Céline Merlin-Brogniart

Christine Liefooghe
email: christine.liefooghe@univ-lille.fr

Miklós Rosta
email: miklos.rosta@uni-cornivus.hu

Márton Katona
email: marton.katona@uni-cornivus.hu

Merlin Céline
email: celine.merlin@univ-lille.fr

-Brogniart

Value Co-creation and Innovation in the New Service Economy

In the context of social innovation, collaborative governance and in particular innovation networks has gained importance. This paper focuses on the potential for scaling up according to the institutional arrangements and context of different countries. A grid for analyzing the degree of state control of citizens' and local initiatives is proposed in order to study the different forms and intensity of scaling up.

Introduction and Context

Given increasingly scarce financial resources and the new demands of citizens for services, governments are in search of solutions to continue providing public services while reducing costs.

One of these solutions consists in encouraging different actors (associations, social entrepreneurs, citizens...) to develop innovations with a public service objective. Concurrently, the third sector is developing social solutions in response to needs not met by the market or by the government. These solutions require the collaboration of various actors, including the public sector. These initiatives lead to the networking of stakeholders from the public and private sector. When these initiatives are successful, the question of generalizing these initiatives to a larger scale arises.

The purpose of this paper is to analyse the role of the stakeholders, and particularly the public actor, in designing, commissioning, delivering, controlling, and upscaling, collaborative social innovation.

In the research field, studies on governance networks have been developed since the early 1990s. Initially focused on the contribution of networks in effective policy making, then on the role of governance for democratizing public policy making, the third wave of research focuses on how governance networks may contribute to the innovation in the public sector (Sorensen Torfing, 2010). In addition, Desmarchelier et al, (2020) observed that an overall trend towards the "tertiarization of innovation networks", which is reflected in the proposal of new forms of organizations in which hierarchy is replaced by horizontal networks, and more attention is given to multi-criteria assessments.

Among the three paradigms of public administration that reflect the different modes of coordination (traditional public administration, new public management and new public governance), this trend corresponds to the New Public Governance approach in which public administrations becomes equal partners to private actors and citizens in value creation.

Our hypothesis is that there are main differences of how these social innovation networks emerge, operate and deliver services to citizens in different institutional settings. These institutional arrangementsrules of the gamecan be scrutinized in a given time and place. The formal institutions are shaped by the government which decide on public policies. However, decision-making of the state is not fully free due to path dependency and the informal institutions of the given society.

In order to explore this hypothesis, several case studies concerning collaborative governance have been studied in two countries with different institutional contexts, different temporality of centralization/decentralization and political context: Hungary and France.

Literature review: social innovation, collaborative governance, institutional arrangements, and scaling processes

We use as a framework the literature on public service innovation networks, as well as the literature on political economy and institutional economics. Different patterns of institutional arrangements and coordination mechanisms [START_REF] Acemoglu | Economic origins of dictatorship and democracy[END_REF][START_REF] North | Institutions, institutional change and economic performance[END_REF]) could be in favour of innovation networks and entrepreneurial activities, or on the contrary, could undermine them [START_REF] Baumol | Entrepreneurship: productive, unproductive, and destructive Journal of political economics[END_REF][START_REF] Pasquier | Régionalisations et régionalismes dans une Europe élargie : les enjeux d'une comparaison est-ouest[END_REF]. On the other hand, countries are anchored in different welfare regimes, thus the degree of State intervention in collaboration innovation networks depends on the country's history. The relationship between the state and the economy has an impact on the management of social issues [START_REF] Esping-Andersen | The three worlds of Welfare Capitalism[END_REF]). These coordination mechanisms, between these rather local innovation networks and the State, may influence the capacity of scaling up innovation.

The second part of the theoretical framework concerns the notion of scale-up. The perception of innovation has evolved over time. Compared to technology adoption, more attention is now given to the multi-dimensional nature of innovation and the consequences of interdependent changes on a broader systems, and consequently, on the possibility of diffusion of innovations: Scaling up requires different levels of scale, the involvement of multiple stakeholders, and can result in different types of organization of the dissemination process [START_REF] Schut | Science of Scaling: understanding and guiding the scaling of innovation for societal outcomes[END_REF]. Scaling of innovation involved different processes [START_REF] Wigboldus | Using a Theory of Scaling to Guide Decision Making. Towards a Structured Approach to Support Responsaible Scaling of Innovations in the Context of Agrifood Systems[END_REF]. The process of upscaling refers to the creation of conducive conditions and policies for scaling at higher levels. The process of outscaling refers to the spreading of something within the same sphere. The process of downscaling is the adaptation of existing practices in a local context.

Finally, in order to better identify the process of innovation and the emergence of these modes of collaborative governance, as well as the scaling processes, we use the findings of [START_REF] Greenhalgh | Diffusion of Innovations in Service Organizations: Systematic Review and Recommendations[END_REF]. This author highlights three processes of diffusion of service innovations (let it happen, help-it happen and make-it happen). According to this author, the Make it happen feature leads to the dissemination of a readymade model to designated adopters; the Help it happen feature creates the conditions for effective diffusion of innovation, but enables adopters to adapt the model to their local conditions; the Let it happen feature allows actors to develop their own solutions, without inducing a model. These features focus on how collaborative networks can emerge and how the network can be structured as a means to facilitate the diffusion of innovation.

Methodology

This study is based on a qualitative research approach applied in different work packages of a European research programme named CoVAL. Five case studies have been carried out, in particular in France and Hungary, on the same social issues (elderly care, education, Immigration, long-term unemployment, environmental protection) with the same "case study framework"1 . The case studies were detected mainly by keyword via the Internet and through literature review. The research method used is in-depth interviews with the key actors of each network.

The case study framework of interviews is composed of five key dimensions: The type of innovation/type of innovation process, the type of Innovation network, Innovation drivers and barriers, Institutional factors and the impacts or performance of the network. Relevant documents from each organization have been analysed as supplementary data.

This paper does not aim at making an empirical contribution about the cases studies but rather to contextualize from a conceptual and theoretical point of view empirical data collected through different work packages. The objective is to discuss the critical role of the State in the co-production of social innovations. If we consider that France and Hungary are rather centralized countries (compared to the federal systems in Germany or the United States) but with two different processes (or stages) in administrative and political regionalization [START_REF] Pasquier | Régionalisations et régionalismes dans une Europe élargie : les enjeux d'une comparaison est-ouest[END_REF], is there any impact in the emergence of social innovation networks and their role in the spatial diffusion of these social innovations?

The role of the government in the diffusion of social innovation related to public service within collaborative governance

The analysis of the Hungarian and French case studies reveals that the historical context of welfare-state formation, and the more recent institutional arrangements (such as decentralization in France or regionalization of public action in Hungary), has an impact on the mechanisms of diffusion of the social innovation created by these networks.

The results indicate that in countries with a state-centred tradition, the state continues to try to control over social innovation networks. In another context, the state can position itself as a driver to solve social problems by providing framework and encouraging stakeholders to develop innovation networks, but too much formalization of support can be prejudicial to the to the spontaneous mechanisms of cooperation.

Dissemination also depends on the social innovation nature and the type of innovation process. Some social innovations could not easily be standardized to be disseminated: a case-by-case basis dissemination taking into account local specificities is often needed. A bottom-up innovation with a strong local character may have more difficulty in becoming generalized than innovation networks set up within the framework of a help-it-happen feature. The latter integrates from the outset methodological tools implemented with the aim of being replicated in several territories.

While communicating success stories of social innovation networks and disseminating the innovation is in the nature of the innovation itself, attempts to upscale these social innovation networks, or to re-internalize innovation projects into public structures, might also have negative consequences on the sustainability of these networks. For example, Top-down projects are sometimes more difficult to be accepted insofar as the actors in the network are not involved from the beginning, in the innovation project. On the contrary, bottom up projects might be interrupted because of a lack of money.

According the theoretical framework described in section 2, we propose a grid of analysis that takes into account: 1) the processes of diffusion of service innovation; 2) the nature of the social problem generally associated with the processes identified, the difficulties associated with each processes; 3) the degree of centralization/decentralization/regionalization of each national institutional settings. The aim is to discuss about the critical role of the state level in the emergence and (spatial or institutional) diffusion of social innovations, that is to say the propensity of a state to keep control despite a discourse in favor of the co-creation of public policies or public services.

Conclusion

This paper shows that, within collaborative governance, the institutional context as well as the degree of government control plays a role in the intensity of scaling up of social innovation related to public service. The actors who create social innovation and the type of public management at work may differ depending on the history of the country.

On the other hand, the degrees of leeway left to private actors (such as private firms, NGOs, associations, foundations, social enterprises, individual service consumers/users and individual citizens), as well as the weight of social actors, depends on the context. In some countries, some social entrepreneurs can easily initiate a solution on a local scale, whether in others countries, it will depend on the law and public prerogatives. If private stakeholders may have a significant role to play in the creativity and initiative of collaborative networks as boundary spanners, or as leaders of the innovation network, the government and more generally the public actors, seems to play an important role in the context and nature of the scaling up of the social innovation. Depending of the country, public actors have a more or less significant role in controlling the accompaniment of projects. The government controls the evolution of institutional arrangements or legislation and therefore has an influence on the development and scaling up of projects.

Merlin-Brogniart C. (2019), Rosta M., Révész E. Katona M., (2019).

Declaration of interest statement

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 770356 "Understanding value co-creation in public services for transforming European public administrations"


Alexandre Pohl

Yannick Donnadieu

Yves Godderis

Cyprien Lanteaume

Alex Hairabian

Camille Frau

Julien Michel

Marie Laugie

John J G Reijmer

Christopher R Scotese

Jean Borgomano

Carbonate platform production during the Cretaceous

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

INTRODUCTION

In the recent years, our knowledge of the geological evolution of the surficial carbon cycle has greatly improved. Among the main advances is the reconstruction of the Phanerozoic atmospheric CO2 [START_REF] Berner | GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2[END_REF][START_REF] Foster | Future climate forcing potentially without precedent in the last 420 million years[END_REF]. The fluctuations of the carbon sink due to continental weathering as well as the change in solid Earth degassing have been at least partly constrained, using models [START_REF] Goddéris | The role of palaeogeography in the Phanerozoic history of atmospheric CO2 and climate[END_REF][START_REF] Brune | Potential links between continental rifting, CO2 degassing and climate change through time[END_REF] or proxies (such as isotopes) [START_REF] Veizer | 87Sr/86 Sr, δ13 C and δ18 O evolution of Phanerozoic seawater[END_REF][START_REF] Cao | Episodic nature of continental arc activity since 750 Ma: A global compilation[END_REF]. One major component of the carbon cycle, however, the sedimentary carbonate sink, has been poorly investigated at the global scale. Many data have been published, regarding carbonate accumulation fluxes [START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF][START_REF] Kiessling | Fluctuations in the carbonate production of Phanerozoic reefs[END_REF], but data compilations and extrapolation at the global scale are scarce.

Carbonate sediments are the receptacle of the atmospheric CO2 that has been removed from the atmosphere by weathering, which can be subsequently recycled along subduction zones [START_REF] Mason | Remobilization of crustal carbon may dominate dominate volcanic arc emissions[END_REF][START_REF] Pall | The influence of carbonate platform interactions with subduction zone volcanism on palaeo-atmospheric CO2 since the Devonian[END_REF]. Carbonate sediment deposition thus reflects many coupled processes. Identifying those processes through geological times is an unparalleled way to check whether we have understood the overall functioning of the carbon cycle or not.

Here we investigate the production by carbonate platforms during the Cretaceous, one of the most prolific periods of carbonate platform development [START_REF] Kiessling | Patterns of phanerozoic carbonate platform sedimentation[END_REF]. We reconstruct temporal variations in platform carbonate deposition based on a new data compilation and subsequently explore the drivers of the temporal trends in Cretaceous carbonate production using a coupled climate-carbon cycle model.

METHODS

Database of shallow-water carbonate preservation rates

We compiled, from published studies, an extensive database of Cretaceous shallow-water marine carbonate preservation rates (see the GSA Data Repository for the full database). The latter were calculated by dividing the estimated sediment thickness by the stratigraphic interval duration. Calculated preservation rates necessarily underestimate actual carbonate production rates. Indeed, neritic carbonate accumulation is limited by depositional accommodation space. In addition, deposits may subsequently undergo dissolution, erosion and compaction, and produced sediments may be exported toward the basin. As a result of all those mechanisms acting to reduce the thickness of the carbonates preserved on the shelves, preservation rates calculated based on the geological record are typically one to several orders of magnitude lower than production rates measured on present-day carbonate-secreting ecosytems such as coral reefs [START_REF] Bosscher | Growth potential of coral reefs and carbonate platforms[END_REF][START_REF] Strasser | Carbonate sedimentation rates today and in the past: Holocene of Florida Bay, Bahamas, and Bermuda vs. Upper Jurassic and lower cretaceous of the Jura mountains (Switzerland and France)[END_REF][START_REF] Schlager | Ordered hierarchy versus scale invariance in sequence stratigraphy[END_REF]. Therefore compiled preservation rates are considered significant underestimations of the actual accumulation rates.

Considering the multiple mechanisms acting to reduce the thickness of the shallow-water carbonates preserved on the shelves, maximum preservation rates are further considered to be the most representative of the original carbonate accumulation flux in ancient times.

The GEOCLIM climate-carbon cycle model

We used the GEOCLIM climate-carbon cycle model (see the Data Repository) to simulate carbonate accumulation fluxes during the Cretaceous. The GEOCLIM model (Donnadieu et al., 2006a) asynchronously couples a carbon cycle box model with a general circulation model. It represents a significant improvement over the zero-dimensional GEOCARB-like models [START_REF] Berner | GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2[END_REF], since continental weathering rates are resolved spatially, which takes into account the continental configuration and sea level [START_REF] Goddéris | The role of palaeogeography in the Phanerozoic history of atmospheric CO2 and climate[END_REF]. The carbon cycle box model is the COMBINE model upgraded following Donnadieu et al. (2006a). It includes a robust representation of the marine sub-cycles of inorganic and organic carbon, oxygen, alkalinity and phosphorus. It explicitly represents the spatial distribution of silicate, basalt and carbonate weathering as a function of climate. The oceans are modeled by 9 "boxes". The accumulation of neritic carbonates takes place exclusively in the box representing the low-to-mid latitude epicontinental photic zone, following Eqn. 1:

𝑭 = 𝒌𝒄𝒓 × 𝑨𝒑𝒍𝒂𝒕𝒇𝒐𝒓𝒎 × (𝛀𝒂𝒓𝒂 -𝟏) 𝟏.𝟕 (1)
where F is the neritic carbonate depositional flux (mol yr -1 ), Aplatform is the shelf area available to shallow-water carbonate deposition, derived from the paleogeographic reconstructions, 𝛀ara is the model aragonite solubility ratio and kcr a calibration constant. This formulation of neritic carbonate accumulation rates has been successfully used in previous studies to investigate the consequences of the demise of carbonate platforms during the Middle-Late Jurassic Transition (ca. 160 Ma;[START_REF] Donnadieu | A mechanism for brief glacial episodes in the Mesozoic greenhouse: Paleoceanography[END_REF] and the effects of the breakup of Pangea on neritic carbonate accumulation (Late Permian to Late Cretaceous; Donnadieu et al., 2006a). The climatic component of GEOCLIM is the FOAM ocean-atmosphere model version 1.5 [START_REF] Jacob | Low frequency variability in a simulated atmosphere-ocean system[END_REF], a mixed-resolution general circulation model that has been routinely used to study climate in deep time, including during the Cretaceous (Donnadieu et al., 2006b;[START_REF] Ladant | Palaeogeographic regulation of glacial events during the Cretaceous supergreenhouse[END_REF].

Simulations were conducted using the Cretaceous paleogeographical reconstructions of [START_REF] Scotese | PALEOMAP PaleoAtlas for GPlates and the PaleoData Plotter Program[END_REF] and [START_REF] Scotese | PALEOMAP Paleodigital Elevation Models (PaleoDEMS) for the Phanerozoic (PALEOMAP Project[END_REF] with deep-ocean bathymetry after [START_REF] Müller | Long-term sea-level fluctuations driven by ocean basin dynamics: Science[END_REF]. Changing solar luminosity values were modeled after the stellar physics of [START_REF] Gough | Solar interior structure and luminosity variations[END_REF]. Earth's orbit around the Sun was circular (null eccentricity) and the obliquity was set to 22°. This orbital configuration provides an equal, annual insolation for both hemispheres with minimal seasonal contrast.

RESULTS

Temporal variations in Cretaceous shallow-water carbonate preservation rates

At first order, Fig. 1 shows a unimodal pattern in neritic carbonate preservation rates during the Cretaceous with background values < 70 m Myr -1 and an excursion to higher preservation rates up to 175-200 m Myr -1 during the mid Cretaceous between 125 Ma (Aptian) and 95 Ma (Cenomanian). This mid-Cretaceous maximum is a robust feature. It was already highlighted by the previous Phanerozoic compilation of [START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF]. It parallels the mid-Cretaceous local maximum in reefal carbonate production identified by [START_REF] Kiessling | Fluctuations in the carbonate production of Phanerozoic reefs[END_REF]. It also corresponds with the development of massive successions of sediments in the Mediterranean Tethys (>100 m thick; [START_REF] Skelton | Rudists and carbonate platforms in the Aptian: a case study on biotic interactions with ocean chemistry and climate[END_REF] and with the maximum in carbonate accumulation identified in the North American, Russian and Siberian platforms [START_REF] Whitten | Cretaceous phases of rapid sediment accumulation, continental shelf[END_REF].

Coupled climate-carbon cycle simulations

The drivers of secular change in platform carbonate production have been the subject of investigation for decades [START_REF] Schlager | The paradox of drowned reefs and carbonate platforms[END_REF][START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF][START_REF] Kiessling | Fluctuations in the carbonate production of Phanerozoic reefs[END_REF]Donnadieu et al., 2006a). From a carbon cycle perspective, global carbonate deposition is tightly linked to changes in continental silicate and carbonate weathering. However, several factors impact the distribution of carbonate deposition between the open ocean and shallow-marine platforms. Debate thus continues as to whether fluctuations in neritic carbonate accumulation rates reflect changing environmental conditions such as global climate, evolving geodynamics (e.g., continental configuration and subsidence) or intrinsic changes such as turnovers in dominant biota, since different carbonate factories are known to be associated with different carbonate production rates (e.g., [START_REF] Lanteaume | Testing geologic assumptions and scenarios in carbonate exploration: Insights from integrated stratigraphic, diagenetic, and seismic forward modeling[END_REF]. Previous attempts to identify these complex relationships over the course of the Phanerozoic failed to reach any definitive conclusions [START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF][START_REF] Kiessling | Fluctuations in the carbonate production of Phanerozoic reefs[END_REF].

Baseline simulations with present-day volcanism

We used the GEOCLIM climate-carbon cycle model (Donnadieu et al., 2006a) to investigate the driving mechanisms for the Cretaceous trend in neritic carbonate deposition with a special focus on the maximum in carbonate accumulation centered at 110 Ma (see Fig. 1).

Simulations were run every 10 Myrs between 150 Ma (Late Jurassic) and 60 Ma (Paleocene).

For each time slice and associated continental configuration, the GEOCLIM model computed the pCO2 value by balancing volcanic degassing with silicate weathering. The GEOCLIM model simulated the associated climatic state and ocean biogeochemistry. Though the neritic carbonate deposition rate was focus of our investigation, the simulated pCO2 was used to evaluate the fit of our simulations to the latest pCO2 reconstruction of [START_REF] Foster | Future climate forcing potentially without precedent in the last 420 million years[END_REF]. The latter criterion was chosen to compare our simulations to proxy data due to the critical role that pCO2 plays on ocean pH and thus carbonate geochemistry.

In our baseline runs, the rate of volcanic degassing was set to the present-day value (6.8 × 10 12 moles of carbon per year; Donnadieu et al., 2006a) (Fig. 2A); only the paleogeography and associated climate varied from one time slice to another. Simulated pCO2 was lower than indicated by the proxy compilation for most of the Cretaceous (Fig. 2B). Yet, an interesting pattern emerged: the bimodal trend observed in the pCO2 compilation between 120 Ma and 60 Ma (grey shading in Fig. 2B) was well reproduced in the baseline runs (black line in Fig. 2B).

This suggests that the temporal variations in pCO2 reconstructed by [START_REF] Foster | Future climate forcing potentially without precedent in the last 420 million years[END_REF] between 120 Ma and 60 Ma may be largely due to the paleogeographical evolution. The total neritic carbonate depositional flux simulated in the baseline runs varied very little between 150 Ma and 60 Ma, showing only a local optimum at 80 Ma (Fig. 2C).

Numerical simulations using Cretaceous volcanic degassing scenarios

In a second step, we used Cretaceous plate models and data compilations to derive volcanic CO2 degassing scenarios, which could help reconcile the simulations with proxy-based pCO2 reconstructions. Such modeling attempt faces limitations associated with the large uncertainties in the reconstruction of Cretaceous volcanic degassing. Indeed, numerous studies have been published trying to reconstruct one of the components of the degassing rate but there is no reconstruction of the total CO2 degassing by the solid Earth at the geological timescale. The lack of an integrated curve leaves us with the necessity to rely on incomplete reconstructions. The rationale that we adopted thus consists in using available constraints to compute total volcanic degassing rates, expressed as ratios compared to the present-day value. We did not try to identify the individual contributions of the different components: subduction zones, rifts, midocean ridges and arc volcanism. Instead, we followed the approach adopted by Berner in his various versions of the seminal GEOCARB(SULF) model [START_REF] Berner | GEOCARB III: a revised model of atmospheric CO2 over Phanerozoic time[END_REF][START_REF] Berner | The phanerozoic carbon cycle CO2 s and O2[END_REF][START_REF] Berner | GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2[END_REF], which consists in scaling volcanic degassing with proxies for geodynamic activity (e.g., subduction length). Although this approach will undoubtedly benefit from advances in geodynamic models in the near future, it has been shown to produce very good results in the GEOCARB model [START_REF] Berner | GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2[END_REF][START_REF] Van Der Meer | Plate tectonic controls on atmospheric CO2 levels since the Triassic[END_REF]. In detail, we derived volcanic degassing rates (Fig. 2A) from the length of subduction zones calculated by Van Der Meer et al. 2017) (CAO17). We also used the C1' and C1'' scenarios of [START_REF] Brune | Potential links between continental rifting, CO2 degassing and climate change through time[END_REF], which consider variable contributions of rifts, mid-ocean ridges, subduction zones and continental arcs.

Our model does not account for the degassing from large igneous provinces (LIPs). It has been shown [START_REF] Dessert | Erosion of Deccan Traps determined by river geochemistry: impact on the global climate and the 87Sr/86Sr ratio of seawater[END_REF] that LIP degassing increases the atmospheric partial pressure of CO2 for durations that do not exceed a few million years after the end of the onset. LIPs also impact the carbonate system through short-term acidification of the ocean, just prior to the response of the weathering system [START_REF] Paris | Geochemical consequences of intense pulse-like degassing during the onset of the Central Atlantic Magmatic Province: Palaeogeography, palaeoclimatology[END_REF]. However, we here explore the response of the carbon cycle to processes acting at a longer timescale, in the order of ten million years.

We tested each of the volcanic degassing scenarios in the GEOCLIM model. The best fit to proxy data was obtained using the subduction-based degassing scenario E92 (Fig. 2B). The neritic carbonate production flux associated with this best-guess scenario displayed a maximum centered on 110 Ma (Fig. 2C) that agreed well with our compilation of Cretaceous preservation rates (see Fig. 1).

Analyzing the drivers of the Mid-Cretaceous maximum in carbonate accumulation

Despite the disparities in the volcanic degassing scenarios (Fig. 2A), most simulations showed that the highest rates of neritic carbonate production occurred during the mid Cretaceous (between ca. 120 and 80 Ma). The mid-Cretaceous unimodal pattern, bounded by an increase in neritic carbonate production in the Early Cretaceous (120-130 Ma) and a decrease in neritic carbonate production in the early Late Cretaceous (80 Ma), was a robust pattern that was shared by different degassing scenarios.

Comparison of the simulations that considered evolving volcanic degassing rates with the baseline runs (color vs. black lines in Fig. 2C) revealed that the lowest-to-mid Cretaceous increase in neritic carbonate production (130-120 Ma), at least partially, relied on an increase in volcanic degassing rates. In addition, a sensitivity test that used a constant area of the neritic environments available for carbonate deposition (dashed magenta line in Fig. 2C) demonstrated that the latter area played a key role in the increase in shallow-marine carbonate production.

Indeed, the area of the continental shelves significantly rose between 130 Ma and 120 Ma in our reconstructions (Fig. 3). This increase resulted from the strong eustatic rise that took place at that time [START_REF] Müller | Long-term sea-level fluctuations driven by ocean basin dynamics: Science[END_REF]. In the E92 scenario, the increasing area of shallow-marine environments strengthened the pattern of carbonate accumulation already imposed by changing volcanism (Fig. 2C), by favoring the accumulation of carbonate in neritic environments at the expense of the open ocean. In other degassing scenarios that did not have a well-defined maximum at 120-110 Ma (i.e., C1', C1'', VDM14, CAO17, EA20), the increasing area of the shallow-marine environments, alone, drove the increase in neritic carbonate production between 130 and 120 Ma (Figs. 2A,C). Regarding the decrease in carbonate production after 80 Ma, two main mechanisms were in play; most scenarios showed a drop in volcanic degassing (Fig. 2A) and a major eustatic fall [START_REF] Müller | Long-term sea-level fluctuations driven by ocean basin dynamics: Science[END_REF] reduced the area of the shallow-marine environments available to neritic carbonate deposition (Fig. 3).

DISCUSSION

Comparison of our simulated trend of shallow-water carbonate production with the updated compilation of preservation rates allowed us to propose a mechanistic explanation to temporal variations in the deposition of Cretaceous shallow-water carbonates. It would be even more interesting and straightforward to compare our simulated fluxes with the volumes (instead of vertical aggradation rates) of shallow-water carbonates produced during the Cretaceous.

Unfortunately, such comparison is hampered by the lack of robust quantification of these volumes. For instance, [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] calculated platform carbonate accumulation fluxes by multiplying the extent of the carbonate platforms mapped by [START_REF] Kiessling | Patterns of phanerozoic carbonate platform sedimentation[END_REF] by globally-uniform preservation rates derived from the compilation of [START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF]. Figure 1C reveals that the temporal trends of carbonate production simulated in GEOCLIM and the preserved volumes reconstructed by [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] largely differ.

The estimates of [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] provide significantly lower values. The low values at least partly reflect the action of dissolution, erosion, compaction and the export of the carbonates toward the basin, which all tend to reduce the thickness of the carbonates deposited on the shelves. Preserved volumes necessarily represent an underestimation of the volumes of carbonate actually produced (see Methods). Regarding the temporal trend, the reconstruction of [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] does not provide any robust quantification of the variation in the production of platform carbonates. Indeed, the approach of [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] consists in multiplying the surface of the carbonate platforms documented in the geological database by a constant (i.e., a uniform rate of vertical aggradation). The authors derived two values for this constant rate from the compilation of [START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF], which provided the lower (using 30 m Myr -1 ) and upper (using 80 m Myr -1 ) boundaries for their reconstructed trend (Fig. 1C). Our updated compilation of preservation rates (Fig. 1), however, reveals that preservation rates cover a very large range of values, from < 10 to 200 m Myr -1 . While it probably reflects the best estimate that can be produced at the global scale based on the current knowledge, the approach employed by [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] neglects the spatio-temporal variations in carbonate accumulation rates and thus exclusively reflects the evolution of the area of the carbonate platforms (compare Fig. 1C and Fig. 3). [START_REF] Skelton | The operation of the major geological carbon sinks[END_REF] conducted similar calculations for the Aptian and Cenomanian.

Only the platforms of the Tethyan region were considered in these calculations, while [START_REF] Dutkiewicz | Sequestration and subduction of deep-sea carbonate in the global ocean since the Early Cretaceous[END_REF] considered the area of the platforms at the global scale. The fact that both studies led to virtually identical values (Fig. 1C), although they focused on significantly different spatial scales, highlights once again the difficulty to estimate the depositional flux by neritic carbonates in the deep time. We argue that, considering the current difficulty to estimate volumes of neritic carbonates produced in ancient times, our reconstructed neritic carbonate preservation rates (Fig. 1) constitute an instructive proxy for the efficiency of the shallow-water carbonate factory in ancient times. The reported temporal patterns are supported by both previous data compilations [START_REF] Whitten | Cretaceous phases of rapid sediment accumulation, continental shelf[END_REF][START_REF] Bosscher | Accumulation rates of carbonate platforms[END_REF][START_REF] Kiessling | Fluctuations in the carbonate production of Phanerozoic reefs[END_REF] and accumulation patterns observed in the field [START_REF] Skelton | Rudists and carbonate platforms in the Aptian: a case study on biotic interactions with ocean chemistry and climate[END_REF].

CONCLUSION

The simulated maximum in mid-Cretaceous neritic carbonate production results from the combination of high volcanic degassing levels and the large shallow-marine realms. Although the precise evolution of carbonate accumulation rates varies from one volcanic degassing scenario to another, the unimodal pattern in neritic carbonate production simulated during the Cretaceous is robust and shows up in most of the scenarios. The model results align well with the temporal trend that emerges from the updated compilation of Cretaceous platform carbonate preservation rates. Our results therefore suggest that the first-order evolution of neritic carbonate deposition during the Cretaceous reflects changes in continental configuration and volcanic degassing. Other mechanisms modulating accommodation space and turnovers in the dominant biota probably played a role as well, but our simulations suggest that the latter processes do not explain the first-order trend in Cretaceous neritic carbonate accumulation. For scenario E92, the simulation represented with the dashed line is identical to the one represented with the solid line except that it uses a constant area of the shallow-marine environments available to neritic carbonate deposition during the Cretaceous. In panel B, background grey shading represents the proxy-based pCO2 reconstruction of [START_REF] Foster | Future climate forcing potentially without precedent in the last 420 million years[END_REF] with LOESS fit, 68 % and 95 % confidence intervals. In panel C, yellow shading and red stars

Late

Palc.

1 0 120 eolog cal t me ( a)

  Such bias concerns both the modeling and data communities. For instance, McKenzie et al. (2016) argue for a dominant role of degassing on the climatic evolution, based on a correlation between the Phanerozoic climate and their curve for the degassing of arc volcanism, although arc volcanism is only one component of the total degassing.

(

  2014) (hereafter VDM14), from the area of subducted lithosphere reconstructed over the last 180 Myrs by Engebretson et al. (1992) (E92), from the slab flux estimated by East et al. (2020) (EA20) and from the continental arc activity compiled by Cao et al. (

Figure 1 .Figure 2 .

 12 Figure 1. Compilation of Cretaceous neritic carbonate preservation rates. The light grey

  platform carbonate accumulation fluxes estimated by Dutkiewicz et al. (2019) and Skelton (2003) (see main text).

Figure 3 .

 3 Figure 3. Area of the shallow-marine environments available to neritic carbonate

1

  GSA Data Repository item 201Xxxx, [Supplementary information, geological database, experimental setup and climate model runs (Sections DR1-DR2, Figures DR1-DR2, and TablesDR1-DR2)], is available online at www.geosociety.org/pubs/ft20XX.htm, or on request from editing@geosociety.org.

ACKNOWLEDGMENTS

The authors thank Dietmar Müller, Peter Skelton and two anonymous reviewers for their thorough reviews that significantly strengthened the present manuscript, and Judith Totman Parrish and Gerald Dickens for editorial handling. A.P. and Y.D. thank the CEA/CCRT for providing access to the HPC resources of TGCC under the allocation 2014-012212 made by GENCI. The research leading to these results was supported by a Marie Sklodowska-Curie International Fellowship under Grand Agreement no. 838373. The authors thank B. Suchéras-Marx (CEREGE) for interesting discussions on the calcifying plankton during the Cretaceous, P. Maffre (GET) for his assistance in setting-up our Cretaceous configuration of the GEOCLIM model and S. Brune for providing degassing scenarios.


Camille Girard-Tercieux

Isabelle Maréchaux

Ghislain Vieilledent

Raphaël Pélissier

Rethinking the role of intraspecific variability in species coexistence

Keywords: Coexistence, Intraspecific-variability, high-dimensional-niche, spatial-structure, Performance, Competition

Abstract:

How species coexist while competiting for the same resources is a long-standing question in community ecology, particularly for hyperdiverse communities like tropical forests. In the past decades, intraspecific variability (IV) and its ecological consequences became of major interest, and IV was perceived as a potential mechanism enabling species coexistence, with contrasting results in the literature however.

We argue that taking the nature of IV into account is important to understand its effects on coexistence, and hypothesise that environmental variation alone can produce IV in performance.

Focusing on spatial environmental variation, we build a body of evidence to support this idea. First, we use a theoretical model using virtual data of individual growth across environmental gradients, using less explicative environmental variables in the model than to generate the data. Second we analyse a Eucalyptus clonal dataset in Brazil. Lastly we analyse three datasets from contrasting tropical forests : Paracou in French Guiana (Amazonia), Barro Colorado Island in Panama (Central America) and Uppangala in the Western Ghats in India (Southeast Asia).

The theoretical model shows that observed IV can emerge due to the lower dimensionality of field observations compared with the high dimensionality of the environment, without any intrinsic differences between conspecifics; the clonal dataset analysis shows that IV can emerge from exogenous factors; the tropical dataset analyses show that IV in growth is high in tropical forests, that growth is broadly spatially autocorrelated, which we suppose is a mark of its environmental origin, and that locally, conspecifics have a more similar growth than heterospecifics. This body of evidence shows that IV can emerge from environmental variation and without any intrinsic differences between conspecific individuals. Based on theory, which shows that intraspecific competition must be stronger than interspecific competition to enable species coexistence, we link higher local similarity to higher competition and conclude that intraspecific variability does not preclude this condition, enabling multiple species to coexist in high dimensional and spatially structured environments.

  -Tercieux, CNRS / UMR AMAP (Primary Presenter) Isabelle Maréchaux, INRA Ghislain Vieilledent, CIRAD Raphaël Pélissier, UMR-AMAP Are you currently an ATBC Member?: Yes Do you wish to apply for one of the following awards?: Gentry award for best student oral or poster presentation, New Phytologist Poster Prize for Student Researchers Is your abstract part of a symposium?: No Title: Rethinking the role of intraspecific variability in species coexistence


W Aït-Idir

S Touhami

M Daoudi

J Dillet

J Mainka
email: julia.mainka@univ-lorraine.fr

O Lottin

Oxygen Transport Impedance in a Polymer Electrolyte Membrane Fuel Cell Equivalent Electrical Circuit

Keywords: PEM Fuel Cell, Electrochemical Impedance Spectroscopy, Oxygen Transport Impedance, Electrical Equivalent Circuit Modeling

One common way to interpret the data of Electrochemical Impedance Spectroscopy (EIS) with Polymer Exchange Membrane Fuel Cells (PEMFC) consists in using an Equivalent Electrical Circuit (EEC). There are however various issues in EEC modeling, among which the location and expression of the oxygen transport impedance. In this work, we compare the results obtained using a Randles circuit with those of an EEC where the oxygen diffusion impedance is connected in series with the circuit of the Cathode Catalyst Layer (CCL). In the Randles circuit, the oxygen transport impedance is in series with the charge transfer resistance of the Oxygen Reduction Reaction (ORR), implying that the CCL (pores and/or ionomer) is governing oxygen diffusion. In the other case, the oxygen diffusion impedance is outside of the CCL circuit, which implicates that the Gas Diffusion Layer (GDL) governs oxygen diffusion. In addition, two expressions of the GDL oxygen diffusion impedance were tested: the usual finite Warburg impedance and an alternative expression derived by Kulikovsky that considers the impact of the double-layer capacity on oxygen concentration at the CCL/GDL interface. The parameters obtained with these EEC are used to estimate the main characteristic diffusion length, for various cells and operating conditions. The same trend was observed in all cases: the values of the characteristic diffusion length are found to be of the order of the GDL thickness.

I-INTRODUCTION

In this work, we focus on the interpretation of impedance spectra of PEMFC, i.e. assemblies of a proton exchange membrane, Anode and Cathode Catalyst Layers (ACL and CCL), and two Gas Diffusion Layers (GDL). The most widely used Equivalent Electrical Circuit (EEC) to describe such electrochemical converters is the Randles circuit. Applied to PEMFC, this EEC is an electrical schematization of the membrane, the CCL, as well as -possibly-the cathode GDL through a finite-length Warburg impedance accounting for oxygen transport limitations.

Despite of the wide use of the Randles EEC, its physical relevance remains to be discussed on several points. Regarding oxygen transport limitations, Touhami et al. [1] and Bultel et al. [2] showed for instance that they are located mainly in the GDL [3] when the FC is fed with air. However, some other works point the ionomer layer covering the reaction sites in the CCL as limiting for oxygen transport, especially for electrodes with low Pt loadings -because of high local mass fluxes-and/or when the fuel cell is operating at low relative-humidity [4] [5] [6]. In addition to this obvious absence of consensus, it is worth mentioning that the low frequency impedance is also strongly impacted by oxygen concentration oscillations induced by the measuring signal, and possibly by the water fluxes through the cell [7]. Since these points have been clarified, among others by Schneider [8] [9] et al., Maranzana et al. [10], and Mainka et al. [7], they will be considered as out of the scope of this work. However, it must be kept in mind that oxygen concentration oscillations must eventually be considered should the GDL be identified as limiting for oxygen transport.

Under the hypothesis of oxygen diffusion being limited by the GDL, Kulikovsky showed that the mass transport impedance should differ from the classical finite-length Warburg expression due to the high double-layer capacity Cdl of the porous catalyst layer [11]. Kulikovsky derived an alternative expression which is a generalization of the GDL oxygen transport impedance: it tends toward the classical finite-length Warburg impedance ZW when the double-layer capacity Cdl of the electrode tends toward zero. Note that in any case, the oxygen mass transport impedance through the catalyst layer is assumed negligible, which is consistent with the hypothesis of a thin (surface) electrode that governs the derivation of the Warburg impedance. However, this is not consistent with the usual structure of the Randles EEC, with ZW connected in series with the charge transfer resistance Rct, and both Rct and ZW being connected in parallel with the double-layer capacity Cdl (Figure 1a): if the catalyst layer is indeed considered as a -simpleinterface, one would rather expect to have the Warburg impedance connected in series with both Rct and Cdl (Figure 1a).

Recently, Cruz-Manzo and Greenwood [12] modelled oxygen diffusion through CCL and GDL using a Transmission Line Model (TLM), i.e. a generalization of the Randles circuit [13]. They proposed to include a diffusion impedance in each layer at the cathode side, and choose the finite-Warburg expression for the CCL and the Kulikovsky impedance for the GDL. They obtained similar values of the diffusion resistance when neglecting either the CCL or the GDL. These values correspond to the overall fuel cell diffusion impedance. Our approach was similar, and we discuss the position of the oxygen transport impedance in Randles-like (thin electrode model) circuits. The EEC were tested over a large range of operating conditions and with regular cathode materials, i.e. carbon-supported platinum with loadings varying between 0.1 and 0.4 mg/cm². The impedance spectra were measured on three different cells and four different MEA: two commercial MEA and two homemade MEA. For the sake of simplicity, only one case will be fully described in this work. The impedance spectra were analyzed using two EEC:

• The classical Randles circuit (Figure 1a), for comparison purpose.

• And a modified Randles circuit (Figure 1b) with the oxygen diffusion impedance connected in series to the catalyst layer, i.e. with an oxygen transport impedance located outside the catalyst layer. This is consistent with the assumption that the main limitation to oxygen transport comes from the GDL, and with the hypotheses governing the derivation of both the Warburg and Kulikovsky impedances in a passive media.

We then compared the results obtained with both EEC. Note that the anode was also considered in the impedance models to get a better fit between theoretical and experimental data. This choice was consistent with one of our previous work where we had observed a degradation of the anode [14]. However, in the absence of anode degradation, similar or perhaps better fits may have been obtained using a TLM model for the CCL, i.e. without considering the anode. A more detailed discussion on this point will be presented in a future work.

II-EXPERIMENTAL SETUP

Although the data used in this work were measured over a wide range of operating conditions and using three very different cells, we describe here only those obtained with one of them: a 30 cm² (300 mm×10 mm) cell with identical flow fields on the anode and cathode sides, i.e. 5 parallel straight channels. The channel width and depth were equal to 1 mm and 0.7 mm, respectively. In addition to its simplified geometry, another particularity of this cell lies in the current collection, which is done independently on 20 electrically isolated segments along the channel length: this allows the measurement of the local impedance on each of these segments. A more complete description of this instrumented and segmented cell can be found in our previous work, see for instance [14]. Impedance data were measured in galvanostatic mode, -mostly at 0.5 A.cm -2 -with a perturbation amplitude of 10% for frequencies ranging from 10 mHz to 10 kHz, and with 10 points per decade.

Tailored MEA made by an external supplier with Nafion ® XL membranes were used. The Pt loadings were 0.1 mgPt.cm -2 for the anode and 0.3 mgPt.cm -2 for the cathode. The gas diffusion layers were 235 µm thick Sigracet 28 BC, compressed to 175 µm using PTFE gaskets to control their thickness. The fuel cell temperature was maintained at 80°C. The relative humidities (RH) of air and hydrogen supplied to the cell were 70% and 50%, respectively. The air stoichiometry was set to 2, while for hydrogen it was set to 1.5.

III-ELECTRICAL EQUIVALENT CIRCUITS

Two different EEC were used to analyze the impedance shown in Fig. 1: a classical and a modified Randles EEC standing for the cathode catalyst layer, the other electrical resistances being accounted for through a high frequency resistance Rhf. Rhf is usually associated to the ionic transport resistance of the membrane, although in practice it also includes the contribution of other components such as the GDL and flow field plates, as well as interfaces between them. The Oxygen Reduction Reaction (ORR) in the CCL is modeled through a parallel connection of a charge transfer resistance Rct accounting for the reaction kinetics and a double-layer capacitance Cdl representing the capacity of the porous electrode to store charges in the Electrical Double-Layer (EDL) at the carbon-electrolyte interface. The anode was modelled through a parallel connection of a double-layer capacitance and a charge transfer resistance (hydrogen transport limitations being generally negligible), added in series with the cathode and membrane EEC [14] [13]. The difference between both EEC lies in the position of the oxygen transport impedance ZW or ZK: in the classical Randles configuration ZW is connected in series with the charge transfer resistance (Fig. 1a). Implicitly, this configuration implies that the main limitations to oxygen transport are located in the CCL (i.e. in the pores or in the ionomer layer covering the reaction sites) although in practice, the GDL may also contribute significantly. In the modified Randles EEC, the oxygen diffusion impedance is connected in series with the CCL impedance (Fig. 1b). Although rarely used, this last configuration is consistent with the hypothesis that the GDL is the most limiting component for oxygen transport [1].

The impedance of the oxygen transport through a (passive) porous media is usually accounted for through a finitelength Warburg element ZW [15]. This impedance is derived from Fick's diffusion equations. It is thus based on the assumptions of one-dimensional transport of oxygen and water by binary diffusion only, with as boundary conditions a surface reaction at the CCL/membrane interface (Neumann or second-type boundary condition, the oxygen flux being governed by the current density) and a constant oxygen concentration (Dirichlet or first-type boundary condition) at the CCL/air channel or GDL/air channel interface. The hypothesis of a constant oxygen concentration is reasonable for relatively high stoichiometry ratios [13], i.e. for relatively low currents. The Warburg impedance writes as [15]:

Z W = R d tanh√iωτ d √iωτ d (1)
where Rd corresponds to the diffusion resistance (Ω.cm²), ω = 2πν the angular frequency (rad), τd the characteristic diffusion time (s).

However, Kulikovsky showed that the oxygen transport impedance of the GDL differs from the Warburg impedance due to the high double-layer capacitance of the porous CCL, that actually impacts the faradic current density and the oxygen flux. He derived a modified expression of the oxygen transport impedance as a function of the impedance parameters of the ORR which writes as [11]:

Z K = Z W 1+iωC dl R ct (2)
with Cdl the double-layer capacitance (F/cm²) and Rct the charge transfer resistance (Ω.cm²). This expression can be used to model the impedance of the cathode gas diffusion layer, and it tends toward the Warburg impedance when Cdl tends toward zero.

In the next section, we compare the ability of a classical Randles EEC using a Warburg oxygen transport impedance (Figure 1a) and that of a modified EEC -with the oxygen diffusion impedance connected in series with the CCL impedance (Figure 1b)-to fit various experimental impedance spectra. The mathematical expression of the usual Randles EEC is recalled below [1] [14] [16]:

Z EEC = R hf + ( 1 R ct + Z W + iωC dl ) -1 (3) (a) (b)
And the mathematical expression of the modified EEC (Figure 1b) is given by:

Z EEC = R hf + ( 1 R ct + iωC dl ) -1 + Z W/K (4)
Also, for comparison purpose, we use either the classical Warburg oxygen transport impedance ZW in (4) or the modified expression proposed by Kulikovsky ZK (2). The Kulikovsky expression was not used with the conventional Randles circuit because of the various shortcomings of this EEC mentioned earlier. Regarding the impact of the layer governing oxygen transport (CCL or GDL), the experimental data were equally well fitted using the finite-Warburg impedance, with similar values of the residuals. However, the location of the diffusion impedance impacts visibly the parameters associated with mass transfer (+8% for τ and +22% for Rd, with reference to the values obtained with the Warburg in the CCL) and much more significantly those associated with the ORR kinetics: the charge transfer resistance dropped by 21% and the double-layer capacitance was almost 60% higher. Only the high-frequency resistance remains almost independent from the location of oxygen diffusion impedance, at least in this thin electrode EEC approach. Independently of the expression of the oxygen diffusion impedance (i.e. Warburg or Kulikovsky) considering that the GDL governs oxygen transport increases the contribution of the diffusion to the cell impedance (τ and Rd), while decreasing that of the charge transfer resistance. In addition, it can be seen that the choice of the diffusion impedance has only a slight impact on the other parameters.

IV-RESULTS

To go one step further in the identification of the layer governing oxygen diffusion, the characteristic diffusion length was estimated using the following expression [1]:

𝛿 = (1 + 𝑅 𝑐𝑡 𝑅 𝑑 ) × 𝑗 𝑐𝑒𝑙𝑙 𝜏 4𝐹〈𝐶 𝑂 2 (𝑂)〉 𝑡 (5)
The above equation is obtained using 𝑅 𝑐𝑡 = 𝑏 𝑐 〈𝑗 𝑐𝑒𝑙𝑙 〉 𝑡 ⁄ ; 𝑅 𝑑 = 𝑏 𝑐 𝛿 4𝐹𝐷 𝑒𝑓𝑓 〈𝐶 𝑂 2 (0)〉 𝑡 ⁄ and 𝜏 𝑑 = 𝛿² 𝐷 𝑒𝑓𝑓 ⁄ [14], with jcell the current density (0.5 A/cm² in this case), F the Faraday constant (96 485 C.mol -1 ) and 〈𝐶 𝑂 2 (𝑂)〉 𝑡 the oxygen concentration at the GDL/channel interface, assessed by solving Fick's equation in steadystate [17]:

〈𝐶 𝑂 2 (𝑂)〉 𝑡 = 𝐶 𝑂 2 * - 〈𝑗 𝑐𝑒𝑙𝑙 〉 𝑡 𝛿 4𝐹𝐷 𝑒𝑓𝑓 (6)
with 𝐶 𝑂 2 * the oxygen concentration in the gas channel supposed constant, and Deff the effective oxygen diffusion coefficient, given by 𝐷 𝑒𝑓𝑓 = 𝛿 2 𝜏 𝑑 ⁄ [1]. The porosities of the GDL and the CCL were then determined with 𝜀 𝐶𝐶𝐿 = ( 𝐷 𝑒𝑓𝑓 6.9 10 -6 )

( 2 3 ⁄ )

and 𝜀 𝐺𝐷𝐿 = ( 𝐷 𝑒𝑓𝑓 3.2 10 -5 ) 0.5 [18].

The values obtained using the impedance data of Table I are given in Table II: the characteristic length is much closer to a GDL than a CCL thickness, independently of the location and expression of the oxygen diffusion impedance.

V-CONCLUSION

The characteristic diffusion length of oxygen transport in PEMFC was determined from experimental impedance data considering two EEC differing in the locations (CCL and GDL) and expressions (finite-Warburg and Kulikovsky) of the oxygen transport impedance. This analysis was repeated on three different cells, various current densities and gas stoichiometries. The oxygen diffusion was also identified locally on each segment of the segmented cell. Although they cannot be detailed in this work, the results always stayed consistent: it is most likely the GDL that governs oxygen diffusion in usual operating conditions of PEMFC.

VI-REFERENCES

Figure 1

 1 Figure 1 EECs used to fit the experimental impedance spectra, usual (a) and modified (b) Randles circuits.

Figure 2 .

 2 Figure 2. Experimental Nyquist diagram measured in operando at 0.5 A.cm -2 in the operation conditions described in section II and fitting curves obtained with the EEC depicted in Fig 1.

TABLE I .

 I ESTIMATED PARAMETERS OBTAINED FROM THE EXPERIMENTAL DATA IN FIG 2 USING THE EEC IN FIG 1. COMPARISON BETWEEN THE DIFFUSION IMPEDANCE POSITION (CCL OR GDL) OF WARBURG AND THE COMPARISON BETWEEN WARBURG & KULIKOVSKY IMPEDANCES.

		EXPRESSION.
	Model	R hf

[Ω.

cm²] R ct [Ω.cm²] C dl [mF.cm -²] R d [Ω.cm²] Τ [s] Rct anode [Ω.cm²]

								Cdl anode
								[F.cm -²]
	Warburg CCL	0.072	0.212	19.5	0.262	0.128	0.033	0.011
	Warburg GDL	0.068	0.169	31.2	0.320	0.137	0.024	0.020
	Kulikovsky GDL	0.073	0.168	25.4	0.296	0.137	0.042	0.011

TABLE II .

 II CHARACTERISTIC VALUES OBTAINED WITH THE IMPEDANCE PARAMETERS OF TABLE I.

	Model		Warburg CCL	Warburg GDL	Kulikovsky GDL
	δ [µm]		308	359	302
	Deff [m²/s] 10	-6	1.35	1.92	1.25
	Porosity [-]		0.20	0.32	0.20