Imen Akermi
email: imen.akermi@irit.fr

Boughanem
email: mohand.boughanem@irit.fr

- Rim Faiz

Une approche de recommandation proactive dans un environnement mobile

Keywords: modélisation du contexte, système de recommandation contextuelle, recommandation proactive context modeling, context-aware recommender systems, user modeling, proactive recommendation

Les systèmes de recommandation contextuelle visent à combiner un ensemble de technologies et de connaissances sur le contexte de l'utilisateur pour lui fournir une information pertinente au moment où il en a le plus besoin, c'est ce qu'on appelle la recommandation proactive. Dans cet article nous proposons une approche de recommandation contextuelle et proactive dans un environnement mobile qui apprend implicitement les préférences de l'utilisateur. Nous avons évalué notre approche dans le cadre de la tâche "Contextual Suggestion Track" de TREC 2014. Les résultats que nous avons obtenus sont prometteurs.

Introduction

L'accès aux informations pertinentes, adaptées aux besoins et au profil de l'utilisateur est un enjeu majeur dans le cadre actuel caractérisé par une prolifération massive des ressources d'information hétérogènes. Le développement d'appareils mobiles équipés de plusieurs fonctionnalités telles que la caméra, le WIFI, la géolocalisation et bien d'autres permettent aux systèmes mobiles actuels de recherche d'information d'être hautement contextualisés, pouvant ainsi fournir à l'utilisateur des informations pertinentes au bon moment quand il en a le plus besoin, sans attendre qu'il établisse une interaction avec son appareil. Un système proactif peut prendre la forme d'un guide touristique personnalisé qui se base sur la localisation et les préférences de l'utilisateur pour suggérer à ce dernier des endroits intéressants sans qu'il fournisse sa préférence ou une requête explicite. Cela permettra de réduire les efforts, le temps et l'interaction de l'utilisateur avec son appareil mobile et de présenter les informations pertinentes au bon moment et au bon endroit.

L'efficacité de ce type de système requiert une bonne modélisation des dimensions du contexte et plus particulièrement la modélisation du profil de l'utilisateur. En effet, comme mentionné par [START_REF] Mizzaro | A social approach to context-aware retrieval[END_REF], plusieurs dimensions de contexte, tels que la localisation, le temps, les activités des utilisateurs, leurs besoins, la lumière, le bruit, le mouvement, etc., doivent être pris en compte pour bien capturer tous les facteurs pouvant influencer la recommandation. La véracité et la multiplicité de ces facteurs rend les modèles de contexte trop complexes à implémenter. D'autre part, l'utilisation de peu de dimensions mène à des modèles de contexte incapables de comprendre l'environnement de l'utilisateur [START_REF] Mizzaro | A social approach to context-aware retrieval[END_REF].

Dans cet article, nous proposons une approche de recommandation contextuelle et proactive dans un environnement mobile qui intègre les technologies mobiles et les dimensions spatio-temporelles pour la modélisation d'un profil situationnel de l'utilisateur. En effet, on vise à identifier la bonne information à recommander en fonction de la situation dans laquelle se trouve l'utilisateur.

Cet article est organisé comme suit. Nous présentons dans la section 2 un état de l'art se focalisant sur la recommandation contextuelle. La section 3 présente l'approche proposée. Dans la section 4, nous présentons et discutons les résultats des expérimentations de notre approche sur la collection TREC Contextual Suggestion Track 2014. Nous concluons et énonçons quelques perspectives en section 5.

Etat de l'art

Les systèmes de recommandation proactifs (SRP) comme décrit par [START_REF] Melguizo | What a proactive recommendation system needs -relevance, non-intrusiveness, and a new longterm memory[END_REF], récupèrent de grandes quantités de documents, décident quelle information disponible est probablement en rapport avec les besoins des utilisateurs, et suggèrent ces informations sans une demande explicite de l'utilisateur.

Récemment, plusieurs approches ont été développées pour soutenir la recommandation proactive. On distingue les approches qui se basent sur l'historique de comportement de l'utilisateur pour déterminer ses intérêts. Le comportement de l'utilisateur englobe l'historique de navigation Web/clics [START_REF] Mizzaro | A social approach to context-aware retrieval[END_REF]; les comportements antérieurs de visite de lieux pour les systèmes basés sur la localisation [START_REF] Li | Want a coffee?: Predicting users' trails[END_REF][START_REF] Pu | Location based recommendation for mobile users using language model and skyline query[END_REF] et l'historique des articles lus pour les systèmes de recommandation d'articles d'actualité [START_REF] Ijntema | Ontology-based news recommendation[END_REF][START_REF] Arora | Personalized news prediction and recommendation[END_REF][START_REF] Athalye | Recommendation system for news reader[END_REF][START_REF] Dumitrescu | Improving novelty in streaming recommendation using a context model[END_REF]. D'autres approches de recommandation traitent le contexte de l'utilisateur d'un point de vue centré sur l'activité. Les activités communes utilisées pour construire le profil de l'utilisateur dans ces systèmes pourraient prendre la forme de pages Web ou des documents ouverts [START_REF] Budzik | User interactions with everyday applications as context for just-in-time information access[END_REF][START_REF] Finkelstein | Placing search in context: the concept revisited[END_REF][START_REF] Rhodes | Just-in-time information retrieval agents[END_REF]Prekop et Burnett, 2002;[START_REF] Dumais | Implicit queries (iq) for contextualized search[END_REF][START_REF] Karkali | Match the news: A firefox extension for realtime news recommendation[END_REF] ; de conversation ou l'activité en cours, telles que les messages texte, les appels téléphoniques [START_REF] Popescu-Belis | A speech-based just-in-time retrieval system using semantic search[END_REF] et de l'activité de l'utilisateur à travers les réseaux sociaux tels que le contenu des tweets de l'utilisateur sur Twitter [START_REF] Phelan | On using the real-time web for news recommendation and discovery[END_REF][START_REF] De | From chatter to headlines: Harnessing the real-time web for personalized news recommendation[END_REF][START_REF] O'banion | Social media-driven news personalization[END_REF].

Toutes les approches mentionnées ci-dessus et beaucoup d'autres ont essayé de relever le défi d'inférer le contexte de l'utilisateur et ses préférences, au bon moment et sans son intervention. Cependant, la plupart de ces systèmes rencontrent certaines limites. En effet, diverses approches [START_REF] Bedi | A situation-aware proactive recommender system[END_REF][START_REF] Liu | Personalized news recommendation based on click behavior[END_REF]. Saranya et Sadhasivam, 2012) reposent sur l'historique de comportement passé ou actuel de l'utilisateur tel que son historique de navigation sur internet ou son historique de visite de lieux, pour déterminer ses intérêts. Cependant, on ne peut pas se référer seulement au comportement passé de l'utilisateur car il peut ne pas contenir suffisamment d'informations sur ses intérêts. Un utilisateur peut naviguer sur une page web par hasard ou visiter un endroit particulier sans pour autant porter un intérêt à cet endroit.

Egalement, de nombreuses approches de recommandation [START_REF] Budzik | User interactions with everyday applications as context for just-in-time information access[END_REF][START_REF] Finkelstein | Placing search in context: the concept revisited[END_REF][START_REF] Rhodes | Just-in-time information retrieval agents[END_REF]Prekop et Burnett, 2002;[START_REF] Dumais | Implicit queries (iq) for contextualized search[END_REF][START_REF] Karkali | Match the news: A firefox extension for realtime news recommendation[END_REF] traitent le contexte de l'utilisateur d'un point de vue centré sur l'activité qui peut prendre la forme d'une conversation en cours ou des documents ouverts. Néanmoins, on ne peut pas réduire le profil de l'utilisateur à ces activités. On peut ouvrir un document pour travailler dessus ou avoir une conversation sur un sujet sans pour autant vouloir recevoir des recommandations qui y sont liées. De plus, l'activité sociale d'un utilisateur fournie par les commentaires exprimés à travers ses comptes sociaux ne peut pas fournir suffisamment d'informations pour construire un profil équilibré, car elle pourrait être limitée, voire absente. Ce genre de profilage des utilisateurs contient beaucoup de bruit à gérer et pas assez d'informations pour établir un profil assez complet.

Il existe aussi d'autres limites communes entre les systèmes de recommandation contextuels qui doivent être abordées, telle que, la dépendance à un domaine. En effet, de nombreux systèmes [START_REF] Pu | Location based recommendation for mobile users using language model and skyline query[END_REF][START_REF] Yeung | A proactive personalized mobile news recommendation system[END_REF][START_REF] Quercia | Nurturing social networks using mobile phones[END_REF] dépendent d'un seul domaine (tourisme, cinéma, nouvelles ...) et ont des dimensions de contexte spécifiques à appliquer en fonction du domaine. Cependant, la plupart de ces systèmes reposent presque sur la même combinaison de dimensions qui comprend essentiellement les préférences de l'utilisateur, la localisation, et le temps avec une légère différence sur la façon d'aborder ces dimensions. Par conséquent, de nombreux services liés à des domaines différents peuvent profiter des mêmes informations de contexte sans pour autant encombrer le mobile de l'utilisateur. Notre approche traite ces limites et contribue aux travaux existants en impliquant et en combinant les caractéristiques suivantes:

-La non-dépendance à un domaine particulier: nous couvrons divers domaines dans le processus de recommandation.

-Un système proactif: nous proposons un système de recommandation contextuel et proactif qui peut aider l'utilisateur à faire face aux problème de la surcharge d'information en recommandant une information pertinente qui correspond à ses intérêts personnels au moment où il en a le plus besoin sans attendre que l'utilisateur pose une requête.

Dans notre approche, on vise à identifier l'information adéquate à recommander selon la situation de l'utilisateur.

Une approche de recommandation contextuelle et proactive dans un environnement mobile

L'idée principale que nous proposons est l'intégration des informations relatives à un utilisateur, sa tendance de navigation et les technologies mobiles (GPS, accéléromètre, etc.) afin de recommander de manière proactive des informations pertinentes à l'utilisateur sans avoir à attendre que ce dernier initie une interaction avec son appareil. Nous décrivons dans ce qui suit le modèle de contexte proposé ainsi que le processus de recommandation.

La modélisation du contexte

Nous considérons le contexte comme une représentation multidimensionnelle Contexte= (profil, localisation, temps, activité), composée de quatre dimensions :

-Le profil de l'utilisateur est défini par les préférences de l'utilisateur et ses données démographiques

-Localisation: La position de l'utilisateur définie par des coordonnées GPS -Temps: défini par des étiquettes numériques ou temporelles (matin, soir, ...)

-L'activité de l'utilisateur: l'activité de l'utilisateur en cours Les instanciations de ces dimensions à un moment donné t forment une situation S où la recommandation sera jugée comme nécessaire ou pas. Nous extrayons implicitement les informations relatives à chaque dimension sans l'intervention de l'utilisateur. Nous définissons dans les sections suivantes les différents éléments du processus de modélisation de contexte.

Le profil de l'utilisateur

Nous utilisons un modèle de profil classique (Daoud et al. 2009) défini par deux attributs, les données démographiques; des informations relatives à l'utilisateur telles que le nom, l'âge, etc. ; et les préférences de l'utilisateur par rapport à des centres d'intérêt spécifiques (C). Un centre d'intérêt est représenté par une catégorie et son poids, désignant l'intérêt que porte l'utilisateur à la catégorie en question. Les catégories sont prédéfinies en utilisant « The Open Directory Project Dmoz1 ». profil= {C i ,w i } ; i=1..n Une catégorie est représentée par des termes pondérés extraits à partir de son historique de navigation et les pages qu'il suit sur les réseaux sociaux : C i ={t (i) j ,w (i) j } ; j=1..m

Le temps

Selon le dictionnaire Merriam-Webster2 , le temps est défini comme ″un continuum non-spatial qui est mesuré en termes d'événements qui se succèdent du passé par le biais du présent au futur". Le temps peut aussi être exprimé comme la période mesurée ou mesurable au cours de laquelle une action, un processus ou une situation existe ou continue (Whitrow 1988). Selon la deuxième définition, plusieurs unités de temps sont définies, par exemple, heures, jours, mois et années. La flexibilité de la conception du temps et de sa mesure implique différentes représentations. En effet, le temps peut être représenté comme une variable continue dont les valeurs déterminent les moments précis au cours desquels des items sont évalués par un utilisateur donné. Exemple : un utilisateur A a donné un score à un objet O à un temps t= 1 juin 2010 à 18:05:00 Une autre manière de modéliser le temps est d'identifier des valeurs catégorielles, pour des périodes de temps spécifiques. Par exemple, dans le domaine du tourisme, la variable "saison" peut être exprimée ainsi: saison = {saison chaude, saison froide}. Le temps peut également être modélisé de façon hiérarchique qui permet de définir le degré de granularité de la dimension temporelle.

Exemple:

Jour_semaine = {lundi, mardi,. [START_REF] Dobson | Leveraging the subtleties of location[END_REF], il existe différentes façons de caractériser l'emplacement de l'utilisateur: Position absolue ; Position Relative (à côté de, ...) ; Un nom de lieu ; Une classe nommée qui représente le type du lieu, par exemple, musée, école, etc. Dans notre approche, nous considérons la position absolue et la représentation de classe nommée pour caractériser la dimension spatiale de l'utilisateur. Nous définissons deux niveaux pour cette dimension utilisés dans le processus d'extraction de l'information à recommander: -L'emplacement actuel: il s'agit de l'emplacement actuel de l'utilisateur à un moment donné. -Les endroits liés à l'utilisateur: Ce sont les endroits liés à la vie quotidienne de l'utilisateur (travail, domicile, ...) et qui pourraient être déterminés en étudiant les endroits dans lesquels se trouve l'utilisateur pendant un certain laps de temps.

Le type de l'emplacement actuel peut être déterminé à l'aide de plusieurs outils tels que geonames3 ou le réseau social Foursquare qui attribuent une catégorie à une combinaison de coordonnées GPS donnés. Nous utilisons Foursquare pour déduire les informations de localisation: La catégorie du lieu et son nom.

L'activité de l'utilisateur

L'activité de l'utilisateur actuelle se résume en ce que l'utilisateur fait à un moment donné et peut être déterminée à travers son agenda ou l'application ouverte sur son téléphone portable. Cette dimension est importante dans notre approche et est utilisée pour évaluer si nous pouvons initier le processus de recommandation ou pas. En effet, nous ne pouvons pas recommander des informations, d'une manière imposante, alors que l'utilisateur est toujours à une réunion par exemple.

Le processus de recommandation

Inférence de la catégorie d'information à recommander

Nous considérons que le processus de recommandation implique un jeu de situations qui reflètent une catégorie d'intérêt spécifique caractérisée par les instanciations des dimensions spatio-temporelles et qui sont organisées dans une base de connaissances. Une situation est alors représentée par deux dimensions spécifiques: le temps, plus précisément le jour de la semaine (D w ), et le temps de la journée (D t ) ; et la catégorie du lieu (D l ). Une situation est formellement représentée comme ! = (" # , " $ , " % ).

En effet nous estimons que le besoin de l'utilisateur en information change selon le moment de la journée. Une étude4 réalisée en 2013 révèle que 58% de personnes lisent avant toute chose leurs emails et les actualités le matin. Au déjeuner, les gens préfèrent naturellement trouver le restaurant le plus proche. Par exemple, la situation « déjeuner » est décrite par :

-D l : n'importe quel lieu -D w : n'importe quel jour -D t : tÎ [12,14] La catégorie de l'information à recommander est inférée de la situation actuelle (Exemple : « Restaurant » pour la situation « déjeuner »).

Extraction de l'information à recommander

Afin de récupérer les informations à recommander, une requête q est formulée comme suit : q = (latitude, longitude, catégorie_d'intérêt) La requête est ensuite envoyée à un service basé sur la géo-localisation et choisi en fonction de la catégorie d'intérêt. Par exemple si la situation implique la recommandation d'actualités, on utilise le réseau social Feedly5 pour en extraire les actualités. Si la situation implique la recommandation d'un film, on interroge le réseau social Flixter6 . L'intérêt de l'utilisation des réseaux sociaux pour l'extraction de l'information à recommander réside dans le fait que le filtrage collaboratif y est implicite ce qui assure non seulement la recommandation d'une information pertinente par rapport aux préférences de l'utilisateur mais aussi une information que d'autres utilisateurs recommande. Le résultat de la requête envoyée est exprimé par un ensemble d'items I :

I = {i 1 ,…, i n }.
Si on prend l'exemple de la recommandation d'actualités, l'ensemble I sera représenté par un ensemble d'articles d'actualités : I = {A 1 (titre, contenu), …, A k (titre, contenu)} ; k=1..p Ensuite, nous filtrons à partir de I, les items convenant le mieux aux préférences de l'utilisateur en calculant un score d'utilité de l'item. Ce score combine un score de pertinence thématique de l'item vis-à-vis des préférences thématiques de l'utilisateur et un score géo-pertinence, évaluant l'accessibilité de l'item vis-à-vis de la position actuelle de l'utilisateur. Plus précisément, concernant la pertinence thématique, on considère qu'un item est représenté par un vecteur de mots pondérés (mots existants à partir des éléments textuels décrivant l'item). La pertinence du contenu est calculée par le score de similarité cosine:

Topic &'* (+-. , /0) = 1 +-. (2)
× /0 2 3 245 61 (+-.

(

) 2
)7

3 245

× 6 1 (/0 2 ) 7 3 245

(2)

Où: VC i : Le vecteur termes préférence relatif à la catégorie C i It: Le vecteur termes de l'item i La géo-pertinence n'est utilisée que dans le cas où l'utilisateur doit se déplacer pour se rendre à l'item proposé. Elle est exprimée par un score qui mesure l'accessibilité à l'emplacement de l'item suggéré. L'accessibilité est mesurée comme la distance entre deux coordonnées GPS correspondant à l'emplacement actuel de l'utilisateur et l'emplacement de l'item proposé: (Point 1 (lat1,long1) et Point 2 (lat2,long2)) : 899:;;<><?<0@ = AB × 9

Où : R: The earth radius=6,371Km 9 = C × atanC(D8, E(F G 8)) 8 = sin 7 ((?80C G ?80F) C H ) I cos(?80F) × cos(?80C) × sin 7 ((longC G longF) C H )

La pertinence globale d'un élément à recommander est calculée comme suit :

B:? = J × KLM<9 NO# (+-. , /0) I A (F G J) × 899:;;<><?<0@ (4)

Les items sont classés selon leurs scores de pertinence globale.

Expérimentations

Nous avons évalué notre approche dans le cadre de la tâche « Contexual Suggestion Track 7 » de TREC 2014. Nous présentons, dans cette section, une description générale de cette tâche, ensuite nous exposerons les résultats que nous avons obtenus.

Description de la tâche « Contexual Suggestion Track -CST» de TREC 2014

Cette tâche étudie les techniques de recherche pour les besoins d'information complexes qui dépendent fortement du contexte et des intérêts des utilisateurs. Le but de la tâche est de recommander à des utilisateurs se trouvant dans un contexte donné des lieux qui pourraient les intéresser. Un profil est associé à chaque utilisateur et indique la préférence de l'utilisateur par rapport à un ensemble de suggestions de lieux. Chaque suggestion comprend un titre, une description et une URL associée. Par exemple, une suggestion pourrait être une recommandation d'avoir une bière à la Dogfish Head Alehouse. Un profil est défini par un ensemble de préférences négatives ou positives par rapport à l'ensemble des suggestions de lieux. Chaque contexte correspond à un lieu géographique particulier (une ville). Par exemple, le contexte pourrait être Gaithersburg, Maryland. Le but de la tâche est de retourner pour chaque pair profil/contexte, une liste de lieux intéressants allant jusqu'à 50 lieux. Chaque suggestion doit être adaptée au profil (en fonction des préférences de l'utilisateur) et au contexte (selon l'emplacement).

Construction des profils

Les profils sont construits à partir de la liste de suggestions jugées par l'utilisateur. Chaque suggestion est evaluée selon deux notes, une note pour le titre et la description du lieu et une note pour son site web. Les notes sont données sur une échelle de cinq points sur la base du degré d'intérêt que peut porter cet utilisateur pour le lieu en question: 4 (très intéressé), 3 (intéressé), 2 (Neutre), 1 (Pas intéressé), 0 (Fortement pas intéressé), -1 (Site web ne s'est pas chargé ou pas de score)

Pour construire le profil thématique de l'utilisateur, on identifie, pour chaque suggestion, sa catégorie dans l'API Google Places8 en utilisant l'url qui est associée à la suggestion en question. A l'issue de cette étape, un profil sera alors modélisé comme un ensemble de catégories pondérés qui comportent les termes associés aux suggestions que l'utilisateur préfère : profil= {C i (w i )} ; i=1..n Le calcul du poids assigné à chaque catégorie, pour chaque profil, prend en considération les scores que ce profil a attribués aux suggestions relevant de cette catégorie d'intérêt : P:<QR0(980 Les catégories sont représentées par des termes pondérés qu'on extrait à partir des descriptions des suggestions associées à chaque catégorie.

:QLS@) = 1 AB %U I B $ VAWXY Z [ (5)

Sélection des suggestions

La tâche TREC définit le contexte en fonction des coordonnées GPS fournies dans cette tâche : Contexte= {latitude, longitude}. Pour notre part, on instancie le contexte en exploitant directement les données fournies par la tâche. Pour chaque contexte, on extrait les lieux intéressants en soumettant une requête aux géo-services Google Places et Foursquare9 , formulé comme suit : q= {(latitude,longitude),categorie} Suite à cette requête, on obtient un ensemble de lieux. Un lieu, est modélisé par un objet ayant des attributs spécifiques et qui appartient à une catégorie d'intérêt donné : lieu={nom,url,description ,accessibilité,catégorie} L'accessibilité : représente la distance qui sépare le lieu du contexte représentés par leurs coordonnées GPS (P 1 (lat1,long1) et P 2 (lat2,long2)) et calculée par la formule [START_REF] Rhodes | Just-in-time information retrieval agents[END_REF] . Pour le total des 50 contextes donnés, on a pu extraire à peu près 15 000 lieux d'attraction ce qui fait en moyenne 300 lieux pour chaque contexte qui sont répertoriés sous des catégories.

Appariement Profils/Suggestions

Le processus de sélection des lieux intéressants pour chaque profil-contexte est résumé comme suit : L'évaluation des résultats que nous avons obtenus comporte deux volets : l'évaluation de la pertinence géographique et la pertinence profil. Pour mesurer la géo-pertinence des lieux qu'on a suggérés, on extrait un échantillon V g qui consiste en l'intersection de notre collection de lieux avec les lieux qui ont été évalués géographiquement dans la tâche TREC pour chaque contexte. Nous avons obtenus z+ m z = {|wC lieux en commun, tous contextes confondus. Parmi ces lieux, 4644 ont été évalués géographiquement pertinents. Ce qui implique une précision géographique totale égale à 0,97 et est calculée comme suit : Q:L}S:?:~8r9: = Z>}•:L}B:?:~8r0}+:r€:;

z+ m z (6)
Le tableau 1 présente en détail les résultats. Pour mesurer la pertinence profil, il y avait deux alternatives à considérer. Une première alternative consiste à considérer pour chaque contexte et pour chaque run10 , l'intersection de notre collection de lieux avec les lieux proposés par le run en question, cependant cette intersection donnait quasiment l'ensemble vide vu que nos méthodes d'extractions de lieux sont différentes. Nous avons donc opté pour une solution intermédiaire qui consiste à considérer l'intersection de notre collection de lieux avec l'union des lieux que chaque run a proposés, tous profils confondus. La cardinalité de cette intersection est z+ [ z = ||•Alieux. Ensuite nous avons mesuré pour chaque lieu le niveau d'intérêt qu'il a sollicité de la part des profils en se basant sur le nombre de profils qui ont évalué ce lieu comme pertinent par rapport au nombre d'évaluations totale du lieu en question. Par rapport à la collection obtenue, nous avons obtenu une précision moyenne de 0,56 calculée comme suit:

MSL'<?:}S:?:~8r9: = 1 (r>}M # r>}M}0L0 # ) H zƒ " z #45 z+ [ z (6)
Où :

nb_p l : le nombre de profils qui ont évalué le lieu (l) comme pertinent nb_p_tot l : le nombre total de profils qui ont évalué le lieu (l)

Pour se situer approximativement par rapport aux autres participants, nous avons appliqué cette démarche d'évaluations sur chaque run. On a mesuré pour chaque run et pour chaque lieu que ce run propose, le degré d'intérêt sollicité par les profils en appliquant la formule (6). Le tableau 2 illustre les résultats obtenus pour chaque run.

Conclusion

Le but fondamental des systèmes de recommandations contextuels consiste à combiner le contexte et l'environnement de l'utilisateur dans une même infrastructure pour mieux caractériser les informations dont l'utilisateur a besoin afin d'améliorer le processus de recommandation. Nous avons proposé une approche de recommandation contextuelle et proactive dans un environnement mobile qui permet la recommandation d'éléments pertinents qui répondent aux préférences de l'utilisateur, juste au bon moment sans attendre que l'utilisateur initie une requête. Plus précisément, notre contribution est divisée en deux principales parties: La modélisation d'un profil situationnel de l'utilisateur et la définition d'un cadre d'agrégation pour la combinaison des dimensions contextuelles et sociales. Nous planifions actuellement d'appliquer notre approche au sein de l'entreprise Tunav11 qui développe des produits et des systèmes de navigation et de tracking par GPS, des applications cartographiques et des géo-portails qui offrent à l'utilisateur l'accès à une masse importante d'information géographique. Ces systèmes se diversifient dans différents domaines d'activité dont le transport routier (public, marchandise, taxi, etc.), les travaux, les services, la distribution, la santé, le tourisme. Nous avons comme objectif d'apporter le « just-in-time information » et la dimension contextuelle aux systèmes qui en ont besoin afin de fournir aux utilisateurs des produits personnalisés adaptés à leurs propres besoins et préférences.

  Où :VA;A X -\Apour chaque suggestion s appartenant à cette catégorie d'intérêt C B %U : le score donné au titre et à la description du lieu d'attraction B $ : le score du site web du lieu d'attraction Z [ : le nombre de suggestions appartenant à cette catégorie d'intérêt

  Pour chaque p ] X ^ Pour chaque c _ X ` -Calculer pour chaque suggestion b X A`_ deff'dh]jkd la pertinence globale (selon la formule (4) ) -Normaliser les scores de pertinence globale des suggestions entre 0 et 1 -Extraire les suggestions dont le score de pertinence globale est ≥ 0,5 Et qui appartiennent aux catégories d'intérêt appréciées par le profil : 980:QLS@ $O.mq% rLSu8?<;é v wxy! Où: P: l'ensemble des profils C: l'ensemble de contextes `_deff'dh]jkd : L'ensemble des suggestions relatives au contexte C j 4.2. Résultats:

  Nous adoptons le modèle hiérarchique. Dans notre approche, nous divisons une journée en intervalles de temps (time slots) d'une certaine longueur. C'est selon ces intervalles que nous choisissons entre autre le type d'information à recommander. On représente le temps en 2 niveaux : 1. Temps de la journée (D t ): la journée est divisée en cinq périodes qui sont le matin, le midi, l'après-midi, le soir et la nuit. Ces périodes sont encadrées selon des intervalles de temps répartis sur 24 heures.Le système de positionnement global (GPS) intégré ou installé dans le dispositif mobile permet de définir l'emplacement de l'utilisateur. Cet emplacement est défini en termes de latitude et de longitude. Ces coordonnées GPS ne sont pas les seules caractéristiques que nous pouvons considérer lors de la définition d'un emplacement. En effet, comme indiqué par

	D t = { morning [07:00 , 12:00], midday [12:00 , 14:00], afternoon [14:00 ,
	18:00], evening[18:00 , 22:00], night [22:00 , 00:00]È[00:00 , 07:00] }
	2. Jour de la semaine (D w ): on distingue deux classes qui sont les jours de travail
	(du lundi au vendredi) et le reste des jours (weekend, vacances et jours fériés)
	3.1.3. La localisation

. . , Dimanche} ; temps = {matin, midi, ..., nuit}

Tableau 1. La géo-pertinence (Nb_Total est

  le nombre total des lieux suggérés pour chaque contexte ; Nb_GP est le nombre des lieux géographiquement pertinents ; Nb_NGP est le nombre des lieux identifiés comme géographiquement non pertinents )

	Context ID	Nb_Total Nb_GP Nb_NGP Context ID Nb_Total Nb_GP Nb_NGP
	101	120	118	2	127	86	80	6
	102	74	71	3	128	118	117	1
	103	116	113	3	129	106	106	0
	104	103	100	3	130	35	29	6
	105	58	56	2	131	132	128	4
	106	116	114	2	132	115	111	4
	107	137	132	5	133	49	46	3
	108	80	77	3	134	213	210	3
	109	113	109	4	135	82	75	7
	110	80	76	4	136	60	56	4
	111	63	61	2	137	48	47	1
	112	24	22	2	138	155	152	3
	113	171	165	6	139	35	33	2
	114	68	66	2	140	94	91	3
	115	103	92	11	141	69	67	2
	116	24	23	1	142	114	111	3
	118	79	73	6	143	52	43	9
	119	111	107	4	144	203	202	1
	120	129	127	2	146	99	96	3
	121	111	108	3	147	105	103	2
	122	114	111	3	148	26	26	0
	123	180	180	0	149	204	201	3
	124	198	195	3	150	69	67	2
	125	80	73	7

Tableau 2. Résultats des autres participants

  'après le tableau 2, on note que la précision de la pertinence profil de chaque run par rapport aux lieux qu'ils ont proposés ne dépasse pas 0,25. Cela est expliqué par le fait, que pour chaque run, il y a un grand écart entre le nombre de profils qui ont jugé un lieu (appartenant à un seul contexte) comme pertinent et le nombre de jugements totaux. Généralement, les résultats que nous avons obtenus en appliquant notre approche sont prometteurs et montrent que l'utilisation de la classification par catégories des préférences d'un utilisateur implique une meilleure précision thématique par rapport à ses intérêts. Ces résultats montrent aussi que les choix des paramètres tels que le rayon que nous avons fixé pour l'extraction des lieux par rapport aux contextes sont efficaces. Cependant, cette évaluation n'a mis en examen qu'une partie de notre approche. En effet, la notion du temps n'est pas intégrée alors que cette dimension est considérée dans notre travail.

	id	run	Nb_to	Nb_in	Préc	id	run	Nb_to	Nb_in	Préc
	1	BJUTa	t 1495	t 352	. 0,24	20	simpleScore	t 1496	t 244	. 0,16
	2	BJUTb	1495	327	0,22	0 21	simpleScoreImp	1496	254	0,17
	3	BUPT_01	671	81	0,12	22	tueNet	1497	129	0,09
	4	BUPT_02	704	78	0,11	23	tueRforest	1497	138	0,09
	5	cat	1496	318	0,21	24	UDInfoCS2014_	1495	201	0,13
	6	choqrun	1465	196	0,13	25	1 UDInfoCS2014_	1495	360	0,24
	9	dixlticmu	1496	367	0,25	26	2 uogTrBunSumF	1495	272	0,18
	10	gw1	1466	58	0,04	27	uogTrCsLtrF	1496	199	0,13
	0 11	lda	1496	163	0,11	28	waterlooA	1497	260	0,17
	14	RAMARUN	1497	260	0,17	29	waterlooB	1497	286	0,19
	15	2 RUN1	1494	229	0,15	30	webis_1	1477	269	0,18
	16	run_DwD	1496	181	0,12	31	webis_2	1474	230	0,16
	17	run_FDwD	1496	262	0,18

D

http://www.dmoz.org/docs/en/about.html

http://www.merriam-webster.com/dictionary/time

http://www.geonames.org/

http://blog.marketo.com/2013/07/email-wanted-dead-or-alive-infographic.html

http://feedly.com/index.html#discover

https://fr.flixster.com/

https://sites.google.com/site/treccontext/trec-2014

https://developers.google.com/places/documentation/?hl=fr

https://fr.foursquare.com/

Un run est une application proposé par une équipe pour traiter la tâche « Contextual Suggestion » dans TREC 2014

http://www.tunav.com/

http://www.pasri.tn/ -Le Projet d'Appui au Système de Recherche et de l'Innovation (PASRI), un projet financé par l'Union européenne.

http://www.anpr.tn/ -Agence Nationale de la Promotion de la Recherche Scientifique en Tunisie.

Remerciements

Ce projet est effectué dans le cadre d'une thèse de doctorat MOBIDOC du programme PASRI 12 financé par l'UE et administré par l'ANPR 13 .


H Marzagui

T Cutard
email: cutard@enstimac.fr

Characterisation of microstructural evolutions in refractory castables by in situ high temperature ESEM

Keywords: Refractory castables, Microstructural changes, Environmental scanning electron microscopy

published or not. The documents may come

Characterisation of microstructural evolutions in refractory castables by in situ high temperature ESEM

H Marzagui, Thierry Cutard

Introduction

There is a trend to increase the use of unshaped refractory castables in various industries like steel-making, cement production, energy production and waste incineration. In several applications, they are more economical and easier to use than shaped refractories and they can exhibit excellent mechanical properties. Quality improvement is needed particularly to design durable parts or structures based on these materials.

One of their major characteristics is that they are fired in situ during the starting step of the industrial structure where they are used. It is known that large microstructural evolutions can take place in these refractory castables during their first heating. As they are often based on calcium-alumina cement, some studies have been made on the microstructural evolutions during the firing of calcium-alumina cement bound castables [START_REF] Nonnet | Elastic properties of high alumina cement castables from room temperature to 1600 • C[END_REF][START_REF] Schmitt | Coupling between kinetics of dehydration, physical and mechanical behaviour for high alumina castable[END_REF][START_REF] Sarpoolaky | Influence of in situ phase formation on microstructural evolution and properties of castable refractories[END_REF][START_REF] Simonin | Thermomechanical behavior of high-alumina refractory castables with synthetic spinel additions[END_REF]. Dehydration, conversion of hydrates, crystallisation, sintering are known to occur in these materials when increasing the temperature. Such phase transformations often lead into damage processes by microc-racking and consequently to a non-linear mechanical behaviour [START_REF] Simonin | Room temperature quasi-brittle behaviour of an aluminous refractory concrete after firing[END_REF]. Microsilica is generally added to improve the flaw behaviour during mixing and casting. When heating such calcium-alumina-silica cement based castables, low melting phases appear at high temperature and degrade their high temperature properties. To improve these properties, part of the cement can be substituted by superfine alumina to form an in situ mullite network that contributes to develop a strong binder phase.

Recent works have been published on the thermomechanical behaviour of unshaped refractories and on their links with microstructural evolutions [START_REF] Simonin | Room temperature quasi-brittle behaviour of an aluminous refractory concrete after firing[END_REF][START_REF] Altun | Effect of temperature on the mechanical properties of self-flowing low cement refractory concrete[END_REF][START_REF] Robin | Thermomechanical behaviour of magnesia-carbon refractories[END_REF][START_REF] Schmitt | Tensile behaviour of magnesia carbon refractories[END_REF]. They show a tendance to characterise them by tensile tests and compressive tests because of the large behaviour dissymetry that exists between these two solicitation modes for this material family. Results of these tests are used to identify the coefficients of constitutive equations that are implanted in finite element codes to predict the thermomechanical behaviour of industrial structures. More recently, models coupling microstructural variables and mechanical behaviour have been developed [START_REF] Sarpoolaky | Influence of in situ phase formation on microstructural evolution and properties of castable refractories[END_REF]. This kind of approach indicates the importance of disposing of microstructural data in a wide temperature range concerning these refractory castables.

This paper deals with results of an experimental approach developed to characterise the microstructural transforma-tions and damage processes, which occur in such materials during the first heating and with the help of in situ tests by dilatometry and high temperature environmental scanning electron microscopy. Two commercial refractory castables are considered and the objectives of the study are first to identify the microstructural transformations and the damage processes that occur during the first heating and to then determine their operating temperature range.

Materials and experimental procedures

Two commercial castables are considered. The first one is an ultralow cement bauxite castable (Bau-ULCC) made of bauxite aggregates, fumed silica, ␣-alumina and of a calcium alumina cement. The second is a low cement andalousite castable (And-LCC) made of andalousite aggregates, fumed silica, ␣-alumina and of the same calcium-alumina cement. Both materials are characterised by the same fumed silica content. In the bauxite based castable (Bau-ULCC), the ␣-alumina content in two times higher than in the andalousite based one (And-LCC). Table 1 shows the chemical compositions of the castables supplied by the manufacturer. The high mismatch between the silica contents of the two materials is mainly due the high silica content in andalousite aggregates compared to bauxite ones.

The samples were prepared by mixing the raw materials with controlled water additions and finally cast in moulds under controlled vibrations and immediately wrapped in plastic. They were cured at room temperature during 24 h and then extracted from the moulds before a 110 • C-24 h drying step. Both castables can be considered as constituted of aggregates embedded in a matrix with particle size lower than to 200 m. In order to characterise the microstructural behaviour of the matrix, samples were prepared from dry material mixtures sieved to <200 m. For dilatometry, cylinders were diamond cut at a 8 mm diameter and at a 25 mm length. Tests were performed in a 1600 • C dilatometer (model D-DIL402C, Netzsch), under air, at 5 • C/min heating and cooling rates and with 5 h isothermal dwells before cooling. A field emission gun environmental scanning electron microscope (model XL 30 ESEM-FEG, FEI) equipped with a 1500 • C hot stage was used for in situ

Results

Dilatometry

Fig. 1 shows the dilatometric curves of the two castable matrices during a first thermal cycle up to 1300 • C. During heating, they are both characterised by a series of alternative linear expansion domains and of shrinkage domains. This indicates that these matrices do not only exhibit a thermal expansion but are subjected also to microstructural evolutions which lead to shrinkage mechanisms. Four main domains, in which such mechanisms occur, can be defined. Domain 1, from 150 to 300 • C, in which both materials are characterised by the same amplitude of shrinkage. Domain 2, between 800 and 950 • C, in which the shrinkage of the Bau-ULCC matrix is of higher amplitude than that of the And-LCC matrix. Domain 3, between 1050 and 1150 • C, in which a low amplitude shrinkage is observed for the Bau-ULCC matrix and no evidence of shrinkage for the And-LCC matrix. Domain 4, from 1200 up to 1300 • C, in which an high amplitude shrinkage is observed for the Bau-ULCC matrix and a change of slope is observed for the And-LCC matrix. During the 1300 • C isothermal dwells, both materials exhibit different behaviours: first a regular shrinkage followed by an expansion for the Bau-ULCC matrix and a regular expansion for the And-LCC matrix. During cooling both matrices are characterised by linear thermal contraction behaviours.

Fig. 2 shows the dilatometric behaviour of the two castables during the first heating. Both materials exhibit a thermal expansion behaviour but non-linear domains or slope changes are observed. When reporting on these curves of the four precedent domains, it could be observed that the shrinkage phenomena of the two matrices have an influence on the behaviour of their respective castables, particularly in domains 1, 2 and 4. The amplitudes of shrinkage phenomena are considerably attenuated compared to the matrices.

Figs. 3 and4 show the dilatometric curves obtained on the two matrices for several first heatings at different maximum temperatures. They allow first to observe the reproducibility of the dilatometric behaviour when increasing temperature. Then the irreversibility of the microstructural evolutions associated with each shrinkage domain is proved since linear thermal contraction behaviour is observed during all coolings. Fig. 6 shows the microstructural evolutions in a And-LCC matrix samples during an in situ HT-ESEM test performed up to 1400 • C. An andalousite particule or aggregate (labelled AND) and a tabular alumina aggregate (labelled A) can be seen as embedded in the binder phase. At room temperature, the microstructure was free from any microcrack. Heating up to 150 • C has led to microcrack initiation, particularly at the interfaces between the binder phase and the two types of aggregates. From 150 to 800 • C, this microcracking process continues to occur by microcrack propagation and opening. Two microcracks (labelled 1 and 2 in Fig. 6) propagate through the binder phase and finally join the two aggregates. Between 800 and 1000 • C, these mechanisms continue to occur and larger microcrack openings are observed both for aggregate/binder phase decohesions and for binder phase microcracks. A shrinkage of the binder phase cells, created by the microcrack network, is observed. Between 1000 and 1100 • C, the morphological aspect of the microstructure changes considerably. The granular aspect of the binder phase moves to a more homogeneous one. At 1100 • C, the appearance of a liquid phase can be clearly seen and is responsible of these evolutions. This continues to occur up to 1300 • C and the amount of liquid phase appears as increasing with the temperature. Binder particules, which can be observed on the alumina aggregate at 1000 • C, have begun to convert into a liquid phase at 1100 • C and progressively form liquid droplets on the alumina surface. Furthermore a progressive closing and/or healing of microcracks 1 and 2 is observed in the 1100-1300 • C temperature range. Since 1100 • C, microporosity between the binder phase particules progressively disappears, links or bridges are created between the binder phase and aggregates, crack bridging mechanisms are observed. Those are indications of a liquid phase sintering process in the material. But local volume expansion can take part in these mechanisms too. As an example, no evidence of a decrease of the distance between the andalousite aggregate and the alumina one can be observed in this in situ HT-ESEM image series. If only densification by liquid phase sintering was responsible of the evolutions observed in the 1100-1300 • C temperature range, it should be the case. Fig. 7 shows the microstructural evolutions of another area of the same And-LCC matrix samples during the same in situ HT-ESEM test performed up to 1300 • C but at a higher magnification. This image series focuses on the evolutions of a microcrack that has appeared at 150 • C at the surface of a 20 m in diameter porosity. A progressive microcrack opening occurs when increasing the temperature with an increase of the opening amplitude in the 900-1000 • C temperature range (see Fig. 8). Drastic microstructural changes are again observed in the 1000-1300 • C temperature range. Since 1100 • C, a small amount of liquid phase appears and is accompanied of a progressive disappearance of the binder phase particles. The amount of liquid phase clearly increases at 1200 • C where liquid phase bridges are observed with their characteristic incurved shape (see, for example, the circled area in Fig. 7-1200 • C). At 1300 • C crack bridging is observed (see the circled area in Fig. 7-1300 • C). The shape of this bridge, with straight borders suggests more a crack bridging by the growth of mullite crystals rather than by liquid bridges as observed at 1200 • C.

High temperature environmental scanning electron microscopy

Discussion

The microstructural evolutions characterised during the first heating, both by dilatometry and by in situ high temperature ESEM observations, will now be discussed by considering the four temperature domains previously defined from the matrix dilatometric curves.

In domain 1 (150 • C < T < 300 • C), shrinkage is observed both on the Bau-ULCC matrix and on the And-LCC curves and non-linear expansion curves characterise the two castables. High temperature ESEM observations reveal microcrack initiation, particularly at interfaces between the aggregates and the matrix. This must be related to hydrate conversion and dehydration processes that have been previously identified as operating in this temperature range [START_REF] Nonnet | Elastic properties of high alumina cement castables from room temperature to 1600 • C[END_REF][START_REF] Sarpoolaky | Influence of in situ phase formation on microstructural evolution and properties of castable refractories[END_REF][START_REF] Simonin | Room temperature quasi-brittle behaviour of an aluminous refractory concrete after firing[END_REF][START_REF] Guirado | Thermal decomposition of hydrated alumina cement (CAH 10 )[END_REF][START_REF] Parker | Refractory calcium aluminate cements[END_REF]. Fig. 8 shows the evolution of microcrack openings calculated by digital image processing of ESEM images for the two matrices. It can be clearly seen that microcrack opening increases when the temperature increases.

Between domains 1 and 2, dehydration process generally continue to occur. They can be responsible of the slightly non-linear expansion behaviour observed in this temperature range.

In domain 2 (800 • C < T < 950 • C), the two matrices are characterised by shrinkage, which is more pronounced for the Bau-ULCC one. For the two castables, non-linear expansion curves are observed again. In this domain 2, there is a direct correlation between the shrinkage measured by dilatometry and the acceleration of the dependence of microcrack opening as a function of temperature (see Fig. 8). Evidence of shrinkage was observed for the binder phase cells created by the microcrack network too. The differential thermal expansions between aggregates and matrix can be considered as responsible again. In this temperature domain, sintering starts to occur in the matrix while aggregates continue to expand. Nonnet et al. [START_REF] Nonnet | Elastic properties of high alumina cement castables from room temperature to 1600 • C[END_REF] have already observed a sintering start in CA or CAS cement based castables since 900 • C.

In domain 3 (1050 • C < T < 1150 • C), a low amplitude shrinkage is measured by dilatometry on the Bau-ULCC matrix and no evidence of shrinkage could be detected on the three other materials (And-LCC matrix, Bau-ULCC and And-LCC castables). Drastic changes could be observed in the microstructure of the Bau-ULCC and And-LCC matrix with the help of in situ high temperature ESEM observations. They consist in liquid phase appearance and in a disappearance of the granular aspect and of the microporosity of the binder phase. In this temperature domain, a liquid phase sintering starts to occur in both materials. Presence of microsilica in CA cements is known to lead to liquid formation via low melting phases in the CAS system at such temperatures [START_REF] Sarpoolaky | Influence of in situ phase formation on microstructural evolution and properties of castable refractories[END_REF]. Furthermore, similar shrinkage mechanisms have been observed by Nonnet et al in a CAS cement based castable [START_REF] Nonnet | Elastic properties of high alumina cement castables from room temperature to 1600 • C[END_REF]. The crystallisation of CA 2 as the product of a reaction between CA and alumina is known to occur in this temperature range too and to lead to a relative expansion volume of 13.6% [START_REF] Simonin | Room temperature quasi-brittle behaviour of an aluminous refractory concrete after firing[END_REF]. Thus there is so a competition between two phenomena: expansion due to the formation of CA 2 and shrinkage related to sintering. In the Bau-ULCC matrix, sintering effects are dominant since shrinkage is measured by dilatometry. In the And-LCC matrix evidence of sintering mechanisms are observed on in situ ESEM images but no shrinkage is measured by dilatometry. This indicates that the two competitive effects annuled each other leading to a linear dilatometric behaviour. The same comments can be done on the two castables, which are both characterised by a linear dilatometric behaviour in this temperature domain. In spite of this dilatometric linear behaviour with could suggest a microstructural stability, drastic microstructural changes take place in the material.

In domain 4 (1200 • C < T < 1300 • C), a high amplitude shrinkage is observed for the Bau-ULCC matrix and a only slight deviation from a linear expansion for the And-LCC matrix. It must be remembered that these matrix have different behaviours during the 1300 • C isothermal dwell. The Bau-ULCC one first exhibits a shrinkage before switching to expansion. The And-LCC one is characterised by an expansion behaviour all along the dwell. In situ ESEM observations allow to observe large amount of liquid phase in the two matrices. Fig. 9 shows an illustration of a liquid phase formation in domains 3 and 4 in a And-LCC matrix sample. At 1000 • C, small matrix particles are visible on an alumina tablet. At 1100 • C, liquid phase starts from these particules. Complete fusion of these particles is observed at 1200 and 1300 • C where liquid droplets are clearly seen. Their shape indicates the good wetting behaviour between the liquid phase and alumina. Furthermore, a coalescence of droplets is observed when increasing the temperature that indicates a viscosity decrease of this liquid phase. Liquid phase sintering mechanisms are clearly active in this temperature domain. These in situ observations confirm hypothesis of liquid phase sintering previously given to explain results on CAS cement based castables [START_REF] Sarpoolaky | Influence of in situ phase formation on microstructural evolution and properties of castable refractories[END_REF][START_REF] Simonin | Thermomechanical behavior of high-alumina refractory castables with synthetic spinel additions[END_REF]. Since 1300 • C crystal growth is observed, particularly in the And-LCC matrix. Because of their shape they are expected to be mullite crystals. This hypothesis is reinforced by the results of X-ray diffraction tests performed on the series of And-LCC matrix samples heated at different temperatures. They indicate the appearance of mullite when the temperature is greater or equal to 1300 • C. In this And-LCC matrix, mullite can form either from the andalousite particles or from a reaction between superfine alumina and fumed silica. In the Bau-ULCC matrix, only the second mechanism can occur. The competition between shrinkage mechanisms and expansion ones continues to occur in this temperature domain. The shrinkage ones remain dominant in the Bau-ULCC material and the expansion ones in the And-LCC material. In the two materials, microcrack healing is observed and can be related to the two types of mechanisms. On the one hand those are liquid phase sintering mechanisms that are active in microcrack healing, and on the other hand those are formations of CA 2 and of mullite.

Conclusion

Characterisation of the microstructural evolutions during first heatings of two commercial refractory castables (a bauxite based one and an andalousite based one) has been done by dilatometry and in situ high temperature environmental scanning electron microscopy up to 1300 • C. Investigations have been made both on the castables and on their respective matrices sieved at 200 m. Effects of microstructural changes have been observed by dilatometry with alternative linear expansion domains and shrinkage ones. Four temperature domains, in which shrinkage is occurring, could be defined. A good agreement was obtained between results of dilatometry and of in situ HT-ESEM observations. Important microstructural changes could be seen in these four temperature domains. They deal first with microcrack initiation in the 150-300 • C temperature range due to dehydration mechanisms. Then microcrack opening increases when increasing the sample temperature. An acceleration of these microcrack-opening mechanisms was observed when sintering starts, in the 800-950 • C temperature range. Between 1050 and 1150 • C, liquid phases appear in the material and liquid phase sintering starts to occur. An increase of the liquid phase amount and of liquid phase sintering effects are observed when increasing the temperature up to 1300 • C. Crystal growth was identified as occurring at this temperature too. Above 1100 • C, a competition between shrinkage mechanisms and expansion ones take place. The balance between these two types of mechanisms is not the same for the two studied refractory castables. In situ HT-ESEM observations appear as well suited to follow the microstructural evolutions in refractory castables during thermal cycles.

The complementary between dilatometry and in situ HT-ESEM observations has been seen. As an example, linear dilatometric behaviours have been measured that could suggest a thermal expansion and a microstructure stability. Furthermore, in the same temperature domain, drastic microstructural evolutions have been observed by in situ HT-ESEM. In such cases, the apparent linear dilatometric behaviour is the result of the competition between several mechanisms.

For this type of materials, results of such experiments are useful for a better understanding of their microstructural behaviour and of its influence on the thermomechanical behaviour.

Fig. 1 .

 1 Fig. 1. Dilatometric curves of the two castable matrices during the first heating.

Fig. 2 .

 2 Fig. 2. Dilatometric curves of the two castables during the first heating (only relative to increasing temperature).

Fig. 3 .

 3 Fig. 3. Dilatometric curves of the Bau-ULCC matrix during first heatings at different temperatures.

Fig. 4 .

 4 Fig. 4. Dilatometric curves of the And-LCC matrix during first heatings at different temperatures.

Fig. 5

 5 Fig. 5 shows the in situ HT-ESEM observations that have been made on a Bau-ULCC matrix sample during its first heating up to 1200 • C. This figure clearly illustrates one type of microcracking evolution frequently observed in this material at interfaces between bauxite aggregates and matrix rich areas. Microcracks initiate in the domain 1 (20 • C < T < 300 • C) and progressively open when increasing the temperature above this domain.Fig.6shows the microstructural evolutions in a And-LCC matrix samples during an in situ HT-ESEM test performed up to 1400 • C. An andalousite particule or aggregate (labelled AND) and a tabular alumina aggregate (labelled A) can be seen as embedded in the binder phase. At room temperature, the microstructure was free from any microcrack. Heating up to 150 • C has led to microcrack initiation, particularly at the interfaces between the binder phase and the two types of aggregates. From 150 to 800 • C, this microcracking process continues to occur by microcrack propagation and opening. Two microcracks (labelled 1 and 2 in Fig.6) propagate through the binder phase and finally join the two aggregates. Between 800 and 1000 • C, these mechanisms continue to occur and larger microcrack openings are observed both for aggregate/binder phase decohesions and for binder phase microcracks. A shrinkage of the binder phase cells, created by the microcrack network, is observed. Between 1000 and 1100 • C, the morphological aspect of the microstructure changes considerably. The granular aspect of the binder phase moves to a more homogeneous one. At 1100 • C, the appearance of a liquid phase can be clearly seen and is responsible of these evolutions. This continues to occur up to 1300 • C and the amount of liquid phase appears as increasing with the temperature. Binder particules, which can be observed on the alumina aggregate at 1000 • C, have begun to convert into a liquid phase at 1100 • C and progressively form liquid droplets on the alumina surface. Furthermore a progressive closing and/or healing of microcracks 1 and 2 is observed in the 1100-1300 • C temperature range. Since 1100 • C, microporosity between the binder phase particules progressively disappears, links or bridges are created between the binder phase and aggregates, crack bridging mechanisms are observed. Those are indications of a liquid phase sintering process in the material. But local volume expansion can take part in these mechanisms too. As an example, no evidence of a decrease of the distance between the andalousite aggregate and the alumina one can be observed in this in situ HT-ESEM image series. If only densification by liquid phase sintering was responsible of

Fig. 5 .

 5 Fig. 5. In situ HT-ESEM images at different temperatures during the first heating of a Bau-ULCC matrix sample showing microcracks at aggregate/matrix interfaces and their opening when increasing the temperature.

Fig. 6 .

 6 Fig.[START_REF] Altun | Effect of temperature on the mechanical properties of self-flowing low cement refractory concrete[END_REF]. In situ HT-ESEM images at different temperatures during the first heating of an And-LCC matrix sample showing microstructural evolutions (microcracking, liquid phase appearance, crystal growth and crack healing) when increasing the temperature.

Fig. 7 .

 7 Fig. 7. High magnification in situ high temperature ESEM images at different temperatures during the first heating of an And-LCC matrix sample showing microstructural evolutions in a microcracked area.

Fig. 8 .

 8 Fig. 8. Crack openings as a function of the temperature determined by digital image processing of in situ high temperature ESEM images.

Fig. 9 .

 9 Fig. 9. High magnification and high temperature ESEM images showing liquid phase appearance during the first heating in an And-LCC matrix sample.

Table 1

 1 Chemical analysis and data of the commercial castables

	Castable type	Bau-ULCC	And-LCC
	Aggregate type	Bauxite	Andalousite
	Al 2 O 3 (wt.%)	85	58
	SiO 2 (wt.%)	10	37.5
	CaO (wt.%)	1.1	2.3
	Fe 2 O 3 (wt.%)	1	0.9
	Maximum aggregate size (mm)	5	5
	Water requirement (wt.%)	4.2-5.2	4.5-5.5
	Open porosity (vol.%)	10	6
	Apparent density (kg/m 3 )	2970	2600

Acknowledgements

This work is made in the field of a French research program (PROMETHEREF) for improving the knowledge of thermal and mechanical properties of industrial refractories, involving three industrial partners and five public research laboratories. Authors wish to thank the French Ministry of Industry (Michel Mussino), TRB (Nicolas Prompt, Thierry Joly) and EDF (Patrick Billard, Yves Dutheillet) for their technical and financial support in this program, and Michel Boussuge, coordinator of the program (Centre Pierre Marie Fourt, Ecole des Mines de Paris) for helpful discussions. Authors wish to thank Serge Tovar and Aurélien Mazzoni for their implication in high temperature ESEM observations too.


Raffaele D'elia

Gilles Dusserre
email: dusserre@mines-albi.fr

Sylvie Del Confetto

Nicolas Eberling-Fux

C Dric Descamps

Thierry Cutard

Effect of Dicumyl Peroxide Concentration on the Polymerization Kinetics of a Polysilazane System

The effect of dicumyl peroxide (DCPO) concentration on the polymerization kinetics of a polysilazane system has been investigated through DSC analyses. DCPO acts as polymerization initiator by activating the polyaddition of vinyl groups. The overall heat of reaction is found to be a linear function of the DCPO concentration above 1.5 wt%, due to the addition of the heat of fully initiated polymerization and the heat of DCPO decomposition. Below 1.5 wt% of DCPO, the polymerisation of polysilazane is not fully initiated and only part of the reaction occurs. The resulting overall heat of reaction is therefore lower than that provided by the linear law valid for higher concentrations. A two-reaction kinetic model built on this interpretation leads to a satisfactory representation of the DSC analyses performed for each DCPO concentration between 0.1 and 20 wt%.

INTRODUCTION

Discovered in 1885 [1], polyorganosilazanes encompass a wide variety of silicon carbo-nitrides precursors utilized since the 1950s to prepare ceramic materials [2,3] from a single component [4]. Processed at the liquid state, they are particularly well suited for the preparation of Ceramic Matrix Composites (CMC) by Polymer Impregnation and Pyrolysis (PIP) [5][6][7]. Indeed, this multi-step process involves first the injection of the polymer into a fibrous preform and then the ceramization of the matrix through the pyrolysis of the precursor. The present work is a contribution to the optimization of CMC processed by PIP.

A first step of optimization was performed thanks to several works [8][9][10][11][12][13] aimed to reduce the volatilization of silazane oligomers in polyorganosilazanes formulations. Higher molecular weights were thereby achieved, together with denser polymers in the intermediate material and denser ceramics in the final product. The general molecular structure of polysilazanes is shown in Fig. 1, in an oversimplified way. By changing R 1 and R 2 groups, it is possible to adjust the electronic, optical and rheological properties of the material [14].

More recently, the studies focused on the mechanical and physical in-use properties of polysilazane-derived ceramics [15][16][17][18] or on the reactions involved in the polymer-to-ceramic transformation [19]. However the literature related to the processing properties of the precursors is much less detailed, except properties related to pyrolysis step [5,6]. A few papers investigate the properties of the intermediate polymer. In particular, viscosity is a key feature to design and optimize the PIP process, and is obviously strongly dependent on polymerization. The viscoelastic behavior of polysilazane derived preceramic polymers was investigated by Flores et al. [20,21] and D'Elia et al. [22]. From an industrial point of view, optimizing the process means to reduce the processing time without affecting the material quality, and inter alia requires the crosslinking kinetics to be known, minimized and controlled. Crosslinking of polysilazanes is usually performed by heating at 100-2508C [START_REF] Gmbh | Technical Information: CerasetV R PSZ 20[END_REF][START_REF]KiON Ceraset polyureasilazane and KiON ceraset polysilazane 20 heat-curable resins of KiON Corporation[END_REF], or alternatively by UV radiation [25,26].

Several reactions are involved in the crosslinking mechanism [27] (cf. section "Polysilazane Crosslinking Chemistry"), and some of them can be promoted using the suitable initiator or catalyst. For instance, Flores et al. [20] used tetra-n-butylammoniumfluoride to select a crosslinking mechanism involving dehydrogenation with Si-H and N-H groups to control the glass transition temperature, viscoelastic behavior and thermal stability of the polymer in order to optimize the processing of nonoxide ceramic fibers.

For processing CMC by PIP process, other mechanisms involving reactions without gazeous products (for instance polyaddition of vinyl groups) are more suitable to limit the matrix porosity.

Faster kinetics at lower temperature are made possible by adding a radical initiator, such as organic peroxide, most of the time dicumyl peroxide (DCPO) [START_REF]KiON Ceraset polyureasilazane and KiON ceraset polysilazane 20 heat-curable resins of KiON Corporation[END_REF][28][29][30][31], which is able to initiate polyaddition of vinyl groups [32]. The DCPO concentration recommended to reduce the crosslinking temperature ranges between 0.01 and 5 wt% [START_REF] Schwark | Isocyanate-and isothiocyanate-modified polysilazane ceramic precursors[END_REF][START_REF] Schwark | Thio)amide-modified silazane polymer composition containing a free radical generator[END_REF][START_REF] Schwark | Peroxide-substituted polysilazanes U.S. Patent[END_REF], but a comprehensive study on the effect of peroxide concentration on polymerization kinetics remains mandatory in the framework of material and process optimization.

DCPO is widely used as crosslinking agent in the polymer industry. Owing to a very exothermal heat of reaction (between 666 and 868 JÁg 21 [START_REF] Wu | [END_REF][37][38][39][40]), DCPO decomposition kinetics has been thoroughly studied in many conditions. In most cases, a pseudo-first order kinetic is reported, with reaction order between 3/4 and 1 [START_REF] Wu | [END_REF][37][38][39][40]. However DCPO decomposition kinetics was proved to be sensitive to environment [41]: in the absence of oxygen, DCPO decomposition follows a pseudo-first order kinetics model, whereas an autocatalytic model is more adequate in the presence of oxygen.

The scope of the present paper is to analyze the changes in the polymerization kinetics of a polysilazane system with different DCPO concentrations, with the aim to identify the optimal value and to account for DCPO concentration in a crosslinking kinetic model, on the basis of the autocatalytic model identified in [22] for a DCPO concentration of 1wt%.

EXPERIMENTAL

The commercial polysilazane under study is the ClariantV R KiON V R Ceraset V R PSZ 20. Stored in a dark, cool (48C) and dry place, the shelf-life of this pale yellow liquid is 6 months [START_REF] Gmbh | Technical Information: CerasetV R PSZ 20[END_REF]. Its density ranges between 1 and 1.1 gÁcm 23 , and its viscosity between 180 and 750 mPaÁs at 208C. Once crosslinked between 100 and 2508C, the liquid is converted to a solid polymer consisting of an alternated Si-N backbone with $80% methyl (CH 3 ) and $20% vinyl (CH 5 CH 2 ) side groups as shown in Fig. 2 [START_REF]KiON Ceraset polyureasilazane and KiON ceraset polysilazane 20 heat-curable resins of KiON Corporation[END_REF].

According to the manufacturer, the polymer solidifies after 2 h at 1008C, 1 h at 1508C, 40 minutes at 2008C and 20 minutes at 2508C in air. In an inert gas atmosphere, curing takes a longer time. Curing can be accelerated by addition of dicumyl peroxide (DCPO). The dicumyl peroxide (!98%) used in this work is produced by Sigma Aldrich V R and is stored in a dry, dark and cool place (48C). The chemical formula (C 6 H 5 C(CH 3 ) 2 OOC-(CH 3 ) 2 C 6 H 5 ) of DCPO, is presented in Fig. 3 that shows two benzene rings, four methyl groups (CH 3 ) and the classical peroxide group (O-O) [START_REF]Dicumyl Peroxide -National Center for Biotechnology Informations[END_REF]. Its molar mass is 270.37 gÁmol 21 .

Polysilazane and DCPO are mixed for 1 h at 293 K (208C) using a magnetic stirrer, up to attain the complete dissolution of the peroxide and then stored at 277 K (48C) for 12 h before testing in order to eliminate the air bubbles formed during mixing. Several dicumyl peroxide concentrations were investigated between 0.1 wt% and 20 wt%.

A series of preliminary tests was conducted using a Thermo-Gravimetric-Analysis (TGA) coupled with a Differential Scanning Calorimetry (DSC) under dynamic conditions, with a heating rate of 10 KÁmin 21 , using a TGDSC 111 of SETARAM. The study of dynamic cure kinetics change with peroxide concentration is then performed by Differential Scanning Calorimetry. All DSC tests are conducted on the compounds under dynamic conditions, with a heating rate of 2 KÁmin 21 . DSC tests on DCPO alone were conducted under dynamic conditions, with heating rates of 0.5, 2, 5 and 10 KÁmin 21 . A DSC-Q200 of TA Instruments was used to measure the specific heat of reaction (DH tot ) of the polymer and the specific heat of decomposition of the DCPO (DH DCPO ). The initial mass of the samples ranges between 10 and 20 mg and all tests were performed under continuous N 2 flow (50 mlÁmin 21 ) using a non-hermetic crucible. Temperature and enthalpy were calibrated with pure indium under the same conditions of heating rate, gas flow and crucible as used in the tests. [START_REF] Wu | [END_REF][37][38][39][40]. However, the behavior is quite different with two distinct peaks, whereas literature only reports one single peak. The nature of both peaks was not further investigated in the present study. It is noteworthy that a weak secondary peak has been neglected in [40].

RESULTS AND DISCUSSION

DCPO Decomposition

Actually, an n th -order model with coefficients reported in [START_REF] Wu | [END_REF]37,40,41] (Table 1) is able to properly describe the principal peak occurring in the present experimental results (second peak occurring at higher temperature in Fig. 4). Starting from the parameters reported in [START_REF] Wu | [END_REF]37,40,41] (Table 1) and assuming a pseudo first-order model for the second peak, a first set of parameters, labeled A, has been identified to fit the present experimental data with two uncoupled n th -order model (Eq. 1), each related to a part of the total heat of reaction (f for the second peak and 12f ð Þ for the first one). The set of parameters A considers that 87% of DH DCPO is due to the second peak. The set of parameters A is within the range of values reported in [START_REF] Wu | [END_REF]37,40,41] (Table 1) and provides a heat of reaction for the principal peak, DH 2 , of 904 JÁg 21 , slightly higher than DH DCPO values reported in [START_REF] Wu | [END_REF][37][38][39][40].

_ a DCPO 5k 1 Á e 2E 1 RT Á 12f2a 1 ð Þ n1 1k 2 Á e 2E 2 RT Á f2a 2 ð Þ n2 (1)
Assuming that the first peak does not affect the specific heat flow at the second one, the Kissinger method [43] was applied to identify the energy of activation. A value of 153.1 kJÁmol 21 was found and lead to a second set of parameters, labeled B, still assuming a pseudo first-order model for the principal peak. This method provides the best fit to experimental data and a heat of reaction DH 2 of 831 JÁg 21 (79% of DH DCPO ) was found for the principal peak, within the range of DH DCPO reported in [START_REF] Wu | [END_REF][37][38][39][40]. The value of 153.1 kJÁmol 21 for the energy of activation is significantly higher than those reported in [START_REF] Wu | [END_REF][37][38]40], between 125 and 139 kJÁmol 21 . However Lv et al. [39] found a value of energy of activation between 161 and 203 kJÁmol 21 using the Friedman isoconvertional method.

Polysilazane Crosslinking Chemistry

The crosslinking reactions of polysilazanes involve mainly the groups -CH 5 CH 2 (vinyl), Si-H and N-H. The main reactions, described hereinafter, are polyaddition of vinyl groups, radical reactions of methyl and vinyl groups, hydrosilylation, dehydrogenations and transamination. These reactions take place at different temperature ranges. According to Lavedrine et al. [27], the crosslinking starts at about 1208C with the hydrosilylation reaction (1), followed by dehydrogenation of Si-H with N-H (2). Transamination (3) takes place at approximately the same time, followed by polyaddition of vinyl groups (4), and dehydrogenation with two Si-H groups (5). The radical reactions of methyl and vinyl groups (6) occur at higher temperature, between 200 and 3008C [44].

According to the ATG-DSC analysis conducted on the PSZ20 resin alone, no significant reaction is observed up to 2008C (dashed black line in Fig. 5). However according to TGA analysis (dashed grey line in Fig. 5) a mass loss of 2.5% is observed at 2008C, which is attributed to dehydrogenation of Si-H with N-H groups. Above 2808C, an exothermal reaction starts, with a decrease of mass, which corresponds to the reaction of transamination. The sudden mass loss is produced by the higher mass of the ammonia product (NH 3 ).

The polyaddition of vinyl groups can be activated at low temperature by the addition of a free radical generator as DCPO. According to the literature [16,45], this reaction takes place for a temperature between 50 and 1508C for a polymethylvinylsilazane resin with addition of a peroxide cure initiator. After addition of 1wt% of DCPO, vinyl polyaddition is promoted with regard to dehydrogenation. This inversion in the reaction order should reduce the mass loss at 2008C. According to TGA results (continuous grey line in Fig. 5), mass loss is reduced by more than 60% at 2008C after addition of 1wt% of DCPO, confirming literature results. A sharp exothermic peak is obtained around 1508C.

Heat of Reaction

Figure 6 shows the dynamic DSC scans at 2 KÁmin 21 of the different tested solutions. DCPO concentration (represented by the variable x) ranges from 0.1 wt% to 20 wt%. Two effects are immediately observed with the increase of DCPO concentration: a gradual decrease of the peak temperature (from 1558C for 0.1 wt% to 1218C for 20 wt%), and the occurrence of a second exothermal phenomenon for a concentration higher than 3 wt%.

In Fig. 7 are plotted the DSC scans at 2 KÁmin 21 of the compounds with x values of 1, 5, 10 and 20 wt%, superimposed with the DSC scan of DCPO at 2 KÁmin 21 multiplied by the corresponding x value. A strong correlation is observed between the second peak of the compound and the principal peak of DCPO decomposition (almost the same amplitude), whose kinetics turns out to be slightly faster in the compound. Owing to these results, the second peak arising in the compounds for high DCPO concentrations will be attributed to DCPO decomposition in the forthcoming interpretations.

The first exothermal peak observed for the compound is therefore related to PSZ20 crosslinking. ATG-DSC results plotted in Fig. 5 show that this peak is not correlated to a significant mass loss. Reactions with gaseous products as dehydrogenation and transamination may thus be limited in the presence of DCPO. Moreover, the radical reactions of methyl and vinyl groups are expected to occur at higher temperature, between 200 and 3008C, according to [44]. Hydrosilylation and polyaddition of vinyl groups (promoted by DCPO) might be the principal reactions occurring in the crosslinking mechanism in the temperature range investigated.

According to this interpretation the overall heat of reaction (DH tot ), which represents the time integral of the curves plotted in Fig. 6, can be additively decomposed into two components, related on the one hand to the contribution of PSZ20 crosslinking (initiated by DCPO) and on the other hand to DCPO decomposition. Both components depend on the variable x, i.e. the mass fraction of DCPO. The evolution of the overall heat of reaction is presented in Fig. 8 as a function of DCPO concentration and can be well fitted using a bilinear model (Fig. 8), with coefficients of determination of 0.999 and 0.997 respectively. According to the previous discussion regarding the initiation of vinyl group polyaddition by addition of DCPO, it is important to notice that above a certain value of DCPO concentration, the initiator will simply degrade without interacting with PSZ20, forming radicals that will not combine with vinyl groups. Both terms of the overall heat of reaction are thus proportional to the concentration in the concerned reagent, respectively PSZ20 and DCPO, leading to a linear change of the heat of reaction with x. For low DCPO concentrations (below 1.52 wt%), the overall heat of reaction is lower than expected from this linear law. This is interpreted as a lack of DCPO to interact with all the vinyl groups available in the PSZ20 to complete the crosslinking mechanism related to vinyl groups polyaddition. In any case, to attain a complete degree of polymerization, it will be necessary to heat the system at 200-3008C, where transamination and dehydrogenation reactions will take place, involving Si-H and N-H groups.

Above 1.52 wt% of DCPO, DH tot can thus be expressed as a linear law, Eq. 2, by introducing the specific enthalpy of polymerization, DH p , and the specific enthalpy of decomposition, DH d .

DH tot 5DH p Á 12x ð Þ1DH d Á x if x ! 1:52 wt% (2)
By fitting the experimental data with Eq. 2, it is possible to assess the value of both specific heats of reaction. For x50, the intercept of Eq. 2 gives the specific heat of polymerization, Eq. 3, and the specific heat of DCPO decomposition in the compound is obtained for x51, Eq. 4. DH p 5231:87 J Á g 21

(3)

DH d 5964:92 J Á g 21 (4)
As explained above, when DCPO concentration is lower than 1.52 wt%, which represents the cross-point between both straight lines fitting the experimental data (Fig. 8), the reaction of polymerization will not be complete in the temperature range investigated, because radicals generated by DCPO decomposition will not be numerous enough to interact with all the active vinyl groups available in the system. In this low concentration range, an exponential-type function, Eq. 5, is introduced to account for the partial initiator effect in order to obtain a smooth function over the entire DCPO concentration range, instead of the bilinear one of Fig. 8.

DH tot 5DH p Á 12A 0 Á e 2 x x 0 Á 12x ð Þ1DH d Á x (5)
Despite its phenomenological origin, Eq. 5 can be interpreted as an increase in the probability for a vinyl group to interact with the initiator with higher DCPO concentration. 1 -A 0 would represent the part of all the vinyl groups available in the sample that can be initiated by a single DCPO molecule (when x tends toward zero). The remaining vinyl groups (a part A 0 of the total number) would have more probability to interact with DCPO if the concentration is high, what is described by the exponentialtype function. It is noteworthy that, according to this interpretation, the value of A 0 and x 0 would probably depend on the mass of the sample and on the heating rate.

According to these considerations, Eq. 5 expresses the overall heat of reaction over the whole DCPO concentration range up to 20 wt% with a single continuous and smooth function. Both parameters A 0 and x 0 are identified in such a way that Eq. 5 fits all the experimental data, providing the following values: A 0 5 0.18 and x 0 50.009.

The first term of Eq. 5 describes the transition from a partial polymerization of the system to a full one. The result of this equation for the overall heat of reaction is presented in Fig. 9, where the increase of DCPO concentration initially increases the heat of polymerization (exponential term), and then tends toward a linear decrease related to the decrease of PSZ20 concentration, accounted for by the term (1-x). The heat of decomposition obviously increases linearly with x. It can be checked in Fig. 9 that the experimental data of overall heat of reaction are satisfactorily fitted by Eq. 5 using the previously identified values of DH p , DH d , A 0 , and x 0 .

According to this model it is possible to define the maximum degree of conversion for polymerization reaction, Eq. 6, which will be used in the following section to model the cure kinetics of the system as a function of DCPO concentration.

a pmax 512A 0 Á e 2 x
x 0 (6)

Cure Kinetics Modeling

In a previous work [22], cure kinetics of PSZ20 with 1 wt% of DCPO was modeled using a Kamal-Sourour phenomenological model [46]. The parameters were identified using several isothermal DSC scans, taking into account the initial degree of conversion of the system after an initial heating rate. This model proved to properly describe both isothermal and dynamic scans. However the effect on polymerization of DCPO concentration was not considered, because the DCPO concentration, x, was not included in the model. Moreover DCPO decomposition was not considered.

For these reasons a more complex phenomenological model is necessary to describe the reaction kinetics of this system, taking into account a partial degree of conversion for both reactions of polymerization and decomposition. Reaction kinetics will be modeled using two phenomenological models, representing the decomposition of the dicumyl peroxide and the polymerization of the polysilazane. DCPO decomposition will be modeled using an n th -order model, Eq. 7, where n d is the reaction order and k d is the rate constant that follows an Arrhenius temperature dependence.

_ a d 5k d e 2E d RT Á 12a d ð Þ nd (7)
This model was already successfully applied to the modeling of DCPO decomposition kinetics [START_REF] Wu | [END_REF]37,[39][40][41] with a reaction order close to 1 (cf. section " DCPO Decomposition" and Table 1). The activation energy ranges from 118 to 139 kJÁmol 21 , the reaction order n ranges from 3/4 to 1 and the decomposition enthalpy ranges from 666 to 868 JÁg 21 [START_REF] Wu | [END_REF]37,[39][40][41]. The variability of these parameters depends on the type of identification algorithm used as well as the testing conditions. They are usually obtained for a 99 wt% pure DCPO, analyzed using a highpressure sealed pan to avoid evaporation during scanning. This means that the decomposition products will remain inside the capsule, interacting with the liquid DCPO (fusion point $ 508C). Such conditions of decomposition may not be representative of the decomposition that takes place in the PSZ20/DCPO solution, where further reactions that do not occur in the experiment reported in [START_REF] Wu | [END_REF]37,[39][40][41] could also take place. This may explain that the values of heat of decomposition obtained in [START_REF] Wu | [END_REF]37,[39][40][41] differ of about 10 to 30% from the value FIG. 10. Arrhenius rate constants for the Kamal-Sourour model (from isothermal DSC analyses reported in [22]). identified previously with Eq. 4. For this reason, the values of kinetics model parameters need to be identified from the present experiments performed using several compounds, even if the assumption of an n th -order model will be considered to describe DCPO decomposition. The experimental results obtained using DCPO only have not been used to identify the parameters of Eq. 7. PSZ20 polymerization will be modeled using a Kamal-Sourour phenomenological model [46]. Several authors used this law to model epoxy resins polymerization [47][48][49] or silicone rubber vulcanization [50], because of the autocatalytic and catalytic nature of the reactions driving the crosslinking of these systems. A previous work [22] shows that this model also satisfactorily describes the kinetics behavior of the compound of PSZ20 with 1 wt% of DCPO. This model, slightly modified in Eq. 8, includes two rate constants that follow an Arrhenius temperature dependence. m and n are the reaction orders. The reactions whose kinetics is described by Eq. 8 are assumed to be initiated by DCPO. An increase of initiator concentration acts as increasing the frequency of the interactions, and therefore increases the frequency factor and accelerates the reaction. This effect is described by the factor (x/x ref ) w added in the Kamal-Sourour model, Eq. 8. It is noteworthy that multiplying only the catalytic term by the factor (x/x ref ) w do not allow a proper fitting of the experimental results.

_ a p 5 x x ref w Á k o1 e 2E a1 RT 1k o2 e 2E a2 RT a p m a pmax 2a p À Á n (8)
In Eq. 8, the term a pmax allows accounting for the partial polyaddition of the vinyl groups for low DCPO concentration and for the dilution effect as a function of x, according to Eq. 5.

The overall heat of reaction is thus introduced as a function of x by this way. However this term is not sufficient to describe the shift of peak conversion toward lower temperature with the increase of DCPO concentration. For that reason, the reaction rate, Eq. 8, includes explicitly the dependence to DCPO concentration, x. In Eq. 8, x ref represents the DCPO concentration previously used in [22] to identify the K-S parameters, i.e. 1 wt%. This approach was already used in another paper [START_REF] Ruiz | Modeling of resin cure kinetics for molding cycle optimization[END_REF]. In the present work, an adjustable exponent w is necessary to properly fit the experimental curves over the entire DCPO concentration range.

The parameters of the PSZ20 polymerization model, Eq. 8, are identified from the isothermal DSC scans reported in [22] for a DCPO concentration of 1 wt%. The DCPO decomposition was neglected thanks to the very low concentration in initiator; the same procedure as described in [22] was thus used, but the polymerization heat of reaction identified previously in section " Heat of Reaction" is considered, accounting for a value of a pmax < 1. The rate constants for the present Kamal-Sourour corrected model, Eq. 8, are presented in Fig. 10. The parameters obtained for the Kamal-Sourour model in this paper (Table 2) are slightly different from those obtained in [22], where the effect of the model of decomposition was not taken into account and the maximal degree of polymerization was set to 1. For this reason, in the previous work, the parameters were overestimated with regard to the present work.

The value of the adjustable parameter w is obtained on the basis of the different dynamic scans with various DCPO concentrations. The value of 0.59 is identified in such a way that the temperature at the first peak matches the experiment up to x 5 5 wt%, i.e., PSZ20 polymerization is preponderant in the vicinity of the first peak.

The n th -order model parameters (Eq. 7) are identified using dynamic DSC scans in such a way that the model properly describes the end of the second peak for x > 5 wt%, where PSZ20 polymerization can be considered as complete. An activation energy of 130 kJÁmol 21 is obtained, in the range identified in [START_REF] Wu | [END_REF]37,40,41]. The value of the other parameters (Table 2) are of the same order of magnitude as those reported in [START_REF] Wu | [END_REF]37,40,41] (Table 1).

The parameters of this global phenomenological model, described by the set of Eqs. 5-8, identified using this procedure, are reported in Table 2. According to the parameters presented in Table 2, it is possible to plot the model results under dynamic conditions (2 KÁmin 21 ) for different DCPO concentrations (Fig. 11). The plot for 1 wt% (Fig. 11c) corresponds to the K-S model identified using isothermal conditions and the model of DCPO decomposition, while the other plots are obtained changing the DCPO concentration (parameter x) in Eqs. 5-8.

q5DH p Á 12x ð ÞÁ _ a p 1DH d Á x Á _ a d (9)
In Fig. 11 is presented the modeled overall specific heat flow, q, Eq. 9, (computed using the MatLab V R subroutine ode15s to integrate the set of Eqs. 6-9 and the experimental data (Fig. 11a-g). The contribution of each reaction (PSZ20 polymerization and DCPO decomposition) to the overall heat flow is plotted in Fig. 11h for a DCPO concentration of 10 wt% and shows that each peak is mainly related to one reaction. The model satisfactorily reproduces the shape of the first peak related to PSZ20 polymerization irrespective of the DCPO concentration, as well as the progressive occurrence of a second peak while increasing the DCPO concentration. A more quantitative comparison between model and experiment is carried out in Fig. 12, where the peak temperature is plotted against DCPO concentration (Fig. 12a). The discrepancy between the modeled and measured values of the temperature at the first peak is about 1 K, and reaches 5 K for the second peak. The specific heat flow at peak (Fig. 12b) is also almost perfectly reproduced by the model, excepted for x 5 3, 5, and 10 wt%, where the value at the first peak is significantly overestimated up to 10% for x 5 5 wt%. Despite the satisfactorily results provided by the model concerning the global shape of the curve and the effect of DCPO concentration on the characteristics of both polymerization and decomposition peaks, a significant mismatch between experiment and model is obtained between both peaks, where the model underestimates the specific heat flow for x ! 0.5 wt%. This phenomenon is probably related to the decomposition of peroxide, which may not exactly follow an n th -order model in the compound (cf. section " DCPO Decomposition"), and may also affect the end of polymerization. Indeed the main hypothesis of this model is that both kinetic models are completely uncoupled, neglecting the interaction between peroxide decomposition and polymerization. This model is probably too simplistic and a more mechanistic approach would be unavoidable in order to integrate polymerization dependence upon DCPO decomposition. This could be done introducing a catalytic term inside the Kamal-Sourour equation depending on the degree of conversion of DCPO decomposition. However the mechanisms ruling this phenomenon are not well understood and for this reason a more in-depth analysis should be performed, studying the decomposition/polymerization kinetics under isothermal conditions for a higher DCPO concentration (20 wt%): under these conditions the reciprocal influence of both phenomena could be better understood and a more detailed model could be introduced.

CONCLUSIONS

The polymerization reaction of a polysilazane system was studied in presence or not of DCPO. The reaction without addition of DCPO takes place above 2808C, driven by the reactions of transamination and polymerization of vinyl groups. To accelerate PSZ20 polymerization and reduce the peak temperature, addition of DCPO is necessary. In presence of this initiator, vinyl groups polyaddition takes place around 120-1508C, depending on DCPO concentration. The optimal specific heat of polymerization is obtained for a concentration of 1.52 wt% of DCPO. Above this value the evolution of the overall heat of reaction can be described using a linear law, with a specific heat of DCPO decomposition of 964.92 JÁg 21 and a specific heat of vinyl groups polyaddition of 231.87 JÁg 21 . Under this optimal value, a partial polyaddition reaction is observed, with a specific heat of polymerization depending on DCPO concentration through an exponential law. This describes a low probability of polyaddition initiation for low DCPO concentration. According to this interpretation it is proposed to describe the evolution of the final degree of conversion for both reactions of decomposition and polymerization. Cure kinetics is described according to two phenomenological models: an n th -order model for the decomposition of DCPO and a modified Kamal-Sourour model for the polymerization of PSZ20. A DCPO concentration dependent term is introduced in the Kamal-Sourour model to take into account the evolution of polymerization kinetics with DCPO concentration. This model includes 14 parameters: 4 parameters describe the change in overall specific heat of reaction with DCPO concentration; 6 parameters for the Kamal-Sourour model are identified from a complete characterization reported in [22] involving isothermal and dynamic DSC tests; 3 parameters for the n th -order model to describe the second peak; and one parameter to match the first peak shift with changing DCPO concentration. This model reproduces very satisfactorily the evolution of peak temperatures and intensities of both reactions, although a little mismatch between experimental data and the results of the model is observed between both peaks.

ACKNOWLEDGMENTS

The collaboration with Snecma and Herakles is gratefully acknowledged. This work was supported under the PRC Composites, French research project funded by DGAC, involving SAFRAN Group, ONERA and CNRS (Contract reference number: 1554448A).

NOMENCLATURE a

Overall degree of conversion (compound), dimensionless.

_ a i

Temporal derivative of a i (reaction rate), s

Figure 4

 4 Figure 4 depicts the results of DSC scans performed on DCPO samples at 0.5, 2, 5 and 10 KÁmin 21 . The heat of decomposition, DH DCPO , ranges between 1,002 JÁg 21 (5 KÁmin 21 ) and

FIG. 3 .

 3 FIG. 3. Dicumyl peroxide chemical formula: C 6 H 5 C(CH 3 ) 2 OOC-(CH 3 ) 2 C 6 H 5 [42].

FIG. 6 .

 6 FIG. 6. Specific heat flow versus temperature of PSZ20 with several DCPO concentrations during dynamic DSC scans at 2 KÁmin 21 .

FIG. 7 .

 7 FIG. 7. Comparison of dynamic DSC scans at 2 KÁmin 21 for several compounds with various DCPO concentrations, x, and for DCPO alone weighted by x: (a) x 5 1 wt%, (b) x 5 5 wt%, (c) x 5 10 wt%, and (d) x 5 20 wt%.

FIG. 9 .

 9 FIG. 9. Overall heat of reaction versus DCPO concentration: experimental values (squares) and results of the model (__) accounting for DCPO decomposition (. . .) and polymerization of PSZ20 (-), including a partial polymerization for low DCPO concentrations.

TABLE 2 .

 2 Kamal-Sourour model parameters obtained with isothermal identification (x 5 1 wt%) and n th -order model parameters obtained with dynamic scans (x 5 5, 10, and 20 wt%). Kamal-Sourour model for polysilazane crosslinking k o1 5 1.66 3 10 13 s 21 E a1 5 124.73 kJÁmol 21 m 5 2.54 k o2 5 2.38 3 10 16 s 21 E a2 5 143.12 kJÁmol 21 n 5 1.11 n th -order model for DCPO decomposition (compound) k d 5 5.00Á10 13 s 21 E d 5 130.00 kJÁmol 21 n d 5 1.15

FIG. 11 .

 11 FIG. 11. Model results for several DCPO concentrations compared to experiment: (a) x 5 0.1, (b) 0.5, (c) 1, (d) 3, (e) 5, (f) 10, and (g) 20 wt%; (h) contribution of PSZ20 polymerization and DCPO decomposition to the overall heat of reaction computed for x 5 10 wt%.

FIG. 12 .

 12 FIG.12. Comparison of experimental and computed (a) peak temperature and (b) specific heat flow at peak for both first polymerization peak and second decomposition peak when it exists. The experimental data related to the second peak for x 5 5 wt% are measured at the minimum slope, since there is no local maximum on this curve.

Table 1 )

 1 .

  1,091 JÁg 21 (0.5 KÁmin 21 ). The average value, 1,051 6 37 JÁg21 , is significantly higher than the results of other studies, between 666 and 868 JÁg21

TABLE 1 .

 1 DCPO decomposition kinetics parameters identified from the present results compared with literature data[START_REF] Wu | [END_REF][37][38][39][40][41].DH DCPO (JÁg 21 ) E i (kJ.mol 21 ) k i (s 21 ) n i

	Wu et al. [36]		741.15-750.52	125.35-125.39	3.06-3.12 3 10 12	0.86-0.90
	Wu et al. [37]		666-813	132-139	2.15 3 10 13 to 1.44 3 10 14	0.85-1.00
	Ben Talouba et al. [38]	855.2-867.8	135 6 2	1.18 6 0.017 3 10 10	1.01 6 0.01
	Chen at al. [39]		774-837	161-203	NA	3/4
	Duh et al. [40]		810.5	129.7	1.26 3 10 13	1
	Di Somma et al. [41]	NA	129.9 6 0.2	6.5 6 0.83 3 10 12	1
	Present work		1051 6 37
	Set A	1 st peak (i 5 1)	DH 1 5147	105	5.0 3 10 10	0.5
	f50:87	2 nd peak (i 5 2)	DH 2 5904	139	1.64 3 10 14	1
	Set B	1 st peak (i 5 1)	DH 1 5221	110	2.25 3 10 11	0.58
	f50:79	2 nd peak (i 5 2)	DH 2 5831	153.1	8.81 3 10 15	1

  JÁg21 .DH totTotal specific heat of reaction (compound), JÁg21 . DH 1 Specific heat of decomposition for the first peak (DCPO alone), JÁg 21 . DH 2 Specific heat of decomposition for the second peak (DCPO alone), JÁg 21 . f5 DH 2 Pre-exponential factor for the second peak (DCPO alone), s 21 . k d Pre-exponential factor for DCPO degradation (compound), s 21 . m Pseudo-order of polymerization (autocatalytic component, compound), dimensionless. Specific heat flow measured by DSC, WÁg 21 . R Ideal gas constant, JÁmol 21 ÁK 21 . T Temperature, K if not specified. x DCPO weight fraction in the compound, dimensionless. x 0 Fitting parameter of DH tot x ð Þ for 0 < x < 0:015, dimensionless. x ref DCPO weight fraction used to calibrate the Kamal-Sourour model from isothermal DSC tests in [22], dimensionless. w Fitting parameter that controls the peak temperature shift with varying x, dimensionless.

	k 2
	n	Pseudo-order of polymerization (catalytic compo-
		nent, compound), dimensionless.
	n 1	Pseudo-order of reaction for the first peak (DCPO
		alone), dimensionless.
	n 2	Pseudo-order of reaction for the second peak
		(DCPO alone), dimensionless.
	n d	Pseudo-order of reaction for DCPO degradation
		(compound), dimensionless.
	PSZ20	Commercial designation of the polysilazane resin.
	q
							21 .
		a 1	Degree of conversion for the first peak (DCPO
			alone), dimensionless.
		a 2	Degree of conversion for the second peak (DCPO
			alone), dimensionless.
		a d	Degree of DCPO degradation (compound),
			dimensionless.
		a DCPO	Degree	of	degradation	(DCPO	alone),
			dimensionless.
		a p	Degree	of	polymerization	(compound),
			dimensionless.
		DH d	Specific heat of DCPO decomposition (compound), JÁg 21 .
		DH DCPO	Total specific heat of decomposition (DCPO alone), JÁg 21 .
		DH p	Specific heat of polymerization reactions (com-
		Part of DH DCPO attributed to the second peak, pound), DH DCPO dimensionless.
		A 0	Fitting parameter of DH tot x ð Þ when x tends toward 0, dimensionless.
		DCPO	Symbol for dicumyl peroxide.
		E 1	Activation energy for the first peak (DCPO alone), kJÁmol 21 .
		E 2	Activation energy for the second peak (DCPO alone), kJÁmol 21 .
		E a1	Activation energy of polymerization (catalytic com-ponent, compound), kJÁmol 21 .
		E a2	Activation energy of polymerization (autocatalytic component, compound), kJÁmol 21 .
		E d	Activation energy of DCPO degradation (com-pound), kJÁmol 21 .
		k 01	Pre-exponential factor for polymerization (catalytic component, compound), s 21 .
		k 02	Pre-exponential factor for polymerization (autocata-lytic component, compound), s 21 .
		k 1	Pre-exponential factor for the first peak (DCPO alone), s 21 .

Contract grant sponsor: DGAC; contract grant number: 1554448A.