# Dielectric dispersion of 30% aqueous Ethanolamine solution at microwave frequencies

Ali Hajj, Etienne Savary, Thomas Hauviller, Sebastien Curet, Pascaline Pré

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Ali Hajj, Etienne Savary, Thomas Hauviller, Sebastien Curet, Pascaline Pré. Dielectric dispersion of 30% aqueous Ethanolamine solution at microwave frequencies. European Journal of Microwave Energy, 2024, 1, pp.19-26. 10.18573/ejme.9. hal-04985282

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# Dielectric dispersion of 30% aqueous Ethanolamine solution at microwave frequencies

Hajj A<sup>a,c*</sup>, Savary E<sup>c</sup>, Hauviller T<sup>b</sup>, Curet S<sup>b</sup>, Pré P<sup>a</sup>

## Abstract

Chemical absorption of CO₂ in aqueous amines is the most advanced and widely spread technology to mitigate CO₂ emissions from flue gas streams, however it is plagued by many problems resulting from high temperatures used to regenerate the solvent. Recently, lab-scale studies of MW-assisted regeneration of aminated solvents have shown a promise in decreasing the severity of the regeneration conditions. Still, successful modeling of the regeneration process or the design of a MW-applicator requires knowledge of the dielectric properties of the solvent. In this work the dielectric properties of 30% by weight aqueous ethanolamine (ETA) solution were measured over [915-2450MHz] at two temperatures (20, 60°C). Then the experimental data were accurately fitted with the Cole-Cole dielectric dispersion model. Obtained dispersion parameters show a decrement of the static dielectric constant and the relaxation frequency relative to those of pure water. In addition, the relaxation time distribution parameter approaches zero, implying a very narrow distribution of relaxation times. Predictions show that the solution possesses a considerable conductivity brought about by the protonation of ETA by water. Still, the contribution of the ionic species to the dielectric loss is minimal relative to that of the dipolar rotation mechanism by ETA and water dipoles on the current spectrum of measurement.

© 2024 The Authors. Published by Cardiff University Press.
Selection and/or peer-review under responsibility of Cardiff University
https://doi.org/10.18573/ejme.9

Received: 8th Sep 23; Accepted: 6th Feb 24; Published: 5th June 2024

Keywords: Dielectric properties, Dielectric dispersion, Cole-Cole, MEA, alkanolamine, regeneration

## Introduction

Ever since the industrial revolution, anthropogenic greenhouse gas emissions have intensified leading to a global temperature increase that, if left unchecked, threatens all life on earth. The Sixth assessment report of the IPCC (intergovernmental panel on climate change) has declared that rapid and immediate action is necessary to bring greenhouse gas emissions to net-zero levels by 2050, in order to prevent a temperature-increase of no more than 1.5°C relative to pre-industrial era. The global economy has been and will still be dependent on fossil-fuel sources in the near-future, and so a short-term solution is to decarbonize these emission sources through abatement strategies known as carbon capture (CC) [1]. Chemical absorption of CO₂ into aqueous alkanolamine solutions is one of the most well established CC technologies [2], but despite its level of maturity it suffers from many inherent drawbacks such as high equipment capital cost, amine degradation and the energy penalty to regenerate the solvent [3, 4].

MW irradiation has found many applications in chemical processes [5]. This ensues from the potential for intensifying heating of the process which has already been studied in different processes such as adsorbent bed regeneration [6] or vacuum membrane distillation [7]. Recently, microwave (MW) irradiation has also been used to regenerate CO₂ rich solvents. McGurk [8] tested the cyclic capture capacity of 30%wt ethanolamine (ETA) and found recovery levels that rival that obtained at an industrial scale but considerably lower regeneration temperatures. Bougie[9] characterized the effect of amine mass fraction in the solvent, on the MW-heating rate as well as the energy efficiency of the process. Yang[10] tested the MW-regeneration of dry alkanolamines (ETA, DEA) and found faster regeneration times as well as a 10% improvement in the energy performance in comparison to conduction heating.

The way a medium interacts with electromagnetic (EM) irradiation is characterized by the complex dielectric constant (ε*) shown in (1). (ε') is the relative dielectric and is indicative of the capacitive

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<figure><img src="image_2.png" /></figure>

<footnote><sup>a</sup>IMT Atlantique, GEPEA, UMR CNRS 6144, 44307 Nantes, France</footnote>

<footnote><sup>b</sup>Oniris, Nantes Université, CNRS, GEPEA, UMR 6144, F-44000 Nantes, France</footnote>

<footnote><sup>c</sup>SAIREM, 82, rue Elisée Reclus, 69150 Decines Charpieu, France</footnote>
ability of a material to store electromagnetic (EM) energy. (ε'') is the relative dielectric loss factor, it represents the ability of the material to dissipate EM energy in the form of heat due to friction between the rotating dipoles [11].

$$ε^* = ε_0(ε' - jε'') \quad (1)$$

EM energy is stored by individual molecules of the medium through different mechanisms depending on the frequency of the electromagnetic radiation used. In the MW frequency region, the dipolar rotation and electronic polarization are the dominant mechanisms [12]. Dipolar rotation takes place when an external E-field exerts a torque on the dipoles of the medium which forces them to “relax” by seeking the lowest energy configuration[13]. The relaxation position has been widely accepted to be that of parallel alignment with the E-field [14–18]. This relaxation mechanism is called the slow relaxation mechanism because it occurs at relatively low frequencies, contrary to fast ones (infra-red, optical) which appear at the sub-millimeter (f>100GHz) wavelength region[19].

Dielectric dispersion spectroscopy of alkanolamines has hardly been studied in the literature. Patil [16] studied the dielectric properties of a binary mixture of ETA, DEA at different temperatures, and found alignment/anti-alignment behavior between the dipoles depending on the composition of the mixture. Similar results were found by Jadhavpatil [17] who used the Havrilik-Negami model to fit the dielectric dispersion of aqueous ETA solutions at different temperatures. The obtained Kirkwood corrective factor [20] indicated an anti-parallel alignment of dipoles at high ethanolamine concentrations relative to the ideal mixture. Chiu[21] noticed a positive linear correlation between the static permittivity and the concentration of the hydroxide groups with different alkanolamines. The author also found that the tested binary water- alkanolamine mixtures gave negative excess values of the static permittivity with respect to the ideal mixture over the entire composition range.

Up until now, the few existing studies of MW assisted regeneration of amine solutions have been performed at the scale of a few millimeters. Any future attempt to model the system or to scale-up the regeneration process will forcibly require knowledge of the dielectric properties of the solvent. In this work, the dielectric dispersion of 30%ETA was measured from 915 to 2450MHz using the open-ended coaxial probe method at two different temperatures (20°C, 60°C). The dielectric dispersion spectrum was fitted with the Cole-Cole model, and the obtained dispersion parameters were discussed with respect to those of the pure constituents of the solution.

## Materials and methods

Ethanolamine (C₂H₇NO) (Sigma-Aldrich >98%) and deionized water (DW) were weighed to prepare a 30% by weight aqueous Ethanolamine solution (30% ETA).

The open-ended coaxial probe method was used to measure the dielectric properties of 30% ETA at the spectrum 915-2450MHz. The measurement is based on the readings of the two port network parameters (S₁ᵢⱼ) that vary as a function of the complex dielectric constant and the probe geometry [22]. The dielectric probe (Agilent85070E: high temperature configuration) was linked through a metallic co-axial cable to a vector network analyzer (VNA) (Agilent E5062A ENA-L, 300kHz-3GHz). The probe calibration was done via a three-step procedure with open-air, metallic shorting block, and deionized water at 20°C. Measurements were triggered via a software installed on a computer and results are obtained in a few seconds time. Then, the probe was dipped in a solution of 30% ETA placed in a beaker of volume (125mL) on top of a heating plate. The lateral surfaces of the sample holder were covered by thermal insulation. The liquid height is one order of magnitude higher than what is recommended by the probe manufacturer, and care was taken to ensure that the surface of the probe is free of gas-bubbles that tend to form at high temperatures. An optical fiber was used to verify the temperature at the level of the coaxial probe within the liquid. Dielectric measurements were repeated three times. Drift errors were evaluated by measuring the dielectric properties of DW once per day for three days and results show good reproducibility with the maximum % relative standard deviation of [ε', ε''] with respect to time on the measurement spectrum to be 0.83% and 3.24% respectively.

## Dielectric Dispersion model

The way a medium behaves under an external E-field is denoted by the term relaxation mechanism. It is influenced by many factors such as frequency of the EM radiation, phase of the material, its temperature, composition etc.... At low frequencies dipoles align themselves in geometries that minimize the potential energy of the system. n-alcohols for example are suspected to form chain-like structures [18, 23] while water molecules align in different shapes of clusters such as spherical or parallel sheets[13] the size of which tends to decrease with temperature [24].

Dielectric dispersion models are used to describe the relaxation of a medium as a function of frequency. The most popular models are : Debye [25], Cole-Cole [26], Davidson-Cole [27] and Havrilik-Nagami [28] represented by (2 for (α,β) values of (0, 1); (0<α<1, 1); (0, 0<β<1); (0<α<1, 0<β<1)

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<figure><img src="image_3.png" /></figure>

<footnote>*Corresponding author: Ali Hajj
E-mail address: alielhajj196@gmail.com</footnote>
respectively. The terms “α” or “β” account for the existence of a distribution of the relaxation times [29], which makes the dispersion models more rigorous.

$$ \varepsilon^* = \varepsilon_{\infty} + \frac{\varepsilon_0 - \varepsilon_{\infty}}{(1 - (j\omega\tau)^{1-\alpha})^{\beta}} \quad (2) $$

The Debye model is the simplest and most popular. It assumes rotation diffusion of spherical polar molecules in a viscous medium with a single relaxation time [19, 24]. It is able to produce good quality fits for dielectric data of some polar and organic liquids [16, 18, 23, 30–33]. The Cole-Cole (CC) model is relatively simple but is more rigorous than the Debye model because it takes into consideration a Gaussian distribution of relaxation times [29]. This makes it more adequate to study the properties of highly non-ideal systems such as that of saline water with high concentrations of saccharose [34], or those of near ideal systems of mixtures of n-alcohol and water [23, 35].

The presence of ions in a medium impacts the dielectric behavior, most notably through the increase of the dielectric loss factor by ionic conduction mechanism [36], and the decrease of ε' by the decrease of the number of dipoles participating in the dielectric dispersion [12]. The original dispersion models were modified by many authors [34, 37–39] through the addition of an imaginary term to account for the dielectric loss by ionic conduction.

$$ \varepsilon^* = \varepsilon_{\infty} + \frac{\varepsilon_0 - \varepsilon_{\infty}}{1 - (j\omega\tau)^{1-\alpha}} + j\frac{\sigma}{\omega\varepsilon_0^*} \quad (3) $$

The Cole-Cole dielectric dispersion model with ionic conduction is shown in (3, ε∞ being optical permittivity, ε₀ is the static permittivity, τ (s) is the relaxation time, α is the relaxation time distribution parameter, ω (rd/s) is the angular frequency, σ (S/m) is the DC electrical conductivity, and ε₀* (F/m) the vacuum permittivity. A complex nonlinear least square (CNLS) routine was applied to fit the dispersion model to [e', e''] simultaneously where the objective function is shown in (Eq 5) with subscripts “e” and “m” denoting experimental and model data respectively. Minimization of the objective function (Eq 4) was performed using the Levenberg-Marquart algorithm [40] with the dispersion parameters (ε₀, τ, σ, α) having no dependency on one another. The initial guess for parameter sets was chosen intuitively but carefully. For a lack of better estimation, the optical dielectric constant of the mixture (ε∞,m) was calculated according to Maxwell’s equation ((6) where (n) is the refractive index of 30%ETA at 20°C measured by Ju[41]

$$ E^2 = \frac{1}{n} \sum_{1}^{n} [(\varepsilon'_{n,e} - \varepsilon'_{n,m})^2 + (\varepsilon''_{n,e} - \varepsilon''_{n,m})^2] \quad (5) $$

$$ \varepsilon_{\infty, \text{mix}} = n^2 \quad (6) $$

# Results

## Validation of dielectric measurement method

To validate the measurement technique, the relative permittivity and the dielectric loss factor of DW were measured over the frequency range [915-2450MHz] for the temperatures [20-60°C] by steps of 10°C. Experimental results are plotted along with those from the dispersion model of Debye as shown in Fig. 1 and Fig. 2 respectively. The Debye model uses correlated dispersion parameters taken from Buchner [12].

With regards to ε', the two sets of experimental data agree almost perfectly where %AARD is less than 2% for all temperatures. ε'' displays good agreement with the model, but considerable deviations persist where max %AARD<10% due to the low equipment sensitivity in this range of ε''. The lower limit of measurement on the dielectric loss should be greater than 5% ε' of the liquid under test (LUT) [42]. Gadani [43] observed similar %AARD when validating his measurement technique with DW for the frequency range [0.2-1.4]GHz.

<figure><img src="image_4.png" /><figcaption>Fig. 1: Measured (points) and calculated (lines) relative dielectric constant of deionized water from 20 to 60°C</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2: Measured (points) and calculated (lines) dielectric loss factors of deionized water from 20 to 60°C</figcaption></figure>

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<figure><img src="image_6.png" /></figure>
## Dielectric Dispersion of 30% ETA aqueous solution

The measured dielectric properties of 30% ETA as well as those obtained from the fitted Cole-Cole are plotted in the Cole dispersion diagrams in Fig. 3 and Fig. 4 for T=20°C and T=60°C respectively. Dielectric properties of DW were also plotted using the correlated dispersion properties of Buchner [12] (appendix) in conjunction with the Debye model, and serve as a reference for comparison. The obtained Cole-Cole dispersion parameters are displayed in Table 1.

<table><caption>Table 1: Fitted dispersion properties of 30% ETA, and those of DW at T=20°C and 60°C</caption><thead><tr><th rowspan="2">T</th><th colspan="2">30%ETA</th><th colspan="2">H<sub>2</sub>O</th></tr><tr><th>20 °C</th><th>60 °C</th><th>20 °C</th><th>60 °C</th></tr></thead><tbody><tr><td>ε<sub>0</sub></td><td>69.10</td><td>58.27</td><td>79.93</td><td>66.58</td></tr><tr><td>1-α</td><td>0.93</td><td>0.98</td><td>1</td><td>1</td></tr><tr><td>ε<sub>∞</sub></td><td>1.88</td><td>1.88</td><td>5.99</td><td>4.99</td></tr><tr><td>τ(ps)</td><td>19.2</td><td>8.8</td><td>9.42</td><td>8.76</td></tr><tr><td>σ(S/m)</td><td>0.079</td><td>0.177</td><td>—</td><td>—</td></tr><tr><td>fr (GHz)</td><td>8.28</td><td>18.08</td><td>16.89</td><td>39.84</td></tr><tr><td>E<sup>2</sup></td><td>0.04</td><td>0.01</td><td>—</td><td>—</td></tr></tbody></table>

The table shows that the fitting quality of Cole-Cole model is very good (max E² values of 0.04) and the relaxation time of the solution follows a narrow distribution. It can be inferred from the semi-circular shape of the dispersion diagrams (Fig. 3 and Fig. 4). This is more true for the dispersion at T=60°C having (1-α) being 0.98 than that at 20°C having (1-α) equal to 0.93.

Table 1 shows that there is a decrement of the static dielectric constant ε₀ of 30% ETA with respect to DW. This is due to the fact that pure ethanolamine has lower static dielectric constant (~31.94) [15] than DW (~80) [37]. Although ETA has two hydrogen bonds (NH₂...H/OH...H) per molecule and has a dipole moment (2.37D) [15] greater than that of water 1.8D [19]. Water ultimately has the greater effective dipole moment. Besides, the steric hindrance of ETA shuts out the formation of large H-bonded clusters as in H₂O or n-alcohols which are known to enhance the dipolar moment [13, 15]. Jadhavpatil [17] fitted the dielectric properties of 30% ETA with the model of Havrilik-Negami [28] and obtained ε₀ = 69 at 25°C, in very good agreement with this work (ε₀=69.1 at 20°C).

The Kirkwood correlation factor (g<sub>eff</sub>) was evaluated for 30% ETA system at 20°C using the Kirkwood formula [20] shown in (7). (g<sub>eff</sub>) is a good indicator of the nature of the dipole interactions, therefor we distinguish the following cases:

- g<sub>eff</sub>>1: The dipoles are in parallel alignment and therefor enhance the effective dipole moment.

- g<sub>eff</sub>=1: The dipoles do not interact with another and dipole moment of each molecule is identical to that in the gaseous phase

- g<sub>eff</sub><1: The dipoles are in anti-alignment with one another which decreases the effective dipole moment.

<figure><img src="image_7.png" /><figcaption>Fig. 3: Dielectric dispersion of DW, 30% ETA (Experimental) and 30% ETA (Cole-Cole) at 20°C</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4: Dielectric dispersion of DW, 30% ETA (Experimental) and 30% ETA (Cole-Cole) at 60°C</figcaption></figure>

$$ \frac{4\pi N}{9kT} \left( \frac{\mu_1^2 \rho_1}{M_1} \varphi_1 + \frac{\mu_2^2 \rho_2}{M_2} \varphi_2 \right) g_{\text{eff}} = \frac{(\varepsilon_{0m} - \varepsilon_{\infty m})(2\varepsilon_{0m} + \varepsilon_{\infty m})}{\varepsilon_{0m}(\varepsilon_{\infty m} + 2)^2} \quad (7) $$

In (7 μ is the dipole moment in the gaseous phase, ρ is the pure-component density obtained from Weiland [44], M the molar mass, N is Avogadro's number, k is the Boltzmann constant, φ the volume fraction. The calculated value at T=20°C is g<sub>eff</sub>=2.69, it hints at a dominating parallel alignment between
the dipoles that leads to an increase in the effective dipole moment. This result is in accordance with that of Jadhavpatil[17] who obtained values of g<sub>eff</sub> in the range of [2.7-2.9] for 30% ETA at 25°C. Still, care needs to be taken in the interpretation of g<sub>eff</sub>, in light of its sensitivity to the optical dielectric constant (ε<sub>∞</sub>) [18] that cannot be obtained accurately by fitting to dielectric data in the MW frequency range.

Table 1 shows that the relaxation time increases between H₂O and 30% ETA from 9.42ps to 19.2ps at 20°C respectively, and decreases with temperature increase from 20°C to 60°C as well. This happens on account of ETA having a greater relaxation time in view of its molecular size and higher hydrogen bonding strength [18, 45]. This leads to higher relaxation times than water in the order of 102ps at T=35°C [16]. In addition 30% ETA has a viscosity 2.86 times greater than water at 20°C[44] further impeding the dielectric relaxation of the dipoles in the E-field. With temperature increase, hydrogen bonding strength decrease giving way to smaller H-bonded clusters, and thus a lower relaxation time [24]. The relaxation time measured by Jadhavpatil [17] is 37ps and may be accorded good credibility considering that it was fitted on a more inclusive data set [10MHz-20GHz] than ours [915MHz-2.45GHz]. Still the relaxation values obtained by this author show considerable spread, therefor better accuracy would have been possible had the obtained relaxation values been fitted to a suitable mathematical model. Another very important reason for this discrepancy is due to the fact that Jadhavpatil [17] did not include the ionic conduction term in the dispersion model, which causes the optimization procedure to search for a solution with a higher relaxation time than the true value. This increases the dielectric loss by dipolar rotation mechanism over the spectrum of measurement in an effort to account for that by ionic conduction.

It is clear that the loss factor at T=20°C is higher than that at 60°C for ethanolamine as a function of frequency (Figs. 3 and 4). This happens in consideration of the fact of the spectrum of measurement being closer to the relaxation frequency of the mixture at 20°C than at 60°C, which leads to higher losses by dipole rotation mechanism.

Table 1 shows that 30%ETA solution possesses a non-negligible electrical conductivity at T=20°C and 60°C. The protonation reaction of ETA molecules is the cause as shown in (9). Therefor the dielectric loss factor is augmented by losses from ionic species through the ionic conduction mechanism.

The ionic species in the 30%ETA solution contribute to the dielectric loss factor by 1.55 and 3.2 units at 915MHz ($ε''_{IC} = \frac{\sigma}{\omega\epsilon_0}$) for T=20°C and 60°C

respectively with an expected decrease in their contribution at higher frequencies [36]. It is worth mentioning that ETA is a weak base having pKa=9.5 at T=25 °C [46]. It follows that the electrical conductivity of the solution is low σ=0.72 mS.cm⁻¹ at 20°C [41]; a value in agreement with the one obtained in this work σ=0.79 mS.cm⁻¹. Electrical conductivity at 60°C is almost double that at 20°C. Higher temperatures increase the ion mobility[47] on one hand, and the dissociation constant of ETA (Eq 8) on another [41].

$$MEA + H_2O \leftrightarrow MEAH^+ + OH^- \quad (9)$$

## Conclusion

The dielectric dispersion of 30%ETA was measured using the open-ended coaxial probe technique and the obtained results were fitted with the Cole-Cole model. Obtained dispersion parameters show that the static dielectric constant of 30%ETA is smaller relative to that of pure water, and is inversely proportional to temperature. Similarly, the relaxation time decreased with temperature with an ever more discrete nature as indicated by the higher value of (1-α) at 60°C relative to that of 20°C. Due to the protonation of ETA in water, the solution posses a non-negligible electrical conductivity. The fitted electrical conductivity from the Cole-Cole model shows a considerable contribution of the ionic conduction mechanism to the overall dielectric loss, a contribution that increases with higher temperature and lower EM frequency.

This article covers the dielectric dispersion of 30%ETA free of CO₂. To achieve greater practical utility of the dielectric data, future efforts should complement this work by focusing on dielectric characterizations of the solvent at different concentrations of CO₂. Chosen concentration levels should range in the magnitude of those encountered in a conventional amine scrubbing plant.

## Acknowledgments

The authors would like to thank the ANR (Agence Nationale de la Recherche) for the dedicated funding to project WAVEINCORE to which this work belongs.

## Conflicts of Interest

The authors declare no conflict of interest

<figure><img src="image_9.png" /></figure>

<footnote>*Corresponding author: Ali Hajj
E-mail address: alielhajj196@gmail.com</footnote>
# Appendix

## Notations

<table><tr><td>ε<sup>*</sup></td><td>Complex permittivity</td></tr><tr><td>ε'</td><td>Relative permittivity</td></tr><tr><td>ε''</td><td>Dielectric loss factor</td></tr><tr><td>f</td><td>Frequency (Hz)</td></tr><tr><td>ε<sub>∞</sub></td><td>Optical dielectric constant</td></tr><tr><td>ω</td><td>Angular Frequency (radian/s)</td></tr><tr><td>ε<sub>0</sub></td><td>Relative static dielectric constant</td></tr><tr><td>τ</td><td>Relaxation time (s)</td></tr><tr><td>α</td><td>Cole-Cole Fitting parameter</td></tr><tr><td>σ</td><td>Static conductivity (S/m)</td></tr><tr><td>ε<sub>0</sub><sup>*</sup></td><td>Permittivity of free space (F/m)</td></tr><tr><td>E<sup>2</sup></td><td>Squared Error</td></tr><tr><td>g</td><td>Kirkwood correlation factor</td></tr><tr><td>μ</td><td>Vacuum dipole moment (Debye)</td></tr><tr><td>N</td><td>Avogadro's number(mol<sup>-1</sup>)</td></tr><tr><td>k</td><td>Boltzmann constant (m<sup>2</sup> kg s<sup>-2</sup> K<sup>-1</sup>)</td></tr><tr><td>φ</td><td>Volume Fraction</td></tr><tr><td>n</td><td>Refractive index</td></tr></table>

## Abbreviations

<table><tr><td>IPCC</td><td>Intergovernmental panel on climate change</td></tr><tr><td>EM</td><td>Electromagnetic</td></tr><tr><td>ETA</td><td>Ethanolamine</td></tr><tr><td>DEA</td><td>Diethanolamine</td></tr><tr><td>DW</td><td>Deionized water</td></tr><tr><td>AARD</td><td>Absolute Average Relative Deviation</td></tr><tr><td>CC</td><td>Cole-Cole dispersion model</td></tr><tr><td>LUT</td><td>Liquid Under Test</td></tr></table>

## Subscripts

<table><tr><td>e</td><td>Experimental</td></tr><tr><td>m</td><td>Model</td></tr><tr><td>eff</td><td>Effective</td></tr><tr><td>mix</td><td>Mixture</td></tr><tr><td>IC</td><td>Ionic Conduction</td></tr></table>

## Dielectric properties of Distilled water

The Debye model was used for calculation of the dielectric properties of distilled water. The dispersion parameters function of temperature were obtained from Buchner[12]. The model is valid for T ∈ [0, 55] °C and in the frequency range f < 20.05GHz. The complex permittivity is given by the Debye model:

$$ε' - jε'' = ε_{∞} + \frac{ε_{0} - ε_{∞}}{1 - i2πτf} + \frac{iσ}{2πε_{0}^{*}f}$$

-The relative static dielectric constant is given by the following expression:

$$ε_{0} = 87,85306 * \exp(-0,00456992 * T(°C))$$

-The relaxation time is given by:

$$τ(\text{ps})^{-1} = 5,631 * 10^{-02} + 2,12 * 10^{-03} * T(°C) + 1,86 * 10^{-05} * T^{2}(°C)$$

-The optical relative dielectric constant is given by:

$$ε_{∞} = 6,49 - 0,025 * T$$

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