domain: shs sde

text:
Julie Trottier
email: julie.trottier@cnrs.fr

Challenging the coproduction of virtual water and Palestinian agriculture

The idiom of virtual water feeds a prolific literature now shaping the policies of national administrations and international organizations, including donors. This article explores the manner in which Palestinian agriculture and the concept of virtual water shed light on each other's coproduction. It opens the black box of virtual water to identify the underlying hypotheses. It invalidates these hypotheses using empirical research. Integrating structuration theory to an STS approach, it explores the manner the coproduction of an interpretive scheme, virtual water, is linked to the construction of a structure of power. Within the idiom of virtual water, flows exist only through the international trade of commodities while states are endowed with an annually renewed stock of water. We focus on the real flow of water from its emergence from the earth to its evapotranspiration by a cultivated plant. We demonstrate that social and political variables within water governance determine the volumes of virtual water flows far more than climatic or agronomic variables. The idiom of virtual water portrays Palestinian smallholders as inefficient water users while ignoring the manner they sustain food security and environmental sustainability. It legitimizes export oriented agribusinesses as their mode of production corresponds to the coproduction of the idea of efficiency that underlying the concept of virtual water. These results allow us to reconsider smallholder agriculture as it exists in Palestinian territories and what sort of policies can support it.

Opening the black box of virtual water reveals it treats water as an immobile stock embedded in the natural resources of a state. Within the idiom of virtual water, flows exist only through the international trade of commodities. They do not include the real flow of water from its source, through the land where farmers grow their crops, to the point it evaporates. Naming, defining and mapping are acts of ontological politics. (Mol, 1999) Such acts shape power and authority. The rapid rise of the virtual water literature granted a scientific legitimacy to this concept, simultaneously cementing a social imaginary it embedded.

Science and Technology Studies (STS) have long demonstrated how knowledge and norms are co-produced. In other words, they are constructed through their mutual interactions.

 This article explores the concept of virtual water as a scientific category that is co-produced together with the legitimacy of a specific form of agriculture. This article explores the manner Palestinian agriculture, on one hand, and the concept of virtual water, on the other hand, shed light on their coproduction. It uses in depth fieldwork to challenge virtual water as a hegemonic interpretive scheme that is increasingly shaping our representation of sustainable agriculture and water management. We focus on the trajectories water can bifurcate into between the point it emerges from the earth until the point it leaves

Introduction

The Middle East is considered a water scarce region and has been especially targeted by the discourse on virtual water. Allan has long urged Middle East states to devote their scarce water resources to non agricultural activities generating higher added value. He argued this would allow importing food from states better endowed with water resources, thus ensuring both environmental sustainability and food security. He designated the water necessary to produce such imported crops as "virtual water" because it was imported in a virtual manner together with the crops. [START_REF] Allan | Substitutes for water are being found in the Middle East and North Africa[END_REF] The idiom of virtual water has fed a prolific literature that is now contributing to shape the policies of national administrations and international organizations, including donors. [START_REF] Barnes | Water, water everywhere but not a drop to drink: the false promise of virtual water[END_REF] the system. 1 We demonstrate that social and political variables within water governance determine the volumes of virtual water flows far more than climatic or agronomic variables.

The decision processes, both collective and individual, that determine the paths water will flow into are embedded in both land and water tenure. Our results thus dispel several assumptions upon which the concept of virtual water relies. This article then explores the role this interpretive scheme is playing within a wider structure of signification that portrays agribusinesses embedded in global trade as the only legitimate and successful forms of farming. It demonstrates how it makes Palestinian smallholders appear illegitimate because the manner they sustain food security and environmental sustainability is portrayed as an inefficient use of water. This leads us to reconceptualize water differently. Treating it as a flow instead of a stock allows us to integrate the various institutions it flows through on its path between source and plant. It allows us to reconsider smallholder agriculture as it exists in Palestinian territories and what sort of policies can support it.

Opening and locating the black box

The term "virtual water" was initially coined to designate the water embedded in commodities, such as cereals, that could be traded. [START_REF] Allan | Substitutes for water are being found in the Middle East and North Africa[END_REF] This focus on trade distinguished the concept of virtual water from the pre-existing notion of hydric productivity.

The concept relied on the substitutability of water. Water necessary to produce a crop was deemed to become available for another activity generating more added value if that crop was imported. Champions of virtual water, such as Hoekstra and Chapagain, argued that water scarce states should import water intensive commodities such as food to "save" their resources. They argued that estimating the amount of water needed to produce different crops in various countries was necessary to guide such states' commercial and agricultural policies.

They developed a method based on FAO data on crop water requirements and crop yields. [START_REF] Hoekstra | Globalisation of water resources: international virtual water flows in relation to crop trade[END_REF] 47) It considers that the average specific water demand (SWD) for a given crop (c) in a given state (n) could be calculated by dividing the crop "water requirement" (CWR) with the crop yield (CY):

𝑆𝑊𝐷 𝑛, 𝑐 = 𝐶𝑊𝑅 𝑛, 𝑐 𝐶𝑌 𝑛, 𝑐

The data from the FAO had not been designed to produce calculations of virtual water volumes. It aimed to inform farmers of the maximum yields as a function of irrigation calendars. Using it in this fashion, Hoekstra and Hung were turning it upside down. Their equation supposes that the irrigation calendar deemed by the FAO to maximize yield is systematically used by the farmers. The epistemic community that followed Hoekstra, which we will refer to as the "Delft school of thought", produced a prolific literature to assess the amount of virtual water contained in imported and exported crops. It applied this calculation method without challenging the underlying hypotheses.

These underlying hypotheses where rather extraordinary and wide sweeping. Such a calculation relies on the assumption that water is available on request for every farmer.

Otherwise, farmers cannot provide the irrigation calendar that matches the specific water demand as it appears in the calculation method. This method also assumes that every farmer aims to maximize the vegetal mass. It assumes a monoculture on every plot of land. It assumes that a given crop only yields one product. It assumes that water serves only one use:

the evapotranspiration of the crop that will be sold. Finally, it assumes that only climatic and agronomic variables determine the quantity of water that is necessary to produce a crop.

Such hypotheses rarely resist scrutiny. Agribusinesses with reliable and sizeable infrastructure may benefit from a supply of water on request when operating in very favorable conditions. Palestinian smallholders rely instead on shared springs or farmer managed shallow wells. In the Mediterranean area, spring flow varies widely through the year. This constrains the amount of water a farmer can access, as does the social organization allowing the farmer to access this spring. All Palestinian springs used in irrigation are shared according to "water turns". These are measured in terms of time periods during which the full flow of the spring is usually channeled towards a farmer's plot. Similarly, farmers relying on wells need to share with their neighbors, which constrains their access. As a consequence, most farmers either under irrigate or over irrigate in comparison with the ideal irrigation calendar embedded in the calculation of virtual water volumes. The Delft school recognized its general overestimation of the virtual water content of crops but didn't quantify it. (Chapagain andOrr, 2009, p.1220) Moreover, farmers rarely aim to maximize vegetal mass. They usually prefer maximizing revenue, a goal that sometimes proves to be contradictory with maximizing vegetal mass. Field observation also shows that Palestinian farmers often mix crops within a single plot and often derive two products from the same crop. For example, corn provides cobs that are commercialized while the remaining stalks provide pasture for sheep. Only scientists who have never observed farmers may assume water has only one use. In Egypt, farmers need water to wash the salt off the land otherwise it becomes sterile. (Barnes, 2013, p. 379) Palestinian greenhouse farmers use water in July and August to sterilize the soil. Finally, hypothesizing that climatic and agronomic variables alone determine the quantity of virtual water means assuming that water never flows through human institutions. This begs the question of how water reaches a plot of land after being abstracted. It constitutes a crucial part of the ontological politics of virtual water and will be challenged in the remainder of this article.

The coproduction of virtual water accommodated questionable assumptions because they were convenient for the epistemic community that championed it. Its calculation method proposed that virtual water flows could be detached from their contexts. This created the fictitious mobility of the concept. The controversy surrounding the underlying hypotheses constitutes a clear-cut case of ontological politics. This term designates conflicts involving different assumptions about what exists. (Forsyth and Levidow, 2015, p. 141) Several hypotheses, however challengeable, proved very useful for the rapid rise to hegemony of the concept of virtual water and its accompanying calculation method. Many have demonstrated the inaccuracy of the assumption concerning the distinction between green water, naturally occurring in the soil, and blue water, channeled to the soil through irrigation. (Fernandez, 2008, p. 54) (Perry, 2014, p. 121) Yet, calculations of the water footprint, an indicator the Delft school argues is wider than that of virtual water because it makes explicit the source of water that is used, rely on this distinction. (Hoekstra, Chapagain et al., 2011, p. 167) The Delft school coined the term water footprint to describe the virtual water content embedded in products when they are consumed. It kept the term virtual water to describe water consumed through the production of the goods. The assumption concerning substitutability of water implied that imported virtual water would free up existing water for uses generating greater added value. Yet, examples abound that contradict this assumption. In the 1990s, in Jericho, the casino and the Intercontinental hotel channeled water previously used in irrigation to services deemed to generate a greater added value but most of this revenue actually left Jericho and the Palestinian economy as soon as it materialized. [START_REF] Trottier | Hydropolitics in the West Bank and Gaza Strip[END_REF] The epistemic community that promoted virtual water was concerned with international trade. It coalesced at a time when states had set up large databases concerning importations and exportations. In the 1990s, widespread computational capacities also appeared. This corresponded to a time when the FAO produced its own CROPWAT model that linked agronomic variables with climatic variables accessible online from climate stations around the world. As the databases were collected by states on a national scale, they allowed calculations concerning trade among states. This contributed to the shape global food models adopted. [START_REF] Leblond | Performing an Invisibility Spell: Global Models, Food Regimes and Smallholders[END_REF] Similarly, it shaped the discourse on virtual water, presenting virtual water flows as necessarily calculated over a national scale.

Such a discourse appealed to those who perceived the world as a set of nation states constituting the only forms of social organization capable of exercising power on the national as well as the international scenes. State policy makers were embedded in such institutions.

Scientists usually adhered to this representation, aligning mostly with either of two groups :

those subscribing to neo-liberal ideas and those broadly self described as Marxists. The first group supported an agenda according to which the future depended on such international trade. The second group considered that the forms of social organisation described in this article were inevitably doomed because Capital was going to appropriate their resources. [START_REF] Harvey | The Enigma of Capital and the Crisis of Capitalism[END_REF] The only disagreement between them laid in whether this was the end point.

Both groups disregarded the actual forms of social organisation determining land and water tenure.

A few studies explored virtual water flows among large provinces, such as among the 19 water management areas in South Africa. [START_REF] Dabrowski | Analysis of virtual water flows associated with the trade of maize in the SADC region: importance of scale[END_REF] In such cases, large databases were already available, allowing the calculation over that scalar level.

Thus, availability of data determined the scalar level of the calculations, rather than scientific reasoning. Few pointed out the inadequacy of such a scalar level to produce meaningful information. (Wichelns, 2015, p. 401) The calculation of virtual water is a form of commensuration that proved very popular because it empowered a specific epistemic community. Commensuration means measuring a wide range of variables along the same metric. It may allow comparison when what is measured corresponds to instrumental values but it necessarily distorts substantive values. [START_REF] Espeland | The Struggle for Water, Politics, Rationality and Identity in the American Southwest[END_REF] For example, attributing an economic value to a plot of land seems appropriate for an investor aiming for land speculation. It seems inappropriate for a landholder investing emotional value in his land. The concept of virtual water attributes only a very narrow instrumental value to water. This value is strictly economic and involves only one user dissociated from the context in which he farms. This creates the substitutability of water which allows extracting it from its context. Yet, when considered over an appropriate scalar level, water appears clearly embedded within substantive values. For example, many

Palestinian farmers access water free of charge on the basis of a common property regime developed within the village. To them, water can neither be sold nor bought. It is not substitutable. Moreover, those Palestinian farmers who access water from "well companies" pay for "water hours", yet, they most often benefit from a "payment plan" when they cannot pay. This means that water is made available for them free of charge by their neighbors.

Palestinian communities and families privilege maintaining local solidarity over profitability of a well. This is a substantive value. It resists commensuration. The Delft school could thrive because the epistemic community promoting it viewed water as an economic good and did not explore irrigation over such a scalar level. This allowed the persistence of underlying hypotheses that do not resist scrutiny.

How do Palestinian agriculture and the concept of virtual water shed light on each other's coproduction? In other words, how does virtual water portray Palestinian agriculture?

And how does Palestinian agriculture reveal the power structure that is promoted by the concept of virtual water? When scientists produce scientific claims, they implicitly embed within them the power structures they take for granted. A largely social process then transforms this scientific claim into a scientific fact, thereby "blackboxing" it. [START_REF] Latour | Science in Action[END_REF] Opening the black box of virtual water allows us to show a power structure is embedded in the concept and its accompanying calculation method. Scientists thus reify a political structure. In the case of virtual water, scientists reified a state control over water that rarely exists. They reified an international virtual water trade that would be responsible for food security. Confronting how virtual water depicts Palestinian Agriculture with the results that emerge from fieldwork sheds light on this process.

Deploying the idiom of virtual water to examine Palestinian agriculture leads us to project a homogeneity over the entire territory. It leads us to project scarcity everywhere, ignoring the islands of water abundance that dot the landscape. Palestinian irrigation has been developed from springs managed as common property resources (CPRs) and from wells managed as commons by farmers. The scale over which farmers operate is far smaller than the national territory and their regulation of water access is based on more than economic calculation alone. The idiom of virtual water projects agribusiness practices over the territory, where water is supposed to be bought as an input according to a cost/benefit calculation. The idiom of virtual water doesn't ask where water comes from nor what are the rules to access and to use it. Its inherent distinction between blue and green water assumes that, where green water is abundant, irrigation will be diminished. Fieldwork in the West Bank reveals the opposite. Villages using reliable wells do not practice rainwater harvesting. Where blue water is abundant and cheap or free, farmers rely less on green water, no matter how abundant it is.

Examining Palestinian agriculture to question virtual water shows that this concept treats water as a stock instead of a flow. The calculation method focuses on determining a quantity embedded in a crop. This is a stock. The mobility of the crop is equated with the mobility of that stock. This is why that literature refers to virtual water flows. Examining how water really flows in agriculture is a different matter. From the moment water is abstracted in a well or channeled from a spring, until the point it is evapotranspired through the stomata of a plant, it flows uninterruptedly. Following that trajectory shows water goes through a variety of human institutions. That trajectory determines the appropriate scalar level of analysis. This is the scalar level over which decisions will be made concerning irrigation and water appropriation and management. The second part of this article develops such an approach.

Following the trajectory of water

What happens to water between the moment it emerges from the earth and the moment it evapotranspires through the stomata of a plant? Human and nonhuman actors direct this uninterrupted flow into a variety of trajectories. For example, water may be abstracted from a well managed by a Palestinian "well company", i.e. by a shallow well managed by a collective of farmers owning shares of this company. This locally built institution channels water to a plot whose farmer pays a set fee for one hour of irrigation. This water leaks partly along the network and infiltrates the soil. This leak constitutes a trajectory where part of the abstracted water is "lost" to the farmer paying for the water hour but "gained" by the field that is thus inadvertently watered. This trajectory channels either a non recoverable fraction of the initial full flow into the aquifer acting as a sink, or a recovered fraction to subordinate neighbor consumption. (Lankford, 2013, pp. 147-149) Such a case occurs, for example, if this leaked water is consumed by rainfed olive trees in a neighboring plot.

Once the remaining flow reaches the intended field, part of the water may irrigate the lemon trees serving as a marker dividing plots while the rest of the flow irrigates the avocado trees cultivated in that plot. The water consumed by the lemon trees follows a third trajectory called non-process beneficial consumption while the water consumed by the avocado trees follows a fourth trajectory called process beneficial consumption. A comprehensive examination of the trajectories this water can possibly adopt shows a total of 16 possible paths for water abstracted by the farmer. (Lankford, 2013, pp. 147-149) Diverting water from one of these trajectories into another one can appear to free up water for human and non human actors. These potential gains make up the paracommons. The term includes para to designate the fact resources are potentially available through "efficiency" improvements. It also includes commons to designate the fact that such resources involve a group of users. (Lankford, 2013, pp. 5-16) Channeling a greater proportion of the water flow into one trajectory means reducing the flow into another trajectory.

Our representation of the world constructs our definition of efficiency. How we value one or other of these flows determines our definition of efficiency. For example, a classical definition shows efficiency as the ratio of beneficial consumption, i.e. the volume of water consumed via evapotranspiration of the plants that are cultivated, over the total volume of water that is withdrawn. Another definition of efficiency may show it as the ratio of the beneficial consumption over the total volume of irrigation water that is consumed. Both types of efficiencies could be raised in our earlier example if the lemon trees where chopped off and the leaks repaired. However, this enhanced efficiency could occur simultaneously with an increase in water consumption if the same volume of water keeps on being abstracted. (Lankford, 2013, pp. 47-49) This could occur, for example, if the farmer plants more avocado trees after having chopped off the lemon trees.

Increases in efficiency of water use can be detrimental to food security. Lemon trees serve commonly as dividers between siblings' plots in the West Bank. The lemons they produce provide a useful source of vitamin C to these families. More crucially, khubbiza, a local variety of mallow, commonly grows as a weed in irrigated fields. Palestinian custom considers that these plants should be available to all because they are not cultivated, thus are not produced through human labor. Anyone asking for a landowner's permission to enter his plot in order to pick khubbiza usually receives it. This very nutritious plant provides an important component to the poor's diet. It also generates income for the poor who can pick it and sell it. Thus water that is "lost" as beneficiary consumption in the cultivation of avocadoes may play a very beneficial role in local food security.

Virtual water may represent an increased efficiency in the use of water that is managed as a stock. However, many Palestinian farmers are more constrained by flow management than by stock management. Any reticulation network faces two types of constraints: flow and stock. Farmers in Ain al-Baida, Kardala and Bardala, in the north of the Jordan Valley, are supplied with a constant flow of piped water by the Israeli company Mekorot, as replacement for the springs that dried up when that company sank wells in that village in the early 1970s. [START_REF] Trottier | Le rapport à l'eau et à la terre dans la construction de territoires multisitués: le cas palestinien[END_REF] Their main constraint is flow. They cultivate trees that need irrigation in the summer but are rain fed in winter. They use the flow at their disposal to grow vegetables in greenhouses and in open fields during the winter. This allows them to maximize the use of a constant flow all year round. This is a rational decision to maximize income. But doing this, they do not maximize the use of the yearly stock of water at their disposal. In theory, the overall stock of water they access could allow them to grow a greater vegetal mass as most of their land remains unirrigated and uncultivated. This is not an option for them. Calculating virtual water according to the existing methodology misrepresents the constraints they face.

Following the uninterrupted trajectory of water from the moment it is abstracted, through the many bifurcations it meets, until the point where it evapotranspires allows us to question several aspects of virtual water. The relevant scale over which we need to calculate it, in terms of space and time, changes significantly. Similarly, following this uninterrupted trajectory demonstrates the importance of the decision processes through which water travels before it becomes virtual.

Palestinian cucumbers: an illustration

Cucumbers are a widespread crop throughout the West Bank, which allows comparisons between various ecoregions. The standard calculation of virtual water embedded in cucumbers produced in the West Bank projects a homogeneity over the entire territory.

Everywhere, producing a ton of cucumbers is supposed to have consumed 69 cubic meters of water. This value was calculated using the average of two values for virtual water content for cucumbers in Israel both published by [START_REF] Chapagain | Water Footprints of Nations[END_REF] Hung in 2002 respectively [START_REF] Chapagain | Water Footprints of Nations[END_REF][START_REF] Chapagain | Virtual Water Trade. A quantification of virtual water flows between nations in relation to international crop trade[END_REF] and a coefficient of 0,78 to account for cultivation in a greenhouse.2 [START_REF] Fernandez | Measurement and estimation of plastic greenhouse reference evapotranspiration in a Mediterranean climate[END_REF] Field work carried out in 2014 and 2015 interviewing farmers to reconstitute their irrigation calendar allowed us to estimate the actual volume of water they used and consumed to produce their crop. Map 1 illustrates these results in the case of farmers all using relatively small, piped networks and growing cucumbers in greenhouses using drip irrigation. We initially assumed that the losses on the path between the source and the plant were negligible.

We triangulated our calculations with field measurements of the volume of water flowing from the drippers at the head, middle and tail of the networks. These measurements validated this assumption. determined by climatic variables alone, however, as is illustrated by the differences between Habla and Dhinnaba, both located in the same ecoregion. Dhinnaba cucumbers consume about twice as much water as Habla cucumbers both in winter and summer seasons. This dispels the hypothesis that agronomic and climatic variables alone account for virtual water embedded in a crop.

These results raise the question of which other variables may explain such diversity in the water footprint of Palestinian cucumbers. We included, in the measurement of water consumed to produce the crop, the volume farmers use to sterilize the soil at the height of summer. This practice involves trapping the water flowing from the drippers under plastic sheeting spread on the soil of the greenhouse. The heat then rises to such a level that the soil is sterilized. This water is not evapotranspired by the plants but it is used to grow the crop.

This water is "lost" by the farmer as it follows the trajectory of a "non-recoverable fraction" (Lankford, 2013, pp. 148-149) and seeps into the soil or evaporates. These results demonstrate the crucial need to include the practices of the farmers when determining the calculation method of virtual water volumes. All of the farmers we interviewed used the same sterilizing practice. Subtracting the volume used to sterilize the soil from their overall water consumption would still yield the same diversity among the water footprints of their cucumbers.

Documenting the irrigation calendars used by the farmers demonstrates the variability of virtual water through time. The Delft school has admitted that crop water use depends on the crop calendar and that multiple crop calendars coexist in a single region. (Chapagain and Hoekstra, 2011, p. 750) Yet, it has not integrated this recognition in the calculation method of the virtual water embedded in a crop. Our results demonstrate that the variability between seasons is by itself variable through space. Farmers pick the cucumbers in their greenhouses over several months, producing a few boxes every day. A cucumber picked early in the season did not require the same amount of water as a cucumber picked late in the season. This has never been recognized in the calculations of virtual water flows because the present methods treat virtual water as a stock.

Recognizing that water flows, as illustrated in Figure 1 shows the evolution over time of the virtual water embedded in a cucumber according to the time it is picked. Representing virtual water in this manner leads to policy recommendations that are different from representations of virtual water as a stock. This is explored in the third part of this article.

Institutional as well as individual decision processes guide water through its path, deviating it into either of the 16 trajectories mentioned above. As water flows from the earth to the plant through material infrastructure, it also flows through a variety of property regimes. Palestinian farmers manage their springs and wells as typical CPRs. Yet, when the water reaches their plot or their birka, i.e. their individual pool, it becomes private property.

Map 2 illustrates the great variability of virtual water embedded in the cucumbers produced by different farmers all using greenhouses in the village of Dhinnaba in 2015. The climate doesn't vary within the village and the agronomic variables are identical. This variability can only result from other factors, such as calendar's differences, the source of water and individual strategies. These farmers receive water from different local wells all managed in a similar fashion through "well companies" run by farmer-owners. Dhinnaba farmers carry out stock management, as opposed to the Bardala farmers constrained into flow management. In Dhinnaba, each farmer purchases hours of water from one well to which his plot is connected. A farmer phones the well operator a day ahead to ask for a slot to receive one hour of water. He is billed monthly by the well accountant for the number of hours he has used. The well companies in Dhinnaba sold their water in 2015 at an hourly rate varying from 80 to 100 New Israeli Shekels. As the flow varied from well to well, this meant a price varying from 1 to 1,33 New Israeli Shekels per cubic meter. Each well has a yearly quota, so farmers irrigate only when they consider their crop needs it. As opposed to their colleagues in Bardala, Dhinnaba farmers are free to use more one month and less the next one. Each farmer follows different practices according to his situation. Some are full time farmers, others are civil servants who finish work at 14:00 and farm in the afternoon. Some inherited their land from their fathers, some rent it, others bought it. This led them to adopt different practices with very different formal efficiencies that led to very different water consumptions. Social and economic variables thus appear to determine the volumes of virtual water embedded in a crop far more than climatic and agronomic variables.

The social and political mechanisms affecting the volumes of virtual water embedded in a crop need to be examined. Observing the flow of water along its path from the earth to the plant reveals these mechanisms. Each village has a distinct history shaping its water tenure and land tenure. From 1950, when they divided their tribal land into private plots, until 1967, all of Bardala irrigating farmers held rights to a water "turn" from one of 15 springs shared with Ain al-Baida and Kardala villages. The population fled to Jordan during the war of 1967. Those owning the land appropriated by Mehola, an Israeli settlement, were unable to come back to farm it again. In Bardala, absentee water right holders were kept on the list for the water "turns". Anyone wishing to use the turn of an absentee must rent it for a year at a price decided collectively within the village. This practice continues to this day in spite of the fact that all the springs disappeared in 1972 after the Israeli water company, Mekorot, drilled a well in the village. Since then, Mekorot, having recognized its responsibility for the disappearance of the springs, provides a constant flow of water in gauges located exactly where the springs used to flow. Farmers replicated over the gauges the common property regime previously deployed over the springs.

In neighboring Ain al-Baida, absentees were removed from the water "turns". Those villagers able to return home benefited from a shorter rotation of the spring's use. They decided they would include the returnees anew within this rotation once they came back. In 2014, a Bardala farmer wishing to rent the water turn of an absentee paid the right holder an annual fee of 400 Jordanian Dinars. 3 The right holder was often born abroad and had never seen the village. Consequently, Bardala farmers, who access water at a sizeable cost, make different decisions from their neighbors in Ain al-Baida, who access it for free. Similarly, the complex land tenure entails a variety of choices concerning water use. In Al Jalama, a farmer who cultivates his cousin's land does not pay rent because the land belongs to his family. Yet, he pays the absentee landowner's fee to the Israeli Authorities because his cousin is forced in exile as a refugee. Throughout the Jordan Valley, many farmers are sharecroppers but on the western side of the West Bank, most people either rent or own the land they farm. These various forms of land tenure systematically affect the decisions made concerning the 16 types of pathways water will be allowed to follow between the moment it emerges from the earth and the moment it reaches the plants. This determines the volume of virtual water embedded in a crop.

The construction of the separation wall since 2002 and the rapid urban sprawl around Palestinian villages is now driving the interaction between water tenure and land tenure. Map 3 shows the village of Habla, where much of the agricultural land now lays on the "wrong" side of the wall.

3 In 2015, 400 Jordanian Dinars were equivalent to 560 US dollars. This is a sizeable sum for a farmer. As a matter of comparison, Palestinian agricultural labor in the Jordan Valley was remunerated 50 New Israeli Shekels per day of work by both Israeli settlements and Palestinian land owners. This daily wage amounted to 13 US dollars. Renting one mawdud of water, i.e. one unit of a water rotation from a gauge, was thus equivalent to the wages for 43 full days of work.

Map 3: Land and water uses in the West Bank village of Habla -the colored plots and the wells were the sites where investigations and measurements were made in this village Each plot is linked to a specific well managed by a local "well company". The land lying on the other side of the wall becomes difficult or impossible to access for a farmer. Depending on its location, its irrigation or its cultivation sometimes becomes forbidden. Simultaneously, land lying inside the wall but close to the heart of the villages of Habla and Ras Attiya becomes prey to urban sprawl. As a result the wells that supplied these lands are less solicited than they used to be. They now abstract far less than their quota. Farmers in quest of land now develop a "pioneer front" east and north of Ras Attiya, where land remains available. They build terraces where sheep had roamed through rain fed olive trees until recently. They connect to wells closest to their new plots. These wells have become oversubscribed and cannot satisfy all the users even when operating at full capacity. Under-irrigation thus increases. The quotas are attributed to individual wells, not to the entire area. So a well that under-pumps its quota cannot transfer its quota to an over-solicited well. The technical constraints of these wells also limit their pumping capacity in any case.

These interactions between land and water tenure impact the flow of water between the moment it is abstracted in wells in Habla and the moment it reaches the stomata of cultivated plants to evaporate. Neither the 2002 water law nor the 2014 decree 14 relating to West Bank. The Palestinian Authority does not have the institutional capacity to exercise social control over the management of water. This does not mean that water is not managed efficiently. Farmer run "well companies" and commons managing springs both show a great efficiency. But their definitions of efficiency diverge from the definition underlying the concept of virtual water and its standard calculation method.

The role of virtual water in constructing structures of power

The first section of this article opened the black box of the concept of virtual water and of the manner it is assessed quantitatively. It identified the underlying hypotheses. The second section of this article followed in detail the actual trajectory of water from the point it leaves the soil up to the point it evapotranspirates through the leaves of cultivated plants or otherwise leaves the system. This detailed study invalidated the hypotheses both underlying the concept of virtual water and its calculation method. We now integrate elements of structuration theory to an STS approach in order to explore the manner power relations pervade the processes of coproduction of a scientific discourse in the construction of legitimacy in water use.

The present formulation of virtual water limits the type of criticism that can be formulated concerning water use. It makes those actors deploying their strategy at the national scale very visible and legitimate. For example, al-Bira wastewater treatment plant has been the first to operate in the West Bank since 2013. It produces treated wastewater still unused in agriculture. Consequently, the project of a pipeline bringing treated wastewater from al-Bira, located at about 800 meters altitude directly to al-'Uja, located at about 200 m below sea level, appears as enhancing water efficiency. This treated wastewater is presently released in the environment. It penetrates the soil and is used as green water by nature and by a succession of farmers between the ridge, where al-Bira is located, and the Jordan Valley. In other words, this water is used many times by a variety of actors, whether human or nonhuman. The project of a pipeline would eliminate all of these uses, allowing only a single use before water trickles towards the Dead Sea acting as a sink. Treated wastewater is a new resource, a typical paracommon, which is the target of competing appropriation mechanisms.

The pipeline would reduce the overall efficiency of water use, yet thanks to the calculation method to assess virtual water, it would appear as raising the overall efficiency of water use at the national level.

Those actors promoting the project of a pipeline to bring treated wastewater to al-'Uja include individuals who purchased cheap land around that village when its spring nearly disappeared in 2011. (Trottier, 2013, p. 163) Well versed in "donor speak" and well integrated in the social arenas that elaborate projects for foreign donors, these Palestinian investors don't reside in al-'Uja. Foreign donors have devoted very large sums to the Palestinian water sector since 1994. [START_REF] Le More | International assistance to the Palestinians after Oslo : political guilt, wasted money[END_REF] Harnessing the discourse of virtual water allows individuals wishing to access those funds to shroud their projects in an illusion of water efficiency.

Similarly, as the idiom of virtual water projects uniformity over the entire territory, it automatically legitimates an institution such as the Palestinian Water Authority (PWA) which produces a discourse aimed at the national scale. Yet the law and decree that it upholds don't harness the various forms of local water management. As a result, they are neither implemented nor implementable.

The present formulation of virtual water makes those actors deploying their strategy at the scale of a village invisible and illegitimate. This phenomenon is akin to the manner global food models make smallholders invisible. [START_REF] Leblond | Performing an Invisibility Spell: Global Models, Food Regimes and Smallholders[END_REF] Virtual water is calculated as a stock embedded in the land which disappears through evapotranspiration.

Farmers and other actors interacting with this flow between these two points play a crucial role. Their actions determine which part of the flow is directed to one or other of the 16 possible trajectories. At first sight, their management may seem inefficient. Yet, when they direct water into a trajectory that benefits wild plants, the neighboring village's well or their neighbor's field, they are, however inadvertently, maintaining a solidarity with human and nonhuman neighbors. Their actions are portrayed as inefficient by the idiom of virtual water.

It hypothesizes that food security can only result from importing food from abroad that embeds less virtual water. Much of what appears to be inefficient water management contributes to other mechanisms that maintain local food security. Often, "improvements" to the irrigation infrastructure to enhance water efficiency proved detrimental to mechanisms that maintain local food security. For example, switching an open canal system to a pressurized pipe system ensures a greater portion of the incoming water leaves through evapotranspiration of the crop. But it decreases the portion of water that seeped in the ground and contributed to pasture for sheep, to khubbiza or to the neighboring village's well.

As an interpretive scheme, virtual water sheds much light on the interactions between the construction of a structure of signification and the accompanying construction of a structure of domination. Structuration theory shows that discursive mechanisms link structure and agency. [START_REF] Jabri | Discourses on Violence Conflict analysis reconsidered[END_REF] The production of meaning occurs through the construction of interpretive schemes which, when hegemonic, support a structure of signification. The latter reinforces the structure of domination. These structural properties of social systems constrain agency. They determine the degree of freedom of the actors, their capacity to act and even to think and be aware of their condition. In the case of virtual water, the prolific publications, detailing the stock embedded in various crops, support a structure of domination where international trade ensures both food security and sustainable development. Within such a structure of domination, smallholders are doomed. Within the accompanying structure of signification, their contribution to food security and sustainable development has never been considered. The manner virtual water is framed makes their interactions with water flows invisible.

Virtual water constitutes an interpretive scheme. It plays a role in a specific structure of signification where agribusinesses bent on exportation are considered the only legitimate, successful forms of farming. As an interpretive scheme produced by scientists, virtual water plays a role at the interface between our representation of nature and our construction of the social order. This interpretive scheme is thus an important part of the coproduction of both the discourse on efficient use of water in agriculture and the political management of water deemed to be sound. Any discourse concerning the environment relies on an underlying ideology. [START_REF] Forsyth | Critical Political Ecology: the politics of environmental science[END_REF] When knowledge concerning the environment circulates and is implemented, it is unavoidably transformed. [START_REF] Goldman | Knowing nature : conversations at the intersection of political ecology and science studies[END_REF] Similarly, an outwardly neutral indicator of water efficiency becomes a ruthless tool to classify farmers as either "successful" or "inefficient" and to justify policies promoting only the first category.

Map 4 shows the virtual water embedded in cucumbers produced by farmers selected on the basis of their classical efficiency. The representation in Map 4 differs significantly from that of Map 1. In all four villages, some farmers achieve rates of virtual water that are lower than that calculated using the standard method. Such farmers are portrayed as efficient and successful. A public policy based on the concept of virtual water would seek to support them. Yet, these farmers may not necessarily be integrated in the overall redistribution of the flow of water that inevitably occurs between the origin of water and the plant, in an especially beneficial manner for their local environment. Their actual contribution to food security may be much less than that of another farmer deemed inefficient according to this indicator. The idiom of virtual water nevertheless portrays them as the most capable of contributing to food security because the stock of water involved in producing their crop is smaller than the stock of water other farmers from their villages need to produce the same crop. As such, virtual water is not an appropriate indicator to discuss food security. It ignores the benefits of non-process beneficial consumption of water, allowing, for example, lemon trees and khubbiza to grow.

The calculation of virtual water as a stock feeds into the prevalent representations of water negotiations between Israel and the Palestinian Authority. Instead of focusing on the joint management of an uninterrupted flow, these negotiations have always treated water as a stock. The Oslo agreements attributed fixed volumes of water from each of the three West Bank aquifers to each of the two parties. Such a representation of water as an immobile resource is preposterous. For example, in Habla, farmers do not harvest rainwater from the rooftops of their greenhouses because the local wells provide water at 1 New Israeli Shekel per cubic meter, making the equipment to collect rainwater uncompetitive. In many plots, rainwater is channeled straight from greenhouses' rooftops into a ditch that brings it into Israel. The water Habla farmers bring to their plots is counted as part of the quantity attributed to the Palestinians, yet, once it has penetrated the ground, it flows into Israel. This phenomenon is even larger in locations were submersion irrigation is practiced, such as in Battir, and Wadi Fukin villages, situated next to the Green Line that demarcates the limit of Israel according to the 1949 armistice agreement.

Overcoming the limitations imposed by such a narrowly defined structure of signification is necessary. The danger of naturalizing the policy discourse based on virtual water is real. Naturalizing its specific definition of efficiency empowers state engineers as the only persons capable of establishing water rights and distribution schedules. (Boelens and Vos, 2012, p. 22, 24) It denies the knowledge accumulated by farmer managed institutions that have sometimes proved their resiliency over centuries. It legitimates a structure of domination where a merchant economy alone exists whereas Palestinian irrigating farmers, like millions of smallholders around the world, are very much embedded in a human economy. A merchant economy rearranges goods and its actors use money to accumulate wealth. A human economy creates, destroys and repositions humans, using money to create, maintain or interrupt relations among persons. [START_REF] Graeber | Debt The first 5,000 years[END_REF] A large part of food security for Palestinians depends on a human economy that involves "inefficient" uses of water.

Palestinian smallholders are facing the penetration of a merchant economy, especially since 2008, into domains previously managed by a human economy. The idiom of virtual water prevents us from understanding how this is affecting them.

Epistemic communities and Palestinian water

The literature on Palestinian water originates from three main epistemic communities.

Within area studies, water is usually treated as an immobile resource which needs to be carved out quantitatively between two opposing parties, Israel and the Palestinian Authority.

Many practitioners subscribe to this representation. Saeb Erekat, the present secretary general of the Palestinian Liberation Organization, stated in 2015 that establishing the borders would automatically solve the water problem. This would be the case if water remained static underground. But water keeps flowing irremediably, borders or no borders.

Within the water engineering literature, the concept of virtual water is so entrenched that framing water as a stock that can be exchanged through international trade is taken for granted. Virtual water is presented as an inexpensive adjustment deemed necessary because "[A]ny advances made in irrigation will translate into gains in other sectors -which often have higher economic returns or added value like industry, public water supply and sanitation or environmental services -which at present are not benefiting globally from water captured by irrigation." (Lopez-Gunn and Llamas, 2008, p. 228) Such wishful thinking is easily invalidated by field observations. Most often, "advances in irrigation" mean that water previously wasted in the process is redirected from one of the 16 possible trajectories into the only one that leads to the cultivated crop. It rarely leads to an increase in water availability for other users. [START_REF] Lankford | Resource Efficiency Complexity and the Commons[END_REF] This was demonstrated in Jericho in the 1990s as detailed earlier in this article. It was also demonstrated in Yemen when free American grain entered the country as food aid, leading farmers in the Sa'ada basin to forgo the irrigation of wheat and turn to growing alfalfa, a crop that consumes much more water. [START_REF] Lichtenthaler | Political Ecology and the Role of Water, Environment, Society and Economy in Northern Yemen[END_REF] Virtual water has been described as a myopic notion. [START_REF] Wichelns | Virtual water and water footprints: Compelling notions but notably flawed[END_REF] Farsightedness may describe it better. It allows a vision from afar, but so blurry a representation from up close that it becomes quite misleading.

Within the political ecology literature, or more broadly, the social science literature, the narrative opposing Capital and communities often dominates. "Communities" are usually not defined, but expected to protest against large companies such as multinational food-chain companies. [START_REF] Vos | Virtual Water Trade and the Contestation of Hydrosocial Territories[END_REF]) Such a literature identifies the "paradigm of bourgeois economics hiding in virtual water." (Gialis and Mavroudeas, 2014, p. 9) It usually remains remote from fieldwork and rarely explores the "communities" that are expected to protest against Capital. It often projects upon the commons a will to resist capitalism. [START_REF] Dardot | Commun. Essai sur la révolution au XXIè siècle[END_REF] Yet, fieldwork usually dispels this idea. A community that constructs a common concerning an object, such as Palestinian farmers do concerning water, seek an interaction with the state, when one exists, and with capitalism, concerning other objects. It doesn't seek to organize resistance against the state. Typically, Palestinian farmers who participate in the careful management of their commons whether they be springs or well companies, also receive tap water from either Mekorot, the Israeli national water company or from the municipality. The latter is usually supplied by a variety of sources, including Mekorot. When farmers rely on the free water from a spring managed as a common, they see no contradiction with selling their products on the market. Their maintenance of their common usually does not mean an opposition to capitalism outside of that common.

Conclusion

Opening the black box of virtual water allowed us to identify the underlying hypotheses both of the concept of virtual water and the method to assess it quantitatively. Our field research invalidated these hypotheses. Integrating structuration theory to an STS approach proved useful to explore the manner the coproduction of an interpretive scheme, virtual water, is linked to the construction of a structure of power. Virtual water, as an interpretive scheme, feeds a structure of signification that determines which farmers are "successful" because they are "efficient". This article demonstrated that the coproduction of virtual water as a concept legitimizes export oriented agribusinesses and portrays smallholders as inefficient. It makes their contribution to food security and environmental sustainability invisible.

Our approach frees us from such representations as it treats water as a flow. Water "lost" between source and plant, by one farmer, often feeds another user, whether human or non human. The decision processes, determining the various trajectories of water between source and plant, impact the virtual water content of a crop far more than climatic or agronomic variables. Such decision processes are both individual and collective in the Palestinian context. Analyzing them reveals the multiple interactions within agriculture that ensure food security, environmental sustainability, even housing security. It demonstrates that the appropriate scalar level to consider efficiency in water use is determined by the path water follows between source and plant.

Policies based on standard calculations of international virtual water flows unavoidably harm smallholders because it ignores the manner such farmers are embedded in redirecting water flows. Understanding the manner the coproduction of this concept is linked to the coproduction of a structure of domination is necessary to understand the context within which smallholders exert their agency. It allows us to understand their constraints and their definitions of efficiency. It allows us to understand their contribution to sustainable development. Policies need to build on such mechanisms.in order to succeed.

Map 1 :

 1 Average quantity of virtual water for one ton of cucumbers (m 3 /ton) four villages located across the three main aquifers of the West Bank discussed in this article. The values labeled "Winter season" and "Summer season" are measured on site.

  Figure one illustrates the water consumption of two farmers each growing the same variety of cucumbers over one dunum in the same greenhouse over two seasons, in two different villages. They both consume twice as much water in one season compared to the other. Yet one produces yields per cubic meter of water for the two seasons that are comparable. The other has 1/3 difference in his yields.

Figure 1 :

 1 Figure 1: Water volume (m 3 ) used per dunum and per season to produce 1 ton of cucumbers in each of two West Bank villages: Bardala and Habla

Figure 2 :

 2 Figure 2: Yield of cucumbers (kg) per cubic meter consumed during each season in each of two West Bank villages: Bardala and Habla

  Figure 2. Yield of cucumber per season for 1 m³ (in kg)

  the water law, both promulgated by the Palestinian Authority have been implemented in the

Map 4 :

 4 Average quantity (m 3 /ton) of water consumed by 1 ton of cucumbers produced by "efficient" farmers in four villages located across the three main aquifers of the West Bank

Table 1 -

 1 Average volume of virtual water in cucumbers in m 3 /ton in each of four West Bank villages Map 1 shows virtual water embedded in cucumbers as an average of the values emerging from our field work in each of four villages, Habla, Dhinnaba, Al-Jalama and Bardala, located across the three main aquifers of the West Bank. The volumes of virtual water embedded in cucumbers appear in Table1. The measured values demonstrate (1) a significant variability compared with the values calculated using the standard method, (2) a significant variability across space and (3) a significant variability across seasons. The Delft school acknowledged the variability of the virtual water content of a crop within the territory of a large state.(Chapagain and Orr, 2009, p. 1220) Our results demonstrate a great variability within a very small territory. While Bardala farmers demonstrate a greater efficiency than expected by the standard calculations, Dhinnaba summer cucumbers consume over four times the volume expected through the standard calculations. Agronomic variables are constant here. However, climate variables vary between these locations. Bardala is located in the Jordan Valley, 100 meters below sea level, but Dhinnaba is located 100 meters above sea level on the western slope of the West Bank. Such variability through space cannot be

	Village	According to	Measured on site	Measured on site	No of plots
		standard method	Winter season	Summer season
	Habla	69	70	126	3
	Dhinnaba	69	138	251	14
	Al-Jalama	69	73	73	3
	Bardala	69	42	39	2

Water leaves the system either through evapotranspiration through the leaves of plants, through evaporation from the soil or through reaching a sink such as the sea

The web tool of the Water footprint network produces a different value (33.1 m

/ton of blue water + 58.1 m 3 /ton of green water) for cucumbers in the West Bank, "Water footprint assessment tool: Production assessment", http://waterfootprint.org/en/resources/interactivetools/water-footprint-assessment-tool/ (accessed 18 November 2016). The web tool only presents values for open field cultivation. Greenhouse conditions reduce evapotranspiration by 22%. The value from the web tool thus yields 70,9 m 3 /ton for cucumbers in greenhouse conditions. In any case, using the figure from the web tool or from the standard valued averaging 69 m 3 /tonne does not change any point in the discussion that follows.


Isabelle Billard

Ali Ouadi

Clotilde Gaillard

Is a universal model to describe liquid/liquid extraction of cations by use of ionic liquids at reach?

A general chemical model describing the extraction mechanism of cations from an acidified aqueous phase toward an ionic liquid phase in which an extracting agent is dissolved is proposed. On this basis, fits are made which recover very satisfactorily the variation of the distribution ratio as a function of [HNO 3 ] for several experimental data sets from the literature. This chemical model is discussed and compared to another model.

Introduction

Liquid/liquid extraction of cationic entities is experiencing a renewed interest from the academic world through the introduction of Ionic Liquids (ILs). [1][START_REF] Billard | Handbook on the Physics and Chemistry of Rare earth[END_REF][START_REF] Binnemans | [END_REF] These solvents, composed solely of ions, offer some distinctive properties rendering them very appealing: [START_REF] Wasserscheid | Ionic liquids in synthesis[END_REF] Most ILs in use display very low vapour pressure and no flammability, by contrast to molecular solvents that often present low flash points and high volatility. In addition, it has been recognized that using ILs in replacement of traditional molecular solvents greatly enhances extraction efficiencies of many well-known extracting agents. [START_REF] Dai | [END_REF][6][7] Thanks to the increasing number of studies already performed, it is now acknowledged that metal extraction in such systems occurs through an extraction mechanism very different from that at work in molecular solvents. 1,8 However, the question remains whether extraction in ILs obeys a "universal" chemical scheme or not that could be summarized through the introduction of a limited number of chemical equilibria, as was already done long ago for the extraction of metallic cations towards molecular solvents.

Taking advantage of our experimental work devoted to the extraction of actinides from acidified aqueous phases towards ILs, 9,10 we propose a general model composed of a set of chemical equilibria, describing the extraction process occurring in aqueous phases/IL phase.

According to this model, fits of experimental D (distribution ratio) variations [10][11][12][13] versus the acidic (HNO 3 ) initial concentration of the aqueous phase are performed, demonstrating the very good quantitative agreement between our model and these data.

Applicability of this model to any extraction system involving cations and IL phases is then discussed and is compared to a second model proposed by another group. 11

Reference systems 2.1 Definitions and systems under study

In the following, extraction systems of interest will be denoted as: M m+ /HX//E/IL, where M m+ refers to the cation to be extracted, HX is the acid used, E is the extracting entity, irrespective of its form (molecular, ionic, protonable or not) and IL is the ionic liquid. A list of acronyms and abbreviations used for the names of the compounds E can be found at the end of this paper. We will use the term "system" for extraction data obtained with the same cation, same acid, same extracting agent but different ILs, while we will use the term "series" for extraction data obtained for a given IL in a system. In this work, we consider only systems for which no significant extraction is observed for M m+ /HX//IL. In other words, in the systems under study, the extracting agent, E, is responsible for the extraction and the IL solvent acts solely as a reception phase. The cationic and anionic parts of an IL are denoted as Cat + and Ani -, respectively. [X] and designate the equilibrium concentration of X in the aqueous and IL phase, respectively, while subscript "init" refers to the initial values of the concentration.

Selected experimental systems

In order to test our model, we chose two extraction systems for which a rather large set of experimental data is available in the literature. The data we consider are the experimental variations of the extraction ratio, D, as a function of [HNO 3 ] init , for a fixed concentration of E.

The experimental details of importance to this work are presented in tables 1 and 2.

The first system is UO 2 2+ /HNO 3 //TBP/C 1 C n imTf 2 N (n = 4, 5, 8, 10), where TBP is tributyl phosphate. The experimental data, redrawn from the works of Dietz et al., 12 Giridhar et al. 13 and Billard et al. , Am 3+ and an impressive list of lanthanide elements can also be found. [22][23][24] Therefore, the uranyl data (n = 4, 5, 8, 10) of this study are representative of a general trend.

The data illustrated in fig. 2 for Ca 2+ /HNO 3 //DCH18C6/C 1 C n imTf 2 N (n = 5, 8, 10) also present an evolution of the boomerang shape from n = 5 to n = 10 and, in addition, present a shoulder (or levelling) of the D variation in the approximate acidity range 0.5 -3M

for n = 8 and 10, which is thus denoted as regime III. Similar variations with a shoulder have been obtained for Sr 2+ and Ba 2+ , 11 so that the system we chose is also representative of a rather large wealth of data.

It is our opinion that all data cited above, where the element, the extracting agent and the IL phase are varied, display intrinsic similarities which we believe to be more significant than their differences. To our view, this is more than a coincidence and is the signature for a common mechanism underlying the various extraction profiles, which is accounted for through our model.

Chemical modelling

General model

There is a list of physical phenomena and chemical reactions that should be considered whatever the extraction mechanism itself could be.

First, the cation, M m+ , may experience complexation with X -, the acid counteranion introduced in the aqueous phase to avoid hydrolysis and precipitation. This acid may be either fully dissociated (HCl, HClO 4 etc.) or not (HNO 3 , H 2 SO 4 etc.).

Second, although the system is biphasic, mutual solubilities of IL and water have been evidenced, together with transfer of acid to the IL phase, even in the absence of E. 25 Therefore, depending on the chemical structure of E, its protonation in the IL phase may be considered, owing to the presence of H + ions arising from acid solubility.

As a consequence, the corresponding equilibria, with their corresponding equilibrium constants K Z , are written as follows:

-Successive complexations of M m+ in the aqueous phase:

(eqs. 1-i, K i )
-Partial dissociation of the acid:

(eq. 2, K HA )

-Protonation of the extracting agent:

(eq. 3, K 3 )
Then, we propose the extraction mechanism to proceed through three generic equilibria:

( (eqs. 4-i, K 4-i )
With 0 ≤ i < m and (k+l) = m-i (eqs. 5-i, K 5-i )

With i > 0 (eq. 6, K 6 )

This model is an extension of our previous proposal, which we successfully applied to the study of UO 2 2+ /HNO 3 //TBP/C 1 C 4 imTf 2 N 10 and UO 2 2+ /HNO 3 //malonamide/C 1 C 4 imTf 2 N. 9 As compared to this first model, there are three main differences. First, we now consider that all the positively charged complexes MX i (m-i)+ might be (but not necessarily are) extracted through a cationic exchange mechanism involving a combination of the H + and Cat + species present in the IL phase (eqs. 4-i), while we previously restricted the extraction of positively charged species to the naked ion M m+ solely. Second, in a similar way, we consider now all the negatively charged species, [MX (m+i) ] -to be possibly extracted through an anionic exchange involving i Ani -anions (eqs. 5-i), while we previously restricted the anionic exchange to the sole first negatively charged complex. Third, we also consider the extraction of neutral species (eq. 6), an option that was not included in our two previous attempts. 9,10 In principle, there should be no need to separate within three different equations (4, 5 and 6) the extraction process of positively charged, neutral and negatively charged species, but this

...) 3 , 2 1, (i ] [ ) (        i m i m MX iX M bH ) (      b b a a X H X H EH     H E ] [ ) ( ) (             iAni E MX E q Ani i X i m M i q i m m   ] [ ) ( ) (               lH kCat E MX E p H l Cat k MX i m p i i m i ] [ E MX E r mX M r m m     
would be at the cost of an increased complexity in the writing and in the number of indices and variables. As such, our model is as general as possible.

In the following subsections, a qualitative discussion of the model is first made, demonstrating its ability to recover the data of the reference systems. Next, we briefly describe and discuss the mathematical and chemical assumptions made in order to derive a mathematically tractable relationship linking D, the distribution ratio, to the experimental [HNO 3 ] init values in view of a quantitative approach to the data. Then, we give details on the programming details and fitting procedure. In the results section, we first present some calculations evidencing the contribution of each extraction equations (3, 4, 5 and 6) to the overall D calculations. Finally, our fitting results for the reference systems are presented, together with a general discussion.

Qualitative discussion of the model

The decrease in D versus [HNO 3 ] init at low acidities is qualitatively described by the combination of eqs. 1-i plus 4-0 alone. At very low acidities, the metal cation is extracted according to eq. 4-0 but, as [HNO 3 ] init increases, the metallic entity is blocked into non extractable species, thus leading to a decrease of D. On another hand, an increase in D at high acidities is qualitatively described through eqs. 5-i or eq. 6. As [HNO 3 ] init further increases, equations of type 5-i (or 6) become dominant and the presence of X -in the extraction equation leads to an increase in D. Therefore, by simply considering eqs. 1-i, 4-0 and 5-i (or 6), it is possible to qualitatively describe the boomerang shape experimentally observed.

Changing the IL cation to a more hydrophobic one (for example by increasing the alkyl chain length on the imidazolium ring) induces a lower Cat + equilibrium concentration in the aqueous phase, which in turn leads to a lower extraction ratio according to eqs. 4-i (provided k ≠ 0), as compared to a more soluble Cat + . Consequently, it is expected that D values at low acidities are decreasing as the hydrophobicity of the IL cation increases. In this case, the dominating character of the anionic (eqs. 5-i) or neutral extractions (eq. 6) becomes evident at lower HNO 3 values, so that the turnover concentration is expected to decrease as the hydrophobicity of the IL cation increases. Finally, as the IL cation is not involved in eqs. eqs. 4-i (i > 0). Under this hypothesis, depending on the relative values of all the involved equilibrium constants, there could be a range of [HNO 3 ] init values for which the intermediate species is dominating the aqueous speciation and is thus efficiently extracted, while the extraction of the anionic (or neutral) species through eq. 5-i or eq. 6 is not yet dominant.

Under these chemical conditions, a leveling off (i. e. shoulder) of the distribution profile is expected.

We now turn to a quantitative approach of our model.

Mathematical modelling

The chemical system described in section 3.1 can be translated into mathematical equations, following a procedure previously published 9 and according to a few hypotheses:

1) Activity coefficients are considered to be constant

2)

The ligand and H + in the IL phase are in large excess as compared to the metal.

3)

The concentrations of Ani -and Cat + in the IL phase are introduced in the equilibrium constants, which are thus conditional equilibrium constants.

Taking account of the activity coefficients for the numerous species of the system is a difficult task. For the aqueous phase, the Specific Interaction Theory (SIT) is a wellestablished procedure, [START_REF] Guillaumont | Update on the chemical thermodynamics of uranium, neptunium, plutonium, americium and technetium[END_REF] but faces the problem that there are neither experimental nor tabulated data for the two IL ions, Cat + and Ani -, thus preventing the use of this method. In addition, to the best of our knowledge, there is no theoretical approach to activity coefficients in IL phases so far. We thus decided to assume constant activity coefficients.

The second assumption is in line with chemical conditions usually prevailing in extraction experiments. However, in case of a protonable ligand, it may be envisioned that at very high acidities of the aqueous phase, the protonation constant (eq. 3) is so high that the "free" ligand concentration is no longer in large excess as compared to the initial metal concentration. This leads to an intricate mathematical system which is much more difficult to solve and we thus limit our study to the case of "low" protonation constants, i. e. to free ligand in excess even at the highest acidities investigated in this work, although protonated ligand species can be considered.

Program structure, fitting procedure and specific cases investigated

Under the frame discussed in the above section, one can derive an analytical expression for D, as a function of the initial concentrations of the chemicals and of all the equilibrium constants.

This expression is then implemented in a Fortran routine in view of data fitting (i. e. some parameters are set free in a minimization process) or calculations (i. e. all parameters are fixed). All fitting results presented here are based on the minimization of the   , using the Simplex and Migrad subroutines available on the CERN library, and defined as:

(eq.7)

Where N is the number of data points and D exp and D calc are the experimental and calculated D values, respectively. The errors associated to the parameter values (see tables 1 and 2) were obtained as the values inducing an increase of 5 % in the  2 . All  2 values are provided with 3 significant digits.

In a first step, we performed calculations in order to decipher the contributions of some of the equations to the overall D values. The results are presented in section 4.1. In a second step, we performed fits of the reference systems. The overall number of parameters to be fitted is high. For a +2 charged metal ion, assuming two successive complexations with X - and extraction of two positively charged, one neutral and one negatively charged species, the total number of parameters amounts to twelve (K 1-1 , K 1-2 , K 4-0 , K 4-1 , K 5-1 , K 6 , p, p', q, r plus k and k' in eqs. 4-0 and 4-1), notwithstanding of a possible protonation constant for the ligand, K 3 , while the data sets under study contain 8 to 13 experimental data points. Therefore, we fixed some of the parameters according to the following considerations:

i) Only two successive uranyl-nitrate complexes have been evidenced in the literature, [START_REF] Lange | Lange's handbook of chemistry[END_REF] thus equations of type 1-i are restricted to 1-1 (formation of the positively charged species [UO 2 (NO 3 )] + ) and 1-2 (formation of the neutral species [UO 2 (NO 3 ) 2 ]). In the case of calcium, only one nitrate complex is known [START_REF] Lange | Lange's handbook of chemistry[END_REF] thus limiting the model to eq. 1-1 (formation of [Ca(NO 3 )] + ). These successive nitrate complexation constants have been fixed to their thermodynamical published values. [START_REF] Lange | Lange's handbook of chemistry[END_REF] In addition, we will consider HNO 3 to be fully dissociated.

ii) Both TBP and DCH18C6 are assumed to be non protonable moieties in ILs, so that K 3 is set to zero in eq. 3. TBP protonation in molecular solvents is well-known and so is crown-ethers protonation. However, considering the ionic nature of ILs, the situation might be different in such media and it would be difficult to assign a specific structural form to the extracted acid, if any. Our previous study on the effect of TBP onto acid extraction 25 Therefore, we think it is justified both on an applied logic (number of parameters) and on an experimental basis to neglect ligand protonation in this work. Note however that the specific effect of ligand protonation is investigated in sect. 4.1.

iii) As such, the model accounts for several ligand stoichiometries in the extracted complexes (p, q and r in eqs. 4-i, 5-i and 6). However, as the data sets under investigations have all been acquired for fixed initial ligand concentrations, parameters p, q and r cannot be reasonably fitted from these data alone. All these parameters have thus been fixed to 1. As a consequence, the associated equilibrium constants become conditional constants that should not be over interpreted.

iv) The initial concentration of TBP and DCH18C6, together with the initial concentrations of UO 2 2+ and Ca 2+ , have been fixed to the published experimental values.

Concentrations of uranium or calcium indicated in the references as "at the trace level" have been arbitrarily fixed at 10 -7 M. In agreement with data previously published for C 1 C 4 imTf 2 N, 9,25 we assume that is a linear increasing function of [HNO 3 ] init . We also assume the slope of this variation to be identical for all the ILs under consideration in this work, and we fix the ratio value to 0.94, ie: = 0.94 (eq. 8)

v) The solubility of Tf 2 N -in water as a function of [HNO 3 ] init has been measured in C 1 C 4 imTf 2 N according to a procedure described in the supplementary materials. The experimental variation (see supplementary material) was fitted with a linear law and the solubility of Tf 2 N -in the other ILs was assumed to obey the same linear law, i.e:

(eq. 9)

Finally, we limited the possible extraction equilibria to 4-0, 4-1, 5-1 and 6 only.

According to these assumptions, the number of parameters is thus decreased to 6 (K 4-0 , K 4-1 , K 5-1 , K 6 , k in eq. 4-0 and its equivalent k' in eq. 4-1). The latter two have been allowed to take integer values only. Each series has been fitted independently and various trials have been performed. In particular, apart from the "general" fits with all parameters liable to variation, we also performed "limited" fits, for which some of the equilibrium constants were set to zero to investigate the effect of a restricted model onto the goodness of the fits.

Results and discussion

Individual contributions to the model

In Figs. 3 to 5, we present the calculated D variations for various "ideal" cases that are documented in Table 3. Figure 3 is dedicated to the contributions of equation 4-0 or equation 5-1 as the unique extraction equilibrium, to the effect of equations 4-0 and 5-1 taken together and to a comparison with eq. 6 alone. For all these calculations, two successive complexation equilibria in the aqueous phase have been additionally considered, that mimic the realistic uranyl case. The qualitative description given in section 3.2 for the boomerang shape and the change in [HNO 3 ] TO is in close connection with the plots. Furthermore, it can be seen that eq.

6 alone is not equivalent to eqs. 4-0 and 5-1 taken together. This is due to two main reasons: in eq. 6, neither [Cat + ] nor [Ani -] are implied, while these quantities have an impact in eqs. 4-0 and 5-1 through the variations expressed in eq. 9, and the different stoichiometric coefficients for X -(2 in eq. 6 and 3 in eq. 5-1) are directly related to the slope of the D increase as a function of [HX] init .

Then, Figures 4 and5 present the effect of the ligand protonation, for an ideal case close to the uranyl system (Fig. 4) or to the calcium case (Fig. 5). For K 3 = 0, the shoulder obtained is in line with the quantitative description in section 3.2. As K 3 is increased, the concentration of the free ligand is decreasing in the whole acidic range so the D values decrease, even at the lowest acidity of the aqueous phase. In Fig. 4, increasing the protonation of the ligand leads to an opening of the boomerang angle, a situation that has already been experimentally observed in the system UO 2 2+ /HNO 3 //malonamide/C 1 C 4 imTf 2 N. 9 In Fig. 5, the protonation of the ligand has a dramatic impact onto the D values at high acidities so that eventually the D plot resembles the traditional bell shape obtained in molecular solvents. In view of fitting boomerang shapes as illustrated in fig. 1, the data plotted in Figs. 4 and5 a posteriori justify neglecting K 3 .

Fittings

Tables 1 (uranyl case) and 2 (calcium case) display all the fitted values and the relevant data while Figs. 1 and2 present the fitted curves together with the experimental data sets. In the tables, the  2 values have been limited to three significant digits. In some cases, the fitting routine converges solely with a nil value of some of the parameters. These are indicated in the tables under the notation "ltz" (lowered to zero). For Ca 2+ /HNO 3 //DCH18C6/C 1 C 10 imTf 2 N, allowing all parameters to be free leads to convergence problems, due to a strong correlation between K 6 and K 5-1 , while the other parameters appear to be reasonably defined. Therefore, we performed two different fits, one fixing K 6 = 0 and the other one fixing K 5-1 = 0. These two parameter sets gave almost identical  2 values (less than 2 % relative difference) and almost indistinguishable plots.

As can be seen, the fits recover quite nicely the experimental trends for all the series.

Discussion

Uranium system:

Although obtained for rather different metal concentrations and at two different research groups, the two series for although the hydrophobicity of the IL cation increases with the alkyl chain length, the system seems to favor exchange of IL cations, in large excess, rather than exchange of H + , that are present in small quantities. However, this lowering of K 4-0 could also be interpreted as the evidence for a difference in the solvation energy of the [UO 2 .pTBP] 2+ species in the various ILs. It is probable that these two effects contribute to the lowering of D as a function of n at low acidity. Conversely, the fact that a unique K 5-1 value is able to account for all the data in Fig. 1 (average value: 6.2x10 -2 ) would indicate that the solvation energy of the species [UO 2 (NO 3 ) 3 .qTBP] -is more or less identical, whatever the IL. Finally, it is interesting to note that extraction of a neutral species is not to be considered in this system, whatever the IL. This is in line with the spectroscopic evidences that have been provided, demonstrating that the uranyl neutral species [UO 2 (NO 3 ) 2 .2TBP] is not present in extracted IL phases. 10,14 As mentioned previously, the data investigated here do not allow determining the exact values of k and ℓ in eqs. 4-i. In order to get some insight onto this question, measuring the D variation at a fixed acidity, as a function of added C 1 C n imCl in the aqueous phase is needed. 1,[START_REF] Billard | Handbook on the Physics and Chemistry of Rare earth[END_REF] To the best of our knowledge, such an experimental test has not been performed yet for the system UO 2 2+ /HNO 3 //TBP/C 1 C n imTf 2 N. In UO 2 2+ /HNO 3 //TBP/(CH 3 ) 3 NCH 2 CH 2 OMeTf 2 N, the cationic exchange has been proved to proceed through exchange of one H + and one Cat + , 14 but such a result cannot be transferred to our system with full confidence, owing to the differences in the hydrophilicity of the two ILs.

Calcium system: The situation is more intricate in this case. In particular, for the last series (C 1 C 10 imTf 2 N), K 6 is needed to recover the experimental variations, which was not the case for the uranyl system. It was not necessary to assume extraction of the first calcium-nitrato complex in C 1 C 5 imTf 2 N to fit the data, while the experimental variations could not be reproduced without this assumption for n = 8 and 10. The speciation calculated in the IL Finally, the major difference between the calcium and uranyl systems is the appearance of neutral extraction for calcium in C 1 C 10 imTf 2 N. Again, the reason why this is not true for the uranyl system is not understood at the moment, although it is most probably related to the ligand rather than to the metallic entity.

General discussion: Our chemical model is able to reproduce the experimental variations of the two chosen systems. In particular, the model is able to reproduce the changes in the D vs and for +1 ions (Na + , K + , Cs + ). 11,[START_REF] Dietz | [END_REF]29 This proposal is based on three distinct pathways. Two of them correspond to cationic exchange, either with H + or Cat + ions and the third one corresponds to ion pairing, (i.e. extraction of a neutral species) the relative balance between the three pathways being dependent on the chemical conditions (IL nature, ion to be extracted, nature of E etc.). Obviously, two of the suggested exchange processes, i. e. cationic exchange through H + and cationic exchange through Cat + , correspond to our proposal. In fact, these authors categorize cationic exchange under two different equations (i.e. pathways), while we merge these two in the more general equation written in the form of eq. 4-i. In this sense, we consider that the two models perfectly agree on the question of cationic exchange. Note however that our model accounts for mixed cationic exchange of the type k H + and ℓ Cat + and takes into account extraction of +3 or +4 ions, such as Am 3+ or Pu 4+ , thus being more general than the one proposed by Dietz and co-workers.

[
Clearly, the irreducible difference between the two models lies in the proposal of either ion pairing alone or anionic exchange together with ion pairing. Besides, the two proposals are in qualitative agreement with the data discussed in the present work, because under the assumption of ion pairing between M 2+ and two nitrate ions, an increase in the nitric acid concentration will lead to an increase in D, as in the case of anionic exchange involving three nitrates, as demonstrated through our simulations. However, as clearly shown in fig. 3, the slope of the D increase depends on the assumption made and, in the case of the uranyl system and in two out of three of the calcium series, our study shows that ion pairing is not occurring, while anionic exchange has to be considered to recover the data.

The difference between the two models is more than anecdotal because following one or the other of the two hypotheses, very different ways to tackle the question of pollution of the aqueous phase by IL solubilization as a by-side effect of the extraction mechanism can be envisioned. If ion pairing occurs alone, then one should always favor this mechanism, by using ILs with long alkyl side-chains 30 and/or fluorinated anions. 31 Attempts performed under these lines did not prove to be very efficient, possibly indicating that ion pairing is not a dominant mode of extraction, whatever the IL chosen. Actually, we also note that Ca 2+ /HNO 3 //DCH18C6/C 1 C 10 imTf 2 N is the less efficient system in view of Ca(II) extraction, at any acidities. Furthermore, this implies that extraction should always be performed at the highest achievable acidities in order for ion pairing to be dominant over cationic exchange and to get reasonable extraction distribution ratios. This may prove to be irrelevant in some industrial envisioned cases. By contrast, if anionic exchange can substitute to cationic exchange at high acidities, then ion exchange cannot be avoided but one may take advantage of it following two different strategies. First, one may favor cationic exchanges involving cheap sacrificial ions, introduced on purpose in the IL phase, such as Na + or NH 4 + . Attempts in this way have already been performed and proved to be quite efficient, although not replacing Cat + back transfer up to 100%. 32 Second, one may also observe that the best sacrificial ion is H + , which is already present in the IL in large amounts, thus not requiring any additional chemical to be introduced in the system. In view of system optimization, one has to understand in details the reasons driving the cationic exchange through either m Cat + , 6,33 m H + , 9,34 or mixed Cat + /H +9, 14 exchange as already been observed in the literature, in order to conceive extraction systems occurring with H + exchange only.

Conclusion

We system. Actually, spectroscopic data have already proved that the extracted species at high acidities in UO 2 2+ /HNO 3 //TBP/IL 10,14 differs from the neutral UO 2 (NO 3 ) 2 .TBP 2 extracted in dodecane, 10,14 thus confirming the need of anionic exchange at high acidities at least for some cases but the relative experimental abundances of the two models is still unknown, which will require a lot of additional experimental work. Spectroscopic studies appear to be a very promising way to solve this question and more work on this topic is underway in our group.

List of acronyms and abbreviations used.

M m+ ] (M) [E] (M) K 4-0 ℓ for K 4-0 K 4-1 ℓ for K 4-1 K 5-1 K 6  2 ref. C 1 C 4 imTf 2 N 4.2x10 -4* 1.1* 1.4x10 -3 (± 0.2x10 -3 ) 0 ltz n. a.
6.2x10 -2 (± 0.6x10 -2 ) ltz 8.58x10 -2 13 C 1 C 4 imTf 2 N 10 -3* 9x10 -4 (± 1x10 -4 ) 6.7x10 -2 (± 0.7x10 -2 ) 7.91x10 -2 10 C 1 C 5 imTf 2 N 10 -7 1.2* 6.8x10 -4 (± 0.9x10 -4 ) 6.5x10 -2 (± 0.7x10 -2 )

1.08x10 -1 12 C 1 C 8 imTf 2 N 3.4x10 -5 (± 0.4x10 -5 ) 5.9x10 -2 (± 0.6x10 -2 ) 6.83x10 -2 C 1 C 10 imTf 2 N ltz n. a. 3x10 -5 (± 2x10 -5 ) 0 5.6x10 -2 (± 0.6x10 -2 ) 6.97x10 -2 Table 1. Uranyl case. For all the fits: K 1-1 = 1.99 and K 1-2 = 0.07; p = q = r = 1; K 5-2 = 0. 2.4x10 -4 (± 0.3x10 -4 ) 0 ltz n. a. 1.7x10 -3 (± 0.3x10 -3 ) ltz 7.69x10 -2 11 C 1 C 8 imTf 2 N 8x10 -3 (± 1x10 -3 ) 1 6.2x10 -2 (± 0.7x10 -2 ) 1 5.4x10 -4 (± 0.5x10 -4 ) 3.84x10 -2 9 (± 1) 2 5.7x10 -2 (± 0.7x10 -2 ) C 1 C 10 imTf 2 N 3.1x10 -6 (± 0.7x10 -6) 0 4.3x10 -2 (± 0.7x10 -2) 0 4.8x10 -2 (± 0.6x10 -2 ) 5.40x10 -2 Table 2. Calcium case. For all the fits: K 1-1 = 1.9 and K 1-2 = 0; p = q = r = 1; K 5-2 = 0. K 3 = 0 (see text). *: as from the reference paper. ltz: lowered to zero by the fitting program n. a.: not applicable Table 3. Fixed values of the parameters for the calculations displayed in figs. 3 to 5. For all the calculations: p = q = r =1, [M m+ ] init = 10 -7 M (see text). 3 (see text).

The numbering refers to the first colomn in Table 3 and the arrows indicate the turnover concentration. 3 (see text).

The numbering refers to the first colomn in Table 3. 3 (see text).

The numbering refers to the first colomn in Table 3.

5-i and 6 ,

 6 a change in Cat + should not have too much impact onto the extraction at high acidities, provided the IL anion is kept constant. All these features are in perfect qualitative 3 //TBP/C 1 C n imTf 2 N (see section 2.2). Qualitative description of D plots displaying a shoulder as in the case of Ca 2+ /HNO 3 //DCH18C6/C 1 C n imTf 2 N (n = 8, 10) is basically possible on the same pattern, plus the extraction of an intermediate species, through

  has shown that TBP (1.1 M in C 1 C 4 imTf 2 N) has only a slight effect onto HNO 3 extraction (i. e. as compared to the quantities that are solubilised in the IL phase in the absence of TBP) and that this effect is hardly visible, owing to experimental uncertainties, below [HNO 3 ] init = 7.5 M. To the best of our knowledge, there are no similar data for DCH18C6 but we note that for the this work ([DCH18C6] = 0.1 M) the depletion in H + in the aqueous phase due to a possible ligand protonation would also be hardly detectable through titration.

  C 1 C 4 imTf 2 N give similar fitted values, which indicate good data quality. The K 4-0 values significantly decrease as a function of n, the alkyl chain length, until the value is set to zero by the fitting routine. For n = 10, the cancellation of K 4-0 is compensated by the extraction of a +1 charged species, through K 4-1 . As the number of exchanged H + remains constant to 0 from n = 4 to 10, this corresponds to an extraction mechanism evolving from exchange of two IL cations for n = 4, 5, 8 to one single IL cation for the more hydrophobic IL cation (n = 10). It has to be recalled that the extraction of positively charged species occurs solely at low acidities of the aqueous phase. Under these chemical conditions, the quantity of H + present in the IL phase is low, whatever the IL, and

  phase from the fits (n = 8 or 10) shows that below [HNO 3 ] init = 0.1 M, the dominating extracted species is [Ca.pDCH18C6] 2+ , while [Ca(NO 3 ).qDCH18C6] + is dominant in the range ca. 0.1 M up to 2-3 M, above which the main species is either Ca(NO 3 ) 3 .rDCH18C6] -(n = 5, 8) or [Ca(NO 3 ) 2 .rDCH18C6] (n=10). It is quite difficult to interpret this result and the reasons why C 1 C n imTf 2 N (n = 8 or 10) would accommodate the species [CaNO 3 .pDCH18C6] + better than C 1 C 5 imTf 2 N remains unclear at the moment.In addition, change in the ℓ values for K 4-0 , corresponding to a change in the nature of the exchanged cations, makes comparison from one set of fitted values to another quite difficult. However, by comparison of the uranyl and calcium cases, we note that C 1 C 5 imTf 2 N favors IL cation exchange whatever the metal/extracting agent couple, while C 1 C 8 imTf 2 N and C 1 C 10 imTf 2 N accommodate both IL cation and H + exchanges in the presence of calcium/DCH18C6 but only IL cation exchange in the presence of uranyl/TBP. Considering the identical charges of the metallic cations of this study, and the very similar complexation constants K 1-1 for the two, such a difference should rather be ascribable to the difference in the ligand but the physical reasons are unclear.

C 1 C

 1 n im + :1-methyl, 3-n-alkyl imidazolium CMPO: octyl(phenyl)-N,N-diisobutylcarbamoylmethyl(phosphine oxide) Cyanex-272: commercial compound, based on phosphinic acid DCH18C6: dicyclohexano-18-crown-6 ether HOPO: 2-hydroxypyridine-N-oxide ImPTf 2 N: diethyl-2-(3-methylimidazolium)ethylphosphonateTf 2 N R 1 R 2 R 3 R 4 N + : tetraalkylammonium ion TBP: tributyl phosphate Tf 2 N -: bis(trifluoromethanesulfonyl)imide T-DGA: tripodal diglycolamide IL phase [

  K 3 = 0 (see text). *: as from the reference paper. ltz: lowered to zero by the fitting program n. a.: not applicable IL phase [M m+ ] (M) [E]

Figure

  Figure #plot K 4-0 K 4-1 K 5-1 K 3 ℓ in eq. 4-0 K 6 [E] init (M) K 1-1 K 1-2

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Experimental data for the reference system UO 2 2+ /HNO 3 //TBP/C 1 C n imTf 2 N. Data redrawn after 13 (○: C 1 C 4 imTf 2 N), after 10 (•: C 1 C 4 imTf 2 N) and 12 (▲: C 1 C 5 imTf 2 N; ◊: C 1 C 8 imTf 2 N and ■: C 1 C 10 imTf 2 N). Solid lines: simulations (see text).

Fig. 4 .

 4 Fig. 4. Calculations of the D variations according to the values displayed in Table3(see text). The numbering refers to the first colomn in Table3.

Fig. 5 .

 5 Fig. 5. Calculations of the D variations according to the values displayed in Table3(see text). The numbering refers to the first colomn in Table3.

  10 are displayed in figure 1. The second system is Ca 2+ /HNO 3 //DCH18C6/C 1 C n imTf 2 N (n = 5, 8, 10), where DCH18C6 is a crown-ether.11 The data, redrawn from the work of Hawkins and co-workers, are displayed in figure2. TO , D is sharply increasing as a function of [HNO 3 ] init (regime II). The turnover acidity value depends on the nature of the IL cation, while the D variation in regime II is independent of the IL cation nature. Such a behaviour is not limited to uranyl or 2+ ions, as Am 3+ /HNO 3 //Cyanex-272/C 1 -C 10 imTf 2 N16 or Am 3+ /HNO 3 //T-DGA/C 1 C n imTf 2 N (n = 4, 6, 8),17 Pu 4+ /HNO 3 //octyl-1,2-HOPO/C 1 C 8 imTf 2 N,18 Th 4+ /HNO 3 //diglycolamide/C 1 C n imPF 6 (n = 4, 6, 8),19 Pu 4+ /HNO 3 //DOAImTf 2 N/C 1 C n imTf 2 N (n = 4, 6)20 and Pu 4+ /HNO 3 //ImPTf 2 N/C 1 C 4 imTf 2 N 21 also evidence a clear boomerang shape. Other examples for Pu 4+ , UO 2 2+

	These two systems have been chosen because they correspond to different cations and two different extracting agents and also provide interesting experimental features as a function of the alkyl chain length of the IL phase. The "boomerang" variations observed for the system UO 2 also be found for UO 2 2+ /HNO 3 //TBP/R 1 R 2 R 3 R 4 NTf 2 N, 14 UO 2 2+ /HNO 3 //diglycolamide/C 1 C n imPF 6 (n = 4, 6, 8) 15 and UO 2 2+ /HNO 3 //malonamide/C 1 -2+ /HNO This boomerang shape is quite common in the literature. Actually, such variations can C 4 imTf 2 N. 9

3 //TBP/C 1 C n imTf 2 N (n = 4, 5, 8, 10) can be qualitatively described by defining two zones. At low acidities, D is either decreasing or constant as a function of [HNO 3 ] init (regime I), the exact values being dependent of the cationic nature of the IL. Above a turnover acidity value, denoted as [HX]

  HNO 3 ] init pattern as a function of the nature of the IL cation, as depicted in figs.1 and 2, with

	extraction mechanisms of variable importance. Although this success does not prove that this
	model is a fully correct description of the extraction processes actually occurring, it is
	nevertheless a very encouraging result.
	Another suggestion has been made, in view of qualitatively describing the extraction
	data for Ca 2+ discussed in the present work, together with similar data obtained for Sr 2+ , Ba 2+

  propose a chemical model, based on cationic, neutral and anionic exchange, which is able to recover a large number of extraction data for systems of the form M m+ /HX//E/IL. The restricted version of this model proposed by other authors and solely considering cationic and ion pairing, appears to be insufficient to quantitatively describe the UO 2 2+ /HNO 3 //TBP/C 1 C n imTf 2 N system, and part of the Ca 2+ /HNO 3 //DCH18C6/C 1 C n imTf 2 N

Acknowledgments

The financial support of the French program ANR is greatly acknowledged (LILAT project). Dr. M. Sypula is thanked for the NMR data.

Supplementary materials

1-butyl-3-imidazolium bis(trifluorosulfonyl)imide (C 1 C 4 imTf 2 N) was purchased from Solvionic (purity: 99.5%, Verniolle, France) and dried prior to use according to a published procedure. 35 0.5 mL of the IL phase was contacted with 0.5 mL of an aqueous phase of variable nitric acid concentration. Both phases were contacted in a mechanical shaker at room temperature (293K±1) for three hours followed by 2 min centrifugation. The concentration of Tf 2 N -(see figure below) in the aqueous phase was measured using 19