# Dielectric behaviour of an epoxy network cured with a phosphonium-based ionic liquid

Thibaut Lefort, Jannick Duchet-Rumeau, Sébastien Livi, Damien Bachellerie, Sébastien Pruvost

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Thibaut Lefort, Jannick Duchet-Rumeau, Sébastien Livi, Damien Bachellerie, Sébastien Pruvost. Dielectric behaviour of an epoxy network cured with a phosphonium-based ionic liquid. Polymer, 2021, 222, pp.123645. 10.1016/j.polymer.2021.123645. hal-03279986

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# Dielectric behaviour of an epoxy network cured with a phosphonium-based ionic liquid

Thibaut Lefort¹,², Jannick Duchet-Rumeau¹, Sébastien Livi¹, Damien Bachellerie² and Sébastien Pruvost¹,*

1 Univ. Lyon, INSA Lyon, UMR CNRS 5223, IMP Ingénierie des Matériaux Polymères, F-69621 Villeurbanne, France

2 SuperGrid Institute SAS- 23, rue Cyprian, BP 1321 - 69611 Villeurbanne, France

## ABSTRACT

Phosphonium based ionic liquids (ILs) have been previously shown as a new emerging class of initiator of epoxy prepolymers. The present study aims at investigating the influence of ILs on the dielectric behaviour of epoxy-IL systems by dielectric spectroscopy. Here, the content of IL incorporated in the epoxy prepolymer has a significant impact on the final properties of the polymer networks displaying a high glass transition temperature (Tg> 160 °C). The excess of IL (> 10 phr) acts as a plasticizer agent decreasing the Tg and leading to the formation of heterogeneities. Moreover, the study of α and β conventional relaxation modes by dielectric spectroscopy highlighted an increase of chain mobility due to IL excess. A ω relaxation mode has been noticed with the addition of high content of IL, probably relating to heterogeneities of the network. Unlike the most of polymer systems, the study of the DC conductivity by the application of an Arrhenius law demonstrated a thermal activation mechanism, independent from the free volume and the glass transition phenomenon. A discussion on the identification of charge carriers has been finally proposed.

## 1 INTRODUCTION

Ionic liquids (ILs) are molten salts composed of an organic cation and an organic or inorganic anion with a melting temperature below 100°C. Due to their low vapour pressure, their good chemical and thermal stabilities, the endless number of cation-anion combinations, their high ionic conductivity and their ability as a solvent [1] [2]. ILs have recently attracted a great interest in the material science. Moreover, their low melting temperature as well as their tuneable viscosity allow them to be compatible with polymer process temperature. These properties make them attractive in a wide range of applications, such as electrolytes [3] [4] [5] [6] [7], lubricants [8] [9] [10], plasticizers and materials additives [11] [12].

Very recently, few authors investigated the ability of ILs to initiate the homopolymerization of epoxy prepolymers [13] [14] [15]. The first studies have reported that imidazolium and pyridinium based ILs were able through their decomposition products (the imidazolium is decomposed into an imidazole)
to open the epoxy ring of a prepolymer, and form an adduct including an alkoxide anion. Then the alkoxide propagates until the formation of a three-dimensional network by anionic polymerization [13].

Different mechanisms have been proposed for phosphonium based ILs. In fact, Silva *et al.* showed that a phosphonium IL combined with a bis 2,4,4-(trimethylpentyl)phosphinate anion was able to initiate the polymerization without any decomposition step [16] [17]. The authors suggested a nucleophilic attack from the phosphinate anion on the oxirane group, generating the alkoxide anion, required for the propagation. They highlighted a highly reactive system, requiring only a few amounts of IL (> 5 phr) in order to achieve a complete epoxy conversion. Thus, epoxy network was developed, exhibiting good mechanical performances and thermal stability with high glass transition temperatures (>140 °C for 10 phr of IL) compared to conventional epoxy-amine thermosets [16]. Maka et al. studied epoxy nanocomposites based on epoxy with the same IL as Silva et al, i.e a phosphonium/phosphinate combination [18].

Thereafter, Nguyen *et al.* have compared epoxy network initiated with the same phosphonium IL denoted ILTMP and a phosphonium based IL including a diethyl phosphate counter-anion also able to initiate the epoxy polymerization. Although they have exhibited a high glass transition temperature (114 °C for 10 phr of tri(butyl)ethylphosphonium diethyl phosphate) with a better thermal stability than an epoxy-amine system, they remained less interesting due to their lower reactivity and final glass transition temperatures compared with the phosphinate anion based system [17].

Previous studies on electrical properties of epoxy/IL systems were mostly dedicated to electrolyte solutions. For this purpose, ILs were added: (i) as classic curing agents (in stoichiometric conditions with the epoxy prepolymer) [7] [19] [19] [20]; (ii) in large excess leading to low glass transition temperatures [7] [19] [21]; (iii) or simply to another matrix than a polyepoxide one (more conventional for electrolytes, as PEO) [6]. Finally, dielectric properties and conduction mechanisms were not especially investigated after an anionic homopolymerization, for which the IL is involved in the curing process.

The present study investigates the dielectric behaviour of epoxy/IL systems according to the network properties obtained after the anionic homopolymerization. The curing process was investigated by DSC measurements for different contents of IL. The morphology of the network was also studied by TEM and related with DMA measurements. Finally, the dielectric measurements were performed by dielectric spectroscopy. For the first time, all the results were compared to a conventional epoxy/anhydride system.

# 2 EXPERIMENTAL

## 2.1 MATERIALS

An epoxy prepolymer based on diglycidyl ether of bisphenol A (DGEBA) was purchased from Huntsman (Araldite CY 225). A methyl-tetrahydroptalic anhydride (MTHPA) hardener was also provided by Huntsman (Aradur HY 925) and used as comparison in stoichiometric conditions (80 phr, phr: per hundred resin). An imidazole based catalyst is also present in the anhydride formulation. The ionic liquid (IL) denoted ILTMP was supplied by Solvay (Cytec® IL104) and is made up of a trihexyl(tetradecyl)phosphonium cation, associated with a bis 2,4,4-(trimethylpentyl)phosphinate anion. The Table 1 summarizes the structure and characteristics of the used materials.
Dielectric Analysis (DEA) was carried out using an XM Ametek Solartron spectrometer, in a sample cell and a cryogenic system provided by the Janis Research Company. Characterized samples are disk-shaped with a thickness of 1 mm. Gold electrodes were sputtered on both sides to ensure good electrical contacts. The diameter of the electrodes is equal to 25 mm. A voltage of +/- 5 V was applied at a frequency from 1 MHz to 0.1 Hz and a temperature range from -100 to 200 °C (isothermal step every 3 °C). Relative permittivity and dielectric loss were evaluated, as well as the real part of the conductivity and the equivalent DC conductivity from the low frequencies at high temperature. The DC conductivity $\sigma_{DC}$ was calculated from the low frequency plateau of the real part $\sigma'$ of the complex conductivity, defined as:

$$ \sigma'_{AC} = \omega\varepsilon'' \qquad (1) $$

Where $\omega$ and $\varepsilon''$ are respectively the angular frequency ($\omega = 2\pi f$, with f the frequency) and the imaginary part of the complex permittivity.

The dielectric relaxation modes were analysed by using a Cole-Cole model, expressed by the equation (2).

$$ \varepsilon^*(\omega) = \varepsilon_{\infty} + \frac{\Delta\varepsilon}{1 + (j\omega\tau)^{\alpha}} \qquad (2) $$

With $\alpha$ the shape parameter describing the symmetric broadening of the relaxation peak, $\tau$ the relaxation time at the angular frequency $\omega$, and $\Delta\varepsilon = \varepsilon_s - \varepsilon_\infty$ with $\varepsilon_\infty$ and $\varepsilon_s$ respectively the infinite and static permittivities.

The fragility index was defined by Angell et al. [22] and is calculated from equation (4). The fragility index m allows to classify as “strong” (low m value and Arrhenius-like behaviour or “fragile” (higher value of m and deviation from the Arrhenius behaviour):

$$ m = \left. \frac{d(\log \tau)}{d(T_g/T)} \right|_{T=T_g} \qquad (3) $$

# 3 RESULTS AND DISCUSSION

## 3.1 CURING BEHAVIOUR OF EPOXY/IL SYSTEMS

The curing process of epoxy/IL systems was followed by DSC measurements. Unlike conventional hardeners, the IL does not form a bridge between epoxy macromolecules, but acts as an initiator of an anionic homopolymerization (the IL anion will stand chemically linked to the epoxy network after the polymerization) [16]. Figure 1 shows the heat flow corresponding to the exothermic reaction of the epoxy anionic homopolymerization induced by the IL. Characteristic temperatures and exothermic enthalpies are summarized in Table 2.
<figure><img src="image_2.png" /><figcaption>Figure 1: DSC thermograms of epoxy/IL systems for different contents of IL.</figcaption></figure>

Whatever the concentration of IL, an exothermic peak representative of polymerization appeared. Associated enthalpy ΔH increases with the increase of the IL content and reaches a maximum of 81 kJ/epoxy equivalent (388 J/g) for 10 phr of LI, which appears to be the optimal ratio required to achieve a full polymerization. This content also leads to the highest glass transition temperature (110 °C), suggesting that the excess of IL will not take part in the polymerization process for IL contents higher than 10 phr but will act as a plasticizer decreasing the glass transition temperature [17]. The second temperature ramp does not show a residual exothermic peak. The highest temperature of the Tg2 glass transition (110 °C) is also obtained for 10 phr, values in agreement with the literature [16] [17] [18] [23]. No glass transition temperature has been detected for 4 and 6 phr of LI suggesting an incomplete polymerization, due to the lack of LI in the reactive mixture.

<table><caption>Table 2: Characteristic temperatures, and exothermic energies depending on the IL content.</caption><thead><tr><th>ILTMP content (phr)</th><th>Onset temperature (°C)</th><th>Peak temperature (°C)</th><th>ΔH (J/g)</th><th>ΔH (kJ/ee)</th><th>Tg2 (°C)</th></tr></thead><tbody><tr><td>4</td><td>106</td><td>151</td><td>82</td><td>16</td><td>-</td></tr><tr><td>6</td><td>105</td><td>146</td><td>229</td><td>46</td><td>-</td></tr><tr><td>8</td><td>104</td><td>140</td><td>364</td><td>75</td><td>99</td></tr><tr><td>10</td><td>111</td><td>136</td><td>388</td><td>81</td><td>110</td></tr><tr><td>12</td><td>102</td><td>131</td><td>369</td><td>79</td><td>103</td></tr><tr><td>14</td><td>98</td><td>129</td><td>372</td><td>81</td><td>96</td></tr><tr><td>20</td><td>103</td><td>142</td><td>342</td><td>78</td><td>95</td></tr><tr><td>Anhydride (80 phr)</td><td>130</td><td>167</td><td>297</td><td>102</td><td>95</td></tr></tbody></table>

The decrease of the onset temperature can be attributed to the initiation of the homopolymerization from the phosphinate anion as well as the initiator effect of the phosphonium cation. Indeed, Smith *et al.* highlighted the ability of phosphonium based compounds to act as latent accelerator of the epoxy polymerization [24]. They suggested the formation of active species from hydrogen bonded phosphonium/epoxy complexes.
In optimum conditions, the IL leads to a more reactive system than the anhydride, exhibiting a lower onset temperature (111 and 130 °C for respectively 10 phr of IL and 80 phr of anhydride), as well as a higher exothermic heat (366 and 297 J/g for respectively 10 phr of IL and 80 phr of anhydride). As a conclusion, DSC results highlighted the ability of the IL to be used as an initiator of the homopolymerization as it was previously suggested in the literature. An optimum content was established around 10 phr, above which a plasticizing effect due to the IL excess appears.

## 3.2 MORPHOLOGY OF EPOXY/IL NETWORKS

The morphologies of epoxy networks containing ILTMP were evaluated by TEM and presented in Figure 2 for different contents of IL (6, 12 and 20 phr). Clusters probably due to IL agglomeration are observed for 6 and 12 phr of IL. These observations are confirmed in several works highlighting the ability of ILs to generate a phase-separated morphology into thermosets or thermoplastic matrices when the miscibility threshold is exceeded [23] [25]. A phase separation phenomenon or large IL rich zones are observed for 20 phr: the darkest phase can be probably attributed to a highly IL-concentrated phase coming from the excess of IL which did not take part in the polymerization process.

<figure><img src="image_3.png" /><figcaption>Figure 2: TEM observation of epoxy systems for different contents of ILTMP.</figcaption></figure>

From dynamic mechanical measurements on all epoxy networks with and without ILTMP, Figure 3 and Figure 4(A), display the storage modulus $E'$, loss modulus $E''$ and dissipation factor $\tan \delta$ as a function of temperature. Table 3 summarizes the main relaxation temperature $T_\alpha$ associated with the glass transition and the cooperative movement of macromolecular chains observed on the $\tan \delta$ curve (Figure 4 (A)) and the rubbery modulus $E'_R$.

The plateau obtained at high temperature on the storage modulus, corresponding to the rubbery modulus, is drastically increased for epoxy/IL systems (154 and 20 MPa for respectively 8 phr of IL and 80 phr of anhydride), suggesting a higher crosslink density of epoxy/IL systems due to the homopolymerization.
<figure><img src="image_4.png" /><figcaption>Figure 3: Storage modulus and loss modulus as a function of temperature for different contents of IL compared to the epoxy/anhydride system.</figcaption></figure>

Epoxy/IL systems exhibit high $\alpha$ relaxation peak temperatures (> 160 °C between 6 and 12 phr) with a maximum of 165 °C achieved for 8 phr of IL. This content is different from DSC measurements for which a maximum glass transition (2nd ramp) was obtained for 10 phr. Indeed, the DSC ramp from -100 to 200 °C (10 °C/min) is not representative of the real curing process applied in oven. Whatever, the optimized content must be between 8 and 10 phr of IL.

<table><caption>Table 3: Thermomechanical behaviour of epoxy networks cured with IL.</caption><thead><tr><th>ILTMP content (phr)</th><th>T<sub>α</sub> (°C)</th><th>E'<sub>R</sub> (MPa)</th></tr></thead><tbody><tr><td>6</td><td>160</td><td>151</td></tr><tr><td>8</td><td>165</td><td>154</td></tr><tr><td>10</td><td>162</td><td>164</td></tr><tr><td>12</td><td>159</td><td>173</td></tr><tr><td>16</td><td>144</td><td>131</td></tr><tr><td>20</td><td>132</td><td>125</td></tr><tr><td>Anhydride (80 phr)</td><td>132</td><td>20</td></tr></tbody></table>

While keeping a high rubbery modulus whatever the IL content, the $\alpha$ relaxation peak temperature $T_\alpha$ is drastically decreased as the IL content increases (from 162 to 132 °C for respectively 10 and 20 phr). As previously observed by DSC, the IL leads to a plasticizing effect since the IL excess do not take part in the polymerization process. The excess of IL causes a wider relaxation peak, illustrated by the normalization of the relaxation peak as a function of its amplitude and temperature in Figure 4 (B). The epoxy network heterogeneity increases with the IL content, result supported by the heterogeneities previously observed by TEM (clusters apparition whose size depends on the IL content).
<figure><img src="image_5.png" /><figcaption>Figure 4: (A) Loss tangent in function of temperature, (B) normalization of α relaxation peak.</figcaption></figure>

DMA results highlight the ability of IL to generate stiff epoxy network displaying high glass transition temperature (≈160 °C). Nevertheless, IL excess drastically reduces the temperature of α relaxation due to its plasticizing effect. When the IL content increases, the broadening of the tan δ peak proves the formation of a more and more heterogeneous environment around relaxing entities.

## 3.3 DIELECTRIC BEHAVIOUR OF EPOXY/IL NETWORKS

### 3.3.1 Relaxations analysis

Dielectric behaviour was investigated by dielectric spectroscopy. Figure 5 shows relative permittivity and dielectric loss as a function of temperature at 10 Hz. Several mechanisms appear:

i. The localized mobility of branched molecular segments induces the β *relaxation mode* at low temperature. It is mainly associated to hydroxyether groups from the epoxy prepolymer chain [26] [27]. Its temperature at the maximum of tan δ is close to the epoxy/anhydride system and does not seem to be modified by the IL content.

ii. The α *relaxation mode* is the dielectric manifestation of the glass transition. It is associated with the cooperative and delocalized mobility of macromolecular chains. Although it clearly appears as a shoulder on dielectric loss for the epoxy/anhydride system, the α mode is not visible on dielectric loss for IL-containing samples. Indeed, this relaxation mode is hidden by conduction phenomenon occurring at high temperature.

iii. *Conduction mechanisms* σ arise at high temperature and conceal the α relaxation on dielectric loss. It increases with the IL content.

iv. A *relaxation mode* called ω is observed between the β and α relaxation modes for the highest contents of IL (16 and 20 phr ILTMP). This relaxation is not well understood and some authors attributed this relaxation to the dielectric manifestation of some heterogeneities in the network [28] [29]. This relaxation seems to be sensitive to water uptake in epoxy systems and associated with the motion of cyclohexyl units in epoxy-anhydride networks [30].
<figure><img src="image_6.png" /><figcaption>Figure 5: (A) Relative permittivity and (B) dielectric loss for different contents of IL, f = 10 Hz.</figcaption></figure>

A Cole-Cole model was applied to the different relaxation modes. Arrhenius plot of relaxation time from α and β modes are shown in Figure 6.

a) α Relaxation

The frequency dependence of the relative permittivity and the dielectric losses between 80 and 200 °C for 10 and 20 phr IL is shown in *Supporting Information (Figure S1)*. A temperature jump in relative permittivity, associated with the α relaxation, is observed in Figure 5 and appears to be greater for 20 phr of IL. The large increase of permittivity at low frequency is due to the contribution of conduction, identified by a slope of (-1) on the dielectric losses.

The application of a Cole-Cole model added to the conduction slope makes it possible to discriminate
the α relaxation from the conduction contribution on the dielectric loss. The parameters α and Δε are
reported in *Supporting Information (Table S1 and Figure S3)*. The α parameter, characteristic of the
distribution width of the relaxation time, is usually independent on temperature [31]. The width of
the distribution does not appear to vary with the amount of IL (about 0.40). However, the α
relaxation is broader than one of the stoichiometric system epoxy/anhydride (about 0.50). These
results are in agreement with the dynamic mechanical analysis, for which a wider α relaxation peak is
also observed for epoxy/LI systems (Figure 4).

The Δε factor and its temperature dependence increase with the amount of IL. A strong dependence
is observed for 20 phr of IL, with a permittivity jump greater than 20. This increased temperature
dependence when the amount of LI increases matches with the relative permittivity jump observed
in Figure 5. The Δε factor of the Cole-Cole model is proportional to the number of dipoles involved in
the relaxation process [31]. It is therefore sensitive to the concentration, the nature and the
environment of these dipoles. The increase of the Δε factor is consistent with an increase of the
network mobility in the presence of IL as the number of available dipoles increased with the IL
content. At a given temperature, this mobility is also shown in Figure 6 (A) by a decrease of
relaxation time when the IL content increases (or by a time shift towards low temperatures). The
temperature dependence of the Δε parameter, which is increased as the amount of IL increases
(significantly decreased from 37 to 23 between 110 and 144 °C for 20 phr), could be explained by the
intervention of conduction mechanisms in which the dipoles associated with the relaxation mode α
would be involved. Therefore, they would no longer contribute to the permittivity jump.
The relaxation time of the α relaxation in Figure 6 (A) are higher for epoxy/IL networks than the epoxy/anhydride one. It is due to the homopolymerization generating a network with a high crosslink density, and, thus, a low chain mobility compared to epoxy/anhydride copolymerized network. The discussion will focus on this point. The results from the VFT law applied for 8 and 20 phr are shown in *Supporting Information (Table S2)*. The T~v~ temperatures deviate slightly from the Tg-Tv = 50°C case commonly observed for polymers and for the epoxy/anhydride system proposed in this study. Parameter D is characteristic of the deviation from a VFT law to an Arrhenius law (respectively from a “fragile” to “strong” behaviour). In the present case, it appears to be sufficiently low (close to 1) to express a VFT behaviour. On the other hand, the fragility index m of the epoxy/IL systems is much lower than the epoxy/anhydride system (respectively 30 and 64). According to Angell’s argumentation, it seems to indicate epoxy/IL are “stronger” which seems to be inconsistent with the value of D [22]. Calorimetric measurements and the Donth approach based on the Adam and Gibbs theory could be interesting to determine the cooperativity length [32] [33].

<figure><img src="image_7.png" /><figcaption>Figure 6: Arrhenius plots of relaxation time for (A) the α relaxation mode (lines correspond to a VFT law application), and (B) the β relaxation mode.</figcaption></figure>

b) β relaxation

Relaxation time from β mode is plotted in Figure 6 (B). The temperature dependence of the
relaxation time of epoxy/IL systems appears to be close to the conventional epoxy/anhydride and
suggests a similar contribution of the hydroxyether groups. The parameters derived from Arrhenius
law are shown in Table 4. According to the Arrhenius law, a decrease of the activation energy with
the IL content appears from 0.66 to 0.53 eV for respectively 8 and 20 phr of IL-TMP, common value
observed for sub glass relaxation. An activation energy value close to the epoxy/anhydride system is
obtained for small amounts of IL (8 phr). The contribution of the lateral groups thus appears similar
and not altered when the IL is not in excess. When there is an excess of IL, the higher mobility of the
P=O groups associated with free anions could explain an additional contribution and the decrease of
the activation energy when the IL amount increases.
<table><caption>Table 4: Activation energies from β relaxation mode.</caption><thead><tr><th>ILTMP content<br>(phr)</th><th>E<sub>A-β</sub><br>(eV)</th></tr></thead><tbody><tr><td>8</td><td>0.66</td></tr><tr><td>10</td><td>0.63</td></tr><tr><td>12</td><td>0.62</td></tr><tr><td>16</td><td>0.57</td></tr><tr><td>20</td><td>0.53</td></tr><tr><td>Anhydride (80 phr)</td><td>0.69</td></tr></tbody></table>

### c) ω relaxation

The ω relaxation mode is only observed for high content of IL (16 and 20 phr). Due to multiple and complex overlaps obtained for 20 phr, only results for 16 phr of IL were available for data processing. The relative permittivity as a function of temperature is shown in Figure 7 (A) at different frequencies. This relaxation mode occurs for temperatures between the β and α modes (Figure 7 (B)). Its activation energy was calculated from an Arrhenius law and estimated at 0.67 eV. This value is similar to the activation energies obtained in Table 4 for the β relaxation mode of the epoxy/IL and epoxy/anhydride systems (respectively 0.66 eV for 8 phr ILTMP and 0.69 eV for the anhydride) and, thus, suggests mechanisms close to the sub glass relaxation process, i.e. localized dipoles involved in the relaxation. This relaxation may be attributed to the previously observed heterogeneities and will be discussed from this point of view.

<figure><img src="image_8.png" /><figcaption>Figure 7: (A) β and ω relaxation modes for different frequencies between 1 and 100 Hz (indicated by the arrow from low to high frequencies) for 16 phr ILTMP, and (B) Arrhenius plots of all relaxation modes for 16 phr ILTMP, compared to the epoxy/anhydride system.</figcaption></figure>

### 3.3.2 Electrical conductivity

The real part $\sigma'_{AC}$ of the complex conductivity is shown in Figure 8 between 80 and 170 °C for different contents of IL. A DC conduction plateau is observed at low frequency for all formulations. The DC plateau appears for temperatures lower than $T_α$ previously reported. A steady plateau is obtained from 110 °C at 0.1 Hz for 8 phr of IL while the corresponding $T_α$ is equal to 162 °C. Thus, it means that conduction mechanism occurs at low temperature even below the glass transition.
<figure><img src="image_9.png" /><figcaption>Figure 8: AC conductivity from dielectric spectroscopy for different contents of IL-TMP.</figcaption></figure>

The Arrhenius plot of the DC conductivity calculated from equation (2) is presented in Figure 9 for different contents of IL and compared to the epoxy/anhydride system. The DC conductivity is increased by one order of magnitude on the whole range of temperature when the anhydride hardener is substituted by 12 phr of IL-TMP, and increased by two orders of magnitude or more with the substitution by 20 phr of IL.

<figure><img src="image_10.png" /><figcaption>Figure 9: Arrhenius plot of the DC conductivity from dielectric spectroscopy.</figcaption></figure>
DC conductivity in polymers is usually fitted by a VFT law defined by equation (5) [34] [35].

$$ \sigma_{VFT} = \sigma_0 e^{\frac{-DT_v}{T-T_v}} \quad (4) $$

With $\sigma_0$ a pre-exponential factor, D a strength parameter quantifying the deviation from the VFT law toward Arrhenius, $T_v$ the Vogel temperature, and T the temperature. This expression from Adams-Gibbs theory suggests an activation mechanism principally led by segmental mobility of the polymer host, i.e. depending on the glass transition (with $T_v$ usually considered as [T$_g$ - 50°C]). The VFT parameters as a function of IL content are reported in *Supporting Information (Table S3)*. Unlike the epoxy/anhydride system, the curvature of DC conductivity from epoxy/IL networks does not illustrate a VFT behaviour. It is confirmed by the high values of D parameters, indicating a deviation from the VFT law towards an Arrhenius behaviour. Consequently, $T_v$ values are senseless and far lower from [T$_g$-50 °C]. One could immediately think that the curvature loss would come from a VFT law shifted towards higher temperatures, due to higher glass transition temperatures of epoxy/IL networks. Nevertheless, the $\alpha$ temperature for 20 phr of IL is about 132 °C, which is equal to the $\alpha$ temperature of the epoxy/anhydride system. Thus, another explanation will be proposed and discussed later.

## 3.4 DISCUSSION

An optimized epoxy/IL network seems to be obtained by adding between 8 and 10 phr of IL, for which the highest reaction enthalpy and glass transition temperature were reported by DSC and DMA. The theory of rubber elasticity can't be strictly applied on the rubbery modulus since the original theory is based on several hypothesis which are not totally fulfilled in epoxy/IL systems [36]. Moreover, its validity is linked to the study of homogeneous systems, which is not the case for the highest IL contents exhibiting a separation phase. However, the increase of the rubbery modulus can be associated with the high crosslink density of the network and/or to additional interactions involved in the epoxy/IL systems compared to the epoxy/anhydride one. A simple calculation of the theoretical mass between crosslinks is proposed in *Supporting Information (Figure S5)*, according to the initiation and propagation schemes presented in Figure 10. Mass between crosslinks of 184 g.mol$^{-1}$ and 267 g.mol$^{-1}$ were calculated for respectively 10 phr of IL and 80 phr of anhydride, which is correlated with the increase of the rubbery modulus.
<figure><img src="image_11.png" /><figcaption>**Figure 10:** Initiation and propagation of the epoxy homopolymerization: the successive reactions of epoxy groups generates ether segments explaining the high crosslink density compared to classical epoxy/anhydride network.</figcaption></figure>

As a conclusion from DSC and DMA results, a 2D network architecture can be proposed in Figure 11. Two points are highlighted in this simplified illustration: (i) the high cross-linking density, and consequently the large number of cross-linking points; (ii) the position and steric hindrance of the IL (approximate size scale of cations and anions relative to the prepolymer). The low mass between crosslinks calculated from the epoxy/IL system could be explained by the contribution of -O-CH₂-sequences generated between crosslinks by the propagation step of the homopolymerization [37] (Figure 10).

<figure><img src="image_12.png" /><figcaption>**Figure 11:** 2D representation of an epoxy network induced by anionic homopolymerization in presence of IL: (blue) IL anion, (red) IL cation, (black) prepolymer; (green) crosslinks.</figcaption></figure>
Several phenomena were observed and associated with dielectric relaxation modes of epoxy/IL networks:

* An increase with IL content of the chain mobility involved in the α relaxation process, principally due to a plasticizing effect induced by the excess of IL from the polymerization process. On the other side, a “strong” behaviour has been identified according to the Angell’s argumentation (low fragility index). It is in agreement with results from conductivity which does not seem to depend on segmental mobility.

* The activation of the β relaxation mode is enhanced by the presence of IL. It could be due to the steric hindrance of the IL near the hydroxyether groups involved in the relaxation process. P=O dipoles from the IL would also contribute to this relaxation mode.

* A ω relaxation mode is observed between the α and β relaxations. It is similar to the most known but controversy ω relaxation observed in several studies [38] [39] [40] [29]. Indeed, authors were able to associate it with various mechanisms: the heterogeneity of the network, the presence of moisture, or the mobility of aromatic nuclei or of hydroxyether groups. In the present study, the water absorption may probably not be the cause due to the sample storage in dried atmosphere. Activation energies indicate a dielectric relaxation close to sub glass relaxations, i.e. associated with hydroxyl dipoles orientation. In order to broaden the discussion, FTIR measurements were performed in the wavelength range corresponding to hydroxyl groups (3000-3700 cm⁻¹). An additional contribution seems to appear at 3300 cm⁻¹ when the amount of IL increases. The involvement of -OH groups of epoxy network in interactions with IL could be responsible for this absorption peak [41]. However, their involvement is not trivial, since the absorption peak is also observed for the neat IL. It could therefore be attributed to intrinsic cation/anion interactions of the IL. Consequently, we tend to explain the increase in amplitude of the ω relaxation. We assume that the network is more and more heterogeneous as the IL content increases. The broadening of the tan δ proves it. Previous works tend to demonstrate that the presence of ω relaxation can be due to the absorption of small amount of water inside the network generating heterogeneities in the network where the molecular mobility is higher in these zones (mobility of cyclohexyl units for example). By analogy, we can make the hypothesis that IL promotes the mobility of small units like cyclohexyl ones leading to this ω relaxation on dielectric measurements. FTIR measurements could confirm this result showing the existence of cation/anion interactions. We discard the hypothesis of water absorption for two reasons : first, dielectric measurements were done on dried samples and the second temperature run still exhibits the relaxation and second, the IL introduced into the network is hydrophobic as much as the network itself (energy surface measurements confirmed this result).
<figure><img src="image_13.png" /><figcaption>Figure 12: FTIR-ATR analysis for different ILTMP</figcaption></figure>

DC conductivity analysis have shown that conduction phenomena occurred far below the glass transition temperature of epoxy/IL networks. Moreover, the temperature behaviour of the conductivity of these new systems does not follow a traditional VFT behaviour. A thermal activation mechanism has to be considered by the application of an Arrhenius law, defined by the equation (6).

$$ \sigma_{Arrh} = \sigma_0 e^{-E_A/k_B T} \quad (6) $$

The corresponding Arrhenius parameters are reported in Table 5. The activation energy E<sub>A</sub> decreased with the addition of IL. The activation energies, higher than 1, probably indicate a conduction process essentially led by ionic conduction [42]. Nevertheless, the charge carrier identification is not trivial:

* At first sight, it would be easy to identify the ionic contribution essentially coming from the mobility of the IL (cation and/or anion). But the ions molecular weight (respectively 483 and 289 g.mol<sup>-1</sup> for the cation and anion) are similar to the prepolymer molecular weight. Their 3D representations are shown in Supporting Information (Figure S6). Moreover, these masses are of the same order of magnitude as the approximated mass between crosslinks previously calculated. Consequently, IL mobility may be complicated in such highly crosslinked epoxy networks.

* A contribution of proton conduction is an option since hydroxyl groups are initially found in the epoxy prepolymer [43].

* Ionic impurities coming from the DGEBA or IL preparation would also contribute to ionic conduction process [44].

<table><caption>Table 5: Parameters of the Arrhenius law applied to DC conductivity for different contents of IL.</caption><thead><tr><th>ILTMP content<br>(phr)</th><th>σ<sub>0</sub><br>(S/m)</th><th>E<sub>A</sub><br>(eV)</th></tr></thead><tbody><tr><td>8</td><td>7.3 10<sup>9</sup></td><td>1.49</td></tr><tr><td>10</td><td>2.9 10<sup>9</sup></td><td>1.45</td></tr><tr><td>12</td><td>1.2 10<sup>9</sup></td><td>1.38</td></tr><tr><td>16</td><td>2.5 10<sup>8</sup></td><td>1.29</td></tr><tr><td>20</td><td>3.2 10<sup>6</sup></td><td>1.06</td></tr></tbody></table>
Finally, the IL mobility is probably not the main contribution to the DC conductivity. It would more probably act as a promotor of ionic conduction (proton and small ionic impurities) due to: (i) its plasticizing effect, increasing the network mobility in the range of the glass transition temperature and for higher temperatures; (ii) the orientation of IL's ionic interactions, favouring the conducting ions towards the electric field.

## 4 CONCLUSION

The substitution of conventional hardeners by ionic liquids has a significant influence on the epoxy polymerization process, the network and its final solid properties. Previous studies highlighted the ability of IL to initiate an epoxy homopolymerization. In this study, strong relationships have been established between the epoxy network morphology and, for the first time, its dielectric behaviour. The main results and conclusions of this work are: (i) an increase of the macromolecular mobility due to the IL excess; (ii) the emergence of a ω relaxation mode identified as the dielectric manifestation of heterogeneities of the network generated by the excess of IL in the network; (iii) a significant increase of the DC conductivity until 2 decades higher than a conventional epoxy/anhydride system, and obtained from temperatures much lower than the glass transition; (iv) a thermal activation mechanism of the ionic conduction defined by an Arrhenius behaviour. The present study highlighted the potential of epoxy/IL system for insulation application requiring an interesting electric conductivity even below the glass transition temperature (for example to reduce static charge accumulation) while maintaining excellent solid properties, with a high crosslink density combined to a high glass transition temperature ($T_g$>160 °C). This innovative route can be also considered in order to enhance electrical conductivity below the glass temperature.

## 5 ACKNOWLEDGEMENTS

The authors acknowledge Pierre Alcouffe and the Consortium Lyon Saint-Etienne de Microscopie (CLYM, FED 4092) for the access to the microscopes.
This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01)

*This manuscript is in honor of the 50 year anniversary of the French Polymer Group (Groupe Français des Polymères – GFP).*

*This work is also dedicated to Professor Jean-Pierre PASCAULT, famous scientist of thermosetting polymers. He was a friend of ours.*
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