Etienne Pihan
email: etienne.pihan@cea.fr

Mickael Albaric
email: mickael.albaric@cea.fr

Gabrielle Regula
email: gabrielle.regula@univ-amu.fr

Nathalie Mangelinck-Noël
email: nathalie.mangelinck@im2np.fr

Attempt to correlate dislocations network and distribution to macroscale plane rotations in <001> cast-mono ingots

Keywords: silicon, cast-mono, dislocations, crystal orientation, X-ray diffraction, sub-grain boundaries Highlights

Attempt to correlate dislocations network and distribution to macroscale plane rotations in cast-mono ingots

Etienne Pihan, Mickael Albaric, Gabrielle Regula, Nathalie

Introduction

In the cast-mono silicon (cm-Si) process, a pavement of monocrystalline seeds is placed at the bottom of the crucible in order to take up the initial orientation of the seeds [START_REF] Stoddard | Casting Single Crystal Silicon: Novel Defect Profiles from BP Solar's Mono2 TM Wafers[END_REF]2]. Efficiencies measured on cm-Si were first limited due to the presence of structural defects such as parasitic grain nucleation on the walls of the crucible [START_REF] Trempa | Mono-crystalline growth in directional solidification of silicon with different orientation and splitting of seed crystals[END_REF][START_REF] Oliveira | Formation mechanism and properties of twinned structures in (111) seeded directionally solidified solar grade silicon[END_REF] generally by twin formation. Nowadays, the main issue that remains is the control of structural defects like dislocations that can lead to the downgrading of the wafers. Indeed, thanks to seeding, cm-Si shows improved properties [START_REF] Stoddard | Casting Single Crystal Silicon: Novel Defect Profiles from BP Solar's Mono2 TM Wafers[END_REF], but an inhomogeneous distribution of dislocation clusters often results from the contact boundaries of the seed plates [START_REF] Trempa | Mono-crystalline growth in directional solidification of silicon with different orientation and splitting of seed crystals[END_REF][START_REF] Oliveira | Cellular dislocations patterns in monolike silicon: Influence of stress, time under stress and impurity doping[END_REF][START_REF] Oliveira | Recombination Activity of 2D Extended Defects in Monolike Silicon[END_REF]. Dislocations can be either arranged in cellular patterns, in the entire cm-Si ingot and are known as background dislocations [START_REF] Oliveira | Cellular dislocations patterns in monolike silicon: Influence of stress, time under stress and impurity doping[END_REF] or generated on the top of the seeds [START_REF] Tsoutsouva | Segregation, precipitation and dislocation generation between seeds in directionally solidified mono-like silicon for photovoltaic applications[END_REF][START_REF] Tsoutsouva | Mono-like silicon ingots grown on low angle misoriented seeds: Defect characterization by synchrotron Xray diffraction imaging[END_REF], at their junctions on precipitates [START_REF] Tsoutsouva | Segregation, precipitation and dislocation generation between seeds in directionally solidified mono-like silicon for photovoltaic applications[END_REF] and propagate vertically along the growth direction [START_REF] Trempa | Mono-crystalline growth in directional solidification of silicon with different orientation and splitting of seed crystals[END_REF][START_REF] Autruffe | Dislocation generation at nearcoincidence site lattice grain boundaries during silicon directional solidification[END_REF][START_REF] Ekstrøm | Structure and dislocation development in mono-like silicon[END_REF][START_REF] Autruffe | Coincident site lattice bi-crystals growth-Impurity segregation towards grain boundaries[END_REF]12,[START_REF] Trempa | Influence of grain boundaries intentionally induced between seed plates on the defect generation in quasimono-crystalline silicon ingots[END_REF] generating the formation of sub-grain boundaries (SGBs).

In a cm-Si ingot, dislocation cells and SGBs are inserted inside a giant grain generated by the use of large monocrystalline seeds (often larger than 150 x 150 mm 2 surface) making difficult by any characterization technique to cover the wide range of spatial dimensions (from dislocations to grains).

Two dislocation structures are characterized in <001> cm-Si material: a cellular network and complex tilt boundary domains. They differ drastically in terms of electrical activity, which is a major concern for photovoltaic (PV) application. The cellular structure is present in high carrier lifetime areas [START_REF] Oliveira | Influence of processing parameters on the generation and propagation of electrically active crystalline defects in monolike silicon[END_REF] and the complex tilt boundary structure (SGBs) is present in poor carrier lifetime areas [START_REF] Lantreibecq | Détermination de la nature et de l'origine des défauts cristallins dans le silicium monolike[END_REF]. The latter is detected by characterization techniques probing the carrier lifetime such as microwave photoconductance decay (MW-PCD) or photoluminescence (PL) imaging. This is most likely due to the difference of several orders in terms of dislocation density (much higher in sub-grains domains), and of the character of the dislocations.

Dislocations organized in cells and sometimes called background dislocations are either supposed to be associated to thermal gradients during heating and solidification [START_REF] Oliveira | Cellular dislocations patterns in monolike silicon: Influence of stress, time under stress and impurity doping[END_REF] and/or could be frozen-in upon ingot cooling [START_REF] Jiptner | Thermal stress induced dislocation distribution in directional solidification of Si for PV application[END_REF][START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF]. As mentioned above, many local sources for SGBs have been found in the vicinity of the seeds and are systematically depicted as grown-in defects as they multiply along ingot height by increasing the total SGB length, the corresponding surface coverage and the tilt misorientation between subdomains. Lantreibecq et al. [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF] have shown by stressing cm-Si samples in situ in a transmission electron microscope that isolated dislocations (a/2<110>{111} dislocation segments in the cell network) are as mobile as dislocations in Czochralski (Cz) ingots whereas edge type a/2<110> dislocations aligned vertically in SGBs are sessile. Nevertheless, unanswered questions remain, including: why dislocation density in cells is drastically reduced at the seed re-growth interface? Which driving force generates the new threading dislocations in SGBs? Indeed, the multiplication cause is unclear as there is no energy reduction if edge <110> dislocations result from two a/2<110> {111} dislocations by elastic reaction. Krause et al. [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF] have shown that dense dislocation networks in cellular form in the seeds (far from side local sources) could result in sub-grains in the grown area and have correlated this area in seeds to (100) orientation tilt change measured by XRD. The origin of the tilts was attributed by the authors to stress-induced plastic deformation of the seeds, possibly originating from an uneven crucible bottom. This work aims to contribute to the understanding of the mechanisms behind on the one hand, the dislocation network formation and on the other hand, the resulting electrically active crystalline defects in cast-mono ingots grown along the <001> axis. The dislocation array is correlated to the deformation measured by XRD, and the extension of the deformation to the grown volume is analysed. For that purpose, large scale (15.0 cm wide seed and grain) crystal rotation is probed in the seeds. Additionally, those analyses are extended to the grown ingot to check if the crystal orientation is tilting. Rocking curve imaging (RCI) is carried out using synchrotron radiation on wafers of a neighboring brick to study the (001) rotation link with the dislocation networks.

Experimental methods

Cast mono samples

Ingots of various scales grown with the cast-mono process show that their edges are much more prone to defect multiplication with ingot height [START_REF] Oliveira | Recombination Activity of 2D Extended Defects in Monolike Silicon[END_REF][START_REF] Oliveira | Influence of processing parameters on the generation and propagation of electrically active crystalline defects in monolike silicon[END_REF][START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF][START_REF] Cabal | CRYSTALMAX Silicon for High Efficiency / Low-Cost Solar Cells[END_REF]. For this study, the ingot is chosen because it has been extensively characterized [START_REF] Oliveira | Influence of processing parameters on the generation and propagation of electrically active crystalline defects in monolike silicon[END_REF][START_REF] Lantreibecq | Détermination de la nature et de l'origine des défauts cristallins dans le silicium monolike[END_REF][START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF][START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF] and is representative of SGB multiplication along the height in side bricks which is an issue met and identified by industrials trying to develop cm-Si [START_REF] Huang | Growth and Defects in Cast-Mono Silicon for Solar Cells: A Review[END_REF]. The cm-Si ingot used in this study is a 85 kg ingot grown with Cz seeds. The seed pavement is made of four 15.6  15.6 cm 2 main seeds with growth axis oriented in <001> ±2°. The saw damage layer resulting from the preparation of the seeds is removed by KOH etching. A quarter of this ingot has been precisely characterized by PL imaging, dislocation etch pit observation and SGB length measurements. The results and experimental details can be found in [START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF]. At brick scale, PL characterization reveals that electrically active SGBs mainly affect the quality of the top of the ingot.

In order to be able to measure an orientation tilt by X-ray (θ/2θ) method, areas of a cm-Si with no significant SGBs are required in order to be able to acquire a unique diffraction peak angular position. Three slabs from a brick A representing a quarter of ingot are used for XRD measurements (Figure 1.a). The initial Cz seeds orientation is <001> orientation normal to the surface with a precision better than 2° (standard PV specifications). A slab labelled S is chosen in the seed (ingot height H = 0.7 cm), another labelled SG at the start of growth (H = 1.4 cm) and the third one labelled HG close to half of total ingot height (H = 8.9 cm). At 8.9 cm height, the sub-grains cover less than 10% of the grain surface and are mainly positioned at ingot corners (opposite corner to the 0 reference in Figure 1.c) whereas no significant formed SGB can be detected by PL in the seed. Only a small area of SGBs is detected in the SG slab (Figure 1.b bottom right). Each slab is grinded before polishing and chemical attack is used to reveal dislocation etch pits. The brick D from the same ingot (Figure 1.a) is cut into wafers and characterized by rocking curve imaging to probe the different scales required for comparison of orientation tilts in the dislocation cell network [START_REF] Oliveira | Influence of processing parameters on the generation and propagation of electrically active crystalline defects in monolike silicon[END_REF] with the XRD measurements.

Figure 1: (a) Sketch of the 85 kg cm-Si ingot from which brick A is extracted for /2 XRD measurements on three thick slabs cut at H = 0.7 cm, 1.4 cm, and 8.9 cm. Brick D is used for RCI analysis; Photoluminescence images of the 15.6  15.6 cm 2 samples for start of growth (SG) at H = 1.4 cm (b) and half ingot (HG) at H = 8.9 cm (c). Grey scale contrast of the PL images indicates higher (bright) and lower (darker) carrier lifetimes regions. The color legend red, blue and yellow in this paper, refers to half height (HG), start of growth (SG) and seed (S), respectively.

X-ray diffraction (θ/2θ) measurements

The deformation in cm-Si material is measured by X-ray diffraction (XRD) in θ/2θ configuration. Delta Technologies Int'l GMWS (550-300) equipment is used for a measurement of the misorientation with respect to the <001> crystallographic orientation along two X and Y sample axes (Figure 2).

The origin is taken at the ingot center (0 in Figures 1 and2) and X and Y axes are named as depicted in Figure 2.b. According to the seed crystallographic orientation, X is deviated 30° from <110> direction as represented in Figure 2b. The slabs at H = 0.7 cm and 1.4 cm are in one 15.615.6 cm 2 piece and allow probing with our X-ray (θ/2θ) measurement system θx along the X-axis and θy along the Y-axis (Figure 2.a). The slab at 8.9 cm was cut into 25 squared 3.13.1 cm 2 sub-areas and is used to probe biaxial deformations θx and θy for X and Y axes. The nine squared sub-areas used in this study are shown in the image insert in Figure 2.b together with their schematic positions superimposed on the PL image of the sample. Macroscale-length crystal orientation rotations are extrapolated from the slopes of the local misorientation as a function of the distance in either X or Y axes. Altogether, the sample choice allows to probe <001> orientation tilts along two ingot axes (X and Y), seed / growth interface and tilts during growth.

As each slab is grinded prior to measurements, any orientation variation within a sample cannot be attributed to inaccurate flatness of the sample (flatness translated in angle is better than 0.01 degree). Nevertheless, a sample horizontal plane positioning error can exist for each sample compared to the others from both the slab cutting and the grinding step. Considering at maximum a difference of 200 µm on one side of the horizontal slab surfaces, we estimate the surface sample horizontal plane positioning to be better than 0.07 degree even in the worst case. Moreover, an error of the pre-positioning is possible depending mainly on the mechanics (including ball centering), of the order of 0.1 degree. A double measurement of each side after rotating the sample by 180 degrees eliminates this pre-positioning error . For this study, it was possible to reduce the error δ for all measurements on the HG sample thanks to sub-area geometry. An error of less than 0.05 degree is obtained for the HG sample and is lower than 0.1 degree in the case of fullsize S and SG samples for which only one single measurement can be done per position.

Rocking curve imaging (RCI)

This technique can be interpreted as a fully quantitative version of X-ray topography [START_REF] Philip | Three-dimensional rocking curve imaging to measure the effective distortion in the neighbourhood of a defect within a crystal: an ice example[END_REF]. The spatial distribution of the plane structure distortion can be visualized through a series of Xray diffraction topographs recorded at successive rocking angles, which provides a rocking curve of each pixel of the image, from which maps of the integrated intensity, full width at half maximum (FWHM) and peak position (PP) can be generated. These maps measure the local plane distortion.

For rocking curve data acquisition, the wafer sample is positioned to diffract the Si (0 0 4) reflection in the horizontal scattering plane, and the diffracted beam images are recorded with 2.10 -4 degree angular steps by using a CCD camera with optics giving a 1.87 µm image pixel size. The data are treated to extract the maps of integrated intensity and from a peak adjustment, the full width at half maximum (FWHM) and peak position (PP) for each pixel [START_REF] Tsoutsouva | Characterization of defects in mono-like silicon for photovoltaic applications using X-ray Bragg diffraction imaging[END_REF]. The peak position maps provide information on tilts and misorientations. Lattice parameter is assumed to remain homogeneous in the ingot and hence all peak position variations can be attributed to plane orientation tilts.

From the FWHM, the local density of non-geometrically necessary dislocations can be estimated from the Hirsch's formula [START_REF] Hirsch | Mosaic structure[END_REF]:

𝜌 = 𝛽 2 9𝑏 2 (1)
where is the FWHM value and b is the norm of the Burgers' vector of usual glide dislocations.

The RCI data used here are collected to study the dislocations cells in cm-Si ingots. The FWHM maps were discussed in [START_REF] Autruffe | Dislocation generation at nearcoincidence site lattice grain boundaries during silicon directional solidification[END_REF][START_REF] Oliveira | Influence of processing parameters on the generation and propagation of electrically active crystalline defects in monolike silicon[END_REF] in terms of local lattice distortion between cells. Here, the focus is on the PP measurements that give local quantitative values to be compared to the misorientation measurements performed by <001> XRD. The FWHM maps are used to assess the presence of dislocations cell network in the studied areas.

Results

(001) orientation gradient measurement by XRD

The misorientation of {001} lattice planes relatively to the sample surface normal as a function of distance to the center of the ingot are plotted in Figure 3 along the two perpendicular X and Y sample axes. For all samples, it is possible to measure θx and θy along X and Y axes, respectively (Figure 3.a and d). For HG sample, which is cut into sub-areas accordingly to Figure 2.b, additional measurements are performed for θx along the Y axis (Figure 3.b) and θy along the X axis (Figure 3.c). A similar <001> orientation scan on an unused Cz seed results in a flat one value profile for each θx and θy only depending on the cutting planes. Here, all <001> orientation components θx are contained within the [+0.8°; +2.0°] range and θy within the [-0.1°; -0.9°] range thus extending over a range much wider than our accuracy (±0.1 degree).

Looking first at θx results along X axis in Figure 3.a, a linear trend variation along the scan directions X is observed for the three samples revealing the presence of crystal misorientation as a function of the distance from the center of the ingot. Surprisingly, the absolute values of θx and the slope Δθx/Δx do not vary monotonically with ingot height. The sample taken at a position close to the start of growth shows lower values for both absolute value of the misorientation and slope. Keeping aside the absolute values which are more difficult to compare, the orientation gradients (slope Δθx/Δx) are compared. It appears that the seed orientation gradient falls in between the gradient at the start of growth and at half growth meaning that reorganization of the crystal structure along the ingot width and height is taking place at some stages of crystal growth or cooling.

A somewhat similar behavior is found in Figure 3.d for θy measurements along the Y axis. Here again θy and the slope Δθy/Δy do not evolve monotonically with the ingot height. An exception to the linear trend for θy as a function of Y axis is found for sample SG. Here an abrupt change of both the value of θy and sign of Δθy/Δy is observed for Y values between 4.5 cm and 7.5 cm. Values for θy below 4.5 cm are lower than for S and SG samples as is the case for θx along X axis. For Y larger than 7.0 cm, θy values and slope lie in between values for S and HG samples of θy. This exception to the linear behavior is discussed in §4.1 and seems to be associated to liquid silicon infiltration in between ingot seeds. θx (resp. θy) is a rotation around Y axis (resp. X axis). As θy scan along X axis of HG sample in Figure 3.c contains much less radial variation (<0.1°) than θx, we can assert that for this sample, the rotation of the crystal lattice is mainly a rotation around the Y axis along the X direction. From Figure 3, it is found that average crystal orientation gradients Δθx/Δx along X direction and Δθy/Δy along Y direction are significantly larger than Δθy/Δx and Δθx/Δy (Table 1). In the HG sample, an orientation gradient of (-0.04 ± 0.01) degree/cm along X axis and a perpendicular orientation gradient of (-0.05±0.01) degree/cm along Y axis are measured. At mid ingot height, Figure 2.b reveals that some sub-grains are present at ingot edge in that sample. No direct relation with sub-grains can be established using only the XRD experiments. However, significant amounts of SGBs are detected by PL at positions where deformation are larger. Tracking growth axis <001> misorientation over large distances (> 10 cm) shows the existence of small crystal rotations with values of about 0.01 degree/cm with, in the end, quite large misorientation due to the long-distance range it applies and to a cumulative effect. From ingot center to the edge, misorientation change in the same grain in the HG sample is approximately Δθx=0.5° and Δθy=0.6° along X and Y axis, respectively. As each of those misorientations component θx and θy are mainly orthogonal, the top left of the sample in Figure 2.b has a misorientation above one degree relatively to the bottom right corner. For this ingot brick A, the measurements tend to show that {001} plane curvature can be biaxial or axi-symmetrical. Solid/liquid interface shape could be a parameter related to deformations either through interface phenomena or through thermal gradient induced stress in the solid. Here crystal plane curvature is opposite to the interface shape curvature, which is convex. The same method of XRD measurements was applied to other cm-Si samples without SGBs. First, orientation gradients were hardly measurable meaning that cm-Si with low sub-grain amount are not prone to large orientation tilts compared to the one reported in the present manuscript. Second, cm-Si ingots with both concave and convex interface shapes (60kg G2 ingots) were also characterized. No direct relation between melting and solidification interface curvature and crystal orientation gradient curvature sign was found.

The XRD measurements confirm the presence of large-scale plane rotations in seeds of cm-Si as in [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF]. Additionally, slight orientation changes at seed / start of growth interface and further increase of the measured orientation changes with ingot growth are observed. Moreover, a general trend for a linear orientation gradient is observed for the main rotations θx along X, and θy along Y. Deformations can be associated to dislocation networks or linked to the microstructure. In those samples, three types of defects were identified in reference [START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF]: micro twins, background dislocations, and sub-grains (i.e. dislocations walls). No significant sub-grains are present, from PL and etch pit characterizations in the chosen positions where XRD measurements are performed. Thus, those orientation gradients could be associated either to background dislocation density, either to micro-twins.

Orientation gradient measurement by RCI

This technique is carried out to investigate the potential relation between crystal plane curvature, micro-twins and background dislocations organized in cells.

On the brick D from the same ingot, 3  3 mm 2 samples were extracted from the wafers and measured by RCI selecting the Si (0 0 4) planes. Two types of maps are presented in Figure 4. First, the FWHM map (Figure 4

Discussions

Singularities in the orientation gradient slope

In this sub-section the measured orientation gradient θy sign change observed in Figure 3.d for SG sample and plotted in Figure 5 is discussed. A large view optical image after surface etch pit revelation by chemical attack is also used for the discussion. The etch pit image contrast is inversed (areas with more pits appear whiter). The surfaces measured by XRD are identified as blue rectangular areas. At that scale, individual etch pits are not resolved. However, it is possible to conclude that the pit density decreases from the ingot center (left side) to the ingot edge. At the ingot edge, some sub-grains are also visible as continuous lines forming approximate squares with dislocation walls aligned along <110> directions. In-between the two measurements at 4.5 and 7.5 cm, an orientation change occurs that requires a larger crystal deformation. A 1-2 mm wide linear area inclined to the sample edge with darker contrast indicates that in this linear area, there is a lower density of dislocation etch pits. The top side of the etch pit image in Figure 5 is also a seed junction area of the pavement. In the S sample, the remaining seed junction is still present and two behaviors are observed along the Y axis. Between the ingot center O and the location of low etch pit area E, the gap in-between seeds is infiltrated by liquid silicon whereas seed junction is not infiltrated after low etch pit area E in Figure 5. A more localized switch between low/high etch pit density areas is also captured in the S sample. Those observations tend to show that the abrupt change in the <001> crystal orientation is related to seed infiltration, maybe through a local change of mechanical boundary limit conditions (free deformation in unfilled seed junction area) of the seeds. One hypothesis to explain our observations is that non-uniform infiltration could generate different local strain conditions at the level of the seeds.

Also surprising is the fact that the abrupt orientation change observed in the SG sample (Figure 5 and blue plot in Figure 3.d) is not present in the S sample neither transferred to the grown-in ingot. In fact, in the measurement on the following HG slab, the main orientation gradient (slope of the red curve in Figure 3.d) is similar to the two point measurements close to center of SG sample and no trace of an orientation discontinuity is captured by our local measurements at ingot height 8.9 cm. Similarly, the slope of θy in SG sample far from the center is similar to the one in the seed. A change of (001) orientation gradient slope with a locally higher orientation gradient in seed was found in Krause et al. [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF] and correlated to a higher dislocation density and lower cell size characterized by etch pit on a vertical plane of similar samples. In [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF], it also corresponded to a position upon which sub-grain could develop along ingot height. In this work, the local change of θy and of the sign of the slope of Δθy/Δy, is not accompanied by subgrain development in the upper ingot (see PL imaging insert in Figure 5 taken from the corresponding area in the HG sample). The origin of this abrupt orientation change is unknown to the authors and might not be directly compared to the case studied in [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF]. Indeed, it is worth noting that in our sample, area of interest differs from [START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF] from the fact that the misorientation was voluntarily not measured in areas where SGBs are developing, but instead, in areas free from this kind of defects, in order to be able to measure orientation gradient evolution along width and height. One possible reason why defects are not transmitted to the grown ingot in the form of subgrains might arise from the time sequence during growth. In fact, it is likely that the deformation in the SG sample took place close to the seed junction after the start of growth and was not propagated to the solid liquid interface.

Correlation between large scale and local misorientation measurements in relation to the cellular array of dislocations

(001) orientation variation across cm-Si samples can be described as a linear orientation gradient by both XRD ( §3.1) and by RCI ( §3.2). Both techniques characterize very different length scales. Orientation gradients extending over 10 cm distance are characterized by XRD on thick samples (> 5 mm) and continuous orientation changes are quantified by RCI over millimeters of wafers samples with angular precision of 2.10 -4 degree. Given the lower accuracy of the XRD system, the crystal orientation gradients can be measured by XRD only by the cumulative effect of the gradient over the large grain distance. In Figure 6, both measured (001) orientation gradients are compared as a function of the ingot height. Both gradients measured by both techniques on very different scales are of the same order of magnitude between 10 -2 and 10 - 1 degree/cm. As measurements are performed on similar but neighboring brick, a one to one correlation is not expected.

Interestingly, the fact that both measurements are of same order of magnitude suggests that the background dislocations, organized in cellular network as checked by RCI FWHM results ( §3.2), can be at the origin of the orientation gradient at large distance. In our sample consisting of one large grain, it results in relatively large misorientations of more than one degree between domains belonging to the same grain for the only slab HG. Considering sub-grain multiplication from bottom to the top of cm-Si or multi-crystalline (mc-Si) ingots the assumption of an almost perfect, static crystal around sub-grains, implies that those are probably self-multiplying with little interactions with the perfect main crystal. Nevertheless, interactions are mandatory in proposed models [START_REF] Oriwol | Smallangle subgrain boundaries emanating from dislocation pile-ups in multicrystalline silicon studied with synchrotron white-beam X-ray topography[END_REF] and some mobile dislocations interactions with SGBs walls were observed by TEM [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF]. This work might slightly change the perspective as we characterize frozen-in crystal orientation changes over: large distance, several sample axes and along ingot height. Considering the epitaxy over a sub-grain surface, the tilt of the surrounding grain with height surely requires SGB properties evolution with height. In other words, orientation change of the bulk of the grains might be connected to the not well-known subgrain multiplication and densification mechanisms with ingot height.

From a photovoltaic application perspective, the defects in the measured areas do not have a strong impact on the PV efficiency. Indeed, background dislocations in cellular form are hardly captured by carrier lifetime measurement techniques due to a much smaller effect on lifetime than denser sub-grains. Recently, µ-PL was used to characterize defects in particular, sub-grains and dislocations, in silicon ingots [START_REF] Nguyen | Micrometer-Scale Deep-Level Spectral Photoluminescence From Dislocations in Multicrystalline Silicon[END_REF][START_REF] Krenckel | Propagation of Crystal Defects during Directional Solidification of Silicon via Induction of Functional Defects[END_REF]. P. Krenckel [START_REF] Krenckel | Propagation of Crystal Defects during Directional Solidification of Silicon via Induction of Functional Defects[END_REF] observed by µPL a cm-Si monocrystalline area containing dislocations cells and found that the cellular dislocation structure is recombination active to some extend but also conclude that it is unclear if it could limit the material quality for solar cells. Nevertheless, several properties of sub-grains deleterious for the PV properties might be underlined in the view of this new result. For (001) cm-Si growth, the number of dislocations in sub-grain domains are increasing in two ways: by increasing the number of SGBs (walls) and by densifying the dislocations constituting the grain boundaries (increase of misorientation of grain boundaries by rotation about <001> growth axis [START_REF] Ekstrøm | Structure and dislocation development in mono-like silicon[END_REF]). In ref [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF], a sub-grain domain visible by PL on a vertical section was shown to rotate at a rate of 0.12°/cm about the <001> growth axis. Axis rotation differs in SGB from the one measured in the cellular area. Nevertheless, both crystal rotation in this SGB and the measured horizontal large-scale orientation gradient can be considered of similar order of magnitude (measurement in [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF] was made toward the top of ingot). In this work, Figure 6 shows that the orientation gradient increases with height. Additionally, TEM analysis [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF] shows that dislocations forming sub-grains in <001> cm-Si are <001> edge dislocations (Lomer type similar to [START_REF] Bauer | Recombination at Lomer Dislocations in Multicrystalline Silicon for Solar Cells[END_REF]) and lead to sub-grain lattice rotation about <001>. Such dislocations might be formed by elastic reaction of mobile dislocations belonging to different slip planes [START_REF] Lantreibecq | Subgrains, micro-twins and dislocations characterization in monolike Si using TEM and in-situ TEM[END_REF]. The junctions of deformed domains between the cellular and the sub-grain structure are of peculiar importance to check a potential relation to electrically active SGB structure formation. The time at which each defect is formed is a key parameter in this analysis. Sub-grains are believed to be grown-in defects, propagated and multiplied at the solid/liquid (S/L) interface whereas dislocations organized in cells are supposed to have been mobile dislocations frozen-in at some time upon cooling [START_REF] Jiptner | Evaluation of residual strain in directional solidified mono-Si ingots[END_REF].

The growth over FZ seed and cm-Si seed were compared during the heating and growth process through in-situ and post-growth characterization [START_REF] Becker | Investigation of subgrains in directionally solidified cast mono-seeded silicon and their interactions with twin boundaries[END_REF]. The presence of sub-grains with misorientations up to 3° was observed in the regrown part of the cm-seeded sample whereas such behavior was not observed in the regrown part of similar experiments performed with seeds issued from zone melting. It was deduced from observations in [START_REF] Becker | Investigation of subgrains in directionally solidified cast mono-seeded silicon and their interactions with twin boundaries[END_REF] that the cellular dislocation network, present in cm-Si used as a seed, must carry some kind of deformation in relation with the SGB generation. Here we go further by characterizing a large-scale deformation in the form of an orientation gradient that can extend over two different axis. Nevertheless, a clear understanding of physical relation between dislocation cell network and SGB remains an open question.

Orientation gradient and equivalent geometrically necessary dislocations

In this sub-section, the geometrically necessary dislocations (GND) are evaluated to accommodate the measured orientation gradients and their evolution along ingot height is discussed. The FWHM map obtained from RCI (see §3.2) gives local distortion which is not necessarily associated to an organization of the dislocations. This is the non-geometrically necessary dislocations and measures somehow the required density to accommodate distortion with dislocations having possibly Burgers' vectors in opposite directions. On the contrary, the presence of the orientation gradient about <001> can be modelled by an ordering of dislocations at large scale with a summing up effect of dislocations having the same sign of their Burgers' vector edge component. A density of geometrically necessary dislocations can be estimated from the orientation gradient measured by XRD and by RCI peak position values for angle variation lower than 1° by: ρ~2θ/xb (3) where θ/x is the orientation gradient and b is the norm of the Burgers's vector [START_REF] Zhang | Effect of crystallographic orientation on structural response of silicon to femtosecond laser irradiation[END_REF].

Results of GND estimated from equation (3) are summarized in table 2 for the main deformation θx along X axis for the three samples characterized by XRD and for one sample characterized by RCI. The relative trends between samples are well captured here and as for figure 6, the more precise RCI peak position analysis comforts the XRD ones. From table 2, it follows that the GND density required to accommodate measured orientation gradients are in the order of some 10 4 cm -2 . This is in fairly good agreement with literature for best quality areas from electrical point of view in cm-Si. Looking first at the S sample, post-growth dislocations density in those seeds (> 10 5 cm -2 [START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF]) is significantly over calculated GND (3.10 4 cm -2 ). Therefore, there are far enough dislocations in seeds to explain the presence of a crystal lattice tilt. Moreover, a majority of dislocations in seeds does not contribute to the main deformation along the X axis (θx). At the start of growth from the seed, the difference between dislocation density in seeds and GND required to accommodate the orientation gradient in the seed can be a first source of reduction of the density of dislocations at seed / growth interface in cm-Si ingots whereas further discussions on the mechanisms are needed [START_REF] Lantreibecq | Spatial distribution of structural defects in Cz-seeded directionally solidified silicon ingots: An etch pit study[END_REF][START_REF] Krause | Plastic deformation as an origin of dislocations in cast mono[END_REF]. It was found by simulations of a G2 cm-Si ingot process [START_REF] Lantreibecq | Thermomechanical Stress Modelling during Melting and Solidification of a Monolike Ingot Process[END_REF], that the thermal stress in seeds is high at the start of melting step, minimum at the start of growth and then increases during crystal growth because of radial heat flow toward solid silicon. The decrease of geometrically necessary dislocation density at start of growth could fit with this stress decrease between melting and start of growth. Nevertheless our results do not reveal a significant increase of GND density with ingot height and thus with increasing stress during growth. To discuss it further, we would need more information on the time sequence of orientation gradient defect formation. In-situ observation of silicon growth may give fruitful additional information there. In such experiments, before the growth starts on the seed, in the course of melting, and at the very start of growth, the surface of remaining seeds close to S/L interface is a location of active dislocation movements [START_REF] Dias | Dislocation Dynamics in Monocrystalline Si near the Melting Point Studied in Situ by X-Ray Bragg Diffraction Imaging[END_REF][START_REF] Becker | Simultaneous X-ray radiography and diffraction topography imaging applied to silicon for defect analysis during melting and crystallization[END_REF]. Additionally, a darker contrast in the topographic images is also observed at the seed growth interface during those in-situ experiments, thus revealing a localized stress field around the seed / growth interface [START_REF] Becker | Simultaneous X-ray radiography and diffraction topography imaging applied to silicon for defect analysis during melting and crystallization[END_REF]. There is a possibility that reorganization of dislocations in seeds in the vicinity of the S/L interface and at the start of growth could provide the mechanism for the density reduction and orientation gradient evolution at the large grain scale due to the induced high dislocation mobility. Anyhow, a mechanism must be responsible to the fact that between S and SG samples, the crystal is tilting with a dependence on distance from the ingot center.

Conclusion s

Crystal deformation measurements relatively to the [001] growth axis are performed on cm-Si ingot samples by XRD (θ/2θ) over large scale and by RCI. XRD reveals the presence of orientation gradients in the seed, at the start of growth and at mid ingot height. Orientation gradients up to (0.05 ± 0.02) degree/cm extending over 12 cm inside the single cast-mono grain are measured. It is essential to note that within this area investigated by XRD, no significant electrical defects are visible from MWPCD and PL mappings. Nevertheless, dislocations are present and organized in cells. The measured large-scale orientation gradient is quite continuous and constant over each sample axis. One exception with a localized change of slope of the deformation field inside the sample at start of growth is associated with the infiltration of silicon in between seeds. Surprisingly, this higher deformation volume is neither captured by XRD in the seed nor transmitted up in the ingot as a local deformation or sub-grain appearance. By RCI analysis, an orientation gradient of the {001} planes over 3 mm wide samples can also be measured. This gradient is attributed to the presence of a cellular dislocation network and its linear trend has been confirmed with high accuracy. Localized disruptions in the linear trend can be related to the presence of the dislocation walls perpendicular to the orientation gradient scan direction and to micro-twins.

The misorientation between individual cells was previously believed to be a localized misorientation between unit dislocation cells quantified by RCI FWHM without taking into account a large-scale order. In this work, (001) XRD large scale misorientation measurements are compared to more localized and much more precise RCI measurements on the neighboring brick. The fairly good correlation strongly suggests that background dislocations in a cellular form can create the observed organized orientation gradient over large distance. In our sample consisting of one grain, it results in relatively high misorientations between domains belonging to the same grain (greater than one degree) by summing two perpendicular deformations over two perpendicular horizontal axes.

The geometrically necessary dislocation (GND) density to accommodate the measured orientation gradients are evaluated in the order of some 10 4 cm -2 which corresponds to experimental data in the literature in regions of re-growth from seeds without sub-grains in cm-Si. For seeds, post-growth dislocation density is significantly higher than the calculated GND. The fact that a majority of seed dislocations does not contribute to its main deformation may be one significant parameter influencing the reduction of dislocations at seed re-growth interface during cm-Si seeding process.

An enthusiastic perspective of the present work would be to investigate whether the orientation gradients measured in the cm-Si grain are connected to the SGBs domains through misorientation mappings around sub-grains domains. For this, a larger scale RCI on complementary vertical and horizontal sample fields might be the ideal tool to investigate in depth potential relations between orientation gradients in the area where dislocations cells are present as well as the sub-grain domains. In-situ studies could also contribute to explain the transmission of dislocations at the S/L interface and the dynamics of sub-grain formation.

Figure 2 :

 2 Figure 2: Sketch of θx and θy defined as the misorientation of {001} planes relatively to the sample surface normal (a), X and Y axes are taken along the edges of the 15.6 cm size slab with origin at the ingot center, and measurements are performed at (X, Y) positions at a distance of 1.5 cm from the edges (see dotted line) (b). θx and θy (X and Y directions, respectively) are measured for all samples.

Figure 3 :

 3 Figure 3: Misorientation relative to <001> as a function of the distance to the center of the ingot along the X and Y axes. θx in X direction (a) θx in Y direction (b) θy in X direction (c) θy in Y direction (d). Seed (S), start of growth (SG) and half ingot (HG) labels correspond to ingot heights of 0.7 cm, 1.4 cm and 8.9 cm, respectively.

  .a) gives the local plane distortion between cells in degrees. The local deformations are arranged in a cellular form that corresponds to cellular arrays of dislocations. The corresponding peak position map (Figure 4.b) reveals the presence of an orientation gradient from bottom left to the top right of the reconstructed map. A line scan along the white arrow in Figure 4.b shows that the peak position gradient is almost linear (Figure 4.c). On top of the linear trend for the variation of the peak position, abrupt changes of the PP are related to the presence of dislocation cell walls perpendicular to the scan line. Indeed, the position of the abrupt PP changes (see for example the PP variations between P1 and P2) correspond to the dislocation cell walls revealed by the FWHM map. The vertical bands clearly seen on the right side of Figure 4.a reveal the presence of micro-twins. The corresponding local orientation difference at their level is also revealed on the PP map (Figure 4.b). The micro-twins are not modifying the general trend of the evolution of the crystal orientation presented in Figure 4.c.

Figure 4 :

 4 Figure 4: RCI measurements on 3 × 3 mm 2 cm-Si wafer from brick D at ingot height 11 cm; (a) FWHM (full width half maximum) map; (b) corresponding peak position (PP) map; (c) graph corresponding to the line-scan along the white arrow in b). Positions P1 and P2 are indicated in (a) with red arrows. g=004.

Figure 5 :

 5 Figure 5: θy in Y direction for the SG sample (H = 1.4 cm), etch pit scanner image with XRD measurement positions (blue vertical rectangles) at SG sample surface. Note that the etch pit image has an inverse contrast meaning that areas of higher pit density appear whiter. PL imaging of corresponding area in half growth (HG) sample. The grey horizontal straight line corresponds to a GB induced by a seed junction of the pavement.

Figure 6 :

 6 Figure 6: Plot of the average large-scale orientation gradients Δθx/Δx and Δθy/Δy measured on brick A samples compared to the peak position evolution measured by RCI on wafer samples (3 × 3 mm 2 ) from brick D as a function of the ingot height.

Table 1 :

 1 Summary of the average orientation gradients for each orientation component and direction extracted from Figure3, as a function of the ingot height H. *See Figure3.d, there are two different slopes over sample length.

	H	dθx/dx	dθx/dy	dθy/dx	dθy/dy
	cm	° /cm	° /cm	° /cm	° /cm
	0.7	-0.03 ± 0.02	N.A.	N.A.	-0.01 ± 0.02
	1.4	-0.02 ± 0.02	N.A.	N.A.	*
	8.9	-0.04 ± 0.01	0.01 ± 0.01	0.00 ± 0.01	-0.05 ± 0.01

Table 2 :

 2 Summary of the estimated GND density from equation (3).

		<001>	Estimated
	Ingot height	orientation
		gradient	GND
	cm	°/cm	cm -2
	0.7 (XRD)	-0.03 ± 0.02	~ 3.10 4
	1.4 (XRD)	-0.02 ± 0.02	~ 2.10 4
	8.9 (XRD)	-0.04 ± 0.01	~ 4.10 4
	11 (RCI)	0.021 ± 0.001	~ 2.10 4

Acknowledgements

The authors would like to thank the team of the ESRF BM05 beamline for its support and in particular, Thu Nhi Tran and José Baruchel.

Funding

RCI were performed at ESRF by T.N. Tran-Thi and V.A. Oliveira in the frame of a CEA funded Carnot project/SiDeRA.

Author contributions


Asma Grira

Cornelia Amarandei

Claudiu Roman

Oumaya Bejaoui

Nouha Aloui

Gisele El Dib

Cecilia Arsene

Iustinian G Bejan

Romeo I Olariu

André Canosa

Gisèle El Dib

Alexandre Tomas
email: alexandre.tomas@imt-nord-europe.fr

Gas-Phase Ozone Reaction Kinetics of C-5-C-8 Unsaturated Alcohols of Biogenic Interest

Keywords: unsaturated alcohols, Green Leaf Volatile (GLV), ozonolysis, absolute kinetic method, relative kinetic method, Structure Activity Relationship (SAR) approaches

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

Introduction

It is widely accepted that ozone plays a key role in controlling both atmospheric chemistry and climate change. This is due to its oxidative and light-absorbing properties which present a threat for all the ecosystem elements [START_REF] Reich | Quantifying Plant Response to Ozone: A Unifying Theory[END_REF]2 and to its role in producing hydroxyl (OH) radical which initiates the majority of oxidation processes in the atmosphere [START_REF] Finlayson-Pitts | Atmospheric Chemistry of Tropospheric Ozone Formation: Scientific and Regulatory Implications[END_REF] . Therefore, ozone reactivity has been a subject of intensive studies and continues to be of significant concern worldwide. Background ozone concentrations in remote areas are generally within a few µg m -3 , yet, in many locations, they have been shown to increase steadily in the past decades partly due to increased global emissions of nitrogen oxides (NOx) and volatile organic compounds (VOCs) [START_REF] Bortz | Water Vapor, and Temperature in the Upper Tropical Troposphere: Variations over a Decade of MOZAIC Measurements[END_REF][START_REF] Sicard | Spatiotemporal Trends in Ground-Level Ozone Concentrations and Metrics in France over the Time Period 1999-2012[END_REF][START_REF] Jenkin | Trends in Ozone Concentration Distributions in the UK since 1990: Local, Regional and Global Influences[END_REF][START_REF] Cooper | Multi-Decadal Surface Ozone Trends at Globally Distributed Remote Locations[END_REF] .

Unsaturated alcohols or alkenols are VOCs emitted by numerous plants due to biological activity (photosynthesis, transpiration…) and cell decomposition [START_REF] Kleist | Irreversible Impacts of Heat on the Emissions of Monoterpenes, Sesquiterpenes, Phenolic BVOC and Green Leaf Volatiles from Several Tree Species[END_REF] . More specifically, C6 and C9 compounds have been shown to be ubiquitous species characterizing the emissions of plants, with stronger releases under biotic and abiotic stresses with transient emission rates up to 2 orders of magnitude larger than monoterpenes [START_REF] Heiden | Emissions of Oxygenated Volatile Organic Compounds from Plants Part I: Emissions from Lipoxygenase Activity[END_REF] . Once in the atmosphere, the double bond present in the carbon skeleton makes such alcohols quite reactive towards the atmospheric oxidants, thus contributing to the oxidative capacity of the atmosphere. While reactions of unsaturated alcohols with OH radical are relatively well known [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] , reactions with ozone have been less investigated and uncertainties remain on their reactivity and atmospheric impact. These latter reactions make unsaturated alcohols relatively short-lived (atmospheric lifetimes around minutes to hours) [START_REF] Atkinson | Gas-Phase Tropospheric Chemistry of Volatile Organic Compounds: 1. Alkanes and Alkenes[END_REF] and usually associated with the formation of organic acids [START_REF] Horie | Gas-Phase Ozonolysis of Alkenes. Recent Advances in Mechanistic Investigations[END_REF] , organic hydroperoxydes [START_REF] Hellpointner | Detection of Methyl, Hydroxymethyl and Hydroxyethyl Hydroperoxides in Air and Precipitation[END_REF] , and secondary organic aerosols [START_REF] Dwyer | The Gas-Phase Ozonolysis of 1-Penten-3-Ol, (Z)-2-Penten-1-Ol and 1-Penten-3-One: Kinetics, Products and Secondary Organic Aerosol Formation[END_REF] (SOA) which often appear as a haze over forests [START_REF] Graedel | Terpenoids in the Atmosphere[END_REF] .

Regarding O3 + alkenols literature kinetics data, only ambient temperature rate coefficients have been reported. The kinetics of cis-2-penten-1-ol was first investigated by Grosjean and Grosjean [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] , but the obtained value for the rate coefficient (1.69±0.25)×10 -16 cm 3 molecule -1 s -1 is inconsistent with two more recent studies [START_REF] Dwyer | The Gas-Phase Ozonolysis of 1-Penten-3-Ol, (Z)-2-Penten-1-Ol and 1-Penten-3-One: Kinetics, Products and Secondary Organic Aerosol Formation[END_REF][START_REF] Kalalian | Temperature Dependent Kinetic Study of the Gas Phase Reaction of Ozone with 1-Penten-3-Ol, Cis-2-Penten-1-Ol and Trans-3-Hexen-1-Ol: Experimental and Theoretical Data[END_REF] which reported (1.15±0.07)×10 -16 cm 3 molecule -1 s -1 and

(1.05±0.20)×10 -16 cm 3 molecule -1 s -1 , respectively. The O3 kinetics of trans-2-hexen-1-ol was recently studied by Gibilisco et al. [START_REF] Gibilisco | FTIR Gas Kinetic Study of the Reactions of Ozone with a Series of Hexenols at Atmospheric Pressure and 298[END_REF] and Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] . The obtained rate coefficients differ by almost a factor of 3, with values of (0.60±0.07)×10 -16 cm 3 molecule -1 s -1 and (1.66±0.22)×10 -16 cm 3 molecule -1 s -1 , respectively. The rate coefficients for the reaction of O3 with trans-3-hexen-1-ol measured by Gibilisco et al. [START_REF] Gibilisco | FTIR Gas Kinetic Study of the Reactions of Ozone with a Series of Hexenols at Atmospheric Pressure and 298[END_REF] , Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] and Kalalian et al. [START_REF] Kalalian | Temperature Dependent Kinetic Study of the Gas Phase Reaction of Ozone with 1-Penten-3-Ol, Cis-2-Penten-1-Ol and Trans-3-Hexen-1-Ol: Experimental and Theoretical Data[END_REF] are (5.83±0.86)×10 -17 , (6.19±0.72)×10 -17 and (6.24±1.37)×10 -17 cm 3 molecule -1 s -1 , respectively. For cis-3-hexen-1-ol, the study of Grosjean et al. [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Alcohols, Esters, and Carbonyls[END_REF] is about twice higher than those of Atkinson et al. [START_REF] Atkinson | Rate Constants for the Gas-Phase Reactions of Cis-3-Hexen-1-Ol, Cis-3-Hexenylacetate, Trans-2-Hexenal, and Linalool with OH and NO3 Radicals and O3 at 296 ± 2 K, and OH Radical Formation Yields from the O3 Reactions[END_REF] , Gibilisco et al. [START_REF] Gibilisco | FTIR Gas Kinetic Study of the Reactions of Ozone with a Series of Hexenols at Atmospheric Pressure and 298[END_REF] , Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] , and Chen et al. [START_REF] Chen | An Experimental Kinetic Study and Products Research of the Reactions of O3 with a Series of Unsaturated Alcohols[END_REF] , raising the concern about the kinetic rate coefficients obtained for cis-2-penten-1-ol by Grosjean and Grosjean [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] . The rate coefficient for the reaction of O3 with trans-4-hexen-1-ol was measured only by Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] , who reported (1.05±0.21)×10 -16 cm 3 molecule -1 s -1 . For 1-octen-3-ol ozonolysis, to the best of our knowledge, only Li et al. [START_REF] Li | Kinetic Study of the Gas-Phase Reaction of O3 with Three Unsaturated Alcohols[END_REF] investigated the kinetics. Table S1 summarizes the above available literature data.

The objective of this work was thus to investigate the ozone kinetics of a series of seven unsaturated alcohols from C5 to C8:

𝑐𝑐𝑐𝑐𝑐𝑐 -2 -penten -1 -ol + O 3 → Products (1) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐 -2 -hexen -1 -ol + O 3 → Products (2) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐 -3 -hexen -1 -ol + O 3 → Products (3) 𝑐𝑐𝑐𝑐𝑐𝑐 -3 -hexen -1 -ol + O 3 → Products (4) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐 -4 -hexen -1 -ol + O 3 → Products (5) 1 -octen -3 -ol + O 3 → Products (6) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐 -2 -octen -1 -ol + 𝑂𝑂 3 → Products (7)
Two complementary experimental setups were implemented using absolute and relative kinetics methods.

The results will help resolving the inconsistencies noted above on the rate coefficients and better understand the atmospheric impacts of such compounds in the context of increasing O3 background concentrations and climate change. Note that this work represents the first investigation of trans-2-octen-1-ol + O3 kinetics. Further, developing structure-activity relationships (SAR) for atmospheric chemistry models needs consistent and extended kinetic databases to which the present work aims to contribute, especially the effect of the position of the double bond with respect to the -OH functional group. Four different SAR approaches proposed in the literature [START_REF] Atkinson | Kinetics and Mechanisms of the Gas-Phase Reactions of Ozone with Organic Compounds under Atmospheric Conditions[END_REF][START_REF] Calvert | The Mechanisms of Atmospheric Oxidation of the Alkenes[END_REF][START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF][START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] were tested against alkenols ozonolysis kinetics, including the present results.

Experimental part

Pseudo first order kinetic set-up (Douai Teflon chamber)

A series of kinetic experiments for cis-2-penten-1-ol, trans-2-hexen-1-ol, trans-3-hexen-1-ol, cis-3-hexen-1-ol, 1-octen-3-ol and trans-2-octen-1-ol were performed in a Teflon chamber of about 300 L at a temperature of 296±2 K and atmospheric pressure of purified air [START_REF] Szabo | Kinetics of The •OH-Radical Initiated Reactions of Acetic Acid and Its Deuterated Isomers[END_REF][START_REF] Crunaire | Use of Cw-CRDS for Studying the Atmospheric Oxidation of Acetic Acid in a Simulation Chamber[END_REF] . This chamber is equipped with inlet and outlet ports used for introducing reactants and taking samples from the reaction mixture. All the connections between the reaction chamber and the instruments were operated via Teflon tubes. Liquid aliquots of alcohols were first vaporized in the chamber under a stream of pure air and the mixture was left to stabilize for ∼1h. Preliminary tests were dedicated to the study of alcohol stability in the reactor. Wall losses of alcohols appeared to be negligible in the present conditions (loss rate < 3% per hour for all alcohols). Ozone was produced separately by an O3 generator (C-Lasky C-010-DTI) based on electrical discharge on pure zero air flow. After stabilization of the alcohol inside the chamber (1σ of three measurements by Fourier Transform Infrared (FTIR) spectroscopy below 3%), a few tens of mL of O3 were sampled with a gas syringe and added to the reaction mixture under a high flow of air (about 20 L min -1 ), thus enhancing the prompt mixing of the reactants and starting the reaction.

Pseudo-first order conditions were set up with alcohol initial concentrations [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 ((0.34-3.6)×10 14 molecules cm -3 ) in excess (at least 10 times higher) over that of ozone [𝑂𝑂 3 ] 𝑡𝑡 0 ((1.4-17)×10 12 molecules cm -3 ). The alcohol concentration can thus be assumed to be constant during the experiment. Eq. 1 describes the ozone concentration decay taking into account the ozone wall loss rate (kw in s -1 ).

-

𝑑𝑑[𝑂𝑂 3 ] 𝑡𝑡 𝑑𝑑𝑡𝑡 = 𝑘𝑘 × [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 × [𝑂𝑂 3 ] 𝑡𝑡 + 𝑘𝑘 𝑤𝑤 × [𝑂𝑂 3 ] 𝑡𝑡 (Eq. 1)
with k the rate coefficient for the reaction between the studied alcohol and O3 and [𝑂𝑂 3 ] 𝑡𝑡 is the concentration of ozone at time t. Eq. 1 can be simplified into:

- 𝑑𝑑[𝑂𝑂 3 ] 𝑡𝑡 𝑑𝑑𝑡𝑡 = 𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 × [𝑂𝑂 3 ] 𝑡𝑡 (Eq. 2)
where kobs = k × [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 + kw is the pseudo-first-order rate constant. Integrating Eq. 2 yields:

𝑎𝑎𝑡𝑡 � [𝑂𝑂 3 ] 𝑡𝑡 0 [𝑂𝑂 3 ] 𝑡𝑡 � = 𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 × 𝑡𝑡 (Eq. 3)
Plotting 𝑎𝑎𝑡𝑡 � Primary products from reactions of unsaturated compounds with O3 are mainly carbonyls [START_REF] Johnson | The Gas-Phase Ozonolysis of Unsaturated Volatile Organic Compounds in the Troposphere[END_REF] .

Potential interferences from these carbonyls in the O3 analyzer are expected to be negligible since the absorption cross section ratios between ozone and carbonyls at 253.7 nm (detection wavelength of the O3 analyzer) are in the range of 400 to 4000 [START_REF] Turnipseed | Use of a Heated Graphite Scrubber as a Means of Reducing Interferences in UV-Absorbance Measurements of Atmospheric Ozone[END_REF] . Hence, carbonyl absorption will be negligible compared to that of ozone. Consistently, Peters et al. [START_REF] Peters | Development of a New LOPAP Instrument for the Detection of O3 in the Atmosphere[END_REF] found no interferences for commercial ozone monitor for a series of VOCs including alcohols and carbonyls.

Concentrations of cis-2-penten-1-ol, trans-2-hexen-1-ol, trans-3-hexen-1-ol, cis-3-hexen-1-ol, 1-octen-3-ol and trans-2-octen-1-ol were measured in the following IR ranges, respectively: 960-1081 cm -1 , 956-1032 cm -1 , 934-1000 cm -1 , 997-1096 cm -1 , 913-940 cm -1 , and 900-1050 cm -1 .

Relative rate kinetic set-up (Iasi ESC-Q-UAIC reaction chamber)

A series of kinetic experiments for trans-2-hexene-1-ol, trans-3-hexen-1-ol, cis-3-hexen-1-ol, and trans-4-hexene-1-ol were performed at 298 K and 1 atm of air pressure, using the facilities of the Environmental Simulation Chamber made out of Quartz from "Alexandru Ioan Cuza" University of Iasi (ESC-Q-UAIC), Romania. The reactor consists of three quartz tubes with a total length of 4.1 m and a total volume of 760 L. The homogeneous mixture of compounds inside the reactor is achieved by two Teflon fans. The reactor can be evacuated down to 10 -2 mbar. Both ends are closed with anodized aluminum flanges and are provided with multiple inlet and outlet ports.

A Bruker Vertex 80 FT-IR spectrometer was used for collecting IR spectra over a White type mirror system with an optical path length of 492 m at a resolution of 1 cm -1 . A more detailed description of the reactor can be found in literature [START_REF] Roman | Investigations into the Gas-Phase Photolysis and OH Radical Kinetics of Nitrocatechols: Implications of Intramolecular Interactions on Their Atmospheric Behaviour[END_REF] . The relative kinetics method was employed for rate coefficient measurements using trans-2-butene and cyclohexene as reference compounds with k(trans-2-butene+O3) = (2.00±0.50)×10 -17 cm 3 molecule -1 s -1 [START_REF] Mcgillen | Database for the Kinetics of the Gas-Phase Atmospheric Reactions of Organic Compounds[END_REF] and k(cyclohexene+O3) = (7.44±1.86)×10 -17 cm 3 molecule -1 s -1 36 . 1,3,5-Trimethylbenzene was used as OH scavenger in concentrations such that more than 90% of any OH radicals produced was suppressed during the ozonolysis of unsaturated compounds. For trans-3-hexene-1-ol only, two other additional scavengers were employed: cyclohexane and di-butyl ether. The reason was to check whether or not the nature of the scavengers plays any role in this study. Preliminary tests to measure wall depositions of trans-2-hexene-1-ol, trans-3-hexen-1-ol, cis-3-hexen-1-ol, and trans-4-hexene-1-ol revealed the following wall loss rates (kWL): (4.93±0.45)×10 -5 s -1 , (4.35±0.50)×10 -5 s -1 ,

(5.08±0.51)×10 -5 s -1 and (6.04±0.53)×10 -5 s -1 , respectively. No wall deposition was observed for the reference compounds. In the gas-phase system, besides the reaction of alkenols with ozone, reference compounds would also react with ozone (reactions ( 8) and ( 9)):

𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑐𝑐 -2 -butene + O 3 → Products (8) cyclohexene + O 3 → Products (9)
For the unsaturated alcohols and reference compounds the following kinetic equations are valid in the relative method approach:

- d[𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 d𝑡𝑡 = 𝑘𝑘 × [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 × [𝑂𝑂 3 ] 𝑡𝑡 + 𝑘𝑘 𝑊𝑊𝑊𝑊 × [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 (Eq. 4) - d[𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 d𝑡𝑡 = 𝑘𝑘 𝑟𝑟𝑟𝑟𝑟𝑟 × [𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 × [𝑂𝑂 3 ] 𝑡𝑡 (Eq. 5)
where [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 and [𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 are the concentrations of the alcohols and reference compounds at time t. Integrating and combining these two equations yields the following relation between the alcohols and reference concentrations and the O3 reaction rate coefficients:

ln [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 -𝑘𝑘 𝑊𝑊𝑊𝑊 × (𝑡𝑡 -𝑡𝑡 0 ) = 𝑘𝑘 𝑘𝑘 𝑟𝑟𝑟𝑟𝑟𝑟 ln [𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 0 [𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 (Eq. 6)
where [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 and [𝑡𝑡𝑟𝑟𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑡𝑡𝑐𝑐𝑟𝑟] 𝑡𝑡 0 are the initial concentrations of unsaturated alcohols and reference compounds, k and 𝑘𝑘 𝑟𝑟𝑟𝑟𝑟𝑟 are the rate coefficients of the reaction of alcohols and reference compounds with ozone.

The initial concentrations were estimated based on the weighted amounts injected into the reaction chamber, as the difference of the syringe weights with the liquid compound and without liquid compound measured right after the injection, leading to the following average values (in molecules cm -3 , where the uncertainties are two standard deviations): (7.37±0.39)×10 [START_REF] Hellpointner | Detection of Methyl, Hydroxymethyl and Hydroxyethyl Hydroperoxides in Air and Precipitation[END_REF] for alcohols, (8.12±1.62)×10 [START_REF] Hellpointner | Detection of Methyl, Hydroxymethyl and Hydroxyethyl Hydroperoxides in Air and Precipitation[END_REF] for trans-2-butene, (4.69±0.78)×10 [START_REF] Hellpointner | Detection of Methyl, Hydroxymethyl and Hydroxyethyl Hydroperoxides in Air and Precipitation[END_REF] for cyclohexene. Regarding OH scavengers, their concentrations (in molecules cm -3 ) were calculated based on the volume injected:

2.30×10 15 for 1,3,5-trimethylbenzene, 3.00×10 [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] for cyclohexane and 5.60×10 [START_REF] Graedel | Terpenoids in the Atmosphere[END_REF] for di-butyl ether.

The OH scavenger concentration was estimated to suppress up to 90% of OH radicals considering the initial concentrations of the alcohols and reference compounds and their reactivity toward OH radicals [START_REF] Calvert | The Mechanisms of Reactions Influencing Atmospheric Ozone[END_REF] .

The target alcohols, references and OH scavengers were obtained commercially with the following purities: cis-2-penten-1-ol (Aldrich, > 96%), trans-2-hexen-1-ol (Aldrich, ≥ 95%), trans-3-hexen-1-ol (Aldrich, 97%), cis-3-hexen-1-ol (Fluka, > 98%), 1-octen-3-ol (Aldrich, ≥ 98%), trans-2-octen-1-ol (Aldrich, 97%), trans-4-hexen-1-ol (Aldrich, 97%), trans-2-butene (Aldrich, 99%), cyclohexene (Aldrich, 99%), 1,3,5-trimethylbenzene (Aldrich, 98%), cyclohexane (Carl-Roth, > 99.5%), di-butyl ether (Aldrich, 99.3%). They were used as received without further purification. At Iasi ESC-Q-UAIC, synthetic air (Messer-Griesheim, 99.999%) and oxygen (Messer-Griesheim, 99.999%) were used while ozone was produced photochemically by passing a flow of O2 over a VUV-Hg lamp mounted inside a tube and connected to the reactor. Extra pure zero air was produced in Douai with pure air generator (Claind AZ 2020) with relative humidity RH < 2 ppm, CO and CO2 < 80 ppb.

Results and discussion

Rate coefficients

An example of pseudo-first order kinetic plots representing kobs as a function of [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 is displayed in Figure 1 for trans-2-octen-1-ol. The kinetic plots for the other 5 alkenols are provided in Supporting Information (Figures S7-S11). All plots show very good linearity with close to zero intercepts. The ozone rate coefficients obtained from the slope of these plots are (in 10 -17 cm 3 molecule -1 s -1 ): 11.0±2.0 for cis-2-penten-1-ol, 12.0±2.0 for trans-2-hexen-1-ol, 6.4±1.0 for trans-3-hexen-1-ol, 5.8±0.9 for cis-3-hexen-1-ol, 2.0±0.3 for 1-octen-3-ol and 8.4±1.3 for trans-2-octen-1-ol. Quoted uncertainties are two standard deviations and represent the statistical error on the ozone decays (about 5%) combined with the uncertainty coming from alcohol concentrations (of about 15%, both statistical and systematic errors). The final uncertainty on k, Δ(k), was calculated using the error propagation method through Eq. 7 and is about 16% for each rate coefficient.

∆(𝑘𝑘) 𝑘𝑘 = � � ∆𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 � 2 + � ∆[𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 [𝑡𝑡𝑎𝑎𝑐𝑐] 𝑡𝑡 0 � 2 (Eq. 7)
Studies performed in Iasi by using the relative kinetic method measured simultaneously the reference decay and the degradation of hexenols during the ozonolysis. S15) shows a maximum of 5% difference between the measured and literature rate coefficients ratios (kcyclohexene+O3/ktrans-2-butene+O3), this slight difference being covered by the proposed uncertainties. One could notice the very good agreement between the O3 rate coefficients obtained for trans-3-hexen-1-ol when three different OH radical scavengers were used. These results proved that the effect of OH radical could be suppressed by using any of the scavengers. [START_REF] Dwyer | The Gas-Phase Ozonolysis of 1-Penten-3-Ol, (Z)-2-Penten-1-Ol and 1-Penten-3-One: Kinetics, Products and Secondary Organic Aerosol Formation[END_REF] and Kalalian et al. [START_REF] Kalalian | Temperature Dependent Kinetic Study of the Gas Phase Reaction of Ozone with 1-Penten-3-Ol, Cis-2-Penten-1-Ol and Trans-3-Hexen-1-Ol: Experimental and Theoretical Data[END_REF] who found (1.15±0.07)×10 -16 cm 3 molecule -1 s -1 and (1.05±0.20)×10 - 16 cm 3 molecule -1 s -1 , respectively, while about 33% lower than the study from Grosjean and

Grosjean [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] of (1.69±0.25)×10 -16 cm 3 molecule -1 s -1 . All previous literature studies used the absolute kinetics method except Kalalian et al. [START_REF] Kalalian | Temperature Dependent Kinetic Study of the Gas Phase Reaction of Ozone with 1-Penten-3-Ol, Cis-2-Penten-1-Ol and Trans-3-Hexen-1-Ol: Experimental and Theoretical Data[END_REF] , who used the relative method. Grosjean and Grosjean [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] carried out only three experiments under 55% relative humidity using cyclohexane as scavenger with no variation of the initial alkenol concentration, leading to probably less reliable results. A higher rate coefficient value may also point to unknown secondary losses such as impurities in cis-2-penten-1-ol. Yet, with a stated purity of 99%, [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] the 1% impurity should have reacted with O3 at a fairly high rate coefficient of about 5×10 -15 cm 3 molecule -1 s -1 in order to yield the 30% higher cis-2-penten-1-ol + O3 rate coefficient measured by Grosjean and Grosjean [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Aliphatic Alcohols[END_REF] . Reactions of Criegee Intermediates (CI) with alkenols may also be evoked as potential additional loss of alkenols. In the absence of kinetics data, an alkenol + CI rate coefficient of about 1×10 -13 cm 3 molecule -1 s -1 can be estimated based on the reactivity of CI with alkenes [START_REF] Buras | Direct Kinetic Measurements of Reactions between the Simplest Criegee Intermediate CH2OO and Alkenes[END_REF] and alcohols [START_REF] Mcgillen | Criegee Intermediate-Alcohol Reactions, A Potential Source of Functionalized Hydroperoxides in the Atmosphere[END_REF] For trans-2-hexen-1-ol, a rate coefficient of (1.2±0.2)×10 -16 cm 3 molecule -1 s -1 was obtained by the absolute kinetic method and (1.27±0.11)×10 -16 cm 3 molecule -1 s -1 by the relative rate kinetic approach. Both investigations are virtually similar and are in good agreement with the last study by Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] ((1.66±0.22)×10 -16 cm 3 molecule -1 s -1 ) while significantly larger (about a factor of two) than Gibilisco et al. [START_REF] Gibilisco | FTIR Gas Kinetic Study of the Reactions of Ozone with a Series of Hexenols at Atmospheric Pressure and 298[END_REF] who found (5.98±0.73)×10 -17 cm 3 molecule -1 s -1 . However, in this latter study, it was mentioned that OH radicals were not sufficiently scavenged and the results should be considered with caution. Gibilisco et al. [START_REF] Gibilisco | FTIR Gas Kinetic Study of the Reactions of Ozone with a Series of Hexenols at Atmospheric Pressure and 298[END_REF] corrected the obtained rate coefficients by inclusion of self-canceling terms of -khexenol∫[OH]dt and -kreference∫[OH]dt based on the assumption that references have identical rate coefficients against ozone and similar OH radical yields of 26% as reported for isoprene and trans-3-hexen-1-ol.

For trans-3-hexen-1-ol and cis-3-hexen-1-ol where the double bond is further from the -OH group compared to trans-2-hexen-1-ol, lower rate coefficients are obtained in the present work, (6.4±1.0)×10 -17 and (5.8±0.9)×10 -17 cm 3 molecule -1 s -1 , respectively, when employing the pseudofirst order kinetic method and (5.01±0.30)×10 -17 and (4.13±0.34)×10 -17 cm 3 molecule -1 s -1 when using relative rate kinetics. Experimental evidence for other unsaturated alcohols [START_REF] Dwyer | The Gas-Phase Ozonolysis of 1-Penten-3-Ol, (Z)-2-Penten-1-Ol and 1-Penten-3-One: Kinetics, Products and Secondary Organic Aerosol Formation[END_REF][START_REF] Gai | Kinetics of the Gas-Phase Reactions of Some Unsaturated Alcohols with Cl Atoms and O3[END_REF] as well as quantum chemistry calculations [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] supports a higher rate coefficient when the double bond is in α position with respect to the -OH functional group, as is the case with trans-2-hexen-1-ol. It should be noted that both 3-hexen-1-ol isomers (cis-and trans-) display a relatively similar reactivity towards O3, while literature reviews on alkene + O3 kinetics indicate that trans-isomers are generally more reactive than cis-due to a higher pre-exponential factor [START_REF] Treacy | Reactions of Ozone with Unsaturated Organic Compounds. Berichte Bunsenges[END_REF][START_REF] Grosjean | Rate Constants for the Gas-Phase Reaction of Ozone with 1,2-Disubstituted Alkenes[END_REF] . Consistently, a slightly higher rate coefficient value can be observed for the trans-isomer in comparison with the cisisomer, though this conclusion could be encompassed if the uncertainties level is considered. It is important to mention that rate coefficient values obtained for 3-hexen-1-ol isomers agree within 30% with the literature values obtained by using different methods and simulation chambers as those used in present investigations (see Table 2). However, most of the difference could be explained considering the assumed errors of about 20% of the reference rate coefficients used in the relative rate method. As for cis-2-penten-1-ol, only three experiments were performed by Grosjean et al. [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Alcohols, Esters, and Carbonyls[END_REF] for cis-3-hexen-1-ol with no variation of the initial alkenol concentration. This may explain the discrepancies observed for kcis-3-hexen-1-ol+O3 between Grosjean et al. [START_REF] Grosjean | Rate Constants for the Gas-Phase Reactions of Ozone with Unsaturated Alcohols, Esters, and Carbonyls[END_REF] , on the one hand, and the other studies (including the present work), on the other hand.

The kinetic values for trans-4-hexen-1-ol (in cm 3 molecule -1 s -1 ) are in good agreement for both reference compounds ((14.1±1.7)×10 -17 with trans-2-butene and (13.9±1.8)×10 -17 with cyclohexene) and with Lin et al. [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] ((10.5±1.4) ×10 -17 ) considering the uncertainties. In an attempt to compare the rate coefficient of trans-2-hexen-1-ol, trans-3-hexen-1-ol and trans-4-hexen-1-ol, a virtually similar reactivity for trans-2-hexen-1-ol and trans-4-hexen-1-ol is observed while the rate coefficient for trans-3-hexen-1-ol is about three times lower.

For 1-octen-3-ol, our value is in excellent agreement with the only literature data from Li et al. [START_REF] Li | Kinetic Study of the Gas-Phase Reaction of O3 with Three Unsaturated Alcohols[END_REF] .

Finally, the present work reports the first O3 rate coefficient for trans-2-octen-1-ol.

As observed in many studies on alkenes + O3 reaction kinetics [START_REF] Avzianova | Temperature-Dependent Kinetic Study for Ozonolysis of Selected Tropospheric Alkenes[END_REF][START_REF] Leather | Temperature-Dependent Ozonolysis Kinetics of Selected Alkenes in the Gas Phase: An Experimental and Structure-Activity Relationship (SAR) Study[END_REF] , a higher degree of alkyl substitution of the double bond generally leads to a higher rate coefficient. Considering all rate coefficients known for alkenols + O3 (Table S1) suggests that it is also the case for alkenols. Note that the highest k value is for 3-methyl-2-buten-1-ol (> 4.39×10 -16 cm 3 molecule -1 s -1 ) which is a tri-substituted compound. This phenomenon has been explained by an inductive effect produced via the enhancement of the π-orbital electron density for higher substituted compounds, leading to a lowering of the activation energy.

In the case of unsaturated compounds, the hydroxyl function group is expected to induce an electron-donating effect on the adjacent bonds, thus enhancing the electronic density of the double bond and increasing the reactivity of the unsaturated compound. Comparing the O3 reactivity of alkenols with that of the corresponding alkenes as a function of the distance between -OH and C=C displays a puzzling picture, as shown in Figure 3. While for 1-alken-3-ols, the rate coefficient ratio k(O3+alkenol)/k(O3+alkene) is higher than 1, as expected, the reverse is observed for all other alkenols. The highest ratio of about 2 is calculated for 1-octen-3-ol/1-octene and 1-nonen-3-ol/1nonene. Mason et al. showed that C3 to C10 1-alkenes all react with O3 with rate coefficients around 1×10 -17 cm 3 molecule -1 s -1 without any effect of the carbon chain length [START_REF] Mason | Rate Constants for the Gas-Phase Reactions of NO3 Radicals and O3 with C6-C14 1-Alkenes and 2-Methyl-1-Alkenes at 296 ±[END_REF] . Interestingly, the present results indicate that the substitution by OH at the α-position to the C=C bond in 1-alkenes increases the rate coefficient up to a factor two. In addition to the electron-donating effect of the -OH group, this may be due to the formation of a strong pre-reactive complex through hydrogen bond interaction between O3 and -OH [START_REF] Lin | Kinetics and Mechanisms of Gas Phase Reactions of Hexenols with Ozone[END_REF] . Noteworthy, 2-alken-1-ols like 2-penten-1-ol (which are αalkenols) do not show such reactivity increase between alkenes and alkenols, probably due to steric effects. Further experimental and theoretical investigations of reaction mechanisms of α-alkenols + O3 may help understanding their reactivity.

Structure-Activity Relationships (SAR)

Rate coefficients can be estimated using different methods involving structure reactivity relationships. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] to heteroatomic unsaturated VOCs.

The different SAR approaches cited above were applied to evaluate their suitability as alternative tools for rate coefficient estimation for the reactions of unsaturated alcohols with ozone. Where applicable, the experimental values were calculated by averaging rate coefficients obtained in the present work by the pseudo-first order approach and the relative rate kinetic method. In Table 3, the experimental k values (kexp) can be compared with the calculated values obtained using the different SAR approaches (kSAR) on the investigated compounds. The earliest methodologies proposed in the literature on SAR estimations of rate coefficients show large discrepancies with the experimental results. Poor agreement was also noticed when using the SAR approach from Pfrang et al. [START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF] (except for 3-hexen-1-ol isomers) despite the more complex methodology involved.

Using McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] methodology (details are provided in the Supplementary Information), a very satisfactory estimate is obtained for cis-2-penten-1-ol, trans-2-hexen-1-ol and trans-2-octen-1-ol, with agreement with our results between 2% and 20%. For the others alkenols, the ratios kSAR/kexp vary between 0.29 and 0.59. The strongest disagreement is obtained for trans-4-hexen-1-ol (kSAR/kexp = 0.29) for which the experimental finding is three times larger than the calculated rate coefficient. Because of the distance between -OH and C=C in trans-4-hexen-1-ol (-OH is in δ position towards C=C), no inductive effect is considered in the SAR calculation. Consistently, the experimental rate coefficient of the corresponding alkene (trans-2-hexene) with O3 (1.53×10 - 16 cm 3 molecule -1 s -1 ) [START_REF] Calvert | The Mechanisms of Reactions Influencing Atmospheric Ozone[END_REF] is close to that obtained in the present work for trans-4-hexen-1-ol (1.40×10 - 16 cm 3 molecule -1 s -1 ). Therefore, the low kSAR/kexp ratio reflects a weakness in the SAR method, probably regarding a change in the reaction mechanisms as suggested by McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] . Based on the overall agreement, it is suggested that the SAR method from McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] estimates the rate coefficients from ozonolysis of unsaturated alcohols much closer to the experimental data than the other above-mentioned approaches.

Ozonolysis rate coefficients were also computed for a range of other alkenols using the SAR method from McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] . Values are reported in Figure 4 as a function of experimental ones (see Table S1). Besides the compounds already included in McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] analysis (with updated values from Kalalian et al. [START_REF] Kalalian | Temperature Dependent Kinetic Study of the Gas Phase Reaction of Ozone with 1-Penten-3-Ol, Cis-2-Penten-1-Ol and Trans-3-Hexen-1-Ol: Experimental and Theoretical Data[END_REF] and the present work), fourteen new compounds were added (see

Atmospheric implications

The rate coefficients determined in the present work allow calculating the lifetime τ of alkenols in the atmosphere when reacting with O3, using τ = 1/(k×[O3]). Assuming an average ozone concentration of 1.6×10 12 molecules cm -3 (about 65 ppb at 295 K and 1 atm) [START_REF] Dayan | Atmospheric Pollution over the Eastern Mediterranean during Summer -a Review[END_REF] leads to lifetimes of a few hours (Table 4). The corresponding lifetimes when reacting with OH, NO3 and Cl can be similarly calculated and are reported also in Table 4. Comparing with OH, NO3 and Cl reactions indicates that ozonolysis is a competitive oxidation process, especially during the night and at low NOx environments where OH and NO3 concentrations are low, respectively. In addition, in the perspective of increasing ozone concentrations in the future [START_REF] Lin | US Surface Ozone Trends and Extremes from 1980 to 2014: Quantifying the Roles of Rising Asian Emissions, Domestic Controls, Wildfires, and Climate[END_REF] , an increasing impact of ozonolysis may be expected in the degradation of alkenols.

Conclusions

The rate coefficients of a series of seven unsaturated alcohols with ozone have been determined using two complementary setups, allowing both absolute and relative kinetics methods to be employed. Good agreement has been obtained between the two methods. Alkenols appear to have high reactivity with ozone with lifetime in the hour range. Rate coefficients show a strong and complex dependence on the structure of the alkenol, particularly the relative position of the OH group towards the C=C double bond. Four SAR approaches were tested against the investigated compounds, the most recent from McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] displaying the best results. Yet, efforts are still needed to better understand the reaction mechanisms and unravel the links between the structure and the reactivity of alkenols with O3.

Supporting Information

Details for evaluating SAR rate coefficients using McGillen et al. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] [START_REF] Pfrang | Structure-Activity Relations (SARs) for Gas-Phase Reactions of NO3, OH and O3 with Alkenes: An Update[END_REF] (for trans-4-hexen-1-ol, the OH group being far from the C=C double bond, the SAR from Pfrang et al. [START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF] for alkenols was not used but that developed for alkenes by Pfrang et al. [START_REF] Pfrang | Structure-Activity Relations (SARs) for Gas-Phase Reactions of NO3, OH and O3 with Alkenes: An Update[END_REF] ). [START_REF] Grira | Kinetic Measurements of Cl Atom Reactions with C5-C8 Unsaturated Alcohols[END_REF] and Rodriguez et al. [START_REF] Rodríguez | Kinetics and Mechanism of the Atmospheric Reactions of Atomic Chlorine with 1-Penten-3-Ol and (Z)-2-Penten-1-Ol : An Experimental and Theoretical Study[END_REF] ; e Average of Gibilisco et al. [START_REF] Gibilisco | OH-Initiated Degradation of a Series of Hexenols in the Troposphere. Rate Coefficients at 298 K and 1 Atm[END_REF] and Davis and Burkholder 59 ; f Pfrang et al. [START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF] ; g Average of Grira et al. [START_REF] Grira | Kinetic Measurements of Cl Atom Reactions with C5-C8 Unsaturated Alcohols[END_REF] and Gibilisco et al. [START_REF] Gibilisco | Rate Coefficients at 298 K and 1 Atm for the Tropospheric Degradation of a Series of C6, C7 and C8 Biogenic Unsaturated Alcohols Initiated by Cl Atoms[END_REF] ; h Average of Gibilisco et al. [START_REF] Gibilisco | Atmospheric Sink of (E)-3-Hexen-1-Ol, (Z)-3-Hepten-1-Ol, and (Z)-3-Octen-1-Ol: Rate Coefficients and Mechanisms of the OH-Radical Initiated Degradation[END_REF] ; Peirone et al. [START_REF] Peirone | Relative Rate Coefficient Measurements of OH Radical Reactions with (Z)-2-Hexen-1-Ol and (E)-3-Hexen-1-Ol under Simulated Atmospheric Conditions[END_REF] and Gibilisco et al. [START_REF] Gibilisco | OH-Initiated Degradation of a Series of Hexenols in the Troposphere. Rate Coefficients at 298 K and 1 Atm[END_REF] ; i Average of Gibilisco et al. [START_REF] Gibilisco | OH-Initiated Degradation of a Series of Hexenols in the Troposphere. Rate Coefficients at 298 K and 1 Atm[END_REF] , Jimenez et al. [START_REF] Jiménez | Photooxidation of Leaf-Wound Oxygenated Compounds, 1-Penten-3-Ol, (Z)-3-Hexen-1-Ol, and 1-Penten-3-One, Initiated by OH Radicals and Sunlight[END_REF] , Atkinson et al. [START_REF] Atkinson | Rate Constants for the Gas-Phase Reactions of Cis-3-Hexen-1-Ol, Cis-3-Hexenylacetate, Trans-2-Hexenal, and Linalool with OH and NO3 Radicals and O3 at 296 ± 2 K, and OH Radical Formation Yields from the O3 Reactions[END_REF] and Davis and Burkholder 59 ; j Average of Pfrang et al. [START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF] and Atkinson et al. [START_REF] Atkinson | Rate Constants for the Gas-Phase Reactions of Cis-3-Hexen-1-Ol, Cis-3-Hexenylacetate, Trans-2-Hexenal, and Linalool with OH and NO3 Radicals and O3 at 296 ± 2 K, and OH Radical Formation Yields from the O3 Reactions[END_REF] ; k Grira et al. [START_REF] Grira | Kinetic Measurements of Cl Atom Reactions with C5-C8 Unsaturated Alcohols[END_REF] ; m Pfrang et al. [START_REF] Pfrang | Structure-Activity Relations (SARs) for Gas-Phase Reactions of NO3, OH and O3 with Alkenes: An Update[END_REF] ; n Pfrang et al. [START_REF] Pfrang | Gas-Phase Rate Coefficients for Reactions of NO3, OH, O3 and O( 3 P) with Unsaturated Alcohols and Ethers: Correlations and Structure-Activity Relations (SARs)[END_REF] ; -: no data represent other alkenols (14 compounds). Rate coefficients for alkenes are from Calvert et al. [START_REF] Calvert | The Mechanisms of Atmospheric Oxidation of the Alkenes[END_REF] while those for alkenols are reported in Table S1. [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF] and Supplementary Information) vs those determined experimentally at 298 K (see Table S1). The solid line is a linear regression over all the data (26 data) going through zero. The uncertainty on the slope corresponds to 2 standard deviations (2σ). One compound, 3-methyl-2-buten-1-ol, was excluded from the linear regression (see main text). represent other alkenols (14 compounds). Rate coefficients for alkenes are from Calvert et al. [START_REF] Calvert | The Mechanisms of Atmospheric Oxidation of the Alkenes[END_REF] while those for alkenols are reported in Table S1.

Accepted manuscript / Final version

  . The comparison of the rate of alkenol + O3 (rO3 = k×[O3]×[alc], with k = 1.1×10 -16 cm 3 molecule -1 s -1 in the case of cis-2penten-1-ol and [O3] = 1×10 12 molecules cm -3 ) with the estimated rate of alkenol + CI (rCI = kCI×[CI]×[alc] with kCI = 1×10 -13 cm 3 molecule -1 s -1 and [CI] estimated at 1×10 6 molecules cm -3 ) leads to a ratio of about 1000. This value indicates that alkenol reactions with CI are probably not significant in the present chamber experiments. Hence, the possible discrepancies in the rate constants between the present work and literature values cannot be explained by CI reactions with alkenols.

(

  trans-2-octen-1-ol 8.40×10-17

Table 4 :τ

 4 Comparison of atmospheric lifetimes of unsaturated alcohols with respect to removal by O3, OH radicals, NO3 radicals and Cl atoms. Average concentrations used: [O3] = 1.6×10 12 molecules cm -3 47 , [OH] = 2×10 6 radicals cm -3 50 , [NO3] = 5×10 8 radicals cm -3 51 , [Cl] = 10 4 atoms cm -3 52 . Values in italic correspond to SAR calculations. Cl (h) cis-2-penten-1-ol 11.0 1.

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Relative kinetic plot of ozone reaction with trans-2-hexen-1-ol versus (•) cyclohexene

Figure 3 :

 3 Figure 3: Relationship between O3 rate coefficient ratio and number of carbon atoms between -

Figure 4 :

 4 Figure 4: Ozonolysis of alkenols: rate coefficients calculated by SAR (see McGillen et al. 27 and

Figure 1 :

 1 Figure 1: Kinetic plot of trans-2-octen-1-ol ozonolysis.

Figure 2 :

 2 Figure 2: Relative kinetic plot of ozone reaction with trans-2-hexen-1-ol versus (•) cyclohexene

Figure 3 :

 3 Figure 3: Relationship between O3 rate coefficient ratio and number of carbon atoms between -

Table 2

 2 compares the rate coefficients obtained in the present work (absolute and relative methods) with literature data, where available. The rate coefficient obtained for cis-2-penten-1-ol ((1.1±0.2)×10 -16 cm 3 molecule -1 s -1 ) is in excellent agreement with the determinations of O`Dwyer et al.

  Atkinson and Carter 24 applied a methodology used by the US Environmental Protection Agency under the AOPWIN (Atmospheric Oxidation Program for Windows) to estimate ozone rate coefficients. Calvert et al. 25 developed SAR methods using the groupadditivity approach and factors contributions. Pfrang et al. 26 used correlations and rate coefficients for basic structures multiplied by group reactivity factors for corresponding substituents. More recently, a new SAR method was developed implying the contribution of inductive effect of heteroatoms and total steric effects based on the earlier work of McGillen et al. 46 on alkenes and extended by McGillen et al.

Table S1 ,

 S1 compounds in italic). It can be seen that calculated rate coefficients are within a factor of 2 of the experimental rate coefficients. A linear regression (forced through zero) on the data yields a slope coefficient of 0.64±0.11 (2σ uncertainty), indicating that SAR calculated rate

coefficients are mostly lower than experimental ones. As stressed above, this may suggest unknown changes in reaction mechanisms of alkenol ozonolysis. Additional experiments are clearly needed to better characterize these mechanisms and improve structure activity relationships.

Table 1 :

 1 CPER Climibio), and the European Fund for Regional Economic Development. AG is grateful for a PhD grant from Brittany Region and IMT Nord Europe. AG, GED, AC and AT are grateful to the INSU-LEFE-CHAT program for funding this research. CAr, IGB, RIO and AT acknowledge the financial support from European Union's Horizon 2020 Research and Innovation Framework Program, through the EUROCHAMP-2020 Infrastructure Activity Grant (grant agreement No 730997). CAr, IGB, RIO, CAm and CR and acknowledge the Operational Program Competitiveness 2014-2020, Axis 1, under POC / 448 / 1 / 1 Research infrastructure projects for public R&D institutions / Sections F 2018, through the Research Center with Integrated Techniques for Atmospheric Aerosol Investigation in Romania (RECENT AIR) project, under grant agreement MySMIS no. 127324 for its co-support. All the authors are thankful to the PHC Brancusi program for funding the OzOA project (38385UD). Experimental results from the relative kinetic measurements employed in the present study for the ozonolysis of a series of alkenols.

	methodology, ambient

Table 2 :

 2 Rate coefficients obtained in the present work using the absolute rate (pseudo first order) method (AR) and relative rate method (RR) compared with literature data.

	Alcohol	k × 10 17 (cm 3 molecule -1 s -1 ) a	Reference
		11.0±2.0 (AR)	This work
		16.9±2.5 (AR)	Grosjean and Grosjean 16
	cis-2-penten-1-ol	11.5±0.7 (AR)	O`Dwyer et al. 14
		10.5±2.0 (RR)	Kalalian et al. 17
		12.0±2.0 (AR)	This work
		12.7±1.1 (RR)
	trans-2-hexen-1-ol	6.0±0.7 (RR)	Gibilisco et al. 18
		16.6±2.2 (AR)	Lin et al. 19
		6.4±1.0 (AR)	This work
		5.01±0.30 (RR)
	trans-3-hexen-1-ol	5.8±0.9 (RR)	Gibilisco et al. 18
		6.2±0.7 (AR)	Lin et al. 19
		6.2±1.4 (RR)	Kalalian et al. 17
		5.8±0.9 (AR)	This work
		4.13±0.34 (RR)
		10.5±0.7 (AR)	Grosjean et al. 20
		6.4±1.7 (RR)	Atkinson et al. 21
	cis-3-hexen-1-ol	6.0±0.9 (RR)	Gibilisco et al. 18
		5.5±0.7 (AR)	Lin et al. 19
		6.05±0.38 (RR)	Chen et al. 22
		5.78±0.65 (AR)
		14.0±1.2 (RR)	This work
	trans-4-hexen-1-ol	10.5±1.4 (AR)	Lin et al. 19
		2.0±0.3 (AR)	This work
	1-octen-3-ol	1.9±0.2 (AR)	Li et al. 23

Table 3 :

 3 The comparison of different SAR methods and the ratio of kexp/kSAR. kexp are the average of the absolute and relative rate coefficients obtained in the present work, where applicable.

	Alcohol	kexp (this work)

  Atkinson and Carter 24 , b Calvert et al. 25 , c Pfrang et al. 26 , d McGillen et al. 27 , e Pfrang et al.

	1.38×10 -17 c	0.16
	0.99 ×10 -16 d	1.18
	2.00×10 -16 a	2.38
	1.90×10 -16 b	2.27

a

  this work (average of absolute and relative determinations); b Orlando et al.[START_REF] Orlando | Rate Coefficients and Product Yields from Reaction of OH with 1-Penten-3-Ol, (Z)-2-Penten-1-Ol, and Allyl Alcohol (2-Propen-1-Ol)[END_REF] ; c Average of Pfrang et al.[START_REF] Pfrang | Night-Time Tropospheric Chemistry of the Unsaturated Alcohols (Z)-Pent-2-En-1-Ol and Pent-1-En-3-Ol: Kinetic Studies of Reactions of NO3 and N2O5 with Stress-Induced Plant Emissions[END_REF] and Zhao et al.[START_REF] Zhao | Kinetics Studies of the Gas-Phase Reactions of NO3 Radicals with Series of 1-Alkenes, Dienes, Cycloalkenes, Alkenols, and Alkenals[END_REF] ; d Average of Grira et al.

			5	1.17 b	1.2	2.34 c	2.4	3.00 d	93
	trans-2-hexen-1-ol	12.3	1.4	0.81 e	1.7	1.56 f	3.6	3.45 g	81
	trans-3-hexen-1-ol	5.71	3.0	1.05 h	1.3	2.67 f	2.1	3.24 g	86
	cis-3-hexen-1-ol	4.97	3.4	1.12 i	1.2	3.58 j	1.6	3.04 g	91
	trans-4-hexen-1-ol	14.0	1.2	0.534 m	2.6	2.93 f	1.9	-	-
	1-octen-3-ol	2.00	8.6	0.16 n	8.7	0.0099 n	560	4.03 k	69
	trans-2-octen-1-ol	8.40	2.0	0.28 n	5.0	0.20 n	28	-	-

a

Accepted manuscript / Final version

Acknowledgements

The Center for Energy and Environment acknowledges funding by the French ANR Agency under contract No. ANR-11-LabX-0005-01 CaPPA (Chemical and Physical Properties of the Atmosphere), the Région Hauts-de-France, the Ministère de l'Enseignement Supérieur et de la

 [START_REF] Mcgillen | Structure-Activity Relationship (SAR) for the Prediction of Gas-Phase Ozonolysis Rate Coefficients: An Extension towards Heteroatomic Unsaturated Species[END_REF]and Supplementary Information) vs those determined experimentally at 298 K (see Table S1). The solid line is a linear regression over all the data (26 data) going through zero. The uncertainty on the slope corresponds to 2 standard deviations (2σ). One compound, 3-methyl-2-buten-1-ol, was excluded from the linear regression (see main text).