Farida Souiah

Monika Salzbrunn

ISSRC Simon Mastrangelo

Hope and disillusion. The Depiction of Europe in Algerian and Tunisian Cultural Productions about Undocumented Migration

Keywords: undocumented migration, harraga, Algeria, Tunisia, cultural production, music, imaginaries

Combining digital humanities, cultural studies and migration studies, this chapter analyses the depiction of Europe in Algerian and Tunisian cultural productions about undocumented migration. These cultural productions are used as gateway to imaginaries of migration and imaginative geography. Europe first appears as a fortress and a land that is especially hard to reach as well as a land where everything is possible: a land of freedom where one can succeed and be accomplished. However, Europe is not only the land of hope but also the land of disillusion. Cultural productions about undocumented migration sometimes portray the loneliness of migrants or the racism that they face. These works also speak of the economic hardships, as well as the fear of being expelled from this land that they risked so much to reach.

Finally, the present chapter provides a constructive alternative to mechanistic approaches in migration and diaspora studies. We will analyze the different artistic strategies for expressing the agency of the harragas, that are rooted in their imagination, but still evolving in a specific political, social and economic context.

Borders between North Africa and Europe are increasingly difficult to cross because of the implementation of restrictive migration policies [START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF]. Despite these restrictions, migrants and refugees attempt to leave their home country without passports or visas, often on boats, and usually at a great risk to their lives. The Mediterranean Sea has become the deadliest migration route in the world (IOM, Missing Migrants Project 2016). In the Maghrebi dialects, those who leave without documentation are called harragas, literally "those who burn" 1 the borders. This name reflects that fact that they do not respect the mandatory steps for legal departure. Also, they figuratively "burn" their papers to avoid deportation once in Europe.

This form of migration-harga (the burn)-is a source of inspiration for many artists [START_REF] Peraldi | S'arracher : la harraga des mineurs en Algérie[END_REF]. Songs (Salzbrunn, Souiah and Mastrangelo 2015a;[START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF], films, and many forms of art have depicted harragas [START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF]. The discourse about migration and borders in art stands in contrasts to political and media discourse mainly because it focuses on the narratives of the migrants themselves [START_REF] Canut | Les voix de la migration. Discours, récits et productions artistiques[END_REF]. In addition, some harragas post content online that is related to their migratory desires and their "adventures" [START_REF] Bredeloup | L'aventurier, une figure de la migration africaine[END_REF][START_REF] Timera | Aventuriers ou orphelins de la migration internationale[END_REF][START_REF] Gaibazzi | The Quest for Luck: Fate, Fortune, Work and the Unexpected among Gambian Soninke Hustlers[END_REF][START_REF] Bachelet | Irregular Sub-Saharan Migrants in Morocco : Illegality, Immobility, Uncertainty and 'adventure' in Rabat[END_REF]. For example, they create create pages dedicated to this topic on Facebook, where they also post and comment on footage shot during their journey across the Mediterranean. They also share the videos they create using images and songs they find on the web [START_REF] Salzbrunn | Digital humanities. Empowering through Art and Music. Tunisian Representation of Europe through Music and Video Clips[END_REF]. In this chapter, we purposely choose not to distinguish between "high art" and "low art," nor between "art" and "non-art." Therefore we will invoke the notion of "cultural productions" to refer to songs, books, paintings, videos, collages and Facebook posts about harga. These cultural productions, which are both digital and non-digital, are used as gateway to imaginaries of migration 1 The verb "to burn" in Arabic can mean "to free ride", "to jump a queue" or to "run a light". [START_REF] Martin | À la quête des OPNI (objets politiques non identifiés). Comment traiter l'invention du politique ?[END_REF](Martin , 2003)).

These imaginaries are "culturally shared and socially transmitted representational assemblages that interact with people's personal imaginings and are as used as meaningmaking devices and world-shaping devices" (Salazar 2014: 124). Moreover, "They are imaginary in a double sense: they exist by virtue of representation or implicit understandings, even when they acquire immense institutional force; and they are the means by which individuals understand their identities and their place in the world" (Gaonkar 2002: 4). A focus on mechanistic economic visions and macro-political approaches have dominated the study of migration [START_REF] Wihtol De Wenden | Vers un droit universel à la mobilité[END_REF]. The study of imaginaries as an important factor in the decision to migrate is quite recent and remains rare despite the pioneering work done by Abdelmalek Sayad (1975). In his article "El ghorba: From original sin to collective lie," he describes the mythification of migration in rural Kabilya and notably the collective misrecognition of the migrants' life as workers in France [START_REF] Sayad | El ghorba: From original sin to collective lie[END_REF]. Various social scientists have subsequently analysed social imaginaries in relation to the decision to migrate [START_REF] Barrère | La modernité et l'imaginaire de la mobilité : inflexion contemporaine[END_REF][START_REF] Bredeloup | L'aventurier, une figure de la migration africaine[END_REF][START_REF] Camacho | Migrant Imaginaries: Latino Cultural Politics in the U.S.-Mexico Borderlands[END_REF][START_REF] Friese | Ya l'babor, ya mon amour: Raï, Rap and the Desire to Escape[END_REF][START_REF] Karoui | Les mirages de l'émigration au miroir du cinéma égyptien[END_REF][START_REF] Lacroix | L'imaginaire migratoire chez les jeunes Marocains[END_REF][START_REF] Mbodji | Imaginaires et migrations. Le cas du Sénégal[END_REF][START_REF] O'reilly | The Role of the Social Imaginary in Lifestyle Migration: Employing the Ontology of Practice Theory[END_REF][START_REF] Poulet | De Paris à Dakar, discours croisés et enjeux autour de la mémoire de l'expérience migratoire[END_REF][START_REF] Ragaru | Imaginaires et itinéraires migratoires bulgares en Europe. Une introduction[END_REF]Salazar 2010aSalazar , 2010b[START_REF] Salazar | Migrating Imaginaries of a Better Life… Until Paradise Finds You[END_REF][START_REF] Salzbrunn | Undokumentierte Mobilität (Tunesien-Schweiz) und digital-kulturelle Ressourcen nach dem Arabischen Frühling[END_REF][START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF][START_REF] Timera | Aventuriers ou orphelins de la migration internationale[END_REF][START_REF] Vigh | Wayward Migration: On Imagined Futures and Technological Voids[END_REF]. Following Salazar, this article builds on the observation that "The motivations to cross boundaries are usually multiple, but they are largely linked to the capacity of migrants and their social networks to imagine other places and lives" (Salazar 2011: 577).

Analysing images and representations is even more crucial in a postcolonial migratory context. As Edward Said argues, "Just as none of us is outside or beyond geography, none of us is completely free from the struggle over geography. That struggle is complex and interesting because it is not only about soldiers and cannons but also about ideas, about forms, about images and imaginings." (Said 1993: 7) Inspired by Said's concept of imaginative geography, we study the images of Europe in Algeria and Tunisia as rooted in a specific power relation. However, this article breaks with a focus on the images of the dominant and how they perceive and construct the "others" and "otherness". Rather, it focuses on the imaginative geography of those who are socially, politically and geographically at the margins: the subaltern.

This article also treats Algeria and Tunisia together rather than employing a comparative perspective, since the representations of Europe in cultural production in Algeria and Tunisia contain similar themes 2 . In both cases, the images of Europe are neither homogeneous nor consistent. Europe first appears as a fortress and a land that is especially hard to reach. The cultural productions about harga also evoke Europe as the land where everything is possible: a land where one can succeed and be accomplished. Some of these works depict a picturesque Europe, while others focus on material gain such as money and cars. Europe also appears as the land where one can free oneself from social pressure and where one can for example, drink and flirt openly. However, Europe is not only the land of hope but also the land of disillusion. Cultural productions about harga sometimes portray the loneliness of migrants or the racism they experience on the other side of the Mediterranean. They also speak of the economic hardships they face, as well as the fear of being expelled from this land that they risked so much to reach. Finally, the present chapter provides a constructive alternative to mechanistic approaches in migration and diaspora studies. We will analyse the different artistic strategies employed to express the agency of the harragas, which is rooted in the force of their 2 This chapter is based on data collected for a Ph.D. thesis about harga and contestation in Algeria [START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF] and on data collected as part of a project directed by Prof. Monika Salzbrunn and funded by the Swiss National Science Foundation entitled "Undocumented Mobility and Digital-Cultural Resources after the 'Arab Spring'". Simon Mastrangelo is completing his Ph.D. as part of this project and Farida Souiah is a postdoctoral fellow. As part of her dissertation, Souiah interviewed 30 harragas and their family members in Oran and Mostaganem. She analyzed Algerian artistic productions such as songs, movies, novels, paintings, political cartoons, etc.) during eight months of fieldwork in 2011. The results of the "Undocumented Mobility and Digital-Cultural Resources after the 'Arab Spring'" project are based on three years of ethnographic fieldwork in Tunisia, Europe and in the digital space: we notably analyzed a corpus of 54 Tunisian songs and 20 private and public pages on Facebook.

imagination, but also draws on a specific political, social and economic context.

Europe as Fortress

Cultural productions about harga often depict restrictive migration policies and visa restrictions. Mobility constraints are notoriously more difficult for the citizens of the Global South, as all passports do not have the same "power": they do not grant the same rights to their holders. For instance, in 2016, German and French passports allow their holders to visit 158 and 156 countries respectively. That is, their holders were allowed on foreign soil without a visa (or by getting a visa directly at the border), whereas an Algerian can visit only 48 countries and a Tunisian 61 countries in similar conditions. The right to mobility is fragile and highly unequal [START_REF] Barry | Free Movement: Ethical Issues in the Transnational Migration of People and of Money[END_REF][START_REF] Corradi | Le droit à la mobilité: nouvel horizon pour penser les migrations[END_REF][START_REF] Golash-Boza | Causes and consequences of international migration: sociological evidence for the right to mobility[END_REF][START_REF] Miaille | L'état du droit à la mobilité[END_REF][START_REF] Pécoud | International Migration, Border Controls and Human Rights: Assessing the Relevance of a Right to Mobility[END_REF][START_REF] Wihtol De Wenden | Vers un droit universel à la mobilité[END_REF], 2013). While some are denied the right of entry in the Global North because they are perceived as potentially "undesirable" migrants [START_REF] Agier | Gérer les indésirables : Des camps de réfugiés au gouvernement humanitaire[END_REF], borders are less constraining for other subjects-even if their passport does not grant them the right to mobility-who have resources such as money, qualifications, or networks.

Social scientists have document the closing of borders and the restrictive migration policies that comprise the basis of unequal mobility, noting that migration policies shifted in the 1970's [START_REF] Massey | Worlds in Motion: Understanding International Migration at the End of the Millennium[END_REF]). This "historical moment" marked the entry in a "new migration world" where migration policies were primarily understood as tools of control [START_REF] Guiraudon | Controlling a New Migration World[END_REF]. Indeed, since the 1970's, migration has been perceived mainly as a problem since migratory flows are generally unplanned [START_REF] Cvajner | Theorizing Irregular Migration: The Control of Spatial Mobility in Differentiated Societies[END_REF]. This negative perception of migration directly impacted the mobility regime. Those who claim to stay for a short period of time are now suspected of presenting false motives and secretly harbouring a desire for a more permanent migration. According to Paolo Cuttitta, the imposition of visas is the primary instrument of migration control policies [START_REF] Cuttitta | Le monde-frontière. Le contrôle de l'immigration dans l'espace globalisé[END_REF]. Moreover, individuals are systematically suspected if they belong to a country of emigration or that is politically unstable.

As Didier Bigo notes, this suspicion makes "the granting of a visa (…) an exception to the exclusion" and "obeys a logic of rarity "in the minds of those who deliver them" (Bigo 2010: 254).

Due to the restrictive and unequal nature of migration policies, cultural production on harga predominantly represents Europe as a land that is hard to reach or even as a fortress. Seen from the harragas' point of view, Europe is a place of rejection and exclusion, where one is deemed unworthy of a visa. Harragas are on the "wrong" side of both the geographical and social divide; because they are mainly young urban men without professional qualifications, getting a visa for Europe is almost impossible. For the European consulates, they are a "migratory risk" if not a "security threat." How does this system of (im)mobility shape the representations of Europe in Tunisian and Algerian cultural productions?

To answer this question, we looked at several pieces of art and at the artistic production published on various Facebook pages. The first of these cultural productions is a work by Zineddine Bessaï, a graphic designer and a visual artist born in Algiers in 1985. He graduated from the Graduate School of Fine Arts in Algiers in 2010 and his work is often tinged with humour. In this piece, he takes inspiration from the urban environment of Algeria, notably from daily life in popular neighbourhoods and the language used on the street. One of his pieces about harga is entitled "H-Out: the guide to immigration. The "H" stands for harragas and the title implies that harragas are kept out of Europe. Moreover, "Hût" is a transliteration of the plural of the word "fish" into dialect. This play on words allows the artist to reference to a popular expression among the harragas who say they would rather be eaten by fish than by 203 worms 3 . This expression emphasizes the fact that these individuals are ready to die trying to leave, and see this fate as preferable to rotting in Algeria. This work is composed of two pieces. One of the two pieces is a map of the world that represents the migratory imagination of young Algerians. The map's key is written in both the Algerian dialect (using the Latin alphabet) and in French. The French version offers more-or less accurate translations of dialect. In addition to this map, there is a collage in which the artist depicts three harragas. The work, with the full title of "H-out: the guide of immigration," is supplemented by a leaflet in which the artist explains his approach, including the centrality of the popular expressions. Bessaï could not go to England for the opening of the exhibition because his visa was denied [START_REF] Sheerin | Zineddine Bessaï denied entry into UK[END_REF]. Unsurprisingly, perhaps, Bessaï deals extensively with the topic of visas. He links the restrictive visa policy to harga. In "H-out," the body of the three harragas is made of a Schengen short stay visa application form -those applications that often lead to a visa refusal or which are never even completed by the would-be migrants who are convinced that getting a visa is impossible.

In this depiction, the artist has drawn a cross in the place where the harragas heart would be. This pictogram usually indicates something that is harmful or irritating. In Bessaï's work, this image is associated with the need to obtain a visa. It is also present in the map that composes "The Immigration Guide H-out." This map represents space as it is experienced by harragas. For example, Europe is called "Schengen Oropa." In Europe and North America, there are numerous white crosses on a red background. The green places -indicating that Algerians can travel to the country without a visa application -are rare on this map. The artist also chooses to physically represent the boundaries by a double barbed wire that cuts the map in half and separates the South from the North. The border runs to the south of the United States, Spain, France of Italy and Australia. Yet in order to indicate that the boundary remains porous, and to express his opposition to the limits placed on mobility, the artist draws pairs of scissors at various points near the border to indicate that it could be "cut off", in other words, crossed.

Another body of work that deals with harga is found in Algerian and Tunisian literature.

In his novel, "He Will Have Mercy on Us" (Il aura pitié de nous), published in 2004, Roshd Djigouadi, evokes the visa issue and mobility constraints in a very subtle manner. The story is set in the early 2000s. The hero narrator, Adel, is an Algerian hittiste 4 who lives on petty crimes and small jobs. He recounts his boredom, his unhappiness, his sexual frustration and his desire to leave Algeria. The novel opens when Adel meets Omarou, a Malian migrant who is travelling through Algeria to try to reach Europe. The reader follows a few months of the life of Omarou, Adel and his friends in a popular neighbourhood (houma), of Algiers. Adel dreams of migrating, but does not take any action to leave Algeria, while Omarou works hard, mainly doing construction work to collect the money he needs to get to Europe. Adel wishes he was born a few years earlier, when it was still possible to migrate. In fact, he is able to use the mobility system as a means of income; at dawn he wakes, gets in line at the French consulate in Algiers, and charges those who are applying for a visa in order to take his place in line.

When one of his friends asks why Adel why he never bothers to ask for a visa himself despite his frequent visits to the consulate he answers: "I am a free man; I don't need a visa. A little bit of salty water is not going to bother me" (Djigouadi 2004: 31). However, despite these flippant comments, the narrator compares Europe to a fortress and the Mediterranean Sea to a cemetery. Here, he expressed a vision vision of Europe similar to that found in Bessaï's work.

Yet the notable difference is that Adel clearly decides to ignore the reconstruction of borderlines and the introduction of visa (which was not foreseen in the French-Algerian Evian treaty of 1962 and which was introduced in 1986 by the French government).

Algerian [START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF] and Tunisian (Salzbrunn, Souiah & Mastrangelo 2015a) music both invoke the theme of constraints on mobility. In terms of musical genre, this phenomenon is seem mainly in Algerian raï 5 and Tunisian mizwed6 , while both countries have a tradition of 4 "Untranslatable term, a mix of French and Arabic, connotes the young Algerians who hang out, leaning against the walls (heit), whose 'task' is to support the walls. Because schools are overcrowded and unemployment runs high, many young Algerians are forced into the street" ('Abd al-Haq, Verges and Hiltermann 1995: 14). 5 Raï (the word literally means "opinion" in North African dialects) is an Algerian popular musical genre that originally arose in the city of Oran [START_REF] Virolle-Soubiès | Le raï entre résistances et récupération[END_REF]. Because of its topics -among which feature alcohol, love and sex -and the music scene that it emerged in -cabarets, raï has a subversive dimension. Raï is also known internationally as part of the "word music" genre [START_REF] Nooshin | Music and the Play of Power in the Middle East, North Africa and Central Asia[END_REF]. politicized rap. For example, the Algerian rapper Lotfi Double Kanon describes a world where borders are closed. Cheb Belkheir sings that he is tired of "regrets" and begs for "Schengen".

In Algerian street language "regrets" refers to visa denials (in reference to the formula of politeness "We regret to inform you…") while "Schengen" refers to the short-stay visa common to the Schengen Area. Abdelkader Boukabouss repeats that he has neither a passport nor visa. He accuses European countries (that he does not name) of "cherishing" visas while harragas risk their lives. For the singer Reda Taliani, if young Algerians risk their lives while trying to reach Europe, it is because they cannot get a visa to travel legally.

The representation of passports and visas are a recurring theme on the Facebook pages about harga. The administrators and the members post pictures of EU passports, often with euros, highlighting the resources they embody. The administrator posted a picture of two passports laying on coins. On the image, it is written in dialect, using a mix of Arabic and Latin alphabet, "Give me a visa and leave me". Few weeks later, the administrator posted a collage made of several images among which many refer to the mobility constraints, notably passports with the inscription "denied" in French, Arabic and English and migrants in detention centers.

It is interesting to note that this collage does not focus only on the Mediterranean but evokes the Mexican-US border case -testifying to the existence of a global space where people endure similar circumstances. The road to "Paradise" or to "Italy" is also a common image used by artists on Facebook, even though the authors are aware of the fact that the living conditions are extremely difficult on the other shore of the Mediterranean Sea.

Cultural productions and Facebook pages about harga reflect the frustration of those who are marginalised by the visa system. They are both a reflection of migratory imaginaries even while they also influence these expectations. Therefore, it is not surprising that we found the singing, a type of bagpipe(...). Mizwid is a music which looks to rural, 'popular' song types for its roots, yet developed in Tunisia's capital city. Thus it is an urban 'popular' music, which uses rural instruments, rhythms and musical modes, in complete contrast to its 'classical' counterpart" (Stapley, 2006, p. 244). This genre of music has long been associated with marginalized groups. a very similar discourse among the harragas that were interviewed and observed as part of our fieldwork. For example, Sofiane was 30 years old in 2011, when he tried to leave Algeria on a small boat that was arrested at the Spanish shores, near Almeria. When asked about visas he said "I did not ask for a visa. They will not give me a visa. They give visas to people with money, merchants and businessmen. They give visas to old people, married people and retired people. They don't give visas to people like me. Why would I bother asking for a visa?" (Sofiane, 30 years old, Oran, 2011). Ali, who tried to leave Tunisia in 2011 when he was 17 years old, considers visa constraints to be inhuman. He implicitly evokes mobility as a right and denounces this regime inequality: "Explain something to me. You are a human being and I am a human being. You are French and I am Tunisian. You can come here and a have a coffee with me with only your ID card (…). Why do I need a visa if I want to visit you? Are you better than me? Why can you come to my country and visit it with your ID card? (…) How are you better than me? It took 9 months to conceive you and it took 9 months to conceive me" (Ali, 21, Tunis, 2015). The argument of social (in) justice is frequently expressed by Tunisians who desire equal treatment between themselves and the Europeans who visit their country.

Mobility is a discriminating factor both at an international level (between the Global North and the Global South) as well as within Algeria and Tunisia where those who have economic and cultural resources have facilitated access to obtaining a visa. In cultural productions and online forums "Burning" the borders and discrediting the visa system is a form of resistance to the unequal access to international mobility. It is a form of agency. Especially since migration is also a way to escape the hardship of daily life and experience a land where one may encounter new opportunities.

Europe as a Land of Opportunity

Media and political discourses about migration, especially undocumented migration, often emphasize the naïveté of the migrants, pointing to their gullibility and belief in an "Eldorado".

Originally, this expression referred to a legendary lost city with abundant wealth, and it has been a persistent myth since the 16 th -17 th century and the conquest of the New World. Today, the Eldorado is a metaphor for a place where one can become wealthy quickly, notably in a migratory context. The belief that migrants are misled by their own imaginaries is so strong that the International Organization for Migration (IOM) set up a program named Salemm (Solidarity with Children of the Maghreb and the Mashreq) in Morocco, Tunisia and Egypt.

The goal of the program is to depict the lives of undocumented migrants in Europe. The IOM finances cultural activities, notably plays, music and film workshops to try to contradict the depiction of Europe as an Eldorado7 .

Cultural productions about harga often evoke Europe as an abstraction, a place that is "over there," or a region that is beyond the Mediterranean Sea. Some North Africans also use colloquial expressions such "Bled el-ghir" which means the country of the others, or "Bled elgaouri" and "Bled el-roum" (Western country) to refer to European countries. The places that are the most depicted in cultural production by Algerians and Tunisias are: France (especially Paris), Italy (either as a country, in terms of specific cities such Milan and Rome, or islands such as Lampedusa), and Spain (particularly Barcelona, Malaga and Almeria). Artists depict these locations as picturesque, invoking monuments, landmarks, sunrises and sunsets. As Noel Salazar has argued (2011), the use of these symbols suggests a link between touristic imaginaries and migratory imaginaries. One of the few differences between Algerian and Tunisian cultural production is found in which countries the artists choose to invoke. While France is a common reference in both bodies of work, Tunisian cultural production tends to focus mainly on Italy, whereas Algerian representations often look to Spain. This point can be easily explained by an analysis of the migratory flows. Algerian and Tunisian migrations are postcolonial migrations [START_REF] Nair | Postcolonial theories of migration[END_REF] and France remains the main country of residence for the Algerians and Tunisians living abroad (MPC Team, 2013). Italy and Spain have become coveted destinations-largely but not exclusively-for undocumented migrants. For obvious geographical reasons these countries are also transit countries for migrants who come by boat.

Migrants leaving from the western Algerian shores go to Spain, whereas Migrants leaving from East Algeria and Tunisia tend to have Italy as their destination, or at least a transit country in their migratory journey. The other European locations that are often depicted-though less as a destination than a space of transit-is Lampedusa. This island is features most prominently in Tunisian cultural production. In his song "Harka", Mr Mustapha describes the itinerary of young man who wants to leave Tunisia, he sings about him:

"He has only one thing on his mind, it's the sea His brain is tired. He wants to rest He has only one way on his mind, it's Lampedusa's way".

Lampedusa is seen as the door to Europe. Many Facebook pages names mention the island in their title and many collages and photographs explicitly mention Lampedusa. In his very stimulating work on Lampedusa, Paolo Cuttita documents the "borderization" of the island and defines it as the "theatre of the border play" [START_REF] Cuttitta | Le monde-frontière. Le contrôle de l'immigration dans l'espace globalisé[END_REF].

One of the most recurring images in music videos and Facebook posts about harga stages a young man who is looking away at the sea. A sentence is often written on the picture in order to explain the hopes of the young man who embodies all harraga. For example, in the picture below, we can see a shirtless young man wearing a cap who looks at the sea. Over the image, in red capital letters is written, "L'avenir ray mor Lebhoor". This sentence, which is a emigration resonates with one of the images mentioned earlier.

The notion of an Eldorado is omnipresent in the Bessaï's artwork discussed earlier. His map is an anamorphic map or a cartogram; in other words, it is not an accurate depiction of geographical space, but rather corresponds to the imaginary cartographies of the harragas. As such, the size and location of the countries are distorted. For example, sub-Saharan Africa conspicuously absent while Spain and Italy (especially Sardinia and Sicily) occupy most of the map. France, Germany, the United Kingdom, Canada and the United States also appear prominently. In addition, this map evokes the notion of an Eldorado through two main elements: first, images of women's silhouettes and second, the inscription of western currencies. The legend of the map indicates that the silhouettes of young women correspond to "E'zels/Blondates," which the artist translates as "Western beauty/blondes" in the French version of map key. "E'zels" actually means "gazelle," the animal, which also designates a woman in Arabic dialect and is used to emphasizes her beauty and her grace. According to the map key in the dialect version, the monetary signs (dollars, euros and pounds) correspond to "El Khedma w'deviz", which literally means "Work and foreign currencies." In the map key in French, the artist chooses to translate this by "Zone de puissance économique" which is roughly equivalent to the English phrase, "Zone of Economic Influence." In any case, Bessaï's imagined geography reflects the image of the Western Eldorado, a place where one can meet women and earn money.

The focus on women is related to the fact that most harragas are young men 8 . Gender norms in their home country also play a role. As argued by Benjamin Davis and Paul Winters in the case of Mexico, social and cultural norms influence the decision to migrate: 8 Even though the current share of women in the world's international migrant population is close to one half (GEMMA Gender and Migration, European Commission, FP7), some types of migration remain predominantly masculine and others feminine.

Social norms regarding gender roles play an important role in promoting or hindering migration by females and males. The patriarchal family system accepts and foments male migration, but hinders female migration. Fathers are more likely to resist the migration of daughters, and husband the accompaniment of their wives and children, even years after first leaving home (Davis & Winters 2001: 10).

The predominance of young men among harragas are also due to the the specific obstacles women face in embarking for Europe. The ways in which potential harragas obtain information on migratory strategies and the fact that they meet with one another (and with smugglers) in places of specifically male sociality also explain the small proportion of females.

Women also face specific risks when departing from an isolated beach, in the middle of the night, in a group that is mostly comprised of men. In addition, if their attempt at crossing the Mediterranean fails, it is often difficult for them to go back and live under the family roof because of the social stigma of female undocumented migrants. 9

In cultural productions about harga, femininity is mainly represented through the two symbolic figures of the mother and the western woman. In Merzak Allouache's film Harragas (2009), the expectations of migrants are closely associated with freedom and women. While their boat is drifting, Rachid, one of the main characters has a vision and sees a party that is taking place on a yacht. At the back of the boat, looking at Rachid, is a beautiful young woman who is wearing an evening dress and raises her glass. Later on, when they arrive in Spain, Rachid calls one of his friends to inform him that they made it and asks him to tell Agnèswhom the spectator of the film has not yet met -that he arrived and to put a beer in the fridge for him. Pictures of women soccer fans are often posted on the Facebook pages about harga. 9 During our fieldwork in Algeria and Tunisia, it was very challenging to identify and contact female harragas. There were rumors about Mrs So-and-so having left on a boat. However this data was always very difficult to verify and female harragas were impossible to meet. Analyzing the obstacles we faced during fieldwork is informative: It is hard to contact female harragas not only because there are fewer of them, but also because they encounter specific obstacles and a social stigma.

In one picture below, we see the colours of the Italian flag in the background. In the foreground is a collage of women supporters and three sentences written in different languages. In the Tunisian dialect, one can read, "I will leave and not come back. Sailor do a good deed," referring directly to harga. In French, the phrase seems addressed to a loved one: "You are my life. I will cross the sea just to spend my life with you." The last sentence, in Italian, is a message of love directed at a European country "I love you Italy". It is important, however, to put these pictures of women posted on Facebook in perspective. It is probable that other pages where mainly young men post-even if they have different interests and origins-will also have their fair share of pictures of attractive young women.

Western women are more rarely mentioned in the songs about harga where these individuals are often portrayed as chasing after material success. This points to the second feature of Europe indicated in Bessaï's map ("El Khedma w'deviz") since being able to afford a car is a reoccurring theme. In their song "Mchaou" ("They are gone"), the Tunisian rapper Balti says:

"He wanted to try his luck He wanted to bring back [money] as the others did He wanted to make his mother happy He wanted to stuff his pockets."

To better understand the representations of Europe, one must also study how these cultural productions portray the countries from which migrants are departing. These texts and songs deal with the daily lives of harragas in Tunisia and Algeria, and they focus on hardships rather than the possibility of finding an Eldorado. In this respect Tunisia and Algeria, despite their different political itineraries and economies, are depicted in a similar fashion. YouTube videos and on Facebook pages portray Algeria and Tunisia as countries where hogra is highly present and almost overwhelming. In dialect, the word "hogra", a word which literally means "contempt" or "disdain". It also has a broader meaning, designating an abuse of power that creates frustration and the feeling of being powerless. Harragas are portrayed as feeling trapped at the margins of a corrupt and unequal socio-economic system that offers them no prospects of improvement. Therefore the positive representations of Europe often serve as a foil to Tunisia and Algeria; unlike North Africa, Europe appears as a place where it is possible to achieve one's dreams through work and resilience. Fantasizing about Europe is also way to escape the hardships of their daily lives. This is why Djigouadi's characters allow themselves to believe the tall tales about migration. It also explains one of the main representations of harraga found online, which is the image of a young man turning his back and looking at Europe. We imagine that he is dreaming of economic accomplishments, but also individual and emotional freedom.

These representations resonate with the discourses of the harragas that we met during our fieldwork. Talking about his perspectives in Europe, Ali, whom we met earlier, argued that "Out there in Europe, you can find a job. Their lives are better than ours. I swear, their lives are better than ours" (Ali, 21, Tunis, 2015). He goes so far as to say that being jailed in Europe is better than being free in Tunisia. We interviewed Mohammed, a 23 year-old Algerian from Mostaganem who worked as a street vendor, in 2011. At that time, he had already tried to leave Algeria by boat. Although he did not succeed the first time 10 , he was still determined to migrate.

When we asked him about how he imagined his life in Europe, he replied: "I cannot tell you. I will see when I get there. It is not easy there either. It's hard but I have friends, harraga, who made it, they are accomplished now: they are married, they have kids, they are no longer undocumented, they have a car … They are doing well and they left by boat. I have seen them leave" (Mohammed, Mostaganem, 2011).

Mohammed's position allows us to nuance the representation of Europe as an Eldorado. While he communicated his belief that it was possible to succeed in Europe, he clearly did not want to appear naive or gullible. Consequently, he distanced himself from the myth of Eldorado and acknowledged that it might be hard to make it on the other side of the Mediterranean.

Cultural productions about harga, especially songs, deal with the life's of those who want to migrate and what they hope to leave behind in North Africa such as their marginality, their boredom and their lack of prospects, more than they focus on with what Europe has to offer (Salzbrunn, Souiah and Mastrangelo 2015a;[START_REF] Souiah | Musique populaire et imaginaire migratoire en Algérie[END_REF]. Even when they do evoke the European Eldorado it seems to be in opposition to their country. Cultural production in North Africa is full of actors who seek to transcend borders in order to physically or psychologically escape their social condition. 10 Two small boats left that day full of young men from the same neighborhood in Mostaganem. Mohammed was maneuvering one of the two boats. He had the skills to do so because his father was a fisherman and he had worked with him for a few years. The other boat was steered by one of his neighbors, Hicham. Hicham's boat overturned and the Algerian coast guard intervened and rescued the harraga, but one of them died. During this rescue mission, the coast guards arrested the migrants on Mohammed's boat and the survivors on Hicham's boat. They were convicted for attempting to "exit the country illegally" (Algerian Penal Code, Article 175bis), for which they were dealt a six-month suspended prison terms and a fine of 60,000.

A Land of Tragedy and Disillusion

Along with these positive representations of Europe as an Eldorado or at least as a place where one can become accomplished, there are also negative representations of Europe that circulate in cultural production about harga. Many of these works highlight the economic difficulties and racism that undocumented migrants may face in Europe, giving them a sober tone. The disillusion seems to strike the migrants as soon as they step foot in Europe or even earlier, when

Europe remains a distant hope. In his political cartoons about harga, Dilem highlights humorously the difficult economic situation of some European countries. In his cartoon "Greece; a new destination for harragas" he goes against the myth of the Eldorado. The drawing represents a group of harragas on a boat that is close to reaching its destination. On the horizon, the migrants can already see Greece, including an archaeological site and a sign that reads "ruins" The caricaturist associates Greece's archaeological sites-the ruins-with the catastrophic situation of Greek economy. Moreover, confronted with the social and economic situation of Greece, the harragas are under the impression that they never left Algeria. One of them says, "Damn… We went back to Algeria" Humorously, this caricature deals with the economic crises that shook Europe through the emblematic example of Greece.

The island of Lampedusa serves as a gateway to Europe that portends ambiguous or even tragic consequences. In his song "El-harga," DJ Danger asks: "Oh Lampedusa, are you the problem or the solution?". In his mizwed song Ahmed El-Amri blames the island directly as he sings, "I was not expecting that, oh Lampedusa, you made us wanderers and you made our mothers cry." He says that the island turned them into a spectacle, a sinister joke for the Italians. On Facebook pages about harga, the internet users do not only share music videos and collages, they also share documentaries or television coverage of the issue of harga. One clip that is most frequently shared is an extract of report broadcasted in 2011 on the French TV channel France 2 from the show called Envoyée spécial11 . The ten minutes extract (taken from a longer, 45 minute report) deals with the migrants' living conditions in Lampedusa. It shows that some prefer to sleep outside rather than in the crowded facilities that are supposed to welcome the migrants. In an interview with a reporter, one of the young man simply says "Lampadusa sucks." The reporter asks him: "Are you disappointed"? His answer is again to the point: "Yes." The images of migrants trapped in poorly managed and crowded "reception" centres have durably marked the imaginaries of migration. Indeed, Lampedusa has become the symbol of Europe's failed migration policy.

In Algerian popular music, the songs depicting Europe negatively are mainly written from the perspective of a parent or someone who tries to persuade a loved one not to leave. For example, the raï singer El Hindi tries to dissuade young people from migrating by boat, insisting on the economic precariousness that they will find in Europe. He warns the harragas:

"You pay 150,000 dinars in order to sleep on card boxes in the street." In the same vein, Houari

Benchenet embodies an undocumented migrant who bitterly regrets leaving Algeria. He is homeless, works on the black market, and is mistreated by his employer. Moreover, he lives in constant fear that the authorities will ask to see his papers. A second song by Houari Benchenet aims to destroy the myth of the Eldorado and is written from the perspective of someone who wants to dissuade young people from leaving by boat. The narrator recounts: "Rome, London, Paris and Malaga are not a paradise". This theme is not limited to Algerian songs but can also be found in Tunisian music.

Sabrina, the only female rapper we studied, writes songs from the perspective of someone who migrated and then returned. She explains that she left full of hope but did not find anything positive on the other side of the Mediterranean Sea. She raps: "It's not true.

Ghorba is not a good life. Open your eyes. It's not paradise. Lose your illusions." Some passages in Djigouadi's novel, He Will Have Mercy on Us (Il aura pitié de nous), also refute the Eldorado myth. He points out to the racism that the harragas confront. When Omarou attacks Adel's passivity and the fact that he does not do anything to try to leave Algeria, Adel responds by mocking the young Malian's desire for Europe: "You're annoying me Omarou, I am already fed up with you. If God is willing, I will get married here, I will live here, and I will die here. I leave this shitty West and it's consumerist society to them."12 For him, the West is contemptuous and unreachable. Mocking Omarou's expectations, he asks, "Do you think that they will be waiting for you with a coffee and a residence permit?" Migrants potentially face not only economic hardship, but also the loneliness that results from the absence of their families and their friends. Thus, many works evoke those left behind, especially their mothers, and how they have suffered due to their son's absence. In the songs written from the perspective of the harraga who left, the singers often directly address their mothers, apologizing and telling them how much they miss them.

Migrants who

have not yet left North Africa, such as Brahim, express their awareness that it can be very difficult to find a job in Europe and that newcomers can face precarious living conditions. He says: "There is misery. There is despair. You can end up sleeping outside" (Brahim, 24, Oran, 2011). Malek even mentions racism as a violence that he is ready to face:

"I would rather be called 'filthy Arab'. I would rather live abroad, anywhere, not only in France and I will let them insult me: 'filthy Arab'" (Malek, 23, Oran, 2011). Hadj, another young man that we interviewed, sarcastically jokes that undocumented migrants are a godsend for European employers because they accept low salaries free of charge (Hadj, 26, Oran, 2011).

This last representation of Europe as a place of suffering and loneliness resonates with Abdelmalek Sayad's work, which nevertheless recognizes the agency of migrants [START_REF] Sayad | El ghorba: From original sin to collective lie[END_REF]. Indeed, if they are ready to endure the hardships of migration, this is because it still seems to be a better outcome than suffocating back home, where there are no no prospects. The focus on the hardships undocumented migrants face in Europe reflects the power structure and the rejection of migration in Europe. This rejection is even stronger when the migrants are undocumented young men without a university degree, and who are perceived as Muslims. The negative representations of Europe thus do not dissuade migrants from crossing the Mediterranean. This should perhaps lead us to re-evaluate programs such as IOM's Salemm, as well as policies that aim to deter migrations by reducing so-called "incentives" and making the conditions of migration even more difficult13 .

Conclusion: Europe, at the crossroads of hope and disillusion

This chapter has analysed the varied representations of Europe in the art and digital images relating to harragas. Indeed, these works point to the agency of migrants who continue to search for Eldorado or land of opportunities. Europe appears as the promise for a normal life with employment, marriage and material security (which would allow for the migrant to help family members left behind). Yet Europe is also depicted as a destructive destination since the harragas realise that they may pay a high price and risk their lives only to arrive on a no-man's land like Lampedusa. The spectre of bad living conditions, loneliness and racism are always present. Nevertheless, harragas who are aware of these possible consequences still pursue their emigration plans so that cultural production in North Africa is replete with examples of actors who cross borders and seek to escape their social conditions. The ways in which individuals navigate the tension between hope and disillusion underscores their agency and their capacity to search for a "good life" [START_REF] Salzbrunn | Undokumentierte Mobilität (Tunesien-Schweiz) und digital-kulturelle Ressourcen nach dem Arabischen Frühling[END_REF]). Thus, focusing on the representations by individuals offered us a vision of undocumented migration that is considerably more nuanced than the mechanistic models prevailing in Europe, that are based on the figure of homo oeconomicus and a narrow form of economic determinism.

Figure 1 :

 1 Figure 1 : Zineddine Bessaï, H-out: le guide de l'immigration (2010)

  Bessaï's work has been exhibited at the Museum of Modern and 3 Yakûlni el-hût wa ma yakûlnich ad-dûd. Contemporary Art in Algiers and at the Museum of European and Mediterranean Civilizations in Marseille. It was also shown at Corner House gallery in Manchester. Ironically, Zineddine

Figure 3 :

 3 Figure 3: Facebook page "7ar9a", posted on 10 December 2014

Mizwed "is a type of popular 'folk' song which takes its name from the main instrument used to accompany

IOM, Salemm project, http://www.salemm.org/fr/fr-projet (accessed on 22 December 2016).

"Les naufragés de la révolution", Envoyé spécial (2011), [TV programme] France 2.

"Tu m'emmerdes Omarou, tu me fatigues d'avance. Si Dieu veut, je me marierai ici, je vivrai ici et je crèverai ici. Je leur laisse leur Occident de merde avec leur société de consommation (…)."

For example, in March 2017, the mayor of Calais in France forbade the distribution of free meals in his city because he thought that it was an incentive for migrants to come.

Taliani, R. (2013), Gayeb el-khbar.

mix of French and North African dialect means "Future is only behind the sea." The belief in an Eldorado also represents the possibility of dreaming. Djigouadi's novel, He Will Have Mercy on Us (Il aura pité de nous), also evokes this Eldorado. Adel and his two friends, Kamel and Ali, tell stories about emigrants. Although those stories are not plausible, the three young men allow themselves to believe in certain tall tales about migration. Ali tells his two friends a story so implausible that they initially doubt him. However, Adel and Kamel end up being carried away by the story: "But, without daring to confess to each other, one wants to believe in it; We end up believing. It is such a pleasant 'hope of elsewhere'" (Djigouadi 2004: 109). Adel compares these tales to a kind of addiction. The same representation can also be found in popular music, always in link to this state of waiting. In the song "Ya babor" (Oh boat) by Liberta, the singer who embodies a migrant says: The posture of this young man, sitting in front of the sea, allowing himself to dream of


A new correlation for the relative permittivity of polar compounds and its application to the NRTL-PRA EoS for modeling of mixtures containing water and salts

Isabelle Raspo, Evelyne Neau, L Avaullée

A new correlation for the relative permittivity of polar compounds and its application to the NRTL-PRA EoS for modeling of mixtures containing water and salts I. Raspo 1 , E. Neau 1 , L. Avaullée 2 1 Aix Marseille Univ., CNRS, Centrale Marseille, M2P2, 38 rue Joliot-Curie, 13451 Marseille, France 2 TOTAL-CSTJF, Av. Larribau, Pau, France tel. +334 9111 8546, e-mail: Evelyne.neau@univ-amu.fr

The NRTL-PRA EoS [1] was recently extended to the modeling of phase equilibria in mixtures containing alcohols and light gases with water and strong electrolytes [2]. For this purpose, the residual term of the original model was modified in order to describe all the interactions between solvents and ions with only two contributions: the SMR term, specific of "Short and Middle Range" interactions between solvents and salts, and the LR relation proposed by Pitzer-Debye-Hückel [3], for the description of "Long Range" electrostatic interactions.

The first problem encountered in the development of this model concerned the estimation of the relative permittivity, () r T  , of the polar salt-free solvent mixture which appears in the LR term. In particular, it was observed that classical correlations proposed in literature [4][5][START_REF] Haynes | CRC Handbook of Chemistry and Physics[END_REF] for water and methanol with sodium chloride led to "strange" behaviors of the permittivity, especially for water, at temperatures greater than 350 K.

Taking into consideration "data generated" from various literature correlations ([4] for water, [5] for methanol and CRC tables [START_REF] Haynes | CRC Handbook of Chemistry and Physics[END_REF] for other alcohols), a generalized function for r  was proposed for polar compounds in [2] with two objectives: first, to obtain the best representation of the "experimental domain" defined by the CRC tables; second, to allow a "reasonable extrapolation" of the relative permittivity r  at high temperatures, it means up to 600 K (as required for the modeling of VLE of methane or carbon dioxide mixtures with water and salts near the water critical temperature). Rather satisfactory VLE results were obtained in such conditions [2]. However, a further critical comparison between real experimental data and the estimations proposed in [2] of the relative permittivity of water in a very wide temperature range (from 250 K to 680 K) gave evidence of strong discrepancies above 400 K. A similar comparison, using obviously a more restricted data set, was also performed with methanol and led to the same conclusions.

The purpose of this work was therefore the development of a general correlation of () r T  based on a substantial amount of experimental data in a wide temperature range up to 823 K. A comparison between results obtained from the various methods is presented for water and methanol.

The last step of the work concerned the application of the proposed correlation to the modeling of phase equilibria by means of the NRTL-PRA model [2]. Due to the presence of water in all mixtures previously considered (alcohols and light gases with water and strong electrolytes), a new estimation of group contribution interaction parameters between solvents and ions was required. A good agreement with experimental data is obtained for VLE representations.


Gerald R Kneller

Konrad Hinsen

Memory effects in a random walk

Keywords:

come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

The protein structure-function relationship is one of the basic concepts in structural biology and it has for several decades driven the determination of protein structures by X-ray and neutron crystallography as well as by nuclear magnetic resonance (NMR) techniques. It was soon recognised that protein function requires dynamic structures, [1][2][3][4] and one can observe a change in paradigm over the last years, admitting that protein function does not necessarily require well-defined structures. One speaks here of intrinsically disordered proteins (IDP), where the term "disorder" describes the absence of well-defined secondary structure elements and may concern the whole protein or parts of it. [5][6][7][8] In contrast to well-structured proteins, for which more than 140000 structures can be found at present in the Protein Data Bank 9 , much less is known about the possible conformations of IDPs. Information comes here essentially from computer-generated models which are compatible with experimental data from structural NMR and small angle diffraction techniques. Corresponding data bases are being built up 10,11 and start to become exploitable from a statistical point of view. One can therefore search for criteria that allow a distinction between structured and unstructured proteins on a purely statistical basis. Since protein structure data bases contain structures and structure ensembles of different proteins, such statistical models should be based on the conformation of the protein main chain only. The simplest example is the polymer chain model by W. Kuhn, 12 which consists of equidistantly spaced point-like monomers and which can be transposed to proteins by associating each C α -atom along the protein main chain with a monomer of the Kuhn chain. We note here that that due to the rigid geometry of peptide bonds, the distances between consecutive C α -atoms in proteins have an almost constant value of 0.4 nm. The polymer configurations in Kuhn's model are random chains, where all monomers are placed randomly at the fixed distance to their respective predecessor along the polymer chain. These freely jointed chains lead to a Gaussian model for the probability distribution of finding a monomer at a distance r from a given monomer and they can be interpreted as trajectories of Brownian particles whose subsequent positions in time correspond to the monomer positions along the polymer chain. The Markovian character of Brownian motion reflects the fact that the position of each monomer depends only on the position of its predecessor. The Gaussian chains thus have "zero folding memory". Kuhn's model was the motivation for the present work, where the concept of folding memory will be used in order to distinguish between ensembles of well-structured and (partially) unstructured proteins (IDPs).

II. PROTEINS AS DISCRETE PATHS

In the standard discrete path representation of proteins, each residue is represented by its C α -atom. In the following, we will both this standard representation and an alternative one, in which secondary structure elements (SSEs) are essentially filtered out. SSEs are characterised by a regular winding of the protein main chain with a typical period between 2 and 4 monomers (residues) and thus lead to a priori "trivial" folding memory effects on that scale. Our straightened path representation replaces SSEs by the axis around which the main chain is wound. This axis can be obtained using the ScrewFrame algorithm. 13 The global fold of a protein is described as a succession of screw motions aligning successive discrete Frenet frames along the C α -trace. The centres for the constructed screw motions then define a "polymer chain" along the protein axis. In contrast to the C α -trace, where the distances between adjacent C αatoms are nearly constant, ∆ ≈ 0.38 nm, the distances between adjacent screw motion centres vary and are considerably shorter. The protein axis polymer chain may be associated with a Rouse chain, where the monomers are connected by springs. 14 The left part of Fig. 1 illustrates the construction of the screw motion centres (blue points) from a C α -trace (red points) which has the form of an ideal helix, such that the corresponding screw motion centres lie on a straight axis (except for the first and the last one). The two Frenet frames shown in black define the screw motion from "monomer" 2 to 3. For N C α -atoms there are N -1 screw motion centres. The right part of the figure shows the corresponding analysis for myoglobin (PDB structure code 1AB6). It is important to note that ScrewFrame is applicable to any C α -trace, i.e. also to β-strands, which are "flat helices", and for unstructured parts of a protein. Secondary structure elements are characterised by recurrent screw motion parameters and in particular by a straight axis joining the screw motion centres. The ScrewFrame algorithm leads effectively to a tube model for proteins (indicated in transparent grey), where the local tube axis is defined by the succession of screw motions centres and the local radius by the radius of the respective screw motion. The tube can be considered as excluded volume of the protein main chain. In polymer physics, tube models are used to explain the slow dynamics of reptation, 15,16 where the tube represents the space accessible to a single polymer inside the polymer matrix forming its environment, but the reptation model is obviously not a valid picture for the dynamics of protein main chains.

III. DIFFUSIVITY OF PROTEIN PATHS A. Mean square displacements

Starting from the analogy between polymer models and discrete stochastic paths, we consider first the ensemble-averaged mean square displacement (MSD)

W (n) = 1 N x -n Nx-1-n k=0 (x(k + n) -x(k)) 2 , (1)
where N x is the number of steps in the discrete path, x(k) (k = 0, . . . , N x -1), and n = 0, . . . , P N x to obtain good statistics. For our calculations we used P = 100. The brackets in (1) denote an average over the protein structures in the given ensemble, where each protein structure counts equally. This weighting scheme, which corresponds to unconstrained maximum entropy weighting [START_REF] Papoulis | Probablity, Random Variables, and Stochastic Processes[END_REF] , is very different from thermal averaging of configurations in statistical mechanics, where each configuration is weighted with a Boltzmann factor. Eq. ( 1) is constructed in complete analogy with time-dependent MSDs, as they are for example calculated from single particle tracking in biological systems or from molecular dynamics simulations. MSDs of discretely sampled trajectories are traced as a function of the time lag n ≡ n∆t, where ∆t is the sampling step, whereas the MSDs presented in this paper are traced as function of the dimensionsless "residue lag". In this context, it may appear more appropriate to speak of "mean square distances" instead of "mean square displacements", because we are not considering moving particles. However, we keep the first term in order to maintain the analogy with trajectory analyses. Fig. 2 shows the MSD as a function of residue lag for well-structured and unstructured proteins. In the first case we used protein structures from the ASTRAL data base [START_REF] Chandonia | [END_REF]19 and in the second from the pE-DB data base. 10 The diffusion coefficients indicated in the plot have been obtained by fitting a linear expression of the form

W (n) = 2Dn + a (2)
to the MSD data for n ≥ 20. This offset appears clearly in the data for well-structured proteins and corresponds roughly to the maximum length of protein secondary structure elements. Practically no differences can be found between the MSDs for the C α -trace and the protein axis, but the diffusion coefficient for unstructured proteins is about ten times larger than for well-structured proteins. We find D ≈ 0.18 nm 2 /res. in the first case and D ≈ 0.017 nm 2 /res. in the second. Using the the polymer-trajectory analogy, the asymptotic linear form of W (n) for both well-structured and unstructured proteins corresponds to "normal diffusion". From this point of view they behave like Gaussian chains or, equivalently, like trajectories of Brownian particles. As we will show in the following, the local behaviour is, however, very different.

B. Displacement autocorrelation functions

In order to investigate the local properties of our two polymer models for well-structured and unstructured proteins, we make use of a well-known relation between the time-dependent MSD for a diffusing classical particle and its velocity autocorrelation function (VACF), c vv (τ ) = v(0) • v(τ ) . Assuming stationarity of the VACF one derives 20

W (t) = 2 t 0 dτ (t -τ )c vv (τ ), (3)
were . . . denotes a classical ensemble average over the phase space of the diffusing particle. The VACF itself fulfils an equation of motion of the form 21

ċvv (t) + t 0 dτ κ v (t -τ )c vv (τ ) = 0, ( 4
)
where the memory kernel κ(t) v can be formally expressed by the microscopic forces acting on the diffusing particle and between the solvent particles. In the following, only use the general form of the equation of motion ( 4) is of importance. At the velocity level, the motion of a Brownian particle is described by the Langevin equation, v(t) + γv(t) = f s (t), where f s (t) is white noise, γ > 0 a friction constant. The memory kernel has the form κ v (t) = γδ(t), where δ(t) is the Dirac delta function. Brownian motion is thus "memory-less" and the VACF has the form c vv (t) = |v| 2 exp(-γt). We will now investigate which kind of VACF and corresponding memory function will emerge from the polymer paths representing well-structured and unstructured proteins.

The VACF becomes here in fact a discrete displacement autocorrelation function (DACF),

c dd (n) = 1 N d -n N d -1-n k=0 d(k + n) • d(k) , (5)
where d(k) = x(k+1)-x(k) (k = 0, . . . , N d -1) and N d = N x -1. Using that the convolution is commutative, the memory function equation ( 4) is replaced by the discrete version

∆c dd (n) + P k=0 w(k)c dd (n -k)κ d (k) = 0, (6)
for n = 0, . . . , P N d . Here w(k) are integration weights according to the second order (trapezoidal) rule for numerical integration, w(0) = w(P ) = 1/2 and w(k) = 1 for k = 2, P -1, and ∆ denotes a numerical derivative of second order. Eq. ( 6) represents a triangular linear system of equations for κ d (k) (k = 0, . . . , P ), which can be solved recursively. The second order approximation for numerical integration and differentiation ensures that, to a good approximation,

κ d (n) ∝ λδ 0n , if c dd (n) = c dd (0) exp(-λn) and N d >
∼ 100. Figure 3 shows the DACFs for well-structured (upper panel) and unstructured proteins (lower panel). In contrast to the MSDs, there is a clear difference between the DACFs corresponding, respectively, to the C α -trace and the protein axis. The DACFs for the protein axis do not display the fast initial oscillations which are seen in the DACFs for the C α -trace and which are particularly pronounced for well-structured proteins. These oscillations can be attributed to the presence of secondary structure elements, in which the direction of the displacements changes periodically with residue lags of approximately 2 (β-strands) to 4 (α-helices). The fact that the oscillations are less pronounced for unstructured proteins than for well-structured ones is simply due to the fact that unstructured proteins contain fewer secondary structure elements.

The DACF for the protein axis of well-structured proteins has a striking similarity with the VACF of simple liquids. A surprising result of Rahman's historic simulation of liquid argon [START_REF] Rahman | [END_REF] was that the VACF for such a system does not decay exponentially, as for the Langevin model, but displays damped oscillations which are ascribed to rattling motions of the diffusing molecules in the cage of nearest neighbours. The lag time corresponding to the first minimum corresponds here to the typical time for a reversal of its velocity. In analogy, the DACF for the protein axis of well-structured proteins displays a pronounced minimum for residue lags of about n = 18, which means that the displacement vector d tends to invert its direction after 18 consecutive steps. The ScrewFrame protein axis may here be considered as an analogue of a simulated (discrete) Molecular Dynamics trajectory. Knowing that typical secondary structure elements have about a length of 18, such a behavior could be explained by the typical "helixloop-helix" successions in well-structured proteins such as myoglobin. The term "helix" must here be understood in the sense of the ScrewFrame algorithm, i.e. as a regular secondary structure element, a category that includes α-helices and β-strands. To investigate this point in more detail, we have computed the DACFs for the protein axis of well-structured proteins separately for sub- ensembles of protein structures containing, respectively, essentially α-helices and β-strands and recording in both cases histograms for the lengths of these secondary structure elements. Fig. 4 shows clearly that the first minima of the axis DACFs are correlated with the maximum lengths of the secondary structure elements, which confirms the hypothesis that the first minimum of the DACF reflects effectively the recurrent "helix-loop-helix" motif in globular well-structured proteins. Since this motif is less present in IDPs, the minimum of the corresponding protein axis DACF is less pronounced.

The frequency of the "helix-loop-helix" motif should also be reflected in the memory kernel of the DACF. Fig. 5 shows the memory kernels for protein axis DACFs of well-structured proteins and unstructured proteins. Although the difference is small, it is systematic: The memory function corresponding to the DACF of wellstructured is systematically larger than its counterpart for unstructured proteins, indicating stronger "folding memory". The slight oscillations in the latter case should not be overinterpreted since they might be artefacts due to insufficient statistics.

IV. CONCLUSIONS

Our study shows that suitably defined polymer models for proteins enable a meaningful statistical analysis of their folding properties on the basis of "polymer paths". Each path is here a succession of points that represent the residues, and two types of paths are considered: 1) the C α -representation, where each residue is represented by its C α -atom, and 2) the ScrewFrame representation, where each residue is represented by the projection of the C α position onto an appropriately constructed protein main axis. The resulting paths are analyzed within a theoretical framework that is inspired by the theory of the generalized Langevin equation. We show in particular that the memory functions associated with the displacement autocorrelation function along the protein chain display much stronger "folding memory" for wellstructured proteins than for IDPs. Although the statistical basis for unstructured proteins is still fairly small, the theoretical framework allows for discriminating between ensembles of well-structured and unstructured proteins. The next step will be to develop suitable simple memory function models which explain the the data at least semiquantitatively and which have a physical interpretation.

FIG. 1 :

 1 FIG. 1: Left: Exact helicoidal trace of Cα-atoms (red points) and corresponding screw motion centres (blue points). The figure also shows two consecutive Frenet frames (black arrows), which are attached to Cα-atoms 2 and 3, respectively. Right: Cα-trace and corresponding screw motion centres for myoglobin (PDB structure code 1AB6). The local radius of the gray tube is defined by the radius of the corresponding screw motion.

  FIG. 2: Mean square displacement as a function of residue lag for well-structured and unstructured proteins. In both cases the MSDs are shown for the Cα-traces and for the protein axes.

FIG. 3 :

 3 FIG. 3: Upper panel: DACFs for well structured proteins comparing the Cα-traces and protein axes. Lower panel:The same for unstructured proteins.

FIG. 4 :

 4 FIG. 4: Upper panel: DACFs for the protein axis of well structured proteins containing essentially α-helices and histogram for the lengths of the latter. Lower panel: The same for β-strands.

FIG. 5 :

 5 FIG.5: Memory kernel of the protein axis DACF for wellstructured proteins and unstructured proteins.

Supplementary Material

See supplementary material for the complete source code of our analysis software with the input and output datasets.


Aurélie U Ortiz

Marie-Anne Springuel-Huet

François-Xavier Coudert

Alain H Fuchs

Anne Boutin

Predicting mixture coadsorption in Soft Porous Crystals: Experimental and theoretical study of CO 2 /CH 4 in MIL-53(Al)

Keywords: metal-organic frameworks, adsorption, structural transition, breathing, thermodynamics, gas mixture adsorption

We present a synergistic experimental and theoretical study of CO2/CH4 mixture coadsorption in breathing metal-organic framework MIL-53(Al). Mixture adsorption experiments were performed and their results were analyzed by comparing them to predictions made from pure-component adsorption data using the Osmotic Framework Adsorption Solution Theory (OFAST). The analytical model, fully validated for the first time, was then used to predict coadsorption properties as a function of temperature, pressure and mixture composition. The phase diagrams obtained show a surprising nonmonotonic behavior.

Porous metal-organic frameworks (MOF) are a topical class of materials that display an extremely large range of crystal structures and host-guest properties, potentially giving them a major impact in many areas of science and technology. 1,2,[START_REF]Themed issue: metal organic frameworks[END_REF] In particular, they have potential applications in the fields of heterogeneous catalysis 4 and adsorptive separation of fluids. 5,6 Much attention has recently been focused on a fascinating subclass of metal-organic frameworks that behave in a remarkable stimuli-responsive fashion. These Soft Porous Crystals 7 (SPC) feature dynamic crystalline frameworks displaying reversible, large-amplitude structural deformations under external physical constraints such as temperature, 8 mechanical pressure 9 or gas exposure. 10,11 A number of these materials have been proposed as candidates for processes of adsorption separation of mixtures containing CO2, a crucial step in the capture and sequestration of carbon dioxide from flue gas. These include members of the MIL-53 materials family, which can oscillate between two metastable structures (a large-pore form, lp, and a narrow-pore form, np) upon adsorption, a phenomenon called breathing.

While many authors have stated that soft porous crystals are good candidates for adsorptive gas separation, such predictions are usually based solely on looking at their pure-component adsorption properties. Direct measurements of gas mixture adsorption selectivities are scarce, 12,13,14,15 and the larger parameter space involved in such studies is hard to fully explore experimentally. The Osmotic Framework Adsorption Solution Theory (OFAST) was recently proposed as an attempt to fill this void and allows theoretical prediction of mixture coadsorption in flexible nanoporous materials, based on their pure-component adsorption properties alone. 16 We present here a combined experimental and theoretical study of the coadsorption phase diagram of a CO2/CH4 mixture in MIL-53(Al), investigating the evolution of the breathing as a function of temperature, pressure and mixture composition. The theoretical predictions are in good agreement with the experiments, thus validating the OFAST model for such simple gas mixtures.

Experimental methods.

The sorption experiments of a mixture of carbon dioxide and methane were carried out at various temper-atures (253, 273, 292 and 323 K) and pressures (ranging from 0.5 to 9.5 bars) using an "Intelligent Gravimetric Analyser" (IGA system) from Hiden Isochema. This instrument allows dynamic multicomponent gas sorption experiments in both pressure and flow control modes.

The MIL-53(Al) sample (about 36 mg, of the same origin as the one used in ref 17) was deposited in a mesh container suspended from a hook (constituting one part of the balance). The whole is placed in a stainless steel chamber of 1.8 L. Prior to sorption measurements, the sample was activated at 423 K overnight under a helium flow.

The uptake-release isotherms were measured, at fixed temperature and total gas pressure, as a function of the gas composition which was varied step-by-step. The "uptake" branch corresponds to the increase of the molar fraction of carbon dioxide from 0 to 100%, the "release" branch to the decrease of this ratio. A total gas flow of 100 cc/min was used for all the experiments. Typically, the measurement of an uptake-release isotherm takes 7 to 30 h. 14 to 35 data points were measured for each isotherm.

To perform the experiments at 253 K, 273 K and 323 K, the chamber was placed in a thermostatic bath containing an ethylene/glycol mixture whose temperature was controlled with an accuracy of 0.5 K.

Theoretical models. The coadsorption isotherms for the CO2/CH4 mixtures were calculated from pure-component data available from the literature 17 using the Osmotic Framework Adsorbed Solution Theory (OFAST). 16 This method couples the description of the adsorbed mixture as an ideal solution in each possible host structure (following the IAST prescriptions put forth by Myers and Prausnitz 18 ), and the thermodynamic equations of the osmotic ensemble describing the equilibrium between guestloaded host structures. 19 The osmotic ensemble (Nhost, µads, σ, T) is the thermodynamic ensemble pertinent to the description of the adsorption of fluids (and fluid mixtures) into flexible porous frameworks. Its control parameters are the number of molecules of the framework, Nhost; the chemical potential of the fluids, µads; the mechanical constraint exerted on the system, σ (which in simple isotropic cases without external stress reduces to the total fluid pressure, P); and the temperature, T. In the case of most soft porous crystals, the flexibility displayed is due to multistability: the material may alternate between different preexisting metastable structures, the stability of which is influenced by guest loading. In this case, the osmotic subensemble can be used to describe the system in equilibrium between the host phases k, i.e. the volume V of the system can only take a finite number of values {Vk}. 20 For each host structure k, the subosmotic thermodynamic potential upon adsorption is given by:

Ω os 𝜇𝜇, 𝑃𝑃, 𝑇𝑇 = 𝐹𝐹 host 𝑇𝑇 + 𝑃𝑃𝑉𝑉 - 𝑁𝑁 ads (𝑇𝑇, 𝜇𝜇) d𝜇𝜇 (1)
where Fk host (T) is the free energy of the guest-free phase k of the material, and Nk ads (T,µ) is the total quantity of all adsorbed species in host structure k. The former term can be calculated from purecomponent experimental data, 21 while the latter is calculated using (or, to be more accurate, approximated by) ideal-solution equations using pure-component isotherms as their input. 22 The OFAST method naturally extends to the analysis of temperature dependency provided that temperature-dependent purecomponent data is available. This can be achieved by fitting experimental data using well-behaved isotherm models and Arrhenian temperature dependencies, as done in the case of xenon adsorption in MIL-53(Al) by Boutin et al. 23 In this work, we used the model parameters provided by a previous mixed experimental/theoretical adsorption study of CO2 and CH4 in MIL-53(Al), 17 without any modification or readjustment.

Experimental isobars-isotherms at 273 K. We report in Figures 1 and 2 the evolution of total adsorbed fluid mass, i.e. mads = mads(CO2) + mads(CH4), measured in weight %, as a function of mixture composition for the CO2/CH4 mixture in MIL-53(Al) at 273 K and various values of total gas pressure (from 0.5 to 9.5 bar). These measurements, performed with both x(CO2) increasing from 0 to 1, and then decreasing back to 0, yield monotonic curves: the total adsorbed mass increases with CO2 composition for all measurements reported in this work, as a consequence of the much larger affinity of carbon dioxide than methane. Thus, we call the isobar-isotherm curves upon CO2 composition increase the uptake curves, and the curves obtained upon decreasing CO2 molar fraction (or increasing methane composition) the release curves. Among the eight isobars-isotherms measured at 273 K, those at 2.75, 3.5 and 4 bar (Fig. 2) each feature two steps (the first one being very small at 4 bar). These steps are associated with hysteresis loops and are indicative of a breathing structural transition induced by the adsorption of the mixture. For pressures lower than 2.75 bar, a single transition is observed, while at high pressure (P ≥ 8 bar), no transition is seen. This demonstrates the complexity of the behavior of the flexible MIL-53(Al) upon mixture adsorption, as well as the difficulty of attributing these breathing transitions from isotherms without any addition structural evidence, e.g. from in-situ X-ray diffraction.

The data obtained for x(CO2) = 0 or 1 from these coadsorption isotherms (i.e. pure methane or carbon dioxide) were compared to pure-component adsorption data previously published 17 (Fig. S2). The agreement is very good over the entire pressure range, with slight differences inside the hysteresis loop for CO2. The amount adsorbed depends strongly on the history of the system. Thus, the amount adsorbed in a given set of thermodynamic conditions depends on whether it is measured as part of a pressure swipe at fixed x, or by varying x at fixed pressure. In particular, we experimented with various treatments of our sample and found that the most reliable way to fully convert it completely into its lp form at room temperature is to "activate" it at high CO2 pressure (pure CO2, 9.5 bar, 273 K) rather than under a vacuum. This is due to the fact that the large-pore form of MIL-53(Al) is more stabilized under CO2 adsorption at high pressure than in the evacuated sample. This is consistent with the fractions of lp and np phases measured by in-situ X-ray diffraction during CO2 adsorption and desorption by Serre et al. 24 In particular, this can been seen by the difference in the points of the uptake and release branches in Fig. 2a, where the sample was exposed to pure CO2 at 5 bar (thus converting it fully into the lp phase) between the measurement of the uptake and release curves.

Pressure-composition phase diagrams -Comparing experiments and theory.

To shed some light into the influence of mixture composition on the breathing of MIL-53, we plotted each step observed on the experimental isotherms at 273 K (Figs. 1 and2) on a pressure-composition diagram. 16 For each step, we considered that the composition of the transition at equilibrium must lie inside the hysteresis loop, and marked the two extremes of the loop as bracketing the transition. This experimental (P, x) diagram is reported on Figure 3. In parallel, we calculated the theoretical diagram predicted by the OFAST method, 16 using the adsorption parameters derived from experimental data in our previous work for pure-component CO2 and CH4 adsorption. 17 This theoretical diagram, reported in blue on Fig. 3, is in excellent agreement with the experimental transition ranges (the magenta bars). While the OFAST method had previously been validated only on a limited set of coadsorption selectivities from dynamic breakthrough measurements on this system, 12 the present experimental work provides a direct validation of this recent theoretical model on the full range of molar fraction, pressure and temperature (the latter will be detailed below).

The (P, x) phase diagram fully explains the complex behavior of the system and the features of the isotherms in Fig. 1 and2. These isotherms correspond to horizontal lines in the diagram. At low pressure, one transition is observed upon increase of CO2 mole fraction, going from the open form to the closed form (CH4 does not induce breathing at this temperature). At intermediate pressure, two successive transitions are seen (lp-np-lp), as MIL-53 is open with both gases, but can be closed by a mixture of the two. At higher pressure, no breathing is observed anymore. Some striking features of this pressure-composition diagram can be highlighted. Firstly, the evolution of the material's reopening pressure (the np-to-lp transition) with the CO2 molar fraction is nonmonotonic, unlike that of the lower-pressure lp-to-np breathing. This has the consequence that the reopening pressure for the material is, in a large range of composition, larger for the mixture than for the CO2 itself. In other words, mixing CO2 (which triggers breathing) with CH4 (which does not) increases the pressure domain of the breathing phenomenon. This feature, first predicted in our earlier theoretical work, 16 is confirmed experimentally with this study. This is due to the fact that addition of CH4, which does not trigger breathing at this temperature but contributes to the increase in total gas pressure. A second notable feature is the relatively low value of the critical breathing composition, i.e. the minimum concentration at which breathing can be observed. Less than 5% of CO2 added to a flow of CH4 is enough to trigger the breathing of MIL-53(Al) under adsorption at pressures between 1.5 and 4 bars, while the material does not breathe with pure CH4 at this temperature. Indeed, because the affinity of CO2 for the framework is so much higher than that of CH4, it adsorbs preferentially, and even a small amount is sufficient for the breathing to take place. This has important practical consequences for the design of adsorptive gas separation processes using soft porous crystals, as it shows that traces of gases with a strong adsorption enthalpy can drastically modulate the structural transitions (gate opening or breathing) of flexible frameworks upon adsorption. In particular, we expect this behavior to be even stronger with more polar adsorbates, such as water and hydrogen sulfide.

Influence of temperature on the adsorption isotherms. In order to study the effect of temperature on mixture coadsorption, we measured uptake and release isobars-isotherms on the same system at 253, 292 and 323 K, for a variety of pressures from 0.5 to 8 bar. These 16 isotherms are plotted in Figures S3 to S5. For each temperature, the pressure-composition phase diagram was calculated using the OFAST method, and the transitions observed experimentally were reported on top. All three diagrams are displayed on Figure 4. The overall agreement is good, especially considering that the theoretical OFAST diagrams are drawn solely from purecomponent data, without any reparametrization. Minor deviations from the experimental values are observed at low CO2 molar fraction, which we attribute to the large sensitivity of the OFAST equations to x(CO2) in this domain, amplifying possible deviations of the adsorbed mixture from the Ideal Adsorbed Solution Theory.

The four (P, x) phase diagrams, ranging from 253 to 323 K, display a clear evolution of the breathing phenomenon with temperature. The lowest temperature, 253 K, is very close to the maximal temperature for which CH4 can induce breathing, which is 245 K. 17 Consequently, the critical breathing composition of the mixture is close to 0: it takes minute amounts of CO2 to favor the narrow-pore structure and make the material breathe. Moreover, since the low temperature favors adsorption at lower pressure, the pressure span of the diagram is restricted to 0-8 bar. By increasing temperature, we heighten the free energy difference between the lp and np phases, enhancing the stability of the lp phase (Slp > Snp) and making it harder for the adsorbates to trigger structural transitions. Thus, the critical composition increases with temperature, reaching 20% at 323 K. In addition, the diagram sees a global shift to higher pressure, as Henry constants diminish with temperature. Thus, the peak in breathing pressure, at intermediate compositions, becomes less marked. Finally, it is seen that the hystereses between the two phases become more pronounced, with larger isotherm loops, which can also be linked to the larger free energy difference, and thus the larger free energy barriers, between the lp and np phases.

Exploration of the three-dimensional parameter space. The OFAST model being a fast, analytical method for the calculation of phase stability and mixture coadsorption, it allows to perform calculations in the entire (T, P, x) parameter space. This is an important feature for the simulation and optimization of adsorption processes, as well as to guide the experimental exploration of the large multi-dimensional parameter space. In particular, it allows the optimization of operating parameters for designing adsorption separation columns and processes, e.g. by using equilibrium data as an input to simulations of adsorption column dynamics. Thus, phase diagrams of MIL-53(Al) upon CO2/CH4 adsorption can be presented as three-dimensional objects, though those are difficult to visualize. We present on Figure 5 the evolution of the (T, P) phase diagrams with mixture composition, which are cuts of the 3D diagram along constant-composition planes. We can thus see how the material breathes in the presence of various mixtures.

Plotted on the same scale, it appears that the domain of stability of the np phase is smaller for methane than for carbon dioxide, both in terms of pressure and temperature range. As it was already seen on the constant-temperature diagrams, the breathing pressure ranges extend for intermediate compositions to values larger than for the pure component; this effect is observed at all temperatures. Moreover, we can see that the role of the gases is not symmetric: the phase diagram is much more sensitive to the presence of a small fraction of CO2 in CH4 than it is for mixtures mostly composed of carbon dioxide. This sensitivity is particularly highlighted by the difference between the phase diagrams for pure methane and 20% CO2, which have very different extensions in terms of pressure (2 bar vs. 11 bar) and temperature (245 K vs. 315 K). We will direct further investigations into the influence of traces of polar gases in mixtures, as well as the limits of validity of the Ideal Adsorbed Solution Theory for such dissymmetric mixtures.

We performed a synergistic experimental and theoretical study of the adsorption of CO2/CH4 mixtures in the soft porous crystal MIL-53(Al), exploring the three-dimensional parameter space of pressure, temperature and mixture composition. We demonstrated an experimental methodology to construct (P, x) phase diagrams for this breathing material, and showed that the OFAST method allows to analyze this data. This fully validated this analytical treatment of mixture adsorption. Furthermore, we predicted the flexibility of the material in the full (P, T, x) parameter space. We highlighted the dissymmetry in the role of CO2 and CH4 in the mixture, and the very high sensitivity of the breathing pressures to the mole fraction of CO2 in almost-pure CH4. Finally, we showed that the shape of the (P, T) phase diagram for MIL-53 upon gas adsorption is very generic, and valid for gas mixtures as well as pure components.

Figure 1. Experimental uptake and release isobars-isotherms of a mixture of CO2 and CH4 in MIL-53(Al), as a function CO2 molar fraction, at 273 K. Each curve corresponds to a fixed value of total gas pressure, ranging from 0.5 to 9.5 bar. Open symbols correspond to increasing CO2 fraction ("uptake"), full symbols to decreasing ("release"). Experimental pressures for structure transitions are in magenta (width corresponds to the experimental hysteresis loop). Green vertical ranges indicate the purecomponent transition pressure. 17 The theoretical diagram predicted by the OFAST model is reported as the blue line.

Figure 2 .

 2 Figure 2. Experimental uptake and release isobars-isotherms of a mixture of CO2 and CH4 in MIL-53(Al), as a function CO2 molar fraction, at 273 K. (a) P = 2.75 bar; (b) P = 3.5 bar; (c) P = 4 bar.

Figure 3 .

 3 Figure 3. Pressure-composition phase diagram for MIL-53(Al) with a CO2/CH4 mixture at 273 K, indicating the region of stability of the npphase (in gray) and lp phase (in white). Experimental pressures for structure transitions are in magenta (width corresponds to the experimental hysteresis loop). Green vertical ranges indicate the purecomponent transition pressure.17 The theoretical diagram predicted by the OFAST model is reported as the blue line.

Figure 4 .

 4 Figure 4. Pressure-composition coadsorption phase diagram for a CO2/CH4 mixture at 253, 292, and 323 K in MIL-53(Al). See caption of Fig. 3 for the color code.

Figure 5 .

 5 Figure 5. Temperature-pressure phase diagram of MIL-53(Al) upon adsorption of a CO2/CH4 mixture, with increasing CO2 molar fraction.Dashed lines correspond to pure component diagrams.

Funding Sources

This work was partly funded by the Agence Nationale de la Recherche project SOFT-CRYSTAB (ANR-2010-BLAN-0822).

ASSOCIATED CONTENT

Supporting Information. Figures of the lp and np structures of MIL-53(Al), coadsorption isobars-isotherms and full set of model parameters. This information is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author * fx.coudert@chimie-paristech.fr

ACKNOWLEDGMENT

The authors thank Dr. Andrei Nossov for expert technical assistance. Dr. T. Loiseau and professor G. Férey are gratefully acknowledged for providing us with the MIL-53(Al) sample.