Ludovic Charpentier
email: ludovic.charpentier@promes.cnrs.fr

Danying Chen

Johann Colas

Frederic Mercier

Michel Pons

Didier Pique

Gael Giusti

Jean-Louis L Sans

Marianne Balat-Pichelin

Multilayer multifunctional advanced coatings for receivers of concentrated solar power plants

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Introduction -Context

The market of the concentrated solar power plants is extending and several commercial plants are operating using steam-based Rankine cycles below 870 K. A major improvement can be achieved by using gas-based Brayton cycles that could ideally heat an air coolant beyond 1070 K, which requires the use of high-temperature materials for solar surface receivers [START_REF] Poživil | A pressurized air receiver for solar-driven gas turbines[END_REF].Heat exiting from the Brayton cycle could be then sent to a steam generator following a secondary Ranking cycle. A recent paper has shown that the combination of gas-based Brayton, steam-based Rankine and organic-based Rankine cycles could afford to reach an efficiency (defined as the ratio of the electric power produced to the incoming solar power) of 33% [START_REF] Sachdeva | Thermodynamic analysis of solar powered triple combined Brayton, Rankine and organic Rankine cycle for carbon free power[END_REF].

The efficiency of the solar receiver to convert the incoming solar flux into thermal energy mainly relies on two radiative properties: [START_REF] Poživil | A pressurized air receiver for solar-driven gas turbines[END_REF] the solar absorptivity  which determines the fraction of the incoming solar flux that could be absorbed, and (2) the total emissivity  that determines the radiative thermal losses. An ideal receiver would present an absorptivity close to 1 and an emissivity close to 0. This is difficult to obtain because solar spectrum and blackbody emittance areas overlap when the temperature is increasing. Additionally, the formation of an oxide layer can seriously affect satisfactory native properties, as already observed for TaC [START_REF] Charpentier | The impact of the oxidation on the optical properties of TaC[END_REF].

Nickel-based Inconel alloys are limited by their poor oxidation resistance in air at temperature above 1000 K. Various authors reported the oxidation behavior of Inconel 718 [START_REF] Greene | Oxidation of Inconel 718 in air at high temperatures[END_REF], Inconel 625 [START_REF] Kumar | Studies on the oxidation behavior of Inconel 625 between 873 and 1523 K[END_REF][START_REF] Seo | SiO 2 and MoSi 2 formation on Inconel 625 surface via SiC coating deposited by cold spray[END_REF], and Inconel 617 [START_REF] Kim | Oxidation characteristics and oxide layer evolution of alloy 617 and Haynes 230 at 900 °C and 1100 °C[END_REF] at temperature up to 1620 K. They observed the formation of porous chromia oxide layers following a parabolic kinetics, but the Inconel 617 loses mass after 36h oxidation in air at 1373 K due to the spallation of this porous chromia layer [START_REF] Kim | Oxidation characteristics and oxide layer evolution of alloy 617 and Haynes 230 at 900 °C and 1100 °C[END_REF]. Ceramics like SiC are resistant to oxidation at higher temperatures (1470 to 1770 K), but are sensible to cracking, which would quickly break the solar modulus [START_REF] Leray | Etude du comportement thermique et thermomécanique des récepteurs solaires sous haut flux radiatif[END_REF].

Recently, we developed High Temperature Chemical Vapor Deposition (HT-CVD) to coat a metallic alloy with a ceramic AlN coating at 1400 K [START_REF] Pons | High temperature chemical vapor deposition of aluminum nitride, growth and evaluation[END_REF]. Optimization of this process could enable the synthesis of new composite materials that combine the main advantages of the metallic substrate (machinability and resistance to thermal stresses) and the main advantages of ceramic coating (improvement of the radiative properties and oxidation resistance). The aim of this work is to investigate the oxidation resistance and the high temperature radiative properties of such composite materials.

Materials and methods

Two kinds of substrates are selected for the high temperature chemical vapor deposition of AlN coatings: (1) a molybdenum-based alloy named TZM (Goodfellow Metal, 99 wt% Mo, 0.5wt% Ti, 0.1wt% Zr and C) and (2) an oxide dispersion strengthened (ODS) FeCrAl alloy named Kanthal APMT (Sandvik, Kanthal, 22 %t Cr, 5wt% Al, 0.1 wt% Y, 0.1 wt% Zr and Fe (balance)). In the analysis below, it is convenient to denote these two substrates by TZM and APMT respectively. The choice of TZM as substrate material is due to its similar thermal expansion coefficient to those of SiC and AlN in the temperature range of 800-1600 K [START_REF] Touloukian | Thermal Expansion -Metallic Elements and Alloys[END_REF][START_REF] Touloukian | Thermal Expansion -Nonmetallic Solids[END_REF]. APMT is selected as an alternative substrate material for its superior oxidation resistance up to 1500 K, which allows the study of the optical properties of the coatings at high temperature. AlN coatings (40 µm) are grown by HTCVD at around 1400 K and 2000 Pa using NH 3 (99.999%) and AlCl 3 (in-situ formed via chlorination of high purity Al pellets (99.999%) and Cl 2 (99.999%) at 800 K) as precursors. The ratio N/Al, defined as the NH 3 /AlCl 3 ratio in the gas phase, is fixed to 3 to promote the growth of large grains [START_REF] Pons | High temperature chemical vapor deposition of aluminum nitride, growth and evaluation[END_REF]. SiC coatings are deposited at 1400 K using SiH 4 and C 3 H 8 as percursors, but an intermediate AlN layer is required to avoid the carburation and/or silicidation of the metallic substrate. The thickness of the intermediate AlN and SiC coatings are 15 and 80 µm respectively.

We carry out our experiments using two solar facilities previously described. The first one is the "REacteur Hautes Pression et Température Solaire" (REHPTS) [START_REF] Charpentier | High temperature oxidation of SiC under helium with low-pressure oxygen-part 1: sintered α-SiC[END_REF], the second one is the "Moyen d'Essai et de DIagnostic en Ambiance Spatiale Extrême" (MEDIASE) [START_REF] Paulmier | Physico-chemical behavior of carbon materials under high temperature and ion irradiation[END_REF][START_REF] Balat-Pichelin | Emissivity measurements on carbon-carbon composites at high temperature under high vacuum[END_REF][START_REF] Brodu | Efficiency and behavior of textured high emissivity metallic coatings at high temperature[END_REF]. Both reactors are located in Odeillo, at an altitude of 1500 m, so that the surrounding atmospheric pressure is 87 kPa. Concentrated solar fluxes are of interest to generate thermal shocks with temperature rates up to 100 K s -1 during heating and cooling.

The coated and uncoated samples are oxidized inside REHPTS. The temperature (whose level can be adjusted by a shutter as previously described [START_REF] Charpentier | High temperature oxidation of SiC under helium with low-pressure oxygen-part 1: sintered α-SiC[END_REF]) is measured using a monochromatic (5 μm) optical pyrometer Ircon Modline 7 that has been previously calibrated on a blackbody. The temperature measurement is ranged from 1400 ± 15 K to 2500 ± 25 K and the duration of each temperature plateau is 20 min. A video camera enables an in situ filming of the experiments. The mass variation expressed in mg cm -2 is obtained from the weighting of the samples before the experiments and after each plateau.

The solar concentrated radiation heats the samples placed inside the MEDIASE facility at the focus of the 1 MW solar furnace and previously described [START_REF] Paulmier | Physico-chemical behavior of carbon materials under high temperature and ion irradiation[END_REF][START_REF] Balat-Pichelin | Emissivity measurements on carbon-carbon composites at high temperature under high vacuum[END_REF][START_REF] Brodu | Efficiency and behavior of textured high emissivity metallic coatings at high temperature[END_REF]. A CI Systems SR-5000N spectroradiometer measures the normal spectral emissivity on the back face of the sample on a range from 1.4 to 14 µm at various temperatures in the 1100-1600 K interval and these measurements are integrated on the 1.4-2.8 µm and 1.4-14 µm intervals according to equation ( 1) and ( 2):

(1) (2)
where is the spectral solar irradiance AM1.5 [START_REF]Reference Solar Spectral Irradiance: Air Mass 1.5[END_REF] and is the blackbody emittance at T that can be computed from Planck's law. The average emissivities given by equations ( 1) and ( 2) are respectively the approximate values of the solar absorptivity  and of the total emissivity , the / ratio being of interest to analyze the thermal equilibrium of materials in extreme solar environment [START_REF] Balat-Pichelin | Emissivity measurements on carbon-carbon composites at high temperature under high vacuum[END_REF]. A bi-color pyro-reflectometer developed at PROMES-CNRS in order to get the real temperature of a surface with unknown or variable emissivity [START_REF] Hernandez | Experimental validation of a pyroreflectometric method to determine the true temperature of an opaque surface without hampering reflections[END_REF] measures the temperature. The pyroreflectometer and the spetroradiometer have also been previously calibrated on a blackbody.

In this work, radiative properties measurements are performed in air on coated and uncoated Kanthal APMT at temperatures from 1100 to 1500 K, the same sample being exposed at increasing temperatures. The time required to reach the desired temperature and to get stable emittance values is generally around 5 minutes. Nevertheless, the first measurements we performed on uncoated materials requested a longer time and presented important deviations due to the in situ growth of an oxide layer that would affect the radiative properties (up to 50% deviation can be observed due to the advancement of the oxidation). Measurements are therefore performed on the uncoated alloy that was previously oxidized in air inside a muffle furnace during 100 h at 1370 K, so that the influence of in situ oxidation in air would be less significant.

Room temperature optical measurements are also performed to investigate the consequences of the high temperature treatments on the optical properties of the materials, using two apparatus. The Perkin-Elmer Lambda 950 is used to perform reflectivity measurement in the solar spectrum range, from 0.25 to 2.5 µm. SOC 100 HDR is used to perform reflectivity measurements in the far infrared region, from 2 to 25 µm. From these measurements the spectral emissivity can be deduced and it can be integrated on 0.25-2.5 µm and 0.25-25 µm according to equations similar to the eqs. ( 1) and ( 2) to access the values of  and  at room temperature. These room temperature measurements are performed on a wider wavelength range that the measurements done in MEDIASE, so both analyses are complementary.

The surface evolution is observed using Scanning Electron Microscopy (SEM), with a Hitachi S-4500 apparatus.

Results

The first results show the difficulties to protect TZM from fast oxidation: smokes of gaseous molybdenum oxide appeared and provoked a significant drop in the signal measured by the optical pyrometer as shown in figure 1 (a) and (b). The temperature was difficult to estimate due to this opacification but should not have been higher than 1200 K. kinetics, which is due to the growth of a dense and protective alumina scale [START_REF] Badini | Oxidation of FeCrAl alloy: influence of temperature and atmosphere on scale growth rate and mechanism[END_REF][START_REF] Liu | Modeling of Oxidation Kinetics of Y-Doped Fe-Cr-Al Alloys[END_REF]. The coating reduces the oxidation kinetics during the first hour, then an increase is observed during the last cycle.

The growth of alumina does not affect the aspect of the AlN-coated sample, whereas one glassy silica layer recovers the AlN/SiC-coated one. Cracks are observed through the coating (figure 2e), these cracks may favor the oxygen diffusion and therefore enhance the sample oxidation. These cracks formed due to the thermo-mechanical stresses generated by the large temperature variation from 300 to 1400 K.

Residual stresses measurements in AlN coating and growing Al 2 O 3 layer are performed by Raman spectrometry and photoluminescence at room temperature. Fifteen thermal cycles in thirty hours are performed from 1373 K to 300 K during this experiment in a conventional furnace. It is shown that the stress in the AlN layer is always compressive and increases from -1.7 GPa before oxidation to -2.7 GPa after 30 hours. In the growing Al 2 O 3 layer, the stress is also compressive with a mean value of -2.3 GPa. These high values come from a complex dependence on the high thermal stresses developed during cooling and creeping rate of the metal substrate at high temperature. However, these values remain lower than the theoretical compressive strength of AlN (-2.81 to -3.2 GPa [START_REF] Subhash | Mechanical behaviour of a hot pressed aluminum nitride under uniaxial compression[END_REF][START_REF] Heard | Mechanical behaviour of polycrystalline BeO, Al 2 O 3 and AlN at high pressure[END_REF]) and Al 2 O 3 (-4 GPa [START_REF] Subhash | Mechanical behaviour of a hot pressed aluminum nitride under uniaxial compression[END_REF]). For the experiments carried out in the REPHTS, the thermal shocks are higher and cracking of the films occurs. The complete modeling including thermal stresses, high temperature creep and oxidation will be published later.

Figure 3 presents the optical properties at room temperature of the uncoated, AlN and AlN/SiC coated APMT, before and after oxidation in the REHPTS or in the muffle furnace. Figure 3 a) shows that the AlN coating makes the spectral emissivity increase in the solar spectrum and also in the infrared region. A short-time oxidation (4 cycles of 20 minutes) does not significantly affect these properties. Nevertheless, a thicker oxide layer grown after 100 h exposure in the muffle furnace at 1373 K leads to a significant drop in the spectral emissivity. Figure 3 b) shows that the AlN/SiC coating has better optical properties than the AlN coating, with an improvement of the spectral emissivity in the solar spectrum range and a smaller increase in the infrared domain. The calculated solar absorptivity and total emissivity at 300 K (figure 3 c)) confirm that the AlN and AlN/SiC coatings improve the solar absorptivity, but long-term oxidation of AlN provokes the inversion of the spectral selectivity, with a total emissivity that gets higher than the solar absorptivity.

Finally, figure 4 presents the high temperature emissivity measurement in air using the MEDIASE setup. At around 1350 K, the spectral emissivity of the coated APMT is higher than the one of the oxidized APMT (figure 4 a). Whereas the spectral emissivity of the AlN/SiC coated material tends to decrease when the wavelength increases, the one of the AlN coated material tends to increase. This is confirmed by figures 4 b) to d): at 1350 K the AlN-coated materials present a lower value of  1.4-2.8

than  1.4-14 , 0.75 vs 0.8 respectively. So the spectral selectivity of AlN-coated materials does not look promising. At the opposite, the AlN/SiC coating seems promising to increase the solar absorptivity, keeping a satisfying spectral selectivity: at 1330 K,  1.4-2.8 is higher than  1.4-14 , 0.95 vs 0.85 respectively. It is worth mentioning that SiC oxidized in air into SiO 2 , and this slight oxidation does seem to affect these radiative properties. Nevertheless, the appearance of cracks observed on figure 2 e) prevents currently the analyses of the long-term evolution of these properties in air.

Conclusions

We have presented here the first results on the influence of a ceramic coating on the oxidation resistance and optical properties of metallic alloy. We did not succeed in preventing TZM alloys from severe oxidation in air due to the difficulty to fully recover the defects of TZM substrates, nevertheless the results on APMT have shown that the AlN and AlN/SiC coatings could reduce the oxidation kinetics of the substrate. Thermal shocks generated may crack the coating. The roomtemperature optical and high temperature radiative measurements have shown that the AlN coating is not the ideal material for high temperature solar receivers due to the decrease of its solar absorptivity after long term oxidation (> 100 h). AlN/SiC coatings seemed to improve the solar absorptivity of the substrate while maintaining an interesting spectral selectivity.

Our next investigations will therefore mainly aim at reducing the thermal stresses in the coating by reducing the heat rate conditions or developing other accommodation layers. The direct growth of SiC on pre-oxidized APMT is now under development regarding this axis.

Figure 1 (

 1 figure 2 a). The oxidation of the uncoated sample follows a diffusion controlled semi-parabolic

Figure 1 .

 1 Figure 1. a) Video caption of the oxidation of AlN/TZM sample after 7 minutes exposure in air b) Pyrometer signal measured during the experiment c) SEM image of the section of an as-coated TZM samples, showing uncovered defects.

Figure 2 .

 2 Figure 2. Weight changes with time of the coated and uncoated APMT samples oxidized in air at T ≈ 1400 K (a) and SEM images (SE mode) of the AlN-coated (b-c) and AlN-SiC coated (c-d) APMT samples before (b, d) and after (c, e) 80 minutes oxidation in air.

Figure 3 .

 3 Figure 3. Spectral hemispherical emissivity at 300 K of uncoated and AlN-coated APMT, before and after oxidation inside REHPTS (4 cycles of 20 min. at 1490 K) or muffle furnace (100 h at 1373 K) (a), spectral hemispherical emissivity at 300 K of uncoated and AlN-SiC coated APMT (b) and roomtemperature solar absorptivity , total emissivity  and evolution of the / ratio (c) for the 5 presented samples.

Figure 4 .

 4 Figure 4. Spectral normal emissivities measured in air at T ≈ 1350 K for oxidized and coated APMT (a) and variations with T of the integration on the 1.4-2.8 µm wavelength interval (≈ ) (b), of the integration on the 1.4-14 µm wavelength interval (≈) (c) and of the ratio of  1.4-2.8 on  1.4-14 (≈ /) (d)

Acknowledgments

This work was supported by the French "Investments for the future" program funded by the French National Research Agency (ANR) under contracts ANR-10-LABX-22-01-SOLSTICE and ANR-10-EQPX-49-SOCRATE, and by the 2MAC-CSP project also funded by the ANR under contract ANR-16-CE08-0019. We also thank Christophe Escape from PROMES-CNRS and Yonko Gorand from the University Perpignan Via Domitia (UPVD) for their help for the reflectivity measurements and SEM imaging, respectively.

Supplementary Material Available:

A schematic representation of the multilayer system together with the description of the Raman and photoluminescence measurements used to determine the residual stresses are provided.


Marie-Dit Asse

A.-M Farnet

ACTING ON THE VEGETATION TO REDUCE THE RISKS RELATED TO MINING WASTE DEPOSITS: ECOTECHNOLOGICAL APPROACH ON THE LIGNITE WASTE HEAP OF "LE DEFENS" (OHM BASSIN MINIER DE PROVENCE)

OBJECTIVE

The objective of this study was to analyze the effect of the various types of vegetation present on the heap on the quality and the stability of the substrate of the heap slopes, on the fire risk and to assess the quality of the runoff water on the lignite waste heap in order to recommend the most appropriate ecotechnological actions to limit the environmental risks. Grassland seemed to be the most appropriate vegetation type to reduce:

• Superficial landslide and substrate water erosion thanks to its dense and relatively homogeneous vegetation cover • Fire risk due to its water retention capacity and its biological type diversity

The use of pioneer local, nurse and engineer herbaceous plant species could be an interesting solution to stabilize the unvegetated slopes of the heap.

The gradual conversion of the Aleppo pine stand to a non-coniferous woody stand with grassland under tree canopy could limit the risks of fire spread and landslides.

Moreover the strict respect of regulation of access to the heap without all-terrain vehicles may limit soil erosion and potential ion transfer. The lignite waste heap named "Le Défens", located on the territory of the OHM Bassin Minier de Provence, is subject to hazards related to this mining waste deposit characteristics: superficial landslide hazard, non-negligible fire risk and risk of contamination transfer by substrate and water erosion. However, today it is accessible to the public and is the place of many practices despite the potential dangers.

MAIN RESULTS

ENVIRONMENTAL

•

  Poor substrate quality despite a relatively homogeneous vegetation cover • Presence of an erosion facies = preferential paths of water flow but low transfer of substrate element to water runoff • Soil and plant water contents, vegetation composition and structure may alter fire risk Grassland (East of the waste heap) Aleppo pine stand (West of the waste heap)

  Territory of the Bassin minier de Provence

	Aerial view of the lignite	A lignite waste heap
	waste heap of "Le Défens"	completely integrated in
	(Meyreuil)	the local landscape

  ://www.ohm-provence.org/spip.php?rubrique5 Google Earth screenshot with the contours of the heap in red 1 Master Envi'Terre mention Biodiversité Ecologie Evolution parcours Ingénierie Ecologique finalité Ecotechnologies et Bioremédiation, promo18-19, Marseille, France, 2 Aix Marseille Univ, Avignon Université, CNRS, IRD, IMBE, Marseille, France, 3 Aix Marseille Univ, CNRS, LCE, Marseille, France, 4 Aix Marseille Univ, IRD, LPED, Marseille, France.

	CONTEXT
				N
	Châteauneuf-le-Rouge Rousset MEYREUIL
	Bouc-Bel-Air Gardanne	Fuveau	Peynier	Trets
	Gréasque Simiane -Collongue	Belcodène
	Mimet
	Cadolive Peypin
	La Destrousse	Urban areas
			Industrial and
			commercial areas

https


Edouard Rahir

the New York John Pierpont Morgan

Bussy-Rabutin's Book of Hours

Prince's Gate. Rahir placed in Morgan's hands a notorious little manuscript, the socalled "Book of Hours" of Roger de Rabutin, comte de Bussy (1618Bussy ( -1693)). This transaction ended a two-century odyssey during which the volume had passed from one aristocratic and/or bibliophilic owner to the next, steadily gaining in fame and value along the way. It first appeared on the market in December 1783, at the sale of the library of the duc de La Vallière. The very long and detailed description in the sale catalog presented the book as "one of the most precious, most interesting, and most curious that can be seen." It surfaced again at sales held in 1872 (vicomte de Lostanges-Beduer), 1879 (Ambroise Firmin-Didot), and 1897 (Henri Bordes). The acquisition by Pierpont Morgan gave the manuscript a permanent home and ensured that henceforth it could indeed "be seen" by the public. Yet its preservation and accessibility have gone largely unnoticed: while Bussy studies have blossomed in recent decades, no scholar seems to have personally examined his legendary Livre d'heures.

more likely that he was hinting at another work, which he may have heard about without knowing exactly what it contained. In 1659, Bussy-Rabutin had already been briefly banished to his estates following an orgy during Holy Week, which purportedly included obscene parodies of Christian rites and hymns. Did he commit even more impieties where Catholicism rhymed with eroticism? It was Boileau's posthumous editor Claude Brossette who first openly asserted the existence of a libertine and satirical book of hours to clarify the poet's cryptic allusion. But he evidently hadn't seen it either and provided a misleading description. The manuscript's occasional appearances in the late 18th and 19th centuries finally allowed for first-hand inspection, but the discussion remained contradictory and inconclusive.

As we prepare to celebrate Bussy-Rabutin's 400th birthday (on Friday, April 13), his "saints" deserve a fresh look and renewed critical efforts. The Morgan has generously granted permission to share some photos of its manuscript for the purpose of increasing awareness and facilitating scholarly analysis. The interpretation that follows reflects my attempt to come to grips with this magnificent and mysterious object and is presented here as a working hypothesis awaiting corroboration or refutation.

Measuring 4 1/2 by 3 inches (115 x 73 mm), the book contains 35 vellum leaves, of which 24 are blank except for a golden border. On two leaves (f. 12 and 16), an identical border surrounds faint traces of calligraphy; the text begins on the recto and continues on the verso, followed by a crowned monogram (LI and RC, respectively, with both letters mirrored and intertwined). The monogram RC also appears on the verso of f. 7, in a white oval surrounded by blue lozenges on a golden background. The crowns surmounting the monograms are those of a marquis (f. 7), a duke (f. 12), and a count (f. 16). On the verso of the remaining leaves (f. 9, 13,17,20,23,26,29,32) are full-page miniatures of saints (4 female, 4 male), painted inside a broad golden border like the one on f. 7. The recto of these leaves is entirely blank. By its contents and structure, the manuscript resembles a distinct section of traditional Horae, usually found at the end of the volume: the "Suffrages" or "Memorials" in which images of selected saints are accompanied by ejaculations and short prayers. Bussy's book included at least two such prayers, composed in French prose and calligraphed in Roman script, but they were scrupulously erased by scraping the ink off the vellum. Past bibliographers managed to decipher some fragments, including "Ainsi soit il" (Amen) at the end of both oraisons.

Information

When seen in UV light, the text on the verso of each folio becomes almost fully legible, but only a few disconnected words emerge on the recto, which has twice as many lines and would typically include references to the saint and his or her story. One can suspect that each prayer presented at least some risqué double-entendre (if not, why take such pains to erase it?), but for now this remains open to speculation. came up with a slew of famous names, from Anna of Austria and the duke of Buckingham to Mme de Montespan and Louis XIV. A penciled note in the Morgan's curatorial file points in a more fruitful direction, suggesting that these miniatures "relate to paintings in the Bussy-Rabutin chateau." Indeed, just like the manuscript has been preserved and can be consulted in New York, many of the hundreds of portraits assembled by Bussy have survived and can be seen in his château in Burgundy. The juxtaposition of the miniatures with the full-size paintings is illuminating, as long as we keep in mind that painted portraits are not photographs and that their degree of "resemblance" to each other and to the sitter can vary greatly. The male saints in the manuscript are Sebastian, John the Baptist, Louis, and George. I am inclined to identify them as follows: Bussy-Rabutin himself, the duc de Candale, the prince de Condé, and, perhaps, the comte de Guiche. (All four also appear in the Histoire amoureuse.) But the correlation between the miniatures and the paintings in the château may be less direct in these cases: Guiche, for example, is not represented in the château, and Condé's portrait seems to have been added belatedly. To recognize the Great Condé (rather than Louis XIII) in the figure of Saint Louis, one needs to consider his youthful likenesses, such as those painted in 1645 by Juste d'Egmont. The moustache in the miniature is very similar to that worn by Condé in a 1653 depiction by David Teniers the Younger. The satirical portrait of the prince in the Histoire amoureuse presents him as having "lively eyes, a hawk's and sharp nose, hollow lean cheeks, a long face and the physiognomy of an eagle, frizzled hair, his teeth were ill set and nasty…" On the other hand, Bussy describes himself with "great sweet eyes, a handsome mouth, a something hawkish nose, an open face, and a happy physiognomy, fair, clear light hair."

Posing as Saint Sebastian allows him to exhibit both his virility and his tenderness. It is safe to assume that all the miniatures embellish and soften the traits of their models, shown here not as military heroes but as martyrs of Love. The sequence of the miniatures suggests an arrangement by couples: Montglas and Bussy, d'Olonne and Candale, Châtillon and Condé, Fiesque and Guiche. The repetition of the monogram RC on f. 7 and f. 16 seems to emphasize the union between the comte de Bussy (Roger) and the marquise de Montglas (Cécile), the likely dedicatee of the volume. The monogram LI, surmounted by a ducal crown, could refer to the prince de Condé (Louis) and the duchesse de Châtillon (Isabelle). Its placement on f. 12, however, does not make sense; its logical position would be on f. 25, following Saint Catherine. I suppose that the two leaves with text were separated from the rest in order to facilitate the erasure operation, after which they were retained for the painted monograms, but not both re-inserted in their original place. The current, very luxurious binding (tan morocco with red morocco doublures and "all-over" pointillé gold tooling) appears to be somewhat later and closely resembles bindings attributed to the workshop of Luc-Antoine Boyet. It may have been commissioned by Nicolas-Joseph Foucault (1643-1721), one of the foremost bibliophiles of his day, who, ten months before his death, presented the manuscript to one of Bussy-Rabutin's daughters. Once the text of the prayers is erased, there is nothing terribly scandalous about these "Hours." It was common in the 17th century for rich and pious patrons to be represented with a saint's attributes; Bussy-Rabutin himself once posed as Saint Julian of Brioude (a 4th-century martyr) in a painting displayed in a local church. This practice extended to illuminated prayer books, such as those executed by the calligrapher Nicolas Jarry. Too little is known about the work of French miniaturists of the time, but a name that comes up in this context is that of Louis Du Guernier (1614-1659), a Protestant and founding member of the Académie royale de peinture et de sculpture. In 1688, the art historian André Félibien praised Du Guernier's human and painterly qualities and affirmed that he had no rival when it came to "the force and resemblance of a head." Among his works on vellum mentioned by Félibien is a "book of prayers" created around 1646 for Henri II de Lorraine, duc de Guise, in which "all the fairest ladies of the Court" were represented en saintes. After the death of Louis Du Guernier in January 1659, his younger brother Pierre continued the family tradition and, according to Félibien, also achieved renown for the beauty of his portrait miniatures. I am not ready to venture an attribution to a specific artist nor to precisely date the Morgan manuscript. A cluster of signs point to the Du Guernier family and to the period 1658-1660: years during which Bussy not only composed his novel but also participated in the fashionable craze for written portraits, indulged in parodic Alleluias, and began decorating his residences in Burgundy. The little book of saints may well predate the Histoire amoureuse des Gaules as well as the decor of the Tour dorée, the "golden tower" which continues to astonish visitors of the Bussy-Rabutin château today.

Whatever its genesis, this illuminated mock hagiography adds another brilliant facet to Bussy's life and works.

Volker Schröder Saint Patrick's Day, 2018

  f. 16v, MS M.370, The Morgan Library & Museum. Left: in normal light / Right: in UV light, digitally enhanced Whereas this textual erasure continues to thwart our curiosity, the images have remained splendidly intact and cry out for recognition. The 1783 catalog offered just one identification, seeing Louis XIII in the figure of Saint Louis, and left it up to the "amateurs" to guess the identity of the other models. Later writers took the bait and

  1

  The four female saints represented in the manuscript, clearly distinguished by their traditional attributes, are the virgin martyrs Cecilia, Dorothy, Catherine of Alexandria, and Agnes of Rome. On the basis of the paintings in the château of Bussy-le-Grand, I propose to identify the real-life models of these miniatures as the marquise de Montglas, the comtesse d'Olonne, the duchesse de Châtillon, and the comtesse de Fiesque.Montglas (whose first name was Cécile) was Bussy's great love; she dumped him following his disgrace, and her likeness and infidelity haunt the entire decor of his château. Fiesque was Montglas' and Bussy's close friend and a prominent Précieuse. D'Olonne and Châtillon are the protagonists of the two main parts of the Histoire amoureuse des Gaules, appearing under the pseudonyms Ardélise and Angélie. The novel also features Montglas ("Bélise") and Fiesque ("Fésique").

  Left: Saint Dorothy (f. 17v, MS M.370, The Morgan Library & Museum) / Right: Catherine-Henriette d'Angennes, comtesse d'Olonne (Château de Bussy-Rabutin) Left: Saint Agnes (f. 29v, MS M.370, The Morgan Library & Museum) / Right: Gilonne d'Harcourt, comtesse de Fiesque (Château de Bussy-Rabutin)

  Left: Saint Louis (detail of f. 26v, MS M.370, The Morgan Library & Museum) / Right: Louis II de Bourbon, prince de Condé, by Juste d'Egmont (Château de Chantilly, Musée Condé) Left: Saint Sebastian (f. 13v, MS M.370, The Morgan Library & Museum) / Right: Roger de Rabutin, comte de Bussy, attributed to Juste d'Egmont (Château de Bussy-Rabutin)

Fly

  -leaf, MS M.370, The Morgan Library & Museum

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O Sandre

C Ménager
email: menager@ccr.jussieu.fr

J Prost

V Cabuil

J-C Bacri

A Cebers

Shape transition of giant liposomes induced by an anisotropic spontaneous curvature

Keywords: numbers: 75.50 Mm, 87.16 Dg, 82.65 Dp, 82.70 Dd, 83.50 Pk

We explore how a magnetic field breaks the symmetry of an initially spherical giant liposome filled with a magnetic colloid. The condition of rotational symmetry along the field axis leads either to a prolate or to an oblate ellipsoid. We demonstrate that an electrostatic interaction between the nanoparticles and the membrane triggers the shape transition.

Phospholipidic bilayers are the basic structural element of most biological membranes. In water these bilayers can form closed vesicles also called liposomes. Due to this analogy with cells, liposomes are commonly used in biophysical studies. In spite of the obvious simplification it implies, artificial liposomes are used to mimic some biological phenomena in well defined, low component environments [1]. For example, analogies have been found between shapes of red blood cells (discocytes, stomatocytes, echinocytes, spherical ghosts) and shapes of synthetic liposomes. Most shapes have a spherical topology and an axis of rotational symmetry: spheres, prolate ellipsoids, dumbells, pear shapes, oblate ellipsoids, discocytes, stomacytes. Other shapes have a symmetry axis of finite order (starfishes), no symmetry axis (3 axed ellipsoids), or another topology (torus). The transformations between those shapes can be triggered by an external parameter: temperature [2,3], gravity [4], a pH gradient [5,6] or a photochemical reaction [7]. The area-differential-elasticity model (ADE) enables the attribution of all morphologies to domains in a single phase diagram [8]. The two control parameters are: (i) the spontaneous curvature c 0 which reflects the asymmetry between the two sides of the bilayer ; (ii) the 'reduced volume' v which quantifies the ratio of volume to area (high v for an inflated vesicle, low v for a flaccid one). It was shown in [9] that a vesicle can move from one equilibrium shape to another by subtle changes of c 0 , i.e. by perfusion of different sugars (in osmotic equilibrium). In reference [10] the authors theoretically consider asymmetric bilayers in contact with colloids, but they do not include any angular anisotropy.

In this article, we describe an anisotropic spontaneous curvature due to magnetic nanoparticles placed in the interior of giant liposomes. An aqueous solution of those particles is an ionic ferrofluid [11]. The liposomes filled with such a ferrofluid are called 'magnetoliposomes'. Here, we observe magnetoliposome shapes under a magnetic field of low intensity (400 Oe). In some cases liposomes elongate in the direction of the magnetic field (Fig. 1(a)), while in others they are compressed at their poles (Fig. 1(b)). In the following, we describe the relevant experimental parameters determining the shape: the concentration of magnetic nanoparticles inside the liposome (C p ), the salt concentration of the medium (C s ), the radius of the liposome (R 0 ) when spherical (with no field) and its axes a and b under deformation. Qualitatively, oblate deformations occur for small, weakly magnetized liposomes, at low ionic strengths. On the other hand, prolate deformations are observed for large, highly magnetized liposomes in salty media. In the last section we propose a model to explain this transition between prolate and oblate shapes.

Preparation of the magnetoliposomes

The phospholipid constituting the membrane is 1-2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) purchased as powder from Avanti Polar Lipids. The process used to encapsulate the ferrofluid inside the liposomes with maximal efficiency differs slightly from usual ones: the first step is to pre-hydrate the phospholipid film with the colloidal solution of ferrofluid, and then swell it with pure water. A small amount of perfectly dry powder (around 1mg) of DOPC is mixed with 10µL of the aqueous dispersion (pH 7) of magnetic nanoparticles (γFe 2 O 3 ) and spread and sheared with a glove finger on a glass support (Petri dish) to obtain an oily orange film. This film is presumably a lamellar phase swelled with charged particles. Immediately following the shearing, 1 mL of distilled water is poured onto the film of fat to start the spontaneous swelling of liposomes. Samples are placed in a water bath at 45°C and observed after half an hour with an optical microscope (Leica 40x, NA 0.65). Pictures from a CCD camera are digitized with a frame-grabber (LG-3, Scion Corp., Frederick MD). Most of the liposomes prepared this way are quasi-spherical with diameters ranging from 10 to 100 µm. Their interiors are orange-colored and their membranes exhibit thermal fluctuations.

Measurement methods

There is heterogeneity in the colloid entrapment yields of different liposomes. First, the film pre-hydrated with the colloid is mixed manually and hence the particles are not dispersed homogeneously. In addition, liposomes in the same sample can also differ in their 'histories': their membranes close at different times during the swelling process, which competes with the simple diffusion of the ferrofluid by water (without entrapment in a closed membrane). Thus, the concentration C p of magnetic nanoparticles encapsulated in a given liposome must be measured independently. Therefore we make magnetophoresis experiments. Briefly, the method consists in applying a controlled magnetic field gradient. The intensity of the field gradient is 100 Oe cm -1 , and the geometry of the field lines is described in detail in [12,[START_REF] Sandre | Cebers in Giant Vesicles[END_REF]. Because magnetoliposomes have a higher magnetic susceptibility χ than the surrounding liquid, they move towards increasing field intensity. Their velocity is constant and corresponds to the balance of the magnetic force and the drag force exerted by the outer fluid. For ellipsoidal shapes the two forces have analytical expressions, which allows a precise measurement of χ.

= χ

. The magnetization at saturation of γFe 2 O 3 , m s =360 Oe, and the average volume of a nanoparticle V p are known from former studies [START_REF] Bacri | [END_REF].

Maghemite particles have diameters of the order of 10 nm. Their surface is coated by citrate ligands so that they bear negative charges at pH 7: this is essential for the colloidal stability of the ferrofluid. With no precaution, the concentration of tri-sodium citrate in ferrofluids is rather high (C s 0 ≈90 mM) because of the non adsorbed citrate species in solution in equilibrium with the citrate ligands. This can be decreased by dialysis through a cellulose membrane (Spectra/Por MWCO 12-14000, ROTH, France). With this method, the salt concentration C s 0 is reduced to 3 to 80 mM as obtained from the measured conductivity of the ferrofluid. In the same way as the nanoparticles, the electrolyte is also diluted in the vesicles compared to the initial ferrofluid. We make the assumption that the sodium citrate salt and the nanoparticles have identical entrapment yields:

0 0 p p s s C C C C =
. By contrast, if the sodium and citrate ions were not entrapped as efficiently as the particles (e.g. due to their faster diffusion before the bilayers close), then the electrolyte would be homogeneously diluted when adding pure water. For instance, starting with a ferrofluid of C s 0 =80 mM would lead to magnetoliposomes in a liquid bath with a salt concentration C s =0.8 mM. The suspension of magnetoliposomes would then have a moderate electrical conductivity (≈1mS cm -1 predicted). This is not observed experimentally, as the measured conductivity is less than 40 µS cm -1 . Therefore we conclude that the electrolyte is indeed co-encapsulated with the magnetic colloid in the liposome interiors.

Dimensions of magnetoliposomes are measured by optical bright field microscopy using image analysis software (Image, NIH). It is well known that the projected area of giant liposomes is smaller than the true surface of the membrane [15], the difference being absorbed by thermal undulations. The effect of a moderate tension is to flatten the fluctuations. Quasi-spherical vesicles can change their shape at constant volume by using the excess area hidden in the fluctuating membrane. In our case, tension originates from magnetic polarization forces acting on the magnetoliposomes. The shape of a liposome submitted to a magnetic field can be described by an ellipsoid with axial symmetry around the field direction. A slight deviation from the rotational symmetry is observed by confocal microscopy (Fig. 2). Giant liposomes filled with a ferrofluid have indeed a higher mass density than the suspending bath:

-3 3 4 cm g 10 5 10

- - × - ≈ ρ ∆
. Thus they are somehow flattened by gravity 0 g  in the z direction. In the next section we develop a simple theory that ignores gravity by considering only axisymmetric ellipsoids. In a standard approximation, shapes are predicted in the zero gravity limit, and gravitational corrections are considered afterward [8,16]. The dimensionless number b K R g g 4 0 0 ρ ∆ = has been introduced in [4] to predict deformations of vesicles due to gravity (K b is the membrane bending modulus). Magnetoliposomes have g values between 10 -3 and 1. This is why the largest ones are not perfectly axisymmetric. Nevertheless, we can clearly distinguish between prolate and oblate shapes, either elongated or flattened in the y direction (parallel to the applied magnetic field). We also point out here the discrepancy of our case with spontaneous transitions between a prolate and an oblate shape reported in [16]. In the latter case, the axis of rotational symmetry also flickers from parallel to perpendicular to the bottom surface of the observation chamber. In the shape transition triggered by a magnetic field, both prolate and oblate ellipsoids keep their axis parallel to In summary, the following experiments have been performed. First, we synthesize different ferrofluids with fixed particle concentration C p 0 , and varying ionic concentrations C s 0 . Then we encapsulate these ferrofluids in giant vesicles, thereafter characterized by optical microscopy. We measure their radius R 0 in the quasi-spherical state. Then we use a home built setup of magnetophoresis to simultaneously measure the ellipsoidal deformation under a magnetic field (value of e 2 and its sign), and the velocity under the field gradient (perpendicular to the field direction). As explained above, with these measurements we can calculate the concentrations C p and C s in individual liposomes.

Theory

The overall shape of a liposome subjected to a field H 0 must minimize the total free energy, which is the sum of the magnetic energy E m , the bending energy E b, and the surface energy of the vesicle ( )

τ π S R -4 0 2
, where τ is the membrane tension, and S the surface area of the vesicle. The idea is to calculate the free energy of an initially spherical liposome deformed at constant enclosed volume into an axisymmetric ellipsoid. In the expansion of the free energy as a function of the ellipticity, the terms of order higher than e 2 are neglected. The surface energy thus disappears since it varies as e 4 .

The magnetic term is proportional to the liposome volume. It is related to the shape through the where χ is the magnetic susceptibility of the encapsulated liquid. Using a standard expansion of D as a function of e [START_REF] Chikazumi | Physics of Magnetism[END_REF], one obtains the approximate expression:

( )

2 3 0 2 0 45 4 constant e R H E m πχ - ≈ (2)
This magnetic energy is decreased by positive values of e 2 , and thus it favors a prolate deformation.

In the following we show that the prolate/oblate transition under magnetic field is driven by a competition between the magnetic energy E m and the bending energy E b . The strong influence of the ionic strength on the deformation suggests that electrostatic interactions are involved between the charged nanoparticles and the slightly charged membrane. We make here the assumption that some charges exist on the DOPC phospholipidic bilayers. This assumption is supported by previous studies which report: i) the existence of a weak negative ζpotential of a few mV for vesicles made of natural egg lecithin [START_REF] Carrion | [END_REF] or synthetic phosphatidylcholine lipids [19]; and ii) the evidence of electrostatic repulsion between pure phosphatidylcholine bilayers, measured with a Surface Force Apparatus [20].

The behavior of charged membranes has been studied extensively in theoretical papers [21,22,23]. The electrostatic contributions to the bending modulus K b and to the spontaneous curvature c 0 have been considered in [24] in the Debye-Hückel approximation of the electrostatic potential and in the case of electrically uncoupled leaflets. It appears that electrostatic repulsion produces an enhancement of the bending modulus compared to the uncharged case: surface charges make the bilayer stiffer. The spontaneous curvature c 0 characterizes the bilayer asymmetry [25]. It has been derived in reference [24] for a bilayer bearing different surface charge densities on its two sides. In that case the salt concentrations were identical inside and outside the vesicle, and hence the Debye lengths as well. Here we develop another model that fits better to the case of magnetoliposomes:

asymmetry comes from two different screening lengths κ i -1 and κ o -1
, inside and outside respectively.

In a suspension of magnetoliposomes, the outer phase is a usual salt solution, while the inner phase is a complex colloidal system combining the salt and the charged magnetic nanoparticles. In order to obtain a simple solution of this problem, we describe this inner phase as a mixture of electrolytes: -the particles (concentration C p ), identified as magnetic polyions with an effective charge Z -the other ions (charge Z i for type i) having the same concentration C s i as in the suspending bath. In the outer phase, electrostatic interactions are screened by the ions (in practice sodium and citrate, but no particles) above a standard isotropic Debye length

2 1 2 2 1 4           = ∑ - i i i w o e Z C kT π e κ
, where e w is the dielectric constant of water (e w =78.5). Inside the liposomes, the decay length of electrostatic interactions is denoted κ i -1

and takes into account all the charged species, salt ions and nanoparticles. The modifications on the bending modulus and on the spontaneous curvature are estimated using the same approach as in [24]. At first we calculate the electrostatic energy E el of a simple body -an infinite cylinder with radius R -then we expand it as a function of R. Finally we identify the terms with the standard expression of the bending energy, supposing that these expressions remain the same for a body of general geometry:

2 0 2 3 2 3 2 2 2 1 2 1 8 3 8 3 2 1 2 1 1 1 4 2 1 2       - ≡         + + - + + ≈ c R K R R R R R E el b o i o i i o w el κ κ κ κ κ κ e πσ π (3)
The elastic constants are derived in the assumption of a slight difference between κ i and κ o . The bending modulus is then Here σ denotes the surface charge density. It is inferred that σ is the same on both monolayers, because the pH is buffered inside and outside by the citrate salt. The asymmetry between the two sides of the membrane arises from different electrolyte compositions inside and outside the vesicle. This small difference has a negligible effect on the modulus, but it is dominant for the spontaneous curvature.

In the model of a liposome filled with a ferrofluid, we make an additional approximation. We suppose that the difference between κ i and κ o is due only to the presence of nanoparticles inside, and their absence outside. In other words, we neglect the difference of salt concentrations inside and outside, responsible for a classical isotropic c 0 . The model focuses on the field dependence of the inner Debye length κ i -1

. The concentration profile of nanoparticles near the inner leaflet of the membrane is indeed sensible to  H . Thus, a magnetic term has to be added in the linearized Poisson-Boltzmann equation. Due to that the calculation of the electrostatic energy of the membrane in the presence of the magnetic field turns out to be rather complicated problem since simultaneous solution of the electrostatic and magnetic field equations is involved. As result at the curvature expansion of the electrostatic energy of the membrane its anisotropy arising due to the magnetic interactions appears. This electrostatic energy curvature expansion is carried out in the forthcoming publication [27]. Its results confirm the conclusions of much simpler model described below. The simple model is based on the assumption of the locally flat membrane and the reduction of the solution of the coupled electrostatic and magnetostatic field equations to 1D approximation. Obtained in such way screening constants are substituted in the expressions of the bending elasticity constant and spontaneous curvature leading to the anisotropic curvature elasticity energy of the membrane. Further consideration is carried out in the frame of the simple model. We begin by solving the magnetostatic problem in a flat membrane geometry, with a magnetic field at an angle α with the normal to the plane of the membrane. Let x be the coordinate in the direction normal to the membrane.

Because the vesicle radius is three orders of magnitude larger than the particles sizes, we can neglect the membrane curvature and the finite size of the nanoparticles. Thus we denote the nanoparticle concentration C p (x) at a distance x from the membrane, the x component of the field H x (x), and the electric potential ψ(x). Far away from the membrane those variables tend respectively towards C p , H 0 cos(α) and zero. The solution of Maxwell

equation 0 4 = + ) M H ( div   π is: p p p p x ) x ( C C ) cos( H ) x ( H χ π χ π α 4 1 4 1 0 + + = (5)
The net flux of nanoparticles in the x direction is then calculated using their mobility u under an osmotic, an electrophoretic and a magnetophoretic force:

x H H ) x ( uC x ) x ( C ukT x Z ) x ( uC J x x p p p p x ∂ ∂ χ ∂ ∂ ∂ ∂ψ + - - = (6)
At equilibrium, J x =0 and: compares the two pressures acting on the membrane: the magnetic pressure calculated at the liposome poles ( 2 2 0 2 πχ H ) and the osmotic pressure exerted by the nanoparticles (C p kT). Numerical values of λ range from 10 -3 to 5×10 -2 , as seen in Table 1. Looking back to the electrostatic potential ψ(x), an anisotropic decay factor can be defined, including the screening by all the charged species:

( ) ( ) x Z ) x ( C x ) x ( C ) x ( C kT ) ( cos H C ) x ( C kT p p p p p p p p ∂ ∂ψ ∂ ∂ χ π α χ π χ π - =         + + +
2 1 2 1 1       + + = ) ( cos d ) ( o i α λ κ α κ (8) It depends through d Z C Z C p i s i i = ∑ 2 2
on the ionic strength of the dispersion and through λ on its magnetic characteristics. The anisotropic part of κ i is negligible as long as the screening is dominated by the salt ions, i.e.

for high ionic strengths (small d). In the opposite case, the angular dependence of the distribution of particles induces an angular dependence of

) ( i α κ
, and hence of c 0 (α ) . The largest screening length turns out to be on the poles. The reason for that is rather simple. Since the magnetic pressure acting near the poles pushes the magnetic polyions to the membrane it augments near it the concentration of the charges having the same sign as on the membrane and thus diminishes the ecranization of charges on it. An increase of the screening length near the magnetic poles (α=0 and α=π) decreases locally the spontaneous curvature: qualitatively, the oblate shape is favored because it has a lower curvature at the poles than at the equator. Equations ( 4) and ( 8) enable one to derive the spontaneous curvature at any angle α:

( )       + - + ≈ ) ( cos d d d ) ( c o α λ κ α 2 0 1 1 1 3 (9)
We can now calculate precisely the bending energy of the membrane,

( ) ∫       - + + = dS ) ( c R R K K E el b b b 2 0 2 1 1 1 2 1 α
. It involves the two local principal radii of curvature R 1 and R 2 of the bilayer [25]. Due to the dependence of the bending elasticity modulus on the screening constant and its anisotropy described by the relation (8) anisotropic under the action of the magnetic field, the bending elasticity modulus of the membrane is also anisotropic. Nevertheless its account is not necessary at the calculation of the curvature elasticity energy of the vesicle up to the first order terms in 2 e since the direct calculation shows that its contribution in that approximation disappears exactly. That is why for the bending elasticity modulus the is assumed, what does not reflect the dependence of the modulus on the magnetic field strength and its direction. As before, we look at an ellipsoidal deformation of a quasi-spherical vesicle.

Integration leads to:

( ) ( ) ( ) 2 2 0 3 2 1 405 32 e R d d K K E o el b b b κ λ π - + + ≈ (10)
Exact treatment of the electrostatic energy of the vesicle under the action of the magnetic field carried out in [27] shows that besides the anisotropies of the elastic modulus discussed above, there is specific 3D efect leading to the anisotropy of the bending modulus depending on the tangential component of the magnetic field strength.

Howewer its contribution to the electrostatic energy is negligible since it does not contain -in comparison with the expression (10) -a multiplier 2 0 0 ) ( R χ which, as it follows from data in Table 1, is very large. E b enters in the expansion of the total free energy with the same order in e 2 as the magnetic energy E m , but with the opposite sign. Indeed it is possible to explain a prolate deformation or an oblate one depending whether E m or E b is predominant.

Results and discussion

The experimental measurements of R 0 and χ on given liposomes are computed in Eq. (1) to get the slopes in the expansion of E m as a function of e 2 . Then we convert the values of χ into particle concentrations C p , inferring a mean value for the nanoparticles diameters D=12×10 -7 cm, or equivalently a magnetic susceptibility per particle χ p =8.6×10 -19 cm 3 . The salt concentration is deduced by C s =C s 0 C p /C p 0 . From stoichiometry it follows that Z 1 =3

and C 1 =C s for the citrate anions, Z 2 =1 and C 2 =3C s for the sodium cations. Then we calculate the electrostatic decay factor κ o caused by the salt ions only. The two parameters λ and d appearing in the anisotropic term of ) ( i α κ are computed from the values of χ, C p , C s and Z=25, a reasonable estimate of the net charge per particle (including the adsorbed counterions). The surface charge density of the bilayer is inferred to be σ=800 ues cm -2 .

It represents about 1% of negatively charged lipids. Finally we compute E b /e 2 from Eq. (10). The ratio of the two competing terms E b /E m is plotted vs. C s on Fig. 3. For the higher ionic strengths where the screening of charges is the strongest, the magnetic term dominates the electrostatic contribution to the bending energy: the deformation is indeed prolate. The field dependent elongation has been analyzed in a former work in order to determine the bending modulus of the DOPC bilayer, K b =(8.6±0.8)×10 -13 dyn cm [26]. But a dilution of the ions in the bulk by two orders of magnitude is sufficient to reverse the ratio of E b and E m , thus explaining the oblate shape. The critical value for this ratio is 1, and it clearly separates the graph into domains of prolates and oblates. The scatter of Fig. 3 is due to two parameters, other than C s , that vary in a polydisperse suspension of magnetoliposomes: the vesicle radius R 0 and the encapsulated particle concentration C p (or equivalently the λ-parameter). For example the magnetic energy E m varies like 10) because of the polydispersities of R 0 and λ. This gives the residual scatter in the data. However the sensitivity on C s is fully established: C s is varied over two orders of magnitude, and this inverts the weights of E b and E m in the total energy. The set of values for the guessed parameters -Z, χ p (or equivalently D) and σ -is reasonable. The point that needs to be further discussed in our model is the approximation of a flat interface to derive the magnetic field H x (x) as given by Eq. ( 5). Complete treatment of the problem based on the curvature expansion of the electrostatic energy of the membrane of the arbitrary shape is carried out in [27]. Results obtained completely confirms qualitative picture considered above. It should be remarked that results obtained for the anisotropy of the spontaneous curvature in the frame of the complete treatment shows the coincidence with qualitative simple model even up to the numerical coefficient. Therefore current model is sufficient to point out that the electrostatic double layer of membrane is deformed by the magnetic field via its effect on the charged magnetic nanoparticles.

We have reported an original shape transition of giant magnetic liposomes triggered by the ionic strength.

The transition between prolate and oblate ellipsoids has already been observed under an applied ac electric field

[28]: the vesicles are prolate in the 'conductive regime' (low frequency) and oblate in the 'dielectric regime' (high frequency). It has also been predicted for an applied magnetic field: Helfrich showed that the sign of magnetic anisotropy of the lipid molecules themselves leads either to prolate or oblate deformations [25,29].

However the magnetically induced ellipticity has been far too small to be detected experimentally, even in a strong field H 0 =10 4 Oe (1 Tesla). Here we have taken advantage of the magnetic properties of the encapsulated solution to improve the coupling between the magnetic field and the bending energy of the vesicles. The main result of our theoretical description is an anisotropic distribution of particles at the neighborhood of the membrane when a field is applied. Both the Debye screening length at the inner monolayer and the spontaneous curvature of the bilayer maintain this anisotropy. This model corresponds to the regime of electrostatic interaction between a weakly charged phospholipid bilayer and ionic encapsulated species. This might be an important point for the description of biological membranes which are surrounded by charged mesoscopic objects and embedded in salty media. Gravity is along the z axis. The hot spots are lipid-particle aggregates that either settle at the bottom of the cell or make chains attracted by the strongly magnetized giant liposome.

  To get the particle concentration C p , we use the ferrofluid property of superparamagnetism: the susceptibility is the product of C p and the susceptibility per particle



  H . Let a be the semi- axis parallel to the magnetic field  H and b the value of the two other semi-axes perpendicular to  H . The two types of deformations and their amplitudes are characterized by a single parameter of ellipticity: positive for an elongated liposome (prolate ellipsoid) and negative for a compressed one (oblate ellipsoid).

  demagnetizing factor D(e): O. Sandre, C. Ménager, J. Prost, V. Cabuil, J.-C. Bacri, and A. Cebers, Phys. Rev. E 62, 3865 (2000) Author manuscript DOI: 10.1103/PhysRevE.62.

  -Boltzmann theory and the Debye Hückel approximation, a solution is found for a small variation of nanoparticle concentration around the bulk value ( δC x C x ). Then the linear dependence of δC p (x) with the electrostatic potential ψ(x) becomes anisotropic,

3 0 R.

 30 and the anisotropic bending energy E b like 2 0 R . The scatter of the data has been reduced by plotting on Fig. The error bars estimate the uncertainty in our measurements (shape analysis, magnetophoresis and conductimetry). It is impossible to fit all the data with a single simulation of Eqs. (1) and (

Fig. 1 :

 1 Fig. 1: The two competing shapes of magnetoliposomes subjected to a magnetic field (amplitude H 0 =400 Oe, field direction along the arrow); (a) prolate ellipsoid for a high ionic strength ferrofluid (C s 0 =85 mM); (b) oblate

Fig. 2 :

 2 Fig. 2: Cross-sections of an oblate magnetoliposome in the three principal planes xy, xz and yz. A stack of 150 pictures in the sample plane (xy) is taken every 0.5µm along the z axis with a confocal microscope (TCS4D, Leica). The lipid bilayer is labelled with the fluorescent dye Di-6-ASPBS (N-(4-sulfobutyl)-4-(4-(dihexylamino)styryl)pyridinium). Excitation is provided by the 488nm line of an Argon laser, and fluorescence is collected through a fluorescein filter set. The ellipsoid semi-axes are a=19µm and b=32.5µm. The ferrofluid has a low ionic strength (C s 0 =5 mM). The white arrow indicates the magnetic field (intensity H 0 =200 Oe).

Fig. 3 :

 3 Fig. 3: Ratio of the two competing terms E b /E m in the expansion of the free energy as a function of ellipticity. They are calculated for oblate (open markers) and for prolate (filled markers) liposomes using both experimental data (C p , C s , R 0 ) and assumed parameters (see text). Solid line is plotted from Eqs. (1) and (10) for typical values R 0 =15 µm and λ =5×10 -3 .

Table 1 :

 1 Examples of numerical data for oblates (clear cells) and prolates (shadowed cells). R 0 and e 2 are measured by optical microscopy. The parameters d and λ are calculated from experimental measurements of the concentrations C s and C p . The last three columns contain important features of the model: the screening length κ o -

	25.2	-0.397	0.96	3.0×10 -3	45	8.4	280
	13.3	-0.596	0.62	4.8×10 -3	29	2.2	230
	21.4	-1.17	0.62	3.2×10 -3	36	4.0	280
	24.6	-0.845	0.19	3.1×10 -3	20	0.73	380
	22.5	0.496	0.19	5.3×10 -3	15	0.32	290
	50.4	0.343	0.19	2.8×10 -3	21	0.85	400
	21.1	-1.31	0.14	1.5×10 -3	24	1.3	600
	31.6	0.466	0.11	2.3×10 -3	17	0.45	540
	14.1	0.536	0.074	4.5×10 -2	3.2	3.1×10 -3	150
	13.0	0.586	0.056	6.1×10 -3	7.8	4.2×10 -2	440

due to the salt ions only, the ratio of the electrostatic contribution to the bending modulus of membrane, and the local value of the spontaneous curvature radius at the magnetic poles (α=0 and α=π).

Acknowledgments

We thank J. Mertz and E. Karatekin for reading the manuscript and M. Blanchard-Desce for the gift of Di-6-ASPBS. O. Sandre, C. Ménager, J. Prost, V. Cabuil, J.-C. Bacri, and A. Cebers, Phys. Rev. E 62, 3865 (2000) Author manuscript DOI: 10.1103/PhysRevE.62.3865