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惰性气体原子间相互作用势比较研究

孙素蓉 王海兴

引用本文:
Citation:

惰性气体原子间相互作用势比较研究

孙素蓉, 王海兴

A comparison of interatomic potentials for noble gases

Sun Su-Rong, Wang Hai-Xing
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  • 原子间相互作用势是预测惰性气体输运性质的必要输入条件. 文章对描述惰性气体原子间相互作用的Lennard-Jones势、指数排斥势、Hartree-Fock-Dispersion-B (HFD-B)势和唯象势的形式和特点进行了分析. 基于Chapman-Enskog方法, 计算得到了惰性气体在300–5000 K温度区间内基于四种原子相互作用势的黏性和热导率, 并与文献报道的实验和理论计算结果进行了比较. 研究结果表明, 基于Hartree-Fock排斥理论与色散理论发展起来的HFD-B势能够合理反映惰性气体原子相互作用的趋势与特征, 因而可以较好地预测惰性气体的宏观输运性质.
    Prediction of transport properties of noble gases requires the calculation of collision integrals, which depend on interatomic potentials as the input. However the accuracy of transport properties depends largely on the accuracy of interaction potentials. So different interatomic potentials of noble gases are compared in order to get the accurate transport properties. The forms and characteristics of Lennard-Jones, exponential repulsive, Hartree-Fock-Dispersion-B (HFD-B), and phenomenological model potentials that are used to describe the atomic interactions between noble gases are analyzed in this paper. Then the calculation method of transport properties is presented. Viscosities and thermal conductivities of noble gases based on these four potentials are obtained using Chapman-Enskog method in the temperature range for computation from 300 to 5000 K. It can be seen from the results that the interaction potentials have a great influence on the calculated results of transport properties. There are great differences between the results obtained using different interaction potentials. These differences of the calculated results can be explained according to the performance of interaction potentials. Results calculated with Lennard-Jones potential are always much lower in the high temperature range due to its overestimated repulsive part, and the exponential repulsive potential gives unreasonable results at low temperatures because there is no attractive well in this potential. Therefore, the accurate interatomic potentials for noble gases can be obtained only by comparing the calculated results with published experimental and theoretical data of other researchers. It can be found that the results obtained by HFD-B potential agree well with previously experimental and theoretical data. So it is apparent that the HFD-B potential in light of Hartree-Fock repulsion and dispersion theory can provide a realistic description of the trends and features of interatomic potentials, allowing accurate theoretical calculations to be made for transport properties of noble gases.
    • 基金项目: 国家自然基金(批准号: 11275021, 11072020)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11275021, 11072020).
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    Pirani F, Albertı M, Castro A, Teixidor M M, Cappelletti D 2004 Chem. Phys. Lett. 394 37

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    Bruno D, Catalfamo C, Capitelli M, Colonna G, Pascale O De, Diomede P, Gorse C, Laricchiuta A, Longo S, Giordano D, Pirani F 2010 Phys. Plasmas 17 112315

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    Miller E J, Sandler S I 1973 Phys. Fluids 16 491

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    Sandler S I, Mason E A 1969 Phys. Fluids 12 71

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    [45]

    Devoto R S 1973 Phys. Fluids 16 616

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    Devoto R S 1966 Phys. Fluids 9 1230

    [47]

    Ghorui S, Heberlein J V R, Pfender E 2008 Plasma Chem. Plasma P 28 553

    [48]

    Ghorui S, Heberlein J V R, Pfender E 2007 Plasma Chem. Plasma P 27 267

    [49]

    Murphy A B 2000 Plasma Chem. Plasma P 20 279

    [50]

    Dawe R A, Smith E B 1970 J. Chem. Phys. 52 693

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    Maitland G C, Smith E B 1972 J. Chem. Eng. Data 17 150

    [52]

    Jody B J, Saxena S C, Nain V P S, Aziz R A 1977 Chem. Phys. 22 53

    [53]

    Bich E, Millat J, Vogel E 1990 J. Phys. Chem. Ref. Data 19 1289

    [54]

    Kestin J, Knierim K, Mason E A, Najafi B, Ro S T, Waldman M 1984 J. Phys. Chem. Ref. Data 13 229

    [55]

    Jain P C, Saxena S C 1974 J. Phys. E: Sci. Instrum. 7 1023

    [56]

    Guevara F A, McInteer B B, Wageman W E 1969 Phys. Fluids 12 2493

    [57]

    Murphy A B, Arundell C J 1994 Plasma Chem. Plasma P 14 451

    [58]

    Saxena V K, Saxena S C 1968 Chem. Phys. Lett. 2 44

    [59]

    Chen S H P, Saxena S C 1975 Mol. Phys. 29 455

    [60]

    Nain V P S, Aziz R A, Jain P C, Saxena S C 1976 J. Chem. Phys. 65 3242

    [61]

    Saxena V K, Saxena S C 1969 J. Chem. Phys. 51 3361

    [62]

    Goldblatt M, Wageman W E 1971 Phys. Fluids 14 1024

    [63]

    London F 1930 Quantum 10

    [64]

    London F 1937 Trans. Faraday Soc. 33 8b

  • [1]

    Chapman S, Cowling T G 1970 The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge: Cambridge University Press)

    [2]

    Hirschfelder J O, Curtiss C F, Bird R B 1954 Molecular Theory of Gases and Liquids (New York: John Wiley and Sons, Inc)

    [3]

    Pirani F, Albertı M, Castro A, Teixidor M M, Cappelletti D 2004 Chem. Phys. Lett. 394 37

    [4]

    Maitland G C, Rigby M, Smith E B, Wakeham W A 1981 Intermolecular Forces: Their Origin and Determination (Oxford: Clarendon Press)

    [5]

    Amdur I, Harkness A L 1954 J. Chem. Phys. 22 664

    [6]

    Amdur I, Mason E A 1954 J. Chem. Phys. 22 670

    [7]

    Amdur I, Mason E A 1955 J. Chem. Phys. 23 2268

    [8]

    Amdur I, Mason E A 1955 J. Chem. Phys. 23 415

    [9]

    Amdur I, Mason E A 1956 J. Chem. Phys. 25 624

    [10]

    Jones J E 1924 Proc. Royal Soc. London Series A 106 46

    [11]

    Murphy A B 1995 Plasma Chem. Plasma P 15 279

    [12]

    Aziz R A, Nain V P S, Carley J S, Taylor W L, McConville G T 1979 J. Chem. Phys. 70 4330

    [13]

    Aziz R A, Meath W J, Allnatt A R 1983 Chem. Phys. 78 295

    [14]

    Aziz R A, Slaman M J 1989 Chem. Phys. 130 187

    [15]

    Aziz R A 1976 J. Chem. Phys. 65 490

    [16]

    Aziz R A 1993 J. Chem. Phys. 99 4518

    [17]

    Devoto R S, Li C P 1968 J. Plasma Phys. 2 17

    [18]

    Kannappan D, Bose T K 1980 Phys. Fluids 23 1473

    [19]

    Aubreton J, Elchinger M F, Rat V, Fauchais P 2004 J. Phys. D: Appl. Phys. 37 34

    [20]

    Wang H X, Sun S R, Chen S Q 2012 Acta Phys. Sin. 61 195203 (in Chinese) [王海兴, 孙素蓉, 陈士强 2012 物理学报 61 195203]

    [21]

    Murphy A B 1997 IEEE Trans. Plasma Sci. 25 809

    [22]

    Devoto R S 1969 AIAA J. 7 199

    [23]

    Murphy A B, Tam E 2014 J. Phys. D: Appl. Phys. 47 295202

    [24]

    Bose T K 1988 Prog. Aerosp. Sci. 25 1

    [25]

    Amdur I, Mason E A 1958 Phys. Fluids 1 370

    [26]

    Monchick L 1959 Phys. Fluids 2 695

    [27]

    Liuti G, Pirani F 1985 Chem. Phys. Lett. 122 245

    [28]

    Cambi R, Cappelletti D, Liuti G, Pirani F 1991 J. Chem. Phys. 95 1852

    [29]

    Bruno D, Catalfamo C, Capitelli M, Colonna G, Pascale O De, Diomede P, Gorse C, Laricchiuta A, Longo S, Giordano D, Pirani F 2010 Phys. Plasmas 17 112315

    [30]

    Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F 2007 Chem. Phys. 338 62

    [31]

    Ahlrichs R, Penco R, Scoles G 1977 Chem. Phys. 19 119

    [32]

    Hepburn J, Scoles G, Penco R A 1975 Chem. Phys. Lett. 36 451

    [33]

    Aziz R A, Chen H H 1977 J. Chem. Phys. 67 5719

    [34]

    Tang K T, Norbeck J M, Certain P R 1976 J. Chem. Phys. 64 3063

    [35]

    Douketis C, Scoles G, Marchetti S, Zen M, Thakkar A J 1982 J. Chem. Phys. 76 3057

    [36]

    Song B, Wang X P, Wu J T, Liu Z G 2011 Acta Phys. Sin. 60 033401 (in Chinese) [宋渤, 王晓坡, 吴江涛, 刘志刚 2011 物理学报 60 033401]

    [37]

    Aziz R A, Janzen A R, Moldover M R 1995 Phys. Rev. Lett. 74 1586

    [38]

    Aziz R A, Slaman M J 1986 Mol. Phys. 58 679

    [39]

    Aziz R A, Slaman M J 1986 Mol. Phys. 57 825

    [40]

    Hirschfelder J O, Taylor M H, Kihara T, Rutherford R 1961 Phys. Fluids 4 663

    [41]

    Miller E J, Sandler S I 1973 Phys. Fluids 16 491

    [42]

    Sandler S I, Mason E A 1969 Phys. Fluids 12 71

    [43]

    Mason E A 1957 J. Chem. Phys. 27 75

    [44]

    Curtiss C F, Hirschfelder J O 1949 J. Chem. Phys. 17 550

    [45]

    Devoto R S 1973 Phys. Fluids 16 616

    [46]

    Devoto R S 1966 Phys. Fluids 9 1230

    [47]

    Ghorui S, Heberlein J V R, Pfender E 2008 Plasma Chem. Plasma P 28 553

    [48]

    Ghorui S, Heberlein J V R, Pfender E 2007 Plasma Chem. Plasma P 27 267

    [49]

    Murphy A B 2000 Plasma Chem. Plasma P 20 279

    [50]

    Dawe R A, Smith E B 1970 J. Chem. Phys. 52 693

    [51]

    Maitland G C, Smith E B 1972 J. Chem. Eng. Data 17 150

    [52]

    Jody B J, Saxena S C, Nain V P S, Aziz R A 1977 Chem. Phys. 22 53

    [53]

    Bich E, Millat J, Vogel E 1990 J. Phys. Chem. Ref. Data 19 1289

    [54]

    Kestin J, Knierim K, Mason E A, Najafi B, Ro S T, Waldman M 1984 J. Phys. Chem. Ref. Data 13 229

    [55]

    Jain P C, Saxena S C 1974 J. Phys. E: Sci. Instrum. 7 1023

    [56]

    Guevara F A, McInteer B B, Wageman W E 1969 Phys. Fluids 12 2493

    [57]

    Murphy A B, Arundell C J 1994 Plasma Chem. Plasma P 14 451

    [58]

    Saxena V K, Saxena S C 1968 Chem. Phys. Lett. 2 44

    [59]

    Chen S H P, Saxena S C 1975 Mol. Phys. 29 455

    [60]

    Nain V P S, Aziz R A, Jain P C, Saxena S C 1976 J. Chem. Phys. 65 3242

    [61]

    Saxena V K, Saxena S C 1969 J. Chem. Phys. 51 3361

    [62]

    Goldblatt M, Wageman W E 1971 Phys. Fluids 14 1024

    [63]

    London F 1930 Quantum 10

    [64]

    London F 1937 Trans. Faraday Soc. 33 8b

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出版历程
  • 收稿日期:  2014-10-16
  • 修回日期:  2015-03-20
  • 刊出日期:  2015-07-05

惰性气体原子间相互作用势比较研究

  • 1. 北京航空航天大学宇航学院, 北京 100191
    基金项目: 国家自然基金(批准号: 11275021, 11072020)资助的课题.

摘要: 原子间相互作用势是预测惰性气体输运性质的必要输入条件. 文章对描述惰性气体原子间相互作用的Lennard-Jones势、指数排斥势、Hartree-Fock-Dispersion-B (HFD-B)势和唯象势的形式和特点进行了分析. 基于Chapman-Enskog方法, 计算得到了惰性气体在300–5000 K温度区间内基于四种原子相互作用势的黏性和热导率, 并与文献报道的实验和理论计算结果进行了比较. 研究结果表明, 基于Hartree-Fock排斥理论与色散理论发展起来的HFD-B势能够合理反映惰性气体原子相互作用的趋势与特征, 因而可以较好地预测惰性气体的宏观输运性质.

English Abstract

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