Background and objectives: Malaria, a potentially life-threatening disease, is the most prevalent endemic infectious disease worldwide. In the modern era, the spectrum of glomerular involvement observed in patients after malarial infections remains poorly described.

Design, setting, participants, & measurements:

We therefore performed a retrospective multicenter study to assess the clinical, biological, pathological and therapeutic characteristics of patients with glomerular disease demonstrated by kidney biopsy in France within three months of an acute malaria episode Results: We identified 23 patients (12 men), all but one of African ancestry and including 10 patients with concomitant human immunodeficiency virus (HIV) infection. All the imported cases were French citizens, living in France who had recently travelled back to France from an endemic area and developed malaria after their return to France. Eleven patients had to be admitted to an intensive care unit at presentation. Plasmodium falciparum was detected in 22 cases and Plasmodium malariae in one case. Kidney biopsy was performed after the successful treatment of malaria, a mean of 24 days after initial presentation. At this time, all patients displayed acute kidney injury, requiring kidney replacement therapy in 12 cases. Nephrotic syndrome was diagnosed in 17 cases. Pathological findings included focal and segmental glomerulosclerosis (FSGS) in 21 cases and minimal change nephrotic syndrome in two patients.

Among patients with FSGS, 18 had collapsing glomerulopathy (including nine cases of HIVassociated nephropathy). In four patients, immunohistochemistry with an antibody targeting P. falciparum histidine-rich protein-2 demonstrated the presence of the malaria antigen in tubular cells, but not in podocytes or parietal epithelial cells. An analysis of the apolipoprotein L1 risk genotype showed that high-risk variants were present in all seven patients tested. After a mean follow-up of 23 months, eight patients required kidney replacement therapy (kidney transplantation in two cases), and mean eGFR for the other patients was 51 mL/mn/1.73m 2 .

Conclusions:

In patients of African ancestry, imported Plasmodium infection may be a new causal factor for secondary FSGS, particularly for collapsing glomerulopathy variants in an APOL1 high-risk variant background.

Introduction

Malaria is a major public health concern worldwide, affecting many millions of people living in tropical areas and causing a significant number of deaths annually [START_REF] Askling | Management of imported malaria in Europe[END_REF]. Endemic malaria has been eradicated in European countries, and the malaria cases notified in France are generally imported cases in travellers returning from or migrants moving to France from countries in which malaria is endemic. Acute kidney injury (AKI) is one of the most feared and severe lifethreatening complications, affecting 1% to 4% of all patients, and up to 60% of patients with severe malaria [START_REF] Burdmann | Acute kidney injury due to tropical infectious diseases and animal venoms: a tale of 2 continents[END_REF][START_REF] Van Wolfswinkel | Neutrophil gelatinase-associated lipocalin (NGAL) predicts the occurrence of malaria-induced acute kidney injury[END_REF]. A broad spectrum of glomerular lesions has been described in association with malaria, but the pathophysiological relationship between these two conditions has been little investigated [START_REF] Barsoum | Malarial acute renal failure[END_REF][START_REF] Van Velthuysen | Glomerulopathy associated with parasitic infections[END_REF]. Early studies, performed in patients with Plasmodium malariae (P. malariae) infection, found that immune complex-mediated membrano-proliferative glomerulonephritis (MPGN) was one of the most frequent causes of nephrotic syndrome in Africa [START_REF] Van Velthuysen | Glomerulopathy associated with parasitic infections[END_REF][START_REF] Elsheikha | Epidemiology, pathophysiology, management and outcome of renal dysfunction associated with plasmodia infection[END_REF][START_REF] Yashima | Mesangial proliferative glomerulonephritis in murine malaria parasite, Plasmodium chabaudi AS, infected NC mice[END_REF]. The spectrum of glomerular damages associated with Plasmodium falciparum (P. falciparum) infection is less common and has not been described in detail [START_REF] Barsoum | Malarial nephropathies[END_REF]. The main pathological lesions appear to be immunoglobulin A nephropathy [START_REF] Yoo | Immunoglobulin A nephropathy associated with Plasmodium falciparum malaria[END_REF], eosinophilic glomerulonephritis [START_REF] Walker | Eosinophilic glomerulonephritis in children in Southwestern Uganda[END_REF], minimal change nephrotic syndrome [START_REF] Rangwani | Minimal change disease and malaria[END_REF] and collapsing glomerulopathy [START_REF] Kute | Collapsing glomerulopathy and hemolytic uremic syndrome associated with falciparum malaria: completely reversible acute kidney injury[END_REF][START_REF] Niang | Collapsing glomerulopathy and haemophagocytic syndrome related to malaria: a case report[END_REF][START_REF] Sehar | Collapsing Focal Segmental Glomerulosclerosis in a Patient with Acute Malaria[END_REF]. We therefore retrospectively assessed the data for 23 patients with biopsy-proven glomerular disease in a context of imported malaria, with the aim of describing the clinical, biological pathological, and therapeutic characteristics of these cases, as well as their outcome. We also performed, in four patients, immunohistochemistry studies with an antibody targeting P. falciparum histidine-rich protein-2 (HRP-2), to determine whether P. falciparum was present in the kidney tissue at the time of glomerular disease diagnosis.

Materials and methods

Patients and kidney function evaluation

We conducted this retrospective study by sending a questionnaire to all French nephrology departments, asking them to identify patients with biopsy-proven glomerular disease following acute malaria episode (kidney biopsy performed within three months of Plasmodium infection).

The main indications of for kidney biopsy were significant proteinuria (urine protein/creatinine ratio (uPCR) > 1.5 g/g) associated with renal impairment. This study was performed in accordance with the ethical standards of the Helsinki Declaration, and was approved by our local institutional review board (IRB 412 Mondor No. 00003835) and by the Comité de Protection des Personnes d'Ile de France IV (No. 2016/25NICB). We included 23 adult patients from 10 nephrology departments seen between 1998 and 2019. Demographic, clinical, biological and histological data obtained at the time of malaria diagnosis and at kidney biopsy were assessed for each patient (supplementary information). Nephrotic syndrome was defined as an uPCR exceeding 3 g/g and a serum albumin concentration below 3.0g/dL Acute kidney injury (AKI) and chronic kidney disease were defined according to Kidney Disease Improving Global Outcome (KDIGO) criteria [START_REF]Kidney Disease: Improving Global Outcomes (KDIGO) Acute Kidney Injury Work Group: KDIGO clinical practice guideline for acute kidney injury[END_REF][START_REF] Disease | Improving global outcomes (KDIGO) CKD work group: KDIGO clinical practice guideline for the evaluation and management of chronic kidney disease[END_REF]. The genotyping data for two risk alleles (the G1 and G2 variant alleles) of the gene encoding apolipoprotein L1 (APOL1) were systematically noted, when available [START_REF] Freedman | Gene-gene and gene-environment interactions in apolipoprotein L1 gene-associated nephropathy[END_REF]. Follow-up data are listed in supplementary information.

Plasmodium infection

The positive diagnosis of malaria was based on blood tests (thick and thin blood smears Giemsa stained and observed by microscopy) (supplementary information). The results of parasitaemia levels and species identification confirmed by polymerase chain reaction (PCR) were noted when available. Patients were considered to have severe malaria if they met the recently updated World Health Organisation (WHO) criteria for severe malaria on admission or during hospitalisation [START_REF]Guidelines for the Treatment of Malaria[END_REF].

Kidney biopsy examination and immunohistochemistry study.

All patients underwent a kidney biopsy for the exploration of proteinuria with an associated impairment of kidney function, within three months of acute Plasmodium infection. Minimal change nephrotic syndrome was diagnosed as previously described [START_REF] Vivarelli | Minimal Change Disease[END_REF]. Focal and segmental glomerulosclerosis (FSGS) was classified according to the Columbia classification [START_REF] Vd | Pathologic classification of focal segmental glomerulosclerosis: a working proposal[END_REF]. The morphological features of collapsing glomerulopathy (including HIV-associated nephropathy (HIVAN) in HIV-infected patients) were defined as previously described [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF]. We investigated whether the Plasmodium directly infected some kidney cells and the possible presence of parasitised red cells in the kidney parenchyma at the time of biopsy, by performing immunohistochemistry with a monoclonal antibody targeting P. falciparum HRP-2 (Meridian Life Science,Inc, Memphis, TN, USA) on frozen kidney biopsy sections fixed in ethanol [START_REF] Genrich | Fatal malaria infection in travelers: novel immunohistochemical assays for the detection of Plasmodium falciparum in tissues and implications for pathogenesis[END_REF] (supplementary information).

Results

Demographic, clinical and biological characteristics of patients with biopsy-proven glomerular disease occurring after imported Plasmodium infection

We retrospectively identified 23 patients (12 men and 11 women) with a mean age 47 years (range: 24-66 years). Their demographic, clinical and biologic data at the time of Plasmodium infection are summarised in Table 1. All but one of the patients were of African ancestry, and 10 patients had concomitant HIV infection, newly diagnosed in three cases and known for some time in the other seven. All the cases were French citizens, living in France who had recently travelled back to France from an endemic area and developed malaria after their return to France. Mean CD4+ T-lymphocyte count in the 10 patients with HIV infection was 345/mm 3 , (range: 17 to 910/mm 3 ). At the time of the bout of malaria, four HIV-positive patients were on HAART, which successfully controlled the viral infection, with undetectable levels of HIV in all cases (Table 1). Five HIV-positive patients had positive HIV viral load (2.10 4 to 2.10 6 copies/mL). One patient tested positive for hepatitis C virus (viral load: 5.7 viral copies/mL) and one patient was positive for hepatitis B virus (viral load: 260 copies/mL). The Plasmodium species responsible for malaria were P. falciparum in 22 cases (96%) and P. malariae in one case, and mean parasitaemia was 7% (range 0.3 to 29%). Severe malaria infection led to 11 patients (48%) being initially hospitalised in an intensive care unit (ICU) for malaria management. The specific treatments administered for malaria are listed in Table 1. The main results for kidney function parameters, immunological findings and other relevant laboratory investigations at the time of kidney biopsy are shown in Table 2. All patients displayed AKI (stage 1 in one patient, stage 2 in two patients and stage 3 in 20 patients). AKI required kidney replacement therapy with haemodialysis in 12 patients and the other 11 patients presented significant alterations of kidney function with a mean creatinine level of 4.9 mg/dl (range: 1.3 to 9.6mg/dl). Seventeen of the 19 patients for whom data were available (90%) presented nephrotic syndrome. Mean uPCR and serum albumin levels in the total population were 9.49 g/g (1.7 to 27g/g) and 2.0 g/dl (0.7 to 4g/dl), respectively. Immunological tests, performed in 23 cases, yielded unremarkable results in all but three patients, two of whom had type II cryoglobulinaemia with low levels of complement fractions, whereas the third had a monoclonal immunoglobulin G (IgG) kappa (κ)spike

Underlying glomerular lesions

The mean time between acute malaria episode and kidney biopsy was 24 days (7 to 80 days).

In all patients, kidney biopsy was performed after the successful management of malaria, as demonstrated by an absence of parasitaemia after treatment, in all cases. Kidney pathology findings are shown in Table 3. The most frequent glomerular lesion, found in 21 patients (91%), was FSGS, but two patients (9%) had typical features of minimal change nephrotic syndrome (including one patient with P. malariae infection). The collapsing glomerulopathy variant was identified in 18 patients (Figure 1a) whereas lesions were classified as not otherwise specified (NOS) histological variants in three patients (Figure 1b). In the 10 patients with concomitant HIV infection, collapsing glomerular lesions were consistent with HIVAN diagnosis in nine cases, whereas the kidney biopsy specimen from the last HIV patient demonstrated the presence of NOS FSGS lesions. Of note, two patients had a previous history of biopsy-proven HIVAN (13 months and 60 months before the malaria episode) considered to be in remission under HAART until the relapse in a context of Plasmodium infection. In one case, HIVAN recurrence was diagnosed in a context of HAART withdrawal. Interestingly, three patients were found to have collapsing glomerulopathy despite good control of HIV infection. In one case, HIVAN lesions were associated with glomerular damage suggestive of additional MPGN lesions with immunoglobulin monoclonal IgG κ deposits. An electron microscopy study was performed for this patient and revealed non-organized dense subendothelial osmiophilic deposits, suggestive of proliferative glomerulonephritis, with monoclonal IgG deposits but no tubuloreticular inclusion. In one patient, HIVAN was associated with thrombotic microangiopathy lesions in a context of severe hypertension. In two patients with cryoglobulinaemia, no glomerular lesions suggestive of cryoglobulinaemia-related glomerulonephritis were found on biopsy. In HIVnegative patients, collapsing glomerulopathy was the most frequent pattern of glomerular injury (nine patients, 69%). Excluding patients diagnosed with minimal change nephrotic syndrome, the percentage of glomeruli displaying segmental and sclerotic lesions was 64% (from 12.5 to 100%). In patients with collapsing glomerulopathy (regardless of HIV status) the mean percentage of glomeruli displaying segmental or global collapse was 50% (from 4 to 100%).

Non-neoplastic lymphoplasmacytic infiltration was found in the interstitium in 18 patients (78%). Acute tubular necrosis (ATN) lesions were found in 15 patients (65%). Microcystic tubular dilatation was observed in 15 patients, including nine diagnosed with HIVAN and six HIV-negative patient (Figure 1c). Mild arteriolar hyalinosis was a frequent histological finding, present in 15 patients, mostly in those with collapsing glomerulopathy not associated with HIV infection (eight of nine patients).

Detection of P. falciparum protein in kidney parenchyma

P. falciparum was the species potentially implicated in the glomerular diseases occurring after malaria in 96% of cases. We therefore used an anti-HRP-2 antibody to determine whether parasite was present in the kidney parenchyma of 4 of these patients. The positive control, P. falciparum-infected red blood cells, is shown in Figure 2a. Immunohistochemistry revealed the presence of the parasite antigen in the lumina of the tubules (Figure 2b) of the four patients analysed, and in the tubular cells cytoplasm (Figure 2c) in one patient. By contrast, podocytes, parietal epithelial cells and glomerular endothelial cells were negative, in all tested cases (Figure 2d). We observed no endocapillary staining suggestive of the presence of circulating infected red blood cells. The negative controls are shown in Figures 2e and2f.

Treatment and follow-up

Some of the patients therefore underwent additional analyses to assess the likelihood of FSGS being caused by a secondary process (Table 2). APOL1 risk allele variants were studied in seven patients, all of whom tested positive (four patients were homozygous for the G1/G1 genotype and three had the compound heterozygous G1/G2 genotype). Serological tests for parvovirus B19 were performed in 14 cases. Four patients tested positive for specific IgM antibodies whereas concomitant serum PCR assays yielded negative results. At the time of kidney biopsy, HAART had been started in three of the HIV-infected patients, reintroduced in one case and modified in six (Table 4). Steroid therapy was introduced in 10 patients, including one with HIVAN associated with MPGN and the two patients diagnosed with minimal change nephrotic syndrome. An immunosuppressive regimen was added in two patients. After a mean follow-up of 23 months (0.5 to 220 months), only four of the patients were considered to present a complete remission of nephrotic syndrome. At the end of follow-up, kidney replacement therapy was required in eight patients: maintenance intermittent haemodialysis was performed in six cases and the other two underwent kidney transplantation. All these patients had severe AKI at the time of kidney biopsy (stage 3 of the KDIGO classification in all cases) and seven were already on dialysis at initial nephrological evaluation. One patient died from septic shock one month after kidney biopsy. It was possible to stop kidney replacement therapy in five of the remaining 15 cases. Mean estimated glomerular filtration rate (eGFR) of these 15 patients was 51 mL/mn/1.73 m 2 at the end of follow-up (ranging from 9.5 to 113 mL/mn/1.73 m 2 ).

Discussion

The main clinical, biological, pathological and therapeutic characteristics of travellers with biopsy-proven glomerular disease after imported malaria have never been investigated in detail.

In this retrospective French survey, we found that FSGS was the most frequent glomerular lesion observed in this setting. We also demonstrated that the most frequent morphological variant of FSGS was collapsing glomerulopathy, observed in 18/23 cases.

The mean time between the onset of Plasmodium infection and the histological diagnosis of glomerular disease was 24 days. This relatively long interval probably reflects the severity of malaria, as ICU admission was required for 11 patients at initial presentation, and 22 patients were considered to have severe malaria infection according to WHO criteria. AKI is a relatively frequent complication of severe malaria and is associated with higher mortality rates [START_REF] Trang | Acute Renal Failure in Patients with Severe Falciparum Malaria[END_REF]. The pathophysiological processes underlying AKI due to malaria seem to be multifactorial, involving haemodynamic instability, immune-mediated kidney injury, metabolic disturbances, and/or the sequestration of parasitised red blood cells in the kidney vasculature leading to ischemic ATN (4). Regardless of the underlying glomerular disease, our pathological study showed that ATN lesions were present in 61% of patients. Given the potential role of ischaemic injury in collapsing glomerulopathy pathogenesis [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF], we can hypothesise that ischaemia related to P. falciparum infection may act as an additional factor triggering glomerular involvement in these patients. We also observed lymphoplasmocytic cell infiltration into the interstitial area in 78% of cases, suggesting that interstitial inflammation and systemic immuneinflammatory processes may also contribute to AKI (4).

The predominance of collapsing glomerulopathy among the glomerular lesions in these patients may also be a key factor associated with the high frequency of AKI in our cohort [START_REF] Schwimmer | Collapsing glomerulopathy[END_REF].

Collapsing glomerulopathy, a severe clinicopathologic type of glomerular injury considered to be a distinctive variant of the FSGS spectrum, was initially described in Afro-Caribbean populations, mostly in patients with HIV infection (classic HIVAN) [START_REF] Schwimmer | Collapsing glomerulopathy[END_REF] but also in some patients not infected with HIV [START_REF] Weiss | Nephrotic syndrome, progressive irreversible renal failure, and glomerular "collapse": a new clinicopathologic entity?[END_REF]. The list of known underlying processes associated with collapsing glomerulopathy is continuing to grow [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF], but it has rarely been reported in a context of acute malaria [START_REF] Kute | Collapsing glomerulopathy and hemolytic uremic syndrome associated with falciparum malaria: completely reversible acute kidney injury[END_REF][START_REF] Niang | Collapsing glomerulopathy and haemophagocytic syndrome related to malaria: a case report[END_REF][START_REF] Sehar | Collapsing Focal Segmental Glomerulosclerosis in a Patient with Acute Malaria[END_REF]. Several potential confounding causal agents of collapsing glomerulopathy could be considered in our study. In 10 patients, Plasmodium infection occurred in a context of HIV infection, and collapsing glomerulopathy is the main glomerular feature in patients diagnosed with HIVAN [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF]. Compelling evidence has been reported, demonstrating a direct role for HIV viral proteins in affected kidney parenchymal cells, promoting HIVAN [START_REF] Ross | Advances in the pathogenesis of HIV-associated kidney diseases[END_REF][START_REF] Swanepoel | Kidney disease in the setting of HIV infection: conclusions from a Kidney Disease: Improving Global Outcomes (KDIGO) Controversies Conference[END_REF]. Unfortunately, we did not perform in situ hybridisation to detect HIV in kidney tissues. Interestingly, HIV infection was successfully controlled in four patients on HAART therapy at the time of HIVAN diagnosis suggesting that the trigger was not HIV infection but malaria infection. One HIV-infected patient displayed FSGS lesions without the other pathological characteristics of HIVAN, highlighting the specific role of P. falciparum in podocyte injury. Infection with parvovirus B19, another agent that has been implicated in FSGS and/or collapsing glomerulopathy [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF][START_REF] Moudgil | Association of parvovirus B19 infection with idiopathic collapsing glomerulopathy[END_REF][START_REF] Tanawattanacharoen | Parvovirus B19 DNA in kidney tissue of patients with focal segmental glomerulosclerosis[END_REF], was investigated in 14 patients. Four patients (29%) tested positive for IgM antibodies, suggesting recent infection. In our series, we cannot definitively exclude the possibility of a role of parvovirus B19 infection in the pathogenesis of glomerular disease due to the absence of DNA extraction and amplification on kidney tissue.

Moreover, only two of our patients displayed clinical or biological features of autoimmune disease. These two patients had cryoglobulinaemia, but their kidney lesions were consistent with collapsing glomerulopathy, associated with TMA lesions in one patient and minimal change lesions in the other.

Our findings therefore suggest that infection with P. falciparum (96% of the cases considered here), may be a crucial trigger for FSGS/collapsing glomerulopathy development in patients of African ancestry. The only patient in this cohort not of African descent was diagnosed with minimal change nephrotic syndrome. Recent studies have demonstrated that Afro-Caribbean individuals carrying APOL1 risk alleles have a higher risk of developing several types of glomerular injury leading to chronic kidney diseases [START_REF] Genovese | Association of trypanolytic ApoL1 variants with kidney disease in African Americans[END_REF][START_REF] Kopp | APOL1 genetic variants in focal segmental glomerulosclerosis and HIV-associated nephropathy[END_REF][START_REF] Kormann | Roles of APOL1 G1 and G2 variants in sickle cell disease patients: kidney is the main target[END_REF][START_REF] Larsen | Apolipoprotein L1 risk variants associate with systemic lupus erythematosus-associated collapsing glomerulopathy[END_REF]. We investigated APOL1 risk genotype in seven patients from whom DNA samples were available. Strikingly, all of them were positive for high-risk alleles. There is growing experimental evidence to suggest that the kidney-specific expression of the APOL1-G1/G2 risk variants may interfere with normal podocyte homeostasis [START_REF] Ma | Localization of APOL1 protein and mRNA in the human kidney: nondiseased tissue, primary cells, and immortalized cell lines[END_REF][START_REF] Beckerman | Transgenic expression of human APOL1 risk variants in podocytes induces kidney disease in mice[END_REF][START_REF] Kumar | Disruption of APOL1-miR193a Axis Induces Disorganization of Podocyte Actin Cytoskeleton[END_REF]. Unfortunately, the retrospective nature of this study and the limited number of patients tested for APOL1 genetic variants suffers are inherent limitations to the approach used here that weaken our presumptions concerning the potential role of APOL1 polymorphism in the occurrence of glomerular injury. The potential role of malaria in the two patients with P. falciparum infection and minimal change nephrotic syndrome remains more speculative. Minimal change nephrotic syndrome is generally considered to be an idiopathic glomerular disorder potentially triggered by immunological stimuli, leading to secondary podocyte dysfunction [START_REF] Sahali | Immunopathogenesis of idiopathic nephrotic syndrome with relapse[END_REF]. Electron microscopy analyses are not routinely performed in the context of MCNS at French nephrology centers. Light and immunofluorescence microscopy findings were highly suggestive of this diagnosis, but differential diagnoses could not be definitively ruled out. In our two patients, it remains difficult to determine whether minimal change nephrotic syndrome and malaria should be considered as a related disorder or as a fortuitous association. Plasmodium infection is associated with a profound dysregulation of the immune response [START_REF] Ortega-Pajares | The Rough Guide to Monocytes in Malaria Infection[END_REF], and we cannot, therefore, exclude the possibility that an increase in the production of pro-inflammatory cytokines interferes with normal podocyte biology, leading to subsequent nephrotic syndrome like it has already been described in other settings such as hemophagocytic syndrome [START_REF] Thaunat | Nephrotic syndrome associated with hemophagocytic syndrome[END_REF].

In order to test the hypothesis of a direct role of the parasitic infection on kidney disease, we searched for Plasmodium in the kidney cells of our patients, by performing immunohistochemistry with an antibody specifically targeting a P. falciparum protein, in four patients. We detected parasites protein in the tubules, but obtained no evidence of parasitized red blood cell adhesion to the capillary glomerular endothelium or of the presence of parasites in podocytes. Nevertheless, the lack of detection of a P. falciparum-specific protein in the glomeruli at the time of kidney biopsy (mean of 24 days between malaria infection and kidney biopsy) does not rule out the possibility of the parasite playing a key role in early stages of glomerular injury. Consistent with this hypothesis, CMV infection may be considered a second hit for de novo collapsing glomerulopathy despite the absence of glomerular staining for CMV [START_REF] Chang | Donor's APOL1 Risk Genotype and "Second Hits" Associated With De Novo Collapsing Glomerulopathy in Deceased Donor Kidney Transplant Recipients: A Report of 5 Cases[END_REF]. The presence of parasite antigens in the tubular lumen and tubular cell cytoplasm after the virus has been eradicated remains surprising. We can hypothesise that, as in HIV infection [START_REF] Canaud | The kidney as a reservoir for HIV-1 after renal transplantation[END_REF], the kidneys may act as a reservoir of malaria infection despite undetectable parasitaemia.

Further studies based on PCR tests on urine should be considered to determine whether this non-invasive method could be used for the diagnosis of persistent Plasmodium infection in the kidneys. Furthermore, we cannot exclude the possibility that HRP-2 detection in the kidney parenchyma is related to degradation products resulting from Plasmodium lysis.

Collapsing glomerulopathy is a particularly aggressive form of FSGS that responds poorly to steroid therapy [START_REF] Albaqumi | Current views on collapsing glomerulopathy[END_REF][START_REF] Thomas | Clinical and pathologic characteristics of focal segmental glomerulosclerosis pathologic variants[END_REF]. In our study, after a mean of 23 months of follow-up, notwithstanding the initiation of steroid treatment in 10 cases, eight of the patients in the total population progressed to end-stage renal disease requiring kidney replacement therapy, and another four patients displayed severe decreases in eGFR. Previous studies in patients with collapsing glomerulopathy showed that the increase in ESRD risk was correlated with the degree of interstitial fibrosis, the number of glomeruli with collapsing lesions, proteinuria and creatinine levels [START_REF] Laurinavicius | Collapsing glomerulopathy in HIV and non-HIV patients: a clinicopathological and follow-up study[END_REF][START_REF] Valeri | Idiopathic collapsing focal segmental glomerulosclerosis: a clinicopathologic study[END_REF]. Twenty of the patients from our cohort had stage 3 AKI at initial presentation, and all but one of the patients displayed severe kidney impairment at the time of biopsy. In addition, in 16 patients, more than 20% of the glomeruli presented collapsing lesions, and 12 patients had more than 20% interstitial fibrosis. Overall, these data may explain the poor kidney outcome of patients with glomerular disease after Plasmodium infection.

In conclusion, our study suggests that, in patients of African ancestry, imported malaria can be added to the spectrum of underlying processes promoting FSGS lesions. Our immunohistochemistry study results do not support a direct role for P. falciparum in glomerular damages. P. falciparum infection seems to act as a trigger for FSGS occurrence in patients with genetic susceptibility factors and/or pre-existing viral infection

Table 1 Demographic and clinical data at the time of malaria

 1

	HIV: human immunodeficiency virus, ICU: intensive care unit, AKI: acute kidney injury, %P:
	parasitaemia expressed as a percentage, ARDS: acute respiratory distress syndrome
	*Neurological criteria: neurological involvement including impaired consciousness and/or
	prostration and/or multiple convulsions

Table 2 Clinical and biological data at the time of kidney biopsy

 2

	AKI: acute kidney injury, KDIGO: Kidney Disease Improving Global Outcome, UPCR: urine
	protein/creatinine ratio, Cryo: cryoglobulinaemia, IgGk: monoclonal immunoglobulin G kappa.
	ApoL1: apolipoprotein L1
	* Two patients with anuria

Table 3 : Kidney biopsy findings

 3 arteriolar hyalinosis was scored as follows: + mild ++ moderate +++ severe ** In one patient with HIV infection, renal biopsy findings were consistent with not otherwise specified variant. In one case HIV associated nephropathy lesions were associated with additional membranoproliferative glomerulonephritis lesions. In one case, HIV associated nephropathy lesions were associated with thrombotic microangiopathy lesions.

	Number of glomeruli (n=23)	16 (range 6-30)
	Obsolescent glomeruli (%) (n=23)	11% (range 0-50 %)
	FSGS lesions (%) (n=21/23)	64% (range 12.5-100%)
	Collapsing lesions (%) (n=18/21)	50% (range 4-100%)
	Interstitial fibrosis (%) (n=23)	18% (range 0-50%)
	Interstitial infiltrate (n=23)	18 (78%)
	Interstitial edema (n=23)	7 (30%)
	Tubular microcyst dilatation (n=23)	15 (65%)
	Acute tubular necrosis (n=23)	15 (65%)
	Arteriolar hyalinosis* (n=23)	15 (65%)
	Definitive pathological diagnosis**
	FSGS	21 (91%)
	Collapsing glomerulopathy	18
	(including HIV associated	9
	nephropathy)
	Not otherwise specified variant	3
	Minimal change disease	2 (9%)
	FSGS: focal segmental glomerulosclerosis

*

Table 4 : Treatment and follow-up

 4 min/1.73m² (range 9.5-113 ml/min/1.73m²) HAART: highly active antiretroviral therapy, RAS: renin-angiotensin system, eGFR: estimated glomerular filtration rate, KRT: kidney replacement therapy * Death occurred in one patient one month after kidney biopsy Disclosures : Dr. Audard reports receiving personal fees from Addmedica outside of the submitted work

	HAART initiation in HIV patients	10 (100%)
	(n=10)
	Steroids (n=23)	10 (43%)
	RAS inhibitors (n=23)	11 (48%)
	Cyclosporine (n=23)	2 (9%)
	Mean follow-up (months) (n=23)	23 months (range 0.5-220 months)
	Complete remission of nephrotic	4 (18%)
	syndrome (n=22/23)
	Kidney status at last follow-up
	(n=22/23)*
	Hemodialysis	6 (27%)
	Kidney Transplant	2 (9%)
	Mean eGFR at last follow-up visit	51 ml/
	in those not needing KRT (n=15)
	(ml/min/1.73m²)

Acknowledgments :

We would like to acknowledge all the nephrologists and kidney pathologists involved in the medical care of the patients included in the present study. We thank Julie Sappa for editorial assistance.

Legends to figures

2f: Absence of staining in a negative control consisting of a HIVAN patient without malaria (x200). Similar results were obtained for patients with acute tubular necrosis unrelated to malaria.

Supplementary information

Material and Methods

Patients and renal function evaluation

Identification of patients, demographic clinical and biological data

We included 23 adult patients from 10 nephrology departments (Henri Mondor Hospital (Créteil), Tenon Hospital, Necker Hospital, Georges Pompidou European Hospital, Bichat Hospital, Association pour l'utilisation du Rein Artificiel (Paris), Foch Hospital (Suresnes), André Grégoire Hospital (Montreuil), Conception Hospital (Marseille), Huriez Hospital (Lille)) seen between 1998 and 2019. The patients at each hospital were identified on the basis of electronic medical records, including the renal disease and clinical diagnosis databases. For all patients, the demographic data recorded included age, sex, ethnicity and coinfections with hepatitis B virus, hepatitis C virus and human immunodeficiency virus (HIV). For patients with HIV infection, HIV viral load (copies/mL), CD4 + T-lymphocyte counts, and the use of highly active antiretroviral therapy (HAART) were reported. Levels of complement fractions C3, C4 and the total hemolytic activity (CH50) of the serum were determined for all patients. Serum protein electrophoresis and immunological tests, including tests for anti-neutrophil cytoplasm antibodies, anti-nuclear antibodies and anti-DNA antibodies were systematically performed.. High-risk APOL1 genotypes were defined as two risk alleles in any combination (homozygous G1/G1, homozygous G2/G2, or compound heterozygous G1/G2). All patients tested for APOL1 risk alleles gave written informed consent.

Follow-up

Follow-up data included renal function evaluations (estimated glomerular filtration rate (eGFR) or the need for renal replacement therapy and the outcome of underlying glomerular disease, based on proteinuria at the last follow-up visit. Complete remission of nephrotic syndrome was defined as the normalisation of urinary protein-creatinine ratio (uPCR) (< 0.3 g/g), and an albumin concentration >3.0g/dL. Specific treatments for underlying glomerular disease (steroid therapy and/or immunosuppressive agents) were specified for all patients.

Plasmodium infection

The results of parasitaemia levels and species identification confirmed by polymerase chain reaction (PCR) were noted when available. The antimalarial drugs administered and the type of hospitalisation unit to which patients were initially admitted (conventional medicine unit or intensive care unit (ICU)) were recorded for all patients.

Renal biopsy examination and immunohistochemistry study.

Diagnosis of underlying glomerular diseases

Minimal change nephrotic syndrome was diagnosed on the basis of an absence of visible alterations on light microscopy examination, and an absence of immunoglobulin and/or complement deposits in immunofluorescence studies [START_REF] Vivarelli | Minimal Change Disease[END_REF] Immunohistochemistry with a monoclonal antibody targeting P. falciparum HRP-2

We used P. falciparum-infected red blood cells fixed in ethanol as the positive control, and the primary antibody was omitted as a negative control. We also assessed the specificity of staining on clinically relevant negative controls: two kidney biopsy specimens from patients diagnosed with HIVAN diagnosis in the absence of malaria and two kidney biopsy specimens from patients with acute tubular necrosis (ATN) not related to malaria infection.


Francesca Frontini Praxiling
email: francesca.frontini@univ-montp3.fr

Carmen Brando
email: carmen.brando@ehess.fr

Joanna Byszuk
email: joanna.byszuk@ijp.pan.pl

Ioana Galleron
email: ioana.galleron@sorbonne-nouvelle.fr

Diana Santos
email: d.s.m.santos@ilos.uio.no

Ranka Stanković
email: ranka.stankovic@rgf.bg.ac.rs

Named Entity Recognition for Distant Reading in ELTeC

which started in 2017, has among its main objectives the creation of an open source, multilingual

Introduction

The Distant Reading for European Literary History (COST Action CA16204) kicked off in 2017 with the goal of using computational methods of analysis for large collections of literary texts. The objective is to establish shared practices in the application of innovative computational methods, while at the same time reflecting on the impact that such methods have on our capacity to raise and answer new questions about literary history and theory. More details are to be found on the Action's website 1 .

One of the most ambitious deliverables of this COST Action is the creation of a multilingual open source collection, named European Literary Text Collection (ELTeC). In its final version, the corpus will contain at least 10 linguistically annotated subcollections of 100 novels per language (1840-1920 2 ), that is at least 1,000 full-text novels. To make subcollections representing particular languages as comparable as possible, the novels are selected to represent a) various types of novels as to their length: short stories, epic novels, b) five twenty-year time periods within the examined time span, c) text of various levels of canonicity, as judged by the number of reprints, and d) as equal as possible ratio of female and male authors. As of now, a first version of the ELTeC corpus has been collected and published with a light TEI encoding 3 , with more language collections to be included in the further releases throughout the duration of the Action. Since obtaining more works for some language collections is possible, the Action also plans the publication of the extended ELTeC (including more texts per language or ones published slightly before the assumed time span) estimated to take the total number of full-text novels to at least 2,500.

A case study on Named Entity annotation was carried out in the Working Group 2 "Methods and Tools" (WG2), with an aim of establishing common annotation guidelines -which are specifically oriented to answering a set of scholarly research questions identified by the Action participants -and testing a selection of NER tools, in order to assess their capacity of automatic reproduction of such annotation, a task crucial for annotating corpora of this and bigger sizes.

In this abstract we shall introduce the desiderata for the NE annotation, the current state of the multilingual NE corpus and of the annotation, describe the evaluation framework and provide preliminary results for a selection of NE systems. Finally, we will discuss the relevance of these activities with respect to the CLARIN community as well as to the CLARIN services and tools, with some ideas for possible collaboration.

2 Developing the NE layer of the ELTeC corpus 2.1 Desiderata and annotation set NER is a well known task in NLP, and there are several sets of guidelines for performing NER annotation (see among others [START_REF] Nadeau | A survey of named entity recognition and classification[END_REF][START_REF] Chinchor | Overview of MUC-7[END_REF][START_REF] Ldc | ACE (Automatic Content Extraction) English Annotation Guidelines for Entities[END_REF][START_REF] Santos | HAREM: An Advanced NER Evaluation Contest for Portuguese[END_REF][START_REF] Zupan | Annotation guidelines for Slovenian named entities: Janes-NER[END_REF]), establishing a number of categories and rules for creating annotated corpora, so that automatic algorithms can try to replicate such annotation. However, NER is a preliminary module for other tasks, such as information extraction. The philosophy guiding the definition of the best known NE guidelines is mostly geared towards very specific scenarios, such as extraction of events in news or scientific texts. Their application to literary texts is therefore not straightforward, despite current attempts at producing new annotation guidelines and datasets [START_REF] Bamman | An Annotated Dataset of Literary Entities[END_REF].

Within the context of the COST action, WG34 came up with a set of research questions in order to help with the definition of a more targeted set of annotations. A first set of desiderata emanates from the idea that a novel is an epic set in the private space of a bourgeois home, something which demands researchers to be able to detect indicators of social structure and roles, such as honorifics, names of professions, etc. Another set of research topics touches upon questions about identity, otherness, but also the distinction between urban and rural spaces, which require the annotation of demonyms, as well as a higher granularity in the annotation of toponyms, to facilitate detecting different types of locations (cities vs villages and countryside)5 . Finally, questions about cultural references, role models and cosmopolitanism can only be answered if references to works of art, authors, folklore and periodical publications are detected.

Such considerations led to the inclusion of categories such as demonyms (DEMO), professions and titles (ROLE), works of art (WORK) in the tagset, alongside more canonical categories, such as person names (PERS), places (LOC), events (EVENT), organisations (ORG) (see Table 1). However, this annotation was later simplified to avoid nested annotations and overlap.

Current state of the corpus

The NE annotation of the corpus is part of the plan for the so called level 2 annotation, which will also include morpho-syntactic and direct speech annotation. At this moment, WG2 carries out the NE annotation for a subset of languages: Czech (cze), German (deu), English (eng), French (fra), Hungarian (hun), Norwegian (nor), Portuguese 6 (por1, por2), Slovene (slv), and Serbian (srp). For each language involved, a sample collection was prepared from the novels already available in ELTeC. Every languagespecific collection contains 20 files, each of which is composed of excerpts from one novel. Each file is made up of five ~400-word passages randomly selected from the novel. The annotation teams worked on the same set of guidelines, using the BRAT 7 annotation tool, but of course some adaptations were necessary due to differences between languages. When two persons worked on the same collection, we performed cross-checking. The latest version of the annotated NE corpus is available online, together with the latest version of the annotation guidelines 8 . For more information we refer also a recent paper [START_REF] Stankovic | Named Entity Recognition for Distant Reading in Several European Literatures[END_REF] presented at the DH Budapest 2019 conference. The results of the latest round of annotations (May 2019) are presented in Table 1.

Testing automatic NER

Another important activity of WG2 is testing existing tools to assess their capacity to reproduce the envisaged annotation. At this stage testing is performed without previous domain adaptation, and with a preference for tools that are easy to install and use. The rationale behind this choice is to evaluate whether literary scholars without advanced technical skills will be able to use existing NLP technologies in their research.

In this study, we focused on four collections only, in English, French, Portuguese and Serbian, these being the languages the authors of this paper are most familiar with. This first evaluation round allowed us to develop a common evaluation set up. For each collection, we tested two tools: one common for all (spaCy 9 ), and another one language specific (Stanford-NER for English 10 , SEM for French 11 , PALAVRAS-NER for Portuguese [START_REF] Bick | Functional Aspects in Portuguese NER[END_REF] and SrpNER for Serbian). BRAT outputs were compared to annotations produced by these tools by using a shared evaluation script, thus guaranteeing the consistency with the agreed upon strategy for identifying hits and misses in terms of entity detection.

In this first round the evaluation of string detection was strict (segments must match exactly); but we are planning to perform a second round with relaxed evaluation. Only the PERS and LOC tags were mapped to similar categories of NER tools, and evaluated. The performance of the tools was evaluated separately for each tag.

NER results and analysis

Current evaluation results are presented in Table 2. These preliminary results show the difficulty of the task of NE-annotation of literary novels. A strict evaluation of detection is often penalising for PERS, because of honorifics which we chose to include in our annotation, and is further complicated by the fact that the XML annotated input was processed as such by tools which often expect plain text12 . In most cases, LOC seems to be less problematic for the pre-trained models. We follow with some remarks for each specific language. Portuguese: It was expected that off-the-shelf Named Entity recognisers that were developed for modern Portuguese would perform significantly worse in the por2 collection. This was confirmed for PALAVRAS-NER, which showed lower performance for por2, but not for spaCy. This NER system had considerably lower results than PALAVRAS-NER, but no significant performance drop between the two sets (in fact, for PERS it fares even better for por2). We believe this is because only the easy cases are catered for by spaCy, and those cases do not depend too much on ortography. English: In spaCy, tokenization issues due to TEI XML tags included in tokens account for 16% of PERS and 38% for LOC errors. It also misses a lot of PERS (21%) due to undetected honorifics (Mr/Mrs/Miss). Stanford NER has better precision for LOC than spaCy and has no problems with TEI XML tags. For both models, some additional training and fine tuning would be needed for better performances.

7 https://brat.nlplab.org/ see also [START_REF] Stenetorp | brat: a Web-based Tool for NLP-Assisted Text Annotation[END_REF]. 8 http://brat.jerteh.rs/#/eltec-simplified/ 9 We used the out-of-the-box model for all languages except for Serbian, for which none was available. 10 https://nlp.stanford.edu/software/CRF-NER.shtml 11 https://www.lattice.cnrs.fr/sites/itellier/SEM.html French: The manual corpus contains many PERS and fewer LOC annotations. However, spaCy-fra annotates too many LOC hence the low precision for this category, and SEM-fra annotates too few PERS, hence the low recall for this category. In general, there are many detection issues in particular with entities including determiners. Despite the better performance, spaCy-fra has an odd behaviour due to parsing, tokenising, presence of XML tags, capital letters in the beginning of sentences, and it recognises entities composed of more than 4 tokens, which are actually rare. Serbian: SrpNER is a rule based system and the best NER tool for Serbian. 11% of missing annotations are related to PERS multiword units with honorifics "g./gda." (Mr/Mrs). For LOC, missing annotations are celestial bodies, names of the streets and facilites. With the Serbian spaCy model, about 7% of errors are related to TEI XML tags, much fewer than with the English model, as the training set included TEI annotated text. Further improvements are foreseen.

Relationship to CLARIN and conclusion

The creation, annotation and publication of the ELTeC corpus falls clearly within the scope of CLARIN activities, and ties with CLARIN are already assured by individual participants in the COST action (such as Tomaž Erjavec, Slovenian National Coordinator). Nevertheless, the presentation of the corpus at the CLARIN conference represents an opportunity to discuss further avenues for collaboration. Following the FAIR principles and CLARIN best practices, we identify the following points.

The final version of the manually checked NE subset of the ELTeC corpus, as described in this paper, represents a new reference resource in the domain of literary NE annotation, especially for the broad spectrum of languages 13 included. As such, its preservation and visibility should be ensured. When it comes to the publication and preservation of the whole richly annotated ELTeC collection once it is completed (a goal set to be achieved with the end of this Action in 2021), the final decision is yet to be made, with current interest in Textgrid 14 and GAMS 15 . Collaboration with CLARIN should ensure the visibility of the resource, by means of metadata harvesting to the CLARIN Virtual Language Observatory and by listing the corpus in initiatives such as the CLARIN Resource Families.

The usability of the ELTeC collection could be further enhanced by making it a part of the Federated Content Search initiative (especially with the further addition of the morpho-syntactic and semantic 13 Not all languages in ELTeC have been made the object of NE annotation so far, but future additions are envisaged. 14 Textgrid [https://textgridrep.org/], a repository supported by the Göttingen State and University Library (SUB) and the Gesellschaft für wissenschaftliche Datenverarbeitung Göttingen mbH (GWDG); now a CLARIN C-centre.

15 http://gams.uni-graz.at/ layer). This should be facilitated by the fact that our COST action is planning to publish the corpus also on the TXM platform 16 , which already implements CQP queries. Last but not least, the collaboration could touch upon the question of NLP tools and services, their usability and domain adaptation. Given the fact that for most languages only parts of the ELTeC corpora can be manually annotated, what can CLARIN do to achieve quality automatic processing for the rest of the corpus? And more generally, how can this help in creating ad hoc models for similar texts which are not yet included in the ELTeC collection? Right now CLARIN offers easy to use services to process texts, such as the CLARIN Switchboard and Weblicht. However, NER is not yet available for most languages, and when it is, it generally does not support the processing of TEI-XML texts, something which constitutes a major issue in processing as shown in our results. Moreover, the NER models that are currently available are not necessarily adapted for literary studies and do not allow for the annotation of all of the NER categories demanded by ELTeC design.

The presentation will describe the current state of the ELTeC corpus, with a focus on the NE manually annotated subset and on the tests carried out with various NER modules, and will constitute an opportunity to discuss the aforementioned points with experts from CLARIN ERIC and the various national consortia.

Table 1 :

 1 Data on the manually NE-annotated corpus.

		DEMO EVENT LOC ORG OTHER PERS ROLE WORK
	cze	163	5	275	0	0	1150	454	0
	deu	66	2	323	12	0	973	458	4
	eng	56	7	198	37	0	1184	203	25
	fra	77	3	262	22	128	900	244	18
	hun	29	7	152	20	0	1091	367	7
	nor	4	8	83	25	3	990	201	10
	por1	17	9	351	19	0	940	490	54
	por2	34	1	256	30	7	1059	347	7
	slv	133	54	336	37	0	1230	620	2
	srp	121	18	185	11	0	985	301	4
		700	114 2425	213	138 10514	3685	131

Table 2 :

 2 Results of the strict evaluation, per language and category.

		Cat	Correct	Missing	Spurious	Precision	Recall	Excess
	SEM-fra	LOC PERS	73 82	112 512	84 115	0.465 0.416	0.395 0.138	0.535 0.584
	SPACY-fra	LOC PERS	103 329	78 194	468 297	0.180 0.526	0.569 0.629	0.820 0.474
	PALAVRAS-por1	LOC PERS	223 816	63 90	44 86	0.835 0.905	0.780 0.901	0.165 0.095
	SPACY-por1	LOC PERS	225 465	84 256	440 374	0.338 0.554	0.728 0.645	0.662 0.446
	PALAVRAS-por2	LOC PERS	151 857	67 133	91 285	0.624 0.750	0.693 0.866	0.376 0.250
	SPACY-por2	LOC PERS	157 569	57 236	396 393	0.284 0.591	0.734 0.707	0.716 0.409
	Stanford-eng	LOC PERS	98 649	100 535	126 399	0.438 0.619	0.495 0.548	0.563 0.381
	SPACY-eng	LOC PERS	98 536	100 648	170 240	0.366 0.691	0.495 0.453	0.634 0.309
	SrpNER-srp	LOC PERS	107 718	78 267	19 158	0.849 0.820	0.578 0.729	0.151 0.180
	SPACY-srp	LOC PERS	57 553	128 432	104 315	0.354 0.637	0.308 0.561	0.646 0.363

Proceedings CLARIN Annual Conference 2020

Working Group 3, dedicated to Literary Theory and History https://www.distant-reading.net/wg-3/

At this stage Entity Linking is not envisaged for our corpus, and in any case it would not easily solve the problem of distinguishing between types of populated places for past or fictional locations in novels.

For Portuguese, two sets of novel excerpts are available: por1 comprises canonical novels, in modern ortography, while por2 was created from novels with old ortography, non-canonical.

This evaluation scenario is realistic in the context of Digital Literary Studies, where digital editions with a minimal TEI encoding are to be further enriched using NLP tools, to be then analysed by literary scholars.


Mohamed Souheib Chebil

Guillaume Bouaoulo

Salma Pierre Gerard

El Euch

Hervé Issard

Emmanuel Richaud
email: emmanuel.richaud@ensam.eu

Mohamed Souheib Chebil

Salma El

Oxidation and unzipping in ELIUM resin: Kinetic model for mass loss

Keywords:

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Manufacturing of large composite parts with short processing times, low external heating is a continuous challenge in several industrial sectors such as marine industry (hull and bridges of race boats), aeronautic and aerospace industry, renewable energy (wind turbine blade) [START_REF] Arhant | Marine composites -design and performance[END_REF] .

ELIUM® resin is one of the youngest members of organic matrices. The polymer is obtained from a low viscosity [ 2 , 3 ] reactive mixture of polymer solution of (meth)acrylic monomers (MMA, Alkyl acrylic) and acrylic copolymer chains (viscosity of 100 cPs) and possibly other comonomers [4] . Its polymerization is activated by a ketone peroxide as thermal initiator and can be achieved at room temperature with the presence of an iron salt-based catalyst [START_REF] Bhudolia | Optimizing polymer infusion process for thin ply textile composites with novel matrix system[END_REF] . The final material has thus two advantages: both fastness and simplicity of radical polymerization (comparable for example to unsaturated polyesters) together with the toughness of acrylic copolymer such as poly(methyl methacrylate (PMMA) where a sub-glassy mobility [START_REF] Sondhau | β-Relaxation of PMMA: tip size and stress effects in friction force microscopy[END_REF] allows a better toughness than in other composite matrices (vinylesters, unsaturated polyesters or epoxies [START_REF] Obande | Mechanical and thermomechanical characterisation of vacuum-infused thermoplastic-and thermoset-based composites[END_REF] for example) .

The last open issue is the long-term stability of ELIUM® resin. Apart papers dealing with water ageing [ 7 , 8 , 9 ], the thermal ageing case remains open to the best of our knowledge. Given the structural commonality with Polymethylmethacrylate (PMMA), thermal degradation is expected to induce both random chain scissions together with chain ends unzipping. However, it remains to assess the possible differences in kinetics with PMMA. Apparent degradation parameters were previously assessed for PMMA under anisothermal conditions [ 10 , 11 ] but it is tricky to predict the isothermal degradation of ELIUM® from those apparent kinetic parameters established from very high degradation temperature. Moreover, the predicting lifetime requires to understand the macromolecular changes induced by ageing [START_REF] Gilormini | A statistical theory of polymer network degradation[END_REF] .

That is the reason why we decided in this paper:

-to focus on isothermal degradation first under nitrogen and then in presence of oxygen, -to perform isothermal degradation only, -to propose a kinetic model running for degradation under air and under nitrogen basing on the elementary steps of degradation.

Experimental

Materials

Two kinds of ELIUM® resins (ELIUM® V1 and V2) were studied. Their approximate structure is depicted in Fig. 1 . ELIUM® V2 differs from ELIUM® V1 by the addition of a divinyl groups working as a crosslinker and methacrylic acid used for improving ther- mal stability. In other words, ELIUM V1 is a "thermoplastic resin" whereas ELIUM® V2 is processed in liquid state but gives a thermoset network after curing. ELIUM® V1 was supplied as films of about 100 μm thickness. ELIUM® V2 was supplied as 4 mm plates and about 50 μm films were samples using a Leica microtome.

A PMMA commercial grade (VM100, also supplied by Arkema) was used as a "model system". About 350 μm thickness films were prepared by compression molding using a Gibitre press by heating for 3 minutes at 200 °C under 220 bars and using wedges to get right thickness.

Ageing condition

Samples were isothermally aged in thermal analysis cells of TGA device (see after) under either pure nitrogen or pure oxygen supplied by a 50 ml min -1 gas flow. Some complementary tests were performed in ventilated ovens at 150, 180 and 200 °C (supplied by SCS) on ELIUM V2 plates to check the thickness of oxidized layer (TOL).

Characterization

Thermogravimetric measurements (TGA)

TGA measurements were performed using a Q500 apparatus driven by QSeries Explorer (TA Instruments). Isothermal measurements were performed either under 100% N 2 or 100% O 2 atmosphere supplied by a continuous 50 ml min -1 gas flow. Isothermal degradation was performed at a constant temperature ranging from 230 to 310 °C.

Differential Scanning Calorimetry measurements (DSC)

DSC measurements were performed using DSC Q10 apparatus (TA instruments) using the following procedure: samples were first isothermally degraded in situ either under 100% N 2 or 100% O 2 atmosphere. After cooling to 40 °C, they were heated at a 10 °C min -1 so as to determine the glass transition temperature (T g ) value.

Gel Permeation Chromatography measurements (GPC)

GPC measurements were performed on a WATERS 717 + Autosampler Instrument in THF (1 ml min -1 ) equipped with a Waters 2414 Refractive Index detector on samples previously in situ aged in TGA cell (see above). Average molar masses are given in polystyrene equivalent.

Optical microscopy

Optical microscopy was used for measuring the Thickness of Oxidized Layer (TOL) for aged bulky samples. After polishing the samples to get a smooth surface, a ZEISS Axio Imager A2M optical microscope was used to obtain the TOL ((Thickness of Oxidized Layers) values.

Results

Stability under N 2

Mass loss on PMMA, ELIUM® V1 and V2 were monitored isothermally at different temperatures (from 230 to 310 °C) versus time exposure under 100% N 2 atmosphere in TGA cell (NB: for PMMA, some experiments were done in duplicate and triplicate for checking the repeatability). Results are presented in Fig. 2 .

They call for the following comments: 1 at very low exposure times, a very fast decrease is observed with an initial mass loss close to 10%. In ELIUM®, it seems that the initial part is mainly due to residual monomers. The residual mass was expressed as:

m m 0 = m v + m p m v 0 + m p 0 (1)
Where m v is the masse of residual (non polymerized) monomers, m p of the volatile compounds released due to polymer decomposition. As depicted in Appendix 1 ( Fig. 10 ) and discussed later, m p decreases following an apparent first order kinetics, and it seems reasonable to assume that it is also the case for m v . If so:

m m 0 = m v 0 . exp ( -k v .t ) + m p 0 . exp ( -k obs .t ) m v 0 + m p 0 ( 2
)
with k v >> k obs so that at early times :

d dt m m 0 ∼ -k v . m v 0 m v 0 + m p 0 (3)
Whereas, at longer times, with m p >> m v :

ln m m 0 ∼ exp ( -k obs .t ) (4)
Both equations will be used to extract apparent rate constants of degradation. k v was shown to be hardly temperature dependent but this is not surprising since the loss of residual monomers occurs meanwhile the cell temperature is equilibrating to the ageing temperature.

2 in a second stage, mass decreases with an auto slowed down kinetics. A pseudo first order kinetics is observed for PMMA and 3 (see ''Discussion"). NB: the number of experimental points is lowered for better clarity. fits acceptably in a first approach for ELIUM® in the medium conversion degrees (up to almost 50% mass loss).

3 in a first approach, PMMA and ELIUM® display some comparable trends: for example, at 250 °C, about 20% of the initial mass is lost after 20 h aging under 100% N 2 for both materials. At 270 °C and 290 °C, the mass loss after 20 h is in both cases close to 40% and 65%. More in detail, ® V2 which is more stable than ELIUM® V1 possibly in link with the presence of some comonomers, which will be depicted in terms of rate constants for depolymerization in the following.

To better understand the mechanisms responsible for mass loss, DSC measurements were performed in order to measure the change in glass transition value and investigate the architecture of degraded materials. Fig. 3 depicts thermograms of virgin and aged PMMA and ELIUM® V1 resin having undergone a thermal exposure in situ under nitrogen. Corresponding T g changes are given in Fig. 4 a together with values for samples degraded in presence of oxygen. Under nitrogen, the glass transition temperature remains almost constant within the experimental uncertainties (contrarily to ageing oxygen, as it will be seen later). A small increase can even be observed, maybe due to the evaporation of residual monomers (see above). This observation seems also to be true at temperatures higher than 250 °C (i.e. 270 and 290 °C) for different exposure times. One sees that despite significant mass loss levels (up to 30% at 290 °C after 4 h exposure), T g depletion remains relatively low (about 5 °C). As it will be seen later, this is in line with the existence of a predominant unzipping mechanism i.e. a chain ends depolymerization.

Contrarily to ELIUM® V2 which is a thermoset resin i.e. insoluble, PMMA can be easily analyzed by GPC as illustrated in Fig. 5 for PMMA aged at 250, 270 and 290 °C during 2 h. The measured molar masses for samples aged at 250, 270 and 290 °C under N 2 for 2h are given in the Table 1 . They confirm that decrease in molar mass is low which suggests that volatile segments come for the chain ends as is will be tentatively justified later.

Investigation of the stability under oxygen

The stability of samples under oxygen was first investigated by determining the thickness of oxidized layer at several temperatures ( Fig. 6 ) for 4 mm thick plates aged in ovens under air. This latter was estimated as the total thickness of the dark edge of samples by optical microscopy. For summarizing: -There is no evidence of cracks occurring within the oxidized layer and favoring the propagation of this latter towards deeper layers [START_REF] Colin | Interaction between cracking and oxidation in organic matrix composites[END_REF] . The measured Thicknesses of Oxidized Layers (TOL) are given in Table 2 . -TOL takes an almost constant value depending only on temperature and certainly external oxygen concentration. Despite lower than in recently developed thermoset matrices (~1500-20 0 0 μm in epoxidized linseed oil thermosets [START_REF] Richaud | Epoxidized linseed oils based networks. Case of thermal degradation[END_REF] ), its value is clearly higher than in other thermosets (for instance less than 300 μm for vinyl esters, 600 μm in unsaturated polyesters [START_REF] Arrieta | Thermal oxidation of vinyl es-ter and unsaturated polyester resins[END_REF] ) degraded in comparable conditions. -As previously described in literature [START_REF] Celina | Oxidation profiles of thermally aged nitrile rubber[END_REF] , TOL decreases when increasing temperature.

Those values were tentatively extrapolated at temperatures under investigation (250-290 °C) using Arrhenius equation. One sees that oxidation would hardly be controlled by oxygen diffusion for samples below 300 μm at 290 °C so that in the following, investigations will be performed on 50 μm thin ELIUM® V2 obtained by microtomy, 150 μm ELIUM® V1 films obtained by casting reactive mixture between two plates, and 350 μm PMMA films obtained by compression molding. Moreover, the control of oxygen diffusion has only a low impact on the main conclusions of this paper.

The effect of oxygen on thermal ageing was thus investigated for example by performing isothermal TGA under pure oxygen. They are directly compared with TGA under nitrogen at the same 3 .

temperatures in Fig. 7 . According to a preliminary interpretation, it seems that the presence of oxygen induces an auto-accelerated mass loss mechanism but in the earlier exposure time, the "pure" thermal mechanism is prominent.

Those experiments were completed by measuring the T g changes (related to polymer backbone modifications) after isothermal ageing runs. Corresponding results are given in Fig. 4 . Both PMMA and ELIUM® V1 present a strong T g changes in those conditions (about 20 °C decrease after 2 h aging). This confirms the instability of acrylic resins at high temperatures under O 2 . Those strong T g changes indicate the presence of chain scissions randomly located in PMMA, and presumably in ELIUM as well. Those latter are confirmed by GPC measurements ( Fig. 5 ) leading to the molar mass values for samples aged at different times given in Table 2 .

Last, two GC-MS analyses (subcontracted in 2MATECH, Aubière, France) were performed on gaseous compounds evolved by samples aged 1h at 250 °C either under N2 or air in hermetic vials. In both cases, MMA was found to be the predominant volatile compounds ( Fig. 10 ).

Discussion

The aims of this section are:

-to compare the nature of the mechanism under nitrogen and in presence of oxygen, -to propose a kinetic modeling working for ELIUM® V1, ELIUM® V2 and PMMA with parameters related to the thermal stability, -to adapt this kinetic model for ageing either under inert atmosphere or in presence of oxygen.

Nature of the mechanisms involved under inert atmosphere or in presence of oxygen

The most striking facts are that under oxygen, average molar mass decreases fast in conjunction with a higher level of mass loss whereas values expressing the macromolecular architecture (M n , T g ) remains almost constant for ageing under inert atmosphere despite the occurrence of mass loss ( Fig. 8 ).

Interestingly, for a given mass loss level, the corresponding decrease of glass transition is higher for ageing in presence of oxygen than for ageing under inert atmosphere. For discussing this result, let us recall that glass transition changes with molar mass as follows [START_REF] Fox | Second-order transition temperatures and related proper-ties of polystyrene. I. Influence of molecular weight[END_REF] :

T g = T g ∞ -k FF / M N (5)
Where T g ∞ is the "fictive" value for a PMMA sample with an infinite molar mass, and k FF is the Fox Flory constant (114 °C and 200 K kg mol -1 values for PMMA are given in [START_REF] Cardenas | High-conversion polymerization. I. Theory and application to methyl methacrylate[END_REF] ). M n changes with the concentration in chain scissions:

-For random chain scissions [START_REF] Saito | Effects of high energy radiation on polymers II. End-linking and gel fraction[END_REF] 1

M N - 1 M N0 = s (6)
-For chain end scissions (unzipping)

M N = M N0s . M N . M 0 [START_REF] Chilali | Effect of water ageing on the load-unload cyclic behaviour of flax fibre-reinforced thermoplastic and thermosetting composites[END_REF] (where M 0 is the molar mass of the monomer unit). It comes:

-For chain ends scissions

T g -T g0 = - k F F . M 0 M N0 • s 1 -s. M 0 (8)
i.e. at low conversion degrees

d T g /ds = -k F F . M 0 / M N0 (9)
-For random chain scissions

T g -T g0 = k FF . s (10)
i.e. at low conversion degrees d T g / ds = -k FF [START_REF] Gao | Kinetics of thermal degradation of poly(methyl methacrylate) studied with the assistance of the fractional conver-sion at the maximum reaction rate[END_REF] Since M 0 << M N0 , it means that a limited number of chain scission has a strong effect on molar mass for random chain scissions compared to chain end scissions.

According to literature, there are three main mechanisms at the origin of unzipping ( Scheme 1 ): random chain scissions [START_REF] Madras | Degradation of Poly(methyl methacrylate) in Solution, Indus[END_REF] followed by the ejection of monomers located at chain ends ( Scheme 1 a).

-scissions located on weak sites such as head to head moieties (possibly in the middle of chains -Scheme 1 b). In principle, this reaction occurs even at low temperature (around 200 °C) [START_REF] Kashiwagi | Effects of weak linkages on the thermal and oxidative degradation of poly(methyl methacrylates)[END_REF] . -unzipping occurring directly at chain ends holding double bonds [START_REF] Hu | The effect of end groups on the thermal degradation of poly(methyl methacrylate)[END_REF] ( Scheme 1 c and 1 d), those latter being expected since no transfer agent was used for ELIUM® manufacturing. According to the glass transition and molar mass changes (see previous section), we assumed that unzipping occurs mainly at the chain ends, consistently with other results [START_REF] Madras | Degradation of Poly(methyl methacrylate) in Solution, Indus[END_REF] . In other words, it seems to us that: under inert atmosphere, the mechanism is an unzipping mechanism occurring by chain ends, consistently with literature data [START_REF] Bekanova | Thermal stability of RAFT-based poly(methyl methacrylate): A kinetic study of the dithiobenzoate and trithiocarbonate end-group effect[END_REF] .

-under oxygen, the unzipping mechanism is complicated by the fact that alkyl radicals can simultaneously undergo unzipping and react with oxygen and induce a degradation mechanism where chain scissions can occur simultaneously on the polymer chain.

Degradation mechanism under inert atmosphere

According to many previous researches, it can be considered that the auto-decelerated shape of mass loss curves for PMMA [ 21 , 24 ] based polymers obeys a first order kinetics:

dm dt = -k obs . m (12)
Observed apparent rate constants (k obs ) can be assessed from first order diagrams (see Fig. 2 ). Corresponding values are plotted in Fig. 9 together with values for PMMA either from this work or from literature [ 21 , 24 ].

In a first approach, data measured in this work in the same temperature range for PMMA, ELIUM® V1 and ELIUM® V2 are relatively comparable. They reasonably fit with the Arrhenius law, with apparent activation energy equal to 113.5 kJ mol -1 (PMMA studied in this work) or ~140 kJ mol -1 for ELIUM® V1 and ELI-UM® V2. Reversely, data from [ 21 , 24 ] seem responsible for a certain distortion in the Arrhenius diagram with a higher activation energy (~200 kJ mol -1 ). This curvature can be explained as follows: at higher temperature, initiation results either from chain end or random chain scission (whereas only the first one exists at temperatures below 300 °C). As it will be seen later, since the apparent rate constant for depolymerization is a function of rate constant for elementary steps ( Eq. [START_REF] Saito | Effects of high energy radiation on polymers II. End-linking and gel fraction[END_REF], the existence of those two competing mechanisms can result in a curvature in Arrhenius diagram [ 25 , 26 ].

According to those data, ELIUM® V2 resin seems slightly more stable than ELIUM® V1 towards the unzipping degradation, which can be explained as follows: ELIUM® V2 reactive mixture contains a slight percentage of 1,4 butanediol dimethacrylate and methacrylic acid working which may act as depolymerization inhibitors (the effect of ethylene glygol dimethacylte is illustrated in [START_REF] Bate | A new approach for measuring the rate of pyrolysis of cross-linked polymers: evaluation of degradation rate constants for cross-linked PMMA[END_REF] ).

The "first order" plot ( Fig. 2 ) and the apparent rate constant allow easily to screen and characterize the stability of acrylic resins. However, it remains quite empirical since it does not really take into account the chemical mechanisms at the origin of mass loss (as it will be seen later, this is needed to predict the degradation under air). A more complete (but simplified) mechanism is summarized here below:

1 As discussed above, initiation would start by chain ends.

2 Depropagation (« unzipping ») leads to monomer release ( Scheme 2 ).

3 Last, termination corresponds to the reaction between two radicals to form a "stable" chain ( Scheme 3 ). It can involve sec-ondary and tertiary radicals ( Scheme 1 a-1 d). The coupling of tertiary radicals ( Scheme 1 d) creates an unstable head to head group likely to initiate further degradation. In a first approach, this latter reaction was neglected compared to the other reactions [ 28 , 29 ] so that we do not have to add a new initiation reaction (with a supplementary kinetic parameter) in the model.

Assuming a bimolecular termination process, this derived kinetic model is thus: Ends → P °(k i ends ) P n °→ P n-1 °+ M (k DP ) (subscripts correspond to residual polymerization degree of chains) P °+ P °→ stable product (k t )

In this last case, it can for example be shown:

d [ P • ] dt = k i ends [ ends ] -2 k t [ P • ] 2 ( 13
)
is the concentration in chain ends likely to initiate depolymerization (vinyl groups for example). For PMMA, it might be close to ρ 0 /M n0 at t = 0 (where ρ 0 is the polymer density and M n0 its initial average number molar mass). Under the assumption that steady state is quickly reached, it gives:

[ P • ] = 1 2 k b • k i ends • ρ 0 M n ( 14
)
The concentration of released monomers [M] is given by:

d [ M ] dt = -k DP . [ P • ] (15)
Which leads to the theoretical expression of mass loss rate for unzipping:

d m m 0 dt = - M m ρ 0 • d [ M ] dt = - M m ρ 0 • k DP • k i ends • ρ 0 2 k t . M n ( 16
)
Where M m is the mass of the monomer released from unzipping.

In the (empirical) first order model, one has:

[ M ] = [ M ] 0 . exp ( -k obs . t ) ( 17
)
Scheme 3. Termination for unzipping.

Scheme 4. Fate of alkyl radicals under air.

i.e. at low conversion degrees:

[ M ] / [ M ] 0 ∼ 1 -k obs . t (18)
So that this kinetic model converges with the empirical first der model at steady state where following equality is

k obs = M m ρ 0 k DP • k i ends • ρ 2 k t . M n ( 19
)
It suggests that Eq. 19 can be used as a simplified relationship to estimate the relative orders of magnitude of k i , k DP , k t from the apparent k obs value estimated in Fig. 2 .

In order to estimate all the rate constants, the differential system was solved using Scilab® software with the script given in "Supplementary Informations". The strategy is to identify rate constants from the fitting of data given in Fig. 2 . In order to minimize the number of adjustable kinetic parameters, some values (k t , [ends] 0 ) related to elementary steps were fixed as discussed below. The missing values must verify (at least roughly) Eq. 19.

In the case of radical PMMA polymerization, the rate constant between two alkyl radical ended PMMA chains is k t ~5.10 7 l mol -1 s -1 [START_REF] Achilias | Development of a general mathematical framework for modeling diffusion-controlled free-radical polymerization reactions[END_REF] . There is no reason, for us, to consider there is any difference with PMMA.

Since PMMA and ELIUM® resins display an almost common behavior (apart the release of free monomers), we decided to consider that:

-in PMMA, the initial concentration in chain ends is ρ 0 /M n0 1/60 mol l -1 .

-in ELIUM® resin, this concentration is the same. In fact, even if this is an approximation, it can be easily verified that model simulations remain almost the same provided that the quantity k i /M n0 remains constant.

Using those rules for rate constants, the rate constant for unzipping can thus be estimated. They allow to fit mass loss curves ( Fig. 2 ) and are thus expected to express the reactivity of each system.

It can be verified that k obs (derived from Fig. 2 ) and k obs * (derived from Eq. 19 ) are relatively close. In other words, despite some approximations made for the concentration of radicals in steady state, it validates the proposed kinetic model. k DP is found to verify Arrhenius law with an activation energy E aDP ~100 kJ mol -1 , which can be discussed as follows: for propagation reaction in PMMA polymerization, the activation energy (E aP ) is reported to be about 25 kJ mol -1 [START_REF] Begum | Modeling methyl methacrylate free radical polymerization in nanoporous confinement[END_REF] meanwhile the reaction enthalpy for polymerization reaction is H r ~-60 kJ mol -1 [START_REF] Roberts | Heats of polymerization. a summary of published values and their relation to structure[END_REF] . It is hence not surprising to observe E aDP ~E aP -H r .

According to [START_REF] Zhou | Dependence of thermal stability on molecular structure of RAFT/MADIX agents: a kinetic and mechanistic study[END_REF] , the rate of scission of chain ends for a PMMA synthesized by Reversible Addition Fragmentation chain Transfer (k i ) is given by 1.06 × 10 6 × exp(-77600/RT) s -1 . In a certain way, it could be considered that RAFT agents are chosen so as to make possible the "reactivation" of PMMA chain [START_REF] Bekanova | Thermal stability of RAFT-based poly(methyl methacrylate): A kinetic study of the dithiobenzoate and trithiocarbonate end-group effect[END_REF] end into radical living forms so that k i is expected here to be lower, in good agreement with the values we used for our model. Reversely, the activation energy of initiation reaction is found lower than in ref [START_REF] Inaba | Effects of initial molecular weight on ther-mal degradation of poly(methyl methacrylate): Part 1-Model 1[END_REF] (more than 200 kJ mol -1 ) where unzipping is studied at high temperature where random chain scission might be the main initiation mode.

Since k i is in part unknown, this investigation was completed by a parametric study (see "Supplementary Informations" file). For summarizing, there is an interplay between all rate constants so that many set could acceptably fit the experimental data. However, an accurate simulation of the curve cannot be obtained if one significant error (for example a factor 2 on one rate constant) is made, because it cannot be compensated by changes on other parameters.

Interestingly, k DP is found lower for example for ELUM V2 than ELIUM V1. This might be in link with the presence of comonomers working as "internal stabilizers". In the future, a more thorough description of the unzipping reaction would be based on a scheme closed to copolymerization process:

---M 1 -M 1 • → ---M 1 • + M 1 k DP 11 ---M 2 -M 1 • → ---M 2 • + M 1 k DP 21 ---M 1 -M 2 • → ---M 1 • + M 2 k DP 12 ---M 2 -M 2 • → ---M 2 • + M 2 k DP 22
Where M 1 is MMA and M 2 a comonomer, such as typically k DP11 >> k DP12 for example.

Degradation mechanism in presence of oxygen

According to Scheme 4 , two kinds of alkyl radicals can be generated during PMMA or ELIUM® thermolysis and both can react with oxygen to give a hydroperoxide.

Table 3

Kinetic parameters for degradation used for fitting mass loss curves ( Figs. 2 and7 ). k obs comes from Fig. 2 andk obs * from Eq. 19.

T ( °C)

[V] (mol l -1 ) k v (s -1 ) k i (s -1 ) k DP (s -1 ) k t (l mol -1 s -1 ) k obs (s -1 ) k obs * (s -1 ) k 1 (s -1 ) k 2 (l mol -1 s -1 ) k 3 (l mol -1 s -1 ) k 5 (l mol -1 s -1 ) ELIUM V2 230 1 2.3 ×10 -3 1.1 ×10 -5 110 5.0 ×10 7 4.9 ×10 -7 4.1 ×10 -7 7.0 ×10 -4 1.0 ×10 5 320 5.0 ×10 From a kinetic point of view, the rate constant for the reaction P °+ O 2 → POO °(k 2 ) is reported to be about 10 8 l mol -1 s -1 [START_REF] Denisov | Oxidation and Antioxidants in Organic Chemistry and Biology[END_REF] whereas the solubility in polymers is about 10 -3 mol l -1 [START_REF] Higashide | Permeability to oxygen of poly(methy1 Methacrylate) films containing silane-treated glass flakes[END_REF] . The balance between the rate of oxidation and unzipping is given by k 2 [O 2 ]/k DP ~10 5 /k DP and clearly exceeds 1 for all temperatures under investigation. In other words, an oxidation mechanism takes place and predominates. However, MMA is the main volatile product (like under inert atmosphere) meaning that radicals are mainly located by chain ends meanwhile random chain scission seem to co-exist with chain ends unzipping. Basing on existing literature, a speculative mechanism can be proposed (see "Appendix 2"), despite more analytical data are needed to validate it. We thus tried to model the effect of oxygen on mass loss rate by adding the mechanisms (summarized as 1, 2, 3 and 5 reactions) derived from the Basic Autooxidation Scheme to the unzipping scheme presented in the previous section. The complete scheme becomes:

Initiation by thermolysis : Ends → P • ( k i )

Depropagation : P n • → P n -1 • + M ( k DP )
Bimolecular termination :

P • + P • → stable product ( k t )
Initiation by hydroperoxides decomposition :

POOH → 2P • + H 2 O + Volatile ( k 1 ) Propagation : P • + O 2 → POO • ( k 2 ) Propagation : POO • + PH → POOH + P • ( k 3 ) Bimolecular termination : P • + POO • → inactive product ( k 5 )
Of course, this is a simplified view of the complete degradation mechanisms: or example the termination between POO °and POO °is not taken into account here. This latter actually predominates under enhanced oxygen pressures [START_REF] Richaud | Effect of oxygen pressure on the oxidation kinetics of unstabilised polypropylene[END_REF] which is not the case here, and adding it to the mechanistic scheme would induce a supplementary parameter to be determined.

In a first approach, it was chosen to present here the "simplest" scheme (with the advantage of a very limited number of adjustable kinetic parameters. This mechanistic scheme leads to the following differential system:

d [ P • ] dt = k i [ P H ] -2 k t [ P • ] 2 + 2 k 1 [ P OOH ] -k 2 [ P • ] [ O 2 ] + k 3 [ P OO • ] [ P H ] -k 5 [ P • ] [ P OO • ] ( 20
)
d [ P OO • ] dt = k 2 [ P • ] [ O 2 ] -k 3 [ P OO • ] [ P H ] -k 5 [ P • ] [ P OO • ] ( 21
)
d [ P OOH ] dt = -k 1 [ P OOH ] + k 3 [ P OO • ] [ P H ] + k 5 [ P OO • ] [ P • ] (22)
We assumed here that termination between P °and POO °generates dialkylperoxides kinetically equivalent to hydroperoxides in term of decomposition.

The mass of released volatiles (i.e. reactive substrate with abstractable hydrogen to generate hydroperoxides POOH) is given by:

d m p / m p0 dt = - M 0 ρ ( k i [ P H ] + k DP [ P • ] ) + 32 ρ k 2 [P • ][O 2 ] - 18 + M 1 ρ k 1 [ P OOH ] (23)
And for unpolymerized volatiles groups:

d m v / m v 0 dt = - M 0 ρ ( k v ap [ V ] ) ( 24
)
M 0 is the molar mass of a monomer unit released from unzipping reaction (100 g mol -1 ). M 1 is the molar mass of a volatile compound ejected from the decomposition of alkoxy. This is an adjustable parameter since many kinds of volatiles are released (see for example Scheme 5 ). The overall mass changes are thus given by:

dm dt = m v 0 × d m v / m v 0 dt + m p0 × d m p / m 20 dt m v 0 + m p0 ( 25
)
The corresponding script is given in Supplementary Information file. To simulate the experimental results, it remains now to assess the kinetic parameters as explained below:

1 The oxygen concentration is on the order of [O 2 ] = 10 -4 l l -1 mmHg -1 = 0.003 mol l -1 [START_REF] Higashide | Permeability to oxygen of poly(methy1 Methacrylate) films containing silane-treated glass flakes[END_REF] .

2 k 3 (for the POO °+ PH → POOH + P °) propagation reaction corresponds to a mechanism involving chain methylene predominates. Using the relation reported by Korcek [37] : log k 3 ( 30 • C ) = 16 . 4 -0 . 0477 . BDE (26) E 3 = 0 . 55 ' ( BDE -261 . 5 ) [START_REF] Bate | A new approach for measuring the rate of pyrolysis of cross-linked polymers: evaluation of degradation rate constants for cross-linked PMMA[END_REF] k 3 and E 3 were calculated using BDE = 395 kJ mol -1 (i.e. a value close to the case of methylenic groups in PE). Interestingly, E 3 < E aDP which means that unzipping is favored at high temperature whereas oxidation would predominate at lower temperatures and possibly in use conditions. [START_REF] Van Rijswijk | Review : reactive processing of textile fiber-reinforced thermoplastic composites -an overview[END_REF] According to [START_REF] Gillen | General solution for the basic autoxidation scheme[END_REF], the reactivity of alkyl is very high which justifies that k t (P° + P° ) ~k 5 (P° + POO° ) with an activation energy close to 0.

Finally, three adjustable parameters remain:

-k 1 expresses the (un)stability of hydroperoxides. This value is not, to our knowledge, documented in PMMA. Its value is directly linked to the length of the "induction period" for mass loss (see Fig. 6 ). -k 2 is usually reported to be about 10 8 l mol -1 s -1 , and it is usually observed k 2 ~k 5 . Its value is not observed to be temperature dependent. Here, k 2 was adjusted in particular to fit the slope of the main mass loss stage under oxygen. Its value was found lower but this difference can originate from the simplifications in the mechanistic scheme. -M 1 value also triggers the shape of mass curve after induction period. On one side, the molar mass of volatiles is low for compounds envisaged in the mechanism given in Appendix 2 (69 g mol -1 for formaldehyde + carbon dioxide, 102 g mol -1 for methyl pyruvate), but on the other side, chain scissions occurring on two close units can generate bigger volatile species.

Here, M 1 was arbitrarily fixed equal to 85 g mol -1 but it is clear that a more thorough identification of volatiles are needed.

The final set of rate constants permitting a fair fitting of degradation under oxygen starting from the degradation model under oxygen is given in Table 3 . We emphasize that a deeper insight in the understanding of the mechanism is required to justify those rate constants in terms of structure-properties relationships.

Conclusions

This paper investigates the thermal degradation under nitrogen or in presence of oxygen of ELIUM® resins, together with PMMA chosen as a model system. Degradation was monitored in situ by TGA (mass loss), together with a study of macromolecular architecture by T g measurements using DSC and molar mass measurement by GPC. Experimental data showed that thermal degradation under nitrogen displayed two significant features: it is auto-decelerated with minor changes on polymer skeleton whereas degradation in presence of oxygen displays an auto-acceleration and strong macromolecular changes. It led us to a first kinetic model derived from the mechanistic scheme for unzipping (depolymerization) under inert atmosphere with supplementary reaction derived from the basic autoxidation scheme under oxygen. Despite the use of a limited number of adjustable parameters, reasonable simulations can be obtained at least for the moderate conversion degrees (up to 50% mass loss) with kinetic parameters being almost the same for PMMA and ELIUM® resins. The next step would be to better precise for example the depropagation step in the case of ELIUM® resins which are very often copolymers so that depropagation step is actually comparable to the scheme established for co-oxidation or copolymerization.

Declaration of Competing Interest

We hereby confirm that we have no conflict of interest with the paper Appendix 1. First order diagrams for mass loss curves oxygen" or in ref [START_REF] Song | Thermal oxidative degradation of poly(methyl methacrylate)[END_REF] ) and the faster degradation ( Fig. 6 ) observed under oxygen compared to under nitrogen.

Another mechanism can be envisaged. It is based on the radical of CH groups hold by repetitive units randomly located in the polymer chains for example by many kinds of radicals (for example HO °, or peroxy radicals…). Three reactive groups can be envisaged:

-methyl in α position if tertiary carbons, which should be very stable, -methylene -CH 2 , and methyl groups in α position of ester, which are expected to be more reactive.

It is difficult at this stage to quantify the relative proportion of reactions involving C-H (2) and C-H (3) groups. Both C-H actually would display bond dissociation energy close to 390 kJ mol -1 [ 37 , 40 ]. However, at elevated temperatures such as investigated here, it seems that they can easily lead to 1a or 1b radicals. For example, after a radical attack, a -O-CH 2 °radical would be generated ( Scheme 6 ). Its decomposition could generate formaldehyde together with a carboxyl radical. This latter decomposes into a tertiary radical that will undergo a chain scission to regenerate 1a and 2a radicals so that the unzipping can go on. It explains why, even under air, methyl methacrylate is the major volatile product (see [START_REF] Richaud | Effect of oxygen pressure on the oxidation kinetics of unstabilised polypropylene[END_REF] ).

If we consider now the alkyl radicals coming from the radical attack of methylenes, it seems also that they can rearrange by beta scission and give 1a radicals ( Scheme 7 a) [START_REF] Colom | Properties of PMMA artificially aged[END_REF] .

In other words, the initiation reaction can be summarized as follows:

POOH → PO • + HO • HO • + R -H → P • + H 2 O PO • → volatile + P •
The decomposition of POOH is supposed to be the limiting step whereas the decomposition of radicals is supposed to be very fast. Finally, we have: POOH → 2P • + H 2 O + volatiles For the propagation reaction, according to Billingham [START_REF] Broska | Accelerating effect of poly(methyl methacrylate) on rubber oxidation, Part 1: A chemiluminescence study[END_REF] or Schnabel and coll [START_REF] Song | Thermal oxidative degradation of poly(methyl methacrylate)[END_REF] , the reactivity of chain methylenes could prevails and induces the formation of hydroperoxides, decomposing as described in Scheme 7 b. It justifies why chain scis-sions would occur randomly (see "4.1. Nature of the mechanisms involved under inert atmosphere or in presence of oxygen"). Since each P °radical created from C-H abstraction rearrange into a "chain end radical", it can be considered that POO °+ RH → POO °+ P °.

Those reactions justify to implement the Basic Autoxidation Scheme (see part "4.3. Degradation mechanism in presence of oxygen").

CRediT authorship contribution statement

Mohamed Souheib Chebil: Data curtion, Formal analysis, Investigation, Writing -original draft. Guillaume Bouaoulo: Data curtion, Formal analysis. Pierre Gerard: Data curtion, Methodology, Writing -original draft. Salma EL Euch: Funding acquisition, Methodology, Project administration, Supervision. Hervé Issard: Funding acquisition, Methodology, Project administration, Supervision. Emmanuel Richaud: Formal analysis, Investigation, Conceptualization, Methodology, Project administration, Supervision, Writing -original draft.

Fig. 1 .

 1 Fig. 1. Schematized structure of ELIUM V1 (a) and V2 (b).

Fig. 2 .

 2 Fig. 2. Kinetics of mass changes for PMMA (a) and ELIUM® V1 and V2 (b) under N 2 at different tem peratures. For Figs. 1 a and 1 b, dashed lines correspond to best kinetic model with rate constants given in Table3(see ''Discussion"). NB: the number of experimental points is lowered for better clarity.

Fig. 3 .

 3 Fig. 3. DSC traces of unaged and ELIUM® and PMMA aged 2 h under N 2 at 250 °C.

Fig. 4 .

 4 Fig. 4. T g changes of PMMA and ELIUM® V1 versus exposure time at 250 °C under N 2 (a) and as a function of temperature for different exposure times under N 2 (b).

Fig. 5 .

 5 Fig. 5. GPC measurements for PMMA samples aged under N 2 or O 2 at different temperatures.

Fig. 6 .

 6 Fig. 6. Optical microscopy images of the oxidized layer at (a) 200 °C 3 weeks and (b) 180 °C 15 weeks (b) for ELIUM® V2 samples.

Fig. 7 .

 7 Fig. 7. Comparison of mass loss monitored by TGA under nitrogen and oxygen for 50 μm ELIUM® V2 films at several temperatures. Full and dashed lines correspond to kinetic modeling respectively under oxygen and nitrogen with rate constants given in Table3.

Fig. 8 .

 8 Fig. 8. T g changes vs mass loss for ELIUM® V1 resin aged under nitrogen and oxygen.

Scheme 1 .

 1 Scheme 1. Initiation mechanism of thermal degradation.

Fig. 9 .Scheme 2 .

 92 Fig. 9. Arrhenius diagram for apparent rate constants of thermal decomposition under nitrogen atmosphere.

Fig. 10 .

 10 Fig. 10. First order diagrams for kinetics of mass changes for PMMA (a) and ELIUM® V1 and V2 (b) under N 2 at different temperatures. The slopes are related to the first order mass loss equation (see "Discussion") and are given inTable 3 as k obs .

Table 1

 1 Measured molar mass after ageing at different temperatures under 100% N 2 or 100% O 2 atmosphere.

	Ageing conditions	M w (kg mol (1 )	M n (kg mol -1 )
	0 h (not aged)	123.7	60.6
	2h -250 °C -N 2	125.3	64.7
	2h -270 °C -N 2	124.2	67.1
	2h -290 °C -N 2	108.2	51.5
	2h -310 °C -N 2	68.9	28.8
	1h -250 °C -O 2	57	8.6
	2h -250 °C -O 2	13.3	2.6
	15 h -250 °C -O 2	2.1	1.3

Table 2

 2 Measured TOL on ELIUM® V2 samples (up to 3 months aging for the highest values).

	Temperature ( °C)	150 °C	160 °C	180 °C	200 °C
	TOL (μm)	1100-1300	1100-1200	760-870	550-830

Table 3

 3 as k obs . Oxidation mechanism involving the methylene group.

	Scheme 7.

According to Scheme 4, two kinds of alkyl are formed and lead to at least two kinds of hydroperoxides, the possible decomposition products of which being given in Scheme 5: Scheme 5. Decomposition of hydroperoxides in PMMA and ELIUM® resin. Scheme 6. Oxidation mechanism involving methyl ester group.

However, one sees that such a mechanism only converts 1a alkyl radicals into 2a ones, and 2a into 1a, i.e. that reactive species remain located on chain ends. It does not explain why molar mass of PMMA chain decrease very fast (see our results in "4.1. Nature of the mechanisms involved under inert atmosphere or in presence of