Frédéric Dumur

Stéphane Reculusa

Michal Mruczkiewicz

Mathias Perrin

Laurence Vignau

Sophie Fasquel
email: sophie.fasquel@ims-bordeaux.fr

Multilayer Langmuir-Blodgett films as diffractive external 3D photonic crystal in blue OLEDs

Keywords:

Three-dimensional Langmuir-Blodgett films made of silica beads are theoretically and experimentally investigated in order to improve the relatively small efficiency of blue OLEDs. Using films made of 5 layers of beads, we fabricated OLEDs emitting at 476 nm, and measured a gain of around 40% on their external quantum efficiency. An optical model has been developed to accurately handle the fact that the organic emitting layer and the photonic extraction layer are separated by a distance greater than 1000 wavelength. The latter also permits to describe rapidly this three-dimensional optical OLED cavity, without redoing all the numerical simulations when the optical properties of the organic layers are changed (material index, thicknesses).

Introduction

Since the discovery of the green electroluminescence of tris(8-hydroxyquinoline)aluminum Alq3 by Tang and van Slyke in 1987 [START_REF] Tang | Organic electroluminescent diodes[END_REF], a revolution in the field of photonics on basis of organic materials has been initiated, and led to the production of OLED-based displays at the industrial level. Today, one important topic concerns the fabrication of highly emissive blue OLEDs, in particular for the development of full-color displays and lightings [START_REF] Yang | Recent advances of the emitters for high performance deep-blue organic lightemitting diodes[END_REF][START_REF] Zhu | Blue fluorescent emitters: design tactics and applications in organic light-emitting diodes[END_REF][START_REF] Huang | The development of anthracene derivatives for organic light-emitting diodes[END_REF][START_REF] Yook | Organic materials for deep blue phosphorescent organic light-emitting diodes[END_REF][START_REF] Xiao | Recent progresses on materials for electrophosphorescent organic light-emitting devices[END_REF]. These devices typically consist in a stack of organic layers sandwiched between one metallic (Aluminum) and one transparent (ITO) electrode. When a voltage is applied, holes and electrons are injected within the organic layers and recombine in a specific layer, namely the Emissive Layer (EML), turning electrical power into light. It is particularly difficult to fabricate high performance blue emitters because of their intrinsically wide bandgaps. Indeed, charge injection is hindered by the mismatch of EML energy levels with those of the adjacent layers. Besides, the produced light turns out to be strongly coupled to the optical modes of the metallo-dielectric stack waveguide, and tends to remain inside the medium of high optical index. This total internal reflection effect that occurs both in conventional planar bottomemitting organic and inorganic light emitting devices is responsible for the low outcoupling efficiency [START_REF] Benisty | Impact of planar microcavity effects on light extraction-Part I: basic concepts and analytical trends[END_REF][START_REF] Benisty | Impact of planar microcavity effects on light extraction-Part II: selected exact simulations and role of photon recycling[END_REF][START_REF] Meerholz | Outsmarting waveguide losses in thin-film light-emitting diode[END_REF][START_REF] Tsutsui | Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer[END_REF][START_REF] Madigan | Improvement of output coupling efficiency of organic light-emitting diodes by backside substrate modification[END_REF][START_REF] Chutinan | Theoretical analysis on light-extraction efficiency of organic light-emitting diodes using FDTD and mode-expansion methods[END_REF] -Typically 20% of the electrogenerated photons are coupled to free space [START_REF] Meerheim | Quantification of energy loss mechanisms in organic light-emitting diodes[END_REF]. Most of the remaining 80% excite lossy guided modes in the organic material, as well as a complex set of surface waves at the metal / organic interface, often denoted "surface plasmon" [START_REF] Lozan | Anomalous light absorption around subwavelength apertures in metal films[END_REF], that eventually dissipates as heat. In order to increase the yield, it has been proposed to introduce a patterned structure to improve light outcoupling [START_REF] Saxena | A review on the light extraction techniques in organic electroluminescent devices[END_REF].

Patterning the inner layers of large area OLEDs for internal outcoupling is a challenge [START_REF] Shi | Nano-honeycomb structured transparent electrode for enhanced light extraction from organic light-emitting diodes[END_REF], and may also have incidence on the color of the final OLED [START_REF] Ishihara | Organic light-emitting diodes with photonic crystals on glass substrate fabricated by nanoimprint lithography[END_REF]. Therefore, we choose to structure the outer surface of a bottom emitting OLED, for technological reasons [START_REF] Zhang | Very high efficiency phosphorescent organic light-emitting devices by using rough indium tin oxide[END_REF][START_REF] Kumar | Outcoupling efficiency enhancement in organic light emitting diodes via nano-structured indium tin oxide and nano-phosphors[END_REF][START_REF] Kumar | Enhancement of light extraction efficiency of organic light emitting diodes using nanostructured indium tin oxide[END_REF][START_REF] Bai | Outcoupling of trapped optical modes in organic light-emitting devices with one-step fabricated periodic corrugation by laser ablation[END_REF]. In many cases, the outcoupling layers are made of microstructures such as microparticles [START_REF] Bathelt | Light extraction from OLEDs for lighting applications through light scattering[END_REF], microlenses [START_REF] Greiner | Light extraction from organic light emitting diode substrates: simulation and experiment[END_REF], micro and nano-voids assembled in a monolayer [START_REF] Koh | Enhanced outcoupling in organic lightemitting diodes via a high-index contrast scattering layer[END_REF], or periodic structures deposited on top of the glass substrate [START_REF] Sun | Enhanced light out-coupling of organic light-emitting devices using embedded lowindex grids[END_REF]. However, some of these nanopatterned diffractive grating structures involve complex and expensive elaboration processes, far from the stringent requirements of ease of fabrication for OLEDs mass production. Some disordered extraction layers [START_REF] Koh | Enhanced outcoupling in organic lightemitting diodes via a high-index contrast scattering layer[END_REF] are easier to fabricate, but their optical properties may be difficult to model, leading to tough engineering steps in order to optimize the yield of the device. Besides, it is unsure that their fabrication would be reproducible at large, industrial scale. The Langmuir-Blodgett (LB) technique, on the contrary, is a very attractive way of producing ultrathin films with a precise control of the thickness, pattern size and shape [START_REF] Reculusa | Synthesis of colloidal crystals of controllable thickness through the Langmuir-Blodgett technique[END_REF][START_REF] Massé | Elaboration of photonic crystal heterostructures by the Langmuir-Blodgett method[END_REF]. Besides, recent results show that this technique can be scaled up, using a roll-to-roll method [START_REF] Parchine | Large area 2D and 3D colloidal photonic crystals fabricated by a roll-to-roll Langmuir-Blodgett method[END_REF], to make films of large surface containing several layers of dielectric beads, that could be stick onto an OLED to improve its yield, and may even be compatible with flexible OLEDs. The spatial periodicity of the extraction film, and therefore, of the whole OLED, permits to model their optical properties accurately and rapidly. To do this, we have extended to three dimensions the incoherent reflection/transmission formalism which is typically used to simulate OLEDs as unidimensional [START_REF] Schmidt | Efficiency analysis of organic light-emitting diodes based on optical simulations[END_REF][START_REF] Shcherbakov | Rigorous S-matrix approach to the modeling of the optical properties of OLEDs[END_REF][START_REF] Schmidt | Extracting the emitter orientation in organic lightemitting diodes from external quantum efficiency measurements[END_REF] or two-dimensional [START_REF] Bienstman | Modeling gratings on either side of the substrate for light extraction in light-emitting diodes[END_REF] systems. In particular, our model decouples the influence of internal layers and external coating, and permits to evaluate rapidly the OLED efficiency for different internal architectures (e.g. different EML thicknesses or point source location), without redoing all the computations. This leads to a better understanding of the mechanisms at stake, and makes it possible to obtain quantitative predictions on the improvement of light extraction, in which the 3D optical but also the 1D electrical OLED architecture plays an important role.

In Section 2, the fabrication of the device (extraction layer and then OLED) is detailed. Section 3 deals with the numerical model. Results are discussed in section 4.

Experimental details of fabrication

The experimental procedure can be divided in two main steps. First, a Langmuir-Blodgett film is deposited on one side of a glass substrate, and in a second step, the OLED is fabricated by evaporation on the other side. Note that the beads are bound together and to the substrate strongly enough so that no exceptional care had to be taken when handling the device during the fabrication steps.

Synthesis of silica particles and formation of the Langmuir-Blodgett film

As described in the literature, bare or surface-modified colloids presenting an amphiphilic behavior can be spread at an air-water interface and form a Langmuir Blodgett Film (LBF), thus behaving like surfactants or other molecules with a hydrophilic-hydrophobic balance. After compression with a mobile barrier, a compact monolayer of particles can then be obtained and transferred on a large variety of substrates, provided these ones are hydrophilic. In this work, we have used silica particles that were prepared following classical Stöber recipes [START_REF] Reculusa | Synthesis of colloidal crystals of controllable thickness through the Langmuir-Blodgett technique[END_REF]. Whereas 300 nm beads were synthesized in one single step, 600 nm beads were obtained after a growth-seeded process to get the targeted final size. In a second stage, the bare silica particles were surface-modified using a large excess of aminopropyltriethoxysilane, making them dispersible in the chloroform-ethanol mixture used for the spreading. Langmuir-Blodgett experiments were carried out on a NIMA trough with a maximum working area of 1.2 cm 2 and the particles were compressed until a surface pressure of 8 mN m-1. Then, small glass pieces (1 cm2) coated with ITO on one single side were cleaned cautiously with ethanol and chloroform in an ultrasonic bath during a few minutes. After drying, two slides were put together with their ITO sides facing each other and attached to the dipping system. This allowed the transfer of the Langmuir film only onto the non-ITOcoated sides, the latter being carried out with a fast immersion and a slow upstroke (1 mm min-1) through the air-water interface. Under these conditions, deposition of one single monolayer at each cycle can be achieved and by repeating the process several times, it is possible to get LBF with a very precise number of particle layers (up to 5, in this work), and a homogeneous thickness over a large scale. Figure 1(a) and Fig. 1(b,c) show SEM views at different scales of the LBF deposited on glass. Figure 1(d) displays a picture of the final iridescent devices.

OLED fabrication

After LBF deposition on one side of the glass substrate, OLEDs where fabricated on the other (uncoated) side. All materials (including the light emitting material BSB4, also named BSB-Cz in some studies [START_REF] Setoguchi | Suppression of roll-off characteristics of electroluminescence at high current densities in organic light emitting diodes by introducing reduced carrier injection barriers[END_REF][START_REF] Zhang | Capacitance-voltage characteristics of a 4,4′-bis[(Ncarbazole)styryl]biphenyl based organic light-emitting diode: Implications for characteristic times and their distribution[END_REF][START_REF] Aimono | 100% fluorescence efficiency of 4,4′4′-bis[(N-carbazole)styryl]biphenyl in a solid film and the very low amplified spontaneous emission threshold[END_REF][START_REF] Yokoyama | Molecular orientation in small-molecule organic light-emitting diodes[END_REF]) used for the device fabrication were purchased from Lumtec with the best purity available and used as received. OLEDs were fabricated onto cleaned indium tin oxide (ITO) coated glass substrates with sheet resistance of 10-12 Ω/sq. Prior to organic layer deposition, the ITO substrates were successively washed with acetone, ethanol and isopropanol in an ultrasonic bath for 10 min before surface treatment with UV-ozone plasma for 20 min. This treatment had no effect on the LBF deposited on the other side of the substrate. Organic layers were then sequentially deposited onto the ITO substrate at a rate of 2-4 Å/s under secondary vacuum. Aluminum cathode was deposited through a shadow mask by thermal evaporation. Device structure is the following: ITO was used as the transparent anode / MoO 3 (10 nm) as the hole injection material/ MoO3: 4,4'-bis(4-(9H-carbazol-9yl)styryl)biphenyl (BSB4) (20 wt%, 10 nm) as the hole-transport layer, BSB 4 (130 nm) as the emission layer(EML)/2,9-dimethyl-4,7-diphenyl-1,10-henanthroline (BCP) (20 nm) as the hole-blocking layer/ tris(8-hydroxyquinolinato)aluminium (Alq 3 ) (40 nm) as the electron transporting material/ LiF (1 nm) as the electron injecting material and Al (80 nm) as the cathode. The Electroluminescence (EL) spectra, CIE (Commission Internationale de l'Eclairage) coordinates, current-voltage and brightness-voltage characteristics of the devices were recorded with an EQE Measurement System (model C9920-12) of Hamamatsu Photonics K.K. The device architecture, the chemical structures of the materials that were used in this work, as well as the EL spectrum and the color of the OLED are presented in Fig.

Optical modeling

Flat OLEDs, without extraction layer, can be modeled in a simple and accurate way, as a unidimensional multilayered waveguide coupled to an electric dipole, that mimics one emitting molecule [START_REF] Chance | Lifetime of an emitting molecule near a partially reflecting surface[END_REF][START_REF] Chance | Molecular fluorescence and energy transfer near interfaces[END_REF][START_REF] Wasey | Efficiency of spontaneous emission from planar microcavities[END_REF]. The knowledge of the Green function of such multilayered media [START_REF] Kourkoulos | Accurate approximation of green's functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves[END_REF][START_REF]Organic Light-Emitting Diodes (OLEDs) Materials, Devices and Applications[END_REF] permits to compute rapidly some essential physical quantities such as the far field radiation diagram, the EQE, and the amount of energy coupled to the lossy guided modes [START_REF] Schmidt | Extracting the emitter orientation in organic lightemitting diodes from external quantum efficiency measurements[END_REF][START_REF] Bienstman | Modeling gratings on either side of the substrate for light extraction in light-emitting diodes[END_REF], including surface plasmons [START_REF] Lozan | Anomalous light absorption around subwavelength apertures in metal films[END_REF].

However, it is much more difficult to build a model that also takes accurately into account the three-dimensional external PC layer above the thick glass substrate. In particular, it is clearly impossible to model the whole device (OLED + LBF) with direct numerical methods such as Finite Elements (FEM) or Finite Difference in Time Domain (FDTD), as the computation domain would be much too large (the substrate between organic layers and LBF is more than 1000 wavelength thick).

To overcome this problem, one assumes that the extraction layer, placed over thick and rough glass, reflects light incoherently towards the EML. Then, the emission rate of a molecule is not modified by the presence of LBF [START_REF] Schmidt | Extracting the emitter orientation in organic lightemitting diodes from external quantum efficiency measurements[END_REF][START_REF]Organic Light-Emitting Diodes (OLEDs) Materials, Devices and Applications[END_REF], and the variations of EQE are only due to a change of outcoupled power, but not of Purcell factor. Under this realistic hypothesis, one can solve the problem numerically in two main steps [START_REF] Yang | near-to-far field transformations for radiative and guided waves[END_REF].

First, the flat OLED, without LBF, will be modeled, and its radiation diagram will be computed -see 3.1. Then, the transmission coefficients of a LBF on a glass substrate, without OLED will be computed -see 3.2. Combining these studies, one can estimate the optimal parameters of the LBF (pattern, number of layer), for a given OLED architecture. Finally, a more rigorous and quantitative description of the OLED with LBF will be presented -see 3.3.

Modeling an OLED without LBF

Using a numerical model developed previously [START_REF] Schmidt | Efficiency analysis of organic light-emitting diodes based on optical simulations[END_REF][START_REF] Shcherbakov | Rigorous S-matrix approach to the modeling of the optical properties of OLEDs[END_REF], based on the theory of Chance, Prock and Silbey [START_REF] Chance | Lifetime of an emitting molecule near a partially reflecting surface[END_REF][START_REF] Chance | Molecular fluorescence and energy transfer near interfaces[END_REF], we compute the Green function of one dipole source in a multilayered planar medium, to evaluate the radiation diagram of the OLED [START_REF] Hanson | Dyadic Green's function for a multilayered planar medium -A dyadic eigenfunction approach[END_REF][START_REF] Kourkoulos | Accurate approximation of green's functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves[END_REF][START_REF] Yang | near-to-far field transformations for radiative and guided waves[END_REF] in a semi-infinite glass slab, see Fig. 3(a).

The OLED we study has a thick EML (130 nm) that cannot be modeled with a single dipole source, as usually done for EML as thin as 10 nm [START_REF] Schmidt | Efficiency analysis of organic light-emitting diodes based on optical simulations[END_REF][START_REF] Shcherbakov | Rigorous S-matrix approach to the modeling of the optical properties of OLEDs[END_REF]. A distribution of dipoles should instead be considered, what leads to two main differences compared to thin EML OLEDs.

Firstly, as the exciton distribution is generally not uniform in thick EML [START_REF] Novotny | Principles of Nano-Optics[END_REF], all the elementary dipoles will not emit with the same intensity. We observed experimentally that removing the hole blocking BCP layer, the charges recombine in Alq 3 , resulting in a green emitting OLED. This means that in the EML, the holes' mobility is larger than electrons' and that the recombination zone of the OLED is asymmetric, and shifted towards the BCP / EML interface. For the sake of simplicity, we shall use a uniform probability density (constant over a width Δ) to model the exciton distribution, see section 3.3.

Secondly, each elementary emission site is located at a different distance from the metal cathode, and has therefore a different radiation diagram [START_REF] Novotny | Principles of Nano-Optics[END_REF]. Figure 3 describes this effect, showing the radiation diagram of the light emitted by one dipole placed at different location inside the EML -each location corresponds to a different color. The dipole orientation also influences both the far field polarization and intensity [START_REF] Novotny | Principles of Nano-Optics[END_REF][START_REF] Flämmich | Oriented phosphorescent emitters boost OLED efficiency[END_REF]. Therefore, the elementary contributions of a dipole either parallel -see Fig. 3(b) -or perpendicular -see Fig. 3(c) -to the XY stack plane have been studied. Eventually, the total energy emitted by the OLED is obtained by summing these contributions with a weight 2/3 for parallel and 1/3 for perpendicular dipole. When the dipole is parallel to the stack, the far field characteristics depend on the polar and azimuthal angles -denoted respectively θ and ϕ , see inset Fig. 3(a). To take into account the uncorrelated emission of randomly oriented molecules, we made averages on ϕ , so that the emitted energy, see Fig. 3(b,c), now depends only on θ . Looking at the numerical results, one notices an important variation of the angular spectrum when the dipole location changes inside the EML. As the exciton distribution is shifted towards the BCP / EML interface, the main contribution to OLED light come from the molecules located between the BCP / EML interface and the middle of EML (see the black, blue and red lines, that corresponds respectively to a distance of 75 nm, 100 nm and 125 nm from the cathode). Therefore, the emission has a maximum around 60 θ ≈ °, above the total internal reflection (TIR) angle for outcoupling to air, θ TIR = arcsin (1/n) ~44° -n = 1.45 is the glass refractive index.

Consequently, an important part of the light emitted by the exciton recombination in the OLED cannot escape to air and remains strongly coupled to the guided modes of the stack. In order to improve the performance of the device, one needs to find a way to extract the light emitted around 60 θ ≈ ° in the glass substrate.

Optical properties of the multilayered Langmuir-Blodgett film

It is known that guided resonances in photonic crystal slabs [START_REF] Peres | Frequential and temporal analysis of two-dimensional photonic crystals for absorption enhancement in organic solar cells[END_REF][START_REF] Fan | Analysis of guided resonances in photonic crystal slabs[END_REF] permit to couple guided modes to free space, thanks to a periodic array of dielectric or metallic inclusions. Simple models of light extraction based on this effect have been proposed [START_REF] Peng | Improving light extraction of organic light-emitting devices by attaching nanostructures with self-assembled photonic crystal patterns[END_REF], in which a Bragg condition permits to evaluate the minimum grating period that permits to extract light out of an OLED. However, neither the bead index and shape, nor the number of bead layers do not play any role in such model, and in the following, we shall use a more quantitative approach.

Using FEM simulation [START_REF] Fietz | Complex k band diagrams of 3D metamaterial/photonic crystals[END_REF]51], one can compute the power transmission and reflection coefficients of the complex LBF structures that were fabricated, see Fig. 4. To do this, we considered a plane wave, TE or TM polarized, that is incident on the LBF coating, modeled using periodic boundary conditions and perfectly matched layers (PML) [START_REF] Fietz | Complex k band diagrams of 3D metamaterial/photonic crystals[END_REF]51]. The wave direction is described by two angles, see Fig. 4(c): θ, the polar angle between incident ray and the normal to the stack planes, and φ, the azimuthal angle between one principal direction of the hexagonal lattice, and the projection of the ray on the stack plane.

Computation results are presented Fig. 4. A first example, see Fig. 4(e), shows, for 0 ϕ = , that some energy can be transmitted above the TIR angle, when a LBF is present, whereas it could not be transmitted without LBF. The corresponding field maps, for an angle arbitrarily chosen: θ inj = 54.5°, above TIR limit, are shown in Fig. 4(d). One can clearly see that the light transmission is associated to a resonance in the PC beads (right hand side figure), whereas no light comes out if LBF is absent (left hand side figure). This is precisely the guided resonance effect [START_REF] Peng | Improving light extraction of organic light-emitting devices by attaching nanostructures with self-assembled photonic crystal patterns[END_REF] in a LBF, which is responsible for the outcoupling above TIR angle.

In order to investigate the LBF properties, the transmission has been computed for different bead diameters, D -that are identical to the PC period -, different angles of incidence (θ, φ) and polarizations. The results are presented Fig. 4(a,b), where the diameter is shown in units of wavelength: D/λ, and, for the sake of clarity, the transmission has been averaged on φ and on incident polarization. For both the monolayer, Fig. 4(a), and the pentalayer LBF, Fig. 4(b), one observes a high and a low transmission zone, respectively below and above TIR angle. The limit, at TIR angle, tends to fade out when the number of layer increases -compare Fig. 4(a) and Fig. 4(b). Both for a monolayer and a multilayer, transmission is possible above TIR angle, and is stronger (i) when five layers are used instead of one, (ii) when D/λ increases. Note this last observation is in agreement with the fact that the number of resonances in photonic crystal slabs increases with D/λ [START_REF] Peres | Light trapping efficiency of organic solar cells with large period photonic crystals[END_REF], each resonance above TIR angle being responsible for a transmission peak [START_REF] Fan | Analysis of guided resonances in photonic crystal slabs[END_REF]. Note that, in the limit where D>> λ, many resonances are present so that the LBF would be described in a more appropriate way by geometrical optics, neglecting polarization effects [START_REF] Greiner | Light extraction from organic light emitting diode substrates: simulation and experiment[END_REF].

From the results of section 3.1, one knows that the optimal LBF needs to show a high transmission around θ = 60°. It turns out that one observes several local maxima of transmission around θ = 60°, for the 5-layers LBF, see Fig. 4(b). Two of them respectively corresponds to the periods D = 300 nm and D = 600 nm. More precisely, as most of the emitted energy lies between the wavelength of 440 nm and 540 nm, see Fig. 2(b), the corresponding ratio D/ λ lie between 0.55 and 0.68 -when D = 300nm -; between 1.1 and 1.36 -when D = 600 nm. We represented these intervals by white ellipses on Fig. 4(a) and Fig. 4(b). For monolayer LBFs of the same period -see the ellipses on Fig. 4(a) -, one notice that transmission above TIR angle is much smaller. This simple analysis shows that one can expect a better extraction with five than with one layer LBFs, for the OLED we fabricated. Looking at Fig. 4(a), one does not expect a strong improvement with the monolayer LBF when D = 300 nm, whereas for D = 600 nm, a local maximum of transmission is present around θ = 60°, so that this monolayer LBF is expected to slightly improve outcoupling. Note that these trends have been confirmed by experiments (see section 4), and more detailed simulations (see section 3.3).

Finally, if one combines the information on the radiation pattern without LBF -see section 3.1 and Fig. 3 -, and the LBF transmission, one can find an optimal sphere diameter by matching the angle where emission is maximum to the angle where LBF transmission is maximum. This simple optimization criterion assumes that the outcoupling gain is due to an increase of the transmission above TIR angle, and that the transmission below TIR angle do not play an important role. This is the case, for example, if the dipole radiation diagram is narrow enough, and its peak is located above TIR angle, see e.g the red curve Fig. 3

(b).

This method is rapidly scalable to other colors, as the properties of the LBF only depends on the ratio D/λ. Then, once the shape of LBF is fixed (i.e. number of layers, refraction index of the spherical inclusion), one can compute its transmission for all ( , ) θ ϕ and polarization states, and find out the optimal pattern size for any OLED architecture. Obviously, this technique can be generalized to any shape of the periodic lattice as well. However, it has some limitations. Indeed, while LBF improves transmission above TIR angles, one notice that it gives worse results than bare glass at small θ angles, especially when the LBF contains several layers of beads -compare Fig. 4(a) and Fig. 4(b). Then, the possible gain due to guided resonances observed above TIR angle could be ruined by a transmission loss, if the dipole source also radiates at small angles. This points out a limitation of the previous methodsection 3.1 and 3.2 -, where only the angle of maximum emission (here, θ = 60°) has been considered.

Modeling a three-dimensional OLED cavity with LBF

In order to overcome this limitation, we will now present a more elaborate model.

One now considers that each plane wave emitted by the molecules bounces back and forth in the organic and substrate slab, reflecting at each roundtrip on the organic / aluminum coating, and outcoupling a fraction of its energy at each refraction on the outer interface. This will permit to take all the outcoupled rays into account, and not only those that are directly transmitted through the LBF. A priori, the problem can be complex, as many rays can come out of one single scattering process (see Fig. 5). ), which propagates towards the organic layers (in this example two plane waves are created, and i = 1 or i = 2). This backward propagating plane wave reflects on the organic/metal multilayer and bounces upwards with an angle (θ b1 i , φ b1 i ), etc…. At each roundtrip, a transmission occurs and energy leaks out of the stack.

To implement this ray tracing method, one organizes the different contribution to extracted light in a tree structure, where every node corresponds to a scattering process. The tree is then explored using an algorithm of the "deep first search" type [START_REF] Cormen | Introduction to Algorithms[END_REF]. This permits to compute the total power as a path integral, written as in the form of a continued product:

( ) ( ) ( ) 0 0 0 0 0 0 , 0 0 1 1 1 1 2 2 ( , ) , 1 , ;
;

1 tot t b i i i t b i i j j j k P P T R R T R R T θ ϕ θ ϕ θ ϕ θ ϕ θ ϕ θ ϕ θ ϕ   =      +          + + … …               (1)
where the notation ( )

1 1 2 2
;

t b i i j j
R R T θ ϕ θ ϕ represents the product of top, bottom reflection coefficients and transmission coefficient during the elementary path that goes from ray i of 1st scattering process to ray j of 2nd scattering process. Note that reflection and transmission coefficients also depend on the polarization state of the incident light, and not only on the direction of the incident ray. ). Indeed, their contribution can be factorized, and the continued product then reads:

0 0 0 0 , ( , ) 1 l tot res t b l loop l l T P P P R R θ ϕ θ ϕ ∈     = +   -       (2)
where R b and R t are the reflection coefficients of the bottom and top interfaces, and T the transmission coefficient. P res is the residual power coming from rays which do not form simple closed loops and is computed by summing on the successive scattering processes, until numerical convergence is reached.

A key point in the model is that 0 0 ( , )

P θ ϕ on one hand, and the reflections and transmission coefficients of the photonic structure on the other hand, are independent. This means that once the photonic structure has been characterized, see section 3.2, it is fast to evaluate the OLED efficiency for different situations, corresponding for example, to different point source locations, different arrangements (index, thicknesses) of the organic layers.

We have just described the excitation of a periodic layer made of a complex stack of glass spheres, by a plane wave issued from a unique point source. However, to model the OLED and compare with experimental results, we now need to consider many independent punctual sources, distributed in the zone where excitons recombine [START_REF] Gather | Measuring the profile of the emission zone in polymeric organic light-emitting diodes[END_REF], see 3.1. The total extraction gain shall then be obtained by integration over different location of the thin dipole sheet inside the thick EML.

Let us focus here on the best extracting LBF, of period D = 600nm with 5 layers of beads (similar results have been found for the other LBFs). Fig. 6(a) (see the black dashed line) shows that, in the present architecture, a maximum of extraction could occur with a large enhancement (≈220%), if the source were a thin layer of dipoles located at the center of EML, see the red line Fig. 3(b). Note that similar dependency on the source location has been observed for flat OLEDs with thin EML, in the ideal case where all the energy trapped in the substrate is extracted (using a semi-spherical macroextractor, see [START_REF] Schmidt | Extracting the emitter orientation in organic lightemitting diodes from external quantum efficiency measurements[END_REF].). In this later work, the thin EML (10 nm) acts as an infinitesimal sheet of dipoles, and its location was varied by changing the thickness of the ETL, whereas in our case, the EML is thick (130 nm) so as to improve the resistance of the device to high voltage. Eventually, total extraction gain shall be computed by integration on the exciton distribution [START_REF] Ruhstaller | Advanced Numerical Simulation of Organic Light-Emitting Devices, Optoelectronic Devices and Properties[END_REF]. These later have been studied theoretically [START_REF] Knapp | Numerical simulation of charge transport in disordered organic semiconductor devices[END_REF][START_REF] Erickson | Investigating the role of emissive layer architecture on the exciton recombination zone in organic light-emitting devices[END_REF] and experimentally [START_REF] Erickson | Investigating the role of emissive layer architecture on the exciton recombination zone in organic light-emitting devices[END_REF][START_REF] Kalinowski | Determination of the width of the carrier recombination zone in organic light-emitting diodes[END_REF] and depends on the OLED structure, as well as hole and electron mobilities. Using a simple step distribution (constant exciton density over a width Δ), we evaluated the OLED gain, Fig. 6(b), and obtain a good agreement with experimental results, see Table 1, for some reasonable width of 60 nm of the exciton distribution.

Results and discussion

To assess the outcoupling efficiency of the LBF, blue OLEDs were fabricated with a benchmark fluorescent emitter i.e. BSB 4 . Two types of silica beads -300 and 600 nm of diameter -were used, to make monolayer, bilayer and pentalayer films, organized by the Langmuir-Blodgett technique.

Reference devices without light-outcoupling layer were also fabricated to evidence the benefits of these nanostructures. OLEDs were fabricated according to the method described in the experimental section with configuration: ITO/MoO 3 (10 nm)/ MoO3:BSB 4 (20 wt%, 10 nm), BSB 4 (130 nm)/ BCP (20 nm)/ Alq 3 (40 nm)/ LiF (1 nm)/ Al (80 nm). The measured characteristics are presented in Table 1.

Prior to investigations on a possible increase of light scattering, electrical characteristics of the pristine devices and devices with a LB Film (LBF) were examined. As evidenced by a careful control of their I-V (current/voltage) curves, OLEDs characteristics were clearly identical, guaranteeing that the modification of the EL intensity only arises from the capping layer. Device performances with and without optical outcoupling layers have been verified in three separate batches with multiple OLEDs per batch. Electroluminescent characteristics were first examined for OLEDs capped by a monolayer of silica particles with either D = 300 nm or D = 600 nm. As can be seen from Table 1, for the whole range of current density examined, the Power Efficiency (PE) as well as the EQE were sensibly enhanced upon introduction of a monolayer LBF with D = 600 nm. Enhancement factors of 1.13 (Power Eff x ) and 1.21 (EQE x ) were measured, respectively for the PE and the EQE. The improvement of the EL performance was much smaller for OLEDs capped with a monolayer LBF with period D = 300 nm (see Table 1) and no further investigations were carried out on LBF of 300 nm period.

In parallel to the electrical characteristics, one could wonder if the LBF also influences the spectral characteristics of the emitted light. This phenomenon has been observed for OLED with internal extractors [START_REF] Shi | Nano-honeycomb structured transparent electrode for enhanced light extraction from organic light-emitting diodes[END_REF][START_REF] Ishihara | Organic light-emitting diodes with photonic crystals on glass substrate fabricated by nanoimprint lithography[END_REF] and is a general feature that can arise when a resonator of any size (here the OLED stack with or without photonic crystal) is coupled to an emitter [START_REF] Yang | Analytical formalism for the interaction of two-level quantum systems with metal nanoresonators[END_REF]. This could lead to an unwanted modification of the spectrum of emitted light [START_REF] Ishihara | Organic light-emitting diodes with photonic crystals on glass substrate fabricated by nanoimprint lithography[END_REF], that could even depend on the driving current. Such phenomenon was not observed here, as the spectral shape and OLED color, see Fig. 7(b), remain unaffected by the injection rate. This indicates that no significant shift of the recombination zone with the driving voltage was present, which is a sign of a good confinement of excitons within the emissive layer. Simply, careful examination of the EL emission revealed that the EL spectrum of the capped OLEDs is slightly broader than the EL spectrum of the uncapped OLEDs, see Fig. 7(a). This is a known phenomenon, attributable to interference effects [START_REF] Riel | Phosphorescent top-emitting organic light-emitting devices with improved light outcoupling[END_REF]. Note that this observation is in agreement with the hypothesis used section 3, that the EQE gain is not due to a change of Purcell factor but of light outcoupling. In the two cases we studied, the EL intensity was maximum at 476 nm with a full width at half maximum (FWHM) of 73 nm. A blue light with CIE coordinates of (0.15, 0.24) was obtained.

Then, a second series of devices was fabricated, using now a 5-layers LBF. Similarly, we observed that the EL spectrum almost does not change when the OLED is caped, but the EQE enhancement now reached a factor of 1.38 (see Table 1). This result is consistent with the aforementioned theoretical calculations (factor of 1.4). An enhancement factor of 1.32 was also determined for the power efficiency (see Table 1). At first sight, one can be surprised that the turn-on voltage is slightly higher for the 600nm pentalayer OLED than for the monolayer OLEDs. In fact, by increasing the thickness of the light outcoupling layer from one to five layers of silica spheres, one also increases its absorption -the glass beads always have some tiny losses. This additional loss channel shifts the detection threshold of 1 cd/m 2 to a slightly higher voltage.

Figure 8 shows the enhancement of power efficiency and EQE for devices with one or five layer LBF and the reference device, as a function of the driving current. We also observed an improvement of the current efficiency (cd/A), the PE (lm/W). Finally, let us mention that for a given voltage, a higher luminance was measured for OLEDs with a 5-layer LBF, compared to OLEDs with a monolayer LBF and reference OLED. For exemple at 11.2V, the brightness of devices with a LBF was ca. 3-times higher than that of the pristine devices, with a luminance increasing from 10400 cd/m 2 to 30200 cd/m 2 .

Conclusion

In summary, we propose to increase the efficiency of blue OLEDs by putting a structured 3D coating elaborated by Langmuir-Blodgett technique on the outer side of the OLEDs, and we obtain a EQE gain close to 40%. Additionally, we have shown that the LBF period can be determined by a simple matching condition between the direction of light emission in the glass substrate, and the angle where LBF transmission is maximum. Then, we extended to three dimensions the well-known unidimensional model of OLED cavities, taking advantage of a decoupling between emission and extraction processes. In this way we are able to model complex photonic structures, which are optically thick, taking into account all the rays diffused by the extraction coating. The experimental results, in agreement with the numerics, show that it is important to use a multilayered film, that can be fabricated at large scale and low cost e.g. by roll to roll processes [START_REF] Parchine | Large area 2D and 3D colloidal photonic crystals fabricated by a roll-to-roll Langmuir-Blodgett method[END_REF], but not by spin-coating techniques [START_REF] Peng | Improving light extraction of organic light-emitting devices by attaching nanostructures with self-assembled photonic crystal patterns[END_REF]. Perspectives could concern the design of 3D OLED such as bio-inspired architectures [START_REF] Kim | Biologically inspired organic light-emitting diodes[END_REF] and OLED with thick emissive layers for which a joint work on electrical and optical modeling is necessary, as the exciton distribution will have an influence on the optimal LBF period.

Funding

French National Research Agency (ANR)( ANR-10-EQPX-28-01/Equipex ELORPrintTec, and ANR-13-BS08-0003 / PhotoLighT), State of Aquitaine, SMOLED project (number 2014 -1R6306).

Fig. 1 .

 1 Fig. 1. Sample SEM pictures of the Langmuir Blodgett pentalayer (a,c) and monolayer (b) of 300 nm diameter silica spheres. Picture (d) shows the final devices, each containing four OLEDs. The colour variations of the different samples are due to an iridescence effect that depends on the surface orientation.

2

 2

  .

Fig. 2 .

 2 Fig. 2. a) Scheme of the fabricated device. b) Formula of the fluorescent material, BSB 4 , EL spectrum and color of the active material.

Fig. 3 .

 3 Fig. 3. Radiation pattern of one dipole source in an OLED with thick emissive layer. Panel (a) is a scheme of the simulated device, where a semi-infinite glass medium has been considered. The detailed structure is given Fig. 2(a). An inset (bottom) shows the coordinate system, with a polar, θ , and azimuthal, ϕ , angle. For each simulation, one single point source is placed inside the EML, at different distance from the cathode (75 nm -black -, 100 nm -blue -, 125 nm -red -, 150 nm -green -, 175 nm -orange -, 200 nm -turquoise). Panel (b,c) show the energy emitted in a direction θ (see panel (a)), towards the bottom of the OLED, by a unitary dipole oriented either parallel (b) or perpendicular (c) to the XY plane of the stack. Averages on ϕ have been made in the case the dipole is parallel to the stack (panel (b)) -see text. The energy emitted at

Fig. 4 .

 4 Fig. 4. Optical properties of the multilayered Langmuir-Blodgett film. Panel (a), shows the power transmission of a monolayer LBF at wavelength λ as a function of the pattern period / D λ , and of the θ angle, after averaging on TE-TM incident polarization and ten values of the azimuthal angle φ between 0 and 60 . Panel (b), shows the transmission for a pentalayer LBF. The modes excited by the blue emitter when D = 300 nm or D = 600 nm, and 60 θ ≈ ° are marked with an ellipse (see text). Panel (c) is a scheme of the simulated structure. Panel (d) shows the norm of electric field, in arbitrary units, with (right-hand side) and without (left-hand side) extraction layers. A plane wave is injected (from top to bottom) at λ = 476 nm, with a direction φ = 0, θ inj = 54.5 > θ TIR (see the dashed line panel (e)). Dimensions on field maps in panel (d) are in microns. No light is transmitted towards the bottom half space (air) for the reference. With one LB layer (right hand figure), extraction is associated with excitation of photonic crystal resonances (hot spots) in the glass beads of 600 nm diameter. Similar results are obtained for a 5-layer photonic crystal. Panel (e) shows the power transmission for φ = 0, varying θ, for the reference (without LBF) -dotted grey -, the 300 nm period LBF (red) and 600 nm period LBF (black). Monolayers are represented in solid lines, pentalayers with dotdashed lines.

Fig. 5 .

 5 Fig. 5. Scheme of light propagation in the multilayer with LBF. One of the plane wave emitted by some point source propagates through glass with angles (θ 0 ; φ 0 ). It reflects a first time on the 3D photonic crystal to create several plane waves at angles (θ 1 i ; φ 1 i

P

  θ ϕ is the power radiated by the point source in the layered material. To accelerate this ray tracing procedure, we look for loops that occur when (

Fig. 6 .

 6 Fig. 6. panel (a): extraction gain (dashed line) obtained when only one thin layer of dipoles emits. Dipole are randomly oriented and placed inside the EML, at different distances from the BCP/EML interface of an OLED covered with a 5-layers LBF of period D = 600 nm (see the scheme in inset). The colored background symbolizes a uniform exciton distribution, of width Δ. In panel (b) the total extraction gain is shown. It has been obtained by integration of local gain on the exciton distribution.

Fig. 7 .

 7 Fig. 7. a) Electroluminescence spectra of OLEDs with a LBF with spheres of 600 nm (blue solid line) and reference device (black dashed line). b) Variation of EL spectra and CIE coordinates with the applied voltage.

Fig. 8 .

 8 Fig. 8. Effect of the LBF on OLEDs characteristics. Reference device and OLEDs with one and five layers of 600 nm silica particles are compared. Power efficiency (PE, lm/W) and External Quantum Efficiency (EQE, %) are represented (respectively in green and orange plots) as a function of the current density.

Table 1 . Summary of EL characteristics of the fabricated OLEDs

 1

	Device	V turn-on (V) [a]	CIE (x,y) [b]	λ EL (nm)	L [c] (cd/m 2 )	Current eff. [c] (cd/A)	Power eff. [c] (lm/W)	EQE (%) [c ]	Power eff x	EQE x
	Reference device	4.2	0.163, 0.255	477	10900 (12.2 V)	2.41	0.76	1.37	1	1
	Monolayer LBF (D = 300 nm)	4.3	0.166, 0.252	478	12200 (12.2 V)	2.43	0.80	1.43	1.05	1.04
	Monolayer LBF (D = 600 nm)	4.1	0.162, 0.249	477	21700 (11.8 V)	2.77	0.86	1.66	1.13	1.21
	Bilayer LBF (D = 600 nm)	4.2	0.161, 0.254	478	25320 (11.2)	2.81	0.99	1.70	1.22	1.24
	Pentalayer LBF (D = 600 nm)	4.7	0.163, 0.250	478	30200 (11.2 V)	3.43	1.00	1.89	1.52	1.38
	EQEx (resp. Power Effx) is the EQE (resp. Power efficiency) enhancement factor vs. the reference device without LBF. a) Turn-on voltage at a brightness of 1 cd/m 2 . b) Values measured at 100 mA/cm 2 . c) Maximum value.


Daria V Berdnikova

Tseimur M Aliyeu

Stéphanie Delbaere

Yuri V Fedorov

Gediminas Jonusauskas

Valentin V Novikov

Alexander A Pavlov

Alexander S Peregudov

Nikolay E Shepel'

Fedor I Zubkov

St Ephanie Delbaere

Nikolay E Shepel' A , Fedor

I Zubkov

Оlga A N Fedorova

Regio-and stereoselective [2+2] photocycloaddition in Ba2+ templated supramolecular dimers of styryl-derivatized aza-heterocycles

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

Introduction

Organic compounds comprising a cyclobutane motif represent an important class of natural metabolites that have been found in various terrestrial and marine species [1,[START_REF] Dembitsky | 1. b) Dembitsky VM[END_REF]. The majority of natu rally occurring cyclobutane derivatives demonstrates remarkable biological activity making them promising lead structures for the creation of novel anticancer, antibacterial and fungicidal drugs [START_REF] Dembitsky | 1. b) Dembitsky VM[END_REF]. Besides that, cyclobutanes are important synthetic intermediates providing atom economic one step transitions from simple to complex structures that is especially important in the total syn thesis of natural products and other intricate molecules [3].

High practical importance of cyclobutane derivatives stimulated the development of synthetic approaches to these compounds. The most commonly applied method of the cyclobutane scaffold con struction is photochemical [2þ2] cycloaddition of two ethylene double bonds that may occur in the inter or intramolecular way [3c,4]. Nevertheless, a straightforward application of the photoin duced [2þ2] cycloaddition in the synthesis of complex biologically related molecules is hindered in many cases by its low regio and stereoselectivity. To manage this problem, three main methodolo gies allowing performance of [2þ2] cycloaddition reactions in a regio and stereoselective manner have been applied. The classic methodology is based on the attachment of appropriate sub stituents managing the preferred direction of the photochemical cycloaddition by steric and electronic effects [5]. In some cases, stereoselectivity of the photocycloaddition can be reached through chiral induction provided by introduction of chiral auxiliaries [5]. The second methodology relates to an emerging class of catalytic [2þ2] cycloadditions that have been extensively developing within the last decade [6]. This group of reactions includes both photo chemical and non photochemical transformations that are assisted by various catalysts, such as Lewis acids, amines or transition metal complexes, and lead to formation of enantiomerically enriched cyclobutanes. The third methodology is based on the supramolec ular preorganization of substrate molecules that provides fixation of the reactive bonds in the desired mutual position prior to the cyclization process. In this field, several reports are devoted to the solid state template directed synthesis of cyclobutanes managed 1 by confinement of the substrates in metal organic frameworks and hydrogen bond templates [7], zeolites [8], nanocages [9]. There are a few examples of the reversible single crystal to single crystal cyclobutane ring formation upon irradiation of stilbenoids in their crystal state [10]. In solution, supramolecular catalysis has been applied for complexes of macrocyclic hosts with photoactive guests that undergo stereospecific [2þ2] photocycloaddition directly inside the host cavity [11]. Another type of supramolecular preorganization for [2þ2] photocycloaddition was realized by self assembly of the substrates in solution assisted by the metal cation coordination, hydrogen bonding, pep stacking interaction and partial covalent linking. The examples of the latter approach, however, are still rather rare [12e20].

Herein, we present simple yet efficient variation of the latter method resulting in the regio and stereoselective light induced formation of cyclobutane derivatives in the series of crown containing styrylheterocycles 1ae4a (Chart 1). The key process providing the closure of a cyclobutane ring is an intermolecular [2þ2] photocycloaddition of the ethylene double bonds taking place upon irradiation of the supramolecular dimers of 1ae4a (Chart 1). Noticeably, the photoreaction yields only one of eleven possible isomers of the cyclobutane product. Formation of the head to head dimeric complexes of 1ae4a is driven by a delicate balance between the pep stacking interaction of the heterocyclic fragments and the sandwich type coordination of Ba 2þ cations by two 15 crown 5 ether residues. To estimate the role of the stacking interaction we varied the heterocyclic residue increasing the sur face area from pyridine to phenantroline. The effect of the sandwich type coordination with barium cations on the formation of dimers was studied by comparison with magnesium cations, whose size fits well to the 15 crown 5 ether cavity excluding the possibility of "sandwich" formation. Metal cation complexation, supramolecular dimerization and photocycloaddition reaction of compounds 1ae4a were investigated by absorption spectroscopy, steady state and time resolved fluorescence spectroscopy as well as 1D and 2D NMR techniques.

Results and discussion

Steady state optical spectroscopy studies

Absorption spectra of styryl derivatives 1ae4a exhibit intense long wavelength absorption bands at the spectral region of 300e400 nm (Fig. 1; Table 1; Figures S1eS7,ESI) that are associated with an intramolecular charge transfer from the electron rich crown residues to the electron poor heterocyclic fragments. The absorption maxima of compounds 1ae4a shift to longer wave length with increasing electron withdrawing effect of the hetero cyclic part in the series 1a < 4a < 2a < 3a. Addition of Ba(ClO 4 ) 2 or Mg(ClO 4 ) 2 to the acetonitrile solutions of 1ae4a results in the blue shift of the absorption bands due to binding of Ba 2þ and Mg 2þ cations by crown ether oxygen atoms involved in the chromophoric system of the ligands (Fig. 1; Table 1; Figs. S3eS7,ESI). In the case of Chart 1. Chemical structures of 1a 4a and schematic representation of their supramolecular dimerization in the presence of Ba 2þ . Mg 2þ , the inclusion complexes of 1:1 stoichiometry (metal/ligand) are formed due to the fine coincidence of the sizes of 15 crown 5 ether and magnesium cation [21,22]. At the same time, the cavity of 15 crown 5 ether is too small for binding of the barium cation. Therefore, in the presence of Ba 2þ formation of sandwich type complexes of 1:2 stoichiometry (metal/ligand) is expected (Chart 1) [21,22]. Spectrophotometric titrations of 1ae4a with Ba(ClO 4 ) 2 and Mg(ClO 4 ) 2 in acetonitrile and following treatment of the ob tained data confirmed the expected stoichiometries and allowed to determine stability constants of the complexes (Table 1).

Irradiation of the acetonitrile solutions of styryl derivatives 1ae4a with filtered light (l 365 nm) resulted in the decrease of the absorption intensities along with a slight blue shift of the ab sorption maxima that is indicative of the formation of the photo stationary mixtures of E and Z isomers of 1ae4a (Scheme 1; Figs. S1 and S2, ESI) [23].

Photolysis of 1ae4a under the same conditions in the presence of 0.5 eq. of Ba(ClO 4 ) 2 led to more pronounced and more compli cated spectral changes. At first, a fast decrease of the absorption intensities of the long wavelength absorption bands and a slight blue shift of the absorption maxima were observed as in the case of E Z photoisomerisation of styryl derivatives 1ae4a. Prolonged irradiation of the barium complexes of 1ae4a (l 365 nm) caused the disappearance of the long wavelength absorption bands in the spectral region of 300e400 nm indicating destruction of the con jugated chromophoric system. At the same time, new significantly blue shifted bands appeared at 230e350 nm that is the charac teristic absorption region of non conjugated aromatic and hetero aromatic fragments (Fig. 1; Figs. S5eS7,ESI). To explain this observation, we assumed that dimeric complexes L 2 $Ba 2þ undergo the [2þ2] photocycloaddition reaction of the ethylene double bonds resulting in the formation of cyclobutane derivatives 1be4b, in which conjugation between aromatic rings is disrupted by the cyclobutane ring closure. (Scheme 1). Kinetic studies on the photochemical reactions of the complexes of 1a and 3a with Ba(ClO 4 ) 2 were carried out upon irradiation at 313 nm or 365 nm depending on the position of the absorption maxima of the cor responding species. Analysis of the kinetic data allowed us to determine the values of the quantum yields of the forward and reverse photoisomerisation and photocycloaddition reactions (Table 2). No cyclobutane species was detected in control experi ments with Mg 2þ cation that does not form dimeric complexes with 1ae4a. Thus, irradiation (l 365 nm) of the complexes L$Mg 2þ just led to the decrease of the intensity of the long wave length absorption bands with a small blue shift of the absorption maxima (Figs. S3eS4, ESI), as it was observed for free 1ae4a.

Therefore, supramolecular preorganization of the ligands 1ae4a in the Ba 2þ templated supramolecular dimers is the key process managing the occurrence of [2þ2] photocycloaddition.

NMR spectroscopy studies

Since binding of the barium cation to the crown ether residue has an intermediate rate in the NMR timescale, the addition of Ba(ClO 4 ) 2 to the solutions of styryl derivatives 1a-4a in CD 3 CN resulted in severe broadening of their 1 H NMR spectra at room temperature, owing to chemical exchange between various possible complexes. While at lower temperature (233 K) the intermolecular exchange is slow enough to allow observing the signals of complexes with different barium to ligand ratio (Fig. S15, ESI), the irradiation of these mixtures with 365 nm light produced heavily overlapped NMR spectra of the photocycloaddition and E Z photoisomerisation products and their barium complexes. The spectra are dramatically simplified if a small amount of D 2 O (15% v/ v) is added to the sample and if the measurements are performed at room temperature, as the presence of water shifts the dynamic exchange processes to the high rate regime (Fig. 2).

In all cases, the main photochemical process was the formation of the only one cyclobutane derivative of 1be4b, as revealed by the presence of two doublets in a characteristic region of the cyclo butane ring protons (4.5e5.5 ppm), and the only side process was the E Z isomerization of the initial compounds. Notably, irradiation (l 365 nm) of compounds 1ae4a in the absence of barium species resulted in the E Z isomerization only, and no products of photo cycloaddition were detected that is in agreement with the steady state optical spectroscopy data (vide supra).

The processes occurring upon addition of barium ions and following photoirradiation were analyzed by NMR in more details for 4 quinoline derivative 2a. The addition of 0.5 eq. of Ba 2þ to a solution of 2а in CD 3 CN caused two distinctive sets of signals to appear in the 1 Н NMR spectrum (Fig. S15b, ESI); those are assigned to two isomers of sandwich (2a) 2 $Ba 2þ complexes with different Scheme 1. Photochemical transformations of styryl derivatives 1a 4a and their complexes with Ba 2þ and Mg 2þ . orientations of the styryl fragments (Fig. 3a andb) [19]. In both cases, the downfield shift of the signals of the heterocyclic protons suggests the de shielding influence of a neighboring aromatic fragment of the second styrylheterocyclic fragment, which is possible only in a sandwich like coordination geometry. Further increase of the concentration of the metal ions results in a new set of signals (Fig. S15, ESI) assigned to a conventional 1:1 complex (Fig. 3c).

While the irradiation of different isomers of sandwich complexes would result in different products of photo cycloaddition, in our experiments, only one cyclobutane isomer out of eleven possible [24] (Fig. 4) is formed. The presence of only two signals in the region of cyclobutane protons (4.5e5.5 ppm) limits the plausible structures to the symmetric ones, thus excluding isomers 2, 3, 8 and 9. Given the origin of the product, i. e. the ge ometry of the sandwich dimers, it leaves only four structures of the cyclobutane products with crown ether moieties located on the same side of the cyclobutane ring (compounds 1, 6, 7, 11 on Fig. 4). Indeed, the formation of all other isomers is less probable, as the corresponding L 2 $Ba 2þ sandwich complexes will not be stabilized by the p p stacking of heteroaromatic fragments. The L 2 $Ba 2þ complexes shown on Fig. 3a andb would lead to cyclobutane de rivatives 6 (rctt) and 11 (rtct), respectively, in the absence of E Z photoisomerisation, and to isomers 1 (rccc) and 7 (rccc), respec tively, if E Z photoisomerisation would occur. The relative positions of the protons in the cyclobutane structure can be identified with the aid of the two dimensional NMR ROESY (Rotating frame nu clear Overhauser effect spectroscopy) pulse sequence, in which the intensity of cross peaks in 2D spectra depends on the distance between the corresponding nuclei [25]. Generally, rссс and rtct isomers would have stronger through space interactions between protons H a,a' and H b,b' than for rctt one (Fig. 5): in rссс, all protons H a , H a' , H b , H b' are close to each other, as they are located on the same side of the cyclobutane ring, whereas in rtct isomer there are twice as many H a H b interactions as in rctt isomer. On a more quantitative level, the relative intensity of the ROE type cross peaks between different protons may be estimated from the ratio of distances between them; the pair of protons with a well determined inter nuclear distance may be used as a reference. [START_REF] Neuhaus | The nuclear overhauser effect in structural and conformational analysis[END_REF] The approximate geometries of three possible isomers, as obtained by quantum chemical calculations using MM2 force field, were used to estimate expected H a (H a' ) e H b (H b' ) cross peak intensities relative to the cross peak of the neighboring aromatic protons H 5 and H 6 (~2.5 Å). The comparison with the experimental data (Table 3; Fig. S19,ESI) shows that the product 2b is an rctt isomer (Fig. S20, ESI). Moreover, the value of the scalar coupling constant 3 J Ha- Hb 6.6 Hz obtained from lineshape simulation of 1 Н NMR signals using DAISY module of Topspin 3 software (Fig. S21,ESI) is also indicative of a transoid geometry of H a and H b protons in 2b [START_REF] Rappoport | The chemistry of cyclobutanes[END_REF].

Time resolved fluorescence spectroscopy studies

Time resolved fluorescence measurements showed the mono exponential fluorescence decay for free ligands 1a, 3a, 4a, whereas for ligand 2a two distinct fluorescence lifetimes were observed (Table 1). Most likely, the existence of two lifetimes for 2a corre sponds to the occurrence of two photoinduced processes in the exсited state, namely, the equilibration of syn and anti populations (reflecting orientation of the 4 quinoline moiety with respect to the double bond) and following E Z photoisomerisation [START_REF] Würthner | [END_REF]. Complexation of 1ae4a with Mg 2þ shortened the first fluorescence lifetime for all compounds and additionally led to the appearance of the second component for 3a and 4a. We assume that the second lifetime arises from the occasional formation of labile sandwich like structures of 2ae4a complexes with Mg 2þ due to the stack ing interactions between the heterocyclic fragments and the ex change of magnesium cations between the two crown ether units [18]. Complexation of the ligands with Ba 2þ resulted in the appearance of new very characteristic long living components in the timescale of 1000e3600 ps for compounds 2ae4a that were assigned to the formation of the tight syn sandwich dimers with the Ba 2þ cation (Table 1). Shorter lifetimes were associated with the relaxation of the monomeric and/or loose syn complexes as well as possible anti conformers of 4 quinoline derivative 2a.

The value of the longest relaxation time of the exited state correlates with the bulkiness of the moving molecular fragments on the E Z isomerization pathway. In other words, formation of the sandwich complexes in the presence of Ba 2þ cations hinders large amplitude rotations due to the tight stack arrangement of the molecules in the supramolecular dimers. This fact results in the increase of the excited state (fluorescence) lifetimes. Surprisingly, no long living component was detected for styrylpyridine deriva tive 1a upon complexation with the cation. The most possible reason for this is quite weak pep stacking interaction between the small aromatic systems of the pyridine rings that does not allow a long living sandwich dimer of 1a to be formed. On the other hand, irradiation of the complex (1a) 2 $Ba 2þ still yields the single isomer of the cyclobutane species 1b as it does in the cases of 2ae4a. We assume, therefore, that the sandwich dimer of (1a) 2 $Ba 2þ is formed, but it possesses high conformational lability that is reflected by the absence of the long living fluorescence lifetime. However, the lifetime of (1a) 2 $Ba 2þ in the favorable conformation appears to be sufficient for the occurrence of the regio and stereoselective [2þ2] photocycloaddition.

Conclusions

In summary, we have demonstrated that the regio and ster eoselectivity of [2þ2] photocycloaddition can be controlled in so lution in an all supramolecular way by means of the appropriately balanced non covalent interactions. Thus, the [2þ2] photo cycloaddition of the crown derivatized styrylheterocycles takes place only in their supramolecular dimeric complexes, in which a favorable arrangement of the reactive C]C double bonds is pro vided. The supramolecular dimerization is managed by pep stacking interaction of the heterocyclic fragments and sandwich type coordination of Ba 2þ cations by two 15 crown 5 ether

Experimental section

Crown derivatized styrylheterocycles 1ae4a were synthesized according to published protocols [29,30]. 1 H and 13 C NMR spectra were recorded from CD 3 CN solutions using Bruker Avance 500 and Avance 600 spectrometers. The chemical shifts were referenced using the residual signals of the deuterated solvents. The tempera ture was calibrated using standard methanol sample. Samples in CD 3 CN were irradiated in NMR tubes (5 mm) at 295 K in a home built apparatus that has been previously described [31]. The filtered emission spectrum of a 1000 W XeeHg high pressure short arc lamp (Oriel) (optical filter: L.O.T. Oriel 365FS10e50:

354<l < 378 nm with l max 365 nm and T 25) was focused on the end of a silica light pipe (length 6 cm, diameter 8 mm), leading the light to the spinning sample tube, inserted into a quartz Dewar. After irradiation, the tube was transferred into the NMR spectrometer. To monitor the pathways of the photoreactions, the spectra were recorded at regular time intervals. The concentration of each photoproduct was obtained from the ratio of peak intensities. Absorption spectra were recorded on a Varian Cary 100 double beam spectrophotometer. Preparation and handling of the solu tions were carried out under red light. Photochemical reactions were carried out with a high pressure Hg vapor lamp (120 W) and an immersed Hg photoreactor (125 W). Kinetic studies on the phototransformations of the complexes were performed using a diode array fiber optic spectrometer AvaSpec 2048. Complex for mation of 1ae4a with Mg(ClO 4 ) 2 and Ba(ClO 4 ) 2 was studied by a spectrophotometric titration method in acetonitrile at 20±1 C; the stability constants of the complexes were determined from the photometric data using the SpecFit 32 program.

The fluorescence excitation light pulses for the time resolved measurements were obtained by frequency doubling and tripling of a Ti:sapphire femtosecond laser system (Femtopower Compact Pro) output. The depolarized excitation light was used to excite the samples. The highest pulse energies used to excite fluorescence did not exceed 100 nJ and the average power of excitation beam was 0.1 mW at a pulse repetition rate of 1 kHz focused into a spot with a diameter of 0.1 mm in the 10 mm long fused silica cell. The fluo rescence emitted in the forward direction was collected by reflec tive optics and focused with a spherical mirror onto the input slit of a spectrograph (Chromex 250) coupled to a streak camera (Hamamatsu 5680) equipped with a fast single sweep unit M5676, temporal resolution 2 ps. The convolution of a rectangular streak camera slit in the sweep range of 250 ps with an electronic jitter of the streak camera trigger pulse provided a Gaussian (over 4 de cades) temporal apparatus function with a FWHM of 20 ps (for more details see ESI).

Note

Authors declare no competing financial interests.

Fig. 1 .

 1 Fig. 1. Absorption spectra of 4a, its sandwich complex (4a) 2 Ba 2þ and photocycloaddition product 4b Ba 2þ (c 4a 20 mM, l 365 nm, irradiation time 30 min) in MeCN at 20 C.

Fig. 2 .

 2 Fig. 2. 1 H NMR spectra in CD 3 CN (600 MHz) of the mixture 2a þ 0.5 eq. Ba 2þ irradiated for 2 h (l 365 nm) at 233 K (a), RT (b) and RT with addition of 100 ml D 2 O (c) and the spectrum of the isolated cyclobutane product 2b (d).

Fig. 3 .Fig. 4 .

 34 Fig. 3. Possible outcomes of Ba 2þ complexation with styryl derivatives 1a 4a.

Fig. 5 .

 5 Fig.5. Proton-proton through-space interactions in cyclobutane isomers. For clarity, the cyclobutane moiety is shown as a plane.

Table 1

 1 Absorption maxima l abs , fluorescence lifetimes t fl and stability constants logK of 1a 4a and their complexes with Mg 2þ and Ba 2þ in MeCN at 20 C.

	logK

Compound

l abs /nm t fl /ps

Table 2

 2 Quantum yields of the E-Z-photoisomerisation (4 1 ), Z-E-photoisomerisation (4 2 ), forward (4 3 ) and reverse (4 4 ) [2þ2] photocycloaddition reactions of the supramolecular dimers L 2 Ba 2þ at different irradiation wavelengths (l).

	Compound	l, nm	4 1	4 2	4 3	4 4
	(1a) 2 Ba 2þ	313	0.42	0.50	0.12	-a
	(3a) 2 Ba 2þ	313	0.36	0.45	0.20	0.0044
	(3a) 2 Ba 2þ	365	0.52	0.40	0.08	0.0014
	a Not determined due to low absorption of (1b) 2 Ba 2þ at 313 nm.

Table 3

 3 Experimental and theoretical ROE-cross-peak intensity for possible isomers of 2b. No [2þ2] photocycloaddition occurs in the complexes of the ligands with Mg 2þ due to the smaller size of the Mg 2þ cation excluding the sandwich complex formation. Notably, for all studied compounds only one cyclobutane isomer out of eleven possible is formed. The obtained results represent a promising synthetic approach towards construction of the cyclobutane ring of the desired structure and conformation.

		ROE-cross-peak intensity
	H-5 H-6 (reference)	1.00
	1 (rccc)	1.65
	7 (rccc)	3.30
	6 (rtct)	0.67
	11 (rctt)	0.33
	Experimental value	0.33

Acknowledgements

This paper was financially supported by the Ministry of Education and Science of the Russian Federation on the program to improve competitiveness of People's Friendship University (RUDN University) among the world's leading research and education centers in the 2016e2020 and RFBR 15 03 04695 (optical studies). The NMR measurements were performed with the support of the grant of the President of Russian Federation (project MK 6320.2016.3).


Maylis Stepanov
email: anatoli.stepanov@im2np.fr

S Orio

Bertaina

C.-E Dutoit

S Bertaina

M Orio

M Dressel

A Stepanov

Charge-ordering induces magnetic axes rotation in organic materials (TMTTF) 2 X (with X = SbF 6 , AsF 6 , and PF 6 )

Keywords: 71.27.+a Strongly correlated electron systems, heavy fermions, 75.85.+t Magnetoelectric effects, multiferroics, 76.30.-v Electron paramagnetic resonance and relaxation organic salt, electron paramagnetic resonance, charge-ordering, loss of the symmetry centre

Charge-ordering induces magnetic axes rotation in organic materials (TMTTF) 2 X (with X = SbF 6 , AsF 6 , and PF 6 )

Quasi-one-dimensional systems such as organic chargetransfert salts have been intensively studied during the last decades. Among these organic salts, (TMTTF) 2 X molecules, where X represent a inorganic anion, exhibit a very rich phase diagram [1] and display phase transitions such as antiferromagnetic, charge-ordering, spin-peierls, etc. They cristallize in the triclinic 1 P space group with two donor molecules and one anion in the unit cell. TMTTF molecules are arranged in a "zig-zag" configuration, forming stacks along the a direction and layers in ab plane which alternate with the anion X along the c axis. Charge-order- ing (CO) is observed in these compounds at T CO = 65 K, 105 K [2], and 154 K [3] for X = SbF 6 , AsF 6 , and PF 6 , respectively.

Here, we report a continuous wave (cw) electron paramagnetic resonance (EPR) study of (TMTTF) 2 X (X = SbF 6 , AsF 6 , and PF 6 ). The rotation of g-factor principal axes was observed in these three salts when the temperature decreases from 300 to 4 K. This rotation is considerably enhanced below the charge-ordering transition. We discuss the possible origin of this rotation by comparing experimental results with those obtained from our quantum chemical cal-culations performed with density functional theory (DFT). When considering only a thermal contraction of the TMTTF structure, as temperature decreases, the DFT calculations show a rotation of about 4-5° between T = 300 and 4 K. But when a uniform anion displacements due to the charge ordering transition were considered [4] we obtain a much stronger rotation ranging up to 26 in the case of (TMTTF) 2 SbF 6 salt, in fair agreement with the experimental data.

Single crystals of (TMTTF) 2 X were prepared by standard electrochemical method [START_REF] Montgomery | Organic Conductors[END_REF] and were needle-shaped with typical dimensions of 3×0.1×0.5 mm. X-band EPR measurements were performed on a cw Bruker EMX spectrometer operating at about 9.6 GHz and equipped with a continuous flow cryostat covering the temperature range from 4 to 300 K. The microwave power supplied into the cavity was below 1 mW in order to avoid saturation of the EPR signal. The modulation frequency was set at 100 kHz and its amplitude was chosen between 0.1 and 1 G to prevent distortion of the EPR signal due to over-modulation. The sample was fixed on quartz suprazil rod with the a axis parallel to the rotation axis, in addition the a direction being oriented along the microwave magnetic field mw h . A small amount of DPPH was used as g-factor marker. The sample holder was rotated around the a axis every 5° with an accuracy of 0.25°. For each set of measurements a fresh crystal was used.

Quantum chemical calculations have been performed by DFT method using the ORCA program package [START_REF] Neese | [END_REF]. The g factor was obtained from single point calculations, combing the hybrid functional B3LYP [7,8] and the EPR-II basis set, as a second derivative property of the energy with respect to the external magnetic field and the electron magnetic moment [9][10][11][12]. To analyze our experimental results, we have introduced an orthogonal coordinate system with * a , * b , and * c axes such as * a , * b , and * c are the principal axes of the g factor. We choose the * a axis of our coordinate system to be parallel to the long axis of the studied crystal which according to [13] is parallel to the crystallographic a axis. Independently, by EPR measure- ments, we have checked that the * a axis is one of the prin- cipal axes of the g factor. Therefore, the two other g-factor principal axes should be in the plane perpendicular to the * a axis, and are denoted * b and * c axes. Note that the * b and * c axes are not fixed by the symmetry elements of the point group in considered low symmetry crystals.

Figure 1 shows a representative angular dependence of the g factor in the * b * c plane taken at different tem- peratures for (TMTTF) 2 SbF 6 sample. We observe a clear g-factor anisotropy which is in agreement with previous results [13]. We assign the minimum of g-factor value in * * b c plane to the * b axis and the maximum to the * c axis. To simplify our analysis the room temperature (RT) curve of ( ) g θ is chosen as a reference and we set the magnetic field orientation * || H b as = 0 θ ° in the laboratory coordinates at 300 K.

Our main finding is that the * b axis continuously ro- tates when the temperature decreases. For instance, as seen in Fig. 1, the position of the * b axis is close to θ = 19 in (TMTTF) 2 SbF 6 at T = 30 K. This difference in the * b axis position is denoted ( ) T ∆θ and is plotted in Fig. 2. Interestingly, the ∆θ temperature dependence is not monotonic, and is characterized by two different behaviors in two distinct temperature intervals. Between RT and T CO , ∆θ reaches at most 5-6° with a slow variation. In contrast, between T CO and 4 K, the ∆θ temperature dependence is much more important, and at low temperature the ∆θ reaches up to 22° for (TMTTF) 2 SbF 6 . This latter behavior can be attributed to charge-ordering phase transition.

To explain the observed rotation calculations were performed using experimental crystal data obtained at different temperatures from previous studies [14,15] as input parameters. They were conducted to compute the g-factor parameters and the corresponding spin density distributions. Above T CO , the charge is equally distributed between two neighbouring TMTTF molecules. Below T CO , there is a charge disproportion between two TMTTF molecules causing the loss of the symmetry centre.

In Fig. 2 in addition to the observed temperature dependence of ∆θ we show the one predicted by DFT calculations. Consistently with experiments, the calculations Fig. 2. Experimental temperature dependence of the * b axis posi- tion as compared to its position at RT for (TMTTF) 2 X (X = = SbF 6 , AsF 6 and PF 6 ). The calculated * b axis position due to the thermal contraction of TMTTF is represented by ∆θ calc. scen. 1 and due to the thermal contraction of TMTTF and uniform anion displacements is represented by ∆θ calc. scen. 2. Charge-ordering induces magnetic axes rotation in organic materials (TMTTF) 2 X reveal two different behaviors of ( ) T ∆θ in two distinct temperature intervals. When considering only thermal contraction of the molecular structure between 300 K and T CO , calc ( ) T ∆θ varies slowly up to 4-5° as temperature decreases (scenario 1). If now one considers a uniform anion displacement of about 10% towards the charge rich TMTTF [4,16] below T CO , calc ( ) T ∆θ reaches up to 26° for (TMTTF) 2 SbF 6 (scenario 2), 18° for (TMTTF) 2 AsF 6 and 12° for (TMTTF) 2 PF 6 , respectively, in a good agreement with experiment.

In conclusion, quasi-one-dimensional charge-transfert salts (TMTTF) 2 X with X = AsF 6 , PF 6 , and SbF 6 , have been studied by cw X-band EPR and data have been interpreted by quantum chemical calculation. We observed the g-factor principal axes rotation when the temperature decreases. To explain this behavior, quantum chemical calculations were performed using the DFT method. Our computational study has revealed two distinct temperature behaviors of ∆θ in a good agreement with experimental results. We argue that the charge ordering transition in (TMTTF) 2 X crystals induces a strong g-factor axis rotation around the a axis.

This work was supported by CNRS's research federation RENARD (FR3443) for EPR facilities.

Fig. 1 .

 1 Fig.1. A representative g-factor angular dependence for (TMTTF) 2 SbF 6 at different temperatures when the static magnetic field is applied perpendicular to the a axis. The evolution of the position of the * b g is indicated by a dashed line.

© C.-E. Dutoit, S. Bertaina, M. Orio, M. Dressel, and A. Stepanov, 2015

Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 11

Low Temperature Physics/Fizika NizkikhTemperatur, 2015, v. 41, No. 11