Influence of carbon nanofibers electric conductivity on infrared extinction capability

Using method of moment, the calculating model of electric current distributing and scattered electric field for carbon nanofibers is established in this paper. Based on it, the expression of absorption cross section, scattering cross section and extinction cross section are got. The relationship between infrared extinction cross section of carbon nanofiber and electrical conductivity is analyzed and calculated by using Matlab. The results show that the infrared extinction cross section increases with electrical conductivity increase and peak value appeares when wavelength is longer than the length of carbon nanofiber. The electrical conductivity on peak value is related to wavelength. Keywordscarbon nanofibers; infrared extinction; absorption; scattering; extinction coefficient


INTRODUCTION
Smoke is a simple and effectual means of laser passive interference, and the infrared smoke materials should be taken on the better infrared extinction capability. Carbon nanofiber is a new kind of materials with good capability of electromagnetic wave absorption. It not only has the characteristic of common gas phase growth carbon fiber, but also has the characteristic of low density, high electrical conductivity, large specific surface and high specific intensity. In infrared band, the length and wavelength of carbon nanofiber is the same order. It can generate not only scattering attenuation, but also absorption attenuation. In modern warfare, carbon nanofiber has been a new kind of infrared smoke interference materials. To explore the applications of carbon nanofibers in passive interference by smoke screen, the integral equation of induced cueernt for carbon nanofibers is established based the electromagnetic field theory.

The integral equation for carbon nanofiber
To carbon nanofiber, the radius is much shorter than the length and incidence wavelength. The induced current inside carbon nanofiber is uniform distribution along the axisl direction and no component is in radial direction. According to the axial symmetry, the axisl direction current can replace the total induced current I. Suppose the length direction as Z axis, the scattered field produced by the axisl direction current in r point is following: is Green function.
The carbon nanofiber produces the conduction current by field: , nei E is the internal field, V is carbon nanofiber conductivity; the dielectric property of the materials can also produce polarization current[1] then the total induced current is: The relationship between the induced current and the internal field of the carbon nanofiber is: The field and internal field of the materials is the same along the Z axis.The field is composed by incidence field Ei and scattered field Es and the boundary condition is

carbon nanofiber extinction cross section
In far field condition, According to formula (1), the carbon nanofiber scattered field is

K P H
To unit amplitude incidence wave, the scattered field can be obtained from above and the carbon nanofiber scattering cross section is

Calculation and discussion
The code of carbon nanofiber induced current, scattered field and extinction cross section are programmed based on Matlab. The relationship between infrared extinction cross section of carbon nanofiber and electrical conductivity is analyzed and calculated. The calculation conditions are: 10, 50 , 5 , 50 r a nm L m N H P . The calculation result is as followed Fig.1.
The results show that when the wavelength is 2μm, extinction cross section increases fast with electrical conductivity increase. When , carbon nanofiber absorbs the incidence wave more than the scattered wave. When , extinction effect is mainly the scattering effect, absorbing effect is weak. When the wavelength is 5μm, the extinction cross section peak value appeares near the electrical conductivity . The absorbing effect is tapered with electrical conductivity increasing, the scattering effect is enhanced and the extinction cross section reduces little. When the electrical conductivity is near 7 1 1 10 m : , the extinction cross section keeps constant. When incidence wavelength is 14μm and 20μm, the extinction cross section has peak value. It is , the extinction effect mainly is scattering effect. So, the longer the wavelength is, the larger the electrical conductivity span of absorbing extinction is. Fig.1 Relationship between electrical conductivity and extinction cross section

Conclusion
According to the electrical conduction and dielectric characters of carbon nanofiber, the electromagnetic field integral equation is built. The integral equation is solved and the expression of absorption cross section, scattering cross section and extinction cross section are got. The relationship between infrared extinction cross section of carbon nanofiber and electrical conductivity is analyzed and calculated based on Matlab. The results show that the infrared extinction cross section increases with electrical conductivity increase and peak value appeares when wavelength is longer than the length of carbon nanofiber. The electrical conductivity on peak value is related to wavelength. The analysis results can supply the theoretical basis for IR smoke materials in preparation and selection.