Bo Wang

Vincent Perrichot

Edmund A Jarzembowski

Preface:Cretaceous ecosystems trapped in amber

Preface:Cretaceous ecosystems trapped in amber

Bo Wang 1 , Vincent Perrichot 2 , Edmund A. Jarzembowski 1 1 State Key Laboratory of Palaeobiology and Stratigraphy, Nanjing Institute of Geology and Palaeontology and Center for Excellence in Life and Paleoenvironment, Chinese Academy of Sciences, 39 East Beijing Road, Nanjing 210008, China.

2 Univ. Rennes, CNRS, Géosciences Rennes, UMR 6118, F-35000, Rennes, France. Amber-bearing deposits are among the most important Konservat-Lagerstätten, providing unique windows into ancient terrestrial ecosystems. Several new amber biotas have been discovered recently from which various sometimes specialized and bizarre looking animals and plants have been reported; these discoveries naturally attract the attention of palaeontologists, palaeoecologists, biologists, and, most certainly, the public at large. Moreover, research based on amber has greatly developed in the past decade and is becoming increasingly multidisciplinary with the application of new methodology and approaches (e.g., µCT imaging, integrative phylogeny), increasing the importance of amber inclusions in broader evolutionary studies.

This special issue of Cretaceous Research contains 13 papers that reflect some of the latest advances in the study of various aspects of the ancient ecosystems preserved in Cretaceous ambers. Exceptional plant and animal fossils are reported or reviewed, with insights into the novel morphological and ecological functions they reveal. The papers encompass 10 insect orders, including Blattodea (cockroaches), Coleoptera (beetles), Hymenoptera (wasps), Neuropterida (Neuroptera (lacewings), Megaloptera (alderflies) and Raphidioptera (snakeflies)), Odonata (dragonflies), Tarachoptera In addition to the highly diverse insect taxa in amber deposits, Ostracoda (seed J o u r n a l P r e -p r o o f shrimps) and Jungermanniopsida (liverworts) are also discussed in this issue. [START_REF] Piovesan | Organic inclusions in Brazilian Cretaceous amber: the oldest ostracods preserved in fossil resins[END_REF] report several ostracods encapsulated in a Brazilian Cretaceous amber sample, representing the oldest ostracods preserved in a fossil resin.

Palynological analyses of amber-containing limestones of the Crato Formation (Araripe Basin, Northeastern Brazil) suggest that the extinct coniferous Family Cheirolepidiaceae was the possible botanical source of this fossil resin. Based on two newly discovered and exquisitely preserved gametophytes in Kachin amber, [START_REF] Li | Re-appraisal of two fossil Frullaniaceae species (Marchantiophyta, Porellales) from the mid-Cretaceous Burmese amber[END_REF] provide a detailed investigation and re-appraisal of two previously described species of Frullaniaceae (leafy liverwort family). Last but not least, Feldberg et al.

(2021) review all other currently recognized leafy liverwort species (Jungermanniopsida) from Cretaceous ambers and provide a useful key, as well as describing a new species from Kachin amber.

We are grateful for the critical reviews of the many referees that led to much improved revised manuscripts, to the technical editors of this volume, and we are especially indebted to Dr Eduardo Koutsoukos for revision and editing of the papers, which greatly improved their quality.

(

  extinct insects) and Trichoptera (caddisflies). A particular focus is made on the abundant, extraordinary Kachin (Burmese) amber biota which has been extensively studied in the past decade, providing invaluable advances towards our understanding of evolutionary patterns on a tropical Tethyan island. Most papers also compare and contrast the past diversity offered by various Cretaceous amber deposits worldwide, including those from the Lower Cretaceous of the Middle East (Lebanon and Jordan), England, Spain and Myanmar (Hkamti); the mid-to Upper Cretaceous of France; and J o u r n a l P r e -p r o o f the Upper Cretaceous of Russia (Taimyr), Azerbaijan, USA (New Jersey), Canada and Myanmar (Tilin). These all augment the 8 species in 5 genera newly described from mid-Cretaceous Kachin amber.Thus Peris (2020) reviews all Cretaceous amber Coleoptera and shows how beetles are a useful tool for studying community and trophic structure as well as generating evolutionary implications for the whole ecosystem. Additionally,[START_REF] Wu | The first representatives of Lucaninae from mid-Cretaceous Burmese amber based on two new species of Anisoodontus gen. nov. (Coleoptera: Scarabaeoidea: Lucanidae)[END_REF] report the first occurrence of the Lucaninae (Coleoptera; stag beetles) from mid-Cretaceous Kachin amber, suggesting an origin and early diversification of the subfamily before the Late Cretaceous.[START_REF] Zhao | Termite communities and their early evolution and ecology trapped in Cretaceous amber[END_REF] review the termites (isopteran Blattodea) and related inclusions in Cretaceous amber, with insights into their early eusociality, feeding habits and associates (termitophiles), demonstrating their significance for understanding the termites' early evolution, ecology and behaviour.[START_REF] Zheng | Odonatans in lowermost Cenomanian Kachin amber: updated review and a new hemiphlebiid damselfly[END_REF] describes a new hemiphlebiid damselfly and further clarifies the position of 11 odonatans of previously equivocal familial assignment, all from Kachin amber.[START_REF] Wichard | Order Tarachoptera in mid-Cretaceous Burmese amber (Insecta, Amphiesmenoptera)[END_REF] review the extinct order Tarachoptera, which is exclusively confined to inclusions in Burmese amber. By summarizing all tarachopterans, they provided an emended diagnosis of the order and establish its placement within the superorder Amphiesmenoptera, also including Lepidoptera (butterflies) and Trichoptera.[START_REF] Luo | Enervipraeala nigra gen. et sp. nov., an umenocoleid dictyopteran (Insecta) from mid-Cretaceous Kachin amber[END_REF] briefly discuss the internal taxonomy of the beetle-like extinct family Umenocoleidae (actually related to cockroaches) in which they report a new genus and species based on a well-preserved specimen from Kachin amber.[START_REF] Wichard | Overview of the caddisflies (Insecta, Trichoptera) in mid-Cretaceous Burmese amber[END_REF] provides an overview of the Trichoptera in Kachin amber, providing taxonomic clarification of 10 Cretaceous caddisfly families. Furthermore,[START_REF] Wichard | Overview of the caddisflies (Insecta, Trichoptera) in mid-Cretaceous Burmese amber[END_REF] andWang et al. (2021) report four new species in three genera of caddisflies. Away from panorpoids,[START_REF] Lu | The Neuropterida from the mid-Cretaceous of Myanmar: a spectacular palaeodiversity bridging the Mesozoic and present faunas[END_REF] give a review of our present knowledge of the systematics, phylogeny, and palaeoecology of Neuropterida from Kachin amber, and also provide a world checklist and faunal analysis of other Cretaceous amber Neuropterida, highlighting a significantly higher Cretaceous diversity of this now archaic (and charismatic) insect group. Rasnitsyn and Öhm-Kühnle (2021) review the non-aculeate (non-eusocial) hymenopterans and suggest that a major infraordinal transformation took place during the first half of the Late Cretaceous based on the gradual loss of extinct families in successive amber assemblages.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

J o u r n a l P r e -p r o o f


Vincent Raulin

Pierre-Franc ¸ois Gimenez

Yufei Han

Valérie Viet

Triem Tong

Towards a Representation of Malware Execution Traces for Experts and Machine Learning

Keywords: malware analysis, dynamic analysis, visualization, data representation

Dynamic analysis is a common technique to analyze the run-time behavior of software and identify malware (malicious software). Execution traces typically contain the list of system calls with their parameters, the list of accessed files, etc. Several representations have been proposed to organize these data better and help both human experts and automated tools analyze them effectively. This paper reviews these representations and identifies four research problems that the first author plans to investigate during his Ph.D.

I. INTRODUCTION

In recent years, the number of malware (malicious software) has been increasing rapidly. Every year commercial antiviruses manufacturers make reports on their annual activities, including malware evolution data, which shows a tremendous amount of new malware per month [5]. With this rising threat, adapted defenses must be organized.

Malware analysis is the domain of computer science focusing on identifying and understanding malware. The identification task consists of distinguishing malware from benign software (also called goodware), whereas the understanding task goes further and consists of studying the program's behavior. Both tasks can be approached in different ways. Static analysis is the study of the code of the malware without execution. Dynamic analysis is based on the monitoring of the software execution. Hybrid analysis can mix both techniques.

This study will focus on dynamic analysis. This analysis is generally done with a controlled environment that collect information about the execution, for example with the Cuckoo [START_REF]Cuckoo sandbox[END_REF] sandbox which returns an execution report. This report is very rich and can contain many different types of information which is not easy to handle right away for experts of malware analysis tools (for example, Machine Learning (ML) models).

Machine learning has been successfully applied to various domains such as image and language processing and can be used in execution traces analysis. In that case, a learning algorithm is fed with the collected data as an input to learn a model and then perform a task, for example detecting whether sample is a malware or classifying a malware into a family -virus, trojan, ransomware, etc. The transformation of the execution traces of a sample into the input data of a malware analysis system can have a large impact of the model's performances. Besides, these representations are not only useful for ML techniques: they can also be used by a human expert to understand the behavior of a malware. Many representations [START_REF] Alptekin | TRAPDROID: Bare-Metal Android Malware Behavior Analysis Framework[END_REF], [START_REF] Anderson | Graph-based malware detection using dynamic analysis[END_REF], [START_REF] Ding | A malware detection method based on family behavior graph[END_REF], [START_REF] Grimmer | Intrusion Detection on System Call Graphs[END_REF]- [START_REF] Kolosnjaji | Deep Learning for Classification of Malware System Call Sequences[END_REF], [START_REF] Wang | Heterogeneous Graph Matching Networks for Unknown Malware Detection[END_REF], [START_REF] Wunderlich | Comparison of System Call Representations for Intrusion Detection[END_REF] of execution traces have been proposed, with various advantages and limits.

This article presents a survey of malware execution representations and points out their limitations. This brings us closer to the goal of the Ph.D. of the first author, that is to build a representation of a program behavior that is robust to evasion attacks, can encompass executions traces from various mainstream Operating Systems (OSes), be useful for an expert to manually review and reflects all malicious actions of an execution trace.

The paper is structured as follow. Section II presents a survey of malware execution representations. Section III points out several research questions related to representation and discusses them. Finally, Section IV concludes this article and presents the goal of this Ph.D. thesis.

II. SURVEY OF MALWARE EXECUTION REPRESENTATIONS

Our work focuses on defining and extracting efficient feature representations from dynamic traces of malware samples. The first subsection focuses on the different sources for monitoring information. The second subsection summarizes proposed representations of this information.

A. Sources of information

Most works on dynamic analysis [START_REF] Sihwail | A survey on malware analysis techniques: Static, dynamic, hybrid and memory analysis[END_REF] collect system call traces while executing a malware sample. Indeed, they are the main medium of interaction between a program and the host OS, and their traces can provide accurate detection output of malicious payloads [START_REF] Chen | Automatic Ransomware Detection and Analysis Based on Dynamic API Calls Flow Graph[END_REF], [START_REF] Ding | A malware detection method based on family behavior graph[END_REF], [START_REF] Grimmer | Intrusion Detection on System Call Graphs[END_REF], [START_REF] Kolosnjaji | Deep Learning for Classification of Malware System Call Sequences[END_REF], [START_REF] Park | Fast malware classification by automated behavioral graph matching[END_REF], [START_REF] Wunderlich | Comparison of System Call Representations for Intrusion Detection[END_REF]. Their parameters are also an important source of information [START_REF] Ding | A malware detection method based on family behavior graph[END_REF], [START_REF] Park | Fast malware classification by automated behavioral graph matching[END_REF], [START_REF] Xiao | Malware Detection Based on Deep Learning of Behavior Graphs[END_REF]. Monitoring disk access, network ports, and OS activity inside a virtual machine have also been proposed [2], [START_REF] Alptekin | TRAPDROID: Bare-Metal Android Malware Behavior Analysis Framework[END_REF], [START_REF] Wang | Heterogeneous Graph Matching Networks for Unknown Malware Detection[END_REF]. Finally, physical properties like CPU usage [START_REF] Piplai | Knowledge Enrichment by Fusing Representations for Malware Threat Intelligence and Behavior[END_REF] or CPU power consumption [START_REF] Bridges | Towards Malware Detection via CPU Power Consumption: Data Collection Design and Analytics[END_REF] can also be monitored. But such information does not concern interactions with the OS, which is out of scope for this study.

For expert and classifier systems to better analyze these data, one needs to organize them inside a representation. The following subsection proposes a literature review of such representations.

B. Representations of monitoring information

We identified four families of representation, depending on how they organize the information, and thus what parts of a program's behavior they highlight.

1) Representing the order of actions: A classical representation directly uses time series of system calls without parameters [START_REF] Kolosnjaji | Deep Learning for Classification of Malware System Call Sequences[END_REF], [START_REF] Wunderlich | Comparison of System Call Representations for Intrusion Detection[END_REF]. This representation is already used in execution reports. N-grams (sequences of n system calls) or word embedding vectors (a machine-learning-based technique) [START_REF] Kolosnjaji | Deep Learning for Classification of Malware System Call Sequences[END_REF], [START_REF] Wunderlich | Comparison of System Call Representations for Intrusion Detection[END_REF] are then extracted to conduct malware analysis. A graph structure inspired from Markov chains has also been proposed [START_REF] Chen | Automatic Ransomware Detection and Analysis Based on Dynamic API Calls Flow Graph[END_REF], [START_REF] Grimmer | Intrusion Detection on System Call Graphs[END_REF], where each vertex denotes a system call and each edge is labelled by the probability to chain two system calls in the observed executing traces. This representation was extended by [START_REF] Grimmer | Intrusion Detection on System Call Graphs[END_REF] to consider n-tuples of system calls. The size of this representation does not depend on the sample or the size of the execution traces.

2) Representing the actions on objects: Parameters of system calls allow to better characterize the behavior of a program. For example, one can identify whether a "open file" system call concerns the same target file as the "write into file" system call executed later. Several representations track objects, e.g. files, sockets, threads, etc, manipulated by system calls as parameters or return values. [START_REF] Ding | A malware detection method based on family behavior graph[END_REF] defines a graph where each vertex is a system call and a directed edge links every pair of consecutive system calls that manipulate the same object in the sequence. Another work [START_REF] Park | Fast malware classification by automated behavioral graph matching[END_REF], [START_REF] Xiao | Malware Detection Based on Deep Learning of Behavior Graphs[END_REF] consists of multiple time series, one for each set of system calls manipulating the same object.

3) Representing the interactions between objects: Several works rely on multiple other sources of information from the interactions with the system, e.g. network traffic, contacted IPs/URLs/domains, file access (with modifications) for better understanding malware behaviors. In [START_REF] Alptekin | TRAPDROID: Bare-Metal Android Malware Behavior Analysis Framework[END_REF], processes, threads, files and sockets are included in the representation. Furthermore, system calls are replaced by more accurate actions. For example, a call to "open" with a file descriptor will be replaced by "open file" with the corresponding file object, thus a sequence is transformed in a categorized (by type of objects it handles) version. From that point, a sequence of system calls is processed for each monitored thread. This sequence is then categorized, and all the objects it interacts with are formatted to include practical information (i.e., the mode this file is opened with, which process spawned which one, what thread contacted which IP on what port, etc.). Sadly, we do not have much more information on how the actual graph is built.

4) Representing the interactions between processes from different programs: The work from [START_REF] Wang | Heterogeneous Graph Matching Networks for Unknown Malware Detection[END_REF] proposes a graphstructured representation based on the monitoring of multiple processes on several machines.This is a heterogeneous graph with three node types: file, process and socket. There are three kinds of edges: from a process to a socket (if that process uses this socket to communicate), from a process to a file (if that process interacts with it) and from a process to another one (if the former creates the latter). This malware representation can identify a suspicious process by comparing its behavior with benign processes. It can also be used to analyze the behavior of a malware with respect to the files it handles, the processes it spawns and the IP address it contacts. For example, it could help identify a remote C&C (Command and Control) server.

Finally, VirusTotal's database exploration graph [2] is a representation that entails the interactions between a malware and other entities (file, IP, domains, etc.), both via internet and via the file system.

III. DISCUSSIONS ON RESEARCH PROBLEMS

The previous research efforts try to achieve different objectives. However, they do not necessarily address all of the open problems that we raise as below.

A. How to make a representation more robust to evading techniques?

The detector's resilience to evasion techniques is an issue that can determine the accuracy level of ML-based malware detection models. Our study will only consider evasion techniques as tricking an analyzing tool to make a malware appear benign while still executing its payload. For example, changing individual API calls (by replacing them with equivalent ones or adding dummy system calls) can easily alter system-callsequence-based representations and transition graphs. This attack can evade the ML-based detector and yet preserve the functionalities of the malicious payloads [START_REF] Fogla | Polymorphic blending attacks[END_REF], [START_REF] Kucuk | Deceiving Portable Executable Malware Classifiers into Targeted Misclassification with Practical Adversarial Samples[END_REF], [START_REF] Stokes | Attack and Defense of Dynamic Analysis-Based, Adversarial Neural Malware Detection Models[END_REF]. On the other hand, by feeding a heterogeneous graph-based malware representation to an ML detector, we expect to mitigate such functionality-preserving evasion attacks. Furthermore, we expect such a representation to unveil evading techniques used in non-ML-based malware analysis, such as camouflage and mimicry attacks.

B. How to make a representation abstract enough to make it cross-platform?

A common issue with current malware detection is the scarcity of dataset on less-targeted mainstream OS such as macOS or Linux. This issue concerns all the aforementioned works that are platform-specific because they rely notably on system calls. To alleviate this problem, we propose to design a cross-platform representation that could be used to represent software behavior from multiple OSes. This would allow to learn to recognize a certain family of malware very common on a certain platform and then use this detector on a different platform where this family is much more rare. Reaching this goal relies on the semantic level of the representations, as abstracting the meaning of system calls is necessary for a cross-platform representation and the objects an OS handles are most often not specific to any particular platform. This will also be required to reach the goal of III-D.

C. What elements make the representation of an execution trace visually exploitable for a human expert?

A visual representation can help an expert quickly assess the behavior of a software and understand its features by organizing its information to facilitate the search. The representations presented in Section II could be improved in that regard. On the one hand, it is difficult to make logical connections between actions represented by a time series of system calls. On the other hand, the system call transition graph has a manageable constant size but the expert cannot see the exact chaining of actions anymore, discarding any indepth analysis. Representations that focus on system objects (files, network, etc.) can reveal how a software interacts with its environment. However, the expert may miss essential information because such graphs are generally too large. The most polished visual representation is the Virus Total's relation graph. However, it doesn't include the nature of interactions or the order of actions, so it is not suited for behavior analysis. The approach based on object monitoring is promising, but we expect the size of such representation to be the main challenge. Our line of research will investigate how to help the expert navigate such representation using, for example, recommendations, graph pruning, or graph collapsing. D. How to ensure a representation reflects all the malicious actions of a malware infection event?

In an execution trace report, the information used for malware analysis might not be presented in an exploitable way i.e. the related information might not appear directly linked.

For instance, representations in system call sequences (with parameters or not) show that the order of actions is a relevant information. Indeed it is missing in the transition graph representations, as some of the related actions do not directly follow each other.

Furthermore, the representations that include the system call parameters show that what matters is not only the order of operations in the sequence, but also the order of operations on objects (files, IPs, locks, etc).

Moreover, many programs will use multiple threads and/or processes, and a sequence representation is designed to represent a single sequence of actions. Heterogeneous information graph representations address that, and besides, this allows to make links between these threads/processes, via the objects that they handle to interact. Thus, these objects represent the interactions a sequence of actions has with the system at a higher level.

Finally, Virus Total's representation shows that we cannot get rid of the actions. By only showing the related objects, and not their interactions, nor the order of interactions, this is not enough to explain what happened during an execution.

IV. CONCLUSION AND GOAL OF THE PHD

This article surveys what is done in terms of representations of software execution traces. It unveils four research questions that the literature deals with insufficiently (or sometimes not at all). The Ph.D. thesis of the first author will therefore focus on proposing a new representation that encompasses all suspicious actions while being readable for human experts. Furthermore, this representation based on higher semantics should be less prone to evasion techniques and general enough to be cross-platform.


Pauline Vitoux

Thierry Tassaing
email: t.tassaing@ism.u-bordeaux1.fr.

Francois Cansell

Samuel Marre

Cyril Aymonier

In Situ IR Spectroscopy and Ab Initio Calculations To Study Polymer Swelling by Supercritical CO 2

The CO 2 sorption and polymer swelling of hydroxytelechelic polybutadiene (HTPB) and poly(ethylene glycol) (PEG) have been investigated as a function of temperature and CO 2 pressure by combining in situ nearinfrared spectroscopy with molecular modeling. The results reported here for the PEG-CO 2 system are in a very good agreement with literature data hence validating our experimental procedure. It has been found that CO 2 sorption and swelling effect is more important for PEG than for HTPB. For both polymers, an increase of temperature leads to a strong decrease of both the CO 2 sorption and swelling. In order to identify at a molecular level the nature and strength of intermolecular interaction occurring between CO 2 and the polymers, ab initio calculations have been performed on model structures, representative of the main functional group of the polymer, and their complex with CO 2 . Trans-3-hexene (3-Hex), propyl methyl ether (PME) and methoxytrimethylsilane (MTMS) have been selected to mimic the functional groups of HTPB, PEG and polydimethyl siloxane (PDMS), respectively. The last system has been chosen since previous works on the swelling of PDMS by high pressure CO 2 have revealed the high ability of CO 2 to swell both uncrosslinked and crosslinked PDMS. The calculated stabilization energies of the MTMS-CO 2 , PME-CO 2 , and 3-Hex-CO 2 dimers indicate that CO 2 interacts specifically with the three moieties through a Lewis acid-Lewis base type of interaction with the energies displaying the following order: E(MTMS-CO 2 ) )-3.59 > E(PME-CO 2 ) )-3.43 > E(3-Hex-CO 2 ) )-2.5 kcal/mol. Since the solubility of CO 2 in the corresponding homopolymers follows the same order, it is evidenced that the stronger the interaction between CO 2 and the polymer, the higher the CO 2 sorption. Therefore, even if one cannot exclude the influence of free volume and chain flexibility of the polymer, it appears that the solubility of CO 2 in the polymer is predominantly governed by the interaction between CO 2 and the polymer. Although the same trend is observed for the swelling of the polymer as a function of the CO 2 pressure, we have found that for a given value of CO 2 sorption, the swelling of the polymer depends on its nature, meaning that the swelling is not only governed by the CO 2 -polymer interaction but also by other intrinsic properties of the polymer.

Introduction

The use of supercritical carbon dioxide (scCO 2 ) as a substituent to harmful solvent systems for both chemical syntheses and polymer processing has been the subject of a particular attention in the last years. [1][2][3][4][5][6][7] Indeed, its critical coordinates are easily accessible (T c ) 31 °C, p c ) 7. 38 MPa, F c ) 0.468 g • cm -3 ), and CO 2 is nonpoisonous, nonflammable, chemically inert, inexpensive, and easily available. In addition, scCO 2 exhibits a good solubility in a number of polymers; increasing the CO 2 pressure induces a significant increase of the initial volume of the polymer (swelling) and modifies its morphological and functional properties. In other words, the addition of small amounts of compressed CO 2 to the polymer phase results in substantial changes of its physical properties such as its viscosity, permeability, interfacial tension, and glass transition temperature. Thus, carbon dioxide can be used as a temporary plasticizer, facilitating the absorption of additives into polymers. Another great advantage of scCO 2 compared to traditional organic solvents is that it leaves quickly the polymer during the depressurization of the system, without any solvent residue. Consequently, the stage of drying, necessary when using a liquid solvent, is nonexistent here. This polymer processing method has found a large number of applications in various fields such as particle formation, foaming, and blending as well as impregnation of active chemical species that have been recently reviewed in the literature. 2,3,8 Therefore, understanding the mechanisms underlying the CO 2 solubility and diffusivity in polymers, as well as their subsequent swelling in all these processes is of great importance as they are expected to provide a wide range of opportunities in polymer processing for the plastics industry.

A large variety of polymers have already been investigated such as poly(ethylene glycol) PEG, polydimethyl siloxane (PDMS), poly(methyl methacrylate) PMMA, polystyrene (PS), polycarbonate (PC), polyethylene terephthalate (PET). 9-14 Some reviews 2,3 present good literature data surveys on CO 2 -polymers systems, showing that the solubility of scCO 2 in a polymer can be either negligible or reach a weight percentage of about 40%, depending on its nature. To get such CO 2 sorption data, various methods have been developed such as the barometric, gravimetric, and the frequency modulation methods. 2 More recently, spectroscopy techniques such as attenuated total reflectioninfrared (ATR-IR) [15][16][17] and near-infrared (NIR) transmission spectroscopy 18 have proven very effective in the simultaneous measurement of CO 2 sorption and polymer swelling, according to the CO 2 pressure, for many polymers.

Although it is not easy to rationalize the current state of the art on the understanding of the polymer-CO 2 phase behavior, it is now generally admitted that the affinity of CO 2 for a polymer is mainly related to intermolecular interactions occurring between CO 2 and the polymer, even if in some cases the chain flexibility as well as the free volume of the polymer has a greater effect on the solubility than the gas-polymer interactions. 19 These specific intermolecular forces and their relationship with CO 2 sorption were investigated qualitatively by few authors using FTIR spectroscopy. 20,21 However, no quantitative relationship between the nature and the strength of the interactions between the polymer and CO 2 and its ability to swell the polymer has been reported at this point. Indeed, to the best of our knowledge, the molecular origin of the ability of CO 2 to swell a polymer has only been little investigated in detail for fluoropolymers 22 and polyethylene 23 using molecular modeling methods. In particular, the work on polymer-gas mixtures reported by van der Vegt 23 was aimed to determine quantities like solvation Gibbs energies, enthalpies, and entropies using molecular dynamics simulations, as well as the contributions of polymer reorganization and penetrant binding to the solvation enthalpy (the interactions among the dissolved penetrants may be ignored). Thus, in the solvation process, there is a competition between the work required to create a cavity in the polymer (that implies a polymer reorganization) and the binding energy between the solute and the polymer. For weak interacting gases like He, Ne, and H 2 , the energy associated with the polymer reorganization processes dominates over the solute binding interaction with the polymer, rendering positive values of the solvation enthalpy. However, an opposite behavior was found for CO 2 , where the solute binding interaction was found to be predominant.

These considerations prompt us to investigate at the molecular level how far the sorption of high-pressure CO 2 in model polymers is correlated to the nature and strength of the CO 2 -polymer interaction. In this purpose, we have chosen to investigate three different polymers, namely PDMS, PEG, and hydroxytelechelic polybutadiene (HTPB) (Figure 1). The choice of these model systems was driven by our wish to study different homopolymers that can be more or less swollen by scCO 2 . First, previous studies concerning the swelling of PDMS by high pressure CO 2 have revealed the high ability of CO 2 to swell both uncrosslinked and crosslinked PDMS. Swelling values of PDMS by CO 2 as high as 60% at 50 °C and 10 MPa have been reported. 11,16 The second polymer, PEG, can be considered as an intermediate system as it can be swollen by CO 2 by up to 25% at 40 °C and 10 MPa. 10,24 Finally, we have studied HTPB, which is expected to have a lower swelling rate. Although PEG has already been the subject of numerous investigations, it has been considered in this study as a validation system for our experimental procedure, which has been further applied to determine the swelling and CO 2 sorption of HTPB. Finally, literature data concerning PDMS have been compared to our results obtained for PEG and HTPB. In this work, we have chosen to use in situ NIR transmission spectroscopy for a quantitative determination of the CO 2 sorption and swelling of PEG and HTPB in scCO 2 . Performing transmission spectroscopy in the spectral range 4000-10 000 cm -1 has some advantages over the traditional mid-infrared spectroscopy, as previously shown by Guadagno et al. 18 In particular, molar absorption coefficients of combination bands are expected to exhibit little sensitivity upon temperature and pressure conditions, 25,26 which is not the case for fundamentals. For example, Buback et al. 27 have shown that the molar absorption coefficient of combination bands of CO 2 were almost independent of the CO 2 density. Therefore, this spectral region has been often used for concentration measurements. Besides, the use of in situ NIR spectroscopy makes it possible to detect impurities that could be present

Experimental Section

2.1. Chemicals. PEG (Mw ) 400 g/mol) was purchased from Sigma. Hydroxytelechelic polybutadiene or HTPB R45 HT (Mn ) 2600 g/mol) was provided by Arkema. Structures of the polymers are displayed in Figure 1. Carbon dioxide N45 (purity 99.95%) was supplied by Air Liquide.

2.2. Infrared Setup. The infrared absorption measurements were performed on a Biorad interferometer (type FTS-60A) equipped with a dual source capability (a globar and a tungsten halogen source), two different beamsplitters (a KBr/Ge and a quartz plate) and a DTGS (deuterated triglycine sulfate) detector in order to investigate the spectral ranges (400-6500 cm -1 ) and (3000-11500 cm -1 ), respectively. Single beam spectra recorded with a 2 cm -1 resolution were obtained after the Fourier transformation of 50 accumulated interferograms.

The near-infrared absorption experiments were performed using a homemade stainless steel cell 29 equipped with four cylindrical sapphire windows with a path length of 6.7 mm. The sealing was obtained using the unsupported area principle. The windows were positioned on the surface of a stainless plug, while a 100 µm Kapton foil placed between the window and the plug compensated for any imperfections between the two surfaces. Teflon O-rings were used to ensure the sealing between the plug and the cell body. The cell was heated using cartridge heaters disposed in the periphery of the body of the cell. Two thermocouples were used, the first one located close to a cartridge heater for the temperature regulation and the second one close to the sample area to measure the temperature of the sample with an accuracy of about 2 °C. The cell was connected via a stainless steel capillary to a hydraulic pressurizing system that allows the pressure to be raised up to 50 MPa with an absolute uncertainty of (0.1 MPa and a relative error of (0.3%. The stabilization of the operating conditions was controlled by recording several consecutive spectra.

Experimental Procedure.

The cell was first filled with the polymer, then pumped under vacuum in order to remove any trace of water in the polymer and finally heated up to the required temperature. The spectra were recorded for the raw

Computational Details

Calculations were performed on three model structures, namely MTMS, PME, and 3-Hex, selected to mimic the functional groups of PDMS, PEG and HTPB, respectively (Figure 1). The initial configuration used for MTMS, 30 PME, 31 and 3-Hex 32 was the lowest energy conformer previously reported by authors who investigated the conformational properties of these molecules using ab initio and density functional theory (DFT) calculations. Preliminary geometry optimizations were carried out using a semi empirical model (AM1 33 ) to determine the most stable conformations of the MTMS-CO 2 , PME-CO 2 and 3-Hex-CO 2 adducts. These semiempirical calculations were carried out using the AMPAC software. 34 The lowest energy adducts obtained at the AM1 level were further investigated using an ab initio method implemented in the Gaussian 2003 package. 35 Calculations of geometries and energies reported in this paper were carried out at the secondorder Moller-Plesset level (MP2), which includes explicitly the effects of electron correlation. 36 The augmented correlationconsistent polarized valence double basis sets (aug-cc-VDZ) proposed by Dunning and co-workers were used in these calculations. [37][38][39][40] Geometry computations were not subjected to a particular symmetry constraint, excepted for isolated CO 2 (D ∞h symmetry). Stabilization energies of the adducts investigated in this paper were calculated using the "supermolecule" method as the difference in energy between each adduct and the sum of the isolated monomers. The basis set superposition errors (BSSE) were calculated using the full counter-poise method of Boys and Bernardi. 41 Molden was used to display the optimized geometry of the isolated moieties and the complex. 42

Results and Discussion

4.1. Near-Infrared Absorption Spectra. The infrared spectra of HTPB subjected to CO 2 were recorded for pressures up to 25 MPa and for three different temperatures: 40, 100, and 150 °C. Figure 2a illustrates the spectral changes in the wavenumber range 4400-6200 cm -1 that occur with an increasing CO 2 pressure. A number of significant peaks associated to combination or overtones of the polymer can be observed in the spectral range 4400-4800 and 5500-6200 cm -1 . Increasing the CO 2 pressure leads to a decrease of the intensities of the polymer bands (for example at 4720 and 6105 cm -1 ), whereas the intensity of the CO 2 peaks, characteristic of CO 2 sorbed into the polymer (for example at 4950 cm -1 ), increases. Note that the three more intense peaks observed in Figure 2a (centered at 4480, 5660, and 5820 cm -1 ) are saturated in our experimental conditions and cannot be used for our purpose. Besides, the peaks centered at 4600, 4660, 4720 strongly overlap, making it difficult to extract accurate quantitative information from these contributions. Consequently, we have used the peak centered at 6105 cm -1 to determine the swelling of HTPB subjected to scCO 2 . Concerning CO 2 , we can detect two peaks at 4950 and 5100 cm -1 that are assigned to the combination modes ν 1 + 2ν 2 + ν 3 and 2ν 1 + ν 3 of the CO 2 in the polymer, inducing potentially a non-negligible effect on the swelling of the polymer.

Meanwhile, ab initio calculations have been performed in order to obtain information on the nature of the polymer-CO 2 intermolecular interactions. Although statistical mechanical simulations are well adapted to get insights of the phase behavior of polymer-gas mixtures, ab initio calculations are preferred in order to compute accurate interaction energies. The calculations have been performed on model structures that are representative of the main functional groups of the backbone of PDMS, PEG, and HTPB (Figure 1). The equilibrium geometries of these model structures and their complexes with CO 2 , in particular, on methoxytrimethylsilane (MTMS), propyl methyl ether (PME), and trans-3-hexene (3-Hex), representative of PDMS, PEG, and HTPB, respectively, have been investigated. Note that such an approach does not take into account neither the polymer-polymer interaction, the CO 2 -CO 2 interaction nor the solvent accessible surface area 28 of CO 2 in connection with the free volume of the polymer. However, it was previously reported 22,23,28 that in the case of CO 2 , these effects may be less relevant than the CO 2 -polymer interactions. Therefore, we have decided to use such accurate method in order to rationalize the relation between the nature and strength of the polymer-CO 2 interaction and the concentration of CO 2 that can be incorporated into the polymer. polymer, then CO 2 was added up to the highest desired pressure. The system was kept under isobaric and isothermal conditions for a long period of time (typically from a few hours at high temperature up to 2-3 days at 40 °C) in order to ensure that the equilibrium was achieved. After recording the spectrum, the pressure was decreased to a lower value. For each pressure, the equilibrium was considered to be achieved when no change of the spectral bands was noticed. molecule, respectively. [START_REF] Herzberg | Molecular Spectra and Molecular Structure: Infrared and Raman Spectra of Polyatomic Molecules[END_REF] Because of the weak intensity of the peak at 5100 cm -1 , we have used the band at 4950 cm -1 to estimate the evolution of the weight percentage of CO 2 incorporated into the polymer as a function of the CO 2 pressure. The near-infrared spectra of PEG 400 subjected to CO 2 was recorded the same way for pressures up to 20 MPa and for two different temperatures, 40 and 150 °C (see Figure 2b). In this case, we have used the peak centered at 4850 cm -1 to determine the swelling of PEG, while using the band centered at 4950 cm -1 to estimate the evolution of the weight percentage of CO 2 incorporated into the polymer. 18 the polymer swelling can be calculated via the absorbance of a specific band of the polymer before and after exposure to CO 2 , using the following procedure, according to the Beer-Lambert law:

Where A 0 , A, C 0 , and C are the absorbances of polymer bands and concentrations of polymer before and after exposure to CO 2 , respectively, and l is the path length of the cell.

Finally, after combination of these three equations, the swelling S is given by On the basis of the above considerations, we have selected the peak centered at 6105 cm -1 to determine the swelling of HTPB.

The integrated areas A 0 and A of this band were calculated in the wavenumber range (6080-6170 cm -1 ). In the case of PEG, we have used the peak centered at 4850 cm -1 . However, the swelling was determined from the variation of the maximum absorbance of this peak instead of its integrated area.

b. CO 2 Sorption. In order to determine the concentration of CO 2 (C CO2 ) incorporated into the polymer, we have applied the Beer-Lambert law using the integrated absorbance of the ν 1 + 2ν 2 + ν 3 band of CO 2 centered at 4950 cm -1 as follows where ε is the molar absorption coefficient (L • mol -1 • cm -2 ) associated to the ν 1 + 2ν 2 + ν 3 band of CO 2 , C is the concentration of CO 2 (mol • L -1 ), and l is the path length of the cell (cm). The wavenumber range considered for the integration of the ν 1 + 2ν 2 + ν 3 band extends from 4880 (ν′) to 5030 cm -1 (ν′′). The molar absorption coefficient was estimated in previous investigations 27 on pure CO 2 and was found to be constant over a wide range of density (up to 0.9 g • cm -3 ) and temperature (27 to 227 °C). Thus, the molar absorption coefficient of this peak was assumed to be the same when CO 2 swells the polymer and we have used for the considered wavenumber range a value of 10 L • mol -1 • cm -2 . For a straightforward comparison with the literature data, the weight percentage of CO 2 (% mass CO 2 ) sorbed into the polymer matrix was calculated using the following expression: 18 Where F pol (mol • L -1 ) represents the density of the polymer and S the swelling of the polymer after exposure to CO 2 , obtained from the ratio ∆V/V (see above). Because of the presence of a weak peak of HTPB located at about 4960 cm -1 (see Figure 2a), the spectrum of pure polymer at the considered temperature was subtracted for all registered spectra. 4.3. CO 2 sorption in HTPB and PEG. The weight percentage of sorbed CO 2 calculated using eqs 5 and 6 is reported in Figure 3 as a function of pressure at 40, 100, and 150 °C for HTPB and at 40 and 150 °C for PEG in Figure 4. For comparison, we have displayed in Figure 4 the results obtained by Guadagno et al. 18 and Gourgouillon et al. 10 for PEG 400 at

A 0 ) ε • C 0 • l (1) A ) ε • C • l (2) C 0 C ) V + ∆V V ) 1 + ∆V V ) 1 + S (3) S ) A 0 A -1 (4) ∫ ν' ν'' A(ν) • d(ν) ) ε • C • l (5) % mass CO 2 ) C CO2 C CO2 + F pol 1 + S ( 6
)
If V is the volume of the polymer before exposure to gas and V + ∆V is the volume of the polymer during exposure to gas, one can write case of HTPB at 40 °C, the weight percentage of sorbed CO 2 increases with the pressure to reach a plateaulike value of about 15% at 10 MPa indicating that above this pressure, no more CO 2 can be incorporated into the polymer. A similar increase with a much less pronounced plateau-like behavior is observed for the measurements performed at higher temperatures (100 and 150 °C) but for a given pressure, an increase of temperature causes a decrease of the weight percentage of CO 2 incorporated into the polymer.

In the case of PEG, it appears clearly that the weight percentage of CO 2 sorbed, displaying the same plateau behavior as a function of CO 2 pressure, is higher than in HTPB and found to be about 20% at 10 MPa. Although small discrepancies are observed between the different sets of data, probably due to the different experimental and analytical methods employed, an overall good agreement is obtained between our data and that previously reported. Similarly to the case of HTPB, an increase of temperature causes a decrease of the weight percentage of CO 2 incorporated into the PEG, for a given pressure.

Thus, since the solubility of CO 2 is higher in PEG than in HTPB, CO 2 -ether interactions are expected to be stronger than CO 2 -double CdC bond interactions. The nature of the molecular interactions responsible for the differences in the solubility of CO 2 into PEG and HTPB are investigated by means of quantum calculations in the Section 4.5.

Swelling of PEG and HTPB.

The swelling of the polymer calculated using eq 4 is reported as a function of pressure at 40, 100, and 150 °C for HTPB in Figure 5 and at 40 and 150 °C for PEG in Figure 6. For comparison, we have displayed in Figure 6 the results obtained by Guadagno et al. 18 for PEG 400 at 40 °C. In the case of HTPB at 40 °C, the swelling increases with the pressure up to a maximum value of about 15% reached for a pressure of 15 MPa, above which CO 2 cannot swell additionally the polymer. A similar behavior is observed for the measurements performed at higher temperatures (100 and 150 °C). However, for a given pressure an increase of temperature causes a decrease of the polymer swelling. Considering the PEG, the swelling increases with the pressure up to a value of about 35% reached at a pressure of 20 MPa. Similarly to HTPB, an increase of temperature for a given pressure causes a decrease of PEG swelling. Finally, according to the CO 2 sorption, the comparison of Figures 5 and6 clearly shows that PEG swelling is higher than that measured for HTPB.

Analysis of the Polymer-CO 2 Interactions from Ab Initio Calculations: Structural and Energetic Considerations.

In order to investigate at a molecular level how the solubility of CO 2 in PDMS, PEG, and HTPB is correlated to the nature and strength of the CO 2 -polymer interaction, we have performed ab initio calculations on three model structures, namely MTMS, PME, and 3-Hex, chosen to mimic the functional groups of PDMS, PEG, and HTPB, respectively. Although these quantum chemistry methods do not allow modeling the entire polymer the way it could be done through statistical simulations, accurate interaction energies between CO 2 and the characteristic functional groups of polymers can be obtained. Let us emphasize that high level quantum mechanical methods (accounting for electron correlation effects) are required in order to compute accurate energies as the interactions in these systems are expected to be weak. Therefore, in order to calculate the geometry of the isolated PME-CO 2 , MTMS-CO 2 , and 3-Hex-CO 2 pairs, we have performed ab initio calculations at the second order Moller-Plesset perturbation theory (MP2) using Dunning's aug-cc-pVDZ basis set. Figure 7 shows the optimized structures of the three dimers with the more relevant calculated structural parameters. Note that the initial configurations used for the PME, the 3-Hex, and the MTMS molecules, taken as the lowest energy conformers reported in previous studies, are almost unchanged upon complexation with CO 2 . However, the isolated CO 2 molecule, which has a d ∞h symmetry and a CdO bond length of 1.18022 Å, is systematically perturbed upon complexation, in particular concerning the O)CdO angle (cf. Figure 7).

In the case of PME-CO 2 dimer, CO 2 is found to be above the oxygen atom of PME for which the donating lone pair interacts with the carbon atom of CO 2 . Such configuration reveals a Lewis Acid-Lewis Base (LA-LB) type of interaction where PME plays the role of a Lewis base and CO 2 the role of a Lewis acid. Such configuration is consistent with previous calculations performed on ether-CO 2 complex. [START_REF] Vanginderen | [END_REF]45 The calculated binding energy of the complex, corrected for the BSSE, is found to be approximately -3.43 kcal/mol, which is in good agreement with that reported in the literature for the methyl butyl ether (MBE)-CO 2 complex 45 (-3.49 kcal/mol at the MP2/ aug-cc-pVTZ level). Such interaction energy is not negligible and evidence the good affinity of ether function with CO 2 as it has been found for polymer containing ether group. [45][46][47] Similarly to the PME-CO 2 adduct, CO 2 is found to be above the oxygen atom of MTMS in the MTMS-CO 2 dimer, which unveil a LA-LB type of interaction. However, the calculated binding energy corrected for the BSSE is found to be -3.59 kcal/mol, which is a value slightly higher than the one found for the PME-CO 2 complex. Therefore, this higher energy of interaction could account for the significantly higher solubility of CO 2 in PDMS 16 than in PEG. Note that the solubility of CO 2 in PDMS has been found to be about 25% at 50 °C and 10 MPa. 11,16 Considering the 3-Hex-CO 2 dimer, the CO 2 molecule placed itself above the double bond of the 3-Hex molecule, the π electron of the CdC double bond interacting with the carbon atom of CO 2 . The calculated binding energy of the complex, corrected for the BSSE is about -2.5 kcal/mol. This value is lower than the ones reported for both PME-CO 2 and MTMS-CO 2 complexes, which could a posteriori explain why the solubility of CO 2 in HTPB is lower than in PEG and PDMS.

In order to evaluate the influence of the model structure on the energy of interaction between CO 2 and a CdC double bond, we have performed the same calculations using ethene, trans-, and cis-dimethyl ethene as model structures of CdC double bond.

The optimized structures, calculated energies, and structural parameters are reported in Figure 8. The main features concerning the optimized structures are the same for all complexes: CO 2 is found to placed itself above the CdC double bond, its main axis being almost parallel to the H-CdC-H plane, the angle between the main axis of CO 2 and the CdC bond depending on the model structure.

Concerning the ethene-CO 2 complex, the structure is found to be in agreement with previous reported calculations. 48 Also, the energy of interaction between CO 2 and ethene is found to be the lowest one of the series of ethene derivatives, about -1.5 kcal/mol. The calculated energies reported for the cis-and transdimethyl ethene are found to be almost the same (about -2.3 kcal/mol) and very close to the value calculated for the 3-Hex-CO 2 complex (-2.5 kcal/mol). Thus, whatever the model structure used to mimic the HTPB-CO 2 interactions, it appears that the interaction between CO 2 and a CdC double bond is lower than the LA-LB interaction occurring between CO 2 and an ether group. Therefore, from these calculations, we have shown that the intermolecular interactions occurring between CO 2 and our model structures display the following energy order: E(PDMS-CO 2 ) > E(PEG-CO 2 ) > E(HTPB-CO 2 ).

Since the solubility of CO 2 in these polymers follows the same order, we can consider that it is mainly driven by the CO 2 -polymer interaction. Such conclusion is consistent with previous theoretical investigations, 22,23,28 evidencing that other factors such as polymer-polymer interactions, CO 2 -CO 2 interactions, as well as the solvent accessible surface area of CO 2 in connection with the free volume of the polymer have a much smaller influence on the ability of CO 2 to be sorbed into the polymer. Therefore, in order to obtain the higher gas sorption in a given polymer, the choice of an appropriate gas that will afford strong interactions with the main functional group of the polymer is required.

4.6. Analysis of the Correlation between CO 2 Sorption and Polymer Swelling. In order to determine how the swelling of the polymer and the CO 2 sorption are correlated, we have reported in Figure 9 the swelling percentage of PDMS, PEG, and HTPB as a function of the weight percentage of CO 2 sorbed into the polymer. For a given temperature in the pressure range investigated in this study, one can notice an almost linear dependence of the swelling of PEG and HTPB as a function of the weight percentage of CO 2 sorbed into the polymer. Such correlation has been found and discussed by other authors for semicrystalline polymers in supercritical CO 2 . 49,50 The temperature seems to have almost no effect on the slope of these curves. However, for a given weight percentage of CO 2 sorbed into the polymer, the swelling of PEG is higher than that observed for HTPB. In the case of PDMS, the swelling and CO 2 sorption are not linearly connected, and it appears that the swelling is higher than PEG and HTPB when the CO 2 sorption is above 25%.

Therefore, as expected above, the swelling of the polymer appears to be correlated to the CO 2 sorption since a higher CO 2 sorption will induce a higher swelling of the polymer. However, the correlation observed between the swelling and the CO 2 sorption is system specific and depends on several physical properties of the polymer such as the degree of crystallinity and crosslinking, the cohesivity (or the surface tension), the viscosity, and the chain flexibility.

Conclusion

Our experimental results extend the suitability of NIR spectroscopy, introduced in ref 18, to determine the CO 2 sorption and polymer swelling as a function of temperature and CO 2 pressure. In particular, the swelling and CO 2 sorption reported here for the PEG-CO 2 system are in a very good agreement with literature data. In addition, new results have been obtained for this system at higher temperature, while the swelling and sorption for the HTPB-CO 2 system were reported for the first time. It has been found that the CO 2 sorption and swelling rate of PEG is higher than that measured for HTPB. In addition, the CO 2 sorption and swelling rate of both polymers are much lower upon an increase of temperature. Ab initio molecular orbital calculations on model structures and their complexes with CO 2 have been performed in order to identify at a molecular level the nature and strength of intermolecular interactions occurring between CO 2 and PDMS, PEG, and HTPB, which may be responsible for the observed differences in the solubility of CO 2 in these polymers. Results of energy calculations of the MTMS-CO 2 , PME-CO 2 , and 3-Hex-CO 2 dimers indicate that CO 2 interacts specifically with the three moieties through a Lewis acid-Lewis base type of interaction with the energies displaying the following order: E(MTMS-CO 2 ) ) -3.59 > E(PME-CO 2 ) ) -3.43 > E(3-Hex-CO 2 ) ) -2.5 kcal/mol. Since the solubility of CO 2 in the corresponding homopolymers follows the same order, we can claim that the solubility of CO 2 in the polymer is mainly governed by the interactions between CO 2 and the main functional group of the polymer. This means that the stronger the interaction between CO 2 and the polymer, the higher the CO 2 sorption. Thus, it appears that even if one cannot exclude the influence of free volume and chain flexibility of the polymer, the role of such property seems to be less significant than the interaction between CO 2 and the polymer (as reported elsewhere 22,23,28 ).

Accordingly, the same trend is observed for the swelling of the polymer as a function of the CO 2 pressure. However, we have found that for a given CO 2 sorption in a polymer, its swelling depends on the nature of the polymer. The swelling is certainly not only controlled by the CO 2 -polymer interactions but also by other specific properties of the polymer such as its cohesivity (or the surface tension), its viscosity, and the chain flexibility.

Figure 1 .

 1 Figure 1. Structures of the polymers and their corresponding model structures.

4 . 2 .

 42 Data Processing for the Determination of CO 2 Sorption and Polymer Swelling. a. Polymer Swelling. As previously proposed by Guadagno et al.,

Figure 2 .

 2 Figure 2. IR absorption spectra of HTPB (a) and PEG (b) at different pressures of scCO 2 and constant temperature. The arrows indicate the intensity variation upon increasing the pressure. The asterisks show the peaks used for the determination of the CO 2 sorption and the polymer swelling.

Figure 3 .

 3 Figure 3. Weight percentage of CO 2 incorporated into polymer matrix of HTPB at 40 (b), 100 (9), and 150 °C (2) as a function of the pressure of scCO 2 .

Figure 4 .

 4 Figure 4. Comparison of weight percentage of CO 2 incorporated into polymer matrix of PEG at 40 (b) and 150 °C (2) as a function of the pressure of scCO 2 with literature data.

Figure 5 .

 5 Figure 5. Swelling percentage of HTPB at 40 (b), 100 (9), and 150 °C (2) as a function of the pressure of scCO 2 .

Figure 6 .

 6 Figure 6. Comparison of swelling percentage of PEG at 40 (b) and 150 °C (2) as a function of the pressure of scCO 2 with literature data.

Figure 7 .

 7 Figure 7. Optimized structure (MP2/aug-cc-pVDZ level) of the trans-3-hexene-CO 2 (A), propylmethylether-CO 2 (B), and the methyltrimethylsilane-CO 2 (C) dimer.

Figure 8 .

 8 Figure 8. Optimized structure (MP2/aug-cc-pVDZ level) of the ethene-CO 2 (A), cis-dimethyl ethene-CO 2 (B) and trans-dimethyl ethene-CO 2 (C) dimer. Values in parentheses are reported for the molecule without CO 2 .

Acknowledgment. The authors acknowledge DGA for the

was also supported by CNRS through the PEPS07-33. Finally, we wish to thank two unknown referees for fruitful comments on the manuscript.


Anandi Srinivasan

Rebecca A Musgrave

Mathieu Rouzières

Rodolphe Clérac
email: clerac@crpp-bordeaux.cnrs.fr

John E Mcgrady

Elizabeth A Hillard
email: elizabeth.hillard@icmcb.cnrs.fr

A Linear Metal-Metal Bonded Tri-Iron Single-Molecule Magnet

The linear trinuclear complex cation [Fe 3 (DpyF) 4 ] 2+ was prepared as [Fe 3 (DpyF) 4 ](BF 4 ) 2 2CH 3 CN. With large Fe-Fe distances of 2.78 Å, this complex demonstrates intramolecular ferromagnetic coupling between the anisotropic Fe II centers (J/k B = +20.9(5) K) giving an S T = 6 ground state and exhibits single-molecule magnet properties.

Ferromagnetic coupling (FM) can also be observed in direct metal-metal interactions, particularly for valence-delocalized iron clusters, ‡ which often exhibit maximal ground spin states. 4 The simplest examples include di-iron paddlewheel complexes, such as an Fe I -Fe I complex with an intermetallic distance of 2.127 Å (S T = 3), 5 mixed-valent Fe II -Fe I complexes 6 with distances of ca. 2.2 Å (S T = 7/2), and two Fe II -Fe II complexes with distances of 2.287 and 2.462 Å (S T = 4). 7 The face-sharing bioctahedral S T = 9/2 complex [(Me 3 tacn) 2 Fe 2 (μ 2 -OH) 3 ] 2+ , has yet a longer Fe-Fe distance of 2.510 Å. 8 Eventually, the Fe-Fe distance becomes too large to mediate spin coupling; as in Fe 2 (-DPhBz) 2 ( 2 -DPhBz) 2 (d Fe-Fe = 3.124 Å), with a magnetic moment compatible with non-interacting S Fe = 2 centres. 7a Clusters with three iron ions can adopt a triangular or, more rarely, a linear arrangement of atoms. Examples of high-spin triangular complexes include the mixed-valent S T = 11/2 Fe 3 (and related S T = 19/2 Fe 6 ) clusters, with FeFe distances ranging from ca. 2.4 to 2.7 Å. 9 Maximal spin states have also been predicted for linear iron clusters, 10 although only four such compounds have been reported. Recently, a trinuclear compound with three bridging 2,6bis[(trimethylsilyl)amido]pyridine ligands was obtained with FM coupling between the Fe II centers (2.442 Å). 11 Additionally, the tetranuclear complexes Fe 4 (tpda) 3 Cl 2 12 and Fe 4 (tpda) 3 Br 2 , 13 with mixed bridging-chelating tripyridyldiamido modes and long Fe-Fe distances of > 2.9 Å, were modelled as consisting of two FM coupled Fe 2 pairs, with antiferro-magnetic (AF) inter-pair interactions. In 1998, a tri-iron cluster with a similar mixed coordination mode, [Fe 3 (DpyF) 4 ](PF 6 ) 2 , (DpyF = dipyridylformamide), was reported to have a room-temperature T value of 16 cm 3 K mol -1 , much higher than that expected for three isolated Fe II centers, once again suggesting FM coupling between the Fe II spins. 14 Motivated by our interest in the magnetic properties of linear clusters, 15 we have prepared the BF 4

-analogue [Fe 3 (DpyF) 4 ](BF 4 ) 2 to study its static and dynamic magnetic properties. [Fe 3 (DpyF) 4 ](BF 4 ) 2 2CH 3 CN (1, Figure 1) was synthesized using an adaptation of the literature protocol, 14 by refluxing LiDpyF, FeCl 2 and TlBF 4 in THF and recrystallizing the ensuing pale yellow precipitate from the diffusion of diethyl ether into an acetonitrile solution (ESI). It crystallizes in the space group I4/m (Table S1) such that the four fold axis is co-linear with the metal axis and the central Fe II ion is bisected by a glide plane perpendicular to the metal axis, giving one unique Fe(1)-Fe(2) distance of 2.7838( 5) and 2.7742(6) Å at 270 and 100 K, respectively. The cation displays distorted octahedral terminal Fe II sites and a tetrahedrally distorted square planar central Fe II ion (Table S3). The terminal Fe(1)N distances average 2.191[2] Å for both temperatures, while the central Fe(2)N(2) distance is 2.1436( 18) and 2.1431( 18) Å (Table S2), consistent with HS Fe II centres and similar to those reported for [Fe 3 (DpyF) 4 ](PF 6 ) 2 . 14 One of the BF 4 -anions and the solvent molecules could not be modelled atomistically; solvent masking in Olex 2 16 suggested the presence of two acetonitrile molecules per formula unit.

The static magnetic susceptibility, , was measured on a polycrystalline sample of 1 mixed with mineral oil (Figure 2). The T value at 300 K is 15.3 cm 3 K mol -1 , significantly higher than the sum of Curie constants for three uncoupled high-spin Fe II centers (9.0 cm 3 K mol -1 for g = 2). Upon decreasing the temperature, the T value increases continuously, reaching a maximum value of 25.8 cm 3 K mol -1 at 22 K, revealing dominant FM coupling between the three Fe II S = 2 spins. The maximum value is higher than that expected from an S T = 6 system (21.0 cm 3 K mol -1 , g = 2), suggesting the contributions from orbital momentum, leading to a g factor higher than 2 (as expected for high-spin octahedral Fe II centers). Below 20 K, the T value at low field (0.1 T) decreases slightly to reach a minimum value of 21.7 cm 3 K mol -1 at 1.85 K, likely due to magnetic anisotropy is the molar magnetic susceptibility (M/H) per complex and T the temperature) in an applied dc magnetic field of 0.1 and 1 T for 1. Inset: Field dependence of the magnetization for 1 below 8 K. Solid lines are the best fits to the model described in the text.

and/or AF interactions between cation moments. Variable field magnetization data below 8 K (Figure 2, inset and Figure S1), do not saturate even at 7 T, reaching a maximum value of 10.7

 B, lower than the 12  B expected for an S T = 6 species. This high field feature, and the nonsuperposition of the M = f(HT -1 ) curves (Figure S1), strongly suggest the presence of a significant magnetic anisotropy. In the literature, magnetic data for linear iron clusters have been treated either using an exchange-coupled model, when FM exchange is weak (|J/k B |<50 K) 7b,12 or a delocalized macrospin model in the strong coupling limit (|J/k B |>300 K). 9a,9c In the present case, a simple macrospin model would not capture the temperature dependence of the T product (Figure 2), and therefore the experimental data were fitted numerically (PHI 17 ) considering the following anisotropic Heisenberg Hamiltonian:

where J denotes the intramolecular interaction between Fe II spins, is the spin operator for each metal ion centre (S Fe = 2) and D is the axial ZFS parameter. The best fit parameters, J/k B = +20.9(3) K, D/k B = -6.2(2) K and g = 2.23 (5), reproduce well the experimental data shown in Figures 2 andS1. Notably, the fit was not significantly improved by incorporating a rhombic ZFS parameter or intermolecular interactions in the model and degraded strongly upon forcing D to be positive. The estimated FM interaction in [Fe 3 (DpyF) 4 ](BF 4 ) 2 2CH 3 CN (J/k B = +20.9 K) is slightly larger than in Fe 4 (tpda) 3 X 2 (J/k B = +10.1 to +15.4 K), 12,13 which possess longer Fe-Fe distances (> 2.9 Å vs. 2.78 Å).

Further insight into the ground state electronic structure on the cation in 1 was obtained using density functional theory (DFT) as implemented in ORCA v.4.2.1, 18 using X-ray coordinates adjusted to D 2d symmetry without further optimization. The performance of DFT in describing exchange coupling has been reviewed extensively, 19 and the choice of functional has a substantial impact, particularly in cases where the ground state involves FM exchange. Following recommendations from Illas et al., 20 we discuss here results obtained with the hybrid B3LYP functional, 21 and the sensitivity of the results to other choices is discussed in ESI. We have identified a number of different FM configurations with S T = 6, along with a broken-symmetry (AF) state which is an approximate quintet with M S = 2. The lowest-energy configuration does indeed prove to be FM ( 13 B 2 , S T = 6): The Fe II manifold of Kohn-Sham orbitals is shown in Figure 3, with only the -manifold shown here for simplicity. The orbital array shows the 15 metal-based orbitals split into a lower band of 10 that are approximately Fe-N non-bonding and a higher band of 5 that are Fe-N antibonding. The very different local coordination environments of the terminal and inner Fe II ions (octahedral and distorted square-planar, respectively), lead to different high-spin electronic configurations: for the two terminal Fe II ions, the 6 th (spin-) 3d electron occupies a orbital (1a 1 and 1b 2 in Figure 3), while for the inner Fe II ion, the 6 th electron occupies a orbital (1b 1 ), with Fe-Fe  character. The  manifold therefore makes a FM contribution to exchange coupling through a spin delocalization/double exchange mechanism (see inset in Figure 3), while the  manifold makes an AF superexchange contribution according to the Goodenough-Kanamori rules, albeit a weak one due to the limited  overlap. The sum of the two components, FM coupling in the  manifold and weak AF coupling in , gives rise to the FM alignment observed in the magnetic measurements.

The electronic structure can be mapped onto the Heisenberg ladder using a broken-symmetry state with M S = 2, where the spin moment on the central Fe ion is inverted relative to the FM ground state. While the near orbital degeneracy of the Fe II ion complicates the mapping of spin-state energies onto a simple Heisenberg-type Hamiltonian, 22 we can use the computed energies of the S T = 6 and M S = 2 states to extract an estimate of the exchange coupling constant, J/k B = +43.2 K (ESI). While this number is higher than the experimental value of +20.9 K, it is within the normal range of accuracy shown by DFT in the FM regime.

The dominance of FM coupling, the detection of magnetic anisotropy and a negative D value led us to investigate potential SMM properties. In the absence of an external dc-field, no frequency dependence in either the in-phase (') or out-ofphase (") component of the ac susceptibility was observed above 1.8 K with ac frequencies up to 10 kHz (ESI). The application of an external dc-field led to appearance of frequency and temperature dependent ac signals (Figures 4 and S2, ESI), revealing the slow dynamics of the magnetization and consequently, its SMM properties. The ' vs.  and " vs.  data at 1.9 K in different dc-fields (Figure S2, ESI) and at different temperatures under 0.2 T (Figure 4) were fit to the generalized Debye model 23 to obtain the field and temperature dependence of the magnetization relaxation time () characteristic of this S T = 6 SMM (Figure S5). To analyse the paramagnetic relaxation, four mechanisms are usually invoked: quantum tunneling of the magnetization (QTM), 24,25 Orbach-type (i.e., thermally activated, Arrhenius behavior), [25][START_REF] Gatteschi | Molecular Nanomagnets[END_REF][START_REF] Van Vleck | [END_REF] Raman 27 and direct 28 processes. The paramagnetic relaxation rate (τ -1 ) can be then decomposed in four terms: possessing their own thermal and dc-field dependences with a collection of eight independent parameters: Considering that the magnetization relaxation is observed in a small experimental window (0.02-1 T, 1.8-3 K, 0.115-10 kHz; Figure S5), it is unreasonable to try to extract accurately the whole set of parameters. Nevertheless, a few hypotheses can be formulated by a simple analysis of the relaxation time. At low dc-field (Figure S5a), the characteristic frequency decreases from 10 kHz at 0.02 T down to 140 Hz at 0. Therefore, the paramagnetic relaxation in 1 seems to be dominated by Orbach-type and QTM pathways. Between 1.8 and 3 K, the ln(τ) vs. T 1 plot (Figure S5b) is linear and thus compatible with a thermally activated relaxation with a preexponential factor, τ 0 , of 9(1) × 10 9 s and an energy gap, ∆ eff /k B , of 22(1) K. Nevertheless, this value is ten times lower than that expected (∆/k B = DS T 2 /k B = 223 K) from the estimated magnetic anisotropy (D/k B = -6.2 K) and the spin-ground state (S T = 6) suggesting that our experimental window may cover a crossover regime between these two relaxation pathways.

In conclusion, [Fe 3 (DpyF) 4 ](BF 4 ) 2 2CH 3 CN contains a rare example of a linearly-disposed trinuclear cluster cation, with ferromagnetically coupled Fe II ions and an S T = 6 ground state, consisting of singly-occupied nearly degenerate metal-based molecular orbitals. The FeFe distance (2.8 Å) is amongst the longest observed to mediate FM coupling. The magnetic data was modeled with an anisotropic Heisenberg Hamiltonian, giving J/k B = +20.9(3) K and D/k B = -6.2(2) K. The combination of the strong magnetic anisotropy and the energetically wellseparated ground state likely yield the SMM properties, which appear to involve QTM and Orbach-like relaxations.

Electronic Supplementary Information (ESI) available: Synthesis, crystallography, Shape analysis, magnetic measurements and theoretical calculations. See DOI: 10.1039/D1CC05043E. Structures of 1 at 270 and 100 K can be found in the Cambridge Structural Database CCDC 2025912-2025913.

Conflicts of interest

There are no conflicts to declare.

Figure 1 .

 1 Figure 1. Thermal ellipsoid (50%) diagram of the cation in 1 at 270 K from single crystal X-ray diffraction data.

Figure 2 .

 2 Figure 2. Temperature dependence of the T product (where 

Figure 3 .

 3 Figure 3. Kohn-Sham orbital energy diagram for the 13 B 2 ground state of [Fe 3 (DpyF) 4 ] 2+ . Interactions with , ,  and ' symmetry are mediated by , , and orbitals, respectively. Eigenvalues and eigenfunctions shown are for the spin- manifold. Isosurfaces are shown only for the orbitals of  and  symmetry that are involved in Fe-Fe exchange coupling. The schematic configurations shown in the inset illustrates the FM and AF contributions of double-and superexchange in the  and  manifolds, respectively.

Figure 4 .

 4 Figure 4. ac frequency (left) and temperature (right) dependence of the real ', top) and imaginary ('', bottom) parts of the ac susceptibility for 1 at 0.2 T, for ac frequencies of 10-10000 Hz and 1.8-10 K. Solid lines on the ' and '' vs. ν plots are generalised Debye fits 23 of the ac data used to extract the temperature dependence of the relaxation time (Figure S5) as well as α, ν,  0 ',   ' and  0 '-  ' (Fig. S4.)

  3 T suggesting the presence of QTM relaxation, even if a Raman process cannot be completely excluded with C 2 > C 1 . Above 0.3 T, the relaxation time is only weakly field dependent, in disagreement with direct (in H 4 or H 2 ) or Raman (in H 2 with C 2 << C 1 ) mechanisms.

Acknowledgements

This work was supported by the CNRS, the French Ministry for Higher Education, Research and Innovation, the Regional Council of Nouvelle Aquitaine, the University of Bordeaux, Quantum Matter Bordeaux and the EU Horizon 2020 Research and Innovation Programme under grant agreement No. 752684. We thank S. Exiga and V. Bulicanu for technical assistance.