E Charkaluk

A Constantinescu

J J Thomas

NUMERICAL APPROACH IN THERMO MECHANICAL FA TIGUE

This paper presents a global approach of thermomechanical design in the automotive industry based on four dif f erent aspects: the loading definition, the modelling of the constitutive law and of the damage and a failure criterion. This approach is applied on cylinder heads and on exhaust manifolds submitted to transient thennal loading and permits to predict the cracked area as well as the lifetime. The main hypothesis and the different aspects are detailed and results on automotive parts are presented.

I INTRODUCTION

The study of metallic structures submitted to high temperatures began really in the 50's with the development of the aeronautic industry and with the development of the nuclear power stations.

Metals were then submitted to temperatures higher than half the melting temperature, where mechanical characteristics are significantly modified and numerous damage mechanisms are encountered. Tbermomechanical loadings induce then often inelastic cyclic strains on the structures.

Metal fatigue studies came then from the high cycle domain to the low cycle one. Many research were realised on this topics : understanding and modelling of the p hysical phenomena, development of constitutive laws, development of high temperature test rig, ... In the same time, numerical computation became more and more efficient and permits simulations of complex loadings, but structures submitted to thennomechanical loading inducing multiaxial stress and strain states were not extensively studied. In the automotive industry, predictive method for such structures are necessary to limit the number of physical prototypes and then the development time of components.

A design approach is based on four particular aspects : the load ing definition, the model ling of the material behaviour and of the damage under cyclic loading and the definition of the failure of the structure. The loading associated to the material behaviour provide the mechanical response of the structure and this one permits the determination of the lifetime through a damage indicator, lifetime depending of the failure criterion.

Two particular automotive components are concerned in this paper : aluminium alloy cylinder heads and cast iron exhaust manifolds. The thermomechanical loading correspon ds to the start and stop cycles of the engine. Ln a first part, main hypothesis and choices necessary for the global approach are detailed. The n, the applicatio n of those choices in the design method are pr esented : the prediction of lifetime of complex structures submitted to thermomechanical loading is possible as soon as geometry is known.

A GLOBAL APPROACH IN THERMOMECHANICAL DESIG

Loading definition

The structure is essentially submitted to a thermal cyclic loading representing the start and stop of the engine and the mechanical part of the loading is static. Them1al loading definition is a key 1 feature of the design approach because the accuracy of the thermal loading determines the accuracy of the mechanical response of the structure and then the lifetime [I].

Mechanical behaviour

Lot of works were realised in France on viscoplasticity coupled with damage (continuum damage mechanics) during the 70's with Lemaitre and Chaboche [START_REF] Lemaitre | Mecanique des Materiaux So/ides[END_REF]. However, this type of approach has some drawback: the complexity of the models with a lot of temperature dependant parameters, the complexity of the tests and of the calibration of the parameters and large time computations induced by the coupling. Results of Sermage et al. [START_REF] Sermage | Multiaxial creep-fatigue under anisothermal conditions[END_REF] shows that this coupling is often not necessary. For all !hose reasons, this approach uncouples damage and malerial behaviour. The conslilulive law is viscoplastic with a Linear kinematic hardening and the parameters (5 or 6 per temperature) are identified on the stabilised cycle of the characterisation tests. The numerical implementation used a totally implicit algorithm which permits large time increment and relatively small computation time.

Damage

Many parameters influence the damage mechanisms in thermomechanical tests : temperature, mean stress, mean strain, dwell time, ... To assess the lifetime of structures, two different ways are possible. The first one consists in parametric approaches which gives a direct relation between lifetime and mechanical and/or physical parameters, like Manson-Coffin law [START_REF] Manson | Behaviour of materials under conditions of thermal stresses[END_REF][START_REF] Coffin | A study of the effects of cyclic thermal stresses on a ductile material[END_REF] for example.

The second way is based on the continuum damage mechanics initially developed by Rabotnov on creep damage. Creep-fatigue interaction laws were then developed by Chaboche [START_REF] Chaboche | Determination des durees de vie des aubes de turbines a gaz[END_REF] for the aeronautic industry. As previously mentioned, those laws are complex and require many tests to identify the temperature dependant parameters.

For this reason, parametric laws seem to be preferable for their simplicity but require the determination of physically based damage indicators consistent with the mul1iaxial state of stress and strain in the structures and independent of temperature.

Failure criterion

The last aspect concerns the definition of a failure criterion. The objective of the design in the automotive context is to avoid a macroscopic -i.e. at an engineer scale -crack initiation which can conduct Lo a fault in the engine during Lhe lifetime of the vehicle. As long as a crack is confined in an elementary volume of material, its propagation is governed by the local mechanical fields. As soon as its size becomes greater than this volume, its propagation is governed by the structure. This is the definition of a failure in our context.

In this approach, initiation an d propagation are not stw;/ie d separotely; the failure is d efine d ot !he scale of the structure and in !he same manner for a specimen, a cylinder head or an exhaus/ manifold.

MECHANICAL MODELLING OF THE MATERIAL IN THE STRUCTURE

Context

The modelling of the material behaviour has to be realised with the objective of a structural computation. Therefore, the key feature of the modelling is to be representative of the material in the structure, this implies a choice of representative tests conditions (temperatures, loading rates, ... ) as well as representative specimens (microstructure, process, ... ).This is a crucial part of the characterisation and the modelling. Different type of uniaxial tests are used for the characterisation of the model and the calibration of its parameters: isothermal monotonic tests (tension, creep), isothermal cyclic tests at different strain rates and non isothermal cyclic tests. To validate the models and the calibration in a multiaxial non isothermal context, tests on simple structures are necessary. For example, thermal fatigue tests are realised on specimen submitted to thermal cyclic loading by Joule effect. Then, tests on components (thermal shock) can validate the complete approach of design. This requires controlled and known test conditions which is not simple because of the complexity of an engine bench test. This particular point will be detailed in the case study.

2 Constitutive law and calibration of parameters

The studied structures, in cast iron for the exhaust manifolds and in aluminium alloy for cylinder heads, are submitted to thermomechanical cycles between the room temperature and a maximal one close to 0,3 to 0,5 the melting temperature (typically 800°C for the cast iron and 300°C for the aluminium alloy). In this range of temperature, the material, plastic at low temperature, becomes viscoplastic as the temperature increases.

The modelling of the constitutive law has to integrate this phenomenon. Therefore, different models can be used : a classical viscoplastic model with only one inelastic strain similar to those developed by Chaboche [START_REF] Lemaitre | Mecanique des Materiaux So/ides[END_REF] or a two layer viscoelastic-elastoplastic model which permits to have two inelastic strains, viscous and plastic [START_REF] Charkaluk | Lois de comportement viscoplastiques anisothermes pour calculs cycliques sur structures[END_REF]. In our studies, both models were used and compared

The main difficulties of viscoplastic constitutive laws are the multiaxial translation of the equations and the numerical implementation in a FE code like ABAQUS/Standard. For both viscoplastic models presented above, an implicit scheme was chosen which permits large time increments and a stability of the computed mechanical response of the structure [START_REF] Charkaluk | Lois de comportement viscoplastiques anisothermes pour calculs cycliques sur structures[END_REF].

The other difficulty is encountered with the calibration of the models parameters. The classical way consists in an identification at each tested temperature and a linear interpolation between the identified temperatures. Yerger et al. [START_REF] Verger | On the simulation of large viscoplastic structures under anisothermal cyclic loadings, JUTAM Creep in structures[END_REF] showed that non isothermal tests are necessary for the calibration because of the parameters coupling of such models of viscosity (Norton-Hoff laws). As models are implemented and parameters are identified, structural computations are possible.

Damage modelling

The damage under thermomechanical cyclic loading is modelled with an energetical approach. Indeed, the dissipated energy density per cycle (plastic work) is one possibility to define the damage in this context. Results coming fr om literature we:: re synthesised by Ve:: rge:: r d al. [START_REF] Verger | A macroscopic crack initiation criterion in multiaxial tbermomechanical fatigue[END_REF] and presented plastic work versus the number of cycles to failure for different material at different temperatures. The same trend as Hal ford's results [1 O] was observed. For particular steels, temperature seems to have an influence on the results. However, it was shown that the positions are also close for the studied ciist-iron [I I]. Similar results have heen ohtained for aluminium [I 2]. Let us now remark that the dissipated energy per cycle can be extended to a multiaxial load path as:

T t.1�{x) = Ja(x,t )• t(x, I)• dt 0
where cr and e are stress and strain tensors, T the cycle period. Moreover the obtained function is not explicitly temperature dependant and can therefore easily integrate a non isothermal approach.

More details are given in [START_REF] Charkaluk | Fatigue design of structures under tbennomechanical loadings[END_REF] which show that this criterion can be simply used on numerical simulations.

CASE STUDY

Materials and tests

The studied materials are:

• a spheroi"dal graphite cast iron with molybdenum and silicon addition named SiMo cast iron. This material is 11sed in the case of the exhai1st manifolds.

• a A356 aluminium alloy (with silicon and magnesium addition) with a thermal treatment T7 used for the cylinder heads.

Different type of fatigue tests were realised on specimens and on components:

• isothem1al strain controlled LCF tests at different temperatures between I 00°C and 700°C

for the cast iron and between I 00°C and 300°C for the aluminium alloy. The strain rate was I 0-3 s-' for all tests and the different total strain ranges were taken between ±0,25% and ±1%.

• thermal fatigue tests corresponding to the figure I. The maximal temperature, obtained in the middle of the specimen, varied from 40°C and 700°C in the case of the cast iron and between 75°C and 300°C in the case of the aluminium alloy. The spatial gradient was approximately 30-40°C/mm and the heating rate was approximately 20°C.s-• for the cast iron and 7,5°C.s-1 for the aluminium alloy (see [I] for more details).

• engine bench tests on components (thermal shock). Those tests are realised for the validation of all the engine (cylinder head, crankshaft, exhaust manifold, ... ) under thermomechanical loading corresponding to the start and stop cycles. One of the difficulty consists in the detection of the cracks as soon as they appear (macroscopic initiation), when this detection is possible.

Results

The LCF tests permit to construct the design curve, based on the energetic criterion. The numerical results obtained from the simulation of the thermal fatigue tests and of the thermal shocks are then compared with this design curve (see figure 3). The approach consists in the analysis of the stabilised response of the structure as this response can be considered representative of the total cyclic damage during all the test f I 1 l On figure I and 2, the cracked area observed after the tests on components are compared with the predicted cracked area. A good prediction can be denoted on exhaust manifold as well as on cylinder head. It can be underlined that simple stress analysis (von Mises) or strain analysis (plastic strain range) do not permit such a prediction [I]. Moreover, on the figure 3, one can observe a good agreement between the experimental and estimated lifetime for both type of tests on specimen and on automotive parts. This shows the great interest of this approach in thermomechanical design of complex structures.

Figure I :

 I Figure I: results on exhaust manifolds. The numerical simulation (b) indicates an initiation on the inner shell of the component. The experimental results (a) shows the final macroscopic crack.

Figure 2 :

 2 Figure 2: results on cylinder head. The crack initiates in the intervalve bridge (a) and this area is detected by the numerical simulation (b).

  /' " I.

  '

.

Figure 3 :

 3 Figure 3: comparison between estimated and experimental lifetime on specimen and on components. Three type of results are synthesised : isothermal LCF tests on specimen, thermal fatigue (TF) tests on specimen and engine bench tests (thermal shock) for exhaust manifolds and cylinder heads.CONCLUSIONThis paper presents a global approach of thermomechanical design in the automotive industry based on four different aspects: the loading definition, the modelling of the constitutive law and of the damage and a failure criterion. This approach was applied on cylinder heads and on exhaust


Marie Barale

Muriel Escadeillas

Gregory Taupier

Yann Molard

Clément Orione

Elsa Caytan

Rémi Métivier

Julien Boixel
email: julien.boixel@univ-rennes1.fr

Nondestructive All-Optical Readout through Photoswitching of Intramolecular Excimer Emission

Keywords: Photochromism, Dithienylethene, Luminescence, Pyrene, Two-photon excitation

come

successes, ranging from biomedicine to smart molecular materials. [START_REF] Costil | Directing Coupled Motion with Light: A Key Step Toward Machine-Like Function[END_REF][START_REF] Van Dijk | Molecular Machines for Catalysis[END_REF][START_REF] García-López | Light-Activated Organic Molecular Motors and Their Applications[END_REF] Photochromic molecules stand as efficient molecular light-switches since they are able to undergo reversible photoreactions by absorbing photons of suitable frequencies, which promotes different deactivation paths such as the formation of new chemical bonds and/or transforming their configuration leading to modulation of properties like electronic gap, polarity, or geometry. As far as molecular motion is concerned, the targeted photochrome must undergo photo-modulation of geometrical changes.

Azobenzene derivatives are the most studied due to their large geometrical changes upon light irradiation but suffer from low thermal stability. [START_REF] Crespi | Heteroaryl Azo Dyes as Molecular Photoswitches[END_REF] We learned during the journey of photoactivatable molecules that the specifications of reversibility, fatigue-resistance and non-destructive readout are crucial toward operating photo-responsive molecular systems, particularly in the fields of bio-imaging or molecular data storage. [START_REF] Wu | Photocontrolled Multiple-State Photochromic Benzo[b]phosphole Thieno[3,2-b]phosphole-Containing Alkynylgold(I) Complex via Selective Light Irradiation[END_REF][START_REF] Dortaj | High-Speed and High-Contrast Two-Channel All-Optical Modulator Based on Solution-Processed CdSe/ZnS Quantum Dots[END_REF][START_REF] Xie | Lanthanide-Doped Heterostructured Nanocomposites toward Advanced Optical Anti-Counterfeiting and Information Storage[END_REF] Besides, the choice of an optical output signal appears both beneficial and challenging. [START_REF] Crespi | Heteroaryl Azo Dyes as Molecular Photoswitches[END_REF][START_REF] Irie | A Digital Fluorescent Molecular Photoswitch[END_REF][START_REF] Irie | Photochromism of Diarylethene Molecules and Crystals: Memories, Switches, and Actuators[END_REF] Among the all-optical molecular systems reported to date for the photo-control of linear or nonlinear [START_REF] Boixel | Second-Order NLO Switches from Molecules to Polymer Films Based on Photochromic Cyclometalated Platinum(II) Complexes[END_REF] optical output, a common design combines photochromic and fluorescent units, where the fluorescence emission is modulated by the photochromic reaction. Among the various photochromic compounds known to date, the dithienylethenes (DTE) are the most suitable for fluorescence photoswitching owing to their excellent thermal stability and fatigue resistance. [START_REF] Irie | Photochromism of Diarylethene Molecules and Crystals: Memories, Switches, and Actuators[END_REF][START_REF] Fukaminato | Single-Molecule Fluorescence Photoswitching of a Diarylethene-Perylenebisimide Dyad: Non-Destructive Fluorescence Readout[END_REF][START_REF] Fukaminato | Digital Photoswitching of Fluorescence Based on the Photochromism of Diarylethene Derivatives at a Single-Molecule Level[END_REF][START_REF] Berberich | Toward Fluorescent Memories with Nondestructive Readout: Photoswitching of Fluorescence by Intramolecular Electron Transfer in a Diaryl Ethene-Perylene Bisimide Photochromic System[END_REF][START_REF] Fukaminato | Photochromism of Diarylethene Single Molecules in Polymer Matrices[END_REF] The "ON"/"OFF" readout process is Depending on the nature, the structure and the environment of the dyad, the usually observed destructive fluorescence readout can be due to, i) the fluorescence quenching process by excitation energy transfer which can trigger the cycloreversion reaction of the DTE unit, ii) the contribution of the triplet state in the photocyclization reaction or iii) the competition between fluorescence emission and photocyclization reaction. [START_REF] Boixel | Second-Order NLO Switches from Molecules to Polymer Films Based on Photochromic Cyclometalated Platinum(II) Complexes[END_REF][START_REF] Roberts | Linker-Dependent Metal-Sensitized Photoswitching of Dithienylethenes[END_REF][START_REF] Zhao | Photochromic DTE-Substituted-1,3-Di(2-pyridyl)benzene Platinum(II) Complexes: Photomodulation of Luminescence and Second-Order Nonlinear Optical Properties[END_REF] To overcome this issue, several strategies have been proposed, such as readouts using the changes of the refractive index or IR absorption at the wavelengths out of the switching unit, [START_REF] Zhao | Photochromic DTE-Substituted-1,3-Di(2-pyridyl)benzene Platinum(II) Complexes: Photomodulation of Luminescence and Second-Order Nonlinear Optical Properties[END_REF] stabilized signals by means of acid or base reactions, [START_REF] Boixel | Sequential Double Second-Order Nonlinear Optical Switch by an Acido-Triggered Photochromic Cyclometallated Platinum(II) Complex[END_REF] switching by photoinduced electron transfer, 20 molecular polarity, or supramolecular conformational changes. While efforts have been made to reduce competitive processes to luminescence photoswitching, it is still very challenging to completely suppress the destructive readout in DTE-based systems.

We report herein an efficient approach combing photo-triggered geometrical change and alternative one-and two-photon excitations (OPE an TPE).

The photo-modulation of molecular motions have already been investigated with overcrowdedalkene-based systems, 11,28,29 azobenzenes 30 and diarylethenes, [START_REF] Hashimoto | Photoswitching of an Intramolecular Chiral Stack in a Helical Tetrathiazole[END_REF] as examples. Herein, inspired by the elegant work of Hashimoto et al., [START_REF] Hashimoto | Photoswitching of an Intramolecular Chiral Stack in a Helical Tetrathiazole[END_REF] on the photo-modulation of the excimeric emission of pyrene, we report the new pyrene-based DTE A(o) (Scheme 1). In A(o), the two pyrenes can face each other in the open's DTE form, thus leading to static excimer emission. Upon ring-closure reaction, the pyrene introduced on the inner position will be moved apart from the lateral pyrene, thus avoiding the possibility of excimer. To benefit from a large molecular movement upon photocyclization the DTE must be functionalized at the lateral and internal positions, as the changes in distance between the two lateral positions upon photochromism is only 1 Å. However, reports on DTEs functionalized at the lateral and internal positions are rare due to the synthetic challenge that represents such an unsymmetrical functionalization. [START_REF] Hashimoto | Photoswitching of an Intramolecular Chiral Stack in a Helical Tetrathiazole[END_REF][START_REF] Fukaminato | Molecular Design Strategy toward Diarylethenes that Photoswitch with Visible Light[END_REF] Thus, design of A(o) is expected to give higher propensity of excimer emission in comparison to a symmetrically substituted DTE. [START_REF] Hu | Synthesis and Photochromic Properties of Triazole-Bridged Dithienylethene Compounds with Pyrene Units[END_REF] Nonlinear optical processes such as stepwise and simultaneous TPE have been reported to enhanced the cyclo-reversion reaction of DTE. [START_REF] Luchita | Efficient Photochromic Transformation of a New Fluorenyl Diarylethene: One-and Two-Photon Absorption Spectroscopy[END_REF][START_REF] Sotome | Efficient Cycloreversion Reaction of a Diarylethene Derivative in Higher Excited States Attained by Off-Resonant Simultaneous Two-Photon Absorption[END_REF] However, for both TPE processes, the photocyclization reaction is known to be ineffective. Knowing that TPE produces specific one-photon forbidden excited states, the combination of one-and two-photon excitations can allow to selectively trigger the photochromism and collect the excimer emission in A(o), respectively. This opens the way of an unprecedented non-destructive fluorescence readout with orthogonal light stimuli i.e.; one-photon irradiation (UV and visible) employed to control the photochromic reaction and two-photon excitation (730 nm) used to probe the fluorescence. Besides, TPE can provide precise three-dimensional visualization deep within the samples using low-energy photons.

The targeted DTE A(o) and the reference B(o) (Scheme 1) are obtained via a convergent synthesis strategy, allowing their early functionalization at will (see ESI). [START_REF] Boixel | Sequential Double Second-Order Nonlinear Optical Switch by an Acido-Triggered Photochromic Cyclometallated Platinum(II) Complex[END_REF][START_REF] Boixel | Contrasted Photochromic and Luminescent Properties in Dinuclear Pt(II) Complexes Linked through a Central Dithienylethene Unit[END_REF] The two thiophenic sides of the DTE B(o) are firstly prepared separately through classical cross-coupling reactions.

Finally, the two thiophene derivatives are bridged by the perfluorocyclopentene via stepwise nucleophilic substitutions. From B(o), the deprotection of the acetylenic arm followed by a

Sonogashira cross-coupling with the 1-bromopyrene yields the bis-pyrene DTE A(o).

The geometry optimization of compound A(o) was performed using the B3LYP hybrid functional with the D3BJ model to describe weak interactions, and the 6-31G(d,p) basis set, using the Gaussian 16 software (Figure 1). 37 The anti-parallel conformation of A(o) was found to be the most stable, confirming a majority of anti-parallel conformations in solution. In this conformation, the two pyrenes are facing each-other, at a distance of 3.5 Å, evidencing their possible interaction in the ground state and their capacity to form an excimer in the excited state.

Scan calculations performed at the B3LYPGD3BJ / 6-31G level of theory allowed us to estimate the rotational energy barrier around the thiophene -perfluorocyclopentene bridge. It was estimated at 75 kJ.mol -1 for the C10-C3' bond and 161 kJ.mol -1 for the C6-C3 bond (Figure 1). The latter being superior than 100 kJ.mol -1 , the rotation around the bond is indeed blocked at roomtemperature, agreeing the observed experimental behavior. [START_REF] Li | Separation of Photoactive Conformers Based on Hindered Diarylethenes: Efficient Modulation in Photocyclization Quantum Yields[END_REF] Interestingly, the interchromophoric distance of 3.5 Å found between the two pyrenes in A(o) leads to ground state interactions, whereas similar distances calculated in PDI dimers exhibit monomer-like absorption feature likely due to higher rigidity and slip stacks. [START_REF] Kim | π-Stacking-Dependent Vibronic Couplings Drive Excited-State Dynamics in Perylenediimide Assemblies[END_REF] One can notice that in A(o), the two differently branched pyrenes allow an optimized overlap with very short slip stacks of 1.4 Å and 0.73 Å along the short and long pyrene axes respectively. 2Figure and the related data are summarized in Table 1. The absorption spectrum of reference compound B(o) is characterized by two sets of bands in the UV region gathering -* transitions on the DTE core and on the pyrene moiety i.e., from 250 to 300 nm (S0-S3 for pyrene) and from 300 to 400 nm (S0-S2 for pyrene). [START_REF] Maeda | Alkynylpyrenes as Improved Pyrene-Based Biomolecular Probes with the Advantages of High Fluorescence Quantum Yields and Long Absorption/Emission Wavelengths[END_REF] The S0-S2 excitation in 2-substituted pyrene was described as "pyrene-like", regardless of the electronic nature of the substituent, due to a node in the HOMO and LUMO orbitals at the 2-position. [START_REF] Crawford | Synthesis of 2-and 2,7-Functionalized Pyrene Derivatives: An Application of Selective C-H Borylation[END_REF] As a matter of fact, the S0-S2 transition of B(o) exhibits structuration with characteristic vibrational spacing of 1400 cm -1 (Figure 2). The vibrational structure of the S0-S3 transition cannot be seen due to the overlapping with transitions belonging to the DTE core. Complete 13 C, [START_REF] Fukaminato | Single-Molecule Fluorescence Photoswitching of a Diarylethene-Perylenebisimide Dyad: Non-Destructive Fluorescence Readout[END_REF] F and 1 H NMR assignments have been established, and through space interactions observed for A(o) (Figure S22) support this [ … ] interaction between the pyrene as well as TD-DFT calculations (vide infra). For A(o), [START_REF] Feringa | The Art of Building Small: From Molecular Switches to Motors (Nobel Lecture)[END_REF] H- [START_REF] Fukaminato | Single-Molecule Fluorescence Photoswitching of a Diarylethene-Perylenebisimide Dyad: Non-Destructive Fluorescence Readout[END_REF] F-correlation experiments gave clear signals of through space interactions between protons located on the thiophenes and fluorine of the bridge (Figure S23). The protons of methyl groups at the 4-or 2-position of the thiophene ring (4Me or 2Me) show through space interaction with the fluorine 7a (F7a) or 7b (F7b) respectively, thus indicating a blocked configuration of the thiophene group around the C6-C3 bound. The proton H4' of the second thiophene group shows through space correlations with both F9a (weak)

and F9b (strong), consistent with a rotation around the C10-C3' bound (fast in NMR timescale), but with a preferential anti-parallel conformation. This is corroborated by [START_REF] Feringa | The Art of Building Small: From Molecular Switches to Motors (Nobel Lecture)[END_REF] H NOESY experiments revealing spatial proximity of H4' with both 4Me and 2Me but also clear correlations between the protons of 4Me and the protons at the ortho positions of both pyrenes (Figure S24).

The latter result evidences that the two pyrenes point in the same direction and are thus facing each-other. Similar 1 H/ [START_REF] Fukaminato | Single-Molecule Fluorescence Photoswitching of a Diarylethene-Perylenebisimide Dyad: Non-Destructive Fluorescence Readout[END_REF] F NMR correlations are monitored between fluorine F7 and protons 2-4CH3 for B(o) (Figure S25) indicating a hindered rotation around the C6-C3 bound.

Table 1. Absorption and emission data for A and B.

Open form PSS (irr = 365 nm) and 575 nm respectively were analyzed numerically, providing the photochromic quantum yields o→c and c→o for A and B, as listed in Table 1. The photocyclization quantum yields o→c were found at 0.680.09 and 1.000.08 for A(o) and B(o). Such high values of o→c are likely due to the hampered thiophene's rotation that favored the anti-parallel form ratio. [START_REF] Yamada | Tetrathienyl Corannulene Compounds with Highly Sensitive Photochromism[END_REF] The quantum yields corresponding to the cycloreversion reaction (c→o) induced at 575 nm are much lower and very similar for both A and B (0.0330.002 for A(c) and 0.0400.002 for B(c)), as commonly observed for such DTE derivatives. The introduction of substituents (Me, t Bu) in the 4-positions of the thiophene rings has shown to be effective in increasing photocyclization quantum yields close to unity. [START_REF] Irie | Photochromism of Dithienylethenes with Electron-Donating Substituents[END_REF] The fluorescence properties of the DTE-based pyrene derivatives A and B were investigated in solution at room temperature with a concentration of c.a. 10 -6 M, diluted enough to exclude intermolecular excimer (Figure S30). The monopyrene compound B is non-emissive due to rapid competitive ring-closure reaction triggered by irradiation of UV light, which agrees with the photocyclization quantum yield determined at almost unity (Figure 3, bottom). However, the DTEbased bispyrene A exhibits excimeric emission (Figure 2, Table 1). The emission spectrum of A(o)

abs a [nm] (e×10 3 [M -1 cm -1 ] em a,b [nm] (em [%],  c [ns]) abs a [nm] Conversion c [%] o→c (365nm), c→o (365nm), c→o (575nm)
shows a broad band centered at 490 nm attributed to the intramolecular excimer and corresponding to 5 % of photoluminescence quantum yield. Upon irradiation at 350 nm and reaching the PSS, the solution of A shows a decrease of the excimer emission intensity of about 70 % (Figure 1 and Figure 3, bottom). The observed emission profile is likely an admixture of several radiative deactivation processes, accounting for: i) remaining amount of the anti-parallel conformer, ii) various plausible parallel conformers with both centered pyrene (structured) and charge transfer (broad) emission profiles. On can notice that because the pyrenes are functionalized at 2-positions (thiophenyl and alkynyl-thiophene groups), their emission energies appear at lower energy than a non-functionalize pyrene. [START_REF] Crawford | Experimental and Theoretical Studies of the Photophysical Properties of 2-and 2,7-Functionalized Pyrene Derivatives[END_REF] Moreover, this pyrene's emission cannot originate from A(c) because; i) it is expected to be quenched by the closed DTE core, ii) a concomitant increase of the pyrene's emission is not observed upon the photocyclization process. The remaining excimer emission (≈ 30 %) at the PSS is due to the presence of residual open isomers, as the photoconversion is not quantitative (≈ 75 %). Upon irradiation at 580 nm the initial emission spectra is fully recovered. The excimer emission of A(o) is recorded upon two photon excitations with the same solution (TPE: 700 nm < ex < 800 nm). One can notice that no TPE emission signal was observed for B in same conditions. Remarkably, the TPE spectra of A exhibits an emission band at the same energy as the excimer emission recorded upon OPE, without any residual structured emission of monomeric pyrene (Figure 3). In this system, the TPE measurement selectively probes the excimer, likely due to symmetry rules (Figure 3, bottom). [START_REF] Mcclain | Two-Photon Molecular Spectroscopy[END_REF] The output intensity of two-photon excited fluorescence (TPEF) was linearly dependent on the square of the input laser intensity, confirming the nonlinearity of the absorption process. A shows a modest two-photon absorption cross section of 90 GM, typical for pyrene systems (Figure S33 and Table S1). Interestingly, while the emission intensity of OPE decreases upon consecutive emission spectra acquisitions due to the competition with the ring-closure reaction (Figure S31), the emission recorded on two-photon excitation remains stable (Figure S32). The robustness of A toward TPE allowed us to perform an all-optical switching experiment where OPE was employed to trigger the photochromic reaction and TPE was used to record the "ON" or "OFF" signal, over 10 cycles without any loss of readout (Figure S35).

A(o)

To conclude, we report herein the synthesis of original unsymmetrical DTE-based pyrenes, with a complete characterization and assignment of their composition. We also confirmed the face-to- General information, synthesis way and characterization, NMR and emission experiments.

23 Scheme 1 .

 231 Scheme 1. Representations of A(o) and B(o) (top), and the photo-modulation of the static excimer

Figure 1 .

 1 Figure 1. side (left) and top (right) view of the calculated structure of compound A(o).

Figure 2 .

 2 Figure 2. top: Absorption spectra of A and B in their open and at the photostationary state (PSS)

  Photochromic cycles

  The photochromic activity of the DTE A and B have been investigated by means of UV-visible absorption and NMR experiments. Interconversions between the open and closed forms are triggered by 365 and 575 nm light irradiations, respectively.The initial colourless solution of B(o) turns dark blue upon irradiation at 365 nm with the emergence of two characteristic absorption bands in the visible, i.e.: a large band centered at 582 nm and a shoulder at 383 nm, respectively attributed to the S0-S1 and S0-S2 transitions on the closed DTE unit (Figure2).[START_REF] Irie | Photochromism of Diarylethene Molecules and Crystals: Memories, Switches, and Actuators[END_REF] These features attest the formation of the closed isomer B(c). One can notice that the energies and shapes of the broad bands in the visible are identical for A(c) and B(c). This is explained by the formation of a sp 3 carbon at the central position upon ring-closure reaction, which prevents any electronic communication with the closed DTE core. Monitoring the ring-closure reaction by 1 H NMR spectroscopy gives access to the percentage of conversion at the photostationary state (PSS under irradiation at 350 nm), that are 75 % and 90 % for A and B, respectively. The ring-closure and ring-opening photokinetics were recorded by means of a UV-visible spectroscopy set-up. The resulting absorption time-profiles under continuous irradiation at 365

Figure 3 .

 3 Figure 3. top: Normalized fluorescence spectra of A by OPE or TPE at 365 and 730 nm,

  parallel << anti-parallel) Compound B (parallel <<< anti-parallel)

  face arrangement of the pyrenes in A(o) prior to the photo-physical investigation. The close proximity of the pyrenes in A(o) gives rise to the excimeric luminescence, both upon OPE and TPE. As we expect, upon ring-closure reaction the internal arm undergoes a movement that brings pyrene moieties apart, inhibiting the excimer luminescence. Also, we discovered that the additional methyl at position 4 of the thiophene (right side) advantages the extremely effective photochromic behavior and promotes the pyrenes stacking. Finally, the efficient photo-modulation of the excimeric luminescence combined with the selective and stable response to TPE, allows us to record the non-destructive readout fluorescence by alternative exposure to OPE and TPE. We believe that our original approach of preparing such unsymmetrical DTE-based chromophores demonstrates an alternative and promising way to design fluorescent molecular photoswitches with non-destructive read-out behavior, by taking advantage of the molecular motion that takes place in the internal position. This work may open new perspectives in photo-triggered sensing, superresolution bio-imaging, and light-fueled molecular machines. ASSOCIATED CONTENT Supporting Information.

ACKNOWLEDGMENT This work was supported by financial supports from the CNRS and the University of Rennes 1. The PhD grant of the first author has been provided by the University of Rennes 1. This work was granted access to the computing resources of CINES (Montpellier, allocations 2020-AP010811752, 2021-A0100805032). Part of this work has been performed using the PRISM core facility (Biogenouest©, UMS Biosit, Université de Rennes 1-Campus de Villejean-35043 RENNES Cedex, FRANCE

Notes

The authors declare no competing financial interests.