Terahertz absorption in graphite nanoplatelets/polylactic acid composites

The electromagnetic properties of composite materials based on poly(lactic) acid (PLA) filled with graphite nanoplatelets (GNP) were investigated in the microwave (26–37 GHz) and terahertz (0.2–1 THz) frequency ranges. The maximum of the imaginary part of the dielectric permittivity was observed close to 0.6 THz for composites with 1.5 and 3 wt.% of GNP. The experimental data of complex dielectric permittivity of GNP/PLA composites was modelled using the Maxwell-Garnett theory. The effects of fine dispersion, agglomeration, and percolation in GNP-based composites on its electromagnetic constitutive parameters, presence, and position of THz absorption peak are discussed on the basis of the modeling results and experimental data. The unique combination of conductive and geometrical parameters of GNP embedded into the PLA matrix below the percolation threshold allow us to obtain the THz-absorptive material, which may be effectively used as a 3D-printing filament.


Introduction
Progress in the research of modern composites, as well as the achievement of very promising mechanical and electro magnetic (EM) properties, are often related to use of various types of nanostructural carbon fillers. Many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13] showed that nanocarbon inclusions can significantly affect the EM response of composites and provide an effi cient way to tune their properties in a wide frequency range. Especially in the last decade, there has been rapid develop ment in the fields of graphene THz devices, metamaterials and absorbers [14][15][16].
A GNP is the high aspect ratio and high conductive mat erial having a form of thin flakes of graphite. The typical diameter and thickness of GNPparticles provided by dif ferent manufacturers vary in the range D = 2-20 μm, and H = 4-20 nm. The high aspect ratio, as well as the high elec trical conductivity of GNP particles, generally define their EM properties in the microwave and THz ranges and make these carbon additives very promising for solving problems related to effective broadband absorption and shielding of EM radiation. In particular, PLA filled with GNP, carbon nano tubes, and other nanocarbons is one of the best candidates to produce layered structures or structures with different sophisticated geometries via additive manufacturing (see for example [25][26][27]).
Recent works have showed [21,24] that the EM properties of polymer composites based on a GNP may be effectively described in the microwave range using the MaxwellGarnett (MG) theory for randomly dispersed conductive ellipsoids in a dielectric matrix. The local fields, as well as the depo larization factors for ellipsoids, can be easily calculated by analytical formulae [28]. In this case, the ellipsoid is a uni versal particle-it may be considered in the limited case as a sphere, needle, and disk, and widely used for the prediction of EM properties of composites from statics and up to the optical range [29,30].
In the present communication, we will consider the poly mer 3Dprinting suitable composites with GNP content below the percolation threshold and assume that GNP parti cles may be approximated as flattened conductive ellipsoids. This assumption is in good agreement with previous similar investigations in the microwave range [19,21,24]. Moreover, the lateral dimensions, as well as the effective conductivity of GNP particles, make them especially interesting for the tera hertz frequency range. The results of simple modelling based on the MG theory presented below predict the high absorp tion ability of such composites near 1 THz. A similar peak for carbon nanotube composites was predicted and exper imentally observed in [31,32].
The terahertz absorption maximum near 2.2 THz was recently observed experimentally in polyethylenebased com posites with different sp 2 carbon inclusions [22], associated according to quantum chemistry calculations with particular features in the vibrational spectra of graphene. We discuss an alternative origin of the absorption peak related to the unique combination of the geometrical and conductive properties of GNPs. Moreover, in the present communication, we focus first of all on composites suitable for 3Dprinting, which are particularly important for practical applications. This paper is organized as follows: the second sec tion describes details of modelling based on the Maxwell Garnett theory. This formalism is then applied to explain the experimental data for the EM response of the GNP/PLA composites. The third section presents the fabrication of the composite materials and their experimental characteriza tion. The experimental results related to the electromagnetic response of GNP/PLA composites in the microwave and tera hertz ranges, comparison of the theoretical predictions and the experimental observations are presented in section 4. The last section of the manuscript is devoted to the discussion of the presented results, together with the effects of percolation and agglomeration in real composites. The conclusion part sum marizes the general results most important to the further prac tical usage of the materials studied.

Maxwell-Garnett modelling
Let us consider the mixture of conductive randomly oriented ellipsoidal particles in the dielectric matrix. In the case of a low concentration of filler (below 10%), the MG approach [29] is often applied to predict the dielectric permittivity of such a composite material. In the classical form of MG theory, the effective dielectric permittivity of a mixture is dependent on the dielectric permittivity of inclusions. But usually nano carbon fillers (carbon nanotubes, onionlike carbon, GNPs, carbon black and their agglomerates) are characterized in terms of polarizability α [31,32] (here, we use the definition of polarizability as a coefficient connecting electric field E and a dipole moment of inclusion p = αε 0 E, ε 0 = 8.85 × 10 12 F m −1 is vacuum permittivity, where the units for polarizability are (m 3 )). Throughout the paper, MG formulas are written in terms of inclusions polarizability and the effective dielectric permittivity of a composite is [29] (all equations below were written using SI units and assume an exp[iωt − ikz] harmonic time convention): where ε m is the dielectric permittivity of the matrix, n is the volume concentration of ellipsoids with semiaxes a, b, c, α i is the polarizability of inclusions in the i = a, b, c directions, N i is the depolarization factor along the iaxis, and V is the volume of ellipsoid. The polarizability of conductive (i.e. with static conductivity σ) ellipsoid surrounded by media with the dielectric permittivity ε m is [29] where ν is the frequency. The depolarization factors N i for i = a, b, c directions may be calculated as [28]: It is important to note again that the above presented MG equations are written in terms of polarizability of inclu sions, which is more suitable for a nanoscaled carbon filler. Nevertheless, a similar and equivalent MG approach in terms of dielectric permittivity of inclusions was successfully applied for the prediction and description of EM properties of GNP/epoxy composites in the 8-18 GHz range [21,24].
Due to strong dependence (see equation (2)) on the depo larization factor, the polarizability of conductive inclusion is maximal in the direction parallel to the largest lateral dimen sion. Particularly, the frequency dependence of polarizability α b = α c of the flattened conductive ellipsoidal particle with diameter D = 2b = 2c = 1.4 μm, thickness H = 2a = 17 nm and static conductivity σ = 9000 S m −1 in vacuum calculated using equation (2) is presented in figure 1. The polarizability α a have significantly smaller values in comparison with α b , and their contribution at low frequencies (up to 5 THz) can be neglected. Below, by default, we will consider and discuss the polarizability of inclusions along the largest lateral dimension.
Let us analyse figure 1 together with equation (2). First of all, we see that in the static limit when ν → 0, the polarizability is the real number. The value of equa tion (2) converges to classical values of static polarizability of the conductive particle in the external electric field parallel to the largest lateral size of the particle. For example [28], in the case of a sphere of radius R, it is α s = 4πR 3 , in the case of a disk of diameter D (much larger than thickness H) α d = 2D 3 /3, and in the case of a needle of length L (which is much larger than radius R) It is important to note that the static polarizability is proportional to the largest lateral dimension raised to the third power, and the volume V of the particle used in equation (1) is proportional to R 3 , D 2 and L in the case of spheres, disks, and needles, corre spondingly. Therefore, we clearly see that the high aspect ratio particles (disks and needles) much more significantly affect the EM properties of the composite in comparison to the spheres with the same volume fraction.
Next, from examination of figure 1, we can see that the imaginary part of polarizability has a maximum at the critical frequency ν c . Above this frequency Im(α), which is related to the Ohmic losses in conductive particles, starts to domi nate. The physical origin of them is caused by the delay in the molecular polarization of filler with respect to a changing electric field in a composite medium. The trivial solve of equation ∂ ∂ν Im(α i (ν, σ)) = 0 gives the simple expression for critical frequency According to equation (1), the maximum of Im(α) for con ductive particles originates from the corresponding maximum of Im(ε eff ) in the composite. For example, for composite materials based on the spherical graphite particles (σ = 120 kS m −1 ) in the dielectric matrix with ε m = 2.5, the maximum of Im(ε eff ) is located in a very high frequency range-near 360 THz. Nevertheless, from equation (4), it is clear that by modifying the conductivity of filler, their shape and aspect ratio, it is possible to smoothly change the position of the Im(ε eff ) maximum and shift them to much lower frequencies.
Particularly, the flake structure of GNP, as well as the smaller value of conductivity (∼10 kS m −1 [21,24]), expects the posi tion of the absorption maximum near 1 THz (figure 1).
It is important to note that very often the experimental data of ε for composites below the percolation threshold may be satisfactorily fitted by the Debye relaxation formula [4,33]: where τ is the relaxation time, ε s is the static permittivity, and ε ∞ denotes the limiting highfrequency permittivity. The fitting parameters τ , ε s , ε ∞ are obtained from experi ments. It is important to note that the expressions for di electric permit tivity ε eff calculated using equation (1) and ε D calculated using equation (5) have a similar form after simplification, and the parameters of the Debye model may be retrieved as ε s = lim The is easy to calculate from the critical frequency ν c . Now let us apply equations (1) and (2) for a typical size and conductivity of GNP fillers and check how they can modify the dielectric permittivity of the composite. From the electromagnetic point of view, the most important parameters are the aspect ratio and conductivity of particles. The typical frequency dependence of the dielectric permittivity of the composite, including 1.5 wt.% of particles with conductivity σ = 9000 S m −1 and various aspect ratios (AR = diameter/ thickness = b/a) is presented figure 2.
From figure 2(a), we can clearly see that the AR of the filler particles plays a crucial role in the EM response of the composite. The increase of AR leads to a significant increase of both components of dielectric permittivity ε = ε − iε . For visualization of limits for ε and ε obtained within the presented here modelling, the same curves are displayed in the Cole-Cole representation in the inset of figure 2(a). Additionally, in accordance with equation (4), the absorption maximum shifts to the lowfrequency region.
A typical frequency dependence of the dielectric permit tivity of the composite including 1.5 wt.% of particles with AR = 80 and various conductivity σ is presented in figure 2(b). From this figure, we can clearly see that a decrease in conduc tivity leads to a decrease of position of the Im(ε) peak. This is again the consequence of equation (4). Nevertheless, the change of σ leads to a shifting of the peak but the shape of dielectric permittivity spectra remains the same. All curves from figure 2(b) in the Cole-Cole representation are equiva lent (they are plotted in figure 2(a) inset by red color). It is important to note that a possible way to change the conduc tivity is by doping of the carbon filler during the manufac turing process.
All theoretical observations prove the possibility to observe a terahertz absorption maximum in composites with well dis persed GNP particles inside the polymer matrix. These results are in good agreement with [22,31,32,34]. Application of the presented formulae for composites with typical GNP param eters (aspect ratio, size, conductivity, etc) shows that these samples are good for terahertz absorption, due to the presence of ε maximum near 1 THz.

Fabrication of composites and their characterization
In the present communication, we used a polymer matrix suitable for further 3D printing applications. Particularly, the poly(lactic) acid polymer (PLA) Ingeo 700 1D from Nature Works, USA, was used as a matrix polymer for the preparation of composite materials samples. GNPs produced from Times Nano (TNGNPs), China, were used as fillers for the prep aration of nanocomposites [35]. The source GNPparticles have a thickness in the range 4-20 nm and a diameter in the range 5-10 μm.
The samples were prepared using the following procedure. The PLA 700 1D was dissolved in chloroform in a ratio of 1:3. Suspensions of GNPs were prepared in 200 ml chloroform by ultrasonic mixing and added to the dissolved PLA. The final mixture was mechanically stirred for 60 min and dried in a vacuum oven for 24 h at 70 °C. Compositions with θ = 0%, 1.5% and 3% wt. of GNP in PLA in the form of a 1 mm thick plane parallel plate were prepared by this solution blending technique. The physical parameters, most important for fur ther 3D printing applications of the samples under study, are presented in table 1.
The transmission electron microscopy (TEM) analysis of GNP/PLA composites was made by TEM JEOL JEM 2100 in the bright field (BF) mode at the accelerating voltage 200 kV. Results of the TEManalysis show that the composite consists of separated GNP particles in the PLA matrix. The typical TEMimage of the obtained composites is presented in figure 3(a). The particles have a complex multilayergra phenebased structure, reminiscent of crumpled paper. The typical lateral size of GNP inclusion is 1-2 μm ( figure 3(a)). The thickness of multilayergraphene forming the GNP was analysed using scanning electron microscopy (SEM) (made by a S4800 Hitachi microscope). The values of the thickness vary in the range of 5-20 nm ( figure 3(b)) in good correspond ence with the manufacturer data sheet [35]. Due to breaking during high power sonication treatment, the average diameter of particles was decreased to several microns. Rarely, a few agglomerates of contacting GNP particles with lateral lengths around 4-5 μm were observed at 1.5 wt% filler content.
The typical Raman spectra of GNP/PLA composites is shown in figure 4. Measurements were performed by a Raman spectrometer Nanofinder HE (LOTIS TII, BelarusJapan) with a 600lines/mm grating and 473 nm laser excitation. The peaks observed at 1363, 1576 and 2743 cm −1 , originating from the GNP, 871 and 2996 cm −1 , are contributed by the PLA matrix. The largest G 1576 cm −1 peak is typical for high ordered graphite.
The electromagnetic response of GNP/PLA compos ites was experimentally investigated in the Kaband (26-37 GHz) using a scalar network analyser ELMIKA R2408R. All measurements were carried out in a 7.2 × 3.4 mm wave guide system described in detail in our recent work [10]. The di electric permittivity ε was then calculated based on the methodology described in [36].
THz measurements were carried out using a commercial THz timedomain spectrometer 'TSpec' by EKSPLA. A 1050 ± 40 nm wave length pumping laser having a 50-150 fs pulse duration and more than 40 mW output power at approx imately 80 MHz pulse repetition rate was used to excite a photoconductor antenna and produced THz radiation up to 2 THz. The spectrometer, THz emitter, and detector consist of a microstrip antenna integrated with a photoconductor (low temperature grown GaBiAs) and silicon lens. The sample in the form of a plane parallel plate was placed between the emitter and detector normally to the initial EM wave. The THz detector output is proportional to the instant electrical  field strength of the THz pulse during the ultra short pumping pulse. The Fourier transform of the waveform of electrical field of the THz radiation gives the frequency dependence of the complex transmission coefficient of the investigated sample used for ε calculations [36].

Experimental results
The results of the calculation of the dielectric permittivity from the experimentally measured data in the microwave and THz ranges are presented in figure 5 with scatters. First of all, the maximum of ε is clearly seen near ν c = 0.6 THz in figure 5. The absolute value of ε increases with GNP content. The real part of dielectric permittivity has a pronounced bend near 0.6 THz. The absorption coefficient of 1 mmthick composites was about 85% at 0.6 THz.
Results of modelling are in good agreement with the exper imental data. In the next section, we will discuss the general features of GNP based composites, effects of percolation and agglomeration, together with an overview and outlook for their possible practical use.

Discussion
As we mentioned above, the composites with GNP content below the percolation threshold were investigated. To observe THz absorption, the maximum composite should be prepared with a very high level of GNP distribution homogeneity, i.e. particles should be isolated from each other. It is very difficult to realize in practice, due to problems with the agglomeration of carbon particles [37,38]. Additionally, at higher concentra tions, the percolation occurs. The next subsection will discuss the influence of these effects on the appearance and position of the THz absorption peak.

Effect of agglomerates
Agglomerates and connected particles may be considered as structures with a higher aspect ratio and lower effective conductivity. The effective conductivity decreases due to the presence of contacts between particles. The agglom erates and connected particles form a percolation network with complex structured conductive regions. They may be considered as prolonged particles [21] with increased effec tive AR. According to equation (4), both of these param eters lead to a significant decrease of ν c . To demonstrate the effect of agglomerates, we consider a mixture of 1.5 wt.% of the above mentioned GNP particles and 0.15% of agglomerates with diameter D = 2b = 2c, macroscopic length L = 0.2 mm and conductivity σ = 3000 S m −1 . In this case of the multiphase mixture, the sums in equation (1) should include terms for all fractions in the composite. The dielectric permittivity spectra for one and twocomponent of agglomerates/GNP/PLA composite are presented in figure 6(a). One can see that at low frequencies, the contrib ution of agglomerates is dominated and in the range 5-50 GHz (see the grey region in figure 6(a)), both comp onents are decreasing with frequency as it was observed, for example, in [19,21,24].
In the Cole-Cole representation (figure 6(b)), the spectra have a form of two engaged hemispheres. When the content of the filler increases, a number of agglomerates also increases. In this situation, the large hemisphere merged with the smaller one in figure 6(b) and THz peak spread and became invis ible. Moreover, the contribution of the agglomerated or per colated particles will be excluded from the highfrequency absorption peak and should be taken into account at low frequency absorption. In this case, the frequency spectra of ε will be dominated by the contribution of agglomerates and the highfrequency THzpeak will be significantly dumped. That is why it is very important to prepare well the dispersed GNP composites to observe highfrequency THz absorption phenomena. This situation was widely discussed in [21,24], where authors used a mixture of oblate and prolate ellipsoids to explain the EM properties of similar GNP/epoxy compos ites at lower frequencies (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18). Actually, from the pre sent analysis, we can clearly see that a well dispersed GNP/ PLA composite may be used as a selective THz absorber transparent for microwave radiation.

Effect of percolation
When the concentration of filler reaches the percolation threshold agglomerates or arrays of connected particles start to be comparable to the lateral dimension of the whole sample, the material starts to be conductive in DC. The description of EM processes in agglomerates is a complex problem, which may be solved within percolation theory and through applying timeconsuming MonteCarlo modelling [39].
Nevertheless, to understand the general features of broad band dielectric permittivity spectra of percolated compos ites, it is possible to assume that the dielectric permittivity of the matrix in percolated composites starts to be complex ε * m = ε m − iσ s /(2πνε 0 ), where σ s is the static conductivity of the composite. In this case, Im(ε eff ) has singularity at ν → 0. A comparison of the corresponding spectra of the composite consisting of 1.5% of GNP particles inside the neat PLA matrix and inside the matrix with dielectric permittivity ε * m and σ s = 1 S m −1 is presented in figure 6(c). As can be seen from the figure, the percolation generally affects the imagi nary part of the dielectric permittivity, whereas the real part is influenced very slightly, decreasing at low frequencies due to shunting of conductive particles by the conducting matrix. The THz absorption maximum may be potentially observed in percolative composites, for small values of conductivity σ s . Let us examine spectra from figure 6(c) in the Cole-Cole representation (see the inset of figure 6(c)). The position of the singularity is very important for the possibility of exper imental THz peak observation. If σ s is less than ∼1 S m −1 , the singularity moves to the right from the red curve and the THz peak starts to be more pronounced. If σ s is increased then the singularity shifts to the left, and the terahertz absorption peak in that case disappears.
Summarizing this section, we can conclude that the contrib ution of agglomerates plays a dominate role in the formation of Re(ε) at lower frequencies in percolative com posites (including arrays of connected particles forming the percolation paths, agglomerates and isolated particle). The particles included to conductive paths are mainly respon sible for Im(ε) values and isolated particles form the THz absorption peak.

Conclusions
The EM properties of PLA/GNP composites were investi gated in the microwave (26-37 GHz) and terahertz (0.2-1 THz) frequency ranges. We pointed out that a unique com bination of conductive and geometrical parameters of GNP allow us to obtain the THzabsorptive material, which may be used as a 3Dprinting filament. The preparation proce dure, as well as dispersion control in this case, play crucial roles. Simple relations between the position of the absorp tion maximum and geometrical and conductive parameters of inclusions were derived on the basis of MG modelling. An absorption maximum was experimentally observed near a frequency of 0.6 THz for the GNP/PLA composites with 1.5 and 3 wt.% of graphite fillers, which is below the per colation threshold. The experimental data were fitted using MG formulae. Effects of percolation and agglomeration in GNPbased composites were discussed in view of respon sibility for electromagnetics constitutive parameters of the GNP comprising composites and the position of the THz absorption peak.