Nelly Leblond

Performing an invisibility spell: global models, food regimes and smallholders

Nelly Leblond (Université Paul Valéry) Julie Trottier (CNRS) Abstract:

The present construction of global representations of food and farming is problematic. For example, how can we "know" the world needs to double food production although we cannot foresee a food crisis? How can we estimate investment opportunities while failing to quantify their impacts on smallholders? Global models constrain the manner we perceive the food regime as they produce such representations. We need to identify the causal relations embedded inside models' equations and why they are arrayed in this fashion. This paper combines actor network theory and structurationist theory to analyse a sample of 70 global models. It locates the modules and equations of these black boxes in the sociotechnical and political context of their production. A bibliometric analysis finally sketches the overall epistemic community that drove models into success or extinction. Dominant global models recycle equations, modules and databases to effectuate narrow worlds. They make smallholder farming invisible in spite of its prevalence around the world. They do not address food needs and construct pixellated representations of under utilized land. They systematically favour large scale agricultural trade and investments in production and productivity. This reflects the structure of signification modelers adhere to as well as the structure of domination they are embedded in. Securing clients ensures the success of global models independently from their validation. The paper demonstrates the manner modeling is a social practice embedded in power relations. Considering simultaneously the structure of domination formalized inside models and surrounding modeling is crucial. Future research should investigate how various actors resort to global models to champion their goals. It should question the policy recommendations drawn from such models and their relevance as decision support tools.

Word Count: 9624 words

Introduction

A food regime is defined as a structure of production and consumption of food on a world scale, including the explicit and implicit rules that govern it [START_REF] Friedmann | The political Economy of Food: A Global Crisis[END_REF]. As such, a food regime is a structure of domination, according to the idiom of structurationist theory [START_REF] Jabri | Discourses on Violence Conflict analysis reconsidered[END_REF]. Global models aim to represent food production and consumption around the world. They play a pivotal role in the construction of specific patterns of production and consumption, a role which goes far beyond representing these patterns. Which actors want these models, for which purposes, and how they use them needs to be examined at the same time as we study the manner these models attempt to represent the world. The "co-production" of scientific knowledge designates the process whereby the latter both embeds and is embedded in social identities, institutions, representations and discourses [START_REF] Jasanoff | States of knowledge : the co-production of science and social order[END_REF]. This article investigates the co-production of global models and the food regimes as well as some of the consequences of this co-production.

Science is a social practice. The multiplicity of knowledge productions concerning the environment or agriculture makes the practice of environmental science and the study of food production and consumption even more complex than that of classic laboratory fields. Scientists are unavoidably influenced by the perceived needs of those who try to "apply" environmental knowledge. They are also influenced by the widely circulating knowledge claims made by scientists and others within and outside their fields. As a result, scientific practice cannot be understood in isolation from the processes of knowledge circulation and application [START_REF] Goldman | Knowing nature : conversations at the intersection of political ecology and science studies[END_REF].

Actor network theory (ANT) has argued against defining a priori the context within which actors interact. It has distinguished entities and actors on the basis of their connections with other entities and other actors [START_REF] Latour | Reassembling the Social: An Introduction to Actor-Network-Theory[END_REF]. This has proved immensely useful to study the role of agency, whether human or non human. Its unfortunate side effect, however, is to neglect power interactions among various actors. If interactions are not examined within their wider context, the power imbalances within which actors evolve can go unnoticed. We risk ascribing an agency to people acting under duress, for example. Structurationist theory reconciles the consideration of human agency with the consideration of structures of domination within society [START_REF] Jabri | Discourses on Violence Conflict analysis reconsidered[END_REF][START_REF] Jabri | The Postcolonial Subject[END_REF]. Both agency and structure need to be examined when we turn to human interactions with the environment such as occurs in agriculture [START_REF] Trottier | A wall, water and power: the Israeli 'separation fence[END_REF]. Harnessing this approach allows us to shed new light on the manner global models contribute to the global food regime.

The term "black box" designates a scientific claim once it has been turned into an unquestionable scientific fact, or a machine after it has been made to work [START_REF] Latour | Science in Action[END_REF]. This paper opens 70 "black boxes" as it analyses a sample of global models and examines the causal relations that are put into equations inside them. It locates these causal relations in the context within which the models were produced. It questions the silences within these models. It shows the specific worlds that such models produce as well as the policy recommendations they can or cannot lead to. It questions the types of government embedded in such models. The paper then examines the links among the numerous models that often borrow modules or equations from one another. This sheds light on the struggles or extinction of alternative models. Finally, the paper turns to the epistemic communities that have championed various models. The article argues that the co-production of global models and the food regime means that models effectuate the world far more than they represent it.

Understanding the causal relations embedded within global models of food production and consumption allows us to identify which agency can actually be exerted according to these models. It also allows us to identify which actors are effectively silenced because their agency cannot be represented by these models. Our study demonstrates that the models who became dominant were the ones who enrolled most allies, exactly as ANT expects. It also demonstrates that those models who succeeded in enrolling most actors were embedding specific power interactions within their equations. They contributed to constructing a structure of signification that suited a specific structure of domination, exactly as structurationist theory expects. Thus, successful global models posited the only possible development of the food regime occurs through international trade and through targeted investments, for example on the basis of potential yields.

Beyond shedding light on the manner models contribute to the food regime, this article shows the usefulness of combining ANT and structurationist theory. These two approaches have tended to shun each other when tackling such complexity.

Global Models: Opening the Black Box

What is inside a model? For the purposes of this article, a model is understood strictly as a set of computerized, mathematical relations that link variables within functions purporting to explain, describe, judge or predict. This paper examines models that deal with food consumption and production at the global scale. Each model puts forward a number of causal relations linking variables such as economic demand, agronomic practices, climatic conditions, and population growth, to represent the global picture. The manner these causal relations are formulated and arrayed is shaped by the structure of signification the modelers favour. Structurationist theory defines a structure of signification as the overall production of meaning achieved by the creation and repeated use of interpretive schemes to describe the world and our actions within it [START_REF] Jabri | Discourses on Violence Conflict analysis reconsidered[END_REF]. A structure of signification emphasizing interactions among states produces a world scale depiction of the food regime. A structure of signification emphasizing interactions, such as climate change, among a much greater variety of actors around the world produces a global scale depiction of the food regime. Which variables modelers choose to integrate and how they arrange them into causal relations allows us to distinguish four main categories of models: economic models, biophysical models, integrated models and hybrid models, as illustrated in table 1.

Our sample of 70 global models was built through a literature review of large scale modeling of food and farming including grey literature on the different modeling enterprises. We applied a broad sampling method taking into account both academic models and those developed by think tanks, international institutions and ministries. The purpose of this sample is to characterize the practice of global modeling rather than to identify the "representative" models [START_REF] Becker | La prise en compte de cas inhabituels dans l'analyse sociologique : les conseils de Hughes[END_REF]. Out of an initial set of 90 models , 20 were discarded because of lack of information, limited focus on food and farming issues, or limited spatial scale. Early warning systems of food and farming and monitoring of food insecurity were also excluded because they do not offer a formalization of food and farming systems but rather a collection of indicators. Such representations were not considered as global models for the purpose of our exercise.

Place Table 1 here.

Global economic models focus on the exchanges of agricultural products. They initially relied on a set of national modules, usually those of main exporting or importing states such as the United States, Canada or Australia, and an additional module describing the "rest of the world". Such modules are connected through international market functions where demand and supply meet and thus determine physical and economic equilibrium prices. Economic models thus rely on pre-existing national scale models and data bases. By the 1970s, time series oriented models had started harnessing the latter to extrapolate past trends in order to predict future trends. Later, models based on a general equilibrium theory, relying on price to balance demand and supply supplanted them.

Global biophysical models focus on the production potential of the planet from an agronomic point of view. Their equations link physical variables such as rainfall, temperature, and surface properties to calculate the quantity of biomass that can be produced. They can be theory based and determine the yield strictly on the basis of agronomy theory, or data driven. In this case, they rely on the statistical analysis of datasets to identify the main contributions to the crop yields. Data bases the Food and Agricultural Organization of the United Nations (FAO) collected across countries served to elaborate the first biophysical models. Later, the ecophysiological measurements carried out in experimental stations around the planet and remote sensing data fed them further.

Global integrated models focus on the interactions between human activities, as economic models do, and the environment, as biophysical models do. Two main sorts of integrated models have emerged. Homogeneous models have been developed, each by a single team, often using system dynamics modeling. These have tended not to include prices, favouring kilocalories instead, for example. They have also tended to extinction. Heterogeneous models have been developed by several teams, each contributing its own module to the overall model. They link modules from each of economic and biophysical models, gathering variables that are measured in different units such as kilocalories, dollars or cubic meters. These have tended to include prices. And they have fared much better than homogeneous models.

Global hybrid models overlap broad sets of factors, whether economic, physical or social, as layers of pixels. Most land use datasets integrated in global models have a 5-arc minute resolution, in other words the pixels represent around 100 km² or 10 000 ha. Hybrid models use the pixel as the basic unit of analysis instead of the state. Yet the state often remains the central unit of data gathering even within global datasets. The representations that emerge from these models thus sometimes express divisions along national borders even when this was not intended.

Locating the causal relations embedded in the models

Locating the causal relations, embedded in each category of models, in the political and economic context within which the models emerged, is important. It sheds much light on why these causal relations were put forward. Once it is enshrined inside an equation within a model, a causal relation becomes essentialized, i.e. the fact that it is a socially constructed depiction of reality no longer appears. Instead, this causal relation appears as a "law of nature". Locating the construction of the models, together with the specific causal relations they embed, allows a more critical understanding of the role models play in the coproduction of the food regime.

National research institutions and national planning agencies were at the forefront of the development of economic models. The Ministry of Agriculture Forestry and Fisheries in Japan produced the World Basic Food Model in 1974 and later IFPSIM i . The United States Department of Agriculture (USDA) developed the World Grain-Oilseed-Livestock Economy model (GOL) and SWOPSIM in the 1970s. The Institut National de la Recherche Agronomique (INRA), in France, developed MISS. Such models emerged then because datasets and adequate computing facilities became available. Researchers and planners turned to datasets produced by national accounting concerning exports, imports, inputs and outputs as well as to datasets concerning elasticities (Josling et al., 2010). Most industrialized, capitalist states set up such datasets in the 1950s to inform national policy. This was a state driven process where economists and civil servants defined categories to analyse and manage the economy. Keynesianism dominated at that time, and both economists and civil servants usually considered the state was in charge of regulating economic markets [START_REF] Desrosières | Managing the Economy[END_REF].

The development of global economic models occurred at a time when controversy raged concerning national agricultural subsidies and the liberalization of international agricultural trade. Several western countries were producing more than they could consume and favoured a liberalization of international exchanges. American economists perceived models as a pragmatic tool to guide policies [START_REF] Benedictis | Between Scylla and Charibdys: Agricultural Economists' Navigation Around Free Trade and Protectionism[END_REF][START_REF] Armatte | La science économique comme ingénierie[END_REF]. As the development of the categories and of the datasets was only carried out in northern states, it fitted their economic structure where agriculture is industrialised and food commercialized. This left the rest of the world in a void, both from the point of view of data and the development of appropriate categories to describe widespread activities, such as smallholder agriculture. However, the dominant ideology, soon after the second world war, promoted a technological solution to the food problem, one where agricultural technology and increased production should end hunger [START_REF] Cornilleau | La sécurité alimentaire comme problème global : généalogie, acteurs, institutions et expertises[END_REF]. Information concerning smallhoder agriculture seemed unimportant because, as a relic of the past, it would soon be transformed into more efficient, scientifically driven systems.

As opposed to economic models, that were state driven, global biophysical models were driven by international initiatives. Spurred by the 1972 Limits to Growth report, international organisations sought to establish the carrying capacity of the planet. They urged scientists to turn away from national food self-sufficiency and to think globally. Wageningen University developed MOIRA in 1972 and the International Institute of Applied Systems Analysis (IIASA) produced the most detailed biophysical model, the Global Agro Ecological Zones project. FAO collected worldwide datasets, establishing the first satellite databases to map cultivated areas around the world. In the 1970s, the carrying capacity was believed to be determined strictly by physical and technical constraints. Environmental research later demonstrated that the carrying capacity of any ecosystem is also a function of human practices. Biophysical models predated that understanding and the causal relations they embed reflect this. The rise of system dynamics and the cold war both fostered the rise of global integrated models. Protecting the global environment could rally both east and west around a common goal, thereby appeasing tensions. Global modeling was appealing because this representation of the world dis-embeds production and consumption data from their local political context and thus appears apolitical. The causal relations it embeds in its equations are deeply political, but the overall tool appears to be neutral and technical [START_REF] Taylor | How do we know we have global environmental problems? Science and the globalization of environmental discourse[END_REF]. The IIASA was thus located in Vienna, aiming to gather scientists from communist and capitalist states, seeking to respond to the Limits to Growth report with the development of new models.

Global hybrid models proliferated especially after 2000. This was a time when satellite produced datasets became easily available for all, as well as Geographic Information System (GIS). Financial deregulation and new doctrines promoting intervention inside state affairs withered away the Westphalian structure of the international community. The state ceased to appear as the basic building block and the only legitimate actor. Hybrid models such as the food density map of FAO [START_REF] Matuschke | Rapid urbanization and food security: Using food density maps to identify future food security hotspots[END_REF] reflected this change as they replaced a world composed of a collection of states with a world composed of a collection of pixels.

In recent years, all four types of models underwent a "spatial turn", i.e. they integrated GIS and undertook to project their results on grids of pixels. This approach was championed by the World Bank Development Report in 2009 which insisted on economic geography. This systematic spatialisation has several consequences. It projects homogeneity on any area represented by one pixel, thereby erasing anything that exists only at a smaller scale. The grid size becomes extremely important in making small scale farming systems invisible or not [START_REF] Trottier | Donors, Modellers and Development Brokers: The Pork Barrel of Water Management Research[END_REF][START_REF] Chouquer | Terres porteuses entre faim de terres et appétit d'espace[END_REF].

As we located the production of models within their political and economic contexts, it is worth also locating the extinction of some models. Economic models based on statistical series fell into disuse because they could not model prices and simulate market dynamics. World Bank economists judged them inferior because they considered the market was central to the world food system and food security. Models, for example LAWM, which included radical changes such as land redistribution scenarios, were deemed unrealistic and later fell into oblivion [START_REF] Bernardini | The Bariloche world model as an infeasibility sutdy[END_REF]. Actually, any model that could not target and secure the loyalty of clients, was doomed. Siegmann noted that finding clients for a model was very problematic unless it catered specifically to their practical concerns, such as economic forecasts [START_REF] Siegmann | World Modeling . Report for UNESCO[END_REF].

Which silences within these models? Any scientific discourse is based on the silence of its object [START_REF] Foucault | The Archaeology of Knowledge[END_REF]. Ignorance is part of the construction of science, either as a driver or as a product [START_REF] Proctor | A missing term to describe the cultural production of ignorance (and its study)[END_REF]. Scientific practice, by selecting information, highlighting pathways or stabilizing methods, can produce numerous silences, inadvertently or deliberately. All four categories of models embed important silences. We will mention only three, which have far reaching consequences: silence on the context of the data, silence on non-monetary exchanges, and silences on food needs.

All data used in these models is necessarily disembedded from its context. Agricultural systems appear as starting points and evolving only under the pressure of variables such as prices, technological features and trade policies. As a consequence all previous subsidies and state support that shaped these production systems are essentialized, i.e. they are made to appear as a part of nature. In these models, a Californian agrobusiness heir to decades of free water channelled thanks to infrastructure funded by the American taxpayer is indistinguishable from a Malian farm practicing subsistence agriculture. The essentialisation of socially constructed phenomena prevents models from integrating their evolution. These models use databases structured according to categories that were defined to address agricultural marketing in the 1950s or 1970s. Thus, food production and consumption that is not based on monetary exchanges does not exist within the representation produced by these models. The term family farming designates a form of organization of agricultural production "characterized by organic links between the family and the production unit and by the mobilization of family labor, excluding permanent employees" (Bélières et al, 2015, p.20). Quantifying family farming and on-farm consumption is notoriously difficult. However, statistics from 81 countries gathering 84% of the world population show that 85% of agricultural holdings, i.e. 373 million holdings, are family farms under 2 ha [START_REF] Bélières | Family Farming Around the World. Definitions, contributions and public policies[END_REF][START_REF] Bélières | Family Farming Around the World. Definitions, contributions and public policies[END_REF]. This is far smaller than the usual grid size used by global models, around 10 000 ha. Undeniably, the bulk of basic food production in these countries originates from family farms, with an important on-farm consumption and contribution to the livelihoods of extended families. Models are particularly ill equipped to represent the contribution of family farming.

Finally, the manner the modelers pictured the food regime shaped the equations within the models. These usually rely on food prices as a proxy to food access. Drawing on the datasets produced by national accounting, they calculate the point at which demand meets supply. Food demand is a function representing the amount of food an individual wishes to buy at a given price. The demand expressed by someone who has no money at all is necessarily satisfied, even when he is starving to death. The demand expressed by an individual matches his needs only if the market prices for satisfying them are affordable for that person. Food needs include both a quantitative dimension, as individuals require a minimum number of calories, and a qualitative dimension. Indeed, individuals require a variety of foods to avoid malnutrition and to maintain the cultural processes in which food is embedded. Dominant models make needs invisible because they only focus on demand. Obesity is also made invisible, because the causal relations framed within the models do not allow to represent it either. Yet, obesity is a major problem within the food regime. Models most widely used are therefore structurally incapable of addressing food needs.

In short, the silences within these models are important and are part of their structure. They contribute to represent a specific food regime. Many other silences could be identified. For example cattle raising is often under-represented, especially extensive pastoralism, because the land used for this activity is difficult to represent. Access to infrastructure necessary for distribution and exchange capacity is rarely represented within these models.

Which worlds do these models produce?

All four categories of global models construct a very specific paradigm to understand a food regime, thereby portraying very few options for its development. They contribute to the co-production of narrow worlds.

Global economic and integrated models rely on a world structured into states, which they reproduce within the representations they generate. Hybrid and biophysical models rely on sets of pixels that do not show state borders. Thus, hybrid and biophysical models represent Europe as a global wheat basket whereas economic models represent it as a collection of states or economic regions producing and trading wheat. None of them represent the trade of crops within states from one region able to produce it to another unable to produce it, such as the trade of olives between the south and the north of France, for example.

Global economic models and modules place states and exchanges among states at the centre of the world they produce. For example, the Basic Linked System (BLS) model, links national markets to a world market [START_REF] Fischer | The basic linked system of the food and agriculture program at IIASA: An overview of the structure of the national models[END_REF]. Through iterations, they balance national demands and supplies showing different elasticities. Unavoidably, this iteration process concludes that countries with a lower marginal cost of production will specialise in this production. Development can only mean a greater international food trade. Yet, currently, international food trade represents only a small fraction of food production. Less than 15% of cereals produced in the world are currently exchanged on world food markets, for example (FAO, 2015). These models thus effectuate a world where international food trade is the dominant development path in spite of the fact it remains marginal.

Biophysical and hybrid models produce sets of pixels, each of which is independent from the other. They co-produce a world where intervention is possible over various spaces without any need for these spaces to match the boundaries of a state. For example, global datasets allow identifying "climate risk hot spots" where climate change is most likely to impact agricultural yields negatively [START_REF] Deryng | Simulating the effects of climate and agricultural management practices on global crop yield[END_REF]. Adaptation strategies such as planting new crops, for example, can then target specific zones that might straddle a national border or be a small subset of a larger national space [START_REF] Lobell | Prioritizing Climate Change Adaptation Needs for Food Security in 2030[END_REF]. These models thus effectuate a world where state sovereignty does not matter much.

The spatial turn, which most models underwent after the 2000s, has had an especially far reaching consequence. Projecting datasets on grids of pixels has produced under-utilized lands and vacant lands. Dominant models do not include land uses such as pastoralism or non-monetarized agriculture in their inputs or their outputs. The homogeneity projected on each pixel, usually representing 10 000 ha, masks a great diversity of resource access and property regimes. Fine grain representations can show clusters of farms smaller than 10 ha, but, for several reasons, such representations are not integrated in global models. First of all, high resolution datasets exist concerning some regions of the world, such as Europe, but not the entire world. As a result, their integration in a global model is problematic. Moreover, they require prohibitive processing capacities. Mixed pixels allow considering several land uses within an area smaller than that represented by the pixel. However, neither agronomy, economic or ecological theory is yet capable of integrating this category of "mixed pixel" within the calculations carried out by the models. As a result, those smallholders who are active over a scalar level smaller than that represented by a pixel are made invisible. Vacant land is thus constructed within a representation that shows intervention on any portion of space as possible or even desirable.

Finally, these models represent very poorly transport infrastructure, which is crucial for the exchange of agricultural products. The world they construct is one where transport is not problematic, where the trade-offs between transport infrastructure and other land uses, whether agricultural or environmental, are negligible.

In summary, all four categories of models produce simplified worlds where few interventions are possible and only partially assessed. In global economic models and integrated models centred on equilibrium theory, the only possible development of the food regime involves monetarized agricultural production and international trade. In global biophysical models and hybrid models, vacant yet potentially productive land replace large stretches of smallholder agriculture and pastoralism. They produce worlds where intervention can be elaborated on portions of space anywhere on the planet. Therefore, the policy recommendations they can lead to are worth examining to understand the role they play in the construction of the food regime.

How global models constrain the scope of potential policy recommandations

The mechanisms whereby models function restrict greatly the sort of policy recommendations they can lead to. They are unable, structurally, to inform policy that would include smallholder agriculture because the categories they rely on under-represent it. However, since the 2000s their pixelated design allows them to promote investments in any area on the basis of its biophysical and economic potential, regardless of its political or social context. The contract "Lessons for the large-scale acquisition of land from a global analysis of agricultural land use" between the IIASA and the World Bank illustrates this. It produced tables of results expressed as potentially available good quality land rated according to its accessibility, defined as reachable within 6 hours of road travel, and its population density [START_REF] Fischer | Farmland Investments and Food Security[END_REF]. This report assessed, in dollars, the profitability of investments by calculating the ratio of potential production over present production.

The causal relations embedded in models lead them to recommend policies that sometimes satisfy demand but never address food needs. Economic models seek to balance demand and supply. They do not seek to end hunger. They cannot recommend policy targeting the poor, whose demand is automatically satisfied because they don't have money to spend on food. Hybrid models produce policy recommendations where the aim of food policies is transformed from an effectivity principle, such as ending hunger, to an efficiency strategy, such as maximising profitability of investment. These models are useful to produce policy recommendations to support investors. They cannot possibly contribute to policy recommendations to support livelihoods they make invisible.

The manner malnutrition has been embedded in models' equations locks them into productivist policy recommendations, whereby the quantity of food produced should be increased in order to decrease malnutrition. Yet, malnutrition and famine systematically result from access problems, often in situations where production is unproblematic (Sen 1981). The International Food Policy Research Institute (IFPRI) developed a partial equilibrium model, IMPACT, in 1995, to promote investment in agricultural research. IMPACT calculates the production of a foodstuff so as to equilibrate the food demand, a curve determined by consumer prices, per capita income and elasticities, instead of by the population's needs. The model thus mechanically produces greater food demand where revenues grow and under-nutrition where they are weak. This partial equilibrium model uses two indicators to represent hunger: food availability and child malnutrition. Food availability is expressed in terms of quantity of food per person as kg or calories per day. Child malnutrition is expressed in terms of the percentage of children between 0 and 5 years of age whose weight was under two standard deviations in comparison with the standards of the World Health Organisation. This is illustrated in Figure 2.

The structure of the model links child malnutrition to a single endogenous variable: food availability. The other variables in the equation are exogenous, in other words, these values are fed as entry data into the model. As a result, hunger cannot be reduced in the model unless food availability, understood here as meaning production, is increased. Therefore IMPACT automatically leads to a policy recommendation of increasing food production.

Simultaneously, IMPACT produces vacant lands. Its representation of food production is based on national and subnational agricultural statistics merged with remote sensed cropland data. [START_REF] Robinson | The international model for policy analysis of agricultural commodities and trade (IMPACT): Model description for version 3[END_REF] Both are inadequate to grasp small scale farming. IMPACT also fails to take into account on-farm consumption and the livelihoods of the rural population. Therefore, the model inevitably leads to the representation of underproductive land. It simultaneously promotes policy recommendations according to which investments should be made in agriculture to satisfy an ever increasing food demand. Therefore it promotes land uses competing with the ones actually in place, all in the name of ending hunger, which it doesn't address. The second part of this article will return to IMPACT, showing that this equation to represent malnutrition was carried over into several subsequent models.

Which types of government do these models embed?

Global models play a crucial role in the government of the food regime. The term governmentality was coined to describe a type of political rationality whereby technology and knowledge are deployed to organise human populations in order to steer them into a certain type of behaviour [START_REF] Foucault | Entre production et institutionnalisation des idées: La réforme de la politique agricole commune[END_REF]. Global models participate in a governmentality that has global ramifications, whether intended or not.

The first economic models were produced at a time when the United States sought to re-route the surplus it produced towards developing countries through food aid. America thus sought to ward off communism and promote national models of agro-industrialization as a path to development in poor countries [START_REF] Mcmichael | A food regime genealogy[END_REF]. Global models that found clients in the 1970s shared this vision of the food regime. They focused on international markets, technologies, free trade and national growth. They embedded the mechanisms their clients wanted to put in place.

Are global models now embedding a new food regime? As they have switched from state to pixel as their basic unit since the spatial turn, they are compatible with the corporate food regime McMichael argues has now arisen. The latter is based on free trade rules, the persistence of subsidies in northern countries and decreased agricultural regulations in southern countries. It operates through the corporatization of agriculture, the appropriation of land for agro-exporting, and the displacement of small-holders to a pool of impoverished labour. Global representations identifying fertile spaces to invest and urban populations to feed effectuate this food regime.

So, what is inside a model? After opening the black box and locating the causal relations embedded in their equations as well as their silences, we conclude that they are both products of science and producers of the food regime. A food regime is a political structure, a political project. This political project lies inside the models, structuring the causal relations they embed in their equations. In the co-productionist idiom, this is typical of scientific discourses, which systematically embody both what the world is and what it ought to be [START_REF] Jasanoff | Designs on nature : science and democracy in Europe and the United States[END_REF]. The important point here is that the models that fared well, those that didn't drift into extinction, embody a food regime that relies on international exchanges of foodstuff, where subsistence agriculture doesn't exist, where only demand matters, instead of needs, and where the only path forward lies in investments in agricultural production and productivity. Such models construct a world that welcomes what is often described as land grabs.

Do models breed?

Anyone wishing to represent world food production and consumption can pick among a vast number of global models. However, this does not mean a similarly high number of independent assessments.

Proliferation and reproduction

Models are rarely constructed independently from other models. They are based on similar equations and thus rely on similar hypotheses. Dominant global economic models are based on equilibrium theory. They incorporate little real-time data and simulate poorly the vulnerability of households to price shocks. As a result, none of them can either analyse or predict a food crisis, such as occurred in 2008 [START_REF] Headey | Was the global food crisis really a crisis? Simulations versus selfreporting[END_REF]. Global biophysical models are based on independent pixels, each of which is supposed to be optimized. They all tend to promote crops according to the biophysical potentiality of the land within each of these pixels, without consideration for the knowledge and experience local farmers might or might not have. Conversely, these models do not include retroactions of large scale monocropping, such as vulnerability to pests or the dependency on the price of the crop.

Global models share the same datasets. The Global Trade Analysis Project (GTAP) database, which contains bilateral trade information, transport and protection linkages, is used by thousands of economic modelers around the world. Most models also use FAO datasets for food production and consumption. This restricts the possibility of assessing the quality of the datasets and other parameters as they outnumber greatly the independent observations that are available. The hegemonic position of a few institutions and data bases thus leads global models and their results to be used in spite of the impossibility to validate them.

More crucially, the modules of one global model are often recycled from one model to another. It seems models can breed and produce several generations of offspring, each new model carrying the same equations as the previous generation in the manner living organisms carry DNA. Some modelers like to refer to the need to "have models marry other models" (Cornilleau, forthcoming). The IMPACT model's family tree illustrates this quite well. Produced by the think tank IFPRI in the 1990s, it was reused in 2002 as the IMPACT-WATER model, after being linked ("married") to a water module (Water Simulation Model). In 2009, it was once again coupled: IMPACT married the DSSAT cropping system model to assess some impacts of climate change. The equations it carried, such as the equation used to calculate child malnutrition examined earlier were thus transmitted to its descendants. This is illustrated in Figure 3.

Global models may converge in their results, but their consanguinity means their convergence does not indicate their validity as two models cannot be used to achieve a triangulation concerning a given result.

Alternative models?

The deficiencies of dominant global models, such as their inability to consider needs instead of demand and their structural inability to perceive or predict a food crisis should spur the development of alternative models, embedding other hypotheses and causal relations within their equations. So we should expect alternative models to emerge and challenge the dominant ones. Much scientific effort has been actively devoted to this goal. Yet, no "new guard" of models is presently emerging to challenge successfully the "old guard".

Part of the explanation for the absence of alternative models lies in the economics of modeling. It is a very costly activity in terms of time, datasets and infrastructure. "Building an applied trade model is a costly exercise, which tends to require several man-years of dedicated work on database construction, theory formulation, parameter estimation and computer implementation. In addition, the size of the investment implies that the basic design choices are to a large extent irreversible. Once a particular route has been chosen, the switching cost may become prohibitive" (Van Tongeren et al., 2001, pp. 167-168). Once datasets exist for a certain type of models, most probably, future models will converge to that standard type.

Can we find examples of alternative models in spite of this path dependency? Yes, and studying their destiny sheds light on the reasons why a model rises to dominance or becomes extinct. The example of Agrimonde is worth pausing over. A foresight study launched by the Centre de Coopération Internationale en Recherche Agronomique pour le Développement (CIRAD) and INRA in 2006, Agrimonde is based on a biophysical model, Agribiom, that estimates production and needs along a variety of scenarios (Dorin et al., 2011). As opposed to most models, it is not based on equilibrium theory. It relies on a direct match between the kilocalories that are produced and those that are needed. Several scenarios radically different from those of other models were produced. They include normative considerations such as sustainable food production and the reduction of inequalities in food and health. Most importantly, this model proposed to follow the flow of calories instead of prices.

Although Agrimonde did contribute to the global debate on the food regime, its international impact was quite limited. The scenarios based on the "sufficiency narratives" were especially difficult to integrate in the broader debates [START_REF] Labbouz | Sécurité alimentaire et futurs de l'agriculture mondiale[END_REF]. Instead of maximising production, such scenarios set as an aim the limitation of production once repletion has been achieved, i.e. once the food needs of the population have been satisfied. This was not an appealing aim for many members of the modeling community. Moreover, entering modeling platforms proved very difficult for this model because it had very different structural properties. Regrettably, a model that is "too original" cannot be integrated while one that recycles modules, equations and datasets used in previous models is easily welcomed.

We conclude that, yes, models do breed. They have proliferated within a very small genetic pool. But they have not done this on their own. Their interactions with modelers and users were crucial in this process. Models may marry, but these are arranged marriages were modelers are matchmakers. The reasons a model may become dominant or extinct are largely found in the interactions within the epistemic community producing and using models.

Epistemic communities and their models

The term "epistemic community" designates the networks of professionals with a recognized competence and expertise in a specific field, who appear legitimate to produce relevant knowledge necessary to support public policies in that field [START_REF] Haas | Introduction: Epistemic Communities and International Policy Coordination[END_REF]. The economists, engineers, computer programmers and systems analysts who elaborate global models make up such an epistemic community. The interactions among them, between them and their clients as well as between them and their models have largely contributed to shaping both what these models are and their fates in the larger construction of the food regime.

The rise of modeling relying on system dynamics, economic theory and large datasets took place initially in the United States in a variety of fields. It led to a hegemony of rational choice theory and of models as an inevitable tool to manage large systems. This process occurred in the United States in the 1970s in the field of water management, for example [START_REF] Espeland | The Struggle for Water, Politics, Rationality and Identity in the American Southwest[END_REF]. The rise to hegemony of the modeling approach was possible because its promoters managed to convince clients of the usefulness of their models. And this was possible because their clients shared the world view expressed by the modelers.

When asked why does a model become dominant or extinct, a modeler often answers that models that become extinct did so because they were bad models. This begs the question of what is a bad model. As opposed to hydrological models, global food models cannot be calibrated. Indeed, no independent dataset exists which can allow us to confront the results generated by a global food model. When the model IMAGE-2 was run to simulate the period from 1900 onwards, it reflected very accurately the situation. But its authors became aware the datasets they used to validate their model had been reconstructed by models structurally similar to IMAGE-2 [START_REF] Costanza | Integrated Global Models[END_REF]. Their exercise was thus futile. Global climate models face similar problems of data availability, yet they undergo numerous validation processes [START_REF] Edwards | Global Climate science, uncertainty and politics: Data-Laden Models, Model-Filtered data[END_REF][START_REF] Guillemot | Connections between simulations and observation in climate computer modeling. Scientist's practices and "bottom-up epistemology" lessons[END_REF]. The rich network of weather stations around the world allow climate modelers to attempt a validation process which is only partially undertaken by global food modelers. Thus, a model is not "bad" because it cannot be calibrated or because it has been invalidated. A model is "bad" because the epistemic community has not found it to be useful.

How does an epistemic community sift through existing questions and methods to produce the ones it deems useful? This social process involves interactions between modelers, their peers and their clients. For example, when six American agricultural economists, among whom Tim Josling and Alex McCalla, created the International Agricultural Trade Research Consortium (IATRC) in 1978, they were spearheading macroeconomic modeling. With funding from the Ford Foundation, this think tank tackled a fundamental problem: their partial equilibrium models relied on world market prices as inputs. But the United States and Canada's contribution was so overwhelming that their domestic policies determined the prices of world cereal markets. The outputs thus contradicted the inputs. The IATRC needed to develop a new method [START_REF] Josling | Precursors to IATRC[END_REF]. It organised comparisons between several international models produced by the FAPRI, the USDA, the University of Michigan and the IIASA and the INRA. The IATRC economists shared the conviction that free trade was necessarily good and a completely liberalised agricultural sector would necessarily function best. They borrowed from other models only what was compatible with this premise.

A number of these American modelers pursued their work within international institutions. Tim Josling, for example, went on to FAO to set up data bases of two indicators: Producer and Consumer Subsidy Equivalent (PSE and CSE). PSE estimates the transfers from domestic consumers and taxpayers to farmers under a set of agricultural policies. These indicators introduced a distinction between subsidies deemed to impact markets prices and subsidies that didn't impact market prices. This method was then carried over to the OECD in 1982 and led to the MTM model, a macroeconomic model that quantifies the impact of state support in terms of trade distortion. This process led to two important transformations. First, the concepts of "decoupling" and of "trade distortion" became hegemonic (Fouilleux, 2000). They are based on the premise that agricultural markets exist as autonomous entities, quite independently of the social and political contexts in which agriculture is carried out. Second, international equilibrium models were effectively black boxed as the necessary tools to represent world markets and assess the effects of PSE and CSE in terms of price distortions. Modelers in effect penetrated their future clients when they joined institutions in the late 1970s dedicated to policy making. There, they shaped datasets and approaches that informed later models these institutions were to call upon.

Modelers joined international institutions at a time when the latter developed macroeconomic models. This allowed these institutions to remain visible as producers of knowledge and to acquire credibility within the new paradigm of world food security. In the 1970s, FAO defined food security in terms of adequate availability in spite of crop failures or price fluctuations. The models estimated such availability strictly in terms of revenues and food prices. Though such an estimation shrinks the broader understanding of food security as defined by international institutions, it allowed them to take part in the new paradigm. For example, in 1993 FAO developed the WFM, a partial equilibrium model based on the IFPSIM model. By the end of the 1990s, an international network of macroeconomic modeling was sharing its datasets located in FAO, the World Bank, the USDA, the OECD, and the GTAP. This network also shared its paradigmatic formulation whereby individual utilities aggregate into the global well being, a process made possible by the equilibrium of national and international markets.

More recently, institutions such as FAO have changed their policy and now want to act as critical purchasers of strategically chosen pieces of research, instead of producers of research. As modelers have been migrating to international institutions early on, the clients of modelers have themselves often been modelers for a long time.

Epistemic communities from bibliometric analysis

The overall epistemic community working on food and agriculture at the global scale is so vast and its academic production is so large that a bibliometric analysis can be useful to provide an overview of its structure. We used the free access software CorTexT to identify networks of authors, and cited authors. (http://www/cortext.net) We analysed two corpuses of scientific papers, one dealing with global food security, the other with international agricultural trade. We composed each corpus from ISI Web of Knowledge over the period between 1974 and 2011. We used the keyword search "World Food Security OR Global Food Security" and identified 1763 papers. We used the keyword search "International Food Trade OR International Trade Agricult*" and identified 1814 papers. We used CorTexT to analyze the meta-data of these publications. The CorTexT platform reveals and maps the links between authors, concepts, references and institutions. This allowed us to locate modelers and global models in the overall epistemic community focused on food and agriculture at the global scale.

Figure 4 shows the map produced by CorTexT using the international trade corpus. The authors and institutions cited appear in red circles. The blue circles indicate the authors who publish. The size of the circles is proportional to the number of citations or publications. The large circles thus indicate influential sources of legitimate knowledge. Institutions such as FAO, the World Bank, the WTO, the USDA, the OECD, the WTO and the WHO as well as the European Commission therefore appear prominently as sources of knowledge.

Anthropological fieldwork in the World Bank highlights this strategy [START_REF] Goldman | Imperial Nature, The world bank and struggles for social justice in the age of globalization[END_REF]. Modelers such as Kym Anderson, Arjen Hoekstra, Tim Josling, Mark Rosegrant, Will Martin, and Jikun Huang appear as important sources of knowledge who both publish a lot and are cited a lot.

Although this corpus was not constructed using a keyword containing "model" or "modeling", by far the most prominent scientists contributing legitimate knowledge are modelers. Institutions that produce the datasets used in their models also figure prominently as sources of legitimate knowledge. This is testimony to the weight of global models in the scientific discourse concerning food and agricultural international trade. Of course, such a bibliometric analysis cannot show users of global models, such as private corporations, who do not publish. It also shows disproportionately authors who publish in English language journals. Additionally, it reflects metadata rather than content and modelers may also publish articles unrelated to modeling. In spite of these limitations, this bibliometric analysis demonstrates the numerous interactions between modelers, data providers and institutions using global models. Such thick networks are indicative of a thriving epistemic community.

Conclusion

Global models of food production and consumption appear to be neutral and apolitical. Yet, when we open them and examine the causal relations their equations express, their political nature becomes apparent. Such power relations were essentialized, i.e. made to appear natural, because they match the world view of the modelers and of the model users. Models that became dominant use prices as a proxy for needs, thereby representing only demand instead of needs. They use elasticities to calculate the development food production should follow. This means that states, or regions, with the lowest marginal production cost for a given foodstuff are inevitably invited to specialise in that production and international trade is inevitably supposed to grow. Dominant models use a representation of malnutrition that links it to food production, thereby leading mechanically to recommend a greater production to solve this problem. Recent dominant models represent the world as a series of pixels. The grid size within pixel based representations erases all production units smaller than a pixel from the map. These are all important constructions of power relations. The representations successful models generate suit several features that match a very specific structure of domination.

Clearly, models that rose to prominence did so because they circulated in dense networks of modelers and users. Alternative models that attempted to track the flow of calories, for example, were unable to integrate such thick networks. Their contribution to the debate concerning the global food regime thus remained marginal. Successful models embedded and thus promoted a structure of domination that suited their users' conception of a legitimate government of food production: one that led to ever increasing international trade and showed investments in agriculture and agricultural productivity as solving hunger.

Smallholders seem erased from the representation of global food production within dominant global models. Yet, the overwhelming importance of smallholder farming is undeniable both in terms of food production and in terms of its role within commercial farming. Indeed, the individuals involved in commercial farming as laborers, for example, are often simultaneously engaged in subsistence farming. The structural difficulty for dominant global models to include smallhoder farming raises the question of their usefulness.

Global models that rose to dominance proved very successful at constructing a representation of the world that legitimizes the activities of certain actors, such as foreign investors who claim to develop potential yields in places suffering from inefficient or inexistent agriculture. They also legitimize productivist policies and the promotion of a deregulated international market of agricultural products. Yet, the same models show grave deficiencies. They are structurally unable to predict a food crisis such as arose in 2008. So, the success of global models stems from their capacity to effectuate a world that matches both the structure of signification modelers adhere to and the structure of domination their clients champion.

Global food production models that rose to dominance did so because the epistemic community that generated them enrolled enough users into a dense network. An approach rooted in actor network theory allowed us to demonstrate this. These models embedded very specific power relations within the causal relations expressed by their equations. This led them to promote a very specific food regime that matches a global structure of domination the users of these models sought to establish. An approach rooted in structurationist theory allowed us to demonstrate this. Combining both of these approaches was necessary to understand the contribution of global models to the food regimes. They effectuate the food regimes their champions wish to establish far more than they describe the existing world in a "neutral" fashion.

Acknowledgements :

The authors wish to thank Agrobiosphere programme of the Agence Nationale de la Recherche for supporting the project Of Lands and Waters ANR-12-AGRO-0002-01

help with Cortext, and P.B.


Stéphane Dassin

Michel Dumon

Françoise Mechin

Jean-Pierre Pascault

THERMOPLASTIC POLYURETHANES (TPUs) WITH GRAFTED ORGANOSILANE MOIETIES: A NEW WAY OF IMPROVING THERMOMECHANICAL BEHAVIOR

Keywords: thermoplastic polyurethanes (TPUs), grafting, alkoxysilanes, hydrolytic condensation, thermomechanical properties

Organosilanes were grafted on thermoplastic polyurethanes (TPUs) using an internal mixer or reactive extrusion. The reaction described here proceeds in two stages, with the help of a diisocyanate as a coupling agent to create allophanate junctions between TPU chains and an aminosilane. Such materials could then be crosslinked by a hydrolytic condensation mechanism, resulting in increased thermomechanical properties. The starting TPU was at first carefully characterized. Using the plastograph, the different stages (reactions between TPU and diisocyanate, isocyanate-grafted TPU and aminosilane, but also between TPU and aminosilane alone) were then studied separately, together with the influence of several essential parameters (time, temperature, rotating speed, etc). Optimal conditions for a well-controlled grafting process were defined, and the different ways of crosslinking the TPU chains were compared.

INTRODUCTION

Thermoplastic polyurethanes (TPUs) are obtained from the reaction of long, soft hydroxyl-terminated oligomers (polyols) with excess diisocyanates and short diols often termed chain extenders. Most of the time, and especially when the synthesis is carried out in two stages, alternating soft and hard segments are obtained and the thermodynamic incompatibility between them usually induces a two-phase structure with soft domains containing mostly the polyol moieties, and hard domains made up of diisocyanate-chain extender sequences (1)(2)(3)(4)(5)(6)(7)(8). This particular structure, together with the variety of reagents (chemical nature and molar mass) and stoichiometries that can be used result in versatile engineering properties and a wide range of materials (elastomers, thermoplastics, and both) can be prepared; phase separation being the essential parameter for controlling the final thermomechanical behavior. TPUs are thus widely used for high-performance applications, especially when high tear and tensile strength or good wear and abrasion resistance are required. However, these properties are strongly jeopardized as soon as the service temperature of the material exceeds 70 to 80°C, mostly because of creep phenomena.

In this work, we tried to improve the working temperature of a commercial TPU by creating well-controlled chemical crosslinks; the idea was to have an easily processable material (i.e. to preserve its thermoplastic character) with an improved thermomechanical behavior. Moreover, the modification had to be feasible via an industrial processing, e.g. reactive extrusion.

Apart from rubber vulcanization, the most common technique to crosslink linear chains is radical crosslinking initiated by peroxides or by high-energy radiation [START_REF] Rees | Encyclopedia of Polymer Science and Technology[END_REF]. In addition, the use of organo-functional silanes crosslinkable by moisture cure increased after the development of the SIOPLAS ® [START_REF] Scott | [END_REF] and MONOSIL ® (11) processes. In this case vinyltrimethoxysilane (VTMO) is grafted onto linear polyethylene (PE) chains. A peroxide is added to promote this reaction, which is usually carried out with an extruder. Other polymers, such as ethylene-propylene copolymers, EPR or ethylene-propylene-diene terpolymers, EPDM (12,13), and even PVC (14)(15)(16) can be grafted in the same way. After this processing, the silane-grafted PE can then be crosslinked on demand through the action of water that hydrolyses the alkoxy groups, with subsequent condensation to yield silsesquioxane bonds. Such a process thus allows making self-crosslinkable PE with thermoplastic forming technologies, which are more advantageous in comparison with vulcanization technologies. However a catalyst, generally di-n-butyltin dilaurate or an organic acid (12,17) has to be incorporated during the initial processing to obtain acceptable crosslinking rates. Therefore the procedure is unfortunately not suitable for TPUs because the radical VTMO grafting is inadaquate, and also because the usual catalysts described above induce a total degradation of the TPU chains during processing.

A new process for grafting reactive moieties onto TPU chains was recently described in the literature and also by our laboratory (18,19). These works describe the reaction of diisocyanates with urethane groups in TPU chains, which result in the creation of allophanate branching units. In the present work, we tried to perform these reactions in a well-controlled manner, in order to leave pendant isocyanate groups which could then react with aminoalkoxysilanes to generate the same silane-grafted structure obtained for polyethylene via the SIOPLAS ® process. The proposed scheme is depicted in Figure 1.

EXPERIMENTAL

Materials and methods

The thermoplastic polyurethane (TPU) used in this study was a commercial, polyester-type TPU (Estane 58277, BFGoodrich). The reagents used for grafting were 4,4'diphenylmethane diisocyanate, MDI (Desmodur 44M, Bayer) and 3-amino-propyl trimethoxysilane, γ-APS (Dynasilan Ammo, Sivento) and were used as received. Both are very fluid liquids at the processing temperature (typically 170-190°C). An important issue was the time for homogeneously mixing the reactive components, since the TPU is still very viscous at such temperatures. However, experiments were quite reproducible and numerous pieces of materials taken from various parts of the blend always led to consistent results.

Size exclusion chromatography (SEC) was performed in THF, using a Waters chromatograph equipped with 3 microstyragel columns (Millipore HR1, HR2 and HR3) with double detection (differential refractometry and UV absorption), and referring to polystyrene standards.

The chemical structure was investigated by 1 H and 13 C Nuclear Magnetic Resonance (NMR, Bruker 400MHz spectrometer) and Fourier Transform Infra Red spectroscopy (FTIR, Nicolet Magna 550) between 4000 and 400 cm -1 . Differential Scanning Calorimetry (DSC) was carried out using a Mettler TA 3000 calorimeter. The samples (15-20 mg) were placed in aluminum pans and heated up at 10 °C/min from -100 °C to 230 °C. Dynamic mechanical properties were measured in tensile mode with a Rheometric Scientific RSAII apparatus using a frequency of 1Hz, from -100 to 230°C (3°C/min).

Sample preparation

Before modification, the TPU was dried 24 hours at 80°C. For its processing, an internal mixer (HAAKE Plastograph Rheomix 600P) was used to study grafting through torque and internal temperature variation. After a given reaction time, t, the modified TPU was recovered and quickly cooled back to room temperature between two plates for further analysis.

Before MDI modification, thin films of the materials were at first analyzed by FTIR to detect any possible NCO groups resulting from chain degradation. After the reaction, several pieces of the TPU/MDI blend were either directly analyzed by SEC, or sometimes immediately placed in a solution of 99% tetrahydrofuran (THF) and 1% di-n-butylamine (DBA). In so doing, the monoamine neutralizes the residual NCO groups, which could otherwise cause some side and crosslinking post-reactions. As amine groups are in large excess compared with NCO groups ([NH]/[NCO]>20), we consider that each isocyanate group reacts with one amine group and that residual MDI is completely transformed into its di-adduct, DBA-MDI-DBA. The torque variation can then be compared with the instantaneous molar mass distribution as a function of the reaction time, t.

As for studies on allophanate formation (20)(21)(22) the amounts of grafted and crosslinked structures were evaluated indirectly on the basis of the gel fraction in tetrahydrofuran (THF). With silane it was also possible to evaluate the degree of crosslinking after exposure of the silane-grafted TPU in an oven at 70 °C with 95 % RH (relative humidity) for 7 days. The gel content values were determined after extraction with THF for 48 h by comparison of the chromatographic peak area with that of the unmodified TPU.

RESULTS AND DISCUSSION

Characterization of the starting material

The number average molar mass of the raw TPU was evaluated by SEC ( n M = 46000 +/-2000 with respect to a polystyrene calibration). In order to have a better control over the future grafting reactions, we tried at first to have a precise image of the chemical structure of this material, using FTIR and mainly 1 H and 13 C NMR. From these analyses, it could be concluded that the soft segment was based on adipic acid and 1,4-butanediol (BDO), whereas the diisocyanate was 4,4'-diphenylmethane diisocyanate (MDI) extended with BDO to yield the hard segments. More precisely, the peak integrations of the 1 H spectrum (Fig. 2)

were compatible with the structure depicted in Figure 3 and their corresponding attributions indicated in Table 1. From these data, it is indeed not possible to determine separately the lengths of the soft (parameter m) and hard (parameter x) segments, respectively; however the average length ratio m/(x+1) can be calculated. Depending on the peak integration used, it appears that:

1.62 < 1 x m + < 1.69 or 1 x m + ≈ 1.66
From this value, two characteristic features for the starting TPU can be deduced: i) the urethane equivalent weight, M u = 334 g.mol -1 (meaning that the average number of urethane bonds per chain is about 140)

ii) the hard segment proportion, about 44 wt% Such a structure is consistent with the thermal transitions, T g (glass transition temperature) and T m (melting temperature) determined by DSC. For this TPU, T g was measured at -21°C (see Figure 4a). The melting zone associated with T m does not appear as a characteristic narrow endothermic peak as for semi-crystalline polymers, but more as a weak, broad peak between 80 and 160°C. T g is in general about -70°C for pure polyadipates (23), whereas it was found equal to 107°C for a pure MDI/BDO hard segment (24); using a simple Fox-type equation, and assuming the polymer is totally amorphous and homogeneous, T g could be roughly evaluated as: With w s = 56% and w h = 44%, it comes out that T g = -18°C. The actual value is only slightly lower: the soft domains are thus far from being pure, but rather a nearly homogeneous mixture of the "soft" and "hard" segments, consistently with their very comparable lengths; while other transitions presumably associated with a small semicrystalline hard domain appear at higher temperature. Both transitions are also visible in the dynamic mechanical spectrum (Fig. 4b). In this graph, it appears clearly that although the mechanical properties of this material are quite good below 70-80°C, it would be impossible to use it above these temperatures without some modification.

TPU/γ-APS systems

In a first step, we examined the possibility of grafting the organosilane directly onto the TPU chain, without the help of a coupling agent. The TPU was at first "molten" at 170°C for 5 min; at the end of this time, no NCO group could be detected by FTIR analysis. Then, γ-APS (0.16 mol/kg TPU, or [NH 2 ]/[ureth.] = 0.054) was added all at once. Instantaneously, the torque showed a strong decrease resulting from a much more fluid blend. Unfortunately, SEC (Fig. 5) revealed that although γ-APS had been totally consumed after 5 min, the whole polymer peak had simultaneously moved towards lower molar masses. This can be attributed to exchange reactions between urethane and amine groups, resulting in chain scissions:

NH-C-O O + H 2 N-R NH-C-NH-R + O OH with -R = -(CH 2 ) 3 -Si(OCH 3 ) 3
Even after a one-week-long hydrolytic condensation (70°C, 95% RH), the gel content of this modified material did not exceed 40 to 50%. Consequently, the use of a diisocyanate as coupling agent turned out to be necessary.

TPU/MDI systems

In order to avoid the above degradation, the use of a coupling agent is required and it is obviously necessary to add it before the aminosilane. MDI was chosen for this purpose and the systems based only on MDI and the TPU were studied, to be able to define precisely the first stage of the future process.

Typical curves obtained for torque and material temperature as a function of time are

shown in Figure 6. During the few minutes that follow MDI loading, the torque increases and finally reaches a plateau. Several samples were collected (see Fig. 6) and directly analyzed by SEC, with the corresponding chromatograms displayed in Figure 7. The first sample collected during the torque rise 2 minutes after MDI loading clearly shows some residual diisocyanate;

this is less and less visible along the plateau, but in the same time the distribution progressively broadens towards high molar masses with an increasing shoulder at t elution ≈ It appears that MDI conversion is always limited to a value that depends on this speed. The best results are obtained for 100 rpm, for which over 90% of the initial amount of MDI have been consumed at the end of the experiment. The initial reaction rate is also increased when using increasing rotating speeds. In fact, with increasing speed a better mixing is rapidly achieved and leads to a more homogeneous system. However, one must keep in mind that increasing shear also induces an increase in the material internal temperature. The effect of the assigned temperature was studied in the same way at 30 rpm, and we observed that for a higher temperature (i.e. 190°C) the torque began to rise but then decreased back to almost its initial level (see Figure 9a). The molar masses of the various samples were measured and plotted as a function of reaction time in Figure 9b; it comes out that w M increases regularly at 170°C; whereas it remains almost constant at 190°C and increases only slightly at 180°C. This last behavior might be the most desirable for a well-controlled MDI grafting, since the sharp increase in w M at 170°C is probably associated with strong chain coupling with a chance of gelation; whereas at 190°C, rearrangements and chains scissions due to the thermoreversibility of the urethane bond (24)(25)[START_REF] Eisenbach | GÜNTER in Advances in Elastomer and Rubber Elasticity[END_REF][START_REF] Koberstein | [END_REF](28)(29)(30)(31) presumably become non-negligible and result in partial but irreversible degradation of the material due to the excess NCO groups released in that case.

In any case, the above experiments prove that the first stage of the proposed process is very delicate, and that a compromise needs to be found between three essential parameters: assigned temperature, shear level and MDI reaction time.

TPU/MDI/γ-APS systems

The complete process was finally studied, still with the help of Haake plastograph. A typical curve obtained for successive additions of MDI and γ-APS to the raw TPU is shown in Determination of the optimal r 1 Figure 11 displays the insoluble fraction of the material obtained by grafting the starting TPU with MDI (t = 2 min) and γ-APS, after press molding (170°C, 4 min), hydrolysis and condensation of the alkoxy groups (70°C; 95% RH; 7 days). Several r 1 values were used, while r 2 was kept constant (r 2 = 2, overall isocyanate excess). Quite logically, it appears that with increasing r 1 , increasing final gel contents are obtained. However we have also checked the insoluble fraction before water reaction, just after press molding. These data are also depicted in Figure 11, and show that above r 1 ≈ 0.105, a small insoluble fraction is already present at the start. This presumably results from premature and uncontrolled gelation due to excess isocyanate functions that induce chain coupling, either by a direct grafting reaction or by reaction with the air moisture; in this case a hydrolyzed NCO group would yield an amine, which should immediately react with another grafted isocyanate moiety. The last part of the increase in the final gel content observed for hydrolysed samples is thus probably due to this initial fraction, which is associated with isocyanate functions that did not react with the aminosilane but can still create a crosslink, hence the change in the slope of the curve. Therefore, a narrow optimal range can be defined for r 1 , which corresponds to the maximal value that will not allow this undesired premature gelation. For r 2 = 2 and t = 2 min, < r 1 optimal ≈ 0.10-0.11.

Determination of the optimal r 2

In the following experiments, a constant value of r 1 = 0.107 was used. γ-APS was added after varying MDI reaction times, t, or in different amounts, i.e. with varying r 2 values.

Considering the effects of t (see Fig. 10), SEC allows the same kind of observation as for experiments with TPU/MDI systems and di-n-butylamine (see above and Fig. 7 & 8): for increasing values of t, Figure 12 shows that the polymer peak progressively broadens towards high molar masses (revealing the beginning of chain coupling reactions), while the sharp peak associated with the γ-APS-MDI-γ-APS adduct simultaneously decreases. The value of t was then set to 2 min, which corresponds to the beginning of the first torque plateau (Fig. 10) with no visible change in the shape of polymer peak (Fig. 12).

Varying amounts of aminosilane were then added and reacted with the MDI-grafted TPU for about 3 min in the plastograph (i.e. the necessary time to reach a stable torque), and the final materials were then collected and analyzed by size exclusion chromatography.

If the initial isocyanate concentration is i 0 , then at time t:

• concentration of residual (non-reacted) MDI = x

• concentration of reacted MDI = y = α + β with -concentration of once-reacted molecules = α and -concentration of twice-reacted molecules = β

• concentration of isocyanate functions i = 2x + α (1)
with i + α + 2β = 2x + 2α + 2β = i 0 (2)
The optimal amine amount one should add at this time is thus:

a 0 = i = 2x + α = i 0 (1 -p) (3)
with p = isocyanate conversion. This means that the optimal value for r 2 is:

r 2 optimal = p 1 1 - (4)
Therefore, a 0 and r 2 optimal depend on time t and on the reactivity ratio between both isocyanate functions of a MDI molecule towards urethane groups under our experimental conditions. In contrast, using too high or too low amounts of aminosilane can result in material degradation:

• if a 0 > i (i.e. r 2 is too low) , some residual amine will remain with an initial concentration a = a 0 -2xα; these functions can then induce some chain scissions

• if a 0 < i (i.e. r 2 is too high), some residual isocyanate functions will be left with a concentration equal to 2x + α -a 0 ; as reported above, these functions can cause premature gelation before the end of the full process.

The above considerations were well illustrated by three experiments using r 2 = 4/3, 2 and 4. In Figure 13, the variation of the torque for these three samples was represented as a function of time, for r 1 = 0.107 and t = 2 min. For the highest r 2 (i.e. the lowest amount of aminosilane), the torque increased to a high value. For r 2 = 2, it reached a reasonable plateau, whereas the torque dropped to a non-measurable value for the lowest value of r 2 (i.e. the highest amount of aminosilane). This last behavior was also partially due to a very bad mixing between the highly viscous MDI-grafted TPU and a high amount of hyperfluid silane. Some improvement was brought by a progressive (instead of instantaneous) γ-APS addition; but even in this case the final torque was very low.

All these observations were confirmed by the size exclusion chromatograms of the final materials depicted in Figure 14. In this figure, it appears clearly that using r 2 = 2, the final mass distribution, although slightly broader than the initial, was centered exactly on the same elution volume; whereas the whole distribution had moved to higher molar masses for r 2 = 4, and to lower masses for r 2 = 4/3.

It comes out that using r 1 = 0.107 and t = 2 min, r 2 optimal = 2. This is obviously not independent of the fact that with r 2 = 2 and t = 2 min, r 1 optimal was found in the range 0.10 to 0.11. In fact, with given temperature and rotating speed, r 1 and r 2 are parameters linked by a relation depending on time t, but for a given t, several (r 1 , r 2 ) pairs can presumably fit.

Characterization of the final materials after hydrolytic condensation

Once grafted with MDI and aminosilane, the TPU was found to be very stable under room atmosphere, in the absence of catalyst. The materials could be kept several months without the appearance of any gel fraction.

Material hydrolysis

In contrast, the alkoxysilane groups were easily hydrolyzed, simply by aging the materials under a hot and humid atmosphere. For this purpose, 2mm-thick plates were kept at 70°C and 95% RH for several days, without hydrolysis catalyst. This procedure was chosen to reproduce typical industrial conditions. Figure 15 displays the increase in the insoluble fraction (solvent: THF). The gel content increased rapidly during the first 4 days, after what the crosslinking rate slowed down, yet without completely stopping. The use of a catalyst (stearic acid for instance) allows a faster and complete crosslinking in 1-2 days.

But Figure 15 also shows that the easiest and fastest way of obtaining a complete crosslinking of the material is simply to graft it only with MDI and leave it under room atmosphere; a TPU grafted with MDI (r 1 = 0.107, 170°C, 30 rpm) and allowed to stand without protection was indeed found to be 100% crosslinked after 4 days. In fact, the air moisture partially hydrolyses the pendant isocyanate groups:

N-C-O O NCO O=C NH + H 2 O N-C-O O NH 2 O=C NH + CO 2
The resulting amine groups rapidly combine with other isocyanate functions, yielding aromatic-aromatic urea groups. This phenomenon finally results in the complete crosslinking of the material. However it is very difficult to control this process, and thus the use of an aminosilane remains necessary if a self-crosslinkable, but still thermoplastic material is desired.

Thermomechanical behavior of the final materials

The dynamic mechanical properties of the initial and final materials were finally analyzed and compared. Figure 16 displays the storage moduli and loss factors of the starting TPU and of this material grafted either with MDI alone (r 1 = 0.107), then hydrolyzed in air for several days, or successively with MDI and γ-APS (r 1 = 0.107, t = 2 min and r 2 =

2) and hydrolyzed in a steam oven (70°C, 95%RH) for 7 days. For a better comparison, the starting TPU represented here was aged one week under the same conditions, which resulted in some plasticization by water, with a lower modulus between Tg and 70°C (see

Fig. 4b & 16).

Both crosslinked materials, instead of flowing above ~ 120-130°C, show a new modulus plateau. However the silane-crosslinked polymer has a lower insoluble fraction (about 85%) than the MDI-crosslinked sample (100%). The connecting "bridges" between TPU chains are also longer and softer for the silane-based material. This can explain why the "plateau modulus" of the silane-crosslinked sample above 120°C is slightly lower (at 160°C, E' = 2.73 MPa for this material, whereas the MDI-crosslinked sample shows E' = 3.97 MPa).

However at higher temperatures (above 200°C), a total collapse of the modulus of the MDIcrosslinked sample is observed, while that of the silane-based material seems to hold a little longer: as an illustration, the values of tanδ at 200°C are respectively 0.73 (MDI) and 0.27 (silane). This behavior probably reveals the destruction of the network structure, which is based on several types of thermally reversible bonds (urethane, allophanate and urea). In fact, both networks contain the same urethane and allophanate bonds, and apart from the stable silsesquioxane linkages the only difference can be found in the nature of the urea bonds, either aromatic-aromatic (MDI-crosslinked material) or aliphatic-aromatic (silanecrosslinked material). In the literature, aromatic-aromatic urethanes have been reported to be thermally less stable than aromatic-aliphatic ones (28); if this was also the case for ureas, then one could account in this way for the slight extra-gain in thermal stability observed for the silane-based material. However the main advantage of this procedure remains the better control of the grafting and crosslinking process.

Finally, the use of increasing amounts of diisocyanate and silane logically results in ever-increasing moduli. Figure 17 shows the values of E' obtained for varying amounts of modifiers (with a constant r 2 = 2). The corresponding gel contents are reported in Figure 11 and Table 2. For the first 4 samples, the curves are quasi-identical up to ~ 100°C, with only a very slight difference in the principal mechanical transition (Tg increases slightly with the amount of modifiers). Then these curves diverge, with the highest amounts of modifiers logically leading to the most crosslinked materials and thus to the highest moduli. The case of the fifth sample (MDI or γ-APS: 0.40 mol/kg TPU, r 1 = 0.268) is different: the E' curve of this sample is strictly parallel to that obtained with 0.16 mol/kg TPU, but well above. This sample, in contrast to all others, already presented an insoluble fraction before water exposure, attributed to some side reactions of the excess diisocyanate molecules during press molding (see above). Apparently, this phenomenon rather affects the first modulus drop (associated with the soft amorphous domains) than the transitions at higher temperatures. As the grafting reaction can only take place on urethane groups and consequently should affect more the mobility of the "hard" segments (HS), these side reactions must thus be enabled only on those HS present in the amorphous phase. In contrast concerning the separated hard domains, grafting would only be possible on their boundaries, without affecting their internal morphology (since the same mechanical transition is always present at the same temperature).

Industrial transposition

Preliminary attempts (32) to define a near-industrial continuous process were made with a CLEXTRAL twin-screw co-rotating extruder (length/diameter L/D ratio: 36; diameter D = 25 mm). The modified material was chilled by water and granulated. With such a processing machine, a better mixing is rapidly achieved, due the high rotating speed (200 rpm). By adjusting the temperature & screw profiles, output, as well as the MDI feeding zone (hopper or first zone), it will thus be possible to redefine the important parameters (MDI reaction time, t, and global stoichiometric ratios, r 1 and r 2 ) to obtain the desired grafted material.

CONCLUSION

The feasibility of a controlled crosslinking of Thermoplastic PolyUrethanes (TPUs) was demonstrated. Using the classical isocyanate chemistry, it was possible to create well-defined allophanate branching points, which allowed in a second stage the grafting of trialkoxysilane moieties. In this way, "self-crosslinkable" (in the presence of moisture), but still thermoplastic materials could be obtained, that can be considered analogous to polyethylene grafted via the SIOPLAS ® process.

The reaction conditions for an optimal grafting were defined with the help of a mixer, by monitoring the torque and internal temperature as well as the molar mass distribution during the process. After pointing out the necessary use of a diisocyanate coupling agent to be able to graft the aminosilane without damaging the material, several important parameters were studied. The mixture temperature, shear level and MDI reaction time are equally essential for a good control of the process. After the first stage, the optimal amount of aminosilane to be added depends on these three parameters, and must be carefully adjusted.

The thermomechanical behavior of these materials was greatly improved once they were crosslinked. A simple grafting with only the diisocyanate is sufficient to obtain a completely crosslinked material; however the grafted materials are unstable, whereas the silane-grafted TPUs remain easily processible until the final crosslinking stage that proceeds on demand in the presence of moisture via a soft and well-controlled reaction.

This new process should now be transposed to more industrial conditions by use of a twin-screw extruder. The parameters studied previously with the mixer can be used to define the new processing conditions; preliminary experiments already gave good results for the preparation of self-crosslinkable TPUs via a continuous process. Moreover, the process designed here should a priori apply to any polymer bearing labile H atoms; as well as to polymer blends, e.g. in order to crosslink a dispersed phase in situ. Comparison with a MDI-grafted TPU (r 1 = 0.107) under room atmosphere (….□….). Comparison with a MDI-grafted TPU (r 1 = 0.107) under room atmosphere (….□….).

-C-O-CH 2 -CH 2 -CH 2 -CH 2 -O-C-CH 2 -CH 2 -CH 2 -CH 2 -C-O-CH 2 CH 2 O O O m CH 2 CH 2 NH-C-O-CH 2 NH-C-O-CH 2 -CH 2 -CH 2 -CH 2 -O-C-NH CH 2 O O O

22. 5

 5 min, until an insoluble fraction finally appears for long reaction times (t = 15 min, insoluble fraction = 20 wt%). These observations are compatible with the second isocyanate functions of grafted MDI molecules starting to react with urethane groups born by other TPU chains, yielding first branched molecules with double or triple average molar mass, and finally some insoluble fractions. In order to have a more precise idea of the global MDI conversion during this reaction, new experiments were run and the collected samples were immediately neutralized with excess di-n-butylamine and quenched back to room temperature. Even with low amounts of MDI, the resulting DBA-MDI-DBA adduct yields a sharp peak easily detectable in size exclusion chromatograms. This was used to plot the time-conversion curves depicted in Figure8, obtained with varying rotating speeds.

Figure 10 :

 10 Figure 10: in this case, MDI was reacted during a time t and γ-APS was then added, roughly

Table 1 : 1 H

 11 NMR analysis of the unmodified TPU (DMSO d6, 25°C, 400 MHz)

  to the structure proposed in Figure1

Figure 1 :Figure 2 : 1 HFigure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 12134567 Figure 1: Proposed method for the preparation of a self-crosslinkable TPU

Figure 8 :

 8 Figure 8: Conversion of MDI molecules deduced from the decrease in the DBA-MDI-DBA

Figure 9 :

 9 Figure 9: Effect of the assigned temperature on the grafting of TPU chains with MDI

Figure 10 :Figure 11 :

 1011 Figure 10: Material temperature () and torque (▬▬) variation observed during the

Figure 12 :

 12 Figure 12: Size exclusion chromatograms of the starting TPU ( ) and of the TPU reacted

Figure 13 :

 13 Figure 13: Torque variations recorded during the reaction of the TPU (170°C, 30 rpm)

Figure 14 :

 14 Figure 14: Size exclusion chromatograms of the starting TPU ( ) and of this TPU reacted in

Figure 15 :

 15 Figure 15: Insoluble fractions obtained for the TPU grafted with MDI and -APS (r 1 = 0.107; r 2 = 2, t = 2 min) during hydrolytic condensation (•, 70°C, 95% RH).

Figure 16 :

 16 Figure 16: Storage moduli (a) and loss factors (b) of the starting TPU aged 7 days at (70°C,

Figure 17 :Figure 1 :

 171 Figure 17: Storage moduli of the starting TPU aged 7 days at (70°C, 95%RH) ( ) and of

Figure 2 :

 2 Figure 2: 1 H NMR spectrum (DMSO d6, 400 MHz) of the starting TPU

Figure 3 :

 3 Figure 3: Proposed chemical structure for the starting TPU

Figure 4 :Figure 5 :

 45 Figure 4: DSC analysis [a), 10°C/min] and dynamic mechanical properties [b), 1 Hz,

Figure 6 :Figure 7 :

 67 Figure 6: Material temperature () and torque (▬▬) variation observed during the

Figure 8 :Figure 9 :

 89 Figure 8: Conversion of MDI molecules deduced from the decrease in the DBA-MDI-DBA

Figure 10 :Figure 11 :Figure 12 :Figure 13 :

 10111213 Figure 10: Material temperature () and torque (▬▬) variation observed during the

Figure 14 :Figure 15 :

 1415 Figure 14: Size exclusion chromatograms of the starting TPU ( ) and of this TPU reacted in

Figure 16 :

 16 Figure 16: Storage moduli (a) and loss factors (b) of the starting TPU aged 7 days at (70°C,

Figure 17 :

 17 Figure 17: Storage moduli of the starting TPU aged 7 days at (70°C, 95%RH) ( ) and of

Table 2 :

 2 Insoluble fractions obtained for the starting TPU and for this TPU grafted with MDI and γ-APS (r 2 = 2). All the materials were pressed (170°C, 4 min) and aged for 7 days (70°C,

	95%RH)
			insoluble fraction
	modifier amount			final insoluble
		r 1	after press molding
	(mol/kg TPU)			fraction (wt%)
			(wt%)
	0	0	0	0
	0.04	0.027	0	25
	0.08	0.054	0	48
	0.16	0.107	0	84
	0.40	0.268	13	95

ACKNOWLEDGEMENTS

The authors wish to thank Marie-France LLAURO (NMR laboratory, FR CNRS # 2151, Solaize) for performing the NMR analyses. Financial support from Didier LAGNEAUX (GEMOPLAST s.a., Frontonas), together with fruitful advice and discussions, are gratefully acknowledged.