1. Introduction

Polycaprolone (PCL) and polylactide (PLA) are widely used in biomedicine for wound covering and prosthetics, including tooth implantation[1, 2]. The main advantages of these materials are their biocompatibility and slow degradation accompanied by release of water and carbon dioxide; the latter fact makes these polymers a perfect ecologically pure packing material. Therefore, the study of the electrical and dielectric properties of these materials, in particular, the absorption of electromagnetic waves of different frequency bands, is of great scientific and practical interest. Data on the preparation process and material characterization, including dielectric properties of PCL and PLA, are presented elsewhere [316]; for example, data on the dielectric properties of pure PCL and PLA at frequencies from to 10⁶ Hz[3,4], and data on the properties of PLA in the frequency band 0.5–10 GHz[5]. However, there are no data on the dielectric properties of PCL and PLA and their nanocomposites in the millimeter (MM) wave band. The importance of these data is associated, in particular, with a recent increase in the application of MM waves in medicine [29]. We have measured for the first time the dielectricproperties of crosslinked poly-ε-caprolone (cPCL) and PLA, as well as their composites with carbon nanotubes (CNTs), in the frequency range from 85 to 118 GHz and in the range of temperatures from 20 to 90℃.

2. Materials

1. The samples of crosslinked poly-ε-caprolone (cPCL) and its nanocomposites were fabricated at the Southwest Jiaotong University, Chengdu, PRC [26] by the reaction of PCL diol with methacrylic anhydride [27].

2. The samples of PLA and its nanocomposites were fabricated at the École Nationale Supérieure de Chimie de Lille, France. The synthesis of PLA was done by reactive extrusion via ring opening polymerization of L,L-lactide using a continuous single-stage process [28].

3. Measurement Methods

The propagation constant of electromagnetic waves traveling in an infinite medium with complex refractive index is given by

(1)

where the decay constant (Np/m) and the phase constant are related to the real n and imaginary κ parts of the refractive index by the formulas

(2)

(3)

Here is the wavenumber in vacuum and λ is the wavelength in vacuum. Thus, having determined and experimentally, we can find the parameters n and κ of the medium under test.

The measurements were carried out in the range of frequencies from 85 to 118 GHz by a panoramic VSWR and attenuation meter based on an RG4-14 oscillator. The block-diagram of the setup is shown in Figure 1.

Figure 1. Block diagram of the setup

Here, 1 is a panoramic VSWR and attenuation meter based on an RG4-14 oscillator, 2 is a directional coupler for the incident wave, 3 is a directional coupler for the reflected wave, 4 is a waveguide bend, 5 is a transmitting horn, 6 is a receiving horn, 7 is a directional coupler for the transmitted wave, 8 are detector sections, 9 is a matched load, 10 is a test sample of thickness l, and 11 is an indicator.

The measurement setup is implemented on a rectangular waveguide of cross section of 2.4-by-1.2 mm; the cross section of horn 5 is 10-by-10 mm, and the cross section of horn 6, 14-by-14 mm. The increased cross section of the receiving horn allows one to receive almost all the power propagating in a spacing of 50 mm between the horns, where the transverse dimension of the field increases due to diffraction.

We measured the power transmission T and reflection R coefficients of the materials 24, 25. For a sample thickness of l, which actually guarantees the absence of interference in a sample (for absorption in a sample of more than 5–7 dB), the coefficients T and R are related to the propagation constants by the formulas

(4)

(5)

where is the propagation constant in vacuum (in air).

From (4) we can determine the decay constant α in the medium:

(6)

Substituting this value of into (2), we obtain the imaginary part κ of the refractive index of the sample:

(7)

To determine the real part n of the refractive index of the sample, we apply (5), which in our case is transformed to

(8)

Solving this equation, we derive a formula for finding n:

(9)

The complex dielectric constant of the medium is related to its complex refractive index by the formula , from which we obtain an expression for determining the real ε₁ and imaginary ε₂ parts of the dielectric constant of the sample under test:

(10)

(11)

4. Measurement Results

4.1. Investigation of Samples of cPCL and Its Nanocomposites

Table 1. Dielectric properties of CPLC and nanocomposites in the frequency band 90–100 GHz Sample no. n ε1 ε2 T, oC 1 1.7 0.0030 2.9 0.010 25 1.8 0.0045 3.2 0.015 45 2 2.7 0.13 7.1 0.7 25 2.7 0.16 7.1 0.8 45 3 2.7 0.003 7.1 0.016 25 2.7 0.005 7.1 0.029 45 4 2.3 0.010 5.3 0.05 25 2.4 0.017 5.8 0.08 45

We have measured the dielectric characteristics of four samples: 1, pure сPCL; 2, сPCL containing 5% of multiwall CNTs (MCNTs); 3, сPCL containing 15% of Fe₃O₄; and 4, cPCL containing 3.75% of MCNTs and 11.25% of Fe₃O₄.

The dielectric properties of cPCL were measured in the temperature interval T = 25–45℃. In [3], when studying pure cPCL at frequency of 100 kHz, the authors observed an increase in ε₂ with temperature in the interval from 35 to 50℃. In our experiments carried out in the frequency band of GHz, we also observed an increase in ε₂ in this temperature interval with a maximum at T = 45℃ in all the samples. The results of these measurements are presented in Table 1. Note that, within the measurement accuracy (3% for n and 15% for κ), we did not observe any dielectric dispersion in this frequency band.

Table 1 shows that the maximal increase in κ and ε₂ is caused by the introduction of carbon nanotubes into cPCL. The introduction of Fe₃O₄ did not lead to a noticeable change in the absorption of the samples.

4.2. Investigation of Samples of PLA and Its Nanocomposites

The results of the measurements of the dielectric properties of PLA and its nanocomposites are presented in Table 2. Here sample 1 is pure PLA, sample 2 is PLA prepared with 1% of MWNT of diameter 40 – 60 nm, and length of 515 m with melamine and sample 3, PLA prepared with 1% of the same MWNT without melamine.

The measurements were carried out in the same frequency band as those of the cPCL samples but in a larger temperature interval (T = 25–90℃), because, in the temperature interval of 50–90℃, the authors of [3] observed an increase in the ε₂ of pure PLA with a maximum at 85℃. We also observed an increase in ε₂ in all the samples (pure PLA and its nanocomposites) in this temperature interval.

Table 2. Dielectric properties of PLA and its nanocomposites at frequency of f = 96 GHz Sample no. n ε1 ε2 T, oC 1 1.66 <0.01 2.76 0.01 25 1.66 0.02 2.76 0.06 90 2 4.0 0.40 15.70 3.20 26 4.0 0.44 15.60 3.50 90 3 3.7 0.69 13.40 5.10 24 3.7 0.71 13.30 5.30 90

Table 2 shows that, for the same concentration of MWNTs, the sample with melamine exhibits much lower absorption, which can be attributed to the formation of aggregates of nanotubes when preparing a sample in the absence of melamine. This assumption has been confirmed by the electron microscope examination of the samples carried out at École Nationale Supérieure de Chimie de Lille, France, by Professor S. Bourbigot.

Moreover, in the case of sample 3, we revealed a dispersion of ε₁ and ε₂: both these functions decrease as frequency increases. For example, at frequency of 96 GHz (see Table 2), these parameters amount to 13.4 and 5.1 at 24℃ and 13.3 and 5.3 at 90℃. At frequency of 116 GHz, ε₁ and ε₂ took the respective values of 12.4 and 4.6 at 24℃ and 12.3 and 4.8 at 90℃. This fact points to the Debye character of dispersion in sample 3, the Debye frequency being lower than the frequency at which the measurements are carried out.

5. Discussion

5.1. Samples of cPCL and Its Nanocomposites

Earlier we have investigated the dielectric characteristics of samples 14 at frequencies from to 2 10⁶Hz by a BDS40 broadband dielectric spectrometer (Novocontrol) [10]. The results of these measurements are presented in Figures 25.

Figure 2. Real part of permittivity of cPCL and its nanocomposites at frequencies Hz

Nanocomposites have much greater ε₁ than pure cPCL at frequencies of 0.110 Hz. For all samples, ε₁ measured at frequencies about 3•10⁶ Hz is greater than the values of ε₁ obtained in our MM wave measurements (ε₁ = 713 at 3•10⁶ Hz for nanocomposites and 6 for pure cPCL). This means that there is a marked dispersion of ε₁ in all samples at frequencies from 3•10⁶ Hz to 80 GHz.

Figure 3. Imaginary part of permittivity of cPCL and its nanocomposites at frequencies Hz

Figure 3 shows that, at frequencies about•10⁶ Hz, all the samples have practically the same ε₂ = 0.1. Samples 1 and 3 have much less ε₂ (Table 1). On the other hand, the values of ε₂ of samples 2 and 4, which contain multiwall CNTs, are much greater than those in Figure 3. This means that multiwall CNTs exhibit marked dispersion of ε in all the samples at frequencies from 3•10⁶ Hz to 80 GHz.

Figures 4 and 5 present the imaginary parts of permittivity of samples 2 and 1 at frequencies 10^-13•10⁶ Hz without regard to conductivity σ.

Figure 4. Imaginary part of permittivity of sample 2 at frequencies Hz without regard to conductivity σ

Figure 5. Imaginary part of permittivity of sample 1 at frequencies Hz without regard to conductivity σ

In the MM wave band (Table 1), the contribution of to ε₂ is much less. On the contrary, for sample 2 with multiwall CNTs, ε₂ in the MM waves range is high due to the dielectric dispersion in multiwall CNTs at frequencies between 3•10⁶ Hz and 80 GHz.

5.2. Samples of PLA and Its Nanocomposites

These samples were investigated by TEM microscopy at the École Nationale Supérieure de Chimie de Lille, France, by professor S. Bourbigot.

Figures 6 and 7 present 200 nm TEM microscope images of the samples of PLA+1%MWNT (without melamine) and PLA+1%MWNT (with melamine), respectively.

The sample of PLA+1%MWNT (with melamine) is characterized by a much more uniform distribution of MWNT without aggregation of nanoparticles compared with the sample of PLA+1%MWNT (without melamine). This is the reason for the difference in ε₂ of these two samples in Table 2.

Measurements of the dielectric properties of PLA+1%MWNT (without melamine) and PLA+1%MWNT (with melamine) by the resonance method at frequency of 11 GHz [10] confirmed the difference between the absorption in these two samples.

The dielectric permittivity of PLA+1%MWNT (without melamine) at frequency of 11 GHz is ₁ = 9.16 and ₂ = 3.23.

The dielectric permittivity of a PLA+1%MWNT (with melamine) at frequency of 11 GHz is ₁ = 4.36 and ₂ = 0.30.

Figure 6. TEM microscopy picture of PLA+1%MWNT (without melamine) sample

Figure 7. TEM microscopy picture of PLA+1%MWNT (with melamine) sample

6. Conclusions

We have carried out the measurements of the dielectric properties of biocompatible and biodegradable crosslinked polycaprolone and polylactide polymers and their nanocomposites at frequencies from 85 to 118 GHz and in the temperature interval in which the samples show considerable dependence of absorption of electromagnetic waves on temperature. We have found that the complex dielectric permittivity of PCL and its nanocomposites increases with temperature in the interval from 40 to 50℃, while that of PLA and its nanocomposites increases in the interval from 85 to 90℃. The samples of PLA with carbon nanotubes prepared with melamine show much lower absorption compared with the same samples prepared without melamine. The latter fact can be attributed to the formation of clusters of nanotubes in these samples.

These materials may find application, in particular, in medical diagnostics and therapy with the use of MM waves [29].

ACKNOWLEDGEMENTS

We are grateful to Professor S. Bourbigot for supplying and TEM microscopy investigation of PLA samples and useful discussions.

This work was supported by the Russian Foundation for Basic Research, project nos. 10-02-13310-RT_OMN and 11-02-93965-YuAR_a.