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弹性碰撞截面是研究粒子间相互作用的关键参数之一, 有助于揭示气体绝缘的微观机理. 本文基于 R 矩阵理论计算了24种气体分子在0—15 eV下的弹性碰撞截面, 提取了最低共振态能量、峰值等截面特征参数. 对比了SF6, CF2Cl2, i-C3F7CN碰撞截面的计算值与实验值, 首次给出了i-C3F7CN在0—1 eV的低能碰撞截面; 分析了F取代和碳链长度对截面参数的影响, 最终研究了截面特征与绝缘强度间的关联性. 结果表明, 计算得到的各分子最低shape共振态能量与现有研究数据一致, 均方误差为0.181; F取代时, 共振态能量逐渐增大、峰值逐渐减小; 碳链延长则与之相反. 分子最低共振态能量、截面峰值与气体绝缘强度有较强关联, 分子的最低共振态能量越低, 对应的截面峰值越大, 其绝缘强度越高. 通过分析分子中低能弹性碰撞截面特征, 可定性评估气体绝缘强度.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.
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Keywords:
- insulation strength /
- R-matrix method /
- cross-section /
- resonances
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图 1 R矩阵内外区划分示意图
Fig. 1. Schematic diagram of dividing the inner and outer of the R-matrix method.
图 2 SF6分子shape共振和core-excited共振
Fig. 2. SF6 molecular shape resonance and core-excited resonance.
图 3 SF6计算结果 (a) 弹性碰撞截面; (b)本征相位曲线图
Fig. 3. Calculation results of SF6: (a) Elastic collision cross-section; (b) eigenphases diagrams.
图 4 CF2Cl2计算结果 (a) 弹性碰撞截面; (b)本征相位曲线图
Fig. 4. Calculation results of CF2Cl2: (a) Elastic collision cross-section; (b) eigenphases diagrams.
图 5 i-C3F7CN计算结果 (a) 弹性碰撞截面; (b)本征相位曲线图
Fig. 5. Calculation results of i-C3F7CN: (a) Elastic collision cross-section; (b) eigenphases diagrams.
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
Fig. 6. Calculation results of F-substituted molecules: (a) Elastic collision cross-section; (b) eigenphases diagrams.
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
Fig. 8. Trend of cross-section characteristic parameters with insulation strength: (a) F-substituted molecules; (b) carbon chain extended molecules; (c) 24 molecular scatter plots.
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
Fig. 7. Calculation results of carbon chain extended molecules: (a) Elastic collision cross-section; (b) eigenphases diagrams.
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 
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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)Er 分子 最低共振态
位置/eV实验值或
计算值/eV峰值/
(10–16 cm2)Er 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
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