Jean Baptiste Regnet
email: regnet@geologie.ens.fr

Jerome Fortin

Aurélien Nicolas

Matthieu Pellerin

Yves Gueguen

Elastic properties of continental carbonates: From controlling factors to an applicable model for acoustic-velocity predictions

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INTRODUCTION

Carbonate rocks are convoluted and heterogenous media by nature. This inherent complexity is a main concern when deciphering seismic data for subsurface characterization. The relations and correlations between elastic properties and carbonate rock type or rock physical properties (porosity, mineralogy...) is of primary importance to interpret and understand seismic sections and acoustic logs (Anselmetti et al., 2001;[START_REF] Kenter | Acoustic behavior of sedimentary rocks: Geologic properties versus Poisson's ratios[END_REF]Regnet et al., 2015a). Only then, the source of reflectivity on seismic lines can be identified and fully understood, as so the parameters used to calculate impedance models for synthetic sections [START_REF] Anselmetti | Controls on sonic velocity in carbonates[END_REF][START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF]. It is common knowledge that many parameters as the dominant mineralogy, pore type and pore shape, porosity and pore fluid, rock fabric, influence the elastic properties of carbonate rocks in general (among the many publications available, see in particular [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Assefa | Velocities of compressional and shear waves in limestones[END_REF][START_REF] Verwer | Acoustic properties of carbonates: Effects of rock texture and implications for fluid substitution[END_REF][START_REF] Weger | Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[END_REF][START_REF] Fournier | Critical porosity and elastic properties of microporous mixed carbonate-siliciclastic rocks[END_REF][START_REF] Fournier | Elastic properties of microporous cemented grainstones[END_REF]Regnet et al., 2015aRegnet et al., , 2015b)). The attempt to define reliable correlations between all those physical properties becomes a dilemma and sometimes an obstacle when trying to disentangle the seismic or log signature in carbonate succession.

The discovery of deep and ultra-deep water giant fields in offshore Brazil has put continental carbonate deposits under the spotlight, as they account for a large portion of the production [START_REF] Bruhn | Campos basin: reservoir characterization and management -Historical overview and future challenges[END_REF]. Yet, the lack of non-marine carbonate reservoirs throughout the geological record means their physical properties are poorly documented and thus poorly understood. Furthermore, the extensive use of seismic imaging or 3D seismic imaging technics and their results on the offshore Brazil deposits are sometime delicate to handle due to the overlying thick sequence of salt ("pre-salt deposits") [START_REF] Bassant | The stratigraphic architecture and evolution of the Burdigalian carbonate-siliciclastic sedimentary systems of the Mut Basin, Turkey[END_REF][START_REF] Thompson | Lacustrine carbonate reservoirs from Early Cretaceous rift lakes of Western Gondwana: Pre-salt coquinas of Brazil and West Africa[END_REF]. The origin of continental carbonates is a subtile interplay between physicochemical and biological precipitation of carbonates, that can be coupled with a strong influence of clastic mineralogical inputs. The result is a mineralogical commixture, coupled to a wide heterogeneity of pore types usually inherited from the great diagenetic potential of carbonate rocks (from cementation and dissolution to recrystallisation or dolomitization...) Taking into account this natural complexity, we propose new elements of reflexion on the controlling parameters of elastic properties in continental carbonate rocks, gathered from various localities in the world (outcrops and subsurface). Compressional-wave velocity (Vp) and shear-wave velocity (Vs) measurements under confining pressure, alongside with porosity, mercury injection measurements, X-Ray Diffraction (XRD) and petrography are used to characterize the samples. Then, based on the experimental results and the insights gained from the controlling factors, we suggest a simple analytical model based on the effective medium theory, for acoustic velocity predictions in those rock media.

METHODOLOGY

Samples described in this study are assembled from different outcrops and subsurface analogues of pre-salt carbonates.

COMPOSITION characterization

Texture, composition and pore space/type were characterized on both thin sections (with luminescent-died epoxy impregnation) and with observations carried out on the macroscopic scale.

X-RAY Diffraction (XRD) analyses were conducted on 40 samples were petrography suggested a complex mineralogical composition. The semi quantitative interpretation is done with Quanta software. For sake of simplicity, only three dominant mineralogical assemblages are discriminated regarding their known effect on the elastic properties: calcite, dolomite, and the quartz-clay assemblage (Anselmetti et al., 1997[START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Kenter | Acoustic behavior of sedimentary rocks: Geologic properties versus Poisson's ratios[END_REF]. Grain density of the samples is determined with a Micromeritics Accupyc 1330 helium pycnometer.

PHYSICAL properties

The petrophysical measurements are conducted on sixty five 1.5-inch (3.81 cm) diameter plugs. The effective porosity in the plugs is measured by means of helium expansion porosimetry. Mercury injection porosimetry was performed using an Autopore IV 9500 porosimeter on 20 samples. It can generate pressures from 3.103 to 200 MPa, providing access to pores with throat diameters of 360 μm to 0.03 μm. Gas permeability was measured in a steady state permeameter with nitrogen (N2).

Compressional-wave and Shear-wave velocities (Vp and Vs respectively) measurements are performed under dry conditions and at different hydrostatic pressures (2.5,5,10,20 and 40 MPa) in a loading and unloading path (hysteresis loop). The two wave types propagate along the sample axis at a frequency of 1 MHz (Ultrasonic domain). The measurement accuracy is estimated to be within 3%. The elastic moduli (bulk modulus K, shear modulus G, ...) are inverted from the velocity measurements and the dry bulk density. 2) Lithoclastic to bioclastic wackestones-packstones contain partially dolomitized lithoclasts of various size (silt-sized to large sand-sized quartz and clay) (Figure 1E). Bioclastic fraction consists of eroded and rounded shell fragments from ostracods to gastropods. The grains are embeded in a calcite-rich matrix, although some small sized blocky calcite cements might occur between them. Most of the porosity is interparticular, corresponding to parts that have not been cemented. Some dolomite cement reduced and biomoldic porosity is also regularly present, as microporosity in the matrix (Figure 1F). (3) Microbial bindstone refers to stromatolite deposits and consist of micritic laminae of algal or microbial origin (framework). Layers alternate from calcite cemented to micritic ones that can contain detrital minerals (mostly quartz and clay, but also feldspars or muscovite) (Figure 2A). Porosity is mostly intercrystalline (50µm large pores) and some vuggy pores can occur in layers that are coarser crystalline and which rather correspond to solution enlarged veins that have been partially infilled by cement (Figure 2B

RESULTS

MICROSTRUCTURES

& C).
Microporosity is not widespread and is limited to micritic intervals, following the laminations (Figure 2D). ( 4) Biomicrite shrubs represent travertines schrub samples with arbustiform framework or honey-comb like structures of algal origin (Figure 2E & F). Grains are mostly small peloids and detrital grains (mainly quartz) that are present all over this rock type and are found along the lamination. Some rhomb shape crystals point to a dolomite mineralogy.

Porosiy is mainly vuggy as well as interparticular. Dessication-like cracks regularly occur around few grains, as well as some circular pores. Some of the micritic layers possess welldeveloped microporosity.

MINERALOGICAL composition

Optical observations reveal a complex mineralogical mixing where calcite, dolomite and detrital minerals (quartz and clay mostly) co-exist. Few samples (18) have a pure mineralogical composition with almost 100% of calcite or dolomite (Figure 3). Those pure mineralogical composition are associated with bioclastic 'coquina' grainstones (calcite mineralogy) and in a lesser extent, with bioclastic wakestones-packstones (dolomite oriented).

The two other rock types (stromatolite laminite and biomicrite schrubs) are strongly affected by detrital quartz or clay inputs (indisolubles in Figure 3) and by dolomite recrystallization.

POROSITY, permeability and mercury injection

Porosity displays a wide range of values from 1% to 39% with a median value of 13%, and permeability data show a cloudy distribution, over several orders of magnitude, between 10 -3 and 4445 mD (Figure 4). As it is often the case in carbonate rocks, the porositypermeability relationship deviates strongly from a clear linear or power-law correlation. When considering the rock-type, Figure 4A shows a large superposition of the porosity-permeability properties regarding the texture, and the permeability range for one texture can be relatively high (4 orders of magnitude). The porosity-permeability evolution trend of Bioclastic wakestones-packstones appears to be well-constrained. The influence of dominant pore-type on permeability is not clear even if microporous samples tend to have the lowest values at a given porosity range (Figure 4B). The intercrystalline to moldic porosity (sensu [START_REF] Lucia | Carbonate reservoir characterization : An integrated approach[END_REF] samples display a wide variation of fluid flow properties as the two pore types coexist in different relative proportions respect to one another.

Given the strong diagenetic overprint through solution-enlarged pores, inconsistencies between helium and mercury injection porosity values are expected and observed (Figure 5A).

The later ones are largely under-estimated in the high porosity domain (> 20%). This could show that most of the pore space in high porosity samples is supported by larger pores that are not investigated by mercury injection measurements (such as solution-enlarged interparticular pores, vuggs or moulds). This presence of larger porous inclusions is supported by the derivative of the cumulative intrusion curves with respect to pore-throat diameter (PTD, Figure 5B &C). They show skewed and unimodal distribution of PTD when Hg-porosity is equivalent to Gas porosity (orange dots and curves, Figure 5A &B), with clearly one single family of pores and subsequent mercury filling through pores with smaller size. On the opposite, "non-consistent porosity" sample (blue dots and curves, Figure 5A &C) curves display a plurimodal and wide distribution of PTD, except the one with a rather unimodal and a wide peak distribution (red curve, Figure 5C) which also displays a higher mercury porosity respect to the gas porosity one.

To make sense of those results, and the role played by the pore throat diameter on the fluid path and flow, we perform simple calculations using a permeability model where the PTD value at the main peak is the one that controls the fluid flow. Doing so, we will disregard for the other peaks even if it may not be so accurate as irreversible changes in the microstructure can happen with hydro-mechanical coupling under high stresses. Guéguen and Dienes (1989) derived expressions for the permeability based on a statistical model made of interconnected pipes that are located at random points in space, with specific geometrical properties (length and radius). In this medium, the permeability depends on the statistical mean values of the pipe radius and length, and of course, on the pipe density.

Summarizing their results, the authors come up with the following relation for the permeability:

² 32 1 r K   (1)
where r is the mean pipe radius and ϕ is the porosity. Considering here that we deal with peak-like distributions, we take r = dc/2 for the mean pipe radius. Here, we assume again that fluid flow is driven by the critical diameter, even if the physical background of the statistical model is very different from a percolation model. This model worked particularly well in other carbonate rocks (Casteleyn et al., 2011). Figure 6 shows a fairly good permeability prediction (orange dots) when porosity measurements are consistent. The PTD is then a good proxy for permeability. When considering other samples, and especially the "nonconsistent porosity" ones (blue dots), calculated permeability is largely under-estimated. This comes from the omission of other pore families in the calculation that are likely to greatly influence the fluid-flow.

ACOUSTIC properties

High pressure P-wave velocity measurements show that a distinction can be made between velocity paths that remain more less constant and stabilize (terminal velocity) with an increasing pressure (black-dashed cruves, figure 7) and velocity paths that significantly increase with an increasing pressure (red curves, figure 7). This phenomenon can possibly be explained by the presence of microcracks or crack-like pores within the samples, that tend to close during the progressive loading [START_REF] Fortin | Effects of pore collapse and grain crushing on ultrasonic velocities and Vp/Vs[END_REF]Regnet et al., 2015aRegnet et al., , 2015b;;[START_REF] Nicolas | Brittle and semibrittle behaviours of a carbonate rock: influence of water and temperature[END_REF]. For the later samples, velocities never stabilize suggesting that 40 MPa is still far from the complete closing pressure (Pclosure) of microcracks. It is noteworthy that the loading pressure-velocity path is steeper than during the release path, resulting in a non-hysteresis loop. This effect shows that the elastic limit has been reached for some of the samples, and that some microcracks, crack-like pores or brittle mechanisms might occur during the loading path. This crack-related effect will be discussed later in the paper.

P and S-wave velocities range from 2725 to 6377 m/s and from 1606 to 3444 m/s respectively (Figure 8A). Here, total porosity controls the acoustic velocities as they decrease with increasing porosity. However, velocity dispersion at a given porosity is quite huge and reach 2300 m/s for P-waves and 1200 m/s for S-waves.

Both bulk (K) and shear moduli (G) follow the same linear trend as acoustic velocities with total porosity (Figure 8B). The scattering of values on K modulus is more or less 50%, especially for low porosities (< 20%). Poisson's ratio show no correlation with porosity but a cloudy distribution (Figure 7C). Variations go from 0.11 to 0.36, with most of the values centered around 0.30. The grain densities, ranging from 2.63 to 2.85 g/cm³, but centenred to calcite values (2.70 g/cm³, [START_REF] Mavko | The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media[END_REF]. This result along with observations made on the Poison's ratio goes with the observed complex mineralogical composition of the samples.

Here, mineralogies that can push the grain density towards lower values are quartz and clay

(2.65 g/cm³ and 1.58 to 2.6 cm³, respectively [START_REF] Mavko | The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media[END_REF]. Heavier mineralogies that occur in the samples is dolomite (2.88 g/cm³). Even within the same mineralogy, the grain density can vary. Carbonates for example are associated with fabric alternations where sparite crystals can be more dense than micritic fabrics [START_REF] Pentecost | Travertine[END_REF].

DISCUSSION

In carbonate rocks, elastic properties are a complex product of several parameters which together control range and absolute values of velocity. In the next sections, we discuss and bring insight into the velocity-controlling factors of continental carbonate rocks, compare their significance, and propose an adequate model to predict them.

FACTORS controlling velocity in continental carbonate rocks

PRESSURE and cracks

In many cases, P-wave velocities are known to be pressure and crack-density dependant [START_REF] Fortin | Effects of pore collapse and grain crushing on ultrasonic velocities and Vp/Vs[END_REF]Regnet et al., 2015aRegnet et al., , 2015b;;[START_REF] Nicolas | Brittle and semibrittle behaviours of a carbonate rock: influence of water and temperature[END_REF]. When considering the used isostatic pressure range (2.5 MPa to 40 MPa), velocity dispersion values become more and more centered to zero, as porosity increases (Figure 9A). This marks the diminishing role of cracks in terms of velocity dispersion and more rounded porous inclusions towards high porosity values.

The evolution of acoustic velocities can be interpreted theoretically and quantitatively considering a porous rock as a mixture of solid grains, spherical pores and penny-shaped cracks. By inverting the crack densities, a quantitative description of crack-induced velocity dispersion is then accessible. Here, we understand crack density as a statistical generalization of porosity for non-spherical inclusions. An elongated pore between two grains will be considered a crack [START_REF] Guéguen | Effective elastic properties of cracked rocks-An overview[END_REF][START_REF] Mallet | Effective Elastic Properties of Cracked Solids: An Experimental Investigation[END_REF][START_REF] Ghabezloo | A micromechanical model for the effective compressibility of sandstones[END_REF].

Using [START_REF] Kachanov | Elastic solids with many cracks and related problems[END_REF], the effective elastic properties of the porous rock may be expressed as a function of the overall porosity Φ and the crack density ρc. The crack density is defined as:

   n i i c c V 1 3 , 1  (2)
where N is the total number of cracks embedded in the representative elementary volume (REV) V and ci is the radius of the ith crack. One can note that from equation 2, the dominant aspect of the crack density is the crack length c and not the number of cracks per unit of volume, which can be non-intuitive.

Following [START_REF] Kachanov | Elastic solids with many cracks and related problems[END_REF] and [START_REF] Fortin | Effects of pore collapse and grain crushing on ultrasonic velocities and Vp/Vs[END_REF], the effective bulk modulus K (in dry conditions) can be expressed as:

), 2 1 ( 2 1 1 1 0 0 0          h K K c (3)
where K0 is the bulk moduli of the crack-free matrix, ν0 is Poisson's ratio of the crack-free matrix, ρc is the crack density and h is a factor given (for a penny-shaped geometry) by: . ) 2 / 1 ( 9) 1 ( 16

0 2 0      h (4)
The elastic properties K0 and ν0 of the solid matrix and embedded pores were estimated from velocities measured at Pc = 40MPa, a pressure far below the crack closing pressure for some of the samples (red curves, Figure 7), as the velocities keep building up beyond this point. In other words, this value of 40 MPa should be seen as a lower bound limit of the crack closing pressure for the considered samples, and the calculated crack densities as minimum values.

Here, crack density takes values between 0.2 and 0.6, and mostly close to zero in the high porosity domain (> 20%, Figure 9B). Also, the samples with the highest crack density value are largely clustered to the main porosity-velocity trend. This means that most of the initial cracks are closed at an isostatic pressure of 40 MPa, and that residual cracks that would have been closed beyond 40 MPa, should not influence the velocity that much.

Following [START_REF] Walsh | The effect of cracks on the compressibility of rock[END_REF], the crack closure pressure Pcl for isotropic stress state can be related to the crack aspect ratio defined as ξ = w/2c, where w is the crack aperture:

. ) 1 ( 4

2 0 0     E P cl (5)
Using the elastic values (E0 and ν0) of the crack-free material at Pcl = 40 MPa and equation 5, the minimum crack aspect ratios ξ fall between 5.10 -4 and 4.10 -3 , and rise from low to high porosity values (Figure 9C). This result is somehow expected as the pore and crack aspect ratios become larger when porosity rises. It is noteworthy that in dry case, crack aspect ratio has little influence on the elastic properties, where they become paramount in saturated conditions due to fluid content/microstructure coupling (local fluid-flow from cracks to pores, also called "squirt-flow", O' Connell and Budiansky, 1977).

Following [START_REF] Guéguen | Effective elastic properties of cracked rocks-An overview[END_REF], if cracks are assumed to be characterized by a penny-shape geometry, the crack porosity is given by:

   c crack 2  , ( 6
)
where ξ is the average crack aspect ratio defined as c w 2 /   . Taking ξ values and crack density values inverted at Pc = 40 MPa, the initial crack porosities between 0 and 0.4% (Figure 9D). Finally, crack density or their aspect ratio have limited effect on the elastic properties and should not be taking into account when it comes to the origin of velocity dispersion.

ROCK fabric and pore type

In carbonate rocks, the depositional settings and diagenetic pathway are known to form special rock fabrics with characteristic velocity patterns. Here, the dataset being an assemblage of samples from various locations, both the depositional setting and the diagenetic evolution is obviously not the same from one sample to another. Thus, an effect of the rockfabric (texture, facies, composition) on the porosity-velocity trend is hardly expected, as shown by Figure 10A. Litho-Bioclastic packstones are rather positioned on a lower porosityvelocity trend, partly due to their detrital mineral fractions (Figure 3).

Several studies have shown that acoustic velocity dispersion in carbonate rocks can be explained by the variability of pore types and geometries [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Weger | Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[END_REF]). Here, pores are mainly composed of a (1) Intercrystalline-Moldic mixing, and (2) vugs (from several tens of mm to 1 cm) and does not explain the entire variability of P-wave velocities, even for the highest porosities (Figure 10B).

MINERALOGY

The difference between the elastic properties of calcite and dolomite is high enough so that, similar to siliciclastic rocks, some control of the mineralogical composition on the velocity of carbonate rocks might be expected. Total porosity controls the overall elastic response here, but the mineralogical overprint is a good candidate to explain the wide variability of the acoustic wave velocities at a given porosity (Figure 11). The lower porosityvelocity trend is dominated by samples with medium to large quartz/clay proportions (12% to 80%). The presence of minerals of detrital origin (here, mostly quartz and clay) is diffused in the rock-fabric and thus directly effect the elastic properties. Collectively, this observation is consistent with the results of [START_REF] Anselmetti | Controls on sonic velocity in carbonates[END_REF] and [START_REF] Kenter | Parameters controlling sonic velocities in a mixed carbonate-siliciclastics Permian shelf-margin (upper San Andres formation, Last Chance Canyon, New Mexico)[END_REF], who show that, for a given porosity, mixed carbonate and siliciclastic minerals (> 5% in proportion) have lower velocity than pure carbonate rocks.

On the opposite, dolomitized samples are not only found in the higher trend as one should expect, but also centered in the average trend of the dataset (Figure 11). This show that the effect of dolomitization on the elastic properties is much more diluted, as the associated features of dolomitization also strongly modify the existing pore geometry and the total porosity as well (Anselmetti et al., 1997;[START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF]. Note that mixed quartz-clay and dolomite samples are also roughly centered on the average porosity-velocity trend. Then, although the mineralogical effect on elastic properties is strong and clear for calcitesiliciclastic mixing, it becomes reduced when dolomitization occurs. In this case, and despite the differences in porosity, elastic properties might also depend on the pore geometry as reported in a near-pure calcite travertine succession where stiff inclusions are dominant [START_REF] Soete | Acoustic properties in travertines and their relation to porosity and pore types[END_REF] (Figure 11). Linking elastic properties to anyone parameters becomes then impossible as the velocity signal is averaged, and the dataset being composed of samples with rather different diagenetic pathways and evolution.

When time comes to extrapolate those results to other continental carbonate successions or units, not much material is available. Yet, in the literature, the clastic mineralogical mixing is somehow very common: this can be easely explain, as the sources for detritic input are high in those type of sedimentary systems [START_REF] Soete | Acoustic properties in travertines and their relation to porosity and pore types[END_REF][START_REF] Thompson | Lacustrine carbonate reservoirs from Early Cretaceous rift lakes of Western Gondwana: Pre-salt coquinas of Brazil and West Africa[END_REF][START_REF] Ronchi | Continental carbonates as a hydrocarbon reservoir, an analog case study from the travertine of Saturnia, Italy[END_REF][START_REF] Teboul | Origins of elements building travertine and tufa: New perspectives provided by isotopic and geochemical tracers[END_REF]. This means that the highlighted control of the mineralogy, and especially the siliciclastic mixing, on the elastic properties could be globalised and extended to other continental carbonate systems. Yet, the lack of non-marine carbonate reservoirs throughout the geological record means their physical properties are poorly documented and thus poorly understood. The long-term objective is to find modernday analogues to further increase our understanding and knowledge of continental carbonates, driven by the concept that "the present is the key to the past" [START_REF] Thompson | Lacustrine carbonate reservoirs from Early Cretaceous rift lakes of Western Gondwana: Pre-salt coquinas of Brazil and West Africa[END_REF].

MODELING elastic parameters of continental carbonate rocks

One of the objectives here is to propose a model simple enough to obtain closed formulations for bulk moduli but yet sophisticated enough to take into account the elastic moduli of the minerals, porosity, and pore shape. There are several approximate schemes to do this, commonly known as effective medium theory. Among them, the differential effective medium theory proposed by [START_REF] Mclaughlin | A study of the differential scheme for composite materials[END_REF][START_REF] Norris | A differential scheme for the effective moduli of composites[END_REF][START_REF] Salganik | Mechanics of bodies with many cracks[END_REF][START_REF] Zimmerman | Elastic moduli of a solid with spherical pores: New self-consistent method[END_REF], calculates the effective elastic moduli when inclusions are introduced into the medium in small amounts. The effective moduli is then re-calculated at each step, leading to a pair of differential equations for the effective bulk and shear moduli. Those predictions will always be included into the upper and lower bounds derived [START_REF] Hashin | Note on a variational approach to the theory of composite elastic materials[END_REF]. Even at high inclusion concentrations, this approach produce accurate results (Saenger, Kruger, & Shapiro, 2004[START_REF] Saenger | Effective elastic properties of fractured rocks: Dynamic vs. static considerations[END_REF]Carvalho & Labuz,c1996;Zimmerman, 1991a;[START_REF] David | Elastic moduli of solids containing spheroidal pores[END_REF]. Here, we propose to use asymptotic expressions for both compressibility and shear compliance of realistic pore aspect ratios, that lies between the limiting cases of cracks and nearly spherical pores [START_REF] David | Elastic moduli of solids containing spheroidal pores[END_REF]. The solution of those asymptotic expressions are a bulky and heavy sum of logarithm expressions and rational functions of the Poisson's ratio. However, those expressions can be substantially simplified, without losing accuracy, by retaining only the unbounded terms (see David et al., 2011 for details). This brings in final expressions of the form:

, 1 1 1 1 ln 1 1 ln ln 8 5 3 4 1 ln 4 3 2 0 2 5 0 4 0 3 2 0 2 0 1 0                                                                                                    c c c c c c (7) , 1 1 1 1 ln 1 1 ln 2 1 2 1 ln ln 9 10 2 0 2 5 0 4 0 3 2 0 2 0 1 0 0 0                                                                                                               C C C C C K K (8)
where α is the pore aspect ratio, ρc the crack/inclusion density, ν the Poisson's ratio of the sample, ν0 the Poisson's ratio of the considered matrix (without inclusions), K the sample bulk

                                                         
                                                                 C C C C C (10)
The crack density is related to the total porosity Φ by , 3

4 c    (11)
The volume occupied by cracks is small, but their compliances can be quite large, since they are inversely proportional to their aspect ratio. To obtain inverted P-wave velocities, we first calculate Poisson's ratio ν of the sample in eq. 7, and then injecting the result in eq. 8 to obtain the K/K0 term.

As the key controlling parameter on elastic properties is the mineralogical composition (MC) of the sample, we first ran the simulations considering the three dominant MC (dolomite, calcite and quartz, see Table 1 for detailed values). We consider the case where the medium contains randomly oriented pores with aspect ratios between 10 -2 (crack-like pores) and 0.4 (oblate spheroids). Keep in mind that theoretically, changing the value of α involves changing the overall porosity and crack/inclusion density. The effect of the later on the elastic properties becomes dominant in low pore aspect ratio domains (eq. 11). Yet, this crack/inclusion density is allowed to vary from 0 to 2. The porosity varies from 0% to 40%, in the same range that the experimental data. Results of simulations are shown in Figure 12, and main trends are compared to experimental data. When porosity is zero, predicted P-wave velocities correspond to those found and measured in pure dolomite (Figure 12A), calcite (Figure 12B) or quartz (Figure 12C) and depend on used values of K0 and ν0 respectively. For all the three MC, the model logically predicts a decrease of P-wave velocities as porosity increases and we found the usual concave-upward evolution. The role of the pore aspect ratio and their associated compressibility differences and tendencies is also well captured. When the aspect ratio value decreases, the pores become more compliable to dynamic deformation as the wave propagates trough the rock. The first decreasing steps, from α = 0.4 to α = 0.3 when considering dolomite and calcite MC slightly shift the porosity-velocity trend downward (ΔVp < 500 m/s at a given porosity value). This observation especially stands for the dolomite and calcite MC, and slightly differs when considering a quartz composition where the porosity-velocity relationship trend is lowered during the first changes in pore aspect ratio. In dolomite and calcite MC, the trend shifting through lower P-wave velocities drastically increases when the pore aspect ratio takes values below 0.3, and drops to its lower value when α = 10 -2 . The crack/pore density value increases and becomes paramount at low α where we observed the higher velocity drops (from 6500 m/s to 2000 m/s with only a 5% variation in total porosity with α = 10 -2 , Figure 12B). Overall, the fit between predicted trends and the experimental data is fairly good, especially for calcite and quartz matrix mineralogy, and considering aspect ratios between α = 0.35 and α = 0.15. (Figure 12B &C).

To go further, we then predict the P-wave velocity of each sample using their associated porosity, and elastic parameters calculated and inferred from the mean mineralogical composition (XRD data). As an example, the matrix bulk modulus K0 of a sample with 60% of calcite, 30% of dolomite and 10% of quartz is considered to be the harmonic mean of each mineral bulk value, respectively. The comparison between predicted and measured velocities are presented in Figure 13A & B, for two distinct aspect ratio values. Dispersion is calculated in absolute value and is the normalized difference between predicted and measured velocities, in percent. When α = 0.15, the P-wave prediction is fairly good with an average dispersion of 13.6% (Figure 13A). This dispersion beyond the average (green-dashed line) is lower for porosity below 15%, and increases for highest values where P-wave velocities are almost constantly under-estimated. When increasing the aspect ratio to a value of 0.3, the average dispersion is equivalent (14.1%, Figure 13B) but is rather constant through porosity changes.

The resulting predicted trend is also very similar to the experimental one, and becomes even closer to it in high porosity domain, where dispersion slightly decreases. Finally, it appears that the best prediction is a combination of two aspect ratio values where α = 0.15 when porosity is below 15% and α = 0.3 for higher porosity (Figure 14). This somehow arbitrary cut-off in the α value gives the best result in terms of dispersion which decreases to 9% when considering low porosities (< 15%).

In some cases, and despite the aspect ratio variation in both simulations, the model fails to accurately (beyond the average value) predict the P-wave velocities. This probably means that another factor is at stake beside mineralogy. The concerned samples do not belong to any particular texture association, but instead often correspond to samples with a large proportion of vuggy pores or characterized by rather "rounded" biomoldic pores (Figure 14 & 15). Those two kind of porous inclusions are clearly an issue for the model, which fails to capture their "positive" feedbacks on the elastic properties, where crack-like pores have "negative" effects.

This can be easily explained by the limitation of the effective medium approach which oversimplifies the reality by failing to account for the intrinsic variability of the pore aspect ratio from one inclusion to another.

CONCLUSION

The objectives here were (1) to propose new insights into the factors controlling elastic properties in continental carbonate rocks, and (2) to suggest a simple analytical model based on the effective medium theory, for acoustic velocity predictions in those media.

(1) Total porosity controls the overall elastic response here, but the mineralogical overprint is a good candidate to explain the wide variability of the acoustic wave velocities at a given porosity. The presence of minerals of detrital origin is diffused in the rock-fabric and thus directly effects the elastic properties. This observation is also in good agreement with previous studies on the matter. On the other hand, the effect of dolomitization on the elastic properties is much more diluted, as the associated features of dolomitization also strongly modify the existing pore geometry and the total porosity. When trying to extrapolate those results to other continental carbonate successions or units, not much material is available. Yet, in the literature, the clastic mineralogical mixing is somehow very common. This can be easily explain, as the sources for detritic input are high in those type of sedimentary systems. This means that the highlighted control of the mineralogy, and especially the siliciclastic mixing, could be expected and extended to other continental carbonate systems.

(2) The proposed model, based on the elastic moduli of the minerals, porosity and pore shape, is working fairly well when we consider the case where the medium contains randomly oriented pores with aspect ratios between 10 -2 (crack-like pores) and 0.4 (oblate spheroids).

Overall, the fit between predicted trends and the experimental data is fairly well, especially for calcite and quartz matrix mineralogy, and considering aspect ratios between α = 0.35 and α = 0.15. In some case, and despite the aspect ratio variation in both simulations, the model fails to accurately (beyond the average value) predict the P-wave velocities. This probably means that another factor is at stake beside mineralogy. This can be easily explained by the limitation of the effective medium approach which oversimplifies the reality by failing to account for the intrinsic variability of the pore aspect ratio from one inclusion to another. The (Guéguen & Dienes, 1989). Data points are discriminated regarding measurements consistency of porosity (orange and blue, from Figure 5). (Guéguen & Dienes, 1989). Data points are discriminated regarding measurements consistency of porosity (orange and blue, from Figure 5).

  Microstructural observations reveal a large variation of sedimentary texture. Samples can be grouped into four texture association based on their composition and structures. (1) Bioclastic grainstone (coquinas) are characterized by an intense calcite cementation, with a non-negligeable overprint of chalcedony (the silicified spots are always several millimeters in cross-section) (Figure 1A & B). Due to the cementation, the outline of the coquina shells have been obliterated but is still visible in the large calcite crystals. Porosity is uniformly widespread and essentially intercrystalline or moldic, and occurs where the cementation of cavities is uncomplete. Few samples have been microsparitized, revealing a minor microporosity fraction (Figure 1C & D). (

  modulus and K0 the matrix bulk modulus without inclusions,

FIGURE CAPTION Figure 1 :

 CAPTION1 FIGURE CAPTION

Figure 2 :

 2 Figure 2 : Pre-salt analogue samples A, B, C & D -Microbial bindstone showing micriticlaminae of algal or microbial origin. Porosity is mainly intercrystalline (Yellow-ish areas is B and C), with localised microporosity in some laminae, following lamination (green luminescent, D). E & F -Biomicrite schrubs characterized by arbustiform porosity framework with mainly large vuggy pores (P., E & F). Rhomb shape crystals point to a dolomite mineralogy (white arrows, F).

Figure 3 :

 3 Figure 3 : Ternplot of mineralogical compositions inferred from XRD measurements. Only the three dominant mineralogical assemblages are considered. The indisolubles contain both quartz and clay mineralogies. Samples are discriminated regarding their microstructural association.

Figure 4 :

 4 Figure 4 : Porosity-Permeabiliy properties of the pre-salt analogues. Permeability data show a skewed distribution, over several orders of magnitude. This relationship deviates strongly from a clear correlation. A -Data points are discriminated by textures. B -Influence of dominant Pore Types.

Figure 5 :

 5 Figure 5 : A -Porosity measurement consistency, between helium and mercury injection. The later ones are almost constantly under-estimated. B & C -Pore throat diameter extracted from mercury injection measurements. Orange and blue color match with the associated dots in figure A.

Figure 6 :

 6 Figure6: Permeability calculation using a statistical model of interconnected pipes, randomly located in space(Guéguen & Dienes, 1989). Data points are discriminated regarding

Figure 7 :

 7 Figure 7 : P-wave velocity paths (loading and unloading) of the high pressure measurements, between 2.5 MPa and 40 MPa. Black-dashed and red curves indicate the velocity stability or increase with presure, respectively. Note that the hysteresis loop is not perfect between loading and unloading cycle.

Figure 8 :

 8 Figure 8 : A -P & S-wave velocity evolution with porosity at 40 MPa. B -Bulk and Shear modulii evolution with porosity inverted from velocities at 40 MPa. C -Poisson's ratio evolution with porosity inverted from velocities at 40 MPa. D -Bulk and Shear modulii evolution at 40 MPa with measured grain density.

Figure 9 :

 9 Figure 9 : A -Evolution of normalized P & S-wave velocity dispersion with porosity at 40 MPa. B -P-wave velocity evolution with porosity. Data are discriminated with crack density value inverted from velocities between 2.5 and 40 MPa. C -P-wave velocity evolution with porosity. Data are discriminated with crack aspect ratio value closed at 40 MPa. D -P-wave velocity evolution with porosity. Data are discriminated with initial crack porosity value.

Figure 10 :

 10 Figure 10 : A -Influence of texture association on the scattering of P-wave velocities at 40 MPa. B -Influence of pore type on the scattering of P-wave velocities at 40 MPa.

Figure 11 :

 11 Figure 11 : P-wave velocity evolution through porosity variation. Data points are discriminated with their quartz/clay content (dot color, associated with the side colobar), and with their dolomite content (dot size). Two mineralogical domains are individualized (calcitedolomite mixing and calcite-quartz mixing zones). Evolution trend collected from Soete et al., 2015 showing velocity-porosity relationship where stiff pore inclusions are dominant is also reported in the figure.

Figure 12 :

 12 Figure 12 : Analytical simulation of P-wave velocity using the crack-like pores model from David et al., 2011. Simulations are done on three different matrix mineralogies (A -dolomite, B -calcite and Cquartz) for a wide range of aspect ratio values from α = 10-2 to α = 0.34.

Figure 13 :

 13 Figure 13 : Analytical simulation of P-wave velocity for two fixed aspect ratio values (A -α = 0.15 and B -α = 0.3). Simulations take into account the porosity and the mean mineralogy inferred from XRD analysis, for each sample. Dispersion is the normalized difference between prediction and measurements.

Figure 14 :

 14 Figure14: Analytical simulation of P-wave velocity for two fixed aspect ratio values (α = 0.15 between 0% and 15% porosity, and α = 0.3 beyond 15%). Simulations take into account the porosity and the mean mineralogy inferred from XRD analysis, for each sample.Dispersion is the normalized difference between prediction and measurements. White dots are sample characterized by vuggy and « rounded » biomoldic porosity.

Figure 15 :

 15 Figure 15 : Example of samples characterized by high dispersion value regardless the aspect ratio cut-off (white dots, figure 13). A & B -Bioclastic wackestone-packstone with rather rounded, stiff pores of moldic origin. C & D -Biomicrite schrubs displaying large vuggyframe pores.

Figure 1 :

 1 Figure 1 : Pre-salt analogue samples A, B, C & D -Coquina grainstones characterized by large, intensely recrystallized coquina shells (Cq., A, B, C & D). Porosity is mostly interparticular (P., picture A & B), with few microporosity (black and white arrows, C & D). Nonnegligeable proportion of chalcedony (Ch., A & B). E & F -Lithoclastic to bioclasticwackestone-packstone, characterized by partially dolomitised bioclasts (Bc., E), quartz grains (white arrows, E) and clay (Cl., E). Porosiy is interpaticular and biomoldic (yellowish areas and P., F).

Figure 2 :

 2 Figure 2 : Pre-salt analogue samples A, B, C & D -Microbial bindstone showing micriticlaminae of algal or microbial origin. Porosity is mainly intercrystalline (Yellow-ish areas is B and C), with localised microporosity in some laminae, following lamination (green luminescent, D). E & F -Biomicrite schrubs characterized by arbustiform porosity framework with mainly large vuggy pores (P., E & F). Rhomb shape crystals point to a dolomite mineralogy (white arrows, F).

Figure 3 :

 3 Figure 3 : Ternplot of mineralogical compositions inferred from XRD measurements. Only the three dominant mineralogical assemblages are considered. The indisolubles contain both quartz and clay mineralogies. Samples are discriminated regarding their microstructural association.

Figure 4 :

 4 Figure 4 : Porosity-Permeabiliy properties of the pre-salt analogues. Permeability data show a skewed distribution, over several orders of magnitude. This relationship deviates strongly from a clear correlation. A -Data points are discriminated by textures. B -Influence of dominant Pore Types.

Figure 5 :

 5 Figure 5 : A -Porosity measurement consistency, between helium and mercury injection. The later ones are almost constantly under-estimated. B & C -Pore throat diameter extracted from mercury injection measurements. Orange and blue color match with the associated dots in figure A.

Figure 6 :

 6 Figure6: Permeability calculation using a statistical model of interconnected pipes, randomly located in space(Guéguen & Dienes, 1989). Data points are discriminated regarding measurements consistency of porosity (orange and blue, from Figure5).

Figure 7 :

 7 Figure 7 : P-wave velocity paths (loading and unloading) of the high pressure measurements, between 2.5 MPa and 40 MPa. Black-dashed and red curves indicate the velocity stability or increase with presure, respectively. Note that the hysteresis loop is not perfect between loading and unloading cycle.

Figure 8 :

 8 Figure 8 : A -P & S-wave velocity evolution with porosity at 40 MPa. B -Bulk and Shear modulii evolution with porosity inverted from velocities at 40 MPa. C -Poisson's ratio evolution with porosity inverted from velocities at 40 MPa. D -Bulk and Shear modulii evolution at 40 MPa with measured grain density.

Figure 9 :

 9 Figure 9 : A -Evolution of normalized P & S-wave velocity dispersion with porosity at 40 MPa. B -P-wave velocity evolution with porosity. Data are discriminated with crack density value inverted from velocities between 2.5 and 40 MPa. C -P-wave velocity evolution with porosity. Data are discriminated with crack aspect ratio value closed at 40 MPa. D -P-wave velocity evolution with porosity. Data are discriminated with initial crack porosity value.

Figure 10 :

 10 Figure 10 : A -Influence of texture association on the scattering of P-wave velocities at 40 MPa. B -Influence of pore type on the scattering of P-wave velocities at 40 MPa.

Figure 11 :

 11 Figure 11 : P-wave velocity evolution through porosity variation. Data points are discriminated with their quartz/clay content (dot color, associated with the side colobar), and with their dolomite content (dot size). Two mineralogical domains are individualized (calcite-dolomite mixing and calcite-quartz mixing zones). Evolution trend collected from Soete et al., 2015 showing velocity-porosity relationship where stiff pore inclusions are dominant is also reported in the figure.

Figure 12 :

 12 Figure 12 : Analytical simulation of P-wave velocity using the crack-like pores model from David et al., 2011. Simulations are done on three different matrix mineralogies (A -dolomite, B -calcite and Cquartz) for a wide range of aspect ratio values from α = 10 -2 to α = 0.34.

Figure 13 :

 13 Figure 13 : Analytical simulation of P-wave velocity for two fixed aspect ratio values (A -α = 0.15 and B -α = 0.3). Simulations take into account the porosity and the mean mineralogy inferred from XRD analysis, for each sample. Dispersion is the normalized difference between prediction and measurements.

Figure 14 :

 14 Figure14: Analytical simulation of P-wave velocity for two fixed aspect ratio values (α = 0.15 between 0% and 15% porosity, and α = 0.3 beyond 15%). Simulations take into account the porosity and the mean mineralogy inferred from XRD analysis, for each sample. Dispersion is the normalized difference between prediction and measurements. White dots are sample characterized by buggy and « rounded » biomoldic porosity.

Figure 15 :

 15 Figure 15 : Example of samples characterized by high dispersion value regardless the aspect ratio cut-off (white dots, figure 13). A & B -Bioclastic wackestone-packstone with rather rounded, stiff pores of moldic origin. C & D -Biomicrite schrubs displaying large vuggy-frame pores.

ACKNOWLEDGMENT

This work is part of a Postdoctoral Fellowship funded by TOTAL R&D Carbonate Team.

Authors are very grateful to Rudy Swennen and the KU Leuven team for carrying the petrographical (thin-section analysis), mineralogical (XRD) and petrophysical analysis. With regard to the latter, density analysis was carried out at KU Leuven, while poroperm analysis was done at Panterra BV (the Netherlands) and the Vp & Vs measurements were performed at the VU Amsterdam.

concerned samples do not belong to any particular texture association, but instead often correspond to samples with a large proportion of vuggy pores or characterized by rather "rounded" biomoldic pores.

APPENDIX A

Supporting information table containing the petrophysical data presented in this article. Table A1 is organized by sample name with one column per petrophysical properties and derived parameter from our laboratory measurements.


Guillaume Erbland

Yohan Gisbert

Gwénaël Rapenne

Claire Kammerer
email: kammerer@cemes.fr

Expedient synthesis of thioether-functionalized hydrotris(indazolyl)borate as an anchoring platform for rotary molecular machines

Keywords: scorpionate ligand, indazole, reductive sulfidation, indium, molecular motor Preprint

Major improvements in the synthesis of surface-mounted rotary molecular machines based on ruthenium(II) complexes are reported. The development of a one-pot indium(III)-mediated "Ndeprotection / ester reductive sulfidation" sequence allowed step economy, reproducibility and high efficiency in the synthesis of the thioether-functionalized tripodal ligand. Switching to the thallium salt of hydrotris(indazolyl)borate and to microwave heating further optimized the preparation of the common intermediate in the modular synthesis of symmetric and dissymmetric molecular motors and gears. The penta(4-bromophenyl)cyclopentadienyl ruthenium(II) key precursor is now reproducibly synthesized in 5 steps and 31% overall yield on the longest linear sequence. Subsequent five-fold Suzuki-Miyaura coupling with ferroceneboronic acid led to a new C5-symmetric penta-ferrocenyl molecular motor.

Introduction

The field of artificial molecular machines has witnessed a tremendous development over the last two decades, with an initial impetus related to the synthesis of mechanically interlocked systems allowing to control the motion of (at least) one of their components. [1,2] Among nanomachines, artificial molecular motors are expected to transform the supplied energy into a unidirectional translational or rotational motion, ultimately leading to recovery of the work performed. [3] Pioneering examples of chemicallyand light-fuelled rotary motors were reported as early as in 1999 by the groups of Kelly [4] and Feringa, [5] respectively, exhibiting controlled unidirectional motion in solution. Although many very elegant molecular rotary motors using chemical or light energy have been developed ever since [3] and have shown interesting applications, [6] the exploitation of electronic energy is still rare and only scarce examples have been reported at the single molecular scale [7][8][9] or in self-assembled monolayers. [10] Sykes and co-workers employed a butyl methyl sulfide single-molecule chemisorbed on a Cu(111) surface as a rotor and used the tip of a Scanning Tunneling Microscope (STM) to trigger an electrically-driven rotation. [7] As a result, one of the enantiomeric surface-bound molecules underwent rotary motion with 5% directionality, which has been ascribed to the intrinsic chirality of the STM tip. In 2011, Feringa incorporated four overcrowded alkene-based motors acting as wheels into a molecular car scaffold and proved that the electrically-driven rotary motion of the motors can be converted into directional translation of the nanovehicle on a Cu(111) surface. [8] In this context, we reported the design and synthesis of electron-fueled molecular motor 1 displaying a dissymmetrically-substituted cyclopentadienyl rotor, a scorpionate ligand as the stator and a ruthenium(II) center as a joint allowing the rotary motion of the upper part with respect to the lower one (Figure 1). [11] The tripodal stator was functionalized with thioether groups to ensure a strong anchorage on gold surface via chemisorption. This molecular motor was indeed studied at the single molecule scale at low temperature (5 K) under Ultra-High Vacuum (UHV) by STM. [9] The latter was used not only to image the molecular motor, but above all to trigger its rotation via the injection of tunneling electrons. Most importantly, it was discovered that the dissymmetric character of the rotor, with four phenyleneferrocenyl groups and a truncated tolyl arm, is of paramount importance. On the one hand, it allows a direct monitoring of the rotation (and of its direction) by following the position of the shorter arm, which serves as a tag. On the other hand, it was discovered that this dissymmetry induces a reversible behaviour, with a direction of rotation which depends on the location of the tip during the pulse (above one of the longer ferrocenyl-appended arms, or above the shorter truncated arm).

This motor belongs to a broader family of motors that have been reported along the years (Figure 1). [12] This family mostly involves C5-symmetric rotors, with arms of various lengths and nature. [11,13] Indeed, while the dissymmetric motor 1 displays a diameter of about 2 nm with a single para-phenylene separating the cyclopentadienyl and ferrocenyl units, several motors with longer arms have been reported. These C5-symmetric rotors included phenylethynyl linkers [13b] but also insulating groups such as bisethynyl trans-platinum(II) [13b] or bicyclooctyl [13c] spacers. Moreover, most of the motors had been originally designed to be deposited on insulating oxide surfaces and therefore display ester anchoring groups. However, the technology is currently not mature enough to address horizontally an electron-fueled rotary motor located between two electrodes on an insulating surface (i.e. a nanojunction). Our efforts are thus currently focused on the development of new symmetric and dissymmetric structures of motors and gears, [12b,c] specifically designed for an optimal interaction with metallic surfaces such as gold (Scheme 1).

Scheme 1. Structure of symmetric (R1 = R2) or dissymmetric (R1 ≠ R2) molecular motors and gears, and related retrosynthetic analysis leading back to common key intermediate 2.

From a retrosynthetic point of view, all the structures including a C5-symmetric rotor stem from key intermediate 2, displaying aryl bromide functions on each arm, ready for various cross-coupling reactions. This strategy was successfully applied to the synthesis of our family of symmetric motors, starting from pentaphenylcyclopentadiene (Scheme 2). [11] The latter is first brominated on the phenyl para-positions and on the cyclopentadiene core using neat bromine giving an hexabrominated compound (3) in a nearly quantitative yield. Subsequent oxidative addition on ruthenium(0) cluster Ru3(CO)12 leads to complex 4, [14] in accordance with the method reported by Connelly and Manners. [15] Conversion of this piano-stool complex into the key intermediate 2 is finally achieved via ligand exchange in the presence of the potassium salt of thioether-functionalized hydrotris(indazolyl)borate (5.K). Although this synthetic route suffers from the low yield of the last step, it allows the formation of the cyclopentadienyl-Ru(II) complex, which appeared impossible under other tested conditions due to the strong steric hindrance of the five phenyl rings attached to the cyclopentadienyl core. By contrast, the synthesis of the dissymmetric motor 1 (with R1 = Fc and R2 = Me) involved the introduction of the tolyl group corresponding to the truncated arm at a very early stage. [11] In addition to an evident lack of modularity, it was observed that the oxidative addition of the dissymmetric cyclopentadienyl bromide on the Ru3(CO)12 cluster was less efficient (43%) than with the corresponding symmetric precursor 3 (78%). This tendency was confirmed by other attempts with cyclopentadienyl bromides involving one longer and potentially coordinating arm. [16] In view of future developments of dissymmetric motors and gears based on the ruthenium cyclopentadienyl scaffold, the latter approach is not reliable and modular enough. It is thus envisioned to exploit penta-bromide key intermediate 2 and perform a first statistical single cross-coupling to generate the differentiated arm. The remaining four activated positions could then undergo cross-couplings reactions to yield various dissymmetric rotors. This renewed strategy towards dissymmetric motors and gears highlights the need for important amounts of key intermediate 2. It thus appeared necessary not only to increase the efficiency of the coordination of the tripodal ligand (only 20%, Scheme 2) but also to optimize the synthesis of potassium hydrotris[6-((ethylsulfanyl)methyl)indazolyl]borate 5.K by itself. The latter is a bifunctional platform combining anchoring groups and coordinating sites pointing in opposite directions. The anchoring groups are necessary to efficiently restrict the possible translation, rotation and rocking motions of molecules on a surface. While a single binding point only prevents translation motions and a second one additionally blocks the rotation of the molecule, a minimum of three points of anchoring are necessary to preclude rocking motion. In our design, the rigid hydrotris(indazolyl)borate scaffold bears three functional thioether pendant groups well oriented at the 6-position of the indazole core to very efficiently immobilize this platform on metallic surfaces such as gold, silver or copper (Scheme 1). On the opposite side of the ligand, three nitrogen atoms belonging to the indazole cores are available to coordinate a metal center such as ruthenium. This tripodal chelating unit thus allows the covalent binding of coordination complexes on a surface, as in the surface-mounted molecular gears or motors reported previously. [12] Furthermore, lifting the metallic center away from the surface allows minimizing interferences caused by metal-surface interactions. In this context, rotors (in the case of rotary motors) or cranked wheels (in the case of gears) can be efficiently deposited, anchored and studied without almost any interaction with the surface, which is particularly important for Scanning Probe Microscopy experiments.

Herein we present our results towards higher efficiency and step-economy in the preparation of tripodal ligand 5 and of the ruthenium penta-bromide derivative 2, which serves as a central platform in the modular synthesis of various molecular motors and gears. As an application, the synthesis of a new symmetric penta-ferrocenyl motor with three thioether pendant groups (Scheme 1, R1 = R2 = ferrocene) is reported.

Results and Discussion

As mentioned above, one of our aims was to optimize the synthetic route towards hydrotris(indazolyl)borate 5 in terms of efficiency and reproducibility. Indeed, the preparation of such scorpionate ligand involved 7 steps starting from 3-amino-4-methylbenzoic acid (Scheme 3). [17] The latter was almost quantitatively protected as an ethyl ester and subsequently converted to the 1Hindazole 8 by a Jacobson reaction followed by acidic hydrolysis of the intermediate acetamide 7 (64% over two steps). Functional group manipulation to convert the ethyl ester into the desired ethyl thioether then involved the reduction of the ester to the corresponding alcohol 9, bromination and subsequent nucleophilic substitution with ethanethiol. The thioether-appended 1H-indazole 10 was finally reacted with KBH4 under solvent-free conditions at 200 °C to afford selectively the potassium hydrotris(indazolyl)borate KTp 4Bo,6-CH2SEt (5.K) which was purified by sublimation of unreacted indazole 10.

Scheme 3. Synthetic route toward the potassium salt of hydrotris(indazolyl)borate 5.K, starting from 3amino-4-methylbenzoic acid.

This synthetic sequence has been intensely used in our group as a standard way to prepare indazolederived scorpionate ligands carrying either ester (from a direct reaction between KBH4 and 8) or thioether anchoring groups. Now that our main interest lies in molecular machines to be studied on metallic surfaces, it was desirable to renew the synthetic route towards thioether-appended indazole 10, especially as a lack of efficiency and reproducibility of the ethanethiol-mediated nucleophilic substitution was observed throughout the years.

Improved synthetic route to thioether-appended indazoles

Interestingly, Sakai et al. recently reported the direct conversion of esters into sulfides via an indiumcatalyzed reductive sulfidation reaction (Scheme 4). [18] The ester is directly reacted with the appropriate thiol in 1,2-dichloroethane (1,2-DCE) in the presence of a catalytic amount of indium(III) iodide as Lewis acid and an excess of 1,1,3,3-tetramethyldisiloxane (TMDS) as reducing agent. [19] After overnight heating, thioethers deriving from aliphatic and aromatic esters and thiols are obtained in good to excellent yields.

Scheme 4. Example of the indium(III)-catalyzed reductive sulfidation of methyl p-methylbenzoate with

1-octanethiol, as reported by Sakai et al. [18] This method is thus of high synthetic utility since it avoids the common sequence involving the reduction of the ester, subsequent conversion of the alcohol into a (pseudo)halide and final substitution by a sulfur nucleophile.

The efficiency and the scope of this transformation drew our attention since this would allow the direct conversion of indazolyl ester 8 to thioether 10 (Scheme 3) in a single step (instead of three), although Sakai et al. did not mention any test on heteroaromatic derivatives.

In order to prevent the coordination of free 1H-indazole to the In(III) center, the reaction was first tested with the N-acetyl-protected indazolyl ester 7. When reproducing the conditions reported by Sakai et al., i.e. 10 mol% indium(III) iodide in combination with ethanethiol (1.2 equiv.) and 1,1,3,3tetramethyldisiloxane (TMDS, 3 equiv. i.e. 6 Si-H equiv.) in 1,2-dichloroethane at 60 °C for 20h, a complex mixture was obtained as observed by 1 H NMR spectroscopy of the crude product (Table 1, entry 1). Careful analysis revealed the presence of traces amounts of unconverted starting material (7). Since no further signal corresponding to an acetamide moiety was detected, it was concluded that the expected N-acetyl protected indazole carrying the ethyl thioether function had not been formed. To our delight, it appeared that the free 1H-indazole scaffold bearing the thioether function was present in the mixture, although in traces amounts. This indicates that the desired reductive sulfidation takes place, although with a concomitant deprotection of the N-acetyl group which most probably consumes both the thiol and the silane. Indeed, increasing the quantity of thiol and silane to 2.2 and 6 equivalents, respectively, the free 1H-indazole 10 was gratifyingly formed as major product and isolated in 57% yield (entry 2). To check if the possible coordination of the free 1H-indazolyl ester 8 or thioether 10 formed during the reaction might deactivate the indium(III) catalyst and thus hamper the reaction, indium(III) iodide was introduced in slight excess (1.1 equivalent) compared to the substrate (entry 3). Under otherwise unchanged conditions, only a minor improvement of the isolated yield was obtained (65%). In this reaction, a by-product (13) was formed in a ratio of 1:4 compared to product 10 according to the 1 H NMR spectrum of the crude mixture. This by-product had already been observed in various amounts under catalytic conditions and corresponds to the N-ethyl derivative of 10. The N-ethyl moiety in 13 most probably results from a direct reduction of the acetamide group, as already reported under similar conditions. [20] To overcome this unproductive side reaction, the quantity of nucleophile was increased to 4 equivalents and the desired free 1H-indazole 10 was obtained as a single product in 86% yield (entry 4). Finally, in view of the synthesis of scorpionate ligands on a large scale, the same reaction was run on 1.5 g (compared to 150 mg in entries 1-4) to give rise to thioether indazole 10 in a comparable 85% isolated yield (entry 5).

Table 1. Optimization of the reaction conditions for the direct conversion of indazolyl ester 7 to thioether 10, [a] in one single step instead of four.

Entry

InI3 (equiv.) EtSH (equiv.) (Me2SiH)2O (equiv.) Yield (%) [b] 1 0.1 1.2 3 Traces 2 0.1 2.2 6 57 [c] 3 1.1 2.2 6 65 [c] 4 1.1 4 6 86 5 [d] 1.1 4 6 85

[a] The reactions were run on a 150 mg (0.65 mmol) scale unless otherwise stated. [b] Isolated yield unless otherwise stated. [c] Byproduct 13 resulting from the direct reduction of the N-acetyl group into an N-ethyl moiety was detected in the crude mixture. [d] The reaction was run on a 1.5 g (6.5 mmol) scale.

Application of the reaction conditions for the reductive sulfidation of esters developed by Sakai et al. and subsequent optimization now allow for a direct conversion of N-acetyl indazolyl ester 7 into the corresponding N-deprotected indazolyl thioether 10 in high yield and in a single step. This one-pot deprotection / reductive sulfidation not only shortens the synthetic route towards tripodal ligand 5.K but also avoids the tedious isolation of 1H-indazolyl ester 8. The thioether-functionalized indazole ( 10) is now very conveniently prepared in three steps on the gram scale starting from 3-amino-4-methylbenzoic acid in a reproducible 70% overall yield (Scheme 5), instead of six steps and a non-reproducible overall yield of 12 to 36% previously.

Scheme 5.

Optimized synthetic route yielding the key penta-bromide rotor 2 in 5 steps and 31% overall yield in the longest linear sequence (instead of 8 steps and maximum 4% yield previously).

Following this improvement, the reproducibility of the synthesis of the hydrotris(indazolyl)borate salt 5.K and the efficiency of the subsequent ligand exchange to yield key intermediate 2 were tackled.

Beneficial use of the thallium salt of the tripodal ligand as intermediate in the synthesis of rotor 2

Hydrotris(pyrazolyl)borates and by extension hydrotris(indazolyl) borates, are mostly prepared by heating an excess of the appropriate pyrazole (respectively indazole) with KBH4 or NaBH4 under neat conditions, as described above for the synthesis of the potassium salt 5.K. [21] However, the thallium(I) salts of such derivatives have appeared as mild and valuable reagents for the transfer of the scorpionate ligands onto various transition metals, as they exhibit a lower reducing ability than the corresponding alkali metal salts. [22] The crystallinity of the thallium(I) complexes also renders their isolation more easy, and we thus envisioned the synthesis of the thallium salt TlTp 4Bo,6-CH2SEt 5.Tl. The thallium salts of scorpionate ligands are usually obtained by cation exchange, reacting the alkali metal salt with TlNO3.

In 2008, two new methods were reported by Kitamura et al.: i) preparation and isolation of thallium borohydride TlBH4 and subsequent reaction with pyrazole or indazole derivatives [23] or ii) a solvent-free one-pot method using KBH4 and Tl2SO4 in a 2:1 ratio to yield the thallium hydrotris(pyrazolyl)-or hydrotris(indazolyl)borate via an in-situ cation exchange. [24] Given the toxicity of thallium(I), the latter one-pot procedure was selected to avoid the isolation of the thallium borohydride reagent. Indazole 10 was thus reacted in the presence of potassium borohydride and thallium sulfate to give rise to thallium hydrotris(indazolyl)borate 5.Tl in 54% yield (Scheme 5). Generating the thallium salt instead of the potassium salt leads to a comparable yield (54% vs 55%, respectively) but avoids the tedious and nonreproducible sublimation procedure as the thallium salt is efficiently recrystallized. However, the main advantage of using the thallium intermediate 5.Tl lies in the ligand exchange step. Indeed, the reaction of 2 equivalents of thallium hydrotris(indazolyl)borate 5.Tl with 1 equivalent of the ruthenium cyclopentadienyl complex 4 in THF at 100 °C for 48h afforded the target compound 2 in 67% yield, compared to 20% with the potassium salt 5.K under otherwise similar conditions (Scheme 2). To our delight, the efficiency of this reaction was even further increased to 82% replacing classical heating with microwave heating (100 °C, 3 x 10 min) in acetonitrile as solvent (Scheme 5).

The indium(III)-mediated one pot deprotection / reductive sulfidation sequence followed by the preparation of the thallium salt of the scorpionate ligand has significantly shortened the synthetic route to the penta-bromide rotor 2 and increased its efficiency. Indeed, this key building block towards molecular motors and gears is now prepared in 5 steps in 31% overall yield in the longest linear sequence, compared to 8 steps and a maximum 4% overall yield formerly.

Extension of the indium(III)-mediated methodology to the synthesis of ester-appended scorpionate ligands

During our work towards the reductive sulfidation of indazolyl ester 7, it was observed that the deprotection of the N-acetylindazole to give the corresponding 1H-indazole 8 occurs prior to the effective transformation of the ester. Deprotection of the N-acetyl protecting group is most commonly performed under drastic basic (hydroxide, alkoxide) or acidic (HCl) conditions, [START_REF] Greene | Protective Groups in Organic Synthesis, Third Edition[END_REF][START_REF] De Rouville | [END_REF] provided that these conditions are compatible with additional functional groups. For instance, in our synthetic route towards hydrotris(indazolyl)borates, the crude N-acetylindazole obtained via the Jacobson reaction was deprotected using concentrated HCl at 60 °C (Scheme 3). The 1H-indazole 8 was obtained in a moderate 64% yield over two steps, and it was observed that a significant amount of product was lost during the acidic deprotection step, possibly via hydrolysis of the ester.

Since the amide function appears more reactive than the ester towards In(III)/TMDS/EtSH reaction conditions, the possible selective deprotection of the indazole core under mild conditions was investigated.

Table 2. Screening of conditions for the N-deprotection of N-acetylindazole 7 and corresponding blank experiments. [a] Entry InX3 t (h) Conv. (%) [b] Yield (%) [c] 1 InI3 16 100 28 [d] 2 In(OAc 8 [h] InCl3 48 0 -

[a] The reactions were run on a 150 mg scale (entries 1-5) or on a 75 mg scale (entries 6-8). [b] Conversion of the starting material 7 as determined by 1 H NMR spectroscopy. [c] Isolated yield. [d] The desired product 8 was formed along with reductive sulfidation product 10 (13% isolated yield) and other unidentified products, as observed by 1 H NMR spectroscopy of the crude product.

[e] Not determined. [f] Ethanethiol was omitted.

[g] Nethylindazolyl ester 14 and the desired product 8 were obtained in the crude mixture, in a 2:1 ratio. [h] 1,1,3,3-Tetramethyldisiloxane was omitted.

In a first test, the slight excess of indium(III) iodide (1.1 equiv.) was maintained while the amounts of ethanethiol and TMDS were reduced to 1.2 and 3 equiv. respectively, in order to favor the single reaction of the amide function (Table 2, entry 1). After 16h at room temperature, the starting material was fully converted but a mixture of products was obtained, including 10 resulting from the N-deprotection / reductive sulfidation sequence. The desired deprotected indazolyl ester 8 was isolated in 28% yield. Less reactive indium(III) species were tested next in order to avoid the conversion of the ester moiety.

In the presence of indium(III) acetate and triflate, the conversion was very low after 4h at room temperature (entries 2 and 3). Conversely, indium(III) chloride promoted a smooth reaction with 91% conversion of the starting material after 20h (entry 4). Increasing the reaction time to 48h led to full conversion and the desired deprotected 1H-indazole 8 was isolated in a satisfactory 96% yield (entry 5). Blank experiments were next carried out in order to assess the role of each reagent. As expected, omission of the Lewis acidic indium(III) species totally prevented the reaction (entry 6). In the absence of thiol, the major product was N-ethylindazolyl ester ( 14), resulting from the complete reduction of the carbonyl moiety to the corresponding methylene (entry 7). [20] Finally, the reducing agent is also crucial in this procedure as no reaction occurs in the absence of hydrosilane (entry 8). It is thus assumed that this deprotection reaction is formally a reductive sulfidation of the acetamide moiety, with the indazole core playing the role of the leaving group.

With these new deprotection conditions in hand, indazolyl ester 8 is now efficiently synthesized in 79% overall yield starting from 3-amino-4-methylbenzoic acid (Scheme 6), as compared to the 63% obtained previously (Scheme 3). The preparation of ester-appended hydrotris(indazolyl)borate 11.K, used as stator in studies on insulating surfaces, will benefit from this improvement implying an increase from 43% to 54% of the overall yield on this four-step sequence.

Scheme 6. Optimized synthetic route towards the potassium salt of ester-functionalized hydrotris(indazolyl)borate 11.K.

Test-reaction: Synthesis of a new molecular motor and last major improvement using microwave activation

So as to probe the efficiency of a complete synthetic sequence up to molecular machines, the preparation of the new molecular motor 12 incorporating a symmetric rotating subunit was tackled (Scheme 7).

The penta-bromide rotor 2, displaying a thioether-functionalized tripodal ligand, was submitted to Suzuki-Miyaura coupling conditions in the presence of a large excess of ferroceneboronic acid, using palladium diacetate / SPhos as catalytic system, potassium phosphate as base in anhydrous toluene. Penta-aryl bromide 2 thus underwent five successive Suzuki-Miyaura couplings to give rise to the desired penta-ferrocenyl molecular motor 12 in 17% yield after 48h at 100 °C (Scheme 7, classical heating).

Considering the future preparation of motors and gears that may involve more complex and expensive boronic acid derivatives, decreasing the amount of such partner was highly desirable. New reaction conditions were thus developed, involving 7.5 equiv. of ferroceneboronic acid (i.e. 1.5 equiv. per aryl bromide), sodium tert-butylate (22.5 equiv.) as base and [1,1'-bis (diphenylphosphino)ferrocene]dichloropalladium PdCl2(dppf) (20 mol% per aryl bromide) as catalyst in anhydrous toluene. Microwave heating at 135 °C for 1 h gave rise to the desired penta-ferrocenyl product in a highly satisfactory 45% yield (Scheme 7, microwave heating). This step leads to the formation of five new C-C bonds in a single synthetic operation, with a yield of 85% per Suzuki-Miyaura cross-coupling in spite of the steric hindrance. These new coupling conditions now allow an expedient synthesis of this symmetric molecular motor, displaying short ferrocenylphenylene arms, in 6 steps in the longest linear sequence with an overall yield of 14%.

Scheme 7. Synthesis of the new molecular motor 12 via a five-fold Suzuki-Miyaura cross-coupling under classical or microwave heating.

The new molecular motor 12 was fully characterized and exhibits free rotation at room temperature as shown by NMR spectroscopy. Its properties will be investigated by Scanning Probe Microscopy techniques in the near future.

Conclusions

In this work, high efficiency and step-economy was achieved in the preparation of thioetherfunctionalized hydrotris(indazolyl) borates to be used as anchoring platforms in surface-mounted rotary molecular machines, but also as a general platform to anchor various metallic centers on gold, silver or copper surfaces. Indeed, the development of a one-pot "N-deprotection/ ester reductive sulfidation" sequence allowed the direct conversion of the N-acetylindazolyl ester precursor into the corresponding 1H-indazolyl thioether in a single high-yielding step mediated by indium(III) iodide. The thioetherfunctionalized indazole is now very conveniently prepared in three steps on the gram scale starting from 3-amino-4-methylbenzoic acid in a reproducible 70% overall yield, instead of six steps and a nonreproducible overall yield of 12 to 36% previously. Furthermore, milder conditions involving indium(III) chloride and the same TMDS/EtSH system were identified for the selective cleavage of the N-acetyl protecting group leading to the free 1H-indazolyl ester in excellent yield, which is of interest for the synthesis of ester-appended scorpionate ligands.

In view of the synthesis of families of ruthenium(II) complexes based on a thioether-functionalized stator and a penta-aryl cyclopentadienyl rotor, the preparation of the penta(4bromophenyl)cyclopentadienyl common intermediate was improved to reach 31% overall yield in the longest linear sequence (5 steps), instead of a maximum of 4% (over 8 steps) previously. A five-fold Suzuki-Miyaura cross-coupling of this key precursor gave rise to a new C5-symmetric molecular motor with five ferrocenylphenylene arms, proving that molecular machines can now be obtained efficiently in 6 steps via our renewed synthetic route. The modular synthesis of various symmetric and dissymmetric molecular gears, exploiting the same synthetic strategy, is now underway.

Experimental Section

General methods: All commercially available chemicals were of reagent grade and were used without further purification. Isoamyl nitrite, anhydrous 1,2-dichloroethane, anhydrous THF, anhydrous acetonitrile, anhydrous toluene, ethanethiol, potassium phosphate and sodium tert-butoxide were purchased from Aldrich. 3-Amino-4-methylbenzoic acid, potassium borohydride, thallium(I) sulfate and 1,1'bis(diphenylphosphino)ferrocenepalladium(II) dichloride (dichloro-methane adduct) Pd(dppf)Cl2CH2Cl2 were purchased from Acros. Trichloroindigane, triiodoindigane and ferroceneboronic acid were purchased from Alfa Aesar. 1,1,3,3-Tetramethyldisiloxane and palladium(II) acetate were purchased from ABCR. Potassium acetate was purchased from Lancaster, acetic anhydride from Fluka and 2-dicyclohexylphosphino-2'-6'-dimethoxybiphenyl (SPhos) from TCI. Compounds 3, [14] 4, [14] 6, [17] and 11.K [17] were prepared according to the corresponding published procedures. All reactions were carried out using standard Schlenk techniques under an argon atmosphere. Thin layer chromatography (TLC) was performed on pre-coated aluminum-backed silica gel 60 UV254 plates (Macherey-Nagel) with visualization effected using ultraviolet irradiation ( = 254, 366 nm). Flash column chromatography was carried out on 230-400 mesh silica gel (Aldrich) unless otherwise stated. Microwave reactions were carried out using CEM Discover LabMate. NMR, IR and mass spectra were recorded by the appropriate services of the Toulouse Institute of Chemistry (ICT -FR2599). NMR spectra were recorded with a Bruker Avance 300 or Avance 500 spectrometer and full assignments were made with the assistance of COSY, HMBC and HSQC spectra when necessary. 1 H and 13 C NMR chemical shifts (δ) are reported in ppm relative to the signal of tetramethylsilane (TMS). Residual solvent signals were used as an internal reference. Coupling constants (J) are given in Hz and the following abbreviations have been used to describe the signals: singlet (s); doublet (d); triplet (t); quadruplet (q); quintuplet (quint); multiplet (m). The numbering system used for the assignment of signals in new compounds 5.Tl, 7 and 12 is provided in the supporting information document, along with the corresponding spectra. IR spectra were recorded with a Nicolet 6700 FTIR-ATR. Only selected characteristic peaks are recorded. High-resolution mass spectra (HRMS) were performed with a Waters GCT Premier spectrometer for desorption chemical ionization (DCI/CH4) and with a Waters Xevo G2 QTof spectrometer for electrospray ionization (ESI). Melting points were measured with a Krüss M5000 melting-point apparatus or with a Kofler hot bench and are uncorrected. UV/Vis spectra were recorded with a Shimadzu UV-26000 spectrometer (sh=shoulder, ε [mol -1 dm 3 cm -1 ] is reported in parentheses).

Compound 2:

In a dry tube designed for microwave irradiation and under argon, compound 5.Tl (160 mg, 0.20 mmol, 2.0 equiv.), ruthenium(II) complex 4 (110 mg, 0.10 mmol, 1.0 equiv.) were introduced and degassed anhydrous acetonitrile (4 mL) was added. The tube was sealed and the reaction mixture was heated under microwave irradiation at 100 °C for 3 x 10 min. A pressure of 5 bar was achieved due to the CO evolution and this pressure was released between heating cycles. The completion of the reaction was monitored by TLC. The resulting mixture was diluted with CH2Cl2 and filtered through a pad of silica gel. The solvents were removed under reduced pressure and the residue was purified by column chromatography (CH2Cl2/cyclohexane gradient from 0:100 up to 30:70) to afford compound 2 (128 mg, 0.08 mmol, 82%) as an orange solid. Rf=0.3 (CH2Cl2/cyclohexane 30:70); 1 H NMR (300 MHz, CD2Cl2, 25°C): δ=7.88 (bs, 3H), 7.80 (d,4 J = 0.5 Hz,3H),7.35 (dd,3 J = 8.4 Hz, 4 J = 0.5 Hz, 3H), 7.21 (m, 20H), 7.04 (dd, 3 J = 8.4 Hz, 4 J = 1.4 Hz, 3H), 3.90 (s, 6H), 2.46 (q, 3 J = 7.4 Hz, 6H), 1.27 (t, 3 J = 7.4 Hz, 9H); 13 C NMR (125 MHz, CD2Cl2, 25°C): δ=143.6, 140.2, 137. 8, 135.1, 132.1, 130.6, 122.3, 122.0, 121.9, 120.0, 110.9, 87.1, 37.4, 25.3, 14.3; UV/Vis (CH2Cl2): λmax (ε)= 298 (26800), 312 nm (25600 mol -1 dm 3 cm -1 ); HRMS (ESI+): calcd for C65H54BBr5N6RuS3 [MH] + :1528.8674, found: 1528.8652. The data match those reported in the literature. [11] Thallium hydrotris{6-[(ethylsulfanyl)methyl]indazol-1-yl} borate (5.Tl): 6-[(Ethylsulfanyl)methyl]-1H-indazole 10 (530 mg, 2.76 mmol, 3.0 equiv.), KBH4 (61 mg, 1.11 mmol, 1.2 equiv.) and Tl2SO4 (285 mg, 0.565 mmol, 0.6 equiv.) were successively placed in a dry Young-type Schlenk tube. The mixture was stirred at 140 °C for 1h under an argon stream in an open system, and the Schlenk tube was then sealed and heated for 2h at 180 °C. The mixture was allowed to cool to room temperature. The Schlenk tube was connected to an argon line, and the internal pressure, which had been raised by the evolution of hydrogen gas, was carefully released. Subsequent heating of the closed system during 3h at 180 °C followed by cooling to room temperature yielded a white solid. Chloroform (10 mL) was added and the resulting suspension was transferred to a conical centrifuge tube. After centrifugation at 3000 rpm for 30 min, the supernatant (8 mL) was separated and 8 mL of chloroform were added. The operation was repeated three times. The combined supernatants were evaporated to dryness. The residue was solubilized in a minimum amount of CH2Cl2, and MeOH was then added (v/v = 1:1). The thallium salt 5.Tl crystallized by slow evaporation to give white crystals (392 mg, 0.496 mmol) in 54% yield. 1 H NMR (300 MHz, CD2Cl2, 25°C): δ=8.05 (d, 4 J = 0.8 Hz, 3H, Ha), 8.01 (m, 3H, Hd), 7.62 (dd, 3 J = 8.3 Hz, 4 J = 0.8 Hz, 3H, Hb), 7.11 (dd, 3 J = 8.3 Hz, 4 J = 1.4 Hz, 3H, Hc), 3.93 (s, 6H, He), 2.46 (q, 3 J = 7.4 Hz, 6H, Hf), 1.25 (t, 3 J = 7.4 Hz, 9H, Hg); 13 C NMR (75 MHz, CD2Cl2, 25°C): δ=144.9 (C2), 137.6 (C1), 133.5 (C5), 122.7 (C7), 122.5 (C4), 121.0 (C3), 112.4 (C6), 37.0 (C8), 25.7 (C9), 14.7 (C10); HRMS (ESI-): calcd for C30H34BN6S3 [M-Tl] -:584.2136, found: 584.2136.

Ethyl 1-acetyl-1H-indazole-6-carboxylate (7):

A dry three-necked round bottom flask was successively charged with ethyl 3-amino-4-methylbenzoate 6 (2.0 g, 11.2 mmol, 1.0 equiv.), anhydrous toluene (50 mL), potassium acetate (1.1 g, 12.3 mmol, 1.1 equiv.) and acetic anhydride (3.8 mL, 40.5 mmol, 3.6 equiv.). Isoamyl nitrite (3.0 mL, 22.3 mmol, 2.0 equiv.) was then added dropwise over 15 min. The resulting gelatinous mixture was stirred and heated at reflux for 16h with a 15% NaOH trap. The completion of the reaction was monitored by TLC. The solution was then evaporated to dryness to give an orange-brownish solid. The crude product was dissolved in 50 mL of CH2Cl2, filtered on a pad of silica gel and concentrated under reduced pressure. The residue was purified by column chromatography (CH2Cl2/pentane gradient from 30:70 up to 70:30) to give compound 7 (2.1 g, 9.2 mmol) as an orange solid in 82% yield. Rf=0.6 (ethyl acetate/cyclohexane 30:70); m.p. 95 °C; 1 H NMR (300 MHz, CDCl3, 25°C): δ=9.07 (m, 1H, Hd), 8.15 (d, 4 J = 0.9 Hz, 1H, Ha), 8.02 (dd, 3 J = 8.3 Hz, 4 J = 1.4 Hz, 1H, Hc), 7.75 (dd, 3 J = 8.3 Hz, 4 J = 0.8 Hz, 1H, Hb), 4.43 (q, 3 J = 7.1 Hz, 2H, Hf), 2.80 (s, 3H, He), 1.43 (t, 3 J = 7.1 Hz, 3H, Hg); 13 C NMR (75 MHz, CDCl3, 25°C): δ=171.0 (C8), 166.3 (C10), 139.4 (C1), 138.8 (C2), 131.5 (C5), 129.0 (C7), 125.5 (C3), 120.7 (C4), 117.2 (C6), 61.6 (C11), 23.1 (C9), 14.5 (C12); IR (ATR): ṽ=1715 cm -1 (C=O); HRMS (DCI/CH4): calcd for C12H13N2O3 [MH] + :233.0926, found: 233.0935.

Ethyl 1H-indazole-6-carboxylate (8):

In a dry Schlenk tube under argon were successively added ethyl 1-acetyl-1H-indazole-6-carboxylate 7 (150 mg, 0.65 mmol, 1.0 equiv.), trichloroindigane InCl3 (157 mg, 0.71 mmol, 1.1 equiv.) and anhydrous 1,2-dichloroethane (2 mL). Ethanethiol (60 µL, 0.78 mmol, 1.2 equiv.) and 1,1,3,3tetramethyldisiloxane (TMDS) (353 µL, 1.94 mmol, 3.0 equiv.) were then successively added and the reaction mixture was stirred at room temperature for 16h. The completion of the reaction was monitored by TLC and the reaction medium was then evaporated to dryness. The crude product was dissolved in CH2Cl2 (10 mL), transferred to a separatory funnel and water (3 mL) was added. The layers were separated and the aqueous phase was then extracted with CH2Cl2 (3×5 mL). The combined organic layers were dried over anhydrous MgSO4, filtered, and concentrated under reduced pressure. The crude material was purified by column chromatography (ethyl acetate/cyclohexane 1:1). to afford compound 8 (118 mg, 0.62 mmol) as a white solid in 96% yield. Rf=0.32 (ethyl acetate/cyclohexane 30:70); m.p. 125°C; 1 H NMR (300 MHz, CDCl3, 25°C): δ=10.25 (br s, 1H), 8.28 (m, 1H), 8.15 (d, 4 J = 0.8 Hz, 1H), 7.88 (dd, 3 J = 8.5 Hz, 4 J = 1.3 Hz, AB system, 1H), 7.81 (dd, 3 J = 8.5 Hz, 4 J = 0.8 Hz, AB system, 1H), 4.44 (q, 3 J = 7.1 Hz, 2H), 1.44 (t, 3 J = 7.1 Hz, 3H).; 13 C NMR (63 MHz, CDCl3, 25°C): δ=166. 8, 139.5, 135.0, 129.0, 125.7, 121.6, 120.7, 112.1, 61.3, 14.4; IR (ATR): ṽ=3317 (N-H), 1688 cm -1 (C=O). The data match those reported in the literature. [17]

6-[(Ethylsulfanyl)methyl]-1H-indazole (10):

In a dry Schlenk tube under argon were successively added ethyl 1-acetyl-1H-indazole-6-carboxylate 7 (150 mg, 0.65 mmol, 1.0 equiv.), triiodoindigane InI3 (352 mg, 0.71 mmol, 1.1 equiv.) and anhydrous 1,2-dichloroethane (2 mL). Ethanethiol (0.2 mL, 2.6 mmol, 4.0 equiv.) and 1,1,3,3tetramethyldisiloxane (TMDS) (0.7 mL, 3.9 mmol, 6.0 equiv.) were then added and the reaction mixture was heated at 60 °C during 16h. The completion of the reaction was monitored by TLC and the reaction medium was evaporated to dryness. The crude product was dissolved in CH2Cl2 (10 mL), transferred to a separatory funnel and water (3 mL) was added. The layers were separated and the aqueous phase was then extracted with CH2Cl2 (3×5 mL). The combined organic layers were dried over MgSO4, filtered and concentrated. The product was purified by column chromatography (ethyl acetate/cyclohexane 20:80) to yield compound 10 (107 mg, 0.56 mmol, 86%) as a white solid. Rf=0.3 (ethyl acetate/cyclohexane 30:70); m.p. 66-67°C; 1 H NMR (300 MHz, CDCl3, 25°C): δ=10.09 (bs, 1H), 8.05 (d, 4 J = 0.9 Hz, 1H), 7.71 (dd, 3 J = 8.3 Hz, 4 J = 0.9 Hz, 1H), 7.44 (m, 1H), 7.18 (dd, 3 J = 8.3 Hz, 4 J = 1.4 Hz, 1H), 3.87 (s, 2H), 2.46 (q, 3 J = 7.4 Hz, 2H), 1.25 (t, 3 J = 7.4 Hz, 3H); 13 C NMR (63 MHz, CDCl3, 25°C): δ=140. 4, 138.0, 134.4, 122.7, 122.4, 120.8, 109.6, 36.3, 25.4, 14.3; IR (ATR): ṽ=3183 cm -1 (N-H); HRMS (DCI/CH4): calcd for C10H13N2S [MH] + :193.0799, found: 193.0799. The data match those reported in the literature. [17] Compound 12: Conditions A (classical heating): In a dry Schlenk tube under argon, penta-arylbromide 2 (26 mg, 17 µmol, 1.0 equiv.), palladium(II) acetate (3.9 mg, 17 µmol, 1.0 equiv.), K3PO4 (72 mg, 340 µmol, 20 equiv.), ferroceneboronic acid (156 mg, 680 µmol, 40 equiv.) and 2-dicyclohexylphosphino-2'-6'dimethoxybiphenyl (SPhos) (14 mg, 34 µmol, 2.0 equiv.) were successively introduced and degassed anhydrous toluene (1.5 mL) was added. The resulting suspension was stirred at 100 °C for 48 hours and the completion of the reaction was monitored by TLC. The reaction mixture was allowed to cool to room temperature, filtered on a neutral alumina pad (using CH2Cl2) and evaporated in vacuo. The residue was purified by column chromatography (neutral alumina, CH2Cl2/cyclohexane 30:70) followed (if required) by a recrystallization in a heptane/MeOH mixture (1:1). Complex 12 was obtained as an orange-red solid (6 mg, 2.9 µmol, 17%).

Conditions B (microwave irradiation): In a dry tube designed for microwave irradiation and under argon, penta-arylbromide 2 (50 mg, 33 µmol, 1.0 equiv.), 1,1'-bis(diphenylphosphino)ferrocenepalladium(II)dichloride dichloromethane PdCl2(dppf)CH2Cl2 (27 mg, 33 µmol, 1.0 equiv.), sodium tertbutoxide (71 mg, 740 µmol, 22.5 equiv.), ferroceneboronic acid (57 mg, 246 µmol, 7.5 equiv.) were successively introduced and degassed anhydrous toluene (3.6 mL) was added. The tube was sealed and the reaction mixture was heated under microwave irradiation at 135 °C for 1h (a pressure of 5 bar was achieved). The reaction mixture was allowed to cool to room temperature, filtered on a neutral alumina pad (using CH2Cl2) and evaporated in vacuo. The residue was purified by column chromatography (neutral alumina, CH2Cl2/cyclohexane 30:70) followed (if required) by a recrystallization in a heptane/MeOH mixture (1:1). Complex 12 was obtained as an orange-red solid (30 mg, 15 µmol, 45%). Rf=0.2 (CH2Cl2/cyclohexane 30:70, SiO2); 1 H NMR (500 MHz, CD2Cl2, 25°C): δ=8.11 (br s, ~3H, Ha), 7.92 (bs,3H,Hd),7.36 (m,13H,Hb and Hh),7.20 (d,3 J = 8.5 Hz, 10H, Hi), 6.99 (dd, 3 J = 8.4 Hz, 4 J = 1.3 Hz, 3H, Hc), 4.55 (dd, 3 J = 1.9 Hz, 4 J = 1.8 Hz, 10H, Hj), 4.24 (dd, 3 J = 1.9 Hz, 4 J = 1.8 Hz, 10H, Hk), 3.94 (s, 25H, Hl), 3.90 (s, 6H, He), 2.48 (q, 3 J = 7.3 Hz, 6H, Hf), 1.28 (t, 3 J = 7.3 Hz, 9H, Hg);

Figure 1 .

 1 Figure 1. Structure of the unidirectional and reversible tetraferrocenyl molecular motor 1 and of symmetric Ru(II)-based molecular motors incorporating ester anchoring groups on the scorpionate ligand, and arms of various lengths and nature connected to the cyclopentadienyl core.

Scheme 2 .

 2 Scheme 2. Synthesis of key intermediate 2 starting from pentaphenylcyclopentadiene.

Acknowledgements

This work was supported by the University Paul Sabatier (Toulouse, France), the Centre National de la Recherche Scientifique (CNRS), the Agence Nationale de la Recherche (ANR) (ACTION project ANR-15-CE29-0005) and the European Union by the H2020 FET-OPEN project MEMO (Mechanics with Molecules, Grant N°766864).