C Nouguier-Lehon

Effect of the grain elongation on the behaviour of granular materials in biaxial compression

Keywords: C. Nouguier-Lehon, C. R. Mecanique ? ? ? (2011) Granular material, particle shape, biaxial test, rotations Matériau granulaire, forme des particules, essai biaxial, rotations

In this paper we study the effect of the grain elongation on the shearing behaviour of dense granular materials by means of 2D numerical simulations of biaxial compression tests, using the Contact Dynamics method. The case of grains with hexagonal shapes (and four possible different elongations) is studied in comparison to the case of a sample with circular grains. For the studied shapes, samples with polygonal grains exhibit initial densities higher than the sample with discs, and the initial density decreases when the grain elongation increases. The friction angle at the residual state increases linearly with the particle elongation ratio. The cumulative rotations of discs are higher than those of polygons. Finally, in the case of elongated hexagons, the grains with highest rotations are located along thin bands because the shear bands are thinner and more persistent for these shapes. To cite this article:

Introduction

The discrete element method (DEM) has been widely used since the last thirty years to improve the understanding of physical phenomena controlling the behaviour of granular materials. It allows to access to the microstructural parameters such as contact forces between particles, that are difficult to experimentally measure. The majority of simulations were initially performed on samples of either discs in 2D or spheres in 3D (we can cite [START_REF] Oda | Mechanics Of Granular Materials: An Introduction[END_REF][START_REF] Kuhn | Structured deformation in granular materials[END_REF][START_REF] Ltzel | Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell[END_REF][START_REF] Rothenburg | Critical state and evolution of coordination number in simulated granular materials[END_REF][START_REF] Ltzel | Comparing simulation and experiment of a 2D granular Couette shear device[END_REF][START_REF] Luding | Micro-macro transition for anisotropic, frictional granular packings[END_REF] among others). But, it is well known that the particle shape is a characteristic that has a great influence on the behaviour of such media [START_REF] Cleary | The effect of particle shape on hopper discharge[END_REF][START_REF] Cleary | DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge[END_REF][START_REF] Guo | Shear strength, interparticle locking, and dilatancy of granular materials[END_REF][START_REF] Tsomokos | Effect of grain shape and angularity on the undrained response of fine sands[END_REF]. Indeed, the possibility that grains are in contact through multiple contact points (due to roughness, angularity or nonconvexity of the particles) and the eventual grain elongation modify the behaviour of these materials. Several image analyses techniques and 3D surface reconstructions are nowadays available, that can be used in order to catch with remarkable precision the actual grain shape. However, the real shape of particles may be very complex and it is important to reproduce, in a rather simple way in numerical simulations, the main features of particle non-sphericity.

More recently, many numerical simulations were performed in order to study the effect of particle shape [START_REF] Rothenburg | Micromechanical features of granular assemblies with planar elliptical particles[END_REF][START_REF] Matuttis | Discrete Element Methods for the simulation of dense packings and heaps made of spherical and non-spherical particles[END_REF][START_REF] Antony | Influence of particle shape on the interplay between contact signatures and particulate strength[END_REF]. For instance, Mirgahsemi et al. [START_REF] Mirghasemi | Influence of particle shape on engineering properties of assemblies of two-dimensional polygonal-shaped particles[END_REF] performed numerical simulations with samples composed of 500 regular polygons (from triangles and squares to polygons with 11 edges) showing that samples made of angular particles are denser than samples with rounded particles. Azéma et al. [START_REF] Azéma | Force transmission in a packing of pentagonal particles[END_REF] showed that the existence of face-to-face contacts in a sample made of pentagonal particles leads to an higher anisotropy for the force transmission (with strong force chains essentially carried by face-to-face contacts). In previous works [START_REF] Nouguier-Lehon | Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis[END_REF][START_REF] Nouguier-Lehon | Structural changes in granular materials: the case of irregular polygonal particles[END_REF], we analysed the behaviour of samples composed of different grain shapes (circular, isotropic and anisotropic polygonal shapes). Our results clearly show the existence of a steady state of void ratio, of the shear strength and texture anisotropy, whatever the grain shape, as that has been found again by [START_REF] Peña | Influence of particle shape on sheared dense granular media[END_REF] from shear test simulations with samples of convex polygons. The effect of induced anisotropy was also studied by Alonso-Marroquín et al. [START_REF] Alonso-Marroquín | Role of anisotropy in the elastoplastic response of a polygonal packing[END_REF] analysing the behaviour of polygons with adjusted shapes to model the behaviour of the marble.

In the present study, we analyse the effect of particles elongation, by performing 2D numerical simulations of biaxial compression test and using samples made of irregular hexagons with different aspect ratio. A sample of discs was also generated in order to compare with the behaviour of circular particles. First we present the numerical program and the specimen preparation. Then we analyse the effect of grain elongation on the initial state and on the global and local mechanical behaviour.

Numerical procedures

Numerical method

The programs used for these simulations are based on the Contact Dynamics (CD) method [START_REF] Moreau | Some numerical methods in multibody dynamics: Application to granular materials[END_REF][START_REF] Jean | The non-smooth contact dynamics method[END_REF][START_REF] Moreau | Numerical aspects of the sweeping process[END_REF][START_REF] Radjaï | Contact Dynamics as a nonsmooth discrete element method[END_REF], i.e. a Discrete Element Method that allows to model granular assemblies as a collection of rigid or deformable bodies in contact with dry friction, without the introduction of elasticity at contacts (cf. smooth DEM [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF]). In the CD method, the impenetrability condition and the friction law are treated by using the non smooth relations of Signorini and Coulomb, which link the relative velocity at the contact impulsion. To take the collisions into account, normal and tangential coefficients of restitution are introduced, respectively denoted e N and e T , with values between 0 and 1. Pure elastic shocks are considered for e N = e T = 1, while the entire energy vanishes during impact for e N = e T = 0. Finally, the equations of motion are discretised by an implicit algorithm, that allows to choose larger time steps than the smooth DEM. The CD method has been used in very various fields from Civil Engineering to Biomechanics: among others we can cite the modelling of the ballast behaviour [START_REF] Saussine | Modelling ballast behaviour under dynamic loading, Part 1: A 2D polygonal discrete element method approach[END_REF] and of rock avalanches [START_REF] Taboada | Rock-soil avalanches: theory and simulation[END_REF], the study of masonry structures [START_REF] Chetouane | NSCD discrete element method for modelling masonry structures[END_REF], or the analyse of cytoskeleton structuration [START_REF] Maurin | Mechanical model of cytoskeleton structuration during cell adhesion and spreading[END_REF]. Comparisons between simulations performed with the CD method and smooth DEM showed that both numerical methods give similar results for quasistatic tests [START_REF] Nouguier-Lehon | Analysis of granular material behaviour from two kinds of numerical modelling[END_REF][START_REF] Kadau | Influence of particle elasticity in shear testers[END_REF]. The particle elongation [START_REF] Mitchell | Fundamentals of Soil Behavior[END_REF] can be defined as the ratio b a , where a is the diameter of the smallest circle containing the particle and b is the diameter of the largest circle included in the particle (figure 1). So the elongation ratio b a is the inverse of the aspect ratio, a parameter also used to characterize the particle elongation, that is defined as the ratio of the largest particle size to the smaller one. For a circular particle, b a = 1 and the higher the particle elongation the smaller the ratio b a . Starting from the same particle size distribution (d min = 0.66 cm, d max = 2 cm and a uniform distribution in particle surface fraction), the polygons are generated in order to obtain particles having, for a given diameter, the most elongated shape. To avoid the effect of particle roundness, all the polygonal shapes have six edges. The two first vertices are put diametrically opposed on the circle of a in diameter (points A 1 and A 2 in figure 1). Then, the four latest vertices will be on the lines tangent to the circle of b in diameter and parallel to this line A 1 A 2 . To avoid regular hexagons, these vertices are chosen in a random way between the two extremal cases which are on one hand the point located on the large circle (point P 1 in figure 1) and on the other hand the point such as the small circle is the inscribed circle (point P 2 in figure 1). In this work, we studied five different values of the elongation ratio: b a = 1 (circular particle); 0.8; 0.7; 0.6 and 0.5. The most elongated hexagons have thus their largest dimension twice the smallest one.

Shape characterization and sample generation

The granular sample is contained inside a box with rigid walls and the grains are perfectly rigid in these numerical simulations. Since each sample is made of grains with different shapes, we used a sample creation leading to the densest state (maximal relative density). First, a sample of non contacting discs is generated with the particle size distribution chosen and they are then replaced by hexagons so that a = 2r. The hexagons are set with a random orientation, a random velocity and normal and tangential coefficients of restitution equal to 1 in order to have chocks without energy dissipation. The gravity and the coefficients of friction µ g between grains and µ w between walls and particles are set to zero. The sample is isotropically compressed with the same constant velocity applied to the top and the right walls. To avoid a looser area in the center of sample, this displacement is regularly stopped so that the particles are evenly distributed inside the box, before pursuing the compression until a state of isotropic stress is reached. Five different samples with 4995 grains are generated: four of them are made of hexagons and the last one is made of discs. The figure 2 shows zoom in samples for every assemblies generated with the polygonal shapes. This generation procedure allows to obtain homogeneous samples in respect with the density and to avoid a preferential direction of contact normal (figure 3), that would happen if the particles were deposit in the gravity field, especially in that case of elongated particles [START_REF] Nouguier-Lehon | Structural changes in granular materials: the case of irregular polygonal particles[END_REF][START_REF] Hidalgo | Granular packings of elongated faceted particles deposited under gravity[END_REF]. Moreover, it was also verified that the orientation of particles was randomly distributed: figure 4 shows the polar distributions of the hexagons largest axis orientations. Figure 5 shows the effect of grain elongation on the initial void ratio e 0 . We can note that, for the studied shapes, the sample made of discs ( b a = 1) is the loosest sample, which is consistent with previous numerical studies about the effect of particle angularity [START_REF] Mirghasemi | Influence of particle shape on engineering properties of assemblies of two-dimensional polygonal-shaped particles[END_REF][START_REF] Azéma | Force transmission in a packing of pentagonal particles[END_REF]. When the particle shape slightly deviates from the circular shape ( b a = 0.8), the initial void ratio decreases to reach a minimum for b a = 0.7, which corresponds to an aspect ratio a b ≈ 1.5. It is the same result as [START_REF] Donev | Unusually dense crystal packings of ellipsoids[END_REF][START_REF] Donev | Underconstrined jammed packings of nonspherical hard particles: ellipses ans ellipsoids[END_REF][START_REF] Ng | Particle shape effect on macro-and micro-behaviors of monodisperse ellipsoids[END_REF] who obtained, experimentally and numerically, the densest packing for ellipsoids with an aspect ratio equal to 1.5. For lower elongation ratio, the initial void ratio increases. The angularity of polygons allows first to reach a denser initial state, but the particle elongation reduces this ability and for very elongated particles, a larger initial void ratio is expected, as observed by [START_REF] Hidalgo | Granular packings of elongated faceted particles deposited under gravity[END_REF][START_REF] Donev | Unusually dense crystal packings of ellipsoids[END_REF][START_REF] Donev | Underconstrined jammed packings of nonspherical hard particles: ellipses ans ellipsoids[END_REF].

Results

Analysis of initial states

We can also remark in figures 3 and 4 that the samples made of hexagons with b a = 0.8 and b a = 0.7 present distributions of contact directions and particle orientations with more fluctuations, in spite of the isotropic procedure used to generate the samples. This is because these hexagons are almost regular and only very slightly elongated. So, during the sample preparation, they arrange themselves with face-toface contacts having almost all the same orientation. As a consequence, these samples also exhibit a more variable orientation distribution. It would be interesting to generate samples containing more particles and to test the repeatability of specimen creation in order to see whether a preferential direction emerges.

Mechanical behaviour in biaxial compression

The biaxial compression tests are performed for a constant confining stress σ 0 = 10 kPa by applying a constant horizontal velocity V 1 onto the right wall. To avoid dynamics effects, the velocity V 1 is chosen such as the inertia parameter I defined from [36] is small enough: I = ε m σ0 ≤ 10 -3 . The coefficients of friction are set to 0.5 between particles and kept to zero between walls and particles. For these quasistatic simulations, the contact network slowly evolves, so the restitution coefficients are decreased to e N = 0.2 and e T = 0.1.

Figures 6 and7 show the stress-strain curves and the volumetric behaviour of samples during the biaxial compression. Since the samples are dense, the evolution of q p = σ1-σ2 σ1+σ2 as a function of the axial strain ε 1 exhibits a peak followed by a softening leading to a residual state. The behaviour of the discs sample is different from the behaviour of hexagons samples: the shear resistance and the dilatancy are greater for the samples made of non-circular particles. Angularity and particle elongation allow a better mobilization of friction at contacts and restrict grain rotation, as it will be shown in the following section.

The effect of elongation on the value of the internal friction angles at peak Φ peak and at the residual state Φ * is shown in figure 8, where sin Φ = σ1-σ2 σ1+σ2 . The sample made of hexagons with b a = 0.7 exhibits the larger Φ peak value, that can be connected with the fact that it is also the densest sample. Then Φ peak decreases with b a . We observe a linear increase of the internal friction angle at the residual state Φ * in the range of the particle elongation examined here. The same result was observe by Ng [START_REF] Ng | Particle shape effect on macro-and micro-behaviors of monodisperse ellipsoids[END_REF] for samples made of ellipsoids with similar aspect ratios. In our study, the procedure chosen to generate the hexagons does not allow to model particles with b a greater than 0.8. So we can not predict the evolution of Φ * and Φ peak for samples composed of particles whose shape gradually approaches a circular one. On the other hand, it would be interesting to simulate samples with more elongated particles ( b a < 0.5) to check whether the linear increase of Φ * is confirmed or whether there is a value of b a from which it no longer increases.

Discussion

A lot of results found in the previous section can be explained by the particle angularity allowing them to exhibit face-to-face contacts. At the initial state, the samples made of polygonal particles are denser because this angular shape is able to better fill up the voids than the circular one. But beyond the elongation ratio b a = 0.7 these face-to-face contacts are less and less possible (there are 15% of face-to-face contacts in the sample with b a = 0.8, whereas there are only 10% in the sample with b a = 0.5) because the prevailing mechanism is the volume exclusion while it is negligible for a small deviation from the circular shape [START_REF] Azéma | Stress-strain behavior and geometrical properties of packing of elongated particles[END_REF]. So, the initial void ratio increases for the samples made of the most elongated hexagons.

This ability for the angular particles to have face-to-face contacts also restricts the grain rotation during the biaxial compression. For the sample of discs, 77% of grains have a cumulative rotation (from the initial state to ε 1 = 20%) greater than ±15 • , while less than 50% of hexagons rotate more than 15 • in absolute value for the same axial strain ε 1 , whatever their elongation ratio. Moreover, these large rotations are not distributed in the same way for the discs than for the polygons: large rotations are uniformly distributed inside the sample of discs (figure 9) but are located along thin bands for the samples of hexagons (figure 10). This phenomenon is linked with the width and persistence of shear bands, which is not the same in samples of discs and samples of polygons. They are more spread in the case of circular particles and are very volatile. In figure 11 the large cumulative rotation of discs is shown for strain increments of 5%. One can see that zones where the cumulative rotation is large move depending on the strain amplitude. On the contrary for samples made of angular grains, shear bands are thinner [START_REF] Gerolymatou | Energy-rates for granular materials: discrete characterization[END_REF] and they change very little during the deformation, as shown in figure 12. This is consistent with the result obtained by [START_REF] Kuhn | Structured deformation in granular materials[END_REF], [START_REF] Iwashita | Micro-deformation mechanism of shear banding process based on modified distinct element method[END_REF] and [START_REF] Mohamed | Comprehensive study of the effects of rolling resistance on the stress-strain and strain localization behavior of granular materials, Gran. Matter[END_REF] which performed numerical simulations on samples of discs but by introducing some rolling resistance at contact points in order to reproduce a high gradient of particle rotation along the shear band, as it is found in actual sand. Finally, we can note that for these hexagonal particles, the rotations have the same direction inside a given shear band (anticlockwise or clockwise), this confirms the importance of sliding contacts (increasing the mobilization of friction) for these elongated shapes.

Conclusions and perspectives

Numerical simulations of biaxial compression were performed on samples composed of either hexagons or discs in order to analyse the effect of particle angularity and elongation. The mechanical response of these samples was analysed in particular in comparison to that of a sample of circular particles. Our results show that particle shape modify the global and local behaviours of these granular materials. -For the range of b a ratio studied and for the same initial confining pressure, the samples made of angular particles are denser than the sample made of circular particles, but the particle elongation reduces this ability and density of samples with hexagons decreases with their elongation.

-Samples made of angular particles exhibit larger shear strength and dilatancy due to the face-to-face contacts that restrict rotations and the friction angle at the residual state is found to linearly increase with the particle elongation, for the range of b a ratio studied. -The large rotations are distributed inside the whole sample of discs whereas they are located inside thin bands for the samples made of angular grains, because the shear bands are thinner and more persistent in these media. Therefore, DEM simulations using only circular or spherical particles seem too restrictive. If the introduction of rolling resistance is an attractive solution [START_REF] Iwashita | Micro-deformation mechanism of shear banding process based on modified distinct element method[END_REF][START_REF] Mohamed | Comprehensive study of the effects of rolling resistance on the stress-strain and strain localization behavior of granular materials, Gran. Matter[END_REF], the difficulty of this strategy lies in choosing the value of such a parameter. Taking into account the non-circular shape of the particles (angularity and elongation) allow to introduce into the numerical model only parameters whose physical origin is clear.

Further analyses are presently under way in order to correlate these results with the evolution of some local parameters (coordination number, anisotropy of contact forces) and to clarify the effect of particle elongation. Comparisons with the results obtained for samples made of some other shapes (octagons [START_REF] Chaze | Effect of grain shape on the behaviour of granular materials in biaxial compression[END_REF], clumps made of overlapping discs [START_REF] Saint-Cyr | Effect of shape nonconvexity on the shear strength of granular media[END_REF][START_REF] Szarf | Influence of the grains shape on the mechanical behavior of granular materials[END_REF], rectangles with rounded caps [START_REF] Azéma | Stress-strain behavior and geometrical properties of packing of elongated particles[END_REF]...) are also in progress, in order to extend this analysis and to generalize the effect of the grain shape on the mechanical behaviour of granular materials.

Figure 1 .

 1 Figure 1. Construction of an irregular hexagonal shape with an elongation ratio b a .

Figure 2 .

 2 Figure 2. Zoom in the assemblies made of elongated hexagons at the initial state.

Figure 3 .

 3 Figure 3. Polar distributions of normal vector orientation in the initial configuration for every elongation ratio.

Figure 4 .

 4 Figure 4. Polar distributions of hexagon orientations in the initial configuration for every elongation ratio.

Figure 5 .

 5 Figure 5. Initial void ratio e 0 as a function of the elongation ratio b a .

Figure 6 . 2 σ 1 +σ 2 as a function of the axial strain ε 1 Figure 7 .

 62217 Figure 6. Evolution of qp = σ 1 -σ 2 σ 1 +σ 2as a function of the axial strain ε 1 for the sample of discs and 3 samples of elongated particles.

Figure 8 .

 8 Figure 8. Effect of the elongation ratio b a on the friction angle at peak Φ peak and at the residual state Φ * .

Figure 9 .

 9 Figure 9. (a) Cumulative rotation of discs from initial state to ε 1 = 20%. The discs which rotate more than 15 • anticlockwise are filled in black and respectively in white if it is a clockwise rotation. (b) Relative displacement of discs from initial state to ε 1 = 20% showing the location of zones associated to large displacements.

Figure 10 .

 10 Figure 10. (a) Cumulative rotation of hexagons with b a = 0.5 from initial state to ε 1 = 20%. The grains which rotate more than 15 • anticlockwise are filled in black and respectively in white if it is a clockwise rotation. (b) Deformation after ε 1 = 20% of an initial regular grid imprint on the sample of hexagons with b a = 0.5 at the initial state, showing the location of the most distorted zones. (c) Relative displacement of hexagons with b a = 0.5 from initial state to ε 1 = 20% showing the location of zones associated to large displacements. The cases of hexagons with b a > 0.5 are similar.

Figure 11 .

 11 Figure 11. Cumulative rotation of discs (a) from initial state to ε 1 = 5% and (b) from ε 1 = 5% to ε 1 = 10%. The grains which rotate more than 5 • anticlockwise are filled in black and respectively in white if it is a clockwise rotation.

Figure 12 .

 12 Figure 12. Cumulative rotation of hexagons with b a = 0.2 (a) from initial state to ε 1 = 5% (b) from ε 1 = 5% to ε 1 = 10% (c) from ε 1 = 10% to ε 1 = 15% and (d) from ε 1 = 5 15% to ε 1 = 20%. The grains which rotate more than 5 • anticlockwise are filled in black and respectively in white if it is a clockwise rotation.

Email address: cecile.nouguier@ec-lyon.fr (C. Nouguier-Lehon).

Acknowledgements

This work is a part of the CEGEO program, a french national research project.


Aline Cohen De Lara

Séparer pour mieux soigner : le travail du psychanalyste en institution spécialisée

La première psychanalyse d'enfant de D.W. Winnicott était celle d'un délinquant suivi au sein d'une institution qui n'a pas toléré les actes transgressifs de ce garçon. Il a d'ailleurs inventé un diagnostic qui l'aurait considérablement aidé dans sa pratique : « Enfant pour qui je ne peux rien », préconisant la nécessité d'une prise en charge par la société, d'une prise en main de l'enfant, afin de ne pas le laisser tomber comme son environnement initial a pu le faire. Dans la tendance antisociale, l'enfant cherche quelque chose de bon qu'il a expérimenté et qui lui a été retiré. Pas de privation mais une séparation, un retrait qui « a dépassé la durée pendant laquelle l'enfant est capable d'en maintenir le souvenir vivant », nous dit Winnicott.

La notion de séparation est ainsi présente dans la tendance antisociale, renvoyant à l'idée d'une rupture de continuité, une rupture de l'environnement interdisant à l'enfant la possible prise en charge de lui-même, c'est à dire l'adaptation à soi même, à sa propre destructivité. À travers la tendance antisociale : « l'enfant cherche (…) la stabilité de l'environnement qui pourra supporter la tension résultant du comportement impulsif ; c'est la quête d'un environnement perdu, d'une attitude humaine qui, parce que l'on peut s'y fier, donne la liberté à l'individu de bouger et d'agir et de s'exciter 1 » écrit Winnicott. La tendance antisociale est un signe d'espoir et c'est à cet espoir que la société en général et plus spécifiquement les thérapeutes d'enfants au sens large doivent répondre, sauf à considérer que ces formes d'expressions sont "sans objet", sans destinataire, et à réprimer.

J'aimerai évoquer avec vous, non pas les incidences pathogènes des séparations sur le fonctionnement psychique de l'enfant, mais la dimension potentiellement thérapeutique de la séparation, lorsqu'elle est proposée dans le cadre de placements en institution. Cet exposé est issu de mon expérience de psychanalyste auprès d'enfants placés au centre thérapeutique « Le coteau G. Amado », un ITEP qui était spécialisé dans la prévention les risques d'évolution vers la psychopathie et la délinquance.

Lorsque l'on se penche sur les histoires personnelles de ces enfants agités et violents, ayant recours aux comportements comme symptômes manifestes de leurs souffrances psychiques, on retrouve toujours dans leurs anamnèses des séparations concrètes, petites ou grandes, des discontinuités d'investissement multiples. On se demande alors quel peut être le bénéfice d'une séparation de plus, aussi « lourde » que celle proposée par un placement. Quelles conséquences cela va-t-il avoir sur le fonctionnement de ses enfants ? Ne faudrait-il pas au contraire renforcer des liens déjà très malmenés en maintenant coute que coute l'enfant dans son milieu de vie. C'est pourtant suite aux difficultés rencontrées dans les prises en charges en ambulatoire et face à des situations de crise intense que nos partenaires des secteurs en viennent à envisager la séparation de l'enfant d'avec sa famille. L'internat du Coteau avait pour spécificité d'utiliser la séparation comme un outil thérapeutique 2 , en proposant une séparation longue, venant réactiver d'autres séparations afin d'en tenter une élaboration après coup. Situation pour le moins paradoxale, où ces enfants ayant déjà vécu de nombreuses ruptures étaient séparés de leur milieu familial pendant un trimestre, sans retour à la maison, mais avec des visites régulières de la famille. Paradoxe aussi quand, face à des vécus d'exclusion et de rejet, une intensification factuelle de la séparation était proposée, entrainant souvent un désir de réappropriation de l'enfant par ses parents permettant un travail de reprise. Pourtant, le paradoxe a été pour moi de constater que cette situation de séparation a pu être un levier thérapeutique souvent bénéfique, quand elle était pensée par une équipe pluridisciplinaire et surtout travaillée psychiquement avec l'enfant et ses parents. Certes, les risques de clivage et de ruptures peuvent alors être accentués. D'où la nécessité d'un travail de reprise régulier par les professionnels durant les réunions, bien sur, mais aussi au sein de la vie institutionnelle au sens large, "dans les couloirs", dans ces espaces « interstitiels » potentiellement thérapeutiques. Si j'insiste sur ce point, c'est qu'actuellement au sein des institutions soignantes de tous ordres, le temps nous est compté, tout doit être 3 Kahn L. ( 2008) "Les petites choses. Enfants du Coteau, temps de guerre", in penser/rêver, n°14, L'inadaptation des enfants et de quelques autres, Édition de l'Olivier, p. 14. ; Ibid. pp. 18-21. Les périodes d'intense destructivité de Sonia à mon égard me laissaient comme terrassée, totalement impuissante à l'aider par les moyens classiques de la psychothérapie. Comment jouer avec quelqu'un qui n'en est pas, ou plus capable, comment lui montrer, en suivant R.

Roussillon, que le jeu « soutient la part d'illusion nécessaire à la vie psychique, (et) permet de transformer les situations les plus douloureuses en situations "bonnes à symboliser". » Il appartient au travail psychanalytique, nous propose t'il de « retrouver les traces du jeu (qui n'a pas pu historiquement avoir lieu) pour créer les conditions qui permettent que le jeu potentiel puisse être régénéré et qu'il puisse redéployer ses virtualités symbolisantes » . 9

Jouer, c'est accepter de régresser. Mais cette régression est insupportable pour ces enfants, puisqu'elle renvoie à leur vécu d'impuissance, aux failles narcissiques douloureuses, à un risque d'intrusion et de passivité insupportables, eux qui ont souvent constitué des carapaces de guerriers insensibles, tout-puissants, pour affronter leurs réalités. J'ai souvent eu l'impression que mon travail de psychanalyste avec ces enfants n'était qu'une longue négociation, toujours remise sur le tapis de jeu à chaque séance. Peu de playing car sans règles, c'est prendre le risque de tomber dans l'arbitraire, la folie de la toute-puissance de la pensée et le risque encouru de la perte totale des limites. Quelques games parfois qui avaient le mérite d'apaiser un temps la situation. Un temps seulement, car comment accepter la contrainte des règles et, pour le psychanalyste, ces jeux sans fin où toujours il perd, quels que soient les dés. Rien ne doit être laissé au hasard, tout doit être sous contrôle omnipotent.

Recevoir, contenir, et survivre à la destructivité, tel est souvent l'essentiel des parcours psychanalytiques avec ces enfants. Lier la destructivité à l'objet, mais dans l'actualisation du transfert, c'est-à-dire sur l'objet de transfert et pendant longtemps ne jamais nommer l'objet du transfert. Il faut accepter et tolérer d'être un objet de transfert, (un "objeu") 10 , prêter notre présence et notre fonctionnement psychique, sans quasiment jamais évoquer directement les objets premiers d'investissement. Au début de ma pratique, je pensais qu'il fallait verbaliser, trouver les mots qui semblaient faire défaut à ces enfants, interpréter le transfert, lier ces mouvements psychiques aux imagos parentales perceptibles à partir du contre-transfert. Le constat a été rapide, en lieu et place de l'apaisement attendu, l'excitation redoublait et les 12 Green (2005) op. cit.,p. 32. 13 D.W. Winnicott (1971), Playing andreality, tr. fr. Jeux et réalité, in Éditions Gallimard, 1975. Lorsque la réalité vient confirmer ce vécu intrapsychique, comment croire alors à leur potentialité de restauration ? La réponse de l'objet est fondamentale, même imparfaite, elle tente d'être "suffisamment bonne". Sonia venait d'avoir 14 ans, elle allait mieux quand nous avons décidé d'un commun accord d'interrompre la psychanalyse. Par la suite, elle est revenue à plusieurs reprises me rencontrer, pour "avoir de mes nouvelles" disait-elle. Elle a souhaité me revoir lors du décès de sa mère, en présence de sa famille d'accueil, elle y tenait, comme si pour eux aussi, je devais être inscrite dans son parcours au centre. Elle voulait, je crois, vérifier que j'avais survécu à sa force destructrice. Plus tard, lorsqu'elle a su que je quittais l'institution, elle a demandé à me rencontrer. Elle souhaitait savoir ce que je ferai de son dossier. Nous l'avons regardé et retracé ensemble notre cheminement en ce lieu. Elle a décidé de l'emporter avec elle puisque je partais. Quand à 21 ans elle a quitté le placement familial, elle a organisé une petite fête où elle m'a convié. Je n'ai pas beaucoup hésité, j'y suis allée et ce soir-là, elle m'a demandé comment j'avais fait pour la supporter. Elle se souvenait essentiellement de ces moments de destructivité, lorsqu'elle disait de moi que j'avais une "sale gueule" à l'époque où le visage de sa mère était de plus en plus déformé par la maladie. Je lui ai répondu qu'à ce moment-là, je savais que tout en s'adressant à moi, elle s'adressait aussi à travers moi, à quelqu'un d'autre et à elle-même. Et que si elle avait pu le faire, c'était parce que nous savions que, malgré tout, nous nous aimions bien toutes les deux. Je ne sais pas si j'ai trouvé les mots justes pour évoquer ces mouvements transférentiels, ce sont ceux qui me sont venus et je crois qu'elle était prête à les entendre. J'ai en tout cas la conviction que de son côté, il était maintenant possible pour elle de revenir l'espace d'un instant sur ces temps forts de sa psychanalyse et s'interroger sur son fonctionnement psychique et le mien. Elle pouvait au moment où elle se séparait officiellement de ce lieu de soin et de vie ainsi que des individus qui l'avaient accompagné, évoquer sa destructivité et constater de visu qu'elle n'avait pas tout détruit autour d'elle et qu'elle était aussi capable de réparation à travers cette invitation. Nous étions toutes les deux ce jour là prêtes à nous séparer.

De mon côté, la séparation d'avec ce lieu de soin a pris du temps, un temps psychique qui n'a pas correspondu avec le temps réel d'une séparation qui nous a été imposé du dehors par des instances administratives qui ont détruit un outil original et je crois thérapeutique. J'ai souhaité aujourd'hui plus de dix ans après rendre hommage au travail mené pendant des années par l'ensemble de l'équipe du Coteau-G. Amado à Vitry sur Seine.

  Dans ces formes psychopathologiques, les sujets luttent contre la massivité potentielle de leurs investissements objectaux idéalisés. D'où la nécessité d'un dispositif qui offre un espace thérapeutique élargi où peuvent être perçus et entendus, venir se projeter et se déplacer, se jouer et se donner à voir en des lieux et selon des modalités différentes, les effets de ces investissements de nature transférentielle. Cet environnement thérapeutique peut rendre possible la diffraction du transfert sur de nombreux intervenants, évitant ainsi la condensation du transfert sur la seule personne du psychanalyste. Cette diffraction, qui complexifie la situation psychanalytique individuelle, est pourtant nécessaire tant les mouvements transférentiels susceptibles d'apparaître sont massifs, violents, en tout ou rien, menaçants pour le sujet, mouvements qui ne trouvaient jusqu'alors de dérivation que dans les agirs, les 2 Cet internat était l'une des institutions du Centre Thérapeutique « Le Coteau -Georges Amado » à Vitry Sur Seine, cf. Cohen de Lara A. (2001) « Ces enfants dits inadaptés », in dir. Arfouilloux J. C., Diatkine G., Fréjaville A., Éducation et maltraitance, PUF, Monographies de la Psychiatrie de l'enfant, 2001, 137-148.comportements. Pour L. Kahn, qui a longtemps travaillé au Coteau, le psychanalyste « ne pouvait vraiment laisser se développer dans le transfert le jeu des forces pulsionnelles que parce qu'il savait qu'il y avait une forme d'environnement qui, par ailleurs, allait endiguer l'instabilité. […] D'une certaine façon, ces traitements n'étaient possibles que parce qu'il y avait un véritable environnement pour l'analyste » 3 . Ce cadre contenant, « facilitant » et fiable, au sein duquel les traitements psychanalytiques peuvent avoir lieu, exerce une fonction médiatrice et protectrice, nécessaire et indispensable pour prendre le risque du transfert, du côté du sujet, et pour tolérer l'intensité de ce transfert, du côté du thérapeute. Car c'est précisément contre le risque du transfert que luttent ces patients qui ne peuvent pas psychiquement se laisser aller à vivre des sentiments aussi intenses, à se faire confiance et à avoir confiance en l'objet. A. Green fait de « la confiance en une espérance d'un possible dans l'avenir » 4 une des conditions de possibilité d'analyse. Dans ces situations de séparation, la question de la confiance semble exacerbée par les vécus antérieurs de défaillance des objets d'investissement. Pourquoi investir à nouveau alors même que de multiples expériences ont montré les risques encourus lors de séparations, pourquoi raviver des blessures narcissiques profondes et toujours actuelles ? Quels que soient ces vécus de défaillance antérieurs, la fidélité aux premiers objets d'investissement reste très active tant que l'enfant n'a pas pu les resituer à une place qui lui permette de s'en séparer psychiquement et d'exister sans trop de souffrances. Cette fidélité aux parents suscite des conflits d'appartenance chez les enfants et ce d'autant plus qu'ils doivent aussi investir les autres adultes qui les ont en charge, avant même de pouvoir investir leur psychanalyste. Ainsi, si une alliance thérapeutique peut s'instaurer, elle doit d'abord avoir lieu avec ces multiples intervenants afin de constituer un des éléments du cadre thérapeutique.

4

  Green A. (2005) "Le syndrome de désertification psychique", in Le travail du psychanalyste en psychothérapie, Dunod, Paris, pp. 23. quantifié et spécifié, ce qui laisse peu de place pour les échanges informels, pour ce travail de lien entre les soignants. Or, c'est aussi de cela que ces enfants en particulier ont besoin, que les adultes qui les ont en charge, qui prennent soin d'eux, échangent entre eux, à propos d'eux et du reste. « On parle d'un enfant » dirait J.L. Donnet 5 . La dimension thérapeutique ne doit pas être réduite au temps concret passé auprès d'un patient. Que fait l'objet quand il s'absente, vers quel autre objet se tourne-t-il quand il n'est pas là ? C'est ici la question de la scène primitive qui peut se rejouer pour l'enfant et qui peut être reprise dans un travail élaboratif au sein des séances de psychanalyse individuelle. La séparation et l'exclusion peuvent être tolérées si l'enfant sent et peut penser qu'il reste présent dans la pensée de l'objet qui s'absente. « L'investissement maintenu de l'objet en l'absence de celui-ci, suppose la réciproque […] la représentation de l'existence d'un investissement maintenu par les objets parentaux eux-mêmes » écrit Roussillon. 6 Sans tomber dans l'idéalisation des prises en charge institutionnelles, c'est pourtant la présence soignante de plusieurs intervenants qui ont des liens entre eux, qui non seulement rend possible la diffraction du transfert tout en contenant les risques de clivage, mais aussi favorise l'intériorisation du tiers par l'enfant, et donc l'accès à un possible traitement des problématiques de séparations et de leurs incidences sur le fonctionnement. Une autre particularité de l'internat du Coteau était la durée du placement fixée à deux années de séjour, c'est à dire une autre séparation, programmée cette fois-ci à l'avance. Deux ans pour une psychothérapie, qu'advient-il du temps psychique, du temps d'instauration d'un processus ? L'inconscient est atemporel. Comment investir une relation et a fortiori une relation de transfert lorsque l'on sait que le terme est déterminé d'avance ? Cette durée était une des conditions du cadre thérapeutique global. Une forme d'instance surmoïque limitante, de fonction tierce au sein de la relation duelle qui s'engageait. Ce temps de séparation déterminé correspondait à des paramètres externes au fonctionnement psychique, tout comme le temps déterminé d'une séance. Pas d'arbitraire ici, mais une condition établie d'avance, en dehors de l'enfant et du thérapeute, puisque c'était une des conditions d'acceptation du placement en internat. "Vous entrez et vous en sortirez". Condition porteuse de séparation mais aussi d'issue, quelle qu'elle soit. Cela pouvait représenter pour certains enfants un obstacle à l'indication de psychanalyse individuelle, d'où l'importance d'une évaluation fine par un tiers avant toute décision. Elle s'avérait être un moteur thérapeutique dans de 5 Cité par Roussillon R. (2010), in La naissance de l'objet, pp. 36. 6 Roussillon R. (2010) Ibid. pp. 35. nombreux cas. Au sein même de la psychanalyse individuelle, cette condition du cadre permettait que l'actualité de la séparation liée au placement tout comme celles à venir puissent être pensées, réactivant souvent des représentations et des affects liés aux séparations antérieures. Parfois déniée par l'enfant, la séparation d'avec l'institution ne devait pas l'être pour le thérapeute qui participait de ce cadre global. Une fois ce cadre externe mis en place et plus ou moins accepté, ou toléré, par l'enfant et sa famille, il devient possible d'envisager une psychanalyse individuelle pour certains, même si les risques de rupture sont toujours présents et susceptibles de s'actualiser du fait même des mouvements induits par le processus mais aussi des évènements de la réalité extérieure. Car ce qui rend les prises en charges de ces enfants complexes, c'est aussi parce que des évènements de la réalité externe viennent envahir la séance, trop de réalité empêchant l'instauration d'une autre scène, scène psychique, théâtre privé, au sein duquel la réalité psychique pourrait se jouer. D'où la nécessité que cette réalité externe et les incidences qui en découlent soient elles aussi prises en charge par d'autres professionnels tout au long du traitement. Filtrée par ce cadre thérapeutique global, la réalité externe peut partiellement être mise à la porte de la séance. Partiellement cependant… Sonia entre à l'internat à l'âge de 6 ans du fait de troubles du comportement et surtout d'une situation de crise familiale intense. Durant la première année, elle semblait n'investir pleinement ni sa psychanalyse ni l'institution. Le processus thérapeutique était d'autant plus long à s'instaurer que les relations entre les parents ne cessaient de se dégrader. La mère, atteinte d'un cancer avancé, souhaitait le placement de sa fille afin de lui permettre de poursuivre une scolarité en milieu protégé. Le père était lui extrêmement méfiant, avec un vécu de persécution à peine dissimulé. Il était contre le placement, contre la thérapie mais aussi contre un retour à la maison, conscient qu'il était de son impossibilité à s'occuper de ses enfants ; situation paradoxale s'il en est pour cette petite fille qui ne savait qui satisfaire. La séparation proposée par l'internat était douloureusement vécue par tous, enfant, famille et professionnels et nous avons dès le début de la seconde année envisagé un retour à la maison, afin que Sonia puisse vivre auprès de sa mère dont l'état de santé ne s'améliorait pas. Psychiquement, je me sentais dans une impasse : comment investir cette enfant, comment penser une continuité autrement qu'en essayant, à partir d'un matériel chaotique et peu symbolique, de tisser des fils d'une séance à l'autre. Sonia n'avait pas souhaité que je rencontre ses parents au début du traitement, elle ne voulait pas que nous puissions voir sa mère dont le visage était défiguré par la maladie et qui avait le plus grand mal à s'exprimer. C'est devant l'éventualité d'un retour à la maison qu'elle a tenu à ce que je les rencontre. Ce passage par la réalité concrète est souvent nécessaire en psychanalyse d'enfants. Pour Sonia, cette rencontre a contribué à sceller une alliance thérapeutique malgré le chaos que fut ce cheminement en psychanalyse et les nombreux bouleversements et drames qui ont égrené le parcours de cette enfant tout au long des placements, dont les décès successifs de ses parents. Cette alliance a rendu possible que nous engagions puis poursuivions ce travail jusqu'à l'adolescence. Après deux années à l'internat, Sonia est retournée vivre un temps chez elle en continuant d'être prise en charge à l'externat du Coteau. La psychanalyse a pu se poursuivre, tant bien que mal. En effet, à plusieurs reprises et pendant de longues périodes, en lien avec l'aggravation de la maladie de la mère et la séparation des parents, Sonia mettait tout en oeuvre pour fragiliser et empêcher le déroulement de ses séances, jusqu'à monter les autres enfants pour que collectivement ils cessent de fréquenter leurs analystes. Elle mobilisait ainsi l'ensemble de l'équipe et tout le monde savait que l'heure de ses séances approchait. Si elle refusait parfois d'y venir, le plus souvent elle hurlait son refus dans les couloirs, tournait autour de mon bureau pour finir par y entrer et se blottir derrière moi en criant que je la forçais à être là et en m'intimant l'ordre de la laisser sortir. Conduites et propos paradoxaux puisque, bien sûr, rien concrètement ne l'empêchait de le faire, sauf la force du lien transférentiel, un transfert paradoxal au sens d'Anzieu, dans ces moments où ses objets premiers d'investissement étaient particulièrement fragiles et où une décision de placement familial était prise. Pour J.L. Donnet, dans le conflit opposant le moi et le surmoi, il est plus facile pour le moi « de se défendre contre l'accusation venant du dehors, (à partir de laquelle il a pu accéder jadis à la capacité de mensonge, condition d'une liberté de penser,) que contre l'accusation du dedans, détentrice du devinement parental. (…) C'est pourquoi le détour par la projection de l'accusation est un temps transférentiel nécessaire pour l'établissement d'une scène de tribunal interne 7 ». En développant la question de la conscience morale à travers le concept de surmoi et en introduisant la notion de sentiment inconscient de culpabilité même chez les criminels, Freud 7 Donnet J.L. (1995) Le surmoi, t. I, in Monographie de la Revue Française de Psychanalyse, Paris : PUF, p. 46. a ouvert la voie à une compréhension et un traitement possible des actes délictueux 8 . Or, une des caractéristiques majeures du surmoi pour Freud est l'indifférenciation entre les actes et la pensée. Cette caractéristique a des incidences sur les modalités thérapeutiques et nous rappelle combien nos interventions se doivent d'être au plus près du mode de fonctionnement inconscient, où acte et pensé sont indistincts. « Au commencement était l'acte » écrit Freud à la fin de Totem et tabou. R. Roussillon évoque lui le langage de l'acte, un acte qui serait à entendre comme une adresse à autrui. C'est à l'objet de prendre acte, à l'objet de rencontrer subjectivement ces actes, et de leur donner une fonction de communication, une valeur signifiante. Certains recours aux actes peuvent se comprendre comme des tentatives d'actualisation, de mise « au présent du moi » selon l'expression de Winnicott, de ce qui n'a pas trouvé de lieu psychique, de ces « fueros » qui n'ont pas été intégrés par la psyché, qui n'ont donc pas non plus été refoulé, mais réprimé. Le travail avec ces enfants m'a conduit à désapprendre certains principes thérapeutiques, en particulier le sens dévolu à la cure psychanalytique classique, qui cherche la levée du refoulement. Avec ces enfants, pas ou trop peu de refoulement justement. Faut-il alors éduquer, au sens Freudien d'élever des digues contre la pulsionnalité ? Faut-il travailler dans le sens de la mise en place du refoulement ou dans le sens de sa levée ? Lorsque les actes sont omniprésents et que le conflit est externalisé hic et nunc sans déplacement possible, les psychanalystes doivent savoir modifier leurs modalités d'interventions pour s'adapter à ces enfants, à leur quasi absence d'associativité et de jeu symbolique, à la confusion entre les actes et les pensées.

  à mes parents, ni à mon monde interne » semblait me dire Sonia à travers ses explosions quand je tentais de faire des liens. Lorsque la capacité à maîtriser la réalité interne est défaillante, le besoin de maîtriser la réalité externe devient intense. Le psychanalyste doit durant tout un temps supporter d'être maîtrisé, malmené, tout en tentant de s'en dégager partiellement pour trouver des voies de déplacement et de créativité. Il n'est pas évident 9 Roussillon R. (2008) Le jeu et l'entre-je(u), Paris : PUF, p. IX et X 10 Roussillon R. (1997), "La fonction symbolisante de l'objet", in Revue Française de Psychanalyse, LXI, 2, 399-415.

  psychiquement d'être utilisé comme un objet malléable. Souvent, le recours à d'autres objets potentiellement malléables ne parvient pas à s'opérer : que d'ébauches de dessins, combien de pâte à modeler, de bricolages amorcés pour tenter de figurer quelque chose.Rétrospectivement, il me semble que c'est lorsque je renonçais à chercher à comprendre, à trouver du sens à ce qui se produisait en séance, que je retrouvais un degré de liberté suffisant pour qu'un dégagement s'opère et que j'éprouvais à nouveau la "capacité d'être seule" en présence de l'autre 11 . Alors parfois une autre modalité de réponse me venait à l'esprit. Ce fut souvent le cas avec Sonia, lorsque je me mettais à écrire et à dessiner pour moi. Le dossier de Sonia était d'ailleurs rempli majoritairement de mes productions, pas de squiggle ici, peu de co-construction du moins dans les traces concrètes laissées par elle dans mon bureau.Nous nous sommes fréquemment interrogés avec l'équipe sur la pertinence à poursuivre ce traitement. Au final, je dirais que c'est Sonia qui l'a maintenu, de façon là aussi paradoxale, en mobilisant les adultes de l'institution et en ne cessant de crier que j'étais là, toujours et encore là, à l'attendre inutilement, alors même qu'elle devait investir sa famille d'accueil et que sa mère partait vivre loin pour essayer de se soigner. Comme toutes celles menées avec ces enfants insupportables dirait A. Fréjaville, cette psychanalyse était passionnante, aussi intense que les investissements transférentiels, et ce malgré le vécu d'impuissance, les sentiments parfois d'être totalement inutile dans sa fonction, nié dans son altérité, annulée dans son existence même, malgré la haine ressentie dans le contre-transfert, pour reprendre les termes si justes de D.W. Winnicott. C'est là qu'intervient le nécessaire recours au tiers, le tiers institutionnel, le travail d'équipe mais aussi le tiers externe de la supervision. « Une règle sans exception : Tenir et endurer sans faillir et sans se durcir. Pour le reste, être vigilant quant à la tentation d'attitudes réparatrices et, surtout, veiller au maintien d'une qualité d'écoute qui comporte par elle-même et en elle-même son pouvoir -moins de compréhension que de témoignage » écrit A. Green 12 . « Survivre », écrivait D.W. Winnicott, pour qui l'utilisation de l'objet implique qu'il soit détruit dans le fantasme 13 mais qu'il survive. Or, ces enfants ont le vécu d'avoir détruit l'objet, d'être des objets destructeurs de leurs figures parentales, sans restauration possible. 11 Winnicott D.W. (1958), "La capacité d'être seul", in De la pédiatrie à la psychanalyse, Payot, Paris 1969.

Freud S. (1916), « Quelques types de caractères dégagés par le travail psychanalytique, III Les criminels par conscience de culpabilité », in OEuvres Complètes, Psychanalyse, XV, Paris : PUF, 2005.


Michele Serri

Matteo Mannini

Lorenzo Poggini

Emilio Vélez-Fort

Brunetto Cortigiani

Philippe Sainctavit

Donella Rovai

Andrea Caneschi

Roberta Sessoli

Low temperature magnetic force microscopy on single molecule magnet-based microarrays

The magnetic properties of some single molecule magnets (SMM) on surfaces can be strongly modified by the molecular packing in nanometric films/aggregates or by interactions with the substrate, which affect the molecular orientation and geometry. Detailed investigations of the magnetism of thin SMM films and nanostructures are necessary for the development of spin-

2 based molecular devices, however this task is challenged by the limited sensitivity of laboratory based magnetometric techniques and often requires access to synchrotron light sources to perform surface sensitive X-ray magnetic circular dichroism (XMCD) investigations. Here we show that low temperature magnetic force microscopy (LT-MFM) is an alternative powerful laboratory tool able to extract the field dependence of the magnetization and to identify areas of in-plane and perpendicular magnetic anisotropy in microarrays of the SMM Terbium(III) bisphthalocyaninato (TbPc 2 ) neutral complex grown as nanosized films on SiO 2 and Perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA), in agreement with data extracted from non-local XMCD measurements performed on homogeneous TbPc 2 /PTCDA films. KEYWORDS. Magnetic Force Microscopy; molecular magnetism; magnetic anisotropy; patterning; dipolar field ; Terbium double decker MAIN TEXT Single molecule magnets (SMM) are magnetic systems featuring slow relaxation of the magnetization at low temperature that gives rise to a dynamic hysteretic behavior; this effect is coupled with the occurrence of resonant quantum tunneling mechanism that widen the potential interest of those objects for the development of novel molecular spintronics devices. [1][2][3] Recent research efforts have been directed towards the organization of SMM units onto surfaces, [4][5][6] which represents a milestone for the realization of solid state devices. The interaction with the surface can affect molecular packing and orientation, significantly modifying the magnetic response of a molecular film. Magneto-optical techniques, 7,8 in particular X-ray magnetic circular dichroism (XMCD), 9,10 are the most employed techniques to characterize thin films, the 3 latter achieving sub-monolayer sensitivity but requiring the access to special facilities (synchrotron light sources). If spatial resolution is also required, such as in sub-micrometric devices, scanning probe techniques can be employed. Spin polarized STM [11][12][13] and inelastic electron tunneling spectroscopy (IETS) 14,15 have provided detailed information on magnetic properties of isolated magnetic molecules on surfaces but they require very demanding experimental conditions and instrumentation.

Magnetic force microscopy (MFM) is an affordable technique to probe the local magnetization of materials and can access information at nanometric length scales that are relevant for molecular spintronic devices, offering superior spatial resolution compared to scanning superconducting quantum interference device (SQUID) and scanning Hall probe microscopy. 16,17 MFM has been extensively used to study, as well as to manipulate, the domain structure of ferromagnetic inorganic films [18][19][20] and micro-or nano-structures, [21][22][23] or vortexes in superconductors. [24][25][26] The application of this technique to molecular magnetic materials is however largely unexplored and most of the studies in the literature are limited to room temperature and lack a systematic field dependent characterization at low temperature, [27][28][29][30] which is necessary to evaluate the magnetic properties of the material and rule out topographic or electrostatic spurious contributions to the MFM measurement.

Notable exceptions are the recent report of Lorusso et al. where MFM has been used to extract the low temperature magnetization curve of micrometric aggregates of a paramagnetic gadolinium acetate complex, 31 or that of Pinilla-Cienfuegos et al., who have investigated the magnetic switching of ferromagnetic (T c ≈ 40 K) Prussian blue analogue (PBA) nanoparticles of different sizes. 32,33 PBA nanoparticle patterns were also magnetically imaged at low temperature 4 using scanning hall probe microscopy by Ghirri et al. 34 To the best of our knowledge there are no reported examples of MFM characterization of a SMM system at low temperature.

In this work we demonstrate that a carefully prepared nanostructure of Terbium(III) bisphthalocyaninato neutral complex (TbPc 2 hereafter) can be characterized using MFM, obtaining a local magnetization curve and an unprecedented lateral resolution of the dipolar field distribution of the molecular nanostructures. TbPc 2 (Figure 1a) is a single ion-based SMM with large total angular momentum, J=6, and a strong magnetic anisotropy with the easy axis of magnetization perpendicular to the planes of the phthalocyaninato ligands. Thanks to its stability it can be thermally sublimed to a variety of substrates, often maintaining the SMM behavior 9,35,36 or being influenced by specific magnetic substrates. 3,37 In this study we have also profited of the possibility to control the molecular orientation in the film by tuning the molecule-substrate interactions. Weakly interacting materials and amorphous or rough surfaces favor a standing orientation of the phthalocyaninato rings, where the easy axis lies parallel to the film. This characteristic would be disadvantageous for the realization of spintronic devices and it is not ideal for MFM measurements, since the easy axis is generally oriented in random directions in the plane of the film, suppressing the net magnetic moment of the sample and potentially reducing effects such as magnetoresistance. 38 In order to prepare an optimized sample for a LT-MFM characterization (see Supporting Information, SI hereafter, for details of samples preparation), we deposited the SMMs-on a templating agent 39 constituted by a thin film of Perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA, Figure 1b), which is known to induce a planar orientation of phthalocyanine molecules. This approach has been earlier adopted for TbPc 2 by the group of Salvan 40 that reported an enhancement at room temperature of the magnetic circular dichroism of this molecule when deposited on PTCDA 5 compared to SiO 2 /Si substrates. More recently, by combining Cantilever Torque Magnetometry (CTM) and X-Ray Natural Linear Dichroism (XNLD), some of us 41 showed that TbPc 2 films deposited on PTCDA are strongly ordered with the phthalocyanine (Pc) plane parallel to the surface resulting in out-of-plane magnetic anisotropy that is maintained in samples several tens of nm thick. the inset shows the smaller opening of the hysteresis at B=0 T compared to the film on PTCDA.

Prior to a local characterization of these samples, in order to allow a detailed comparison of the MFM features and the magnetic and hysteretic behavior of TbPc 2 at the nanoscale, we performed a characterization of the angular dependence of the magnetic hysteresis of TbPc 2 films on different substrates using circularly polarized X-ray synchrotron radiation at the ID32 beamline at ESRF synchrotron. 42 The upper part of Figure 1c shows the absorption spectra of circularly polarized X-rays measured at 7 K at the M 4,5 Tb edge in a 20 nm TbPc 2 film on a 20 nm PTCDA layer with a magnetic field of 3 Tesla oriented normal to the sample (θ=0°). The lower part of Figure 1c compares the normal incidence X-ray circular magnetic dichroism (XMCD) spectra of this sample with a thick TbPc 2 (100 nm) film on polycrystalline gold. The dichroism detected at normal incidence (θ=0°) on the topmost layers of a relatively thick film of TbPc 2 on PTCDA, expected with preferential orientation of the easy axis perpendicular to the film, is larger than then the dichroism of the thick film deposited on gold. Topmost layers of this deposit contain TbPc 2 molecules sitting in standing configuration analogously to thick films on aluminum foil. 35 These evidences are consistent with the results of our recent investigation of these materials by 7 CTM and XNLD. 41 The dichroic ratio is therefore strongly enhanced in the film grown on PTCDA, reaching a maximum at E=1240 eV close to 150% of the isotropic XAS. This result is comparable with the XMCD previously measured in TbPc 2 monolayers on gold 35 in which molecules are known to have a flat orientation of the phthalocyanine ring. 43 Following the XMCD experiments, we measured the magnetic hysteresis loops of the two samples at the two orientations by recording the field dependence of the XMCD at the energy of the maximum dichroism (1240 eV). The sample on PTCDA (Figure 1d) shows an open hysteresis loop with the characteristic butterfly shape of the TbPc 2 single molecule magnet, which is caused by the high spin relaxation rate at zero applied field due to resonant quantum tunneling. The hysteresis is remarkably wider that previously observed in monolayers on gold, 35 which is partly due to the different experimental conditions (temperature and field sweep rate that strongly alter the SMM behavior) but can also indicate a slower relaxation rate on PTCDA compared to the monolayer on gold, analogously to what has been recently found by Dreiser et al. on MgO. 44 At θ=45° the magnetic moment is reduced due to the Tb anisotropy. In the thick film on gold (Figure 1e), the hysteresis opening is greatly reduced at θ=45°, while in the hard direction (θ=0°), the magnetic moment is almost suppressed and the hysteresis is negligible.

The different molecular orientation and magnetic response of TbPc 2 molecules on different substrates was then exploited in a multiple shadow masking process to generate a superstructure of arrays of microdots with different (in-plane and out-of-plane) magnetic anisotropy. If patterning is a necessary step to create a topographic and magnetic profile easily detected in scanning force microscopy, the original superstructure we designed here further enhances the magnetic contrast by allowing a direct comparison between identical topographic structures with expected different magnetic signal. We deposited PTCDA by sublimation through a 2000 mesh 8

Cu TEM grid, with square holes 7.5 μm wide spaced by 5 μm, in contact with a silicon substrate.

Subsequently, a pattern of TbPc 2 dots was created with a smaller TEM grid, consisting of Cu grids (200 mesh) covered by a carbon film perforated in a regular pattern of circular holes with 1.2 μm diameter and 1.3 μm separation. We notice that TbPc 2 is expected to maintain their orientation on both PTDA and Si independently to the thickness of the deposit. 41 The topography of the structures was checked with atomic force microscopy (AFM) at room temperature and during the MFM measurement at low temperature (Figure 2a) revealing an array of TbPc 2 dots with a truncated cone shape of average height of 24 nm and half-height diameter of 1.7 μm, distributed over PTCDA squares of 12 nm height.

The TbPc 2 /PTCDA structures were cooled down to a temperature of 10 K in a field of 4

Tesla and studied with MFM, configured with a phase locked loop (PLL) feedback on the cantilever oscillation and a dual pass measurement where each line of the image is scanned twice, the first time tapping the surface to record the topography and the second at a lift height of 85 nm from the sample and following the firstly acquired profile to isolate long range magnetic interactions from the morphology contribution. In the PLL mode, the magnetic contrast is measured as the shift f of the cantilever resonance frequency from a reference value; here f was set to 0 at the center of the dot on PTCDA. High coercivity MFM probes (ASYMFMHC, nominal H c 0.5 T/μ 0 at room temperature) were used in the experiment.

Figure 2b shows the MFM signal measured at 10 K applying an out-of-plane field of 4 T on a 12.6  12.6 μm 2 area containing both TbPc 2 dots on PTCDA and on bare silicon, as highlighted by the topography image in Figure 2a simultaneously acquired. The MFM image shows a sharp difference of the magnetic contrast between TbPc 2 structures grown on differently 9 treated substrate areas, which can also be appreciated in the frequency shift profiles presented at the bottom of Figure 2b. As expected, the dots on the templating agent show the largest magnetic contrast due to the perpendicular orientation of the TbPc 2 easy axis, while the dots on silicon exhibit much lower net magnetization due to the unfavorable in-plane orientation of the easy axis. The magnetic origin of the measured signal was confirmed by measurements in zero field, after performing a demagnetizing sequence, which showed negligible contrast (data in Figure S2 and Figure S4 in SI). Interestingly, MFM imaging of the dots grown across the boundaries of the PTCDA squares show the transition of the magnetic anisotropy from one orientation to the other within the same dot. This demonstrates the capability of the MFM measurement to perform a local magnetic characterization on a scale significantly smaller than the size of the dots.

Furthermore, it shows how neighboring film domains of different orientation are magnetically uncoupled, which is a consequence of the paramagnetic nature of TbPc 2 .

10 12 This distribution indicates that the magnetic moments of the sample and the tip are not collinear and, because of the perpendicular magnetization of TbPc 2 on PTCDA, 41 we conclude that it is due to the design of the microscope used in this study, where the MFM probe is mounted at a tilt angle of 15° with respect to the sample normal and the magnetic field direction, as schematically shown at the top of Figure 3c. This effect is probably reinforced by the strong anisotropy of the MFM tips used here (CoPt/FePt), which are likely to magnetize along the tip axis rather than the field direction, as well as by the relatively sharp edges of the truncated cone structures which result in a highly pronounced spatial dependence of the demagnetizing field. These distinctive features of our experiment may explain why this effect has not been observed in a similar study of Gd(ac) 2 microdots. 31 In support of this interpretation, we show at the bottom of Figure 3c a simulation of the magnetic force gradient, proportional to the MFM signal, calculated on a saturated TbPc 2 dot at an angle of 15° from the normal (details in the experimental section, see SI).The simulated image reproduces the crescent shaped features of the MFM image, although the magnetic point dipole tip model used in the calculation also predicts features that are likely averaged out by finite size of the probe used experimentally (nominal radius 32±7 nm). By using a more detailed model of the tip magnetization, or by calibrating the tip response, 45,46 one should be able to obtain a better qualitative agreement with the experimental image and, more importantly, to quantitatively assess the local magnetization distribution in the sample.

A simpler TbPc 2 microarray, containing dots 50 nm high grown on a continuous 20 nm PTCDA layer on silicon, has been prepared (see Figure S1 The field dependence of the MFM signal was studied at 5.9 K in these microarrays of TbPc 2 .

Crescent shaped features, analogous to those previously discussed, were observed with 3 T at a probe lift height of 71 nm (Figure 4a). In this second set of measurements performed again in dual pass mode, the lift height was further optimized and slightly decreased to further enhance the sensitivity to magnetic signal still minimizing the contribution due to short range interactions.

The magnetic contrast showed a marked field dependence which is highlighted by the series of images shown in Figure 4c, measured between 3 T and -3 T. At fields above the coercivity of the tip both the tip and the sample are magnetized in the same direction, giving rise to MFM contrast insensitive to the field sign. An inversion of the contrast is expected when only one of the two interacting elements, the tip and the sample, has inverted its magnetization; however, this was not evident in our measurement due to the weakness of the signal at low field. Contrary to previous data, a small residual signal was detected in zero magnetic field (figure 4d-1), which may have a topographic origin, due to the shorter tip sample distance used in this measurement, or may be caused by an inhomogeneous surface potential 47 or an incomplete demagnetization of the magnet.

With the aim of extracting the magnetization curve of a single dot from MFM images, we developed an original method to analyze the MFM data, based on the partition of the image into three regions. These correspond to the areas where the tip experiences: (A) the strongest attractive forces (red colored crescent in the left half of the dot), (B) moderate attractive interaction (the yellow-green zone inside the dot), and (C) the strongest repulsive forces (purple colored crescent outside the right half of the dot). A set of three data-masks named A, B and C 14 (Figure 4b), defining the three regions, has been created with an algorithm (see experimental section in SI for details) starting from the image measured at 3 T, which has the strongest magnetic signal. When an external field is applied along an easy direction, as in the case of the TbPc 2 dots on PTCDA, the stray field of the sample should not change its spatial distribution but only its magnitude, hence it is legitimate to use the data-masks obtained at 3 T on images acquired at different fields. MFM images were aligned with the one at 3 T using the respective topography as reference. Then, on each image, the distribution of the resonance frequency shift values f respect to the initial one (f 0 ) in each of the three regions of the image was fitted with a Gaussian peak, obtaining a triad of peak positions (f A , f B , f C ) and widths (σ A ,σ B , σ C ), representing respectively the characteristic frequency shift and the spread of values in each of the three regions. The distance between any pair of peaks i, j (Δf i,j = f i -f j ) measures the variation of the force gradient between the regions i and j, which is proportional to the magnetization of the dot, while the sum of the widths of the peaks in the selected pair (σ i +σ j ) was used to evaluate the uncertainty in the measurement, which depends both on the experimental noise and the choice of the masks. The f C and f A components, which correspond to the regions of maximum repulsive and attractive interaction, provided the lowest relative error and were used to construct the single dot magnetization curve shown in Figure 4e, to be compared to the hysteresis loop measured by XMCD. Both curves were normalized to the value measured at saturation (B=3T). The values obtained by MFM are shown as black spheres, numbered to express the measurement sequence.

Since the tip magnetization follows the sign of the field above its coercivity, the MFM values measured at negative field have been multiplied by -1 for a better comparison with the XMCD data; the original values are also shown in blue color. with the butterfly hysteretic behavior detected by XMCD, the MFM detected bistability will require future additional investigations, being the differences small when compared to the error bars and, in the low field region, convoluted with the tip hysteretic behavior. Furthermore, the timescale of an MFM-detected magnetization measurement, which takes place in hours, is significantly longer than the one employed in synchrotron experiments that have been carried out at T=7 K. The lower temperature used in MFM test is expected to slightly increase the opening of the hysteresis cycle thus suggesting that lower temperature experiments should to be performed in the future even if the effect of resonant quantum tunneling occurring in TbPc 2 systems can limit this strategy.

In conclusion, our parallel investigation based on synchrotron radiation and magnetic force microscopy showed that the single molecule magnet properties of thin films of TbPc 2 can be greatly improved when the orientation of the anisotropy axis is controlled via a templating 17 layer of PTCDA. The hysteresis loop of the templated film shows in the XMCD measurement a wider opening than previously observed in monolayers deposited on Au(111) 35 and HOPG, 9 which exhibit a molecular orientation similar to the films on PTCDA considered here. This result is in line with the recent reports 36 showing that the addition of an insulating decoupling layer between TbPc 2 and a metallic substrate improves the spin relaxation times. PTCDA is not insulating and exhibits a n-type semiconductor behavior, 48 however its interaction with the SMM is expected to be much weaker than in the case of a metallic substrate, hence the reduction of the spin relaxation rate and the widening of the hysteresis. 25

Table of Contents Graphic and Synopsis

The local magnetic anisotropy and the field dependence of the magnetization of a specifically designed multilayered microarray structure including the Tb-double decker Single Molecule Magnet has been studied by low temperature magnetic force microscopy (LT-MFM) and results

have been compared with X-ray magnetic circular dichroism data. An MFM-image analysis protocol for the extraction of magnetic information has been developed and proposed as a valuable tool for in line analysis of molecular or inorganic nanostructures.

Figure 1 a

 1 Figure 1 a) TbPc 2 molecule; carbon atoms are shown in black, nitrogen in blue, terbium in

Figure 2 a

 2 Figure 2 a) Topography of the TbPc 2 dot microarray on patterned PTCDA layer on silicon,

Figure 3 a

 3 Figure 3 a) Topography image of a single TbPc 2 dot on PTCDA and profiles along the

  in SI). On this sample an extra characterization has been performed by Time of Flight Secondary Ion mass spectrometry (ToF-SIMS) in order to carefully evaluate the chemical distribution of the two species and the 13 13 presence of intact SMM; the spatial distribution of the detected molecular peak of TbPc 2 and PTCDA in the sample, reported in Figure S1, further confirmed the quality of the sample.

Figure 4

 4 Figure 4 a) MFM image of a 50 nm thick TbPc 2 dot on a continuous (20 nm) PTCDA layer at

  ABBREVIATIONSLT-MFM, low temperature magnetic force microscopy; XMCD, X-ray magnetic circular

Funding Sources


Véronique Raverot

Pauline Perrin

Philippe Chanson

Emmanuel Jouanneau

Thierry Brue

Gérald Raverot

Prolactin immunoassay: does the high-dose hook effect still exist ?

Keywords: prolactin, hook-effect, immunoassay, prolactinoma, macroprolactinoma

. The objective of our study was to evaluate if the mention of the high dose hook effect is relevant in actual practice.

Methods: A serum from a patient with giant macroprolactinoma was assayed by using all the different reagents available in France in 2020 on native serum and after dilution. Technical inserts from manufacturers were reviewed to study information of analytical principles, numbers of steps, and mention to high dose hook effect if necessary.

Results: Fourteen reagents were studied; all were two-site immunometric assays, mostly in 1 step (11/14). One tested reagent was sensitive to high dose hook effect leading to falsely low prolactin concentration when measured on native serum.

Conclusion:

The high-dose hook effect still exists. The evolution of reagents may lead to new reagents sensitive to this effect in the future. We therefore advise that this hook effect be mentioned in the recommendations.

Introduction

Measurement of prolactin in clinical laboratories is an important part of the management of patients with pituitary adenoma. Prolactin is known to be sensitive to various analytical interferences, including the high-dose hook effect, like other biochemical markers known to undergo large amplitudes of concentration variation. In the presence of extremely high concentrations of prolactin, the reagent antibodies can become saturated and fail to form a sandwich, leading to a lower than expected prolactin result [START_REF] Haddad | Interpretation of common endocrine laboratory tests: technical pitfalls, their mechanisms and practical considerations[END_REF]. This uncommon analytical pitfall, which did not exist in older competitive assays, has been described in sandwich assays, also called two-site immunometric assays when handled in one step [START_REF] Melmed | Diagnosis and treatment of hyperprolactinemia: an Endocrine Society clinical practice guideline[END_REF]6]. This known phenomenon can be avoided by using sandwich assays that run in two steps (including a wash step before the addition of the second antibody), or by diluting the samples when using sandwich assays that run in one step [START_REF] Vilar | Pitfalls in the Diagnostic Evaluation of Hyperprolactinemia[END_REF][START_REF] Haddad | Interpretation of common endocrine laboratory tests: technical pitfalls, their mechanisms and practical considerations[END_REF].

The high-dose hook effect is mentioned in most recent articles discussing prolactin assay and management of pituitary prolactin adenomas [START_REF] Petersenn | Diagnosis and management of prolactinomas: current challenges[END_REF][START_REF] Saleem | Prolactin Biology and Laboratory Measurement: An Update on Physiology and Current Analytical Issues[END_REF][START_REF] Vilar | Pitfalls in the Diagnostic Evaluation of Hyperprolactinemia[END_REF]. However, articles describing case reports or series of high-dose hook effects in prolactin assay are mostly old or poorly documented [START_REF] Petersenn | Diagnosis and management of prolactinomas: current challenges[END_REF][START_REF] St-Jean | High prolactin levels may be missed by immunoradiometric assay in patients with macroprolactinomas[END_REF][START_REF] Yener | Misdiagnosis due to the hook effect in prolactin assay[END_REF][START_REF] Unnikrishnan | The 'hook effect' on serum prolactin estimation in a patient with macroprolactinoma[END_REF][START_REF] Petakov | Pituitary adenomas secreting large amounts of prolactin may give false low values in immunoradiometric assays. The hook effect[END_REF][START_REF] Schofl | Falsely low serum prolactin in two cases of invasive macroprolactinoma[END_REF][START_REF] Barkan | Giant pituitary prolactinoma with falsely low serum prolactin: the pitfall of the "high-dose hook effect": case report[END_REF][START_REF] Fleseriu | Giant invasive pituitary prolactinoma with falsely low serum prolactin: the significance of 'hook effect[END_REF]. Although few changes in the principles of immunoassays have occurred since these cases, most of the reagents have evolved. The objective of our study was to evaluate if the mention of the high dose hook effect is relevant in actual practice. We therefore propose to describe the different reagents currently available for the measurement of prolactin, to study the manufacturers' recommendations concerning the high-dose hook effect and to test these reagents in order to establish whether or not this high-dose hook effect in the measurement of prolactin still exists.

Methods

Reagents and protocol: Selection of French laboratories representative of the different techniques listed on the Probioqual (a French association for the promotion of quality control in medical biology) survey report of December 2020 was made thanks to the help of the specialized biochemistry group of the French society of nuclear medicine and Probioqual in order to be exhaustive of prolactin reagents used in France in 2020. These different laboratories agreed to provide us with the technical data sheets of the suppliers and to perform prolactin measurement on sample that we dispatched, on native serum firstly and after dilution 1:10 or more, as practiced in the laboratory when necessary.

Blood sample preparation:

A single patient diagnosed with a giant macroprolactinoma was informed and agreed to participate to make this study possible. Serum samples were aliquoted and stored at -20°C until analysis. The volume of sample provided to participating laboratories was large enough (500 µL) to allow measurement on native serum and after dilution on all tested systems. Data collected: Prolactin values obtained on native serum and after dilution were collected.

The technical data sheets were reviewed to study informations of analytical principles: competitive or two-site immunometric assays; number of steps for the two-site immunometric assays : one step or two steps (with a wash step) ; linearity range; mention to high dose hook effect if necessary; and concentration until which the high dose hook effect is not supposed to occur.

Results

In the survey of December 2020, Probioqual received 464 results for prolactin measurement.

Reagents were from 11 manufacturers. Two manufacturers used the same reagent on different analyzers: Architect and Alinity from Abbott were combined in one analyzers and the same for Cobas e601 and e801 from Roche. Samples with elevated prolactin concentration have been sent to 16 French laboratories to test the 14 reagents (ie also to test different analyzers from Abbott and Roche). Probioqual combined answers from those different analyzers using the same reagent (cf figure 1 andtable1) and obtained 14 different analytical systems.

The careful analysis of the insert technical notice allowed an up to date evaluation of the prolactin reagent situation in 2020's:

-All reagents used two-site immunometric assays with different labels (radioactivity, chemilumininescent, electrochemiluminescent…).

-The reactions are in 1 (78.6% = 11 reagents/14) or 2 (21.4% = 3 reagents/14) steps.

-The linearity range vary from 190 to 470 µg/L depending the manufacturer.

-All the one step reagents mentioned the high dose hook effect in their notice (100%).

-The theorical concentration until high-dose hook-effect is not observed vary from 9520 µg/L to 50 000 µg/L depending the manufacturer.

Prolactin measurement: When perform on native serum, one reagent was sensitive to high dose hook effect and gave a result of 150 µg/L below the linearity range of the assay and all the other were reported as "above the upper limit of the assay". Results obtained after dilution varied from 17900 µg/L to 86900 µg/L depending on the reagent used (table 1). The reagent sensitive to high dose hook effect gave result of 17900 µg/L after dilution compared to 150 µg/L on native serum. This reagent is a two-site radio-immunometric assay in one step from Beckman used in France by 2 laboratories (2 results out of 464 in the Probioqual's survey).

Except value obtained with Vista reagent, all the results obtained after dilution were above the prolactin value announced by the manufacturer as not sensitive to high dose hook effect.

These results validated the absence of a high dose hook effect with the different reagents.

Result obtained with Vista from Siemens led to 30800 µg/L and the limit not sensitive to hook effect was announced at 50000 µg/L.

Discussion

To our knowledge, this is the first study to determine whether the high-dose hook effect still exists with current reagents for prolactin measurement. In guidelines dealing with the management of prolactin adenomas, this analytical interference is always mentioned because it can sometimes lead to a wrong diagnosis and subsequently to wrong treatment [START_REF] Petersenn | Diagnosis and management of prolactinomas: current challenges[END_REF], based on old publications.

A review of actual manufacturers' package inserts showed that the methodologies are based on two-site immunometric assays, which are suitable for prolactin determination. These assays, born with the discovery of monoclonal antibodies, are more sensitive and specific than previous competitive assays, but are subject to interferences that did not exist with competitive techniques, high dose hook effect for instance. This interference can be avoided by using sandwich assays that run in two steps or by diluting the samples when using sandwich assays that run in one step [START_REF] Vilar | Pitfalls in the Diagnostic Evaluation of Hyperprolactinemia[END_REF][START_REF] Haddad | Interpretation of common endocrine laboratory tests: technical pitfalls, their mechanisms and practical considerations[END_REF]. Dilution of suspected elevated concentration samples is not easy to handle in routine conditions. Interactions between clinicians and laboratories are very important; clinicians must be aware that prolactin result might be affected by an analytical interference. Some manufacturers developed some two-site immunometric assays in one step with no wash step, called homogenous phase (for example TRACE® (Time-Resolved Amplified Cryptate Emission). These technologies are supposed not being sensitive to high dose hook effect since the signal is measured several time during the reaction, but the supplier still mention in the insert that the hook effect is not observed until a notified concentration Our study is the first one, which tested all the current available reagent. It is reassuring to observe that no hook effect occurred with modern reagent. The one from Beckman which was sensitive to high dose hook effect is an old immunoradiometric assay (IRMA) which should not be use anymore, since IRMA do not improve prolactin measurement performances.

Several case reports mentioned IRMA reagent sensitive to high dose hook effect [START_REF] St-Jean | High prolactin levels may be missed by immunoradiometric assay in patients with macroprolactinomas[END_REF][START_REF] Petakov | Pituitary adenomas secreting large amounts of prolactin may give false low values in immunoradiometric assays. The hook effect[END_REF][START_REF] Fleseriu | Giant invasive pituitary prolactinoma with falsely low serum prolactin: the significance of 'hook effect[END_REF][START_REF] Comtois | Immunoradiometric assays may miss high prolactin levels[END_REF].

We observed in this study that not all the IRMA reagent are sensitive to hook effect since that among reagents which were tested in this study, 2 were based on IRMA methodology and the one from Diasource was not sensitive to hook effect on the sample tested. Many other cases reports were seen with chemiluminescent technologies [START_REF] Unnikrishnan | The 'hook effect' on serum prolactin estimation in a patient with macroprolactinoma[END_REF][START_REF] Schofl | Falsely low serum prolactin in two cases of invasive macroprolactinoma[END_REF][START_REF] Barkan | Giant pituitary prolactinoma with falsely low serum prolactin: the pitfall of the "high-dose hook effect": case report[END_REF].

The case reports published in the literature are difficult to use: the vast majority do not mention the reagent used [START_REF] Yener | Misdiagnosis due to the hook effect in prolactin assay[END_REF][START_REF] Unnikrishnan | The 'hook effect' on serum prolactin estimation in a patient with macroprolactinoma[END_REF][START_REF] Barkan | Giant pituitary prolactinoma with falsely low serum prolactin: the pitfall of the "high-dose hook effect": case report[END_REF], and many cases are old with reagents that are not or no longer available. They reported that high dose hook effect is more frequent in male, which is due to the larger size of the adenoma at the time of diagnosis, and larger amount of prolactin.

In future publication describing high dose hook effect or other interferences, the mention of the reagent used should be mandatory to allow a better understanding of the real systems.

This study allowed us to verify that this interference did not occur with reagents running with two steps thanks to a wash step before the addition of the second antibody [START_REF] Fleseriu | Giant invasive pituitary prolactinoma with falsely low serum prolactin: the significance of 'hook effect[END_REF]. Although it is theorically the easiest way to avoid the hook effect [START_REF] Vilar | Pitfalls in the Diagnostic Evaluation of Hyperprolactinemia[END_REF][START_REF] Haddad | Interpretation of common endocrine laboratory tests: technical pitfalls, their mechanisms and practical considerations[END_REF], two steps reaction is used in less than 25% of the answers collected by Probioqual in France. One major inconvenient in immunoanalysis is that reagent and analyzer are combined and it is not possible to use a 2 steps reagent if the analyzer is not adapted to it.

A major strength of this study is that the concentration of the studied sample was higher than the concentration mentioned by the manufacturers as a limit until there was no hook effect; except with one reagent (Vista Siemens). This validated the study design which was to exceed the concentration mentioned by the manufacturers. One strength of this work is that all the data sheets could be modified to take into account this new prolactin threshold; except the Vista's one.

A limitation of our work is that Probioqual's data reflect reagents used in France at the time of the survey but not the proportion of data obtained with all these reagents in clinical activities.

Laboratories working with clinicians from pituitary centers may have selected reagent not sensitive to high dose hook effect. In addition, this situation is actual and we cannot preclude the future, no one knows what future reagent will appear and one should continue to check for this interference [START_REF] Melmed | Diagnosis and treatment of hyperprolactinemia: an Endocrine Society clinical practice guideline[END_REF].

An unexpected finding of the study was the diversity of the results obtained on the same sample: concentrations as different as 17900 to 86880 µg/L were measured on a unique sample despite adoption of World Health Organization's third international standard (IS) for prolactin 84/500, recently replaced with the 4 th IS 83/573 [START_REF] Ferguson | WHO International collaborative study of the proposed 4th International Standard for Prolactin[END_REF]. This lack of commutability between method has already been reported [START_REF] Saleem | Prolactin Biology and Laboratory Measurement: An Update on Physiology and Current Analytical Issues[END_REF]. This confirms the need to follow the prolactin decrement during a medical treatment with the same reagent. In 2020's, standardization of prolactin measurement needs to be done and follow by manufacturers.

Conclusion

Although extremely rare, the high dose hook effect should be mentioned in prolactin measurement in order to prevent it from being forgotten. If it is no longer mentioned, it will no longer be taught. With the multiplication of biochemistry technical platforms, the use of new reagents (not tested here) and untrained biologists/clinicians may lead to situations where the management of the patient would be altered because of this high dose hook effect.

Figure 1 :

 1 Figure 1 : Proportion of users of the different techniques (results extracted from Probioqual data). Framed names, techniques in 2 real steps; underlined name, technique TRACE

Acknowledgments

We thank Probioqual who allow us the use of their datas and Drs Marc Barba; Florence Boux de Casson; Anne-Sophie Gauchez; David Guenet; Jean Guibourdenche; Isabelle Lacroix; Cindy Lauro; Mathieu Pecquet; Antoine Pilon; Christel Pissier; Caroline Richet ; Rémi Segues; Séverine Trabado and Alice Veauville who handled prolactin concentration measurement on analyzer available in their laboratories.

Statements and Declarations

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Véronique Raverot and Pauline Perrin. The first draft of the manuscript was written by Véronique Raverot and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

The authors did not receive support from any organization for the submitted work.