G Violano
email: guido.violano@poliba.it

A Chateauminois

L Afferrante

Adhesive contact of randomly rough surfaces: experimental and numerical investigations

The contact mechanics of soft matters is strongly affected by short-range adhesive interactions, which can lead to large deformations and contact instabilities.

In this work, we present both experimental and numerical investigations of the adhesive contact between soft elastic bodies with a Greenwood and Williamson (GW)-like roughness. To investigate the coalescence of neighbour contact spots, surfaces have been designed with overlapping spherical asperities. Normal contact experiments are carried out by using a homebuilt device. Numerical simulations are performed with the Interacting and Coalescing Hertzian Asperities (ICHA) model, conveniently modified to take account of adhesion according to the Johnson, Kendall & Roberts (JKR) theory.

Introduction

Adhesive contact of soft elastic bodies is of great interest in several engineering applications, ranging from bionispired adhesives [START_REF] Geim | Microfabricated adhesive mimicking gecko foot-hair[END_REF][START_REF] Dening | Adhesion control by inflation: implications from biology to artificial attachment device[END_REF], soft robots [START_REF] Germann | Stretchable electroadhesion for soft robots[END_REF][START_REF] Iida | Soft robotics: challenges and perspectives[END_REF], stretchable electronics [START_REF] Tang | Adhesion between highly stretchable materials[END_REF][START_REF] Rogers | Materials and mechanics for stretchable electronics[END_REF].

Surface roughness is known to widely affect the interfacial properties of materials. Modeling adhesion between rough soft elastic media is a tricky challenge. The tribological properties of soft matter are strongly characterized by complex phenomena, e.g., the elastic instabilities raising at the jump into contact [START_REF] Wu | The jump-to-contact distance in atomic force microscopy measurement[END_REF].

The classical contact mechanics theories are used to describe the simple case of the contact between two elastic spheres. Johnson, Kendall & Roberts (JKR) theory is commonly used to estimate adhesion between compliant soft bodies with short-range adhesive interactions [START_REF] Johnson | Surface energy and the contact of elastic solids[END_REF]. On the other hand, Derjaguin, Muller & Toporov (DMT) theory is widely used to characterize the contact between hard bodies with long-range adhesive interactions [START_REF] Derjaguin | Effect of contact deformations on the adhesion of particles[END_REF].

Several models have been developed in the framework of JKR theory. Fuller & Tabor (FT) model [START_REF] Fuller | The effect of surface roughness on the adhesion of elastic solids[END_REF] is an extension of the classical Greenwood & Williamson (GW) multiasperity theory [START_REF] Greenwood | Contact of nominally flat surfaces Proc[END_REF], in which adhesion is modeled according to JKR theory. GW model is based on the assumption that all the asperities have the same radius of curvature and elastic coupling is negligible. Refs. [START_REF] Afferrante | Elastic contact mechanics of randomly rough surfaces: an assessment of advanced asperity models and Persson's theory[END_REF][START_REF] Violano | Contact of rough surfaces: modeling adhesion in advanced multiasperity models[END_REF] showed that neglecting lateral interaction of asperities and coalescence of merging contact spots can lead to a significant underestimation of the contact area even at very small load.

Moreover, Persson [START_REF] Persson | Adhesion between an elastic body and a randomly rough hard surface[END_REF] developed a theory of adhesion between an elastic solid and a hard randomly rough substrate taking into account that partial contact may occur between the solids at all length scales. He found that "even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact may still be several times larger than when the adhesion is neglected."

Degrandi-Contraires et al. [START_REF] Degrandi-Contraires | Cassie-Wenzel-like transition in patterned soft elastomer adhesive contacts[END_REF] showed that the contact behavior between a flat PDMS surface patterned with cylindrical pillars and a spherical indenter can be accurately described by applying JKR theory with an effective adhesion energy depending on the roughness of the substrate. However, recently Acito et al. [START_REF] Acito | Adhesive contact of model randomly rough rubber surfaces[END_REF], performed classical JKR tests on rubber samples with a GW-type roughness. They demonstrated that the findings of Degrandi-Contraires et al. [START_REF] Degrandi-Contraires | Cassie-Wenzel-like transition in patterned soft elastomer adhesive contacts[END_REF] cannot be extended to their surfaces because "the separation of length scales between the microasperity contacts and the macroscopic contact region is insufficient to allow for the use of a JKR model-based approach with an effective adhesion energy."

In the present paper, we experimentally investigate the adhesive contact of a smooth glass lens and a rubber substrate with a well-defined rough surface. Roughness is textured by a set of spherical microasperities with identical radius of curvature, like in a GW-type surface. A similar study has been performed in Refs. [START_REF] Acito | Adhesive contact of model randomly rough rubber surfaces[END_REF][START_REF] Yashima | Normal contact and friction of rubber with model randomly rough surfaces[END_REF], but we have removed the non-overlapping constraint between the asperities.

A numerical study is then performed by exploiting two multiasperity models. The first one is a discrete version of FT model, in which the geometry and the position of each single summit is determined rather than using the statistics of the asperities distribution. The second model is the Interacting and Coalescing Hertzian Asperities (ICHA) model [START_REF] Afferrante | Interacting and coalescing Hertzian asperities: a new multiasperity contact model[END_REF], which takes account of both elastic coupling and coalescence of merging asperities. Moreover, both models are conveniently developed to consider adhesion according to a slightly modified JKR theory [START_REF] Ciavarella | Effect of Tabor parameter on hysteresis losses during adhesive contact[END_REF], which considers the jump into contact instabilities.

Recently, a version of the ICHA model incorporating adhesion according to DMT theory has been presented in Refs. [START_REF] Violano | On DMT methods to calculate adhesion in rough contacts[END_REF][START_REF] Violano | On the DMT adhesion theory: from the first studies to the modern applications in rough contacts[END_REF]. Such model proved to be very accurate in the assessment of the main contact quantities when contact occurs between rough hard elastic bodies with low surface energy. However, for soft materials the assumption of neglecting surface deformations due to adhesion is no longer valid. In this case, a JKR-type approach is certainly more appropriate [START_REF] Violano | Modeling the Adhesive Contact of Rough Soft Media with an Advanced Asperity Model Tribol[END_REF].

Adhesion of surfaces with GW-like roughness

Here we present the results of an experimental campaign aimed at investigating the adhesive normal contact between a spherical smooth indenter and a nominally flat rubber substrate with roughness described by a GW-type geometry. Specifically, spherical identical microasperities are randomly distributed both spatially and in height. Differently from previous works [START_REF] Acito | Adhesive contact of model randomly rough rubber surfaces[END_REF][START_REF] Yashima | Normal contact and friction of rubber with model randomly rough surfaces[END_REF], adjacent spherical bumps can overlap and coalescence of merging contact spots occurs during loading experiments.

In Ref. [START_REF] Acito | Adhesive contact of model randomly rough rubber surfaces[END_REF], the effect of lateral interaction between the asperities has been numerically investigated for the sphere-on-flat adhesive contact. Specifically, it was observed that the contribution of the elastic coupling becomes less important when increasing the standard deviation of the asperities height. In such case, a classical discrete FT multiasperity model is accurate in describing the area-load relation.

In this work, we instead want to investigate both elastic coupling and coalescence effects. For this reason, different patterned surfaces have been numerically designed and PDMS samples has been accordingly modeled. Experimental measurements of the contact area and microcontacts distributions are then compared with the numerical predictions of a discrete version of the FT and ICHA models.

Experimental details

Classical JKR-like tests have been carried out between an optically glass lens and a rubber substrate. The glass indenter, which is assumed to be smooth, has a radius of curvature of 103.7 mm. The rubber substrate is made of PolyDiMethylSiloxane (PDMS). One PDMS sample has been manufactured by cross-linking at 70 • C for 24 hours a mixture of Sylgard 184 and Sylgard 527 liquid silicones, with a 0.35:0.65 weight ratio.

The top of PDMS sample is textured with three patterned rough surfaces. In particular, roughness is characterized by spherical microasperities having the same radius of curvature. Patterned surfaces have been obtained by moulding PDMS in PolyMethylMethAcrylate (PMMA) forms milled using ball-end mills with a radius of 100 µm. Smoothening of the spherical cavities of the PMMA molds has been performed by exposing them to a saturated CHCl 3 vapor for 30 minutes. A part of the PDMS sample has been kept smooth to allow measurements of the elastic modulus and the adhesion energy.

Three surfaces have been generated with a squared nominal area of 8 mm 2 , where asperities are randomly distributed with a density of 2.9 × 10 7 m -2 . Asperities heights follow a Gaussian distribution with standard deviation of 5 µm. For the first surface, asperities are collocated with a non-overlapping constraint, which has been removed for the other two surfaces. For these surfaces, coalescence phenomena may occur during loading experiments.

Indentation tests of the glass lens on the smooth part of the PDMS sample were performed and the contact radius vs load data were fitted according to JKR theory. Figure 1 shows the contact radius vs applied load relation. The fitting line allows to evaluate the values of the composite elastic modulus (E * = 1.21 MPa) and adhesion energy (∆γ = 0.037 J/m 2 ).

Normal contact experiments have been performed under controlled load conditions. In particular, the glass indenter is fixed to a vertical translation stage by a double cantilever beam of known stiffness (290 N/m). The contact load is measured from the deflection of the cantilever, which is detected by means of a high resolution optical sensor (Philtec D64-L).

Contact pictures are recorded at fixed load steps, ranging between 0.01 -0.05 N, with a incremental step of 0.01 N. Both the indenter and the PDMS sample are transparent. During the contact loading, illuminating in transmission with a white LED diffusive panel, microcontacts appear as bright disks (figure 2). The measure of the area of each microcontact is performed by using standard image thresholding techniques. The total contact area A is then obtained by summing up all microcontact areas.

Further details about the experimental setup can been found in Refs. [START_REF] Acito | Adhesive contact of model randomly rough rubber surfaces[END_REF][START_REF] Yashima | Normal contact and friction of rubber with model randomly rough surfaces[END_REF].

Experimental results and comparison with numerical predictions

Contact measurements have been performed on three different patterned surfaces. One (pattern A) presents a random spatial distribution of asperities with a non-overlapping constraint, the others (pattern B and pattern C) are instead characterized by the presence of overlapping asperities.

In the design of patterns B and C, we introduced a constraint regarding the minimum distance between the apex of two neighboring asperities. The minimum distance is equal to 0.8 and 0.6 times the radius of the microasperities for patterns B and C, respectively.

A useful quantity to characterize the surface roughness is the correlation length ξ, which gives the average distance that one has to travel on the surface topography (and in a random direction) in order to no longer be on the same bump. Specifically, ξ is related to the variogram H(d), being d a horizontal lag value. H(d) can be defined as the squared difference in height between two random points at a distance d where h(x i ) is the height of a point located at a random position x i and N is the total number of measurements. In figure 3,H(d) is shown for the three patterned surfaces; calculations have been performed on rough profiles extracted from the surface topography in x and y directions, respectively. The correlation length ξ is equal to the distance at which H(d) is no longer dependent on the value of d. For our surfaces, we find that ξ is always of the same order of magnitude of the microasperities radius. However, the presence of overlapping bumps (patterns B and C) leads to a little decrease in ξ.

H(d) = 1 2 1 N N -1 i=0 [h(x i ) -h(x i + d)] 2 , (1)
Figure 4 shows the contact area A as a function of the applied load F for the three patterned surfaces. Numerical calculations have been performed with the FT-discrete and ICHA models.

For each load level, five repetitions of the test were performed on each patterned surface and at the same location on the pattern. Data were obtained close to adhesive equilibrium as after each load increment the system was keeped at rest for a long time (1000 s). Curves show non-linearity and, at given load, higher contact areas are detected for the surfaces B and C, where coalescence occurs. We notice that exposition of the spherical cavities of the PMMA molds to a saturated CHCl 3 vapor causes a little increase in the nominal radius of curvature of the asperities resulting in slightly larger values of the contact area at the higher loads. In all cases, numerical and experimental data are in good agreement. The inclusion of the elastic coupling in the ICHA model, leads to greater values of the contact area with respect to the FT-discrete model. This is in agreement with previous findings [START_REF] Afferrante | Elastic contact mechanics of randomly rough surfaces: an assessment of advanced asperity models and Persson's theory[END_REF][START_REF] Violano | On DMT methods to calculate adhesion in rough contacts[END_REF].

For pattern A, the predictions of the ICHA and FT-discrete models are very close, especially in the range of small loads. For patterns B and C, greater differences are observed due to coalescence of merging asperities. In the range of loads considered in the experiments, differences are not significant as the number of overlapping contact regions is quite small. However, we remember that the effect of coalescence is instead very significant when roughness develops on several length scales [START_REF] Violano | On DMT methods to calculate adhesion in rough contacts[END_REF].

Figure 5 shows the contact spots at increasing load steps (F = 0.01, 0.03, 0.05 N) for pattern C. The first three images (a-c) refer to the contact regions observed during the experiments (we removed the background and highlighted contact spots in blue). The other figures (d-f) show the contact spots distribution predicted by the ICHA model. The inset in the figure shows a superposition of the numerical contact areas (red circles) with the experimental ones (blue disks) at the load value F = 0.05 N. The coalescence of microcontacts is well detectable, so as the replacement of the merging contact spots with an equivalent macro-region that occurs in the ICHA model.

Conclusions

In this work, we present experimental investigations of the adhesive contact between a 'rigid' smooth sphere and nominally flat surfaces with GW-like roughness. To capture the coalescence of contact spots, surfaces were designed with overlapping spherical bumps of identical radius of curvature.

Experimental data are then compared with the numerical predictions of an ad-hoc multiasperity model, which takes account of both elastic interactions between asperities and coalescence of merging contact regions. The model is based on JKR theory, which is conveniently modified to consider jump into contact instabilities.

The observed agreement is very good; however, at this initial state, we performed tests and calculations only for the loading phase; therefore, further studies and developments are required to test the reliability of the model.

2 j πR j r 2 ij a 2 j -1 + 2 - r 2 ij a 2 j arcsin a j r ij - 1 πa j E * 8πa 3 j E * ∆γ arcsin a j r ij (A.2)
is the displacement due to the elastic coupling. The term ŵi takes into account that the displacement on the easperity i depends on the contributions of all the contacting asperities n ac . In equation (A.2), r ij is the distance between the asperities i and j.

The classical JKR model predicts the first contact occurs when the approach is equal to zero. However, Wu [START_REF] Wu | The jump-to-contact distance in atomic force microscopy measurement[END_REF] founded that jump-on occurs at a critical gap

∆ ON = 1 -2.641µ 3/7 (A.3)
where is the range of attractive forces and µ = ∆γ 2 R/E * 2 1/3 /ε is the so-called Tabor parameter [START_REF] Tabor | Surface forces and surface interactions[END_REF].

On the base of the Wu's findings, Ciavarella et al. [START_REF] Ciavarella | Effect of Tabor parameter on hysteresis losses during adhesive contact[END_REF] suggested to add the effect of van der Waals interactions in the JKR theory, by using equation (A.3) for the jump-on critical distance. Therefore, one can assume that a contact raises when the gap between an asperity and the half-space becomes smaller than the jump-on distance.

The first estimate of the asperity contact radius is done by inverting the JKR relation δ = a 2 R -2πa∆γ E * . Then, after a further increase in the penetration η i , the contact radius is increased by the quantity

∆a i = η i 2a i /R i -π∆γ/(E * a i ) (A.4)
We further recall that, according to the method developed in Ref. [START_REF] Afferrante | Interacting and coalescing Hertzian asperities: a new multiasperity contact model[END_REF], asperities with overlapping contact spots are replaced with a new equivalent one, which maintains the same total contact area of the suppressing asperities. The position of the new asperity is defined by keeping unchanged the volume centroid, and its radius of curvature R eq is empirically assumed

equal to R 2 i + R 2 j 1/2
. Finally, the height h eq of the new equivalent asperity is defined so that the contact radius of the corresponding contact spot returns effectively the area πa 2 eq at the given separation.

The total contact area and the total load are obtained by summing up the contributions of all the asperities in contact. In this respect, we recall that the contact load F i exerted on the spot of radius a i is calculated with the JKR formula

F i = 4 3 E * a 3 i R i -8πE * ∆γa 3
i , where R i is the radius of the asperity i, E * is the composite elastic modulus and ∆γ is the interface energy of adhesion.

Figure 1 .

 1 Figure 1. The contact radius a 3/2 /R as a function of the applied load F/a 3/2 . Results are referred to normal contact experiments between the glass spherical indenter (R = 103.7 mm) and the smooth PDMS sample. Experimental measurements are denoted with markers, while the solid line is obtained by fitting data with JKR theory.

Figure 2 .

 2 Figure 2. Image in transmission of the contact between the spherical indenter and a patterned rough surface (compressive load F = 0.05 N). The inset shows the coalescence of merging contact spots.

Figure 3 .

 3 Figure 3. The variogram H(d) for the three patterned surfaces. The correlation length is calculated in x (solid line) and y (dashed lines) directions. We obtained ξ = 120 µm for the pattern A and ξ = 100 µm for the patterns B and C.

Figure 4 .

 4 Figure 4. The true contact area A (m 2 ) as a function of the applied load F (N). Results refer to normal contact experiments between a spherical indenter and three different patterned rough surfaces. Five contact repetitions have been performed in the same location of the patterns. Experimental measurements are denoted with circular markers. The FT-discrete and ICHA models predictions are shown with blue dotted line and red solid line respectively.

Figure 5 .

 5 Figure 5. Experimental (blue disks) and numerical (red circumferences) microcontact spots. Results are shown for the pattern C, at loads F = 0.01 N (a, d), 0.03 N (b, e) and 0.05 N (c, f).The inset shows a superposition of the measured contact spots with the numerical one predicted at the same level of applied load. The length of the rectangle in the inset is equal to 1 mm.

  a

Acknowledgements L.A. and G.V. acknowledge support from the Italian Ministry of Education, University and Research (MIUR) under the program "Departments of Excellence" (L.232/2016).

Appendix A. Numerical model The Interacting and Coalescing Hertzian Asperities (ICHA) model is an advanced multiasperity model aimed at studying the contact between rough surfaces. It showed to be quite accurate and efficient in predicting the main contact quantities in adhesionless cases [START_REF] Muser | Meeting the Contact-Mechanics Challenge[END_REF][START_REF] Afferrante | Elastic contact mechanics of randomly rough surfaces: an assessment of advanced asperity models and Persson's theory[END_REF] and in presence of adhesion modeled with a DMT-type approach [START_REF] Violano | Contact of rough surfaces: modeling adhesion in advanced multiasperity models[END_REF][START_REF] Violano | On DMT methods to calculate adhesion in rough contacts[END_REF]. In the present work, we have instead used a different version of the ICHA model, in which adhesion is modeld according to the JKR theory [START_REF] Violano | Modeling the Adhesive Contact of Rough Soft Media with an Advanced Asperity Model Tribol[END_REF]. Specifically, following the JKR formalism, the normal displacement w i of the elastic half-space at the location of the asperity i can be written as


Dr David Augros

Dr Corinne Comoy

Dr Yves Fort

Frédéric Leroux

Dr Armen Panossian
email: armen.panossian@unistra.fr

Frédéric R Leroux

Dr Frédéric R Leroux

Dr Frédéric R Leroux

Frederic Leroux
email: frederic.leroux@unistra.fr

The winding road towards an atropo-enantioselective 'ARYNE coupling'

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Introduction

In contrast to the well-studied and successful enantioselective trapping of organolithiums with various activated electrophiles, enantioselective carbolithiations have been less studied. [1] In the latter reactions, the electrophilic partner is a non-activated prochiral olefin and the nucleophilic one is most often an alkyllithium. Yet, aryllithium nucleophiles have also been studied in this reaction, leading to a broad range of enantioselectivity, usually with sparteine employed as the chiral ligand for lithium. [2] Concerning the electrophile, however, apart from olefins, there are only a few reports on alkynes as reaction partners for enantio-retentive carbolithiations, although some of the latter involve an enantioselective lithiation as the first step, rendering the whole sequence enantioselective. [3] Formally, ortho-arynes [4] could be seen as a peculiar case of reaction partner for carbolithiation, with the p system of the transient arynes being much more reactive than in standard inactivated alkenes or alkynes. However, unlike alkenes whose p system is orthogonal to the atomic plane, thus allowing re/si face differentiation, the electrophilic p system of an ortho-aryne is coplanar with the arene ring. Hence, steric distinction in the course of the enantioselective carbolithiation step would be much more challenging with arynes, especially since the triple bond is strongly bent, thus moving away substituents from the incoming nucleophile (Scheme 1). For some years now, we have been interested in the access to biaryls from ortho-arynes, [5] more exactly in the reaction of aryllithiums and ortho-arynes generated in situ upon halogen/lithium exchange, a chain process that was termed the 'ARYNE coupling', which is in fact a specific case of carbolithiation. [6] We were particularly interested in the development of atroposelective versions of this coupling, in order to access axially chiral biaryls; so far, we have explored the post-coupling deracemization or desymmetrization [7] or the atropo-diastereoselective coupling (Scheme 2). [8] In the present paper, we will describe our preliminary attempts towards the atropo-enantioselective version of the reaction (Scheme 2), which is highly challenging on several aspects: 1) As mentioned above, enantioselective carbolithiations have not been studied intensely, in particular on alkynes as electrophiles, and are unknown for arynes and 2) The control of selectivity would be more difficult with arynes than with alkenes or linear alkynes, as stated earlier; 3) Enantioselective reactions of arynes are scarce; [9] 4) Atropo-enantioselective creation of a biaryl bond from an aryllithium as precursor has also been scarcely reported. [10] Scheme 1. Schematic comparison of the carbolithiation of arynes with aryllithiums, of alkynes and of alkenes.

Results and Discussion

In our previous efforts for the development of an atropostereoselective ARYNE coupling by means of chiral sulfoxides, oxazolines or diether auxiliaries attached to the aryllithium nucleophile, we were unable to achieve concomitantly high yields and high diastereoselectivities. [8] The most efficient approach appeared to be the use of a chiral oxazoline as chiral auxiliary, leading to moderate diastereoselectivity but satisfying yield, and allowing efficient separation of atropodiastereomers as well as post-functionalization of the biaryl moiety, as demonstrated in the formal synthesis of each enantiomer of natural product steganacin with high enantiopurity. [8b-d] As a new attempt for stereocontrol of the organolithium species, we decided to assess the L-proline-derived (S)-[(2methoxymethyl)pyrrolidine-1-yl]methyl auxiliary (SMP-methyl), which had successfully been used in the diastereoselective derivation of ferrocene. [11] In this case, when targeting the biaryl core of (-)-steganacin, we gratifyingly obtained both a high yield (86%) and an optimal atroposelectivity, with only one detectable atropo-diastereomer; furthermore, the product could be analyzed by X-ray diffraction crystallography, allowing determination of the configuration of the newly created chiral axis and proposition of a stereochemical rationale (Scheme 3). [12] Unfortunately, all our attempts to remove efficiently the chiral auxiliary by quaternarization, oxidation or coordination of nitrogen followed by benzylic substitution or oxidation proved fruitless.

Scheme 2. The ARYNE coupling and its atroposelective versions.

Considering the additional steps required for installation and transformation of a covalently bound chiral auxiliary and the difficulties we encountered, an enantioselective process involving a chiral ligand of lithium seemed much more appealing. Towards this end, a few solvents were assessed as a replacement for THF, which is usually employed in this reaction. The aim was to use a less coordinating solvent, to favor complexation of lithium by the potentially chiral ligand. As reaction partners, we selected 1a as aryne precursor and achiral 2-aryloxazoline 4a as pronucleophile so as to mimic the conditions of a working atropo-diastereoselective ARYNE coupling. As a slight difference, the pronucleophile was iodinated to ensure efficient formation of the aryllithium in other solvents than THF, by iodine/lithium exchange instead of bromine/lithium exchange or direct lithiation. With these partners in hand, the coupling promoted by butyllithium was shown to proceed in all solvents tested, namely THF, toluene, diethyl ether and even dichloromethane, although with modest yields in the latter two solvents. Interestingly, toluene afforded formation of the product in a very good 91% yield, which is in line with our previous studies, [8c,6f,6g] and even in higher yield than in THF in this case. When tert-BuLi was used in place of BuLi in toluene, a much lower 34% conversion was observed by 1 H NMR (Table 1).

Scheme 3. Atropo-diastereoselective coupling with the SMP-methyl auxiliary and comparison with previous work with oxazolines.

We then evaluated a small series of bidentate ligands, achiral or chiral, nitrogen-or oxygen-based (Table 2). It was shown indeed in our previous work on the coupling of 3-thienyllithium and 1,2benzyne that some ligands could have a dramatic accelerating effect in toluene as solvent. [6f,g] The ligand was added to the reaction mixture after the full formation of the aryllithium nucleophile, the resulting mixture was stirred for 5 minutes and the aryne precursor 1a was finally introduced. While in the absence of ligand, 91% yield of the coupling product 5a were achieved, employing 0.2 equiv. of TMEDA (L1) led to 76% yield, and a full equivalent of L1 afforded a complex mixture, in which only traces of 5a were detected (entries 1-3). The racemic analogue L2 based on trans-cyclohexane1,2-diamine similarly furnished a low yield of 5a under either substoichiometric or stoichiometric conditions (entries 4-5). The BINAM-derived analogue L3 unfortunately proved insoluble under the reaction conditions. We were hopeful concerning the well-known ligand sparteine, [13] which proved efficient in enantioselective carbolithiations by aryllithiums. [2] Disappointingly, its (+)enantiomer L4 also led to a complex mixture and only traces of 5a. Moving to oxygen-based ligands, we assessed the lithium salt of (S)-BINOL L5, obtained by reaction of 2 equiv. of BuLi with (S)-BINOL. Similarly to the case of L3, we encountered solubility issues and had to add some THF during the formation of L5; this allowed us to obtain the coupling product 5a with 71% yield, albeit in racemic form. Tomioka's diether ligand L6, which was successful in other strategies to access axially chiral biaryls via organolithiums, [10a,10b,14,10c] gave a racemic product under substoichiometric conditions (0.2 equiv.), but, gratifyingly, 11% ee of 5a under stoichiometric conditions with an honorable 60% yield, thus proving the concept of the atropo-enantioselective ARYNE coupling mediated by a chiral external ligand of lithium (entries 9-10). The structurally related ligand L7, [10c,2k] which is also a diether analogue of L2, afforded a much lower yield of 5a, which was contaminated with an unidentified side-product in small amounts preventing accurate determination of the enantiomeric excess, although the latter remains low (≤19%, entry 11). Toluene tBuLi (2 equiv.) [b] Traces [c] [a] Isolated yield, or conversion into the product estimated by 1 H NMR given in parentheses. [b] Pronucleophile 4a was added onto a -78 °C solution of tBuLi in toluene. [c] Degradation of the reaction mixture.

Following this first hit in terms of enantioselectivity, we tackled the variation of reaction conditions for the atropoenantioselective coupling. We had to target coupling partners leading to biaryls that would be at least trisubstituted in ortho positions of the biaryl junction, in order to ensure, as much as possible, their configurational stability. [15,[START_REF] Mazzanti | For a selected approach to determine the relative size of orthosubstituents of a biphenyl[END_REF] Initially, we selected sesamol-derived pronucleophile 4b, displaying two different oxygen-based substituents, inert towards organolithiums, in ortho positions of the masked carbanion, which would stabilize the latter without internal coordination of the lithium cation, [17] but could allow intermolecular coordination. Considering the unknown degree of aggregation of the chiral aryllithium, we wished indeed to depart from the case of the coordinating oxazolinyl group, presumably leading to smaller and more rigid aggregates, which would have a different impact on enantioselectivity. As reaction partners, we chose 1c-d, which were shown to be the most efficient benzyne precursors for ARYNE couplings taking place in toluene as solvent [6g] (Table 3).

In this series of experiments, the time required for full formation of the aryllithium nucleophile had been ascertained by separate tests. In the absence of added ligand, the coupling showed low efficiency, with at best 26% conversion into the desired biaryl 5b (entries 1-3). The main products observed were 4b and 4b', resulting respectively from re-iodination (by iodine/lithium exchange on 1c-d) and hydrolysis (either by the n-or sec-butyl iodide generated in the first stage of the reaction or during the final aqueous quench) of the aryllithium. We then assessed a few chiral ligands in this reaction, namely (+)-sparteine L4, Tomioka's diether L6 and bis-oxazoline L8. In all cases, the yield of 5b remained quite low due to the formation of sideproducts 4b and 4b' mentioned above, as well as of the rather unexpected 1,2-diiodobenzene 1c', which we never observed in coupling experiments carried out in THF as solvent. Disappointingly, L4 repeatedly afforded a racemic product (entries 4-7), whereas, on the contrary, L6 repeatedly gave 10% ee (entries 9-13). Ligand L8, which had not been tested yet, was unable to produce the biaryl (entry 8). These modest yields and low enantioselectivities could not be improved by changing the nature of the alkyllitihium base (entries 4-5 and 9, 12-13), the order of addition of reactants for the formation of the chiral aryllithium (entries 5-7), the nature of the benzyne precursor and the length of the mixing time in the presence of the ligand (entries 10-11). Note that, upon addition of a ligand, the yield of 5b tends to increase, as well as those of iodinated side-products 4b and 1c', whereas the yield of the protonated nucleophile 4b' tends to decrease. [a] ee [b] 1 --91% -

2 L1 0.2 76% - 3 L1 1 (Traces) [c] - 4 L2 0.2 24% - 5 L2 1 18% - 6 L3 0.2 n.
d. [d] -7 L4 1 (Traces) [c] -

8 L5 0.2 71% [e] 0% 9 L6 0.2 67% 0% 10 L6 1 60% 11% 11 L7 1 12%
≤19% [f] n.d. = not determined.

[a] Isolated yield, or conversion into the product estimated by 1 H NMR given in parentheses. [b] Enantiomeric excess determined by chiral phase HPLC. [c] Complex mixture. [d] The ligand proved insoluble under the reaction conditions. [e] THF (0.125 mL /mL toluene) was added to help solubilize L5. [f] The product could not be perfectly purified from traces of an unidentified side-product. ee [b] Side-products/ Yields or (conv.) [a] Isolated yield, or conversion into the product estimated by 1 H NMR given in parentheses. [b] Enantiomeric excess determined by chiral phase HPLC. [c] tBuLi was added to a mixture of 4b and L4. [d] 4b was added to a mixture of tBuLi and L4. [e] tBuLi was added to a mixture of 4b and L6.

The formation of product 1c' from benzyne had already been documented under different reaction conditions, either via a postulated radical mechanism [18] or by attack of iodide on benzyne followed by trapping of the 2-iodoaryl carbanion by an electrophilic iodine source (I2 or IF). [19] In our case, we presume that a mechanism similar to the latter one accounts for the formation of 1c', with the nucleophilic iodide being lithium iodide, generated upon iodine/lithium exchange on 4b by tBuLi or protonation of the aryllithium with n-or sBuI; and the electrophilic iodine source being 1c-d or the re-iodinated 4b.

The fact that 1c' is formed only in the presence of a ligand would then be explained by the complexation of LiI or of the resulting 2-iodophenyllithium, respectively solubilizing the former in toluene and stabilizing the latter, overall favoring their availability for further reactions (Scheme 4). Interestingly, an additional experiment involving 4b, BuLi and 1c in the absence of ligand but in the presence of added lithium iodide (1 equiv.) gave 31% of 5b but no diiodo compound 1c'. The low enantioselectivities obtained in the coupling of 4b and 1c-d led us to reconsider the structure of the aryllithium nucleophile. Whereas 4b shows little steric distinction between the methoxy group and the dioxole ring, the latter being moreover quite flat, we were hoping that 4c, bearing on either side of the masked carbanion a small methoxy group and a large and spherical trifluoromethyl substituent, would allow a better differentiation in the stereoselective course of the nucleophilic attack onto the aryne. Additionally, the presence of the bulky CF3 group would impede a dynamic interconversion of atropo-diastereomeric biaryllithium/chiral ligand complexes by axial epimerization, leading to dynamic thermodynamic or kinetic resolutions as potential alternative scenarii for the enantioselection of the process. Thus, 4c was opposed to aryne precursors 1c and 1a (Table 4). Interestingly, although the aryllithium resulting from bromine/lithium exchange on 4c was not fully soluble in toluene, the reaction in absence of ligand still managed to produce the desired biaryls 5c and 5d (entries 1 and 4 respectively). The yield was moderate for 5c, the main side-product being 3-trifluoromethylanisole formed by protonation of the aryllithium derived from 4c. Some other sideproducts were detected in small amounts in 19 F NMR with chemical shifts close to the one of the desired biaryl 5c, suggesting the formation of isomers arising from equilibration of the 2-lithio-2'-methoxy-6'-trifluoromethylbiphenyl intermediate towards more stable biphenyllithium isomers -with lithium ortho to OMe or CF3-caused by a too long residence time before trapping by iodine from 1c. On the other hand, biaryl 5d was obtained in a very good 89% yield (entry 4), especially when considering the very high steric congestion around the aryl-aryl bond due to the bulky iodo, trifluoromethyl and trimethylsilyl ortho substituents. [START_REF] Mazzanti | For a selected approach to determine the relative size of orthosubstituents of a biphenyl[END_REF] Chiral ligands were then assessed in these reactions. (+)-Sparteine L4 failed to afford the expected coupling products (entries 2 and 5). Tomioka's diether L6 proved more successful, with similar 59% and 55% yields of 5c and 5d (entries 3 and 6 respectively). In the reaction of entry 3, 5c was formed in very low ee, while side-product 6, whose structure was confirmed by X-ray diffraction crystallography (Figure 1), was isolated in 13% yield and presumably formed by an unexpected homocoupling of 4c upon loss of CF3 -to generate an aryne. [20] This side-product was not detected when using 1a, which gratifyingly led to 17% ee of 5d when using ligand L6 (entry 6). When 2 equiv. of L6 were employed instead of one (entry 7), the ee remained sensibly the same, but the yield was twice lower, presumably due to the enhancement of the nucleophilicity or basicity of lithium-based intermediates upon coordination, leading to side-reactions as in the formation of 1c' (vide supra). We also varied the temperature in the complexation stage of the aryllithium nucleophile with L6 and observed a small decrease in ee when their mixing temperature was lowered (entries 6, 8-9), possibly implying a less efficient complexation; indeed, the reaction proceeds already well in the absence of ligand (entry 4). Finally, employing diether L7 gave almost identical results in terms of yield and ee of 5d than when using the structurally related L6 (entries 10 vs 6). One would thus favor the use of L6 since it is much more easily accessible and is moreover UVactive, allowing a better tracking and recovery of the ligand at the end of the reaction. [a] Isolated yield, or conversion into the product estimated by 1 H NMR given in parentheses. [b] Enantiomeric excess determined by chiral phase HPLC. [c] 2 equivalents of L6 were used. [d] The temperature of the reaction medium was decreased from 0 °C to -78 °C as soon as the ligand had been added to the mixture, which was then stirred for 60 min at -78 °C before addition of 1a. [e] The temperature of the reaction medium was decreased from 0 °C to -78 °C prior to the addition of the ligand, and only then the resulting mixture was stirred for 60 min at -78 °C before addition of 1a.

Figure 1. Structure of side-product 6 and X-ray diffraction crystallographic picture (ellipsoids at the 50% probability level).

Considering the specific increments for ortho substituents MeO, F3C and TMS (respectively 4.6, 9.5 and 9.4 kcal/mol) [START_REF] Mazzanti | For a selected approach to determine the relative size of orthosubstituents of a biphenyl[END_REF] one could estimate, by coarse but erroneous additivity, a rotational barrier of at least 23.5 kcal/mol for the key biaryllithium intermediate leading to 5d. The actual value, which should be even higher, would render axial epimerization extremely slow in the temperature range of the reaction. Hence, a dynamic resolution as mentioned earlier seems improbable. Accordingly, the enantioselectivity of the reaction would either arise from a selective attack of the aryllithium/chiral ligand complex onto the aryne, or by a non-selective attack onto the aryne followed by a non-dynamic kinetic resolution in the trapping of the biaryllithium/chiral ligand complex by an iodine atom provided by the aryne precursor. Finally, a combination of both scenarii, operating at the same time, is also possible.

Conclusion

In summary, we have engaged in the development of an atropoenantioselective version of the so-called ARYNE coupling, which would lead to axially chiral biaryls starting from haloarenes, halogenated ortho-aryne precursors, alkyllithiums and chiral ligands for lithium. This targeted process was expected to be highly challenging due to the lack of precedents in enantioselective carbolithiations of alkynes in general, and of arynes in particular, and to the very little number of reports on enantioselective reactions of arynes and on the atropoenantioselective construction of a biaryl bond from an aryllithium. And indeed, the task proved difficult. Gratifyingly, we were able to obtain a proof of concept, with a handful of reactions affording the desired atropo-enantioenriched products with up to 17% ee. Among the few ligands screened, Tomioka's diether based on a hydrobenzoin core offered the best compromise in terms of synthetic access, enantioselectivity, efficiency and practicality. Yet, the scope of the reaction and enantioselectivity remain to be improved, and the mechanism for enantioselectivity remains to be elucidated. Corresponding efforts are underway in our laboratories.

Experimental Section

General procedure for the ARYNE coupling

BuLi (1 equiv.) or tert-BuLi (2 equiv.) was added dropwise to a stirred solution of the pronucleophile 4a, 4b or 4c (1 equiv.) in the desired anhydrous solvent (0.25 M) at the specified temperature. The mixture was stirred for a known time and was then cooled down to -78 °C. A precooled -78 °C solution of the aryne precursor 1a, 1c or 1d (1 equiv.) in the same solvent (0.25 M) was then cannulated into the first one. The mixture was stirred overnight (ca. 15 h) from -78 °C to r.t. and then quenched with water and extracted thrice with Et2O. The combined organic layers were dried over Na2SO4, filtered and evaporated to dryness to give the crude material, which was then purified by flash chromatography on silica gel to afford the pure biaryl product.

SynBioN synthesis platform of the L2CM UMR 7053, Université de Lorraine, for the preparation of batches of aryne precursors 1a-b. We are thankful to the analytical services of the Université de Strasbourg for elemental analysis, high resolution mass spectroscopy analysis and X-ray diffraction crystallography.

Keywords: Arynes • Aryllithiums • Biaryls • Axial chirality • Ligand effects

Scheme 4 .

 4 Scheme 4. Tentative rationale for the formation of 4b' and 1c'.

Table 1 .

 1 Assessment of solvents in a model ARYNE coupling

	Entry	Solvent	AlkLi (nb equiv.)	Yield	or
				(conversion) [a]
	1	THF	BuLi (1 equiv.)	59%
	2	Et2O	BuLi (1 equiv.)	34%
	3	DCM	BuLi (1 equiv.)	36%
	4	Toluene	BuLi (1 equiv.)	91%
	5	Toluene	tBuLi (2 equiv.)	(34%)
	6

Table 2 .

 2 Evaluation of ligands in the ARYNE coupling

	Entry	Ligand	x equiv.	Yield	or
				(conversion)

Table 3 .

 3 Variation of parameters in the atropo-enantioselective ARYNE coupling of 4b with benzyne

	Entry	1	AlkLi (nb. equiv.)	t1 (min)	t2 (min)	Ligand	Yield or (conv.) [a]

Table 4 .

 4 Variation of parameters in the atropo-enantioselective ARYNE coupling of 4c

	Entry	Aryne precursor	Ligand	T (°C)	t (min)	Product	Yield or (conv.) [a]	ee [b]
	1	1c	-	-	-	5c	46%	-
	2	1c	L4	-78	60	5c	n.d. (traces)	n.d.
	3	1c	L6	0	30	5c	59%	<5%
	4	1a	-	-	-	5d	89%	-
	5	1a	L4	0	60	5d	n.d. (traces)	n.d.
	6	1a	L6	0	60	5d	55%	17%
	7	1a	L6 [c]	0	60	5d	26%	14%
	8	1a	L6	0/-78 [d]	60	5d	32%	13%
	9	1a	L6	-78 [e]	60	5d	68%	10%
	10	1a	L7	0	60	5d	54%	16%
	n.d. = not determined.

Acknowledgements

We gratefully acknowledge the French Agence Nationale de la Recherche (ANR) (grant number ANR-14-CE06-0003-01, ChirNoCat), the CNRS, the Université de Strasbourg, the Université de Haute-Alsace and the Université de Lorraine for financial support. We also acknowledge Sandrine Adach of the

Yves Fort received his Ph.D. in 1983 under the supervision of Prof. J.-P. Pete (Reims University). He successively held a postdoctoral and a CNRS researcher he moved then to the Swiss Federal Institute of Technology in Lausanne (EPFL). He joined in 2003 the CNRS as Research Associate and was promoted CNRS Research Director in 2009. he moved to the ICIQ (Tarragona, Spain)

Entry for the Table of Contents

The enantioselective addition of aryllithiums onto arynes, leading to axially chiral biaryls in the absence of transition metals, was investigated by means of chiral ligands of lithium. Biaryls with a high degree of steric congestion around the aryl-aryl bond could be obtained.