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# Assessing the Impact of the Off-Stoichiometric Epoxy/Amine Ratio on the Curing Kinetics and Properties of Space-Grade Disulfide-Based Vitrimer Resins

Joséphine de Calbiac, Philippe Olivier, Rima Sfar Zbed, Marina Torres, Marion Broutelle, Mathias Destarac, Marc Guerre

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## ► To cite this version:

Joséphine de Calbiac, Philippe Olivier, Rima Sfar Zbed, Marina Torres, Marion Broutelle, et al. "Assessing the Impact of the Off-Stoichiometric Epoxy/Amine Ratio on the Curing Kinetics and Properties of Space-Grade Disulfide-Based Vitrimer Resins." ACS Applied Polymer Materials, 2025, 7 (8), pp. 5271-5279. 10.1021/acsapm.5c00637. hal-05072950

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https://hal.science/hal-05072950v1

Submitted on 29 Oct 2025

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# Assessing the impact of off-stoichiometric epoxy/amine ratio on the curing kinetics and properties of space-grade disulfide-based vitrimer resins

Joséphine de Calbiac,<sup>a,b,c</sup> Philippe Olivier,<sup>c*</sup> Rima Sfar Zbed,<sup>d</sup> Marina Torres,<sup>a</sup> Marion Broutelle,<sup>a</sup> Mathias Destarac,<sup>b,d</sup> and Marc Guerre,<sup>b*</sup>

Corresponding authors: *philippe.olivier@iut-tlse3.fr*; *marc.guerre@cnrs.fr*

**KEYWORDS:** vitrimers, epoxy, space, disulfides, off-stoichiometric

**ABSTRACT:** Carbon fiber-reinforced polymer composites are widely used in space structures due to their lightweight nature and excellent thermal stability. However, repairing manufacturing defects in cross-linked thermosets remains a significant challenge. In this regard, Vitrimers offer a promising alternative by combining the mechanical strength of thermosets with the reprocessability of glass. These materials feature a dynamic network structure, allowing them to behave like traditional thermosets at operational temperatures while exhibiting fluid-like properties at elevated temperatures. In this study, a space-grade epoxy thermoset matrix was transformed into a high-Tg vitrimer (Tg ≈ 200°C) for potential use in composite applications. The vitrimer chemistry relies on disulfide exchange reactions, facilitated by an industrially available reagent (4-AFD). Rheological and reactivity characterization tests were performed to ensure that the crosslinking kinetics in the presence of dynamic bonds remain compatible with existing composite manufacturing processes. These measurements enabled the development of Time-Temperature-Transformation (TTT) diagrams, providing precise insights into the polymerization process. To enhance repairability, off-stoichiometric formulations (epoxy/amine = 1/1.2) were explored to optimize both the curing process and vitrimeric properties. The applicability of kinetic models to off-stoichiometric systems was also assessed. Notably, even under off-stoichiometric conditions, the resin maintained a high Tg of 175°C while exhibiting excellent mechanical properties and improved reprocessability. Additionally, the outgassing properties remained identical to those of the stoichiometric reference. These findings highlight the potential of off-stoichiometric epoxy/4-AFD formulations as viable matrix materials for composite applications. By offering improved reprocessability without compromising thermal or mechanical performance, these materials present a compelling alternative to traditional thermosets for high-performance aerospace applications.

## 1. Introduction

Vitrimers are an emerging class of crosslinked materials with remarkable healing and recycling properties<sup>1-6</sup>. Their ability to reorganize their molecular structure in response to temperature has led to their development for applications such as self-healing coatings<sup>7-9</sup> and advanced composite materials<sup>10-12</sup>, offering significant advantages over conventional

thermosets. Among the various dynamic chemistries explored over the years<sup>3,4,10,13</sup>, certain limitations, such as limited large-scale availability and high costs, have hindered a broader industrial implementation of this new class of materials. In this context, disulfide chemistry, which is readily available and found in molecules such as 2-hydroxyethyl disulfide<sup>14,15</sup>, 4-Aminophenyl disulfide (4AFD)<sup>16-19</sup> or

<footnote><sup>a</sup> CNES, Centre National d'Etudes Spatiales, 18 avenue Edouard Belin, 31400 Toulouse, France</footnote>

<footnote><sup>b</sup> Laboratoire Softmat, Université de Toulouse, CNRS UMR 5623, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France.</footnote>

<footnote><sup>c</sup> Institut Clément Ader, Université de Toulouse, UT3, UMR CNRS 5312, 3 Rue C. Aigle, 31400 Toulouse, France</footnote>

<footnote><sup>d</sup> IRT Saint Exupéry, Bâtiment B612, 3 rue Tarfaya, CS 34436, 31405 Toulouse cedex 4, France</footnote>
cystamine²⁰,²¹, has been particularly developed. The presence of functional groups facilitates the integration of this dynamic chemistry into various common chemical processes, including polyurethanes, polyesters, epoxies and others, to name a few ²²⁻²⁵. 4AFD was found to be of particular interest as a hardener in epoxy formulation. It can be directly used as a common hardener, with a reactivity comparable to that of regular amines, while imparting dynamic properties through the introduction of disulfide moieties within the backbone. Disulfide exchange reactions can then be triggered through different stimuli including UV radiation or thermal activation. For high-Tg and bulk polymers, thermal activation is often preferred since activation via irradiation is limited by factors such as penetration depth and is generally only effective for low-Tg materials and coatings¹⁶,²⁶,²⁷. Additionally, thermal activation ensures a reduction in viscosity beyond glass transition temperature (Tg) of the material while effectively promoting dynamic exchanges.

In a seminal paper, 4AFD has been implemented in a DGEBA-based formulation with epoxy vitrimer network of a mid-high Tg value of 130°C which demonstrated excellent reprocessing and repairability under thermal stimulus ²⁸. This disulfide-based vitrimer formulation was then extensively applied in composite manufacturing such as pultrusion, impregnation, or RTM, with carbon fiber or Al₂O₃ particles ²⁹⁻³¹.

In most studies involving 4AFD ³²⁻³⁴, an off-stoichiometric ratio was predominantly used with a 20% excess of 4AFD relative to the epoxy resin. The excess of dynamic hardener is crucial for significantly accelerating dynamic exchanges, as materials with a stoichiometric ratio exhibit comparatively slower dynamic behavior. The addition of excess hardener affects not only the efficiency of dynamic exchanges but also results in materials with a slightly lower Tg, reduced crosslink density, and a lower degradation temperature ²⁸. While the precise mechanisms behind this acceleration remain unclear, it is likely due to a combination of increased mobility and a higher concentration of dynamic groups. Although the influence of these off-stoichiometric conditions on typical physicochemical parameters is relatively well-known, no data currently exist on the real impact of this excess on the kinetics of epoxy-amine curing or the overall mechanical properties [17]. For instance, the influence of this modification on the Di Benedetto equation or, more broadly, on Time-Temperature-Transformation (TTT) diagrams ³⁵ is so far barely known.

This parameter is often overlooked while it is of paramount importance. For instance, an excess of amine in a non-stoichiometric network may increase the proportion of chain branching due to the presence of a higher number of formed hydroxyl groups. This would create an internal catalysis effect, facilitating nucleophilic attack on the secondary amine and leading to a network with a distinct macromolecular structure, as demonstrated by several research groups³⁶,³⁷.

In this study, we provide a comprehensive characterization of three formulations consisting of 4AFD and a space-grade epoxy resin, designed for use in filament winding process. These formulations differ in stoichiometric conditions and glass transition temperature, allowing a detailed investigation into the impact of 1:1 and 1:1.2 stoichiometries on both reactivity and final properties. Particular emphasis is given to the effects of stoichiometry on the Time-Temperature-Transformation (TTT) diagram, which is widely used in composite manufacturing to optimize processing conditions. Mechanical properties were also characterized, with specific attention to factors critical for space applications such as outgassing.

## 2. Experimental

### 2.1. Materials

Epoxy resin (HTG 240) was purchased from Resoltech. 4-aminophenyl disulfide (4AFD, 98 % purity) was purchased from Molekula group. 1,6-Hexanediol diglycidyl ether (HDE, 98 % purity) was purchased from Sigma-Aldrich.

### 2.2. Vitrimers preparation

The three formulations were prepared according to the following weight ratios: 100:58.21 for HTG240-V-1/1 and 100:69.84 for HTG240-V-1/1.2.

The HTG240-mod-V resin was prepared by mixing 10% HDE with the industrial HTG240 resin, followed by a resin-to-hardener mixing ratio of 100:64.15.

Basically, to ensure a highly homogeneous mixture, the various components were weighed using a precision scale and then mixed at room temperature. The mixture was then gradually heated from 50 to 80°C, checking for the melting of 4AFD and ensuring no lumps were formed.

### 2.3. Methods and characterisations

**Densities** were obtained using the Density Determination Kit Sartorius YDK03 at room temperature. The reported results are averages of three measurements.

**Differential scanning calorimetry (DSC)** analyses were performed with a DSC 25 TA instruments under nitrogen atmosphere at different isotherms and/or ramps in standard mode.

**Thermogravimetric analyses (TGA)** were performed with a TG 209 F3 Tarsus Netzsch under air at a heating rate of 10°C/min from 30 °C to 400 °C.

**Rheological analyses** were performed with a MCR 302 Anton Paar rheometer. Oscillatory measurements using parallel plates of 25 mm diameter with a gap of 1 mm, an angular velocity of 10 rad/s and a strain of 1 % were typically used.

**Dynamic Mechanical Analyses (DMA)** were performed with a DMA+ 100 Metravib under air at a heating rate of 3 °C/min from 25 °C to 250 °C. Measurements were performed in tensile mode with a static strength of 2 N, a frequency of 1 Hz and a displacement of 15 µm, on rectangular samples measuring 40.0 x 10.0 x 2.5 mm.
**Tensile tests** were performed with an INSTRON 4466 in accordance with the ISO 527-2 standard, on two samples per system. Extensometer was used ensuring high measurement accuracy of the strain. The curves presented in the article are representative examples, selected as the closest to the average of all measurements

**3 point bending tests** were performed with an INSTRON 4466 in accordance with the ISO 178 standard on four samples per system.

**Conductivity experiments** were made via Laser Flash Analysis (LFA), under Helium atmosphere and at different isotherms from 25°C up to 220°C on rectangular samples of 10 x 10 x 1.2 mm.

**Outgassing tests** were conducted on CNES micro-VCM equipment in accordance with ECSS-Q-ST-70-02C standard. Vacuum was performed at a value of 10⁻⁵mbar and at 125°C during 24h. Samples were sized at 10*10mm and had an average weight of 100mg.

## 3. Results and discussion

### 3.1. Curing kinetics

The formulations described in this study are based on an epoxy resin known as HTG240, specifically developed for use in space applications. HTG240 is primarily composed of N,N,N',N'-tetraglycidyl-4,4'-diaminodiphenylmethane (TGDDM). This resin also incorporates an aliphatic epoxy component, 1,6-hexanediol diglycidyl ether (HDE), at a concentration of approximately 10-50%, reducing the Tg of the resulting materials

The epoxy equivalent weight (EEW) of HTG240 was determined to be 106.67, based on NMR titration (see Supporting Information for detailed calculations). Additionally, NMR analysis confirmed the HDE concentration to be approximately 10%. The required amount of 4AFD curing agent was then calculated from the resin's EEW to obtain two distinct formulations (see figure S1 for detailed calculations).

HTG240-V-1/1 maintains an epoxy-to-amine stoichiometric ratio of 1:1. HTG240-V-1/1.2 uses an off-stoichiometric approach with a 20% excess of amine content. A 20% formulation strikes an optimal balance between the dynamic properties of vitrimers and the network structure of crosslinked materials. A 1:1 ratio lacks sufficient dynamic behavior, leading to poor vitrimer properties, while a 1:1.3 ratio results in overly low crosslink density. For comparative purposes, an additional formulation (HTG240-mod-V-1/1) was prepared with a 1:1 stoichiometric ratio but included 10 phr (parts per hundred resin) of HDE to reduce Tg. This approach made it possible to achieve a Tg similar to that of the HTG240-V-1:1.2 formulation but preserved the 1:1 stoichiometric ratio.

<table><caption>**Table 1.** Experimental Kamal-Sourour kinetic parameters for each formulation</caption><thead><tr><th></th><th>HTG240-V-1/1</th><th>HTG240-V-1/1.2</th><th>HTG240-mod-V-1/1</th></tr></thead><tbody><tr><td>E1 (kJ/mol)</td><td>62.6</td><td>67.8</td><td>57.2</td></tr><tr><td>E2 (kJ/mol)</td><td>65.1</td><td>45.7</td><td>59.4</td></tr><tr><td>A1 (s<sup>-1</sup>)</td><td>3.28E+04</td><td>1.34E+05</td><td>4.69E+03</td></tr><tr><td>A2 (s<sup>-1</sup>)</td><td>8.27E+05</td><td>2.83E+03</td><td>7.29E+04</td></tr><tr><td>m</td><td>1.47</td><td>1.43</td><td>1.05</td></tr><tr><td>n(T)</td><td>0.0143T-0.794</td><td>0.00725T+0.0109</td><td>0.00841T-0.164</td></tr></tbody></table>

The curing kinetics of all three formulations were first evaluated and compared. First, the total reaction enthalpy and the overall reactivity of each formulation were evaluated through dynamic DSC (Figure 1A and S2-S4). HTG240-V-1/1.2 is slightly more reactive than the other two, while HTG240-V-1/1 and HTG240-mod-V-1/1 exhibited a similar behaviour. Moreover, similar enthalpy values of 630 ± 17 J/g, 610 ± 8 J/g and 563 ± 14 J/g were obtained for HTG240-V-1/1, HTG240-V-1/1.2 and HTG240-mod-V-1/1, respectively. This indicates that despite the exothermicity which must be managed for composite processing and scale-up, the off-stoichiometric formulation does not exhibit more exothermic behaviour than the stoichiometric analogue. The higher reactivity of HTG240-V-1/1.2 compared to stoichiometric formulations can be attributed to the excess of primary amine and its greater reactivity compared to secondary amine. The primary-to-secondary amine ratio differs at the initial stage and throughout the polymerization process for both formulations. This variation may significantly influence the overall reactivity of the system and, consequently, the resulting network structure 38,39.
<figure><img src="image_3.png" /><figcaption>Figure 1. (A) heat flow (full lines) and corresponding conversion (dashed lines) as a function of time during dynamic curing (10°C/min) for HTG240-V-1/1, HTG240-V-1/1.2 and HTG240-mod-V-1/1. (B) Evolution of the reaction rates as a function of conversion for isotherm at 180°C.</figcaption></figure>

Isothermal DSC experiments were also conducted for each formulation (see Figures S5 to S7). As for other studies on high Tg epoxy materials, the DSC curves clearly show limited conversion at certain temperatures due to vitrification phenomenon (S2 to S7) 31,40.

For each formulation, the phenomenological Kamal-Sourour model (Equation [1]) was applied. This model is commonly used to predict the reaction conversion as a function of temperature and time in the curing of epoxy/amine resins 41.

$$ \frac{d\alpha}{dt} = (k_1 + k_2\alpha^m)(1 - \alpha)^n \quad [1] $$

with $d\alpha/dt$ the reaction rate, $k_1$ and $k_2$ the reaction rate constants following an Arrhenius-type dependence on temperature, $\alpha$ the fractional conversion and m and n the reaction orders.

This model was specifically applied to isothermal DSC analysis (Figure S5 to S7) 42. Based on this fitting, typical Kamal-Sourour parameters were determined via a Nelder-Mead direct search method. The model was validated across all three formulations. The linear fit of K1 and K2 to the Arrhenius plot demonstrated its applicability to both the 1:1 and

1:1.2 ratios, with a strong correlation coefficient of 0.95, indicating high predictive accuracy.

The parameters obtained for both HTG240-V-1/1 and HTG240-mod-V-1/1 were very similar (Table 1). The activation energies, respectively E1 and E2, were close in value and consistent with those reported in previous studies on stoichiometric epoxy/amine ratios 31,43.

In contrast, the HTG240-V-1/1.2 formulation exhibited a more pronounced difference in both activation energies and pre-exponential factors. The pre-exponential factors for HTG240-V-1/1.2 followed a trend where A2 > A1, whereas the stoichiometric formulations showed the opposite trend, with A2 < A1. A significant disparity is also observed between E1 and E2 for the off-stoichiometric ratio, with E2 being much lower than E1. This suggests that the off-stoichiometric ratio alters the reaction mechanism, potentially influencing the reaction rate associated with E2, which is connected to an internal autocatalytic reaction induced by the formation of hydroxyl groups. The higher concentration of primary amines in the formulation seems to accelerate the release of hydroxyl groups, thereby enhancing the autocatalytic reaction and altering the overall temperature dependence of E2. These results are confirmed by Fig. 1B where the reaction rate peak is observed for a conversion of 0.45 for HTG240-V-1/1.2 in contrast to a value of 0.3 for stoichiometric formulation.

The polymerisation exhibits an overall order (m+n) of 2.5 at processing temperature (100-170°C), nearing 3 at high temperature (>170°C), as also observed by Abuín and coworkers 44 (see Figure S8). In their study, they investigated the effect of high amine/epoxy ratios (up to 3:1) on the applicability of the kinetic model. Their results confirmed an overall reaction order of 2.5, which is independent of the amine/epoxy ratio.

The second empirical model used in this study to characterize the complete curing of the resins is the Di Benedetto equation [2], which gives the evolution of Tg as a function of conversion $\alpha$:

$$ Tg = Tg_0 + (Tg_\infty - Tg_0) \frac{\lambda\alpha}{1 - (1 - \lambda)\alpha} \quad [2] $$

With Tg the glass transition temperature at a given conversion, $Tg_\infty$ the glass transition temperature for the fully cured resin, $Tg_0$ the glass transition temperature at $\alpha=0$, and $\lambda$ a structure-dependent parameter that should be comprised between 0 and 1.

The $\lambda$ parameter primarily serves as a fitting parameter rather than a fundamental physical constant providing a better representation of Tg trends in polymerization processes. It provides information on the curvature evolution of the glass transition temperature (Tg) with conversion. The lower the lambda factor, the more pronounced the curvature of Tg evolution with conversion. Conversely, when $\lambda$ equals 1, a linear evolution of Tg with conversion is observed.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Evolution of the glass transition temperature with conversion for HTG240-V-1/1, HTG240-V-1/1.2 and HTG240-mod-V-1/1 and corresponding fitting curves to Di Benedetto model.</figcaption></figure>

Isothermal DSC measurement conditions were designed to extract data points for the Di Benedetto equation, achieving specific conversions from $α=0.1$ to 0.9 (based on the verified Kamal-Sourour model). After an initial isothermal curing step, the resin sample was rapidly cooled and a dynamic heating ramp was applied in order to determine $T_g$ for each conversion-controlled material. The obtained residual enthalpy provided the degree of cure (Figure S9 to S11). This allowed for the plotting of the Di Benedetto curve across the full range of conversion (Figure 2). The $λ$ parameter was then extracted through curve fitting and compared to the calculated value obtained from $ΔC_p/ΔC_p^0$$^{45}$ as proposed by Pascault and Williams (with $ΔC_p$ and $ΔC_p^0$ the heat capacity of the non-polymerized resin and the heat capacity of the full polymerized resin, respectively). See Table 2 for $λ$ values and Figure 2 for Di Benedetto plotting and fitting (detailed measurements of $ΔC_p$ and $ΔC_p^∞$ are given in figures S12 to S14).

Stoichiometric formulations exhibit a gradual increase in $T_g$ at low conversions due to the increasing molecular weight of the epoxy resin. At high conversions and beyond the gel point, the most pronounced $T_g$ increase results from the rise in crosslinking density. For stoichiometric HTG240-V-1/1 and HTG240-mod-V-1/1, $λ$ equals 0.45 and 0.48, respectively. These values fall within the range given by Di Benedetto for his model and correspond well to the experimental values of $ΔC_p/ΔC_p^0$. On the contrary, for HTG240-V-1/1.2, the fitting to Di Benedetto model generates a $λ$ value of 1.03. This value does not align with the $λ$ approximation of Pascault and Williams which is equal to $ΔC_p/ΔC_p^0$. In addition, while $T_g$ becomes more sensitive to changes at higher conversions in stoichiometric formulations, off-stoichiometric conditions exhibit an almost linear dependence$^{46}$. This phenomenon has hardly been documented, likely due to the strict application of stoichiometric ratios in conventional practices of the di Benedetto model. Nonetheless, since these curves are based on experimental data, the expression of $T_g$ as a function of network conversion can be plotted for further use but cannot be considered

valid for the 1/1.2 ratio, even though it approaches the outer boundary limit.

<table><caption>**Table 2.** Heat Capacity and determination of $λ$ parameter</caption><thead><tr><th></th><th>ΔCp0<br>J/g.K</th><th>ΔCp∞<br>J/g.K</th><th>ΔCp ∝<br>ΔCp0</th><th>λ</th></tr></thead><tbody><tr><td>HTG240-V-1/1</td><td>0.767</td><td>0.348</td><td>0.454</td><td>0.450</td></tr><tr><td>HTG240-V-1/1.2</td><td>0.457</td><td>0.350</td><td>0.766</td><td>1.03</td></tr><tr><td>HTG240-mod-V-1/1</td><td>0.584</td><td>0.290</td><td>0.496</td><td>0.480</td></tr></tbody></table>

Rheology analyses can also be conducted to compare the reactivity of different formulations. These analyses provide information such as gel time, determined by the crossover point between $G'$ and $G''$ (Figures S16 to S18). The gel time is determined across a range of temperature (120-160°C) and has a logarithmic temperature dependence (Figure S15). These values (see table S1) show that the crosslinking of HTG240-V-1/1.2 is, on average, 15% faster than that of stoichiometric networks. This result is consistent with previous findings demonstrating the faster reactivity of the formulation with an excess of amine$^{47}$. Experimental $α_{gel}$ values correspond to a classical epoxy/diamine network, averaging 0.55$^{45}$. However, these values are significantly higher than the theoretical values predicted by the Flory-Stockmayer equation (0.37-0.41) due to certain approximations. Indeed, the difference in reactivity of the epoxy and formation of defects during curing, such as intramolecular cyclization, are not considered in this model. In addition, methods such as the Winter-Chambon criterion$^{48}$, although more time consuming than the crossover point between $G'$ and $G'$, is more precise to strictly evaluate gel time. Nonetheless, the use of an excess of amine clearly induces higher $α_{gel}$ as anticipated by the Flory-Stockmayer equation (See supporting information for the calculation of theoretical $α_{gel}$ values).

Kamal-Sourour and Di Benedetto models can thus be interconnected to provide an overall view of the polymerization of each tested resin. Time-Temperature-Transformation diagrams (TTT) show the behavior of the resin at any time and for any applied temperature.

This diagram allows estimating the required durations for the material to gel and vitrify and is very useful for composite manufacturing, where the curing state of the resin has to be controlled at any time of the process.$^{31,49}$

To achieve the highest conversion and consequently the best mechanical and thermal resistance, vitrification should occur as late as possible. This is because, in a glassy state, there is a significant decrease of chain mobility and then polymerization is driven by diffusion phenomena and no
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Comparison of the TTT diagram of HTG240-V-1/1 (orange), HTG240-V-1/1.2 (blue) and HTG240-mod-V-1/1(yellow) based on Kamal-Sourour and Di Benedetto kinetic models fitted to experimental data.</figcaption></figure>

longer by kinetic factors. At the gel state and during the stage between $t_{gel}$ and $t_{vitrification}$, chain mobility is reduced, although certain mobility is still preserved in comparison with the glassy state. However, gelation must be approached with caution because it is a determinant parameter in the crosslinked material, since it may generate residual stress and possible porosity caused by the viscosity increase and volumetric variations of the resin.

TTT diagrams are constructed based on the above-described models and the correlation with experimental data was in good agreement (See Figure S19-S21 for detailed TTT diagram of each formulation and Figure 3 for comparison). However, some part of the diagram, particularly at high temperature, deviate from experimental data due to the diffusion phenomenon, which is not accounted for in the model ⁴¹. This phenomenon does not hinder the resin's usability in various processes, such as impregnation, as it occurs at moderate temperatures (between room temperature and 80°C). At high temperatures, HTG240-V-1/1.2 exhibits significantly higher reactivity, reaching a conversion of 0.99 at 180°C in 20 minutes, whereas stoichiometric formulations require 32 minutes for the same conversion—an acceleration of approximately 37%. As a result, HTG240-V-1/1.2 possesses an efficient advantage in composite processing, while still maintaining a sufficiently long curing time to prevent defects during impregnation. Comparison also shows that $Tg_∞$ for HTG240-V-1/1.2 and HTG240-mod-V-1/1 are similar enough allowing the vitrimeric properties of both resins to be compared regardless of the temperature used.## 3.2. Mechanical characterization

Following kinetic studies, the mechanical properties of each material were tested. DMA curves exhibited in Figure 4 showed the characteristic $T_α$, which are 213°C, 186°C and 178°C for HTG240-V-1:1, HTG240-V-1/1.2 and HTG240-mod-1/1, respectively (Figure 4).

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Elastic modulus (E') and corresponding tan δ (E''/E') measured in 3-point-bending versus temperature at a heating rate of 3°C/min for all three formulations HTG240-V-1/1, HTG240-V-1/1.2 and HTG240-mod-V-1/1.</figcaption></figure>

The results align with calorimetry measurements, exhibiting the same trend across formulations. The off-stoichiometric and modified resins exhibited a lower E' (1.37 GPa) compared to the stoichiometric formulation (1.66 GPa), measured at 50°C. Additionally, HTG240-V-1/1 displayed greater elasticity than HTG240-V-1/1.2 and HTG240-mod-1/1, as indicated by its lower tan δ peak height.
The excess of amine led to increased molecular mobility and a less densely crosslinked structure, imparting the material with a more viscous response at high temperature.

Furthermore, a secondary tan delta relaxation was observed in HTG240-V-1/1 and HTG240-V-1/1.2 resins. This effect is attributed to vitrimer relaxation, where macroscopic flow is predominantly governed by dynamic exchanges rather than glass transition flow. Additionally, this relaxation may overlap with potential degradation effects of disulfide bonds, especially for stoichiometric formulation HTG240-V-1/1, which are commonly observed in similar systems at temperatures exceeding 250 °C.

<table><caption>**Table 3.** Young modulus, elongation at break and the maximal stress obtained via tensile and 3-point bending mode for HTG240-V-1/1 and HTG240-V-1/1.2</caption><thead><tr><th></th><th></th><th>HTG240-V-1/1</th><th>HTG240-V-1/1.2</th></tr></thead><tbody><tr><td rowspan="3">Tensile mode</td><td>E (GPa)</td><td>2.45 ± 0.08</td><td>2.38 ± 0.02</td></tr><tr><td>σ<sub>max</sub> (MPa)</td><td>50,0 ± 1</td><td>37,0 ± 7</td></tr><tr><td>ε<sub>max</sub> (%)</td><td>2.72 ± 0.04</td><td>1.40 ± 0.4</td></tr><tr><td rowspan="3">3-point bending mode</td><td>E<sub>f</sub> (GPa)</td><td>2.65 ± 0.01</td><td>2.70 ± 0.2</td></tr><tr><td>σ<sub>max</sub> (MPa)</td><td>74,0 ± 10</td><td>73,0 ± 6</td></tr><tr><td>ε<sub>max</sub> (%)</td><td>3.10 ± 0.6</td><td>2.80 ± 0.4</td></tr></tbody></table>

Since the mechanical characterization of HTG240-mod-V-1/1 exhibited similar behaviour to that of HTG240-V-1/1.2 but with much lower dynamics due to a reduced concentration of dynamic bonds (see reprocessing section below), this formulation was not further characterized. HTG240-V-1/1 and HTG240-V-1/1.2 were then evaluated via tensile tests and showed a comparable Young's modulus, while the elongation at break and the maximal stress decreased by approximately 50% and 30% when using an off-stoichiometric ratio, respectively (Table 3, see figure S23 and S24 for experimental data). These values showed that HTG240-V-1/1 is stiffer than the off-stoichiometric network, due to the higher crosslink density and that HTG240-V-1/1.2 is more brittle than the stoichiometric formulation. This observation could be attributed to the higher concentration of secondary amines in HTG240-V-1/1.2, which promotes physical interactions such as hydrogen bonding, thereby restricting polymer chain mobility.⁵⁰ In 3-point bending resistance, a similar observation was noted.

Conductive properties are also an important aspect to consider. The more thermally conductive the vitrimer is, the less time it will take to obtain the desired shape while reprocessing. In the case of thick material, the conductivity can become an important factor. In our case, conductivity is similar to the typical values of classic epoxy resins and is

slightly changed by the epoxy/amine ratio, where 0.17 W/m.K is determined for stoichiometric formulation against 0.46 W/m.K for off-stoichiometric one. This difference is not significant enough to have a real impact on the vitrimer. Moreover, for future use in composites, fibers will serve as the conductive part, while the contribution of the matrix often becomes insignificant. As observed for other studies³¹, density measurements showed a 15% increase for stoichiometric vitrimers compared to reference network, with an additional 1% for off-stoichiometric material (Table S2).

### 3.3. Vitrimer reprocessing

Reprocessing tests are important for comparing the reproducibility of vitrimer materials. These tests were conducted for each formulation at different temperatures ranging from 190 to 230°C (see table S3). Each formulation was coarsely ground into powder and placed into a rectangular shape mold. It was placed in a hydraulic hot pressat 2T/m² and heated to the desired temperature and maintained for a defined time to achieve complete repairing. At low temperature or temperature near Tg, none of the formulations could be reprocessed. At higher temperature (230°C), HTG240-V-1/1.2 demonstrated a more efficient reprocessing compared to HTG240-V-1/1 and HTG240-mod-V-1/1. Although HTG240-V-1/1.2 and HTG240-mod-V-1/1 exhibited the same glass transition temperature and thus a similar reprocessing range (corresponding to the range of temperature between Tg and Td, where dynamic bonds are exchangeable, Figure S22), poor reprocessability was obtained for HTG240-mod-V-1/1 while HTG240-V-1/1.2 underwent successful reprocessing. This outcome highlights the importance of higher disulfide bond content in the off-stoichiometric formulation which improves the stability of the material for effective reshaping.

Sample pictures after reprocessing highlighted the clear effect of degradation, even for HTG240-V-1/1.2 and at lower temperature than the determined 2w% degradation temperature (Td) obtained by dynamic TGA, that occurs under air at 263°C for HTG240-V-1/1 and 250°C for HTG240-V-1/1.2 and HTG240-mod-1/1 (Figure S25). When it comes to vitrimers, degradation is an important phenomenon to consider. In our previous work, high Tg material showed some reprocessing limitations because of the proximity of Tg and Td³¹. To more precisely assess the thermal stability of both materials, isothermal TGA was conducted under air conditions from 220 up to 270°C. The results given by Figure 5 clearly demonstrate that degradation occurred at a lower temperature than anticipated from dynamic analyses. For an exposure of HTG240-V-1/1.2 at 220°C for 20 minutes, a 1% degradation occurred and after 40 min, a 2% mass loss is recorded (heating is not taken into account). Comparatively, HTG240-V-1/1.2 exhibited faster degradation than HTG240-V-1/1, especially at temperatures >220 °C (Figure 5).⁵¹ This phenomenon is likely attributed to the concentration of disulfide bonds that decreases the degradation temperature of the material. Recent work by Sardon and co-
workers⁵¹ demonstrated, via principal component analysis (PCA), that vitrimers based on aromatic disulfides must be processed over short durations (such as 10 minutes), and at temperatures below 210°C to avoid significant degradation. This clearly highlights the limited reliability of TGA analysis in assessing the thermal stability of vitrimers, as the degradation of dynamic bonds does not necessarily result in the formation of volatile compounds. Nonetheless, reprocessing is the most challenging step, as it requires prolonged time and high pressure. However, reshaping and thermoforming remain feasible for high-Tg materials, as recently demonstrated by our group on RTM6-based epoxy materials³¹.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Isothermal TGA thermograms at temperatures ranging from 220 °C to 270 °C for stoichiometric and non-stoichiometric formulation (full line HTG240-V-1/1, dashed line HTG240-V-1/1.2)</figcaption></figure>

### 3.4. Resistance to specific environments

Space environments undergo very specific conditions, such as no atmospheric pressure and outgassing of any non-reacted molecules present on space structure. Thus, through this experiment, we aimed at evaluating two effects: the influence of dynamic bonds and the effect of stoichiometry on the outgassing properties. For this purpose, no tests were conducted on the HTG240-mod-V-1/1 as it does not provide any new information compared to HTG240-V-1/1 and HTG240-V-1/1,2 on this specific test. In the space industry, ECCS documents (European Cooperation for Space Standardization) are technical standards that define best practices, processes, and requirements for designing, building, and operating space systems⁵². The specific requirements depend on each future thermal environment and the localization of the material during operation but as a first approximation, results have to show a recovered mass loss (RML) of the sample under vacuum that does not exceed 1% of its original mass, and a collected condensable volatile material (CVCM) below 0.1%. For these specifications, both vitrimer formulations fulfilled these criteria (Table 4), with no significant difference between materials with different stoichiometric ratios. This indicates that introducing an excess of amine, leading to the formation of

secondary amines, does not impair the outgassing properties of the material. This can be attributed to the physical interactions of secondary amines, which strengthen the network at low temperatures while resulting in a less cross-linked material.

In the case of epoxy resins, the most abundant contaminant degassed are phenols and aromatic amines, meaning that the disulfide bond of added 4AFD to obtain vitrimer properties does not significantly affect the outgassing properties.

<table><caption>**Table 4.** Outgassing properties of both materials HTG240-V-1/1 and HTG240-V-1/1.2</caption><thead><tr><th>Sample</th><th>TML (%)</th><th>CVCM (%)</th><th>RML (%)</th><th>WVR (%)</th></tr></thead><tbody><tr><td>HTG240-V-1/1</td><td>0.715 ±<br>0.070</td><td>0.00</td><td>0.396 ±<br>0.029</td><td>0.319 ±<br>0.041</td></tr><tr><td>HTG240-V-1/1.2</td><td>0.695 ±<br>0.042</td><td>0.00</td><td>0.377 ±<br>0.007</td><td>0.318 ±<br>0.035</td></tr></tbody></table>

*WVR : water vapor regained

## Conclusion

In this work, a comparison of stoichiometric and off-stoichiometric ratios of an epoxy/amine vitrimer formulation was conducted. Model fitting showed that the use of an excess of amine induces a different kinetic behavior with a difference in activation energy values compared to stoichiometric ratios. The excess of amine also modifies and influences the reaction rate associated with the internal autocatalytic reaction owing to the accelerated formation of hydroxyl groups at the initial stage of the polymerization. Moreover, off-stoichiometric formulation induced a significant change in the Di Benedetto behavior, with the appearance of linear dependency of Tg with conversion. These results combined in a TTT diagram showed that overall, a more reactive behavior of the non-stoichiometric formulation is noticed, with lower $\alpha_{gel}$, a decrease of $Tg_{∞}$ and a linear evaluation of Tg with conversion, characterized by sharper transitions. Reprocessing tests revealed significant limitations. However, the use of an excess of dynamic hardener clearly induces a more efficient reprocessing step, although degradation must be taken into consideration since the increased concentration of dynamic hardener in off-stoichiometric ratios decreases the thermal stability of the corresponding materials. In contrast, outgassing properties—important for space applications—were similar for both formulations, with no clear effect of dynamic moieties on outgassing. This study paves the way for future use of the resin as a matrix in composite materials, enabling control over each step of the polymerization process, particularly during impregnation, where resin properties and curing have a substantial impact on the final composite properties.

## Acknowledgment
The authors would like to thank the French National Centre for Space Studies as well as the IRT Saint Exupéry for their financial support. We extend our gratitude to Guillaume Rioland for his support in conducting the outgassing experiments. Gratitude is also extended to the Clément Ader Institute (ICA) and the Softmat Laboratory for providing the experimental equipment.

## Supporting information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/xx.xxx/

Crosslinking kinetics via DSC experiments and rheological tests, Kamal Sourour fitting, Di Benedetto and experimental determination of lambda factor, detailed Time-temperature-Transformation diagrams, degradation behavior and reprocessing tests, tensile and 3 point bending properties are available in Figures S1-S27.

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<figure><img src="image_8.png" /></figure>

This work highlights the development of a high-Tg vitrimer matrix from a space-grade epoxy thermoset, emphasizing the influence of off-stoichiometric conditions in optimizing curing, evolution of Tg and vitrimeric properties