Maxime Le Goff

Yves Gallet

Nicolas Warmé

Agnès Genevey

An updated archeomagnetic directional variation curve for France over the past two millennia, following 25 years of additional data acquisition

, constitute the French directional database (698 data in all). All but two of these data were obtained using the experimental protocol developed by E. Thellier based on the analysis of large samples and on a magnetic viscosity test that has proved its reliability on numerous occasions. The directions from the entire French database have been precisely defined, with 95% of the α 95 values being less than 1.9°, and ~50% being less than 0.8°. The selection of 286 data with dating

uncertainties of ≤50 years allowed us to compute a new reference directional variation curve for France since the first century BC using sliding windows, the variable durations and shifts of which were adapted to the time distribution of the available data, and the bivariate extension of the Fisher statistics. This shows ample and smooth variations, fairly similar to those previously determined from a much smaller database. The resulting secular variation curve is particularly well suited for use in archeomagnetic dating.

Introduction

Archeomagnetism has developed considerably over the last 20 years. Numerous studies have led to a better understanding of the temporal variations of the geomagnetic field in different parts of the world, although these data still mainly concern the European area (e.g. [START_REF] Schnepp | Archaeomagnetic secular variation in Germany during the past 2500 years[END_REF][START_REF] Gómez-Paccard | The first secular variation curve for the Iberian peninsula. Comparison with other data from Western Europe and with geomagnetic global field models[END_REF][START_REF] Martón | Hierarchical versus stratification statistical analysis of archaeomagnetic directions: the secular variation curve for Hungary[END_REF][START_REF] Tema | Archeomagnetism in Italy: a compilation of data including new results and a preliminary Italian secular variation curve[END_REF][START_REF] Batt | Advances in archaeomagnetic dating in Britain: New data, new approaches and a new calibration curve[END_REF][START_REF] Molina-Cardín | Updated Iberian Archeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF][START_REF] Shaar | The first catalog of archaeomagnetic directions from Israel with 4,000 years of geomagnetic secular variations[END_REF][START_REF] Schnepp | New archaeomagnetic secular variation data from Central Europe. I: Directions[END_REF]. For metropolitan France, in particular, the last two decades have been marked by significant progress in the knowledge of directional variations during the first millennium BC (e.g. [START_REF] Gallet | Three millennia of directional variation of the Earth's magnetic field in western Europe as revealed by archeological artifacts[END_REF]Hervé et al., 2013a) and intensity variations over the past ~3000 years (e.g. [START_REF] Chauvin | Paleointensity of the geomagnetic field recovered on archaeomagnetic sites from France[END_REF][START_REF] Genevey | Intensity of the geomagnetic field in western Europe over the past 2000 years: New data from ancient French pottery[END_REF][START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archeointensity French data[END_REF]2013;2016;Hervé et al., 2013b). In addition to the construction of regional secular variation curves, the densification of the archeomagnetic database (e.g. Korte et al., 2005;[START_REF] Genevey | ArcheoInt: An upgraded compilation of geomagnetic field intensity data for the past ten millennia and its application to the recovery of the past dipole moment[END_REF][START_REF] Brown | GEOMAGIA50.v3: 1. general structure and modifications to the archeological and volcanic database[END_REF] has made it possible to construct global geomagnetic field models that encompass the last few millennia (e.g. Hongre et al., 1988;Korte and Constable, 2005;[START_REF] Hurard | Saint-Pathus (Seine-et-Marne), Les Petits Ormes : longue durée d'occupation du Néolithique à l'époque moderne : mutations d'un habitat rural du Bas-Empire à la fin du premier Moyen Âge[END_REF]Nilsson et al., 2010;[START_REF] Licht | Ensembles of low degree archeomagnetic field models for the past three millennia[END_REF][START_REF] Pavón-Carrasco | A geomagnetic field model for the Holocene based on archeomagnetic and lava flow data[END_REF][START_REF] Constable | Persistent high paleosecular variation activity in southern hemisphere for at least 10000 years[END_REF][START_REF] Sanchez | Modelling the archaeomagnetic field under spatial constraints from dynamo simulations: A resolution analysis[END_REF][START_REF] Hellio | Time-correlation-based regression of the geomagnetic field from archeological and sediment records[END_REF][START_REF] Arneitz | A Bayesian iterative geomagnetic model with universal data input: Self-consistent spherical harmonic evolution for the geomagnetic field over the last 4000 years[END_REF]. All these studies have thus allowed a better characterization of the variability of the geomagnetic field on time scales ranging from a few decades to several millennia. Another reason for the recent spurt of development in archeomagnetism is its ability to provide original dating constraints for archeologically poorly-dated structures (e.g. Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF][START_REF] Pavón-Carrasco | A matlab tool for archeomagnetic dating[END_REF][START_REF] Rouzeau | New constraints on the metallurgical activity at the Morimond Abbey (Haute-Marne) from the archeomagnetic analysis of two excavated brick fireplaces[END_REF][START_REF] Tema | The importance of multidisciplinary dating in rescue excavations: The case of Santhià, Northern Italy[END_REF][START_REF] Schnepp | New archaeomagnetic secular variation data from Central Europe. I: Directions[END_REF] , as well as for a better understanding of the history of volcanoes (e.g. [START_REF] Tanguy | Mount Etna eruptions of the last 2,750 years: revised chronology and location through archeomagnetic and 226 Ra-230 Th dating[END_REF]2009;[START_REF] Hurard | Saint-Pathus (Seine-et-Marne), Les Petits Ormes : longue durée d'occupation du Néolithique à l'époque moderne : mutations d'un habitat rural du Bas-Empire à la fin du premier Moyen Âge[END_REF]. Whether applied to geomagnetic or archeological themes, however, archeomagnetism requires constant improvement in the accuracy and reliability of regional secular variation curves.

First of all, it should be noted that this study focused only on archeo-directional data.

Research in archeomagnetism began in France in the 1930s with the pioneering work of Emile Thellier [START_REF] Thellier | Sur l'aimantation des terres cuites et ses applications géophysiques[END_REF]. Combining instrumental and methodological developments, data acquisition, and the patient establishment of collaborations with archeologists, Thellier's activity led to the construction of the first directional (archeo)secular variation curve for France covering the last two millennia (Thellier, 1981). After Thellier's retirement, Ileana Bucur continued this work, enriching the French archeomagnetic database with ~200 directional data, of which the 120 best dated were used to construct a revised version of the French directional variation curve from the first century BC to 1600 [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF]. Furthermore, I. Bucur has quite often used archeomagnetism as a dating tool, which she has applied to provide dating constraints for archeological burnt structures discovered in situ and poorly dated, and which has enabled her to strengthen her collaborations with archeologists. Since Bucur's retirement (1997), the acquisition of archeomagnetic directional data has continued at the historical archeomagnetism laboratory of Saint-Maur (part of the Institut de Physique du Globe de Paris). The purpose of this paper is to present an update of the Saint-Maur French archeomagnetic dataset, and of the associated reference directional secular variation (DSV) curve covering the last two millennia.

To carry out his archeomagnetic studies, Emile Thellier developed a methodology for the sampling and magnetization analysis that differed significantly from that currently used in paleomagnetism (e.g. Thellier, 1981). Like Ileana Bucur, we have continued to use Thellier's protocol, which was specifically adapted to the nature of the material sampled and the behavior of its magnetization. Practically all other archeomagnetic studies outside our research group are based on different paleomagnetic criteria (e.g., relying on magnetization measurements carried out on small samples and demagnetization experiments). This clearly poses a problem for the classification of the quality of the available archeomagnetic data.

Despite the fact that the French dataset was compiled quite a long time ago [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF], the associated archeomagnetic directional variation curve has often been used as a reference for comparison with other archeomagnetic data. On the other hand, however, the individual archeomagnetic data (i.e., those obtained at the burnt structure level) are viewed with caution and classed as the lowest quality (e.g. [START_REF] Tarling | The global archaeomagnetic database[END_REF][START_REF] Brown | GEOMAGIA50.v3: 1. general structure and modifications to the archeological and volcanic database[END_REF]. For this reason, here, we recall Thellier's experimental protocol and show its perfect adequacy for the detailed recovery of past variations in the geomagnetic field of Western Europe.

An additional 25 years of archeomagnetic sampling

We report new data obtained from 528 burnt structures from different archeological sites, giving a total of 698 directional results when including the 170 data from the Thellier-Bucur database strictly reduced to represent the territory of metropolitan France only (Fig. 1).

The data mainly come from around Paris, in the Ile-de-France region. This uneven geographic site distribution is explained by the fact that one of us (N. Warmé) is an archeologist working at the Ile-de-France center of the Institut National de Recherches Archéologiques Préventives (INRAP). Several archeological sites were intensively sampled for archeomagnetism, such as the localities of Saint-Pathus with its 58 different kilns, and Villiers-le-Sec and Léry, with 35 burnt structures each (Fig. 1; archeological references in Table S1 andText S1). A few other structures were sampled in eastern France (e.g. archeological sites of Wiwerschein (6 structures), Avenay (3), Dizy (3) and Laudrefang (3)) and in southeastern France (e.g.

Montpellier (6), Orgon (1)).

Of the new data, 327 are from domestic kilns. The remaining results come from pottery kilns (77), kilns for tile and brick production (26), lime kilns (17) and others (one bell founding, two drying sheds, hypocaust but also 15 cases of undetermined use). The domestic kilns, which thus represent a little less than two-thirds of the new collection, were mainly found in ancient rural settlements dating back to the High Middle Ages.

All baked clay structures were sampled using the plaster cap method described in Thellier (1967a;1981), [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] and Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF]. This method consists first of isolating several large blocks of baked clay of various sizes from the best preserved and heated parts of the floor of the structure (Fig. 2a). As a very general rule, sampling only the floor of a kiln minimizes the risk of possible distortion in the distribution of magnetic directions that could be produced by wall tilting during burial or excavation. These blocks are then coated with plaster strips to preserve their cohesion (Fig. 2a,b), a practice we have adopted since the early 1990s. On top of each block, depending on its size, one or several plaster caps are molded with a large (~10-cm-diameter) horizontal upper surface (Fig. 2b).

The directions of the local magnetic north and of the sun at a given time are both precisely reported on these horizontal surfaces, the latter orientation providing the direction of the geographic north with a typical accuracy of ±1° (Fig. 2c,d). Note that not all the samples collected could be oriented with respect to the Sun due to adverse weather conditions. Thus, for ~1/3 of the analyzed structures, the local declination was given by the IGRF model at the time and location of sampling. The consolidated and oriented blocks are then removed from the structure and transported to the laboratory. There, the large blocks are cut into separate samples, each with its own plaster cap and, thus, its independent orientation. The oriented samples are finally adjusted and plastered in standard 12-cm-sided molds (Fig. 2e).

Magnetization measurements and experimental protocol

The remanent magnetization of the standard 12-cm-sided samples was measured using a rotating inductometer, especially designed to accomodate their large size (Fig. 2f; e.g. Thellier, 1967b;[START_REF] Goff | Inductomètre à rotation rapide continue pour la mesure des faibles aimantations rémanentes et induites en magnétisme des roches[END_REF]. The sizes of the instrument, the samples and the storage volume required by the number of samples make it impossible to perform the measurements in a zero-field chamber. The entire analytical procedure is performed in the laboratory field, where viscous remanent magnetization (VRM) may interfere with the thermoremanent magnetization (TRM) being sought (Thellier, 1981). We therefore perpetuated Thellier's protocol, in which a viscosity test, involving two magnetization measurements, is performed for each sample. The samples are first left for a minimum of four weeks precisely oriented in the direction of the laboratory field, i.e. in the same magnetic position as the samples had when in situ. This position is referred to as the direct position. After this time interval, the sample magnetization is considered to have 'restored' the (initial) viscous magnetisation acquired since the last cooling of the kiln, which was disturbed by the sampling and laboratory preparation. A first measurement is obtained: M dir . The samples are then left again for ~four weeks, but situated in the opposite direction to the laboratory field (referred to as the 'reverse position'). Now, an opposite four-week VRM is acquired, replacing the four-week direct VRM and part of the initial VRM. A second measurement is taken: M rev . From these two sets of measurements, it is straightforward to determine by vectorial addition and subtraction for each sample both the moment and direction of the TRM (with a small fraction of the initial VRM), here referred to as the TRM Th to underline the fact that it stems from Thellier's method, and the VRM acquired in four weeks. Moreover, a viscosity index (v), expressed as a percentage, is computed from the ratio of the VRM to TRM. Because VRM acquisition follows a logarithmic temporal law (e.g. [START_REF] Dunlop | Rock magnetism, Fundamental and Frontiers[END_REF], the VRM acquired in four weeks represents a very significant fraction of the initial VRM, and Thellier's protocol strongly reduces its parasitic effect on the directional TRM results. A more accurate positioning of the samples relative to the magnetic north in the laboratory for both the direct and reverse steps of the viscous experiments allowed us to increase the rejection viscosity threshold up to 10-12%.

Several examples of VRM and TRM determinations are shown on the Declination-Inclination graphs in Fig. 3. These cases, from six different structures, make it clear that the VRM directions (black symbols in Fig. 3) are very similar to the present-day geomagnetic field direction (yellow circle), while the mean TRM directions (red symbols) form clusters which differ significantly from each other due to the different ages of the structures ranging from the High Middle Ages period to the modern period.

The viscosity test used proved to be very effective in isolating the primary TRM direction and attesting to its stability (e.g. [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF]. This is the case because we only studied short-lived structures, which were abandoned and rapidly buried after their last use, which strongly limits the possibility of secondary magnetization acquisition (except VRM) due, for instance, to partial re-firing. It is worth pointing out that the magnetic viscosity experiments were used here as a 'cleaning' method, similarly to the thermal or alternatingfield demagnetization treatments used in paleomagnetism to analyze the often complex magnetic behavior of much older rocks, or in archeomagnetism on volcanics, in which lightning is a frequent cause of the acquisition of parasitic isothermal remanent magnetization (IRM; e.g. [START_REF] Tanguy | Archeomagnetism of Piton de la Fournaise: Bearing on volcanic activity at La Réunion Island and geomagnetic secular variation in Southern Indian Ocean[END_REF]. In this respect, the directions obtained for the VRM-cleaned TRM clearly cannot be considered simply equivalent to the directions of natural remanent magnetization (NRM). between data from the same archeological site (at Saint-Gilles-du-Gard in southern France), assumed to be of the same age, but obtained after sampling carried out at 35-year intervals (1972/2007), subjected to Thellier's protocol (1972) and the classical paleomagnetic method including thermal demagnetization and TRM anisotropy correction (P. Lanos and J. Thiriot, personnal communication 2011). The two series of three data give mean directions (after transfer to Paris's coordinates, Thellier: Dec.=11.4°, Inc.=56.2°, K=1037 with N sample =18 and α 95 =1.0°; Lanos-Thiriot: Dec=12.4°, Inc=57.1°, K=519 with N sample =50 and α 95 =0.9°) that are identical at the 95%-confidence level (γ=1.1°, γ c =1.6°; [START_REF] Mcfadden | Classification of the reversal test in palaeomagnetism[END_REF], which further testifies to the effectiveness of Thellier's approach.

It is also important to mention the possible effects of magnetic anisotropy. Magnetic anisotropy disturbs the recording fidelity of the geomagnetic direction in two ways: by mechanical action during the manufacture of bricks or tiles (structural or fabric anisotropy) or by the magnetization of the kiln itself (anisotropy of the demagnetizing field also referred to as magnetic refraction; e.g. [START_REF] Aitken | Archaeomagnetism: evidence for magnetic refraction in kiln structures[END_REF]Thellier, 1981;[START_REF] Lanos | The effects of demagnetizing fields on thermoremanent magnetization acquired by parallel-sided baked clay blocks[END_REF]. The first is mainly because, before firing, the clay has been stretched for moulding, while the second is due to the rather thin and elongated dimensions of the magnetized clay layers.

We practically always avoided collecting samples from bricks or tiles found in the kilns. The latter, although (re)-fired during kiln use, could still carry a certain fraction of the primary magnetization they acquired during their manufacture. More importantly, it should be noted that a large proportion of our new results come from domestic kilns dug directly into the ground, in which the original silt was left in place without any moulding. On a single occasion, samples were taken from two brick fireplaces excavated at the Morimond Abbey [START_REF] Rouzeau | New constraints on the metallurgical activity at the Morimond Abbey (Haute-Marne) from the archeomagnetic analysis of two excavated brick fireplaces[END_REF]. In both cases, small samples were carefully prepared and oriented from the bricks, fully thermally demagnetized (with the recovery of two partial-TRM magnetization components) and corrected for TRM anisotropy. Otherwise, we only analyzed samples in which the magnetization is generally considered to be structurally highly isotropic using Thellier's protocol (e.g. [START_REF] Evans | Archaeomagnetic results from southern Italy and their bearing on geomagnetic secular variation[END_REF][START_REF] Kovacheva | Remanence anisotropy effect on the palaeointensity results obtained from various archaeological materials, excluding pottery[END_REF].

On the hand, the effect of the demagnetizing field is very difficult to evaluate and, above all, it cannot be corrected experimentally (unless an equivalent firing of a similar structure/surface, made of the same natural clay, is performed and the resulting samples are collected from the very same zones). This effect depends on the nature and grain size of the magnetic mineralogy and the intensity of the magnetizations (the higher the intensity, the greater the effect), which vary from kiln to kiln. If present in a kiln, the demagnetizing field effect can only be attenuated by taking numerous samples from the entire kiln structure (e.g. Thellier, 1981;[START_REF] Schurr | Archaeomagnetic study of medieval fireplaces at mannheim-Waldstadt and ovens from Herrenchiemsee (southern Germany) and the problem of magnetic refraction[END_REF][START_REF] Soffel | Magnetic refraction studied on two experimental kilns[END_REF]. We mainly sampled the bottom of the kilns; it therefore cannot be excluded that our archeomagnetic directions (and the resulting curve presented below) are slightly biased in inclination (e.g. [START_REF] Schurr | Archaeomagnetic study of medieval fireplaces at mannheim-Waldstadt and ovens from Herrenchiemsee (southern Germany) and the problem of magnetic refraction[END_REF]; however, it should also be noted that the magnetization in the kilns studied was generally on the order of 0.1-1.0 A/m, which is less prone to significant magnetic refraction (e.g. [START_REF] Kovacheva | Remanence anisotropy effect on the palaeointensity results obtained from various archaeological materials, excluding pottery[END_REF].

Description of the new archeo-directional results

Approximately two-thirds of the new archeomagnetic data were obtained for archeomagnetic dating purposes, as the structures concerned had substantial archeological dating intervals (>100-400 years), On the other hand, the results from 140 burnt structures were dated using archeological constraints, in particular from the typo-morphology of ceramics, coins and archives, with sufficient precision and accuracy to be used to improve the French reference directional secular variation curve for the past two millennia (archeological references in Table S1 and Text S1, and see below). All data obtained from dated and poorlydated or undated burnt structures are reported in Table S1 in Electronic Supplement, including those from the [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] database, with a few updates due either to subsequent improvements in the dating of the kilns studied or to the dissociation of some datasets that had been grouped together in the original publication (Table 1 in [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF].

Most of the structure-averaged viscosity index values for these data are between 6% and 8%, with a mean viscosity of ~6.0% (Fig. 5a), and with a typical range of ~2% at the sample level per structure. The mean is higher than that of [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF]'s original database (v mean =3.3%). This difference is due to the much greater number of data obtained from domestic kilns that were added to that database: the viscosity values from 81 artisan (pottery, tile, lime) kilns are among the 100 lowest viscosity indices (v mean =2.6%), whereas the viscosity values from 89 domestic kilns are among the 100 highest values (v mean =9.4%). This probably reflects higher temperatures being reached in artisan kilns. It should be noted that the magenta bars in Fig. 5a show the number of results referred to as abnormal values and rejected by [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF], to which six new data were added. Each of these six data deviates significantly from the age-corresponding segment of the mean DSV curve that we calculated (see below), with a minimum angular distance to the curve of ~6°, up to ~10°. These are the largest angular distances, whereas most of them (i.e. for ~94% of the database) are <3°. The mean TRM directions are particularly well defined, with large Fisher precision parameters (averaging 4253) and small α 95 (averaging ~0.9°). In 95% of the cases, the α 95 values are less than 1.8°, with ~50% being less than ~0.8°(Fig. 5b). Twelve structures provided very small α 95 values of less than 0.4° (minimum of 0.24°) and Fisher parameters up to 32335 (Table S1). Nevertheless, it should be borne in mind that such a high degree of precision is not necessarily a guarantee of data reliability with respect to the geomagnetic field at the given time. It should also be mentioned that, excluding the rare α 95 values >2°, there is no clear systematic relationship between the α 95 values and the associated numbers of samples (Fig. S1a), which means that the small α 95 values are not only the result of a statistical accumulation of data by structure, but they also attest to the quality of the mean direction determinations.

Figure 6 shows the changes in the temporal distribution of the data between the Thellier-Bucur database (Fig. 6a), the new data (Fig. 6b) and the combination of the two datasets retaining only those data (286 values) with dating uncertainties of ≤50 years (Fig. 6c). Although the results from the Thellier-Bucur's database cover all periods from the last two millennia, these are unevenly distributed in time, being concentrated maintly during the Roman period and the Middle Ages after ~900 AD (Fig. 6a). The results from other periods were much rarer, especially from between ~400 and ~900 AD. On the other hand, the age distribution of the new data is strongly biased in favor of the High Middle Ages (with 383 new data from between ~500 and ~1000 AD compared to the previous 47), but unfortunately often with significant age uncertainties (Fig. 6b; see also Fig. S1b and Fig. S2a,b showing the inclinations of all available data, respectively). The age distribution of all the data with dating uncertainties of ≤50 years, however, is quite homogeneous, although there is still less data for the 5th and 15th centuries, and practically no data for after 1700 (Fig. 6c; see also Fig. S3).

The available archeomagnetic directions are illustrated on spherical projections in Fig. 7. All 698 mean directions are shown in Fig. 7a with a color code depending on the α 95 values, and with a change in color signifying a change in the circled areas by a factor of 3, where white<0.5°≤yellow<0.9°≤brown<1.5°≤green<2.6°≤blue. The data with the smallest α 95 values are visibly distributed close to each other and appear to show a preferential path, although no age constraints are provided at this stage. This preferential path is reinforced when a color code is used to specify the dating of the data (but without any further trend calculation). Here, each α 95 circle is colored according to its central date, with a gradation corresponding to its date range. In Fig. 7b,c, the data have been separated into two time intervals, between 100 BC and 1000 AD (Fig7b) and between 1000 AD and 1900 AD (Fig. 7c), in order to avoid confusion resulting from crossing directions around an inclination of ~70° and a declination of ~0°. In particular, this distinction makes a preferred path after 1000 AD more evident (Fig. 7c). On the other hand, the representation chosen in Figs. 7a,b,c suggests that selection of the best-dated data (with dating uncertainties of ≤50 years) did not significantly change the above-mentioned observations (Fig. 7d,e,f), but rather seems to tighten the preferential path (for instance compare Fig. 7b and Fig. 7e; see section 5.1 for further discussion).

It is also interesting to separately illustrate several archeomagnetic datasets obtained from different archeological sites, where a fairly large amount of data had been obtained from each of them. Fig. 8 highlights such a situation for three different archeological sites. It can be seen that each dataset describes a certain segment of secular variation marked by a coherent pattern of directions, mainly with variations in inclination for the Saint-Pathus data (Fig. 8a; [START_REF] Desrayaud | Saint-Pathus (Seine-et-Marne), Le Bois de l'Homme Mort : établissements ruraux antiques et petit temple gallo-romain (fanum) du « Bois de l'Homme Mort » : milieu II e s[END_REF][START_REF] Hurard | Saint-Pathus (Seine-et-Marne), Les Petits Ormes : longue durée d'occupation du Néolithique à l'époque moderne : mutations d'un habitat rural du Bas-Empire à la fin du premier Moyen Âge[END_REF], in declination for the Villiers-le-Sec data (Fig. 8b; [START_REF] Gentili | Villiers-le-Sec (Val d'Oise), La Place de la Ville, document final de synthèse. Afan, Saint-Ouen[END_REF] and in both declination and inclination for the Evreux data (Fig. 8c; [START_REF] Jego | Un « lotissement » gaulois sous le green… Evreux (Eure). Inrap[END_REF]. Independently of their exact dating, these different datasets therefore provide a test of consistency at the archeological-site level for the construction and robustness of the French secular variation curve. The interest in archeology is no less important as a large dataset allows analysis of the occupation phases of an archeological site (duration of the total occupation, discontinuities in occupation, etc.). Although beyond the scope of this study, it should be noted that this aspect of archeomagnetism, based on dense sampling, has generated much interest and effort within our group over the past 25 years.

Discussion

On the need to select the best-dated results

Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF] recently illustrated the limitations of the resolution of a regional mean DSV curve resulting from the accuracy of the archeomagnetic data used to construct the curve. This precision relates to both the accuracy of the directions (as expressed by their α 95 values) and the uncertainties about their dating. The latter uncertainties clearly play a major role in undermining the resolution (see also discussion in [START_REF] Tarling | Archaeomagnetism: An error assessment of fired material observations in the British directional database[END_REF]. To recover all the variability of geomagnetic directions expected for the latitudes of metropolitan France, as can be deduced from the gufm1 model [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF][START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF], the archeomagnetic data would require, on average, a dating accuracy of ~10 years, which is far beyond any reality (and any hope) given the archeological constraints very generally applicable to the structures studied. The abundance of data, from incorporating a large number of data with large age uncertainties, does not make it possible to alleviate this difficulty (there is rather a risk of accentuating it), making it preferable to retain only the bestdated results. It is this selective approach that we choose, retaining only the data with dating uncertainties of ≤50 years.

To further illustrate this point and to complement the information provided by Fig. 7, Fig. 9 shows the available data for two time intervals, between central dates of 450 and 750 AD (Merovingian period; Fig. 9a,b) and between 1000 and 1300 AD (Middle Age; Fig. 9c,d), with and without data with dating uncertainties of >50 years (Fig. 9a resp. Fig. 9b; Fig. 9c resp. Fig. 9d). As in Fig. 7, the α 95 areas were colored according to the date of the data, with a color scale adjusted to their dating uncertainties. It is remarkable how data selection reduces the elongation of the distribution of directions. From Fig. 9a,b, it is obvious that some of the less well dated directions are posterior to the Merovingian period, most probably being dated to the posterior Carolingian period spanning between 751 and the end of the 10th century (which, it should be noted, is not incompatible with the archeological constraints considered).

A similar situation is observed for the results dated between 1000 and 1300 AD (Fig. 9c,d), with some directions being probably either too old or too young in relation to the time segment considered when the dating uncertainties are too large.

Thus, thanks to the data selection performed, we can approach a reference DSV curve with a better resolution; however, it should be borne in mind that the latter remains insufficient for tracing details of the rapid directional variations, on the scale of a century or two, that may have occurred in France over the past few millennia (Le Goff and Gallet, 2019).

Method for a revised French DSV curve

We used the same method developed by Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] to revise the DSV curve.

There are two important and useful aspects to this method. The first aspect is that it involves sliding windows, with durations and time shifts that could be adjusted to accommodate the variable distribution of the data over time. Taking into account the mean dates and dating uncertainties of the individual archeomagnetic data, this amounts to adapting the temporal resolution of the DSV curve, i.e. without considering a uniform regularization, to give an objective view of the current knowledge of temporal variations. The second aspect is that the directions are treated vectorially, in a way very close to that which led to the determination of the different directions themselves (i.e., by using Fisher's statistics). The bivariate calculation takes into account the angular variances of all individual results (as given by their Fisher's K parameters), which means that the higher the dispersion, the larger the α 95 value for the window-mean direction. The 95%-confidence ellipses then contain relevant information both on the dispersion of the data for a certain time window and on the geomagnetic field evolution during this same time interval. It should also be noted that the method of Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] was designed to use the reference DSV curve for archeomagnetic dating purposes. For this reason, it preserves as much as possible a good statistical consistency between the archeomagnetic directions defining the reference curve and any individual direction needing to be dated.

In the method of Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF], the duration of each time window is set according to a statistical weight that is a function of the number of data points present in the window and the proportion of time each data point spends in the window relative to its dating interval. When the DSV curve is calculated, the size of each window is increased from a minimum of 20 years (with a maximum of 110 years) until its statistical weight (i.e., the density of the data) reaches a required minimum value, which, in our study, was chosen as 8 (the same value was considered by Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF]. It should be noted that the minimum statistical weight was 2.5 when a set of 110 directions from the Thellier-Bucur database was used by Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] to calculate the previous French DSV curve between 0 and ~1600. On the other hand, the time shift between two consecutive windows is such that the beginning of the younger window is the central date of the older window. The offset between the central dates of the two windows may then increase with the time extension of the most recent window (i.e., in order to reach the minimum statistical weight).

A more detailed description of the method can be found in Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF].

For each time window, a mean archeomagnetic direction is calculated, after weighting the individual data, using the bivariate extension of Fisher's statistics (Le [START_REF] Goff | Lissage et limites d'incertitude des courbes de migration polaire: pondération des données et extension bivariante de la statistique de Fisher[END_REF][START_REF] Goff | Practical method for drawing a VGP path[END_REF]. In this calculation, unless a bias is introduced by one or a few deviating directions present in a window, the elongation of each 95%-confidence ellipse provides information on the direction and speed of the geomagnetic field drift through the duration of the time window in question.

Description and comparison of the revised French DSV curve with the previous curve

Sixty-four successive time windows were isolated between 100 BC and 1700 AD. Fig 10a shows that they all have approximately the same statistical weight, mainly between 8 and 10, and that their mean duration is ~ 60 years. The resulting DSV curve is displayed on a spherical projection in Fig. 10b (red-white line with the 95%-confidence ellipses in transparent grey; Table S2), together with the individual data used for this calculation (see color code in the figure). The time evolutions of the mean declinations and inclinations, with their 95%-confidence error bands, are also shown in Fig. S3. Schematically, the average curve can be described as follows: a first segment from the first century BC to the 6th century marked by a back and forth evolution of the inclinations (while the declinations remain fairly constant), a second segment marked by a broad, counterclockwise semicircle between ~800 and ~1350 AD, and a third segment between ~1400 and ~1700 AD, in which the directions describe about one third of a clockwise circle, with a curvature similar to that of the previous segment. Note that between ~1700 and ~2000 AD, it is well known that the geomagnetic directions described a tighter clockwise semicircle (double line in pale green, Fig. 10b and details in Table S4; [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF][START_REF] Goff | A reappraisal of instrumental magnetic measurements made in Western Europe before AD 1750: confronting historical geomagnetism and archaeomagnetism[END_REF].

Over the two last millennia, three periods are marked by a clear change in the direction of geomagnetic drift: ~150-350 AD, ~600-800 AD and ~1350-1400 AD. These changes were probably rapid, but the accuracy of the dating of the data remains insufficient (despite the selection criterion) for precisely defining the exact nature of these transitions. Apart from these transitions, the evolution of the mean archeomagnetic directions appears to be very regular, with only two slight inflections towards the 13th century and the middle of the 16th century. Here again, the limited accuracy of the dating of the available archeomagnetic data does not allow us to further discuss the origin of these inflections (Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF].

Finally, the 15th century seems to be marked by the most rapid directional variations, which are underlined by a very strong elongation of the 95%-confidence ellipse of the mean direction, with 1450 AD as the central date. Without challenging this observation, it should however be noted that this is the longest window duration (Fig. 10a) because data for the 15th century are still scarce (Fig. 6).

Figure 11 shows a comparison between the new DSV curve and the previous ones obtained by [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] using sliding windows of fixed duration (80 years) and by [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] using the same database but with sliding windows of various durations. (Note that in the latter study, the confidence ellipses were drawn by considering the weighted number of samples instead of the weighted number of archeomagnetic data available at the structure level, as used in Fig. 10b). Unsurprisingly, the curves are similar, and exactly the same patterns of variation can be observed. Overall, the new curve tends to smooth the rapid fluctuations that previously occurred from one window to the other. In addition, notable differences with now smaller inclinations highlight the period between ~600 and ~850 AD.

Paradoxically, however, it is difficult to know whether these differences correspond to a real improvement in our knowledge of the detailed directional variations, or whether this smoother evolution is rather the result of an increase in the number of data with levels of dating accuracy that are arguably insufficient to trace all the expected variability in the geomagnetic field (Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF]. Nevertheless, whichever option is chosen, the new DSV curve is more robust from a statistical point of view than the old one.

Comparison of the revised French DSV curve with other Western European curves

The new French DSV curve is compared in Fig. 12 with other regional curves established in neighbouring countries, namely Germany [START_REF] Schnepp | Archaeomagnetic secular variation in Germany during the past 2500 years[END_REF], the UK [START_REF] Batt | Advances in archaeomagnetic dating in Britain: New data, new approaches and a new calibration curve[END_REF] and Iberia [START_REF] Molina-Cardín | Updated Iberian Archeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF]. The latter curves are based on databases that cover most of the last two millennia with only a weak influence of the French database (i.e. that of [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF]. In Fig. 12, these curves are presented as calculated by their authors, as it was not our objective to discuss the different techniques used to calculate them (see discussion in [START_REF] Schnepp | Archaeomagnetic secular variation in Germany during the past 2500 years[END_REF][START_REF] Lanos | Hierarchical modelling of archaeomagnetic data and curve estimation by moving average technique[END_REF][START_REF] Lodge | Towards a new approach to archaeomagnetic dating in Europe using geomagnetic field modelling[END_REF][START_REF] Batt | Advances in archaeomagnetic dating in Britain: New data, new approaches and a new calibration curve[END_REF][START_REF] Molina-Cardín | Updated Iberian Archeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF]. Each curve is assumed to reproduce as closely as possible the regional directional variations and it is considered that no particular method of curve calculation can introduce erroneous segments of secular variation. The differences observed in Fig. 12 are therefore due to a potentially different geomagnetic field behavior between the regions considered and/or to differences in the temporal resolution between the different curves, given the different databases and the techniques used for their construction.

Overall, the curves show basically the same patterns of directional variations (Fig. 12). This is not surprising if we refer, for instance, to the historical period for which the direct directional measurements made in France and England over more than three centuries are exactly the same after a correction for latitude (e.g. [START_REF] Alexandrescu | High-resolution secular variation of the geomagnetic field in western Europe over the last 4 centuries: comparison and integration of historical data from Paris and London[END_REF]; see also Le [START_REF] Goff | A reappraisal of instrumental magnetic measurements made in Western Europe before AD 1750: confronting historical geomagnetism and archaeomagnetism[END_REF]. One can also consider the volcanic archeomagnetic data from Vesuvius and Etna (southern Italy) obtained by [START_REF] Tanguy | Archeomagnetic dating of Mediterranean volcanics of the last 2100 years: validity and limits[END_REF][START_REF] Tanguy | Mount Etna eruptions of the last 2,750 years: revised chronology and location through archeomagnetic and 226 Ra-230 Th dating[END_REF]2009), which show the same secular variation pattern as the French DSV. Reasonably, and in accordance with regional (e.g. [START_REF] Pavón-Carrasco | A regional archeomagnetic model for Europe for the last 3000 years, SCHA.DIF.3K: Applications to archeomagnetic dating[END_REF]) and global (e.g. [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF][START_REF] Licht | Ensembles of low degree archeomagnetic field models for the past three millennia[END_REF][START_REF] Nilsson | Reconstructing Holocene geomagnetic field variation: new methods, models and implications[END_REF][START_REF] Arneitz | A Bayesian iterative geomagnetic model with universal data input: Self-consistent spherical harmonic evolution for the geomagnetic field over the last 4000 years[END_REF] geomagnetic field reconstructions, the secular variation has likely remained fairly homogeneous on the Western European spatial scale over the last two millenia.

The differences observed should therefore primarily depend on the different characteristics of the databases (i.e., the number, accuracy and temporal distribution of the data; see also discussion in Le [START_REF] Goff | On the resolution of regional archaeomagnetism: untangling directional geomagnetic oscillations and data uncertainties using the French archaeomagnetic database for dates between AD 1000 and 1500 as a guide[END_REF]. From the corresponding databases, we extracted the 110 (Germany), 759 (UK) and 99 (Iberia) individual directional data (right-hand panels in Fig. 12). On average, the data from these three regions are more scattered than the French data, both at the individual data level (with higher α 95 values) and collectively, at the level of all the data (compare with Fig. 10b). The uncertainties, shown as confidence circles, associated with the mean DSV curves are probably too optimistic, which is a recurrent problem in archeomagnetic field reconstructions (see for instance discussion in Korte et al., 2005;[START_REF] Korte | Improving geomagnetic field reconstructions for 0-3 ka[END_REF]; however, this is particularly critical for the UK curve (Fig. 12c,d). While all the other curves are only based on the corresponding regional database alone, the UK DSV curve is the result of an inversion of the global (worldwide) database, incorporating a significant overweighting of the data from the UK. However, there is a rather paradoxical situation pertaining to the UK curve marked by the absence of mean directions with high inclinations during the period from the ~5th to the ~8th centuries, which are, on the contrary, clearly included in the French and German DSV curves (Fig. 12e,f) and, to a lesser extent, in the Iberian curve (Fig. 12a,b). This seems to be mainly due to the paucity of archeomagnetic data in the UK during this specific time interval (see Fig. 5b in [START_REF] Batt | Advances in archaeomagnetic dating in Britain: New data, new approaches and a new calibration curve[END_REF], as well as their scatter, and this problem is not alleviated by the data available in neighbouring regions, contrary to what the method used by [START_REF] Batt | Advances in archaeomagnetic dating in Britain: New data, new approaches and a new calibration curve[END_REF] might suggest.

The most critical aspect is that the low number of UK data from this period does not result in a significant (expected) increase in the uncertainties associated with the mean directions, which are therefore much too optimistic. In this respect, the angular uncertainties associated with the German DSV curve seem more realistic (Fig. 12a,b). The latter DSV curve does not show the directions with inclinations as low as ~55° between ~1200/1300 and ~1400 AD that are present in both the French and Iberian curves. However, it should be noted that such data are now present in the recently updated archeomagnetic database [START_REF] Schnepp | New archaeomagnetic secular variation data from Central Europe. I: Directions[END_REF].

Figure 12 highlights, in a simple and very general way, the need to homogenize the methods used to estimate regional DSV curves. This is particularly necessary if the secular variation is to be studied on a spatial scale such as that of Europe without resorting to a more global reconstruction of the geomagnetic field, the resolution of which is still limited, or if the significance of the archeomagnetic data obtained from different regions is to be analyzed (i.e., in order to establish a coherent archeological scheme on a scale beyond the framework of a single country). Concerning this last point, it should finally be remembered that the approach developed by Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] is particularly well adapted to the use of the DSV curve for archeomagnetic dating purposes (see also the Bayesian approach developed by [START_REF] Lanos | Bayesian inference of calibration curves: application to archaeomagnetism[END_REF]. Note that the programs allowing the calculation of a DSV curve and its use for archeomagnetic dating using the method developed by Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] are available upon request. S1); in white, only the data with dating uncertainties ≤50 years. The magenta bars show both the data eliminated because their viscosity index is too high (>12%) and the so-called abnormal (VA) values reported by [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] to which we have added six new data because their directions deviate significantly from the age corresponding segments of the mean DSV curve that we calculate (Fig. 10; Table S2). Note that data with viscosity indices >12% are reported only to illustrate the fact that their number is small in relation to the total number of structures analyzed. (b) Histogram of the 95%-confidence circles (α 95 ). In blue, all data ; in white, the data with dating uncertainties of ≤50 years. (Thellier, 1981 ;[START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] (2017) and from the gufm1 model [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF] after 1750 (Table S4). [START_REF] Goff | A reappraisal of instrumental magnetic measurements made in Western Europe before AD 1750: confronting historical geomagnetism and archaeomagnetism[END_REF][START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF]. with that calculated using the same method but with the [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] database (green-white line; Le [START_REF] Goff | On archaeomagnetic secular variation curves and archaeomagnetic dating[END_REF] and that of [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] using sliding windows of fixed duration (blue-grey line).

Concluding remarks

Figure captions

Figure

  Figure 4a,b shows examples of alternating-field (AF) demagnetization up to 20-30 mT

  This study summarized 25 years of research in archeomagnetism carried out in the laboratory created by Emile Thellier. It completes the work of Ileana Bucur with the construction of a new reference curve of the directional variations in the geomagnetic field in France over the last two millennia. It also concludes more than 80 years of research in archeomagnetism carried out at the Saint-Maur Observatory (created in 1880 by Eleuthère Mascart), at a time when the laboratory for the analysis of archeomagnetic directions has just been installed at Chambon-la-Forêt within the French National Magnetic Observatory.

Fig. 1 .

 1 Fig. 1. Location map (Mercator projection) of the archeomagnetic data obtained in

Fig. 2 .

 2 Fig. 2. Different stages of sample collection and preparation in the laboratory (following

Fig. 3 .

 3 Fig. 3. Determination of VRM and TRM direction from six kilns of different ages, with an

Fig. 4 .

 4 Fig. 4. (a),(b) Comparison between the TRM directions from the Thellier method and the

Fig. 5 .

 5 Fig. 5. (a) Histogram of the structure-averaged viscosity indices of all results obtained using

Fig. 6 .

 6 Fig. 6. Age distribution of the data considered in this study. (a) Age distribution of 170

  . (b) Age distribution of the 528 results obtained in our laboratory over the past 25 years. (c) Age distribution of 286 data from the two previous datasets, with dating uncertainties of ≤50 years.

Fig. 7 .

 7 Fig. 7. Spherical projections of the available archeomagnetic directions. (a) All data with a

Fig. 8 .

 8 Fig. 8. Spherical projection of the archeomagnetic directions obtained from three different

Fig. 9 .

 9 Fig. 9. Spherical projection of the archeomagnetic directions with central dates between 450

Fig. 10 .

 10 Fig. 10. The new DSV curve for France for the last two millennia. Only data with an age

Fig. 11 .

 11 Fig. 11. Comparison of the new mean DSV curve calculated in this study (red-white line)

Fig. 12 .

 12 Fig. 12. Comparison of the new French DSV curve (red-white curve) with those previously

Acknowledgments

This study is dedicated to the memory of Emile Thellier, who, a long time ago now, committed MLG to the path of paleo-archeomagnetism research. We are grateful to Ileana Bucur who introduced YG and AG to archeomagnetism. We also thank Jean-Claude Tanguy who, at the same time as this study was being performed, doggedly worked on the archeomagnetism of his beloved Italian volcanoes. We are grateful to Laurent Boissin, Gaétan Gouérou, Lucie Garnier and Aurélia Alligri who carried out some of the archeomagnetic measurements, and all the archeologists who made this study possible. Finally we would like to thank two anonymous reviewers who made useful comments on the manuscript. This work was partly supported by the Fondation Simone and Cino Del Duca of Institut de France ( 2017Research Grant). IPGP contribution no. 4166. Thellier, E., 1967b. A big sample spinner magnetometer. In Methods in Palaeomagnetism, Elsevier Amsterdam, 149-154.

Thellier, E., 1981. Sur la direction du champ magnétique terrestre en France durant les deux derniers millénaires. Phys. Earth Planet. Inter. 24,

recovered from the tables provided by the authors. The 95%-confidence circles of the individual data are shown with the same color code as in Fig. 10b, but also with empty circles for α 95 >5.0°. S3 . In both cases, the grey band shows the associated α 95 Fisher confidence circles.

Supplementary material

The declinations and inclinations of the individual archeomagnetic data (i.e., obtained at the structure level) are also reported using red and blue dots, respectively. The curve segments in magenta (declinations) and cyan (inclinations) covering the past few centuries are constructed using direct magnetic measurements (Table S4).

Table S1. Mean TRM archeomagnetic directions from the Saint-Maur database including the results obtained by Thellier (1981), [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF] and this study. The first two datasets are in italics. Structure number: archeomagnetic data reference number (0-200, from Thellier, 1981;300-399, from Bucur, 1994; from 400 and above, this study). # indicates that either the dating or the grouping of data has been changed from the original publication. Structure Name: name of the archeological structure studied. Ref.: number associated with an archeological reference given in Text S1. * indicates that the archeological information was provided in [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF].

Long. Site (°), Lat. Site (°): location (longitude and latitude) of the structure. Decl. Site (°), Incl. Site (°): declination and inclination of the TRM mean directions at the site locations. Table S3. Interpolation each 10 years of the mean DSV curve detailed in Table S2 (and see text). Same legend as in Table S2. In addition, the corresponding α 95 values are provided in the last column.

Table S4. Historical (direct) DSV curve in Paris determined between 1555 and 1750 by Le [START_REF] Goff | A reappraisal of instrumental magnetic measurements made in Western Europe before AD 1750: confronting historical geomagnetism and archaeomagnetism[END_REF] and from the gufm1 model [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF] after 1750.

Text S1. List of known archeological references associated with the archeomagnetic data detailed in Table S1. Each reference has a number that can be found in the third column of Table S1. All these references are available at dolia.inrap.fr. * indicates that the archeological information was provided in [START_REF] Bucur | The direction of the terrestrial magnetic field in France during the last 21 centuries[END_REF].


Yan Zhang

Ye Zhang

Han Cui

Dr Mihail Barboiu
email: mihail-dumitru.barboiu@umontpellier.fr

Jinghua Chen
email: chenjinghua@jiangnan.edu.cn

Yan Zhang

Ye Zhang

Dr Y Zhang

Prof + H J Cui

Chen

Dynameric Collagen Self-Healing Membranes with High Mechanical Strength for Effective Cell Growth Applications

Keywords: cell growth, collagen, dynamers, dynamic constitutional chemistry, self-healing

  L'archive ouverte pluridisciplinaire

Constitutional dynamic chemistry (CDC) represent an evolutional approach to produce chemical diversity, implementing dynamic molecular/supramolecular interfaces between reversible interacting constituents. [1] CDC has been spreading into different fields, including materials, [2,3] catalysis, [4,5] drug discovery or [6,7] sensing, [8] among others.

Dynamic constitutional materials show practical multi-stimuli (i.e. light, temperature and pH) [9] or inherited self-healing properties, [10] for biomedical, [11] drug delivery, [12] tissue engineering [13] and recyclable plastics [14] applications. Essentially, such features are achieved through supramolecular interactions or dynamic covalent reactions, in which the component connections can be reversibly tuned. Most of the existing dynamic covalent materials are made of synthetic components, such as poly(dimethylsiloxane), [15] methacrylate, [16] polyethylene glycol, [17] and so on. Their biocompatibility is comparatively low to other biodynamers mostly based on chitosan, [18] which may induce inflammation responses when biomedicine related applications are concerned.

Among natural polymers, such as chitosan, gelatin, silk and cellulose, collagen is a main composite in extracellular matrix and contributes as the most abundant protein in mammals. [19a] With its good biocompatibility, high cell affinity and low antigenicity, [19b] collagen has been widely used for biomedical applications, including guided bone regeneration, corneal reconstruction, [20] wound dressing, [21] therapeutic contact lenses, [22] etc. However, pure collagen membranes usually lack desirable mechanical properties, which may bring obstacles for clinical uses. For instance, when barrier membranes are applied for prevention of postsurgical peritoneal adhesion, [23] mechanical stiffness is important to keep the material integrated during all operational procedures. Thus, different approaches have been developed to improve the properties of collagen membranes, for example, addition of cross-linkers such as oxidized polysaccharides [22] or b-cyclodextrin, [24] or mixing with other polymers, [25] including chitosan or cellulose. Despite all these efforts, the reported tensile stress values of the existing collagen membranes were mostly limited to a few MPa, lower than some other membranes from synthetic sources.

Amino-carbonyl/imine reversible chemistry is one of the most frequently adopted approach for building dynamic covalent materials under mild exchange conditions close to physiological environments. [26] Meanwhile, pH can be used to externally switch between condensed imine and hydrolyzed states, which in turn control the polymerization states. [27,28] In the current work, we combined the dynamic polymers -dynamers-with collagen to provide biocompatible mem- branes with good self-healing properties and strong mechanical stiffness for effective cell-growth applications. Upon airdrying method is aimed to be as simple and broadly applicable as possible to obtain thin and compact layer of collagen membranes. This study leads to a greater fundamental understanding of how swelling, self-healing, mechanical strength, degradation, thermostability and cell toxicity can be optimized at the nanoscale to optimize mechanical stiffness of newly designed collagen membranes that hold great potentials for various biomedical applications. The relatively straightforward quantification of mechanical strength of dynameric collagen, relevant to subsequently construct membranes in larger scale based on such probes, is a very important and previously unreported strategy.

Synthesis and Characterization of the Collagen Membranes. Collagen (C) is known for its triple helix structure with three polypeptide strands binding together, where extra amino groups can be found in multiple Lysines for further dynamic modifications. [29] In the current study, various dynameric frameworks cross-linkers were selected to connect the collagen through reversible imine bonds. The cross-linkers themselves were also dynamic polymers synthesized through imine formation reaction, starting from 1,3,5-benzenetricarboxaldehyde (1) core-centers and multi-amino-connectors of different lengths and hydrophilicity (Scheme 1), including short chain diethylenetriamine (2 a), extended chains with 2,2'-(ethylenedioxy)bis(ethylamine) (2 b) and 4,7,10-trioxa-1,13-tridecanediamine (2 c), also polyethylene glycol (PEG) based polymers, such as polyethylene glycol bis(3-aminopropyl) (2 d, M n % 1500) and amino-terminated 4-armed-polyethylene glycol (2 e). Trialdehyde 1 was chosen for its high cross-linking ability, whereas the water solubility of the resulted dynamers is relying on the addition of amines 2 a-e. The ratio between the trialdehyde and amines were set as 1:1 (for 2 a-d) or 1:0.6 (for 2 e), where one third of the aldehyde groups was left for further reaction with amino groups of collagen. The resulted dynameric crosslinkers were firstly dissolved in ethanol to make the stock solutions of 50 mm, which were subsequently mixed with collagen water solution (10 mm) and transferred to Teflon molds for natural evaporation of solvent. After air-drying for 2-3 days at RT, thin layers of dynameric collagen membranes were obtained (Scheme 1).

Fourier transform infrared (FT-IR) spectroscopy was used to analyze the structural changes of the materials. As shown in Figure S1, the vibrational band at 1692 nm of aldehyde groups (1) almost disappeared after cross-linking with collagen and formed the membranes, showing high conversions of the imine formation process. Moreover, the surface morphology of collagen membranes was observed by using scanning electron microscopy (SEM), in which dense and nonporous structures were identified (Scheme 1). From the cross-section images under SEM, the thickness of the membranes was determined to be around 20 mm thinner than the collagen membranes prepared from other methods. [23,30] Tailoring the Mechanical Strength of the Collagen Membranes. The mechanical stiffness of the collagen membranes was measured by placing the samples (3 cm 7 cm) to tensile and compression testers, with a 50 N crosshead at a speed of 5 mmmin À1 at RT (Figure S2). The typical stress-strain curves for all membranes have been illustrated in Figure 1. The membrane composed of pure collagen show the smallest tensile stress (21.9 MPa) and strain at break (2.4 %). The cross-linking with various dynamers improve its mechanical properties. Among the membranes with shorter dynamer cross-linkers, such as 3 a (39.1 MPa, 3.0 %), 3 b (41.7 MPa, 4.8 %) and 3 c (65.1 MPa, 9.9 %), both the values of tensile stress (up to 175 %) and the break strain (up to 400 %) were increased with the length of the amine connectors. This phenomenon can be attributed to the combined effects of dynamically lubricant between the collagen structures and the higher water content from the longer chain dynamers. For the membranes containing polymeric PEG components (3 d,e), their mechanical strengths were even higher. For example, the highest tensile stress (81.7 MPa, + 400 %) was observed from the membrane that linked with 3 e, much higher than most of the other collagen based membranes, [31] accompanied with a break strain of 8.6 % (+ 400 %), probably owing to the amine-terminated fourarm linker, leaving more spots for multiple cross-linking opportunities by imine bonds. On the other hand, the highest break strain was almost 10 times bigger for the membrane 3 d (19.8 %) than the reference membrane C. This can be explained by the longest linker chain between neighboring amines, giving the highest flexibility for the resulted dynameric collagen membrane. However, due to the decreased cross-linking sites, its tensile strength (40.2 MPa) was a bit lower than that of 3 e.

Moreover, to examine the dynameric imine bonding effect during the membrane formation, the imine synthesized from trialdehyde 1 and amine 2 e was reduced with NaBH 4 first and further applied to physically cross-linked collagen. The resulted collagen membrane in which reduced polyamine dynamers would not bind to collagen, showed comparatively lower ten-sile strength, with the maximum value around 75 % of that from membrane 3 e, indicating the importance of inserting reversibly imine bonds between collagen and dynamers during the membrane preparation process. Furthermore, the highest tensile stress and break strain for each collagen membrane have been summarized in Figure 1 b, from which a clear trend of the influences of linker length and dynamer non-bonding effects on the mechanical properties of the membranes can be observed.

Further investigations revealed that the dynameric frameworks 1•2 a-e can form nanoparticles in water, with average diameter ranging from 100-200 nm (Figure S4), as determined by dynamic light scattering (DLS). The comparatively small size of the dynamic particles can provide higher exposure of free aldehyde groups, leading to multivalent effects while interacting with the amino groups in collagen. This can explain the enhanced mechanical strength of this type of cross-linked collagen membranes than the ones made from other methods.

Self-Healing Ability of the Collagen Membranes. The reversibility of the amino-carbonyl/imine reaction enabled the selfhealing properties of the membranes at RT. The membrane 3 a was first fabricated into rod-shaped samples (50 mm 10 mm) and cut into two pieces, which was stained with rhodamine B and methylene blue, respectively, for better visualization effect. Afterwards, the two membrane pieces were put together with slight overlapping, with the presence of a few drops of deion- ized water. As can be seen in Figure 1 a, the two pieces were rejoined after 2 h at RT. Meanwhile, the collagen membrane was cut into a large number of very small pieces, and paved in a Teflon mold with the addition of a few drops of water. After 6 h at RT, one whole self-standing piece of membrane was obtained (Figure 1 c), demonstrating again the strong self-healing and recovery ability of the dynamic covalent membranes. Moreover, a more precise analysis was carried out by cutting membrane 3 a into two pieces, the tensile stress was measured after re-healing the two parts, while comparing to the value of the original membrane. Figure 1 d illustrates that the tensile strain of 3 a was maintained for the re-built membrane, but the mechanical stress was decreased to less than half of the original number, with resulted in a calculated healing efficiency of 44.4 %. This can be explained by the shorter membrane size and stiffer texture after the overlapping of rejoining process. The dry membrane surface also increased the difficulty of the imine exchange reaction under this specific conditions as previously observed for chitosan membranes. [18a] Swelling, Thermostability and Degradation of the Collagen Membranes. The swelling behavior is an important issue related to the cross-linking degree of the membranes and impacting on their performances in an aqueous environment. Therefore, all the freeze-dried collagen membranes were placed in phosphate buffered saline (PBS) solution at 37 8C, and the weight was measured after determined time intervals. Figure 2 a illustrates the change of swelling ratios with time for the prepared membranes. It was clear that the membrane with pure collagen gave the highest swelling ratios due to the lack of cross-linking process. All the other membranes provided lower values, among which, the swelling ratio of membrane 3 c was comparatively lower than the others, probably owing to the good solubility and short length of the dynamic crosslinker contained in the structure. Additionally, the pure collagen membrane was gradually dissolved in water, making difficult to measure the weight after 2 h. These results also demonstrated that the physical stability of the membranes was greatly enhanced after the cross-linking procedure. Appropriate degradation rate is crucial for biomedical membranes. Figure 2 b showed the in vitro degradation profile of the collagen membranes in PBS (pH 7.4) at 37 8C. Generally, fast degradation rate was detected for collagen membranes, C in the first 5 days, with up to 80 % mass loss. The presence of cross-linking slowed down the degradation process, especially for the PEG-based membranes 2 a and 2 d,e, probably coming from the tight dynameric frameworks connections, leading to a higher retention of the membrane masses, up to 23 % after 45 days.

The thermal stability of the collagen membranes were subsequently evaluated. From the thermogravimetric analysis (TGA) two significant weight losses were observed (Figure S5 a): one from 50 to 150 8C, indicating the removal of water from the matrixes; and the other from 250-450 8C, representing thorough decomposition of the materials, with the collagen helix structure completely disintegrated into a random coil polypeptide. The differential thermal gravity (DTG) result was consistent with the TGA profile (Figure S5 b). Meanwhile, an extra valley at 320 8C was detected for the two membranes containing PEG, indicating the decomposition of the PEG part. Furthermore, in the differential scanning calorimetry (DSC) analysis (Figure S5 c), the collagen membrane C showed a denaturation temperature at 107.3 8C, whereas the values for the cross-linked collagen membranes 3 a,b were slightly higher, up to 115.4 8C.

Biocompatibility of the Dynameric Collagen Membranes. The MTT assay was used to study the cytotoxicity of the dynameric collagen membranes. NIH 3T3 cells were treated with gradient-diluted membrane leachates, 100, 50, 25 and 12.5 % of the original concentration, respectively (Figure 3 a). All the leachates from pure collagen increased the cell viability to some extent, which is consistent with the good biocompatibility of collagen itself. After cross-linking, some membrane leachates, for example, 3 c and 3 e with lower concentrations exhibited an enhancement of the cell viability, whereas an slight decrease at above 95 % after 24 h was observed for all the crosslinked membranes with 100 % concentration.&&ok?&& Therefore, the potential toxicity of the possible dynameric frameworks cross-linking did not obviously affect the cell viability in the current case. All the dynamic collagen membranes Besides the membrane leachates, the direct contact tests were also employed to investigate the cytotoxicity of the dynameric membranes. In this experiment, NIH 3T3 cell suspensions were placed directly on the membrane surfaces and incubated for 72 h. All membranes exhibited appreciable stability during the cultivation period. Afterwards, the cells were stained with calcein acetoxymethyl ester (Calcein-AM, green-fluorescence) and propidium iodide (PI, red-fluorescence) for the observation of live and dead cells, respectively. By using confocal laser scanning microscopy (CLSM), cell numbers and morphologies can be clearly observed. As shown in Figure 3 b-g, all the samples of dynameric membranes exhibited similar fluorescence for the live cells, whereas their spindle-shaped morphology showed no difference than the reference sample containing collagen membrane. Very few dead cells (red spots) were observed, demonstrating again the negligible cytotoxicity of the dynameric collagen membranes.

In summary, we have developed a series of dynameric collagen membranes connected through dynamic framework linkers, leading to excellent mechanical strength, self-healing properties and good biocompatibility. Nevertheless, the novel membranes were notably robust, showing self-healing ability even from a crushed status. Meanwhile, by varying the structural composition and length of the dynamic cross-linkers, the stiffness and flexibility of the membranes can be tuned accordingly, in which the tensile strength of the membranes can reach over 80 MPa, more than 400 % higher than that was observed for the reference collagen membrane and highly superior compared to the current state-of-the-art biomaterial sourced membranes. Moreover, the implantation of natural collagen as the starting material also endowed the membrane with good biocompatibility, resulting in more than 90 % viability for NIH 3T3 cells, which can also be directly observed from confocal laser scanning microscopy after live-dead cell staining. The current work provides a new strategy for the design and preparation of biocompatible membranes with excellent properties, which can further lead to broad applications in biomedical fields, such as wound healing, prevention of peritoneal adhesions or tissue regeneration, among others. Dynameric collagen self-healing membranes with high mechanical strength for effective cell growth applications (Barboiu) @MihailBarboiu @enscmchimiemtp SPACE RESERVED FOR IMAGE AND LINK Share your work on social media! Chemistry -A European Journal has added Twitter as a means to promote your article. Twitter is an online microblogging service that enables its users to send and read text-based messages of up to 140 characters, known as "tweets". Please check the pre-written tweet in the galley proofs for accuracy. Should you or your institute have a Twitter account, please let us know the appropriate username (i.e., @accountname), and we will do our best to include this information in the tweet. This tweet will be posted to the journals Twitter account @ChemEurJ (follow us!) upon online publication of your article, and we recommended you to repost ("retweet") it to alert other researchers about your publication.

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Figure 1 .

 1 Figure 1. a) Tensile stress-strain curves collagen C, dynameric collagen 3 a-e membranes and reduced 3 e membrane. b) The highest tensile stress and break strain for each membrane. c) Cutting and rejoining of the self-healing membranes. d) Stress-strain curves of the original and the re-healed membrane 3 a.

Figure 2 .ÝÝ

 2 Figure 2. a) Swelling kinetics and b) degradation profile of the collagen, C and dynameric collagen 3 a-e membranes from PBS (pH 7.4) at 37 8C.

Figure 3 .

 3 Figure 3. a) Cytotoxicity of the collagen membranes on NIH 3T3 cells for 24 h (n = 6). Confocal laser scanning microscopy (CLSM) images of NIH 3T3 cells cultured on b) collagen membrane, C and dynameric collagen membranes: c) 3 a; d) 3 b; e) 3 c; f) 3 d and g) 3 e for 3 days in vitro, cells were stained green with Calcein-AM and red with Propidium Iodide (PI). Scale bar: 50 mm.

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  Biomaterials Y. Zhang, Y. Zhang, H. Cui, M. Barboiu,* J. Chen*

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Acknowledgements

We are grateful for the financial support from Natural Science Foundation of Jiangsu Province (BK20180625), National Natural Science Foundation of China (21574059), National First-class Discipline Program of Light Industry Technology and Engineering (LITE2018-20) and Fundamental Research Funds for the Central Universities (JUSRP51709A).

Conflict of interest

The authors declare no conflict of interest.