碳纳米管非均匀氢等离子体微波吸收的数值模拟

碳纳米管非均匀氢等离子体微波吸收的数值模拟

刘保星，彭志华，谢凝钰，谢卫平，胡林华，张亚楠

(南华大学数理学院，湖南 衡阳 421001)

摘要：提出碳纳米管非均匀氢等离子体薄膜的层状介电模型，探讨等离子体密度分布对碳纳米管氢等离子体微波吸收的影响，运用转移矩阵法求解电磁波的传播方程，计算不同条件下碳纳米管氢等离子体薄膜在0~30 GHz频段的微波衰减系数。随着氢等离子体中自由电子密度分布非均匀性系数a的增加，微波衰减吸收峰值|Attmax|和强烈微波吸收的频宽均明显增大，吸收峰向高频方向移动。结果表明，增大等离子体密度分布的非均匀性，能显著改善碳纳米管氢等离子体薄膜的微波吸收性能。

关键词：碳纳米管；氢等离子体；层状介电结构；转移矩阵法；微波吸收

中图分类号：TB 383.2

基金项目：湖南省自然科学

作者简介：刘保星(1989-)，男，山东济宁人，南华大学数理学院教师，硕士研究生。

通讯作者：彭志华(1962-)，男，湖南邵东人，博士，教授，硕士生导师。

作者简介：蒲斌斌(1992-)，男,甘肃定西人，陇西县首阳中学教师。

Numerical Simulation for Microwave Absorption of Non-homogeneous Hydrogen Plasma in Carbon Nanotubes

LIU Bao-xing,PENG Zhi-hua,XIE Ning-yu,XIE Wei-ping,HU Lin-hua,ZHANG Ya-nan

(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

Abstract:A layered structure model is proposed for microwave dielectric property of non-homogeneous hydrogen plasma in carbon nanotubes film.The influences of non-homogeneous density distribution of hydrogen plasma on microwave absorption of hydrogen plasma in carbon nanotubes films are investigated.Using the transfer matrix method for solving electromagnetic wave propagation equation,the microwave attenuation coefficients of the film are calculated in the frequency range of 0~30 GHz under different conditions.It is found theoretically that with the increase of hydrogen plasma non-homogeneity coefficients a,the maximum attenuation absorption |Attmax| and the frequency bandwidth of strong microwave absorption by the film increases markedly.The absorption peak shifts towards the high frequencies withincreasing.The numerical results show that as the non-homogeneity degree of the hydrogen plasma increases,the absorption of microwave energy will be enhanced in carbon nanotube films.

Key words:carbon nanotube;hydrogen plasma;layered dielectric structure;transfer matrix method;microwave absorption

1引言

现代军事隐身和民用微波防护对吸波材料提出了越来越高的要求。质量轻、力学性能好、具有特殊电磁性能的碳纳米管及其复合材料的合成，为吸波材料开辟了一个新的领域[1-30]。初步研究表明，碳纳米管氢等离子体是具有广泛应用前景的微波吸波与屏蔽材料。

本文在课题组对碳纳米管均匀氢等离子体微波吸收特性研究成果[16-19]的基础上，深入探讨了碳纳米管薄膜中氢等离子体分布的非均匀性对微波吸收的影响。研究结果对于碳纳米管氢等离子体微波吸收剂的优化设计和制备很有意义。

2理论模型

考虑到碳纳米管薄膜对氢气物理吸附的边缘效应[31]，将碳纳米管氢等离子体薄膜视为层状介电结构的介质。薄膜的介电特性在薄膜平面的Y轴和Z轴方向上是均匀的，用ε表示薄膜的电容率，则ε/Z=0,ε/Y=0。而薄膜的介电特性在垂直薄膜平面的X轴方向近似于分层分布。将碳纳米管氢等离子体薄膜沿X轴方向划分为N等份，当N足够大时，可认为每层介质的介电特性是均匀的，如图1所示。

图1　碳纳米管氢等离子体薄膜的层状介电模型

(1)

上式中，v是入射微波的频率、νe为氢等离子体中电子碰撞的有效频率，氢等离子体频率

设碳纳米管氢等离子体薄膜中自由电子的密度分布函数为

(2)

其中n0为碳纳米管氢等离子体的平均自由电子密度，a表示氢等离子体中自由电子密度分布的非均匀性。a越大，自由电子密度分布的非均匀程度越高。

(3)

m=1，2，3…，N

用k表示波数，则对应于Xm-1

(4)

在该薄层介质中，电场传播方程为

(5)

而入射电磁波在碳纳米管非均匀氢等离子体薄膜中的能量衰减为[16]

(6)

其中：

(7)

(8)

3数值计算及分析

(9)

设

(10)

运用转移矩阵可得

(11)

其中

(12)

(13)

当N取值足够大时，即可得到出射微波参数Am的精确解。

设d=0.01m,n0=2.181×1017·m-3,ve=22.0 GHz，对于不同的a值，计算得到碳纳米管氢等离子体薄膜在0~30 GHz频率范围内的微波衰减系数，如图2所示。

取a=1.25，在v=2.63 GHz处有最大衰减吸收|Attmax|=37.24 dB·cm-1。取a=1.05和a=1.125，衰减吸收峰分别出现在2.50 GHz处和2.56 GHz处，对应的|Attmax|分别为33.82 dB·cm-1和35.89 dB·cm-1。当氢等离子体中自由电子密度分布的非均匀性系数a从1.05增大到1.25时，衰减吸收超过30.00 dB·cm-1的频宽从3.11 GHz(1.11~4.22 GHz)增加到11.26 GHz(0.50~11.76 GHz)。显然，随着a的增大，衰减吸收峰向高频方向移动。当a=1(即氢等离子体中的自由电子密度均匀分布)时，在v=2.45 GHz处有衰减吸收峰值|Attmax|=31.26 dB·cm-1。模拟结果表明，等离子体密度分布非均匀程度的增大有利于碳纳米管氢等离子体薄膜对微波的吸收。

图2　a取不同值时，碳纳米管氢等离子体薄膜的微波衰减系数随入射波频率变化的关系

4结论

基于碳纳米管氢等离子体薄膜层状介电模型假设，应用转移矩阵法，数值模拟了碳纳米管非均匀氢等离子体的微波吸收特性。当碳纳米管氢等离子体密度非均匀性系数a从1增加到1.25时，衰减吸收峰值|Attmax|从31.26 dB·cm-1增加到37.24 dB·cm-1，微波衰减系数超过30.00 dB·cm-1的频宽从2.79 dB·cm-1[16]增加到11.26 dB·cm-1。增大等离子体密度分布的非均匀性系数a，能显著提高碳纳米管氢等离子体薄膜的微波吸收性能。取a=1(即氢等离子体中的自由电子密度均匀分布)和n0=2.181×1017·m-3，在2.45 GHz处有衰减吸收峰值|Attmax|=31.26 dB·cm-1，数值结果与已获得的实验数据[9，11]相吻合。

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