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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.
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Keywords:
- Helmholtz free energy /
- complete equation of state /
- polyethylene /
- high pressure and high temperature
[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]
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[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]
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