Dung Di Caprio
email: dung.di-caprio@chimieparistech.psl.fr

Abdelhafed Taleb
email: abdelhafed.taleb@upmc.fr

Fábio D A Aarão Reis
email: reis@if.uff.br

Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

We study the formation of deposits with dendritic morphology using numerical simulations of a model of electrodeposition and diffusion of the adsorbed material. The model considers a diffusive flux of cations in solution, the instantaneous adsorption and reaction in contact with the film surface, and random walks of mobile atoms on

that surface, with a maximum of G hops per atom and a detachment probability ǫ per neighbor at the current position. For low temperature or large current, which correspond to small G, the deposits are similar to diffusion-limited aggregates growing from the flat electrode; for high temperature or very small current, which are represented by large G or ǫ, the deposits have thick rounded columns with sporadic ramification. In these conditions, the growth direction is controlled by the orientation of the electrode and of the cation flux. For balanced conditions of adsorbate diffusion and current (typically 10 2 G 10 4 and ǫ 0.1, but also for larger G and very small ǫ), the films have a hierarchical dendritic morphology with maple leaf shape. The dendrite tips propagate in directions forming 45 • with the electrode and are formed by three concurrent terraces, as a consequence of the simulations in a simple cubic lattice. The average dendrite size increases as a power law of G and is consequently expected to decrease with the applied current. The lowest energy configurations (terraces) are

shown to be stable within the timescale of crystallization of an atomic layer, but the weakly bonded atoms have sufficiently large mobility to create those configurations.

Thus, the dendritic morphology depends on the interplay between the energetics of the crystal and the electric current, which may help the interpretation of dendrite growth with other crystalline structures. The dendrite shape obtained here resembles those observed in some electrodeposited films of gold, zinc, and palladium, and the effect of the electric current on the dendrite size agrees with observations in electrodeposition of silver and gold. Assuming that the adsorbate diffusion is thermally activated, we propose that the average dendrite size is a ratio between an Arrhenius factor and a power law of the current; this suggests a method to estimate the microscopic energy barrier of diffusion, which may differ from the macroscopic activation energy.

Introduction

In materials science, there is a widespread interest in developing micro and nanostructured surfaces with controlled morphology and special physical and chemical properties. Among the prepared morphologies, hierarchical structures such as dendrites have attracted much interest due to their potential for technological applications such as self-cleaning, 1-4 sensing, [START_REF] Wen | Dendritic nanostructures of silver: Facile synthesis, structural characterizations, and sensing applications[END_REF] and catalysis. 6 The open porous structure of dendrite morphology provides high surface area in contact with the solvent and the control of wetting, optical, and magnetic behaviors. [7][8][9][10] The electrochemical methods are among the cheapest and most accurate techniques to control the dendrite morphology, which results from a coupling between the applied potential or current with several processes such as ion diffusion in the electrolyte, reaction kinetics, nucleation, and growth on the electrode. 11- [START_REF] Yang | Shaping particles by chemical diffusion and reaction[END_REF] The sizes and shapes of the dendrites consequently depend on the ion concentration, the physical properties of the electrode, the temperature, and the variations of the electric current. The dendritic films usually have hierarchical configurations with organized micro or nanostructures such as secondary, tertiary, and in some case quaternary subbranches. In works on electrodeposition of copper, silver, and zinc films, the terms leaf-like, feather-like, flower-like, and cauliflower-like were already used to describe dendrite shapes; this reveals the large variety of observed morphologies and suggests a wide range of physical and chemical behaviors. However, depending on the growth conditions, electrodeposited films may also be compact, with low porosity and with relatively smooth surfaces. In other conditions, the films have highly ramified structures with no organization at short lengthscales, which is similar to diffusion-limited aggregation (DLA) [START_REF] Witten | Diffusion-limited aggregation, a kinetic critical phenomenon[END_REF] or diffusion-limited deposition (DLD). [START_REF] Meakin | Diffusion-controlled deposition on fibers and surfaces[END_REF][START_REF] Meakin | Diffusion-controlled deposition on surfaces: Cluster-size distribution, interface exponents, and other properties[END_REF][START_REF] Uwaha | Aggregation growth in a gas of finite density: Velocity selection via fractal dimension of diffusion-limited aggregation[END_REF] Adsorbate diffusion was shown to be relevant in the initial stages of the electrodeposition of films and nanoparticles [START_REF] Berkes | Electrochemical characterization of copper thin-film formation on polycrystalline platinum[END_REF][START_REF] Gründer | Temperature effects on the atomic structure and kinetics in single crystal electrochemistry[END_REF][START_REF] Ustarroz | A generalized electrochemical aggregative growth mechanism[END_REF][START_REF] Desai | Morphological evolution of nanocluster aggregates and single crystals in alkaline zinc electrodeposition[END_REF][START_REF] Xu | Zinc electrodeposition on polycrystalline copper: Electrochemical study of early-stage growth mechanism[END_REF] and for the growth of dendrites. 11, [START_REF] Nishikawa | Evolution of the Morphology of Electrodeposited Copper at the Early Stage of Dendritic Growth[END_REF][START_REF] Fang | Double-interface growth mode of fractal silver trees within replacement reaction[END_REF][START_REF] Aryanfar | Thermal relaxation of lithium dendrites[END_REF] The effects of adsorbate diffusion were also shown in studies of kinetic roughening of compact electrodeposited films. [START_REF] Alamini | Normal versus anomalous roughening in electrodeposited Prussian Blue layers[END_REF][START_REF] Brandt | Substrate effects and diffusion dominated roughening in Cu 2 O electrodeposition[END_REF][START_REF] Mahboob | On the use of atomic force microscopy and scaling analysis to quantify the roughness of zinc electrodeposits produced from an industrial acid sulfate electrolyte containing glue[END_REF] Adatom diffusion was considered in a model of instability development in electrodeposition [START_REF] Aogaki | Morphological instability in nonsteady galvanostatic electrodeposition I. Effect of surface diffusion of adatoms[END_REF] and in kinetic Monte Carlo (KMC) simulations. [START_REF] Liu | Kinetic Monte Carlo simulation of the electrodeposition of polycrystalline copper: Effects of substrates and deposition parameters on the microstructure of deposits[END_REF][START_REF] Treeratanaphitak | Kinetic Monte Carlo simulation of electrodeposition using the embedded-atom method[END_REF] In a recent work, an electrodeposition model with diffusion of adsorbed atoms was proposed and the formation of a non-porous wetting layer on the electrode was studied. [START_REF] Reis | Crossover from compact to branched films in electrodeposition with surface diffusion[END_REF] Here we extend the simulations of that model to study the properties of the porous films that grow on the wetting layer, with special interest in the conditions for growth of hierarchically organized structures, i. e. the dendrites. For very low or very high diffusivity of the adsorbate, highly porous or compact branches are formed, respectively; in both cases, they are oriented perpendicularly to the substrate and do not have any special type of internal organization.

However, for a certain range of model parameters, we show the formation of dendrites with maple leaf shape. These dendrites are formed by stacking atomic planes which spontaneously grow in various directions, but with a self-organization controlled by the crystallography of the material (i. e. by the lattice structure imposed in the simulations). These features are observed if surface diffusion is facile for weakly bonded atoms, but is severely restricted in low energy configurations, which are effectively stable in the timescale of crystallization of each atomic layer. The results are qualitatively compared with those of electrodeposition of silver, copper, gold, zinc, and palladium; in particular, the results are consistent with the effect of the current on the size of the dendrites of electrodeposited silver and gold. We also propose a method to measure the average dendrite size in the simulated deposits and relate this size to the diffusion length of the adsorbed atoms and, consequently, to the temperature and to the applied current.

The rest of this paper is organized as follows. In Section 2, we define the electrodeposition model and present the interpretation of its parameters. In Section 3, we show the simulation results. In Section 4, we discuss the process of dendrite formation and the dependence of dendrite size on physical parameters. In Section 5, a summary of results and conclusions is presented.

2 Model and methods

Model definition

The model is defined in a simple cubic lattice because it allows time consuming simulation of very large deposits (this would be much more difficult with other geometries). The lattice constant is taken as the unit length of the model; its value is assumed to be close to the size of an atom, i. e. some tenths of a nanometer. The size of the lattice in x and y directions is L and periodic boundary conditions are considered in those directions to avoid finite-size effects. The working electrode (substrate) is at the plane z = 0 and lattice sites with z > 0 initially contain a supported electrolyte.

The electrodeposition is modeled as a sequential aggregation of atoms, each one occupying a lattice site. The aggregation of each atom occurs after a sequence of three steps: (i) diffusion of a cation in solution; (ii) adsorption of the cation on the substrate or on the surface of the film, reduction, and formation of a mobile atom; (iii) relaxation by surface diffusion of the mobile atom during a preset time and permanent aggregation of this atom at the final position of this motion.

In step (i), the cation is released at a position (x, y, h max + 45), with randomly chosen x and y, and with h max defined as the maximal value of z of a previously aggregated particle.

The cation executes an unbiased random walk (RW) to nearest neighbor (NN) sites in the electrolyte, as illustrated in Fig. 1(a). During this RW, the position z cannot exceed h max +45, i. e. the cation is reflected if it reaches that height; this condition is necessary because random walkers in three dimensions have a finite probability of moving forever to regions far from the substrate. [START_REF] Montroll | Fluctuation phenomena[END_REF] Step (ii) takes place when the cation reaches a site in which at least one NN is an aggregated atom or a substrate site. In Fig. 1(a), this first contact with the deposit is at the site immediately above the yellow atom. At this position, the electrochemical reaction immediately occurs and the reaction product occupies the same site; this product is termed a mobile atom. Step (iii) is a RW of the mobile atom, which attempts to execute G hops to NN or to next nearest neighbor (NNN) sites, starting at the position where it was produced. There are two conditions for executing a hop attempt. First, it is possible with probability

P hop = ǫ n-1 , (1)
where n is the number of occupied NN of that position (i. e. NN aggregated atoms plus NN substrate sites) and ǫ is termed the detachment probability per NN. Second, a target site is randomly chosen among the NN and NNN sites of the current position and this target site has to be empty and has to have at least one occupied NN. If some of these conditions is not satisfied, the hop attempt is rejected and the mobile atom remains at the current position.

The first condition means that the mobility of the atom is lower (higher) at points with higher (lower) coordination. The condition that the target site has at least one occupied NN means that desorption is not allowed.

Simulation method

Simulations of the model were performed in lattices with L = 1536 until the maximal height reached the value h max = 1480 (in lattice units). Several values of G from 20 to 10 4 were considered, as well as the DLA case (G = 0). The values of ǫ were between 0.02 and 0.25.

For several set of parameters with 20 ≤ G ≤ 10 4 , 100 different deposits were grown, which allows the calculation of accurate distributions of dendrite size. The number of deposits was 10-20 for G = 5 × 10 4 and several values of ǫ because simulation of large values of G consume a long time, which can amount to weeks for a single deposit. For other parameter sets, a few deposits were grown because they aimed only at distinguishing the type of morphology (namely, dendritic or not).

Simulations were run on Nvidia Tesla K80 graphic cards in the CUDA environment for parallelization. In a simulation step, a total of 2496 cations is simultaneously released above the film, corresponding to the number of processors. In this parallel process, more than one mobile atom may reach the same final site due to the slow update of the memory, which does not signal that site as being already occupied. This case is more frequent when ǫ is small and at sites with a large number of neighbours, in which the residence time of a mobile atom is large. In such case, the actual number of deposited particles is counted and the missing number due to multiple particles on the same site is added by performing supplementary depositions.

Interpretation of the model

Step (i) represents the movement of cations in a supported electrolyte, where the electric field is shielded by a high concentration of inactive ions. [START_REF] Wang | Analytical electrochemistry[END_REF] The use of lattice RWs to simulate the motion of the cations is also justified by their small mean free path in solution, even when there is a depleted layer above the growing film.

Step (ii) represents two processes which are assumed to have very high rates (due e. g.

to negligible energy barriers): the adsorption of the cation and the electrochemical reaction.

For this reason, when the cation reaches the film surface, those processes are modeled as an instantaneous transformation of a cation into a mobile atom. Steps (i) and (ii) form the set of rules of the DLD model, in which the reaction product is immediately aggregated at the point of adsorption (G = 0). [START_REF] Meakin | Diffusion-controlled deposition on fibers and surfaces[END_REF][START_REF] Meakin | Diffusion-controlled deposition on surfaces: Cluster-size distribution, interface exponents, and other properties[END_REF] Step (iii) is a simplified description of the effects of adsorbate diffusion. The number of hop attempts of a mobile atom, G, is expected to be proportional to the time of diffusion of the atom before it is incorporated to the growing crystal. If the temperature increases, the diffusion coefficient of such atom increases, then the relaxation to longer distances is possible. Moreover, if a single electrochemical reaction occurs, the rate of cation reduction is proportional to the current, and so is the rate of crystallization (which is the deposition rate); the increase of the current then leads to a decrease in the relaxation time before crystallization. Thus, the increase of temperature or the decrease of the current is represented by an increase of G in the model.

Note that the present model is of limited mobility, since the aggregation position of an atom is chosen before the incidence of another atom. This is the reason for a finite number of hop attempts. Instead, in collective diffusion models, there is simultaneous particle flux and diffusion of all atoms at the surface of the deposit; in this case, there is no constraint for the diffusion time (or diffusion length) of an adatom. However, any adatom is expected to reach a final aggregation position during the film growth because it will be buried below some crystalline layers. This means that it executes a finite number of hops at the film surface.

The algorithm with a sequential aggregation of atoms (limited mobility) is an approximation that allows the simulation of larger systems.

The probability P hop for the mobile atom to hop to a neighboring point represents the effects of the local surface morphology on the atom mobility. P hop = 1 for the mobile atom on a terrace, since the number of neighbors in the crystalline phase is small (n = 1); otherwise, P hop < 1. If ǫ ≪ 1, then the atoms with high coordination have very low mobility.

In electrodeposition, the adsorbate diffusion may be quite complicated and is very different from the adatom diffusion in metal surfaces growing from vapor. For instance, in silver electrodeposition, it was shown that dendrites grow with the formation of an amorphous phase (∼ 5nm thick) at their tips and the subsequent crystallization of that phase. [START_REF] Fang | Double-interface growth mode of fractal silver trees within replacement reaction[END_REF] Molecular dynamics simulations suggest that water absorption is responsible for maintaining the amorphous phase. [START_REF] Fang | Size-dependent structure transformation from amorphous phase to crystal[END_REF] In lead electrodeposition, polycrystalline nanograins are formed in the dendrite tips, but subsequent alignment and aggregation leads to formation of a single crystal and the propagation or splitting of the dendrite. [START_REF] Sun | Structural and morphological evolution of lead dendrites during electrochemical migration[END_REF] Our model assumes that the adatom mobility in those amorphous or polycrystalline phases is controlled by the parameter G, while the preferential crystallization at points with high coordination is mainly controlled by the parameter ǫ.

For the parameter ǫ in Eq. ( 1), a thermally activated form may be proposed as

ǫ = exp (-E b /k B T ), (2)
where E b > 0 is the activation energy and T is the temperature. For low temperatures or large E b , P hop is very small at points where many neighbors are in the crystalline phase (e.

g. n = 3 or larger). For high T or small E b , P hop slowly varies with the coordination number n.

It is important to observe that both G and ǫ increase as the temperature increases. For this reason, the results in which only one of those parameters vary cannot represent effects of varying the temperature. Since only G is expected to depend on the applied current, the qualitative effects of current variations may be interpreted by varying only this parameter.

Note that several works classify electrodeposition processes as diffusion-controlled or reaction-controlled, but this is not applicable to the present model. That classification is possible in systems where the reaction rate varies and where it competes with ion diffusion in the electrolyte to control the film morphology. For instance, the interplay of these processes in the electrodeposition of silver particles was recently discussed. [START_REF] Yang | Shaping particles by chemical diffusion and reaction[END_REF][START_REF] Yang | Quantitatively relating diffusion and reaction for shaping particles[END_REF] However, our model always represents processes with high reaction rate and considers a third process, viz.

diffusion of the adsorbate.

Results

3.1 Film morphology for small G and ǫ For other small values of ǫ, the film morphology is similar to that for ǫ = 0.05. This is shown in the images of Figs. 6(a) and 6(b) for (G = 500, ǫ = 0.02) and G = 10 4 , ǫ = 0.1 , respectively. The leaf-like dendrites thicken as ǫ increases, but this is a relatively small effect.

For instance, as ǫ changes by a factor 5 (from 0.02 to 0.1), the dendrite thickness increases ∼ 20-30%, while a change of G by a factor 5 leads to an increase in the thickness by a factor larger than 3. These effects are quantitatively described in Sec. 3.4.

At dendrite tips, we observe that three concurrent and perpendicular terraces intersect.

Small interaction regime

Here we analyze the simulation results for very large G and ǫ = 0.25. The large values of ǫ are expected to represent deposition in high temperatures or with small bond energy E b ; see Eq. ( 2). Large values of G correspond to high temperatures or to very small applied current.

If G has thermally activated form, then large G may also correspond to small bond energy of atoms on terraces. Thus, a variety of physical and chemical conditions may be associated to large G and large ǫ, but all them are consistent with large mobility of the adsorbed atoms;

this justifies the term small interaction regime.

First consider the film morphology for G = 5 × 10 4 and four values of ǫ, as shown in Fig. 8. In all cases, we observe a thick wetting layer on the electrode, as shown in Ref.

33. For ǫ ≤ 0.05, dendrites with leaf like shape are formed and propagate in (±1, ±1, 1)

directions, as occurred for smaller G. However, for ǫ ≥ 0.1, thick rounded columns grow vertically above the wetting layer, with sporadic ramification.

The range of parameters with dendrite growth

The size of the dendrites

There are four possible orientations of dendrites in our simulations and their sizes and locations change in different realizations. As a dendrite splits, it is difficult to define precisely which atoms belong to the primary or to the secondary one. For these reasons, the distri- bution of dendrite size (or dendrite thickness) has to be measured with some approximation procedure.

All dendrites propagate in some direction with a vertical (z) component. Thus, the size of a horizontal cross section of a dendrite (i. e. a section with constant z) is of the same order of magnitude as the size of a cross section in a plane perpendicular to the propagation direction. Since this direction forms 45 • with the z axis, the two cross sections differ by a factor √ 2. In order to measure the sizes of the horizontal cross sections, we slice the deposit in planes with fixed z (i. e. parallel to the substrate) and, in each slice, we enumerate the clusters of NN connected atoms and calculate the number of atoms (size) s of each cluster.

The identification of connected clusters is done with the Hoshen-Kopelman algorithm with periodic boundaries in the horizontal plane. [START_REF] Hoshen | Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm[END_REF] The slices are taken only at heights in which the porosity reaches a height-independent value; some plots of film density were provided in Ref. 33. The size distributions obtained with this procedure are termed dendrite size distributions, although we understand that the enhancement factor √ 2 is present. For G = 20, there is a peak at s > 1, but the most probable size is also s = 1; the thickening of some branches is not sufficient to organize their structure. For G ≥ 100, a peak at a position s M ≫ 1 is observed and s M rapidly increases with G. For G ≥ 2000, we also observe the gradual formation of a shoulder at a size ∼ 2s M ; this shoulder appears because the masses of two secondary dendrites (near a point of splitting of the primary branch) may collapse into a single cluster in the sliced deposit.

For the smallest ǫ, we obtain α between 0.76 and 0.78. For ǫ = 0.1, a larger α is obtained.

Figure 14: Average dendrite size as a function of G for ǫ = 0.02 (red squares), ǫ = 0.05 (blue triangles), ǫ = 0.1 (green crosses). Dashed lines are least squares fits of the data for fixed ǫ, with slopes 0.75, 0.78, and 0.86, respectively.

Discussion

Comparison with the morphology of electrodeposited films

The dendrite shapes observed here resemble those observed in the electrodeposition of metals by several authors. Flower-like gold nanostructures were obtained in deposition in positive potential on indium tin oxide (ITO) electrode [START_REF] Ye | Electrochemical growth of flowerlike gold nanoparticles on polydopamine modified ITO glass for SERS application[END_REF] and in cyclic voltammetry on ITO surface funcionalized with a biopolymer. [START_REF] Ye | Template-free and direct electrochemical deposition of hierarchical dendritic gold microstructures: Growth and their multiple applications[END_REF] Similar shapes were observed in electrodeposition of zinc and cobalt, [START_REF] Monzon | Nucleation and electrochemical growth of zinc crystals on polyaniline films[END_REF][START_REF] Monzon | Electrosynthesis of iron, cobalt, and zinc microcrystals and magnetic enhancement of the oxygen reduction reaction[END_REF][START_REF] Liu | Anion effects on the solid/ionic liquid interface and the electrodeposition of zinc[END_REF] with formation of stacked layers in zinc dendrite leaves. [START_REF] Monzon | Nucleation and electrochemical growth of zinc crystals on polyaniline films[END_REF] Nanostructures with flower shape were also shown in electrodeposited palladium films. [START_REF] Maniam | Electrodeposited palladium nanoflowers for electrocatalytic applications[END_REF] Despite the simplifications of our model, this comparison shows that the film morphology obtained here is realistic for some materials in certain growth conditions.

The film morphology in the small interaction limit is consistent with that of copper and zinc electrodeposits: 46-48 at short times, thick layers were formed on the electrode; at long times, thick branches with a small number of ramifications points grew above those layers. In those works, the growth was performed near room temperature, but they took several hours, which suggests that the deposited atoms had long times to move at the film surface. Recently, Ref. 49 showed the formation of a compact layer before the growth of thick branched structures in cooper electrodeposition; in this case, the timescales were much smaller (∼ 1s), but the applied current was also very small. In a study of the early stages of copper electrodeposition, it was shown that the layer formed on the substrate has large crystalline domains, but dendrites are subsequently formed by much smaller crystals. [START_REF] Nishikawa | Evolution of the Morphology of Electrodeposited Copper at the Early Stage of Dendritic Growth[END_REF] This is also consistent with the observations of our model, in which the compact layer represents the initial large crystals.

Microscopic processes in the dendrite growth

Fig. 15 shows a simplified scheme of a dendrite tip with three concurrent terraces and illustrates some elementary steps that contribute to the morphology, propagation, and ramification of this dendrite.

A mobile atom on a terrace can move freely on its surface because P hop = 1 (n = 1).

However, for the formation of a terrace, the mobile atoms with low coordination (n = 1 and

2) have to migrate to long distances and aggregate at the terrace borders; thus, G has to be sufficiently large. Since hops to NNN sites are possible, the hops between two perpendicular terraces occur without energy barriers; see Fig. 15(a). This means that the three terraces at The relative stability of growing terraces may be quantitatively explained by comparing the waiting times of the mobile atoms in each neighborhood with their total time of surface diffusion. The average number of hop attempts for an adatom to move from a site with n neighbors is of order P hop -1 = ǫ -(n-1) ; this may be viewed as the waiting time for detachment from a given neighborhood. The ratio between the number of hop attempts G and this waiting time is

r n ≡ Gǫ (n-1) . (4)
If this ratio is large, then the detached atom probably has a large mobility; if this ratio is ∼ 1 or smaller, the detachment is unlikely. Fig. 16 shows the values of r n with n = 1 . . . 5

for points in the upper boundary of the dendrite region of Fig. 10. In other points of the dendrite region, the values of r n are smaller.

For G ∼ 10 2 , after a detachment event, the number of remaining hops of the mobile atom is probably small. This increases the disorder at the film surface because the atom cannot migrate to high coordination sites. For this reason, the organization of the dendrite structure requires small detachment probability ǫ; note the very small values of r n for n ≥ 3 in Fig. 16. For G ∼ 10 3 -10 4 and relatively large ǫ, the motion of atoms with n = 3 or n = 4 is much more probable; see Fig. 16. However, after a detachment event, the mobile atom can still execute a large number of hops because G is large; thus, the detached atom can move to another point with high coordination. Anyway, note that terrace edge detachment (n = 4)

is not frequent because Gǫ 3 30 for all cases in the dendrite region; Fig. 16.

For G > 10 4 , large values of ǫ also have a disordering effect because atoms can frequently move from high coordination sites; thus, the configurations with three concurrent terraces become unstable. For this reason, dendrites are observed only for small ǫ. The data in Fig. 16 shows that atoms with n = 4 (flat terrace edges) are effectively stable and atoms with n = 3 (kink sites) have very low mobility.

The conditions for dendrite growth

When surface diffusion is negligible (very small G), branched films grow from the substrate and no wetting layer is formed. These films have the same structureless shape of the deposits grown with DLD (G = 0). The only noticeable difference is the increase in the lateral size of the branches; see images for G = 20 in Figs. 2(b), 3(b), and 4(b). In all cases, the growth direction is controlled by the orientation of the substrate and of the plane where cations are released (the top of the simulation cell). The spread of the branches is isotropic in the x and y directions and is a consequence of the propagation of correlations, as expected in any kinetic roughening process. [START_REF] Krug | Origins of scale invariance in growth processes[END_REF] For G ∼ 100 and ǫ ≤ 0.1, surface diffusion begins to play an important role. The dendrites have organized structure, in contrast with the randomly growing branches obtained for small G. The diffusion length of the weakly bonded atoms (n = 1 and 2) is significantly larger than the average interatomic distance, which is the unit length of the model. Thus, these atoms can migrate to relatively stable positions and form low energy configurations. As G increases, the mobile atoms can move to longer distances, which explains the increase in the terrace size; Eq. ( 3).

The dendrite shape of maple leaf is a consequence of the particular choice of a simple cubic lattice for the model simulations. The flat terraces are the configurations of lowest energy in this lattice, which explains their relative stability. The orientations of the cation flux and of the substrate only have the effect of excluding dendrite propagation in the -z direction, which is a shadowing effect.

For large G and ǫ, which is the small interaction limit (Sec. 3.2), the branches are thicker, have infrequent ramification, and propagate in the z direction. The atom mobility in the terrace borders is high. The growth direction is again related to the directions of the substrate and of the plane of cation release, but not related to the crystalline structure. Bifurcations are less frequent in the thicker branches because formation of stable configurations in other directions is difficult.

The dendrite morphology is an effect of the combination of the facile diffusion of weakly bonded atoms and the stability of low energy configurations. This stability depends on the energetics of the crystal and on the timescale in which the atoms can move at the dendrite surface. This is the time of G hop attempts in our model. Physically, this is the characteristic time of crystallization of an atomic layer, which depends on the deposition rate and, consequently, on the applied current. In the electrodeposition of a material such as silver or lead, the atoms with high mobility are those of an amorphous or polycristalline phase, respectively, as discussed in Sec. 2.3.

The formation of a secondary branch occurs when a terrace is formed in a direction which is opposite to the direction of one of the terraces of the primary branch. For instance, if the primary branch propagates in the (1, 1, 1) direction, the formation of a terrace with outer normal -y may lead to the formation of a secondary branch propagating in the (1, -1, 1)

direction. This is consistent with the energetics of the lattice structure.

Since G and ǫ are related to the temperature and to the electric current, a balance between these quantities is necessary to provide high mobility to atoms with low coordination and stability of atoms with high coordination. At very low temperature or with very high current, the atom mobility is negligible at all positions, so that the film has the disordered DLA-like features. Moreover, at high temperatures or with very small applied current, the terrace organization is destroyed.

The balance in other physical or chemical parameters to provide dendrite growth was formerly discussed by other authors. For instance, Ref. 15 analyzed the interplay of reaction rate and ion diffusivity in solution in silver electrodeposition. The balance of non-equilibrium conditions in electrodeposition of several materials was also addressed in Ref. 11, which suggested that the slower growth of flat dendrite surfaces could be a passivation effect or an effect of high mobility of atoms on those surfaces. Our model supports the second interpretation: the high mobility of atoms formed in the flat regions permits their migration to points with lower energy and, consequently, low mobility (no passivation effect is considered in our model).

Relation to models of compact film growth

For G ∼ 10 3 or larger, a wetting layer with very low porosity was shown to be formed on the electrode. [START_REF] Reis | Crossover from compact to branched films in electrodeposition with surface diffusion[END_REF] The roughness and the lateral correlation length of this layer vary in time and with distance as power laws with the same exponents of the stochastic growth equation of Villain, Lai, and Das Sarma. [START_REF] Villain | Continuum models of crystal growth from atomic beams with and without desorption[END_REF][START_REF] Lai | Kinetic growth with surface relaxation: Continuum versus atomistic models[END_REF] Those exponents are also the same of the Clarke and Vvedensky (CV) model for solid-on-solid (non-porous) film deposition, [START_REF] Clarke | Growth kinetics and step density in reflection high-energy electron diffraction during molecular-beam epitaxy[END_REF] in which deposition and collective adatom diffusion take place simultaneously.

In the CV model, the atomic flux is collimated and has a rate F . The terrace diffusion coefficient has the thermally activated form

D = h 0 exp (-E s /k B T ), (5)
where E s is an activation energy and h 0 is a constant, and the diffusion coefficient of an atom with another neighborhood is reduced by a factor ǫ per lateral neighbor (i. e. the same factor of our electrodeposition model). The main parameter to describe the competition between these processes is the diffusion-to-deposition ratio 54,55

R ≡ D F , (6)
since adatom diffusion is the mechanism that brings the system to equilibrium configurations and the flux from vapor is the mechanism that drives the system far from equilibrium.

The parameter G of the electrodeposition model has the same qualitative behavior of R as the temperature varies and as the deposition rate varies; in other words, G represents the competition between adsorbate diffusion (which is enhanced by the increase of the temperature) and the applied current (which is proportional to the deposition rate). Ref. 56 presented a simpler version of this model, in which the flux was collimated and each atom could execute G hop attempts, but with solid-on-solid conditions (no overhangs nor pores)

and with ǫ = 0 (irreversible attachment to lateral neighbors). That model produces films with the same morphology of the CV model if G and R are related as

G ≈ AR ν , (7)
where ν ≈ 0.6 and A is a constant of order 10 -1 which has a weak dependence on ǫ. [START_REF] Reis | Dynamic scaling in thin-film growth with irreversible step-edge attachment[END_REF][START_REF] De Assis | Dynamic scaling and temperature effects in thin film roughening[END_REF] Moreover, the average size of the terraces in that model varies as G 1/2 .

Consequences of the scaling of dendrite size

The qualitative relation between G and the electric current (Sec. 2.3) implies that the average dendrite size decreases as the current increases. This is observed in silver electrodeposition, in which dendrites with a feather-like morphology have tips of larger width as the current decreases. [START_REF] Liu | Regulating silver morphology via electrochemical reaction[END_REF][START_REF] Che | Multifunctional silver film with superhydrophobic and antibacterial properties[END_REF] In the electrodeposition of gold of Ref. 41, the decrease of the negative potential (which typically leads to an increase in the deposition rate) led to a change from a morphology with thick leaves to a morphology with thin dendrites. In the copper electrodeposition work of Ref. 60, as the potential decreases to more negative values and the reduction current increases, particles change from compact shape (in close to equilibrium conditions) to flower-like shape with thick leaves, then to feather-like shape with thin branches, and finally to randomly ramifying shape; this evolution is qualitatively consistent with the effect of the current predicted here.

The increase of branch size with the surface diffusivity (for constant growth rate) was predicted by a theoretical approach to instability development in electrodeposition [START_REF] Aogaki | Morphological instability in nonsteady galvanostatic electrodeposition I. Effect of surface diffusion of adatoms[END_REF] and is consistent with the increase of dendrite size with G. In Ref. 61, the study of the initial Li electrodeposition on Cu showed that lower interaction energy between the adatoms was correlated with the formation of homogeneous films, while higher energy favors dendrite growth. In this case, we understand that the lower interaction energy facilitates adsorbate 29 diffusion, which is consistent with our model.

However, the effect of temperature on dendrite thickness is more difficult to predict from our model. Although the temperature increase facilitates the diffusion of the adsorbate, the diffusivity in solution also increases; this may lead to an increase in the deposition rate and a decrease in the time of crystallization of an atomic layer. Depending on the relative changes of diffusivity on the surface and in solution, an increase or a decrease of the diffusion length on the surface may be observed.

Eq. ( 3) shows that the typical width of a dendrite is w ∼ s 1/2 ∼ G α/2 , where α/2 is between ≈ 0.38 and ≈ 0.43. This is the typical width of the terraces in the dendrite tips.

For large G, we obtain w ≪ G 1/2 , which means that a terrace in a dendrite tip cannot attain the same size as a terrace attains in the growth of a compact film with the model of Ref. 56.

Despite this difference, here we propose that G is related to an effective diffusion-todeposition ratio R as a power law, as in Eq. ( 7); however, we assume that the exponent ν may be different from the value 0.6 of the compact films. We will show that this assumption leads to a simple form for s as a function of the temperature and of the current and suggests a framework to analyze experimental data.

From Eqs. (6), (5), and (7), we have G ∼ exp [-νE s / (k B T )]/F ν . Assuming that the deposition rate F is proportional to the electrodeposition current I and using Eq. (3), we obtain the average dendrite thickness as

s ∼ exp (-βE s /k B T ) I β , β = να. (8)
This relation neglects the effect of ǫ on s (this effect was shown to be small in Sec. 3.4).

If s is measured as a function of the current I, for fixed temperature, Eq. (8) predicts s ∼ I -β ; a fit of s versus I then gives an estimate of β. If the current is fixed and s is measured as a function of the temperature, an Arrhenius plot gives an estimate of the macroscopic activation energy βE s in Eq. (8); this procedure is adopted, for example, in the analysis of temperature dependence of lithium dendrite length in Ref. 26. The combination of these estimates provides an estimate of E S , which is an energy barrier for diffusion on the lowest energy surfaces of the dendrites. In this procedure, note that the activation energy βE s obtained in the Arrhenius plot is a macroscopic value which may be different from the microscopic energy barrier E S ; the correction factor β depends on the relation between size and applied current.

Conclusion

We performed numerical simulations of a model of thin film electrodeposition which is designed to describe effects of diffusion of the adsorbed material. This model was introduced in Ref. 33, which analyzed the growth of a wetting layer at short times and the crossover to a regime of porous film growth. Here we analyzed the film structure in this second regime and addressed the conditions for dendrite formation, which is a morphology of interest for several applications.

The conditions of low temperature or large current correspond to small values of the parameter G in our model, which leads to growth of DLA-like structures. High temperature or very small current are represented by large values of the parameters G and ǫ, in which the deposits have thick rounded columns with sporadic ramification. In these limiting cases, the average growth direction of the branches is controlled by the directions of the electrode and of the cation flux.

For 10 2 ≤ G ≤ 10 4 and ǫ 0.1, the films have a hierarchical morphology with dendrites with maple leaf shape; the same morphology is also obtained with larger G, but the detachment probability ǫ has to be small. The dendrite tips are formed by three concurrent terraces and propagate in directions forming 45 • with the electrode. In this regime, there are balanced conditions of adsorbate diffusion and current. The lowest energy configurations (terraces) are stable within the timescale of crystallization of an atomic layer, but weakly bonded atoms have sufficiently large mobility to migrate to terrace borders and increase the terrace sizes. This means that the dendrite morphology and the direction of propagation are controlled by the energetics of the crystal. The particular dendrite shape obtained here is related to the choice of the simple cubic lattice structure, which facilitates the simulation of large systems. Despite this limitation, that shape is similar to those observed in electrodeposition of gold, zinc, and palladium. Moreover, the conceptual framework developed here may be useful for the analysis of dendrite formation with other shapes.

The average dendrite size was shown to increase as a power law of G and to have a small dependence on ǫ. Thus, this size is expected to decrease with the applied current, in agreement with observations in electrodeposition of silver and gold. Assuming that the adsorbate diffusion is thermally activated, we proposed that the average dendrite size is a ratio between an Arrhenius factor and a power law of the current. This result suggests a method to estimate the microscopic energy barrier of diffusion, which may be different from the activation energy obtained from Arrhenius plots of dendrite size.

A common feature of all growth conditions discussed here is the diffusive flux of cations in solution, which leads to preferential attachment at the protuberant parts of the deposit and shadowing of growth at its valleys. This is essential for the formation of branched structures, organized (dendritic) or not (DLA). Dendritic morphology may also be obtained with mixing and reactions of precursors occur as they execute a diffusive motion; however, the large mean free paths and the presence of a depletion layer near the deposit imply a partially collimated flux (although dendrites may be produced in some conditions [START_REF] Gan | Chemical vapor deposition of Bi-Te-Ni-Fe on magnesium oxide substrate and its Seebeck effect[END_REF][START_REF] Gardecka | High efficiency water splitting photoanodes composed of nano-structured anatase-rutile TiO 2 heterojunctions by pulsed-pressure MOCVD[END_REF]

Figure 1 :

 1 Figure 1: (a) A cation (green circle) in the electrolyte executes a RW whose path is indicated (red line with arrows). The cation stops moving when it reaches a site which has a NN aggregated atom (yellow). Other aggregated atoms are shown in blue color and the substrate is in tan color. (b) Possible hops (red arrows) of two mobile atoms (green), with the respective coordination numbers.

Fig. 1 (

 1 b) shows the directions of the possible hops of two mobile atoms in a deposit [note that only one mobile atom is at the surface at each time, thus two mobile atoms are shown in Fig. 1(b) only for the sake of illustration].

Figure 2 :

 2 Figure 2: Images of deposits grown with G = (a) 0, (b) 20, (c) 100, (d) 500, (e) 2 × 10 3 , (f) 10 4 . In all cases, ǫ = 0.05.

Figure 3 :Figure 4 :

 34 Figure 3: Top view of deposits grown with parameters as in Fig. 2: G = (a) 0, (b) 20, (c) 100, (d) 500, (e) 2 × 10 3 , (f) 10 4 . In all cases, ǫ = 0.05.

Figs. 5

 5 Figs. 5(a)-(f) show magnified views of the regions indicated by square boxes in the top views of Figs. 3(a)-(f).For G ≤ 20, there is only random growth and ramification; no organized structure is formed, even in very small lengthscales. Some degree of organization is observed for G = 100, with small terraces formed at the top of the dendrites. For G ≥ 500, we distinctly observe nontrivial structures in the leaf-like dendrites, which are formed by

Figure 5 :

 5 Figure 5: Side views of 100×100×100 size boxes of the areas indicated in Figs. 3(a)-(f): G = (a) 0, (b) 20, (c) 100, (d) 500, (e) 2 × 10 3 , (f) 10 4 . Cyclic palette is used to help visualization of horizontal terraces.

  The top terraces are visible in Figs.5(d)-(f), which also show the nucleation of new terraces on them. Figs. 7(a)-(c) show magnified lateral views of the regions indicated in Figs. 4(d)-(f), respectively, and confirm the presence of the lateral terraces at the dendrite tips. Two

Figure 6 :

 6 Figure 6: Images of deposits grown with (a) G = 500, ǫ = 0.02, and (b) G = 10 4 , ǫ = 0.1.

Figure 7 :

 7 Figure 7: (a), (b), and (c) show lateral views of the dendrite tips shown in Figs. 5(d), (e), and (f), respectively.

Figure 8 :

 8 Figure 8: Deposits grown with G = 5 × 10 4 and ǫ = (a) 0.02, (b) 0.05, (c) 0.1, and (d) 0.25.

Fig. 10

 10 Fig.10shows the type of morphology observed for each simulated value of G and ǫ. That diagram distinguishes three cases: (i) the regime in which dendrites are formed immediately above the compact wetting layer; as defined above, the term dendrite is used here only for the structures with maple leaf shape propagating in (±1, ±1, 1) directions; (ii) the cases in which the branches predominantly grow in the vertical direction with no internal organization; this may include thin branches with many ramifications (DLD-like shape) or thick branches with rare ramification; (iii) the transition cases in which the previous features coexist in the simulation cell. A smaller number of data points is presented for G = 5 × 10 4 because the simulations are very long in this case.In the range 10 2 ≤ G ≤ 2 × 10 4 , the dendrites are observed for all ǫ ≤ 0.1 and possibly for some larger values of ǫ. For much smaller or much larger G, the dendrites are formed only for small ǫ. In Fig.10, the upper bound of the dendrite region (i. e. the set with the largest ǫ for each G) is not symmetric; thus we did not find any simple relation bewteen G and ǫ to characterize that region.

Figure 9 :

 9 Figure 9: Deposits grown with ǫ = 0.25. (a), (d), (g): side view, top view, and detail of the region indicated in the top view, respectively, for G = 500; (b), (e), (h): side view, top view, and detail, respectively, for G = 2 × 10 3 ; (c), (f), (i): side view, top view, and detail, respectively, for G = 10 4 .

Figure 10 :

 10 Figure 10: Film morphology as a function of G and ǫ, with red stars indicating dendrites with maple leaf shape propagating in (±1, ±1, 1) directions, blue circles indicating thin or thick branches with vertical alignment, and green triangles indicating transient structures. Dashed lines are provided as guide to the eye.

Figs. 11

 11 Figs. 11(a)-(f) show slices taken from deposits grown with the same parameters as in

Figure 11 :

 11 Figure 11: Horizontal slices at height z = 900 of deposits grown with parameters as in Fig. 2: G = (a) 0, (b) 20, (c) 100, (d) 500, (e) 2 × 10 3 , (f) 10 4 . In all cases, ǫ = 0.05.

Figure 12 :Figure 13 :

 1213 Figure 12: Dendrite size distributions P (s) obtained from horizontal slices of deposits grown with parameters as in Fig. 2: G = (a) 0, (b) 20, (c) 100, (d) 500, (e) 2 × 10 3 , (f) 10 4 ; in all cases, ǫ = 0.05.

Fig. 14

 14 Fig.14shows the average dendrite size s as a function of G for the values of ǫ ≤ 0.1

Figure 15 :

 15 Figure 15: (a) Terraces formed at the tip of a dendrite propagating in (1, 1, 1) direction. (b) Stable edges and possible hops of particles with 3 or more NNs. (c) Mobile particles with 2 NNs. Red cubes indicate moving cubes with arrows pointing in possible directions of movement. Bullet symbol indicates (NN) cubes interacting with the moving red cube. Red arrows show average movement of more mobile particles. Black and grey arrows indicate main and secondary directions of aggregating particle flux.

Figure 16 :

 16 Figure 16: The ratio r n between the number of hop attempts and the waiting time with n neighbors as a function of G for three different neighborhoods in the upper boundary of the dendrite region.

  chemical (not electrochemical) methods in solution, as illustrated in Ref. 62. Instead, with any bias in the flux, the formation of non-fractal deposits (with finite porosity) is expected at long times, as illustrated by the model of multiparticle biased DLA; 63 see also Ref. 64 for the case of radial growth. In the extreme case of collimated flux, like in molecular beam epitaxy, compact films are formed. With techniques such as metal organic chemical vapor deposition,

  ). (6) Rashid, M. H.; Mandal, T. K. Synthesis and catalytic application of nanostructured silver dendrites. J. Phys. Chem. C 2007, 111, 16750-16760. (7) Yanpeng, X.; Taleb, A.; Jegou, P. Electrodeposition of cobalt films with an oriented fir tree-like morphology with adjustable wetting properties using a self-assembled gold nanoparticle modified HOPG electrode. J. Mater. Chem. A 2013, 1, 11580. (8) Ye, W. C.; Shen, C. M.; Tian, J. F.; Wang, C. M.; Bao, L. H.; Gao, H. J. Self-assembled synthesis of SERS-active silver dendrites and photoluminescence properties of a thin porous silicon layer. Electrochem. Comm. 2008, 10, 625-629. (9) Zhu, Y.; Zheng, H.; Yang, Q.; Pan, A.; Yang, Z.; Qian, Y. Growth of dendritic cobalt nanocrystals at room temperature. J. Cryst. Growth 2004, 260, 427-434. (10) Sun, G.; Dong, B.; Cao, M.; Wei, B.; Hu, C. Hierarchical dendrite-like magnetic materials of Fe 3 O 4 , γ-Fe 2 O 3 , and Fe with high performance of microwave absorption. Chem. General mechanism for the synchronization of electrochemical oscillations and self-organized dendrite electrodeposition of metals with ordered 2D and 3D microstructures. J. Phys. Chem. C 2007, 111, 1150-1160. (12) Qiu, R.; Zhang, D.; Wang, P.; Zhang, X. L.; Kang, Y. S. Tunable electrochemical preparation of cobalt micro/nanostructures and their morphology-dependent wettability property. Electrochim. Acta 2011, 58, 699-706. (13) Qiu, R.; Zhang, D.; Wang, P. Dendritic core shell structure preparation by a facile consecutive electrochemical crystal growth method. Electrochim. Acta 2012, 81, 112-116.

	Mater. 2011, 23, 1587-1593.

(11) Fukami, K.; Nakanishi, S.; Yamasaki, H.; Tada, T.; Sonoda, K.; Kamikawa, N.; Tsuji, N.; Sakaguchi, H.; Nakato, Y.

Acknowledgment F.D.A. Aarão Reis acknowledges support from Brazilian agencies CNPq (304766/2014-3), FAPERJ (E-26/202941/2015), and CAPES (88881.068506/2014-01).

Supporting Information Available

The files animatedshortlat.avi and animatedshortside.avi have movies with lateral and top views, respectively, of growing dendrite tips, generated with G = 10 4 and ǫ = 0.05. This material is available free of charge via the Internet at http://pubs.acs.org/.


Lénaic Rummler

Mariam Abd

El Sater

Nicolas Blanchard

Vincent Bizet
email: vbizet@unistra.fr

Copper-Catalyzed Regiodivergent Borylation of Fluorinated Alkynes and Palladium-Catalyzed Regiospecific Suzuki-Miyaura cross-coupling

Keywords: Borylation, fluorine, alkyne, copper, regiodivergent

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Nowadays, the synthesis of fluorinated molecules is essential in drug discovery and crop science, with roughly 20% of the marketed drugs being fluoro-pharmaceuticals and more than 50% of agrochemicals containing at least a fluorine atom. 1 It is well established that the incorporation of fluorine or fluorinated motifs into organic molecules will modify the physicochemical properties such as lipophilicity and bioavailability for instance ; they are used as bioisosters and therefore enhance biological activities. 2 Hydrometallation reactions are key transformations in modern organic synthesis to control the stereoselectivity depending on the reaction conditions and the concomitant installation of a metal or metalloid for further functionalizations. 3 Several reports about the hydrometallation of R f -alkynes are known in the literature such as hydrostannylation, hydrosilylation, hydrogermylation, hydroboration, hydrocupration or hydroalumination (Scheme 1,a-c). 4 Surprisingly, in all these methods the major product is formed with introduction of the metal/metalloid (M) on the C-α to the CF3 (Scheme 1), while metalation is reversed with biased substrates such as R f -ynoates where the metal is mainly introduced on the C-β to the R f moiety because of reversed polarization. 5  Scheme 1: Hydrometallation of CF3-alkynes Few years ago, we reported an efficient method for the synthesis and the use of CF3-alkynes 1 in regioselective hydrostannylation, germylation and silylation reactions. 4i-j,6 The regioselectivity of the hydrometallation was mainly controlled by the polarization of the alkyne toward the CF3 moiety either under palladiumcatalyzed or radical conditions. More recently, we identified that less polarized alkynes such as ynamides were suitable substrates to perform palladium-catalyzed regiodivergent hydrogermylation and hydrostannylation reactions, where the regioselectivity of the metalation was controlled by the electronic and steric effects of the phosphorus ligands. 7 Unfortunately, such strategy is not applicable to CF3-alkynes 1, however we capitalized herein on the polarization of 1 and the high regioselectivity of the metalation on the C-α to the CF3 to propose highly selective copper-catalyzed regiodivergent borylation reactions of CF3-alkynes (Scheme 1d). The strategy relies on hydrocupration and borylcupration key steps, with HBpin or B2Pin2 respectively, with regioselective introduction of the copper on the C-α to the CF3 in both cases. [START_REF]For analoguous regioselective borylation of ynoates[END_REF] Thermal selective palladium-catalyzed Suzuki-Miyaura cross-coupling was then developed with α-or β-borylated products.

After a short screening of reaction parameters with CF3-decyne 1a (see supporting information for details), we optimized two sets of conditions for the regioselective introduction of pinacolborane (BPin) on the C-α or C-β to the CF3. In condition A, 9 using CuCl (3 mol%), N-XantPhos (3 mol%), NaOt-Bu (6 mol%) and HBPin (1.1 equiv.) after 16 h at 50 °C in THF, we obtained a 95:5 2a:3a ratio with 81% isolated yield for 2a. In condition B, [START_REF] Ms | General procedure condition B: In a dry Schlenk tube under nitrogen equipped with a magnetic stir bar were introduced CuCl (3 mol%, 0.6 mg, 0.006 mmol), NaOtBu (12 mol%, 2.4 mg, 0.024 mmol) and PMe3.HBF4 (6 mol%, 2.0 mg, 0.012 mmol) in dry THF (2 mL). The reaction mixture was stirred for 15 min at room temperature. The reaction is cooled down to 0 °C and bis(pinacolato)diboron (1.1 equiv., 0.22 mmol, 55.8 mg) was added to the solution. The reaction mixture was stirred for 10 min at 0 °C and then the CF3-alkyne 1 (1 equiv., 0.2 mmol) was added, followed by MeOH (2 equiv[END_REF] using CuCl (3 mol%), PMe3•HBF4 (6 mol%), NaOt-Bu (12 mol%), B2Pin2 (1.1 equiv.) and MeOH (2 equiv.) after 3 h at 20 °C in THF, we obtained a 1:>99 2a:3a ratio with 99% isolated yield for 3a. Unfortunately, use of the same ligand for both conditions A and B led to lower regioselectivity, but still with a clear α:β dichotomy by using HBpin or B2Pin2. Noteworthy, we confirmed that no reaction takes place without catalyst, while a 50:50 2a:3a ratio was obtained in the absence of phosphorous ligand with a very low conversion. With the optimized conditions in hands, we investigated the scope and limitations with conditions A and B. In conditions A (Scheme 2), we noticed that the borylation step is moisture sensitive leading occasionally to the formation of reduced product 4. In some cases, the α-borylated products 2 Scheme 2: Regioselective α-borylation of R f -alkynes. a Isolated yield. b Ratio 2:3 and NMR yield determined by 19 F and 1 H NMR with PhCF3 as internal standard.

were poorly stable over purification, so we engaged the crude mixture in direct Suzuki-Miyaura cross coupling at room temperature and isolated corresponding α-arylated products 5 in good yields. Since previous reports mainly investigated aromatic substrates, 4 we mainly explored aliphatic substrates which gave mostly high selectivity ranging from 77:23 to >99:1 α,Z:β,Z. Protected alcohols (1d-e) or amines (1f-g) are well tolerated, as well as silyl groups (1h). Interestingly, the reaction is also compatible with the replacement of the CF3 by a CF2H (1i) delivering α,Z product 2i in excellent 99% yield. An aromatic alkyne substrate was also evaluated leading to a low 55:45 α,Z:β,Z selectivity (5ka:6ka), with a significant amount of protodeborylation product 4. [START_REF]160 MHz): 29.1[END_REF] Conditions B (Scheme 3) were much more robust and excellent selectivities (up to >99:1) were obtained with formation of β,Z isomer (3a-j). The β-arylated product 6 can be easily prepared following a similar two steps sequence, such as for 6ea obtained in 88% over two steps. Surprisingly, reaction with silylated alkyne 1h did not yield adduct 3h, but only isomer 2h was formed instead in excellent 99% NMR yield and probably because of the very hindered TBDMS group which makes the β-position poorly accessible. The regioselectivity drops a little bit with CF2H (3i) in classical conditions, but it rises a bit more up to 9:91 2i:3i by replacing PMe3 by Phox ligand. With aromatic substrates (1k), the BPin adducts 3 were not very robust, and a slight decrease in selectivity was observed up to 10:90 2k:3k, but the corresponding cross-coupling product 6ka was obtained in 57% yield over two steps. In that case replacing the PMe3 by Phox ligand was detrimental and gave a 50:50 mixture of α:β isomers. Based on previous reports, [START_REF]For analoguous regioselective borylation of ynoates[END_REF] we can propose the following mechanisms (Scheme 4): In both conditions, the first step is the formation of the copper active species Cu-H and Cu-BPin (condition A and B, respectively). The key intermediates are resulted from the cis addition of these last species to the alkyne with in both cases selective introduction of the copper on the carbon adjacent to the CF3 (C-α). In condition A, a transmetallation with HBPin delivers compound 2 with concomitant regeneration of the active Cu-H species. In condition B, an alcoholysis with methanol generates compound 3 and Cu-BPin is regenerated by reaction of Cu-OMe with B2Pin2. Scheme 4: Proposed mechanisms for the regiodivergent borylation of CF3-alkyne.

Both conditions A and B were then scaled up on gram-scale (Scheme 5,a) and the catalyst loading was even decreased to 0.7 mol% of copper without noticeable changes in term of regioselectivity and yield. We then tried to on the formation of a vinyl-copper intermediate 7 (in conditions B) and we envisaged to trap this intermediate with electrophile to generate a tetra-substituted fluorinated alkene 8 (Scheme 5,b). Thus, by replacing the as proton source (condition B) by electrophiles such as MeOSnBu3 or MeI, we obtained products 8aa and 8ab in 35% and 69% yields, respectively. [START_REF] Takemoto | For an example of borylstannylation of alkyne[END_REF][START_REF] Alfaro | For an example of 1,2-carboboration of alkyne[END_REF] Scheme 5: Gram scale regiodivergent borylation of CF3-alkynes and trapping of the vinylcopper intermediate with electrophiles. a Isolated yield. b Ratio 2a:3a and NMR yield determined by 19 F and 1 H NMR with PhCF3 as internal standard.

Finally, we confirmed that α-and β-BPin olefins 2a and 3a could be easily engaged in classical Suzuki-Miyaura cross coupling (Scheme 6). [START_REF]General procedure for Suzuki-Miyaura cross-coupling: A dry Schlenk tube under nitrogen equipped with a magnetic stir bar was charged with boronic ester 2 or 3 (1 equiv., 0.2 mmol), Pd(PtBu3)2 (5 mol %, 5.1 mg), and aryl iodide (1.5 equiv., 1.5 mmol), THF (0.25 mL), Cs2CO3 (3 equiv., 0.6 mmol, 195.5 mg) and H2O (60 µL). The mixture was then stirred at r.t. (with 2) or 50 to 75 °C (with 3) until full consumption of the boronic ester as followed by TLC and 19 F NMR. The mixture was quenched by addition of H2O and extracted three times with EtOAc. Organic layers were washed with brine and dried with MgSO4, filtered, concentrated under reduced pressure and purified by silica gel column chromatography delivering products 5 (from 2) or 6 (from 3). (Z)-(1,1,1-Trifluoroundec-2-en-2-yl)benzene 5aa Prepared from (Z)-4,4,5,5-tetramethyl-2-(1,1,1-trifluoroundec-2en-2-yl)-1,3,2-dioxaborolane[END_REF] After a short optimization, we found that using a catalytic amount of Pd(PtBu3)2 and aqueous solution of cesium carbonate in THF was an efficient system to perform crosscoupling of both 2a and 3a with various aryl-and heteroaryliodides. Interestingly, both isomers react differently, α-BPin isomer (2) readily reacts at room temperature while at least 50 °C is needed to transform the β-BPin isomer (3) as confirmed by sequential regioselective cross-coupling from an equimolar mixture of 2a:3a (see supporting information for details). Cross-coupling proved to be effective with electronically diverse aromatic adducts (5aa-ac and 6aa-ac) in good to excellent yields. Heterocycles are also well tolerated (5ad-ae and 6ad-ae). Noteworthy, introduction of 7-aza-indazole substrate in β position (6ad) requires to increase the reaction temperature up to 75 °C to reach a descent yield of 82%. Furthermore, the use of vinylbromide as coupling partner allowed the formation of dienes 5af and 6af in good yields. We propose that the difference of reactivity of 2a and 3a in cross-coupling reaction is mainly due to difference of electronic density of the carbon bearing the BPin in compounds 2 or 3. Due to the high electron-withdrawing effect of CF3 and BPin group, the C-α to the CF3 in compound 2 is relatively electronically enriched and becomes a competent nucleophile. In contrast, the C-β to the CF3 in compound 3 is rather electron depleted and thus a much weaker nucleophile for Suzuki-Miyaura cross-coupling, which means that the reaction requires higher activation energy. Further studies are underway in our group to verify this hypothesis. In conclusion, we have developed an efficient regiodivergent copper-catalyzed borylation of polarized R f -alkynes, thanks to regioselective hydrocupration and borylcupration key steps. We confirmed the possibility to scale-up the reactions on gram scale while decreasing the catalyst loading, and we proved that vinylcopper intermediate could be trapped with electrophiles. Thermal selective palladium-catalyzed Suzuki-Miyaura crosscoupling was also developed to selectively functionalize α-or βborylated olefins.

Scheme 3 :

 3 Scheme 3: Regioselective β-borylation of R f -alkynes. a Isolated yield. b Ratio 2:3 and NMR yield determined by 19 F and 1 H NMR with PhCF3 as internal standard. c Obtained after cross-coupling reaction with PhI (1.5 equiv.), Pd(PtBu3)2 (5 mol%), Cs2CO3 aq. (3 equiv.), 50 °C. d Phox (6 mol%) was used as ligand.

Scheme 6 :

 6 Scheme 6: Thermal selective palladium-catalyzed Suzuki-Miyaura cross-coupling. a Isolated yield. b NMR yield determined by 19 F and 1 H NMR with PhCF3 as internal standard. c Vinylbromide was used as coupling partner. d Reaction performed at 75 °C.

Acknowledgment

The authors thank the French National Research Agency (ANR) for funding the grant of LR, and Emergence@CNRS for funding grant of MAS. The authors also thank Dr. Didier Le Nouen responsible for the analytical platforms and facilities of LIMA (UMR7042 CNRS-Unistra-UHA) who contributed, by his valuable technical and scientific support, to the achievement of this research project.

Funding Information

This work is supported by the ANR HydroMet project, ANR-18-CE07-0020 grant of the French National Research Agency (ANR).

Primary Data

NO.

Supporting Information

YES (this text will be updated with links prior to publication)

Conflict of Interest

The authors declare no conflict of interest.


Michel ; Loreau
email: michel.loreau@gmail.com

Philippe Jarne
email: philippe.jarne@cefe.cnrs.fr

Jennifer B H Martiny
email: jmartiny@uci.edu

Opportunities to advance the synthesis of ecology and evolution

Keywords: Ecology, Evolution, Synthesis, Concepts, Eco-evolutionary dynamics, 20 Rapid environmental change, Adaptation, Levels of biological organisation, Abrupt 21

Despite decades of research on the interactions between ecology and evolution, 26 opportunities still remain to further integrate the two disciplines, especially when 27 considering multispecies systems. Here, we discuss two such opportunities. First, the 28 traditional emphasis on the distinction between evolutionary and ecological processes 29 should be further relaxed as it is particularly unhelpful in the study of microbial 30 communities, where the very notion of species is hard to define. Second, key processes 31 of evolutionary theory such as adaptation should be exported to hierarchical levels 32 higher than populations to make sense of biodiversity dynamics. Together, we argue 33 that broadening our perspective of eco-evolutionary dynamics to be more inclusive of 34 all biodiversity, both phylogenetically and hierarchically, will open up fertile new 35 research directions and help us to address one of the major scientific challenges of our 36 time, i.e. to understand and predict changes in biodiversity in the face of rapid 37 environmental change. 38 39 Although Darwin, the father of modern evolutionary biology, had a strong interest in 40 ecological issues, ecology and evolution developed historically as separate scientific 41 disciplines, each with its own set of concepts, methods and study objects (Futuyma 42 1986). While ecology is broadly concerned with the interactions between living 43 organisms and their biotic and abiotic environment, evolutionary biology focuses on 44 changes in the intrinsic characteristics, or traits, of these organisms through time under 45 changing environments. As a result of this focus, evolutionary biology built a coherent 46 body of theory that gave rise to the so-called "modern synthesis". This synthesis 47 integrated knowledge from genetics, palaeontology, systematics and morphology, but 48 ecology played a relatively small role, even though the influence of ecological 49 processes on evolution was recognised (Huneman 2019). By contrast, ecology 50 developed a wide range of perspectives, from the dynamics of a single population to 51 the functioning of the entire biosphere, but it is arguably still searching for a general 52 synthesis that includes evolutionary thinking at all scales (Loreau 2010). 53 A number of attempts have been made to bring ecology and evolution closer 54 together over the past 60 years or so (e.g. Pimentel 1961; Hutchinson 1965; 55 Antonovics 1976). The recent emergence of the field of eco-evolutionary dynamics 56 has further contributed to this effort by revealing how the reciprocal interactions 57 between ecology and evolution generate eco-evolutionary feedbacks (Fussmann et al.

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 [START_REF] Martiny | Microbiomes in 296 light of traits: A phylogenetic perspective[END_REF], the species level in this 90 hierarchy is ill-defined and differs from that used for most macroorganisms (Rosselló-91 [START_REF] Rosselló-Mora | The species concept for prokaryotes[END_REF][START_REF] Fraser | The bacterial 259 species challenge: making sense of genetic and ecological diversity[END_REF]. Therefore, there is no fundamental 92 difference between changes in the abundance of different microbial "species" through 93 time -the traditional focus of community ecology -and changes in the relative 94 frequency of different microbial "genotypes" -the traditional focus of evolutionary 95 biology. Indeed, some classic examples of eco-evolutionary dynamics, such as 96 Yoshida et al.'s (2003) predatorprey cycles driven by the "rapid evolution" of clonal 97 algae, could be easily reinterpreted as simple ecological dynamics in which the 98 abundance of different algal "species" changes. A similar issue arises in clonal 99 multicellular organisms (e.g. parthenogenetic freshwater snails: [START_REF] Facon | High Genetic 254 Variance in Life-History Strategies within Invasive Populations by Way of 255 Multiple Introductions[END_REF]. 100 Changes in species abundances and changes in phenotype frequencies generate the 101 same type of effect, i.e. changes in mean trait values. Whether these changes in mean 102 trait values take place at the population or community level is largely irrelevant in the 103 case of microbes, as the two hierarchical levels cannot be distinguished 104 unambiguously. Note that this also challenges the distinction between intra-and 105 interspecific competition, which is widely regarded as a key factor explaining the 106 maintenance of biodiversity [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF].

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Many studies have considered microbial evolution in the laboratory, where 108 particular strains can be examined for new mutations and their effects on fitness 109 [START_REF] Lenski | What is adaptation by natural selection? Perspectives of an 286 experimental microbiologist[END_REF] [START_REF] Arevalo | A reverse 224 ecology approach based on a biological definition of microbial populations[END_REF][START_REF] Chase | Maintenance of sympatric and allopatric populations in free-living 239 terrestrial bacteria[END_REF]. Further, the genetic differences 115 between such lineages yield hypotheses about the ecological distinctions between 116 them [START_REF] Arevalo | A reverse 224 ecology approach based on a biological definition of microbial populations[END_REF]. It is even possible now to detect evolution of free-living 117 microbes in the wild. For instance, a strain of Curtobacterium, dominant in the surface 118 soil, was inoculated into microbial "cages" and transplanted into five sites across a 119 temperature and precipitation gradient [START_REF] Chase | Adaptive differentiation and rapid 241 evolution of a soil bacterium along a climate gradient[END_REF]. After just six months in the 120 field, the strain accumulated genomic mutations, and some mutations occurred in 121 parallel across sites, indicating that some mutations were likely adaptive to the new 122 conditions. Together, these advances reveal a previously unknown structure of fine- The second aspect we wish to highlight is that, to achieve greater integration of 140 ecology and evolution, many concepts used in either discipline could be profitably sensu stricto is generally considered as a process leading to higher fitness as a result 147 of natural selection [START_REF] Williams | Adaptation and natural selection: a critique of some current 333 evolutionary thought[END_REF][START_REF] Gardner | The purpose of adaptation[END_REF], while 'adaptedness' denotes the 148 state of being adapted, but the distinction is not always so clear [START_REF] Lewens | Natural selection and adaptation[END_REF]. It would be particularly useful to further extend and generalise the concept of 156 adaptation to wider ecological contexts. For example, soil microbial ecologists use this 157 concept at the community level to describe an increase in overall microbial activity as 158 temperature changes, an approach that integrates across the mechanisms and 159 timescales involved [START_REF] Bradford | Thermal adaptation of decomposer communities in warming 233 soils[END_REF][START_REF] Nottingham | Annual to decadal temperature adaptation of the soil bacterial 303 community after translocation across an elevation gradient in the Andes[END_REF]. This extension of the 160 adaptation concept is fully consistent with that formally proposed by hierarchical 161 adaptability theory [START_REF] Conrad | Adaptability: the significance of variability from molecule to 248 ecosystem[END_REF][START_REF] Lekevičius | Adaptability and functional stability in forest 284 ecosystems: a hierarchical conceptual framework[END_REF]. Hierarchical

  123scale diversity in microbial communities, while clarifying the absence of a distinct 124 species boundary, which makes it difficult to apply classic evolutionary principles.125To overcome this difficulty, we suggest that more attention should be paid in 126 both ecology and evolution to the general fact that evolutionary and ecological 127 dynamics can have similar effects, to the point of being sometimes indistinguishable 128 in microbes. This could contribute to the development of a more integrative conceptual 129 framework that crosses the traditional disciplinary boundaries. Vellend (2016) 130 proposed that community ecology should be rethought in terms of the same 131 overarching processes as population genetics. His innovative view suggested that the 132 two disciplines might proceed in parallel, as they deal with different levels of 133 biological organisation. Microbes invite us to breakdown this distinction further and 134rethink what ecology is and what evolution is (see also[START_REF] West | Social evolution theory 329 for microorganisms[END_REF] for how social 135 evolution could be considered in microbes). We believe this invitation should be seen 136 as a great opportunity rather than a problem -specifically, an opportunity to develop 137 a conceptual framework that accounts for the intertwining of ecological and 138 evolutionary processes more generally.

  141 generalised to the other -they would serve as 'boundary objects' (Star & Griesemer 142 1989) in their conceptual unification. Nosil et al. (2021) provided an example when 143 applying the concepts of stability and resilience, imported from ecology, to 144 evolutionary biology. Here we propose to go in the other direction by extending the 145 concept of adaptation from evolution to ecology. In evolutionary biology, 'adaptation' 146

  149 Moreover, adaptation is traditionally assumed to take place at the individual or 150 genotype level. Even such a strong proponent of individual-level selection as Williams 151 (1966), however, distinguished between 'organic adaptations' and 'biotic adaptations', 152 which help perpetuate a group or population and open up the possibility of clade 153 selection, a controversial issue (Eldakar & Wilson 2011; Goodnight 2015; West et al.

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  162 adaptability theory generalises adaptation to any process that results in improved 163 performance in response to environmental change in a multilevel hierarchical leading to major, readily observable changes in ecosystem structure 190 and functioning. Interestingly, recent ecological theory predicts that simple 191 competitive communities with high variance in species interaction strength produce 192 coalitions of strong and weak interactors that behave somewhat like superorganisms 193 along environmental gradients, with abrupt species turnover and sharp boundaries 194 between communities, despite the absence of strong functional integration (Liautaud 195 et al. 2019). Furthermore, these communities can exhibit directional dynamics in time, 196 i.e., they are characterised by a maturity function that systematically increases over 197 time, as well as community-level selection in space, i.e. they expand across space by 198 replacing other communities with copies of themselves (Bunin 2021). Thus, we may 199 soon have access to performance measures that will allow us to rigorously define 200 adaptation at the community and ecosystem levels in changing environments. 201 Improved integration of ecology and evolution is likely to require a great deal of 202 theoretical and empirical effort to examine how the various ecological and 203 evolutionary processes operate, interact and combine at multiple scales of time, space 204 and biological levels. But this effort is well worth it, as it would bring enormous 205 benefits. In particular, it would help us to address one the major scientific challenges 206 of our time, i.e. to understand and predict changes in biodiversity in the face of rapid 207 environmental change. The ongoing anthropogenic environmental changes are so 208 widespread, rapid and profound that the historically inherited distinction between 209 ecology and evolution might soon become an obstacle to our understanding of the 210 many consequences of these changes. To meet this challenge, ecology and evolution 211 should join forces and build a broader synthesis adapted to our time.

Acknowledgements

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We thank Andrew Hendry, Philippe Huneman and two anonymous referees for their 215 critical but stimulating comments and discussions. ML was supported by the TULIP