Julien Longhi
email: julien.longhi@cyu.fr

Using digital humanities and linguistics to help with terrorism investigations

Keywords: Linguistics, corpus, forensic linguistics, textometry, stylometry

This article seeks to offer a response to the digital transformation of forensic science by employing a tool-based linguistic analysis, integrated into the paradigm of digital humanities. It is a way to scientifically model the analysis of digital texts using digital methods. Computer science comes in support of linguistic skills in order to deal with investigative situations and help analyze criminal acts.

It presents a case report thanks to the analysis of a corpus made up of 23 texts relating to criminal acts related to suspected terrorist groups with links to the far left. The goal is to help investigators by providing results which can help find stylistic similarities or exclusions between texts and thus potentially between the authors of those texts, offering authors profiling hypothsesis that may be included in the investigation process. While linguistics alone cannot solve such cases, a better understanding of language data, including topics, style and grammar, bring additional clues that can be very useful information in the investigation of crimes (linguists can "translate" information to investigators, so that il can be integrated to the investigation). Digital tools provide a form of objectification since they are based on statistical calculations which reveal regularities that are otherwise invisible to the naked eye. These tools, when used properly in investigations, can prove invaluable in extracting "clues" from the linguistic "traces" that make up texts.

Introduction

Humanities and social sciences and especially the emerging field of forensic linguistics are today becoming extremely important in the mechanisms for understanding threats. If, as Ribaux, Walsh, and Margot [1] explain, "it is recognized that forensic case data is still poorly integrated into the investigation and the crime analysis process, despite evidence of its great potential in various situations and studies", this is probably even more true for linguistic data. Following these authors who wish a change of attitude "in order to accept an extended role for forensic science that goes beyond the production of evidence for the court", this paper propose methods that are concretely applicable in risk contexts, in order to detect, characterize, and prevent threatening phenomena. It is possible to consider linguistics as a part of forensic science because it can follow the same process of collecting, analyzing, comparing, interpreting, and reporting linguistic clues in a forensic context. This approach is particularly similar to the typical process for source attribution, ACE-V (used in the field of documents in the 1970s and now systematically used in the field of digital traces): A = analysis (extraction of characteristics); C = comparison of characteristics (e.g. between two texts), identification of concordances and discrepancies; E = assessment of the value of matches (e.g. frequency, rarity, identifying power) and discrepancies (can they be explained or not, if not then exclusion from a common source).

Results allow to answer typical reconstruction questions in investigations:

-Who: can we extract or deduce information about the author(s) of illegal activities (a specific author, a group; or extract information about the author(s), for example age, gender, level of education, etc.)?;

-What: what are the corpora about? Can we use semantic features to understand the specificities of a document? -When: linguistic features can give information on the event/facts (temporality, anteriority/posteriority, etc.).

-Where: sociolinguistic and geographic features can help to understand the origin of the author(s) or the place where they were when they produced the texts; -How: stylistic features can help to understand how a text was produced (for example with a genetic approach); -Why: performativity, intentionality are ways to examine what the goal of a text is.

The proposed paper aims to answer these questions through the prism of linguistics, by analyzing corpora. It will seek to answer, more or less precisely for the moment, these questions: can we characterize one or more authors, or groups of authors (who?); can we reveal thematic regularities in the corpora (what?); do we have geographic or temporal information in the texts studied (where / when?); can we make inferences about the author's intentions and about the means used (why / how)?

In addition, the originality of this work is that it applies to texts in French, whereas most studies in the field focus on analyzing English. Its impacts allow bridging the gap, with extensions in future works, between the qualitative treatment of the threat and its automated processing through large corpora.

More concretely, I shall describe a method for analyzing linguistic meaning based on identifying expression and content regularities from a statistical point of view. This method is part of a forensic science perspective, seeking to lay the foundations of a forensic linguistics which combines quantitative identification with qualitative analysis. The analysis corpus is made up of 23 texts relating to criminal acts which concern especially terrorist groups with links to the far left. The goal is to be able to help investigators with these cases, providing results which can help find stylistic similarities or exclusions between texts and therefore potentially between the authors of those texts.

To achieve the set goals, we need new improved tools that ally qualitative and quantitative analyses. This paper is a case example that can be generalized. To start with the way we can use the tools, Chaski [2] presents different approaches in forensic linguistics:

-Qualitative vs. quantitative; -Prescriptive vs. descriptive; -Analyst-based vs. Machine-based; -Theory-based vs. practice-based.

The adoption of a quanti-qualitative approach made it possible to go beyond the limits of the two separate approaches. This global approach to analysis has been part of the lineage of my work for more than ten years ([3] [4] [5]), with various fields of application. The research initiated in 2015 around security issues testifies more than ever to the relevance of a longitudinal linguistic study: all levels of linguistic analysis can be mobilized to detect, identify, and characterize a threatening phenomenon. I will present different aspects in the "method" section.

For Chaski [START_REF] Chaski | Who's at the keyboard? Authorship attribution in digital evidence investigations[END_REF], dealing with a problematic close to this paper ("Determining who was at the keyboard"), authorship attribution can be approached through several avenues:

-biometric analysis of the computer user; -qualitative analysis of "idiosyncrasies" in the language in question and known documents; -quantitative, computational stylometric analysis of the language in question and known documents.

The second approach, "known as forensic stylistics, could be quantified through databasing", because "without the databases to ground the significance of stylistic features, the examiner's intuition about the significance of a stylistic feature can lead to methodological subjectivity and bias". The third approach, stylometry, "is quantitative and computational, focusing on readily computable and countable language features, e.g. word length, phrase length, sentence length, vocabulary frequency, distribution of words of different lengths". In these two cases, I follow Champod [START_REF] Champod | Overview and Meaning of Identification/Individualization[END_REF], about "Meaning of Identification/Individualization": "the problem of inferring identity of source is more complex than a simple dichotomy between class and individual characteristics", because, from a logical point of view, "the strength to be attached to forensic findings is essentially relative to the case and its value is best expressed using a likelihood ratio. The question of the size of the relevant population -which impact on prior probabilities -and decision thresholds are finally outside the province of forensic scientists but rightly belong to the fact finder".

With the preliminary results presented in this paper, the proposed approach fits the third approach described by Chatsky: it focuses on computable and countable language features (lexical and grammatical; I don't have a database as in the 2 nd approach, but the first corpus of 23 texts can be augmented in future work, to become a reference database). From a general point of view, I follow Coulthard [START_REF] Coulthard | Forensic Linguistics: the application of language description in legal contexts[END_REF] who explains that "there are no specific forensic linguistic tools and […] the best training for a forensic linguist is a course in descriptive and applied linguistics": "each case will normally require a different selection from the basic descriptive linguist's toolbox". Chapter 6 of Coulthard and Johnson [START_REF] Coulthard | An Introduction to Forensic Linguistics. Language in Evidence[END_REF] has examples of forensic analyses focusing on morphological meaning, syntactic complexity, lexico-grammatical ambiguity, lexical meaning, pragmatic meaning, speech-to-writing transformation, narrative analysis and features of non-native language usage" (see also [START_REF] Coulthard | On Admissible Linguistic Evidence[END_REF] for more examples). With these variables, we can try to evaluate their intra and inter-variability: by comparing the intra-variability of the characteristic observed within the texts of the same author with the inter-variability of the characteristic within the text of different authors, we can highlight the useful characteristics (those which are less intra-variable than inter-variable), with the aim of reducing as much as possible the population of possible authors for a text.

Material

The material was given by the French Gendarmerie in order to help investigators with cases involving criminal acts which concerned especially terrorist groups with links to the far left. There are websites where these acts are claimed in writing, giving accounts of the facts (sometimes accompanied by photos), interpreting those facts, justifying them, etc. These texts are of course anonymous, and at this stage, it is not possible to know if the author of the (online) post is the author of the text, whether the author of the text is (part of) the terrorist (group), etc. Nevertheless, being able to characterize the style of these texts, establish similarities, show differences, or linguistically characterize the web pages could help investigators by formulating hypotheses on the possible number of authors or the probability that, for example, texts x, y, z have one, two, or three authors. This addition of linguistic characteristics should help investigators, if they can integrate them into analyzes which are at the same time based on other characteristics (for example physical, in connection with the examination of the crime scene).

Formally, the pages I analyzed came in this form: In this page we can identify a lot of information that is potentially useful to investigators (information which, in the corpus, will become metadata): the place (Couflens), the date of the event (26 April), the date of the post (29 April 2018), the subject (opposition to (contre or "against") the reopening of a tungsten mine). With this example, we see the link with the other information (which makes it possible to answer the questions "who?", "When?", "Where?") not from digital elements (which can be false if the authors take precautions, such as using the darknet) but linguistic information.

Reading the article's introductory paragraph provides us with further details: Figure 2: Beginning of the article illustrated with a photo Thus, the word incendiaires meaning "arsonists" tells us that this is about an arson incident, that a wall has been défoncé or "smashed down", for example.

Methods

Textometry offers an instrumented approach for dealing with corpora, combining quantitative syntheses and analyses which include text [11]. From a functional standpoint, textometry implements differential principles. This approach highlights the similarities and differences observed in a corpus according to the representation dimensions considered (lexical, grammatical, phonetic, prosodic, etc.). In addition to providing sorting procedures and statistical calculations for the study of digital corpora of texts, textometry establishes contextual and contrastive modeling. Thus, the text is characterized by its words in relation to their use in the corpus; the word is characterized by its tungsten mine -26 April"). The website pages were provided by the Gendarmerie in a spreadsheet together with several other pieces of information. The paper has been authorized to use the online pages and the data in them, but the additional information from the Gendarmerie cannot be published. co-occurrences, etc. [START_REF] Pincemin | Sémantique interprétative et textométrie-Version abrégée[END_REF]. Textometry is particularly relevant to corpus exploitation in humanities and social sciences. It simultaneously enables a detailed and global observation of different texts while remaining close to them, and highlights the fact that language is an important observation field for these disciplines. The 23 texts contain a total of 12109 occurrences, 2534 forms with an average of 526 occurrences per text. This corpus size, although modest, is well suited to textometric methods, which makes it possible to compare corpora without having to resort to large training corpora. I consider it is more appropriate to use a word-frequency approach rather than bag-of-words or topic modeling for two reasons:

1) The size of the corpus and the nature of the data (specific texts without a big database to train a model) can be analyzed within the prism of digital humanities using corpus exploration rather than more computational approaches;

2) The analysis of textual data, according to Mayaffre and Vanni [START_REF] Mayaffre | Objectiver l'intertexte ? Emmanuel Macron, deep learning et statistique textuelle[END_REF], "is essentially paradigmatic (tokenization, then selection of tokens according to the dictionary of frequencies, according to the morpho-syntactic label, according to the initial, etc.)" and artificial intelligence "is syntagmatic in essence (contextualization, that is to say the combination or sequentialization or convolution of the token caught in the linearity of the text)", which allows us to take advantage of both the linguistic and grammatical specificities of the corpus, and also the link with the metadata.

Ongoing work aims to combine the two methods and in particular to use convolutional neural networks.

In order to analyze the corpus in a way that would make it possible to analyze both the text produced and the contextual elements and investigative data, I tagged the corpus by putting "variables" (preceded by *) at the top of each document: The addition of * before tags was due to my using the Iramuteq software which provides a set of analysis procedures for the description of a textual corpus. IRAMUTEQ is a GNU GPL (v2) licensed software that provides users with statistical analysis on text corpora and tables composed by individuals/words. It is based on R software and on python language. It is an R INTERFACE for the multidimensional analysis of texts and questionnaires.

One of its principal methods is Alceste. This allows a user to segment a corpus into "context units", to make comparisons and groupings of the segmented corpus according to the lexemes contained within it, and then to seek "stable distributions" [START_REF] Reinert | Une méthode de classification descendante hiérarchique: Application à l'analyse lexicale par contexte[END_REF]. In addition to the Alceste method, Iramuteq provides other analysis tools including prototypical analysis, similarity analysis, and word-cloud analysis. All of these methods allow the users of this tool to map out the dynamics of the discourses of the different subjects engaged in interaction [START_REF] Reinert | Quelques interrogations à propos de l'objet d'une analyse de discours de type statistique et de la réponse 'Alceste[END_REF].

The corpus relating to real cases which the Gendarmerie provided contained 23 texts. These 23 texts were formatted as shown in Figure 3 and then subjected to a statistical analysis. A first basic analysis can be conducted on the frequency of forms (lemmas, see Table 1):

Table 1: Frequency of lemmas 2 in the corpus Methodologically, and from the perspective of a criminal investigation, this software is interesting because it can provide tools for exploring the corpus and not just quantified results. Thus, a user can go back to the corpus in order to see the various forms taken by a lemma or get a concordance, that is, see the forms as they appear in context (examples in Figure 4): 2 A lemma makes it possible to group together different occurrences of a word under the same unit (for example, in Figure 5, the lemma attaque ("attack") groups together the occurrences attaque, attaques; attaquer ("to attack") groups together the various conjugations of the verb; and so on). This is very much an approach to collecting, analyzing, comparing and interpreting data -in this case textual data -which belongs to the forensic science approach, seeking to establish a method that combines identifying phenomena, returning to corpora, conducting linguistic analyses, and exploring phenomena. This first type of analysis has the advantage of providing the users of this software, and therefore potential investigators, with tools for exploring corpora, in particular procedures for counting, reorganizing data, and observing certain quantified phenomena. With this software "Lexical Features" ("single-content words as document features" [START_REF] Mikros | Authorship Attribution and Gender Identification in Greek Blogs[END_REF]) but also grammatical features [START_REF] Charaudeau | Grammaire du sens et de l'expression[END_REF] were used.

With lexical features, we can use a Reinert-type classification proposed by the Iramuteq software: "this classification, implemented for the first time in the Alceste ® software [START_REF] Reinert | Une méthode de classification descendante hiérarchique: Application à l'analyse lexicale par contexte[END_REF], makes it possible to highlight lexical worlds. These discourse structures assume that a statement is a stance that is dependent on the subject but also on its activity and context" [START_REF] Loubère | L'analyse de similitude pour modéliser les CHD[END_REF]. At a methodological level, the vocabulary of the corpus is "used to build a double-entry table listing the presence/absence of the full forms selected in/from the segments; a series of bi-partitions are [then] performed on this table based on a factorial analysis of correspondences." These classifications are very useful for understanding the topics of a corpus through the lexical worlds that compose them. They can be represented with descending hierarchical classifications (DHC).

In terms of the visualization and representation of the results, one can use the factorial analysis of correspondences (FAC): this is a statistical method "that can be applied to contingency tables such as tables resulting from counting different types of vocabulary (table rows) in different parts (table columns) of a corpus of texts" [START_REF] Salem | Tutoriels pour L'analyse Textométrique[END_REF]. We start by "calculating a distance (known as the χ 2 distance) between each pair of texts making up the corpus. These distances are then broken down into a hierarchical succession of factorial axes. […] This method helps obtain synthetic representations of both the distances calculated between texts and those that can be calculated between the textual units that make them up." It is nevertheless important to note that while "the main advantage of FAC lies in its ability to extract from vast data tables that are difficult to grasp simple structures that can approximately reflect large underlying oppositions within a corpus of texts", this is only an "approximation" and the results of previous functions (calculations, tables of figures) must be precisely considered. These visualizations are an issue in the context of research in numerical humanities, which aim, in particular, to make complex results comprehensible through visualizations which are based on metrics and rigorous calculations.

Results and discussion

Two types of results, based on the methods described, can be provided: a lexical classification and a calculation of the proximity/distance between texts.

Lexical classification

With the lexical classification, it is possible to identify major topics (or lexical worlds, [START_REF] Ratinaud | Des mondes lexicaux aux représentations sociales. Une première approche des thématiques dans les débats à l'Assemblée nationale (1998-2014)[END_REF]) which could help group some of the texts together or objectively take into account the subject matter of the texts analyzed. Representing the data in the form of descending hierarchical classifications (DHC) in Figure 5 or factorial correspondence analyses (FCA) will then help visualize the results of the algorithm (see Figure 6). We can thus see that 5 main classes could be identified: these classes, which were based on "text segments", showed that, for example, 18.7% of the text segments within the corpus fell under class 4 related to arson incidents (what the user could interpret through the words feu or "fire", essence or "petrol", allumer or "to light", etc.). 18.7% of the segments also referred to acts connected to animal species in class 2 (humain or "human", sauvage or "wild", animal, etc.). 3 This dendrogram can also be projected onto axes to help identify proximities which may exist between different parts of the corpus (in this case, each of the claim texts) by virtue of their shared connection to lexical worlds (see Figure 6).

3 Other topics are related to energy issues (class 5), the political dimension of actions (class 3) and the issue of discrimination (class 1). The class numbers have no meaning, but their proximity in the dendogram is based on a statistical proximity criterion This way of representing the data does not really allow us to make hypotheses on the stylistic similarity between the texts but rather to see which texts could fall under the same theme (e.g. the four in blue would be related to arson incidents).

While the regularities identified here are mostly thematic and could be the subject of a manual classification, using forensic linguistics in order to see the doxas specific to different texts (i.e. the regularities underlying these texts, whether in relation to what is said or how it is said) helps us to go further in our investigations. Indeed, the links between topics and style is a complex subject.

Mikros [START_REF] Mikros | Authorship Attribution and Gender Identification in Greek Blogs[END_REF] distinguishes three types of thematic analyses in a quantitative perspective: Intra-Topic (IT), Single Cross-Topic (SCT) and Multiple Cross-Topics (MCT). In our case, the advantage of textometry is that the analysis is conducted on the existing corpus, which allows us to do calculations and make connections on the basis of the texts' vocabulary. Thus, the principle of differentiality helps us to measure distances and proximities rather than make classifications, which is relevant to the task at hand. The FCA (Figure 6) shows that classes 2 and 4 seem well separated from the others, while overlaps exist between some others.

Proximity/distance between texts

For this analysis we could use the software to calculate various specificities of each one of the texts so we may measure proximities or differences between them. These calculations could be based on different contexts which were coded using the following metadata:

-Towns as units -Events as units -Websites as units.

This linguistic approach brings more information than basic statistical approach (already well known in these contexts) because it uses specific and adapted statistics for textual analysis, 4 and brings different features (linguistic forms, grammatical categories, etc.). Here, the interpretation of the quantitative results by a linguist makes it possible to assess their significance (knowing that they are not random). This feature produces a factorial correspondence analysis in a contingency table which cross-tabulates active forms (common names, proper names, adjectives etc.) and function words (prepositions, articles) with variables. In this way, each form was assigned a (positive or negative) value in each text, which indicated whether the form was over-or underused in that particular text (Table 2):

Table 2 Specificity table 4 The reference website on textometry defines the principle of calculating specificity as follows: it consists of "normalizing by dividing by the size of the part [which] makes us consider implicitly (or not) that the relative frequencies are representative of the original frequencies (before dividing by size). To this end, by committing as few errors as possible outside any complementary information, relative frequency can be taken to be the likeliest number of occurrences in a part of any size according to a law of normal occurrence. In a way, relative frequency is considered as a mode of normal probability distribution (the middle of the Gaussian bell curve where it is at its highest and therefore its likeliest), i.e. the average (cf. properties of the normal law: average, standard deviation, etc.). However, it so happens that the occurrence probability of a graphic form -or, more generally, a CQL expression -in a part has no reason to behave according to a normal law. That is to say, its distribution does not have to resemble a perfect Gaussian bell curve with an average, standard deviation, etc." Source: http://textometrie.ens-lyon.fr/html/doc/manual/0.7.9/fr/manual43.xhtml Table 2 is of course hard to read and understand since it is made up of 23 columns (one for each text) and very many rows (corresponding to the number of forms). Using the method suggested by Ratinaud [START_REF] Ratinaud | The Brilliant Friend(s) of Elena Ferrante: A Lexicometrical Comparison between Elena Ferrante's Books and 39 Contemporary Italian Writers[END_REF], it "shows the result of a correspondence analysis carried out on the full lexical table which partitions this corpus" according to the towns where the events occurred. This table is a simple contingency table with facts in columns and words in rows. The cells in the table contain the frequency of each word in each row.

The analysis "allows us to project on a 2-dimensional plane the relations" between the towns on the basis of their lexical co-occurrences, i.e. their tendency to have (or not to have) the same words in their texts. With Iramuteq, we could then calculate the distance between the texts according to these variables (textual statistics based on Labbé's intertextual distances). Labbé & Labbé [START_REF] Labbe | Inter-Textual Distance and Authorship Attribution. Corneille and Molie re[END_REF] 5 suggest to consider the "frequency of each type, that is to say, the entire texts (we use the adjective "textual" in order to show that the calculation is on N and not only on V or on a part of V)". Their metric "measures whether two or several texts are relatively far from one another", and their paper presents "a good approximation of the distances between several texts", with mathematical justifications. This graphic visualization of the results makes it easier to interpret the proximities or distances between texts Figure 8).

5 Their work "consider the difference between "token" and "type". The token is the smallest measurable element in a text, and the «type» forms the vocabulary's basic element. For instance, the longest novel in French, Les miseŕables is made up of half a million tokens : its length or extent (noted N), while its vocabulary (noted V) is made up of less than 10 000 normalized and tagged types". A graph of this kind needs to be interpreted very cautiously (because of the instability of linguistic features, that it is necessary to verify by a return to the corpus, in particular because of the phenomena of polysemy), however, it does help us to consider grouping together texts on the basis of their lexical proximity, or excluding them on the basis of their distance. At this stage it is possible to come up with groups of variables (an example of which is shown in Figure 10 -all that is required is to note the proximity or distance between sets). We have seen above that the texts could also be grouped together based on their topics (towns and cities could be grouped together because the lexicon relating to the topics "saturated" the texts with numerous specific terms -for example feu ("fire"), essence ("petrol"), allumer "to light" for arson incidents). In order to examine the style independently of the topics, we could conduct the same type of analysis by taking into account grammatical of the words, rather than lexical aspects (i.e. the proportion of common names, definite articles, indefinite articles, adjectives, etc.). In Figure 9, we can observe other proximities, based on grammatical features. If the user wants more details about the proximities, he can have a look at table 2 and compare specificities of the text (grammatical specificities showed in figure 9, lexical specificities in Figure 8).

We can see the general grammatical specificities (categories) on a graphic (Figure 10): It is my hypothesis that cross-referencing Figures 10 and11 would allow a user/investigator to identify similarities and exclusions by comparing the texts both lexically and grammatically. Thus, in the two graphs above, the texts relating to the events in Limoges and Limoges_Jourdan appeared close to each other (maybe because they use "adj_num" specifically), which could help investigators test the hypothesis of a same author/group of authors for these two incidents.

Similarly, in the same two graphs there were proximities between the cities of Clermont_FD, Crest, and Bellecombe_en_Bauges (with other grammatical or lexical particularities: "pro_ind", pro_rel", "pro_dem", which shows the importance of pronouns). If we can clearly see the potential of such an approach, further step can be taken by providing a tool adapted to the needs of the Gendarmerie, with a specific interface and functionalities for identifying authors and comparing documents. This would include superimposing specific data and metadata on the same graph, in order to more easily observe the connections, and the possible reasons for these connections. This is precisely what was achieved during a research project funded by CHEMI (Centre des Hautes Études du Ministère de l'Intérieur) as part of the 2020 call for proposals in strategic and prospective studies and innovations. The development of a prototype called "Text Print"6 made it possible to lay the foundations of a method and tool adapted to this topic. This tool is still under development but what can be highlighted, apart from documentary and archival benefits, is the implementation of the functionalities mentioned in this article:

-N-grams of terms, grammar, and characters; -Implementing an algorithm for calculating specificities; -Implementing a classification method based on a Convolutional Neural Network trained on specific data (for the moment short online messages).

For example, with the same data used in this paper, the factorial correspondence analyses of the specificities can directly show on the graphic representation (Figure 11) the characteristic words of the parts (in red), and the variables (in blue), and here I choose to combine the lexical words and the grammatical words: Here, we distinguish texts that seem distant from others because of their vocabulary (Saint Martin de Bellevue, Bréau, Gaillac), and we can also make connections, on the basis of lexical words or tool words. The development of such a tool goes hand in hand with a process of mutual acculturation between academic linguists and Gendarmerie experts, aimed at generating new skills in forensic linguistics -a field which is currently absent from investigation teams. Work therefore needs to be done in the long run so that expertise and tools can be provided which can tackle scientific issues pertaining to the community of linguists and meet the expectations and needs of investigators. This means in particular that linguistic results are taken into account in an investigation, and investigators can provide linguists with clear feedback on the usefulness of the analyses, measures, and support they gave during the investigation. Today, I particularly work together with the technicians of the Documents Department of the Criminal Research Institute of the National Gendarmerie (IRCGN) 7 who conduct physico-chemical examinations to determine the composition of the paper supports and inks and, if necessary, carry out comparative reviews. They analyze documents from the perspectives of support, inks and printing techniques. For example, they look for latent traces of fulling, determine printing techniques and authenticate documents. Handwriting and signing fall into the category of printing techniques: these are therefore personal and detailed human products. In this case, as in the forensic linguistics proposed in this article at the level of style, each writer personalizes the writing model that has been taught and develops a personal writing. The careful examination of a sufficient and comparable sample can allow the technician to determine if a contentious writing was produced by a given person (the writer). In the same way, the examination of a textual corpus can allow the linguist to determine if a contentious writing was produced by such a person.

Of course, other types of measurement are also possible. For example, in order to grasp certain specific turns of phrase or ways of saying something, we could use the "repeated segments" feature which helps us see specific uses of strings of several terms (Table 3):

Table 3: Repeated segments (class 1)
This level of analysis is also studied by Wright and Johnson [START_REF] Wright | Identifying idiolect in forensic authorship attribution: an n-gram textbite approach[END_REF]: these collocations and sequential strings of lexical words "can be called 'n-gram textbites', small portions of text that characterise the writing of a particular author". For the authors, these repeated segments "reinforce the benefits of a triangulation of approaches: corpus stylistic, statistical, computational, and case study". The corpus brings attention to textual data; stylistics allows attention of textual diversity; IT offers computation [START_REF] Champod | Overview and Meaning of Identification/Individualization[END_REF] In my collaboration with Cecile Jacob from the IRCGN (https://theconversation.com/la-linguistique-appliquee-aux-enquetes-criminelles-comment-ca-marche-143127#commen t_2294798), I drew parallels between the methods of writing comparison and linguistics in order to validate my approach from a forensic point of view.

of data applied to the case study. In this case, the 3 occurrences of the segment "l affaire de la voiture de" are found in three different texts, which can then lead us to investigate more precisely the similarities between these three texts, and therefore between the three separate cases: Here, textometry provides different ways of conducting syntactic and semantic analyses, which can provide information for observing and interpreting corpora. Using a rigorous method based on building and exploring corpora, linguistics can be a branch of forensic science and help investigators when textual data are exhibits in a case. With these results, investigators can use new hypotheses and, sometimes, find new connections that they would not have spontaneously thought of (for example Limoges and Limoges_Jourdan, or Meylan, Limoges_Jourdan and Arphy_CF_Vallerauge).

Discussion

The discussion concerns the specificity of the work presented here in light of ongoing research conducted in forensic linguistics. According to Coulthard [START_REF] Coulthard | Forensic Linguistics: the application of language description in legal contexts[END_REF], "there is comparatively little work

[done] in France and on the French language". This particularity is probably linked to the status of experts in French courts of law, but it is also, I believe, related to the French scientific context, in particular the fields of linguistics and discourse analysis.

Indeed, in the French intellectual and scientific context, general linguistics was a pioneering and leading science in the birth and development of structuralism (starting with Ferdinand de Saussure's

Course in General Linguistics in 1916). The view according to which socially stable representations attached to a topic impact discourse productions has played an important role in the French research community. As a linguist, Saussure is interested in languages as symbolic formations allowing to signify the specificities of cultures and societies [START_REF] Kharbouch | La séméiotique de Peirce et la sémiologie de Saussure[END_REF]. Foucault [START_REF] Foucault | L'archéologie du savoir[END_REF] states that discourse is a social practice underpinned by areas of conventional knowledge called discursive matrices (formations discursives). A discursive matrix of social stereotypes related to work would, in France, comprise predicates concerning fatigue, money, freedom, constraint, etc. The existence of such matrices would explain why these predicates seem to come up with notable frequency in discourse productions. The study also addresses sociological issues linked to social structure and citizens' perceptions. In Distinction, Bourdieu [START_REF] Bourdieu | La distinction. Critique sociale du jugement[END_REF] aimed to describe the process of entering the social space, and the question of the passage from abstract situations to objective structures, which are nevertheless provisionally reified. If we transpose that analysis of social structure and the analysis of discursive structure, this raises the problem of the reification of forms of discourse since the analyst can lose sight of discursive dynamics (the process of making discourse which is not only a result). Given that meaning is built by different dynamic processes, and according to different constraints, it is crucial to analyze it in context, in relation with the communities that are behind it or that interact, especially online.

Discourse is therefore a field that semiotizes one's understanding of the social world and talking about discourse will include knowledge that speakers have about the social world and the semiotic contribution they bring to their discourse.

The concept of discourse as a semiotization of representations of reality is relevant here since it allows us to conceive of both lexical and grammatical linguistic data as traces left by subjects in their texts. These regularities, similarities, and differences are all elements that can turn traces into clues. Indeed, an expert linguist can make the transition from (linguistic) "trace" to "clue" from a strictly semiotic point of view rather than a legal one [START_REF] Renaut | De la trace langagière à l'indice liguistique : enjeux et précautions d'une linguistique forensique[END_REF]. It seems necessary to develop real skills around the notions of textual semiosis, discursive spaces, or genericity, in order to understand how the linguistic "traces" left in these documents can become linguistic "clues" (in a semiotic way), which can then acquire an interpretable status within the framework of a procedure or an investigation. In some cases a "trace" is mediated, indirect, and transcribed (hearings, reported comments), while in others it is direct but strongly constrained by generic structures and a sociolect (autopsy reports, scene description). However, in all these cases the attention paid to these phenomena could help make the link to forensic science concepts of intra-variability (variability in the language of one people) vs. inter-variability (variability in the language of different peoples). In our study case, features for which inter-variability is larger than intra-variability can be used for identification/association purposes. For that, a clear distinction needs to be made between clue and trace: for Margot [START_REF] Margot | Traçologie: la trace, vecteur fondamental de la police scientifique[END_REF] "the definition of a clue corresponds to a probabilistic view of things":

The material and physical nature of a trace makes it experimentally possible to measure the probability of finding a type of trace in a given situation. This probability varies greatly with the versions of the facts, being dependent on circumstances. It is only on the basis of the knowledge of the possible versions of the facts, or propositions, that the value as a clue or the quality of the information provided by the trace can be measured or assessed (p.79).

We can therefore conclude that there is strong agreement between this explanation of the relationship between trace and clue and the way in which the textometric analysis presented in this paper has worked: indeed, calculating specificity allows us to calculate the probability that an event will occur as many times as we effectively observe it in the part or even more frequently, up to the size of the part. Thus, a linguistic trace meets Margot's definition: "Trace is only an object with no meaning of its own. Its link to a case, and to reasonable hypotheses explaining its presence, in a way gives it its fundamental "raison d'être". It is the observed result that makes the reasoning possible, an inference about a past fact. Thus, a trace becomes a sign when it is used for investigative purposes, or a clue when it is involved in a reconstruction or demonstration" (p.86). The term "sign" is particularly interesting since it is the founding term of semiology, the general science mentioned by Saussure, to which linguistics belongs. One of the additional interests of this research is therefore to offer an application to French corpora, which could be of interest to investigators in the very large French-speaking context (300 million speakers of which 235 million make daily use)

Conclusions

This article has presented the benefits of using linguistics, equipped with computing resources, in the analysis of online criminal content. Of course, linguistics alone cannot solve such cases.

Nevertheless, it is undeniable that the corpus of texts analyzed above offers certain prospects for identifying similarities and differences, proximities and distances between texts. These results can then be submitted to the investigators who can work with linguists to look at different hypotheses in terms of topics, style, and grammar and to better understand language data. Digital tools provide a form of objectification since they are based on statistical calculations which reveal regularities that are otherwise invisible to the naked eye. They also make it possible to benefit from tools developed by linguists (grammatical analyzers, concordancers, dictionaries) and more broadly by the digital humanities (data visualization, corpus exploration). These tools, when used properly in investigations, can be invaluable in extracting "clues" from the linguistic "traces" that make up texts. Some methodological limitations can be easily removed since the proposed approach makes it possible to work both on languages other than French (the software presented here has versions in other languages too, working in the same way since the statistical approach does not require training a model on a particular language) and on larger corpora. If the results seem very case specific, and preliminary at this stage, future research will consolidate the methodology and test it on other cases.

Bibliographical References:

[1] Ribaux O., Walsh Simon J.

Figure 1 :

 1 Figure 1: Example of a claim site 1

Figure 3 :

 3 Figure 3: Corpus and tagging

Figure 4 :

 4 Figure 4: Corpus exploration (software functions), associated forms different forms of the same lemma), and concordance

Figure 5 :

 5 Figure 5: Corpus DHC (classification for the whole corpus)

Figure 6 :

 6 Figure 6: Corpus FCA (representing the *towns according to the topics of the CHD)

Figure 8 :

 8 Figure 8: FCA on the texts' lexical specificities

Figure 9 :

 9 Figure 9: FCA on the texts' grammatical specificities

Figure 10 :

 10 Figure 10: FCA with the grammatical features

Figure 11 :

 11 Figure 11: calculation and FCA with the prototype "Text Print"

  , Margot P. (2006), "The contribution of forensic science to crime analysis and investigation: Forensic intelligence", Forensic Science International 156 (2006) p.171-181. [2] Chaski, C. E. (2008), "The Computational-Linguistic Approach to Forensic Authorship Attribution", In Frances Olsen, Alexander Lorz, and Dieter Stein, (Eds.), Law and Language: Theory and Practice. Düsseldorf University Press, https://www.semanticscholar.org/paper/The-Computational-Linguistic-Approach-to-Forensic-Ch aski/b8bb5ee24b7c5084f61a745153ab1ae2300c1792

This page is accessible at: https://sansattendre.noblogs.org/post/2018/04/29/couflens-france-contre-le-projet-de-mine-de-tungstene-26-avril. The website is called "Sans Attendre Demain" ("Not waiting until tomorrow") and the title of the article reads: "Couflens, France : Contre la réouverture d'une mine de tungstène -26 avril" ("Couflens, France: Against the reopening of a

This project was carried out together with Alexandra Freeman (doctoral student at CY on copyright attribution issues), Jérémy Demange, prototype developer, and Trang Lam, Master's intern.


Kevin Crouvisier Urion

Jean-Pierre Bellat

Gérard Liger-Belair

Régis D Gougeon

Professor Thomas Karbowiak
email: thomas.karbowiak@agrosupdijon.fr

Kevin Crouvisier Urion

Unravelling CO2 transfer through cork stoppers for Champagne and sparkling wines

Keywords: Agglomerated cork stopper, CO2, diffusion, gas transfer

Introduction

Cork has been used for centuries as corking material for wine conservation, from the amphora to the glass bottle. Agglomerated cork stoppers, made of cork particles with adhesives, were developed at the beginning of the twentieth century [START_REF] Pereira | Cork: Biology, production and uses[END_REF], first for sparkling wines and then extended to still wines. Cork particles, calibrated as a function of their mean diameter, form the "body" of the sparkling wine stopper. Since the 1970s, the agglomeration of cork particles has been made with polyurethane (PU) adhesives [START_REF] Franken | Polyurethane hot-melt adhesives for the production of cork stoppers[END_REF] to replace casein glue, which was initially used. In addition, two cork discs are usually glued with an aqueous dispersion of PU on one end of this agglomerated body, thus forming the "mirroir", which is in contact with the wine (Fig. 1).

Such agglomerated cork stoppers are used for the conservation of sparkling wines, such as Champagne, Crémant, Cava, Prosecco, Sekt, but also ciders and beers. Stoppers are highly compressed in the bottleneck. In the case of Champagne wine, this leads to a reduction in diameter of 45 % (from 31 mm to 17.5 mm diameter) [START_REF] Cetie | Bouchage de tirage et d'expédition pour vins mousseux de qualité produits dans des régions déterminées VMQPRD : sur bague couronne verre 29 et 26 mm[END_REF], which corresponds to a reduction of 70 % in volume. After alcoholic fermentation has produced a still "base wine", these sparkling beverages are obtained either from a second fermentation step (using mainly Saccharomyces cerevisiae) or from carbonation, both leading to the presence of CO2 dissolved in the liquid phase. Dissolved CO2 concentrations range from 5 g.L -1 for ciders and beers [START_REF] Faiveley | Stratégies de fermentation appliquées aux boissons[END_REF] up to 12 g.L -1 for carbonated and sparkling wines [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF]. When these beverages are bottled, the thermodynamic equilibrium between the gas-phase and dissolved CO2 causes a partial pressure of gas-phase CO2 in the headspace ranging from about 0.3 to 0.6 MPa (considering a Henry's constant value of 4.4 x 10 -4 mol.m -3 .Pa -1 at 12 °C) [START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. Consequently, the high partial pressure gradient of gas-phase CO2 between the inside and outside of the bottle leads to a CO2 transfer through the stopper, which causes a progressive loss of dissolved CO2 from the liquid phase. Nevertheless, below a partial pressure close to 0.13 MPa in the headspace (at 12 °C) [START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF], corresponding to a critical concentration of dissolved CO2 close to 2.5 g.L -1 , a sparkling wine becomes thermodynamically unable to promote effervescence. The precise knowledge of the permeability of a cork stopper with regard to gas-phase CO2 becomes therefore crucial to understand how a bottle of sparkling wine progressively loses its dissolved CO2 content, and therefore its bubbling potential.

The first study dealing with gas transfer through the cork stopper was conducted in the mid-1990s [START_REF] Waters | The role of corks in oxidative spoilage of white wines[END_REF]. Since then, numerous studies have investigated the gas transfer through wine stoppers, in particular to the O2 transfer, because of its impact on wine oxidation [START_REF] Karbowiak | Wine oxidation and the role of cork[END_REF]. Several techniques have been developed to study gas transfer through stoppers, such as coulometric detection, manometric devices, chemiluminescence, SO2 titration, and colorimetric method.

Synthetic stoppers exhibit the highest oxygen transfer rate (from 10 -6 to 10 -4 mmol O2.m -2 .s -1 ), followed by natural cork (10 -7 to 10 -3 mmol O2.m -2 .s -1 ), screwcaps (10 -8 to 10 -4 mmol O2.m -2 .s - 1 ) and technical stoppers (10 -7 to 10 -5 mmol O2.m -2 .s -1 ), at room temperature for an oxygen partial pressure gradient of 0.21 MPa [START_REF] Crouvisier Urion | Gas transfer through wine closures: A critical review[END_REF]. However, only a few studies have addressed the issue of CO2 transfer [START_REF] Brazinha | Gas transport through cork: Modelling gas permeation based on the morphology of a natural polymer material[END_REF][START_REF] Rabiot | Study of the oxygen transfer trough synthetic corks for wine conservation[END_REF][START_REF] Sanchez | Perméabilité gazeuse de différents obturateurs[END_REF][START_REF] Vasserot | Effect of bottle capacity and bottle-cap permeability to oxygen on dimethylsulfide formation in Champagne wines during aging on the lees[END_REF], and only two deal with sparkling wine stoppers [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF][START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. Based on the CO2 concentration decrease in sparkling wine bottles and using modeling (based on Henry's and Fick's laws), the effective CO2 diffusion coefficient has recently been estimated to be between 5 x 10 -11 and 3 x 10 -10 m².s -1 [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF][START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. However, to date, there has been no direct and accurate experimental measurement of the effective diffusion coefficient of CO2 through composite materials such as agglomerated stoppers, in which each part constitutes an individual resistance to gas transfer. Sparkling wine stoppers, made of a body of agglomerated cork particles with two cork discs fixed on one end with two films of adhesive can be considered as an equivalent system composed of five resistances to mass transfer connected in series (Fig. 2). This macroscopic view could obviously be more detailed depending on the scale that is considered. Cork itself is an alveolar material composed of empty closed cells of about 30 µm characteristic dimension with a cell wall around 1 µm thickness. It also contains macroscopic pores called lenticels with a diameter in the millimeter scale. In the case of agglomerated cork stopper, cork particles are surrounded by polyurethane. There is also an intergranular porosity between these particles, which may be either opened or closed. Therefore, it is essential to identify the limiting step for gas transfer and the associated diffusion mechanism. Three mass transfer mechanisms can occur in such a material [START_REF] Crouvisier Urion | Gas transfer through wine closures: A critical review[END_REF]: (i) the molecules move in macropores according to Darcy's law, when the mean free path of the diffusing molecule is lower than the pore diameter; (ii) the molecules diffuse in mesopores following a Knudsen's regime, when the mean free path of the diffusing molecule is larger than the pore diameter; and (iii) the molecules move by jumping from one sorption site to another one in a phenomenon called surface diffusion or solution-diffusion process in the case of polymeric networks [START_REF] Lagorce-Tachon | Diffusion of oxygen through cork stopper: Is it a Knudsen or a Fickian mechanism?[END_REF].

The objective of this study was to measure the effective diffusion coefficient of gas-phase CO2 through an agglomerated cork stopper and then to identify the limiting step to gas transfer depending on the composite material structure. To that purpose, it was necessary to experimentally determine the gas transfer through each part of the sparkling wine stopper. Furthermore, the different parameters that can control the gas transfer, such as the cork particle size, the adhesive content, the presence of cork discs, and the effect of the compression were investigated. The results of CO2 transfer through sparkling wine stoppers are critically analyzed in order to better understand the gas barrier properties of stoppers and to estimate their impact on the shelf life of sparkling wines.

Materials and methods

Material: Cork stoppers

Agglomerated cork stoppers were supplied by the Relvas (Mozelos, Portugal) and Prats & Bonany (Reims, France) companies. Two types of stoppers were studied: stoppers composed of a macro-agglomerated body with two cork discs at one end (referred to as MA2D) and stoppers composed only of a micro-agglomerated cork body (referred to as MI).

Two cork particle size distributions, determined according to the NP ISO 2031:2015 standard, were used to formulate macro-agglomerated (2.5-8 mm diameter) and micro-agglomerated (0.5-2.8 mm diameter) stoppers. An aromatic glue, composed of toluene diisocyanate (TDI) isomers (2,6-TDI and 2,4-TDI), was used at mass ratios (wglue/wcork) of 8 % and 15 % for macro-agglomerated and at 20 % and 25 % for micro-agglomerated stoppers. Agglomerated cork bodies were obtained after polymerization at 120 °C for 45-65 min using an industrial scale processing, based on individual molding. Two cork discs (6 mm thick) were glued at one end of the agglomerated cork body with an aqueous dispersion of PU. They are referred to as "aromatic adhesive for cork body" and "cork disc adhesive", respectively, in the present paper. The resulting stoppers were then sanded down and chamfered to obtain the final cork stopper for sparkling wine. The diameter was reduced to 30 mm to meet the requirements of the bottling machine (TDD Grillat, BM 800).

Gas transfer measurement

The gas transfer through the samples was measured using a homemade manometric device. The equipment and the procedure used to determine the effective diffusion coefficient were previously detailed in [START_REF] Chanut | Fast manometric method for determining the effective oxygen diffusion coefficient through wine stopper[END_REF] [START_REF] Chanut | Fast manometric method for determining the effective oxygen diffusion coefficient through wine stopper[END_REF] . It is based on the pressure measurement in two compartments separated by the sample. For the present work, the initial pressure was fixed at 0.6 MPa of pure CO2 in the first compartment, corresponding to the pressure of CO2 inside a Champagne wine bottle at the end of the fermentation step. The second compartment of the device was maintained under dynamic primary vacuum (0.1 hPa). The pressure drop in the first compartment, due to CO2 transfer through the sample, was recorded over time. The temperature was kept constant at 25 °C. The accuracy of the pressure sensor was 0.01 MPa.

As the calculation of the effective diffusion coefficient requires the knowledge of the solubility of CO2 in the materials, the sorption isotherms of CO2 on the agglomerated cork and on the adhesives were previously determined from 0 to 5 MPa, at 25 °C, using a magnetic suspension balance (Rubotherm GmbH). Rectangular samples (~ 150 mm 3 ) were first outgassed at 25 °C under primary vacuum until mass equilibrium. The gas pressure in the balance was then increased step-by-step (once mass equilibrium was reached for each pressure step). A specific module allowed measuring the gas phase density in order to take into account the buoyancy effect. For each sample, the sorption and desorption isotherms of CO2 were determined, as displayed in Fig. 3, and allows to determine the partition coefficient ψ, defined as the ratio between the concentration of CO2 sorbed on the material (mol.m -3 ) and the concentration of CO2 in the gas phase in contact with the film (mol.m -3 ) at equilibrium.

The different geometries used to determine the effective diffusion coefficient of CO2 according to the sample are summarized in Table 1. To reduce the experimental time, gas transfer was not measured on full-length stoppers, but on reduced-thickness samples. To determine the gas transfer on a full-length stopper, an extrapolation model was applied, following the procedure detailed in Lagorce-Tachon et al. (2016) and Chanut et al (2020) [START_REF] Chanut | Fast manometric method for determining the effective oxygen diffusion coefficient through wine stopper[END_REF][START_REF] Lagorce-Tachon | About the role of the bottleneck/cork interface on oxygen transfer[END_REF], as shown in Fig. 4 for a macro-agglomerated cork body containing 8 % aromatic adhesive. CO2 transfer measurements were carried out on agglomerated corks, both compressed and non-compressed, on the different adhesive films composing the stopper (~700 µm thickness films obtained by polymerization at 20 °C) and on the cork discs. The compressed samples were obtained using a corking machine (TDD Grillat, BM 800) equipped with a special homemade device, which allowed insertion of the cork slice in a sample holder of 17.0 (± 0.5) mm diameter (corresponding to a Champagne bottleneck).

Helium pycnometry

The porosity of the samples has been measured by helium pycnometry with a homemade manometric device. Prior to the measurement, the sample was outgassed under primary vacuum at room temperature. A cork body sample of known apparent volume Vapp

(measured with a caliper) was introduced in the helium pycnometer and the real volume of the sample Vs was determined from pressure measurements. The porous fraction Vp is defined as the ratio of the volume accessible to helium over the apparent volume, according to the following equation:

% / = × 100 (1)
Helium pycnometry was performed at 25 °C on 10 macro-and micro-agglomerated cork bodies (with an apparent diameter of 3.00 ± 0.01 cm and a length of 4.80 ± 0.02 cm, which corresponds to an apparent volume of 34.4 ± 0.3 cm 3 .

Scanning electron microscopy (SEM)

Agglomerated cork stoppers for sparkling wine were observed by SEM using a Jeol JSM 7600F instrument. Prior to imaging, samples were cut with a razor blade and coated with 15-20 nm carbon. A vacuum of 9 x 10 -6 Pa was applied with an accelerating voltage of 15 kV.

Results and discussion

3.1. Effect of particle size and adhesive concentration of the cork body 2. It is noteworthy that the distribution of effective diffusion coefficient values is very large. This is due to the heterogeneity of the porosity of such agglomerated materials, which are composed of cork particles having various sizes and geometries. Both the increase in adhesive concentration and the reduction in the cork particle size lead to a decrease in the mean value of D. A decrease by a factor of 3 (from 3 x 10 -5 to 9

x 10 -6 m².s -1 ) is observed for the macro-agglomerated cork body with an increase in the adhesive content from 8 % to 15 %, and by a factor of 4 (from 8 x 10 -8 to 2 x 10 -8 m².s -1 )

when the adhesive content increases from 20 % to 25 % for the micro-agglomerated cork body (Table 2). Regarding the cork particle size, the reduction from macro (2.5-8 mm) to micro (0.5-2.8 mm) leads to a decrease in the CO2 effective diffusion coefficient by a factor of 375 (from 3 x 10 -5 to 8 x 10 -8 m².s -1 ). This clearly highlights that within the investigated range, particle size is a predominant factor in the reduction of effective diffusion coefficient compared with the increase in adhesive concentration. Nevertheless, the effect of these two factors cannot be fully separated, the micro-agglomerated cork formulation requiring a higher adhesive concentration to obtain an agglomerated body suitable for stopper application.

The decrease in the CO2 effective diffusion coefficient in agglomerated cork with increasing adhesive concentration may be due to the barrier property of the adhesive used for agglomeration. The aromatic PU glue used in sparkling wine stoppers has an average CO2 effective diffusion coefficient value of 8 x 10 -11 m².s -1 (Table 2). This value is in agreement with those found in the literature. Depending on the nature of the monomer used and its content, there is a variation in D values from 7 x 10 -11 to 1 x 10 -10 m².s -1 [START_REF] Galland | Permeability and diffusion of gases in segmented polyurethanes: Structureproperties relations[END_REF].

Our results show that the higher the adhesive content, the better the CO2 barrier property. This effect is probably due to the presence of a continuous adhesive film surrounding the cork particles, which is favored when the particles are small. In addition, the intergranular porosity decreases in the micro-agglomerated cork body with smaller particle size. Moreover, in the latter case, the cork particles are smaller and more spherical in shape than those used for the macro-agglomerated cork. This modification in size and shape induces a reduced intergranular porosity [START_REF] Le Barbenchon | Multi-scale foam: 3D structure:compressive behaviour relationship of agglomerated cork[END_REF][START_REF] Santamarina | Soil behaviour: The role of particle shape[END_REF]. For a deeper understanding of the difference between the macro-and micro-agglomerated cork bodies, it is thus necessary to measure the intergranular porosity. For this purpose, tests were carried out using helium pycnometry on macro-agglomerated (8 % aromatic adhesive) and micro-agglomerated (20 % aromatic adhesive) cork bodies. These measurements give an open porosity of 1.8 % (v/v) for macroagglomerated cork. However, the open porosity was not measurable with this technique in the case of micro-agglomerated cork. This means that micro-agglomerated cork is either nonporous or the porosity is not accessible to helium. This confirms the decrease in porosity observed by SEM when smaller cork particles are used. In macro-agglomerated cork, an important intergranular porosity is visible (Fig. 6a). By contrast, for micro-agglomerated cork, this porosity appears to be absent and the adhesive is obstructing the residual porosity between the cork particles (Fig. 6b), thus contributing to increase the barrier property of agglomerated cork.

Effect of compression

The CO2 barrier properties of agglomerated cork bodies presented above were determined for non-compressed samples (Table 1). In fact, considering the oenological application, the stoppers are compressed in the bottleneck (17 mm diameter). This leads to a total volume reduction of 70 %, and can thus strongly impact the gas transfer. The effect of such a compression level on the CO2 effective diffusion coefficient is reported in Fig. 7 for the macro-and micro-agglomerated corks.

There is a significant reduction in the effective diffusion coefficient for both macroand micro-agglomerated corks when the agglomerated cork body is compressed. The effective diffusion coefficient value decreases by a factor of around 6000 for macro-agglomerated cork (from 3 x 10 -5 to 5 x 10 -9 m².s -1 ) and by a factor of around 1000 for micro-agglomerated cork (from 8 x 10 -8 to 8 x 10 -11 m².s -1 ) (Table 2). The level of compression, as applied in the bottleneck, therefore greatly reduces the transfer of gas through the agglomerated cork body.

This improvement in barrier properties can be explained, in a large part, by the very high reduction in volume. By reducing the intergranular porosity and increasing the tortuosity, the compression slows down the diffusion processes of Darcy and Knudsen. This is particularly true for macro-agglomerated cork for which the intergranular porosity is larger than for micro-agglomerated cork. The decrease in the effective diffusion coefficient due to compression was 6 times larger than for micro-agglomerated cork. In addition, there is also a significant reduction in the width of the distribution, which means that the compression also makes the samples more homogeneous from the diffusion point of view.

Role of the cork discs

Previous investigations have clearly shown that the formulation parameters, as well as the compression, can strongly change the barrier properties of the agglomerated cork body. It is also important to study the role that the two cork discs attached at one end of the cork body may play in the gas transfer through the sparkling wine stopper. The cork disc is punched in the plane perpendicular to the radial direction, and thus it is sprinkled with lenticels, which are channels oriented in a direction parallel to the gas flow. Permeation tests were carried out on single cork discs, but the gas flow is too fast for being measured with our manometric device.

In this case and the CO2 effective diffusion coefficient is taken equal to the value in air (Table 2). Thus, the cork disc alone is not an efficient barrier to the gas diffusion, at least when it is considered non-compressed.

Nevertheless, in the cork stopper, these cork discs are glued together with an aqueous dispersion of PUs. The effective diffusion coefficient of CO2 was measured through a film of ~700 µm thickness of this adhesive. A mean value of 4 x 10 -11 m².s -1 was found (Table 2). In order to get closer to the industrial cork manufacturing process, the effective diffusion coefficient of CO2 was also measured through the two cork discs glued together with a single film of adhesive in between (a sample of ~9 mm thickness was taken from the two discs at the end of a MA2D industrial stopper). In this case, the mean value is 6 x 10 -13 m².s -1 (Table 2). This is very surprising. Such a difference can be explained by the following reasons. i) As we consider no resistance to gas transfer in cork discs, this effective diffusion coefficient is calculated by taking a thickness of adhesive film of 10 µm, roughly estimated from SEM observation (Fig. 8). ii) During the industrial process, the adhesive layer is deposited in excess and can migrate into the lenticels, causing a local increase in the thickness of the adhesive film. iii) Polymerization under industrial conditions differs considerably from that applied under laboratory conditions to obtain a self-supporting film at 25°C. iv) Reactions occurring at the interface between cork and adhesive may locally create an additional barrier to gas transfer. These effects may also explain the large distribution of effective D values measured on this system (ranging from 9 x 10 -14 to 3 x 10 -12 m².s -1 ).

Therefore, it appears that the adhesive film used to glue the two cork discs can act as a significant barrier to the CO2 transfer, provided that the film is sufficiently thick and homogeneous.

3.4. Critical discussion of CO2 transfer in a sparkling wine cork stopper This work allows the determination of the effective diffusion coefficient values for the different parts composing a sparkling wine stopper as well as the formulation and processing parameters that can influence the gas transfer. For a deeper understanding, it is essential to couple these data together in order to elucidate the mechanisms involved in the gas diffusion when considering the material as a whole (Fig. 9).

Gas transfer through the agglomerated cork body

For the gas transfer through the cork body, the CO2 effective diffusion coefficient for a non-compressed macro-agglomerated cork is about 3 x 10 -5 m².s -1 . This very high value shows that the gas diffusion is very fast, probably because of an important intergranular porosity. As the CO2 diffusion coefficient in air is 1.39 x 10 -5 m².s -1 (at 24 °C and 0.1

MPa) [START_REF] Pritchard | Diffusion of coefficients of carbon dioxide, nitrous oxide, ethylene and ethane in air and their measurement[END_REF], it can be assumed that the porosity is totally open along the entire macroagglomerated cork body. In such a case, the diffusion is mainly governed by Darcy's and Knudsen's mechanisms in the intergranular porosity, considering the very high value of D. This is reinforced by the fact that similar effective diffusion coefficients were obtained for O2 on non-compressed macro-agglomerated cork body (data not shown). However, the solutiondiffusion mechanism may also still be involved to cross the cork cell walls as well as the adhesive network at some points. For the micro-agglomerated cork, solution-diffusion process is probably the main mechanism involved and acting as the limiting step to gas transfer (even if Darcy's and Knudsen's mechanisms occur), since the porosity is reduced, leading to a lower CO2 effective diffusion coefficient of around 10 -8 m².s -1 in non-compressed samples. In this case, there is also a difference between O2 and CO2 effective diffusion coefficients, indicating that the solution-diffusion process plays a more important role than in the macroagglomerated cork body (data not shown). In conclusion, the three mechanisms coexist simultaneously and in parallel within the stoppers. On the one hand, the higher the interconnected porosity, the greater the permeability will be governed by Darcy's and Knudsen's mechanisms. On the other hand, the smaller the porosity, or the higher the adhesive concentration, the more the permeability will be governed by the solution-diffusion process, and therefore the gas transfer will be slowed down.

Gas transfer through the cork discs and the adhesive film between them

For the cork discs, Darcy's mechanism is obviously involved in the lenticels oriented in the transfer direction. As above-mentioned, it is experimentally impossible to determine such a high effective diffusion coefficient value with the manometric method. However, considering the lenticels as macropores, it can reasonably be assumed that the effective diffusion coefficient would be at least of the same order of magnitude as its molecular value in air (~ 10 -5 m².s -1 ).

The adhesive film between the two cork discs acts as an efficient barrier to gas transfer. The gas transfer through this film is controlled by a solution-diffusion mechanism.

As we know the values of the CO2 effective diffusion coefficient in the adhesive film between the cork discs (D = 6 x 10 -13 m².s -1 ), the surface area of the film S taken as the section of the bottleneck (m²) and the temperature T (K), the gas flow J (mol.s -1 ) can be calculated as a function of the film thickness L (m) with the following equation:

= × × ∆ × × × 2
where is determined from the CO2 sorption isotherm and corresponds to the partition coefficient, defined as the ratio between the concentration of CO2 sorbed on the material (mol.m -3 ) and the concentration of CO2 in the gas phase in contact with the film (mol.m -3 ) at equilibrium. A value of 0.3 was experimentally determined from the sorption isotherms for the adhesive (Fig. 3).

The dependence of the gas flow on thickness is shown in Fig. 10. From this plot, a critical thickness (Lcrit) was determined by applying the tangent method on the hyperbolic curve and a constant thickness (Lcst) was defined as the thickness value above which the variation in gas flow becomes less than 5 % for each additional micrometer. Above a Lcst of around 20 µm, the gain in barrier property remains very low. By contrast, the gas flow drastically increases for a thickness lower than the Lcrit value (around 5 µm). In the latter case, each micrometer decrease leads to a 20 to 50 % increase in the gas flow. In addition, SEM observations were performed on a cross-section of the two glued cork discs (Fig. 8). The film separating the two cork discs could be distinguished. In the upper disc, a lenticel is partially obstructed by the adhesive. As the adhesive has been deposited in excess, the excess glue has been evacuated at the periphery of the cork disc or through the open lenticular channels, as previously mentioned. Moreover, the adhesive film does not display a homogeneous thickness. It is on average quite thin, around 10 µm thickness (Fig. 8b). It also appears up to three times thicker at some places (Fig. 8c). Furthermore, the average thickness of the film between the two discs lies between Lcrit and Lcst values, as previously defined (Fig. 10), which means that this film globally represents an efficient barrier to gas transfer.

Global effective diffusion coefficient through the full cork stopper

The different parts of the sparkling wine stopper are disposed in series as displayed in Fig. 2. Nowadays, two different cork stoppers are mainly used in the market for sparkling wine. (i) stoppers composed of a macro-agglomerated body with two cork discs at one end (MA2D) and (ii) stoppers composed only of a micro-agglomerated cork body (MI).

Considering their respective assembly, a global resistance to mass transfer R (s.m -1 ) and a global effective diffusion coefficient D (m².s -1 ), can be calculated for these two types of stoppers.

A rather complex case is that of the MA2D stopper, composed of a macroagglomerated cork body of 36 mm, with two cork discs of 6 mm each and two adhesive films of 10 µm each, as shown in Fig. 1. The global resistance to gas transfer is therefore the sum of local resistances corresponding to each part of this stopper (Fig. 2). Unlike the MI stopper, which is considered a homogeneous system with a single effective diffusion coefficient, the MA2D stopper is heterogeneous with, for each part, a corresponding effective diffusion coefficient and a solubility for CO2. Its global effective diffusion coefficient can therefore be determined according to the following equation:

! " ! # ! = ∑ % " % # % & (3)
The values calculated for the global effective diffusion coefficient of each stopper are shown in Table 3, with, for each part composing the stopper, the respective values of thickness, partition coefficient, effective diffusion coefficient and resistance.

In this calculation, the following assumptions have been made. i) The effective diffusion coefficient values used for these calculations are taken from Table 2. It is assumed that that the corresponding effective diffusion coefficient in the cork body is not significantly different for the considered thickness in the cork stopper (as shown in Fig. 4). ii) The D value on one adhesive layer between two cork discs was measured on a non-compressed system. It may be different when compressed. In addition, for the cork disc alone, it was not possible to measure the effective diffusion coefficient on a compressed disc because it breaks during compression. iii) The compression brought by the muselet on the outer part of the stopper is not taken into account. iv) For the cork disc, a partition coefficient of 1 is used as the transfer follows Darcy's mechanism. A value of 0.9 is used for the stopper and 0.3 for the adhesive (Fig. 3). v) The gas transfer that may occur at the cork/bottleneck interface is not considered in this work.

From equation 3, the limiting step to the gas transfer is therefore associated with the part having the strongest resistance to gas transfer (Fig. 2). In this case, this is the adhesive films used to glue the two cork discs (Table 2). Assuming that these films have no defect and have sufficient thickness over the entire disc surface, this is the essential part that is responsible for the barrier properties of MA2D stoppers. The global effective diffusion coefficient of MI stopper was also calculated considering a micro-agglomerated cork body of 48 mm. When considered as non-compressed materials, the global resistance to gas transfer is higher for MA2D than for MI stoppers (Table 3).

However, when used in compressed conditions for sparkling wine conservation, the global effective diffusion coefficient and resistance to mass transfer change. Let us consider a stopper partially inserted in a bottleneck with a penetration depth of 24 mm inside the bottleneck and 16 mm remaining non-compressed outside. The global effective diffusion coefficient D and resistance R calculated in these conditions for the MA2D and MI stoppers are reported in Table 3. Regarding the value obtained, when the stoppers are considered as compressed in the bottleneck, MI stoppers have a resistance to mass transfer 3 times higher than a MA2D stopper.

Liger-Belair et al. were the first to estimate a CO2 effective diffusion coefficient through MA2D cork stoppers for sparkling wine, based on the dissolved CO2 concentration decrease in different Champagne wine vintages (from 2 months to 35 years of storage) [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF][START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. However, they did not focus in detail on the transfer mechanisms acting in such a composite material. In the present work, the detailed study of the agglomerated cork stoppers allows us to clearly identify the limiting step to gas transfer and thus the parameters responsible for providing good barrier properties. The global effective diffusion coefficient value determined in our study is in the same order of magnitude (4 x 10 -10 m².s -1 ) as those reported by Liger-Belair et al. (from 5 x 10 -11 to 3 x 10 -10 m².s -1 ) and measured in situ on different aged Champagne wine samples [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF][START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. The global effective diffusion coefficient calculated from the individual effective diffusion coefficients measured on each part is therefore in good agreement with the global effective diffusion coefficient values obtained from their in situ experiments.

Toward the shelf life prediction of corked bottles of sparkling wine based on CO2 effective diffusion through the stopper

Bubble formation is indeed the hallmark of sparkling wines. The intensity of effervescence and the bubbles' size, two characteristics of paramount importance for sparkling wines lovers, both depend on the level of dissolved CO2 found in a sparkling wine [START_REF] Liger-Belair | The physics behind the fizz in champagne and sparkling wines[END_REF]. Nevertheless, below a critical level of dissolved CO2 close to 2.5 g.L -1 (at 12 °C), namely ' * , a sparkling wine becomes thermodynamically unable to promote any bubble formation under standard tasting conditions (i.e., in a glass, with micrometric particles or glass anfractuosities acting as bubble nucleation sites), as described by Liger-Belair [START_REF] Liger-Belair | Modeling the losses of dissolved CO2 from laser-etched champagne glasses[END_REF]. The precise knowledge of the permeability of a cork stopper with regard to gas-phase CO2 becomes therefore crucial to be able to understand how a sparkling wine will age as time proceeds, especially concerning its progressive decrease in dissolved CO2. In bottles of sparkling wines sealed with cork stoppers, because the partial pressure of gas-phase CO2 in the bottleneck reaches up to 6 bar (at 12 °C), CO2 slowly diffuses from the bottle to the ambient air, either through the cork bulk or through the cork/bottleneck interface. By combining both Henry's and Fick's laws, an exponential decay-type model was found for the theoretical time-dependent level of dissolved CO2 found in champagne during aging (in the MKS system of units) [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF]:

)
' * ≈ ' , -. /-

with 0 C the initial level of dissolved CO2 after corking the bottle, t the aging period of time, τ the timescale of the exponential decay-type model, L the total length of the cork, L V the volume of the liquid phase in the sealed bottle, H k the temperature-dependent Henry's law constant of CO2 (conveniently expressed in mol.m -3 .Pa -1 ) [START_REF] Liger-Belair | Modeling the losses of dissolved CO2 from laser-etched champagne glasses[END_REF], G V the volume of gas phase (the headspace) in the sealed bottle, R the ideal gas constant (8.31 J.K -1 .mol -1 ), T the temperature, D the global diffusion coefficient of gas-phase CO2 through the cork stopper, and S the cross section of the cork stopper (equivalent indeed to the cross section of the bottleneck). The global D values (given in Table 3) are used in this calculation.

Following the exponential decay-type law given by equation 4, it becomes therefore possible to predict the shelf life of corked bottles of sparkling wines (i.e., the time beyond which the concentration of dissolved CO2 fall below the critical concentration of 2.5 g.L -1 required for bubbling) [START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF]. Replacing By replacing in the latter equation each parameter by its numerical value, it becomes therefore possible to approach the maximum period of aging (and therefore a shelf life prediction) beyond which a bottle of sparkling wine could become flat. For a standard 75 cL bottle of sparkling wine initially holding a level of dissolved CO2 close to 12 g.L -1 [START_REF] Liger-Belair | The physics behind the fizz in champagne and sparkling wines[END_REF], the theoretical mean shelf life prediction is in the order of 10 years if the bottle is sealed with a MA2D cork stopper. The distribution is rather large, from 2 to 65 years, if we consider the minimum and maximum values for all the parts composing the stopper, and underlines the crucial barrier role of the adhesive film between the discs. If the same bottle of sparkling wine is sealed with a MI cork stopper, its theoretical mean shelf life prediction is increased to about 30 years. In this case, the distribution is reduced, ranging from 20 to 50 years. A shelf life prediction of 30 years before the sparkling wine would become flat is nevertheless quite hard to verify in situ, because MI cork stoppers have only been used for about two decades only. In contrast, MA2D cork stoppers have been used to seal bottles of champagne and sparkling wines for several decades. Time series data recordings of dissolved CO2 were already done in situ with cuvees sealed with MA2D cork stoppers and aged from several years up to several decades [START_REF] Liger-Belair | Losses of dissolved CO2 through the cork stopper during Champagne aging: toward a multiparameter modeling[END_REF][START_REF] Liger-Belair | Evidence for moderate losses of dissolved CO2 during aging on lees of a champagne prestigue cuvee[END_REF][START_REF] Liger-Belair | Effervescence in champagne and sparkling wines: From grape harvest to bubble rise[END_REF].

The dissolved CO2 content found in these bottles having aged for a much longer period of time than the theoretical shelf life prediction of 10 years was found to be still much higher than the critical level of 2.5 g.L -1 required for bubble formation. Moreover, it is worth noting that the global diffusion coefficients determined under compressed conditions in the present work do not take into account the gas transfer that may occur at the cork/bottleneck interface [START_REF] Lagorce-Tachon | About the role of the bottleneck/cork interface on oxygen transfer[END_REF][START_REF] Karbowiak | Wine aging: A bottleneck story npj[END_REF]. Taking this into account would even more increase the respective global diffusion coefficients, therefore leading to theoretical shelf life predictions even shorter. We are therefore strongly tempted to conclude that the real storage conditions experienced by the corks are in favor of a much better impermeability with regard to gas-phase CO2. This is the reason why Champagne and sparkling wine bottles can age for several decades before they lose their bubbling capacity.

A crucial point also finally unveiled by this work is that, the dry compressed conditions, under which global CO2 diffusion coefficients have been determined in the present work, are still far from the real conditions found in a bottleneck. In a bottleneck, the cork ages in contact with the wine (if bottles are stored horizontally) or in contact with a vapor phase saturated with water and ethanol (if the bottles are stored vertically). Changes in the structure of the cork during aging could therefore alter the way in which CO2 molecules move from the headspace of the bottle to the ambient air, either through the cork stopper, or through the interface between the bottleneck and the cork stopper. Moreover, it is possible that prolonged aging could progressively moisturize the cork stopper, thus filling the pores, and reducing in turn the global diffusion coefficient of CO2 through the cork stopper. Further experiments are needed to fully understand how the global diffusion coefficient of CO2 through cork stopper could change as time proceeds during aging.

Conclusion

This study clearly identified the parameters that can influence the gas barrier properties through sparkling wine cork stoppers. The parameter having the strongest impact on the barrier properties is the compression of the agglomerated cork body, which drastically reduces the effective diffusion coefficient, when applying a 70 % reduction in volume, corresponding to the compression in the bottleneck. Other parameters with a significant impact on the CO2 effective diffusion are the cork particle size along with the adhesive concentration in the agglomerated cork body. The smaller the cork particles and, correlatively, the higher the adhesive concentration, the higher the CO2 barrier property. Both of these associated parameters result in a decrease of the intergranular porosity. Nevertheless, this effect tends to be mitigated when the samples are highly compressed.

The limiting step to gas transfer is the diffusion through the adhesive present both in the network of the agglomerated cork body and in the film between the two cork discs. The diffusion mechanism involved is thus the solution-diffusion process through the adhesive polymeric network. Given these results, it is therefore essential that the adhesive network, particularly that between the two cork discs, is as homogeneous as possible and sufficiently thick to act as an efficient barrier to gases.

Finally, it should be pointed out that the values reported in this study agree rather well with those obtained in real conditions of aging of Champagne wine, even if only the cork stopper is considered. Indeed, the role of the interface between the stopper and the bottleneck, and the surface treatment applied on the stopper were not taken into account. Moreover, the evolution of the mechanical and barrier properties during real bottle aging could also play an important role, in particular when considering the stopper in contact with an hydroethanolic solution. However, this study clearly shows the effectiveness of the cork stopper for the conservation of the sparkling wine and its ability to maintain a sufficient dissolved concentration and partial pressure of CO2 in the headspace over many years.

Fig. 5

 5 Fig. 5 displays the extrapolated distribution for CO2 effective diffusion coefficients

  equation 4 by the critical concentration of dissolved CO2 below which bubble formation would become impossible, and developing, leads to the critical aging period of time, denoted * B t , beyond which bubbling would become impossible through lack of dissolved CO2:

Fig. 1 .

 1 Fig. 1. Detailed structure of agglomerated cork stoppers used for sparkling wines, consisting of macro or micro cork particles, and usually two additional cork discs. The reduction in volume when the cork stopper is inserted into a bottleneck is also indicated.

Fig. 2 :

 2 Fig. 2: The global resistance to mass transfer is the sum of local resistances of each part of the sparkling wine stopper. The resistance to mass transfer ( ) corresponds to the ratio of the thickness ( ) to the effective diffusion coefficient ( ) and the partition coefficient ( ) of each part of the stopper the gas has to go through.

Fig. 3 :

 3 Fig. 3: Sorption-desorption isotherms of CO2 on macro-agglomerated cork, aromatic adhesive and adhesive for cork disk, at 25 °C. The quantity of CO2 sorbed is given in mmol of CO2 per gram of dry matter.

Fig. 4 :Fig. 5 :Fig. 6 :Fig. 7 :Fig. 8 :

 45678 Fig. 4: a) Experimental data and normalized distribution obtained for the CO2 effective diffusion coefficient values measured on 10 mm slices of macro-agglomerated cork body with 8 % of aromatic adhesive. b) Extrapolated distribution of the CO2 diffusion coefficient (-) for a full-length stopper (40 mm) obtained from the experimental distribution (-) on 10 mm slices.

Fig. 9 :

 9 Fig. 9: Comprehensive overview of CO2 effective diffusion coefficient values determined for the different parts comprising a cork stopper for sparkling wine and depiction of the mechanisms involved in the gas transfer. The diffusing mechanisms are only represented for the non-compressed macro-agglomerated cork, but occur in a similar manner in the micro-agglomerated cork and the compressed samples.

Fig. 10 :

 10 Fig. 10: Effect of the film thickness on the CO2 flow through the adhesive film used between the two cork discs. The gas flow was calculated from the Equation 2 for a film thickness from 1 to 60 µ m (each point corresponds to 1 µ m).

Table 1 :

 1 Sample geometry and conditions used to determine the effective diffusion coefficient of CO2 in the different parts composing the sparkling wine stopper.

	Sample part	Geometry	Extrapolated length	Number of replicates
	Agglomerated cork body	Slice of 10 mm thickness	40 mm	15
	Non-compressed	Diameter: 30 mm
	Agglomerated cork body	Slice of 6 mm thickness
			40 mm	10
	Compressed	Diameter: 17 mm
	Adhesive for agglomerated body Non-compressed	Film of ~700 µm thickness	-	10
	Adhesive for cork discs Non-compressed	Film of ~700 µm thickness	-	10
	Two cork discs with the adhesive layer in between	Slice of 9 mm thickness	-
	Non-compressed	Diameter: 30 mm

ACKNOWLEDGMENT

We gratefully acknowledge Prats & Bonany, Relvas and the French Federation of Cork (FFL), as well as the French National Association of Research and Technology (ANRT) for their financial support. This work was also supported by the Regional Council of Bourgogne Franche-Comté and the "Fonds Européens de DEveloppement Régional (FEDER). SEM images were performed at the Laboratoire Interdisciplinaire Carnot de Bourgogne with the help of Frédéric Herbst. We would also like to thank Frédéric Brand, from Louis Bouillot (Boisset company), for his kind help in using the industrial bottling machine for sample preparation.

Table 2: Mean values of CO2 effective diffusion coefficient, D (m².s -1 ), at 25 °C, obtained from the extrapolated distribution to 40 mm length for the agglomerated cork samples or from the experimental distribution for the adhesive film samples. Data in brackets are minimum and maximum values including standard deviation from the corresponding distribution. (n.d.: not determined)

Sample

Mean D (m².s -1 )

Macro-agglomerated 8 % aromatic non-compressed cork body 3 x 10 -5

(1 x 10 -5 -7 x 10 -5 )

Macro-agglomerated 15 % aromatic non-compressed cork body 9 x 10 -6

(3 x 10 -6 -2 x 10 -5 )

Micro-agglomerated 20 % aromatic non-compressed cork body 8 x 10 -8

(3 x 10 -8 -2 x 10 -7 )

Micro-agglomerated 25 % aromatic non-compressed cork body 2 x 10 -8

(1 x 10 -8 -3 x 10 -8 )

Macro-agglomerated 8 % aromatic compressed cork body 5 x 10 -9

(3 x 10 -9 -9 x 10 -9 )

Micro-agglomerated 20 % aromatic compressed cork body 8 x 10 -11

(5 x 10 -11 -1 x 10 -10 )

Aromatic adhesive for cork body (film of ~700 µm thickness) 8 x 10 -11

(2 x 10 -11 -3 x 10 -10 )

Adhesive for cork disc (film of ~700 µm thickness) 4 x 10 -11