<i><b>R</b></i>-matrix theory based calculation of elastic cross-sections of gas molecules and analysis of its correlation with insulation strength

Zhang Xing-Yi; Yang Shuai; Shang Shu-Xiang; Wu Shao-Bo; Wang Hang; Xiao Ji-Xiong

doi:10.7498/aps.73.20241355

Abstract

The elastic collision cross-section is a key parameter in the study of inter-particle interactions, and it helps to reveal the microscopic mechanism of gas insulation. For this reason, based on the R -matrix theory, the elastic collision cross-sections of 24 gas molecules at 0–15 eV are calculated , and cross-section characteristic parameters of the lowest resonance state energy and its peak are extracted. Then the calculated and experimental values of SF₆, CF₂Cl₂, and i-C₃F₇CN cross-sections are compared, and the low-energy cross-section data of i-C₃F₇CN at 0–1 eV are given. Furthermore the effects of Cl-substitution and carbon chain length on the cross-section parameters are analysed. Finally the correlation between cross-section characteristic parameters and insulation strength is investigated. The results show that the lowest shape resonance state energy for each molecule is in better agreement with the existing data within a mean square error of 0.181. For the F-substitution, the resonance energy gradually increases but the peak value gradually decreases, which the carbon chain extension is the opposite to: the resonance state energy gradually decreases but the peak value gradually increases. The lowest resonance energy and peak value are strongly related to the insulation strength. The lower its lowest resonance energy and the larger the corresponding peak value, the higher the molecular insulation strength is. The relevant data can theoretically supplement existing experimental data. This study provides low energy cross-section properties of various insulating gas molecules, which can be useful for qualitatively evaluating the insulating properties of gas molecules and quickly screening SF₆ alternative gases.

Keywords:

Authors and contacts

Hubei Engineering Research Center for Safety Monitoring of New Energy and Power Grid Equipment, Hubei University of Technology, Wuhan 430068, China

Corresponding author: Yang Shuai, ys3254@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52007053) and the Natural Science Foundation of Hubei Province, China (Grant No. 2019CFB144).

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References

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[2]	田双双, 张晓星, 肖淞, 卓然, 王邸博, 邓载韬, 李祎 2018 中国电机工程学报 38 3125 Google Scholar Tian S S, Zhang X X, Xiao S, Zhuo R, Wang D B, Deng Z T, Li Y 2018 Proc. CSEE 38 3125 Google Scholar
[3]	胡世卓, 周文俊, 郑宇, 喻剑辉, 张天然, 王凌志 2019 高电压技术 45 3562 Google Scholar Hu S Z, Zhou W J, Zheng Y, Yu J H, Zhang T R, Wang L Z 2019 High Voltage Eng. 45 3562 Google Scholar
[4]	熊嘉宇, 张博雅, 李兴文, 杨韬, 徐宁 2021 中国电机工程学报 41 759 Google Scholar Xiong J Y, Zhang B Y, Li X W, Yang T, Xu N 2021 Proc. CSEE 41 759 Google Scholar
[5]	郑宇, 周文俊, 朱太云, 任书波, 喻剑辉 2023 高电压技术 49 946 Google Scholar Zheng Y, Zhou W J, Zhu T Y, Ren S B, Yu J H 2023 High Voltage Eng. 49 946 Google Scholar
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[7]	张震, 林莘, 余伟成, 徐建源, 张佳, 苏镇西 2020 高电压技术 46 250 Google Scholar Zhang Z, Lin X, Yu W C, Xu J Y, Zhang J, Su Z X 2020 High Voltage Eng. 46 250 Google Scholar
[8]	王宝山, 余小娟, 侯华, 周文俊, 罗运柏 2020 电工技术学报 35 21 Google Scholar Wang B S, Yu X J, Hou H, Zhou W J, Luo Y B 2020 Trans. Chin. Electr. Soc. 35 21 Google Scholar
[9]	张闹闹, 杨帅, 刘关平, 王航, 肖集雄 2022 高电压技术 48 4323 Google Scholar Zhang N N, Yang S, Liu G P, Wang H, Xiao J X 2022 High Voltage Eng. 48 4323 Google Scholar
[10]	刘关平, 杨帅, 张闹闹, 王航, 肖集雄 2022 高电压技术 48 2208 Google Scholar Liu G P, Yang S, Zhang N N, Wang H, Xiao J X 2022 High Voltage Eng. 48 2208 Google Scholar
[11]	Zhang X Y, Yang S, Liu G P, Wu R, Wu S B 2023 J. Mol. Model. 29 224 Google Scholar
[12]	李鑫涛, 林莘, 徐建源, 李璐维, 陈会利 2017 电工技术学报 32 42 Google Scholar Li X T, Lin S, Xu J Y, Li L W, Chen H L 2017 Trans. Chin. Electr. Soc. 32 42 Google Scholar
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[28]	Fabrikant I I, Eden S, Mason N J 2017 Adv. Atom. Mol. Opt. Phy. 66 545 Google Scholar
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[35]	Goswami B, Antony B 2014 RSC Adv. 4 30953 Google Scholar
[36]	Limao-Vieira P, Blanco F, Oller J C, Muñoz A, Pérez J M, Vinodkumar M, García G, Mason N J 2005 Phys. Rev. A 71 2720 Google Scholar
[37]	Christophorou L G, Olthoff J K 2000 J. Phys. Chem. Ref. Data 29 267 Google Scholar
[38]	Kennerlya R E, Bonham R A, McMillan M 1979 J. Chem. Phys. 70 2039 Google Scholar
[39]	Makochekanwa C, Kimura M, Sueoka O 2004 Phys. Rev. A 70 022702 Google Scholar
[40]	Dababneh M S, Hsieh Y F, Kauppila W E 1988 Phys. Rev. A 38 1207 Google Scholar
[41]	Wang C L, Bridgette C, Wang Y, Sun H, Tennyson J 2021 J. Phys. B-At. Mol. Opt. 54 025202 Google Scholar
[42]	夏涵怡, 杨帅, 王航, 肖集雄 2023 高电压技术 49 4563 Google Scholar Xia H Y, Yang S, Wang H, Xiao J X 2023 High Voltage Eng. 49 4563 Google Scholar
[43]	Christophorou L G, Olthoff J K, Wang Y 2009 J. Phys. Chem. Ref. Data 26 1205 Google Scholar
[44]	Jones R K 1986 J. Chem. Phys. 84 813 Google Scholar
[45]	Underwood-Lemons T, Winkler D C, Tossell J A, Moore J H 1994 J. Chem. Phys. 100 9117 Google Scholar
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[51]	Ehrhardt H, Langhans L, Linder F 1968 Phys. Rev. 173 222 Google Scholar
[52]	Hien X P, Jeon B, Tuan A D 2013 J. Phys. Soc. Jap. 82 03430 Google Scholar
[53]	Ishii I, McLaren R, Hitchcock A P 1988 Can. J. Chem. 66 2104 Google Scholar
[54]	Thynne J C J, Harland P W 1973 Int. J. Mass Spectrom 11 399 Google Scholar
[55]	Burrow P D, Modelli A, Chiu N S 1982 J. Chem. Phys. 77 2699 Google Scholar
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Cited By

图 1 R矩阵内外区划分示意图

Figure 1. Schematic diagram of dividing the inner and outer of the R-matrix method.

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图 2 SF₆分子shape共振和core-excited共振

Figure 2. SF₆ molecular shape resonance and core-excited resonance.

DownLoad: Full-Size Img PowerPoint

图 3 SF₆计算结果　(a) 弹性碰撞截面; (b)本征相位曲线图

Figure 3. Calculation results of SF₆: (a) Elastic collision cross-section; (b) eigenphases diagrams.

DownLoad: Full-Size Img PowerPoint

图 4 CF₂Cl₂计算结果　(a) 弹性碰撞截面; (b)本征相位曲线图

Figure 4. Calculation results of CF₂Cl₂: (a) Elastic collision cross-section; (b) eigenphases diagrams.

DownLoad: Full-Size Img PowerPoint

图 5 i-C₃F₇CN计算结果　(a) 弹性碰撞截面; (b)本征相位曲线图

Figure 5. Calculation results of i-C₃F₇CN: (a) Elastic collision cross-section; (b) eigenphases diagrams.

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图 6 F取代分子的计算结果　(a) 弹性碰撞截面; (b)本征相位曲线图

Figure 6. Calculation results of F-substituted molecules: (a) Elastic collision cross-section; (b) eigenphases diagrams.

DownLoad: Full-Size Img PowerPoint

图 8 截面特征参数随绝缘强度变化的趋势图　(a) F取代; (b) 延长碳链; (c) 24 种分子散点图

Figure 8. Trend of cross-section characteristic parameters with insulation strength: (a) F-substituted molecules; (b) carbon chain extended molecules; (c) 24 molecular scatter plots.

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图 7 碳链延长分子的计算结果　(a) 弹性碰撞截面; (b)本征相位曲线图

Figure 7. Calculation results of carbon chain extended molecules: (a) Elastic collision cross-section; (b) eigenphases diagrams.

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表 1 0—1.0 eV范围i-C₃F₇CN的碰撞截面

Table 1. Collision cross-section of i-C₃F₇CN in the range of 0–1.0 eV.

能量/eV	碰撞截面/ (10^–16 cm²)	能量/eV	碰撞截面/ (10^–16 cm²)
0.01	658.58	0.40	71.53
0.03	227.43	0.45	64.89
0.05	143.86	0.50	62.12
0.07	106.45	0.55	59.14
0.09	88.12	0.60	57.83
0.10	84.86	0.65	55.08
0.12	95.24	0.70	52.86
0.15	230.07	0.75	52.25
0.16	262.53	0.80	51.21
0.17	241.62	0.85	49.85
0.19	179.53	0.90	49.37
0.21	135.73	0.95	48.59
0.23	115.26	1.00	47.95
0.25	105.81	1.05	47.36
0.27	94.79	1.10	49.97
0.30	90.09	1.14	83.43
0.35	79.55	1.15	71.23

DownLoad: CSV

表 2 基于R矩阵计算的分子碰撞截面特征参数与分子相对绝缘强度数据

Table 2. Characteristic parameters of molecular cross-sections based on R-matrix method and relative insulating strength.

分子	最低共振态位置/eV	实验值或计算值/eV	峰值/ (10^–16 cm²)	E_r	分子	最低共振态位置/eV	实验值或计算值/eV	峰值/ (10^–16 cm²)	E_r
CO₂	3.33	3.14^[49]	35.08	0.35	CF₄	8.02	8.87^[44]	27.67	0.41
N₂	1.81	2.32^[50]	65.81	0.38	C₂F₆	4.90	4.60^[53]	39.10	0.78
CO	1.62	1.50^[51]	73.01	0.40	C₃F₈	3.73	3.34^[53]	51.50	0.98
BF₃	3.46	3.88^[52]	22.23	0.40	C₄F₁₀	2.81	2.37^[53]	68.10	1.36
N₂O	1.03	2.34^[49]	100.21	0.47	C₅F₁₂	1.68	1.64^[53]	76.69	1.75
SF₆	0.72	0.85^[42]	60.66	1.00	SO₂	4.40	2.87^[49]	19.88	1.00
i-C₃F₇CN	0.16	0.14^[42]	262.53	2.20	CFCl₃	0.20	0.26^[42]	241.77	1.72
CF₃Cl	1.65	2.00^[44]	47.67	0.53	CF₂Cl₂	0.96	1.02^[42]	63.59	1.10
CCl₄	0.12	~0.0^[43]	306.07	2.36	CH₃CN	2.73	2.82^[47]	64.72	0.80
C₂F₅CN	0.69	1.40^[54]	109.81	2.18	CH₂Cl₂	0.98	1.23^[55]	81.98	0.60
CH₃Cl	3.14	3.45^[55]	33.96	0.31	CHCl₃	0.33	0.35^[55]	184.43	1.67
C₂H₂	2.65	2.60^[56]	54.70	0.42	c-C₄F₈	0.55	0.45^[57]	73.36	1.25

DownLoad: CSV

[1]	满林坤, 邓云坤, 肖登明 2017 高电压技术 43 788 Google Scholar Man L K, Deng Y K, Xiao D M 2017 High Voltage Eng. 43 788 Google Scholar
[2]	田双双, 张晓星, 肖淞, 卓然, 王邸博, 邓载韬, 李祎 2018 中国电机工程学报 38 3125 Google Scholar Tian S S, Zhang X X, Xiao S, Zhuo R, Wang D B, Deng Z T, Li Y 2018 Proc. CSEE 38 3125 Google Scholar
[3]	胡世卓, 周文俊, 郑宇, 喻剑辉, 张天然, 王凌志 2019 高电压技术 45 3562 Google Scholar Hu S Z, Zhou W J, Zheng Y, Yu J H, Zhang T R, Wang L Z 2019 High Voltage Eng. 45 3562 Google Scholar
[4]	熊嘉宇, 张博雅, 李兴文, 杨韬, 徐宁 2021 中国电机工程学报 41 759 Google Scholar Xiong J Y, Zhang B Y, Li X W, Yang T, Xu N 2021 Proc. CSEE 41 759 Google Scholar
[5]	郑宇, 周文俊, 朱太云, 任书波, 喻剑辉 2023 高电压技术 49 946 Google Scholar Zheng Y, Zhou W J, Zhu T Y, Ren S B, Yu J H 2023 High Voltage Eng. 49 946 Google Scholar
[6]	宋佳洁, 李晓昂, 吕玉芳, 袁勰雨, 张乔根, 苏镇西 2020 高电压技术 46 1372 Google Scholar Song J J, Li X A, Lü Y F, Yuan X Y, Zhang Q G, Su Z X 2020 High Voltage Eng. 46 1372 Google Scholar
[7]	张震, 林莘, 余伟成, 徐建源, 张佳, 苏镇西 2020 高电压技术 46 250 Google Scholar Zhang Z, Lin X, Yu W C, Xu J Y, Zhang J, Su Z X 2020 High Voltage Eng. 46 250 Google Scholar
[8]	王宝山, 余小娟, 侯华, 周文俊, 罗运柏 2020 电工技术学报 35 21 Google Scholar Wang B S, Yu X J, Hou H, Zhou W J, Luo Y B 2020 Trans. Chin. Electr. Soc. 35 21 Google Scholar
[9]	张闹闹, 杨帅, 刘关平, 王航, 肖集雄 2022 高电压技术 48 4323 Google Scholar Zhang N N, Yang S, Liu G P, Wang H, Xiao J X 2022 High Voltage Eng. 48 4323 Google Scholar
[10]	刘关平, 杨帅, 张闹闹, 王航, 肖集雄 2022 高电压技术 48 2208 Google Scholar Liu G P, Yang S, Zhang N N, Wang H, Xiao J X 2022 High Voltage Eng. 48 2208 Google Scholar
[11]	Zhang X Y, Yang S, Liu G P, Wu R, Wu S B 2023 J. Mol. Model. 29 224 Google Scholar
[12]	李鑫涛, 林莘, 徐建源, 李璐维, 陈会利 2017 电工技术学报 32 42 Google Scholar Li X T, Lin S, Xu J Y, Li L W, Chen H L 2017 Trans. Chin. Electr. Soc. 32 42 Google Scholar
[13]	孙安邦, 李晗蔚, 许鹏, 张冠军 2017 物理学报 66 195101 Google Scholar Sun A B, Li H W, Xu P, Zhang G J 2017 Acta Phys. Sin. 66 195101 Google Scholar
[14]	Lucchese R R, Gianturco F A 1996 Int. Rev. Phys. Chem. 15 429 Google Scholar
[15]	Berrington K A, Eissner W B, Norrington P H 1995 Comput. Phys. Commun. 92 290 Google Scholar
[16]	Burke P G, Noble C J, Burke V M 2006 Adv. Atom. Mol. Opt. Phy. 54 237 Google Scholar
[17]	Schneider B I, Rescigno T N 1988 Phys. Rev. A 37 3749 Google Scholar
[18]	Takatsuka T, McKoy V 1981 Phys. Rev. A 24 2473 Google Scholar
[19]	Meyer H D 1994 Chem. Phys. Lett. 223 465 Google Scholar
[20]	Wang K D, Meng J, Liu Y F, Sun J F 2015 J. Phys. B-At. Mol. Opt. 48 155202 Google Scholar
[21]	Epée E D M, Motapon O, Darby-Lewis D, Tennyson J 2017 J. Phys. B-At. Mol. Opt. 50 115203 Google Scholar
[22]	Alexandra L, Jimena D G 2019 J. Chem. Phys. 150 064307 Google Scholar
[23]	Carr J M, Galiatsatos P G, Gorfinkiel J D, Harvey A G, Lysaght M A, Madden D, Mašín Z, Plummer M, Tennyson J, Varambhia H N 2012 Eur. Phys. J. D 66 58 Google Scholar
[24]	Tennyson J 2010 Phys. Rep. 491 29 Google Scholar
[25]	Wigner E P 1946 Phys. Rev. 70 15 Google Scholar
[26]	Burke P G, Hibbert A, Robb W D 1971 J. Phys. B-At Mol. Opt. 4 153 Google Scholar
[27]	Bai J Z, Ban Y, Bian J G, Cai X, Chang J F, Chen H F, Chen H S, Chen J, Chen J, Chen J C, Chen Y B, Chi S P 2003 Phys. Rev. Lett. 91 022001 Google Scholar
[28]	Fabrikant I I, Eden S, Mason N J 2017 Adv. Atom. Mol. Opt. Phy. 66 545 Google Scholar
[29]	Thodika M, Mackouse N, Matsika S 2020 J. Phys. Chem. A 124 9011 Google Scholar
[30]	Schulz G J 1973 Rev. Mod. Phys. 45 423 Google Scholar
[31]	CCCBDB http://cccbdb.nist.gov [2024-9-25]
[32]	Frisch M J, Trucks G W, Schlegel H B 2017 Gaussian 16 Users Reference (Wallingford USA: Gaussian) pp33–57
[33]	Chen R, Zhang L, Luo X L, Liang G M 2021 Comput. Theor. Chem. 1203 11348 Google Scholar
[34]	Bach R D, Schlegel H B 2021 J. Phys. Chem. A. 125 5014 Google Scholar
[35]	Goswami B, Antony B 2014 RSC Adv. 4 30953 Google Scholar
[36]	Limao-Vieira P, Blanco F, Oller J C, Muñoz A, Pérez J M, Vinodkumar M, García G, Mason N J 2005 Phys. Rev. A 71 2720 Google Scholar
[37]	Christophorou L G, Olthoff J K 2000 J. Phys. Chem. Ref. Data 29 267 Google Scholar
[38]	Kennerlya R E, Bonham R A, McMillan M 1979 J. Chem. Phys. 70 2039 Google Scholar
[39]	Makochekanwa C, Kimura M, Sueoka O 2004 Phys. Rev. A 70 022702 Google Scholar
[40]	Dababneh M S, Hsieh Y F, Kauppila W E 1988 Phys. Rev. A 38 1207 Google Scholar
[41]	Wang C L, Bridgette C, Wang Y, Sun H, Tennyson J 2021 J. Phys. B-At. Mol. Opt. 54 025202 Google Scholar
[42]	夏涵怡, 杨帅, 王航, 肖集雄 2023 高电压技术 49 4563 Google Scholar Xia H Y, Yang S, Wang H, Xiao J X 2023 High Voltage Eng. 49 4563 Google Scholar
[43]	Christophorou L G, Olthoff J K, Wang Y 2009 J. Phys. Chem. Ref. Data 26 1205 Google Scholar
[44]	Jones R K 1986 J. Chem. Phys. 84 813 Google Scholar
[45]	Underwood-Lemons T, Winkler D C, Tossell J A, Moore J H 1994 J. Chem. Phys. 100 9117 Google Scholar
[46]	Zhang J W, Sinha N, Jiang M, Wang H G, Li Y D, Antony B, Liu C L 2022 IEEE T. Dielect. El. In. 29 1005 Google Scholar
[47]	Hitchcock A P, Tronc M, Modelli A 1989 J. ChemInform. 20 3068 Google Scholar
[48]	Devins J 1980 IEEE T. El. In. 15 81 Google Scholar
[49]	Sanche L, Schulz G J 1973 J. Chem. Phys. 58 479 Google Scholar
[50]	Berman M, Hernan E, Cederbaum L S 1983 Phys. Rev. A 28 1363 Google Scholar
[51]	Ehrhardt H, Langhans L, Linder F 1968 Phys. Rev. 173 222 Google Scholar
[52]	Hien X P, Jeon B, Tuan A D 2013 J. Phys. Soc. Jap. 82 03430 Google Scholar
[53]	Ishii I, McLaren R, Hitchcock A P 1988 Can. J. Chem. 66 2104 Google Scholar
[54]	Thynne J C J, Harland P W 1973 Int. J. Mass Spectrom 11 399 Google Scholar
[55]	Burrow P D, Modelli A, Chiu N S 1982 J. Chem. Phys. 77 2699 Google Scholar
[56]	Jordan D K, Burrow D P 1987 Chem. Rev. 87 557 Google Scholar
[57]	Harland P W, Thynne J C J 1957 Int. J. Mass Spectrom 10 11 Google Scholar
[58]	Fieller E C, Hartley H O, Pearson E S 1957 Biometrika 44 470 Google Scholar

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[7]	Zhang Hong-Ying, Chen De-Ying, Lu Zhen-Zhong, Fan Rong-Wei, Xia Yuan-Qin. Numerical calculation of laser-induced collisional energy transfer in Ba-Sr system. Acta Physica Sinica, 2008, 57(12): 7600-7605. doi: 10.7498/aps.57.7600
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R-matrix theory based calculation of elastic cross-sections of gas molecules and analysis of its correlation with insulation strength

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R-matrix theory based calculation of elastic cross-sections of gas molecules and analysis of its correlation with insulation strength

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