M Andersson

B Espinosa-Arronte

C J Van Der Beek

M Nikolaou

J Lidmar

M Wallin

A vortex solid-to-liquid transition with fully anisotropic scaling

The vortex solid-to-liquid transition has been studied in heavy ion irradiated untwinned single crystals of YBa2Cu3O 7-δ with an inclined applied magnetic field. For magnetic fields tilted at angles about 45 • away from the columnar defects, we find that the electric resistivity in the vortex liquid regime approaches zero with power laws in the reduced temperature T -Tc that have different exponents in all three spatial directions. Since the symmetry in the problem has been broken in two non-collinear directions by i) the direction of the columnar defects and ii) the direction of the applied magnetic field, our findings give evidence for a new type of critical behavior with fully anisotropic critical exponents. A possible view of the vortex topology for the transition is also suggested.

Introduction

The vortex solid-to-liquid transition separates a truly superconducting low temperature phase (vortex solid) from a dissipative high temperature phase (vortex liquid) in the H -T phase diagram of high temperature superconductors. In clean materials, the vortex solid-to-liquid transition is a first order melting transition, while it is believed to turn into a second order glass transition in the presence of strong static disorder. Different types of disorder give different glass behavior, e.g. in superconductors with columnar defects created by high energy ion irradiation, vortices are very effectively pinned when aligned along the columnar defects and less effectively pinned when aligned perpendicular to them, giving rise to a low temperature Bose glass phase [1]. Since the field and the columnar defects break the symmetry, the Bose glass transition is anisotropic with different critical exponents parallel and perpendicular to the columnar defects. This difference is also reflected in the topology of the vortex depinning of a Bose glass; a vortex pinned by a columnar defect is depinned by the creation of a half-loop while a vortex perpendicular to the columnar defect is depinned as it were from a point defect.

For a magnetic field tilted away from the columnar defects at a sufficiently small angle, the vortices will stay on the columns leading to a transverse Meissner effect. In this case, the transverse component of the magnetic field makes the three directions non-equivalent, which should give different critical exponents in all directions [2]. In a recent study on untwinned YBa 2 Cu 3 O 7-δ (YBCO) single crystals with columnar defects and an inclined magnetic field, we

! x ! z ! y H " Figure 1.
The geometry of the experiment. The columnar defects are aligned along the z axis (crystallographic c axis) and the applied magnetic field is tilted with an angle θ in the z -x plane. The resistivity is measured in all three spatial directions.

have found evidence for a regime where the resistivity disappears with power laws that have different exponents in all three spatial directions [3]. However, this occurs at high tilt angles and is not directly comparable to the theoretical results. In order to qualitatively understand the reason for the observed effect, we will discuss the topology of the vortex depinning in these experiments and argue that the depinning topology is likely to be different in all three directions.

Experimental results

Untwinned as-grown YBCO single crystals were irradiated with 1 GeV Pb 56+ ions at the Grand Accélérateur National d'Ion Lourds (GANIL), Caen, France. The fluence of n d = 1 × 10 11 ions cm -2 created randomly distributed amorphous columnar defects, with a density corresponding to a matching field B Φ = Φ 0 /n d = 2.0 T (where Φ 0 is the flux quantum). The beam was incident along the crystallographic c axis (within experimental uncertainty) so that the ion tracks traverse the entire crystal thickness. The disappearance of the resistivity at the vortex solid-to-liquid transition was measured in all three spatial directions when a magnetic field H was tilted by an angle θ as shown in Fig. 1. Using a picovoltmeter as pre-amplifier, a dc voltage resolution below 1 nV was obtained in the measurements. The measurement current (typically 100 µA) was sufficiently low to ensure an Ohmic behavior. ρ x and ρ y were measured on the same sample, while ρ z was measured on a second sample as described in Ref. [3].

When the vortex liquid turns into a glassy vortex solid state below the vortex solid-to-liquid transition temperature T c , the resistivity within the vortex liquid state drops to zero as a power law in |T /T c -1|, i.e.

ρ i = ρ 0 |T /T c -1| s i , i = x, y, z (1)
where we have allowed for the possibility of having different exponents s i in the three spatial directions of the sample. This relation gives a good description of the experimental data at resistivity levels less than 5 % of the normal state resistivity as viewed from the linearity obtained when plotting the inverse of the logarithmic derivative (∂ρ/∂t) -1 = (T -T c ) /s i versus temperature.

The main result of our study is exemplified in Fig. 2, where the three different exponents are shown as a function of angle at an applied field µ 0 H = 1.0 T corresponding to half of the matching field B Φ = 2.0 T. As seen, there exists a range of angles between 45 • and 65 • , where the exponents are almost constant and clearly different from each other. We obtain s x = 4.8 ± 0.4, s y = 4.1 ± 0.4 and s z = 6.0 ± 0.6 in good agreement with the exponents obtained at an applied field of 2 T, where s x = 4.7 ± 0.2, s y = 3.8 ± 0.2 and s z = 6.6 ± 0.3 were found [3]. In the latter case, the range where almost constant values of the exponents were found extended between 25 • and 65 • . This differences in angular ranges may possibly be related to the observation that The angular dependence of the power law exponents obtained from fitting to Eq. 1 for an applied magnetic field µ 0 H = 1.0 T. Note that in the range 45 • to 65 • , the exponents are clearly different and almost constant, suggesting a critical behavior that is anisotropic in all three spatial directions. the accommodation angle θ a defined from the maximum in the resistivity versus angle curve is higher at lower applied fields [4], but this need further investigations.

Another observation from Fig. 2 is that the two exponents s x and s y are different and roughly constant over quite a large angular range (except for angles close to 0 • and 90 • ). The averaged effective Lorentz force on the vortices changes quite considerably in the x direction when tilting the field. Thus, an almost constant s x implies that a model based on a Lorentz force acting on a straight vortex line must be rejected as the cause of our observations. On the other hand, s z is changing considerably as a function of angle, starting from a low value at θ ≈ 0 • , increasing until it reaches a maximum in the regime discussed above, and finally decreasing again. The same trend is seen for a field of 2 T [3].

Discussion

From the results, we see that there is an angular regime where the exponents are constant and clearly different (45 • ≤ θ ≤ 65 • in Fig. 2), i.e. in this regime fully anisotropic scaling is observed. This can be directly related to a general assumption based on different critical exponents for the glass correlation lengths associated with the three spatial directions. More specifically, assuming correlation lengths ξ x = ξ χ , ξ y = ξ and ξ z = ξ ζ where ξ ∼ |T -T c | ν and ν is the static critical exponent and a correlation time for critical scaling down τ ∼ ξ z , one obtains [2,3]. Within this assumption, the only way to obtain three different values of s i is to have different critical scaling exponents of the correlation lengths (1 = χ = ζ = 1), i.e. the observed phase transition must be anisotropic in all three directions.

s x = ν (z -1 + χ -ζ), s y = ν (z + 1 -χ -ζ) and s z = ν (z -1 -χ + ζ)
Let us now speculate about a possible way to visualize the topology of the vortex excitations responsible for the results in Fig. 2. First, it is important to notice that the glass temperature T c in the regime where the exponents are different is, presumably, higher than the melting temperature T m of a pure superconductor as indicated by experimental results [3]. This implies that the transition is controlled by thermal and pinning energies. Thus, elastic energies will be less important and T c > T m may also open up for plastic deformations of the vortex system. Therefore, it seems reasonable to assume that the vortex system can freeze into a staircase vortex structure at T c also for angles θ > θ a . In such a situation, vortex motion can be imagined as shown in Fig. 3, where the direction of the Lorentz forces are shown when the measurement current density j is in the x, y and z direction respectively. With j x, the Lorentz force probes thermal fluctuations out of individual pinning centers along the columns. With j y, the Lorentz force in principle probes thermal fluctuations on the vortex segments in between two columns and on the vortex segments along the columns. However, the first ones are expected to dominate the dynamics due to an easier mode of motion sliding along the columnar defects. Finally, with j z, the Lorentz force probes thermal fluctuations of the vortex segments in between the columns, but in this case vortex motion requires an additional thermal depinning from the columns. As seen, this results in three topologically different modes of vortex depinning, which presumably will have different dynamics leading to different exponents for the disappearance of the resistivity at T c . From the three modes discussed, one would expect the vortex motion to successively become harder in the order y, x, z, which is also reflected by increasing values of the exponents in the same order.

Another view is to neglect the vortex segment in between the columns and only consider the depinning of vortex segments along the columns. On a short length scale, this is then identical to the situation of a transverse Meissner phase, which was studied theoretically in [2]. As indicated above, such an assumption leads to the same relative order between the exponents and can qualitatively explain our results.

Figure 2 .

 2 Figure2. The angular dependence of the power law exponents obtained from fitting to Eq. 1 for an applied magnetic field µ 0 H = 1.0 T. Note that in the range 45 • to 65 • , the exponents are clearly different and almost constant, suggesting a critical behavior that is anisotropic in all three spatial directions.

Figure 3 .

 3 Figure 3. The various ways for vortex motion in a staircase vortex configuration with strong pinning along the columns. Lorentz forces when the current is applied along the x, y and z directions are shown as F x , F y and F z respectively.

Acknowledgements

The authors thank M. Konczykowski for his presence during the irradiation and Ö. Rapp for valuable comments. The work has been supported by the Swedish Research Counsil, the Swedish Foundation for Strategic Research through the OXIDE program and the Göran Gustafsson Foundation.


Emmanuel Virot

Davide Faranda

Xavier Amandolese

Pascal Hemon

Chaotic Dynamics of Flags from Recurring Values of Flapping Moment

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Michael Saidani
email: msaidani@illinois.edu

Bernard Yannou

Yann Leroy

François Cluzel

Harrison Kim

Francois Cluzel

How circular economy and industrial ecology concepts are intertwined? A bibliometric and text mining analysis

Keywords: Circular economy, industrial ecology, bibliometric analysis, text mining, sustainability

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Introduction

While industrial ecology (IE) has been thoroughly theorized and analyzed over the last two decades [START_REF] Cecchin | Relating Industrial Symbiosis and Circular Economy to the Sustainable Development Debate[END_REF], the research around the circular economy (CE) is still emerging and gains increasing traction among businesses, policymakers, and academics (Korhonen et al., 2018a). Yet, this CE concept is not completely new and finds its foundations in several research streams, including the IE. For instance, according to the Ellen MacArthur Foundation (EMF, 2015), the CE paradigm is based on seven "schools of thought", namely: industrial ecology, biomimicry, natural capitalism, regenerative design, cradle-to-cradle, blue economy, performance economy. For the French Environment and Energy Management Agency (ADEME, 2014), industrial ecology is also one of the several pillars to build a circular economy, among ecodesign or product-as-a-service.

In the meantime, it appears that IE has found a second wind in the light of the actual momentum around the shift towards a more CE [START_REF] Cecchin | Relating Industrial Symbiosis and Circular Economy to the Sustainable Development Debate[END_REF]. Moreover, this inclusion of IE within the CE framework is not acknowledged by all. In fact, the connections between CE and IE are still stirring a vivid debate between scholars, through opposite scientific papers [START_REF] Buclet | Ecologie industrielle et économie circulaire: définitions et principes[END_REF][START_REF] Figuière | Écologie Industrielle (EI) et Économie Circulaire (EC). Concurrentes ou complémentaires ? XXXIIèmes journées du développement ATM 2016[END_REF], or by using the online exchange platform ResearchGate (2019) to figure out, e.g., "are circular economy and industrial ecology the same concept?". Also, a special issue of the Journal of Industrial Ecology entitled "Exploring the Circular Economy" published in 2017 [START_REF] Bocken | The Circular Economy: Exploring the Introduction of the Concept Among S&P 500 Firms[END_REF] brought the question of whether industrial ecology is the science of the circular economy.

As circular economy and industrial ecology are therefore still two moving and fuzzy concepts, with no clear boundaries or standardized definitions, this paper aims to brings new insights to the following questions: (i) is circular economy the new industrial ecology, or to what extent it can be considered as such?; and (ii), importantly, how these concepts can be exploited or combined together to achieve a more sustainable development?

In line with the statement of [START_REF] Lifset | Industrial ecology: goals and definitions[END_REF] at the beginning of the 21 st century and emergence of industrial ecology -"Setting out the goals and boundaries of an emerging field is a hapless task. Set them too conservatively and the potential of the field is thwarted. Set them too expansively and the field loses its distinctive identity. Spend too much time on this task and scarce resources may be diverted from making concrete progress in the field. But in a field with a name as provocative and oxymoronic as industrial ecology, the description of the goals and definitions is crucial"the present piece of research aims to provide an update on the positioning between the industrial ecology and circular economy concepts, based on both the pioneered and latest publications covering these topics, using bibliometric and text mining tools to ensure an objective standpoint.

Methodology

First, prior relevant works dealing with the analysis of both circular economy (CE) and industrial ecology (IE) concepts are reviewed and summarized. Then, after identifying and extracting the diverse definitions of a CE and IE, a text mining tool is used to carry out a comparative semantic analysis of these definitions (i.e., to figure out what are the keywords that stand out and how are they related), in order to highlight possible convergences and differentiation. In parallel, a bibliometric analysis is conducted to depict and understand the evolution of published papers from 2000 to 2019 (in top-tier peer-reviewed journals), having the keywords "circular economy", "industrial ecology", or both. Finally, discussions are made on the contributions of these two fields to achieve sustainable development, e.g., to enable and exploit the full potential of ecodesign approaches.

Bibliometric analysis belongs to the scientometry research field, which addresses the quantitative analysis of activity and scientific networks [START_REF] Leydesdorff | Scientometrics and communication theory: Towards theoretically informed indicators[END_REF]. Regarding the text mining analysis, the term frequencybeing an efficient and straightforward text mining method [START_REF] Gaikwad | Text mining methods and techniques[END_REF] is the technique used here to analyze and compare the definitions of circular economy, industrial ecology.

Note that [START_REF] Deus | Trends in publications on the circular economy[END_REF] previously analyzed the current state of publications with the keyword "circular economy" (either located in the title, abstract, or keywords), using bibliometric tools, but without making any bridges with industrial ecology. [START_REF] Türkeli | Circular economy scientific knowledge in the European Union and China: A bibliometric, network and survey analysis (2006-2016[END_REF] also analyzed the evolution of the scientific knowledge on CE, produced in the European Union and in China (most productive regions in this field) using bibliometric, network and survey analysis. Interestingly, our updated and new findings considering both the evolution of publications in IE and CE research streams, are put in parallel with the insights generated by these previous but complementary bibliometric analyses.

Literature survey

Evolution: from industrial ecology to circular economy

Although the initial ideas and first consistent mentions of industrial ecology can be traced back in the early 1950s, the official birth of the "industrial ecology" concept can be related to the scientific paper by [START_REF] Frosch | Strategies for Manufacturing[END_REF] that suggested the need for "an industrial ecosystem" in which "the use of energies and materials is optimized, wastes and pollution are minimized, and there is an economically viable role for every product of a manufacturing process", in accordance to the International Society of Industrial Ecology (ISIE, 2015). The overarching goal was to have industries working together in order to move from a linear to a cyclical closed-loop system. A concrete demonstration of this concept started in 1972 in Denmark, in Kalundborg, and is still ongoing.

Back in the 1990s, industrial ecology was considered in the research literature as an emerging framework. [START_REF] Macarthur Foundation ; Erkman | www.ellenmacarthurfoundation.org/circular-economy/concept/schools-of[END_REF] viewed industrial ecology as a means to implement sustainable considerations in an industrial society. To [START_REF] Røine | Does industrial ecology provide any new perspectives? Reports and Communications from Norwegian University of Science and Technology[END_REF], the most critical challenge in industrial ecology was to unify two main interests: ecological sustainability on the macro level, and business economy profit on the micro level. This means that knowledge from different actors and disciplines are needed to implement necessary processes of change.

Meanwhile, [START_REF] Garner | Industrial Ecology: An Introduction[END_REF] identified future needs for the development of industrial ecology, asking for a clearer definition of this field and its concepts, as it is the case at the moment for the circular economy. And as aforementioned in the introduction, [START_REF] Lifset | Industrial ecology: goals and definitions[END_REF] discussed the challenges of setting out the goals and boundaries of industrial ecology as an emerging field. As a new field, they considered that "industrial ecology is a cluster of concepts, tools, metaphors and exemplary applications and objectives". Note that during this period, several ecodesign methods and tools started to emerge to support the design and development of more sustainable products [START_REF] Pigosso | Ecodesign methods focused on remanufacturing[END_REF].

With this background, [START_REF] Ehrenfeld | Industrial ecology: a new field or only a metaphor[END_REF] questioned whether industrial ecology was a new field or only a metaphor: "in the 10 years since industrial ecology first became a topic of academic interest, it has grown as a field of inquiry and has produced a community of practice in several sectors including academia, business, and government". To [START_REF] Ehrenfeld | Industrial ecology: a new field or only a metaphor[END_REF], even as the shape of industrial ecology becomes clearer, ideas like industrial ecology must become institutionalized to have much effect on the reality of everyday activities.

In 2008, the circular economy paradigm had been being first institutionalized and materialized first in China, as part of the law entitled "Circular Economy Law of the People's Republic of China". The purpose of this law was to promote the CE to improve the use of resources and protect the environment and thus enable sustainable development. It defines the CE as "a generic term used to refer to all reduction, reuse and recycling activities carried out during the production, circulation and consumption process". On this basis, many countries started to incorporate some CE-related topics and objectives in their political agenda. For instance, in France, the CE concept was officially first mentioned during the "Grenelle de l'Environnement" and formalized in 2013 through the creation of the National Institute of Circular Economy [START_REF] Bonet | L'économie circulaire : quelles mesures de la performance économique, environnementale et sociale ?[END_REF].

In a nutshell, [START_REF] Blomsma | The Emergence of Circular Economy: A New Framing Around Prolonging Resource Productivity[END_REF] depicted the stages the circular economy concept has gone through: the period from the 1960s to the 1980s is described as the preamble, the one from the 1990s to the 2010s as the excitement. According to the authors, today's period is facing the validity challenge, and forecasts three possible pathways for the CE: coherence, permanent issue, construct collapse.

Definitions of industrial ecology and circular economy

In the 1990s, industrial ecology was theorized as "a new approach to the industrial design of products and processes and the implementation of sustainable manufacturing strategies" [START_REF] Jelinski | Industrial ecology: concepts and approaches[END_REF]. It was defined as a concept in which an industrial system is viewed not in isolation from its surrounding systems but in concert with them -IE seeking to optimize the total materials cycle from virgin material to finished material, component, product, waste product, and to ultimate disposal. Accordingly, to Erkman (1997), IE is a study aimed at understanding the circulation of materials and energy flows; therefore, IE must first understand how the industrial ecosystem works, how it is regulated and its interactions with the biosphere in order to determine how the industrial ecosystem can be restructured to resemble how natural ecosystems function. Circular economy is also looking for an optimal management of resources throughout the life cycle of systems and is characterized by closed-loop systems, promoting maintenance, sharing, leasing, reuse, remanufacturing, and recycling. CE aims to retain the highest utility and value of products, materials, and resources at all times, in order to minimize the generation of waste (EMF, 2015).

Yet, as for now, there is no standardized or crystalized definition of the CE or IE, which might result in diverse interpretations of these concepts among different stakeholders, and therefore be a hindrance to their actual implementation in industrial practices. Based on their review of 25 definitions of CE, Sacchi Homrich et al. (2018) concluded that this concept came from different epistemological fields, and pointed out a lack of consensus and convergence in the literature. So far, the most comprehensive review has been performed by [START_REF] Kirchherr | Conceptualizing the circular economy: An analysis of 114 definitions[END_REF], identifying and scrutinizing 114 definitions of CE. An interesting finding is that 83 (73%) of these 114 definitions have been proposed between 2012 and 2017, showing how emerging and young the circular economy research field is. According to [START_REF] Kirchherr | Conceptualizing the circular economy: An analysis of 114 definitions[END_REF], such analyses are of the utmost importance to bring more coherence in the circular economy concept, because they argue that significantly varying CE definitions may eventually result in the collapse of the concept. [START_REF] Blomsma | The Emergence of Circular Economy: A New Framing Around Prolonging Resource Productivity[END_REF] depicted the circular economy as an umbrella concept, which can be described as "a broad concept or idea used loosely to encompass and account for a set of diverse phenomena" [START_REF] Hirsch | Umbrella advocates versus validity police: A life-cycle model[END_REF]. Indeed, applied to the circular economy, and the various resource strategies individually related to such a paradigm, this umbrella concept offers a new framing of these strategies by drawing attention to the relationship and complementary between these strategies. Furthermore, [START_REF] Kovács | Circular economy vs. closed loop supply chains: what is new under the sun? Constructing A Green Circular Society[END_REF] analyzed the CE concept in comparison with other related concepts that have been used in other disciplines, such as industrial ecology, or supply chain management, in order to understand what is novel, and how the circular economy extends or combines previous streams of literature. In this line, [START_REF] Blomsma | Collective 'action recipes' in a circular economy -On waste and resource management frameworks and their role in collective change[END_REF] provides an overview of waste and resource management frameworks, developed by a variety of actors, that either inspired the CE concept or that took inspiration from it.

In the following sub-section, the linkages, including convergence, divergence or complementary, between CE and IE are more precisely discussed based on a synthetic literature review. Then, further insights are provided in section 4, based on a new bibliometric analysis of the growing number of publications dealing with CE and IE, and a text mining analysis of their various definitions.

Connections between industrial ecology and circular economy

To [START_REF] Bourg | Perspectives on Industrial Ecology[END_REF], it is not straightforward at first to see the differences between CE and IE, especially since, on the one hand, the main strategic axes of IE are defined as follows: (i) to value waste as a resource; (ii) to loop on material cycles and minimize dissipative emissions; (iii) to dematerialize products and economic activities; and, (iv) to decarbonize energy production. On the other hand, the French Environment and Energy Management Agency (ADEME, 2014) subdivides the CE into seven pillars, namely: (i) sustainable extraction, supply, procurement; (ii) ecodesign (of products and processes); (iii) industrial and territorial symbiosis; (iv) functional economy (i.e., product-as-a-service); (v) responsible consumption; (vi) longer duration of use; and, (vii) recycling and waste recovery. From this standpoint, IE is considered as one pillar of CE, but not that in this case, IE seems mainly to be reduced to the dimension of industrial symbiosis and eco-industrial parks. To [START_REF] Figuière | Écologie Industrielle (EI) et Économie Circulaire (EC). Concurrentes ou complémentaires ? XXXIIèmes journées du développement ATM 2016[END_REF], a global approach is required to achieve the overall objectives of a CE, while a more local approach, e.g., on a region or industrial site, is more relevant for the realization of IE objectives. Also, from an ecodesign perspective, these pillars emerge naturally when considering the question of how to promote optimal use of resources during the product or system design stageecodesign aiming to minimize the environmental impact of a product throughout its life cycle [START_REF] Kim | Research perspectives in ecodesign[END_REF][START_REF] Prieto-Sandoval | Towards a on the circular economy[END_REF], IE is seen as a transitional object (notably from the 1960s to the 2000s) serving the shift from a linear to a circular economy, by moving from an explorative or "cowboy" economy to a regenerative one, through restorative and cyclical steps. IE can indeed be helpful to transition towards a more CE, creating different alternatives for the used materials, components, or energy flows, through sharing, reuse, repair, recycling, or energy recovery. Additionally, [START_REF] Saavedra | Theoretical contribution of industrial ecology to circular economy[END_REF] referred to other IE tools and how they can be used to achieve a sound CE through, e.g., dematerialization, material substitution, pollution prevention, design for environment, or eco-industrial parks. [START_REF] Saavedra | Theoretical contribution of industrial ecology to circular economy[END_REF] actually studied the theoretical contribution of IE in the transition to CE, indicating several aspects in which IE contributes to the CE, such as conceptual, technical and political aspects. Through their review of 43 publications representing the contributions of IE to the development of CE, the authors identified that the evolution of CE would not be possible without the existence of IE concepts and tools. Interestingly, [START_REF] Blomsma | The Emergence of Circular Economy: A New Framing Around Prolonging Resource Productivity[END_REF] exposed a draft of a state-of-the-art research agenda for IE to contribute to the development of CE. To guide the development of the CE concept towards wide implementation and alignment with sustainable development, they mentioned that further integration of social, economic, and system dynamics theories, with is required.

Results: complementary insights from bibliometrics and text mining

Bibliometric analysis

Using the "compare" feature of Google Trends (2020), Figure 1 shows the evolution of the global public interest overtime on CE and IE, through web search (worldwide). The values on the Y-axis represent the search interest relative to the highest point on the chart for the given region and time frame. A value of 100 is the peak popularity for the term. A value of 50 means that the term is half as popular. Likewise, a score of 0 means that the term was less than 1% as popular as the peak.

This chart reveals an ever-growing interest in circular economy from 2012 to the present day, while industrial ecology was more popular in the 2000s, 2012 being the turning point when the popularity of CE started to outpace the number of web searches on IE. A similar story can be told in the world of academic publication, as further analyzed hereafter. Actually, this trend also occurred lately -2016 being the turning pointin the wording used in scientific publications, as illustrated in Figure 2. On the one hand, globally, the circular economy concept seems more easily accessible and understandable to the general public (with the straightforward representation of loops, e.g., the butterfly diagram popularized by the Ellen MacArthur Foundation) and the industrial world (driven by economic profit). On the other hand, the industrial ecology concept seems to be more popular within the scientific and research communities, e.g., through the ISIE, that develop methods, tools, and expertise that can serve to the deployment of a circular economy.

Harzing ( 2007) Publish or Perish software, using Google Scholar queries, has been used to conduct the bibliometric analysis, as illustrated in Figure 2. The six most important international research journals, in terms of the number of publications with CE and/or IE as keywords [START_REF] Deus | Trends in publications on the circular economy[END_REF], have been considered as a relevant and consistent database for the bibliometric analysis, namely: Journal of Cleaner Production; Journal of Industrial Ecology; Resources, Conservation, and Recycling; Sustainability; Progress in Industrial Ecology, and Waste Management. Here are the key takeaways of this bibliometric analysis: (i) overall, the number of publications with the keyword "industrial ecology" has a steady increased from 2001 to 2019; (ii) while the first consistent publications with the keyword "circular economy" began to emerge in the early 2010s, the number of CE-related publications escalated exponentially since 2016; and, (iii) the fact that the number of publications with the keyword "circular economy" surpasses the ones with the keyword "industrial ecology" does not prevent the latter to still increase.

Figure 2. Bibliometric analysis of the publications on circular economy and industrial ecology

Furthermore, investigating on the connections between CE, IE and other keywords in journal publications, interesting trends can be deducted. For instance, searching the number of publications (all journals considered, here) having both the keywords "industrial ecology" and "ecodesign", or "circular economy" and "ecodesign", as listed in Table 1, it has been found (e.g., for the year 2016, where the number of publications with the keywords CE and IE are equal, to make a sound comparison), that the ecodesign approach are more often associate with CE strategies that with IE.

Similarly, still using this reference year (2016) for comparison on the same basis, it has been found that: (i) the keywords "business model" and "policy" are more often associated with CE (971, and 179 publications, with these respective keywords, in all journals, reports, and conference proceedings indexed in Google Scholar in 2016) than with IE (510, and 135 publications, respectively); (ii) the keywords "industrial symbiosis" or "eco-park" are more affiliated to IE (750) than to CE (640). In addition, by analyzing the evolution of CE-related publications produced in the European Union (EU) and in China, [START_REF] Türkeli | Circular economy scientific knowledge in the European Union and China: A bibliometric, network and survey analysis (2006-2016[END_REF] identified the most recurrent themes in the joint CE literature between EU and China, including: resource efficiency, indicators, green finance, food and zero waste, governance. Emerging and most important research fields for CE are product life-cycle extensions, new business models, and political economy, while further research is needed on consumer acceptance, rebound effects, social innovation, societal aspects, alternative economies [START_REF] Türkeli | Circular economy scientific knowledge in the European Union and China: A bibliometric, network and survey analysis (2006-2016[END_REF]. According to the co-citation network between CE and IE papers, depicted by [START_REF] Saavedra | Theoretical contribution of industrial ecology to circular economy[END_REF], CE-based research from an IE perspective can further encourage collaborations between these two research communities. Actually, to accomplish a sustainable transition towards a CE at a macro level, a joint work between the business community, policymakers and institutions is fundamental [START_REF] Saavedra | Theoretical contribution of industrial ecology to circular economy[END_REF].

Text mining analysis

To complement this state-of-this-art bibliometric analysis, a text mining analysis is conducted on the different definitions of CE, IE, and ecodesign, to further identify and discuss common themes or divergences. Two free online tools are used to perform the text mining: (i) Textalyser, to sort out the most used terms in their definitions, as summarized in Table 2; (ii) Wordle to generate illustrative word clouds based on these definitions, as mapped out in Figure 3. Note that all the 70 definitions of circular economy, 35 definitions of ecodesign, and 13 definitions of industrial ecology used here for the text mining analysis are available in Appendix A of Saidani's Ph.D. thesis manuscript (2018).

Through this text mining analysis, although definitive interpretations cannot be drawn, some relevant trends are revealed. Regarding the similarities, both CE and IE concepts use substantially the terms "industrial" and "waste" in their definitions. System thinking is also central in both CE and IE definitions. This makes sense because designing out wastes and closing the loop on industrial products needs a holistic understanding and support. Regarding the differences, the noun "resources" is most often used in CE definitions, while the noun "energy" is more employed in IE definitions. A closer focus on "products" is also noticed on the CE definitions. Moreover, the notions of end-of-life strategies appear in CE definitions through the words "recycling" and "reuse", while IE definitions refer more about the production phase with the word "manufacturing". "Design" strategies (e.g., "design for recycling", design for reuse") are also often mentioned in CE definition In this line, ecodesign is interesting as a micro approach aiming to design and develop environmentally sound products, that can support the realization of CE practices in the long run.

Yet, while circular economy and ecodesign shared some common factors (Pole éco-conception, 2016), through the recommendation of closed-loop supply chain, multi-sectorial collaboration and innovative business models, the former is more focus on a continuous economic growth through sustainable consumption, and the latter on reducing environmental footprint. Indeed, ecodesign methods and tools help to design and develop products so that they can be maintained, reused, remanufactured, or recycled through CE loops. Concretely, ecodesign practices could feed the CE paradigm by making products more easily repairable and longer-lasting, e.g., thanks to the selection of proper materials, modules and connections between components. Note that as a first analysis of these definitions, for simple and straightforward interpretations, only the term frequency mining technique was used, i.e., extracting how frequently a word appears in a document, and its relative importance to the whole set of words. One key limitation is that it can disregard or overlook a lot of information on the syntax and words that are semantically similar. Further studies can be conducted using a more complex text mining technique, such as a cluster analysis [START_REF] Talib | Text mining: techniques, applications and issues[END_REF], e.g. to analyze more specifically the associations between keywords.

Discussion and perspectives

Through bibliometric and text mining analyses, this piece of research brought new insights on the positioning of circular economy within the industrial ecology field, and vice versa. Understanding the evolution and recent trends, as well as clarifying the similarities and divergences between these concepts is essential to ensure proper communication, and adequate implementation, for researchers, industrialists, or policymakers, working on circular economy and industrial ecology. Combining these new findings with the corpus of literature studying these relations, further discussions can be made on the appropriate representations and usages of CE and IE concepts. What is novel and exciting for the CE relies on the traction it gained relatively rapidlycompared to the IE, which barely had a couple of mentions in industrial press releases back in the 1990s or 2000s [START_REF] Bocken | The Circular Economy: Exploring the Introduction of the Concept Among S&P 500 Firms[END_REF] among businesses, industrial practitioners, and policy-making communities [START_REF] Blomsma | The Emergence of Circular Economy: A New Framing Around Prolonging Resource Productivity[END_REF]Korhonen et al., 2018a). Yet, even if an increasing number of firms (e.g., Caterpillar, Renault, or Unilever) are setting and communicating on CE strategies and associated targets implementing in their operational practices, there is still a long way to go for widespread adoption of CE-or IE-centered mindset in many businesses or industrial sectors [START_REF] Bocken | The Circular Economy: Exploring the Introduction of the Concept Among S&P 500 Firms[END_REF][START_REF] Masi | Supply chain configurations in the circular economy: A systematic literature review[END_REF]. In fact, although lot of ecodesign tools are available, their implementation in practice still requires some efforts [START_REF] Mathieux | Ten years of scientific support for integrating CE requirements in the EU EcoDesign Directive: overview and lessons learnt[END_REF].

As such, today is a timely period for researchers, and for sustainability or corporate social responsibility departments in companies, to further build on this momentum and foster the use of ecodesign, industrial ecology tools, to accelerate the transition towards a circular and sustainable economy. Actually, in addition to the boost that CE can benefit from the its inclusion in more and more political agendas [START_REF] Geissdoerfer | The Circular Economy-A new sustainability paradigm[END_REF], the previously developedand now available in various formatstools and methods for industrial ecology (e.g., life cycle assessment, material flow analysis), for innovative business models (e.g., triple-layer business model canvas), are valuable resources that can serve to operationalize the CE In all, these conceptseither circular economy, industrial ecology, ecodesignshould work hand in hand and feed each other to enable and catalyze the sound sustainable management of natural resources in the 21 st century socio-economic world. For instance, the recent integration of CE requirements helped to move forward the EU EcoDesign Directive [START_REF] Peiró | Advances towards circular economy policies in the EU: The new Ecodesign regulation of enterprise servers[END_REF], which was mostly focused on regulating energy consumption, with a large untapped potential into material efficiency [START_REF] Mathieux | Ten years of scientific support for integrating CE requirements in the EU EcoDesign Directive: overview and lessons learnt[END_REF]. As both CE and IE are increasingly acknowledged to be suitable instruments for sustainable development [START_REF] Geissdoerfer | The Circular Economy-A new sustainability paradigm[END_REF][START_REF] Korhonen | Circular economy as an essentially contested concept[END_REF][START_REF] Schroeder | The relevance of circular economy practices to the sustainable development goals[END_REF], it would be relevant in future work to assess more quantitatively how and to what extent CE incentives, strategies, and IE projects are contributing to sustainable development, e.g., through the appropriate combination of circularity and sustainability indicators [START_REF] Saidani | A taxonomy of circular economy indicators[END_REF][START_REF] Kravchenko | A Procedure to Support Systematic Selection of Leading Indicators for Sustainability Performance Measurement of Circular Economy Initiatives[END_REF], in order to foster and monitor such actions.

Figure 1 .

 1 Figure 1. Evolution of the search interest on circular economy and industrial ecology (worldwide)

Figure 3 .

 3 Figure 3. Word clouds of circular economy, industrial ecology and ecodesign definitions

Table 1 .

 1 Number of publications with the keywords circular economy, industrial ecology and/or ecodesign Keywords

		"industrial ecology", AND	"circular economy", AND	"industrial ecology", AND
		"ecodesign"	"ecodesign"	"circular economy", AND
	Year			"ecodesign"
	2011	181	21	12
	2012	222	36	13
	2013	223	51	19
	2014	243	104	46
	2015	244	181	59
	2016	256	282	92
	2017	310	427	129
	2018	297	517	172
	2019	185	600	167

Table 2 .

 2 Most used terms in the definitions of circular economy, industrial ecology, and ecodesign

	Most cited	Circular economy	Industrial ecology	Ecodesign
	words
	#1	economy	ecology	design
	#2	circular	industrial	environmental
	#3	resources	systems	eco
	#4	materials	natural	product
	#5	economic	energy	life
	#6	waste	materials	cycle
	#7	system	economic	process
	#8	use	waste	impacts
	#9	products	human	development
	#10	value	environmental	products
	#...	energy, production, recycling,	products, ecosystems,	environment, integration,
		development, consumption,	manufacturing, industry	stages, reduce, account
		industrial, reuse, design

Acknowledgements

Some sections of this paper are partially based on the introduction section of the Ph.D. thesis manuscript of the lead author (Saidani, 2018). These parts have been reworked, updated, and augmented to provide an independent and self-contained piece of research providing new and stand-alone insights for the research, industrial, and policy-making communities, working on circular economy implementation.


Ewe- Denis Kuzzay

Wei Saw

Fabio J W A Martins

Davide Faranda

Jean-Marc Foucaut

Francois Daviaud

Berengere Dubrulle

New method for detecting singularities in experimental incompressible flows


Ngoc Tuan Nguyen

André Rangel

Véronique Migonney
email: veronique.migonney@univ-paris13.fr.

Prof Migonney ; Véronique

Fbse

Kinetic and degradation reactions of poly (sodium 4-styrene sulfonate) grafting "from" ozonized poly (ɛ-caprolactone) surfaces

Keywords: Degradation, Grafting, Kinetic, Poly (ɛ-caprolactone), Poly (sodium 4-styrene sulfonate)

The covalent grafting of poly (sodium 4-styrene sulfonate) on poly (ɛ-caprolactone) was proved to enhance the bioactivity of this polymer. The aim of this article was to perform kinetic studies of the activation and grafting processes and illustrate the influence of several parameters on the grafting rate and on the degradation of the polymer substrate. Results showed that the active groups created on poly (ɛ-caprolactone) surface by ozonation reach a maximum concentration after a short exposure time. Moreover, a kinetic study of poly (sodium 4-styrene sulfonate) grafting on poly (ɛ-caprolactone) substrate showed that the activation energy of this process was low and the influence of conditions such as pH, monomer concentration, time reaction and grafting temperature was deeply significant for the outcome of the treatment. Besides, ozone oxidation and thermal grafting lead to surface degradation, under certain conditions, for example in the presence of Mohr's salt used as a catalyst to enhance grafting rate. The whole study illustrates that ozone-induced grafting is a strong instrument for surface functionalization, although its parameters should be wisely studied and carefully selected. Poly (sodium 4-styrene sulfonate) functionalization improves bioactivity of poly (ɛ-caprolactone) while decreasing the slowness of its biodegradation.

INTRODUCTION

Biodegradable polymers are widely used in biological applications such as tissue engineering, medical devices (sutures, screws), and drug-delivery systems [START_REF] Woodruff | The return of a forgotten polymer-Polycaprolactone in the 21st century[END_REF]. Amongst them poly (ɛcaprolactone) (PCL) is a slowly biodegradable polymer that was early synthesized in the 1930s. This hydrophobic polyester is and known to provide sutures, patches for therapeutic agents delivery and more recently tissue engineering 3D scaffolds ; it is the object of studies to extend its use to other applications such as the reconstruction of injured anterior crucial ligament (ACL) [START_REF] Woodruff | The return of a forgotten polymer-Polycaprolactone in the 21st century[END_REF] [2] [START_REF] Lam | Evaluation of polycaprolactone scaffold degradation for 6 months in vitro and in vivo[END_REF]. PCL shows an extensive list of advantages when compared to other polyesters including long-term degradation preventing inflammatory degradation products, biocompatibility (FDA approved), easily manufacture.

Previous studies illustrated that immobilizing functional groups on PCL could change surface wettability and induce selective proteins adsorption and bioactivity. In order to enhance cell adhesion, proliferation and differentiation, polymeric surfaces can be functionalized in several ways, for example, surface treatment by oxidation (photo-irradiation, electron-beam [START_REF] Dargaville | High energy radiation grafting of fluoropolymers[END_REF], plasma [START_REF] Gupta | Oxygen plasma-induced graft polymerization of acrylic acid on polycaprolactone monofilament[END_REF], and ozone-induced [START_REF] Fujimoto | Ozone-induced graft polymerization onto polymer surface[END_REF]) or grafting of specific functional groups. This last technique is especially interesting for improving selective interactions between surfaces and target biological species such as cells and proteins but also organic compounds.

Sodium styrene sulfonate (NaSS) is one of the candidates selected to this grafting process due to its demonstrated ability to modulate cell attachment via proteins/material interaction [START_REF] Pavon-Djavid | Bioactive Poly(ethylene terephthalate) Fibers and Fabrics: Grafting, Chemical Characterization, and Biological Assessment[END_REF].

Migonney et al. successfully enhanced in vitro spreading and activity of fibroblast cells on NaSS grafted poly(ethylene terephthalate) and PCL films [START_REF] Pavon-Djavid | Bioactive Poly(ethylene terephthalate) Fibers and Fabrics: Grafting, Chemical Characterization, and Biological Assessment[END_REF] [8] [START_REF] Ciobanu | Radical graft polymerization of styrene sulfonate on poly(ethylene terephthalate) films for ACL application: "Grafting from" and chemical chracterization[END_REF].

To accomplish polymer or copolymer covalent grafting, it is often necessary to realize a surface activation treatment, which will generate active groups from which the grafting or polymerization will occur. Ikada et al. showed that ozone-induced, UV irradiation, and plasma treatment generated peroxides on polyurethane and polypropylene [START_REF] Fujimoto | Ozone-induced graft polymerization onto polymer surface[END_REF] [START_REF] Kulik | Peroxide generation and decomposition on polymer surface[END_REF] and Deopura et al successfully grafted acrylic acid on PCL using oxygen plasma-induced [START_REF] Gupta | Oxygen plasma-induced graft polymerization of acrylic acid on polycaprolactone monofilament[END_REF] activation. Similarly, type I collagen was grafted by Hyon et al. [START_REF] Park | Type I atelocollagen grafting onto ozone-treated polyurethane films: cell attachment, proliferation, and collagen synthesis[END_REF] onto ozonized polyurethane films for fibroblast attachment and proliferation enhancement. The ozonation procedure is a simple method for treating complex polymeric objects such as 3D printing scaffold, woven or non-woven fabric, and fiber bundle of ligament prosthesis. This technique uses the gas/liquid ozone-induced mechanism to treat the surface of a polymer film, generating peroxide groups, which will introduce radicals and, indirectly, produce other activated groups such as carbonyl and carboxyl through thermal decomposition. However, such procedure can produce undesirable side effects to further bioapplications of PCL [START_REF] Fujimoto | Ozone-induced graft polymerization onto polymer surface[END_REF] [10], a biodegradable polyester which hydrolyzing in aqueous medium, especially in an oxidative environment.

In this study, PCL substrates were activated by ozonation and thermal grafted by radical polymerization, kinetic of the ozonation and polymerization reactions were carried out under several conditions. Previous studies of the poly (sodium 4-styrene sulfonate) (pNaSS) radical grafting on PCL were conducted, yet the connection between grafting parameters and degradation was not established [START_REF] Woodruff | The return of a forgotten polymer-Polycaprolactone in the 21st century[END_REF] [3] [START_REF] Lam | Comparison of the degradation of polycaprolactone and polycaprolactone-(β-tricalcium phosphate) scaffolds in alkaline medium[END_REF].

Specifically, this study highlights (1) the influence of the following parameters time, temperature, pH, presence of catalyst, monomer concentration, on the grafting rate of pNaSS exhibiting bioactive functional groups on a biodegradable polymer such as PCL and (2) the influence of the functionalization steps -activation and polymerization -on the degradation of PCL. This detailed study should allow a better understanding of the determining parameters to consider when functionalizing biodegradable polyester for biomedical applications such as ligaments prosthesis, in order to prevent uncontrolled degradation.

MATERIALS AND METHODS

Materials preparation

PCL pellets (60,000 g.mol -1 ) (Sigma Aldrich) were dissolved in dichloromethane (DCM). The PCL solution (60% m/v) was spin-coated (1500 rpm for 30 seconds) and dried at room temperature. PCL films were punched to get 14 mm diameter disks samples. NaSS monomer (Sigma Aldrich) was purified by recrystallization to eliminate polymerization inhibitors [START_REF] Rohman | The grafting of a thin layer of poly(sodium styrene sulfonate) onto poly(e-caprolactone) surface can enhance fibroblast behavior[END_REF]. 90 g of NaSS dissolved in 1.6 L ethanol and 178 mL distilled water (9:1, v/v) overnight. The solution was filtered and the NaSS monomer was let to recrystallize at 4 °C for 24 hrs. Purified NaSS product was dried under vacuum for 6 hours at 30 o C and stored at 4 °C protected from light.

Polymer surface functionalization

The polymer surface functionalization is carried out in two steps: a) Ozonation: Ozone flow produced by an ozone generator (BMT 802 N) (0.6 -0.7 bar, 0.6 L.min -1 ) was introduced in a reactor containing 6 PCL disks and 100 mL of water at 30°C: (i) for 10 min -usual conditions, (ii) for times varying from 5 to 35 min -kinetics study, (iii) for 10 minutes at pH varying from (1 to 12) -pH influence study. b) Polymerization: 6 ozonized PCL disks were rapidly transferred into reaction flask containing 60 mL of argon degassed NaSS water solution at a determined temperature to start the thermal polymerization "grafting from the surface" process. Conditions were as following: (i) 0.7M NaSS solution at 45°C for 1 h in the absence of catalyst (usual conditions) [START_REF] Rohman | The grafting of a thin layer of poly(sodium styrene sulfonate) onto poly(e-caprolactone) surface can enhance fibroblast behavior[END_REF] or in the presence of a catalyst Mohr salt, (ii) 0.7M  NaSS solution at 45°C for times varying from 30 min to 6 hours -kinetics study, (iii) 0.7M NaSS solution at 35, 40, 50 and 55°C for 1htemperature influence study, (iv) 0.2M to 1M NaSS solution at 45°C for 1 hour -monomer concentration effect.

In addition, some experiences of ozonation (10 min, 30°C) and of polymerization (1h, 45°C) were carried at different pH varying from 2 to 12 to study the influence of the pH of ozonation and polymerization solution on the PNaSS GD. pH water solutions were adjusted by using 0.01 mol.L -1 hydrochloric acid or sodium hydroxide solutions.

Characterization

Peroxide density determination by iodine method

Iodine test is a simple method to determine peroxide concentration (PC) on activated substrates using potassium iodide (KI) [START_REF] Fujimoto | Ozone-induced graft polymerization onto polymer surface[END_REF]. The decomposition of peroxided groups present on ozonized PCL films was performed at 45 o C in 5 mL KI (1 mol.L -1 ) solution for 30 min. The original colourless solution turned to yellow after thermal peroxide decomposition and was analysed by UV-vis spectroscopy at 352 nm. Non-ozonized PCL film was used as a reference.

Grafting rate determination by toluidine blue colorimetric assay (TB)

Toluidine blue (TB) colorimetric method used in this study was described by Migonney et al [START_REF] Ciobanu | Radical graft polymerization of styrene sulfonate on poly(ethylene terephthalate) films for ACL application: "Grafting from" and chemical chracterization[END_REF]. TB solution (5 10 -4 mol.L -1 ) was prepared and its pH adjusted to 10. Grafted and non-grafted PCL films (control group) were dyed in 5 mL of TB at 30 o C protected from light. After 6 hours, the samples were washed in 5 mL NaOH (1 10 -3 mol.L -1 ) 3 times and the colorant decomplexed in aqueous acetic acid solution (50 %, v/v) for 24 hours. The de-complexed solution was analysed by UV-vis spectroscopy at 633 nm. The grafting degree (GD) of PNaSS on PCL film was calculated using the following equation:

(mol.g -1 )
Where D is absorbance intensity, V is the volume of acetic acid using de-complexion (mL), A is the area of the sample (cm 2 ), L is the width of the spectroscopy cuvette (1 cm) and ε the angular coefficient from calibration curve (47000 to 50000 L.mol -1 cm -1 )

Contact angle (CA):

The sessile drop technique was used with a DSA10 contact angle measuring system from KRUSS GmbH with 2 solvents: water (polar), and diiodomethane (unpolar) (2 μL, 25 o C, 8s). The surface tension of polymer (γ S ) was calculated to follow Young-Dupre and Fowker's equation.

X-ray photoelectron spectroscopy (XPS):

XPS equipment (Omicron Nanotechnology) with a high power monochromated Al Kα X-ray source was used for the analysis of surface chemical components. The scanning area was 200 µm × 200 µm, 3 different zones of each PCL film samples were investigated. CasaXPS software was used to measure the atomic percentage.

Fourier-transform infrared spectroscopy (FTIR):

Fourier-transformed infrared (FTIR) spectra were acquired using a Perkin Elmer Spectrum Two spectrometer. Samples were uniformly pressed against the ATR crystal (128 scans, 4000 to 400 cm -1 , and resolution of 2 cm -1 ).

Surface morphology

PCL surface morphology was observed using a Hitachi TM3000 SEM system and a MultiMode 8

Atomic force microscopy (AFM) (Bruker, Billerica, USA).

The AFM images were taken in ScanAsyst mode (25 o C, in the air) using a triangular silicon nitrile cantilever (k 0.4 N/m, f 70 Hz). The scanning size on PCL was 1.5 µm x 1.5 µm. Mean roughness was calculated by the following equation: Ra = (Ra is arithmetic average, nm).

The images were analyzed using Gwyddion software.

Size Exclusion Chromatography (SEC)

The average molecular weights of the PCL films samples were determined using a Shimadzu

Prominence instrument LC20AD pump equipped with a SIL-20ACHT autosampler and Shimadzu RID-10A differential refractive index detector (Shimadzu Europa GmbH, Duisburg, Germany). The PCL films were dissolved in tetrahydrofuran (5mg.mL -1 ) and their average molecular weight were measured using a calibration curve plotted using poly(methyl methacrylate) standards. showed that the variation of the GD with the grafting time reaction can be divided in two phases (until 1h and after 1h) the evolution of which depends on the temperature (i) Between 30 minutes and 1 hour of thermal grafting (first phase) the PNaSS GD increased strongly. During this phase it is worthy to note that the higher the temperature the higher the GD -GD 55°C,1h was the highest GD value equalling 56 μmol.cm -2 , GD 50°C,1h and GD 45°C,1h were quite similar around 35 μmol.cm -2 and the lowest GD value was GD 35°C,1h equalled 20 μmol.cm -2 , (ii) During the second phase of the kinetics, two groups of GD evolution were observed: one where the GD reached a plateau value close to the GD value observed at 1h -this is the case for the two lowest temperatures of grafting 35 and 45°C, the other with GD values decreasing from 1h to 6h. The higher the temperature the higher the GD decrease -GD 55°C,6h and GD 50°C,6h

RESULTS

Kinetic and reaction study of the poly (sodium 4-styrenesulfonate) grafting on poly (ε-

were around 20 to 25 μmol.cm -2 .

Influence of the NaSS monomer concentration and of the pH on poly (sodium4styrenesulfonate) grafting on poly (ε-caprolactone)

Influence of the NaSS monomer concentration. The influence of the NaSS monomer concentration was studied from 0.2 to 1 mol.L -1 for 1 hour of thermal grafting at 45 °C (Figure 1C). The results showed that the PNaSS GD increased strongly when the NaSS concentration varied from 0.2 to 0.3 mol.L -1 , and then regardless to the NaSS concentration after 0.3 mol.L -1 , the GD decreased reaching a plateau value around 20 μmol.cm -2 . The optimal value of the monomer concentration for the thermal polymerization grafting of PNaSS on PCL was around 0.3 mol.L -1 .

Effect of pH:

The influence of the pH of the water solutions during the two steps of the grafting process on the PNaSS GD was studied. Results presented in Figure 1D showed two tendencies depending on the grafting process step (i) ozonation step: the variation of the pH of the ozonation water solution induced a variation of the final GD which increased to from 22 to 27μmol.cm -2 when pH increased from 2 to 4 then decreased to 18 and 8 μmol.cm -2 for pH values of 10 and 12 respectively. The maximum value of GD was observed for pH around 4 to 6. (ii) Polymerization step: the PNaSS GD decreased with the increase of the pH value of the NaSS solutionthe lower the pH the higher the GD. The highest GD around 40 μmol.cm -2 was observed for pH 2 and the lowest GD around 26 μmol.cm -2 was observed at pH 6.6.

The results showed that the presence of H + influenced positively the polymerization, and then the GD, by increasing the dissociation of sulfonate groupsless effect of sodium ionsbut had no influence on the generation of peroxide. However, a basic environment during the ozonation step reduced significantly the GD by 80 %.

Effect of Mohr's salt as a catalyst:

Mohr's salt ((NH 4 ) 2 Fe(SO 4 ) 2 •6H 2 O)) (MS) is well known as an effective catalyst for grafting process [START_REF] Ohrlander | The Grafting of Acrylamide onto Poly(εcaprolactone) and Poly(1,5-dioxepan-2-one) Using Electron Beam Preirradiation. I. Influence of Dose and Mohr's Salt for the Grafting onto Poly(caprolactone)[END_REF] [START_REF] Zu | Preparation of cation-exchange membrane containing bi-functional groups by radiation induced grafting of acrylic acid and sodium styrene sulfonate onto HDPE: Influence of the synthesis conditions[END_REF]. In addition, it has been demonstrated to depress the homopolymerization of anionic monomers such as acrylic acid and even of NaSS [START_REF] Rohman | The grafting of a thin layer of poly(sodium styrene sulfonate) onto poly(e-caprolactone) surface can enhance fibroblast behavior[END_REF] [START_REF] Zu | Preparation of cation-exchange membrane containing bi-functional groups by radiation induced grafting of acrylic acid and sodium styrene sulfonate onto HDPE: Influence of the synthesis conditions[END_REF]. The influence of the MS salt catalyst was studied following the variation of the PNaSS GD against MS concentration. Results presented in Figure 2 showed the very significant effect of the presence of MS: at low concentration (0 to 0.1M), GD increased from 32 µmol.cm -2 .h -1 to 300 µmol.cm -2 .h -1 (Figure 2). Nonetheless, for MS concentrations higher than 0.1 % w/w, a plateau value of the GD around 270 µmol.cm -2 .h -1 was observed. This phenomenon can be attributed to a higher incidence of the oxidation reaction of iron (II) to iron (III) during this procedure.

Activation energy determination

The activation energy (AE) of the PNaSS thermal grafting onto PCL has been determined in order to evaluate the reactivity of the generated radicals by the ozonation activation of PCL surface ((hydro) peroxide generation) followed by the thermal lysis of peroxides (radical generation) . This AE was calculated by using the Arrhenius equation (see Figure 3) and was found to equal 16.5 KJ/mol. It is noteworthy that this activation energy is comparable to the AE value observed for NaSS/acrylic acid (AA) grafting onto HDPE (22.2 KJ/mol) [START_REF] Nasef | Kinetic investigations of graft copolymerization of sodiums tyrenesulfonate onto electron beam irradiated poly (vinylidenefluoride) films[END_REF] and NaSS grafting onto PVDF (11.36 KJ/mol) [START_REF] Kitaeva | Radiation graft post-polymerization of sodium styrene sulfonate onto polyethylene[END_REF]. Nevertheless, this value is lower than the AE of

Log

(GD/dt) (µmol.cm -2 .h -1 ) 10 3 / T (K -1 )
13 groups which is better detected in the case of PNaSS grafted PCL film in the presence than in the absence of SM catalyst.

Surface degradation:

SEM and AFM were used to detect the presence of defects (cracks, holes) on PNaSS grafted film which are due to the ozonation reaction and SEC was used to measure the degradation effect of ozonation on the length of the PCL macromolecular chains through the number average molecular weight (Mn) of PCL. Results presented in Figure 5 for SEM, Figure 6 for AFM and Figure 7 for SEC showed that:

(i) SEM. No defect was found on PNaSS grafted film for ozonation time of 10 min followed by 1 hour for grafting when compared to virgin PCL. Degradation effects such as holes on PCL films at the frontier between spherolites started to be observed after 10 min of ozonation and 6 hours of grafting; this phenomenon was amplified when the ozonation time was increased to 30 min and grafting polymerization to 16 hours. The effect of the catalyst during the grafting process was shown to generate cracks along the fibril of the spherolites whatever the concentration of MS:

even at low MS concentration 0.01%, the cracks are visible. Figure 1A showed that peroxide concentration was stable after 10 min ozonation whether extending the ozone exposure time, indicating that the surface is quickly saturated with peroxide groups. To explain these results we decided to analyse the activation energy involved in the grafting process. The analysis of the activation energy determined for the PNaSS grafting reaction on PCL showed low activation energies valuesyet described in the literature for anionic monomers [START_REF] Ali | In vitro toxicity of formocresol, ferric sulphate, and grey MTA on human periodontal ligament fibroblasts[END_REF] [15] [START_REF] Kitaeva | Radiation graft post-polymerization of sodium styrene sulfonate onto polyethylene[END_REF] -which could be opposed with the saturation of the PNaSS grafting degree (GD) after 10min of ozonation. That was assumed to be correlated to the rapid termination of anionic NaSS polymerization. Indeed, comparing the activation energy of PNaSS grafting to the polystyrene grafting on PCL confirm the strong effects of sulfonate groups on the termination reaction [START_REF] Kitaeva | Radiation graft post-polymerization of sodium styrene sulfonate onto polyethylene[END_REF] [17] leading to low GD illustrated by the low S (2p) values obtained by XPS analysis.

Peroxide generation:

Peroxide generation on PCL surface was directly impacted by environmental conditions. Ozone easily decays in water to generate OH • . The pH change influences the reaction speed of ozone oxidation and acid/base equilibrium [START_REF] Crist | Polymer spherulites: A critical review[END_REF], impacting the activity of OH • /O 3 on the PCL surface.

PNaSS grafting reaction.

In the absence of Mohr's salt (MS) catalyst, the polymerization of NaSS ended rapidly as can be seen for the low grafting rate despite increasing monomer concentration. Besides that, the presence of sulfonate was difficult to observe by FTIR. The atomic percentage of S2p was 0.5 % from XPS. Under standard conditions, NaSS grafting on PCL film reach their stables values after 1 hour at 45 -50 o C. Grafting rate at 55 o C incubation could increase by 57 % (Figure 1B), thanks to higher peroxide decomposition.

The concentration of MS drastically impacted the PNaSS grafting rate, because the presence of Fe 2+ leads to significant peroxide decomposition acting as a catalyst. At the same time, Fe 2+ will consume the released hydroxyl radicals (OH • ), decreasing the competitive homopolymerization reaction in solution. The hypothesis could be simply expressed by the following scheme:

In the absence of MS catalyst (P for PCL and M for NaSS monomer)

Initiation:

P n -OOH  P n O • + OH • P n + OH •  P n • + H 2 O Then P n O •  P m • + P k-1

C=O (chain scission of P)

Propagation:

P n • (P m • ) + M  P-M • (P m -M • ) OH • + M  HO-M • Termination: P-M • + HO-M •  P-M-M-OH
In the presence of MS catalyst:

Initiation:

P n -OOH  P n O

P n • (P m • ) + M  P-M • (P m -M • ) OH • + M  HO-M • Fe 2+ + OH •  Fe 3+ + OH -(radical consuming)
Termination:

P n -M • (P m -M • )  P n -M-M-P n (P n -M-M-P m ) (crosslinking) P-M • + HO-M •  P-M-M-OH [START_REF] Gupta | Oxygen plasma-induced graft polymerization of acrylic acid on polycaprolactone monofilament[END_REF], [START_REF] Fujimoto | Ozone-induced graft polymerization onto polymer surface[END_REF], [START_REF] Rohman | The grafting of a thin layer of poly(sodium styrene sulfonate) onto poly(e-caprolactone) surface can enhance fibroblast behavior[END_REF], [START_REF] Ohrlander | The Grafting of Acrylamide onto Poly(εcaprolactone) and Poly(1,5-dioxepan-2-one) Using Electron Beam Preirradiation. I. Influence of Dose and Mohr's Salt for the Grafting onto Poly(caprolactone)[END_REF] However, ferric ions which are cytotoxic and very difficult to remove completely remain on the PNaSS grafted surfaces and are not recommended for biological applications [START_REF] Fargere | Determiniantion of peroxides and hydroperoxides with 2,2-diphenyl-1-picrylhydrazyl (DPPH) application to ozonized ethylene vinyl acetate copolymers (EVA)[END_REF]

Grafting efficiency competition with degradation

Beside the PNaSS grafting reaction, chain scissions of PCL can occur by a hydrolysis process due to ozonation times over 10 min inducing degradation and creation of hydroxyl groups then more wetable PCL surfaces. This competitive hydrolysis reaction led us to analysis more deeply the TB complexation process used to determine the PNaSS GR and the observed BT results. We assume that it is necessary to take the specificity of BT molecules towards the two types of functional groups (sulfonate and hydroxyl) into account: a) specific and quantitative complexation of BT with sulfonate groups and b) unspecific adsorption/interaction of BT with hydroxyl groups. This explained BT values remained increasing for 30 min ozonation whereas the peroxide concentration was unchanged after 10 min and an the increase of O1s % and a decrease of C1s % revealing -OH and -OOH groups produced during both ozonation and grafting processes (see Figure A.1). Moreover, the observed increase of the surface tension can be related to the PCL surface degradation along ozonation time exposure.

MS catalyst effect.

In the presence of MS, the analysis of the GD values in the presence of MS showed that Fe 2+ not only enhanced the PNaSS GD but also the surface degradation as illustrated by numerous cracks along the spherulite crystalline of PC (see Figure 5B). Fe 2+ from MS was shown to decompose peroxide to radicals which participated to NaSS polymerization. However, the Fe 3+ reduction to Fe 2+ occurred directly decomposing peroxide groups leading to chain scission: Figure 8 shows that the grafted PCL surface was smoother when PNaSS grafting was achieved in the presence of MS, indicating that a thicker PNaSS layer was grafted on the PCL substrate; this was correlated to an increase of the PNaSS GD. However, large defects (higher roughness) can also be distinguished, as seen on the texture graph in Figure 8. The defects could reach 60 nm of depth, 0.7 µm of width, and 2-10 µm of length (figure 5B and figure 8A).

P n OOH + Fe 2+  P n O • + Fe 3+
In the absence of MS. Degradation caused by hydrolysis during the ozonation and grafting reactions was occurring with a different mechanism in the absence of the MS catalyst. Radicals (O 3 / OH • ) were shown attacking preferentially the boundaries areas between the spherulite regions. PNaSS grafting with longer ozonation times (over 10 min) promoted hydrolysis creating rougher surfaces (Figure 8) over the whole surface, however, amorphous structures are located at the frontier limit of the spherulites [START_REF] Nie | A Vibrational Spectral Maker for Probing the Hydrogen-Bonding Status of Protonated Asp and Glu Residues[END_REF][START_REF] Woodruff | The return of a forgotten polymer-Polycaprolactone in the 21st century[END_REF]. Therefore, amorphous structures were strongly decomposed by chain scission into small molecules and formed holes (Figure 5A and figure 8Bsize/diameter from 1 to 9.38 µm).

Moreover SEC results, demonstrated that the PCL bulk degradationstrong decrease of M n values happened-for grafted PCL film after 20 min ozonation in the presence of MS (see Figure 7).

CONCLUSIONS

This study was devoted to the analysis of the effects of the different steps -a) activation by ozonation and b) thermal polymerization "from" the surface -parameters of the poly (sodium 4styrene sulfonate) grafting process on the generation of poly(caprolactone) surface degradation.

To achieve this goal, kinetics of ozonation and of poly (sodium 4-styrene sulfonate) thermal grafting were carried out on poly(caprolactone) surfaces under various conditions such as pH, monomer concentration, time and temperature, presence or absence of a catalyst.

The results showed that the activation of the grafting process leading to peroxide generation and radicals on PCL surfaces was limited after 10 minutes of ozone oxidation. This is due to the activation energy of the NaSS grafting which is fairly low (16.5 KJ/mol) and assumed to be due to the action of anionic sulfonate groups on the termination of the polymerization. In addition, the limitation of the peroxide generation on poly(caprolactone) was demonstrated despite the variation of different parameters as the extension of the reaction times of both ozonation and thermal grafting or the pH values of the reactions.

The presence of iron (II) ions was shown to increase substantially the grafting degree of the poly (sodium 4-styrene sulfonate) grafting process. However, the presence of Mohr's salt as a catalyst generated an unexpected degradation of poly(caprolactone) as well as toxic ferric hydroxide as a by-product.

The aim was to constrain the poly(caprolactone) degradation during the functionalization process. This is a key challenge for biodegradable polymers devoted to biomedical applications. The study results demonstrated that both surface and bulk degradation could happen for long ozonation and thermal grafting times, and that the degradation effects are located in amorphous regions for regular grafting and over the whole material in the presence of Mohr's salt.

To summarize, the kinetics and degradation study during the poly(sodium 4-styrene sulfonate) functionalization of poly(caprolactone) provided important information on the degradation of this biodegradable polymer during radical-grafting process. Optimized conditions were determined step to optimize the functionalization of polycaprolactone for further biomedical applications.

) surface 3 . 1 . 1 .

 311 Kinetics of ozonation and poly (sodium4-styrenesulfonate) (PNaSS) grafting on poly (εcaprolactone)(PCL) a) Effect of the ozone exposure on the PNaSS grafting degree (GD) of PCL. Results presented in Figure1Ashowed the effect of the ozonation reaction time on the peroxide concentration generated during the ozonation step and on the PNaSS PCL GD. Results showed that : (i) the peroxide concentration (PO) increased until 10 minutes of ozone exposure after which it reached a plateau value of around 3.2 μmol.cm-2 showing that 10 min of ozonation reaction appears as the optimal time value to get the higher concentration of active species, (ii) the PNaSS GD increased with the time of ozonation in two phases a fast growth during the first 10 minutes (GD varying from 7.5 to 30 μmol.cm -2 ) then a continuous and less fast growth fact until 30 minutes of treatment to reach GD value of 45 μmol.cm -2this continuous increase of GD while the PO concentration is stable after 10 minutes. b) Effect of the thermal grafting reaction time (kinetics) and of grafting temperature on the PNaSS grafting degree of PCL. Figure1Bpresented the evolution of the PNaSS GD with the time of polymerization and with the temperature of the reaction. Results

Figure 1 .

 1 Figure 1. Modulation of the PNaSS grafting degree on PCL -Influence of various parameters (A) ozone activation time on peroxide generation and on PNaSS grafting (polymerization 1 h, 45 °C, [NaSS] = 0.7 mol.L -1 ) (B) polymerization time and temperature (ozonation 10 min, 30 o C, [NaSS] = 0.7 mol.L -1 ) (C) NaSS monomer concentration (ozonation 10 min, 30 °C and polymerization 1 h, 45 °C° (D) pH variation of ozonation and polymerization grafting (ozonation 10 min, 30 °C and polymerization: 1 h, 45 °C, [NaSS] = 0.7 mol.L -1 ).

Figure 2 .

 2 Figure 2. Effect of Mohr's salt concentration on the grafting yield (ozonation 10 min 30 °C and polymerization 1 h at 45 °C, [NaSS] = 0.7 mol.L -1 )

  s salt] (% w/w) poly(styrene) (PS) grafting on PCL which was found to equal 140 to 207 KJ/mol[START_REF] Roth | Effect of pH on H 2 O 2 Production in the Radiolysis of Water[END_REF]; these differences can be explained by the anionic (NaSS, AA) versus neutral (styrene) nature of the monomer. The low AE observed when NaSS was involved can be correlated to the fast saturation (within 1 h) of the grafting process despite a temperature increase (Fig1B) which illustrate a fast termination reaction of the growing PNaSS chains leading to low grafting degree.

Figure 3 . 3 . 3 .

 333 Figure 3. Estimation of the activation energy of pNaSS grafting on PCL surface from Arrhenius plot

  virgin PCL was investigated by contact angle measurements. The water contact angle (CA H20 ) is correlated to the surface energy: the higher the CA the lower the surface energy. The evolution of the water drop spreading out with the ozonation time is presented Figure4A: CA decreased from 87 o to 68 o when the ozone time exposure was increased from 0 to 30 min while the surface energy increased linearly (Figure4B).

Figure 4 .

 4 Figure 4. Evolution of hydrophilicity (A) and surface tension (B) of PNaSS grafted PCL film against the ozonation time (grafting conditions: 1 h/ 45 °C, [NaSS] = 0.7 mol.L -1 ). The sessile drop contact angle method was used (solvents: water and diiodomethane), at 25 °C

Figure 5 .

 5 Figure 5. SEM analysis of ozonated and of PNaSS grafted PCL films: defects caused by ozonation (time ozonation 10 and 30min, 30 o C), grafting (time grafting 1, 6 and 16h, 45 o C) and Mohr's salt presence (0.01, 0.1 and 2.5 %, w/w of Mohr's salt, ozonation: 10min, 30 o C, grafting: 1h, 45 o C). (A) Defects degradation due to ozonation and grafting process; (B) defect caused by Mohr's salt

Figure 6 .Figure 7 .. DISCUSSION 4 . 1 .

 6741 Figure 6. AFM topography images (0.5 µm × 0.5 µm) and roughness cross section of: (A) virgin PCL, and grafted PCL with: (B) 5 min ozonation, (C) 10 min ozonation, (D) 20 min ozonation, (E) 30 min ozonation; Grafting for 1h at 45 o C, 0.7mol.L -1 [NaSS]

Figure 8 .

 8 Figure 8. Topography images, roughness and texture diagram cross section of PNaSS grafted PCL film: (A) in the presence catalyst and (B) in the absence of catalyst

Figure A. 2 .Figure legend Figure 1 .

 2legend1 Figure A.2. FTIR spectra of: (a) PNaSS; (b) virgin PCL; and PNaSS grafted PCL with: (c) 5 min ozonation, (d) 10 min ozonation, (e) 20 min ozonation, (f) 30 min ozonation, (g) 10 min ozonation and Mohr's salt 0.1 % w/w. Grafting conditions: ozonation 30 °C, grafting: 1 h/ 45 o C, [NaSS] = 0.7 mol.L -1 . Styrene sulfonate groups were identified by FTIR on grafted PCL film at 1010 cm -1 peak

Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .

 23456 Figure 2. Effect of Mohr's salt concentration on the grafting yield (ozonation 10 min 30 °C and polymerization 1 h at 45 °C, [NaSS] = 0.7 mol.L -1 ) Figure 3. Estimation of the activation energy of pNaSS grafting on PCL surface from Arrhenius plot Figure 4. Evolution of hydrophilicity (A) and surface tension (B) of PNaSS grafted PCL film against the ozonation time (grafting conditions: 1 h/ 45 °C, [NaSS] = 0.7 mol.L -1 ). The sessile drop contact angle method was used (solvents: water and diiodomethane), at 25 °C Figure 5. SEM analysis of ozonated and of PNaSS grafted PCL films: defects caused by ozonation (time ozonation 10 and 30min, 30 o C), grafting (time grafting 1, 6 and 16h, 45 o C) and Mohr's salt presence (0.01, 0.1 and 2.5 %, w/w of Mohr's salt, ozonation: 10min, 30 o C, grafting: 1h, 45 o C). (A) Defects degradation due to ozonation and grafting process; (B) defect caused by Mohr's salt Figure 6. AFM topography images (0.5 µm × 0.5 µm) and roughness cross section of: (A) virgin PCL, and grafted PCL with: (B) 5 min ozonation, (C) 10 min ozonation, (D) 20 min ozonation, (E) 30 min ozonation; Grafting for 1h at 45 o C, 0.7mol.L -1 [NaSS]

Figure 7 .Figure 8 .

 78 Figure 7. SEC chromatogram analysis: M n and M w of PNaSS functionalized PCL film after a) ozonation and b) PNaSS grafting at different times, c) grafting in the presence of Mohr's salt at different concentrations, d) SEC chromatogram of PCL films under a,b, c conditionspresence of F1, F2, F3 peaks corresponding to degraded macromolecular chains of PCL Figure 8. Topography images, roughness and texture diagram cross section of PNaSS grafted PCL film: (A) in the presence catalyst and (B) in the absence of catalyst

Table 1 .

 1 XPS analysis: atomic percentage measurement for C1s, O1s, S2p of virgin PCL and pNaSS grafted PCL film without catalyst Contact angle. The hydrophilicity of PNaSS grafted PCL after different ozonation times and of

	Atomic %	C 1s	O 1s	S 2p	Na 1s
	Virgin PCL	79.55	20.45	0	0
	Grafted PCL	76.90	22.60	0.50	0

ACKNOWLEDGEMENT

This work was funded as part of the "Future Investment Project" by the French Public Investment Bank (BPI) and the French state -PSPC application -Liga2bio project (VM). I would like to thank Dr. Vincent Humblot from Laboratory of Reactivity of Surface, UMR CNRS 7197, Sorbonne University for the XPS analyses. 25

Appendices