Gabriel Hurel

Jean-Frédéric Diebold

Sébastien Besset

Louis Jézéquel

Messier-Bugatti-Dowty

Influence of the Gyroscopic Effects on Friction Induced Vibration in Aircraft Braking in System

Aeronautical brakes are subject to non-linear unstable vibrations. In particular, two modes appear and present a risk for the structure. Firstly, the whirl modes consist of a rotating bending motion of the axle out-of-phase with the brake torque tube. It is due to a coupling of two bending modes of the axle in orthogonal directions. Secondly, the brake squeal mode resulting from stick-slip or sprag-slip phenomena consists of a rotational motion of the brake around the axle. Those vibrations are not resulting from an external excitation but are friction-induced self-excited. Hence, they are dependent on tribological phenomena specific to carbon disks and are in particular controlled by the friction coefficient µ.

In order to take into account the dynamical aspect in brake design, Messier-Bugatti-Dowty wants to simulate modes and acceleration g's levels. This article deals with the improvement of such a model.

A finite element of the brake exists. It is able to reproduce whirl modes and squeal mode. In order to improve it, physical phenomena must be introduced. Here, the impact of gyroscopic effects is evaluated. For this, an analytical model is built to determine the consequences on frequencies and stability.

Introduction

Friction induced vibrations are present in many applications. Squeaky doors and violins are examples in which noise is created from vibrations due to two interfaces contact characterized with a friction law. In railway and automotive industries, these phenomena are studied for braking systems [START_REF] Kinkaid | Automotive disc brake squeal[END_REF][START_REF] Lorang | Instabilité des structures en contact frottant : Application au crissement des freins à disque de TGV[END_REF]. Indeed, significant energy is involved and vibrations produce important noise and present a risk for the brake structure.

In the aeronautical industry, the objective is not yet to reduce noise but to avoid premature worn and broken equipment. Many tests are performed to check that the brakes do not vibrate, but they are long and expensive. Models are used to predict the brakes' dynamic performance and to understand dynamic phenomena observed during tests, in order to improve design.

Contrary to automotive brakes, aircraft brakes are axisymmetric. A stack of carbon disks, called heat sink, is placed between pistons and torque tube (see Figure 1). Stators secured to the axle and rotors secured to the wheel are arranged alternatively. During the braking phase, a hydraulic pressure is applied on the carbon disks through pistons. This compressive force generates a friction effort between rotors and stators over the entire circumference. It results in a torque, opposed to the wheel rotation. The brake rod transmits the torque to the attach lug linked to the landing gear. The mechanical energy is changed into thermal energy through friction and absorbed by the heat sink [START_REF] Guichard | Freinage à très hautes performances exemple aéronautique[END_REF].

Figure 1: Sectional view of an aircraft brake system [START_REF] Guichard | Freinage à très hautes performances exemple aéronautique[END_REF].

Many braking stops are performed on a test frame. They correspond to landing or taxiing. The brake is attached by the axle, the brake rod and the attach lug. This mechanism is subject to unstable vibrations during the braking. Frequency range is 50 -2000 Hz. During a braking, several different modes may appear. Their levels increase rapidly to reach a stationary limit cycle. Figure 2 shows an example of a braking with appearance of three different modes.

Two types of brake induced vibration may be observed in the low frequency range. The rotation of the brake about the axle called squeal (Figure 3a) results from stick-slip or spragslip phenomena. Unlike stick-slip, sprag-slip [START_REF] Spurr | A Theory of Brake Squeal[END_REF] helps to explain vibrations with a constant friction coefficient and a buttressing of the brake rod. In the first phase, the brake torque induces a flexion of the rod. This energy is relaxed by slipping on the friction interface.

The spin motion of the axle is called whirl (Figure 3b). This complex mode results from the coupling of two bending modes of the axle [START_REF] Hoffmann | A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations[END_REF][START_REF] Sinou | Friction-induced vibration for an aircraft brake system-Part 1: Experimental approach and stability analysis[END_REF]. This coupling depends on the carbon friction coefficient. Several modes of whirl exist depending on order of the mode of the axle.

In order to predict apparition and level of vibrations, a model is needed. A finite element model was built to understand the brake dynamic behaviour [START_REF] Chevillot | Nonlinear transient vibrations and coexistences of multi-instabilities induced by friction in an aircraft braking system[END_REF]. It is able to reproduce the squeal and whirl modes. This model is currently used to identify modes of the structure and perform stability studies.

Finite element model description

This finite element model corresponding to the test configuration is built from CAD. Figure 4 shows the meshed brake system. The frequency range requires parts from the landing gear: axle, brake rod and attach lug.

Figure 4: Finite element model of brake system.

Friction Modeling

For now, the value of rotation speed is not important here because the friction is saturated.

The Coulomb friction law is modelled at disks interface. Contact stiffness k c is introduced to prevent permeation of disks and to retrieve compressive force N . A tangential force T proportional to the normal force and friction coefficient µ is generated (figure 5). This way, the friction coefficient µ is constant on all the disks' surface but the friction force is located where pressure is important [START_REF] Chang | Asymmetric Approach in Solving Aircraft Brake Vibration[END_REF]:

T = µN = µk c (z A -z B ) (1)
Figure 5: Friction modelling at the disks rubbing interface between two nodes A and B.

3 Modal and stability analysis

Computation Technique

The introduction of friction adds to the symmetric stiffness matrix K S an asymmetric matrix µK F .

K = K S + µK F ( 2
)
The system is no longer conservative and energy is brought to the structure from friction. In this case, unstable modes may appear. Actually, dynamic equation is written with mass matrix M, damp matrix C and stiffness matrix K:

M Ẍ + C Ẋ + KX = 0 (3)
Calculating modes (λ i , ϕ i ) is equivalent to solve matrix equation

λ i 2 M + λ i C + K ϕ i = 0 (4)
On a conservative system, eigenvalues λ i are purely imaginary. This is not the case here if µ = 0 because stiffness matrix K is not symmetric. So eigenvalues λ i , are either purely imaginary or complex. In this case, they may be written λ = a + iω where ω is the pulsation of the mode related with the frequency f = 2πω. Parameter a is a modal damping coefficient which determines stability: if a is negative or zero, the system is stable but if a is positive the system is unstable. These two coefficients a and ω are dependent on friction coefficient µ.

A stability analysis can be performed by studying the frequency variation against friction coefficient. An example is given in figure 6.

Results

The finite element model is able to reproduce modes observed during braking test in the low frequency range. The whirl mode appears from a value of the friction coefficient µ. Even if there is a coupling, the model requires an update to retrieve the correct whirl mode.

Improvement of the dynamic model

Different dynamic behaviours of the brake structure are observed for landing stops or taxiing stops during tests. Especially, the whirl mode appears more often during landing stops than taxiing stops. Moreover, the finite element model underestimates the frequency of this mode. The objective of this study is to identify the link between the value of the speed of rotation of the wheel, which is significantly higher in landing than in taxiing stops, and the characteristics of the whirl mode: frequency and stability indicators. Gyroscopic effects could be the root cause of these observations. In order to determine whether these phenomena should be introduced in the finite element model, a study on a simple analytical model is conducted. First, influence of gyroscopic effects without braking on the whirl mode's frequency is evaluated. Then, friction is introduced to quantify its impact on stability for the whirl mode.

Impact of Gyroscopic Effect on Modes Frequencies

Gyroscopic effects are studied on aircrafts engines, where the rotation speed of the rotors is very high. The wheel and brake system may also be subject to gyroscopic effects. Indeed, when landing the wheel rotates with an important speed, especially at the beginning of braking. In addition, the load of the aircraft causes a flexion of the axle perpendicular to the wheel rotation. Both cause a gyroscopic force in the third direction. This study is done to find out if these effects must be injected into the finite element model.

To quantify these effects, a simple model is used (figure 7) with equations used for rotor dynamics [START_REF] Lalanne | Dynamique des rotors en flexion[END_REF]: an axisymmetric cantilever beam free with constant section represents the axle. Rotating parts are considered as a flywheel. This flywheel is represented by its mass is M and its moments of inertia about e x and e y , I 1 and about e z , I 3 . Movements of the beam are allowed in two directions: u and v are the displacements along respectively e x and e y axis. θ and ψ are angles of rotation of the wheel around respectively e x and e y axis. A rotation speed is imposed to the flywheel at pulsation Ω.

Figure 7: Simple model to study gyroscopic effects on wheel and brake system.

The axle is considered as a massless body. Its modal shapes are given by the functions f x (z) and f y (z). The structure can be reduced to two DOF q 1 and q 2 :

u(z) = f x (z)q 1 (5) v(z) = f y (z)q 2 (6) ψ = df x dz (L)q 1 (7) θ = df y dz (L)q 2 (8)
By applying the Lagrange equations, the following system is obtained [START_REF] Lalanne | Dynamique des rotors en flexion[END_REF]:

m 0 0 m q1 q2 + Ω 0 -g g 0 q1 q2 + k 0 0 k q 1 q 2 = 0 (9)
where

m = M + 4I 1 L 2 , g = 8(I 3 -I 1 ) L 2 and k = 4EI f L 3 .
Resolution of the equation 9 gives two solutions corresponding to two pulsation frequencies:

r 1 = iω 1 = i ω 2 0 + g 2 Ω 2 2m 2   1 -1 + 4m 2 ω 2 0 g 2 Ω 2   (10)
r 2 = iω 2 = i ω 2 0 + g 2 Ω 2 2m 2   1 + 1 + 4m 2 ω 2 0 g 2 Ω 2   (11)
The pulsation when the wheel is not rotating is ω 0 = k/m. It is interesting to note the appearance of a coupling between both bending modes. However, there is no modal damping and no preferred mode. The mode shapes are the same as the whirl mode. The second frequency ω 2 corresponds to the case where the vibration mode rotates in the same way as the wheel rotation Ω, it is a direct precession. Conversely, the first frequency ω 1 corresponds to the case where both rotations are in opposite directions, it is reverse precession.

In figure 8, a Campbell diagram shows the whirl modes frequencies against the wheel rotation speed Ω. The maximum speed of the aircraft is reached during landing. At this moment, the impact on frequency of the whirl mode is between 2 and 4%.

Impact of gyroscopic effects on stability

To evaluate the impact of gyroscopic effects on stability [START_REF] Hervé | Analysis of squeal noise and mode coupling instabilities including damping and gyroscopic effects[END_REF], a Coulomb friction law is introduced in the simple model between a rotor secured to the wheel and a fixed stator. When the wheel rotates in ψ, on the one hand, an elastic force reacts on the wheel in ψ and on the other hand the friction creates a resultant force in e y due to inhomogeneous pressure on the disks. This force bends the beam and rotates the wheel in θ. The system equation becomes:

m 0 0 m q1 q2 + Ω 0 -g g 0 q1 q2 + k 11 -µk 12 µk 12 k 11 q 1 q 2 = 0 (12)
A bi-parametric study can be performed with friction coefficient, and speed rotation of the wheel Ω. Figure 9 shows that the coupling of modes happens at µ = 0. The mode associated with positive real part eigenvalue is unstable for µ > 0. When Ω increases, the real parts decrease.

Hence, the gyroscopic decrease the modal damping. This results in a decrease of the growth rate of the whirl modes. However, in the range of the speed of rotation of the wheel, the difference of modal damping between landing and taxiing stops is negligible. Furthermore, the value of damping is not sufficient to explain appearance of instabilities.

Taking into account gyroscopic effects has improved correlation between the model and tests. The table 1 shows that only the whirl mode is concerned. The squeal mode is affected because it does not move rotating parts but parts linked to the landing gear.

Conclusion

Messier-Bugatti-Dowty seeks to better understand the dynamic behaviour of brake systems in order to handle vibration levels. In order to better determine influence of the design, a finite element model is built. This model is able to reproduce complex modes observed through tests such as squeal and whirl modes thanks to insertion of friction terms. However, before simulating its dynamic behaviour during braking, accuracy of the simulated modes frequencies can be further improved. In this paper, gyroscopic effects have been checked. The analytical model shows that taking into account gyroscopic effects can improve the finite element model. The accuracy of frequencies is improved especially for the whirl mode. To introduce these phenomena in the finite element model will be perform in a further work. On the other side, the impact of gyroscopic effects on stability is very low in the range of the speed of rotation of the wheel. They cannot explain the differences between landing and taxiing stops.

Other phenomena like pretension, the boundary conditions on the test frame, clearance in mechanical linkages and hydraulic coupling can considered to get a better representation of the dynamic behaviour of the brake.

Figure 2 :

 2 Figure 2: Example of vibrations during braking with frequency analysis by wavelet.

Figure 3 :

 3 Figure 3: Two modes of vibration on aircraft brake system ((a): squeal mode, (b): whirl mode).

Figure 6 :

 6 Figure 6: Stability analysis for the first whirl ((a): frequency, (b): damping).

Figure 8 :

 8 Figure 8: Campbell diagram with frequencies of the first whirl modes.

Figure 9 :

 9 Figure 9: Whirl 1, (a): Real parts of eigenvalues versus µ and Ω. (b): frequency versus µ and Ω.

Table 1 :

 1 Improvement of the accuracy of frequencies and value of damping in the analytical model.


Nikita K Kulachenkov

Stéphanie Bruyere

Sergey A Sapchenko

Yuri A Mezenov

Dapeng Sun

Andrei A Krasilin

Alexandre Nominé

Jaâfar Ghanbaja

Thierry Belmonte

Vladimir P Fedin

Evgeny A Pidko

Valentin A Milichko

Ultrafast Melting of Metal-Organic Frameworks for Advanced Nanophotonics

come

Introduction

Metal-organic frameworks (MOFs) as novel class of molecular crystals stand out by their unconventional hierarchical structure based on weak and strong interactions between various building blocks such as organic ligands, metal nodes, and solvent molecules. Their co-operation causes MOF compounds to possess an ordered porous structure [1] and softness [2] making them to be perspective materials for many applications in chemistry,[3] biology, [4] and physics in general. [5] Besides this unique combination of properties, one of the most intriguing features of MOFs is the dynamical response of their structure on external stimuli such as pressure, temperature, electric field, and even light. [6] This opens up an ability for efficient utilizing of the MOFs for data storage,[5b-d] controlled filtering,[6c] and nonlinear mechanics.[5e] Meanwhile, under extremal conditions, such stimuli allow the obtaining of new stable structures such as nanometer scale derivatives, [7] which turned out to be very useful for energy storage [7b-d] and catalysis[7e] due to their morphology and nanometer sizes.

The production of functional MOF derivatives, such as amorphous carbon, metal oxides, chalcogenides, phosphides, carbides, or pure metallic nanoclusters, [7a-c] has become one of the most rapidly developing field of nanoscience. However, the approaches to fabricate them are generally based on relatively slow processes such as heating to the melting point within a broad time ranging from nanoseconds to hours. Important is that, these processes limit the synthesis product to the stable structures. In contrast, implementation of nonequilibrium approach of injecting high energy density over a shorter timespan (up to femtoseconds) enables the formation of metastable structures, which are completely new in terms of morphology. Indeed, nonequilibrium processes possess ultrafast melting and cooling rates with complicated dynamics of solidification resulting in dramatic impact on the final morphology and properties of the nanometer scale structures. [8a-d] As a result, this significantly widens the library of nanomaterials and their application in nanophotonics making them competitive with existing nonlinear optical nanomaterials as inorganic nanoparticles[8d] and organic/ inorganic 2D materials.[8e-i] Therefore, research on the effective ways of MOFs conversion to a new kind of derivatives employing ultrafast melting seems to be a substantial step toward synthesis of new nanomaterials with unique functionality.

Here we utilize for the first time an ultrafast melting of MOFs with flexible alkane-chained ligands (Figure 1a) and interpenetrated 3D structure (Figure 2) by femtosecond (fs) IR laser pulses. This allows us to investigate light-matter interactions with regard to the production of new forms of MOF derivatives for nonlinear nanophotonics. We reveal the interplay between the initial MOF structure and the morphology and composition of the derivatives, as well as their nonlinear optical properties. Overall, the proposed approach for ultrafast melting of MOFs leads to conceptually new nanometerscale derivatives and opens up new perspectives for an efficient postsynthetic processing of MOF compounds to yield a family of materials with a rarely described combination of nonlinear optics, and potentially catalytic and energy storage application.

Results and Discussion

As mentioned above, classical approaches to melt MOFs for producing different nanometer scale derivatives, [7a-c] amorphous phases, [9a-e] and MOF glasses[10] (Figure S1, Supporting Information) take much longer time ranging from tens of nanoseconds [11] to hours [10] which is sufficient for reaching the thermal equilibrium. In contrast, under the strong femtosecond optical excitation,[12a] MOFs like other crystalline semiconductors (bismuth,[12b] silicon,[12c] indium antimonide,[12d,e] germanium,[12f ] and gallium arsenide[12g]) should undergo the transition to the state at which few percent of electrons exited from valence to conduction band induce changes in the potential-energy surface and temporary modification of the crystal lattice (Figure 1b). They drastically affect the process of light-induced melting of semiconductors.

The fact that fs melting occurs before the thermal equilibrium (nonthermal melting) between electrons and the lattice through electron-phonon interaction [12] raises the question of the possibility to convert MOFs into new metastable states with new functionality.

Model MOFs

Synthesis

As a model system, we use the series of 3D MOFs (1 to 3) previously synthetized by Barsukova et al.[13] All of them contain 4,4′-stilbenedicraboxylate (sdc 2-) and imidazolyl-based ligands featuring flexible hydrocarbon chains of different lengths (Figure 1a): 1,4-di(1H-imidazol-1-yl)butane (L4) or 1,6-di(1H-imidazol-1-yl)hexane (L6). Compound 1 crystallizes in monoclinic space group P2/c and has quite dense and rigid structure with chemical formula [Cd(sdc)(L4)]•DMF (DMF, dimethylformamide). It comprises sixfold interpenetrated frameworks of a diamond topology (dia). Compound 2 also contains cadmium (II) but has a larger imidazolyl-based ligand L6. Its chemical composition is [Cd(dmf)(sdc)(L6)]•DMF. From structural point of view, the compound is characterized by a very high interpenetration degree (eightfold) of the diamond-type frameworks built from cadmium cations connected through sdc 2-and L6 ligands. Importantly, it crystallizes in a noncentrosymmetric space group P2 1 2 1 2 1 . Compound 3 is zinc(II)-based and its formula is [Zn(sdc)(L6)]•DMF. Its structure also demonstrates eightfold interpenetration of diamond-type frameworks, but it has highest free accessible volume of ≈21% among all three compounds and the smallest crystallographic density of 1.228 g cm -3 as opposed to 1.493 g cm -3 for 1 and 1.387 g cm -3 for 2. It should be noted that MOFs with such complex structures have not been investigated recently as a starting compounds for a postsynthetic conversion. However, despite the intrinsic complexity of these compounds we chose them as starting materials for the experiments expecting some of their structural features (high interpenetration degree and presence of weakly interacting flexible ligands) would play a role in the formation of molten species with new morphology, different from other wellknown MOF derivatives.

Characterization

To perform the ultrafast melting together with optical characterization, we utilize a self-made setup comprising an Yb-doped solid-state femtosecond oscillator (150 fs, 1050 nm, 80 MHz repetition rate) and aligned objectives for laser focusing with simultaneous optical analysis of initial MOF single crystals and nanometer scale objects by commercial photo camera and confocal spectrometer HORIBA LabRam (Figure S2, Supporting Information).

The MOF samples used in this work were obtained solvothermally in accordance with published procedure. [13] The optical measurements allowed us to estimate the bandgap for compounds 1-3 (≈2.9 eV) [13] and revealed high transparency within the visible and near IR range (Figure S3, Supporting Information), which makes them stable to IR irradiation. Moreover, every MOF samples being investigated demonstrate different nonlinear optical effects (Figure 2): a) Single crystals of 1, 2, and 3 demonstrate pronounced nonlinear optical effect such as three-photon luminescence (3PL). In this case, the energy of photons, E 3PL , noncoherently emitted by the crystals, is equal to E 3PL = 3*E ph -E nr , where E ph is an energy of IR photons (1.18 eV) and E nr corresponds to the energy of nonradiative processes. In case of 1, the 3PL spectrum covers the range from 2.2 to 3.1 eV with corresponding cubic slope 2.7 ± 0.2 on excitation intensity (Figure 2a). 3PL signal with the same spectral range and the slope of 3.0 ± 0.1 is also observed for compound 2 (Figure 2b). It should be noted that the most intensive signal of 3PL is observed for this compound (Figure S4, Supporting Information). Regarding compound 3, 3PL can be observed in more specific form (Figure 2c): photoluminescence is characterized by changing shape of spectra with lower slope (2.5 ± 0.3) and strong dependence on the fluence (Figure S5, Supporting Information). b) Intriguing for all compounds we confirm another nonlinear optical effect as second harmonic generation (SHG), i.e., coherently emitting doubled frequencies (1/λ 1 + 1/λ 1 = 1/λ 2 ), where λ 1 and λ 2 are the wavelengths of excitation (1050 nm) and emitted photons (525 nm). This quadratic optical nonlinearity is usually observed for materials having non-centrosymmetric space groups; however, SHG can be also detected for some semiconductors due to surface effects or light-induced breaking symmetry.[12a,14a-c] Concerning compound 1, which has centrosymmetric space group P2c, we detect SHG with quadratic slope of 1.85 ± 0.15 which is appeared under the fluence of ≈0.7-7.5 mJ cm -2 (Figure 2a). The lower limit may be caused by a threshold energy needed for breaking the symmetry,[12a] while the upper limit corresponds to the state when the slop for SHG deviates from quadratic to linear function on the fluence. This behavior can be also explained by sufficient lightinduced structural changes[12a] of compound 1 having weakly interacting flexible alkali-chained ligands. In opposite to 1, single crystals of 2 have non-centrosymmetric space group P2 1 2 1 2 1 and also generate second harmonic radiation at a wavelength of 525 nm with quadratic slope of 1.8 ± 0.2 (Figure 2b). The SHG signal is detected under the broad fluence range from 0.2 to 6 mJ cm -2 . The lower limit is due to the sensitivity of spectrometer, while the upper limit may be caused by the lightinduced structural changes as for 1. Similar to 3PL efficiency (Figure S4, Supporting Information), compound 2 also emits SHG with a maximal efficiency. Finally, compound 3 with centrosymmetric space group Pbcn emits SHG in more specific form: the emission is stepwise and observed at higher fluence threshold of ≈2 mJ cm -2 with the slope of 1.75 ± 0.15. At higher fluence of ≈5.5 mJ cm -2 the signal vanishes. Such deviations of 3PL and SHG signals for 3 can be explained by more dynamic reaction of the compound to the pulsed intense radiation, as its structure comprises the flexible ligands of the maximal length and has the lowest crystal density among all three complexes providing a greater degree of freedom for 3 to change its structure upon irradiation.

Ultrafast Melting: An Overview

Once the preliminary characterization was done, we utilize our setup (Figure S2, Supporting Information) to produce derivatives by exposition of the MOF single crystals to 150 fs IR laser pulses (Figure 3a). By increasing the laser power from 0.2 to 15 mJ cm-2 and measuring the MOF response in terms of structure (Raman scattering), intensity of nonlinear optical signals (3PL and SHG) and dark-field optical imaging, we clearly identify four regimes I-IV (Figure 3b). Further, we consider them on the example of compound 1:

I)

A nonperturbed regime (the fluence up to 7.5 mJ cm -2 ) corresponds to stable signals of SHG (Figure 3d) and 3PL with quadratic and cubic slopes, respectively. The Raman scattering also confirms nonperturbed structure after irradiation with the fluence less than 7.5 mJ cm -2 (Figure 3c). II)

The transition regime (the fluence from 7.5 to 9.5 mJ cm -2 ) is characterized by variation of the intensity of SHG (Figure S5d, Supporting Information) and deviation of the slopes of SHG and 3PL from cubic and quadratic dependence to linear functions, respectively.

The following decrease of fluence yields a transition to regime I, but with lower intensity of SHG (3PL) and is accompanied by a slight color changes of the crystals. These can be caused by formation of crystal defects[9f,g] under irradiation and actually makes the transition I to II irreversible in terms of structure.

III)

The melting regime is appeared with the threshold transition at ≈9.5 mJ cm -2 . This regime is characterized by a step-like melting of the MOF crystals and possibility to produce the particles, which efficiently scatter the light and, hence, have different colors (Figure 4a). Such specific behavior during the melting is similar to the transition between thermal and ultrafast nonthermal melting of crystalline semiconductors under intense fs laser pulses. [12a-e] This hypothesis is also supported by the fact that we can achieve MOF melting under 9 mJ cm -2 with long exposition (more than 10 min), while increase of fluence by 10% to 10 mJ cm -2 results in the snap melting. This observation can also speak in favor of first nonthermal melting of MOFs. IV)

Finally, for the last regime, the burning of the whole crystals (inset in Figure 3b) with creation of small amount of nanometer scale particles can be observed at higher fluence (>11.5 mJ cm -2 ).

Following the concept of ultrafast melting of semiconductors by exiting few percent of electrons from valence to conduction bands, [12] the fraction of excited electrons for each investigated compound could be roughly estimated as following: the ultrafast melting of 1 occurs under 3-6% of exited electrons, while 2.5% and 2.2% correspond to 2 and 3, respectively (for the details, see Supporting Information). The results are in a good agreement with previously reported data on nonthermal ultrafast laser melting of other crystalline semiconductors (Figure 1b and Table S2, Supporting Information). The increase in the number of exited electrons from 2.2% to 3% correlates well with the gradual growth of MOFs crystal density from compound 3 to 1. Moreover, the estimated value of ≈3% for all compounds corresponds well to the values of 3-5% obtained for other materials with melting points (Bi, M.P. 280 °C and InSb, M.P. 530 °C) close to MOFs used in this study (M.P. at ≈400 °C). [13] The crystalline semiconductors with higher melting point (>940 °C) require more than 6% of exited valence electrons (Figure 1b). We can argue that the presence of number of relatively weak bonds, which are involved in the formation of crystal structurer of MOFs, is also responsible for a decreased value of exited electrons needed to weaken these bonds and soften the MOF lattice.

Statistical investigation of the interaction of 40 single crystals of 1, 2, and 3 with fs pulses of different fluence was also performed (Figure 3b). We reveal that compound 1 is more rigid to the increasing fluence than compound 3, while compound 2 was intermediate in terms of stability. The explanation of this effect (i.e., different fluence thresholds for ultrafast melting) can be given with regard to the analysis of ultrafast dynamics of the interpenetrated structure of such MOFs with flexible building blocks, as well as thorough analysis of metal-nitrogen (metal-oxide) strength.

[10a] However, we assume that increase of the crystal density from ≈1.2 to 1.5 g cm -3 and decrease in geometrical length of weakly interacting flexible alkali-chained ligands in a row from 3 to 1 limit the compounds' degree of freedom to react on light and their ability to change their conformation. Therefore, the more rigid compound demonstrates higher fluence threshold for melting by fs light. Concerning the thermal stability under the slow heating (see thermogravimetric analysis, TGA, Figure S6, Supporting Information), [13] there is no evidenced link between TGA data and the threshold for ultrafast melting.

Ultrafast Melting: The Derivatives

Since the regime III has been shown to be the most suitable for producing the particles (Figure 3b), we use fluences of 10, 8, and 7 mJ cm -2 to produce MOF derivatives from compounds 1, 2, and 3, respectively (Figure 4a). To carry out both electron microscopy and optical characterization, the derivatives have been printed on carbon grid and gold substrate. Scanning electron microscopy (SEM, FEI Quanta 200) is used to analyze the average shape and size of MOF derivatives. For compound 1, laser melting mainly provides well-defined spherical particles with diameter distribution from 100 to 1000 nm (Figure 4b). In contrast, compounds 2 and 3 are characterized by irregular shaped structures with characteristic size from 800 to 3800 nm and 500 to 2500 nm, respectively, which can be easily destroyed by electron beam of SEM. Transmission electron microscopy (TEM) and energy dispersive X-ray (EDX) with semi-quantitative elemental analysis are also used to provide insights into the structural and composition properties of the derivatives (Figure 5 and Figure S7, Supporting Information). TEM (JEOL ARM 200F TEM/scanning TEM operating at 200 kV) reveals that derivatives have completely different morphology. In case of 1, two morphologically different types of particles were produced: the amorphized drops (Figure 5k) with metal-organic composition (Figure 5l,m and Table S3, Supporting Information) and homogeneous redistribution of the elements (Figure 5n); and spherical ones (Figure 5a-c,g-j) whose internal structure can be described as core-shell (Figure 5f). The shell represents an amorphized organic phase, which is confirmed by elemental analysis (Figure 5d,e and Table S3, Supporting Information), Raman scattering (Figure 3c), and redshifted 3PL spectra (Figure 6a). Surprisingly, the absence of carbon contamination is verified by Raman scattering, which makes the obtained derivatives to be very different from the reported recently. In the latter case, amorphous carbon becomes a regular product. In contrast, the core of the derivatives has the more complicated morphology as dendrite-like metal-oxide confirmed by TEM and EDX analysis (Figure 5c-j). To the best of our knowledge, such unique core-shell structures have not been previously synthesized from MOFs.

In case of 2 and 3, we produce only the derivatives of irregular shape (Figure S7a,d, Supporting Information) and amorphous phase with metal-organic composition (Figure S7b,c,g,h and Table S3, Supporting Information) confirmed by TEM and redshifted 3PL (Figure 6c). It should be noted that elemental analysis reveals the differences between composition of initial MOFs and all their derivatives (Table S3, Supporting Information), which is in good agreement with results on MOF melting by classical ways.

[10a] The redshifted 3PL signal also confirms the presence of amorphous organic phase, while the existence of cadmium and zinc atoms and their redistribution over the shape of the derivatives is attested by EDX analysis (Figure S7c,h,i, Supporting Information).

To shed light on the reasons for the fundamental difference in the morphology of the derivatives obtained under the ultrafast optical excitation, we analyze the electronic structure of the MOFs by means of density functional theory (DFT) calculations. Figure S9 in the Supporting Information presents the computed projected density of states (pDOS) for 1, 2, and 3 and the respective banddecomposed partial charge densities at the valance band maximum (VBM) and the conduction band minimum (CBM). Calculations underestimate the bandgaps (2.1, 2.0, and 2.2 eV, respectively) for 1, 2, and 3 compared to the experimental values (≈2.9 eV) due to the known shortcomings of the generalized gradient approximatio-type functionals.[14d,e] The results in Figure S9 in the Supporting Information reveal substantial differences in the electronic structure of 1 compared to that of 2 and 3. DFT calculations show that for compound 1 the VBM is mainly represented by the CC bonding πorbitals and the O 2p orbitals. Substantial contribution of Cd orbitals to the valence band close to the Fermi level could also be noted. The corresponding electronic charge densities of VBM show a pronounced delocalization among Cd, O, and the aromatic π-system. The CBM is mainly represented by the π* systems of the ligands with some contributions due to O atoms of the carboxylate moieties.

Both VBM and CBM are delocalized along the structure-forming Cdcarboxylate chains and span throughout the crystal. On contrary, for compounds 2 and 3, the delocalization of the VBM and CBM is limited to defined ligand units. The corresponding electronic charge densities are predominantly contributed by the π and π* aromatic systems of the ligands with only a minor contribution of the orbitals at O sites. In other words, these differences in the electronic structures suggest that upon optical excitation, 1 would undergo a controlled dissociation in the directions determined by the antibonding character of the delocalized CBM. In the cases of compounds 2 and 3, one cannot expect a specific directionality of the crystal melting upon excitation.

Overall, analyzing the gathered experimental and theoretical information, an important assumption can be made. The interaction of MOFs, having an interpenetrated 3D structure and flexible ligands, with fs laser radiation suggests a dependency between thermal stability, crystal density, and electronic structure of the initial MOFs and the morphology of corresponding derivatives. Indeed, among all three analyzed compounds, complex 1 is less stable at low heating rates (TGA, Figure S6, Supporting Information), [13] has higher crystallographic density, and delocalized electronic density. Perhaps these conditions make it easier to break the bonds in the MOF before it gets completely burned, followed by reorientation and reassembly of MOF structural elements into new structures under nonequilibrium conditions. As a result, only this compound can be converted to core-shell metalorganic derivatives, as opposed to compounds 2 and 3, which are more stable to slow heating and less dense. Their derivatives demonstrate a decreased 3PL and SHG signals (see below) and represent the more homogenous metal-organic structures with much higher degree of amorphization to be formed during the ultrafast melting. These structures also cannot be simply considered as amorphous MOFs [9a-e,10] as the elemental composition of the resulting derivatives differs significantly from the chemical composition of the starting materials (Table S3, Supporting Information). Furthermore, the presence of coordination bonds in each nanometer scale derivatives appeared challenging to be confirmed by existing techniques.[9e]

Application

Here we consider the dependence of the functionality of the derivatives, obtained from MOFs with intrinsic nonlinear optical properties (Figure 2), on their morphology. In particular, the derivatives obtained especially from 1 have three key features to be considered for application in nonlinear nanophotonics: metal-organic composition, which is important for efficient photoluminescence and enhanced optical response; nonlinear optical response of initial MOFs; and morphology (core-shell structure, size, and shape) which can drive the interaction of light with wavelengths from ultraviolet to IR range.[7f,15] Therefore, we investigate the interaction of light with single derivatives by linear and nonlinear optical microspectroscopy (Figure 6). Concerning nonlinear optical response, we reveal that 3PL spectra of the derivatives obtained from compounds 1 and 2 are redshifted in comparison to that of initial MOFs (Figure 6a,c). This can be explained by amorphized state of the organic components.

[16] In contrast, derivatives from 3 do not demonstrate any photoluminescence signal that can be explained either by low signal of 3PL or complete destruction of organic components. The signals of SHG are also preserved for derivatives from 1 and 2 due to the well-developed surface,[15d] distorted organic-inorganic structure, [9a] or light-induced broken symmetry. [9a,14a-c].

It is worth comparing the efficiency of SHG from the nanometer scale derivatives obtained from centrosymmetric crystal 1 with that of nanoparticles with (Si) and without (BaTiO3) centrosymmetric space group (Figure S10, Supporting Information). Interestingly, we detect SHG signal from the derivatives, that is just 2 orders of magnitude smaller than that for BaTiO3 nanoparticles[15f ] of the same diameter (430 nm). Compared to centrosymmetric and optically resonant Si nanoparticle with the diameter of 275 nm, for which the well-developed surface of the nanoparticle can be the reason of optical nonlinearity,[15d] MOF derivatives demonstrate the efficiency of the same order of magnitude.

The smaller or bigger Si nanoparticles generate second harmonics with efficiency 1 order of magnitude less (Figure S10, Supporting Information).

Moreover, the ratio of intensities of SHG and 3PL for derivatives and corresponding MOFs (1) is different: SHGderiv/3P Lderiv ≈ 5*SHGMOF/3PLMOF. This effect can be explained by resonant interaction of spherical derivatives of diameter from 100 to 1000 nm and typical refractive index of 2.5 (generally for organic-inorganic materials) with light: high-order Mie-type electromagnetic modes [15] with high quality factor Q (Q = λ0/Δλ, where λ0 is the central wavelength of emission and Δλ is the full width at half maxima) can be optically generated inside such kind of particles supporting an enhancement of intrinsic optical emission.

[15d] We reveal these modes by optical spectroscopy (Figure 6b) from single derivatives in the dark-field geometry (Figure S2, Supporting Information). Indeed, SHG signal with high quality (Q = 138) from derivatives overlaps with high order and same high quality Mie modes,[15c-e] which significantly enhance SHG. Concerning 3PL, this broad spectrum with low quality (Q = 4) cannot be significantly affected by the same Mie modes. This situation is for derivatives from 2, where the low quality of Mie-type modes cannot contribute to enhancement of nonlinear optical response.

Based on these results, one can conclude that the more complicated the morphology of MOF derivatives we have (Figure 5c,g,i), the more efficient linear and nonlinear optical response can be observed. This also raises a question of potential application of amorphous MOFs and the derivatives in photonics. Indeed, recent reports of MOF derivatives application were focused on catalysis and energy storage. In this regard, our study is one of the first demonstration of developed optical synthesis of active nanophotonics components based on metal-organic frameworks.

Conclusion

For the first time the ultrafast melting of 3D interpenetrated MOFs with flexible alkali-chained ligands by femtosecond IR laser pulses was demonstrated as an effective way to produce unique nanometer scale derivatives with complex morphology and enhanced nonlinear optical response. Structurally, the products of this nonequilibrium process can be categorized as complex derivatives representing wellorganized spheres with metal-oxide dendrite core and amorphous organic (noncarbon) shell or as amorphous metal-organic species. An ability to produce such derivatives and the complexity of their morphology are a result of a tradeoff between the crystal density, ligand length and flexibility, electronic structure, and thermal stability of the starting MOF compounds. The analysis of ultrafast melting also reveals that the denser structure with shorter flexible ligand, the higher the fluence threshold for ultrafast melting of such MOFs. Moreover, the delocalization of electronic density contributes to the process of laserinduced melting and results to complexity of the morphology of MOF derivatives. We also demonstrated an enhanced second harmonic generation and three-photon luminescence due to resonant interaction of the 100-1000 nm spherical derivatives with light. The presented data clearly indicate a vast potential of ultrafast melting of MOF for producing new generation of materials for applications in nonlinear nanophotonics and highlight a general methodology for the research on ultrafast melting of other metal-organic framework complexes and related porous materials.

Figure 1

 1 Figure 1. a) Structural formulae of the ligands used to produce compounds 1-3. b) Fraction of electrons to be excited for ultrafast melting of crystalline semiconductors (Table S2, Supporting Information) versus temperature needed for classical melting with thermal equilibrium. 1, 2, and 3present work, Bi,[12b] Si,[12c] InSb,[12d,e] Ge,[12f ] and GaAs.[12g]

Figure 3 .

 3 Figure 3. Ultrafast laser melting of MOFs. a) Scheme of interaction of MOF single crystal with 150 fs 1050 nm laser pulses with 80 MHz repetition rate. b) Four regimes (nonperturbed I, transition II, melting III, and burning IV regimes) of the interaction of MOFs with fs laser radiation with different fluence. As an example, the dependence of SHG intensity (in arbitrary units) and melting efficiency (M.E.) is shown for compound 1 demonstrating the step-like melting. Corresponding images of melted and burned single crystals are shown. Scale bar, 10 μm. For compounds 2 and 3 see Figure S8 in the Supporting Information. c) Raman scattering for single crystal of 1 before and after irradiation by 6 mJ cm -2 , and for single derivatives of 1. d) Stability of SHG signal from single crystal of 1 irradiated by 6 mJ cm -2 for 30 min.

Figure 4 .

 4 Figure 4. Morphology of MOF derivatives. a) Optical images and b) SEM micrographs and diameter distribution for corresponding derivatives obtained from compounds 1, 2, and 3. Scale bars: a) 50 μm and b) 10 μm for 1 and 2, and 5 μm for 3.

Figure 5 .

 5 Figure 5. TEM analysis. a) HAADF (high angle annular dark field) and b) bright field TEM micrographs of MOF derivatives from compound 1. c,g-j) Three zoom in images of the core-shell derivatives. d-f) EDX analysis reveals the elemental ratio, and line scan confirms the core-shell structure. k) Bright field TEM image of the amorphous phase with l,m) corresponding elemental analysis and n) line scan representing the homogeneous element redistribution over the shape. Scale bars: a,b) 1 μm, c) 80 nm, g-j) 200 nm, and k) 200 nm.

Figure 6 .

 6 Figure 6. Optical properties of MOF derivatives. SHG and 3PL spectra from the derivatives of a) 1 and b) 2 normalized by maxima. Inset: Optical image of SHG-3PL signal from single derivative. Scale bar, 2 μm. b,d) Corresponding spectra of scattering of s polarized white light in dark-field geometry on single derivatives with diameter ranging from 500 to 800 nm. The number of resonances (maxima of the curves) corresponds to intrinsic Mie-type modes generated inside the derivatives.[15] Inset: Optical image of derivative irradiated by s and p polarized light. Scale bar: 2 μm.

Acknowledgements N.K.K. and S.B. contributed equally to this work. Authors thank M. O. Barsukova for providing the samples of MOF compounds for the research. V.A.M., N.K.K., and Y.A.M. acknowledge support from the Russian Foundation for Basic Research (Project No. 18-32-20089 mol_a_ved) for optical investigation of MOF derivatives and the Russian Science Foundation (Projects No. 19-79-10241 and 17-19-01637) for investigation the ultrafast melting of MOFs and their composition, respectively. E.P. acknowledges support from the Ministry of education and Science of the Russian Federation (Project 11.1706.2017/4.6). D.S. and E.P. thank NWO (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) for providing for providing access to the SurfSARA supercomputer facilities. S.B., J.G., and T.B. benefited from Programme Hubert Curien-Kolmogorov and would like to thank Dr.-Ing. P. Boulet (Institut Jean Lamour, CC X-Gamma) for XRD measurements. A.N. acknowledges financial support by the Government of the Russian Federation through the ITMO Fellowship and Professorship program.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.


Dr Vijai Meena Santhini

Christian Wäckerlin

Ales Cahlik

Martin Ondráček

Dr Simon Pascal

Dr Adam Matěj

Dr Oleksandr Stetsovych

Dr Pingo Mutombo

Dr Petr Lazar

Dr Olivier Siri
email: olivier.siri@univ-amu.fr

Dr Aleš Cahlík

Pavel Jelínek
email: jelinekp@fzu.cz

Christian Wackerlin

Structures Defined by the Choice of the Transition Metal: Towards a New Class of Antiaromatic Macrocycles

Keywords: coordination modes, diamino-benzoquinonediimine, macrocycle, -d conjugation, scanning probe microscopy

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Introduction

One-dimensional (1D) covalent polymers are of considerable interest in many different technological sectors due to their unique electronic properties. [1][2][3][START_REF]Electronic Materials: The Oligomer Approach[END_REF][START_REF] Llinas | [END_REF][6] The solvent-free synthesis of such nanomaterials at the surface has been emerging as a promising approach to obtain tailored low dimensional materials with atomic precision. Pure organic 1D materials can be obtained through catalyzed C-C coupling reactions on surface from halogenated precursors. [7][8] Alternatively, 1D coordination-polymers (CPs) can be isolated through coordination chemistry, the covalent bond formation resulting from on-surface reactions between metal atoms and suitable linker groups. [9][10][11][12][13][14] One major advantage of this approach is the possibility to tune the properties of the wires by changing the nature of the metal and/or the ligand. In this strategy, the ligand design is crucial since maximizing the conjugation through coordination requires keeping the π-d systems as coplanar as possible. Previous studies reported that low-lying π* orbitals of quinoidal ligands can mix extensively with the valence d-orbitals of a metal center, yielding complexes in which the electrons could be delocalized over both the metal and the ligand. [15][16][17] In this context, 2,5-diamino-1,4-benzoquinonediimines (2HQDI) are particularly appealing because of their fascinating optical properties, [18][19] and remarkable ability to serve as ligand in coordination chemistry. Unlike the N-substituted systems (Nalkyl or N-aryl), [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] the coordination chemistry of the parent (i.e. unsubstituted) molecule 2HQDI in solution has been poorly investigated probably due to its low solubility and specific reactivity that induced unwanted side-reactions. [35] Some of us showed that the absence of N-substituents (no steric hindrance) allows a unique behavior resulting from the stepwise formation of coplanar polynuclear complexes NiQDI with up to 3 repeat units (n ≤ 3) (Figure 1a). [17] The oligomerization reaction proceeds in solution by successive deprotonation/metalation steps from 2HQDI, affording complexes in which each quinoid ligand is linked to two metal centers through two covalent and two coordinative bonds. As a result, the oxidation state of the metal centers is always +II and the π-system of the bridging unit is fully delocalized, forming π-d delocalized systems. [36][37][38][39][40][41] Importantly, the size of the oligomers depends on the nature of the solvent since the oligomerization process stops when the limit of solubility is attained. [42][43] Herein, we explore the reaction between transition metal (TM) atoms (Cr, Fe, Co, Ni and Cu) and 2HQDI directly at the solventfree solid surface under ultra-high vacuum conditions. We anticipated that this approach [44] would overcome the limitations observed in solution and could lead to formation of extended flexible covalent coordination polymers with lengths of hundreds of nanometers. In the course of this study, we also observed a different coordination mode of the metal center to the ligand depending on the metal precursors and/or the nature of the substrate, see Figure 1b. More specifically, a new and remarkable coordination mode of the ligand 2HQDI was observed in the case of reaction with copper, resulting in the formation of wires based on unique (poly) macrocycles, see Figure 1b (Cu2QDI). A combined experimental and theoretical study allowed us to resolve its chemical structure consisting of a 12-membered ring incorporating two copper centers. These macrocycles can be considered as a new class of antiaromatic compounds. [45][46]

Results and Discussion

The metals Cr, Fe, Co and Ni are introduced as neutral metal atoms from an electron-beam evaporator while Cu is provided directly by the Cu substrate (as detailed in the Supplementary Information). The ligand precursor 2HQDI is deposited simultaneously by sublimation, and is let to react on Cu(111) and Au(111) surfaces with the metal atoms. With all metals, isolated 1D metal-organic coordination polymers are obtained. As we show, the {Cr, Fe, Co, Ni} containing CPs are based on four-fold square-planar coordination where the metal atom is coordinated head-to-head between two ligands (MQDI in Figure 1b). Figure 1c(top, middle) shows a representative high-resolution nc-AFM image FeQDI/Au(111), recorded with CO functionalized tip [47,48] revealing a characteristic "x-like" contrast feature in between the molecular units. On the contrary, Cu-CPs are based on two-fold linear coordination motifs where each Cu atom is linked to the nitrogen atoms of the ligand arranged side-by-side (Cu2QDI in Figure 1b), as demonstrated by high-resolution nc-AFM image of Cu2QDI wire on Cu(111) (shown in Figure 1d top, middle) exhibiting a distinct structural contrast. Due to the different arrangement of the molecular building blocks, the periodicity of Cu2QDI (6.8 ± 0.1 Å, Figure S1) along the wire is also noticeably shorter compared to 7.7 ± 0.1 Å for FeQDI. Notably, FeQDI/Cu(111) exhibits a similar AFM contrast as FeQDI/Au(111) (Figure S1), featuring the characteristic "x-like" appearance on the Fe. To confirm the structures, we carried out total energy DFT-B3LYP [50][51] calculations of FeQDI/Au(111), FeQDI/Cu(111) and Cu2QDI/Cu(111) 1D coordination polymers. The lattice vectors of the optimized DFT structures (Figure S2) are in very good agreement with the experimentally acquired values. Furthermore, AFM simulations using the probe-particle model [52] fully reproduce the experimental AFM contrast, see Figure 1c and 1d (bottom). N-N covalent bonding between the ligands can be firmly ruled out, as it would result in a shorter molecule-to-molecule periodicity (5.7 Å from DFT). The dehydrogenation reaction on the surface and simultaneous formation of metal coordinated wires is further supported by XPS measurements (Figure S3) of {Fe,Ni}QDI wires on Au(111) surface and Cu2QDI wires on Cu(111) surface. N1s XP spectra of native 2HQDI on both Au(111) and Cu(111) reveal two components, corresponding to -NH2 and -NH groups. In contrast, for the synthetized {Fe, Ni, Cu2}QDI wires, only one N1s component is observed, showing that all four nitrogen atoms of the ligand have identical chemical environments, consistent with the structures shown in Figure 1b. This also excludes the possibility of hydrogen-bonded wire growth. For Cu2QDI, we could identify 12-membered macrocycles involving twelve π electrons of the ligand. The bridging QDI ligand can be indeed described as two nearly-independent six π electrons subunits chemically connected through two C-C single bonds (the so-called "coupling principle") [START_REF] Dähne | Coupling principles in organic dyes[END_REF] . As a consequence, the Cu2QDI wires are constituted of electronically independent macrocycles linked together through two C-C single bonds, preventing a full delocalization over the wire. Overview STM images of {Cr, Fe, Co, Ni}QDI on Au(111), Cu2QDI on Cu(111) and FeQDI on Cu(111) are displayed in Figure 2. For {Cr, Fe, Co, Ni}QDI on Au(111), very long regular wires easily exceeding lengths of 100 nm can be observed. On Au(111), the wires loosely follow the herringbone reconstruction of the substrate and can be easily manipulated by the STM tip and bent into manifold shapes (Figure S4). This points to their relatively weak interaction with the Au(111) substrate. In the zoom-in STM images (Figure 2), the Cu2QDI wires appear significantly wider compared to the {Cr, Fe, Co and Ni}QDI ones and their periodicity along the wire is visibly smaller (in agreement with the nc-AFM observation). In combination with the known coordination geometry of FeQDI and Cu2QDI determined by nc-AFM (Figure 1c,d Compared to all MQDI wires on Au(111), both types of wires (FeQDI and the Cu2QDI) branch more frequently on Cu(111) and they follow specific directions of the substrate. By analogy with the growth of organic and inorganic 2D materials at surfaces, [53][START_REF] Meiwes-Broer | Metal Clusters at Surfaces[END_REF] the higher frequency of branching suggests that the growth on Cu(111) is more kinetically controlled. This can be attributed to higher diffusion barriers on Cu(111) as compared to Au(111). Interestingly, while FeQDI can be prepared on either Au(111) or Cu(111), we have been unable to prepare Cu2QDI wires on Au(111) by electron-beam evaporation of Cu. We ascribe it to the preferential diffusion of Cu adatoms into the bulk of the Au single crystal.

To understand the origin of the different coordination mechanism of Cu, we analyzed theoretically the formation energies using DFT calculations of free-standing polymers (for details see Figure S5). The FeQDI coordination polymer prefers energetically the 4-fold coordination, while the 2-fold coordination is favorable for Cu2QDI wire, in good agreement with the experimental observation. To get more insight into this trend, we also analyzed the electronic structure of the wires. Note, that our DFT B3LYP calculations reveal a closed-shell ground state of Cu2QDI chain, while in the case of FeQDI, the chain is open-shell with spin S = 1. A detailed experimental and theoretical analysis of magnetic properties of MQDI chains is under investigation and it will be published as a separate scientific paper.

Figures and S7 show calculated projected density of states (PDOS) of free standing FeQDI and Cu2QDI chains respectively. In the case of the FeQDI wire with its four-fold coordination, more dorbitals are involved in the rehybridization with the pz-orbitals of the ligand. Also, in the case of other TM atoms (Cr, Co, Ni), partial filling of their d-orbitals promotes strong hybridization with the ligand field adopting the 4-fold coordination. [17,35] In the case of the two-fold coordinated Cu2QDI chain, only s and dyz orbitals hybridize with pzorbitals of nitrogen atoms of the ligand. Since the fully occupied dorbitals of Cu(I) are reluctant to be involved in the chemical bonding with ligands, the two-fold coordination and thus Cu2QDI structure is preferred. Cu atoms can easily form complexes in +I oxidation state because they are then stabilized by their 3d 10 electronic configuration, unlike Cr, Fe, Co and Ni which prefer oxidation states of +II or higher. The Ni2p3/2 XP spectrum of NiQDI/Au(111) (binding energy 854.5 eV) firmly supports a +II oxidation state (Figure S3). [START_REF] Moulder | Handbook of X-Ray Photoelectron Spectroscopy: A Reference Book of Standard Spectra for Identification and Interpretation of XPS Data[END_REF] In contrast, the Fe2p3/2 binding energy of FeQDI/Au(111) (707.3 eV) is surprisingly low for a Fe(II) ion. The same effect, i.e. high Ni and low Fe binding energy, has been reported for {Fe,Ni}porphyrins, phthalocyanines and related compounds [START_REF] Rieger | [END_REF] and is interpreted as a partial shift of electron density from the substrate to the metal ion, in line with the original explanation of this effect. [57][58][59] Unfortunately, because of the overwhelming substrate signals we cannot study Cu XP spectra of Cu2QDI/Cu(111).

Indeed, the analysis of the electrostatic potential maps of FeQDI (Figure S8a) and Cu2QDI (Figure S8b) (revealing the charge transfer from TMs to the QDI ligand) clearly show that the charge transfer is larger in the case of FeQDI, where Fe in four-fold coordination is typically found in +II oxidation state. Consequently, we conclude that Cu in the Cu2QDI polymer is found in +I state. This observation is consistent with the coordination of the copper center through one covalent and one dative bond with the ligand enabling two isomeric electronic structures as shown on Figure 3a. This allows the delocalization of the π-d electrons over the macrocycle, in contrast to the coordination exclusively through dative bonds as observed in supramolecular complexes. [60] This picture is also supported by DFT calculations. Namely, the calculated band structure shows relatively strong dispersion of both valence and conduction bands resulting in the band width of ~0.5 -1 eV, see Figure S9a and S9b. Also, real space images of electron density of both the valence and conduction bands (Figure S9c and S9d) reveal a strong hybridization of d-orbitals with pz-orbitals of nitrogen atoms on the ligand and delocalization of the electronic states over both TM and ligand. Moreover, the analysis of the bond lengths suggests that in both FeQDI (Figure S10a) and Cu2QDI (Figure S10b) wires, the -system of the quinoidal ligand is strongly delocalized, as shown schematically in Figure 1b. All these findings strongly suggest that the presented 1D coordination polymers exhibit -d conjugation. Next, we provide an analysis of the aromatic character of the macrocycle in the 1D chain Cu2QDI. Figure 3 shows the bond scheme, calculated maps of the nucleus-independent chemical shift (NICS) [61] and the anisotropy of the current induced density (ACID) [62] for free-standing Cu2QDI chain. In the case of Cu2QDI chain, the positive NICS values (Figure 3b) with maxima over the C6 ring of the ligand and the 12-membered macrocycle of +8.6 ppm and +6.6 ppm respectively, indicate that both are antiaromatic in nature. Also the calculated ACID plot of Cu2QDI chain in Figure 3c reveals anticlockwise current density vectors exhibiting paratropic current and thus antiaromaticity, in agreement with the NICS data. Interestingly, the current density vectors of both the C6 ring of the ligand as well as the 12-membered cycle are seen as separate loops, hence substantiating that the backbone of the 1D Cu2QDI chain is formed by individual delocalized macrocycles as depicted schematically in Figure 3a. The antiaromatic character of the quinoidal ligand is also confirmed by a negative harmonic oscillator model of aromaticity (HOMA) value of -0.241 (see Supporting Information for HOMA calculations).

In order to understand the aromaticity of conjugated metallacycles, Mauksch and Tsogoeva have worked out the frontier π-orbital topology rule: "The metallacycle is aromatic (antiaromatic) when the number of π-MOs is even and the π-HOMO is of Möbius (Hückel) topology-and vice versa when the number of π-MOs is odd." [63] The nature of the aromatic stabilization in metallacycles related to the bonding between the transition metals and the adjacent atoms permits two different topologies of the π-d orbital conjugation: Hückel and Mobius topology, where the latter involves the d-orbitals introducing a frustrated phase variation of π-orbitals in the metallacycle. [64] The 12-membered macrocycle in the Cu2QDI chain consists of two dyz metal orbitals which change the phase of adjacent π-orbitals of N atom (see HOMO shown in Figure S9b). The presence of an even (two) number of d-orbitals causing the change of the phase in the cycle avoids the frustration of the πorbital phase in the cycle. Consequently, the π-d conjugation of the macrocycle can be considered as Hückel topology. The 12membered macrocycle in the Cu2QDI chain consists of 8 π-MOs (even) and π-HOMO is of Hückel topology, thus the macrocycle is antiaromatic in nature following the Mauksch and Tsogoeva rule, in agreement with the ACID and NICS analysis. Noteworthy, this rule is strictly applicable for the macrocycles whose number of πelectrons is equal to the number of members in the ring, as discussed recently. [65] In the case of FeQDI, the NICS value (see Figure S11a) for the C6 ring of the ligand as well as the five membered ring containing the metal is negative (with maximal values of -25.7 ppm and -17.5 ppm respectively) exhibiting aromatic character. The negative values of NICS is indicative of a diatropic ring current in presence of a magnetic field, which agrees with the calculated ACID isosurface for the FeQDI chain (see Figure S11b). Nevertheless, we should note that despite relatively large NICS numbers, the ACID plot reveals that the current density is not completely circular on the quinoidal ring. Instead, ACID confirms the existence of two decoupled delocalized π-d electronic systems as schematically depicted in Figure 1b for MQDI. This decoupling is also confirmed by a relatively large bond length alternation within the C6 ring of the ligand (Fig S10). Consequently, the harmonic oscillator model of aromaticity (HOMA) [66] value of the quinoidal ring is about 0.486, predicting a weak aromatic character (for details of HOMA calculations see Supporting Information).

Conclusion

In conclusion, we presented a novel route to the synthesis of long and defect-free 1D coordination -d conjugated polymers, achieved by co-deposition of the 2HQDI molecular precursor and various transition metal (Fe, Co, Ni, Cr, Cu) atoms on metal surfaces under UHV conditions. This approach overcomes the problem of solubility limiting traditional wet chemistry synthesis, and enables to grow up to hundreds of nanometers long defect-free covalent polymers. By high-resolution AFM imaging and theoretical calculations, we demonstrated that all TMs (except Cu) adopt a four-fold coordination motif with nitrogen atoms of the QDI ligand (MQDI). In the case of Cu atoms, we found a new coordination mode of the ligand and the formation of the linear two-fold coordinated Cu2QDI polymer. Our analysis indicates that the electronic states of polymers MQDI (M = Fe, Co, Ni, Cr) fully delocalize over both metal and ligand forming π-d systems. In the case of Cu, we observe a unique formation of Cu2QDI wires based on antiaromatic 12membered macrocycles incorporating two metal centers, chemically connected by two C-C single bonds but electronically independent (no conjugation between the macrocycles), preventing a full delocalization over the wire. We anticipate that the electronic delocalization together with the possibility to incorporate different transition metals provides new route to design π-d polymers of desired magnetic and electronic properties. The on-surface synthesis under UHV conditions provides a unique possibility to further investigate magnetic and electronic properties of individual polymers by means of scanning probe microscopy. [67]

Figure 1 :

 1 Figure 1: (a) Formation of coplanar polynuclear complexes NiQDI in solution (b) On surface formation of structurally distinct four-fold coordinated MQDI (M= Cr, Fe, Co, Ni) wires and two-fold coordinated Cu2QDI wires by dehydrogenative metalation. (c, d) Top: High resolution constant height nc-AFM images (scalebar 1 nm) recorded with CO modified tip of FeQDI wire on Au(111) [Vbias= 1 mV, Aosc= 50 pm] and Cu2QDI wire on Cu(111) [Vbias= 1 mV, Aosc= 50 pm]. Middle: High pass filtered version of the high-resolution images for better clarity superimposed with space filling models (C, H, N, Fe and Cu atoms correspond to grey, white, blue, orange and brown colors respectively.). Bottom: Simulated AFM images of FeQDI/Au(111) and Cu2QDI/Cu(111) coordination polymers.

  , Figure S1), these two properties show that {Cr, Fe, Co, Ni}QDI on Au(111) and FeQDI on Cu(111) are essentially isostructural with square-planar bonding scheme. Most of the individual MQDI wires on Au(111) are truly one dimensional, although branching between two wires occasionally occurs.

Figure 2 :

 2 Figure 2: STM images of {Cr, Fe, Co, Ni}QDI wires on Au(111) and of Cu2QDI and FeQDI wires on Cu(111). The overview images are 200 × 200 nm 2 and the zoom-in images are 8 × 2 nm 2 . Imaging parameters (bias voltage, tunnel current set point): (a) (500 mV, 10 pA); (b) (1.2 V, 10 pA); (c) (500 mV, 20 pA); (d) (-200 mV, 23 pA); (e) (300 mV, 30 pA); (f) (-200 mV, 50 pA); (g) (100 mV, 30 pA); (h) (350 mV, 10 pA); (i) (100 mV, 42 pA); (j) (30 mV, 10 pA); (k) (-400mV, 32 pA); (l) (100 mV, 42 pA).

Figure 3 :

 3 Figure 3: (a) Scheme depicting the bonds and resonating structures of the 12 membered macrocycle in Cu2QDI wires on Cu(111). (b) NICS grid of Cu2QDI/Cu(111). (c) ACID plot of Cu2QDI/Cu(111), black arrow indicating the anticlockwise direction of current density vectors for better clarity. The molecular planes are placed perpendicular to the magnetic field vector. Small green arrows are computed current density vectors.

Acknowledgements

This was supported by GACR Expro 20-13692X. P.J. acknowledges support of the Czech Academy of Sciences through Praemium Academiae award. Ch.W. gratefully acknowledges financial support by the University of Zürich research priority program LightChEC and by the Swiss National Foundation (grant No. P300P2_177755). O.S. thanks the Centre National de la Recherche Scientifique, the Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation. We acknowledge CzechNanoLab Research Infrastructure supported by MEYS CR (LM2018110). Computational resources were provided by the CESNET LM2015042 and the CERIT Scientific Cloud LM2015085, provided under the programme "Projects of Large Research, Development, and Innovations Infrastructures". P.L. acknowledges the support of the Ministry of Education, Youth and Sports of the Czech Republic under Project No. LO1305, the Operational Programme for Research, Development and Education of the European Regional Development Fund (Project No. CZ.02.1.01/0.0/0.0/16_019/0000754).


Daniela Castro Farías

Rodrigo Matsui Serrano

Juan Bianchi Gancharov

Ulises De

Dios Cuadras

José-Alain Sahel

Federico Graue Wiechers

Benedicte Dupas

MD Michel Paques
email: mpaques@15-20.fr

Daniela Castro-Farías

Rodrigo Matsui-Serrano

Juan Bianchi-Gancharov

Ulises De Dios-Cuadras

Federico Graue-Wiechers

Bénédicte Dupas

INDOCYANINE GREEN ANGIOGRAPHY FOR IDENTIFYING TELANGIECTATIC CAPILLARIES IN DIABETIC MACULAR EDEMA

Keywords: Diabetic Macula Edema, Indocyanine Green Angiography, Microvascular Abnormalities, Hard Exudates

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

Aims: During diabetic macular edema (DME), a spectrum of capillary abnormalities is commonly observed, ranging from microaneurysms to large microvascular abnormalities.

Clinical evidence suggests that targeted photocoagulation of large microvascular abnormalities may be beneficial, but their detection is not done in a routine fashion. It was reported that they are better identified by indocyanine green angiography (ICGA) than by fluorescein angiography. Here, we investigated the prevalence and ICGA and OCT features of large microvascular abnormalities in a group of patients with DME.

Methods: Observational study. The fundus photographs, ICGA and structural and angiographic OCT charts of 35 eyes from 25 consecutive patients with DME were reviewed.

Results: Twenty-two eyes (63%) had at least one focal area of microvascular abnormalities showing prolonged ICG staining (i.e. beyond 10mn after injection). In particular, all eyes with circinate hard exudates (n=9) showed foci of late ICG staining in the center of exudates. These areas appeared either as isolated globular capillary ecstasies or as a cluster of ill-defined capillary abnormalities. They were located at a median distance of 2708 µm from the fovea (range: 1064-4583 µm). Their diameter ranged from 153 to 307 µm.

During ICGA, 94% of such large lesions showed an increase in their contrast and apparent size in late frames relative to early frames, while 77% of microaneurysms showed reduced contrast on late frames. OCTA appeared as poorly contributive for the detection of ICG stained lesions.

Conclusion:

Late ICG staining revealing large microvascular abnormalities is commonly observed during DME. Because of their specific angiographic and OCT features relative to microaneurysms, we propose to name them telangiectatic capillaries.

The worldwide epidemic of diabetes challenges the sustainability of health care systems. [START_REF] Varma | Prevalence of and risk factors for diabetic macular edema in the United States[END_REF] Diabetes indeed leads to a variety of metabolic, vascular and neurological complications, among which vision loss is one of the most common as well as one of the most feared by patients. After cataract, macular edema is the second cause of visual loss in patients with diabetes. In Mexico the prevalence of diabetes is around 9.4% 2 with an estimated incidence of 8.8% of diabetic macular edema (DME). [START_REF] González-Villalpando | Incidence and progression of diabetic retinopathy in low income population of Mexico City[END_REF] The canonical lesions of diabetic retinopathy are microaneurysms; however, the spectrum of retinal microvascular abnormalities also comprises large microvascular abnormalities [START_REF] Bresnick | Diabetic macular edema. A review[END_REF][START_REF]Focal photocoagulation treatment of diabetic macular edema. Relationship of treatment effect to fluorescein angiographic and other retinal characteristics at baseline: ETDRS report no 19. Early Treatment Diabetic Retinopathy Study Research Group[END_REF] which can reach a diameter of several hundred microns. [START_REF] Bourhis | Imaging of macroaneurysms occurring during retinal vein occlusion and diabetic retinopathy by indocyanine green angiography and high resolution optical coherence tomography[END_REF] These have been reported in a variety of retinal vascular diseases among which retinal vein occlusion, Coat's disease and macular telangiectasia. [START_REF] Schulman | Large capillary aneurysms secondary to retinal venous obstruction[END_REF][START_REF] Cousins | Capillary macroaneurysms associated with retinal branch vein occlusion[END_REF][START_REF] Parodi | Branch retinal vein occlusion and macroaneurysms[END_REF][START_REF] Battaglia Parodi | Capillary macroaneurysms in central retinal vein occlusion[END_REF][START_REF] Luckie | Adult Coats' disease in branch retinal vein occlusion[END_REF][START_REF] Apostolopoulos | Late complications in branch retinal vein occlusion[END_REF][START_REF] Bastawrous | Medical image. Retinal macroaneurysm following a branch retinal vein occlusion[END_REF][START_REF] Ueda | Usefulness of indocyanine green angiography to depict the distant retinal vascular anomalies associated with branch retinal vein occlusion causing serous macular detachment[END_REF][START_REF] Ogura | Indocyanine Green Angiography-Guided Focal Laser Photocoagulation for Diabetic Macular Edema[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] These lesions have received various terms in the literature, such as capillary macroaneurysms, [START_REF] Bourhis | Imaging of macroaneurysms occurring during retinal vein occlusion and diabetic retinopathy by indocyanine green angiography and high resolution optical coherence tomography[END_REF][START_REF] Schulman | Large capillary aneurysms secondary to retinal venous obstruction[END_REF][START_REF] Cousins | Capillary macroaneurysms associated with retinal branch vein occlusion[END_REF][START_REF] Parodi | Branch retinal vein occlusion and macroaneurysms[END_REF][START_REF] Battaglia Parodi | Capillary macroaneurysms in central retinal vein occlusion[END_REF][START_REF] Bastawrous | Medical image. Retinal macroaneurysm following a branch retinal vein occlusion[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] adult Coats' disease [START_REF] Luckie | Adult Coats' disease in branch retinal vein occlusion[END_REF] or distant retinal vascular anomalies. [START_REF] Ueda | Usefulness of indocyanine green angiography to depict the distant retinal vascular anomalies associated with branch retinal vein occlusion causing serous macular detachment[END_REF] Since the term "macroaneurysm" creates confusion with arterial macroaneurysms, that Coat's disease is clearly a misnomer, and that he term "distant" is inappropriate because these may be found in the macula as well, we will use here the generic term telangiectatic capillaries (TCs).

Following targeted photocoagulation of TCs, anatomical and visual improvement of macular edema has been reported, [START_REF] Ogura | Indocyanine Green Angiography-Guided Focal Laser Photocoagulation for Diabetic Macular Edema[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] which supports the interest of their identification. To optimize their detection, of importance is to take into account the fact that they are better identified by indocyanine green angiography (ICGA) than by fluorescein angiography (FA). [START_REF] Schulman | Large capillary aneurysms secondary to retinal venous obstruction[END_REF][START_REF] Ueda | Usefulness of indocyanine green angiography to depict the distant retinal vascular anomalies associated with branch retinal vein occlusion causing serous macular detachment[END_REF][START_REF] Ogura | Indocyanine Green Angiography-Guided Focal Laser Photocoagulation for Diabetic Macular Edema[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] In particular, ICG staining often persist in late frames; additionally, ICGA seldom leaks out from these lesions which contributes to their high contrast. Improving the knowledge of their clinical characteristics may contribute to improve their identification. Here, in the continuity of previous studies, [START_REF] Cousins | Capillary macroaneurysms associated with retinal branch vein occlusion[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] we further explored the ICGA and OCT features of vascular abnormalities of DME eyes. ICGA was done using the Spectralis scanning laser ophthalmoscope-OCT (SLO-OCT; Heidelberg Engineering, Heidelberg, Germany) using 5 ml of intravenous Infracyanine® (SERB laboratories, Paris, France). A particular attention was paid at obtaining late frames (i.e. at least 10 minutes after dye injection). As a rule, late frames were averaged using the built-in software to improve signal-to-noise ratio. The presence of TCs was evaluated by three experienced retinal specialists (DCF, BD, MP) based primarily on size and ICGA staining. Early, late and wash-out phases were defined as follows: early frames were those showing details of choroidal large vessels; late frames were those showing a uniform background fluorescence of the choroid, and wash-out frames were those showing retinal vessels darker than the background. Each microvascular lesion was classified as microaneurysms or TCs based on its size, assuming that microaneurysms were spherical lesions with an upper size limit of 130µm. [START_REF] Hafner | Dynamic Changes of Retinal Microaneurysms in Diabetes Imaged With In Vivo Adaptive Optics Optical Coherence Tomography[END_REF][START_REF] Lammer | Association of Microaneurysms on Adaptive Optics Scanning Laser Ophthalmoscopy With Surrounding Neuroretinal Pathology and Visual Function in Diabetes[END_REF] The size of the TCs were measured on ICGA images and on OCT using the built-in calipers. Structural OCT also enabled to measure the thickness of the wall of TCs.

METHODS

This observational study was approved by the

OCT angiography (OCTA) images centered on the fovea (6x6mm cubes) were obtained using a DRI Triton OCT device (Topcon, Tokyo, Japan) in a subset of patients. Each en OCT angiogram ICGA and OCTA images were reviewed in a masked fashion by two experienced retinologists (DCF and MP).

RESULTS

Our series comprised 35 eyes with clinically significant DME from 25 type 2 diabetic patients (12 females, 13 males; mean age 61.2 years old). Visual acuities ranged from counting fingers to 20/20 (median, 20/80). Nonproliferative diabetic retinopathy was present in 16 eyes (45.7%), proliferative diabetic retinopathy in 6 eyes (17.1%), and panretinal photocoagulation has been done previously in 13 (37.1%). The mean (±SD) central macular thickness was 282.4 µm (± 145). Ten eyes had grade 1 HEs, 14 had grade 2 and 9 eyes had grade 3 HEs.

In early frames, all microaneurysms were filled by ICG, hence showing a bright contrast, and were most often indistinguishable from TCs. On subsequent frames, TCs typically increased both their apparent size and their contrast with the background, while microaneurysms rapidly reached their peak contrast and did not increase in size (figure 2 and supplementary figure 1). On late frames, 22 eyes (63%) had at least one focal area of ICG staining corresponding to TCs. TCs were located at a median distance of 2708 µm from the fovea (range: 1064-4583 µm). These areas showed variable aspects, from globular, solitary TCs (6 cases) to a cluster of irregularly shaped lesions (18 cases), some subjects 6 having both. In two eyes, progressively increasing ICG leakage from a TC was seen on wash-out frames (figure 3). We compared the ICGA features of microaneurysms and TCs. Among 124 microaneurysms from 5 subjects, all were visible in early frames, but only 23% remained visible on late frames; On the opposite, among 23 TCs, 92% were better detected on late than early frames, because on smaller frames they appeared smaller or even not stained at all.

The median diameter of TCs was 227.5 µm (range: 153-307 µm). The thickness of the wall of globular TCs ranged from 8 to 154 µm (median, 76µm). The lumen of solitary TCs was in all cases filled with reflective material, while its presence was more difficult to assess in irregular TCs due to their smaller size. Clustered TCs showed variable contrast and, when considered individually, were often undistinguishable from microaneurysms. Examples of structural OCTs of TCs are shown in figure 4. We also analyzed the contribution of OCT angiography to the detection of TCs. Figure 5 shows the case of a very large TC which shows marked staining by ICG but poor contrast by OCTA. Overall, there was an inverse correlation between the size of TC and their detection by OCTA: the larger the TC, the less likely they were to be detected by OCTA. OCTA detected 2 out of 4 clustered TC but failed to detect 5 out of 5 globular TC. Among demographic and clinical characteristics (age, sex, duration of diabetes, macular thickness and severity of HEs), only the severity of HEs showed a statistically significant association with the presence of TCs. The prevalence of TCs indeed increased from 4/10 in eyes with grade 1 HEs, to 9/14 in eyes with grade 2 HEs and to all 9 eyes with grade 3 HEs (p=0.03; Chi 2 test). Figure 6 shows a representative example of an eye with grade 3 HEs with TCs in the geometrical center of circinate exudates (see also supplementary figure 1 and2)

Discussion

During retinal vascular diseases a spectrum of microvascular changes may occur, the relationship of which with vascular function is poorly known. We have previously shown that while IGCA and FA both are useful to detect microaneurysms, ICGA is more efficient than FA to detect large microvascular lesions. The interest of ICGA is illustrated by the fact that all cases of circinate exudates showed foci of prolonged, elective ICG staining within them, strongly suggesting that late ICG staining is an indicator of severe rupture of the blood-retinal barrier. Since ICGA is not yet routinely done for the management of DME, many clinical features of TCs still remain to be documented. Here we report the prevalence and OCT and ICGA features of large and/or clustered microvascular abnormalities in a cohort of DME subjects. We found that nearly two third may show late, focal ICG staining of large microvascular abnormalities. Furthermore, we observed that, compared to "classical" microaneurysms, TCs had delayed filling as well as a delayed wash-out. This was more clearly apparent in the largest lesions, some of which retaining ICG even in wash-out frames, that is, up to one hour after dye injection. Overall, the larger the size of TCs, the more there is a temporal shift of ICG staining.

Accordingly, a report on adaptive optics ophthalmoscopy of microaneurysms have showed that some irregularly shaped microaneurysms are incompletely filled by fluorescein. [START_REF] Dubow | Classification of human retinal microaneurysms using adaptive optics scanning light ophthalmoscope fluorescein angiography[END_REF] It can be suggested that such incomplete filling may be due to the presence of intraluminal material as shown by OCT. Therefore, the delayed staining of TCs on ICGA that we observed may be due to the staining of intraluminal material. Histology studies suggested that the nature of this intraluminal material may be either stagnant blood, lipids and/or thrombosis, [START_REF] Stitt | Histological and ultrastructural investigation of retinal microaneurysm development in diabetic patients[END_REF] all of which may show affinity for ICG.

OCTA is gaining interest due to its capacity to noninvasively document the retinal vasculature, and had been reported to be able to document features of diabetic retinopathy with a sensitivity comparable to FA. However, OCTA documents the circulation of red cells rather than the structure of the microvascular anomalies themselves, hence the inherent limitations of OCTA to identify some of the largest TCs. Accordingly, we observed that ICGA and structural OCT were more efficient than OCTA to detect TCs because large TCs may be paradoxically undetectable by OCTA. The combination of wall thickening and intraluminal material accumulation provides a straightforward explanation for the reduced blood flow and hence the absence of detection of some of the largest TCs by OCTA.

The currently recommended first line treatment of DME is intravitreal treatment using either anti-VEGF or steroid. [START_REF] Schmidt-Erfurth | RESTORE Extension Study Group.Three-year outcomes of individualized ranibizumab treatment in patients with diabetic macular edema: the RESTORE extension study[END_REF][START_REF] Elman | Diabetic Retinopathy Clinical Research Network. Intravitreal Ranibizumab for diabetic macular edema with prompt versus deferred laser treatment: 5-year randomized trial results[END_REF][START_REF] Brown | Intravitreal Aflibercept for Diabetic Macular Edema: 100-Week Results from the VISTA and VIVID Studies[END_REF][START_REF] Boyer | Outcomes with As-Needed Ranibizumab after Initial Monthly Therapy: Long-Term Outcomes of the Phase III RIDE and RISE Trials[END_REF][START_REF] Korobelnik | Intravitreal aflibercept for diabetic macular edema[END_REF][START_REF] Boyer | Three-year, randomized, sham-controlled trial of dexamethasone intravitreal implant in patients with diabetic macular edema[END_REF][START_REF] Sophie | Predictors of Functional and Anatomic Outcomes in Patients with Diabetic Macular Edema Treated with Ranibizumab[END_REF][START_REF] Shin | Quantitative evaluation of hard exudates in diabetic macular edema after short-term intravitreal triamcinolone, dexamethasone implant or bevacizumab injections[END_REF][START_REF]The Diabetic Retinopathy Clinical Research Network, Aflibercept, bevacizumab, or ranibizumab for diabetic macular edema[END_REF] On the opposite, randomized trials on targeted laser photocoagulation of microaneurysms in DME did not reach their primary endpoint. [START_REF] Shin | Optical coherence tomography-guided selective focal laser photocoagulation: a novel laser protocol for diabetic macular edema[END_REF][START_REF] Lee | Characterization of microaneurysm closure after focal laser photocoagulation in diabetic macular edema[END_REF] It is interesting to note that in these trials only microvascular lesions identified by FA were included. Therefore, since FA is less sensitive than ICGA for the detection of TCs, large lesions may have been missed. These trials therefore leave open the question of the interest of photocoagulation of large lesions. Pilot studies of treatment of TCs by targeted photocoagulation has reported encouraging results 6, 14-16 yet a randomized trial remains to be done to confirm the efficacy of such procedure. Our results suggest that an optimal strategy aimed at detecting candidates for targeted photocoagulation implies performing ICGA. However, ICGA is somehow invasive, and also implementing ICGA for all DME patients may be challenging for the limited resources of many ophthalmological settings dealing with large populations of patients such as in developed countries. Therefore, identifying subgroups of patients with a high prevalence of TCs may be more pertinent. HEs are a hallmark of chronic macular edema. In the literature, among 24 cases reports of eyes with TCs of different etiologies, severe HEs were present in 11 cases [START_REF] Bourhis | Imaging of macroaneurysms occurring during retinal vein occlusion and diabetic retinopathy by indocyanine green angiography and high resolution optical coherence tomography[END_REF][START_REF] Schulman | Large capillary aneurysms secondary to retinal venous obstruction[END_REF][START_REF] Cousins | Capillary macroaneurysms associated with retinal branch vein occlusion[END_REF][START_REF] Parodi | Branch retinal vein occlusion and macroaneurysms[END_REF][START_REF] Battaglia Parodi | Capillary macroaneurysms in central retinal vein occlusion[END_REF][START_REF] Luckie | Adult Coats' disease in branch retinal vein occlusion[END_REF][START_REF] Apostolopoulos | Late complications in branch retinal vein occlusion[END_REF][START_REF] Bastawrous | Medical image. Retinal macroaneurysm following a branch retinal vein occlusion[END_REF][START_REF] Ueda | Usefulness of indocyanine green angiography to depict the distant retinal vascular anomalies associated with branch retinal vein occlusion causing serous macular detachment[END_REF][START_REF] Ogura | Indocyanine Green Angiography-Guided Focal Laser Photocoagulation for Diabetic Macular Edema[END_REF][START_REF] Paques | Indocyanine-green-guided targeted laser photocoagulation of capillary macroaneurysms in macular oedema: a pilot study[END_REF] supporting a strong association between severe HEs and TCs. This is understandable since TCs are the site of a severe rupture of the blood-retinal barrier, enabling large molecular complexes such as lipoproteins to accumulate in the retina. In our series, the prevalence of TCs was correlated with the severity of HEs, peaking to 100% in presence of circinate HEs. Hence, the more severe the HEs, the more likely there is a TC, suggesting that the presence of severe HEs is a pertinent screening feature.

There are several limits to our study. There is yet no consensual definition of a TC, so their diagnosis may differ among operators. What we termed here TCs was defined primarily by a prolonged, focal ICG staining of a retinal vascular structure larger than a microaneurysm. In the near future cumulative clinical expertise and clinical trials may lead to a more rigorous definition of TCs, which may include structural features such as the thickness of the wall. We indeed observed that some TCs have a considerably thickened wall that may reach more than 100 microns. Another limitation was that our sample was small and comprised only type 2 diabetics with a high prevalence of proliferative diabetic retinopathy, possibly reflecting a poor glycemic control and/or other population-related factors. We had limited access to data on blood pressure and on serum lipids. Therefore, to which extent do these results apply to other populations remains to be determined.

We conclude that telangiectatic microvascular abnormalities showing late ICG staining are commonly observed in DME eyes. Given the fact that photocoagulation of these lesions may be beneficial for treating macular edema, it is of interest to screen eyes with severe DME for their presence. Comparing structural and angiographic OCT may also be of interest to identify photocoagulation targets since the presence of intraluminal material is indicative of BRB rupture.

  Internal Review Board of the Institute Conde de Valenciana. Each patient received oral and written information and gave consent for examination. Consecutive patients diagnosed with clinically significant DME according to the ETDRS criteria 17 were identified. These criteria comprise (1) thickening of the retina within 500 μm of the center of the macula; or (2) hard exudates (HEs) at or within 500 μm of the center of the macula associated with thickening of adjacent retina; or (3) a zone of retinal thickening one disc area or larger, any part of which is within one disc diameter of the center of the macula. HEs were classified as grade 1 (dust-like HEs), grade 2 (aggregated HEs), or grade 3 (circinate disposition and/or foveal accumulation of aggregated HEs). Examples of each grade are shown in figure 1.

Figure 1 .

 1 Figure 1. Grading of hard exudates (HEs) used in the present study.

Figure 2 .

 2 Figure 2. Comparison of early and late ICG staining patterns of microaneurysms and TCs (case 12). Time indicates duration since dye injection. Between the early and late frame, note the fading contrast of the microneurysm, while the TCs increase their contrast (see also supplementary figure 1).

Figure 3 .

 3 Figure 3. Case 4. Illustration of ICG leakage of TC on wash-out frames.

Figure 4 .

 4 Figure 4. Illustration of different presentations of TCs (arrowheads) by ICGA and structural OCT. Top row, case 10; bottom row, case 2. Note the presence of intraluminal material in the case shown in the top row.

Figure 5 .

 5 Figure 5. Case 25. Example of a TC (arrows in successive images) seen by ICGA, structural OCT and OCTA. Note that the TC is better detected by ICGA than by OCTA.

Figure 6 .

 6 Figure 6. Case 5. Left, color fundus photograph showing circinate exudates. Right, late ICG frame showing clustered TC within the ring of exudates (see also supplementary figure 2).

Acknowledgements

Alvaro Rendón, Enrique Graue Hernández and David Lozano Rechy

Supported by the Agence Nationale de la Recherche (ANR-14-CE17-0011-01), the Association Contre l'OVR (www.asso-ovr.fr), the Programme Hospitalier de Recherche Clinique (TalaDMEproject PHRC-N-17-0334), the French Clinical Research Network, the Institut Hospitalo-Universitaire ForeSight and the Comité National Coordination Action Handicap. The funding organizations had no role in the design or conduct of this research.