Chapter 12
Carbon-Nanotube Reinforced Polymers
12.1 Introduction
Our goal in this chapter is to develop electromagnetic models for the inspection of
carbon-nanotube reinforced polymers (CNRPs), along the lines of our work with
CFRPs. Electromagnetic models for carbon nanotube structures are of considerable
current interest. In [134] terahertz wave reflection and transmission from carbon
nanotubes are investigated. The interesting feature is that the dielectric properties
are dispersive, i.e., the permittivity and conductivity are frequency dependent. We
will see that shortly in the next section. In the THz regime, the frequency response
is affected by the number of tube walls, thickness, aspect ratio, filling factor, and
geometrical factor during growth. An extended Drude-Lorentzian model, [31], [66],
is used in [134] to simulate the relative dispersive permittivity of carbon nanotubes
at THz frequencies:
r = c −
ω 2
p
ω(ω − jΓ )
+
ω 2
p1
−ω 2 + jωΓ 1 + ω 2
1
,
(12.1)
where c is the dielectric constant at infinite frequency, ω p , ω 1 , and ω p1 are the
electron plasma, phonon, and oscillator frequency, respectively. Γ and Γ 1 are the
relaxation rate and spectral width, respectively. If we write r = + σ/j ω, where
and σ are real, then it is easy to show that
= c −
ω 2
p
ω 2 + Γ 2 +
ω 2
p1 (−ω 2 + ω 2
1 )
(−ω 2 + ω 2
1 ) 2 + ω 2 Γ 2
1
σ
0
=
ω 2
p Γ
(ω 2 + Γ 2 )
+
Γ 2
1 ω 2
p1 ω 2
(−ω 2 + ω 2
1 ) 2 + ω 2 Γ 2
1
.
(12.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_12
315
Carbon-Nanotube Reinforced Polymers
12.1 Introduction
Our goal in this chapter is to develop electromagnetic models for the inspection of
carbon-nanotube reinforced polymers (CNRPs), along the lines of our work with
CFRPs. Electromagnetic models for carbon nanotube structures are of considerable
current interest. In [134] terahertz wave reflection and transmission from carbon
nanotubes are investigated. The interesting feature is that the dielectric properties
are dispersive, i.e., the permittivity and conductivity are frequency dependent. We
will see that shortly in the next section. In the THz regime, the frequency response
is affected by the number of tube walls, thickness, aspect ratio, filling factor, and
geometrical factor during growth. An extended Drude-Lorentzian model, [31], [66],
is used in [134] to simulate the relative dispersive permittivity of carbon nanotubes
at THz frequencies:
r = c −
ω 2
p
ω(ω − jΓ )
+
ω 2
p1
−ω 2 + jωΓ 1 + ω 2
1
,
(12.1)
where c is the dielectric constant at infinite frequency, ω p , ω 1 , and ω p1 are the
electron plasma, phonon, and oscillator frequency, respectively. Γ and Γ 1 are the
relaxation rate and spectral width, respectively. If we write r = + σ/j ω, where
and σ are real, then it is easy to show that
= c −
ω 2
p
ω 2 + Γ 2 +
ω 2
p1 (−ω 2 + ω 2
1 )
(−ω 2 + ω 2
1 ) 2 + ω 2 Γ 2
1
σ
0
=
ω 2
p Γ
(ω 2 + Γ 2 )
+
Γ 2
1 ω 2
p1 ω 2
(−ω 2 + ω 2
1 ) 2 + ω 2 Γ 2
1
.
(12.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_12
315