    [14]

    Root S, Haill T A, Lane J M D, Thompson A P, Grest G S, Schroen D G, Mattsson T R 2013J.Appl.Phys. 114 103502

    [15]

    Yu J D, Li P, Wang W Q, Wu Q 2014Acta Phys.Sin. 63 116401(in Chinese)[于继东, 李平, 王文强, 吴强2014物理学报63 116401]

    [16]

    Li Y H, Chang J Z, Li X M, Yu Y Y, Dai C D, Zhang L 2012Acta Phys.Sin. 61 206203(in Chinese)[李英华, 常敬臻, 李雪梅, 俞宇颖, 戴程达, 张林2012物理学报61 206203]

    [17]

    Xu S X, Zhang W X 1986Introduction to Practical Equation of State(Beijing:Higher Education Press) p249(in Chinese)[徐锡申, 张万箱1986实用物态方程理论导引(北京:高等教育出版社)第249页]

    [18]

    Zhang L, Li Y H, Yu Y Y, Li X M, Ma Y, Gu C G, Dai C D, Cai L C 2011Physica B 406 4163

    [19]

    Khishchenko K V, Lomonosov I V, Fortov V E 1998High Temperatures-High Pressure 30 373

    [20]

    Bushman A V, Lomonosov I V, Fortov V E, Khishchenko K V, Zhernokletov M V, Sutulov Y N 1996Sov.Phys.JETP 82 895

    [21]

    Tang W H, Zhang R Q 2008Introduction of Theory and Computation of Equations of State(Beijing:Higher Education Press) p224(in Chinese)[汤文辉, 张若棋2008物态方程理论及计算概述(北京:高等教育出版社)第224页]

    [22]

    Wu Q, Jing F Q, Li X Z 2005Chin.J.High Pressure Phys. 19 97(in Chinese)[吴强, 经福谦, 李欣竹2005高压物理学报19 97]

    [23]

    Wunderlich B 1962J.Chem.Phys. 37 1207

    [24]

    Jing F Q 1999Introduction to Experimental Equation of State(Beijing:Science Press) p372(in Chinese)[经福谦1999实验物态方程导引(北京:科学出版社)第372页]

  • [1] Xiao Hong-Yu, Li Yong, Bao Zhi-Gang, She Yan-Chao, Wang Ying, Li Shang-Sheng. Effect of catalyst composition on growth and crack defects of large diamond single crystal under high temperature and pressure. Acta Physica Sinica, 2023, 72(2): 020701. doi: 10.7498/aps.72.20221841
    [2] Tian Chun-Ling, Liu Hai-Yan, Wang Biao, Liu Fu-Sheng, Gan Yun-Dan. Phase transition and equation of state of dense liquid nitrogen at high temperature and high pressure. Acta Physica Sinica, 2022, 71(15): 158701. doi: 10.7498/aps.71.20220124
    [3] Zhang Bu-Qiang, Xu Zhen-Yu, Liu Jian-Guo, Yao Lu, Ruan Jun, Hu Jia-Yi, Xia Hui-Hui, Nie Wei, Yuan Feng, Kan Rui-Feng. Temperature measurement method of high temperature and high pressure flow field based on wavelength modulation spectroscopy technology. Acta Physica Sinica, 2019, 68(23): 233301. doi: 10.7498/aps.68.20190515
    [4] Li Yong, Li Zong-Bao, Song Mou-Sheng, Wang Ying, Jia Xiao-Peng, Ma Hong-An. Synthesis and electrical properties study of Ib type diamond single crystal co-doped with boron and hydrogen under HPHT conditions. Acta Physica Sinica, 2016, 65(11): 118103. doi: 10.7498/aps.65.118103
    [5] Fan Xiao-Bing, Chen Jun-Xiang, Xiang Shi-Kai. Complete equation of state based on specific heat. Acta Physica Sinica, 2016, 65(23): 236401. doi: 10.7498/aps.65.236401
    [6] Fang Chao, Jia Xiao-Peng, Yan Bing-Min, Chen Ning, Li Ya-Dong, Chen Liang-Chao, Guo Long-Suo, Ma Hong-An. Effects of nitrogen and hydrogen co-doped on {100}-oriented single diamond under high temperature and high pressure. Acta Physica Sinica, 2015, 64(22): 228101. doi: 10.7498/aps.64.228101
    [7] Jiang Jian-Jun, Li He-Ping, Dai Li-Dong, Hu Hai-Ying, Zhao Chao-Shuai. Raman spectra based pressure calibration of the non-gauge sapphire anvil cell at high temperature and high pressure. Acta Physica Sinica, 2015, 64(14): 149101. doi: 10.7498/aps.64.149101
    [8] Chen Jun-Xiang, Yu Ji-Dong, Li Ping, He Hong-Liang. Universal function of Grneisen γ and the complete equation of state. Acta Physica Sinica, 2015, 64(8): 086401. doi: 10.7498/aps.64.086401
    [9] Zhang Song-Bo, Wang Fang-Biao, Li Fa-Ming, Wen Ge-Hui. HPHT synthesis and magnetic property of -Fe2O3@C core-shell nanorods. Acta Physica Sinica, 2014, 63(10): 108101. doi: 10.7498/aps.63.108101
    [10] Xiao Hong-Yu, Li Shang-Sheng, Qin Yu-Kun, Liang Zhong-Zhu, Zhang Yong-Sheng, Zhang Dong-Mei, Zhang Yi-Shun. Studies on synthesis of boron-doped Gem-diamond single crystals under high temperature and high presure. Acta Physica Sinica, 2014, 63(19): 198101. doi: 10.7498/aps.63.198101
    [11] Lu Zhi-Wen, Zhong Zhi-Guo, Liu Ke-Tao, Song Hai-Zhen, Li Gen-Quan. First-principles calculations of microstructure and thermodynamic properties of the intermetallic compound in Ag-Mg-Zn alloy under high pressure and high temperature. Acta Physica Sinica, 2013, 62(1): 016106. doi: 10.7498/aps.62.016106
    [12] Li Jun-Jun, Zhao Xue-Ping, Tao Qiang, Huang Xiao-Qing, Zhu Pin-Wen, Cui Tian, Wang Xin. Characterization of TiB2 synthesized at high pressure and high temperature. Acta Physica Sinica, 2013, 62(2): 026202. doi: 10.7498/aps.62.026202
    [13] Li Ying-Hua, Chang Jing-Zhen, Li Xue-Mei, Yu Yu-Ying, Dai Cheng-Da, Zhang Lin. Multiphase equation of states of solid and liquid phases for bismuth. Acta Physica Sinica, 2012, 61(20): 206203. doi: 10.7498/aps.61.206203
    [14] Zhang Zhong-Qiang, Ding Jian-Ning, Liu Zhen, Xue Yi-Bin, Cheng Guang-Gui, Ling Zhi-Yong. Analysis of Interfacial Mechanical Properties of Carbon NanotubePolymer Composite. Acta Physica Sinica, 2012, 61(12): 126202. doi: 10.7498/aps.61.126202
    [15] Chen Xuan, An Zhen-Lian, Liu Chen-Xia, Zhang Ye-Wen, Zheng Fei-Hu. Influence of surface fluorination temperature on space charge accumulation in polyethylene. Acta Physica Sinica, 2012, 61(13): 138201. doi: 10.7498/aps.61.138201
    [16] An Zhen-Lian, Liu Chen-Xia, Chen Xuan, Zheng Fei-Hu, Zhang Ye-Wen. Space charge in surface fluorinated polyethylene. Acta Physica Sinica, 2012, 61(9): 098201. doi: 10.7498/aps.61.098201
    [17] Zhao Yan-Hong, Liu Hai-Feng, Zhang Gong-Mu, Zhang Guang-Cai. Pair interactions of detonation products at high pressure and high temperature. Acta Physica Sinica, 2011, 60(12): 123401. doi: 10.7498/aps.60.123401
    [18] Qin Jie-Ming, Wang Hao, Zeng Fan-Ming, Li Jian-Li, Wan Yu-Chun, Liu Jing-He. Synthesis of MgxZn1-xO under high pressure and high temperature. Acta Physica Sinica, 2010, 59(12): 8910-8914. doi: 10.7498/aps.59.8910
    [19] Huang Xiu-Guang, Fu Si-Zu, Shu Hua, Ye Jun-Jian, Wu Jiang, Xie Zhi-Yong, Fang Zhi-Heng, Jia Guo, Luo Ping-Qing, Long Tao, He Ju-Hua, Gu Yuan, Wang Shi-Ji. Experimental study on shock compression properties of polyethylene. Acta Physica Sinica, 2010, 59(9): 6394-6398. doi: 10.7498/aps.59.6394
    [20] Sun Xiao-Wei, Chu Yan-Dong, Liu Zi-Jiang, Liu Yu-Xiao, Wang Cheng-Wei, Liu Wei-Min. Molecular dynamics study on the structural and thermodynamic properties of the zinc-blende phase of GaN at high pressures and high temperatures. Acta Physica Sinica, 2005, 54(12): 5830-5836. doi: 10.7498/aps.54.5830
Metrics
  • Abstract views:  5670
  • PDF Downloads:  253
  • Cited By: 0
Publishing process
  • Received Date:  15 September 2016
  • Accepted Date:  07 December 2016
  • Published Online:  05 March 2017

/

返回文章
返回