# Dielectric dispersion of 30% aqueous monoethanolamine solution loaded with CO2 at microwave frequencies

A. Hajj, P. Pré, S. Curet

► To cite this version:

A. Hajj, P. Pré, S. Curet. Dielectric dispersion of 30% aqueous monoethanolamine solution loaded with CO2 at microwave frequencies. Journal of Molecular Liquids, 2024, 404, pp.124819. 10.1016/j.molliq.2024.124819. hal-04754811

HAL Id: hal-04754811

https://nantes-universite.hal.science/hal-04754811v1

Submitted on 21 May 2025

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# Dielectric dispersion of 30% aqueous Monoethanolamine solution loaded with CO₂ at microwave frequencies

Hajj A<sup>a,c*</sup>, Pré P<sup>a</sup>, Curet S<sup>b</sup>

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

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

<sup>c</sup>SAIREM, 82, rue Elisée Reclus, 69150 Décines Charpieu, France

## Abstract

In this work the dielectric properties of 30% by weight aqueous monoethanolamine solution (MEA) were measured over the microwave frequency range [915-2450 MHz], for varying conditions of temperature and carbonation ratio. The Cole-Cole dispersion model was fitted to the experimental data to obtain the dielectric dispersion parameters, which were interpreted with the help of the Kent-Eisenberg chemical speciation model. Experimental results show the relative permittivity to be in the same range as distilled water, while the dielectric loss factor is found to be highly elevated such that resulting microwave penetration depths are in the order of few millimeters. Obtained dispersion parameters show the static dielectric constant to decrease with temperature, but to increase with carbonation ratio. The apparent relaxation time follows a similar behavior, higher temperatures allow for a faster relaxation, whereas the increase in carbonation ratio increases the viscous forces thus hindering relaxation. A broadening distribution of relaxation times was observed with higher carbonation ratios as absorption of CO₂ leads to a greater chemical heterogeneity as indicated by the speciation model. The static electrical conductivity of the CO₂-loaded solutions is determined to be two orders of magnitude greater than unloaded monoethanolamine solutions, due to the increase in the concentration of the ionic species with carbonation ratio.

Keywords: Dielectric dispersion, Cole-Cole, MEA, microwave technology, chemical absorption

## 1 Introduction

Critical levels of anthropogenic greenhouse gas emissions have been reached leading to a global temperature increase that poses serious threats to future generations. The Sixth assessment report of the IPCC (intergovernmental panel on climate

<footnote>*Corresponding author.</footnote>
change) has declared that rapid and immediate action is necessary to bring greenhouse gas emissions to net-zero levels by 2050 to prevent a global temperature-increase of no greater than 1.5°C relative to pre-industrial times (Calvin et al., 2023). The problematic surrounding this subject is achieving such a transition without compromising economic growth, national security and living standards (Yu et al., 2008). Global economy has been and will still be dependent on fossil-fuel sources in the near-future, until technologies for sustainable energy sources reach maturity. One solution is to decarbonize these emission sources through abatement strategies known as carbon capture and storage. Chemical absorption of CO₂ into aqueous alkanolamine solutions is one of the most well established carbon capture technologies (Freund, 2003). Regardless of its capture efficiency it is impaired by the high equipment capital cost, amine degradation and the energy required to for solvent regeneration (Abu-Zahra et al., 2007; Wang et al., 2011).

Microwave (MW) irradiation has found many applications in chemical processes (Stefanidis et al., 2014). The advantage it provides is selective, volumetric, and well controlled energy introduction. That led to its employment in many sectors such as food industry (Pielak et al., 2022), manufacturing technology (Kumar Baghel, 2023), and chemical processes (Stefanidis et al., 2014) among others. Recently, MW irradiation has also been tested for the regeneration of CO₂-rich solvents, in the framework of capture and storage, although the encountered studies in literature are performed at the scale of a few milliliters of solvent. (McGurk et al., 2017) studied the MW regeneration of 30%wt. monoethanolamine (MEA) and obtained a dynamic working range ($α_{high}-α_{low}$) that is comparable to those at an industrial scale, albeit at considerably lower regeneration temperatures. (Bougie and Fan, 2018) characterized the effect of amine mass fraction in the absorbent on the energetic performance of regeneration; he found that aqueous 50%wt. MEA solution showed a lower energetic consumption relative to the standard process chemical absorption process. (Yang et al., 2015) tested the MW-regeneration of dry alkanolamines and found faster regeneration times and an improvement in the energy performance in comparison to conduction heating. Till now, the few existing studies of MW regeneration of aminated solutions were performed over a few milliliters. Any scale-up attempt of the process will require knowledge of the dielectric properties of the solvent over a wide range of temperatures and CO₂ loadings.

An exhaustive literature review shows that the dielectric dispersion spectroscopy of alkanolamines has hardly been studied. (Patil et al., 2012) measured the dielectric properties of a binary mixture of MEA, and diethanolamine (DEA) at different MEA mole fractions and temperatures. On the other hand, (Hsieh et al., 2007) studied the dielectric behavior of certain alkanolamines; his findings indicate a strong correlation of static dielectric constant with the concentration of hydroxyl groups. To the best of our knowledge, the only author to measure the properties of aqueous alkanolamines was (Jadhavpatil et al., 2019) who characterized the properties of aqueous MEA solutions at different temperatures and liquid compositions,
however with no CO₂ content. This limits the utility of the author's data in using microwave technologies in the context of carbon capture.

This work focuses on the dielectric characterization of 30%wt. MEA on the frequency range [915-2450 MHz] using the open-ended coaxial probe, at various conditions of temperature and CO₂ loading. The experimental dielectric dispersion spectrum was then fitted with the Cole-Cole dispersion model to obtain the dielectric dispersion parameters. The latter were interpreted with the help of the chemical speciation from the vapor-liquid equilibrium model of Kent-Eisenberg.

# 2 Materials and methods

## 2.1 Sample preparation

Monoethanolamine (C₂H₇NO) (Sigma-Aldrich >98%, CAS No. 141-43-5) and deionized water (DW) were weighed to prepare a 30% by weight aqueous Monoethanolamine solution (30%MEA). The apparatus shown in Figure 1, and adopted by previous authors (Evjen et al., 2017; Shen and Li, 1992), was then used to load the aqueous solution with CO₂. The inlet gas stream, 80 by 20% CO₂ and N₂ respectively, was first saturated with water, then bubbled into a reactor containing 1 liter of 30%MEA solution where the CO₂ in the gas stream reacts with MEA. Outlet stream was analyzed using gas chromatography (INFICON-Fusion, column type U-bond at 60°C, Helium at 186 kPa). Equilibrium was reached when successive readings by the chromatograph showed no variations. Given the exothermic nature of CO₂ chemical absorption (Kim and Svendsen, 2007), the bubbling reactor was placed in a water bath that serves as a heat sink.

<figure><img src="image_2.png" /><figcaption>Figure 1: Apparatus for generating CO₂-loaded 30%wt. MEA aqueous solutions</figcaption></figure>

When the loading procedure is over, the carbonation ratio of the solution – defined in (1) – was determined using Barium chloride (BaCl₂) titration method. This is a classical method for determination of acid gas content first proposed by (Weiland and Trass, 1969) and applied widely by others (Aronu et al., 2011; Jou et al., 1982; Shen and Li, 1992, p. 19). In this method, 5mL of the sample under test is mixed with 10mL hot aqueous BaCl₂ solution (1.4 M). CO₂ is then precipitated under the form of barium carbonate salt (BaCO₃) according to reaction (2).

$$ \alpha = [CO_2]/[MEA] \qquad (1) $$
$$BaCl_2 + CO_2 + H_2O \rightarrow BaCO_{3(s)} + 2HCl \quad (2)$$

After aging for one day in a cooled environment, the precipitate was separated from the liquid by filtration using a filter paper (Whatman 1440-150 mm- grade 40). The filter paper and precipitate were dried in an oven for 2 days at 100°C. Gravimetric measurement allows calculation of the CO₂ content by subtracting the mass of the dried filter paper (measured separately). To validate the experimental procedure, 2g of sodium bicarbonate (NaHCO₃) (Sigma Aldrich ≥99.7%) were dissolved in 100mL of DW, and the solution was tested for its acid gas content (CO₂ under the form of HCO₃⁻) with the described method. Measured CO₂ content is within 5% the true value. Aqueous MEA solutions with different CO₂ loadings were prepared by diluting CO₂-loaded 30%wt. MEA with unloaded ones.

## 2.2 Measurement of dielectric properties

The open-ended coaxial probe method was used to measure the dielectric properties of the CO₂-loaded 30%wt. MEA solution at the spectrum [915-2450 MHz] which incorporates the two main frequencies for MW power applications (915, 2450 MHz) (Pielak et al., 2022). Complex permittivity is inferred from the readings of the two port complex reflection coefficient (Sᵢⱼ) which vary with liquid type and the probe geometry (Misra et al., 1990). The dielectric probe (Agilent 85070E: high temperature configuration) was linked through a metallic coaxial cable to a vector network analyzer (VNA) (Agilent E5062A ENA-L, 300kHz-3GHz). The probe calibration was done via a three-step procedure by measuring the complex reflection coefficient in a three-step procedure: (i)-leaving the probe to open-air, (ii)- connecting a metallic shorting block, (iii)- dipping the probe in deionized water at 20°C. Measurements were triggered via the software and results are obtained in a few seconds time, the option (refresh calibration) was enabled to minimize drift errors. To minimize drift errors the following precautions were taken: constant room temperature was maintained, the coaxial cable connected to the probe was kept at a fixed position, probe was recalibrated at least once per day.

The probe was introduced into a CO₂-enriched 30%wt. MEA solution, placed in a beaker of volume (125mL) and immersed within a temperature-controlled water bath. The external surfaces of the water bath were thermally insulated from all lateral sides and the top side of the beaker was closed with a cap that allows the coaxial cable and the dielectric probe to pass through. The height of the liquid sample is one order of magnitude greater than the minimal level advised by the probe manufacturer (Keysight 85070E: Dielectric Probe kit 200 MHz to 50 GHz 2017). The water bath was heated to a temperature set point. Before triggering the dielectric measurements, thermal equilibrium was verified using an optical fiber connected to a data logger (H201, Rugged Monitoring). Evolution of the sample composition was deemed minor owing to the low volatility of the solution at the temperature range of measurement, the closed sample holder that prevents losses by evaporation, and the constant renewal of the sample every few days.
Measurements were repeated five times and the results were averaged. Good reproducibility is achieved as indicated by the low value of the maximum relative standard deviation (<1%) on [ε', ε''] of CO₂-loaded 30%wt.MEA. To evaluate drift, the properties of DW were measured once per day for three days: maximum absolute average relative deviations on [ε', ε''], over the measurement spectrum on three days, were 0.83% and 3.24% respectively. Some errors on (ε'') is cause by the fact that the measured values of DW fall on the lower limit of the measurement range of this technique (Brodie et al., 2016). Samples with higher lossy character are expected to display lower levels of error.

## 2.3 Dielectric Dispersion model

To characterize the macroscopic interaction of MWs with a medium, the complex dielectric constant (ε*) shown in (3) is used. (ε') is the relative dielectric constant, it is the sum of all individual dipole moments in the system, while (ε'') is the relative dielectric loss factor representing the dissipation of EM energy into heat under a time-harmonic propagating electric field (E-field) (Sadiku, 2001).

$$ \epsilon^* = \epsilon_0^*(\epsilon' - j\epsilon'') \quad (3) $$

Individual dipoles store EM energy by way of different mechanisms. In the MW frequency region, the dipolar rotation and electronic polarization are the dominant mechanisms (Richard Buchner et al., 1999). Dipolar rotation takes place when the external E-field exerts a torque on the dipoles of the medium which forces them to rotate and seek the position that minimizes the applied force (Kemp and Gordon, 2008). The relaxation position has been widely accepted to be that of parallel alignment with the E-field (Ikada, 1969; Jadhavpatil et al., 2019; Kaatze and Lönnecke-Gabel, 1991; Patil et al., 2012; Undre et al., 2012). At microwave frequencies the relaxation mechanism is called the slow relaxation mechanism, while faster ones take place at higher frequencies i.e at the sub-millimeter (f>100GHz) wavelength region (Popov et al., 2016).

The term “relaxation mechanism” is used to denote the behavior of a medium under an E-field. Some key influencing factors are: frequency of the EM radiation, phase of the material, temperature, composition etc.... At MW frequencies, dipoles form networks that minimize the potential energy of the system; n-alcohols are suspected to form chain-like structures (Bao et al., 1996; Kaatze and Lönnecke-Gabel, 1991) while water molecules align in different shapes of clusters such as spherical or parallel sheets (Kemp and Gordon, 2008) the size of which tends to decrease with temperature (Raju, 2003).

Dielectric dispersion models are used to model the relaxation of a medium as a function of frequency, at different operating conditions. We cite those with most popularity: Debye (Debye, 1929), Cole-Cole (Cole, 1955), Davidson-Cole (Davidson and Cole, 2004) and Havrilík-Nagami (Havriliak and Negami, 2007) represented by eq (4) for (n,β) values of (1, 1); (0<n<1, 1); (0, 0<β<1); (0<n<1, 0<β<1) respectively. The terms “n” or “β” account for the existence of a distribution of the relaxation times (Cole, 1955), as well as the asymmetric dispersion behavior of the dispersion. This makes the dispersion models capable of describing more complicated microscopic interactions.
$$ \varepsilon^* = \varepsilon_{\infty} + \frac{\varepsilon_0 - \varepsilon_{\infty}}{(1 - (j\omega\tau)^n)^\beta} \quad (4) $$

The simplest and most popular is the Debye model. One of its main underlying assumptions is the rotational diffusion of spherical polar molecules in a viscous medium having a single relaxation time (Popov et al., 2016; Raju, 2003). It has proven to be able to produce good quality fits for dielectric data of some polar and organic liquids (Bao et al., 1996; Kaatze, 1989; Kaatze and Lönnecke-Gabel, 1991; Kaatze and Uhlendorf, n.d.; Lou et al., 1997; Patil et al., 2012; Winsor and Cole, 1982). The Cole-Cole (CC) model is more complicated than the former but its advantage is being able to account for Gaussian distribution of relaxation times (Cole, 1955). This makes it more adequate to study the properties of non-ideal systems such as that of saline water with high concentrations of saccharose (Bakam Nguenouho et al., 2022), or those of near ideal systems such as mixtures of n-alcohol and water (Bao et al., 1996; Rodríguez-Moré, n.d.).

Ionic presence is consequential to the dielectric behavior of the medium. The most notable contribution is through the increase of the absorbance of MW power quantified by the dielectric loss factor (Falkenhagen, 1931), and the decrease of $\varepsilon'$ by the decrease of the number of dipoles participating in the dielectric dispersion (Richard Buchner et al., 1999). The dispersion models can be modified to account for ionic presence as was done by many authors (Bakam Nguenouho et al., 2022; Klein and Swift, n.d.; Peyman et al., 2007; STOGRYN, 1971) through the addition of an imaginary term to account for the dielectric loss by ionic conduction.

$$ \varepsilon^* = \varepsilon_{\infty} + \frac{\varepsilon_0 - \varepsilon_{\infty}}{1 - (j\omega\tau)^n} + j\frac{\sigma}{\omega\varepsilon_0^*} \quad (5) $$

The Cole-Cole dielectric dispersion model with ionic conduction is shown in (5), $\varepsilon_{\infty}$ being optical permittivity, $\varepsilon_0$ is the static permittivity, $\tau$ (s) is the relaxation time, (n) is the relaxation time distribution parameter, $\omega$ (rd/s) is the angular frequency, $\sigma$ (S/m) is the electrical conductivity, and $\varepsilon_0^*$ (F/m) the vacuum permittivity. The dipolar rotation contributes to the real and imaginary part of the complex dielectric constant, while the ionic conduction (IC) mechanism - most righthand side term- contributes to loss factor.

The Cole-Cole dielectric model, using a complex nonlinear least square (CNLS) routine, was fitted simultaneously to both the real and the imaginary part of the experimental relative complex permittivity. The fitting was performed by way of minimizing an objective function that computes the sum of squared errors between experimental data (subscript “e”) and predicted dielectric properties (subscript “m”) as shown in eq (6). The Levenberg-Marquardt optimization algorithm (Bao et al., 1993) was coded in MATLAB® to find the solution set ($\varepsilon_0$, $\tau$, n, $\sigma$) that allows for this minimization. Initial guess for the algorithm was chosen intuitively but carefully. For a lack of better estimation, the optical dielectric constant of the mixture ($\varepsilon_{\infty,m}$) was calculated from Maxwell’s equation (7) where ($n_{\infty}$) is the refractive index of 30%wt. MEA at 20°C measured by
Ju (Ju et al., 2018). It was stated by (Kaatze and Uhlendorf, 1981) that ($ε_∞$) fitted from dielectric data at the microwave region carry great errors, instead the measurement range should extend to the far infra-red region.

$$ Error^2 = \frac{1}{n} \sum_{1}^{n} [(\varepsilon'_{n,e} - \varepsilon'_{n,m})^2 + (\varepsilon''_{n,e} - \varepsilon''_{n,m})^2] \quad (6) $$

$$ \varepsilon_{\infty, \text{mix}} = n_{\infty}^2 \quad (7) $$

## 2.4 Vapor-Liquid equilibrium model

A vapor-liquid equilibrium (VLE) model predicts the chemical speciation in a multicomponent multiphase system. VLE models are divided into two broad categories: non-rigorous thermodynamic models such as: Kent-Eisenberg, modified Kent-Eisenberg; and rigorous ones such as Deshmukh-Mather, and e-NRTL among others (Aronu et al., 2011). The non-rigorous models have some theoretical background but depend largely on empirical correction factors, this is contrary to the rigorous ones that employ activity coefficients to account for the non-idealities of the system (Suleman et al., 2021).

The Kent-Eisenberg (KE) model, although it is the least accurate, it owes its popularity to being the easiest to implement. Aboudheir (Aboudheir et al., 2003) studied the kinetics of CO₂ absorption in highly loaded aqueous MEA systems, however he used the KE model to calculate the chemical composition of loaded solutions. Similarly, Edali (Edali et al., 2009) and Jamal (Jamal et al., 2006) used this model to calculate the initial concentrations for kinetic absorption into mixed amine system and desorption from 30%MEA respectively. The advantage of introducing a VLE model in the frame of analysis of dielectric properties is that it would allow for insightful interpretations based on the chemical composition of the system at different CO₂ concentrations.

Model input parameters are the total MEA concentration, CO₂ loading (α) and (temperature) T. It is composed of five chemical reactions and three balance equations. The expressions of the apparent equilibrium constants for the involved chemical reactions are provided in the appendix. A total of eight equations are used to solve for eight chemical species: MEA denoted by RNH₂, MEAH⁺ denoted by RNH₃⁺, MEACOO⁻ denoted by RNHCOO⁻, OH⁻, H⁺, HCO₃⁻, CO₃²⁻, and CO₂. The model assumes no interaction between the different chemical species (Suleman et al., 2021), thus the apparent equilibrium constants of the dissociation reactions of: CO₂, H₂O, HCO₃⁻, and CO₃²⁻ are taken directly from literature (Edwards et al., 1978). Those related to MEA - eq (11, 12) - were fitted to experimental VLE data by Kent-Eisenberg (Kent and Eisenberg, 1976) employing a least-squared error procedure which lumps the deviations from the ideal system into the equilibrium constants. The chemical equilibrium in the system is presented by the following reactions:

161 -Dissociation of water

$$ 162 2H_2O \overset{K_1}{\rightleftharpoons} H_3O^+ + OH^- $$

163 -Dissociation of carbon dioxide
$$164 \quad CO_2 + 2H_2O \overset{K_2}{\rightleftharpoons} H_3O^+ + HCO_3^-$$

165 -Dissociation of bicarbonate

$$166 \quad HCO_3^- + H_2O \overset{K_3}{\rightleftharpoons} H_3O^+ + CO_3^{2-}$$

167 -Dissociation of carbamate ions

$$168 \quad RNHCOO^- + H_2O \overset{K_4}{\rightleftharpoons} RNH_2 + HCO_3^-$$

169 -Dissociation of protonated amine

$$170 \quad RNH_3^+ + H_2O \overset{K_5}{\rightleftharpoons} RNH_2 + H_3O^+$$

171 The algebraic equations of the equilibrium reactions are presented as follows:

$$K_1 = [H_3O^+][OH^-] \qquad (8)$$

$$K_2 = \frac{[HCO_3^-][H_3O^+]}{[CO_2]} \qquad (9)$$

$$K_3 = \frac{[H_3O^+][CO_3^{2-}]}{[HCO_3^-]} \qquad (10)$$

$$K_4 = \frac{[RNH_2][HCO_3^-]}{[RNHCOO^-]} \qquad (11)$$

$$K_5 = \frac{[RNH_2][H_3O^+]}{[RNH_3^+]} \qquad (12)$$

172 The equilibrium equations are complemented by the balance equations:

173 -Amine mass balance

$$[RNH_2]_0 = [RNH_2] + [RNHCOO^-] + [RNH_3^+] \qquad (13)$$

174 -Carbon balance

$$\alpha[RNH_2]_0 = [RNHCOO^-] + [HCO_3^-] + [CO_3^{2-}] + [CO_2] \qquad (14)$$

175 -Electroneutrality of solution (Charge balance)

$$\begin{gathered} [RNH_3^+] + [H^+] = \\ [RNHCOO^-] + [HCO_3^-] + [OH^-] + [CO_3^{2-}] \end{gathered} \qquad (15)$$

176 The non-linear system, composed of eight algebraic equations were solved using finite-element method (FEM) in COMSOL® Multiphysics (6.1). The coefficient-form partial differential equation module (PDE) was used to solve the system.

177 The non-linear equations were written as residual terms and solved over a 1D geometry representing the CO₂ loading α ∈ [0-0.8]. Uniform meshing was used for a total of 30 points over the domain, and zero flux boundary condition was used at α=0 and α=0.8. Initial values of the variables were chosen intuitively to have the same order of magnitude as the expected solution under α=0. It should be noted that H₂O concentration was determined after solving the system of equations by performing an atomic balance on Hydrogen before and after CO₂ loading as shown in eqn (16). An underlying condition of this equation is
the isochoric nature of the solution as a function of the CO₂ loading; this can be concluded from the density values reported by Weiland (Weiland et al., 1998).

-Atomic balance on hydrogen

$$2[\text{H}_2\text{O}]_\alpha + [\text{H}^+]_\alpha + [\text{OH}^-]_\alpha + 7[\text{RNH}_2]_\alpha + 8[\text{RNH}_3^+]_\alpha + 6[\text{RNHCOO}^-]_\alpha + [\text{HCO}_3^-]_\alpha = 2[\text{H}_2\text{O}]_{\alpha=0} + 7[\text{RNH}_2]_{\alpha=0} \quad (16)$$

# 3 Results

## 3.1 Vapor-liquid equilibrium model

The VLE model of Kent-Eisenberg was solved for $\alpha \in [0-0.8]$ and for temperature variations from 20 to 80°C. Results show that speciation is overwhelmingly dependent on the CO₂ loading instead of the temperature (not presented here), consequently we will consider the chemical speciation at 20°C on the aforementioned range of $\alpha$. The molar fractions ($x$) of chemical components are plotted in Figure 2 for temperature 20°C. In order to evaluate the accuracy of the model, calculated mole fractions are compared to those obtained experimentally by Poplsteinova (Jakobsen et al., 2005) using NMR spectroscopy; both data sets are plotted in Figure 2. It is clear that there is a good quantitative agreement between experimental and predicted chemical speciation.

Figure 2 also shows that with increased CO₂ loading, concentration of MEA decreases as it is being consumed to produce ionic species, mainly MEAH⁺ and MEACOO⁻ for the region $\alpha<0.5$ while other ionic species have negligible concentrations. At higher loadings, carbamate ions (MEACOO⁻) dissociate to produce more MEA that reacts with CO₂ and H₂O to produce HCO₃⁻; it is only because of this that loadings higher than $\alpha=0.5$ are possible. The concentration of H₂O is not plotted in Figure 2 to preserve the current scale because of the comparatively high molar fraction ($x_{\text{H}_2\text{O}} > 0.825$) than the other chemical species. Still, the concentration of H₂O experiences some decrease with increasing $\alpha$; a drop of 7% was calculated over the range of $\alpha$.
<figure><img src="image_3.png" /><figcaption>Figure 2: Kent-Eisenberg chemical speciation model and experimental values obtained by NMR spectroscopy for 30%MEA from (Jakobsen et al., 2005)</figcaption></figure>

## 3.2 Dielectric properties 30% MEA solution

Deionized water (DW) was used as a standard to verify the dielectric measurement technique. The properties of DW were measured at different temperatures [20-60 °C] by steps of 10 °C and compared with results from Debye model, the latter being complemented with dispersion parameters (ε₀, τ, ε∞) obtained from (Richard Buchner et al., 1999). %AARD on ε' is less than 2% for all temperatures at all frequency points. ε'' displays deviations from the correlation where max %AARD can reach 10%; the reason being the low equipment sensitivity when (ε'' < 5% ε') of the sample under test (Keysight 85070E: Dielectric Probe kit 200 MHz to 50 GHz, 2017).

The dielectric properties of 30% MEA solution were measured over the frequency range [915-2450] MHz at temperatures ranging from 20 to 80°C by steps of 10°C, and α was varied over [0.22-0.55] by steps Δα=0.11. The Debye and Cole-Cole dielectric dispersion models were fitted to the experimental dielectric data by finding the set of parameters (ε₀, τ, (n), σ) that minimizes the squared errors as per eqn (5). Both dispersion models provided good fitting results, but those from Cole-Cole model were privileged due to the greater accuracy in modeling the experimental data. Figure 3, and Figure 4 present the parity plots of the calculated and experimentally obtained relative permittivity and dielectric loss factor respectively at f=915MHz and 2450MHz. It can be observed that deviations between both sets of data is minimal highlighting the quality of the fit and the suitability of the Cole-Cole dispersion to model the dielectric properties of solution.
<figure><img src="image_4.png" /><figcaption>Figure 3: Modeled and experimental relative permittivity of 30%MEA solution at 915MHz (red) and 2450MHz (black) following the Cole-Cole dielectric dispersion model: x, α=0.22; □, α=0.33; Δ, α=0.44; ◦, α=0.55.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: Modeled and experimental dielectric loss factor of 30%MEA solution at 915MHz (red) and 2450MHz (black) following the Cole-Cole dielectric dispersion model: α=0.22; □, α=0.33; Δ, α=0.44; ◦, α=0.55.</figcaption></figure>

### 3.2.1 Dielectric dispersion diagram

Figure 5 and Figure 6 show the experimental and modeled dielectric dispersion of 30%MEA at (T=20°C; α=0.22) and (T=80°C; α=0.55) respectively which represent the extremes of measurement conditions. The total dielectric loss ($ε''_t$) was decomposed into its contributions of dipole rotation ($ε''_{DR}$) and ionic conduction ($ε''_{IC}$) presented in eqns (18-19) respectively. The expression in eq (18) - obtained from (Raju, 2003) - was obtained by separating the real and imaginary terms of the two left-hand side terms of eq (5).

$$ε''_t = ε''_{DR} + ε''_{IC} \qquad (17)$$

$$ε''_{DR} = (ε_0 - ε_∞) \frac{(fT)^n \sin(\frac{n\pi}{2})}{1+2(fT)^n \cos(\frac{n\pi}{2})+(fT)^2n} \qquad (18)$$

$$ε''_{IC} = \frac{\sigma}{\omega\varepsilon_0} \qquad (19)$$
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Figure 5 shows that both mechanisms have comparable contributions to the dielectric loss: at f=915 MHz ionic conduction overtakes the dipolar rotation, this changes at 2450 MHz where higher frequencies hinder ionic conduction contrary to the dipolar rotation that is incentivized due to greater proximity to the relaxation frequency. The increasing contribution of dipolar rotation with frequency shows that the relaxation frequency of the solution is superior to the spectrum of measurement in this study. On the other hand, Figure 6 shows that the contribution of the ionic conduction - to the overall dielectric loss - is immense compared to that of dipolar rotation, values can reach 167.15 versus 8.71 units respectively at 915 MHz. This can be explained by the concentration surge of MEACOO⁻ and MEAH⁺ with higher CO₂ loading as indicated in Figure 2, as well as higher temperatures leading to higher ion mobilities. The decrease of ε''IC from 915 to 2450 MHz is explained with the Falkenhagen (Falkenhagen, 1931) theorem: the central ion- when subjected to a time-harmonic external E-field - experiences a certain mobility, but the surrounding ionic cloud lags behind, thus exerting an opposite relaxation force on the former therefor reducing its mobility with higher frequencies.

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### Effect of (α) on dielectric properties

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The effect of (α) on the dielectric dispersion was studied by plotting the Cole-Cole fit in Figure 7 at (T=20 °C), and (α) c [0.22, 0.55], with a particular focus on the range [915-2450 MHz]. It can be observed that with increased (α) the dispersion curve is shifted upwards and has a greater monotonous decrease. The upward shift is caused by a more dominant lossy character due to increased ionic concentration in the liquid as observed in Figure 2. It is accompanied by a greater steepness; the cause lies in the greater sensitivity of ionic conduction to frequency decrease with higher ionic concentrations. It is interesting to note that with higher carbonation ratios the resemblance to the Cole-Cole dispersion fades, especially at lower frequencies.

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When considering the dispersion on [915-2450 MHz], we observe the curve to stretch to cover a greater range of (ε'). The stretching with increasing (α) is caused by the decrease of the relaxation frequency (more on this in section 3.3.2); The relaxation frequency decreases to values of greater proximity to the spectrum of measurement which causes wider variations of (ε'). This can be contrasted to measurement frequencies that are significantly higher or lower than the relaxation frequency; at such ranges one of two values for (ε') is possible: (ε' = ε₀) at relatively low frequencies, or (ε' = ε∞) at relatively high frequencies. The values of (ε') at 915 MHz are in the range (65-72) units: values that are in the same range as those of water but lower owing to Monoethanolamine possessing a weaker static dielectric constant than water - 31.94 (Ikada, 1969) and 79.93 (Kaatze, 1989) at 20°C respectively.

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### Effect of (T) on dielectric properties

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The effect of temperature on the dielectric dispersion is studied in Figure 8 where temperature is varied along the range [20-80 °C] while fixing (α=0.22). The figure shows that greater temperatures lead to higher dielectric losses (ε''), especially
<figure><img src="image_6.png" /><figcaption>Figure 7: Dielectric dispersion of 30%wt. MEA at T=20°C and $\alpha \epsilon$ [0.22-0.55]</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 8: Dielectric dispersion of 30%wt. MEA at T $\epsilon$ [20-80 °C] and $\alpha$=0.22</figcaption></figure>

## Dielectric loss factor at 915 MHz and 2450 MHz

The dielectric loss factor of [ε"] of 30%wt. MEA were plotted in Figure 9 for different temperatures and carbonation ratios, for (f=915 MHz) and (f=2450 MHz) respectively. In Figure 9, the dielectric loss factors (ε") are shown to be positively influenced by both temperature and carbonation ratio. This is mainly related to ionic conduction dominating the loss factor, with increased ionic content, and ionic mobility. As the temperature increases ionic mobility increases which enforces the lossy character of the solution. It is noteworthy to say however that (ε") has a greater sensitivity to (T) and (α) at 915 MHz than at 2450 MHz: this can be explained by the decreased contribution of ionic conduction at higher frequencies

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<figure><img src="image_8.png" /><figcaption>Figure 9: Dielectric loss factor (ε") of 30wt. MEA solution as a function of temperature and carbonation ratio at f=915 MHz.</figcaption></figure>

### 3.2.2 Penetration depth

The penetration depth of the E-field in the solution was calculated at different temperatures and CO₂ loadings as per the expression given in eq (20) and taken from (Ellison et al., 2017). δₚ (mm) being the penetration depth, c (m/s) is the speed of light in vacuum, and f (Hz) is the frequency of the E-field.

$$ \delta_p = \frac{c}{2\pi f \sqrt{2\varepsilon'}} \left[ \sqrt{1 + \left(\frac{\varepsilon''}{\varepsilon'}\right)^2} - 1 \right]^{-\frac{1}{2}} \quad (20) $$

Figure 10, and Figure 11 present the penetration depth at 915 and 2450 MHz respectively; the obtained values are in the order of a few millimeters which are small in comparison to that of water (11.4cm at 20°C and 915 MHz and 1.6 cm at 20°C and 2450 MHz) These values are calculated using Debye model, the dispersion parameters are provided in the appendix as correlations. Although ε''_t and ε' are greater at 915 MHz, δₚ at this frequency is superior to that of 2450 MHz. Also, observed for both MW frequencies is the decrease of δₚ with temperature and α, this was mainly related to greater mobility of ionic species and the rise of ionic concentration respectively.
<figure><img src="image_9.png" /><figcaption>Figure 10: Penetration depth in 30%wt. MEA function of temperature at different CO2 loadings at f=915 MHz.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 11: Penetration depth in 30%wt. MEA function of temperature at different CO2 loadings at f=2450 MHz.</figcaption></figure>

## 3.3 Dielectric dispersion parameters

The fitted dielectric dispersion parameters (ε₀, τ, n, σ) of the Cole-Cole model are plotted in Figure 12, Figure 14, Figure 15 and Figure 16 respectively as a function of temperature and at different CO₂ loadings. They were approximated by a polynomial of the form shown in eq (21) whose parameters are given in the appendix. The polynomial was provided to obtain better reproducibility of the experimental results and the form of which was chosen arbitrarily to well represent the dispersion properties. The variations of the dispersion parameters are discussed in the ensuing paragraphs.

$$f(T, \alpha) = (aT^2 + bT + c)(d\alpha^3 + e\alpha^2 + f\alpha + g) \quad (21)$$
<figure><img src="image_11.png" /><figcaption>Figure 12: Static dielectric constant of 30%wt. MEA as a function of T and α. Lines, polynomial fittings; (symbols), fitted values: (x), α=0.22; (Δ), α=0.33; (◊), α=0.44; (□), α=0.55.</figcaption></figure>

### 3.3.1 Static relative permittivity (ε₀)

The values of static permittivity shown in Figure 12 appear to decrease with temperature at all tested values of α. It is expected hence higher temperatures contribute to higher thermal energies that decrease the size of H-bonded clusters (Winsor and Cole, 1982). This behavior is able to justify the one observed in Figure 8 where ε' at f=915 and 2450 MHz decreases with increasing temperatures. The decrement of the fitted static permittivity Δε₀ over the temperature range in this study (ΔT=60°C) is in the range of [15.36 - 19.24]; values that are comparable to that of pure water: Δε₀=19.22 (Richard Buchner et al., 1999), or to that of 30% aqueous MEA - Δε₀=18 (Jadhavpatil et al., 2019) over the same temperature range.

Figure 12 also shows that ε₀ has an increasing trend with α which is surprising, although this justifies the trend of experimental results of increasing ε' with higher carbonation ratios (α) - (Figure 7). It is expected that with increasing α, the molecular MEA concentration would decrease as implied from Figure 2, translating to a decrease of the total dipole concentration in the solution. In addition, the augmentation of ionic concentration evokes greater dipole-ion short-range interactions; this leads to irrotational bonding of dipoles by their neighboring ions (Schwartz, 1976), or through the long-range kinetic depolarization described by the Hubbard-Onsanger (Hubbard et al., 1977) theorem. It can therefore be assumed that static permittivity of 30%wt. MEA with no CO₂ content would be higher than that which contains CO₂. The static permittivity of 30%wt. MEA free of CO₂ measured by (Jadhavpatil et al., 2019) and verified locally (not mentioned here) nears 69 units at 25°C, a value that is inferior to results for solutions with carbon content - (Figure 12).

One explanation as to why our results are difficult to interpret is that the measurement spectrum does not extend to sufficiently low frequencies, i.e. the relaxation frequency ($f_r = 1/2\pi\tau$) of the solution is comparable to the spectrum of measurement; accordingly, not enough experimental points are presented at the low frequency region to accurately portray
the static dielectric constant. This is particularly true with lower temperatures and higher $\alpha$; as an example, the dielectric dispersion of the solution at 20°C and $\alpha$=0.55 is plotted in Figure 13. The figure shows that the experimental data points are in the neighborhood of the relaxation frequency, consequently the interpolation of the model to low frequency range may result in mal estimation of the true static dielectric constant. Still, the possibility of ionic polarization contributing to the static dielectric constant cannot be ruled out. While many authors have studied the relaxation of electrolyte solutions, the studies were centered around simple salts. Dielectric studies focusing on electrolyte solutions with more complex ions such as those derived from MEA are not so common, and therefore it is difficult to decisively interpret the obtained results.

Nevertheless, discussions on the static permittivity does not undermine in any way the dispersion model's ability to accurately replicate the solutions' dielectric properties on the frequency range of measurement. The model will be more than sufficient for practical ends such as design of microwave equipment and EM modeling. Its accuracy is clearly demonstrated by the excellent fits shown in Figure 5 and Figure 6.

<table><caption>Table 1: Fitted dielectric dispersion properties for Cole-Cole model</caption><thead><tr><th>T(°C)</th><th>ε<sub>0</sub></th><th>τ(ps)</th><th>σ(S/m)</th><th>n</th><th>fr(GHz)</th><th>Error<sup>2</sup></th></tr></thead><tbody><tr><td colspan="7" style="text-align:center; font-weight:bold;">α=0.22</td></tr><tr><td>20</td><td>71.3</td><td>26.7</td><td>1.8</td><td>0.84</td><td>5.97</td><td>0.1</td></tr><tr><td>30</td><td>70.1</td><td>21.9</td><td>2.2</td><td>0.82</td><td>7.27</td><td>0.1</td></tr><tr><td>40</td><td>67.8</td><td>17.7</td><td>2.7</td><td>0.83</td><td>8.99</td><td>0.1</td></tr><tr><td>50</td><td>69.7</td><td>15.4</td><td>3.1</td><td>0.75</td><td>10.36</td><td>0.0</td></tr><tr><td>60</td><td>66.8</td><td>13.1</td><td>3.6</td><td>0.77</td><td>12.14</td><td>0.0</td></tr><tr><td>70</td><td>63.6</td><td>11.3</td><td>4.3</td><td>0.80</td><td>14.10</td><td>0.0</td></tr><tr><td>80</td><td>60.1</td><td>11.1</td><td>5.0</td><td>0.88</td><td>14.29</td><td>0.0</td></tr><tr><td colspan="7" style="text-align:center; font-weight:bold;">α=0.33</td></tr><tr><td>20</td><td>80.5</td><td>32.0</td><td>2.3</td><td>0.73</td><td>4.97</td><td>0.1</td></tr><tr><td>30</td><td>80.9</td><td>27.5</td><td>2.8</td><td>0.70</td><td>5.78</td><td>0.1</td></tr><tr><td>40</td><td>79.5</td><td>23.0</td><td>3.5</td><td>0.69</td><td>6.92</td><td>0.1</td></tr><tr><td>50</td><td>76.6</td><td>19.4</td><td>4.1</td><td>0.70</td><td>8.19</td><td>0.1</td></tr><tr><td>60</td><td>72.4</td><td>16.4</td><td>5.0</td><td>0.74</td><td>9.70</td><td>0.0</td></tr><tr><td>70</td><td>68.6</td><td>14.3</td><td>5.8</td><td>0.78</td><td>11.10</td><td>0.1</td></tr><tr><td>80</td><td>63.4</td><td>13.0</td><td>6.4</td><td>0.82</td><td>12.24</td><td>0.1</td></tr><tr><td colspan="7" style="text-align:center; font-weight:bold;">α=0.44</td></tr><tr><td>20</td><td>89.6</td><td>38.7</td><td>3.0</td><td>0.67</td><td>4.11</td><td>0.1</td></tr><tr><td>30</td><td>90.6</td><td>35.5</td><td>3.5</td><td>0.64</td><td>4.49</td><td>0.0</td></tr><tr><td>40</td><td>88.3</td><td>28.9</td><td>4.4</td><td>0.64</td><td>5.50</td><td>0.0</td></tr><tr><td>50</td><td>84.1</td><td>23.5</td><td>5.3</td><td>0.66</td><td>6.78</td><td>0.0</td></tr><tr><td>60</td><td>79.3</td><td>19.1</td><td>6.2</td><td>0.69</td><td>8.31</td><td>0.0</td></tr><tr><td>70</td><td>74.7</td><td>16.2</td><td>7.2</td><td>0.74</td><td>9.83</td><td>0.0</td></tr><tr><td>80</td><td>68.8</td><td>15.3</td><td>8.2</td><td>0.86</td><td>10.43</td><td>0.2</td></tr><tr><td colspan="7" style="text-align:center; font-weight:bold;">α=0.55</td></tr><tr><td>20</td><td>92.7</td><td>44.1</td><td>3.6</td><td>0.66</td><td>3.61</td><td>0.0</td></tr><tr><td>30</td><td>92.7</td><td>38.5</td><td>4.3</td><td>0.65</td><td>4.13</td><td>0.0</td></tr><tr><td>40</td><td>82.7</td><td>31.9</td><td>4.8</td><td>0.65</td><td>4.99</td><td>0.0</td></tr><tr><td>50</td><td>84.2</td><td>26.6</td><td>6.1</td><td>0.66</td><td>5.98</td><td>0.0</td></tr><tr><td>60</td><td>87.2</td><td>25.1</td><td>6.9</td><td>0.58</td><td>6.35</td><td>0.1</td></tr><tr><td>70</td><td>75.2</td><td>17.1</td><td>7.8</td><td>0.75</td><td>9.29</td><td>0.0</td></tr><tr><td>80</td><td>72.4</td><td>16.1</td><td>8.5</td><td>0.79</td><td>9.91</td><td>0.0</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>Figure 13: Dielectric dispersion of 30%wt. MEA at T=20°C, α=0.55.

Symbol (o), experimental points; continuous line (—), Cole-Cole model.</figcaption></figure>

### 3.3.2 Relaxation time ($\tau$)

The relaxation time of the solution is shown in Figure 14 as a function of temperature and at different values of $\alpha$. Figure 14 shows that with increasing temperature the relaxation time decreases to reach values in the neighborhood of 10 picoseconds – the relaxation time of water at 20°C (R. Buchner et al., 1999). The reason for this is that higher temperatures lead to weaker and smaller hydrogen bonded clusters, which facilitates faster dissolution of those clusters under a varying E-field (Kaatze and Lönnecke-Gabel, 1991; Raju, 2003; Winsor and Cole, 1982). While increasing temperatures decrease the number of dipoles under the influence of the E-field (lowers static permittivity), the ones that are under this influence are able to relax in a faster manner. This ultimately lowers the relaxation time of the medium, or in an equivalent manner, the increase of the relaxation frequency.

Figure 14 also reveals the increase of the relaxation time of the solution with increasing $\alpha$; the result of two effects at play. The first is the rise of the solution's dynamic viscosity by 31% when $\alpha$ increases from 0.22 to 0.55 at 25°C (Weiland et al., 1998), hence increased viscosity hinders dynamic relaxation (Bakam Nguenouho et al., 2022). The second contributing effect is the interaction of ionic species with the molecular dipoles of the system (MEA, H₂O): molecular dipoles in the solvation shell of ionic species experience an increase/decrease of relaxation time compared to that of the pure solvent. This happens to be the case of aqueous solution of NaCl where the relaxation time of H₂O dipoles in solvation shell of the anionic species (Cl⁻) is lower than that of pure water, contrary to that of Na⁺ where it's higher. The result is a slight reduction in the apparent relaxation time as a function of the salt concentration (Richard Buchner et al., 1999) as has been observed by (Bakam Nguenouho et al., 2022) for aqueous saline solutions. Figure 14 shows the increase of the relaxation time with $\alpha$; so, either
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the viscosity increase had a greater effect on the relaxation time than ion-dipole interactions, or both effects contributed to hindering the dipolar movement ultimately leading to a slower relaxation mechanism (higher relaxation time).

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Results in Figure 14 support the experimental measurements in Figure 7 and Figure 8 where greater α and lower temperatures lead to higher relaxation times thus lowering the relaxation frequency to the measurement range to produce wider dielectric dispersion curves.

<figure><img src="image_13.png" /><figcaption>Figure 14: Apparent relaxation time (τ) of 30%wt. MEA as a function of T and α. Lines, polynomial fittings; (symbols), fitted values: (x), α=0.22; (Δ), α=0.33; (◊), α=0.44; (□), α=0.55.</figcaption></figure>

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### 3.3.3 Relaxation time distribution parameter (n)

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Parameter (n) is plotted in Figure 15 as a function of temperature and at different CO₂ charges. It appears that (n) is inferior to one, implying the existence of a distribution of relaxation times of the solution (Cole, 1955). Another observation is that (n) displays a parabolic trend with temperature, with the lowest value occurring at 40°C<T<50°C, and higher values at the T extremes. Buchner (Richard Buchner et al., 1999) observed a similar non-monotonous trend as a function of temperature for saline solutions over the range of 5 to 35 °C.

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Figure 15 reveals the monotonous decrease of (n) as a function of α; the chemical absorption of CO₂ produces many ionic species, mainly MEACOO⁻ and MEAH⁺ as predicted by the speciation model in Figure 2. The produced ionic species interact differently with the dipoles of the solution (water and MEA) to produce broader distributions of relaxation times. The values of (n) obtained in this study are not uncommon, (Bakam Nguenouho et al., 2022) obtained ones in the order of 0.8 for water and saccharose at 25°C, also (Peyman et al., 2007) obtained a value of 0.83 for an aqueous saline solution having a molarity 4.44 M.
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It appears that the general trend is a broader distribution of relaxation times with increasing solute concentration in the solvent phase. This trend is not respected when different liquids are mixed. Bao (Bao et al., 1993) observed an almost parabolic profile of (n) for an ethanol/water mixture as a function of the mole fraction of water with a value of unity at the pure component extremes. Kaatze (Kaatze and Lönnecke-Gabel, 1991) on the other hand used a Debye model with two relaxation mechanisms (fast and slow) to fit the dielectric properties of binary mixtures of organic solvents at different compositions; for pure components, only one relaxation mechanism sufficed.

<figure><img src="image_14.png" /><figcaption>Figure 15: Distribution parameter of relaxation time function of T and α. Lines, polynomial fittings; (symbols), fitted values (x), α=0.22; (Δ), α=0.33; (◊), α=0.44; (□), α=0.55.</figcaption></figure>

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### 3.3.4 Electrical conductivity (σ)

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The electrical conductivity of 30%MEA solution is displayed in Figure 16 as a function of T and α. The electrical conductivity of loaded solutions are two orders of magnitude greater than for non-loaded ones (0.072 S/m at 20°C) (Ju et al., 2018) owing to ionic presence from the absorption reaction. It appears that σ increases linearly with temperature; temperature rise decreases the viscosity of the solution (Weiland et al., 1998) translating to greater ion mobility as per the Walden equation (Subbiah and Morison, 2018). Additionally, increasing temperatures counteract the ion-pair association through thermal agitation; the latter hinders the formation of neutral ion pairs that are inert to the external E-field (Zhang et al., 2020).
<figure><img src="image_15.png" /><figcaption>Figure 16: Electrical conductivity of 30%MEA solution function of T and α.
Lines, polynomial fittings; (symbols), fitted values: (x), α=0.22; (Δ), α=0.33; (◊), α=0.44; (□), α=0.55.</figcaption></figure>

σ increases with CO₂ charge from α=0.22 up to 0.44. The reason is the linear increase of MEAH⁺ and MEACOO⁻ by reaction of MEA dipoles with CO₂. For α=0.55, σ experiences a more gentle rise with respect to the curve at α=0.44, which is somewhat particular considering that the total ionic content of the solution increases steadily over the entire range of α. In view of the constant viscosity between α=0.44 and 0.55 (Weiland et al., 1998), the diminishing increment of conductivity with α suggests the commencement of ion-pair association.

The effects of α and T on the electrical conductivity justify the experimental results in Figure 7 and Figure 8 respectively, with the dielectric dispersion curve shifting upwards to higher values of ε'' with the increase of these two conditions.

## 4 Conclusion

The dielectric properties of CO₂-loaded 30% by weight aqueous monoethanolamine solution were measured on frequency range [915-2450] MHz at different temperatures and CO₂ loadings. The dielectric dispersion parameters of the liquid were obtained by fitting the Cole-Cole to the experimental data; the formers were then interpreted with the help of the Kent-Eisenberg vapor liquid equilibrium model. Experimental results indicate a high dielectric loss factor that aggravates with higher temperatures and CO₂ loadings, producing penetration depths in the order of few millimeters. The lossy character of the solution is dominated by the ionic conduction, however dipolar rotation can in some instances dominate the loss mechanism. With regards to the fitted dispersion parameters, results indicate that the static dielectric constant ε₀ decreases with temperature but surprisingly enough, it increases with CO₂ loading although the total dipolar concentration is decreasing as shown by the chemical speciation model. The suspected reasons for this behavior are either: extrapolation of the dispersion model beyond the experimental data, or the contribution of the ionic species to static permittivity of the medium. The apparent relaxation time decreases with temperature due to the formation of smaller H-bonded networks but increases with
CO₂ loading by the action of viscosity increase. The solution is shown to experience a broader distribution of relaxation times with increasing CO₂ loading while a non-monotonous behavior is observed with respect to temperature. The electrical conductivity of the solution is increased by the action of increased ionic mobility and concentration with increased temperature and CO₂ loading respectively.

## 5 Acknowledgements

The authors gratefully acknowledge the National Research Agency (ANR) of France for their grant (19-CE05-0027-01), as well as the national association for research and technology (ANRT) of France.

## 6 Appendix

### Notations

<table><tr><td>α</td><td>Carbonation ratio: [CO₂]/[MEA]</td></tr><tr><td>T</td><td>Temperature (°C)</td></tr><tr><td>K</td><td>Chemical equilibrium constant</td></tr><tr><td>ε*</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>n</td><td>Cole-Cole Fitting parameter</td></tr><tr><td>σ</td><td>Electric conductivity (S/m)</td></tr><tr><td>δ</td><td>Penetration depth (mm)</td></tr><tr><td>c</td><td>Speed of light in vacuum (m/s)</td></tr><tr><td>Error<sup>2</sup></td><td>Squared Error</td></tr><tr><td>n<sub>∞</sub></td><td>Refractive index</td></tr><tr><td>x</td><td>Mole fraction</td></tr></table>

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## Abbreviations

<table><tr><td>IPCC</td><td>Intergovernmental panel on climate change</td></tr><tr><td>EM</td><td>Electromagnetic</td></tr><tr><td>E-field</td><td>Electric field</td></tr><tr><td>MW</td><td>Microwave</td></tr><tr><td>MEA</td><td>Monoethanolamine</td></tr><tr><td>DEA</td><td>Diethanolamine</td></tr><tr><td>HCO<sub>3</sub><sup>-</sup></td><td>Bicarbonate</td></tr><tr><td>DW</td><td>Deionized water</td></tr><tr><td>BaCl<sub>2</sub></td><td>Barium Chloride</td></tr><tr><td>BaCO<sub>3</sub></td><td>Barium Carbonate</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>KE</td><td>Kent-Eisenberg</td></tr><tr><td>VLE</td><td>Vapor-Liquid Equilibrium</td></tr><tr><td>MFC</td><td>Mass flow controller</td></tr><tr><td>GC</td><td>Gas chromatograph</td></tr></table>

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## Subscripts

<table><tr><td>e</td><td>Experimental</td></tr><tr><td>m</td><td>Model</td></tr><tr><td>mix</td><td>Mixture</td></tr><tr><td>t</td><td>Total</td></tr><tr><td>IC</td><td>Ionic Conduction</td></tr><tr><td>DR</td><td>Dipolar Rotation</td></tr></table>

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### 6.1.1 Kent-Eisenberg VLE model

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The equilibrium constants used in the K.E VLE model are presented in the equation below with the corresponding parameters for each equation taking the form:

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$$ \ln(K) = \frac{a_1}{T} + a_2 \ln T + a_3 \quad (22) $$

<table><caption>Table 2: Parameters for calculation of the equilibrium constants</caption><thead><tr><th></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>T- Validity(K)</th><th>Reference</th></tr></thead><tbody><tr><td>K<sub>1</sub>(mol/dm<sup>3</sup>)<sup>2</sup></td><td>-13445.9</td><td>-22.4773</td><td>140.932</td><td>273-498</td><td>[52]</td></tr><tr><td>K<sub>2</sub>(mol/dm<sup>3</sup>)</td><td>-12092.1</td><td>-36.7816</td><td>235.482</td><td>273-498</td><td>[52]</td></tr><tr><td>K<sub>3</sub>(mol/dm<sup>3</sup>)</td><td>-12431.7</td><td>-35.4819</td><td>220.067</td><td>273-498</td><td>[52]</td></tr><tr><td>K<sub>4</sub>(mol/dm<sup>3</sup>)</td><td>-3090.83</td><td>0</td><td>6.69425</td><td>298-413</td><td>[53]</td></tr><tr><td>K<sub>5</sub>(mol/dm<sup>3</sup>)</td><td>-5851.11</td><td>0</td><td>-3.3636</td><td>298-413</td><td>[53]</td></tr></tbody></table>

## 6.1.2 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 previous authors (Richard Buchner et al., 1999). Validity of these parameters are for T c [0, 55] °C and in the frequency range f<20.05GHz. The complex permittivity is given by the Debye model:

$$ \epsilon' - j\epsilon'' = \epsilon_{\infty} + \frac{\epsilon_0 - \epsilon_{\infty}}{1 - j2\pi\tau f} + \frac{i\sigma}{2\pi\epsilon_0^* f} \quad (23) $$

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

$$ \epsilon_0 = 87.85306 \exp(-0.00456992 T(^{\circ}\text{C})) \quad (24) $$

-The relaxation time is given by:

$$ \tau(\text{ps})^{-1} = 5.631 \ 10^{-02} + 2.12 \ 10^{-03} \ \text{T}(^{\circ}\text{C}) \\ + 1.86 \ 10^{-05} \ \text{T}^2(^{\circ}\text{C}) \quad (25) $$

-The optical relative dielectric constant is given by:

$$ \epsilon_{\infty} = 6.49 - 0.025 \text{T}(^{\circ}\text{C}) \quad (26) $$

## 6.1.3 Polynomial fit of dispersion properties

The polynomial fit of the dispersion properties of the Cole-Cole model were fitted with the polynomial equation below.

$$ f(T, \alpha) = (aT^2 + bT + c)(d\alpha^3 + e\alpha^2 + f\alpha + g) \quad (27) $$
<table><caption>Table 3: polynomial parameters for dispersion properties of Cole-Cole dielectric dispersion model for 30%MEA function of T and α</caption><thead><tr><th></th><th>ε<sub>0</sub></th><th>τ(ps)</th><th>σ(S/m)</th><th>n</th></tr></thead><tbody><tr><td>a</td><td>-0.0155</td><td>0.0136</td><td>0.00145</td><td>0.000576</td></tr><tr><td>b</td><td>0.418</td><td>-2.87</td><td>0.324</td><td>-0.0486</td></tr><tr><td>c</td><td>319</td><td>197</td><td>9.60</td><td>4.99</td></tr><tr><td>d</td><td>-3.47</td><td>-3.83</td><td>-3.71</td><td>-1.21</td></tr><tr><td>e</td><td>3.12</td><td>3.78</td><td>3.46</td><td>1.56</td></tr><tr><td>f</td><td>-0.643</td><td>-0.724</td><td>-0.675</td><td>-0.727</td></tr><tr><td>g</td><td>0.258</td><td>0.205</td><td>0.134</td><td>0.285</td></tr><tr><td>Error<sup>2</sup></td><td>4.21</td><td>0.80</td><td>0.02</td><td>0.00</td></tr></tbody></table>

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