Prerak Srivastava
email: prerak.srivastava@inria.fr

Antoine Deleforge
email: antoine.deleforge@inria.fr

Archontis Politis
email: archontis.politis@tuni.fi

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

HOW TO (VIRTUALLY) TRAIN YOUR SPEAKER LOCALIZER

Keywords: source localization, direction-of-arrival, image source, directivity, room acoustic simulation

Learning-based methods have become ubiquitous in speaker localization. Existing systems rely on simulated training sets for the lack of sufficiently large, diverse and annotated real datasets. Most room acoustics simulators used for this purpose rely on the image source method (ISM) because of its computational efficiency. This paper argues that carefully extending the ISM to incorporate more realistic surface, source and microphone responses into training sets can significantly boost the real-world performance of speaker localization systems. It is shown that increasing the training-set realism of a state-of-the-art directionof-arrival estimator yields consistent improvements across three different real test sets featuring human speakers in a variety of rooms and various microphone arrays. An ablation study further reveals that every added layer of realism contributes positively to these improvements.

Introduction

Far-field deep learning based speech processing systems often require large amount of training data, as demonstrated by their application to various tasks such as speech recognition [START_REF] Gusev | Deep speaker embeddings for far-field speaker recognition on short utterances[END_REF][START_REF] Huang | Intel far-field speaker recognition system for VOiCES Challenge 2019[END_REF], speaker localization [START_REF] Xue | Sound event localization and detection based on multiple DOA beamforming and multi-task learning[END_REF][START_REF] Grumiaux | A survey of sound source localization with deep learning methods[END_REF], speech enhancement [START_REF] Chen | Multi-channel end-to-end neural network for speech enhancement, source localization, and voice activity detection[END_REF][START_REF] Rao | ConferencingSpeech Challenge: Towards far-field multi-channel speech enhancement for video conferencing[END_REF] and diarization [START_REF] Horiguchi | End-to-end speaker diarization for an unknown number of speakers with encoder-decoder based attractors[END_REF][START_REF] Ryant | The third DI-HARD diarization challenge[END_REF]. For increased generalization, the study in [START_REF] Vincent | An analysis of environment, microphone and data simulation mismatches in robust speech recognition[END_REF] suggest the use of extensive training sets that cover the range of variability found in real test sets. Due to the difficulty of obtaining enough real data with enough diversity, these training sets are typically simulated, an approach called virtually supervised learning in, e.g., [START_REF] Foy | Mean absorption estimation from room impulse responses using virtually supervised learning[END_REF][START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF]. For those applications on which the effect of reverberation is detrimental, such as speaker localization or multi-microphone speech enhancement, the use of room acoustics simulators is widespread since it allows physical modeling of the room impulse response (RIR) from the source to the receivers, which includes the inter-channel differences utilized by the methods as well as reverberation. Depending on the type of simulation method used, diverse data can be generated in terms of source and receiver position, acoustic material characteristics, or room geometry, which is necessary for the generalization of the methods to a wide range of real acoustic scenes.

Among the various room acoustics simulators under use, the most widespread by far rely on the image source method (ISM) for shoebox rooms [START_REF] Allen | Image method for efficiently simulating small-room acoustics[END_REF][START_REF] Peterson | Simulating the response of multiple microphones to a single acoustic source in a reverberant room[END_REF]. Its implementation simplicity and speed allow rapid generation of RIRs for thousands of rooms with randomized dimensions, wall absorption coefficients, and source-receiver positions. More elaborate geometrical [START_REF] Siltanen | The room acoustic rendering equation[END_REF] or wave-based room acoustics simulators [START_REF] Bilbao | Modeling of complex geometries and boundary conditions in finite difference/finite volume time domain room acoustics simulation[END_REF], that allow complex geometries and more accurate modeling of prop-agation effects, are not currently fast enough for this. In the context of supervised learning, they have been used to pre-compute a few large-scale single-channel datasets covering a limited set of conditions only [START_REF] Chen | SoundSpaces 2.0: A simulation platform for visual-acoustic learning[END_REF][START_REF] Tang | GWA: A large high-quality acoustic dataset for audio processing[END_REF]. Even though shoebox ISM simulation employs stronger acoustical simplifications than more advanced room acoustics simulation methods, it has proven useful in training localization models that then perform adequately well on real datasets [START_REF] Chakrabarty | Multi-speaker DOA estimation using deep convolutional networks trained with noise signals[END_REF][START_REF] Adavanne | Sound event localization and detection of overlapping sources using convolutional recurrent neural networks[END_REF][START_REF] Perotin | CRNN-based multiple DoA estimation using acoustic intensity features for Ambisonics recordings[END_REF][START_REF] Diaz-Guerra | Robust sound source tracking using SRP-PHAT and 3D convolutional neural networks[END_REF][START_REF] Nguyen | Robust source counting and DOA estimation using spatial pseudospectrum and convolutional neural network[END_REF]. Most of these studies are using the simplest form of shoebox ISM, namely, broadband omnidirectional sources and receivers and a global wall-and frequency-independent absorption coefficient, which is also the fastest to simulate. More realistic simulation conditions, such as directional sources and receivers and frequency-dependent surface absorption profiles, can be integrated into shoebox ISM with little computational overhead, at the expense of more complex implementation and specification of simulation parameters. Very few studies perform simulations under these more realistic conditions, except when specialized multichannel receivers are used, e.g., spherical [START_REF] Koyama | Spatial data augmentation with simulated room impulse responses for sound event localization and detection[END_REF], Ambisonic [START_REF] Adavanne | Sound event localization and detection of overlapping sources using convolutional recurrent neural networks[END_REF][START_REF] Perotin | CRNN-based multiple DoA estimation using acoustic intensity features for Ambisonics recordings[END_REF], or binaural [START_REF] Ding | Joint estimation of binaural distance and azimuth by exploiting deep neural networks[END_REF][START_REF] Gaultier | VAST: The virtual acoustic space traveler dataset[END_REF].

Despite the widespread use of shoebox ISM-based simulators for training speaker localization systems, the effect of integrating more realistic simulation conditions at training time on the localization performance on real recordings at test time has hardly been studied. Receiver directivity does not only concern specialized multichannel receivers, but also common arrays of omnidirectional microphones above some frequency, due to the microphone mounting or the size of the capsule. Source directivity seems also crucial considering that most methods focus on speech signals, with human speakers being highly directive [START_REF] Gonzalez | Near-field evaluation of reproducible speech sources[END_REF]. Realistic surface absorption profiles can also have a drastic effect on the reverberation reaching the microphones, in terms of spatial distribution and power spectrum. A previous work by the authors showed a significant performance increase on an acoustic parameter estimation task when measured source and receiver directivities and a natural distribution of frequency-dependent absorption coefficients were integrated in the simulations [START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF]. In the context of speaker localization, we are only aware of one recent study [START_REF] Gelderblom | Synthetic data for DNN-based DoA estimation of indoor speech[END_REF] which analyses the effects of speaker directivity and diffuse late reverberation modeling in the simulations. While diffusion showed no significant impact, the source directivity was found to have a positive impact when testing on speech signals convolved with measured directive RIRs.

In this work, we claim that more realistic simulation at training time can significantly improve real-world localization performance, in a wide variety of scenarios. Results on three multichannel datasets of real human speakers captured in various rooms and with various microphone arrays support this claim. The effects of realistic source and receiver directivi-ties and surface absorption profiles at training time are carefully studied in isolation and in combination for each dataset.

The structure of the rest of the paper is as follows. Section 2 introduces the naive and advanced ISM-based simulation modes and Section 3 introduces the real test sets considered in this paper. The experimental setup is described in Section 4 and the results are analyzed in Section 5. We conclude in Section 6.

Image Source Simulation

Generalized Image Source Method

Simulation of multichannel reverberant speech can be expressed as

x[t] = (h * s)[t] + n[t] (1)
where * denotes convolution, h(t) = [h1(t), ..., hM (t)] T the vector of RIRs from the source to M microphones, n(t) = [n1(t), ..., nM (t)] T additive noise and s the dry source signal. RIR generation based on the ISM for shoebox geometries requires at least the dimensions of the (cuboid) room, the source and receiver coordinates, and a global wall absorption coefficient. An extended version of the ISM that takes into account frequency-dependent walls, propagation, and directivity effects can be expressed in the frequency domain as

h(f ) = K k=0 exp(-ȷ2πf r k /cFs) r k • dair(r k , f ) • d k (f ) • gsrc(-r k , f ) • gmic( r k , f ). (2)
Here, c is the speed of sound and Fs is the sampling frequency. r k is the position vector of the k-th image source w.r.t. the microphone array center, r k = ||r k || is the imagesource-to-array distance and r k = r k /r k is the direction unit vector. dair(r, f ) is the distance-dependent air attenuation while d k (f ) is the compound reflection coefficient of all the surfaces that the k-th image has been reflected from. gmic( r) denotes the vector of M microphone directivity responses defined with their phase center at the array center, for direction-of-arrival (DOA) r. gsrc(-r) denotes the source directivity response for direction-of-departure -r. An alternative implementation of the multichannel receivers can instead utilize individual positions, distances, and DOAs for each microphone in the array, and integrate its local directivity excluding inter-channel array propagation effects. That implementation is suitable for open arrays of directional microphones of known directivity, but it is not suitable for more complex directional arrays that include scattering effects, such as spherical arrays or head-related transfer functions.

Advanced v/s Naive Simulation

In the following, we distinguish the naive mode of ISM simulation often used in practice for model training, where a) wall absorption is assumed to be frequency-independent and equal for all 6 room surfaces, i.e., d k (f ) = d o k with o k being the reflection order and b) sources and receivers are assumed to be omnidirectional, i.e., gsrc( r, f ) = gmic( r, f ) = 1. Additionally we define an advanced mode of ISM simulation that incorporates more informed choices on the directivity and absorption components. Regarding absorption, the coefficients in 6 octave bands are drawn from a naturally balanced mix of distributions corresponding to reflective and absorptive wall, ceiling, and floor materials, as described in [START_REF] Foy | Mean absorption estimation from room impulse responses using virtually supervised learning[END_REF][START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF]. These coefficients are then interpolated using half-cosine octave bands in the discrete Fourier domain and turned into minimum-phase responses. Note that both modes of simulation are tuned to yield comparable distributions of reverberation time. Regarding source directivity, the spatially interpolated measured directivities of a head-and-torso-with-mouth simulator (Brüel & Kjaer HATS 4128-C) and two directive loudspeakers (Genelec 8020 and YAMAHA DXR8) taken from the DIRPAT dataset [START_REF] Brandner | DIRPAT-database and viewer of 2D/3D directivity patterns of sound sources and receivers[END_REF] are integrated into the simulation. Regarding microphone array directivities, scenario-based informed choices are made, as detailed in Section 4. These extensions of the ISM are detailed in [START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF] and are currently available as open source code in the branch dev/dirpat of the pyroomacoustics simulator [START_REF] Scheibler | Pyroomacoustics: A python package for audio room simulation and array processing algorithms[END_REF].

Real Test Sets

To examine the impact of increased ISM realism at training time, we evaluate virtually-supervised localization performance on three real datasets of human speakers with spatio-temporal annotations of their activity and position with respect to the microphone array. The selected publicly available datasets are captured in a variety of rooms, and with a different microphone array each. We focus specifically on datasets featuring real human speakers as opposed to ones generated by convolving dry speech signals with measured RIRs. While the latter are commonly used in the speaker localization literature, the former are closer to real world conditions. This study focuses on the most elementary localization task, namely, single-source DOA estimation in [0, 180] • from a two-second signal recorded using a single microphone pair.

VoiceHome-2 [30]

This dataset is specifically made for distant speech processing applications in domestic environments. It consists of short commands for smart home devices in French, collected in reverberant conditions and uttered by 12 native French speakers.

The data is recorded in 12 different rooms corresponding to 4 houses, with fully annotated geometry, under quiet or noisy conditions. It is captured by a microphone array consisting of 8 MEMS placed near the corner of a cubic baffle. For this study, a two-channel sub-array with aperture 10.4 cm is selected, and 360 two-second speech recordings in quiet conditions are used.

DIRHA [31]

This multichannel dataset consists of recordings done in the living room and kitchen of a typical apartment. Microphones in different configurations are placed on the walls and ceiling of the 2 rooms. 6 native English speakers are chosen to speak sentences taken from the Wall Street Journal news text corpus. Annotations of individual microphone positions and speaker positions are provided. For this study, a wall-mounted two-channel microphone array with aperture 30 cm placed in the living room is selected, and 410 two-second speech recordings from the living room are used.

STARSS22 [32]

This dataset contains recordings of naturally acted scenes of human interaction with spatio-temporal annotations of events belonging to 13 target classes, of which speech is a dominant one. This corpus is part of the development set for Task 3 of the DCASE Challenge 2022. It was captured in facilities at Tampere University and at Sony, with the recording, annotation, and organization of acoustic scenes kept similar on both sites. The Eigenmike spherical microphone array is used to deliver the dataset in two spatial formats, one of which is a tetrahedral sub-array of omnidirectional microphones mounted on a rigid spherical baffle. The corpus is more challenging than the other two in the sense that speakers are free to move and turn naturally during discussions, and that it contains intentional and unintentional sound events other than speech with diffuse and directional ambient noise at substantial levels. We carefully preprocessed the data to extract 2,100 two-second non-overlapping speech excerpts from microphones 6 and 10 out of the tetrahedral sub-array, with an aperture of 6.8 cm. The three curated test sets add up to a total of 95 minutes DOA-annotated, two-channel, real human speech recordings.

Scenario-Based Simulation and Training

Model

To select a state-of-the-art learning-based localization method for this study, we examined the extensive literature review in [START_REF] Grumiaux | A survey of sound source localization with deep learning methods[END_REF]. We selected the convolutional neural network architecture proposed by He et al. [START_REF] He | Deep neural networks for multiple speaker detection and localization[END_REF], specifically its most recent version in [START_REF]Neural network adaptation and data augmentation for multi-speaker direction-of-arrival estimation[END_REF], due to its multiple distinguishing features. Namely, it works with arbitrary microphone arrays, it is initially designed for DOA estimation, it has been successfully applied to real speech recordings, it is readily extendable to multiple localization, detection and counting (not addressed in this study), and its architecture is available through open source code. The model is trained over different simulated training sets using the ADAM optimizer with a learning rate of 10 -4 and batches of size 16 for a maximum of 110 epochs, with early stopping on validation sets. We used the same input features as in [START_REF]Neural network adaptation and data augmentation for multi-speaker direction-of-arrival estimation[END_REF], namely, concatenated short-time Fourier transforms with 50% overlap and 42.7 ms windows, except that all the signals considered in this study are down-sampled to 16 kHz, for consistency.

Scenario Based Training

For all the simulated training sets considered, the default air absorption model of pyroomacoustics is used for dair and image sources are simulated up to order 20. A total of 40k shoebox rooms of sizes uniformly drawn at random in [START_REF] Xue | Sound event localization and detection based on multiple DOA beamforming and multi-task learning[END_REF][START_REF] Foy | Mean absorption estimation from room impulse responses using virtually supervised learning[END_REF] × [3, 10] × [2, 4.5] m are simulated, each containing a source and a twomicrophone array placed uniformly at random with a minimum source-array and device-wall distance of 30 cm. The obtained RIRs are convolved with speech excerpts from the Librispeech corpus [START_REF] Panayotov | Librispeech: an ASR corpus based on public domain audio books[END_REF] according to (1), yielding 40k two-second twochannel reverberated speech samples, of which 38k are used for training and 2k for validation. We experimented with supervising the model with sets containing 10k to 60k samples. While a strong performance improvement was observed from 10k to 60k, diminishing returns were hit around 40k. Further improvements may nonetheless be achievable using even larger sets.

Uncorrelated white Gaussian noise and diffuse speechshaped noise convolved with the late part of a random RIR in the same room are added to the reverberated signals. As detailed in [START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF], noise levels are tuned based on reference scenarios according to the source and receiver considered. This yields consistent bell-shaped signal-to-noise ratio distributions in the range [START_REF] Bilbao | Modeling of complex geometries and boundary conditions in finite difference/finite volume time domain room acoustics simulation[END_REF]75] dB with a peak at 40 dB for all of the training sets considered in this study. While a detailed analysis of the specific impact of noise at training time would be of interest, this is out of the scope of this paper. For each of the three real test sets described in Section 3, one naive and one advanced simulated training set is built based on the two modes of simulation described in Section 2 for walls, sources and receivers. For naive sets, ideal omnidirectional receivers are placed at random inside the room using the same apertures as the ones of their corresponding test sets. For VoiceHome-2, the simulated arrays are identical in the naive and advanced sets. This is because MEMS are known to be close to omnidirectional and the directivity of the VoiceHome-2 array is not available. Moreover, early experiments revealed that using mismatched microphone responses at training time was detrimental to the results, a phenomenon also reported in [START_REF] Srivastava | Realistic sources, receivers and walls improve the generalisability of virtuallysupervised blind acoustic parameter estimators[END_REF]. For DIRHA, the advanced simulation places the arrays on the room walls, which is equivalent to simulating microphones with a half-sphere directivity. For STARSS22, the advanced simulation uses the measured directivity pattern of the relevant sub-array of the Eigenmike. 1

Experiments and Results

To evaluate the virtually-supervised localization systems, two complementary metrics are used for each test set, namely, the mean angular error (MAE, in degrees) and the ratio of sources localized with an error less than 10 • (Recall, in %), which showed to be an adequate threshold to prune out outliers. Models trained using naive and advanced simulations are compared to the classical learning-free steered response power with phase transform (SRP-PHAT) localization method, as implemented in [START_REF] Scheibler | Pyroomacoustics: A python package for audio room simulation and array processing algorithms[END_REF].

Simulated Test Sets

We start by comparing the three methods on two test sets simulated in naive and advanced modes under the VoiceHome-2 scenario. The results are shown in Table 1. First, while all the methods perform well on the naive test set, with nearly perfect recall achieved by both trained models, their performance drastically drops on the advanced test set. This suggests that the presence of realistic wall, source and receiver responses significantly hardens the localization task, even under identical noise and reverberation-time distributions. We have not found direct evidence of this in prior literature and believe this could provide a helpful guideline to improve the evaluation of localization methods on synthetic datasets. Second, as expected, the learning-based methods strongly outperform the learning-free one and the advanced model generalizes significantly better to advanced conditions than the naive one. Moreover, the former seems to perform nearly as well as the latter on naive conditions, despite the mismatch. This strengthens the evidence that speaker localization is inherently more challenging in more realistic conditions. The second half of Table 2 presents an ablation study on the proposed advanced simulation strategy. It reveals that removing any of the three considered layers of realism results in noticeable performance loss. One exception is the use of measured source directivity on STARS22, which does not seem to affect performance. One explanation could be that the human speakers in STARS22 perform significant head rotations, which is not modeled by our framework. The use of a measured array directivity seems to have the strongest impact on this dataset, an observation which we have not found in previous literature for such a simple two-element array. On the other two datasets, the positive impact of source directivity previously reported in [START_REF] Gelderblom | Synthetic data for DNN-based DoA estimation of indoor speech[END_REF] is confirmed, while realistic wall absorptions seem to offer a comparable boost in performance. This is new to the best of our knowledge, and may be explained by the presence of diverse real-world rooms in these datasets. The Python code to reproduce these experiments from training data simulation to evaluation is available here: github.com/prerak23/Dir_SrcMic_DOA.

Conclusion

This paper revealed that simulating realistic wall absorption and source/receiver directivities at training time can significantly boost the performance of a virtually supervised speaker localization model across a large test corpus, featuring real human speakers and a variety of microphone arrays and rooms. While these aspects have been mostly ignored in the speaker localization literature, we argue that they can critically benefit both the evaluation of models and their real world applicability. Several research avenues are left to explore. Our preliminary findings revealed that the results are sensitive to the noise distribution at training time, calling for a careful dedicated study of such effects. We also observed that the validation learning curves of models trained on advanced simulation tended to peak earlier than the naive ones. This leads us to believe that there is still room for improvement on the reported results, e.g., by enriching the diversity of directivity profiles through data augmentation. Finally, the inclusion of source and receiver movements at training time or the use of more efficient stochastic late reverberation models constitute worthwhile research directions.

Table 1 :

 1 Localization results on naive and advanced simulated test sets following the VoiceHome-2 scenario.

		Simulated Test Sets
		Naive		Advanced
	Training	↑ Recall ↓ MAE ↑ Recall ↓ MAE
	Naive	96%	2.6 •	74%	8.5 •
	Advanced	95%	3.0 •	80%	6.7 •
	SRP-PHAT	75%	11.1 •	50%	20.8 •

Table 2 :

 2 Localization results on three real test sets achieved by the SRP-PHAT baseline and by the supervised model[START_REF]Neural network adaptation and data augmentation for multi-speaker direction-of-arrival estimation[END_REF] trained using various simulation modes. Mean angular errors (MAE) are displayed with their 95% confidence interval. Bold numbers indicate the best system in each column and the systems statistically equivalent to it. Statistical significance was assessed using McNemar's test for the Recall metric and 95% confidence intervals over angular error differences for the MAE metric.The three methods are compared on the three real datasets. As can be seen in the top part of Table2, advanced training significantly outperforms naive training by 4 to 7 recall points and 2 • MAE margins across all three datasets, despite using the exact same network architecture. It also largely outperforms the classical SRP-PHAT baseline by 15 to 23 recall points and 3 • to 9 • MAE margins. As predicted in Section 3, the STARS22 dataset proved most challenging for all the methods. Note that even under the quiet and static conditions of VoiceHome-2 and DIRHA, the baseline results are far from perfect. This shows that two-channel DOA estimation remains a challenging task in real-world settings.

	Real Test Sets →	VoiceHome-2 [30]	DIRHA [31]	STARS22 [32]
	Methods	↑ Recall ↓ MAE ( • ) ↑ Recall ↓ MAE ( • ) ↑ Recall	↓ MAE ( • )
	SRP-PHAT	70%	9.9 ± 1.5	61%	15.0 ± 2.3	45%	14.9 ± 0.6
	Naive Training	78%	7.6 ± 1.2	77%	8.4 ± 1.4	57%	12.9 ± 0.6
	Advanced Training	85%	5.8 ± 0.8	84%	6.3 ± 1.0	61%	11.4 ± 0.5
	Ablation study
	without wall realism	83%	6.2 ± 0.8	81%	7.5 ± 1.4	59%	12.1 ± 0.6
	without source realism	82%	7.1 ± 1.1	80%	7.8 ± 1.2	63%	11.4 ± 0.6
	without receiver realism	N/A	N/A	78%	8.3 ± 1.5	53%	13.4 ± 0.6
	5.2. Real Test Sets

We used the measured directivity made available by Franz Zotter et al. from Graz University: https://phaidra.kug.ac.at/o: 69292.

Acknowledgements

This work was made with the support of the French National Research Agency through project HAIKUS "Artifical Intelligence applied to augmented acoustic scenes" (ANR-19-CE23-0023). Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).


Solène Guggari

Fiona Magliozzi

Samuel Malburet

Alain Graillot

Mathias Destarac

Marc Guerre
email: marc.guerre@cnrs.fr

Vanillin-based epoxy vitrimers: looking at cystamine hardener from a different perspective

Keywords: Vanillin, epoxy, vitrimers, recyclability, disulfide

Epoxy vitrimers encompass many advantages compared to traditional epoxy materials such as recyclability, repairability and reprocessability. These properties are induced by the incorporation of dynamic reversible covalent bonds. Recently, the incorporation of aromatic disulfide bridges which are dynamic has expanded the development of new eco-friendly epoxy materials. Herein, we studied a bio-based aliphatic disulfide based on cystamine as hardener with a vanillin-derived bio-sourced epoxy to prepare fully bio-based epoxy vitrimers. This article provides a comparative study between cystamine and an aromatic disulfide benchmark hardener issued from petrol ressources. This work demonstrated that the presence of this aliphatic hardener has a significant influence not only on the reactivity, but most importantly, on the resulting dynamic properties. An interesting yet counterintuitive accelerating effect of the dynamic exchanges was clearly demonstrated with only 2 to 20 % of molar fraction of cystamine added to the aromatic disulfide formulation. A similar glass transition was obtained compared to the purely aromatic analogue but relaxation times were decreased by an order of magnitude.

 In view of replacing 4AFD by a more environmentally friendly analogue, the development of bio-based dynamic hardeners also attracted significant attention. Cystamine, a reactive aliphatic diamine disulfide derived from an amino acid,

INTRODUCTION

Thermosets are commonly used for numerous applications such as coatings, electronics, adhesives and composites. Owing to their highly crosslinked polymeric structure there are able to form networks with high dimensional stability, mechanical properties and chemical resistance. [START_REF] Jin | Synthesis and Application of Epoxy Resins: A Review[END_REF][START_REF] Hernandez | Synthesis and Characterization of Bio-Based Epoxy Resins Derived from Vanillyl Alcohol[END_REF] Among them, epoxy resins are the second most widely used thermoset materials after polyurethanes, representing more than 70% of the remaining global market. [START_REF] Hernandez | Synthesis and Characterization of Bio-Based Epoxy Resins Derived from Vanillyl Alcohol[END_REF][START_REF] Auvergne | Biobased Thermosetting Epoxy: Present and Future[END_REF] But due to their irreversible three-dimensional structures, epoxy thermosets cannot be reshaped and recycled after appears as a suitable hardener in the context of dynamic materials. [START_REF] Khalafi | Investigation of the Cure Kinetics and Thermal Stability of an Epoxy System Containing Cystamine as Curing Agent[END_REF][START_REF] Fortman | Rapidly Reprocessable Cross-Linked Polyhydroxyurethanes Based on Disulfide Exchange[END_REF] The curing kinetics and thermal stability of DGEBA-based materials with cystamine as hardener were investigated by Khalafi et al. [START_REF] Khalafi | Investigation of the Cure Kinetics and Thermal Stability of an Epoxy System Containing Cystamine as Curing Agent[END_REF] However, the dynamic properties were not studied and no information was given regarding the reprocessability of materials. Li et al. [START_REF] Li | Covalent Adaptive Networks for Enhanced Adhesion: Exploiting Disulfide Dynamic Chemistry and Annealing during Application[END_REF] developed adaptative adhesives by crosslinking poly((phenylglycidyl ether)-co-formaldehyde) networks with cystamine. They found that this innovative adhesive can overcome internal stresses thanks to disulfide exchange, leading to enhanced adhesive performance but here again, dynamic properties were not investigated.

Recently, cystamine has been used by Fortman et al. [START_REF] Fortman | Rapidly Reprocessable Cross-Linked Polyhydroxyurethanes Based on Disulfide Exchange[END_REF] as co-curing agent for the synthesis of polyhydroxyurethane vitrimers. This work evaluated the dynamic properties but no specific characterization was conducted for pure disulfide exchanges as each network was based on a dual transcarbamoylation / disulfide exchange mechanism. In addition, no comparison was made with regards to the aromatic counterpart 4AFD. In summary, the dynamic properties of pure cystaminebased vitrimers was never investigated and could represent a viable substitute compared to 4AFD.

In this work, epoxy vitrimers based on vanillin with 4AFD and cystamine as disulfide hardeners were synthesized and compared in order to assess the suitability of cystamine as a potential biosourced alternative. The dynamic properties of each material and mixtures thereof were particularly investigated and revealed an unexpected dynamic behaviour EXPERIMENTAL Materials and methods 4-aminophenyl disulfide (4-AFD, 98%) was purchased from Sigma Aldrich. Diglycidyl ether of vanillyl alcohol (DGEVA, SP-9S-5-005, EEW (Epoxy equivalent weight) = 139 g/eq) and cystamine (SP-2-4-001, AHEW (Amine equivalent weight = 38 g/eq) were synthetized and provided by SPECIFIC POLYMERS. DGEVA building block was synthesized through a two-step procedure from vanillin and epichlorohydrin following and already reported protocol. [START_REF] Genua | Build-To-Specification Vanillin and Phloroglucinol Derived Biobased Epoxy-Amine Vitrimers[END_REF] Cystamine was purchased as cystamine dihydrochloride and desalinated following the procedure by Khalafi et al. [START_REF] Khalafi | Investigation of the Cure Kinetics and Thermal Stability of an Epoxy System Containing Cystamine as Curing Agent[END_REF] Tetrahydrofuran (THF), chloroform (CHCl3), dichloromethane (DCM) and 4mercaptoethanol (> 95%) were purchased from Sigma Aldrich and used as received.

Preparation of vitrimers

Following previous works, [START_REF] Genua | Build-To-Specification Vanillin and Phloroglucinol Derived Biobased Epoxy-Amine Vitrimers[END_REF] an excess of disulfide hardener is recommended to exhibit fast enough dynamic exchanges. Hence, 1.2 equivalent of curing agent was introduced in all formulations. This amount was easily calculated from the epoxide equivalent weight (EEW) and amine hydrogen equivalent weight (AHEW), according to equation ( 1):

(1) 𝑝ℎ𝑟 = 1.2 𝑥 𝐴𝐻𝐸𝑊 𝐸𝐸𝑊 𝑥 100
phr, corresponding to the quantity of hardener to add for 100g of epoxy resin, was determined to be 53.6 g and 33.4 g for 4AFD and cystamine, respectively.

Synthetic procedure

In a typical procedure, the epoxy resin (DGEVA, 1 g) was first melted at 100°C for 10 min to afford a viscous resin, easier to manipulate. Then, the diamine hardener (0.536 mg of 4AFD or 0.334 g of cystamine) was added in molar ratio 1/1.2 and stirred mechanically for 5 min at room temperature to afford a homogeneous viscous liquid. The mixture was then cured at 90 °C for 2h

for DGEVA/cyst and at 150 °C for 2 h for DGEVA/4AFD.

Instrumentation Differential Scanning Calorimetry (DSC) was conducted on a Mettler Toledo Differential

Scanning Calorimeter under a constant nitrogen flow rate (50 ml min -1 ). The samples of about 6-10 mg were heated from 20 °C to 250-300 °C at the rate of 10 °C min -1 under nitrogen as a purged gas. Then, the glass transition temperature was measured in the second heating cycle from 20 °C

to 250 °C at the rate of 10 °C min -1 under nitrogen and no residual curing heat was observed.

Isothermal study was conducted at 120 °C, 140 °C and 160 °C for epoxy / 4AFD and at 50 °C, 70 °C and 90 °C for epoxy / cystamine under nitrogen.

Thermogravimetric measurements (TGA) was performed on a DuPont Instruments 951

Thermal Analyzer (USA) using 8-10 mg of the cured sample. Samples were heated under a nitrogen atmosphere (N2) at a constant ramp rate of 10 °C min -1 from room temperature to 800 °C.

Fourier transform infrared spectroscopy (FTIR) was recorded on a Thermo Nicolet NEXUS spectrophotometer equipped with an ATR diamond. All samples were analyzed through 16 scans and within a range of 400-4000 cm-1 for both cured and uncured states.

Cross-linking kinetic experiments were carried out on an Anton PaarMCR302 stress-controlled rheometer using a 20 mm geometry at 2 mm thickness. Crosslinking studies were conducted at a Crosslinking density was calculated by Flory's expression, [START_REF] Hill | Calculation of Crosslink Density in Short Chain Networks[END_REF] as shown in Equation ( 2):

(2) ν = 𝐺′ 𝑅𝑇
where G' is the storage modulus of the thermoset in the rubbery plateau region at Tg + 50 °C, R is the universal gas constant and T is the absolute temperature in Kelvin.

Soluble fraction and swelling ratio

Solubility tests were performed by Soxhlet extraction. Sample of approximately 50 mg of initial mass (mi) was extracted with chloroform during 48 h at 90°C. The swollen samples were weighed to obtain wet sample mass (ms). Then, md was determined after drying procedure in vacuum oven at 120 °C overnight. The soluble fraction and swelling ratio were calculated according to equations

(3) and ( 4):

(3) 𝑆𝑓 = 𝑚𝑖 -𝑚𝑑 𝑚𝑖 𝑥 100 (4) 𝑆𝑟 = 𝑚𝑠 -𝑚𝑖 𝑚𝑖 𝑥 100

Chemical recycling

A small fragment of the epoxy vitrimers DGEVA/AFD and DGEVA/cyst were immersed in a solution of 2-mercaptoethanol 5 wt % in DMF. The system was magnetically stirred at room temperature for few hours, after which the epoxy matrix was completely dissolved. Then the obtained mixture was dried under vacuum at 100 °C for 48 h.

RESULTS AND DISCUSSION

Synthesis and thermal characterization of epoxy vitrimers

Epoxy vitrimers based on dynamic exchanges of aromatic disulfides have already been widely reported in previous works. [START_REF] Azcune | The Effect of Matrix on Shape Properties of Aromatic Disulfide Based Epoxy Vitrimers[END_REF][START_REF] Li | An Investigation on the Performance of Epoxy Vitrimers Based on Disulfide Bond[END_REF][START_REF] Si | Rapidly Reprocessable, Degradable Epoxy Vitrimer and Recyclable Carbon Fiber Reinforced Thermoset Composites Relied on High Contents of Exchangeable Aromatic Disulfide Crosslinks[END_REF][START_REF] Ruiz De Luzuriaga | Transient Mechanochromism in Epoxy Vitrimer Composites Containing Aromatic Disulfide Crosslinks[END_REF][START_REF] Azcune | Aromatic Disulfide Crosslinks in Polymer Systems: Self-Healing, Reprocessability, Recyclability and More[END_REF] However, even though these dynamic systems showed good recyclability and attractive vitrimer properties, the aromatic hardener was still prepared from petrobased compounds. Our objective was thus to provide an alternative to aromatic disulfides by incorporating a cystamine hardener (Figure 1) which can be produced from amino acid and evaluate its impact over materials. The selected epoxy resin (DGEVA) is also bio-sourced and based on vanillin which is one of the most available pure monoaromatic phenol currently produced at an industrial scale from lignin. [START_REF] Nikafshar | A Renewable Bio-Based Epoxy Resin with Improved Mechanical Performance That Can Compete with DGEBA[END_REF] Epoxy vitrimers are prepared following the conditions depicted in Figure 1 from a synthesized vanillin-based diepoxide (DGEVA) and a diamine hardener (cystamine or 4AFD). Amines react with epoxy functions to form tertiary amines and hydroxyl groups with embedded disulfide bonds that can promote dynamic exchanges through thioldisulfide radical exchanges. [START_REF] Matxain | Design of New Disulfide-Based Organic Compounds for the Improvement of Self-Healing Materials[END_REF] The crosslinking is conducted in a low viscosity liquid state, without solvent and does not release any volatile compounds which are important prerequisites for composite manufacturing processes. The reactivity between aliphatic and aromatic amines being significantly different, the chemical reactivity has been carefully evaluated as it represents a crucial part of material design. Recently, Luzuriaga et al. [START_REF] Ruiz De Luzuriaga | Chemical Control of the Aromatic Disulfide Exchange Kinetics for Tailor-Made Epoxy Vitrimers[END_REF] demonstrated that the presence of secondary amines issued from an excess of hardener accelerates the exchange reaction of disulfides into epoxy vitrimers. By mixing the epoxy resin and diamine hardener with a molar ratio of 1:1.2, respectively, the excess of amine is expected to generate about 20 % of partially reacted amine, resulting in -NH-Ar-S-S-structure that have been predicted to be more dynamic than its fully reacted -N-Ar-S-S-analogue. [START_REF] Matxain | Design of New Disulfide-Based Organic Compounds for the Improvement of Self-Healing Materials[END_REF] This strategy has been employed many times in literature to induce swifter disulfide exchanges. [START_REF] Ruiz De Luzuriaga | Epoxy Resin with Exchangeable Disulfide Crosslinks to Obtain Reprocessable, Repairable and Recyclable Fiber-Reinforced Thermoset Composites[END_REF][START_REF] Genua | Build-To-Specification Vanillin and Phloroglucinol Derived Biobased Epoxy-Amine Vitrimers[END_REF][START_REF] Ruiz De Luzuriaga | Chemical Control of the Aromatic Disulfide Exchange Kinetics for Tailor-Made Epoxy Vitrimers[END_REF][START_REF] Martin | The Processability of a Poly(Urea-Urethane) Elastomer Reversibly Crosslinked with Aromatic Disulfide Bridges[END_REF] However, the higher the secondary amine group concentration will be, the lower the Tg. [START_REF] Ruiz De Luzuriaga | Chemical Control of the Aromatic Disulfide Exchange Kinetics for Tailor-Made Epoxy Vitrimers[END_REF] Thus, these off-stoichiometric conditions must be carefully employed in order to not significantly impair materials properties. The 1:1 and 1:1.2 formulations were evaluated for a DGEVA-4AFD vitrimer.

The overall properties were maintained although a slight decrease of Tg (110 °C vs 103 °C) was noticed for 1:1 and 1:1.2 formulations, respectively. In contrast, the dynamic properties were significantly impacted with a decrease of relaxation time from 330 s to 180 s at 190 °C (Figure S1). For this reason, all following materials have been prepared with a ratio of 1:1.2. Then, the reactivity of DGEVA/4AFD and DGEVA/cyst systems was evaluated by dynamic DSC studies.

The two formulations were firstly followed from 20 °C to 200 °C for cystamine and from 20 °C to 300 °C for 4-AFD at a heating rate of 10 °C min -1 (Figure 2a). The onset temperature for DGEVA/AFD was 136 °C vs. 52 °C for DGEVA/cyst meaning that the aliphatic hardener is much more reactive towards epoxy groups (Figure 2a, Table 1). Full conversion was attained at 150 °C for DGEVA/cyst and at 225 °C for DGEVA/AFD at 10 °C min -1 (with an identical reaction time of approximately 13 min (Figure 2b)). The enthalpy values were not in the same order with a lower reaction enthalpy measured for the DGEVA/4AFD network (471 J g -1 ) compared to the DGEVA/cyst network (568 J g -1 ). Moreover, a significant drop of Tg was noticed (Figure 2c) for cystamine compared to 4AFD with values of 53 °C and 103 °C, respectively. This difference can be easily explained by the less rigid structure of cystamine compared to 4AFD. No residual heat flow was observed during the second temperature ramp confirming the complete conversion and infinite characteristics of the obtained Tg.

The apparent activation energy (Ea) is an important kinetic parameter to understand the curing procedure. In order to determine the kinetic parameters of both epoxy networks, DSC analyses were performed at heating rates of 5, 7.5 and 10 °C min -1 from 20 °C to 250 °C. Figure S2 illustrates the obtained DSC thermograms as a function of the heating rate for DGEVA/4AFD (Figure S2a) and DGEVA/cyst (Figure S2c). The Kissinger equation is commonly used to calculate the apparent activation energy of the curing reaction [START_REF] Kissinger | Reaction Kinetics in Differential Thermal Analysis[END_REF] and assumes that the maximum reaction rate occurs at the peak temperature of the exothermic peak of the curing reaction, and the reaction order remains constant during the curing reaction. [START_REF] Khalafi | Investigation of the Cure Kinetics and Thermal Stability of an Epoxy System Containing Cystamine as Curing Agent[END_REF] Based on Kissinger's method, the activation energy can be obtained from Equation ( 5):

(5) ln ( 𝛽 𝑇 2 𝑝𝑒𝑎𝑘 ) = ln ( 𝐴𝑅 𝐸 𝑎 ) - 𝐸 𝑎 𝑅𝑇 𝑝𝑒𝑎𝑘
where R is the universal gas constant, β is the heating rate and Tpeak is the temperature of the exothermic peak. A linear fitting was observed in both cases, suggesting that the experimental data are in good agreement with the Kissinger model. According to the linear regression displayed in Fig. S4, activation energies were calculated from the slope of the equation Ln (β/T 2 peak) = f (1/Tpeak) and 46 and 53 kJ mol -1 were obtained for DGEVA/4AFD and DGEVA/cyst, respectively. The lower Ea of the DGEVA/4AFD system indicated that the curing reaction of DGEVA with the aromatic diamine is less temperature dependent although the difference remains low.

A low glass transition around 50 °C obtained with DGEVA/cyst may provide easy repairing and recycling but could considerably restrain the industrial potential of these materials. [START_REF] Schenk | Vitrimer Composites: Current Status and Future Challenges[END_REF] For this reason, we also investigated the use of a mixture of aromatic and aliphatic hardeners in order to reach sufficiently high Tg and short relaxation times. A series of vitrimers presented in Table 2 were prepared with different ratios of aromatic/aliphatic diamine DGEVA/4AFDxcysty (with x and y standing for the molar fraction of 4AFD and cystamine, respectively). °C at 10 °C min -1 heating rate (Figure 3). It is important to note that DSC thermograms were bimodal due to the difference of reactivity of cystamine and 4AFD with epoxies (Figure S5).

Nonetheless, since the dynamic exchanges occur concomitantly with the curing, network reshuffling should prevent the formation of heterogeneous network. This is clearly visible in Figure 3a with the appearance of a single Tg was observed with different 4AFD/cystamine ratios. Nonetheless, increasing the aliphatic proportion up to 20% has a considerable influence over the glass transition temperature that decreases by more than 20 degrees, reaching 69°C for 40mol%.

The effect of cystamine over dynamic exchanges will be more deeply investigated and discussed in the section dealing with rheological analyses Based on the above-mentioned analyses, the vitrimer materials were then cured following two strategies depending on the proportion of cystamine. A heating cycle at 90 °C was performed for 2 h to prepare DGEVA/cystamine vitrimers. For DGEVA/4AFD the material was cured at 150 °C for 2 h. For all mixtures, from 2 to 40 mol % of cystamine, curing processes were based on the DGEVA/4AFD curing method. All the blends with a mixture of diamine crosslinkers were characterized in following studies.

Thermogravimetric analysis at 5 wt % loss showed that both materials do not degrade up to 250 °C, as depicted in Fig. S6. Nonetheless, the dynamic DGEVA/cyst networks showed a slightly lower degradation temperature of 253 °C versus 280 °C. This effect is less pronounced for 4AFD/cystamine mixtures which exhibited a degradation temperature in the range of 270-280 °C for AFD/cyst compositions ranging from 60/40 to 98/2 (Figure S7). These results show that replacing a fraction of the aromatic hardener with an aliphatic moiety has only a slight influence on the degradation temperature of the resulting materials. Following the above descriptions, crosslinking kinetics and dynamics of exchange were further studied via rheological analyses with regards to the structure/properties relationship of disulfide bonds and mixtures thereof.

Thermomechanical study

To evaluate the reaction kinetics, both crosslinking reactions were studied by rheological analysis. Shear-moduli (G' storage modulus, G'' loss modulus) were measured over time in frequency mode (1 rad s -1 ) at different temperatures such as 30 °C, 40 °C, 50 °C for DGEVA/cyst and 90 °C, 100 °C, 110 °C for DGEVA/4AFD (Figure S8). In agreement with DSC analyses, the reaction with cystamine is considerably faster than with 4AFD. Full crosslinking is achieved within 26 min at 90 °C for the DGEVA/cyst system while more than hours are required at the same temperature to reach a plateau for the DGEVA/4AFD mixture (Figure 4a). As expected, the gel time corresponding to the crossover of G' and G'' tends to be reduced with increasing temperature for both systems, as depicted in Figure S8. According to the gelation theory and assuming that the kinetic rate constant follows an Arrhenius-type dependence, the activation energy of the crosslinking reactions can be extracted by plotting the gel time versus the inverse of the temperature. Through linear regression fitting (Figure 4b), an apparent activation energy of 69 kJ/mol and 63 kJ/mol have been determined for DGEVA/cyst and DGEBA/4AFD, respectively.

These values follow the same trend as ones calculated via the Kissinger model and are reported in Table 3. Rheological studies such as stress relaxation provide a specific fingerprint to evaluate deformation and flow properties of the material. In order to characterize the malleability of our disulfide networks at elevated temperatures, both DGEVA/cyst and DGEVA/4AFD vitrimers were subjected to stress relaxation analyses at high temperatures from 110°C to 170°C and from 170°C to 200°C, respectively. A constant strain of 1% was applied, which is comprised in the linear To better evaluate this effect, these relaxation curves were fitted to a Kohlrausch-Williams-Watts (KWW) stretched exponential decay [START_REF] Williams | Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function[END_REF][START_REF] Fancey | A Mechanical Model for Creep, Recovery and Stress Relaxation in Polymeric Materials[END_REF][START_REF] Ferry | Viscoelastic Properties of Polymers[END_REF] (equation 6, Figure 5a and 5b) and the corresponding relaxation times (τ*), β stretching exponent and fraction of the residual relaxation modulus Gres/G0 were extracted for each temperature (Table S1). The characteristic average relaxation time < τ > of a stretched exponential decay was calculated according to equation 7.

(6) 𝐺(𝑡) 𝐺 0 = 𝐺 𝑟𝑒𝑠 𝐺 0 + (1 - 𝐺 𝑟𝑒𝑠 𝐺 0 )𝑒𝑥𝑝 (-𝑡 𝜏 * ) 𝛽 (7) < 𝜏 >= 𝜏 * Г( 1 𝛽 ⁄ )
𝛽 with Γ the gamma function. [START_REF] Dhinojwala | Retardation of Rotational Reorientation Dynamics in Polymers near the Glass Transition: A Novel Study over Eleven Decades in Time Using Second-Order Non-Linear Optics[END_REF][START_REF] Li | Vitrimers Designed Both To Strongly Suppress Creep and To Recover Original Cross-Link Density after Reprocessing: Quantitative Theory and Experiments[END_REF] A good fitting was obtained for both materials with R² of 0.99 for all relaxation curves. An average β values in the range of 0.60 for DGEVA/cyst and 0.45 for DGEVA/4AFD were obtained indicating a broader distribution of relaxation times for the DGEVA/AFD formulations compared to DGEVA/cyst materials. These beta values are usual for vitrimer materials. [START_REF] Dhinojwala | Retardation of Rotational Reorientation Dynamics in Polymers near the Glass Transition: A Novel Study over Eleven Decades in Time Using Second-Order Non-Linear Optics[END_REF][START_REF] Li | Vitrimers Designed Both To Strongly Suppress Creep and To Recover Original Cross-Link Density after Reprocessing: Quantitative Theory and Experiments[END_REF] A residual relaxation modulus was obtained for DGEVA/4AFD material at temperatures below 190 °C, while DGEVA/cyst is able to completely relax stresses over the whole range of temperature (Gres/G0 < 1 %, 110 -170 °C). This leveling off of the relaxation modulus over time could be caused by the formation of permanent domains due to irreversible side reactions or restricted network mobility.

In addition, significant difference of average relaxation time <τ> can be noticed (Figure 5c) with more than 23 min obtained at 170 °C for the DGEVA/4AFD vitrimers while 22 s was determined for DGEVA/cystamine. Also, when the temperature is increased from 110 to 170 °C for DGEVA/cystamine, <τ> decreased of an order of magnitude. From those relaxation times, the relationship between Ln(<τ>) and 1000/T was fitted to the Arrhenius equation (Figure 5d), and the corresponding viscous flow activation energy was calculated from the slope. Viscous flow activation energy values of 124 kJ/mol and 57 kJ/mol were determined for DGEVA/4AFD and DGEVA/cyst, respectively. As a basis for comparison, Luzuriaga et al. [START_REF] Ruiz De Luzuriaga | Epoxy Resin with Exchangeable Disulfide Crosslinks to Obtain Reprocessable, Repairable and Recyclable Fiber-Reinforced Thermoset Composites[END_REF] calculated an activation energy of 167 kJ/mol for a similar DGEBA/4AFD system but no available data for cystamine is available. In addition to this significant difference of temperature dependency, faster exchange dynamics for DGEVA/cyst is clearly noticeable. This latter result is rather counterintuitive as S-S α-alkyl disulfides are theoretically stronger bonds than aromatic counterparts with a bond dissociation energy of about 68 kcal.mol -1 (butyl-S-S-butyl) versus 46 kcal.mol -1 for 4AFD. [START_REF] Yang | Density Functional Theory Calculations on S-S Bond Dissociation Energies of Disulfides[END_REF] A faster stress relaxation could have been predicted for DGEBA/4AFD as a result of a higher radical concentration available for thiol-disulfide radical exchanges. Indeed, while both materials exhibit 50 °C difference in Tg, all stress relaxation experiments were conducted at Tg + 60 °C, therefore the influence of Tg should be limited. This unexpected phenomenon could be ascribed to the difference of reactivity and stability of the generated radicals (aliphatic vs aromatic) towards disulfides and/or concomitant mechanism with base-catalyzed thiolate anion-mediated exchanges. [START_REF] Yamawake | The Role of Tertiary Amines as Internal Catalysts for Disulfide Exchange in Covalent Adaptable Networks[END_REF][START_REF] Nevejans | The Underlying Mechanisms for Self-Healing of Poly(Disulfide)s[END_REF] This feature is more deeply investigated in the section dealing with 4AFD and cystamine mixtures and will be the focus of a dedicated study with model reactions and DFT calculations.

DGEVA/4AFD appears strongly temperature dependent meaning that topology rearrangement can be achieved within a narrow temperature range. Moreover, the activation energy of DGEVA/cyst implies a more gradual decrease of viscosity with moderate dependence with temperature. It is important to note that for both materials, the presence of molecular dissociation was clearly visible on non-normalized stress relaxation curves (Figure S9). Figure 6 displays the relaxation modulus G0 for both materials as a function of temperature. G0 slightly decreased with temperature in the case of DGEVA/cyst, reducing from 5.9 MPa to 5.1 MPa from 110 °C to 170 °C which is consistent with low molecular dissociation. In contrast, a small temperature change led to a more abrupt decrease of relaxation modulus for DGEVA/4AFD system which decreased from 6.4 MPa to 3.6 MPa from 170 °C to 200 °C. vitrimer is rather kinetically controlled by the associative exchange. To better understand this effect, the synthesized materials reported above in Table 2 with different proportions of cystamine and 4AFD were also investigated by stress relaxation (Figure S10 and fitting parameters in Table S2). Regarding molecular dissociation, the 4AFD/cystamine mixtures showed an intermediate behavior between both references (Figure S11). The proportion of dissociation is gradually decreased with increasing amount of cystamine, with this trend levelling off for DGEVA/4AFD0.80cyst0.20. All Arrhenius curves ranging from DGEVA/4AFD0.98cyst0.02 to DGEVA/4AFD0.80cyst0.20 formulations are summarized in Figure 7a. Increasing the cystamine proportion results in a gradual yet non-linear acceleration of the stress relaxation process. S2). The decrease of β means that the degree of distribution of relaxation time is more significant for 4AFD/cystamine mixture than for DGEVA/cyst reference resulting in an overall increase of the average relaxation time < τ > compared to initial τ*. This The possible better dissociation of the newly formed adduct (/-Ar-S-S-CH2-/) issued from the exchanges between cystamine and 4AFD could be partly responsible for the observed acceleration.

In addition, the faster exchanges evidenced above for aliphatic disulfides in combination with recently reported base-catalyzed thiolate anion-mediated exchanges should not be neglected. [START_REF] Yamawake | The Role of Tertiary Amines as Internal Catalysts for Disulfide Exchange in Covalent Adaptable Networks[END_REF][START_REF] Nevejans | The Underlying Mechanisms for Self-Healing of Poly(Disulfide)s[END_REF] The in situ formation of tertiary aliphatic or aniline amine within the network (i.e. arising from the reaction between amine or aniline with epoxy) with different basicity could also act as internal catalyst. In summary, the underlying mechanism of disulfide exchanges is certainly more complex than anticipated with strong dependency on intrinsic parameters. Thus, instead of giving too much credit to BDE values which were initially used to anticipate the dynamic properties, we Stress relaxation experiments were also conducted on reprocessed samples (R) (Figure S17).

Similar relaxation times were obtained for all vitrimers and an acceleration was even noticed for DGEVA/cyst (R) sample (Table S3). Activation energy (Ea, Figure S18) was identical for DGEVA/cyst (R) but an increase was observed for DEGVA/4AFD (R) (124 to 155 kJ.mol -1 ) and DGEVA/4AFD0.80cyst0.20 (R) (77 to 90 kJ.mol -1 ). While for DGEVA/4AFD (R), the increase is likely related to fitting quality (R² = 0.97), DGEVA/4AFD0.80cyst0.20 (R) showed a good fitting (R²=0.99). For the mixed DGEVA/4AFD0.80cyst0.20 vitrimer, reprocessing seems to modify the underling exchange mechanism with the appearance of important dissociation at high temperature as exhibited on non-normalized curves (Figure S17). We attributed this change to disulfide reshuffling during reprocessing between aliphatic and aromatic disulfides forming a new (/-Ar-S-S-CH2-/) adduct with possible facilitated dissociation. This dissociation at high temperature was not present on the original materials (Figure S11) suggesting that the structure of 4AFD and cystamine remained unaltered during the curing procedure with no or negligible 4AFD/cystamine adduct formation. Finally, a slight decrease of modulus G0 is observed after reprocessing for DGEVA/cyst (R) and DGEVA/4AFD0.80cyst0.20 (R) within the range of G0 dissociation, which means that the dissociation mechanism might not be fully reversible. This important feature suggests that a gradual decrease of modulus could be expected for disulfide vitrimers over multiple recycling steps and this decrease could be directly correlated to the percentage of disulfide dissociation. In contrast, DGEVA/4AFD (R) showed an increased modulus as a result of possible side reactions due to high radical concentration (Table 4). Swelling experiments were also performed in order to assess the network integrity of the vitrimer materials and optimize the degradation conditions with free thiols. The materials were immersed in chloroform and the swelling ratio and soluble fraction were calculated based on equations 3 and 4. Soxhlet extraction was conducted with chloroform at 90 °C for 48 hours. As exposed in Table 4, soluble fractions were similar with only few % for both networks suggesting a good network integrity. In contrast, swelling ratio appears much higher for DGEVA/cyst than for DGEVA/4AFD as a result of the aliphatic nature of cystamine and the higher crosslink density of DGEVA/4AFD vitrimers. DGEVA/4AFD0.80cyst0.20 (R) exhibited swelling properties similar to DGEVA/4AFD reference with a slight increase of swelling ratio arising from the aliphatic content. Overall, the recycled samples showed very similar swelling and gel content properties confirming the successful reprocessing.

Depending on the nature of the dynamic chemical bonds, chemical recycling can be achieved. [START_REF] Zhao | Recyclable and Malleable Epoxy Thermoset Bearing Aromatic Imine Bonds[END_REF] This strategy is very appealing especially for composites industry in view of recovering the fibers using soft depolymerization conditions. In this case, due to the reversible nature of the disulfide crosslinks, our resins could be easily dissolved in the presence of free thiols owing to the thioldisulfide exchange reactions. 57 So, mercaptoethanol was selected to depolymerize the thermosets.

A sample piece of the DGEVA/cystamine and DGEVA/4AFD resins were stirred with 10 equiv. of 5 wt % mercaptoethanol in DMF at room temperature for 4 h and 12 h, respectively. Full degradation of the material was noticed in both conditions. It should be noted that the degradation DGEVA/cyst was much faster than for the aromatic counterpart in agreement with previous observations suggesting a higher reactivity of aliphatic disulfides. Figure 9 and Figure S19 present the full degradation and chemical recycling ability of both vitrimer materials.

CONCLUSION

In conclusion, we report the synthesis of vanillin-based vitrimers with cystamine, a bio-sourced hardener issued from amino acid, as possible alternative to the widely used petro-sourced 4aminophenyl disulfide (4AFD). The newly synthesized and fully bio-sourced vitrimers were strictly compared to petro-sourced counterparts based on 4AFD. Cystamine exhibited much higher reactivity towards epoxy groups but similar activation energies were determined. A significant acceleration of the exchange dynamics was revealed with decreased relaxation times from 23 min to 22 s at 170 °C for 4AFD and cystamine formulations, respectively. This observation was rather counterintuitive as aromatic disulfides were especially designed to exhibit low BDE and thus accelerate exchanges as a result of high radical concentration. In contrast, cystamine-based vitrimers are more dynamic than their aromatic counterparts. This phenomenon was also investigated through 4AFD and cystamine mixtures for which an unexpected accelerating effect was evidenced. Only 20 mol % of cystamine is necessary in 4AFD/cystamine formulations to achieve comparable relaxation times as for the fully cystamine-based analogue. Beyond the biobased character of cystamine, this discovery opens new perspectives as it could enable a fine tuning of the exchange dynamics by simply adjusting the ratio of cystamine in any epoxy formulation. This is especially true since the more flexible segments arising from the aliphatic structure of cystamine considerably impact the Tg with a sharp drop of values from 103 °C to 53 °C (4AFD vs cystamine, respectively). Therein, with only 20 mol % of cystamine in 4AFD-based formulations, similar relaxation times to cystamine-based analogues can be obtained with a competitive Tg of 80 °C. Thus, the exchange dynamics offered by our aliphatic bio-based hardener could become considerably attractive as a viable alternative to the petrochemical-based counterparts with possible suitability for a wide range of applications.

ASSOCIATED CONTENT Supporting Information.

The Supporting Information is available free of charge at https://pubs.acs.org/XXXXXX Stress relaxation experiments, DSC and TGA thermograms, FTIR and images of reprocessed materials.

(57) Takahashi, A.; Ohishi, T.; Goseki, R.; Otsuka, H.

Figure 1 .

 1 Figure 1. Synthesis of DGEVA-based vitrimers with (i) 4AFD and (ii) cystamine as hardener

Figure 2 .

 2 Figure 2. (a) DSC thermograms obtained at a heating rate of 10 °C min -1 for DGEVA/4AFD and DGEVA/cyst vitrimers (b) corresponding degree of conversion with temperature (c) Tg obtained during second heating ramp at 10 °C min -1

Figure 3 .

 3 Figure 3. (a) DSC thermograms recorded for the different 4AFD/cyst formulations (b) Tg measurements determined by DSC analysis for formulations containing from 2 to 100 mol % of cystamine

Figure 4 .

 4 Figure 4. (a) Curing profile of DGEVA/4AFD and DGEBA/cyst at 90 °C with a strain of 1 % and frequency of 1 rad s -1 (b) Comparison Arrhenius plot of DGEVA/4AFD and DGEVA/cyst gel time as a function of temperature

Figure 5 .

 5 Figure 5. Normalized stress relaxation curves of dynamic epoxy networks a) DGEVA/cyst and b) DGEVA/4AFD at different temperatures c) Stress relaxation comparison of DGEVA/4AFD and DGEVA/cyst at 170 °C d) Arrhenius temperature dependence

Figure 6 .

 6 Figure 6. Relaxation modulus G0 as a function of temperature for DGEVA/4AFD and DGEVA/cyst vitrimers These results seem to confirm theoretical expectations: dissociation occurs preferentially with 4AFD aromatic disulfide. As a result, DGEVA/4AFD is presumably based on dual exchange mechanisms involving radical dissociation and associative exchanges, while the DGEVA/cyst

Figure 7 .Figure 8 )

 78 Figure 7. (a) Arrhenius temperature dependence of DGEVA/4AFDxcysty formulations (b) Comparison of stress relaxation behaviour with various proportions of cystamine relative to 4AFD (from 2 to 100mol%) at 170 °C

Figure 8 .

 8 Figure 8. Plots of relaxation times at 170 °C (black) and activation energies (blue) as a function of the proportion of cystamine relative to 4AFD

  recommend to perform full material characterization through stress relaxation and creep experiments. Yet, this simple modification of dynamic structure can enable a fine control of the exchange pathways. Ea values also follow a similar trend yet less drastically with values gradually decreasing from 124 kJ/mol for the 100 % 4AFD reference down to 77 kJ/mol for the DGEVA/4AFD0.80cyst0.20. This discovery is very interesting as it can promote additional level of control of the exchange dynamics without significantly impairing the materials properties. Indeed, the replacement of 4AFD with cystamine decreased the Tg from 103 to 53 °C which can restrain the potential of this material. Therein, by only adjusting the composition of the material, similar relaxation times can be obtained compared to the cystamine reference yet with glass transition in the range of 80°C for the DGEVA/4AFD0.80cyst0.20 composition, for instance. The reprocessability of materials were evaluated through compression molding experiments. DGEVA/4AFD, DGEVA/cyst and DGEVA/4AFD0.80cyst0.20 samples were broken into small pieces and were reprocessed by compression molding in hot press at 150 °C for 1 h, 40 min and 45 min respectively (reprocessed samples now exhibit the acronym (R)). As shown in Figure 9, hot pressing gave access to reshaped objects which have essentially the same mechanical properties. First, recycled materials were analyzed by DSC measurements. As depicted in Table 4, similar Tg was reported for aliphatic or mixed networks (53 °C vs 50 °C and 83 vs 86 for DGEVA/cyst and DGEVA/4AFD0.80cyst0.20, respectively) while a small decrease was noticed for the aromatic network (from 103 °C to 90 °C) (Figure S12-14). FTIR analysis showed no significant modification over reprocessing steps (Figure S15-16).

Figure 9 .

 9 Figure 9. (a) Reprocessing experiments of vitrimer materials via compression molding of DGEVA/AFD and DGEVA/cyst in hot press at 150 °C (b) Chemical recycling in swollen conditions using mercaptoethanol as reactive species

  1 rad s -1 frequency with 1% deformation at 90 °C, 100 °C and 110 °C for epoxy / 4AFD and at 30 °C, 40 °C and 50 °C for the cystamine-based epoxy system.

	Stress relaxation experiments were performed for each cured material to evaluate the rate of
	reorganization. These characterizations were carried out using a 8 mm plate-plate geometry on
	epoxy resin samples with thicknesses of 0.8-0.4 mm. Prior to the experiments, it was checked that
	1% deformation was within the linear range using amplitude sweep experiments at 170 °C. A 1%
	strain was applied for all samples at temperatures ranging from 110 to 200 °C with a constant
	normal force of 5 N. The materials were reprocessed on a lab press instrument (Carver Model C
	laboratory press) at 150 °C under 1 metric ton for 35 to 60 min.

Table 1 .

 1 Overview of composition and physicochemical properties of the synthetized DGEVA/4AFD and DGEVA/cyst vitrimers

	Name	Cystamine	4AFD	Tg DSC	Td (5%)	G' a	𝛥H	Crosslink density b
		%	%	°C	°C	MPa	J g -1	mol m -3
	DGEVA/4AFD	0	100	103	280	1.30	470.9	361.2
	DGEVA/cyst	100	0	53	253	0.766	568.4	240.6

a Storage modulus determined at 1 rad s -1 and Tg +50°C, b Calculated according to equation 2

Table 2 .

 2 Thermomechanical properties of mixture formulations containing various ratios of 4AFD/cyst compared to reference DGEVA materials with 100% 4AFD or 100% cystamine

	Name	Cystamine	4AFD	Tg DSC	Td (5%)	Arrhenius plot Stress relaxation
		mol%	mol%	°C	°C	Ea (kJ mol -1 )	R 2
	DGEVA/4AFD	0	100	103	280	124	0,99
	DGEVA/cyst	100	0	53	253	57	0,99
	DGEVA/4AFD0.60cyst0.40	40	60	69	276	n.d	n.d
	DGEVA/4AFD0.80cyst0.20	20	80	83	277	77	0,99
	DGEVA/4AFD0.90cyst0.10	10	90	90	274	87	0,99
	DGEVA/4AFD0.95cyst0.05	5	95	91	279	109	0,99
	DGEVA/4AFD0.98cyst0.02	2	98	98	280	135	0,99
	n.d : Not Determined

Thermal properties of new formulations were obtained by DSC with a cycle from 20 °C to 250

Table 3 .

 3 Comparative study of Arrhenius calculations of DGEVA/4AFD and DGEVA/cyst

		Crosslinking kinetics	Kissinger method
	Name	Arrhenius plot	Arrhenius plot
		Ea (kJ/mol)	R 2	Ea (kJ/mol)	R 2
	DGEVA/4AFD	63	0.99	46	0.97
	DGEVA/cyst	69	0.98	53	0.99

Table 4 .

 4 Recycling properties of DGEVA/4AFD, DGEVA/cyst and DGEVA/4AFD0.80cyst0.20

		Tg DSC	G0	Ea	R²	Swelling ratio	Soluble fraction
		°C	Pa	(kJ mol -1 )		%	%
	DGEVA/4AFD	103	5.2E6	124	0.99	6	0.5
	DGEVA/4AFD (R)	90	6.7E6	155	0.97	7	0.4
	DGEVA/cyst	53	5.8E6	57	0.99	102	3.5
	DGEVA/cyst (R)	50	4.6E6	56	0.99	103	4
	DGEVA/4AFD0.80 cyst0.20	83	7.1E6	77	0.99	9	0.2
	DGEVA/4AFD0.80 cyst0.20 (R)	86	6.5E6	90	0.99	17	0.3
	With G0 standing for the relaxation modulus at t=0 measured at 180°C, 120°C and 140 °C for
	DGEVA/4AFD,	DGEVA/cyst		and		DGEVA/4AFD0.80
	cyst0.20, respectively.

  Degradable Epoxy Resins Prepared from Diepoxide Monomer with Dynamic Covalent Disulfide Linkage. Polymer 2016, 82, 319-326. https://doi.org/10.1016/j.polymer.2015.11.057.

	4-AFD
	SLOW	FAST
	SLOW	FAST
	CYSTAMINE	SLOW	FAST
		SLOW	FAST
	Crosslinking
	✓ Malleability
	✓ Reprocessability
	✓ Recyclability

For table of content only

A bio-based aliphatic disulfide hardener with accelerating effect was used with vanillin epoxy to prepare a fully bio-based epoxy vitrimers

Funding Sources

Bio Based Industries Joint Undertaking (JU) under grant agreement No 101023190.

ACKNOWLEDGMENT

This work was supported by the VIBES project. This project has received funding from the Bio Based Industries Joint Undertaking (JU) under grant agreement No 101023190. The JU receives support from the European Union's Horizon 2020 research and innovation program and the Bio Based Industries Consortium. This article reflects only the author's view and the JU is not responsible for any use that may be made of the information it contains.

AUTHOR INFORMATION

Corresponding Author

Dr. Marc Guerre, marc.guerre@cnrs.fr