# Thermo-mechanical properties of sustainable resins through a combined experimental and molecular simulation approach

Sébastien Laget, Marie-Noëlle Poradowski, Julien Devémy, Sébastien Garruchet, Alain Dequidt, Patrice Hauret, Patrice Malfreyt

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To cite this version:

Sébastien Laget, Marie-Noëlle Poradowski, Julien Devémy, Sébastien Garruchet, Alain Dequidt, et al. Thermo-mechanical properties of sustainable resins through a combined experimental and molecular simulation approach. Polymer, 2025, 325, pp.128240. 10.1016/j.polymer.2025.128240. hal-05174464

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https://uca.hal.science/hal-05174464v1

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Graphical Abstract

Thermo-mechanical properties of sustainable resins through a combined experimental and molecular simulation approach.

Sébastien Laget, Marie-Noëlle Poradowski, Julien Devémy, Sébastien Garruchet, Alain Dequidt, Patrice Hauret, Patrice Malfreyt

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

Thermo-mechanical properties of sustainable resins through a combined experimental and molecular simulation approach.

Sébastien Laget, Marie-Noëlle Poradowski, Julien Devémy, Sébastien Garruchet, Alain Dequidt, Patrice Hauret, Patrice Malfreyt

* Molecular simulations reproduced the experimental glass transition temperatures and Young's modulus of various epoxy resins.

* The orientational relaxation of epoxy and amine rings is a good descriptor for the Young's modulus

* The width of the distribution of distances between amine functions impacts both the glass transition temperature and the Young's modulus

* The para position of the amine function increases the Young's modulus

* Amines with linear chains show lower glass transition temperatures
# Thermo-mechanical properties of sustainable resins through a combined experimental and molecular simulation approach.

Sébastien Laget<sup>a,b,*</sup>, Marie-Noëlle Poradowski<sup>b</sup>, Julien Devémy<sup>a</sup>, Sébastien Garruchet<sup>a</sup>, Alain Dequidt<sup>a</sup>, Patrice Hauret<sup>b</sup>, Patrice Malfreyt<sup>a,**</sup>

<sup>a</sup>Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000, Clermont-Ferrand, France,
<sup>b</sup>Manufacture Française des Pneumatiques Michelin, 23 Place des Carmes, F-63000, Clermont-Ferrand, France,

## Abstract

Multiple epoxy-amine thermosets, focusing on bio-based epoxy monomers, have been studied using both experimental work and molecular simulations. Glass transition temperature and Young's modulus properties were calculated with both methods to prove the validity of the computational models. We used the molecular simulation to define some descriptors such as the distance between amine groups, number of hydrogen bonds and $\pi$-stacking interactions, degree of rotational freedom of carbon rings. Statistical analysis was performed in order to establish some relationship between the glass transition temperature, Young's modulus and some of these molecular descriptors.

**Keywords:** Molecular simulations, Thermosets, Epoxy - Amine, Glass Transition Temperature, Young's Modulus, Molecular Descriptors, Correlations

## 1. Introduction

Due to their highly cross-linked networks, high mechanical and chemical resistance [1], thermosetting resins called thermosets are key-polymers in a large variety of industrial processes [2] involving composite materials, coating, sealants, paints and adhesives. From high performance applications in the aerospace industry to corrosion resistant coatings, thermoset polymers are chosen for their great versatility[3] and their ability in operating in environments with extreme or variable temperatures [4]. Among thermosets, epoxy resins have many advantages, such as high corrosive resistance and adhesion strength, low curing shrinkage, excellent mechanical, thermal and electrical properties [5]. Epoxy resins can be commonly obtained by chemical reactions of epoxy compounds with curing agents called hardeners. Approximately 90% of the epoxy prepolymer production is based on diglycidyl ether of bisphenol A (DGEBA) (see Fig.1c), which can result from the reaction between bisphenol A (BPA) and epichlorohydrin (ECH) in the presence of sodium hydroxide [6, 7, 8, 9, 5]. BPA, a petrochemical compound, is known as an endocrine disruptor [10] leading to negative impacts for human health and to environmental pollution [11] [12] [13]. Additionally, the irreversibility of the cross-linking reaction make the recycling very difficult further contributing to the global plastic pollution and waste resources[14].

To cover the increasing demand of the composite industry and to reduce the environmental impact of accumulated epoxy waste, a great effort has been done to design either bio-sourced

[15, 16, 17, 18], biodegradable [19], recyclable [20, 21, 22, 23, 24] or user-friendly [25] prepolymers. Vanillin alcohol diglycidyl ether (DGEVA), a compound obtained from wood dust, could be an alternative to DGEBA due to its good thermo-mechanical properties [26, 27, 28]. Another epoxide monomer, triglycidyl ether of phloroglucinol (TGEP) [29, 30, 31] also represents an alternative as a bio-sourced precursor for the design of biodegradable and biocompostable polymer materials (see Fig.1a). The genuine scientific challenge is to design bio-sourced resins from the selection of an epoxy precursor and a curing agent based on the chemical structure of the monomer[32, 33, 34]. Indeed, the prediction of the final properties of the material from the chemical nature of the polymer and hardener requires numerous experiments with different selections of reactants and solvents [35] before reaching the required properties. Even with already available data, this shift toward bio-sourced and user-friendly materials will require significant investment in research to optimize the final material.

The challenging question of predicting the properties of the polymer material from the knowledge of the chemical nature of the prepolymer and the hardener is made harder by the fact that various structural levels [32] namely the chemical nature at the molecular scale and the topology of the cross-linking network are involved in the structure-property relationship[36, 37, 38]. More particularly, what could be the impact of the type and position of functional groups, the strength of intra and intermolecular interactions, the configuration of the polymer chains, the topology of the cross-linking network, the ratio between the prepolymer and hardener on macroscopic properties such as density, glass transition temperature and Young's modulus ?

Such dependencies between structural and molecular parameters and thermo-mechanical properties could be addressed by

<footnote>*Corresponding author: Sébastien.Laget@doctorant.uca.fr</footnote>

<footnote>**Corresponding author: Patrice.Malfreyt@uca.fr</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 1: Molecular structures of epoxy (a-c) and amine (d-k) monomers investigated in this work.</figcaption></figure>

molecular simulations. Indeed, once the molecular interactions are defined by the force field, it is possible to simulate a cross-linked network and extract properties of interest, such as those described above. Identifying relationships between interactions and properties such as density or glass transition temperature is possible but not always straightforward due to the number of factors that describes the resin at the molecular scale. For example, the cooling rate applied in experiments for the measurement of the glass transition temperature is several orders of magnitude slower than the ones used in molecular simulation [39, 40] leading potentially to significant deviations between these both determinations. Nevertheless, a large number of molecular simulations have reported the properties of resins involving various prepolymers and hardeners[41, 42, 43, 44, 45, 46, 47, 48, 37, 38].

In this study, experimental methods and molecular simulations are combined to investigate the thermo-mechanical properties of various bio-based resins. The goal is to identify specific molecular descriptors that can explain the evolution of properties such as density, glass transition temperature, Young's modulus, depending on the nature of the hardener or polymer. We mainly focus on bio-based epoxy monomers, specifically triglycidyl ether of phlorolucinol (TGEP) [49] [27] [30] [31] and diglycidyl ether of vanillyl alcohol (DGEVA)[50] [28] which share structural similarities with the DGEBA monomer characterized by an aromatic core and centrally located epoxy functions. With the epoxydation reaction already optimized in both experimental and MD approach (see Fig.2), the aim is to understand how the molecular structure of reactants affects the final thermo-mechanical properties of the thermoset. To better understand the behavior of the TGEP and DGEBA monomers, both are cured with various amine molecules, each differing by a single structural change. (see Figs.1d-k). The amines are not especially bio-sourced because of the need to use comparable and similar reactants. However, creating a

comprehensive study of the thermoset properties with different molecular structures will help us to understand the impact of functional group and its position on the final properties of the resin. As such, eight amine monomers are used in this study; an aliphatic amine, 1,8 diaminooctane (1,8DAO), an aliphatic with two hetero-atom amine, 2,2'-dioxyethylene-diethylamine (2,2'-DEDA), three cycloaliphatic amines with the reactive group position and their steric hindrance varying, 1,3 bis(aminomethyl)cyclohexane (1,3BAC), 1,4 bis(aminomethyl)cyclohexane (1,4BAC), isophorone diamine (IPDA) and three cycloaromatic amines with different reactive group positions and number of aromatic groups, m-xylylenediamine (MXDA), p-xylylenediamine (PXDA) and 4,4' Diaminodiphenylmethane (4,4'DDM) will be investigated with DGEBA, DGEVA and TGEP epoxy monomers.

The evolution of the glass transition temperature ($T_g$) [51] and Young's modulus (E) [52] [53] [54] [55] [56] [57] are analyzed in relation to that of descriptors such as density, proportion of hydrogen bonds[58], stability of aliphatic and aromatic carbon rings, distance and homogeneity between two amine functions and effect of $\pi$-stacking between aromatic carbon rings. These properties are essential in the characterization of thermosetting polymers and are two key-descriptors for their usage. Indeed, glass transition temperature [59][60] [61] determines the range of temperature over which the material can be used without losing its properties caused by the transition from the glassy state to the rubbery state. For high performances, a suitable $T_g$ would be above 353 K to 373 K. Young's modulus is also a property which informs about the toughness and resistance of the material. Even if the experimental process to obtain these thermo-mechanical properties is well-established [62, 63], the corresponding methodologies for the molecular simulation may lead to some dependencies [64, 65, 65, 66, 67, 39] of the simulated properties on system-sizes, curing reaction, cooling rate and simulation time. Addi-
tionally, for a same resin, it is also possible to observe from ex-
periments some deviations due to the influence of oligomeriza-
tion, curing process or solvent used[30] [68] [31] [49] [69][70].
To remove these uncertainties, every data will be calculated
from this work, with the same experimental and simulation pro-
cess for each thermoset. Experimentally, every epoxy-amine
have their curing rate optimized [71] [72] to maximize the
homogeneity and the conversion rate, while in simulation all
chemical are considered without oligomerisation with a fixed
conversion rate of 95%.

The paper will be structured in the following way: Section 2
describes the experimental and simulation procedures. Section
3 first presents the results of the glass transition and Young's
modulus and then proposes to link the changes on the mechan-
ical and physical properties of the epoxy-amine resin on struc-
tural descriptors. Section 4 contains our main conclusions.

## 2. Experimental and computational procedures

### 2.1. Material studied

A large panel of epoxy and amine monomers are used
to provide a wide variety of molecular structures. These
molecules are shown in Fig. 1. Three epoxy monomers
are the triglycidyl ether of phlorolucinol (TGEP), the
diglycidyl ether of vanillyl alcohol (DGEVA) and the
bisphenol A diglycidyl ether (DGEBA). TGEP was syn-
thesized and provided by SPECIFIC POLYMERS. Two
aliphatic amines, the 1,8 diaminooctane (1,8DAO), and
2,2' ethylenedioxy-diethylamine (2,2'DEDA). Three cy-
cloaliphatic amines, the 1,3 bis(aminomethyl)cyclohexane
(1,3BAC), 1,4 bis(aminomethyl)cyclohexane (1,4BAC) and
isophorone diamine (IPDA). Three cycloaromatic amines,
the m-xylylenediamine (MXDA), p-xylylenediamine (PXDA)
and 4,4' diaminodiphenylmethane (4,4'DDM). 1,8DAO,
2,2'DEDA, 1,3BAC, 1,4BAC, MXDA and PXDA were pur-
chased from Sigma-Aldrich and used as received. In both
experimental and simulation conditions, the reactants are
placed in stoechiometry of function to ensure an optimum
conversion and offer satisfying performance[73] [74]. Working
with epoxy-amine thermoset, each amine group requires two
epoxy groups as shown in Fig. 2[75]. In simulation work, the
conversion rate is fixed at 95% to simulate a well-crosslinked
material without asking for a conversion rate too high, which
would raise considerably the calculation time while potentially
differ from the experimental conversion rate lowered by small
region with an unperfect homogeneity. The curing process is
carried out without using solvents, to ensure the absence of
cavities and air pocket in experimental work, while reducing
the complexity of atomistic simulations. This method found to
be very effective in experimental work with liquid reactants,
but makes it more difficult to reach a great homogeneity with
solid reactants.

Experimentally, the TGEP epoxy (Specific Polymer) is cured
with the 1,8DAO, 2,2'DEDA, 1,3BAC, 1,4BAC, MXDA or
the PXDA amine (TCI Chemicals) and the resulting of the
thermosets are used as a validation of the simulation models.

The DGEVA and DGEBA epoxys, alongside the 4,4'DDM and
IPDA amines are then added to the study on the simulation part
to look deeper in the consequences of the molecular structure
of the reactants on the thermo-mecanical properties of the ther-
mosets.

## 2.2. *Experimental analysis*

2.2.1. *Mixing of the epoxy-amine couple*

For each epoxy-amine couple, the reactants are placed in a planetary mixer (Hauschild, SpeedMixer DAC600) without solvent and blended at the speed of 2000 rpm for 2 minutes. This procedure allows the material to reach a correct homogeneity, both with solid and liquid monomers. For solid amines, the blending time can be increased to reach a satisfactory homogeneity. This method was found to be very effective in experimental work with liquid reactants, however the solid reactants (1,8DAO and PXDA) can impact the final homogeneity and require a larger mixing time. The exact mass varies for each couple and each experiment, between 1 and 10 g of total material. Most of the time, the exothermic reaction started at room temperature within the first couple of minutes, this issue was part of the reason for the removal of solvent to avoid residual pockets within the material, impacting the final results.

2.2.2. *Curing process of the material*

To optimize the final product, the curing process is studied
for each epoxy-amine couple. The raw material, directly after
mixing, is placed under a DSC scan (Netzsh, DSC-300-Caliris)
with two ramps of temperature from 120 K to 520 K with a heat-
ing rate of 50 K min⁻¹, exposing the exothermic reaction linked
to the epoxydation reaction. The first temperature scan high-
lights one or two peaks at temperatures where the epoxydation
reaction takes place. These temperatures are then used follow-
ing the method of A. Tcharkhtchi and al. [76]. The second
temperature scan highlights an approximate value for the glass
transition temperature (see section 2.2.3). The curing process
is the following: for every exothermic peak, a first temperature
plateau is fixed at the beginning of the peak, a second tempera-
ture plateau at the end of the peak, and a last postcured plateau
corresponding to the approximate value of T<sub>g</sub> +20 K. To en-
sure a correct curing time, a DSC scan is performed after every
hour of curing. The reaction is considered as complete when no
peaks are shown at the current curing temperature. This check-
ing method reduces the fusion impact of solid reactants, and
allows a rectification of the temperature levels when two peaks
overlap.

2.2.3. *Glass transition temperature*

The glass transition temperature is determined using a DSC
analysis (Netzsh, DSC-300-Caliris). Samples of 5 mg to 10 mg
are placed in an aluminium crucible with pierced lids under a ni-
trogen atmosphere. Two heating-cooling ramps are performed
with a heating rate of 10 K min⁻¹ under a nitrogen atmosphere.
The temperature ramps are set using the approximate T<sub>g</sub> value
calculated with the curing process optimization. Starting at T<sub>g</sub>
– 100 K to T<sub>g</sub> + 100 K, the final glass transition temperature
<figure><img src="image_5.png" /><figcaption>Figure 2: Epoxydation reaction between an epoxy monomer and an amine reactant.</figcaption></figure>

is determined with the midpoint of the second heating ramp (Fig. 3)

<figure><img src="image_6.png" /><figcaption>Figure 3: DSC curve of the cured TGEP - 1,8DAO thermoset, at a heating rate of 10 K min⁻¹ under N₂ flow.</figcaption></figure>

### 2.2.4. Young's Modulus

The Young's Modulus is determined by a traction test using a Instron Model 5965. The material is molded in a H2 Dumbbell shape (ISO 527,2), cured with the temperature levels defined previously (see section 2.2.2). The cross section of the dumbbell should be 8 mm², however the presence of a concave or a convex meniscus on some materials requires the physical measurement of the cross-section at the breaking point. To determine the correct deformation interval to calculate the Young's modulus, the curve plotting the Young's Modulus and its first derivative as a function of the deformation, given in Fig. S1 in the Supplementary Material, is calculated to find the deformation range with the least variation possible. This method ensures not to take into account the parts where the material is still compressed between the machine's jaws, when these jaws slips slightly before getting a firm grips on the specimen, and remove the impact of both micro-breaks within the material at the start of the test and skin effect close to the breaking point.

## 2.3. Computational procedures

### 2.3.1. Molecular force field

The MedeA® (Material Exploration and Design Analysis) software environment [77] provided by Material Design Inc

was used to create the cross-linked configurations. The PCFF+ [78, 79, 80] force field was used to treat the molecular interactions in the simulation box. The properties reported in this work were calculated with the PCFF+ molecular model indicating that any comparisons with our work must take into account the possible dependence of properties on this model. This model contains intramolecular energy contributions as

$$U_{\text{intra}} = U_{\text{bonds}} + U_{\text{angles}} + U_{\text{torsions}} + U_{\text{impropers}} + U_{\text{coupling}} + U_{\text{nb}} \quad (1)$$

where $U_{\text{bonds}}$, $U_{\text{angles}}$, $U_{\text{torsions}}$, $U_{\text{impropers}}$, $U_{\text{coupling}}$ and $U_{\text{nb}}$ are the covalent bond stretching energy, the bond angle bending energy, the torsion angle rotation energy, the energy penalty due to the deviation from planarity, cross interactions included the dynamic variations among bond, bending and dihedral angle energies and non-bonded interactions, respectively.

The intermolecular interaction between atoms of different molecules and non-bonded interactions between atoms in the same molecule are calculated by using the dispersion-repulsion Lennard-Jones ($U_{\text{LJ}}$) and electrostatic ($U_{\text{ele}}$) energy contributions.

$$U_{\text{inter}} = U_{\text{nb}} = U_{\text{LJ}} + U_{\text{ele}} \quad (2)$$

The electrostatic interactions between two charges $q_i$ and $q_j$ at a distance $r_{ij}$ is represented by the Coulomb potential as

$$U_{\text{ele}} = \sum_{i=1}^{N-1} \sum_{j=i+1}^{N} \frac{q_i q_j}{4\pi\epsilon_0 r_{ij}} \quad (3)$$

where $\epsilon_0$ represents the dielectric constant of the vacuum. These electrostatic interactions are calculated by using the PPPM [81] method.

The dispersion-repulsion energy term is calculated by a 9-6 LJ potential as

$$U_{\text{LJ}}^{9,6} = \sum_{i=1}^{N-1} \sum_{j=i+1}^{N} \epsilon_{ij} \left[ 2 \left( \frac{\sigma_{ij}}{r_{ij}} \right)^9 - 3 \left( \frac{\sigma_{ij}}{r_{ij}} \right)^6 \right] \quad (4)$$

where $\epsilon_{ij}$ and $\sigma_{ij}$ correspond to the energy parameter of the interaction and the Lennard-Jones core diameter. The LJ parameters for the interactions between unlike sites were calculated by using the Waldman-Hagler rules [82] defined as follows for $\sigma_{ij}$ and $\epsilon_{ij}$, respectively.

$$\sigma_{ij} = \left( \frac{\sigma_{ii}^6 + \sigma_{jj}^6}{2} \right)^{1/6} \quad (5)$$
$$ \epsilon_{ij} = 2 \left( \frac{\sigma_{ii}^3 \sigma_{jj}^3}{\sigma_{ii}^6 + \sigma_{jj}^6} \right) \sqrt{\epsilon_{ij} \epsilon_{jj}} \quad (6) $$

### 2.3.2. Molecular dynamics (MD) simulations

The molecular dynamics (MD) calculations were performed using the LAMMPS package [83]. Except if precised otherwise, every MD simulations were performed over 2 ns using the velocity-Verlet integrator with a Nosé-Hoover thermostat [84, 85] at 300 K and 1 bar using the NPT statistical ensemble [86]. The SHAKE algorithm [87] was used to constraint covalent bonds to hydrogen atoms, this allows the use of a time-step of 1 fs Four different cross-linked materials were used for each system. A specimen is a different initial configuration used in the polycondensation process. This means that the four specimens are independent configurations which correspond to the same degree of esterification. The cutoff distance for the van der Waals interactions was set to 12 Å, while the particle-particle particle mesh (PPPM) method [88] with an accuracy of $1 \times 10^{-4}$ and a cutoff distance of 12 Å is considered for the long-range electrostatic interactions.

### 2.3.3. Cross-linking reaction

The molecular modelling of a thermoset polymer starts by establishing the cross-linking process [42] [89]. To this end, multi-steps are required to design a three dimensional network with an high conversion rate. We start by distributing homogeneously monomer molecules in a simulation box and by simulating the epoxydation reaction by creating a covalent bond between the resin and the hardener monomers. The formation of the covalent bond is based on a distance criterion between the two reactive sites at a relative high temperature of 700 K. This strategy was already used in previous molecular simulations [90, 91]. A conversion rate of 0.95 [74] [92] [73] [93] was selected by repeating this process until the conversion value is reached. The temperature of 700 K in the cross-linking process [94] increases the mobility of the molecules within the thermoset, reducing the time to complete the conversion process[95] and allowing the creation of a relaxed and randomized network. The fact of using a relative high temperature avoids the use of more sophisticated approaches such as the incorporation of activation energy calculated from quantum calculations [96, 97, 48], and the addition of catalytic effect in the reaction model [98]. The algorithm used in this work performs very well in obtaining a well cross-linked material with a reasonable calculation time. This gives us the opportunity to investigate more than 60 different thermosets in this paper. Because of the high simulation temperature, close to the thermal decomposition, the cross-linking process is only based on the distance criterion and not on the one that actually takes place in the experimental curing process. [69, 99]. The choice has been made to create the cross-linking process without adding any parasitic oxidation reaction found in experimental curing. The proportion of these oxidation would be too small to be fully considered in this work. The cross-linking process can be described by the following 10 steps :

1. 300 molecules (171 epoxy and 129 amine molecules) are placed in a cubic simulation cell with a density of 0.7 g cm⁻³, a temperature of 300 K and a pressure of 1 atm. This low density means that the molecules can be easily positioned without catenated rings or conflictual placements.

2. each epoxy ring is opened, breaking a carbon-oxygen bond and adding an hydrogen on each side to balance the material

3. the temperature is increased to 700 K, at 1 atm using a NPT simulation to give the system enough mobility for the cross-linking process

4. the cross-linking process starts. Every couple of unreacted epoxy and amine functions within 5 Å is screened, and a covalent bond is created between the reactive carbon of the epoxy and nitrogen of the amine. One hydrogen per reactive atom is removed to keep a balanced material.

5. the system goes through a quick NPT relaxation at 700 K and 1 atm during 10 ps.

6. If the conversion rate of 0.95 is not reached, a loop goes back to the step 4).

7. If the conversion rate is reached, all remaining epoxy rings return to their original state with a closed ring, and the temperature is decreased to 300K.

8. To further relax the cross-linked thermoset, a NPT simulation at 300 K and 1 atm takes place over 1 ns.

9. A 2 ns NPT simulation at 600 K and 1 atm takes place after a temperature ramp from 300 K to 600 K. Rising the temperature allows a rearrangement of the material to remove any metastable conformations.

10. A last 2 ns NPT simulation at 300 K and 1 atm takes place after a temperature drop from 600 K to 300 K. The final simulated material is then used as a starting configuration for the simulation.

Every thermoset studied in this work is cross-linked with a similar reaction between an epoxyde and an amine function. The input parameters such as temperature and search radius remain the same for every cross-linking process. Properties such as density, Young's modulus and hydrogen bonds were calculated at 300 K. In order to limit the dependence of the results on the cross-linking process, the properties were averaged over at least 4 specimen.

## 3. Results and discussion

### 3.1. Glass Transition Temperature

The calculation of the glass transition temperature ($T_g$) can be obtained through the dependence of the specific volume of the resin with respect to the temperature. We take the route of cooling the thermosets from a high temperature in the rubbery state ($T = 700$ K) to a low temperature in the glassy state ($T = 200$ K) at a rate of $20$ K ns⁻¹. It means that the temperature is decreased by steps of 20 K and the average of the specific volume is carried over 1 ns. The glass transition domain (see Fig.4) separates the glassy and rubbery states indicating that $T_g$
has not an unique value but ranges from values characterizing the end of glassy state to the starting of the rubbery state. Three linear fits were carried out on the three domains (rubbery, transition and glassy). The glass transition temperature results from the intercept of the fits of the glassy and rubbery states. For the TGEP-1,8DAO thermoset, as shown in Fig.4, $T_g$ was calculated to 381 K. The experimental cooling rate of 10 K min⁻¹ is of several orders of magnitude slower than that used in molecular simulation. This explains why in other works the simulated $T_g$ values were corrected by empirical contributions calculated via the Williams-Landel-Ferry (WLF) relation [100]. The purpose of corrections is to lower the simulated $T_g$ to match slower cooling conditions.

<figure><img src="image_7.png" /><figcaption>Figure 4: Calculated free volume values of the cross-linked TGEP-1,8DAO thermoset as a function of temperature at a cooling rate of 20 K ns⁻¹ from 700 K to 200 K.</figcaption></figure>

However, the use of universal values [101] for polymers is unrealistic and leads to a wide variability in prediction quality even inconsistent predictions for thermosets [51]. As a result, we do not correct our simulated $T_g$ with any contribution and we focus on the evolution of $T_g$ with respect to the chemical nature of the epoxy amine and of the hardener from experimental and theoretical viewpoints. To be certain of locating $T_g$, we report in Fig.5 the residuals of torsional energy and enthalpy over the 200 K-700 K temperature range. The residual values are defined as the difference between the fitted and actual data. The fitted data were calculated using a least-squares regression method for the enthalpy and torsional energy at different temperatures. Interestingly, the curves of the residual values of both energy contributions show minima located approximately at $T_g$ indicating that both these contributions can help in the determination of the glass transition temperature.

We report in Fig.6 the glass transition temperature of resins obtained from molecular simulations and experiments for different amines cured with the same TGEP epoxy monomer. Fig.6 establishes the inability of correcting the simulated values of $T_g$ by using an identical empirical contribution given that the deviations between experiments and simulations are not identical for each resin. Nevertheless, the trends observed in the experiments are correctly reproduced by the molecular simulations. Indeed, experiments and simulations show that the $T_g$

<figure><img src="image_8.png" /><figcaption>Figure 5: Residuals ($\Delta E$) of torsional energy and enthalpy for a cross-linked TGEP-1,8DAO thermoset at a cooling rate of 20 K ns⁻¹ from 700 K to 200 K.</figcaption></figure>

<table><caption>Table 1: Experimental and simulation values of density, glass transition temperature and Young's modulus for eight epoxy-amine thermosets.</caption><thead><tr><th rowspan="2">Epoxy - Amine</th><th rowspan="2">ρ<sub>sim.</sub><br>(g cm<sup>-3</sup>)</th><th colspan="2">T<sub>g</sub> (K)</th><th colspan="2">E (GPa)</th></tr><tr><th>sim.</th><th>exp.</th><th>sim.</th><th>exp.</th></tr></thead><tbody><tr><td>TGEP - 1,8DAO</td><td>1.18</td><td>393</td><td>358</td><td>3.7</td><td>4.3</td></tr><tr><td>TGEP - 2,2'DEDA</td><td>1.23</td><td>408</td><td>377</td><td>3.6</td><td>4.3</td></tr><tr><td>TGEP - 1,3BAC</td><td>1.20</td><td>435</td><td>437</td><td>3.7</td><td>4.4</td></tr><tr><td>TGEP - 1,4BAC</td><td>1.20</td><td>451</td><td>453</td><td>5.5</td><td>6.1</td></tr><tr><td>TGEP - MXDA</td><td>1.25</td><td>430</td><td>428</td><td>4.2</td><td>4.5</td></tr><tr><td>TGEP - PXDA</td><td>1.25</td><td>425</td><td>418</td><td>5.1</td><td>5.1</td></tr><tr><td>TGEP - 4,4'DDM</td><td>1.21</td><td>420</td><td></td><td>4.0</td><td></td></tr><tr><td>TGEP - IPDA</td><td>1.17</td><td>445</td><td></td><td>4.6</td><td></td></tr></tbody></table>

values of resins formed by linear hardeners are smaller than those formed by hardeners with aliphatic and aromatic rings (see Table 1). Experiments predict a decrease of 20% whereas a decrease of only 10% is given by simulations. To a lesser extent, experiments and simulations agree that $T_g$ of resins with aliphatic rings in amines is slightly higher than that of amines with an aromatic ring as shown in Table 1. The variation of $T_g$ is low and about 5% for both experiments and simulations.

As for the influence of functional group position on $T_g$, this is more difficult to rationalize for two reasons: first, $T_g$ fluctuations due to measurement and calculation uncertainty are more significant than the variations, and second, position has a different effect on aliphatic (1,3 BAC and 1,4 BAC) and aromatic (MXDA, PXDA) rings (see Table 1). The steric hindrance as in IPDA and the number of aromatic rings as in 4,4'DDM do not show significant impact on $T_g$.

We now turn our attention on the influence of the structure of the epoxy monomer on the glass transition temperature. To do so, we report in Fig.7 the values of $T_g$ of three TGEP, DGEVA and DGEBA epoxy monomers cured with three different amines to isolate the influence of the epoxy structure from
<figure><img src="image_9.png" /><figcaption>Figure 6: Glass transition temperature of eight different epoxy-amine thermosets, with experimental (red) and simulation (blue) values. The transparent points correspond to the value of each of the 4 specimen whereas the full blue symbol corresponds to the average value and its standard deviation.</figcaption></figure>

the amine structure. The amines are 1,8 DAO, 1,3 BAC and MXDA representing the linear, aliphatic and aromatic amines, respectively. The values of simulated $T_g$ are also reported in Table 2 for the different resins. Based on the molecular simulation results, we confirm that the linear hardener 1,8 DAO leads to smaller $T_g$ values than aliphatic and aromatic rings for a given epoxy monomer. For example in Table 2, in the case of the TGEP-1,8 DAO, $T_g$ = 393 K whereas it is equal to 435 K and 430 K for 1,3 BAC and MXDA amines, respectively. We find that $T_g$ of aromatic amines is very slightly lower than that of aliphatic ones, whatever the polymer. We also note that $T_g$ of the DGEVA epoxy is the lowest of the three amines by compared to that of TGEP and DGEBA epoxy monomers suggesting that a higher functionality as in TGEP and a larger number of aromatic rings as in DGEBA would likely increase $T_g$.

## 3.2. Young's modulus

Young's modulus is determined by traction testing from experiments. As a consequence, the experimental results are dependent on the stress-strain by using a classic speed on the order of mm min⁻¹. Due to the difficulty to respect the experimental strain rates in molecular simulations, we take the route of using an alternative method based on the fluctuation of the local density [102]. During a simulation, the structural factor $S$ is calculated as a function of the wave vector $q$. The structural factor is then split into a longitudinal ($S_‖$) and transversal direction ($S_⊥$). The demonstration of the operational expressions of the structural factor $S$ has been studied in a previous work [103], using a Fourier components of the displacement fields of particles. The definition of the structure factors is given in the Supplementary Material. The bulk (B) and shear (G) moduli are obtained via the equation 7

<figure><img src="image_10.png" /><figcaption>Figure 7: Simulation glass transition temperatures of nine different cross-linked epoxy-amine thermosets. TGEP (blue), DGEVA (red) and DGEBA (grey) are compared with three different amines as 1,8 DAO, 1,3 BAC and MXDA. The simulation values are averaged over 4 specimens and represented with their statistical fluctuations.</figcaption></figure>

$$ \lim_{q \to 0} S_{\perp}(q) = \frac{2\rho T}{G} \qquad \lim_{q \to 0} S_{\parallel}(q) = \frac{\rho T}{B + 4/3G} \qquad (7) $$

The limit of structural factor when the wave vector tends to zero is calculated by linearly fitting the structural factor $S$ and by acquiring the interception with the vertical axis at $q = 0$. With the assumption of an homogeneous and isotropic linear elastic material, the Young's modulus can be obtained via the bulk and shear moduli calculated previously as:

$$ E = \frac{9BG}{3B + G} \qquad (8) $$

Fig.8 shows the influence of the amine molecular structure on the Young's modulus for TGEP epoxy monomer. The first observation relates to a good agreement between experiments and molecular simulations while at the same time demonstrating a systematic underestimation of simulated values. Indeed, the maximum deviation between experimental and simulated values is about 15% for TGEP-1,3BAC but remains below 10% on average. The main conclusion we can draw from Fig.8 and Table 1 is the impact of the para-position of functional groups in rings on the Young's modulus. Indeed, The Young's modulus of the 1,4 BAC is 38% and 48% higher with respect to the 1,3 BAC amine for experiments and molecular simulations, respectively. In the same way, we observe an increase of the Young's modulus as the amine changes from MXDA to PXDA. However, we do not see correlations between the linearity, aliphaticity and aromaticity and the Young's modulus as observed for the glass transition temperature.

Fig.9 and Table 2 focus on the impact of the epoxy molecular structure on the Young's modulus. First, the TGEP epoxy polymer structure shows the highest Young's modulus regard-
<figure><img src="image_11.png" /><figcaption>Figure 8: Young's modulus of eight different epoxy-amine thermosets obtained from experiments (red) and molecular simulation (blue) values. The 4 simulated values are shown with transparent color while the average value and its standard deviations are represented by solid blue circles.</figcaption></figure>

<table><caption>Table 2: Simulation values of density, glass transition temperature and Young's modulus for nine epoxy-amine thermosets studying the influence of the epoxy molecular structure.</caption><thead><tr><th>Epoxy - Amine</th><th>ρ<sub>sim.</sub><br>(g cm<sup>-3</sup>)</th><th>T<sub>g</sub><br>(K)</th><th>E<br>(GPa)</th></tr></thead><tbody><tr><td>TGEP - 1,8DAO</td><td>1.18</td><td>393</td><td>3.7</td></tr><tr><td>DGEVA - 1,8DAO</td><td>1.18</td><td>387</td><td>3.3</td></tr><tr><td>DGEBA - 1,8DAO</td><td>1.10</td><td>406</td><td>2.8</td></tr><tr><td>TGEP - 1,3BAC</td><td>1.20</td><td>435</td><td>3.7</td></tr><tr><td>DGEVA - 1,3BAC</td><td>1.19</td><td>400</td><td>3.3</td></tr><tr><td>DGEBA - 1,3BAC</td><td>1.12</td><td>439</td><td>3.0</td></tr><tr><td>TGEP - MXDA</td><td>1.25</td><td>430</td><td>4.2</td></tr><tr><td>DGEVA - MXDA</td><td>1.23</td><td>397</td><td>3.9</td></tr><tr><td>DGEBA - MXDA</td><td>1.15</td><td>409</td><td>3.4</td></tr></tbody></table>

less on the structure of the amine whereas the smallest simulated Young's modulus is obtained with the DGEBA epoxy. From a molecular viewpoint, we can argue that an higher functionality in TGEP can lead to a more densely cross-linked thermoset, thus making stronger the intramolecular interactions and increasing the Young's Modulus. For DGEBA, we could assume that either the size which could lead to a less dense cross-linked network or the presence of a quaternary carbon between the two aromatic rings leading to an higher molecular mobility could explain this lowest Young's modulus.

To complete this investigation on the Young's modulus, we also observe that the TGEP epoxy monomer also present the highest density as shown in Table 2 for all the 3 amines whereas the DGEBA epoxy with the smallest Young's modulus (see Fig. 9) also gives the smallest density.

<figure><img src="image_12.png" /><figcaption>Figure 9: Simulated Young's modulus values of nine different cross-linked epoxy-amine thermosets. TGEP (blue), DGEVA (red) and DGEBA (grey) are cured with three different amines 1,8 DAO, 1?3 BAC and MXDA. The simulations are carried out in quadruplicate and the 4 values of Young's modulus are shown along with the average value and its error bars.</figcaption></figure>

### 3.3. Role of the hydrogen bonds

One possible descriptor within the thermosets is the strength of specific interaction such as hydrogen bonds. We calculate the number of hydrogen bonds ($n_{HB}$) in the material by considering the following criteria [104, 105, 106]: one hydrogen bond is retained only if the distance (O-H.O) between the donor and acceptor (oxygen or nitrogen atom) is less than 2.5 Å and simultaneously the angle O-H.O is greater than 150°. $n_{HB}$ was calculated over 2 ns from 2000 configurations saved every 1 ps. $n_{HB}$ was normalized by the number of hydrogen bonds in a box of 1 nm³. All the values of $n_{HB}$ are reported in Table 3. As expected from its number of oxygen and nitrogen atoms (see Figure 1, the maximum number of hydrogen bonds is provided by 2,2'DEDA amine. The minimum of hydrogen bonds is found in 4,4'DDM and IPDA amines whereas the other amines show a number of hydrogen bonds ranging from 2.19 to 2.25$n_{HB}$ per cubic nanometer. More precisely, by comparing to a same linear amine such as 1,8 DAO, the increasing number of hydrogen bonds by 20% due to the presence of two oxygen atoms in the chain, leads to a higher simulated and experimental $T_g$ and a higher simulated density. On the other hand, the lowest number of hydrogen bonds for 4,4'DDM and IPDA amines do not affect properties such as $T_g$, density and Young's modulus.

### 3.4. Role of the π-stacking interactions

We now focus on the calculation of the number of π-stacking in the simulation cell. A case of π-stacking is detected when two aromatic rings centroids are within 4 Å and the angle between the ring normal and vector between the rings centroids is less than 20° [107]. We use the same conditions of simulations than those used for the calculation of $n_{HB}$. The values
<table><caption>Table 3: Calculated values of hydrogen Bonds and π-stacking percentage.</caption><thead><tr><th>Epoxy - Amine</th><th>n<sub>HB</sub><br>(normalized)</th><th>π-Stacking<br>(%)</th></tr></thead><tbody><tr><td>TGEP - 1,8DAO</td><td>2.2</td><td>1.6</td></tr><tr><td>TGEP - 2,2'DEDA</td><td>2.6</td><td>1.5</td></tr><tr><td>TGEP - 1,3BAC</td><td>2.1</td><td>1.4</td></tr><tr><td>TGEP - 1,4BAC</td><td>2.2</td><td>2.1</td></tr><tr><td>TGEP - MXDA</td><td>2.2</td><td>2.9</td></tr><tr><td>TGEP - PXDA</td><td>2.2</td><td>2.8</td></tr><tr><td>TGEP - 4,4'DDM</td><td>1.7</td><td>3.1</td></tr><tr><td>TGEP - IPDA</td><td>1.8</td><td>1.2</td></tr></tbody></table>

must be read as the percentage of rings in a π-stacking configuration compared to the number of aromatic rings within the thermoset. The results are shown in Table 3. The calculated percentages ranging from 1.2 to 2.9% are very weak in the cross-linked networks indicating that this type of interaction cannot lead to strong impacts on the different properties. The maximum value of π-stacking is obtained with aromatic rings in amines (4,4'DDM, MXDA and PXDA) without having values that differ significantly from other amines with linear chains and aliphatic rings. We have not been able to find a direct correlation between this descriptor and the simulated properties.

### 3.5. Impact of the distance between two amine groups

We now pay attention on a structural parameter defined by the distance (d) between amine functions of the same monomer. With the same conditions of simulations than those used for the calculation of n<sub>HB</sub> and the percentage of π-stacking, we calculate an average distribution of all distances over 2 ns by considering the TGEP monomer cured with 6 different amines. We ran 4 independent simulations and the average distribution n(d) is represented with shaded error bars in Fig.10. Three sets of distributions emerge from the analysis. The first set of distributions refer to the amines (1,8 DAO, 2,2'DEDA) with a linear chain with the maximum of the distribution located at 9.3 Å and a distribution width of 4.6 Å calculated with a confidence level of 95%. The second set of distribution including the 1,4 BAC and PXDA amines shows a maximum located at about 7.2 Å with a width of distribution ranging from 1.6 for PXDA to 3.0 for 1,4 BAC amines. This distribution reflects the properties of amines with functional groups in para position. Finally, the third type of distribution of Fig.10 characterizing by maxima at shorter distances (6.4 Å for MXDA and 6.7 Å for 1,3 BAC) expresses the properties of amine functions in meta positions. The distributions of Fig.10 and the position of maximum and width listed in Table 4 show specific distributions specific for linear amines, para and meta positions of amine function groups.

### 3.6. Role of the orientation relaxation of rings

The autocorrelation function (ACF) [108, 109], described in Eq.9, defines how the normal vector of rings $\vec{v}$ in amine and

<figure><img src="image_13.png" /><figcaption>Figure 10: Distributions n(d) of the distance d between amine functions within the same amine monomer in cross-linked TGEP cured with six different amines as indicated in the legend.</figcaption></figure>

<table><caption>Table 4: Position of the maximum of the distribution of the distance between amine groups in the same monomer and width of the distribution calculated with a 95% degree of confidence calculated in TGEP epoxy cured with various amines.</caption><thead><tr><th>Epoxy - Amine</th><th>Max. position<br>(Å)</th><th>Width<br>(Å)</th></tr></thead><tbody><tr><td>TGEP - 1,8DAO</td><td>9.3</td><td>4.6</td></tr><tr><td>TGEP - 2,2'DEDA</td><td>9.3</td><td>4.6</td></tr><tr><td>TGEP - 1,3BAC</td><td>6.7</td><td>4.0</td></tr><tr><td>TGEP - 1,4BAC</td><td>7.2</td><td>3.0</td></tr><tr><td>TGEP - MXDA</td><td>6.4</td><td>3.4</td></tr><tr><td>TGEP - PXDA</td><td>7.3</td><td>1.6</td></tr><tr><td>TGEP - 4,4'DDM</td><td>10.6</td><td>2.8</td></tr><tr><td>TGEP - IPDA</td><td>5.7</td><td>2.3</td></tr></tbody></table>

epoxy molecules are related on average to the preceding vectors over different time lags Δt. It informs us about the evolution of the rotation of the rings over time in the cross-linked thermosets. The autocorrelation function ACF (Δt) of the normal vector $\vec{v}$ for a specific time lag Δt is given by

$$ACF(\Delta t) = \frac{1}{n - \Delta t} \sum_{t=0}^{n - \Delta t - 1} \vec{v}(t) \cdot \vec{v}(t + \Delta t) \quad (9)$$

We used the Fast Fourier transform (FFT) to speed-up the calculation [110]. We used a time lag of 1.7 ns in order to observe significant differences in the time evolution of the rotation of the rings in the different thermosets. A larger time lag would reduce the number of data available to average, creating a bigger uncertainty on the calculated values. Fig.11a shows the autocorrelation functions of the normal vector of the aromatic ring in TGEP, DGEVA and DGEBA epoxy molecules cured with three amines differing with the presence of a linear chain (1,8 DAO), an aliphatic ring (1,3 BAC) and an aromatic ring (MXDA). First, all the curves of Fig.11a show that the autocorrelation of the normal vector decays very slowly reaching values varying from 0.96 to 0.86 after 1.7 ns. Second, the differ-
ent epoxy molecules exhibit slightly different ACF decays. Indeed, we observe that the decay is most marked for DGEBA and to a lesser extent for DGEVA indicating that the tri-epoxidized TGEP molecule maintains the orientation of the aromatic ring over a longer period with respect to bi-epoxidized molecules. We also deduce from Fig.11a that the presence of a covalent bond between the two aromatic rings in DGEBA provides additional flexibility with respect to DGEVA. Third, regardless the epoxy molecule, Fig.11a establishes a more important decay for amines with a linear chain. Fig.11b shows the impact of the position of the functional groups on the ACF decays. Actually, amines with functional groups in para-position shows faster decays of the orientation of the normal vector leading to a greater rotational flexibility. The values of the ACFs after 1.7 ns are given in Tables S1 and S2 of the Supplementary Material.

<figure><img src="image_14.png" /><figcaption>Figure 11: a) Autocorrelation functions of the normal vector of aromatic rings in epoxy molecules with respect to the time lag in cross-linked TGEP-1,8DAO, TGEP-1,3BAC and TGEP-MXDA, DGEVA-1,8DAO, DGEVA-1,3BAC and DGEVA-MXDA, DGEBA-1,8DAO, DGEBA-1,3BAC and DGEBA-MXDA. b) Autocorrelation of the normal vector of aliphatic and aromatic rings in amine molecules with respect to the time lag in cross-linked TGEP-1,3BAC, TGEP-1,4BAC, TGEP-MXDA and TGEP-PXDA.</figcaption></figure>

### 3.7. Spearman Correlation for $T_g$ and Young's modulus

We propose here to establish relationships between the glass transition temperature and Young's modulus and different descriptors calculated from molecular simulations. To this end, we use the Spearman analysis. It results that all correlations are not linear but monotonic. The correlations are conserved if the *p*-value is less than 0.05 [111]. The method is based on the calculation of the critical value of the rank correlation coefficient which depends on the number of investigated points [112]. A positive or a negative Spearman correlation coefficient indicates the direction of the association between the property and the descriptor. In other terms, a positive coefficient means that the property increases with increasing the descriptor. Additionally, the closer the Spearman correlation coefficient is to ±1, the stronger the monotonic relationship between the property and descriptor. For a sample size changing from 36 to 56 points, depending on the property we have simulated, the critical value are as follows: for the meta and para positions, the number of hydrogen-bonds, the percentage of π-stacking and the amine ring rotation, the critical value is 0.330; for the epoxy ring rotation the critical value is 0.291, for the width of the distribution of the distance between amine groups, Young's modulus, glass transition temperature and density, the critical value is 0.264. All the values of the Spearman correlation coefficient along with the *p* values are given in Table 5 for different descriptors obtained from molecular simulations. Only are retained the associations with a *p* value with its historical 0.05 threshold [111].

Fig.12 reports the Spearman correlation coefficients leading to the strongest associations with the glass transition temperature reported in Table 2. Fig.12 and Table 5 clearly establish that the strength of the possible correlations between $T_g$ and the width of the distributions of distance between amines (–0.47), the Young’s modulus (0.42) and the epoxy ring rotation (–0.39) remain moderate. This means that it is very difficult to conclude that one of these descriptors impacts significantly on $T_g$. Access to $T_g$ is therefore mainly limited to experiments and molecular simulation.

Unlike the glass transition temperature, the Spearman statistical analysis show that the Young’s Modulus is very strongly associated with the position of the amine functions in the cyclic amines with a correlation coefficient of 0.87. The correlation is strong for the mobility of epoxy rings (0.79) and the distribution width of distances between amines (0.61). Finally, we observe a moderate monotonic relationship between the Young’s modulus and the density (0.57) and the glass transition temperature (0.42).

## 4. Conclusions

We conducted a study combining molecular simulations and experimental work to determine the thermodynamic properties of epoxy-amine resins. The aim of this combination was to use molecular simulations to find trends in the variation of properties such as glass transition temperature and Young’s modulus but also to find descriptors derived from molecular simulations to interpret them.
<table><caption>Table 5: Calculated Spearman correlation coefficients and *p* values for potential associations between different descriptors and properties such as (*T*<sub>g</sub>) and Young's modulus. The values leading to a significant correlation with a *p* value less than 0.05 and a correlation coefficient greater than their critical value are represented in a bold character. the different descriptors investigated are *T*<sub>g</sub>, density (*ρ*), the number of hydrogen bonds (*n*<sub>HB</sub>), the percentage of π-stacking, the distance corresponding to the maximum of the distribution *n*(*d*) of the distance between amines, the width of *n*(*d*), the final value of the ACFs of the epoxy ring rotation and the amine ring rotation and the Young's modulus.</caption><thead><tr><th></th><th>T<sub>g</sub></th><th>ρ</th><th>n<sub>HB</sub></th><th>π-stacking</th><th>Distance</th></tr></thead><tbody><tr><td></td><td></td><td></td><td>T<sub>g</sub></td><td></td><td></td></tr><tr><td>Coefficient</td><td></td><td>0,12</td><td><strong>-0,33</strong></td><td>0,043</td><td>-0,25</td></tr><tr><td><em>p</em> value</td><td></td><td>0,32</td><td><strong>0,039</strong></td><td>0,79</td><td>0,040</td></tr><tr><td></td><td></td><td></td><td>Young's modulus</td><td></td><td></td></tr><tr><td>Coefficient</td><td><strong>0,42</strong></td><td><strong>0,57</strong></td><td>-0,19</td><td>0,27</td><td>-0,061</td></tr><tr><td><em>p</em> value</td><td><strong>0,0002</strong></td><td><strong>&lt;0,0001</strong></td><td>0,23</td><td>0,095</td><td>0,62</td></tr><tr><td></td><td>Width</td><td>Epoxy ring rotation</td><td>Amine ring rotation</td><td>Meta/para position</td><td>Young's modulus</td></tr><tr><td></td><td></td><td></td><td>T<sub>g</sub></td><td></td><td></td></tr><tr><td>Coefficient</td><td><strong>-0,48</strong></td><td><strong>-0,39</strong></td><td>-0,054</td><td>0,043</td><td><strong>0,42</strong></td></tr><tr><td><em>p</em> value</td><td><strong>&lt;0,0001</strong></td><td><strong>0,0017</strong></td><td>0,0025</td><td>0,86</td><td><strong>0,0002</strong></td></tr><tr><td></td><td></td><td></td><td>Young's modulus</td><td></td><td></td></tr><tr><td>Coefficient</td><td><strong>-0,61</strong></td><td><strong>-0,79</strong></td><td><strong>0,33</strong></td><td><strong>0,87</strong></td><td></td></tr><tr><td><em>p</em> value</td><td><strong>&lt;0,0001</strong></td><td><strong>&lt;0,0001</strong></td><td><strong>&lt;0,0001</strong></td><td><strong>&lt;0,0001</strong></td><td></td></tr></tbody></table>

Molecular simulations were able to reproduce the experimental variations in $T_g$ and Young's modulus as a function of the nature of the epoxy polymer and hardener. For the glass transition temperature, we deduced that $T_g$ of thermosets formed by linear hardeners are smaller than those in hardeners with aliphatic and aromatic rings. However, the impact of linear hardeners is not observed on the Young's modulus. We also investigated the role of hydrogen bonds and π-stacking interactions. For amines with a linear chain, an increasing number of hydrogen bonds leads to a greater $T_g$ and an higher density. The π-stacking interactions which remain however relatively weak in the thermosets investigated here, and the distributions of the distance between amines groups did not impact thermo-mechanical properties.

Finally, the auto-correlation function of the normal vector of rings in epoxy monomers and amine molecule also established that the tri-epoxidized TGEP molecule relaxed more slowly than bi-epoxidized molecules.

We also observed the influence of the amine position on the rotational flexibility of the ring and on the width of the distribution of the distance between amine groups. These two descriptors also impact greatly the thermo-mechanical properties.

To complete this study, statistical Spearman analysis clearly established that the Young's modulus is related to the position of the amine functions in cyclic amines and to a lesser extent to the width of the distribution of amine groups in the molecules and the mobility of the epoxy core rings. For $T_g$, only moderate correlations were found indicating that none of the descriptors studied here has a major and significant impact on this property.

This study raised the ambitious goal of finding molecular descriptors that can impact thermo-mechanical properties of

sustainable resins. Developing relationships between $T_g$ and Young's modulus with molecular descriptors is an important long-term task and our work combining molecular simulations and experiments contributed to meeting this challenge.

## Credit author statement

**Sébastien Laget:** Investigation, Conceptualization, Writing-Original Draft preparation, Writing - Reviewing and Editing
**Marie-Noëlle Poradowski:** Investigation, Conceptualization, Supervision, Writing - Reviewing and Editing **Julien Dévemy:** Methodology, Investigation **Sébastien Garruchet:** Investigation, Conceptualization, Supervision, Writing - Reviewing and Editing **Alain Dequidt:** Methodology, Conceptualization, Supervision, Writing - Reviewing and Editing **Patrice Hauret:** Supervision, Conceptualization, Project administration, Writing - Reviewing and Editing **Patrice Malfreyt:** Conceptualization, Supervision, Writing-Original Draft preparation, Writing - Reviewing and Editing

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.
<figure><img src="image_15.png" /></figure>

Figure 12: Spearman correlation coefficient calculated between the glass transition temperature and descriptors such as the width distribution of distances between amine groups, the Young's modulus, the epoxy ring rotation and the number of hydrogen bonds. The dotted line at 0.4 shows the lower limit of a moderate correlation while the upper limit is 0.6. The histograms in red correspond to negative correlation coefficients whereas the positive coefficients are represented by grey histograms.

<figure><img src="image_16.png" /></figure>

Figure 13: Correlation coefficient values between the Young's modulus and various descriptors obtained from molecular simulations. The different descriptors are the position of the amine groups, the epoxy ring rotation, width of the distribution of distances between amine groups, density, glass transition temperature and the amine ring rotation. The dotted lines show the lower limits of strong (0.6) and very strong (0.8) correlations, respectively. The histograms in red correspond to negative correlation coefficients whereas the positive coefficients are represented by grey histograms.

## Acknowledgment

This work was performed in SimatLab, a joint public-private laboratory dedicated to the modeling of polymer materials. This laboratory is supported by Michelin, Clermont Auvergne University (UCA), CHU Clermont-Ferrand and CNRS. We are grateful to the Mésocentre Clermont Auvergne University for providing computing and storage resources. This work was performed using HPC resources from GENCI-IDRIS (Grant AD010913369R1).

## Supplementary materials

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