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根据DDA算法的有关要求,利用入射波长、粒子形状参数、粒子的有效半径、粒子随波长变化的复折射率等计算石墨烯粒子在红外波段的消光因子和消光系数。
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离散偶极近似方法相对于常见的T矩阵等方法而言,对计算机的要求较低,适用范围更广,程序处理也较为简单,其基本原理如下[13]:
该方法利用大量偶极子组成的阵列来模仿实际粒子,通过求解这些偶极子在入射电磁波照射下的极化度来获得粒子吸收、散射电磁波的性质,粒子对入射电磁场的作用是单个偶极子相互作用累加的结果,可以实现粒子的散射、吸收、消光效率因子(Qsca、Qabs、Qext)和近场等的计算及呈现,且Qext= Qsca+ Qabs。
DDSCAT是由普林斯顿大学的Bruce T. Draine和加利福尼亚大学的Piotr J. Flatau编制的利用DDA算法计算电磁波与任意形状粒子作用引起的电磁吸收和散射问题的Fortran开源程序,可在Windows系统或Linux系统下运行,目前版本为DDSCAT 7.3[14]。
在DDA算法中,粒子的大小用有效半径aeff来描述,也就是与粒子体积相等的球的半径:
$$ {a_{\rm{eff}}} = {\left( {\frac{{{{3}}V}}{{4\pi }}} \right)^{1/3}} = {\left( {\frac{{3N}}{{4\pi }}} \right)^{1/3}}d $$ (1) 式中:V为粒子体积,V=Nd3;N为程序自动划分生成的偶极子的个数;d为偶极子的大小,也就是生成的偶极子立方体的边长。
质量消光系数α是表征烟幕粒子消光性能的重要参数,与消光效率因子Qext存在如下关系:
$$\alpha {\rm{ = }}3{Q_{\rm{ext}}}/(4\rho {a_{\rm{eff}}})$$ (2) 式中:ρ为材料粒子的密度。
利用DDA方法计算一个等效半径为aeff的粒子的消光性能时,偶极子数目N应满足以下条件:
$$N \geqslant \frac{{4\pi }}{3}{\left| m \right|^3}{\left( {k{a_{\rm{eff}}}} \right)^3}$$ (3) 式中:kaeff为粒径参数,kαeff=(2π/λ)αeff,λ为入射波长;|m|为粒子复折射率的模。
利用Windows系统运行下的DDSCAT程序7.3.0版本进行石墨烯粒子红外消光性能的相关数值计算,石墨烯粒子的几何形状可近似为圆片形。在运用DDSCAT 7.3.0程序进行计算时,需要把石墨烯的复折射率数据编译成可执行文件。石墨烯是典型的二维晶体,具有各向异性,选择适合各向异性材料的模型UNIAXICYL进行粒子形状、有效半径等参数设置,选择2个入射波极化方向,取其平均值作为计算结果,并利用粒子的旋转参数计算粒子所有空间取向平均的消光性能。
单层石墨烯的理论厚度仅为0.335 nm,由于实验条件的不同,测量结果也有所差别,一般单层石墨烯的实验测量厚度为0.4~1.0 nm[15]。计算中粒子的尺寸根据石墨烯样品TEM图进行假定。
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计算直径为5 μm、厚度为5 nm的石墨烯圆片粒子在2~14 μm红外波段的消光性能,结果如图5所示。
从图5中可以看出,在2~14 μm波段,石墨烯粒子的质量消光系数保持在2.5 m2/g以上,理论上表明石墨烯具有非常优异的红外消光性能,是粒子对红外散射和吸收共同作用的结果,其中吸收衰减大于散射衰减作用。石墨烯粒子对近红外能够产生较好的衰减效果,是由于与近红外波长相当的粒子产生较强米氏散射引起的衰减[2]。石墨烯粒子对红外表现出较强的吸收衰减,是由于石墨烯具有特殊的电子能带结构,石墨烯的碳原子sp2杂化构成σ键,p轨道上的剩余的一个电子形成大π键,π电子在纳米量级的石墨烯表面可以自由移动,赋予其良好的导电性,在边界条件的约束下受到激发会产生振-转能级跃迁,从而产生新的吸收通道,对红外形成较为强烈的吸收衰减[1]。
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计算不同直径,厚度为5 nm的石墨烯圆片粒子对2、4 μm和10 μm红外辐射的消光性能,结果如图6和图7所示。
图 6 效率因子与石墨烯圆片直径的关系曲线
Figure 6. Relationship between efficiency factor and diameter of round graphene sheet
从图6中可以看出,石墨烯粒子对波长为2、4、10 μm红外的消光效率因子均随着粒子直径的增加而增大,同时粒子也表现出在近红外波段的消光性能较强,明显好于中远红外波段。除石墨烯本身的强吸收作用外,主要是由于在厚度不变的情况下,随着粒子直径的增加,粒子的粒径参数逐渐变大,与近红外波长较为相近,导致其对该波段的米氏散射较强,同时随着粒径参数的增加,粒子的吸收截面变大,有利于对红外的吸收。从图7中可以看出,不同片层直径的石墨烯粒子对于波长为2、4、10 μm红外的质量消光系数范围分别为21.6~17.3 m2/g、17.0~11.5 m2/g、12.4~4.1 m2/g,其中直径0.25~1 μm粒子的质量消光系数最大,直径1~4 μm粒子的质量消光系数随直径的增加逐渐减小,当直径大于4 μm时,石墨烯粒子对各波段红外的消光能力受粒度变化的影响很小。
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计算不同厚度,直径为5 μm的石墨烯圆片粒子对2、4、10 μm红外辐射的消光性能,计算结果如图8和图9所示。
图 8 效率因子与石墨烯圆片厚度的关系曲线
Figure 8. Relationship between efficiency factor and thickness of round graphene sheet
图 9 消光系数与石墨烯圆片厚度的关系曲线
Figure 9. Relationship between extinction coefficient and thickness of round graphene sheet
从图8中可以看出,石墨烯粒子对近红外波段的消光性能好于中远红外波段,对波长为2 μm红外的消光效率因子随着粒子片层厚度的增加而增大,当粒子厚度达到10 nm时,消光效率因子的增加趋于平稳,而对波长为4、10 μm红外的消光效率因子均随着粒子片层厚度的增加而增大。此外,粒子对于波长为2 μm红外的吸收效率因子在厚度4 nm处出现明显的下降趋势,粒子对波长为4 μm红外的吸收效率因子在厚度9 nm处出现不变甚至下降的趋势,而粒子对于波长为10 μm红外的吸收效率因子随厚度增加呈缓慢的增加趋势。研究表明,单层石墨烯的电导率最高,且电导率随着层数的增加而降低并趋于不变[16]。石墨烯对电磁波的吸收衰减主要来源于高电导率引起的介电损耗。随着粒子厚度的增加,电导率有所减小,导致粒子对红外的吸收作用有所减弱,而入射电磁波的频率越高,趋肤深度越小,电磁波在介质中的传输距离越短。因此,2 μm的吸收效率因子比4、10 μm的吸收效率因子更早的表现出较为明显的减小趋势,从而在4 nm处出现了吸收效率因子下降的拐点。从图9中可以看出,不同片层厚度的石墨烯粒子对于波长为2、4、10 μm的红外辐射同样表现出在近、中红外波段具有更大的质量消光系数,而在远红外波段消光能力较弱,这与波长越长越难干扰的规律基本一致。
Complex refractive index and extinction performance of graphene in infrared bands
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摘要: 石墨烯是一种新型二维纳米碳材料,在红外干扰方面具有很大的潜在应用价值,其红外消光特性值得深入研究。文中利用红外椭偏仪测量了石墨烯压片在红外波段的椭偏参数,计算得到其红外波段的复折射率,采用离散偶极近似(DDA)方法计算了石墨烯在2~14 μm波段的效率因子、消光系数与入射波长、粒子直径和厚度的关系。计算结果表明,石墨烯在2~14 μm波段具有优异的红外消光性能,其消光性能主要取决于材料的吸收性能,吸收作用大于散射作用,同时粒子对近、中红外辐射的消光性能明显好于远红外波段;消光效率因子和消光系数随波长增加逐渐减小;消光效率因子随粒子直径的增加而增大,近、中红外波段的消光系数大于远红外波段,其中直径0.25~1 μm粒子的消光系数最大,直径1~4 μm粒子的消光系数随直径增加逐渐减小,直径大于4 μm的粒子对各波段红外的消光能力受粒度变化的影响很小;消光效率因子随粒子片层厚度的增加逐渐增大,近、中红外波段的消光系数随厚度的增加有所减小,而远红外波段的消光系数受粒子厚度变化影响不大。
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关键词:
- 石墨烯 /
- 复折射率 /
- 离散偶极近似(DDA) /
- 红外 /
- 消光系数
Abstract: As a new type of two-dimensional nano-carbon material, graphene has great potential application value in infrared interference, and its infrared extinction characteristics are worthy of in-depth study. In this paper, the ellipsometric parameters of graphene pellet in the infrared bands were measured by infrared ellipsometry, and the complex refractive index was calculated. Subsequent, the relationships between efficiency factors, extinction coefficient and the incident wavelength, diameter, thickness in 2-14 μm wavebands of graphene particles were calculated with discrete dipole approximation (DDA) method. Results show that graphene has excellent infrared extinction performances in 2-14 μm wavebands, and the extinction performance of the particles to near-infrared and mid-infrared radiation is better than that of far-infrared band. The extinction performances mainly depend on the absorption properties of the particles, and the absorption is better than the scattering effect. The extinction efficiency factor and extinction coefficient gradually decrease with the increase of wavelength. The extinction efficiency factor increases with the increase of the particle's diameter. The extinction coefficient in near-infrared and middle-infrared bands is better than that in far-infrared bands, of which the particles with diameter of 0.25-1 μm have the largest extinction coefficient. The extinction coefficient of the particles with diameter of 1-4 μm decreases slowly with the increase of diameter, while the extinction ability of particles with diameter larger than 4 μm is little affected by the change of particle size. The extinction efficiency factor gradually increases with the increase of the thickness of graphene sheet, the extinction coefficient in near-infrared and middle-infrared bands decreases with the increase of the thickness, while the extinction coefficient in far-infrared bands is less affected by the change of particle thickness. -
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