domain: spi phys

text:
Marc Budinger
email: marc.budinger@insa-toulouse.fr

Valérie Pommier-Budinger

Lokman Bennani

Pierrick Rouset

Elmar Bonaccurso

Fabien Dezitter

Electro-mechanical Resonant Ice Protection Systems: Analysis of Fracture Propagation Mechanisms

Recent research is showing growing interest in low-power electromechanical de-icing systems and, in particular, de-icing systems based on piezoelectric actuators. These systems use the vibrations generated by piezoelectric actuators at resonance frequencies to produce shear stress at the interface between the ice and the support or to produce tensile stress in the ice. This paper provides analytical and numerical models enabling a better understanding of the main de-icing mechanisms of resonant actuation systems. Different possible ice shedding mechanisms involving cohesive and adhesive fractures are analyzed with an approach combining modal, stress and crack propagation analyses. Simple analytical models are proposed to better understand the effects on ice shedding of the type of mode, ice thickness, or frequency with respect to cohesive and adhesive fractures.

to propose new solutions that consume less energy or have less bulky power supplies. Among these studies, deicing systems based on piezoelectric systems are a subject of growing interest. The principle is to apply vibrations to the structure that create high-level stresses greater than those required to bring about delamination or cracking of the ice accumulated on the structure [START_REF] Seppings | Investigation of ice removal from cooled metal surfaces[END_REF]. Extensional or flexural modes can be excited and different frequency ranges have been investigated: low frequencies (Hz) [START_REF] Venna | In-Flight De-Icing Self-Actuating Wing Structures with Piezoelectric Actuators[END_REF].. [START_REF] Venna | Piezoelectric transducer actuated leading edge de-icing with simultaneous shear and impulse forces[END_REF], high frequencies (kHz) [START_REF] Palacios | Design, fabrication, and testing of an ultrasonic de-icing system for helicopter rotor blades[END_REF].. [START_REF] Villeneuve | Piezoelectric Deicing System for Rotorcraft[END_REF] and waves (MHz) [16][17]. Paper [START_REF] Budinger | Ultrasonic Ice Protection Systems: Analytical and Numerical Models for Architecture Tradeoff[END_REF] proposes a computational method for estimating amplitude of vibrations to initiate fractures according to the type of mode (extensional or flexural) and to the frequency range. To go further than the prediction of the initiation of de-icing, more work is required to model and understand what happens after the initial cracks or delamination are generated, and how the cracks or delamination can propagate. The fracture propagation mechanisms in the ice or at the ice/support interface involve cohesive failure (which induces cracks) and adhesive failure (which induces delamination). There are currently no studies that model these mechanisms for electromechanical resonant ice protection systems.

In this article, this problem is studied through numerical simulations, analytical modeling and experimental tests on elementary geometries. The supports chosen for modeling and tests are simple plates in order to promote deeper understanding of the phenomena through analytical models. The objective is to obtain models to guide the design or analyze experimental tests. The article focuses on de-icing mechanisms related to resonance modes and does not address electromechanical coupling.

Section II of this article sums up the state of the art concerning the data and models necessary for further developments. Section III develops the computations, based on stress formulas, for estimating the vibration amplitudes leading to the initiation of de-icing. The computations are made for two criteria based on the tensile strength in the ice and on the shear strength at the ice/support interface. Section IV explains general assumptions and introduces the models used in this paper for estimating fracture propagation once de-icing is initiated. It

II. Modeling of Piezoelectric De-icing Systems: State of the Art

This state of the art is limited to the phenomena, data or modeling methods useful for designing and analyzing de-icing systems activated by modal vibrations. Piezoelectric anti-icing systems [START_REF] Li | Effect of ultrasound on frost formation on a cold flat surface in atmospheric air flow[END_REF] or ice accretion characterization systems [20][21] are not considered in this paper.

In order to develop models for the design and analysis of piezoelectric systems, it is interesting to determine the main physical effects involved in de-icing. Many authors have set up video recordings [START_REF] Overmeyer | Actuator bonding optimization and system control of a rotor blade ultrasonic deicing system[END_REF][14] [START_REF] Endres | Experimental study of two electro-mechanical de-icing systems applied on a wing section tested in an icing wind tunnel[END_REF] during their tests. The speed of the fracture phenomena, with time constants lower than milliseconds, is emphasized by the use of fast video cameras. The analyses of the videos highlight two types of phenomena: cracks within the ice (cohesive fracture) and delamination at the ice/support interface (adhesive fracture). The order of appearance of these two phenomena is not always the same [START_REF] Endres | Experimental study of two electro-mechanical de-icing systems applied on a wing section tested in an icing wind tunnel[END_REF]: cohesive fracture then adhesive fracture or adhesive fracture then cohesive fracture. The two phenomena can be consecutive without interruption or can require an increase in voltage magnitude or change of frequency to occur after a first fracture. In the tests reported in the literature, the activation of the support is generally carried out by a sweep over the frequency ranges that can excite extensional [START_REF] Palacios | Design, fabrication, and testing of an ultrasonic de-icing system for helicopter rotor blades[END_REF].. [START_REF] Overmeyer | Actuator bonding optimization and system control of a rotor blade ultrasonic deicing system[END_REF] or flexural [START_REF] Strobl | Feasibility study of a hybrid Ice protection system[END_REF].. [15][22] modes. For all of these modes, it is possible to note a change in the resonance frequency with the thickness of the ice and a significant amplification of the vibrations at resonance. The absorbed current and the quality factor may differ depending on the type of mode [START_REF] Rouset | Comparison of extensional and flexural modes for the design of piezoelectric ice protection systems[END_REF], extensional or flexural.

First of all, modeling requires the characteristics of the ice to be known. Many publications [START_REF] Mohamed | An experimental study on the tensile properties of atmospheric ice[END_REF].. [START_REF] Riahi | The experimental/numerical study to predict mechanical behaviour at the ice/aluminium interface[END_REF] and research projects [START_REF]Efficient ice protection Systems and simulation Techniques Of ice Release on propulsive systems[END_REF] deal with this research area. For high strain rate (higher than 10 -4 s -1 ), ice exhibits macroscopically brittle behavior [START_REF] Druez | The adhesion of glaze and rime on aluminum electrical conductors[END_REF]. The main characteristics useful for our case of applications are thus Young's modulus, density, shear and tensile strengths, and critical energy release rate. These characteristics vary considerably [START_REF] Liu | Ultrasonic-attenuation-based technique for ice characterization pertinent to aircraft icing phenomena[END_REF][21] [START_REF] Mohamed | An experimental study on the tensile properties of atmospheric ice[END_REF].. [START_REF] Riahi | The experimental/numerical study to predict mechanical behaviour at the ice/aluminium interface[END_REF] depending on the type of ice (glaze or rime), the means used to obtain this ice (freezer or wind tunnel), the type of degradation (cohesive or adhesive), and the interface material. As glaze ice is best known, Tables 1 and2 summarize the values of the quantities that are used to carry out the numerical applications or simulations for this ice type, in this article. These values should only be taken as mean values because the literature presents a great variability of results concerning ice properties.

A number of papers put forward analytical or numerical modeling elements. They consist mostly of numerical modal analyses correlated with experimental identification [START_REF] Villeneuve | Piezoelectric Deicing System for Rotorcraft[END_REF]. They can also take the form of frequency analyses which allow the piezoelectric coupling and the damping levels to be taken into account in order to estimate the stress levels at the ice/support interface [START_REF] Palacios | Investigation of an ultrasonic ice protection system for helicopter rotor blades[END_REF]. Other papers couple modal analysis and model reduction to obtain these constraints [18][37]. The phenomenon of fracture propagation is rarely discussed in piezoelectric de-icing papers. It is necessary to turn to the modeling of electro-impulse [START_REF] Sommerwerk | Analysis of the mechanical behavior of thin ice layers on structures including radial cracking and de-icing[END_REF] or electro-thermal [START_REF] Zhang | FEM analysis of in-flight ice breakup[END_REF][35] [START_REF] Bennani | A mixed adhesion-brittle fracture model and its application to the numerical study of ice shedding mechanisms[END_REF] de-icing systems to find models taking cohesive or adhesive fractures into account. To study fracture mechanics, different methods can be chosen and are known to give similar results for linear elastic fracture mechanisms: the stress intensity factor approach [START_REF] Zhang | FEM analysis of in-flight ice breakup[END_REF], the cohesive zone model [START_REF] Sommerwerk | Analysis of the mechanical behavior of thin ice layers on structures including radial cracking and de-icing[END_REF] and the energy balance approach [35][36]. The energy balance approach is used in this paper because of its similarity with energy approaches to determine resonance modes. This approach compares the strain energy release rate called to a critical value : a value of greater than indicates that a crack can grow. Table 2 gives the critical energy release rates (J/m²) commonly used to predict the ability of glaze ice to resist to cohesive or adhesive fractures.

Initiation of De-icing

The target of this section is to recall the conditions that lead to an initiation of de-icing [START_REF] Budinger | Ultrasonic Ice Protection Systems: Analytical and Numerical Models for Architecture Tradeoff[END_REF][37] [START_REF] Pommier-Budinger | Electro-mechanical Resonant Ice Protection Systems. Initiation of Fractures with Piezoelectric De-icing Systems[END_REF]. The support is assumed to be covered by an ice layer of constant thickness made in a freezer. The numerical applications are made for a support thickness of 1.5 mm and an ice layer thickness of 2 mm.

A. Beam Analytical Model

The resonance modes used in the literature for de-icing are essentially in-plane extensional modes and out-ofplane flexural modes. To simplify the analysis, several assumptions are made: support and ice are considered as a thin multilayer beam (1D model). This section summarizes the equations already presented by the authors. For more details on their assumptions and developments, the reader is invited to refer to the corresponding papers [18][37]. Mode shapes are assumed to be identical to that of a uniform beam and boundary conditions are simply supported as in papers [18][37]. Fig. 1 shows the beam under study.

Fig. 1 -Element of the beam under study [18][37]

For flexural modes, the position of the neutral line can be obtained by assuming that the tensile force in a section is zero [START_REF] Timoshenko | Strength of materials Part 1[END_REF]. This results in:

1 2 (1)
Table 3 synthetizes the analytical formulas derived from previous assumptions to compute strains and stresses in the ice, in the aluminum substrate and at the ice/support interface. The formulas of the peak out-of-plane shear stress were obtained by isolating an element of ice of thickness dx subjected to elastic forces, inertial forces and shear forces at the ice/support interface (Fig. 1). The resonance frequencies were obtained by Rayleigh's method using the expression of the strains to estimate the kinetic and potential energies.

B. Beam Analytical Models Analysis

These analytical formulas show that, for extensional modes, the maximum tensile stress in the substrate or in the ice is located on the displacement nodes and the maximum shear stress at the ice/support interface is on the displacement antinodes. For flexural modes, the maximum shear stress is located on the nodes and the maximum tensile stress on the antinodes.

The extensional and flexural modes are compared in [START_REF] Budinger | Ultrasonic Ice Protection Systems: Analytical and Numerical Models for Architecture Tradeoff[END_REF], in particular for their ability to generate stress. For a given frequency and a given displacement, the shear stress level at the ice/support interface and the tensile stress at the top surface of the ice layer are smaller for extensional than for flexural modes. Extensional modes generally appear at higher frequencies (over 15 kHz) and require higher displacements and consequently generally higher power. Thus, to initiate ice delamination or ice fractures while minimizing the displacements (and potentially the consumed power) of the piezoelectric actuators, it is more efficient to excite flexural modes. The set of diagrams in Fig. 2 focuses on the flexural modes and shows, as a function of resonance frequencies:

a) The vibratory magnitude necessary to reach the tensile criterion at the top surface of the ice layer or the shear criterion at the ice/support interface. As higher resonance frequencies entail smaller distances between nodes, higher bending radius and thus higher stresses, the requested magnitudes decrease with frequency. For low frequencies, initiation by crack preferably occurs on the top surface of the ice layer. Initiation by delamination only occurs at higher frequencies. The two phenomena take place simultaneously and cross here at about 40 kHz for an ice layer thickness of 2 mm. For a thickness of 4 mm, the crossing between these two phenomena occurs at approximately 25 kHz.

b) The power per m² necessary to create these vibrations; this power depends on the mechanical losses to be compensated. They are here estimated by assuming a mechanical quality factor equal to 30. This conservative value is observed in practice in the worst cases for structures in aluminum alloy [START_REF] Rouset | Comparison of extensional and flexural modes for the design of piezoelectric ice protection systems[END_REF]. It can be observed that the initiation by tensile criterion can be satisfied with low power, a few tens of W per square meter, at low frequency.

However, this power increases with increasing resonance frequencies and varies with the ice layer thickness. A parametric variation on this thickness shows an optimum thickness of approximately 1 mm for the initiation by surface fracture and 4 mm for the initiation of de-icing by delamination at the ice/support interface.

c) The stress in the support, here in the aluminum alloy, should also be taken into account because it can cause a reduction in the lifetime if it is excessive. It is also an image of the constraints that can be found in the piezoelectric actuators. For the tensile criterion, the stress in the support is directly connected to the ice strength and is thus constant with frequency. For the shear criterion, an increase of the frequency has a positive effect by reducing the stress in the support.

Note: a change in the nature of the ice, e.g. to rime ice with a lower Young's modulus, requires larger vibratory amplitudes in order to initiate the de-icing process and thus higher consumptions and stresses in the support.

C. Comparison with 3D FEM Models and Experimental Tests

The models of the preceding paragraphs revealed two types of fracture during the initiation of de-icing: cracks on the top surface of the ice layer for low frequencies (caused by tensile stress), and delamination at the ice/support interface for high frequencies (caused by shear stress). These results, established with Bernoulli beam assumptions, are compared here with 3D FEM (Finite Element Method) simulations. The use of particular boundary conditions, symmetry on the antinode and anti-symmetry on the node, allows flexural modes to be simulated on a quarter of a wave-length with a form factor allowing fine meshing. A DoE (Design of Experiments) plan varying the overall dimensions and also the shape factor of the mode (ratio of wavelength in one direction over wavelength in the other direction) resulted in Fig. 4. It can be seen that, despite its great simplicity, the beam model makes it possible to represent the tendency of the amplitude necessary for de-icing initiation according to mechanisms n°1 (tensile criterion) and n°2 (shear criterion).

Finally, different experimental tests were performed to compare simulation results with experimental measurements. The test specimen was an aluminum alloy plate 154 x 52 x 1.5 mm 3 with two piezoelectric ceramics (PIC 151 from Physik Instrumente (PI) GmbH-size: 50 x 25 x 0.5mm 3 ) bonded in the middle of the plate (Fig. 3). One ceramic was used as the actuator, the other as the sensor. The plate was tested in free conditions with a uniform ice layer (2 mm-thick). This simple structure allows simulation and experimental results to be compared accurately while limiting uncertainties in the boundary conditions and in the ice profile. The test specimen was tested in a freezer for 3 resonance frequencies (10, 15 and 26 kHz) and 2 types of modes (flexural and extensional).

For each resonance mode, sweeps were made around the resonance frequencies while increasing the voltage until the first fractures appeared. The fractures obtained for the three modes are shown in Fig. 3.

The initiation of de-icing for this bare structure and flexural frequencies around 10 kHz and 26 kHz was caused by tensile stresses. of anti-nodes. The vibratory magnitudes needed to obtain initiation of the de-icing for these modes are given in Fig. 4 and confirm the orders of magnitude of previous calculations. For the mode at 15 kHz, the initiation of deicing was also possible with the same order of magnitude because the resonance mode was not purely extensional:

as illustrated in Fig. 3(c) for the "extensional mode" at 15 kHz, in addition to in-plane displacements, out-of-plane displacements are also present because of non-uniformity in the thickness of the aluminum-ice composite beam.

These tests and other tests for other boundary conditions (clamped) and other forms (leading edge) in an icing wind tunnel are described in greater detail in Pommier-Budinger [START_REF] Pommier-Budinger | Electro-mechanical Resonant Ice Protection Systems. Initiation of Fractures with Piezoelectric De-icing Systems[END_REF]. They confirm that:

• for flexural modes, the tensile criterion dominates at low frequencies for de-icing,

• extensional modes, which are mainly high frequency, show better properties for delamination,

• the order of magnitude of the vibratory amplitudes that initiate de-icing can be determined from the evaluation of linear stresses. In order to study the propagation of fractures, the classical Griffith energy balance approach [START_REF] Schreurs | Fracture Mechanics[END_REF] is used. In the energy balance approach, it is assumed that a certain amount of energy is absorbed by the structure during the formation of an area of fracture surface. When the fracture propagates, a certain amount of stored elastic energy is released. The fracture grows in an unstable way if the released energy is equal to or greater than the absorbed energy.

The strain energy release rate is evaluated by the formula:

1 5 6 7 78 9 :
; <=

with b the depth of the plate, Ui the stored elastic energy, and lf the length of the fracture (Fig. 5). The strain energy release rate is compared with fracture toughness values given in Table 2 to conclude on the rapid propagation of cracks or delamination.

The fracture propagation direction is assumed to be known so that the propagation can be studied. It is also assumed here that the fractures take place for vibrations of constant amplitude (disp in equation ( 2) meaning constant displacement) and that the influence of the kinetic energy can be neglected in the energy balance. In order to verify that the modeling can be placed in a quasi-static framework, the execution time of these fracture phases has to be estimated and compared to the vibration period. This evaluation can be made using the speed of fracture propagation at the fracture tip. In ice, the literature [START_REF] Schreurs | Fracture Mechanics[END_REF] estimates this speed at between 20% and 40% of the speed of sound (defined by > ? /.), thus about s = 1000 m/s. At the ice/support interface, it is assumed that the speed is of the same order of magnitude. The order of magnitude of the time (in μs) necessary to create a crack through the thickness of the ice layer or to delaminate a part of the ice/support interface is negligible up to about 40 kHz (less than 1/10 of a half-period) if the delamination of the surface is limited to 25%. Finally, it is assumed that the variation in compliance of the structure necessary for the energy approach can be evaluated via a modal analysis.

B. Configurations Studied

Fig. 5 describes the four configurations that are studied in the next sections. They enable comparisons to be made for:

• the type of excited mode: flexion or extension.

• the mechanism of initiation of fracture: tensile stress on the surface of the ice (mechanism n°1) or shear stress at the ice/support interface (mechanism n°2).

The objective of this work is to obtain analytical models of the fracture propagation in order to evaluate the potential of each case for de-icing. The phases of cohesive fracture and adhesive fracture in mechanism n°1 are modeled independently, without analyzing either the switch from cohesive fracture to adhesive fracture or the end of delamination.

Fig. 5 -Configurations studied C. Numerical Study of Fracture with Modal Analysis

As an example of the approach followed to study fracture propagation, the propagation of a cohesive fracture (or crack) according to crack length lfy in the ice thickness is investigated for flexural modes of a beam (Fig. 5(a)).

The computations are run for a quarter of wavelength configuration thanks to symmetric and anti-symmetric boundary conditions. The crack is located on an anti-node, starting from the top surface of the ice layer, and the simulations are run for different crack lengths lfy assuming free boundary conditions for the crack. The number of elements along thickness is selected (30-50) in order to ensure a good representation of shear stress. The stored energy is calculated at the resonance frequencies with FEM modal analysis. The FEM modal analysis also allows the stresses and deformations to be computed (Fig. 6). It can be seen that the length of the crack started by the initial vibratory amplitude must be over a certain critical length to enable unstable propagation of the cohesive fracture. Furthermore, the cracking can also stop if the energy release rate is not sufficient. The complete fracture process may therefore require an increase of the initial vibratory amplitudes calculated in the preceding section on the sole criterion of tensile strength. For this case, a vibratory magnitude W0 = 15.5 µm initiates a crack length that generates an unstable crack growth through the whole thickness.

Fig. 6 -2D geometry studied and displacements obtained for a quarter wavelength by modal analysis

Note: the analysis is performed for a cohesive fracture in the ice here but the same type of analysis can be conducted for an adhesive fracture at the ice/support interface. for different de-icing configurations.

V. Analysis of Fracture Propagation with Mechanism n°1, Corresponding to Flexural Modes and Tensile

Criterion

A. Study Case and Objective of the Study

An analysis of the de-icing tests for flexural modes (Endres [START_REF] Endres | Experimental study of two electro-mechanical de-icing systems applied on a wing section tested in an icing wind tunnel[END_REF]) revealed two kinds of fracture propagation, either cohesive and then adhesive, or adhesive and then cohesive. Here, we study the case corresponding to flexural modes represented in Fig. 5(a) and illustrated by the photograph of Fig. 8:

• firstly, cohesive in the ice, just after the initiation of the fracture at the top surface of the ice layer and on the antinode of vibrations.

• secondly, adhesive at the ice/support interface, starting from the base of the fracture initiated just before.

It is often necessary to increase the voltage level to make this appear.

Fig. 8 -Example of cohesive and adhesive fractures for a flexural resonance mode

The first objective here is to determine simplified analytical models describing the cohesive fracture in the ice layer and the adhesive fracture at the ice/support interface, and allowing the elastic energy of the structures to be computed for different configurations of fracture propagation. These models are then used to compute the energy release rate according to the frequency, which can help to analyze the efficiency of de-icing systems using flexural modes and tensile stress.

Zone of adhesive fracture

Cohesive fractures

A simplification is made to obtain these models. The elastic energy is evaluated for only 3 states (Fig. 5(a)):

• state 1: before the cohesive fracture (no fracture in the ice),

• state 2: at the end of the cohesive fracture (crack of the ice through the entire ice layer),

• state 3: at the end of the adhesive fracture (25% of delamination).

We can find a mean value of the mean energy release rate between these states using the relation:

1 5 7 78 9 ≈ 1 5 ∆ ∆8 9 (3)
The two mean energy release rates computed between these three states make it possible to evaluate the cohesive and adhesive fracture potentials. As an example, in Fig. 7(a), the cohesive fracture between states 1 and 2 is characterized by a mean value of G of 0.875 J/m² (value computed for ∆8 9 2mm and ∆ D 1.75 HJ/m . This value is a simple but interesting indicator of the fracture potential of the configuration: with a value of 0.875 J/m² -lower than but close to 1 J/m² -some cohesive fractures can occur but cannot propagate through the entire ice layer.

B. Analytical Computations of the Elastic Energy and Mean Energy Release Rate

The analytical expression of the elastic energy of state 1, i.e. of the structure without fracture, is obtained using the equations of deformation (Table 3):

J 1 2 7> K 1 2 L - & & / 57 7L (4)
with the stress, the strain, and the rotation of a cross section.

,D

1 2 6 3 0 0 3 0 0 : ) " * M " 2 5$ ! (5)
The analytical expressions for states 2 and 3 are obtained using a substitution model based on the VPLM (for Variable Power Law Meta-model) method proposed by Sanchez [START_REF] Sanchez | Dimensional analysis and surrogate models for the thermal modeling of Multiphysics systems[END_REF]. The approach uses response surface models in logarithmic space combined with dimensional analysis. For the problem considered here, the physical variables involved are:

, NO 0 /$ ! ² Q , , " " , , (6)
with hice, halu the thicknesses of the ice and the support, respectively, an the length between 2 nodes, and cice, calu the elasticity of the ice and the support, respectively.

With 5 dimensional variables involving 2 physical dimensions, the application of the Buckingham theorem results in 3 dimensionless variables to express the problem. Moreover, the evolution of the resonance frequency is related to the variation in stiffness and therefore to the elastic energy of the structure. If it is assumed that the modal mass and the vibratory amplitude vary little during fracturing, there is a similarity of evolution between resonance frequency and elastic energy:

1 2 R$ ! ∝ Q O (7)
where

Q O 1 2 1 R T (8)
with K the modal stiffness and M the modal mass of the resonance mode.

Thus the problem can be rewritten in the following form:

! , NO 0 ,D Q O, NO 0 Q O,D Q -D , " , 0 / (9)
Obtaining ! only requires the resonance frequencies to be calculated for the three states of the configuration:

fr,1 for the initial state without fracture, fr,2 after cracking on the entire thickness, fr,3 after delamination of 25% of the surface. The VPLM method [START_REF] Sanchez | Dimensional analysis and surrogate models for the thermal modeling of Multiphysics systems[END_REF] and its associated computer DoE plans [START_REF] Hazyuk | Optimal design of computer experiments for surrogate models with dimensionless variables[END_REF] are used to obtain the approximate analytical expressions of ! for states 2 and 3. The experimental plan to be generated involves the dimensional physical variables , , " , , and the dimensionless numbers D , , 0 . It contains 4 levels for each dimensionless number, which makes 64 points for this experimental plan. The variation ranges of the variables of the problem are given in Table 4. The variation domains defined above can lead to certain unrealistic configurations such as resonance frequencies of the support that are too low and structures that are too fine. An additional constraint, resulting from the calculation of flexural resonance frequency is then added to the problem under study:

" > 2 120 (10)
The expression of the energy after cohesive fracture

!, , / ,D (11)
obtained by the regression method is given by:

obtained by the regression method is given by: These functions have less than 5% average error over the range of study when they are compared to the simulation data. The use of these functions makes it possible to evaluate the evolution of the mean energy release rate, G, as a function of frequency for the cohesive fracture (Fig. 9) and the adhesive fracture (Fig. 10). These evaluations were made for vibratory amplitudes leading to the initiation of de-icing under tensile stress with freezer-type ice (tensile strength of 3 MPa). The evolution of the curves for other strength or amplitude values can be performed by square scaling.

C. Analysis of Results

The analysis of the curves of Fig. 9 and Fig. 10 leads to the following remarks for the de-icing with flexural modes and tensile stress:

• The evolution of these curves as a function of frequency shows that the increase in frequency makes cohesive or adhesive fracturing more difficult;

• A comparison of the values of G with the values of of the state of the art (Table 2) shows that, using the amplitude computed to initiate the fracture, it is possible to make a cohesive fracture grow on the entire ice layer for low frequencies (on Fig. 9, the values of G are greater than 1 J/m² only for low frequencies) but that it is unlikely to make an adhesive fracture grow at the ice/support interface whatever the frequency (on Fig. 10, the values of G are always smaller than 0.5 J/m²). This point corroborates the experimental results, which showed that the propagation of adhesive fractures required higher supply voltage and thus higher power supply in comparison with the voltage or power required for initiating cohesive fractures.

• The variation of ice thickness affects cohesive fractures more strongly: a thick ice layer strongly facilitates a cohesive fracture but has little effect on an adhesive fracture.

Ice thickness

VI.

Analysis of Fracture Propagation with Mechanism n°2 Corresponding to Flexural Modes and Shear

Criterion

Section III of this paper introduces the possibility of a second de-icing mechanism, illustrated on Fig. 5(b), which should appear for higher frequencies than mechanism n° 1: at a vibration node, shear stresses induce a beginning of delamination. Here, we study the propagation of this adhesive fracture at the ice/support interface, using the methodology introduced in sections IV and V where the elastic energy is now evaluated for only 2 states:

• state 1: before the adhesive fracture (no fracture in the ice),

• state 2: at the end of the adhesive fracture on 25% of the ice/support interface surface.

The first point is identical to that of the previous section and the evaluation of the second point using a substitution model leads to the expression for the energy after adhesive fracture according to the substitution model:

with k = 0.92072, a1 = -0.024018, a2 = -0.0048137 and a3 = -0.010926. Fig. 11 also compares the energy release rate, G, for adhesive fractures of mechanisms n°1 and n°2, for the same vibratory amplitude levels. It can be seen that mechanism n°2 has a lower fracture potential and unstable delamination growth is even more unlikely when only the vibration amplitude that initiates the fracture is used.

Higher vibratory amplitude is required to lead to delamination.

The set of pictures from FEM simulations (Fig. 12) makes it possible to understand the difference in energy release rate, G, between the mechanisms n°1 and n°2. These FEM results show the distribution of tensile stresses, shear stresses and stored elastic energy for a bending mode. The spatial zones with high tensile stresses correspond to zones with high stored energy, while zones with high shear stresses correspond to low stored energy. From an analysis of Fig. 11 and Fig. 12, one can understand that fractures of ice occur more easily in zones with high elastic energy. In conclusion, unstable delamination growth through mechanism n° 2 has a low probability.

Shear Criterion

As illustrated in Fig. 3(c), the experiment shows greater delamination for modes having a mixture of displacements in the in-plane (extension) and out-of-plane (flexion) directions. The calculations of section III show that the initiation of delamination is mainly due to the out-of-plane components of these coupled modes. This

Ice thickness section thus focuses on the effect of in-plane deformations on fracture propagation for the two types of mechanisms presented previously.

For the FEM simulations, in order to quantify only the effect of the vibratory components in the plane, boundary conditions are forced on the faces so as to have only extension movements. In order to quantify the maximum effect that can be achieved by these components, the de-icing initiation point is placed at the most favorable position in terms of elastic energy, i.e. at the node of the extensional mode. By taking the approach of sections IV and V, the elastic energy is computed at several points:

• For mechanism n°1 (Fig. 5(c), tensile criterion), with 3 states: initial energy without fracture (state 1), after cohesive fracture in the entire ice layer thickness (state 2), after adhesive fracture on 25% of the ice/support interface (state 3).

• For mechanism n°2 (Fig. 5(c), shear criterion), with 2 states: initial energy without fracture (state 1), after adhesive fracture on 25% of the ice/support interface (state 2).

The cohesive fracture is thus studied between states 1 and 2 of mechanism n°1, and the adhesive fracture between state 2 and state 3 for mechanism n°1 (after a first cohesive fracture) and between state 1 and state 2 for mechanism n° 2 (without initial cohesive fracture).

As previously, the analytical expression for the elastic energy of state 1 (structure without fracture), is obtained using the equations of deformation (Table 3):

,D J 1 2 7> 1 2 ) " * " 2 5 ! (16)
The analytical expressions for the other states are obtained, as in Sections IV and V, using substitution models of FEM simulations. To generate the DoE, the ranges of the ice layer thickness and of the ice and support Young's moduli are the same as previously. To have a similar frequency range, however, it is necessary to adapt the range of the wavelength. The parameter an (distance between 2 nodes) considered here varies between 50 and 300 mm.

The simulation and meta-modeling results are as follows:

• For cohesive fracture through mechanism n° 1 (Fig. 5(c)): state 2 is very close in energy to the initial state 1. This means that extensional modes cannot be used as an enabler of cohesive fracture. If a crack appears before delamination in a de-icing process, it is more likely caused by out-of-plane displacements (and thus flexural modes).

• For adhesive fracture through mechanism n° 1 (Fig. 5(c)): the energy release rate for extensional modes (Fig. 13) is higher than for pure flexural modes (Fig. 10). The two diagrams are drawn with the assumption of an equal vibratory magnitude. The beneficial effect increases with the ice layer thickness. The elastic energy stored at the ice/support interface around extensional modes certainly explains the difference of fracture propagation between the purely flexural and combined extensional-flexural modes.

• For adhesive fracture through mechanism n°2 (Fig. 5(d)): as illustrated in Fig. 13, the energy release rate for extensional modes is low in this configuration. Considering this and previous results, de-icing due to mechanism n° 2 and resulting in fast delamination is less likely to occur than delamination due to mechanism n°1.

• Unlike the energy release rate for flexural modes, that for extensional modes is independent of frequency and thus can be helpful for high frequency de-icing.

Conclusion

The objective of this paper was to set up simplified models for a better understanding of fracture propagation in electromechanical vibratory de-icing systems. To achieve this, various simplifying hypotheses have been used: geometries assimilated to composite beams (support/ice), decoupling of resonance modes (flexion/extension), etc.

A first study concerned the initiation of fractures for de-icing. Models and experimental results show that the initiation of fractures can occur at low frequency using tensile stress or at high frequency using shear stress. The study highlights that the flexural modes are the most suitable to initiate fractures.

Using the vibratory amplitude to initiate de-icing as a starting point, a second study concerned fracture

propagation. An examination of experimental tests highlighted two possible mechanisms for the propagation: one mechanism initiated by tensile stresses and the other by shear stresses. Several proposals have been made for developing models of fracture propagation: energy balance analysis with modal analysis, simplification of the approach by studying the frequency of resonance on some characteristic states, establishing analytical formulations using substitution models. These analytical models made it possible to carry out trend studies, which revealed: the easier propagation of cohesive fractures for low frequency flexural modes, the low probability of de-icing by shear stress, the importance of the presence of elastic energy at the ice/support interface to generate delamination, and the interest of extensional modes to achieve such delamination. These results can be used as design guidelines for new de-icing architectures. They could be extended by further numerical studies not requiring the fracture propagation direction and by studies on more complex geometries, such as plates or leading edges.

2 =

 2 Critical energy release rate, J.m -2 halu = thickness of the support, m hice = thickness of the ice, m hn = position of the neutral line for the flexural mode, m -nodes for the considered mode, -Ui = stored elastic energy, J U(x) = in-plane displacements (for extensional modes), m U0 = anti-node magnitude of in-plane displacements (for extensional modes), m W(x) = out-of-plane displacements (for flexural modes), m W0 = anti-node magnitude of out-of-plane displacements (for flexural modes), m v = speed of sound, m/s x = transverse position over the beam of length a, aircraft or rotorcraft can affect control and cause mechanical failures. Icing occurs when an aircraft flies through clouds in which super cooled droplets are suspended in an atmosphere with an ambient air temperature below the freezing point. The droplets impinge on the aircraft surfaces and freeze, leading to ice accretion. The resulting change in the aircraft geometry can modify wing aerodynamic characteristics (loss of lift, increase in drag) or even damage the engine by ice ingestion. Regarding electrical de-icing systems, electrothermal and electro-impulse technologies are already implemented on aircraft but studies are currently in progress

I

  highlights two different possible fracture propagation mechanisms, the first initiated by tensile stresses and the second by shear stresses. Sections V and VI study fracture propagation for the two mechanisms introduced previously and for flexural resonance modes only. The last section extends the study to extensional modes and compares flexural and extensional modes for fracture propagation.

Fig. 2 -

 2 Fig. 2 -Main values for initiation of de-icing according to tensile and shear criteria

Fig. 3 (

 3 c) represents the mode shape of the corresponding modes where red colors indicate antinodes and blue colors indicate nodes. Positions of cracks initiation (red lines of Fig. 3(c)) correspond to positions

Fig. 3 -Fig. 4 -

 34 Fig. 3 -Experimental tests

Fig. 7

 7 Fig. 7 summarizes the simulation results for a half wavelength of 30 mm. The initial resonance frequency before crack propagation (lfy = 0 mm) is 6.45 kHz. At the end of the cohesive fracture propagation (lfy = 2 mm), the resonance frequency falls to 5.3 kHz. Fig. 7(a) shows the evolution of the elastic energy as a function of the crack length and for a vibratory amplitude, W0 = 11 μm (computed with formulas of section III), enabling the fracture to initiate in the ice. The derivation of this energy gives the energy release rate (Fig. 7(b)) and can be compared to the fracture toughness of the ice (1 J/m², value introduced in Table 2 and represented by the red line on Fig. 7(b)).

Fig. 7 -

 7 Fig. 7 -Elastic energy and energy release rate during cohesive fracture

k

  Nb c a _`^^ Nb c ^ _`^d Nb c d _ ^a^ Nb c a Nb c ^ _ ^^^ Nb c ^ Nb c ^ _ ^d^ Nb c d Nb c ^ … a _ ad^ Nb c d Nb c ^ _`a d Nb c = 0.21669, a1 = -1.7066, a2 = -0.31725, a3 = -0.33617, b12 = -0.68082, b11 = -1.4732, b13 = -0.63382, c121 = -0.36705, c111 = -0.43055, c231 = -0.21696, c131 = -0.25796 and b23 = -0.15783. The expression of the energy after adhesive fracture

  j d _f ^^ghi j ^ e a 0 e d _f dd ghi j d _k dd^g hi j d ghi j ^ (14) with k = 0.16234, a1 = -1.385, a2 = -0.064263, a3 = -0.52435, b13 = -0.30152, b11 = -0.79995, b33 = -0.092924, c331 = 0.12912.

Fig. 9 -Fig. 10 -

 910 Fig. 9 -Estimated mean energy release rate, G, between state 1 and state 2 for cohesive fracture and flexural modes regarding tensile criterion (aluminum 1.5 mm, glaze ice of different thicknesses)

Fig. 11 -Fig. 12 -

 1112 Fig. 11 -Estimated energy release rate, G, for adhesive fracture and flexural modes (between state 2 and state 3 for mechanism n°1 (tensile criterion) and between state 1 and state 2 for mechanism n°2 (shear criterion)

Fig. 13 -

 13 Fig. 13 -Estimated energy release rate, G, for adhesive fracture and extensional modes between state 2 and state 3 for mechanism n°1 (tensile criterion) and between state 1 and state 2 for mechanism n°2 (shear criterion)

Table 1 -Ice properties of glaze ice

 1

	Glaze ice

Table 2 -Strength and critical energy release rate for glaze ice

 2

		Cohesive (glaze ice)	Adhesive (ice/aluminum)
	Strength, cice	3 MPa, for freezer ice	1 MPa, for freezer ice
	Critical energy release rate,	1 J/m²	0.5 J/m²

Table 3 -1D modes formulas

 3

				Extensional modes						Flexural modes
	Displacement	,						# ,		$	$ !	"
						!	"		,			%	&# &
	Peak tensile strain	'	&	&		! "	( "		'	&	&	$ ! % ) "	*	"
	Peak ice tensile stress in ice	'			'	! "	( "	'					) "	* $ !	"
	Peak tensile stress in	'			'	! "	( "	'					) "	* $ !	"
	aluminum
	Peak shear	+ ',						+ ',
	stress at the ice/support	-.			) "	* /	!	"	) "	*	0	2	$ ! ( "
	interface
	Angular frequency			"	1 .	.					) "	* 1	.	23 .
													with
								23	3			0	0
													3	0	0

Table 4 -Variation range for the DoE

 4

	Variables	Units	Variation range
			HH	0.5 5
			HH	0.3 3
	"		HH	15 120
			V"	3 10
			V"	10 210
	D	/	-	1.67 10 XD 1.67 10 D
		< /"	-	2.50 10 X0 2 10 XD
	0	/	-	1.43 10 X	1

Acknowledgements

The present work is partially funded by Toulouse University and Occitanie region. The authors gratefully acknowledge the support of Florent Huet and Marc Wetterwald from Airbus Operation SAS in Toulouse, without which the present study could not have been completed.


Philippe Schaeffer

Lucile Bailly

Estelle Motsch

Pierre Adam
email: padam@unistra.fr

The effects of diagenetic aromatization on the carbon and hydrogen isotopic composition of higher plant di-and triterpenoids: evidence from buried wood

Keywords: Diterpenes, Triterpenes, Early diagenesis, Aromatization, Isotopes, Hydrogen, Carbon, Buried wood

The widely distributed aromatic di-and triterpenoids from higher plants occuring in sediments are formed by diagenetic microbial processes affecting their precursor plant lipids, and these compounds and their stable isotopic composition ( 13 C and  2 H) have the potential to be used for palaeoenvironmental and palaeoclimatic studies. In the present study, the isotopic composition of di-and triterpenoids aromatized to a different extent has been measured to examine the isotopic effects associated with the aromatization reaction. To overcome the possibility of multiple higher plant sources as is generally the case with sedimentary lipids, the  13 C and  2 H values of aromatized di-and triterpenoids from lipid extracts recovered from conifer and angiosperm buried wood have been determined, allowing an unambiguous genetic precursor/product relationship to be insured. The results show that the  13 C compositions of both di-and triterpenes do not seem to be significantly affected by Version non révisée 2 progressive aromatization, whereas the situation is more contrasted with  2 H values. In the case of diterpenoids related to abietic acid, a significant increase of the  2 H values by up to 86 ‰ with ongoing aromatization was measured. This is in contrast to what is expected for dehydrogenated compounds which should be globally more 2 H-depleted than their precursor molecules (e.g., biosynthesized unsaturated fatty acids vs. their saturated precursors). This 2 H enrichment of aromatized diterpenoids could indicate that they represent only minor residual intermediates, the majority of these intermediates having been further degraded by processes favoring the degradation of the 1 H-containing substrates and having a moderately pronounced 12 C/ 13 C selectivity. With triterpenoids, a preservation of the  2 H values was observed whatever the nature and extent of the aromatization process considered, which may be related to enzymatic reactions showing a limited carbon and hydrogen isotopic effect upon aromatization.

INTRODUCTION

The stable carbon ( 13 C) and hydrogen ( 2 H) isotopic composition of n-alkyl lipids from plants (n-alkanes, n-alkanoic acids) in sediments have been actively investigated to acquire plaeoenvironmental and palaeoclimatic information on, notably, the relative contributions of C3 and C4 plants (e.g., [START_REF] Huang | Climate change as the dominant control on glacial-interglacial variations in C3 and C4 plant abundance[END_REF][START_REF] Liu | Summer monsoon intensity controls C4/C3 plant abundance during the last 35 ka in the Chinese Loess Plateau : Carbon isotope evidence from bulk organic matter and individual leaf waxes[END_REF][START_REF] Tanner | C3/C4 variations in salt-marsh sediments: An application of compound specific isotopic analysis of lipid biomarkers to late Holocene paleoenvironmental research[END_REF][START_REF] Agrawal | C4 plant expansion in the Ganga Plain during the last glacial cycle: Insights from isotopic composition of vascular plant biomarkers[END_REF][START_REF] Diefendorf | Extracting the most from terrestrial plant-derived nalkyl lipids and their carbon isotopes from the sedimentary record: A review[END_REF][START_REF] Rao | Relationship between the stable isotopic composition of modern plants and surface soils and climate: A global review[END_REF] or on the reconstruction of past precipitation regimes or temperatures (e.g., [START_REF] Sauer | Compoundspecific D/H ratios of lipid biomarkers from sediments as a proxy for environmental and climatic conditions[END_REF][START_REF] Sachse | Hydrogen isotope ratios of recent lacustrine sedimentary n-alkanes record moderne climate variability[END_REF][START_REF] Garcin | Hydrogen isotope ratios of lacustrine sedimentary nalkanes as proxies of tropical African hydrology: Insights from a calibration transect across Cameroon[END_REF][START_REF] Diefendorf | Extracting the most from terrestrial plant-derived nalkyl lipids and their carbon isotopes from the sedimentary record: A review[END_REF][START_REF] Freimuth | Hydrogen isotopes of n-alkanes and nalkanoic acids as tracers of precipitation in a temperate forest and implications for paleorecords[END_REF][START_REF] Rao | Relationship between the stable isotopic composition of modern plants and surface soils and climate: A global review[END_REF]. The same palaeoenvironmental and palaeoclimatic information may potentially be provided by the determination of the  13 C and  2 H compositions of di-and triterpenic biomarkers from plants in sediments. However, contrary to straight-chain lipids which occur in all plant species, diand triterpenes can sometimes be associated to a specific plant familly or plant species (e.g., [START_REF] Jacob | Millet cultivation history in the French Alps as evidenced by a sedimentary molecule[END_REF]Le Milbeau, 2010;[START_REF] Schnell | Triterpenoids functionalized at C-2 as diagenetic transformation products of 2,3-dioxygenated triterpenoids from higher plants in buried wood[END_REF][START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. Investigation of their carbon and hydrogen isotopic composition might therefore potentially provide additional and more accurate information than that obtained from less or non-specific plant constituents. However, terpenoids generally undergo alteration processes upon diagenesis, such as aromatization which affects the structure of their genuine carbon skeleton and results in the loss of carbon and hydrogen atoms [START_REF] Spyckerelle | Aromatic hydrocarbons from geological sources III. A tetrahydrochrysene derived from triterpenes in recent and old sediments: 3,3,7-trimethyl-1,2,3,4-tetrahydrochrysene[END_REF][START_REF] Laflamme | Aromatized C-2 oxygenated triterpenoids as indicators for a new transformation pathway in the environment[END_REF]Wakeham et al;, 1980;Wolff et al., 1989;[START_REF] Stout | Aliphatic and aromatic triterpenoid hydrocarbons in a Tertiary angiospermous lignite[END_REF][START_REF] Simoneit | Cyclic terpenoids of contemporary resinous plant detritus and of fossil woods, ambers and coals[END_REF]Le Milbeau et al., 2010;[START_REF] Nakamura | Aliphatic and aromatic terpenoid biomarkers in Cretaceous and Paleogene angiosperm fossils from Japan[END_REF][START_REF] Schnell | Triterpenoids functionalized at C-2 as diagenetic transformation products of 2,3-dioxygenated triterpenoids from higher plants in buried wood[END_REF][START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. Since cleavage of several C-C and C-H bonds might be associated to important carbon and hydrogen isotopic effects, a key question arises whether the  13 C and  2 H values of aromatized terpenoids keep or not the original isotopic composition of their biological precursor molecules. This point is of particular interest for studies in which the stable isotopic signatures of lipids are used. In addition, investigation of the carbon and hydrogen isotopic effects associated with aromatization might Version non révisée also potentially give information about the mechanisms involved in these processes which remain largely unknown.

To our knowledge, there are only two studies dealing specifically with the impact of early diagenetic processes on the carbon [START_REF] Freeman | The effect of aromatization on the isotopic compositions of hydrocarbons during early diagenesis[END_REF][START_REF] Jacob | Combined δ 13 C -δD analysis of pentacyclic triterpenes and their derivatives[END_REF] or hydrogen [START_REF] Jacob | Combined δ 13 C -δD analysis of pentacyclic triterpenes and their derivatives[END_REF] isotopic compositions of sedimentary aromatized triterpenoids from angiosperms and one dedicated to the aromatisation processes affecting diterpenoids in coals and mustones (Tuo et al., 2006). Nevertheless, comparison of the  13 C or  2 H values of di-or triterpenoids aromatized to a different extent may occasionaly be found in articles not specifically dealing with the impact of aromatization processes on carbon and hydrogen isotopic composition, this aspect being generally not discussed (e.g., [START_REF] Schouten | The Paleocene-Eocene carbon isotope excursion in higher plant organic matter: Differential fractionation of angiosperms and conifers in the Arctic[END_REF]Tuo et al., 2003;[START_REF] Nakamura | Aliphatic and aromatic terpenoid biomarkers in Cretaceous and Paleogene angiosperm fossils from Japan[END_REF][START_REF] Suzuki | Probable fungal origin of perylene in Late Cretaceous to Paleogene terrestrial sedimentary rocks of northeast Japan as indicated from stable carbon isotopes[END_REF]. The main problem while investigating isotopic fractionation during aromatization of terpenes resides in the fact that a given aromatized terpenoid within a sediment sample might originate from mixed plant sources. It results that the  13 C and  2 H differences between the aromatized intermediate molecules within this sample might be due to fractionation effects associated with the aromatisation process itself, but may also be related to source effects (i.e., contribution of multiple source organisms with different isotopic compositions). To overcome this problem, we have investigated the case of aromatized terpenoids within ancient buried woods samples.

They indeed represent ideal candidates to study the effects of early diagenetic aromatization on carbon and hydrogen isotopic compositions of di-and triterpenoids since all the terpenoid intermediates from a given buried wood sample must be unambiguously genetically related.

We report here the determination and possible significance of the variations of the  13 C and  2 H signatures of aromatic terpenoids from buried wood samples comprising conifer wood (Pinus sylvestris) investigated for diterpenoids, and Quercus robur and Alnus sp. wood for triterpenoids.

Version non révisée

MATERIALS AND METHODS

Samples

Three buried wood samples were collected and analysed for their terpenoid content. They comprise:

Sample 1: Piece of trunk of Pinus sylvestris buried under a mudslide (age : > 4000 BP; SE France).

Sample 2 (cf. [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]: Inner part of an oak trunk (heartwood) unearthed from a palaeochannel of the Rhine river ( 14 C age: ca. 3700 BP; Gerstheim, NE France).

Sample 3 (cf. [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF][START_REF] Adam | Reinvestigation of the structure of a tetracyclic terpenoid from geological samples: A novel marker for fungi involved in the degradation of buried wood[END_REF]: Piece of alder heartwood (Alnus sp.) from a palaeochannel of the Rhine river ( 14 C age: ca. 3700 BP; Gerstheim, NE France).

GC-MS

GC-MS analyses were performed on a Thermo Scientific Trace Ultra gas chromatograph coupled to a Thermo Scientific TSQ Quantum mass spectrometer equipped with a Tri Plus autosampler and a programmed temperature vaporizing (PTV) injector. MS conditions were: source 220 °C, electron ionization (EI) at 70 eV and scanning m/z 50 to 700. GC conditions: HP5-MS column (30 m x 0.25 mm, 0.1 m film thickness) using He as carrier gas (constant flow, 1.1 ml/min); oven program: 70 °C-200 °C (10 °C/min), then to 300 °C (held 40 min) at 4 °C/min).

GC-irmMS

GC-irmMS measurements were carried out on a Delta V Plus mass spectrometer (Thermo Scientific) coupled to a GC Trace GC Ultra gas chromatograph equipped with a Triplus Version non révisée autosampler, an on-column injector, and an Agilent HP5-MS column (30 m x 0.25 mm i.d. x 0.1 µm film thickness), and connected to a ConFlow IV interface system and a GC Isolink II conversion unit, comprising a combustion oven at 1000 °C for  13 C measurements (resp. a pyrolysis oven at 1420°C for  2 H measurements). The temperature program was: 80 °C -310 °C (4°C/min) -isothermal at 310 °C (40 min). Each analysis was repeated 3 x. Before and after each triplicate, the carbon (resp. hydrogen) isotopic composition of a certified n-alkane mixture (Type A5; Arndt Schimmelmann, Biogeochemical Laboratories, Indiana University, USA) was measured and used for calibration. The stability of the measurements was checked using pulses of reference CO2 (resp. H2) prior (5 pulses) and after (3 pulses) each run. H3 + factor was determined every day. The data were analyzed using Isodat 3.0 software. For correction of the  13 C and  2 H values of derivatized lipids, see section 2.7.

Extraction and fractionation of lipids from the pine wood sample

The buried pine tree wood sample was extracted with CH2Cl2/CH3OH (1:1 v/v) according to the procedure described by [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. 975 mg of total lipid extract (TLE) were obtained from 5.52 g of wood, an aliquot of which (240 mg) being derivatized (1.

Ac2O/Pyridine 1:1 v/v; 2. esterification with a solution of diazomethane in Et2O, cf. [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. The derivatized TLE was fractionated on a silica gel column yielding three fractions eluted respectively with CH2Cl2/EtOAc (8:2 v/v) (F1, 168 mg; 2 x dead volume -Dv-); CH2Cl2/AcOEt (F2, 20.5 mg; 2 x Dv), and CH2Cl2/CH3OH (1:1 v/v) (F3; 22.5 mg; 2 x Dv).

Fraction F1 was analysed by GC-MS.

Besides, the remaining underivatized extract (ca. 730 mg) was fractioned on a silica gel column (Dv: 33 ml) to isolate diterpenoid hydrocarbon fractions for determination of their carbon and hydrogen isotopic compositions. Eight fractions were recovered eluting, respectively with cyclohexane (F'1 to F'5, 25 ml each), cyclohexane/CH2Cl2 (1:1 v/v, F'6 and Version non révisée F'7, 25 and 30 ml respectively) and CH2Cl2/CH3OH (1:1 v/v) (F'8; 50 ml). Fractions F'1-F'5 were analysed by GC-MS and GC-irmMS. Fraction F'8 was mainly composed of tetrahydroabietic acid 1 and was further purified on a silica gel column using CH2Cl2/EtOAc (95:5; v/v) as eluent, yielding almost pure tetrahydroabietic acid 1. The latter was silylated (section 2.7) prior analysis by GC-MS and GC-irmMS.

Fractionation of lipids from the oak wood sample

The sample from buried oak wood was extracted as described by [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. An aliquot of the crude extract (40 mg) was fractionated on a silica gel column using CH2Cl2 as eluent yielding, respectively, fraction F1 (11 mg; 3 Dv) and a more polar fraction F2 (5 mg; 3 Dv).

Fractionation of lipids from the alder wood sample

A moderately polar fraction (18 mg) obtained from a buried alder wood sample following a procedure involving extraction, derivatization and elution with CH2Cl2/EtOAc (8:2 v/v) on a silica gel column (cf. [START_REF] Adam | Reinvestigation of the structure of a tetracyclic terpenoid from geological samples: A novel marker for fungi involved in the degradation of buried wood[END_REF] was further fractionated on a silica gel column using successively cyclohexane/CH2Cl2 (8:2; v/v) and EtOAc/CH2Cl2 (8:2; v/v) as eluents, yielding, respectively, an apolar fraction F1 (1.8 mg) containing the aromatic hydrocarbons which was further analyzed by GC-MS and GC-irmMS and a more polar fraction F2 (16 mg) not further investigated.

Derivatization

Fractions containing alcohols, phenols or carboxylic acids were derivatized prior GC-MS and GC-irmMS analysis using pyridine (40 µl) and bis-(N,O-trimethylsilyl)trifluoroacetamide (BSTFA; 150 l, 70 °C, 2 h) having a known carbon and hydrogen isotopic composition of the trimethylsilyl group ( 13 C : -41.14 ‰;  2 H : -154.09 ‰). The solvent and excess reagent Version non révisée were removed under a stream of N2.  2 H and  13 C values of derivatized biomarkers were corrected according to [START_REF] Rieley | Derivatization of organic compounds prior to gas chromatographiccombustion-isotope ratio mass spectrometric analysis: identification of isotope fractionation processes[END_REF] for the added trimethylsilyl group.

RESULTS AND INTERPRETATIONS

Diagenetic aromatization of diterpenoids

GC-MS analysis of the organic extract of the sample of buried Pinus sylvestris (Figure 1) revealed the presence of diagenetic transformation products of diterpenoid acids from the abietane and pimarane series such as tetrahydroabietic acid 1, monounsaturated derivatives of abietic and pimaric acids (2, 3) and dehydroabietic acid 4. The former was the predominant constituent of the fraction and is considered as a typical microbial reduction product formed under anaerobic conditions [START_REF] Reunanen | Long term alteration of pine tar in a marine environment[END_REF][START_REF] Bailly | Identification of guaiacyl dehydroabietates as novel markers of wood tar from Pinaceae in archaological samples[END_REF]. Beside diterpenic acids, various saturated (fichtelite 5), monounsaturated (6), and aromatic hydrocarbons such as 18-norabietatriene 7, tetrahydroretene 8 and retene 9 were detected. Such diterpenic structures are frequently encountered in sediments with a significant contribution of biomass originating from conifers (e.g., Wakeham et al., 1980;[START_REF] Simoneit | Cyclic terpenoids of contemporary resinous plant detritus and of fossil woods, ambers and coals[END_REF][START_REF] Hautevelle | Vascular plant biomarkers as proxies for palaeoflora and palaeoclimatic changes at the Dogger/Malm transition of the Paris Basin (France)[END_REF]Tuo et al., 2006;[START_REF] Nakamura | Aliphatic and aromatic terpenoid biomarkers in Cretaceous and Paleogene angiosperm fossils from Japan[END_REF][START_REF] Suzuki | Probable fungal origin of perylene in Late Cretaceous to Paleogene terrestrial sedimentary rocks of northeast Japan as indicated from stable carbon isotopes[END_REF]. The aromatic compounds 7-9 are postulated to be the result of microbial aromatization processes operative under anoxic conditions (Tavendale et al., 1997a,b;[START_REF] Martin | Recent advances in understanding resin acid biodegradation: microbial diversity and metabolism[END_REF].

For the investigation of the isotopic effects associated with aromatization processes, we have measured the carbon and hydrogen isotopic composition of the aromatic compounds 7, 8, and 9 after chromatographic separation of the total hydrocarbons from the TLE (see below). For comparison, the  2 H and  13 C values of partly reduced compounds such as tetrahydroabietic acid 1, one monounsaturated tricyclic hydrocarbon 6 and fichtelite 5 have been measured. This allowed us to evaluate specifically the influence of decarboxylation on the carbon isotopic composition of diterpenes (comparison between 1 and 5). Because of partial Version non révisée coelutions in GC, determination of the  2 H and  13 C values of the various diterpenoids discussed above could not be performed directly on the lipid fraction shown in Figure 1.

Therefore, further liquid chromatography fractionation was carried out, leading to several subfractions enriched in the diterpenoids of interest and allowing the  2 H and  13 C compositions of compounds 1 and 5-9 to be determined.

The results show that the carbon isotopic composition of the diterpenoids is retained, independently of the diagenetic alteration process considered (decarboxylation, reduction, and aromatization) (Figure 2). On the contrary, the  2 H signatures seem to be strongly affected by these processes, which apparently result in a progressive increase of the D values with ongoing aromatization (from -238 ‰ for 18-norabietatriene 7 to -152 ‰ for retene 9). A similar observation was made by Tuo et al. (2006) in the case of diterpenoids occurring in a series of mudstone samples from the Liaohe Basin (China). Thus, the  2 H values determined for dehydroabietane 10 by Tuo et al. (2006) were generally lower than those measured for the related diaromatic diterpenoid simonellite 11 within the same samples, except in one case.

Hydrogenation processes affecting abietic acid and leading to the formation of tetrahydroabietic acid 1, hydrocarbon 6 and fichtelite 5 in our wood sample (Figure 2) are likely induced by microorganisms, which might explain the slightly lower  2 H values (ca. 25 ‰ difference) between the hydrogenated compounds 1 and 5 and their unsaturated counterpart (6). The D-depletion of the hydrogenated compounds can be explained by the fact that the biological reactions involved in the reduction processes indeed favor the incorporation of 2 H-depleted hydrogen. Such a situation has been observed, for instance, by Chikaraishi et al. (2009) for the biosynthesis of phytol from geranyl geraniol. By contrast, the progressive increase of the  2 H values observed during aromatization of 18-norabietatriene 7

Version non révisée (-238 ‰) to retene 9 (-152 ‰) is more difficult to interpret and will be discussed in detail in section 3.3.1.

Diagenetic aromatization of triterpenoids

Quercus robur

The triterpenoids recovered from the inner part of buried trunk of Q. robur unearthed from a palaeochannel of the Rhine (NE, Gerstheim; France) have been investigated. A detailed molecular analysis of the sample can be found in [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. The predominant aromatized triterpenoids identified (12-17) bear an oxygen functionality at C-2 (Le Milbeau et al., 2010;[START_REF] Schnell | Triterpenoids functionalized at C-2 as diagenetic transformation products of 2,3-dioxygenated triterpenoids from higher plants in buried wood[END_REF][START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF]. These compounds have inherited this uncommon structural feature from the predominant biological triterpenoid precursors 18 and 19 functionalized at both C-3 and C-2 which occur in fresh Q. robur wood. They result from aromatization processes starting in ring D from the triterpenoid skeletons and progressing towards ring A (Figure 3). Two chromatographic fractions, one enriched in the two monoaromatic ketones 14-15 and tetraaromatic phenols 16-17 (Figure 4a) and the other dominated by the alcohols 12 and 13 (Figure 4b) could be separated from the lipid extract of the oak wood sample obtained according to the procedure described in [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF].

These compounds correspond to two triplets of unambiguously genetically related triterpenoids (Figure 3) which are ideal candidates for the evaluation of the effects of aromatization processes on both carbon and hydrogen isotopic compositions. The  13 C and  2 H values of triterpenoids 12-17 are given in Figure 3. Surprizingly, despite the loss of up to six methyl groups from the precursor molecule 19 to its tetraaromatic phenol counterpart 17, neither the carbon, nor the hydrogen isotopic compositions of the different intermediates seem to be significantly affected by these aromatization processes progressing from ring D to ring A.

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Alnus sp.

For comparison, the impact of aromatization processes on the carbon and hydrogen isotopic compositions during aromatization of C-3-oxygenated triterpenes (as opposed C2,C3difunctionalized precursor molecules) following the "classical" pathway starting from ring A and progressing towards ring D (e.g., Wolff et al., 1989;[START_REF] Stout | Aliphatic and aromatic triterpenoid hydrocarbons in a Tertiary angiospermous lignite[END_REF] has been investigated.

For that purpose, the carbon and hydrogen isotopic composition of aromatic triterpenoid hydrocarbons related to lupanol 20 and -amyrin 21 occurring in the organic extract of Alnus sp. wood found at the same site as the oak wood sample have been determined. A detailed analysis of the lipid extract of this sample is presented in [START_REF] Schnell | Contrasting diagenetic pathways of higher plant triterpenoids in buried wood as a function of tree species[END_REF] and [START_REF] Adam | Reinvestigation of the structure of a tetracyclic terpenoid from geological samples: A novel marker for fungi involved in the degradation of buried wood[END_REF]. The partial gas chromatogram of the aromatic hydrocarbon fraction focusing on the pentacyclic triterpenoids is presented in Figure 5. They comprise mono-( 22) (Wolff et al., 1989), tri-(23, 24) and tetraaromatic (25) triterpenoids [START_REF] Spyckerelle | Aromatic hydrocarbons from geological sources III. A tetrahydrochrysene derived from triterpenes in recent and old sediments: 3,3,7-trimethyl-1,2,3,4-tetrahydrochrysene[END_REF][START_REF] Laflamme | Aromatized C-2 oxygenated triterpenoids as indicators for a new transformation pathway in the environment[END_REF]Wakeham et al., 1980;[START_REF] Chaffee | Polycyclic aromatic hydrocarbons in Australian coals-III Structural elucidation by proton magnetic resonance spectroscopy[END_REF], all being closely genetically related (Figure 6). Comparison of the  2 H and  13 C values of the triterpenes from both oleanane and lupane series showed that the hydrogen and carbon isotopic are not significantly affected by the degree of aromatization, as was observed with the triterpenoids from the oak sample (see above). [START_REF] Freeman | The effect of aromatization on the isotopic compositions of hydrocarbons during early diagenesis[END_REF] obtained similar results for carbon isotopes in the case of aromatized triterpenoids occurring in Eocene oil shale samples (Messel formation, Germany). In this case, however, the genetic relationship between the various aromatized higher plant triterpenoids from the same series could not be guaranteed since the triterpenes likely originated from multiple higher plant sources. Regarding 2 H/ 1 H isotopes, there is only one study which is devoted to the comparison of the  2 H composition of triterpenoids aromatized to a different extent in sediments [START_REF] Jacob | Combined δ 13 C -δD analysis of pentacyclic triterpenes and their derivatives[END_REF]. In this study, important variations of up to 100 ‰ could be observed between potential triterpenoid precursors and related aromatized compounds, a difference which we did not observe in our study. However,

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as for the study of [START_REF] Freeman | The effect of aromatization on the isotopic compositions of hydrocarbons during early diagenesis[END_REF], the authors were dealing with triterpenoids extracted from sediments, and for which multiple plant sources with different hydrogen isotopic compositions can be expected.

Evolution of isotopic compositions upon aromatization

Early diagenetic aromatization processes observed in buried wood are triggered by anaerobic microbial processes (e.g., Tavendale et al., 1997a,b;Harder and Foß, 1999;[START_REF] Martin | Recent advances in understanding resin acid biodegradation: microbial diversity and metabolism[END_REF] as demonstrated by incubation experiments involving either diterpenic acids (Tavendale et al., 1997a,b) or triterpenoids (e.g., [START_REF] Trendel | Dégradation de triterpènes dans les sédiments[END_REF]Lohmann, 1988;[START_REF] Lohmann | C-29 tritiated -amyrin : chemical synthesis aiming at the study of aromatization processes in sediments[END_REF]. Therefore, since the formation of aromatized di-and triterpenoids is biologicallymediated, one could envisage that the carbon and hydrogen isotopic shifts induced by these processes have some analogies with those from enzymatic reactions involved in the dehydrogenation of fatty acids via desaturases (e.g., [START_REF] Behrouzian | Application of KIE and thia approaches in the mechanistic study of a plant steraoly-ACP  9 desaturase[END_REF][START_REF] Buist | Fatty acid desaturase: selecting the dehydrogenation channel[END_REF][START_REF] Buist | Deciphering the cryptoregiochemistry of oleate  12 desaturase: a kinetic isotope effect study[END_REF][START_REF] Savile | Cryptochemistry of a Brassica napus fatty acid desaturase: a kinetic isotope effect[END_REF][START_REF] Shanklin | Desaturases : Emerging models for understanding functional diversification of diiron-containing enzymes[END_REF] or in the aromatization of androgen steroids via aromatases (e.g., [START_REF] Simpson | Aromatase cytochrome P450, the enzyme responsible for estrogen biosynthesis[END_REF][START_REF] Akhtar | A review of mechanistic studies on aromatase (CYP19) and 17-hydroxylase-17,20-lyase (CYP17)[END_REF]. Indeed, similarly to the aromatization processes leading from sterols to aromatic steroid hormones such as estradiol, the aromatization of diterpenoids and triterpenoids involves the loss of angular methyl groups. Like for the aromatization of the ring A of androgen steroids, terpenoid aromatization might proceed via the functionalization of the angular methyl groups.

Hydrogen isotopic effects related to the dehydrogenation reactions or loss of methyl groups catalyzed by the enzymes involved have often been investigated in the frame of studies aimed at elucidating their mechanisms, but the carbon isotope effects associated with these reactions are generally not documented. Thus, for instance, in the case of fatty acid desaturases, the hydrogen kinetic isotope effect has been shown to be strongly dependent on the class of enzymes involved. This effect can be important in the case of membrane-bound desaturases (e.g., [START_REF] Savile | Cryptochemistry of a Brassica napus fatty acid desaturase: a kinetic isotope effect[END_REF][START_REF] Buist | Deciphering the cryptoregiochemistry of oleate  12 desaturase: a kinetic isotope effect study[END_REF], but is sometimes negligible with Version non révisée soluble plant desaturases (e.g., [START_REF] Behrouzian | Application of KIE and thia approaches in the mechanistic study of a plant steraoly-ACP  9 desaturase[END_REF][START_REF] Buist | Fatty acid desaturase: selecting the dehydrogenation channel[END_REF]. It should however be noted that the enzymes involved in these biosynthetic pathways bear iron at their active site and are O2-dependent [START_REF] Shanklin | Desaturases : Emerging models for understanding functional diversification of diiron-containing enzymes[END_REF][START_REF] Akhtar | A review of mechanistic studies on aromatase (CYP19) and 17-hydroxylase-17,20-lyase (CYP17)[END_REF], being able to activate C-H bonds aerobically. Therefore, since the early diagenetic aromatization of di-and triterpenes apparently only occur under anaerobic conditions according to incubation experiments [START_REF] Trendel | Dégradation de triterpènes dans les sédiments[END_REF]Lohmann, 1988;[START_REF] Lohmann | C-29 tritiated -amyrin : chemical synthesis aiming at the study of aromatization processes in sediments[END_REF]Tavendale et al., 1997a,b;Harder and Foß, 1999;[START_REF] Martin | Recent advances in understanding resin acid biodegradation: microbial diversity and metabolism[END_REF], it is likely that the enzymatic processes initiating anaerobic aromatization are significantly different and comprise C-H bond cleavage in the absence of oxygen following different pathway(s). These pathways possibly involve the formation of a radical by abstraction of an hydrogen atom as has been described for the enzymes responsible for the biodegradation of hydrocarbons under strictly anaerobic conditions (e.g., [START_REF] Spormann | Metabolism of alkylbenzenes, alkanes, and other hydrocarbons in anaerobic bacteria[END_REF][START_REF] Buckel | Radical enzymes in anaerobes[END_REF][START_REF] Heider | Adding handles to unhandy substrates : anaerobic hydrocarbon activation mechanisms[END_REF][START_REF] Booker | Anaerobic functionalization of unactivated C-H bonds[END_REF]. Nevertheless, regardless of the enzymatic pathway(s) involved (aerobic vs. anaerobic), the isotopic selectivity in the initiation step of the aromatization processes can probably be expected to be similar in aerobic and anaerobic processes and to favor, globally, light isotopes (i.e., 1 H and 12 C vs. 2 H and 13 C).

Hydrogen isotopic composition

In the case of fatty acids biosynthesized by some marine macroalgae, it has been observed by [START_REF] Chikaraishi | Hydrogen isotopic fractionations during desaturation and elongation associated with polyunsaturated fatty acid biosynthesis in marine macroalgae[END_REF] that the  2 H values of saturated fatty acids are significantly increased compared to their unsaturated metabolites, which is probably related to the important hydrogen isotopic effect associated to dehydrogenation reactions induced by membranebound desaturases (e.g., [START_REF] Savile | Cryptochemistry of a Brassica napus fatty acid desaturase: a kinetic isotope effect[END_REF][START_REF] Buist | Deciphering the cryptoregiochemistry of oleate  12 desaturase: a kinetic isotope effect study[END_REF]. In the case of sequential dehydrogenation processes such as those leading from saturated fatty acids to mono-di-, tri and tetra-unsaturated fatty acid analogues, the evolution of the  2 H values of the intermediates was more difficult to predict. According to [START_REF] Chikaraishi | Hydrogen isotopic fractionations during desaturation and elongation associated with polyunsaturated fatty acid biosynthesis in marine macroalgae[END_REF], it appears Version non révisée that these processes depend on the relative fluxes into the various unsaturated products and on the conversion rates, since each dehydrogenation step affecting an intermediate is supposed to result in a 2 H-enrichment of this intermediate relative to the product formed. Similar observations have been made when the hydrogen isotopic composition of alkenones was compared to that of their related dehydrogenated products [START_REF] D'andrea | An efficient method for isolating individual long-chain alkenones for compound specific hydrogen isotope analysis[END_REF][START_REF] Schwab | The measurement of D/H ratio in alkenones and their isotopic heterogeneity[END_REF]. It should, however, be noted that Zhang and Sachs (2007) observed a different trend for the biosynthesis of C18 unsaturated fatty acids from stearic acid by the Chlorophyceae Eudorina unicocca and Volvox aureus. With these organisms, the  2 H values measured for the C18 unsaturated fatty acids were similar or slightly higher than those determined for stearic acid. These authors explained this observation by the fact that the desaturases involved in the biosynthesis of unsaturated fatty acids in these organisms belong to the so called "soluble" desaturases. As mentioned above, the action of these enzymes was indeed shown to induce only very limited isotope effects (e.g., [START_REF] Behrouzian | Application of KIE and thia approaches in the mechanistic study of a plant steraoly-ACP  9 desaturase[END_REF][START_REF] Buist | Fatty acid desaturase: selecting the dehydrogenation channel[END_REF]. In our case, the absence of a significant evolution of the  2 H value of the triterpenoids, whatever the series considered (i.e., lupane vs. oleanane), the aromatization process (i.e., from ring A to ring D or ring D to ring A; Figure 3 and Figure 6, respectively), and aromatization progress (i.e., from mono-to tetraaromatic derivatives), might thus be explained by the fact that the 1 H/ 2 H isotopic effect related to the bacterial enzymes involved in these aromatization processes operating under oxygen-depleted conditions is limited, similarly to the "soluble" desaturases reported from plants.

In the case of the aromatized diterpenoids from Pinus silvestris, the significant increase of the  2 H values observed with increasing aromatization is more difficult to explain in this context.

One would indeed expect the aromatized diterpenes to have lower  2 H values or, as observed in the case of the triterpenoids, almost similar  2 H values than their precursor molecules. The present observation can only be explained if the aromatized diterpenoids identified Version non révisée correspond to minor residual intermediates which have survived overall degradation processes that led to further degradation products not detected in our study or to complete remineralization. Such degradation processes would indeed most likely strongly favor the degradation of 1 H-enriched substrates, resulting in an increase of the  2 H values of the residual aromatic diterpenes. A similar  2 H trend has been reported in the case of the anaerobic biodegradation of aromatic hydrocarbons such as toluene by denitrifying, sulfatereducing and fermenting bacteria using the succinate pathway (e.g., Morash et al., 2001;[START_REF] Meckenstock | Stable isotope fractionation analysis as a tool to monitor biodegradation in contaminated aquifers[END_REF]Vogt et al., 2008). In this connection, it should be noted that the  2 H values determined by Tuo et al. (2006) for dehydroabietane 10 in a series of mudstone samples from the Liaohe Basin were generally lower (except in one case) than those measured for the related diaromatic diterpenoid simonellite 11 within the same samples. This overall trend was thus close to that observed in our sample. Tuo et al. (2006) nevertheless proposed another explanation for this trend, arguing that dehydrogenation processes most likely lead to a 2 H-enrichment of the products relative to the substrate, since hydrogen is preferentially removed during such processes. This is, however, not the case as illustrated by the evolution of the  2 H values of unsaturated lipids formed by dehydrogenation processes induced by desaturases as compared to that of their saturated precursors (e.g., [START_REF] Chikaraishi | Hydrogen isotopic fractionations during desaturation and elongation associated with polyunsaturated fatty acid biosynthesis in marine macroalgae[END_REF][START_REF] D'andrea | An efficient method for isolating individual long-chain alkenones for compound specific hydrogen isotope analysis[END_REF][START_REF] Schwab | The measurement of D/H ratio in alkenones and their isotopic heterogeneity[END_REF]. When a dehydrogenation reaction occurs, the increase of the  2 H value of the remaining substrate relative to that of the unsaturated product formed is due to the fact that the hydrogen isotopic effect mainly affects the hydrogen atom at the C-H position involved in the in the first C-H cleavage reaction (e.g. [START_REF] Buist | Fatty acid desaturase: selecting the dehydrogenation channel[END_REF]Behrouzian, 1996, 1998), this hydrogen atom involved in the desaturation being finally lost.

The  2 H value of the hydrogen atoms from the unsaturated product (or aromatized compound, in our case) formed should thus be almost identical to that of the substrate at the beginning of the reaction, whereas that of the remaining unreacted substrate should progressively increase Version non révisée (Figure 7). In the case of cascade reactions as observed for the diagenetic di-and triterpenoids, it is of importance to note that each intermediate also corresponds to the substrate of the next reaction, the same type of 2 H isotope fractionation applying hence at each step. Furthermore, at each step, the extent of 2 H isotopic fractionation will depend on the yield of the reaction, the  2 H composition of the substrate increasing with increasing yield relative to the product(s) formed. Therefore, given these considerations, it appears that the interpretation of the 1 H/ 2 H signatures of biomarkers formed by diagenetic processes are extremely difficult to interpret in the case of palaeoenvironmental studies (e.g., past climatic changes, palaeohydrology).

Stable carbon isotopic composition

The results show that the carbon isotopic compositions of both di-and triterpenes do not seem to be significantly affected by progressive aromatization, regardless of the nature of the substrate (di-vs. triterpenes), of the process involved (triterpene aromatization progressing from ring A to ring D or from ring D to ring A) and of the number of carbon atom(s) lost during the process (with up to 6 methyl groups lost in the case of tetraaromatic triterpenoids). This suggests that the kinetics of the enzymatic processes for aromatization are not sensitive to carbon isotopic effects. In the same way as that proposed to explain the evolution of the  2 H signatures of terpenoids in relation with intense alteration processes (see above), one might envisage that these degradation processes might potentially also lead to an increase of the  13 C values of the residual, undegraded aromatic terpenes. However, such a trend has not been observed, and might be due to the fact that anaerobic biodegradation processes affecting aromatic hydrocarbons can be significantly more sensitive to hydrogen isotopes than to carbon isotopes, at least in some cases, as demonstrated for the anaerobic biodegradation of toluene (e.g., Morash et al., 2001;[START_REF] Meckenstock | Stable isotope fractionation analysis as a tool to monitor biodegradation in contaminated aquifers[END_REF]Vogt et al., 2008) or with diterpenes (the present study).

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CONCLUSIONS

The stable carbon and hydrogen isotopic composition of aromatic di-and triterpenoid biomarkers from conifer and angiosperm buried wood has been investigated to determine the extent of the isotopic fractionation involved in these diagenetic aromatization processes. Our results indicate that the stable carbon isotopic composition is not significantly affected by aromatization regardless of the substrate (di-vs. triterpenoids), of the processes involved (aromatization progressing from ring A to ring D or from ring D to ring A) and of the number of carbon atom(s) lost during the process. This absence of changes in the terpenoid  13 C signatures may be attributed to the limited sensitivity of the enzymes involved in the biological aromatization processes towards carbon isotopic effects, and indicates that  13 C signatures of aromatic higher plant lipids may thus be used with confidence to trace potential biological sources (e.g., C3 vs. C4 plants).

In the case of the hydrogen isotopic composition of diagenetic terpenoids, our observations are more contrasted, with the diterpenoid  2 H signatures showing a strong increase of the  2 H values with ongoing aromatization, and triterpenoid  2 H composition remaining almost constant whatever the nature and extent of the aromatization process involved. In the case of diterpenoids, the trend observed could be attributed to the fact that the different aromatic diterpenoids analyzed represent extremely minor intermediates which have survived to further degradation/mineralization which affected the majority of the diterpenoid pool. In contrast, the constancy of the triterpenoid  2 H signature suggests that 1 H/ 2 H isotopic effects related to the bacterial enzymes involved in these aromatization processes operating under oxygendepleted conditions is limited, similarly to what is reported for the "soluble" desaturases from plants. The high variability of the 1 H/ 2 H values measured for aromatic terpenoids suggests Version non révisée that the interpretation of the 1 H/ 2 H signatures of biomarkers formed by such diagenetic processes may be extremely difficult to interpret in connection with palaeoenvironmental studies (e.g., climatic changes, palaeohydrology). Tuo, UJ., Wang, X., Chen, J., & Simoneit, B.R.T., 2003. Aliphatic and diterpenoid hydrocarbons and their individual carbon isotopic composition in coals from the Liaohe Basin, China. Organic Geochemistry 34, 1615-1625. Tuo, J., Zhang, M., Wang, X., Zhang, C., 2006. Hydrogen isotope ratios of aliphatic and diterpenoid hydrocarbons in coals and carbonaceous mudstones from the Liaohe Basin, China. Organic Geochemistry 37, 165-176. Vogt, C., Cyrus, E., Herklotz, I., Schlosser, D., Bahr, A., Herrmann, S., Richnow, H.H., Fischer, A., 2008. Evaluation Version non révisée dehydrogenations. Biologically triggered dehydrogenation reactions are generally sensitive to the isotopic composition of the hydrogen atom (H1a biol) involved in the first C-H cleavage reaction and not to that involving the second hydrogen atom (H2a biol) removed during the dehydrogenation step (e.g., [START_REF] Buist | Use of deuterium kinetic isotope effects to probe the cryptoregiochemistry of  9 desaturation[END_REF][START_REF] Buist | Deciphering the cryptoregiochemistry of oleate  12 desaturase: a kinetic isotope effect study[END_REF]. The role on the isotopic composition of the hydrogen atoms not involved in the reaction should be negligible (secondary isotopic effects). It results that the  2 H value of the remaining substrate should increase mainly due to the progressive 2 H-enrichement of the hydrogen at the position involved in the first C-H cleavage reaction whereas the  2 H value of the monounsaturated transformation product should be close to that of the original biological substrate prior dehydrogenation (unless the latter serves as a substrate for further dehydrogenation). Version non révisée

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FIGURE 1

 1 FIGURE CAPTIONS

FIGURE 2 FIGURE 3

 23 FIGURE 2 Scheme showing the genetic relationship between abietic acid and its related diagenetic diterpenoids occurring in buried pine wood. Measured  2 H and  13 C values are

FIGURE 4

 4 FIGURE 4 Partial gas chromatograms (GC-MS) of fraction (a) F1; (b) F2 (cf. section 2.5) isolated from the TLE from a buried oak (Q. robur) trunk (heartwood) sample collected in a palaeochannel from the Rhine river (Gerstheim, NE France). Alcohols and phenols were analysed as trimethylsilyl derivatives.

FIGURE 6

 6 FIGURE 6 Scheme showing the genetic relationship between aromatic triterpenoids 22-25 occurring in buried alder wood found in Gerstheim (NE France). Measured  2 H and  13 C

  Fig. 1

  Fig. 2

Fig. 7

 7 Fig. 7

H r.subs > 2 H biol 2 H unsat > 2 H lost hydro 1 2

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						Enzymatic dehydrogenation
						Preferential removal of 1 H vs. 2 H
			H	H	H	H 2b biol	H 1a biol H 1b biol
			H		H	H 2a biol	H	Biological precursor molecule
			H			H
	Diagenesis Progressive 2 H enrichment			Dehydrogenation	-H 1a H 2a Lost Hydrogen
									2 H lost H1a < 2 H H1a biol
									2 H lost H2a = 2 H H2a biol
	H	H	Remaining substrate H H H H 1a r.subs H 1b r.subs H H 2b r;subs H 2a r.subs H 1 H 2		H H	H 2b unsat H H	2	H H	H 1b unsat transformation product Mono unsaturated H H 1
			2 H H1a biol < 2 H H1a r.subs			2 H H1b biol = 2 H H1b unsat
			2 H H2a biol = / 2 H H2a r.subs			2 H H2b biol = 2 H H2b unsat
			2

ACKNOWLEDGMENTS

D. Schwartz (Université de Strasbourg) is thanked for the gift of the wood sample of Pinus sylvestris, and N. Schneider (Institut National de Recherches Archéologiques Preventives) for the oak and alder wood samples. LB thanks the French "Ministère de l'Enseignement Supérieur et de la Recherche" for a doctoral fellowship. The "Centre National de la Recherche Scientifique" and "Université de Strasbourg" are thanked for financial support.