Pierre Gilormini

Emmanuel Richaud

Jacques Verdu

RADIOCHEMICAL "DEGELATION" OF POLYMETHYL METHACRYLATE NETWORKS

Keywords: Polymer network, Radiolysis, Degelation

Methyl methacrylate-ethylene glycol dimethacrylate networks were synthetized and submitted to radiochemical degradation, with ageing monitored by means of sol-gel analysis. The networks were shown to undergo chain scission predominantly, which leads to their degelation, i.e., the recovery of a thermoplastic-like behavior with loss of all elastically active chains. The degelation dose was shown to increase with crosslink density and the corresponding critical conversion ratio was discussed regarding a recent and general statistical theory that covers radiochemical as well as chemical chain scissions.

Introduction

The degradation of polymeric networks by chain scission is a process that receives an increasing attention in the scientific literature [1][2][3] because it offers the opportunities to recycle materials without downgrading and to regenerate new chemical feedstock. When this process is considered from the point of view of chemical kinetics, the pertinent parameter to characterize the extent of degradation is the conversion ratio y defined by y= N/N 0 , where N 1 Corresponding author.

Tel. : +33 1 44 24 63 37 Fax : +33 1 44 24 63 82 Email : pierre.gilormini@ensam.eu and N 0 are the number of broken bonds and the initial number of breakable bonds, respectively. There are however strong experimental obstacles in general to the determination of low values of y, owing to the analytical problems due to the structure complexity and the insolubility of polymeric networks. This is the reason why degradation is monitored generally by indirect methods aimed at determining the crosslink density x, such as the measurement of the elastic properties in the rubbery state [4][5][6], the solvent swelling ratio of the gel fraction [7], the sol/gel fractions [7][8][9], the molar mass distribution in the sol fraction [10][11][12]. To establish the relationship between the crosslink density and the conversion ratio, it has been assumed that degradation behaves exactly as the reverse of step by step polymerization and then the Flory-Stockmayer theory of network formation could be used [13][14][15], provided that degradation is a "pure" random chain scission (no simultaneous crosslinking). This is generally the case of polyester hydrolysis, which explains why this process has been used to check the theory [6,12].

In the past, attention was focused mainly on the effect of degradation on soluble/insoluble fractions and on the sol composition, but emphasis was put recently on the change of elastic properties, first at low conversions only [5], then in the whole range of conversions during which a gel fraction subsists [6]. In the latter work, analytical expressions were proposed for the crosslink density-conversion ratio relationship, which was illustrated on networks having trifunctional or tetrafunctional crosslinks and for special cases of primary chain length distributions. Experimental checking was performed on trifunctional isocyanate cured polyesters. For a given conversion ratio of the degradation process, it was found that the crosslink density depends on the crosslink functionality f, on the number L of breakable bonds per primary chain and, to a lesser extent, on the shape of the primary chain length distribution.

Special attention was paid to the "degelation" point [12], i.e., the state where the gel fraction vanishes (x=0) and the sample becomes totally soluble. Relatively simple functions of L were obtained [5,6] for the conversion ratio y d at degelation, and some are recalled in Table 1.

When a series of networks differing only by their chain length is available, the determination of their degelation point offers a simple way for checking the theory.

Trifunctional crosslinks Tetrafunctional crosslinks

Homodisperse distribution 1 - 1 2 / 1 - 1 3 / Flory distribution 1 + 1 2 + 2
Table 1. Expressions of the conversion ratio at degelation as a function of the average number L of breakable bonds per primary chain [6].

The radiolysis of polymers containing quaternary carbons in the main chain, polyalkylmethacrylates or polyisobutylene for instance, can be an alternative to polyester hydrolysis in network degradation studies. This is appropriate because it has been established half a century ago that these polymers undergo almost "pure" random chain scission, owing to the very low value of the monomer-monomer bond energy value [START_REF] Bovey | Effect of Ionizing Radiation on Synthetic and Natural Polymers[END_REF][START_REF] Chapiro | Radiation Chemistry of Polymeric Systems[END_REF]. Radiolysis is free of autocatalysis that can complicate the kinetic analysis of hydrolysis [5] and does not depend sharply on irradiation conditions (in the absence of oxidation). It seemed thus interesting to try to check the theory with radical polymerized methyl methacrylate (MMA)-ethylene glycol dimethacrylate (EGDMA) copolymers differing by the molar fraction of comonomers and irradiated by gamma rays.

The radiolysis mechanisms have been elucidated in the case of PMMA [START_REF] Todd | [END_REF]19]. The primary event is the splitting of the chain-ester lateral bond, leading to a tertiary macroradical which evolves by beta scission to give a terminal double bond and the (relatively stable) polymerization radical. The latter can potentially initiate zip depolymerization at elevated temperature but this is unlikely at the temperature of 40°C considered below. The radiochemical yield for random chain scission G(s) is of the order of 2 events per 100eV (about 2 10 -7 mol/J) [START_REF] Schnabel | Aspects of Polymer Degradation and Stabilization[END_REF][START_REF] Thominette | [END_REF][22][23]. Knowing the non-selectivity of radiolytic processes, it can be assumed that this yield takes the same value in tridimensional methyl methacrylate copolymers, except possibly at high crosslink densities where interactions can occur between any MMA monomer unit and the close crosslink mers. We consider two possibilities:

(i) The radiolytic reactions occurring in crosslink mers are negligible, which is probably true for low crosslink densities, i.e., for long PMMA chains. In such cases, the networks would behave as tetrafunctional networks from the point of view of degradation statistics.

(ii) The reactions in crosslink mers are not negligible and must be taken into account in degradation statistics. But what is the radiolysis mechanism in this case? There is no helpful published data on this aspect, to our knowledge. We found interesting to make the following assumption: EGMDA units react like MMA ones, by splitting of the chain-ester bond.

The present paper thus aims at studying the radiolytic degradation of several MMA-EGDMA networks differing by their crosslink density and at characterizing the conversion ratio y d at their degelation point. Two approaches of degradation statistics differing by the assumed mechanisms will then be used to predict degelation, using the statistical theory presented in [6].

Theory

Consider a sample prepared from a mixture of a mass m M of methyl methacrylate (MMA, molar mass M M = 100 g/mol) and a mass m E of ethylene glycol dimethacrylate (EGDMA, molar mass M E = 198 g/mol). The network is composed of two kinds of chains: "long chains" of PMMA containing an average of L monomer units, i.e., L breakable bonds, and "short chains" made of two ester groups interconnected by a dimethylene unit. The question of the number of breakable bonds in "short chains" will be examined later. The average number of breakable bonds in "long chains" is obtained readily by assuming the network is ideal as a first approximation, each EGDMA being thus connected to 4 "long chains":

= ⁄ ⁄ = .
(

) 1
where r denotes the mass ratio m E /m M .

There are two ways of considering the network connectivity as regards degradation. In the first one, the probability of chain scission in the "short chains" is assumed negligible, so that an EGDMA unit plays the role of a tetrafunctional crosslink. The second approach takes scissions in the EGDMA units into account, two "long chains" and one "short chain" are connected to a quaternary carbon which plays the role of a trifunctional crosslink. For the sake of simplicity, it will be assumed in the latter case that "short chains" react like "long chains" by the radiolysis of the chain-ester bond. In other words, short chains would contain 2 breakable bonds with the same radiochemical yield as those of "long chains".

The condition for degelation is detailed now, which is characterized by the conversion ratio y d , i.e., the number of scissions at degelation per initial breakable bond. Let us make first the assumption that only "long chains" carry breakable bonds. The number of scissions induced by an irradiation dose D per unit mass is given by

= ( ) (2)
where G(s) denotes the radiochemical yield of PMMA (in mol/J) and, consequently, the fraction y of the number of breakable sites that have reacted is

= ( ) ⁄ = ( ) (3)
Two subcases can be distinguished: in the first one, all "long chains" bear the same number of breakable bonds and the critical value of y at degelation is given by [

3] = 1 -/ (4)
Actually, L must be an integer in (4), which is not the case for all the samples under study. It seems thus more realistic to suppose that "long chain" lengths are more or less dispersed, L being the average number of breakable bonds per "long chain". We have previously shown [6] that y d would then be larger than in the homodisperse case. For instance, in the case of a Flory distribution, one would have: We make now the alternative hypothesis that scissions can occur in both "long chains"

= (5)
and "short chains". If, as proposed above, the primary event is the scission of the carbonylchain bond, this reaction leads to the same macroradical as the one resulting from PMMA radiolysis (Figure 1a); it must thus react by beta scission. In other words, each radiolysis event in the EGDMA moiety must give two chain scissions (Figure 1b). This, and the presence of two types of breakable chains in the system, requires the following modifications of the model developed in [6], which is quite general and can be applied to any type of chain scission, chemical or radiochemical. Making the assumption that EGDMA has the same radiochemical yield G(s) as MMA, whereas the above approach assumed this yield was negligible, the fraction y of the total number of breakable sites that have reacted for an irradiation dose D is

= ( ) ( ) ⁄ ⁄ ≈ ( ) (6)
since M E /M M is very close to 2. The probabilities for a site on a "short chain" to have reacted is

= ( ) ⁄ = (7)
since there are two breakable bonds per EGDMA, whereas for a site on a "long chain"

= ( ) ( ) ⁄ = ( ) (8)
because of the scissions induced by "short chain" scissions, as detailed above. Therefore, the probability u S for a "short chain" to be unbroken, i.e., for both sites of an EGDMA unit to remain unreacted, is:

= (1 -) (9)
To be uncut, a "long chain" must satisfy two conditions: (i) none of its MMA units has reacted, and (ii) none of the two EGDMA esters at its extremities has reacted and induced a scission on the "long chain". In the case where the chain contains exactly L reactive sites, the probability u L for a "long chain" to remain uncut is therefore:

= (1 -) 1 - (10)
where the coefficient 1 2 ⁄ is due to two possible locations where the second scission takes place when a radiolysis event on a neighboring "short chain" occurs. In the case of a Flory distribution of "long chain" lengths, one would obtain, using a partial result of [6]:

= ( ) 1 - (11)
The expressions of u S and u L will allow expressing the condition for degelation as follows. Let g S denote the probability to reach the gel when starting from a network node through a "short chain". The latter must be uncut and at least one of the "long chains" to which its end is connected must lead to the gel. In the same way, let g L denote the probability to reach the gel when starting from a network node through a "long chain". Like for the definition of g S , this "long chain" must be uncut and at least one of the two chains to which its end is connected (a short one and a long one) must lead to the gel. Therefore, these probabilities are linked by the following relationships:

= [1 -(1 -) ] = (2 -) (12)
and

= [1 -(1 -)(1 -)] (13)
Substituting g S in ( 13) by its expression (12) one obtains:

= - 1 + 4 (14)
The degelation condition corresponds to g L = 0 and, since g S is proportional to g L , g S = 0 results: neither a "long chain" nor a "short chain" can lead to the gel after degelation. By setting equation ( 14) equal to 0, the condition for degelation can thus be written as:

(1 + 2 ) = 1 (15)
which can be solved numerically with respect to y d , by using ( 9), (10) (or (11) for a Flory distribution), (7), and (8).

Experimental

Synthesis

Six networks (

Irradiation

The samples were gamma irradiated by a 60 Co source at moderate temperature (ca 40°C) at 5 Gy/s under air up to irradiation doses ranging from 0.25 to 8 MGy. The irradiations were performed in the SCK CEN laboratory (Mol, Belgium). Several specimens of each network were irradiated simultaneously, and subsets were withdrawn at predefined times, which produced discontinuous results in terms of irradiation dose. Therefore, the degelation dose is bracketed within a finite interval. Equations ( 3) and ( 4) were used to evaluate roughly at what irradiation doses the samples should be withdrawn.

Characterization

Dynamic mechanical analysis

The samples were characterized before irradiation by dynamic mechanical analysis using a DMA Q800 apparatus (TA Instruments) driven by Q Series Explorer. The specimens were submitted to temperature sweep tests using a 2°C/min heating ramp at 1 Hz frequency in tension mode, with a 0.1% strain amplitude and a 0.5 N preload force.

Differential scanning calorimetry

Ca 5 mg samples sealed in standard aluminum pans were characterized by DSC under 50 ml/min nitrogen flow at a 10°C/min rate using a DSC Q10 apparatus (TA Instruments) driven by QSeries Explorer. The glass transition temperature was determined using TA Analysis software. The DSC apparatus was calibrated with an indium standard prior to measurements.

Sol-gel analysis

Two methods were used, which differed by the solvent used, either chloroform at ambient temperature or by refluxing in an acetone-chloroform (50/50) mixture. Immersion of the samples (initial mass m 0 ) was more than 100 hours long (this duration was checked to be sufficient for reaching equilibrium). After immersion, the samples were dried at 90°C in oven till equilibrium was reached (mass m Dry ). The data were used to estimate the insoluble fraction as m Dry /m 0 .

Results

Characterization of initial

The (combined with equation ( 16)) leads to a ratio of of elastically active chains and the concentration of EGDMA.

the value of 2 that would apply to ideal tetrafunctional networks a coefficient of 3 would apply to trifunctional networks (since each EGDMA would the same glassy modulus (ca 3 GPa obtained at 200°C (Table 2) are ( 16)

According to the statistical theory of rubber elasticity, the

the networks before irradiation leads to a ratio of approximately 1.8

of elastically active chains and the concentration of EGDMA.

would apply to ideal tetrafunctional networks, whereas trifunctional networks (since each EGDMA would join two nodes). Therefore, as regards their rubbery elasticity, tetrafunctional and almost-ideal networks where connected to 4 elastically active chains considered in the computations below.

[EGDMA] denotes the concentration in the network where it was measured actually. This is cons by the lack of a sol fraction after the samples were prepared.

The samples were also characterized by DSC, and they all displayed a well visible glass transition. The second scan in Table 2. A similar trend was obs the EGDMA concentration, which suggests ideality than in [24].

networks B(

12 as regards their rubbery elasticity, the samples can be depicted as ideal networks where about 10% of the EGDMA molecules are not connected to 4 elastically active chains. For the sake of simplicity, ideal networks will be considered in the computations below. It may be noted that the above rationale assumes that

[EGDMA] denotes the concentration in the network as well as in the polymerization was measured actually. This is consistent with a complete polymerization ol fraction after the samples were prepared.

The samples were also characterized by DSC, and they all displayed a well visible glass transition. The second scan T g increases continuously with crosslink density A similar trend was observed by Loshaek [24], but with a smaller , which suggests that the networks studied here are closer to the samples can be depicted as 10% of the EGDMA molecules are not

For the sake of simplicity, ideal networks will be It may be noted that the above rationale assumes that polymerization mixture, polymerization suggested

The samples were also characterized by DSC, and they all displayed a well visible continuously with crosslink density, as shown smaller T g increase with that the networks studied here are closer to

Characterization of networks after irradiation

The glass transition temperature of the which confirms that they degrade mainly by chain scission.

Analysis of degelation data

The conversion ratio y d at degelation can be obtained from the theory when the reactivity of EGDMA units is neglected or taken into account by either using equation (4) (or ( 5), for a Flory distribution), or combining (15) with relations (9-10) (or (11), for a Flory distribution).

The corresponding degelation dose D d can then be obtained from either (3) or (6). Figure 6 illustrates the effect of raising G(s) from 2 to 3 10 -7 mol/J in the simulations, still with homodisperse L values, which can be compared with Figure 5. As expected, the degelation dose decreases when the radiochemical yield increases, but the effect is moderate and suggests that a G(s) value slightly above 2 10 -7 mol/J might improve the predictions of the model. Of course, this statement must be balanced by the large uncertainties of the experimental results. Figure 6 also shows the effect of a dispersion of the number of reactive sites on "long chains", illustrated by a Flory distribution, still using G(s)=2 10 -7 mol/J. Except when L=1, where coincidence with the homodisperse case applies, comparison with Figure 5 shows that the degelation dose is increased significantly when dispersed L values are considered, which leads to unsatisfactory results.

Discussion

Globally, the above results confirm that the radiolysis of PMMA networks can be an interesting way to study degelation and there is no apparent contradiction between the experiments and our theory. However, some questions remain open, among which the following ones:

1) About network ideality. Our theory is based on the hypothesis that the networks under study are ideal initially, i.e., free of such defects as dangling chains or loops, for instance.

A non ideal network can nevertheless be considered simply if the concentration of dangling chains is known and if equivalence with a "predegraded" network is reasonable as a first approximation. This would change only the origin of the irradiation dose (as well as the conversion) axis, and the curves in Figures 5 and6 would be lowered.

2) About the reactivity of EGDMA units. It may be noted first that the difference between the degelation doses in the cases of reactive and unreactive EGDMA should vanish when the length of PMMA chains increases, and this is in agreement with Figures 5 and6. This difference remains small for short PMMA chains, indicating that EGDMA units are presumably less reactive than PMMA ones, as already suggested in the comments of where P° and P'° are macroradicals and G° is a microradical; h is the yield of cage recombination. In the case of PMMA, the small radical G° escapes rapidly from the cage, recombination is negligible. In the case of EGDMA, the big radicals resulting from the chain scission are less mobile than G°, they can undergo cage recombination and thus reduce G(s) for this unit.

3) About the effect of a distribution of L values. Primarily, there is no reason to have a uniform distribution of PMMA chain lengths; despite that, the corresponding hypothesis gives better simulation results than a Flory distribution in the domain of long PMMA sequences. A conceivable explanation can be found in the copolymerization kinetics of MMA and EGDMA. As a matter of fact, it can be first recalled that the Flory distribution corresponds to polydispersity ratios close to 2 where species covering more than two orders of magnitude in molar mass coexist. In the cases under study, at least for small to moderate EGDMA/MMA molar ratios, with a reactivity ratio close to unity, PMMA length distribution cannot be so broad; this is the possible reason why the hypothesis of a homodisperse L distribution gives better results.

Conclusion

The degradation by gamma irradiation of PMMA-EGDMA networks differing by their EGDMA concentration, i.e., by the length L of PMMA chains, has been studied by using

Figure 1 .

 1 Figure 1. The mechanisms of chain scission (a) in PMMA and

2 ≈Figure 2 .

 22 Figure 2. Rubbery

Figure 3 .

 3 Figure 3.

Figure 3 .

 3 Figure 3. Glass transition temperature of irradiated

  the irradiated samples are shown in Figure dose. The dose at which a sample becomes totally soluble the last dose D ins at which an insoluble fraction was detected and the first dose the sample was found totally soluble. The values of course, D ins < D d < D sol . It appears clearly that the degelation dose increases wit EGDMA concentration, i.e., it decreases with the number two consecutive EGDMA units in a chain.

Figure 4 . 13 4. 2 .

 4132 Figure 4. Residual insoluble fraction after irradiation of networks B (

Figure 5 .

 5 Figure 5. Degelation dose against average L value for G(s)=2 10 -7 mol/J, a uniform L

Figure 6 .

 6 Figure 6. Degelation dose against average L value with either G(s)=3 10 -7 mol/J and homodisperse L values (non reactive (a) or reactive (b) EGDMA), or G(s)=2 10 -7 mol/J and a

Figure 5 .

 5 Figure 5. A possible explanation is related to the local segmental mobility, which

Table 2 )

 2 were obtained from the bulk polymerization of methyl methacrylate 0.011 to 0.250. Chemicals were purified from the polymerization inhibitor by liquid-liquid extraction by using first a concentrated solution of sodium hydroxide (30 g/l) and then pure water. Then, MMA was vacuum evaporated and EGDMA was dried using anhydrous CaCl 2 . Both reagents were stored at low temperature prior to polymerization.Polymerization was performed in molds made of two glass plates separated by a 2 mm thick Teflon spacer and cautiously sealed with silicone. The reactants (ca 40 g of monomers plus 0.5 g of cumyl peroxide) were injected through the seal with a syringe. The mixture was allowed to polymerize at room temperature during 24 hours, and gelification was evident. The polymerization was ended in oven at 60°C. It was checked that monomer loss by evaporation

	was negligible.
	Sample		L	E rubbery	(°C)	Degel dose
				(MPa)	exp.	(MGy)
	A	0	n.a.	n.a.	108.9	n.a.
	B	0.011 89.1	2.2	112.6 0.25 -0.75
	C	0.027 36.4	3.6	117.0 0.75 -1.25
	D	0.053 18.7	4.7	124.4 1.75 -2.75
	E	0.095 10.4	8.0	131.6	4.25 -5
	F	0.125 7.9	13.0	125.8	5 -7
	G	0.250 4.0	27.5	153.2	> 8

(MMA, M55909-1L grade from Sigma Aldrich) and various amounts of ethylene glycol dimethacrylate (EGDMA, 335681-500ML from Sigma Aldrich), with r = m E /m M ratios ranging from

Table 2 .

 2 Main characteristics of the samples before irradiation, and bracketing of the irradiation doses at degelation.

glass transition temperature and soluble fraction measurements. Special attention was paid to the degelation phenomenon where the polymer becomes totally soluble. This copolymer was chosen because it was expected to react by random chain scission, which has been checked to apply predominantly and which allows trying to check statistical degradation theories. In the frame of a set of reasonable hypotheses, among which the initial network ideality, a reactivity of EGDMA mers comparable to MMA ones, and a radiochemical yield independent of EGDMA content, it was found that the conversion ratio of chain scission at degelation obeys fairly well a recently established and general statistical model for network degradation.


Paulo Ricardo

Gherardi Hein

Gilles Chaix

Bruno Clair

Loïc Brancheriau

Joseph Gril

Spatial variation of wood density, stiffness and microfibril angle along Eucalyptus trunks grown under contrasting growth conditions

Keywords: terrain slope, wind speed, modulus of elasticity, density, MFA, NIR spectroscopy, Environmental control, wood quality

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

INTRODUCTION

As a fast-growing and short-rotation source of wood, the Eucalyptus plantation is the basis for several industries, such as pulp and paper, sawn and engineered products, and -particularly in Brazil -charcoal in "green steel" industries. Although most of the biomass from breeding programs presents an optimal performance for pulp and energy purposes, limited information is available concerning their performance in the timber industry [START_REF] Lima | Variation in compression strength parallel to the grain in Eucalyptus clones[END_REF].

Eucalyptus trunks can present large spatial variation in terms of wood quality due to environmental and genetic factors [START_REF] Raymond | Genetics of Eucalyptus wood properties[END_REF]. Numerous studies have reported similar patterns of radial (Chafe 1986, Oliveira and[START_REF] Oliveira | Variação radial da retratibilidade e densidade básica da madeira de Eucalyptus saligna Sm[END_REF] or longitudinal variation for wood density [START_REF] Quilhó | Within and between-tree variation of bark content and wood density of Eucalyptus globulus in commercial plantations[END_REF]Pereira 2001, Alzate et al. 2005), wood stiffness [START_REF] Cruz | Variações dentro das árvores e entre clones das propriedades físicas e mecânicas da madeira de híbridos de Eucalyptus[END_REF] and MFA [START_REF] Evans | Variation of microfibril angle, density and fibre orientation in twenty-nine Eucalyptus nitens trees[END_REF][START_REF] Lima | Variation in microfibril angle in Eucalyptus clones[END_REF][START_REF] Hein | Radial variation of microfibril angle and wood density and their relationships in 14-year-old Eucalyptus urophylla S.T. Blake wood[END_REF] in the genus Eucalyptus. In short, patterns in pith to bark variability of wood traits from forest plantations are known: wood density and stiffness generally increases while MFA decreases towards the bark [START_REF] Kollmann | Principles of Wood science and technology[END_REF], although reports on the longitudinal variations of these traits for this hardwood are rare. As wood with high density (ρ) and modulus of elasticity (MOE) and low microfibril angle (MFA) normally present higher grades for structural uses [START_REF] Walker | The importance of microfibril angle for the processing industries[END_REF], these trends become more suitable for sawn timber production as trees become older.

According to [START_REF] Zobel | Silvicultural effects on wood properties[END_REF], anything that can change the growth pattern of a tree may result in wood variation and the response of the tree and its wood properties from this change cannot be easily predicted. That is why most researches on wood variation caused by different growing condition are contrasting for many species. For instance, [START_REF] Guilley | The influence of site quality, silviculture and region on wood density mixed model in Quercus petraea Liebl[END_REF] have shown that wood density of Quercus hardly changed with changing environment (five French regions crossed with three site qualities) and type of silviculture (coppice-with-standards and high forest) while [START_REF] Zhang | Spatial patterns of wood traits in Chinaare controlled by phylogeny and the environment[END_REF] reported that the key environmental factor explaining the spatial patterns of wood traits of 618 tree species growing in China was the mean annual rainfall.

Few studies have investigated the environmental effects on the within-tree variation in Eucalyptus wood traits. [START_REF] Downes | Radial variation in Kraft pulp yield and cellulose content in Eucalyptus globulus wood across three contrasting sites predicted by near infrared spectroscopy[END_REF] have investigated the variability of pulp yield and cellulose content within Eucalyptus globulus trunks growing in three contrasting sites. They pointed out that pulp yield and cellulose content were higher in the more productive sites, the wetter ones. Moreover, the trees in these sites exhibited more significant pith-to-bark increases in pulp yield than those in the driest site (less productive). On the other hand, [START_REF] Miranda | Provenance and site variation of wood density in Eucalyptus globulus Labill. at harvest age and its relation to a non-destructive early assessment[END_REF] investigated 9-year-old Eucalyptus globulus from 37 provenances in three sites, reporting that sites did not influence wood density variation. To sum up the general trends in Eucalyptus, [START_REF] Gonçalves | Silvicultural effects on the productivity and wood quality of eucalypt plantations[END_REF] presented a complete review based on a majority of the studies on Eucalyptus describing how silvicultural practices affect the productivity and wood quality. However, information concerning the extent to which specific environmental factors affect wood formation and its properties are limited and contrasting.

To our knowledge, there is no information reporting to what extent the ground slope and the wind speed influence spatial variations in Eucalyptus wood, especially in juvenile wood. Thus, the aim of this study was to better understand the effect of ground slope and wind speed on the spatial variation of ρ, E and MFA of Eucalyptus wood. The strategy here was to use previous NIR calibration models for prediction of ρ, MOE and MFA from spectra measured at different radial and longitudinal positions of Eucalyptus trunks. We studied 6 years old trees because the rotation cycle of Eucalyptus is 6 years for pulp and paper production while 4-5 year-old trees are used for bioenergy purposes in Brazil.

MATERIAL AND METHODS

Vegetal material and sampling

One-hundred fifty (150) 6 year-old Eucalyptus grandis x E.urophylla hybrids growing in three contrasting clonal tests from the Cenibra Company established in Minas Gerais State in Brazil were investigated in this study. Ten (10) hybrids coming from three clonally replicated trials established in contrasting site were investigated. Five individuals per clone were sampled in each clonal test, totalizing 150 trees (10 clones x 3 sites x 5 individuals). Trees were selected among those upright, healthy, without fork. Sites labeled as 302 and 303 present similar weather conditions, but the terrain slope was very contrasting. The location of these two clonal tests is close. The Clonal test 301 is around 200 kilometers distant from others and weather conditions are different, especially the wind speed. According to the classification of Köppen the climate type of the sites is Tropical savanna. The trees were planted in a randomized block design with planting density of 1,667 trees/ha (3 m x 2 m spacing). Trees were planted in 2003 and harvested 72 months later. Figure 1 shows the difference in ground slope between clonal tests while Table 1 describes the main environmental differences between the clonal tests (slope from 0 to 40°, and mean wind speed from 0.9 to 3.2 m/s) and presents the mean values concerning tree growth (mean height between 20.4 to 23.6 m and mean circumference at breast height (CBH) from 57.4 to 67.3 cm). Possibly there are several factors influencing the growing conditions (such as soil qualities for example), but here we considered only the slope of the terrain and the wind speed as the main contrasting factors.

Table 1 and Figure 1 The first log (from the base to 2.4 meters) and five wood discs (thickness: 30 mm) were cut at 0% (around 10 cm from the soil), 25%, 50%, 75% and 100% of the commercial height from each tree (Figure 1-A). The total sampling was composed of 150 logs and 750 discs.

Wood characterization

Resonance sonic tests were performed to determine MOE in 225 clean specimens cut from central boards of the Eucalyptus logs, according to the description reported in Hein et al. (2010a). After the resonance tests, small wood samples were removed from the clearwood specimens for determining wood density (ρ) by the immersion method according to ASTM D2395 procedure (ASTM 2002) and radial sections (thickness: 2 mm) were also cut from the specimens for estimating MFA using X-ray diffraction patterns as described in [START_REF] Hein | Radial variation of microfibril angle and wood density and their relationships in 14-year-old Eucalyptus urophylla S.T. Blake wood[END_REF].

For the resonance tests the specimens were submitted to flexural vibration analyses as described in [START_REF] Brancheriau | Natural vibration analysis of clear wooden beams: a theoretical review[END_REF] and in [START_REF] Hein | Resonance of structural timbers indicates the stiffness even of small specimens of Eucalyptus from plantations[END_REF]. The first four modes of vibration were used for estimating the dynamic transversal modulus of elasticity (MOE) of wood according to the [START_REF] Timoshenko | On the correction for shear of the differential equation for transverse vibrations of prismatic bars[END_REF] motion equation. The analysis of the spectral signal, the selection of the peaks of the natural frequency of vibration of the wood samples and the E estimates were performed using the software BING® (CIRAD,Montpellier,France,version 9.1.3).

The MFA estimates were based on the X-ray diffraction patterns collected on a diffractometer (Xcalibur-I, Oxford Instruments, USA) with CuK α radiation. An X-ray diffraction profile was recorded from 225 radial sections. The formula of [START_REF] Yamamoto | Method of determining the mean microfibril angle of wood over a wide range by the improved Cave´s method[END_REF] was applied in order to estimate the MFA based on the X-ray diffraction pattern.

The repeatability errors of the MOE and MFA measurements were estimated as 5% and 3%, respectively. The detailed procedures for sample preparation and measurements of ρ and MFA are described in [START_REF] Hein | Resonance and near infrared spectroscopy for evaluating dynamic wood properties[END_REF] while those for the elastic modulus are given in [START_REF] Hein | Resonance of structural timbers indicates the stiffness even of small specimens of Eucalyptus from plantations[END_REF].

NIR spectroscopy

The same Bruker spectrophotometer (model Vector 22/N, Bruker Optik GmbH, Ettlingen, Germany) was used in the diffuse reflectance mode for the spectrum measurement. This Fourier transform spectrometer is designed for reflectance analysis of solids using an integrating sphere which measures the diffuse reflected light. This integrating sphere (150 mm² spot) collects light from all angles; thus, the effects of wood texture and other non-homogeneities are minimized. It is also practical that the sphere is "upward looking", with a window on top of the sphere. The diameter of the measured area is 10 mm. A sintered gold standard was used as background. Spectral analysis was performed from 9000 to 4000 cm -1 range at 8 cm -1 resolution. Each NIR spectrum was obtained by means of 16 scans; means were calculated and compared to the gold standard to obtain the NIR spectrum of the sample.

NIR spectra were recorded on the clearwood specimens, on the cubic samples and on the longitudinal-radial sections for calibrating and validating NIR-based models. Partial Least Square (PLS) Regressions were developed to correlate NIR spectra to the laboratory-determined values of ρ, MOE and MFA. The NIR models for predicting the modulus of elasticity are presented and discussed in [START_REF] Hein | Resonance and near infrared spectroscopy for evaluating dynamic wood properties[END_REF] while the calibrations for ρ and MFA are reported in [START_REF] Hein | Estimating shrinkage, microfibril angle and density in Eucalyptus wood by near infrared spectroscopy[END_REF]. Statistical summary of the NIR calibrations for ρ, E and MFA are listed in Table 2.

Table 2 NIR spectra were recorded on local points of the radial surface of the wood discs taking into account the pith-to-cambium variation (Figure 2). The radial strip directions were defined according to the planting line, which correspond to the inclination of the terrain in the sites 301 and 302. Thus, if tension wood occurs, the radial strip will take it totally into account. These NIR spectra were taken using the same experimental settings as described in [START_REF] Hein | Resonance and near infrared spectroscopy for evaluating dynamic wood properties[END_REF] and [START_REF] Hein | Estimating shrinkage, microfibril angle and density in Eucalyptus wood by near infrared spectroscopy[END_REF]. The NIR-based models for estimating wood traits (Table 2) were applied on the NIR spectra taken from the discs in order to estimate MOE, ρ and MFA along the trunk. It is implicit in this approach that the calibration and prediction sets on which these NIR-models are based contain the whole range of variation in the wood disc samples.

Figure 2 NIR spectra were recorded in five positions on the disc from 25% of the tree height because investigating the radial variation of wood traits in more detail was one of the objectives of the project in which this study is inserted. For the other discs NIR spectra were recorded in three positions. Despite the annual rings are not evident in the trees the term inner wood refers to wood formed at the first years while outer wood represent the wood produced during the last year. As the tress investigated in this study present 6 years old, the heartwood formation process is just beginning.

Surface plots

2-D plots presenting the spatial variation of wood traits were developed using the Scilab software (v.5.3.1, http://www.scilab.org/). As NIR models were used to estimate wood traits on specific points along the tree trunk, data were interpolated using the cubic spline method in order to create estimates in a whole tree making it possible to build the surface graphics of the wood traits.

RESULTS AND DISCUSSION

The findings revealed a large spatial variation in wood density, stiffness and microfibril angle among the Eucalyptus trees. This spatial variation in wood trait over the trunk varies according to the growing conditions. Table 3 shows the radial variation of ρ, MOE and MFA along the tree height for all clones.

Table 3

Spatial variation of wood density

Pith to bark variations in wood density were more consistent than those along the trunk. Overall, the wood density strongly varied from pith to cambium at the base (increase of 137.8 kg.m -3 from 460 kg.m -3 near pith to 600 kg.m -3 near cambium) while at 25% of trunk height the increase was of 131.5 kg.m -3 starting from 475 kg.m -3 (Table 3). This trait also increased radially in the upper part of the trunk, but in relatively low magnitude (< 100 kg.m -3 ). The global increase from base to top in wood density showed by the color gradient in Figure 3 is in accordance with the findings reported by Bouvet and Baillères (1995) for Eucalyptus grandis x E. urophylla clones grown in the Democratic Republic of the Congo.

Figure 3 In the present study, the hypothesis is that pith-to-bark increases of the clones vary according to the environmental changes. The pith-to-bark variation in ρ at 25% and 50% of the tree height was higher in trees from the site with a 40° terrain slope (Table 3, values in bold). Our sampling indicates that the higher the slope of the terrain, the greater the magnitude of radial variation of wood density in the intermediate portion of the trunk. At the base and at the top of the trunk, there was no effect of the terrain slope nor wind speed. Figure 3 presents the spatial variation of the wood density inside the trunk emphasizing the radial variation of the clones in 25% of the trees height (A and B).

There was a moderate genetic variation among clones, but clone 4426 seems to present the most particular behavior. Figure 3A shows that clones produce denser wood at the site where the wind speed was higher and the mean annual temperature is lower (clonal test 301, 20°) both in the first (near pith, Figure 3A) and in the last (near cambium, Figure 3B) year of growth. In summary, Figure 3A andB show that the radial increase of wood density of the clones was ~34% higher (Table 3) in the site where the slope is more inclined (clonal test 302, 40°). Thus, variations in wood density of these clones seem to be more influenced by slope than the mean wind speed.

Many studies have shown that environments control one part of the wood variation. There is no similar study on the relationship between terrain slope/wind velocity and wood quality variation for comparing our findings. However few studies on the effect of growing conditions on wood traits variation (especially wood basic density) in Eucalyptus have been done. For instance, [START_REF] Thomas | Temperature effects on wood anatomy, wood density, photosynthesis and biomass partitioning of Eucalyptus grandis seedlings[END_REF] reported a positive relationship between temperature and wood density in Eucalyptus seedlings. However, this relationship is not consistent and further studies are required. [START_REF] Wimmer | Effects of site on fibre, kraft pulp and handsheet properties of Eucalyptus globulus[END_REF] have investigated the wood and Kraft pulp properties of Eucalyptus globulus (eight year-old) planted across three different sites in Australia. They reported higher wood density in E. globulus clones at lower rainfall, lower productivity site (Parkham), compared to the wetter, higher productivity sites (West Ridgley): the wood from the wetter site had on average 11% lower wood density compared with the wood produced in the poor site. [START_REF] Downes | Wood properties of Eucalyptus globulus at three sites in Western Australia: effects of fertilizer and plantation stocking[END_REF] thoroughly investigated this issue using a Eucalyptus globulus in Western Australia. They have evaluated the effects of fertilizer and plantation stocking on the wood properties in trees growing in three sites differing in annual rainfall (620-1100 mm), open-pan evaporation and soil water-holding capacity. According to the findings of [START_REF] Downes | Wood properties of Eucalyptus globulus at three sites in Western Australia: effects of fertilizer and plantation stocking[END_REF], the site with low annual rainfall, the lowest climate wetness index and soil water storage capacity and the slowest diameter growth, provided the trees with the highest mean wood density (648 kg.m -3 ) while trees growing in the site with the highest rainfall, had 10% lower mean wood density.

Spatial variation of wood stiffness

The patterns of variation in MOE and ρ were similar when considering overall values: the radial variation in MOE was higher than those from botton to top of the trees. Modulus of elasticity strongly increased radially from 8,970 to 16,800 MPa at 25% of the height. The increase was also high in the upper part of the trunk: ~5626 MPa and ~3869 MPa at 50% and 75% of the tree height, respectively. Similarly to the wood density, the variation in the tree top was low because these woods were produced recently, some months before harvesting. These findings are consistent with those of [START_REF] Downes | Wood properties of Eucalyptus globulus at three sites in Western Australia: effects of fertilizer and plantation stocking[END_REF] who reported that the modulus of elasticity radially increased from 55% to 174% in Eucalytus globulus wood, depending on the silvicultural treatments.

The spatial variation trends for MOE were different for those for ρ when the tree growing site was taken into account in the analysis. Radial increase of MOE was significantly higher in trees grown in Sites 301 (20 degree slope and high wind speed) and 302 (higher slope degree) when compared to variation in trees from Site 303 (no slope). At 25% of the tree height, the radial increase was ~7500 MPa (~74%, Table 3) in the trees from Sites 301 and 302 while the wood stiffness increased 5760 MPa (~80%, Table 3) from pith to cambium in the site at 0°. However, there was no difference between sites in radial increase of wood stiffness of the base of the trunk.

Variations in wind speed and terrain slope seems to induce changes in elastic modulus. The higher the terrain slope and wind speed in the field, the higher the elastic modulus of the produced wood. These effects are supposed to be similar and cumulative. 3 revealed that the radial increase in MOE is more pronounced at 25% of the tree height. We suppose that this high variation is caused by a shape effect. When a clamped beam with a conical shape is bending, the stress is maximum near the clamped end (depending on the real shape). Thus, the tree produces wood with maximum modulus of elasticity at this address to limit the deformation in this critical region.

The wind causes a cyclic bending the trunk and the outer portion of the trunk is more liable to tension or compression stress variations when the wind is stronger. This can explain why the clones growing at the Site 301 (20 degrees) produced the stiffer (and denser) outer wood (Figure 4B). We assume that the wind speed was the main factor affecting stiffness and causing high increase in wood rigidity towards the cambium. The inclination of 20° also played a role in those variations but is a controlling factor of secondary importance.

Wood stiffness is related to wood density and microfibril angle [START_REF] Evans | Rapid prediction of wood stiffness from microfibril angle and density[END_REF] and wood stiffness increases as density increases and MFA decreases [START_REF] Yang | Prediction of MOE of eucalypt wood from microfibril angle and density[END_REF]. Thus, the knowledge about the factor driving spatial variation in modulus of elasticity can be potentially interesting for sawn timber producers.

Spatial variation in microfibril angle

MFA plays a central role in tree biomechanics. According to [START_REF] Barnett | Cellulose microfibril angle in the cell wall of wood fibres[END_REF] high MFA in the centre of the tree, which were produced when the tree was a sapling, endow the wood with a low stiffness, enabling the sapling to bend in a high wind without breaking. As the tree enlarges, the trunk has to become stiffer to support the increasing weight of the trunk and crown. The lower MFA of the outer wood means that it has a higher stiffness to enable it to fulfil this role.

Here, the trends in MFA variation were inversely similar to those for wood density and stiffness. The microfibril angle of the secondary cell wall decreased, on average, by ~4.4 degrees from pith to bark at 25% of height. Considering the growing conditions, the radial decrease of MFA in the trees grown under high wind speed (Site 301, 20 degrees) was significantly higher at all relative tree heights, except at the base of the trunk.

The wind effect appears to be more evident for MFA variation. The wood of the clones planted at Site 301 have the highest MFA, but the trend is reversed with age and the clones present the lower MFA when they reach 5-6 years old. The radial decrease in MFA (5.2°) at 25% of the relative height of the trees grown on Site 301 was more than 30% above those of the trees from Sites 303 and 302. The trees growing on Site 301 produced the higher MFA values in the inner wood (Figure 5 A) and the lower MFA values in the outer wood (Figure 5 B). At the upper part of the trunk, the difference of radial decrease in MFA between sites was still higher and significant. This spatial variation trend was inversely observed for stiffness and could be attributed to the higher mean wind velocity of the site at 20°, at least partially.

Figure 5 In the study presented by [START_REF] Wimmer | Effects of site on fibre, kraft pulp and handsheet properties of Eucalyptus globulus[END_REF], who have analyzed the wood of eight-year old Eucalyptus globulus clones growing in three sites in Australia, the wood of trees growing in the poor site (Parkham, a lower rainfall and productivity site) presented greater microfibril angles than those from the good site (West Ridgley, a wetter, higher productivity site).

Analyzing these results requires an important consideration: the aging of the meristematic cells that produces the cambium. At the base, the first growth ring is totally juvenile: meristem and cambium had similar age. On the other hand, in the outer ring of the trunk, the cambium was 6 years old while the cambium of the top of the tree was a few months old during the production of the outer wood. The cambial juvenility is frequently less pronounced in the top. These issues are discussed in [START_REF] Thibaut | Mechanics of wood and trees: some new highlights for an old story[END_REF].

Tension wood

It is expected that Eucalyptus trees growing at sloped and/or windy sites produces a special wood called tension wood. This kind of wood is produce by the trees in reaction to an external load such as wind or to conteract an imbalance of the weight which is expected on sloped sites [START_REF] Alméras | Biomechanical design and long-term stability of trees: morphological and wood traits involved in the balance between weight increase and the gravitropic reaction[END_REF]. Tension wood is known to have peculiar composition and organization of the cell wall, especially a low lignin content and microfibril angle nearly parallel to the cell axis. Tension wood is also characterized in numerous species by a thicker fiber wall and fewer and smaller vessels [START_REF] Jourez | Anatomical characteristics of tension wood and opposite wood in young inclined stems of poplar (Populus euramericana CV "Ghoy")[END_REF]) leading to a denser wood (Washusen et al. 2001). The higher density associated to low MFA make tension wood generally stiffer than normal wood [START_REF] Clair | Relationship between growth stress, mechanical-physical properties and proportion of fibre with gelatinous layer in chestnut (Castanea sativa Mill.)[END_REF].

Therefore, all parameters seem to indicate that the denser wood observed in our sampling may be due to the presence of tension wood. It is, however, interesting to notice that angiosperms growing under these conditions should present eccentric growth in the upper side of the leaning trunk or in the side receiving wind [START_REF] Alméras | Biomechanical design and long-term stability of trees: morphological and wood traits involved in the balance between weight increase and the gravitropic reaction[END_REF]. However, the discs studied here did not present eccentric pith. Another point to be mentioned is that darker ring-shaped zones were observed in a few disc samples cut from the three sites. These zones presented collapse after drying which is known to be often associated to tension wood (Washusen and Ilic 2001). One can macroscopically visualize the vessels in the "normal" zone, but in the collapsed zone and/or in the zone where tension wood occurs, it is not possible to see any pores (Figure 6). NIR spectra were not measured in these dark zones. Figure 6 Unfortunately this behavior was observed in some samples a few years after the study had been carried out. The failure of this study was in not examining the likely tension wood formed in the trunks subjected to the action of wind or slope.

CONCLUDING REMARKS

This study established the spatial variation of basic density, stiffness and MFA along Eucalyptus trees. It was possible to compare the variations in wood traits among contrasting sites. The patterns of spatial variation in basic density, stiffness and microfibril angle along the Eucalyptus trunks indicates that wood variability in trunks is not negligible, even for six-yearold trees.

Patterns of spatial variation of wood traits have been reported in many studies. However, the effects of growing conditions on the wood variation are still a matter of debate. In this study, the higher the slope of the terrain, the greater the magnitude of radial variation in wood density, especially around 25% of height. The spatial variation of wood stiffness seems to be sensitive to variation in terrain slope and wind speed. The radial decrease in MFA was more pronounced at the site where the wind speed was high. There was no significant effect of growing conditions on the radial variation at the base and top of the tree for wood density, stiffness and MFA.

Considering the absolute values, the study revealed that clones produce significantly denser wood at the site where the wind speed was higher, the mean annual temperature is lower and the soil type is Inceptisol, both in the inner wood and in the outer sapwood. The trees growing on this site also produced the stiffer (and denser) outer wood and presented the higher MFA values in the inner wood and the lower MFA values in the outer sapwood. This behavior makes the trunks more flexible while thin, and stiffer when grown.

The spatial variation along the trunks presented here indicates that trees are able to adapt their wood to the changing environmental conditions in order to solve biomechanic constraints. Trees growing on sloping ground and under wind produce denser and stiffer wood, attributed to be tension wood. This ability of making wood with high tensile stress naturally provides to the tree an active control of the shape at the trunk base, where the loading forces are the highest [START_REF] Thibaut | Mechanics of wood and trees: some new highlights for an old story[END_REF]. -2.28 b (18.5) -1.26 b (9.9) 301 (20°) -3.81 a (29.5) -5.22 a (40.3) -4.11 a (33.4) -3.74 a (29.4) -2.43 a (18.5) 302 (40°) -3.53 a (27.5) -3.97 b (31.7) -3.41 b (27.7) -2.9 b (22.5) -1.74 b (13.1) overall -3.66 -4.36 -3.67 -2.97 -1.81

Footnote: The radial increase in absolute values for ρ and MOE (or radial decrease for MFA) were compared among sites by the Tukey test at ρ=0.01 threshold (means followed by same letter do not significantly differ). Bold values highlight the higher radial variation.

Figure 4 Figure 4

 44 Figure 4 Figure 4 associated to Table3revealed that the radial increase in MOE is more pronounced at 25% of the tree height. We suppose that this high variation is caused by a shape effect. When a clamped beam with a conical shape is bending, the stress is maximum near the clamped end (depending on the real shape). Thus, the tree produces wood with maximum modulus of elasticity at this address to limit the deformation in this critical region.

Fig 3 -

 3 Fig 3 -Relative spatial variation of wood basic density (kg m -3 ) in Eucalyptus urophylla x E. grandis trees, highlighting the radial variation at 25% of the tree height and the radial variation of the wood density of clones. Top: mean value of all the studied clones. Bottom: Site interaction plot for each clone for the 25% position; A represent wood produced at one year while B the wood produced at 6 years.

Fig 4 -

 4 Fig 4 -Relative spatial variation of modulus of elasticity (MPa) in Eucalyptus urophylla x E. grandis trees, highlighting the radial variation at 25% of the tree height and the radial variation of the wood stiffness of clones at the clonal tests. Top: mean value of all the studied clones. Bottom: Site interaction plot for each clone for the 25% position; A represent wood produced at one year while B the wood produced at 6 years.

Fig 5 -

 5 Fig 5 -Relative spatial variation of microfibril angle (degrees) in Eucalyptus urophyllax grandis trees, highlighting the radial variation at 25% of the tree height and the radial variation of the microfibril angle of clones in the clonal tests. Top: mean value of all the studied clones. Bottom: Site interaction plot for each clone for the 25% position;: A represent wood produced at one year while B the wood produced at 6 years.

Fig 6 -

 6 Fig 6 -Darker ring-shaped zones in wood Eucalyptus samples

Table 2 -

 2 NIR calibrations used for estimating wood basic density (ρ, kg.m -3 ), modulus of elasticity (MOE, MPa) and microfibril angle (MFA, degrees) in 6-year-old Eucalyptus wood.Footnote: Treat: mathematical treatment of NIR spectra; snv: standard normal variate correction; 1 st der: first derivative transformation; R²p: coefficient of determination of prediction (test-set validation); RMSEP: the root mean standard error of prediction (test-set validation); LV: number of latent variables and RPD: ratio of performance to deviation

	Trait	Treat.	R²p	RMSEP	LV	Outliers	RPD	Reference
	ρ	snv+1 st der. 0.80	22.9	3	2.6%	2.32	Hein (2012)
	MOE	1 st der.	0.81	1149	5	1.2%	2.34	Hein et al. (2010)
	MFA	snv+1 st der. 0.75	1.31	5	6.6%	2.10	Hein (2012)

Table 3 -

 3 Radial increase of wood properties (maximum value subtracted from the minimum value) according to the tree height (given in % of commercial height) and growing conditions (see Table1). Values in brackets are radial variation in percentage.

	Wood trait	Site			% of tree height
			0%	25%	50%	75%	100%
		303 (0°) 127.5 a (29.1) 104.4 a (22.2) 88.7 a (18.4)	46.7 a (9.1)	12.4 a (2.4)
	ρ (kg.m -3 )	301 (20°) 141.5 a (29.9) 132.9 b (26.8) 98.1 a (22.0) 302 (40°) 144.4 a (30.7) 157.2 c (34.1) 112.4 b (22.3)	57.2 a (10.6) 46.7 a (8.7)	17.6 a (3.3) 24.7 a (4.7)
		overall	137.8	131.5	97.7	50.2	18.2
		303 (0°)	6599 a (100)	5761 b (57.0) 4800 b (45.1) 2796 b (24.7)	1036 b (9.0)
	MOE (MPa)	301 (20°) 302 (40°) 6382 a (81.5) 7502 a (80.4) 5906 a (56.1) 5908 a (73) 7517 a (73.9) 6171 a (56.6) 4852 a (43.1) 3959 a (37)	2452 a (22.2) 2083 a (20.0)
		overall	6297	6927	5626	3869	1858
		303 (0°)	-3.64 a (27.6)	-3.88 b (31)	-3.5 b (27.9)
	MFA (°)

ACKNOWLEDGMENTS

The author expresses your special thanks to the CENIBRA NIPO-BRASILEIRA for providing trees; to the Department of Wood Science and Technology of the Universidade Federal de Lavras (UFLA, Brazil) for supporting the experimental work and to the Centre de Cooperation Internationale en Recherche Agronomique pour le Development (UMR AGAP and UR BIOWOOEB of CIRAD, Montpellier, France) for laboratory facilities. The authors would like

to thank Arie van der Lee from for assistance for X-ray diffraction measurements. This study was funded by CENIBRA (Celulose Nipo-Brasileira), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil) and CIRAD (UR BIOWOOEB). P.R.G. Hein was supported by CNPq grants (process no. 200970/2008-9). no conflict of interest.

LIST OF FIGURE AND CAPTIONS

LIST OF TABLES

20.4 (28)


K Hammami

H El Feki

O Marsan

C Drouet

Adsorption of nucleotides on biomimetic apatite: The case of adenosine 5 ′ monophosphate (AMP)

Keywords:

This work investigates the interaction between the nucleotide adenosine 5 ′ monophosphate molecule (AMP) and a biomimetic nanocrystalline carbonated apatite as a model for bone mineral. The analogy of the apatite phase used in this work with biological apatite was first pointed out by complementary techniques. AMP adsorption isotherms were then investigated. Obtained data were fitted to a Sips isotherm with an exponent greater than one suggesting positive cooperativity among adsorbed molecules. The data were compared to a previous study relative to the adsorption of another nucleotide, cytidine monophosphate (CMP) onto a similar substrate, evidencing some effect of the chemical nature of the nucleic base. An enhanced adsorption was observed under acidic (pH 6) conditions as opposed to pH 7.4, which parallels the case of DNA adsorption on biomimetic apatite. An estimated standard Gibbs free energy associated to the adsorption process ( G • ads ∼ = -22 kJ/mol) intermediate between "physisorption" and "chemisorption" was found. The analysis of the solids after adsorption pointed to the preservation of the main characteristics of the apatite substrate but shifts or enhancements of Raman bands attributed to AMP showed the existence of chemical interactions involving both the phosphate and adenine parts of AMP. This contribution adds to the works conducted in view of better understanding the interaction of DNA/RNA and their constitutive nucleotides and the surface of biomimetic apatites. It could prove helpful in disciplines such as bone diagenesis (DNA/apatite interface in aged bones) or nanomedicine (setup of DNA-or RNA-loaded apatite systems). Also, the adsorption of nucleic acids on minerals like apatites could have played a role in the preservation of such biomolecules in the varying conditions known to exist at the origin of life on Earth, underlining the importance of dedicated adsorption studies.

Introduction

Apatites are a large group of minerals, generally crystallizing in the hexagonal structure (space group P6 3 /m), and whose main representatives are hydroxyapatite or else fluorapatite. In particular, hydroxyapatite (Ca 10 (PO 4 ) 6 (OH) 2 , HA) is the basic mineral constituent of enamel microcrystals; in contrast, the mineral part of bone (65-75 wt.%, depending on age and sex) and of dentin is composed of a hydrated nonstoichiometric apatite phase formed of nanosized crystals and exhibiting a low degree of crystallinity [START_REF] Gomez-Morales | Progress on the preparation of nanocrystalline apatites and surface characterization: overview of fundamental and applied aspects[END_REF][START_REF] Miculescu | Cortical bone as resource for producing biomimetic materials for clinical use[END_REF]. Besides biological apatites, various studies have been devoted to the preparation, under close-to-physiological conditions (temperature, pH), of synthetic nanocrystalline apatites analogous to bone mineral [START_REF] Vandecandelaere | Biomimetic apatite-based biomaterials: on the critical impact of synthesis and post-synthesis parameters[END_REF][START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF][START_REF] Palazzo | Biomimetic hydroxyapatite-drug nanocrystals as potential bone substitutes with antitumor drug delivery properties[END_REF]. As in bone, "biomimetic" apatite nanocrystals have the particularity to expose a structured but metastable hydrated surface layer, containing labile ions (e.g. Ca 2+ , HPO [START_REF] Pascaud | Interaction between a bisphosphonate, tiludronate, and biomimetic nanocrystalline apatites[END_REF] 2-, CO 3 2-. . .) located in "non-apatitic" environments, as evidenced previously [START_REF] Cazalbou | Poorly crystalline apatites: evolution and maturation in vitro and in vivo[END_REF][START_REF] Eichert | Specific characteristics of wet nanocrystalline apatites. Consequences on biomaterials and bone tissue[END_REF][START_REF] Eichert | Formation and evolution of hydrated surface layers of apatites[END_REF][START_REF] Eichert | Nanocrystalline apatite-based biomaterials: synthesis, processing and characterization[END_REF][START_REF] Rey | Non-apatitic environments in bone mineral: FT-IR detection, biological properties and changes in several disease states[END_REF][START_REF] Rey | Physico-chemical properties of nanocrystalline apatites: implications for biominerals and biomaterials[END_REF][START_REF] Rey | Bone mineral: update on chemical composition and structure[END_REF][START_REF] Rey | Characterization of calcium phosphates using vibrational spectroscopies[END_REF]. These surface ions were also shown to be easily "exchangeable" in solution with ions from the surrounding medium [START_REF] Rey | Physico-chemical properties of nanocrystalline apatites: implications for biominerals and biomaterials[END_REF][START_REF] Drouet | Surface enrichment of biomimetic apatites with biologically-active ions Mg2+ and Sr2+: a preamble to the activation of bone repair materials[END_REF][START_REF] Wu | Phosphate ions in bone: Identification of a calcium-organic phosphate complex by P-31 solid-state NMR spectroscopy at early stages of mineralization[END_REF], leading to very peculiar surface properties [START_REF] Eichert | Book Chapter: Nanocrystalline apatite based biomaterials: synthesis, processing and characterization[END_REF]. Also, surface ions play a primordial role in adsorption mechanisms [START_REF] Al-Kattan | Medical potentialities of biomimetic apatites through adsorption, ionic substitution, and mineral/organic associations: three illustrative examples[END_REF][START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF]. In the field of bone repair materials, these characteristics are important for the interactions between apatite-based implants and the biological environment of implantation. In postmortem conditions, bone diagenesis and bone/DNA interactions are also thought to be modulated/controlled by surface properties of apatite nanocrystals [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF][START_REF] Grunenwald | Novel contribution on the diagenetic physicochemical features of bone and teeth minerals, as substrates for ancient DNA typing[END_REF].

Considering adsorption on apatite nanocrystals, substantial variations of adsorption parameters can be observed depending on the maturation state of the apatite [START_REF] Pascaud | Adsorption on apatitic calcium phosphates for drug delivery: interaction with bisphosphonate molecules[END_REF]. Generally speaking, the adsorption affinity constant tends to increase when the initial maturation time of the apatite substrate increases, while the maximum amount adsorbed decreases. The mineral apatitic matrix plays a crucial role in calcified tissues and biomaterials, and many macromolecules have been classified as initiator or inhibitor of crystal growth although for a given substance the role is not so clear and could depend, for example, on the local concentration or on the state of solute or solid fractions of this given substance [START_REF] Combes | Adsorption of proteins and calcium phosphate materials bioactivity[END_REF]. In the biomaterials field, it has been suggested that molecules interacting with calcium phosphates may play a crucial role in the recruitment of cells and their expression and that they are strongly involved in the biointegration of implants [START_REF] Hlady | Protein adsorption on solid surfaces[END_REF][START_REF] Garcia | Biomimetic surfaces for control of cell adhesion to facilitate bone formation[END_REF]. The utilization of nanocrystalline apatite materials as bone grafts may reduce the need for autologous bone graft, increase the stability of the implant, lead to faster bone regeneration, and facilitate the healing process [START_REF] Jebahi | Biologic response to carbonated hydroxyapatite associated with orthopedic device: experimental study in a rabbit model[END_REF]. In the biomineralization context, the ability of apatite to adsorb various types of molecules (proteins, other biomolecules, and various drugs) can play a determining role in calcified tissues. These phenomena are considered to control in particular apatite nucleation, growth and dissolution in vivo [START_REF] Hauschka | Osteocalcin-hydroxyapatite interaction in the extracellular organic matrix of bone[END_REF][START_REF] Robinson | Crystal growth in dental enamel: the role of amelogenins and albumin[END_REF].

The exploration of adsorption processes is interesting in itself, as it may provide a background for both the fundamental understanding (bio)molecule/apatite interactions and for the development of drug delivery systems based on apatite materials. In the present contribution, we inspected the interaction existing between a model nucleotide, adenosine 5 ′ monophosphate (AMP), and a biomimetic apatite compound. AMP is a nucleotide encountered, as a monomer "building block", in macromolecules of DNA and RNA. Being able to appreciate the type of interaction existing between AMP and apatite surfaces may help understanding the adsorption of the larger DNA or RNA molecules. Apatites and other calcium phosphates nanoparticles have for example been investigated as drug carriers to deliver genetic materials to eukaryotic cells [START_REF] Jordan | Transfecting mammalian cells: optimization of critical parameters affecting calcium-phosphate precipitate formation[END_REF][START_REF] Welzel | Transfection of cells with custom-made calcium phosphate nanoparticles coated with DNA[END_REF]. The interaction between AMP and precipitated calcium phosphate was reported in the 1990s [START_REF] Hermeslima | Adsorption of 5'-adenosine monophosphate onto precipitated calcium-phosphate -effects of inorganic polyphosphates and carbamyl-phosphate, Origins Life Evol[END_REF] but on substrates with undetermined physicochemical features.

AMP is an ester of phosphoric acid and the nucleoside adenosine. It is also the mono-phosphate version of adenosine triphosphate known to control energy storage processes in live cells. From a biochemical viewpoint, 5 ′ -adenosine monophosphate-activated protein kinase (AMPK) is an enzyme that plays a role in cellular energy homeostasis. In the presence of AMP, the activity of AMPK is increased so that AMPK is regulated by AMP [START_REF] Hawley | Complexes between the LKB1 tumor suppressor, STRAD alpha/beta and MO25 alpha/beta are upstream kinases in the AMP-activated protein kinase cascade[END_REF]. The effects of AMP are two-fold: a direct allosteric activation, and making AMPK a poorer substrate for dephosphorylation. Because AMP affects both the rate of AMPK in the phosphorylation positive direction and dephosphorylation in the negative direction, the cascade is ultra-sensitive [START_REF] Hawley | Complexes between the LKB1 tumor suppressor, STRAD alpha/beta and MO25 alpha/beta are upstream kinases in the AMP-activated protein kinase cascade[END_REF]. Nucleotides such as AMP, but also the di-phosphate ADP and tri-phosphate ATP versions, are therefore recognized as important biomolecules in metabolic interconversions. Nucleotide derivatives such as ATP (adenosine triphosphate) can also be present in the extracellular fluid under physiologic circumstances [START_REF] Forrester | Identification of adenosine triphosphate in human plasma and the concentration in the venous effluent of forearm muscles before, during and after sustained contractions[END_REF]. From a more applied viewpoint, the presence of AMP and its interaction with AMPK biochemistry has also tentatively been associated to the control of vascular calcifications [START_REF] Son | Adiponectin antagonizes stimulatory effect of tumor necrosis factor-alpha on vascular smooth muscle cell calcification: Regulation of growth arrest-specific gene 6mediated survival pathway by adenosine 5'-monophosphate-activated protein kinase[END_REF].

The aim of this work was to study the physicochemical interaction existing in solution between the AMP nucleotide and a well-characterized synthetic biomimetic apatite. The interaction phenomena were determined via adsorption reactions involving physicochemical characterization of the liquid and solid phases, including with vibrational spectroscopy techniques (FTIR and RAMAN).

Materials and methods

Synthesis of biomimetic apatite

The synthesis of biomimetic apatite and the analysis of physicochemical features showing their biomimetism to bone mineral was reported previously [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF]. In the present work, a biomimetic carbonated apatite sample analogous to bone mineral was prepared similarly as before, by a double decomposition reaction, at physiological pH and room temperature (22 • C), by mixing a calcium nitrate Ca(NO 3 ) 2 •4H 2 O solution (52.2 g in 750 ml of deionized water) and a solution containing both phosphate solution of ammonium hydrogenphosphate (NH 4 ) 2 HPO 4 and sodium bicarbonate NaHCO 3 (90 g of each in 1500 ml of deionized water). The calcium solution was poured rapidly into the phosphate and carbonate solution. The excess of phosphate and carbonate ions used in these conditions had a buffering effect and allowed the pH to stabilize around 7.4. The suspension was left to mature at room temperature for 7 days and was then filtered on a Buchner funnel, thoroughly washed with deionized water, freeze-dried and stored in a freezer (-18 • C) to avoid further alteration of the apatite nanocrystals. The apatite powder, referred to as "hac-7d", was then sieved and the size fraction 100-200 m was used for all experiments.

Adsorption of adenosine 5 ′ monophosphate (AMP) onto biomimetic apatite

Adenosine 5 ′ monophosphate (AMP) was used as adsorbate in this study, in the form of its dissolved hydrated disodium salt, Na 2 AMP•xH 2 O (purity > 99.0, HPLC grade, Sigma-Aldrich) of formula C 10 H 12 N 5 Na 2 O 7 P. Fig. 1a reports the corresponding developed chemical formula of the anhydrous salt.

The AMP adsorption isotherm (at 22 • C) was constructed by drawing the adsorbed amount N ads versus the equilibrium concentration C eq in solution, varying from 0 to 2 mmol/l. For each datapoint, 60 min of contact was selected as this time was preliminarily shown to allow equilibration of the system. All experiments were run at least in duplicate, and involved the immersion of 20 mg of nanocrystalline apatite powder hac-7d in an AMP solution (5 ml) of increasing concentrations and in KCl 10 -2 M buffer solution, at room temperature and at pH 7.4. In each case, the samples were centrifuged at 5000 rpm for 10 min and filtered onto Millipore (0.2 m). The clear solution was removed via pipetting for analysis. The amount of adsorbed AMP was determined by comparison between the initial amount of AMP dissolved in the adsorption medium and the residual amount present after the selected contact time. Spectrophotometry analyses (Shimadzu UV 1800) were run in the UV domain, by following the optical density (absorption) at 259.4 nm (see Fig. 1b). A calibration curve (correlation factor of 0.9998) was previously drawn for standard solutions of AMP concentrations ranging from 0.0078 to 0.078 mg/ml. All standard solutions were prepared with deionized water.

Physicochemical characterization

The solid phases were subjected to XRD, FTIR/RAMAN, TG-TDA analyses, as well as chemical titrations for Ca and inorganic phosphate and scanning electron microscopy (SEM/EDX) observations. The details are as follows.

X-ray diffraction (XRD) analysis was performed by means of a CPS 120 INEL powder diffractometer equipped with a graphite monochromator and using the CoK ␣1 radiation ( = 1.78892 Å). The samples were scanned in the 2 range from 20 • to 80 • with a step size of 0.02 • and a counting time of 1 s per step. Mean crystallite lengths along the c-axis were then estimated from the (0 0 2) line broadening using Scherrer equation.

An FTIR (Thermo Nicolet 5700) spectrometer was used to study the vibrational features of the compounds. 2 mg of dried sample powder was compacted with 300 mg potassium bromide using a hydraulic pressure. For each spectrum, 64 scans between 400 and 4000 cm -1 were recorded, with a resolution of 4 cm -1 .

Raman analyses of the samples, in the range 400-1500 cm -1 , were generated on a confocal Labram HR800 micro-spectrometer. The samples were exposed in backscattering mode to an AR-diode laser ( = 532 nm) with a power of 17 mW. Measurements were carried out with a spectral resolution of 3 cm -1 . The uncertainty on Raman shifts (<1 cm -1 ) have been calibrated using a silicon standard at 520.7 cm -1 . An optical objective ×100 was used for all analyses, conferring to the system a lateral resolution of 0.7 m and an axial resolution of 2.7 m. The spectra reported in this work are the average of 3 spectral accumulations, each being exposed for 120 s.

The chemical composition of the apatite compound synthesized here was determined from titrations by complexometry for the determination of the calcium content, by spectrophotometry for the total phosphate content (determination of the sum of PO 4 3and HPO 4 2-ions, using the phospho-vanado-molybdenic method [START_REF] Gee | Determination of phosphate by differential spectrophotometry[END_REF] and by coulometric method (UIC, Inc. CM 5014 coulometer with CM 5130 acidification unit) for the carbonate content.

Thermogravimetric analyses (TG-DTA) were performed for evaluating the amount of hydration water contained in the AMP sodium salt, using a Setaram Instrumentation SETSYS evolution system, with a heating rate of 5 • C/min, from 25 • C to 900 • C in air.

The specific surface area, S BET , was determined using the BET method using nitrogen adsorption, on a Tristar II Micromeritics apparatus.

Zeta potential (electrophoretic mobility) was determined at 25 • C using a Malvern Zetasizer Nano Analyzer apparatus, with disposable zeta cells, after dispersion of the powder preliminarily stabilized at different pH values (in the range 6-9.5) and syringefiltered for avoiding the sedimentation of large aggregates (>1 m) during the analyses.

Morphology and particle dimensions/agglomeration state of pure hac-7days and after adsorption of different amounts of AMP were followed using a scanning electron microscope (SEM) LEO 435 VP at a voltage of 15 kV, equipped with an EDX elemental analyzer. Transmission Electron Microscope (TEM) was also performed to observe the constitutive nanocrystals of carbonated nanocrystalline apatite, using a JEOL JEM1400 microscope under 120 kV (current of 76 A). For allowing TEM observations, the apatite sample was suspended in ethanol under ultrasonic treatment prior to direct deposition on a copper grid and air-drying.

Results and discussion

The hac-7d apatite substrate used in this study was first characterized by various complementary techniques as was previously done [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF]. X-ray diffraction (XRD) analysis indicated (Fig. 2a) that the sample was single-phased and composed of a biomimetic nanocrystalline apatite, and the application of Scherrer's formula [START_REF] Patterson | The Scherrer formula for X-ray particle size determination[END_REF] led to the mean crystallite dimensions of ca. 19 nm (length) and ca. 5 nm (width). Thus, analyses revealed physicochemical features very close to those of bone mineral [START_REF] Gomez-Morales | Progress on the preparation of nanocrystalline apatites and surface characterization: overview of fundamental and applied aspects[END_REF][START_REF] Boskey | Bone mineral crystal size[END_REF], with the following other main features: Ca/(P + C) ∼ = 1.36 and %CO 3 ∼ = 3.6 wt.%. SEM observations (Fig. 2b) showed the aggregated shape of the constitutive particles, and the specific surface area measurement by the BET method led to S BET = 180 m 2 /g. Fig. 2c shows the typical plate-like morphology of constitutive crystals for such carbonated apatite, evidencing their nanosize.

The evolution of the amount N ads of AMP adsorbed in KCl 10 -2 M and at T ∼ = 20 • C and pH 7.4 was recorded as a function of the equilibrium concentration C eq in the solution. The exact amount of AMP was corrected by the hydration water contained in the starting sodium salt Na 2 AMP•xH 2 O, where "x" was determined by TG analysis as being equal to 4.6. The resulting adsorption isotherm is plotted in Fig. 3.

Sorption isotherms are usually fitted, by default, using a simple Langmuir equation or the Freundlich or Temkin derived models. However, surface heterogeneities or specific adsorbate/adsorbent interactions may lead to significant deviation from these models, as was pointed out recently in the case of tetracycline adsorption for example [START_REF] Cazalbou | Tetracycline-loaded biomimetic apatite: an adsorption study[END_REF]. The more general Sips model (or Langmuir-Freundlich) may often allow obtaining a better assessment of adsorptive behaviors, due to its broader character. This model can be described by the equation:

N ads = N m • K S • C m eq 1 + K S • C m eq Sips isotherm
where N ads is the amount of AMP adsorbed, N m is the maximal monolayer coverage and where K S and "m" are respectively the Sips constant and exponent parameter. When applied to our experimental dataset, a correlation coefficient of R 2 = 0.9794 was obtained suggesting a relatively good agreement with the Sips model, with the parameters: N m = 0.019 ± 0.006 mmol/g, K S = 1.14 ± 0.98 and m = 1.25 ± 0.45. Despite non-negligible uncertainties, it is interesting to inspect further these values. For example, the maximum adsorbed amount N m reaches 0.019 mmol/g (19 mol/g), which is about 4 times lower than the value found for the adsorption of another nucleotide, cytidine monophosphate CMP (80.8 mol/g) on a similar type of substrate. Since the chemistry of the two nucleotides differs only by the nature of their nucleic bases (adenine being a puric base with two organic cycles, and cytosine being a pyrimidic base with a single cycle), the greater adsorption amount found with CMP can presumably be linked to a greater affinity of the surface for cytosine rather than adenine. It is however at this stage not possible to suggest molecular orientations for AMP or CMP adsorbed on apatite: additional considerations, possibly through molecular dynamics, would be needed. Zeta potential measurements however indicated a somewhat less negative value (-20 ± 2 mV instead of -30.9 ± 1.8 mV at pH 6; and -23.9 ± 1.3 mV instead of -28.6 ± 2.2 mV at pH 9.5) in the presence of adsorbed AMP which agrees well with an increased exposure of the nucleic base on the particle surface, due to adsorption. The order of magnitude of the zeta potential found here for the apatitic substrate is, as can be expected, close to other measures done on similar systems (e.g. [START_REF] Rodriguez-Ruiz | pH-responsive delivery of doxorubicin from citrate-apatite nanocrystals with tailored carbonate content[END_REF]); and in the present study, the zeta potential remained negative in the pH range 6-9.5 even in the presence of adsorbed AMP throughout the adsorption isotherm. This can be linked to the limited amount of adsorbed AMP molecules on the apatitic surface.

Of particular interest also is the value of "m", as it is thought to convey information on the heterogeneous character of the surface and on the positive or negative cooperativity between adsorbed molecules, as was recently reminded [START_REF] Cazalbou | Tetracycline-loaded biomimetic apatite: an adsorption study[END_REF]. A value of "m" greater than one is generally considered to suggest a situation of "positive" cooperativity between adsorbed molecules, whereas the contrary is considered for m lower than unity. Recently Choimet et al. (publication in progress) reported a similar study has been run on the adsorption on biomimetic apatite of another nucleotide, cytidine 5 ′ monophosphate (CMP). In that case, similarly to the present study (m = 1.25), a value of m greater than one (m = 1.20) was obtained for Sips modeling of the adsorption isotherm. Consequently, both AMP and CMP adsorption on biomimetic apatite seem to be accompanied by a favorable positive cooperativity between adsorbed molecules.

The value of the constant K S also conveys some physical meaning, related to the Gibbs free energy of the adsorption process, as was recently reminded and exploited in the case of tetracycline adsorption on biomimetic apatite [START_REF] Cazalbou | Tetracycline-loaded biomimetic apatite: an adsorption study[END_REF]. The following equation allows one to evaluate G • ads from the value of K S (re-repressed for C eq in mol/l):

K S = exp - G • ads RT
This leads to the negative value G • ads ∼ = -22 kJ/mol (uncertainty estimated to ±1 kJ/mol), indicating a favorable adsorption of AMP on biomimetic apatite in standard conditions. This value is similar to those found recently for the adsorption of CMP (-19 kJ/mol) and for tetracycline (-22 kJ/mol) on nanocrystalline apatite: this order of magnitude is consistent with the typical strength of an electrostatically mediated surface-molecule interaction and is found to fall in an intermediate situation between what is generally considered as physisorption and chemisorption.

A previous study on the adsorption of DNA on biomimetic apatite has pointed out the effect of pH on the adsorbed amount [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF]. In particular, an increased adsorption was found when the contact between the substrate and the biomolecules was undergone in acidic conditions. In order to inspect this at a single nucleotide level (as a "building block" of DNA), we investigated here the adsorption of AMP at pH 6. The adsorption isotherm obtained in this acidic condition is plotted in Fig. 4. As evidenced on this figure, for a given equilibrium concentration, the adsorption amount was found to increase significantly upon pH drop from 7.4 to 6. Again, the data were satisfyingly fitted to the Sips adsorption model (R 2 = 0.9988), with however modified parameters as follows: N m = 0.039 ± 0.002 mmol/g, K S = 5.71 ± 1.12 and m = 2.09 ± 0.12. While remaining in the stability domain of apatite, these findings point to a situation where the affinity of the surface for the AMP molecules becomes enhanced in acidic medium, which is evidenced by the significant increase of the constant K S ; also the maximum amount reaches 0.039 mmol/g which is about twice the value found for pH 7.4. The value of "m" close to 2 also depicts a situation with significant cooperativity between adsorbed species, in an even greater scale than at neutral pH.

This effect of pH on the adsorption of nucleotides on biomimetic apatites is, to our knowledge, the first of the kind. It parallels what was previously noticed for the adsorption of DNA [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF], thus suggesting that this effect is not a peculiarity of this macromolecule but that it can probably be ascribed to surface modifications of biomimetic apatites upon acidification. It may be assumed quite reasonably that the protonation of surface phosphate ions is bound to increase noticeably upon acidification of the medium in which it is emerged. This increased protonation may be at the origin of this adsorption enhancement effect, either 1) by moving the surface charge toward more positive values more prone to attract the phosphate end-groups of AMP molecules, or 2) by promoting the release in the solution of protonated phosphate ions (less attracted by calcium due to a diminished charge) and their simultaneous replacement by AMP molecules. Further studies are undergoing on the adsorption of various (bio)molecules onto biomimetic apatite under varying pH values, which should enables us in the future to explain the present observation with more details.

The solids were analyzed after adsorption by vibrational spectroscopy techniques. FTIR analyses (Fig. 5a) showed that the apatite substrate did not undergo noticeable changes upon adsorption, as in all cases the bands characteristic of a carbonated apatite phase were noticed [START_REF] Rey | Characterization of calcium phosphates using vibrational spectroscopies[END_REF][START_REF] Koutsopoulos | Synthesis and characterization of hydroxyapatite crystals: a review study on the analytical methods[END_REF][START_REF] Drouet | Apatite formation: why it may not work as planned, and how to conclusively identify apatite compounds[END_REF][START_REF] Markovic | Synthetical bone-like and biological hydroxyapatites: a comparative study of crystal structure and morphology[END_REF][START_REF] Elfeki | Carbonate ions in apatites -infrared investigations in the NU-4 CO3 domain[END_REF][START_REF] Elfeki | Thermal-decomposition of carbonated hydroxyapatites containing sodium-ions[END_REF]. In particular, the level of carbonation was found to remain unchanged, as could be assessed by the relative intensity of the 3 (CO 3 ) band when compared to 3 (PO 4 ) [START_REF] Grunenwald | Revisiting carbonate quantification in apatite (bio)minerals: a validated FTIR methodology[END_REF]. This was observed independently of the pH value of 7.4 or 6. The chemical environments in the apatite substrate, as followed on the 2 4 (PO 4 ) domain, also remained essentially unchanged by FTIR upon adsorption (Fig. 5b), although the global (averaging) character of these transmission analysis do not lead to specific surface features. The characteristic bands of AMP could not be visualized on these spectra, which can be attributed to the small amount of adsorbed molecules on the surface of the nanocrystals, and to the above mentioned lack of surface-specific analysis by this technique. Moreover, phosphate and carbonate groups from apatite as well as water environments provide many rather intense absorption bands in infrared spectroscopy, which does not facilitate the detection of AMP features.

A complementary analysis was thus carried out by Raman micro-spectroscopy. The bands relative to (adsorbed) AMP become detectable besides those of the apatitic substrate, as can be typically seen in Fig. 6. Interestingly, some of the AMP characteristic bands appear shifted as compared to those of pure AMP (Fig. 6a). This is in particular the case for the relatively intense bands linked to the skeleton vibrations of the adenine ring [START_REF] Koglin | Surface Raman-spectra of nucleic-acid components adsorbed at a silver electrode[END_REF] at 726.9 instead of 732.7 cm -1 (assignable to adenine ring breathing mode [START_REF] Lee | Temperature-dependent Raman and infrared spectra of nucleosides. Part I-adenosine[END_REF]) and at 1339.3 instead of 1333.6 cm -1 (in-plane adenine ring mode [START_REF] Lee | Temperature-dependent Raman and infrared spectra of nucleosides. Part I-adenosine[END_REF]). They point to a situation where the adenine part of the molecule gets modified by the sorption process. Such a shift in Raman band position can be attributed to surface chemical interactions existing between neighboring AMP molecules (as suggested by the positive cooperativity of the Sips model) and/or between AMP and the surface of apatite nanocrystals.

On the other hand, the phosphate group of AMP is responsible for the presence of a rather intense band located, for the AMP sodium salt, around 988 cm -1 . This band is attributable to the vibration mode 1 (PO 4 ) AMP [START_REF] Chinsky | Nucleic-acid derivatives studied by pre-resonance and resonance Raman-spectroscopy in ultraviolet region[END_REF] where the phosphate group is in non-protonated form [START_REF] Rimai | Studies of Raman spectra of water solutions of adenosine tri-, di-, and monophosphate and some related compounds[END_REF]. Interestingly, the Raman spectral region around this position (Fig. 6b) appears significantly modified in the case of AMP adsorbed on apatite, with a clear band rise at ca. 1004 cm -1 and no detection of the 988 cm -1 band. A low intensity Raman contribution at 1005 cm -1 , also attributed to the (non-protonated) phosphate group of AMP, has already been reported for pure AMP [START_REF] Rimai | Studies of Raman spectra of water solutions of adenosine tri-, di-, and monophosphate and some related compounds[END_REF]; and a close analysis of Raman data for the AMP sodium salt used in the present work allows one to detect at 1004 cm -1 a shoulder to the main 988 cm -1 band (Fig. 6b). However, in the case of AMP adsorption onto biomimetic apatite, the contribution at 1004 cm -1 appears enhanced while the 988 cm -1 band does not seem to be present. These observations thus evidence a change in phosphate chemical environments for AMP in the adsorbed state. It therefore indicates that the phosphate group of AMP molecules is also involved in the adsorption process, probably in interaction with calcium ions of the apatite substrate. Note that no obvious band shift was observed on this 1 (PO 4 ) of the apatitic substrate. However, this can probably be explained by the low amount of adsorbed AMP and the relatively low-energy interaction between AMP and apatite as suggested by the G • ads value, "intermediate" between chemisorption and physisorption.

Conclusions

The question of how DNA/RNA or their constitutive nucleotides can adsorb on apatitic substrates, independently of the finality (whether related to bone diagenesis or for nanomedicine for example), is an important concern despite the scarce literature on this topic. In this work we investigated the interaction of a model puric-base nucleotide, adenosine monophosphate (AMP), with a biomimetic apatite substrate preliminarily characterized. This study thus complements previous reports relative to the adsorption of double-brand DNA [START_REF] Grunenwald | Adsorption of DNA on biomimetic apatites: toward the understanding of the role of bone and tooth mineral on the preservation of ancient DNA[END_REF] and of a pyrimidic-base nucleotide: cytidine monophosphate (CMP, Choimet et al., publication in progress). Our data indicate that AMP can adsorb onto biomimetic apatite, and the isotherm can be satisfyingly described by the Sips equation, with an exponent greater than unity suggesting some degree of positive cooperativity between adsorbed AMP molecules. The affinity of the surface for AMP was found to be lower than that for CMP, thus evidencing a role of the nature of the nucleic base, which was indeed pointed out via vibrational spectroscopy analyses. This effect would however probably be absent or at least drastically reduced in the case of double-brand DNA where nucleic bases remain in the interior of the double-helix structure, thus becoming inaccessible to direct surface interaction.

The standard Gibbs free energy related to the adsorption process was estimated to about -22 kJ/mol, and this value falls in between the domains often regarded as "physisorption" and "chemisorption". Interestingly, the adsorptive power of biomimetic apatite toward AMP molecules was found to increase significantly in acidic condition (pH 6) as compared to pH 7.4. This effect parallels the one previously observed for DNA adsorption and suggests an apatite surface modification promoting the adsorption of, at least, such phosphate-terminated molecules.

Spectroscopy analyses run before and after adsorption indicated that the global vibrational features of the apatitic substrate essentially remained unchanged upon AMP sorption, but AMP Raman bands (both phosphate and adenine contributions) were found to be significantly modified, pointing to the existence of chemical interactions between AMP molecules and the surface of apatite nanocrystals, and also possibly among adjacent adsorbed species.

This contribution adds to the works being conducted in view of a better understanding of the interaction between biomolecules and the surface of biomimetic apatites, and especially of DNA/RNA and their constitutive nucleotides. It is expected to prove helpful in disciplines such as bone diagenesis sciences or else nanomedicine, among others. Moreover, the question of the start of life on Earth also rises the question of how nucleotides in formation (as future building blocks for DNA) may possibly have been protected against degradation over time: adsorption onto mineral phases such as apatite may have played a non-negligible role in this preservation process. . .

Fig. 1 .

 1 Fig. 1. (a) Molecular structure of adenosine 5 ′ -monophosphate (AMP) disodium salt, and (b) UV absorption maximum used for titration in solution.

Fig. 2 .

 2 Fig. 2. (a) XRD pattern (with indexation relative to the hydroxyapatite JCPDS card 09-432), (b) SEM observation of the apatite substrate hac-7d prepared in this work, and (c) typical morphology of constitutive nanocrystals (TEM).

4 Fig. 3 .

 43 Fig. 3. Adsorption isotherm of AMP onto nanocrystalline apatite hac-7d, at pH 7.4, 20 • C and in KCl 10 -2 M.

6 Fig. 4 .Fig. 5 .

 645 Fig. 4. Adsorption isotherm of AMP onto nanocrystalline apatite hac-7d, at pH 6, 20 • C and in KCl 10 -2 M (compared to data obtained previously at pH 7.4).

Fig. 6 .

 6 Fig.6. Raman micro-spectroscopy analysis of the hac-7d substrate before or after adsorption (pH 7.4) and of AMP sodium salt: (a) general spectrum in the range 400-1500 cm -1 and (b) zoom around the 1(PO4) apatite vibration domain.

Acknowledgement

The authors thank the University of Sfax for providing financial support to Mr. Khaled Hammami for a doctoral stay in France.