Antoine Doncieux

Frédérique Jankowski

Alexandre Gaudin

Adeline Barnaud

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Certified and peasant seeds: which network for millet seed supply?

III. Results & discussion

Seed origin shapes farmer seed networks After the harvest, seed origin doesn't matter: pearl millet is pearl millet

After the harvest, pearl millet from certified seed circulates for the same reasons as peasant seed 5 .

For instance, Zakat, which is a form of alms-giving, is a religious obligation for all Muslims. It consists to redistribute about 10% of the harvest to those who deserve it (i.e, poor, needy, old or sick person).

In rare cases (5% in our study), pearl millet received under zakat is used as seed 5 . However, no information relating to the origin of seeds is communicated through this practise 5 .

One variety hides another

Over time, certified seed changes status and loses its identity. The perception of the origin of the seed from which the variety is derived differs according to the interlocutor for the same name variety 5,[START_REF] Garine | Effervescence patrimoniale au Sud : entre nature et société 1[END_REF] . Varieties bred by research whose seeds have been certified (i.e,Thialack 2) introduced into a community can be requalified of peasant or even traditional (i.e,Thialack, Tiossan) by farmers if it has adapted well in the locality. As a result, certified seeds saved on-farm by farmers are regarded as peasant seeds for some of them.

Time Thialack 2 Thialack 2 Thialack Tiossan

Pearl millet seed supply seems to be shaped by his certified or peasant origin, both in modalities and networks mobilized by farmers 5 .

Nonetheless, after the harvest, certified and peasant seed are commingled and embedded into an open and complex social network 5 . V. Acknowledgements I. Background n West Africa, government policies has placed particular emphasis on strengthening the seed sector to enhance agricultural productivity, food security and rural well-being of 33 million smallholder farming households. Thus, they support quality-improved seed certified by national seed agencies and released it through private sector such as seed cooperative 1 . However, in small-scale farming societies, farmers usually produce their seed on their own farm (range between 58-99%) [START_REF] Leclerc | Diversity[END_REF] . Among the sources of supply, farmer-to-farmer seed circulation is the major channel [START_REF] Leclerc | Diversity[END_REF][START_REF] Coomes | Food Policy 4[END_REF] . Once inserted, certified seed evolves among peasant seed, outcomes from ancestral crop populations maintained by farmers.

IV. Conclusion

The aim of this study is to characterize farmer seed supply according to the certified or peasant origin of seed and to highlight coexistence modalities of seed supply.

Analyzing coexistence modalities of seed supply between certified and peasant seed through farmer seed networks is a key asset for the development of an innovative governance of plant genetic resources [START_REF] Coomes | Food Policy 4[END_REF] .

I

Data collection: we investigated pearl millet (Pennisetum glaucum (L.) R.Br.) seed circulation networks, which is a major cereal for food security and scarred by a strong sociocultural anchorage. Data were collected in Koungheul Department (Senegal) from an ethnographic fieldwork carried out between march and june 2018 in three muslim villages. A sociometric survey using a snowball-sampling technique was employed with 79 farmers.

II. Methods

(Coopérative Rurale pour le Développement Concerté de Koungheul) database, a cooperative specialized in certified seed production. After asking which pearl millet varieties they grow, farmers were asked for any seed lot sown between 2010 and 2017 1) from whom did they received it to know if it was a certified and / or peasant seed lot, and 2) to whom did they gave a seed lot of their harvest.

Data analysis: pearl millet seed supply was represented using network formalism. Farmer seed networks were splitted according to the certified or peasant origin of the seed and biclustering (stochastic block model (SBM)) were performed to group structurally equivalent nodes 4 . Results from the network representation and the bi-clustering are interpreted and discussed in light of qualitative data.

Label found in certified seed bags. Its and official proof which assures to farmers the high quality of the seeds (purity, germination, etc.) Keur Samba women preparing pearl millet for the Tiéré (couscous in Wolof). Tiéré is an ancestral dish, consumed every morning and evening by the smallholder farming household.

The reasons for the spread of pearl millet (n=538). Circles are proportional to the spread percentages of exchanges

Our results provide a better understanding of farmer seed networks. This study highlights a gap between agricultural policies and local seed management by farmers, results that could feed into the reflection on the governance of plant genetic resources.

  Doncieux A. a,b,d,e , Jankowski F. c,d,f , Gaudin A. a,d & Barnaud A. b,d,e a AgroParisTech, Montpellier ; b IRD, UMR DIADE, Montpellier, France ; c CIRAD, UPR GREEN, Montpellier, France ; d Université de Montpellier, France ; e ISRA, LNRPV, Dakar, Sénégal ; f ISRA, BAME, Dakar, Sénégal Peasant (A) and certified (B) seed acquisition networks. Actors are nodes and edges represent seed flows. Networks are directed, i.e, each directed link corresponds to at least one acquisition event from a seed provider to a seed recipient according to interviewed's declaration. Interviewed farmers are circles, triangles are seed cooperative (one node for each village-based structure). The colors of the nodes represent SBM's result. The size of the node is proportional to the number of the connection between the nodes. The histograms represent the percentage of seed acquisition events (n=229) according to C.1) localisation ; C.2) nature and C.3) social ties between transacting partners.

  all, 229 seed acquisition events were recorded. Seed, whether certified or peasant origin, shapes farmer seed networks (Fig A and B) and modalities of acquisition (Fig C 1:3) are significantly different 5 . On-farm production rates vary according to the certified (36%) or peasant (86%) origin of seed. Certified seed acquisition is also poorly connected (Fig, B ; d=0.026). The SBM distinguishes farmers (in green and beige) from the cooperative (in blue), which provides mainly (90%) certified seed. They are purchased (85%) outside the village (77%) and involves a customer relationship (66%) which means that seed's provider is an unknown person. Farmer-to-farmer seed circulation are anecdotal. Certified seeds are socially isolated due to risk taking (purchase -> indebtedness) and seed cooperative's working methodology. Peasant seed acquisition network is extremely poorly connected (Fig A ; d=0.008). With only one group of nodes, the SBM does not distinguish farmers based on their seed access behavior probably due to the low connectedness of the network. Peasant seeds are obtained within the village (78%), by a nonpurchased way (90% ; i.e, inheritence, gifting) under the tutelage of kinship (68%) from an individual to another (88%).

  Certified and peasant seeds: a coexistence life circuit coming from the harvest. Adapted from Almekinders and Louwaars (1999) Certified seed Peasant seed CoEX project is supported by Agropolis Fondation under the reference 1603-002 through the "Investissements d'avenir" programme (Labex Agro: ANR-10-LABX-0001-01). Support of the ongoing research collaboration through the MIRES network (an interdisciplinary research group developing statistical methods to analyze seed networks) was provided by the Institut National de la Recherche Agronomique (INRA). The authors would like to express their gratitude to the participating farmers and the COORDEC's staff for their collaboration in our study.


domain: chim phys

text:
Radu Tanasa

Cristian Enachescu
email: cristian.enachescu@uaic.ro

Jérôme Laisney

Denis Morineau
email: denis.morineau@univ-rennes1.fr

Alexandru Stancu

Marie-Laure Boillot
email: marie-laure.boillot@u-psud.fr

Unraveling the Environment Influence in Bistable Spin-Crossover Particles Using Magnetometric and Calorimetric First-Order Reverse Curves

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

First-order reversal curves (FORC) method became recently a powerful tool for the characterization of hysteretic behavior in a broad range of materials, starting with magnetic materials [START_REF] Pike | Characterizing Interactions in Fine Magnetic Particle Systems Using First Order Reversal Curves[END_REF] and continuing with ferroelectric 2 or geological samples [START_REF] Pike | First-Order Reversal Curve Diagrams and Thermal Relaxation Effects in Magnetic Particles[END_REF] . For more than a decade, FORC method has been applied for understanding the properties of spin-crossover compounds [START_REF] Enachescu | Forc Method Applied to the Thermal Hysteresis of Spin Transition Solids: First Approach of Static and Kinetic Properties[END_REF][START_REF] Tanasa | First-Order Reversal Curve Analysis of Spin-Transition Thermal Hysteresis in Terms of Physical-Parameter Distributions and Their Correlations[END_REF][START_REF] Enachescu | First-Order Reversal Curves Analysis of Rate-Dependent Hysteresis: The Example of Light-Induced Thermal Hysteresis in a Spin-Crossover Solid[END_REF][START_REF] Rotaru | Pressure Effect Investigated with First-Order Reversal-Curve Method on the Spin-Transition Compounds [Fe x Zn 1-x (btr) 2 (NCS) 2 H 2 O (x = 0.6,1)[END_REF] as well. Spin-crossover (SC) compounds [START_REF] Halcrow | Spin-Crossover Materials -Properties and Applications[END_REF][START_REF] Gütlich | Spin Crossover in Transition Metal Compounds Springer[END_REF] are inorganic molecular compounds, having a d 4 -d [START_REF] Rotaru | Pressure Effect Investigated with First-Order Reversal-Curve Method on the Spin-Transition Compounds [Fe x Zn 1-x (btr) 2 (NCS) 2 H 2 O (x = 0.6,1)[END_REF] transition metal as central ion and situated in an octahedral ligand field. Due to classical thermodynamic reasons [START_REF] Nicolazzi | Thermodynamical Aspects of the Spin Crossover Phenomenon[END_REF] , they can switch between two states, a high spin (HS) state -stable at high temperature and a low spin (LS) state, stable at lower temperature. The two states have different magnetic, optical, mechanical and volume properties making them suitable for applications. [START_REF] Boukheddaden | Quantitative Contact Pressure Sensor Based on Spin Crossover Mechanism for Civil Security Applications[END_REF][START_REF] Létard | Towards Spin Crossover Applications[END_REF][START_REF] Ohkoshi | Light-Induced Spin-Crossover Magnet[END_REF] In the case of strong elastic interactions between spin-crossover units, the transition is accompanied by a thermal hysteresis loop. Though different as origin, the spincrossover thermal hysteresis presents some common features with the hysteresis of magnetic materials, which allowed their study using methods initially developed for ferromagnetism, such as the theoretical Preisach model [START_REF] Enachescu | Static and Light Induced Hysteresis in Spin-Crossover Compounds:Experimental Data and Application of Preisach-Type Models[END_REF] which is the starting point of the experimental FORC technique [START_REF] Enachescu | Forc Method Applied to the Thermal Hysteresis of Spin Transition Solids: First Approach of Static and Kinetic Properties[END_REF][START_REF] Tanasa | First-Order Reversal Curve Analysis of Spin-Transition Thermal Hysteresis in Terms of Physical-Parameter Distributions and Their Correlations[END_REF] . One of these common features is the existence of spin-like domains, which has been proven for spin-crossover complexes in X-Ray Diffraction 15 and Raman spectroscopy [START_REF] Molnár | The Spin-Crossover Phenomenon in the Solid State: Do Domains Play a Role? A Micro-Raman Study[END_REF] or optical microscopy [START_REF] Bonnet | Influence of Sample Preparation, Temperature, Light, and Pressure on the Two-Step Spin Crossover Mononuclear Compound [Fe(Bapbpy)(NCS)[END_REF][START_REF] Sy | Spatiotemporal Investigations on Light-Driven High-Spin-Low-Spin Interface Dynamics in the Thermal Hysteresis Region of a Spin-Crossover Single Crystal[END_REF] experiments. Initial studies using the FORC method on spin-crossover complexes targeted the thermal hysteresis and they successfully described the spin-like domain properties in terms of physical parameters, such as the coercivity (intra-and inter-domain interactions) or bias (energy gap) [START_REF] Tanasa | First-Order Reversal Curve Analysis of Spin-Transition Thermal Hysteresis in Terms of Physical-Parameter Distributions and Their Correlations[END_REF] . Further analysis implied specific cases of kinetic light-induced thermal hysteresis [START_REF] Enachescu | First-Order Reversal Curves Analysis of Rate-Dependent Hysteresis: The Example of Light-Induced Thermal Hysteresis in a Spin-Crossover Solid[END_REF] , systems with dopants [START_REF] Tanasa | Study of Impurities Effect in Spin Crossover Compounds Using First Order Reversal Curves (FORC) Method[END_REF] or pressure hysteresis [START_REF] Rotaru | Pressure Effect Investigated with First-Order Reversal-Curve Method on the Spin-Transition Compounds [Fe x Zn 1-x (btr) 2 (NCS) 2 H 2 O (x = 0.6,1)[END_REF] , while a method to disentangle between kinetic and static components has been proposed as well. [START_REF] Stan | Kinetic Effects on Double Hysteresis in Spin Crossover Molecular Magnets Analyzed with First Order Reversal Curve Diagram Technique[END_REF] The main advantage of the FORC method is that it can be applied directly to experimental data like a characterization tool.

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The behavior of spin-crossover nano-and microparticles showed several differences compared to bulk compounds. Thus, spin-crossover nanoparticles thermal transition is more gradual, shifted towards lower temperature and sometimes incomplete, while the hysteresis loop has a smaller width, vanishes [START_REF] Volatron | Spin-Crossover Coordination Nanoparticles[END_REF] or even may reappear [START_REF] Félix | Enhanced Cooperative Interactions at the Nanoscale in Spin-Crossover Materials with a First-Order Phase Transition[END_REF][START_REF] Raza | Matrix-Dependent Cooperativity in Spin Crossover Fe(Pyrazine)Pt(Cn)4 Nanoparticles[END_REF] in case of a few nanometer size objects. Thus, FORC method was more difficult to apply and the number of studies remains still quite low. Still, the study of nanoparticles present some interesting features, for instance an important reversible component in the hysteretic behavior [START_REF] Rotaru | Size Effect in Spin-Crossover Systems Investigated by Forc Measurements, for Surfacted [Fe(NH 2 -Trz) 3 ](Br) 2 •3H 2 O Nanoparticles: Reversible Contributions and Critical Size[END_REF] , that could be assigned to an anhysteretic effect associated to over-critical size particles as in the case of polycrystalline samples.

Spin crossover nano-or microparticles were generally used as coated with stabilizers or dispersed in various media (surfactants, polymers, glass-forming matrices). The presence of such environment dramatically changes the overall properties of the nanoparticles system. [START_REF] Raza | Matrix-Dependent Cooperativity in Spin Crossover Fe(Pyrazine)Pt(Cn)4 Nanoparticles[END_REF][START_REF] Stoleriu | Thermal Hysteresis in Spin-Crossover Compounds Studied within the Mechanoelastic Model and Its Potential Application to Nanoparticles[END_REF] This initial observation triggered a number of both experimental [START_REF] Mikolasek | Finite-Size Effects on the Lattice Dynamics in Spin Crossover Nanomaterials. I. Nuclear Inelastic Scattering Investigation[END_REF] and theoretical studies [START_REF] Felix | Tuning the Spin Crossover in Nano-Objects: From Hollow to Core-Shell Particles[END_REF][START_REF] Oubouchou | Magnetoelastic Modeling of Core-Shell Spin-Crossover Nanocomposites[END_REF][START_REF] Atitoaie | Study of Spin Crossover Nanoparticles Thermal Hysteresis Using FORC Diagrams on an Ising-Like Model[END_REF] , to figure out the effect of matrix/particle interactions. Moreover an unexpected widening of hysteresis loop have been detected in the case of microparticles embedded in various matrices, which was described as an effect of SC particles-matrix interactions. [START_REF] Tissot | Control of the Thermal Hysteresis of the Prototypal Spin-Transition Fe ii (Phen)2(Ncs)2 Compound Via the Microcrystallites Environment: Experiments and Mechanoelastic Model[END_REF] Experimental reversal curves showed no evidence for a cooperative process but a huge and surprising reversibility, explained as a cut-off / switch on of interactions, determined by the spin dependent particle volume and by the state of the surrounding matrix. [START_REF] Tanasa | Hysteretic Behavior of Fe(Phen)(2)(Ncs)(2) Spin-Transition Microparticles Vs. The Environment: A Huge Reversible Component Resolved by First Order Reversal Curves[END_REF][START_REF] Enachescu | Matrix-Assisted Relaxation in Fe(Phen) (2) (NCS) (2) Spin-Crossover Microparticles, Experimental and Theoretical Investigations[END_REF] Therefore, there is a need for more advanced experimental techniques to probe efficiently the changes in the switch behavior of the particles while interacting with the matrix. The FORC technique appears to be the most appropriate, as it is a powerful sensitive detector of intra-and inter-particles interactions changes. [START_REF] Tanasa | First-Order Reversal Curve Analysis of Spin-Transition Thermal Hysteresis in Terms of Physical-Parameter Distributions and Their Correlations[END_REF] Here we use the FORC method to perform an in-depth study of hysteretic behavior of spin crossover Fe(II) microparticles dispersed in matrices, focusing on the notable deviations from the bulk materials. In addition to standard magnetometry technique showing the unexpected strong effects of matrix/particle interactions, we introduce here a complementary experimental technique based on calorimetric measurements. This technique enables to probe the change of state of both particles and matrix separately

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The Journal of Physical Chemistry and therefore to better disentangle the behavior inherent to the embedding matrices and that of the spin-crossover microparticles. The paper is organized as follows: first we present magnetic and calorimetric studies of the thermal transition of spin-crossover microparticles embedded in glass-forming (or semi-crystalline) matrices -nujol, eicosan and glycerol-, then we present FORCs and FORC distributions in both magnetometric and calorimetric measurements. Methods and results are then discussed.

EXPERIMENTAL SECTION a) Magnetic study of the thermal transition vs. the matrix nature Microparticles of Fe(phen) 2 (NCS) 2 have been synthesized according to a procedure described in Ref. [START_REF] Laisney | Nanocrystals of Fe(Phen)2(NCS)2 and the Size-Dependent Spin-Crossover Characteristics[END_REF] Different characterizations including TEM, IR, Magnetic and XRD measurements confirmed the formation of pure crystalline 1.6(0.4)x1.6(0.4)x0.35(0.15) m 3 particles of the spin-transition compound (see SI for TEM images and powder X-Ray diagrams). The powder was then dispersed [START_REF] Tissot | Control of the Thermal Hysteresis of the Prototypal Spin-Transition Fe ii (Phen)2(Ncs)2 Compound Via the Microcrystallites Environment: Experiments and Mechanoelastic Model[END_REF] in eicosan, nujol or glycerol with a percentage of 2% (magnetism), 49 % (or 4 %, calorimetry) spin active compound with respect to the dispersant. The solidification of eicosan leads to semi-crystalline domains at T m = 310 K as proved by X-ray diffraction. Nujol, a glass-forming oil (T g = 200 K), shows a partial recrystallization between 205 and 270 K [START_REF] Fishman | Conformational Mobility of Small Molecules in Glass-Forming Solutions Studied by Ftir Spectroscopy[END_REF] , while the glass-transition temperature of glycerol is T g ~185-192 K. [START_REF] Chelli | Glycerol Condensed Phases Part I. A Molecular Dynamics Study[END_REF] The magnetic data have been obtained using a SQUID magnetometer (Quantum Design) at a constant magnetic field (5000 Oe), providing a susceptibility signal used to infer the high-spin fraction (denoted here as HS n ), which is the ratio of molecules in the HS state over the total number of molecules. The temperature sweeping rate was 0.3 K•min -1 ; several sweeping rates were considered and no dependence on this parameter was detected.

In Fig. 1, we present thermal transition curves for Fe(phen) 2 (NCS) 2 as powder and as microparticles dispersed in glycerol (main figure), and eicosan and nujol (inset).

While the polycrystalline powder of Fe(phen) 2 (NCS) 2 (see SI for a TEM image) shows a first-order spin-transition with a 2 K hysteresis loop centered around 176 K, microcrystals of Fe(phen) 2 (NCS) 2 dispersed in the selected matrices present a wider hysteresis loop, with a progressive HS-to-LS transition curve shifted toward smaller temperatures values and a LS-to-HS transition curve closely following the one obtained

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The Journal of Physical Chemistry with polycrystalline powder in absence of any dispersing medium. In addition, in the case of particles dispersed in glycerol, two different hysteresis loops can be obtained depending on the previous thermal treatment of the ensemble, respectively if the composite was heated up to 190 or 250 K after the first cooling down. In order to determine the exact nature of the phase formed by the glycerol matrix and to better understand the effect of the thermal treatment on the shape of the hysteresis loop, we have performed Differential Scanning Calorimetry (DSC) experiments, which shall be presented in the next section.

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The Journal of Physical Chemistry Besides magnetic measurements, calorimetric measurements were intensively used to quantitatively evaluate the spin-crossover features [36][37][START_REF] Sorai | Calorimetric Investigation of Phase Transitions Occurring in Molecule-Based Magnets[END_REF][START_REF] Castro | Pulsed-Laser Switching in the Bistability Domain of a Cooperative Spin Crossover Compound: A Critical Study through Calorimetry[END_REF] . Even the idea of spin-like domains mentioned above was initially formulated in the pioneering years of spincrossover phenomenon studies by Sorai and Seki while looking at the heat anomaly during first-order spin transition. 40 This kind of measurement was used to determine relevant thermodynamical parameters, such as the enthalpy or the entropy changes accompanying the thermal transition. We briefly acknowledge that DSC measures the heat flow associated to the speed of progress of the spin transition, rather than the instantaneous fraction of transformed spins measured by magnetometric methods. It is sensitive to the phase transformations of both the microparticules (spin transition) and the embedding matrix (crystallization, melting, glass transition). This is obviously not the case for magnetometry and reflectometry measurements of spin-crossover compounds. [START_REF] Rotaru | Pressure Effect Investigated with First-Order Reversal-Curve Method on the Spin-Transition Compounds [Fe x Zn 1-x (btr) 2 (NCS) 2 H 2 O (x = 0.6,1)[END_REF] Therefore, DSC method is especially suited to study composite systems. Applying various thermal cycling techniques and more elaborate thermal treatments, one can prepare the matrix in well-defined state (liquid, solid, glass) and assess its impact on the microparticles spin-transition. The calorimetric measurements were performed on a TA Instrument Q20 DSC equipped with a liquid-nitrogen cooling system. Three different samples were prepared and loaded in sealed aluminum pans: pure glycerol (m = 6.37 mg), free Fe(phen) 2 (NCS) 2 microparticles (m = 3.3 mg) -both considered as reference systemsand a composite material formed by mixing Fe(phen) 2 (NCS) 2 microparticles (m = 20.8 mg) with glycerol (m = 21.5 mg). The high mass ratio that was chosen for calibration reasons also allowed us to check the preservation of the experimental observations corresponding to 4 wt. %. By convention, the thermograms are presented with the endothermic heat flow up. The heat flow was normalized with respect to the mass of Fe(phen) 2 (NCS) 2 for both the free microparticles and the microparticles embedded in glycerol (so here equivalent to the mass of glycerol), while for pure glycerol, it was normalized to the mass of glycerol. Two different scanning rates were applied (10 K•min -1 and 0.5 K•min -1 ) as specified in the text.

In Fig. 2, we present the thermograms of these three systems acquired during heating at a constant rate (10 K•min -1 ) from 110 to 270 K after an initial cooling down from 273

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to 110 K at the same rate (not shown). For ensuring a better signal over noise response, we used here a percentage of 49% of powder of microparticles with respect to glycerol after checking the qualitative reproducibility of the phenomenon under investigation (49 -4% percentage). The thermogram of glycerol exhibits a jump of the heat capacity (C p = 0.85 J•g -1 •K -1 ) at the glass temperature T g = 194 K (T onset = 192.3 K), immediately followed by a small overshoot (see arrow), which is associated to enthalpic relaxation effects around Tg. Glycerol is a prototypical glass-forming system, and the crystallization could be easily avoided under these thermal conditions, as shown in Fig. 3. The thermal behavior and the measured values are in agreement with the literature for pure glycerol. [START_REF] Zheng | Confinement Effects on the Glass Transition of Hydrogen Bonded Liquids[END_REF] The thermogram of free Fe(phen) 2 (NCS) 2 microparticles exhibits a prominent endothermic peak (see arrow) (T max = 180.5 K, H = 11 J•g -1 = 5.9 kJ•mol -1 ) that corresponds to the LS-HS transition. During cooling, a very similar exothermic peak was observed at a nearby position, giving T 1/2 = 178.5 K for the temperature of the center of the hysteresis loop. This is in agreement with the first-order and highly cooperative character of spin-transition discussed in the previous part concerning the magnetic property. The measured H and T 1/2 parameters are fully consistent with those reported in the literature in case of the structurally characterized Fe(phen) 2 (NCS) 2 materials in the so-called form II. [START_REF] Roux | Pressure-Induced Spin-State Crossovers in Six-Coordinate Fe(II)L(N)L'(M)(NCS) (2) Complexes with L=L' and L Not Equal L': A XANES Investigation[END_REF] T (K) DSC measurements, we can be infer that the matrix and the SC particles are strongly coupled.

In the following, we shall explain the differences in thermal transition observed for glycerol environment after heating up to 190 or 250 K. The different states of glycerol are sketched in Fig. 3, where the enthalpy is plotted over the temperature. While glycerol is solely liquid above the melting point (T m = 291 K), it can exist in different forms at lower temperature. Below T m , the equilibrium phase is crystalline, but glycerol can be usually supercooled in its metastable liquid state. On further cooling, the In Fig. 4, we present the hysteresis loops recorded by DSC for two different cycling conditions. The sample was firstly cooled down from 250 to 100 K (dashed line, noted (a) in Fig. 3) and later cycled between 100 and 190 K (solid lines, noted (b) in Fig. 3). A temperature rate of 0.5 K•min -1 was applied to facilitate comparison with the magnetic measurements percentage. The first cooling branch shows sharp lines (spikes) that dampen and disappear in the subsequent thermograms as long as the system is cycled in the range 100-190 K, but they appear again during the first cooling if the system is This behavior is in line with the magnetic measurements shown in Fig. 1, which also indicated a clear variation of the cooling branch depending on the value of the upper temperature. The origin of this behavior can be hypothesized from a recent DSC study on glass-forming molecular systems. [START_REF] Willart | The Role of Cracks in the Crystal Nucleation Process of Amorphous Griseofulvin[END_REF] Similar thermal spikes due to a discontinuity of the thermal contact arising from the motion of seals aluminium pans were observed during cooling of glassy materials. They were attributed to the formation of cracks in the glassy phase well below T g . Cracks arise from the sudden mechanical release of stresses that develop during deep quenches. As such, they usually appear 50 K or more below the glass-transition temperature. In S.I. we exemplify the broad peak by focusing only on the cooling branch.

In the present study, the spikes appear only a few degrees below the glass transition of glycerol. Under these mild conditions of supercooling, the glycerol matrix unexpectedly developed a significant amount of residual mechanical stresses. We rather infer that during the first cooling, the large volume contraction of the particles associated to the spin transition could not be sustained by the embedding frozen amorphous solid. The spikes associated to some degree of cracking of the matrix, and thus new free volumes, which behaves similar to a rectangular hysteresis loop, denoted as hysteron in the Preisach formalism [START_REF] Mayergoyz | Mathematical Models of Hysteresis[END_REF] (see inset of Fig. 5). The collection of the hysterons forms the socalled Preisach distribution that, in magnetism, offers the statistical distribution either of the switching fields or of the coercivities and the interactions fields of hysterons. [START_REF] Tanasa | First-Order Reversal Curve Analysis of Spin-Transition Thermal Hysteresis in Terms of Physical-Parameter Distributions and Their Correlations[END_REF][START_REF] Enachescu | Static and Light Induced Hysteresis in Spin-Crossover Compounds:Experimental Data and Application of Preisach-Type Models[END_REF] Indeed, the width of the thermal hysteron represents the coercivity, related to intradomain cooperative interactions, while its shift relative to the average transition temperature depends on inter-domain interactions.

is
The FORC distribution is defined as the second mixed derivative of these curves: for heating and cooling modes, respectively.

  2 , ( , )       HS R R R n T T T T T
The distribution of the switching temperatures is statistically stable in the case of noninteracting domains, which makes the FORC distributions to be similar, to the so-called Preisach distributions [START_REF] Stancu | Micromagnetic and Preisach Analysis of the First Order Reversal Curves (FORC) Diagram[END_REF] . Consequently, the FORC distributions in the cooling and heating modes are expected to be the same, as is the case for the pure powder of the spin crossover compound [Fe(btr) 2 (NCS) 2 ].H 2 O, whose typical FORC distributions are indicated in Fig. 6. For an easier comparison, we have represented the heating distribution in the classical Preisach half plane (below T R =T axis) and we have translated the cooling distribution in the half-plane situated above the T R =T axis. We notice then that the warming and cooling mode distributions tend to exhibit the expected mirror symmetry with respect to the T R =T axis. This symmetry can be related to the existence of only intra-domain interactions (a domain can be understood here as an entire particle).

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In addition, we notice that the slope of reversal curves depends on the individual reversal temperature. In the cooling mode, the FORCs are superimposable with the major hysteresis loop up to an unusually high value of HS n , approaching 0.4. For higher HS n values, they direct inside the hysteresis loop, but still remain far from a zero degree slope. In a similar manner, the curves in the heating mode are very close to the major hysteresis branch for a high value of HS n , but start to enter into the hysteresis for smaller HS n .

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The Journal of Physical Chemistry The analysis of the FORC distributions (Fig. 7b-8b-9b-10b) reveals other interesting features. As previously, we represent here the distribution in the two half planes of the Preisach plane, separated by the T R = T line, with the heating distribution below and the cooling distribution above this axis. The long shape of the main peaks is consistent with the progressive widening of the hysteresis loop and could be also connected with possible avalanche-type switchings. [START_REF] Sy | Spatiotemporal Investigations on Light-Driven High-Spin-Low-Spin Interface Dynamics in the Thermal Hysteresis Region of a Spin-Crossover Single Crystal[END_REF][START_REF] Stoleriu | Thermal Hysteresis in Spin-Crossover Compounds Studied within the Mechanoelastic Model and Its Potential Application to Nanoparticles[END_REF] Regarding the different FORC distributions obtained for glycerol when cycling up to 190 and 250 K (Figs. 9, 10 b), they indicate that the saturation should not be considered only as the situation of a fully HS/ LS structure, but also in connection with the environment characteristics (liquid or solid nature, phase stabilization). The differences observed in case of nujol and eicosan, two paraffinic species, are also instructive. Nujol becomes glassy while eicosan remains in a stable crystalline state. Accordingly, the changes in their FORC distributions can be assigned to the differences in the microparticles-matrix interactions as pointed above and thus to the elastic stability characteristics of the two solidified matrices. [START_REF] Nguyen | Fe(Me 2 -bpy) 2 (NCSe) 2 Spin-Crossover Micro-and Nanoparticles Showing Spin-State Switching above 250 K New[END_REF] Another striking observation is the lack of the mirror symmetry in Figs. 7-10, in opposition to the model bulk case where FORC distributions obtained in the heating and cooling modes are rather similar (as shown in Fig. 6). This confirms first the effect of variable interactions between the microparticles and the matrix (as here they replace the classical interdomain interactions). Moreover it also shows that the processes at the two major hysteresis loop branches are different, which confirms the assumption previously made, when discussing only the major hysteresis cycle regarding a cut on /switch off mechanism, which implies the existence of elastic forces between the spin crossover microparticles and the surrounding matrix. Actually, in this case the physical representation of spin-like domains is different from the single-crystal picture, as every spin-crossover microparticle should be regarded as an independent single-domain particle. As stated in the introduction, the volume of individual spin-crossover molecules and consequently the whole microparticle volume diminish during the HS-to-LS transition. Then, the microparticle-matrix interactions vary when the HS-to-LS transition proceeds, due to the change of the spin-crossover microparticles volume, if the matrix is not elastic enough to follow this change. The variation of the matrix-microparticle interactions depends not only on the matrix elasticity and plasticity features, but also on the microparticles size: larger the size, the larger is the absolute variation during the transition and the variation of the distance between microparticle and matrix (see Fig. 11). This determines a variable distribution of interactions during HS-LS transition.

Finally, if the microparticle volume after the HS-LS transition is too small, the distance between its surface and the matrix is so large that these interactions are suppressed and the microparticle does not feel anymore the influence of matrix. However, we expect that some small microparticles, whose absolute size variation is considerably reduced, still keep, at least partially, their connections to the matrix (see Fig. 11 for a schematic representation). We should notice that the inter-domain interaction distribution, as previously defined for spin-crossover compounds is replaced here with particle-matrix interaction. Therefore, while the HS-LS transition corresponds to a particle interacting with the surrounding matrix, the LS-HS transition is closer to that of an open boundary particle.

In the discussion above, we did not considered the presence of interactions between particles mediated by the matrix [START_REF] Raza | Matrix-Dependent Cooperativity in Spin Crossover Fe(Pyrazine)Pt(Cn)4 Nanoparticles[END_REF][START_REF] Stoleriu | Elastic Model for Spin Crossover Nanoparticles in Matrices Proc[END_REF] , as in this case their possible effects are dampened by the particle-matrix interactions. As shown above, the hysteresis obtained for microparticles embedded in matrices is non-cooperative and therefore of a different nature than the cooperative hysteresis of the bulk. Consequently, it is not determined by the interactions mediated by the matrix (which should act similar to a bulk compound where the spin-active molecules interact each other by elastic strains. Here we find out new features elsewhere assigned to the formation of cracks of a glassy matrix (DSC signals) [START_REF] Willart | The Role of Cracks in the Crystal Nucleation Process of Amorphous Griseofulvin[END_REF] under the effect of internal shearing forces (solidification of pressuretransmitting oils) [START_REF] Yokogawa | Solidification of High-Pressure Medium Daphne 7373[END_REF] that are fully relevant with respect to this mechanism because of the change of volume of SC particles.

Another interesting point is the presence of a negative region on the FORC distributions in the cooling mode FORCs , which can be noticed for all matrices.

Generally speaking, negative regions in FORCs distributions were attributed to the change in susceptibility variation between successive curves. Here the susceptibility is

given by the number of microparticles multiplied by their size. According to discussions in previous paragraph, the larger microparticles are the first for which the interactions with the matrix are cut during HS-LS transitions. Consequently, in this case a change in susceptibility variation is possible, as a smaller number of large spin crossover microparticles can count more than a larger number of average size spin crossover microparticles. We have to strengthen that the origin of this negative distribution is different from the negative distributions observed for rate dependent light induced thermal hysteresis in spin crossover compounds [START_REF] Enachescu | First-Order Reversal Curves Analysis of Rate-Dependent Hysteresis: The Example of Light-Induced Thermal Hysteresis in a Spin-Crossover Solid[END_REF] or in the case of potential-driven hysteresis in model electrochemical systems [START_REF] Abou Hamad | New Cyclic Voltammetry Method for Examining Phase Transitions: Simulated Results[END_REF] where it is due to the evolution of the system toward the stable state, even after the direction of change of the control parameter has changed. In order to control the nature of the embedding matrix, two different thermal treatments were applied prior to the DSC-like FORCs experiments. In the first case, the sample was cooled down from 300 to 190 K and then cycled once between 100 and 190 K, in order to prepare glycerol as a glassy matrix with relaxed elastic interactions (no residual spikes as shown in Fig. 4) with the Fe(phen) 2 (NCS) 2 microparticles. The subsequent FORCs were measured for a glassy or very viscous liquid matrix (denoted as case (b) in Fig. 3). In a second case, the sample was cooled down to 100 K and heated up to 270 K. This thermal treatment, which combines a deep quench in the glass and a thermalization in the slightly supercooled liquid promotes the nucleation and the growth of the crystalline phase. The subsequent FORCs were measured for a crystalline matrix (denoted as case (c) in Fig. 3). It can be noted here that the behavior observed upon the first cooling of the composite formed with the glassy or the crystalline matrix is qualitatively unchanged.

The corresponding experimental FORCs measured while heating and that starts from the cooling branch are shown in Fig. 12. The heat flow in Fig. 12a The recording of calorimetric FORCs as heat capacity profiles opened the possibility to represent FORC distributions for calorimetric data. However, there is an important difference compared to the standard method for obtaining FORC distribution: as the heat capacity already corresponds to the first derivative of the HS n with the temperature, only a single derivative is necessary in order to obtain the FORC distributions. The concept of using of a single derivative to get the FORC diagram was theoretically mentioned, however without practical implementation, more than a decade ago, in a study concerning the voltammetric current in electrochemical FORC method [START_REF] Abou Hamad | New Cyclic Voltammetry Method for Examining Phase Transitions: Simulated Results[END_REF] . One has to strengthen that the specificity of this experiment is the quite large temperature step between two consecutive reversal temperatures, due to the necessity to measure all curves in the same conditions and to the time limitations of the experimental device; in the same time the temperature step for a given value of the reversal temperature should be small to obtain smooth curves (representing the first derivative of HS n , as we have explained before). In Fig. 12, we present FORC distributions in the heating mode obtained using calorimetric data for Fe(phen) 2 (NCS) 2 spin crossover microparticles embedded in glassy (when cooling down from 190 K) and crystalline (when cooling down from 270 K) glycerol compounds. Even not so preeminent, the maxima of the distributions are situated at the same value as obtained from the magnetometry curves.

The high/sharp peaks along T R =T line (which are here more clear than in magnetometric FORC discussed previously) are due to the reversible part of the curves.

In the case of the crystalline matrix, a kink is visible for the distribution around 180 K, sign of a different interaction between the spin-crossover particle and the matrix. A complete study of the peculiarities of the FORC technique obtained using the calorimetry experiment will be realized in a further study.

Figure 1

 1 Figure 1 Major hysteresis loop (MHL) for Fe(phen) 2 (NCS) 2 as polycrystalline powder

Figure 2

 2 Figure 2 DSC thermograms recorded on heating after a first cooling down from 273 to

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 70 Paragon Plus EnvironmentThe Journal of Physical Chemistry viscosity of the supercooled liquid is too high to fulfill equilibrium, so that it is eventually stuck into an out-of-equilibrium amorphous solid (glass transition T g = 192 K).

Figure 3

 3 Figure 3 Schematic representation of glycerol stable and metastable phases. The

Figure 4

 4 Figure 4 DSC thermograms of Fe(phen) 2 (NCS) 2 microparticles embedded in glycerol

  indicative of an irreversible change in the microparticles-matrix interactions which necessarily impacts the spin crossover process as previously proposed (cutting-off of elastic interactions). It also introduces extra environment distribution and possible residual stress. The influence of non-relaxed particle-matrix interactions could explain the higher depression of the HS-LS transition along the major hysteresis loop (MHL) cooling branch (see exothermic broad peak in the range 140-150 K for the very first curve starting from a thermally quenched glassy state). The initial state of the composite (giving rise to elastic interactions and mechanical stresses) is recovered when the matrix is allowed to relax in the non-viscous liquid phase at a temperature well above T g (approximately 250 K). These observations support the concepts of cut off/switch on of particles-matrix interactions when cycling through the glass transition of matrices, which were introduced recently in a mean-field model.[START_REF] Tanasa | Hysteretic Behavior of Fe(Phen)(2)(Ncs)(2) Spin-Transition Microparticles Vs. The Environment: A Huge Reversible Component Resolved by First Order Reversal Curves[END_REF] Page 21 of 70 ACS Paragon Plus Environment The Journal of Physical Chemistry c) FORC ANALYSIS OF THE THERMAL HYSTERESIS In order to in-depth analyze the particle-matrix interactions, we have measured firstorder reversal curves for microparticles embedded in glycerol, and for comparison purpose in eicosan and nujol. The FORCs are a specific class of minor hysteresis loops, for which the sweep of the input parameter, temperature here, is reversed once from one of the branches of the major hysteresis loop. For a hysteretic cooperative spin transition, the warming/cooling types of FORC experiments should be distinguished, according to the sign of the thermal variations. The measurements start at a sufficiently high/low temperature, such that the high/low temperature (HS/LS) domain structure is saturated. Then, temperature is lowered/raised until a given temperature * / R R T T , the reversal temperature, and afterwards raised/lowered till reaching full HS/LS structures, in the heating/cooling mode respectively, as illustrated in Fig. 5 for the spin-crossover compound [Fe 0.6 Zn 0.4 (btr) 2 (NCS) 2 ].H 2 O. Typically, the experiment is repeated for several values of n T T values forms the FORC data ( T being the Page 22 of 70 ACS Paragon Plus Environment The Journal of Physical Chemistry temperature at which the HS n is measured for R T , ( * R T ) reversal temperature in the cooling (heating ) branch). The possibility to generate various states within the major hysteresis loop has been previously explained by the existence of the spin-like domains,

Figure 5 Figure 6

 56 Figure 5 Examples of FORCs in warming and cooling modes; inset: typical hysteron

Figure 7 Figure 8

 78 Figure 7 FORCs for Fe(phen) 2 (NCS) 2 microparticles embedded in eicosan. (a) Main

Figure 9 (Figure 10 (

 910 Figure 9 (a) FORCs for Fe(phen) 2 (NCS) 2 microparticles embedded in glycerol for

Figure 11

 11 Figure 11 Schematic representation of particle-matrix interactions during HS-LS

  cumulates the enthalpy LS-HS transition and the heat capacity jump of glass-liquid transition of glycerol, while in Fig.12bit accounts only for the enthalpy of LS-HS transition, glycerol being crystallized.

Figure 12 First

 12 Figure 12First Order Reversal Curves DSC thermograms in the heating mode for

Figure 12

 12 Figure 12 Calorimetric FORC distributions for compound embedded in glassy (a, up)

Figure 10 (

 10 Figure 10 (a) FORCs for Fe(phen)2(NCS)2 microparticles embedded in glycerol for warming mode when cycling up to 190 K (main figure) (b) Corresponding FORC distributions. The temperature scan rate was 0.3 K•min-1.359x480mm (300 x 300 DPI)

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Points to be considered should refer to the matrix transformations with respect to the spin crossover and its combination with size reduction and to the investigation of the effects of light irradiation. The present study can be extended to phase transition in composite [START_REF] Chen | A Facile Route for Preparation of Monodisperse Nanoparticles of One-Dimensional Fe(II)-4-Amino-1,2,4-Triazole Coordination Polymers with Hysteretic Spin-Crossover near Room Temperature[END_REF][START_REF] Bartual-Murgui | Critical Assessment of the Nature and Properties of Fe(II) Triazole-Based Spin-Crossover Nanoparticles[END_REF] and role of moistening in porous materials like silica or chitosan. [START_REF] Voisin | Preserving the Spin Transition Properties of Iron-Triazole Coordination Polymers within Silica-Based Nanocomposites[END_REF]