E F Mohamed

G Awad

C Andriantsiferana

H Delmas

Effect of Salinity and PH on the Industrial Effluent Treatment by Activated Carbon: Modeling of the Kinetic Adsorption and Equilibrium Isotherms

Keywords: Phenol, PHBA, Industrial effluent, Adsorption isotherms, Activated carbon, Temperature, pH, Inorganic Salt, Kinetic

In recent years, interest has been focused on the removal of phenols from contaminated by using a variety of purification techniques. Adsorption of bio-industrial effluent on commercial activated carbon S23 was investigated at ambient conditions. In this wok, phenol and p-hydroxyl benzoic acid (PHBA) was studied as an example of the organic compounds Environmental Management and Sustainable Development

Introduction

Environmental pollution is an emerging threat and great concern in today's context pertaining to its effect on the ecosystem. Industrial effluents often contain various toxic metals, harmful dissolved gases, and several phenolic waste and inorganic compounds [START_REF] Joshi | Minimization of Phenol by Natural Occurrence Adsorbent[END_REF]. The major sources of phenolic waste are petroleum refineries, petrochemical, steel mills, coke oven plants, coal gas, synthetic resins, pharmaceuticals etc. [START_REF] Bazrafshan | Application of adsorption process for phenolic compounds removal from aqueous environments: a systematic review[END_REF]. In general, phenolic compounds emit an unpleasant odor and flavor in concentrations as low as 5 g/l and are poisonous to aquatic life, plants and human as a product of the bio-concentration (Kamble et al., 2008;[START_REF] Navarro | Effect of pH on phenol biosorption by marine seaweeds[END_REF]. Ministry of Environment and Forests (MOEF), Government of India and EPA, has set a maximum concentration level of 1.0 mg l -1 of phenol in the industrial effluents for safe discharge into surface waters, the WHO recommends the permissible phenolic concentration of 0.001 mg l -1 in potable waters [START_REF] Ullhyan | Removal of 2,4-dichlorophenol by simultaneous adsorption and biodegradation (SAB) using low cost adsorbent[END_REF]. A great variety of adsorbents (natural or synthetic) have been used for the removal of organic substances from industrial air effluents and aqueous solutions. Activated carbons are considered as the most effective organics adsorbents with high surface areas [START_REF] Andriantsiferana | Sequential adsorption photocatalytic oxidation process for wastewater treatment using a composite material TiO 2 /activated carbon[END_REF][START_REF] Mohamed | Production of sugarcane bagasse-based activated carbon for formaldehyde gas removal from potted plants exposure chamber[END_REF]Mohamed et al., 2016a[START_REF] Mohamed | Air purifier devices based on adsorbents produced from valorization of different environmental hazardous materials for ammonia gas control[END_REF]. The adsorption capacity of activated carbon for the liquid adsorption of phenolic compounds depends on the solution conditions such as temperature, pH, ionic strength; and the adsorbate concentration [START_REF] Magdy | Removal of three nitrophenols from aqueous solutions by adsorption onto char ash: equilibrium and kinetic modeling[END_REF]. The goal of the present work was firstly to study the adsorption efficiency of S23 commercial activated carbon in the treatment of bio-industrial effluent, and secondly to increase our understanding of adsorption mechanism of the phenols onto activated carbon. To do this, the influence of contact time, temperature, pH, and presence of NaCl on the adsorption equilibrium of phenol and PHBA was investigated. Kinetic models were used to identify the possible mechanisms of such adsorption process. The Freundlich, Langmuir and Jovanovic models were used to analyze the adsorption equilibrium.

Experimental

Reagents

The original industrial effluent wastewater was from the station treatment of SARP INDUSTRIES (Table 1). Two phenolic compounds with different functional groups were studied. These compounds were phenol (-OH) and p-hydroxyl benzoic acid, PHBA (-COOH) (Aldrich Chemical Co. Inc., Milwaukee, WI). All other chemicals used were analytical grade reagents. Commercial activated carbons S23 are obtained from coconut shell (PICA).

MES (105°C) (mg.L -1 ) DCO (mg(O 2 ).L -1 ) COT (mg(C).L -1 ) CIT (mg (C).L -1 ) Na + (g.L -1 ) K + (g.L -1 ) Ca 2+ (g.L -1 ) Cl - (g.L -1 ) NO 3 - (g.L -1 ) SO 4 2- (g.L -1 )

Fe

(mg.L -1 )

Mn

(mg.L -1 )

Zn

(mg.L -1 )

Activated Carbon Characterization

Surface Area and Porosity

Surface area was determined using nitrogen as the sorbate at 77K in a static volumetric apparatus (Micromeritics ASAP 2010 sorptometer). Specific total surface areas were calculated using BET equation.

Boehm Titration

Carbon sample (1 g) was placed in 50 ml of 0.05N of the following solutions: sodium hydroxide, sodium carbonate, sodium bicarbonate, and hydrochloric acid. The excess base or acid was titrated with HCl (0.1 N) or NaOH (0.1 N), respectively. The number of acidic sites was determined under the assumption that NaOH neutralizes carboxylic, lactonic, and phenolic groups; and Na 2 CO 3 neutralizes carboxylic and lactonic groups; and NaHCO 3 neutralizes only carboxylic groups. The number of basic sites was calculated from the amount of hydrochloric acid that reacted with the carbon.

pH at the Point of Zero Charge and Metal Contents

The pH at the point of zero charge (pHpzc) of sample was determined by mass titration method (Canizares et al., 2006). To determine the right concentration of carbon, a titration curve was first obtained. Different carbon concentration slurries in deionised water were prepared, then shaken for 24 h and the final pH of the slurry was measured with the pH meter.

For values greater than 5% wt, the pH value obtained was constant. Therefore, for all samples, this amount of carbon was used and the resulting pH taken as the pHpzc. The values of the metals composition and the elemental analyses of commercial AC S23 samples were obtained from the industrial Supplier (PICA, Veolia group).

Total Organic Carbon

The Total Organic Carbon (TOC) is a parameter for measuring the organic matter present in wastewater. This test is performed by injecting a known quantity of sample into a high temperature furnace in a chemically oxidizing environment. Thus the organic carbon is oxidised to carbon dioxide in the presence of a platinum catalyst. The TOC was measured by TC Multi Analyser 2100 N/C equipment from Analytic Jena with a non-diffractive IR detector. Sample acidification and aeration prior to analysis eliminate errors due to the presence of inorganic carbon.

Adsorption Experiments

Kinetic Study

In order to determine the time required for reaching the adsorption equilibrium, phenol and PHBA solutions were put in contact with the activated carbon S23 for different times, at a constant temperature of 25 C°. For that purpose, a number of samples were prepared by mixing 0.5 g of AC with 2.35 g l -1 of a solution of phenol and others of PHBA (3.38 g l -1 ), shaken, filtered and then analysed by an HPLC apparatus. The amount of phenol adsorbed on the activated carbon samples at different contact times was calculated by the difference between the initial and the final phenol concentrations. The kinetic data obtained from batch studies have been analyzed by using pseudo-first-order and pseudo-second-order models. The first order equation of Lagergren is generally expressed as follows [START_REF] Srihari | The kinetic and thermodynamic studies of phenol15 sorption onto three agro-based carbons[END_REF]:

(1)

Where q e and q are the amounts of pollutant adsorbed (mg g

-1

) at equilibrium and at time t (min), respectively, and K 1 is the rate constant of pseudo-first-order sorption (min -1

). The integrated form of Eq. (1) becomes Eq. ( 2)

(2)

The pseudo-second-order kinetic rate equation is expressed by Robati, 2013, as shown in Eq.

(3):

(3)

Where k 2 is the rate constant of pseudo-second-order sorption (g mg -1

min -1

). The integrated form of Eq. (3) becomes Eq. ( 4) (4)

Adsorption Equilibrium

Phenols solution of different initial concentrations (ranging from 188.22 to 5176.05 mg l -1 ) were shaken with 0.5 g of AC S23 in a 250 ml bottle using the batch bottle-point technique at a constant temperature 25 C° for three days. After equilibrium, samples were filtered, analysed and the amount of adsorbed phenol and PHBA was then deduced.

Modeling of the Adsorption Isotherms

Many models have been used to describe the equilibrium relationship between solute and activated carbon in both single and multi-component systems. The mono-component isotherms were evaluated according to the two parameter models (Langmuir, Freundlich and Jovanovic). The adsorption models constants, the values of which express the surface properties and affinity of the adsorbent, can be used to compare the adsorptive capacity of adsorbents for different compounds.

Langmuir equation is the most isotherm equation used for modelling of the monolayer adsorption data [START_REF] Altaher | Microwave against thermal treatment for manufacturing of activated carbon from agricultural wastes and its use to adsorb methylene blue-equilibrium and kinetic studies[END_REF], is given by Eq. ( 5).

(

) 5
Where q e is the amount of adsorbate taken up on adsorbent at equilibrium (mg g -1 ), C e the equilibrium concentration of the adsorbate in aqueous solution (mg l -1 ), q max and K L are the Langmuir constants, representing the maximum adsorption capacity for the solid phase loading and the energy constant related to the heat of adsorption, respectively.

Freundlich model is used to describe the heterogeneous surface. It is given by Eq. ( 6).

(

) 6
Where K F is the Freundlich constant for a heterogeneous adsorbent, and n is related to the magnitude of the adsorption driving force and to the adsorbent site energy distribution. The value of n indicates favourable adsorption when 1 < n < 10 [START_REF] Altaher | Microwave against thermal treatment for manufacturing of activated carbon from agricultural wastes and its use to adsorb methylene blue-equilibrium and kinetic studies[END_REF].

Jovanovic model is a simple isotherm model for homogeneous surfaces without lateral interactions; this model is suitable for monolayer adsorption and is given by Eq. ( 7) [START_REF] Jaroniec | Statistical interpretation of the Jovanović adsorption isotherms[END_REF]).

(

) 7
Where q is the amount of adsorbate taken up on adsorbent at equilibrium (mg g -1 ), C e the equilibrium concentration of the adsorbate in aqueous solution (mg l -1 ), q max and K are the constants.

82

Nonlinear Least Squares Analysis

Regression of the experimental data to the adsorption isotherm models were performed using a corrected Gauss-Newton algorithm. The procedure calculates the values of the isotherm parameters which minimize the residual sum of squares (RSS):

(8)

Where q ex,i are the elements of the vector q ex containing the given experimental adsorbed phase concentrations, n is data points and q t,i are the corresponding theoretical values calculated by model being studied. The selection of the most adequate model was performed using the Fisher's test. The model selected was the one which exhibited the highest value F calc of Fisher parameter, Eq. ( 9) and having the lowest value of absolute relative errors (AARE), Eq. ( 10).

(9)

(10)

Where q ex is the mean value of the vector q ex and I is the number of adjusted parameters of the model.

Effect of Solution Condition

Effect of Temperature

The effect of temperature in the phenols adsorption experiments were investigated at temperature of 25 and 50 °C. It is important to study the thermodynamic parameters such as the change in the apparent enthalpy, ∆H (KJ/mol) and the Gibbs free energy, ∆G (KJ/mol) and the entropy change, ∆S (KJ/mol K), of adsorption by using the Langmuir constant K L using the following thermodynamic equations (Brucher and Bergstram 1997):

(11) (12)
Where K L denotes the equilibrium constant, R is universal gas constant and T is the absolute temperature in Kelvin. The standards enthalpy ∆H and entropy changes ∆S are respectively determined from the slope and intercept of the plot ln K L against 1/T.

Effect of Solution pH

In order to study the effect of the pH on the adsorption of phenol onto activated carbon, different initial solution pH values (2.2, 7 and 10) maintained by means of ionic buffer solutions (phosphates buffers) were used. The ionic fraction (ionsφ) can be evaluated from equation ( 13):

(13)

Addition of NaCl

The effect of salinity on the phenols removal by activated carbon S23 was studied by adding different amount of NaCl salt to the solutions.

Results and Discussion

Activated Carbon Characterization

Surface area of the activated carbon was found to be 1230 m 2 g -1 (Table 2). The results of Boehm titration was represented in Table 3. The surface function groups was mainly basic groups and the pH was found to be 9.8.The results of the metals content and the elemental analyses of S23 was summarised in Table 4.

Kinetics of Phenol and PHBA Adsorption

Numerous kinetic models have been proposed to elucidate the mechanism by which pollutants may be adsorbed. The mechanism of adsorption depends on the physical and/or chemical characteristics of the adsorbent as well as on the mass transport process. In order to investigate the mechanism of the phenol and PHBA adsorption, the kinetic data have been analysed by using pseudo first-order and pseudo second -order models. In order to quantify the applicability of each model, the correlation coefficient, R 2 , was calculated. The plots of linearized form of the pseudo first-order and pseudo-second-order kinetic equations for phenol and PHBA are shown in Figure 1. The different parameters of both models are summarized in table 5. The results showed that, the correlation coefficient values, r 2 2 were found to be higher than r 1 2 for both phenol and PHBA. In the view of these results, it can be said that the pseudo-second -order kinetic model provided a good correlation for the adsorption of phenol and PHBA (r 2 2 = 0.999) onto activated carbon S23 in contrast to the pseudo-first-order model (r 1 2 = 0.63 for phenol and 0.92 for PHBA). Table 5. Pseudo-first order and Pseudo second order kinetic parameters for the adsorption of phenol and PHBA onto activated carbon S23

Pollutant Pseudo-first order Pseudo-second order q e (mg. g -1 ) K 1 (min -1 ) R 1 2 q e (mg. g -1 ) K 2 (min -1 ) R 2 2 Phenol 1.5646e-4 0.0056 0.6381 357 0.00056 0.9999 PHBA 4.3782e-5 0.0051 0.9241 434 2.9887e-4 0.9999

Equilibrium Isotherms

Adsorption Isotherms of Industrial Effluent

Figure 2 shows the adsorption isotherms of organic pollutants analysed as COT from the industrial effluent onto the commercial AC S23. It can be observed that the concentration of COT was reached to nearly 20 % after the adsorption. The experimental equilibrium data fitted well to the freundlich model. Fitting parameters and regression coefficients obtained are shown in Table 6.

Temperature Effect

It is clear from these Figure 4 that the experimental data fitted well with Langmuir model and the equilibrium adsorption of phenol and PHBA decreases with increasing temperature as revealed by the values of q max , for example, by increasing the temperature from 25 °C to 50 C°, the maximum adsorption capacity for phenol decreased from 434 mg g -1 to 319 mg g -1 (Table 7). It is known that AC has strongly heterogeneous surface. The heterogeneity of the AC surface stems from two sources, namely geometrical and chemical. The geometrical heterogeneity (porosity) is the result of differences in the size and shape of pores, as well as pits, vacancies and steps. Chemical heterogeneity is associated with different functional groups at a surface, and with various surface contaminants. Both the chemical and geometrical heterogeneities contribute to the unique adsorption properties of activated carbon. The effect of carbon surface chemical composition on the adsorption of phenol decreases with rising temperature and geometrical heterogeneity determines adsorption of phenol at higher temperatures. However, at ambient temperature, the influence of surface functionalities is significant. The mechanism of phenol adsorption is also determined by the so-called ''solvent effect''. Adsorption of water by ACs together with the change in the energy of phenol-water interactions with the rise in temperature greatly changes the mechanism of phenol adsorption. [START_REF] Pan | Adsorptive removal of phenol from aqueous phase by using a porous acrylic ester polymer[END_REF]. As shown in the table 7, the negative value of ∆G confirms the feasibility of the process and the spontaneous nature of adsorption.

The negative values of ∆H were, indicating that the adsorption reaction is exothermic. This effect of temperature on the adsorption of phenol is expected for physical adsorption that is exothermic in nature in most cases [START_REF] Sharma | Isotherms describing physical adsorption of Cr(VI) from aqueous solution using various agricultural wastes as adsorbents[END_REF].

Table 7. Thermodynamic parameters for the adsorption of phenols on AC S23

Adsorbate q max (mg.g -1 ) K (L.mg -1 ) ∆G (KJ.mol -1 ) ∆S surface of activated carbon into a negatively charged surface resulting repulsion of negatively charged phenoxide ions and adsorption decreased [START_REF] Machida | Adsorptive Removal of Nitrate from Aqueous Solution Using Nitrogen Doped Activated Carbon[END_REF]. The effect of pH on the removal of the phenol and PHBA using AC S23 is presented in Figure 5. As can be seen in this figure, the adsorption amounts of phenol onto activated carbon increased at neutral solution pH 7 and nonbuffered solution, pH 5.8. At the lower pH, the functional groups on the carbon surface are in the protonated form and high electron density on the solute molecules would lead to higher adsorption. At higher pH, the phenol dissociate, forming phenolate anions, whereas surface functional groups may be either neutral or negatively charged. The electrostatic repulsion between the like charges lowers the adsorption capacities in case of the phenol. This may be due to the dependence of phenol ionization on pH of the medium. Phenols being weak acid (pKa = 9.89) will be adsorbed to a lesser extent at higher pH values due to the repulsive force prevailing at higher pH. A similar trend has been reported for the adsorption of PHBA on the activated carbons. At pH= 2.2 and 3.5, PHBA was found in the protonated form where its pH is lower than 4.8 (p ka ), so its higher adsorption capacity is not only due to the presence of electron attracting group -COOH but also it was adsorbed by donor-acceptor mechanism. At pH= 7, it is partially ionized, having an electron donating group O-and protons which adsorbed preferentially, so it has very weak adsorption capacity. Finally, at pH= 10, higher than p ka , its adsorption capacity is lower since it is completely ionized. These results are in agreement with those reported by [START_REF] Gu | Treatment of hyper-saline wastewater loaded with phenol by the combination of adsorption and an offline bio-regeneration system[END_REF][START_REF] Mohammad | Study of some Effecting Factors on the Removal of Phenol from Aqueous Solutions by Adsorption onto Activated Carbon[END_REF].The pKa values of phenol and PHBA at 30 °C are 9.89 and 4.8, respectively [START_REF] Hameed | Removal of phenol from aqueous solutions by adsorption onto activated carbon prepared from biomass material[END_REF][START_REF] Li | Adsorption of phenol, p-chlorophenol and p-nitrophenol onto functional chitosan[END_REF]. When pH of solution goes beyond the pKa of phenols, phenols chiefly exist as negative phenolate ions, while they are molecules below pKa. Therefore, we consider that phenols effectively adsorbed onto adsorbent are molecules not phenolate anions. Thus, the molecular interactions including hydrogen bonding, hydrophobic interaction and Van der Waals forces are the possible factors for the adsorption of phenols. On the other hand, the higher adsorption capacity in non-buffered isotherm can be interpreted in terms of the competitive adsorption of phenol and the phosphates contained in the buffer system. According to that, when buffer solutions are used to know the pH effects, on the adsorption, the carbon adsorption capacity for the adsorbate is diminished due to the buffer solution uptake.As seen from the results that the equilibrium data for phenol and PHBA at various pH values were well represented by the Frendluich isotherm model. It is seen also that an increase in the salt concentration can increase the adsorption of phenol by activated carbon, but the increase in adsorption was less than 5% at higher phenol concentrations. The proposed mechanisms of the enhanced adsorption involve interactions between water-ion and adsorbate-ion in this system. Sodium chloride dissociates into Na + and Cl -in aqueous solution. There is a strong electrostatic field around the anions and cations, thus, an oriented array of water molecules is formed around these ions. The existence of ions enhances the combining powers between water-water molecules and strengthens the hydrophobicity of the adsorbate in the opposite direction [START_REF] Pan | Adsorptive removal of phenol from aqueous phase by using a porous acrylic ester polymer[END_REF][START_REF] Mohamed | Production of sugarcane bagasse-based activated carbon for formaldehyde gas removal from potted plants exposure chamber[END_REF]) which is beneficial for adsorption. In addition, the water solubility of the hydrophobic compound is reduced by an increase in ionic strength. This effect is known as 'salting-out' [START_REF] Zhang | Effects of ionic strength on removal of toxic pollutants from aqueous media with multifarious adsorbents: A review[END_REF]. The strong influence of salts on the structure of water and water solubility of the adsorbate enhances phenol adsorption onto the surface of adsorbent. It was found that from the application of different models on the equilibrium data for phenol and PHBA, the data fitted well by the Frendluich isotherm model, instead of at high NaCl concentration in the case of PHBA, the experimental data was represented well by Langmuir model.

(KJmol -1 K -1 ) ∆H (KJmol -

Conclusion

The activated carbon S23 can be effectively used as adsorbent for the removal of organic compounds from industrial effluents and different aqueous solutions. The pseudo-first-order and pseudo-second-order kinetic models were used to analyse the data obtained for phenol and PHBA adsorption onto activated carbon S23. The results indicated that the pseudosecond-order equation provided the better correlation for the adsorption data. The solution pH played a significant effect in the organic compounds adsorption. Activated carbon adsorption capacity increased with the decreasing in the solution pH. The adsorption is exothermic process decreased by increasing the temperature. The adsorption capacity of AC was slightly enhanced by an increase of salinity. This study is particularly important for the application of the adsorption process to saline industry wastewater treatment systems.

Figure 1 .

 1 Figure 1. First order (a) and second order (b) kinetics for adsorption of phenol and PHBA onto AC S23

Figure 2 .

 2 Figure 2. Comparison of different isotherms models for COT of the industrial effluent adsorption onto S23 at temperature 25C°: Freundlich model fitting

Figure 3 .

 3 Figure 3. Comparison of different isotherm models for phenol (a) and PHBA (b) adsorptions onto AC S23

Figure 4 .

 4 Figure 4. Adsorption isotherms of phenol and PHBA onto AC S23 at temperature 25 C°and 50 C°: Langmuir model fitting3.4 Effect of Solution pHThe pH of the solution is one of the major factors influencing the adsorption capacity of compounds that can be ionized. Acid or alkali species may change the surface chemistry of the adsorbent by reacting with surface groups. At low pH values, the surface of the activated carbon would be protonated and resulted in a stronger attraction for negatively charge phenolate ions. Phenol, being weakly acidic (pKa = 10), partially ionizes in solution. These

Figure 5 .

 5 Figure 5. Effect of pH on the adsorption of phenol (a) and PHBA (b) onto AC S23 at temperature 25C°: Freundlich model fitting 3.5 Effect of NaCl Figure 6 and 7 show the adsorption behaviour of phenol and PHBA under different NaCl concentration.It is seen also that an increase in the salt concentration can increase the adsorption of phenol by activated carbon, but the increase in adsorption was less than 5% at higher phenol concentrations. The proposed mechanisms of the enhanced adsorption involve interactions between water-ion and adsorbate-ion in this system. Sodium chloride dissociates into Na + and Cl -in aqueous solution. There is a strong electrostatic field around the anions and cations, thus, an oriented array of water molecules is formed around these ions. The existence of ions enhances the combining powers between water-water molecules and strengthens the hydrophobicity of the adsorbate in the opposite direction[START_REF] Pan | Adsorptive removal of phenol from aqueous phase by using a porous acrylic ester polymer[END_REF][START_REF] Mohamed | Production of sugarcane bagasse-based activated carbon for formaldehyde gas removal from potted plants exposure chamber[END_REF]) which is beneficial for adsorption. In addition, the water solubility of the hydrophobic compound is reduced by an increase in ionic strength. This effect is known as 'salting-out'[START_REF] Zhang | Effects of ionic strength on removal of toxic pollutants from aqueous media with multifarious adsorbents: A review[END_REF]. The strong influence of salts on the structure of water and water solubility of the adsorbate enhances phenol adsorption onto the surface of adsorbent. It was found that from the application of different models on the equilibrium data for phenol

Figure 6 .

 6 Figure 6. Effect of NaCl concentration on the adsorption of phenol onto AC S23 at temperature 25 C° and intial pH 6.3: Freundlich model fitting

Table 1 .

 1 Characterization of the studied industrial effluent

	General parameter	Organic matters	Cations	Anions	Metals
	pH	Conductivity
		(ms.cm -1 )

Table 2 .

 2 Characterization of Activated carbon S23

	Activated	BET	Surface	Mesoporous	vol.	Microporous	vol.	Pore	Apparent density
	Carbon	/m 2 g -1		/cm 3 g -1		/cm 3 g -1		 /Å	/kg m -3
	S23	1230		0.04		0.49		17	1013

Table 3 .

 3 Results of Boehm titration for the activated carbon S23

	Activated	Carboxylic	Lactonic	Phenolic	Total acidic	Total basic	pH PZC
	Carbon	group	group	group	sites	sites
		(mM g -1 )	(mM g -1 )	(mM g -1 )	(mM g -1 )	(mM g -1 )
	S23	-	0.1	0.05	0.2	1.00	9.8

Table 4 .

 4 Metal composition and element analysis of AC S23

	Activated Carbon	Metal-content (by ICP)	Elemental analyses (in ppm)
		Zn Ni CO Mn Fe Cu O%	C%	H% N% S%
	S23	13 3	0	5	116 74 2.34 92.28 0.58 0.30	-

Table 6 .

 6 Different parameter values of isotherm adsorption models of phenol, PHBA and TOC after the nonlinear regression analysis Phenol and PHBA Adsorption Isotherms Figure3shows the adsorption of phenol and PHBA on the commercial AC S23. The data were analyzed using Langmuir, Javanovic and Freundlich equations. The results of the regression analysis of the different models evaluated are reported in Table6. The selection of the most adequate model was performed using the Fisher's test. The adsorption phenol equilibrium data fitted Freundlich equation with F calc and AARE values of 31 and 6, respectively. However the highest value of F calc (336) and the lowest value of AARE (3.5) confirm that the adsorption PHBA equilibrium data fitted Jovanovic model.

	Adsorbate	Langmuir					Freundlich					Jovanovic
		q max	K	RSS	F calc	AARE	K (mg 1-	γ (-)	RSS	F calc	AARE	q max	K	RSS	F calc	AARE
		(mg.g -1 )	(L.mg -1 )			(%)	γ .L γ .g -1 )				(%)	(mg.g -1 )	(L.mg -1 )			(%)
	Phenol	434	0.009	14514	9.51	15.96	55.68	0.27	4433	31.13	6.17	335	0.024	37738	3.66	17.00
	PHBA	579	0.003	3122	128.47	4.88	8.21	0.58	17402	11.21	14.04	433	0.004	1191	336.66	3.40
	TOC	218	0.002	224	31.26	16.24	2.75	0.58	224	31.29	11.50	91	0.006	213	32.96	15.32
	(Industrial
	effluent)
	3.2.2

http://emsd.macrothink.org


domain: spi phys info

text:
Martin Robin

Frédéric Jenot
email: frederic.jenot@uphf.fr

Mohammadi Ouaftouh

Marc Duquennoy

Rayleigh modes in a layer-substrate structure with varying degrees of adhesion

Keywords: Adhesion, Non-Destructive Testing, Surface Acoustic Waves, Laser-Ultrasonics, Wigner-Ville distribution

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

Introduction

Thin films are used in numerous industrial domains such as microelectronics to modify the surface properties of layer-substrate structures. The lifetime of these coatings is directly linked to the quality of adhesion at the interface and so it is very useful to develop a Non-Destructive Testing method to characterize the adhesion.

Surface Acoustic Waves (SAW) are well suited to this purpose. For the structures considered, the SAW become dispersive and are known as Rayleigh modes. The contact conditions at the interface influence this dispersion. Laser-Ultrasonics was chosen for its ability to generate and detect acoustic waves without requiring contact as well as for its large frequency bandwidth [START_REF] Sermeus | Determination of elastic and thermal properties of a thin nanocrystalline diamond coating using all-optical methods[END_REF]- [START_REF] Fourez | Non-contact thickness gauging of a thin film using surface waves and a void effect on their propagation[END_REF].

Numerous studies have been published about adhesion testing using acoustic waves, but many concern bulk waves [START_REF] Grossmann | Characterization of thin-film adhesion and phonon lifetimes in Al/Si membranes by picosecond ultrasonics[END_REF]. Most of the papers dealing with SAW focus on piezoelectric transducers to excite and detect these waves [START_REF] Du | Evaluation of film adhesion to substrates by means of surface acoustic wave dispersion[END_REF], [START_REF] Puthillath | Ultrasonic guided wave inspection of a titanium repair patch bonded to an aluminum aircraft skin[END_REF]. Only a few deal with laser sources among which a limited number of studies concerns the influence of adhesion on SAW dispersion curves [START_REF] Mezil | Investigation of interfacial stiffnesses of a tri-layer using Zero-Group Velocity Lamb modes[END_REF]- [START_REF] Bruno | Optimisation des modes de Lamb à vitesse de groupe nulle engendrés par laser et évaluation de structures collées[END_REF]. Most of these studies mention the difficulties in linking the variations in the dispersion to the adhesion due to variations in layer thickness [START_REF] Schneider | Non-destructive evaluation of the mechanical behaviour of TiN-coated steels by laser-induced ultrasonic surface waves[END_REF], [START_REF] Ollendorf | Non-destructive evaluation of TiN films with interface defects by surface acoustic waves[END_REF] and the unknown mechanical characteristics of the glue layer [START_REF] Mezil | Investigation of interfacial stiffnesses of a tri-layer using Zero-Group Velocity Lamb modes[END_REF], [START_REF] Abbate | Coating-bond evaluation using dispersion curves and laser-ultrasonics[END_REF], [START_REF] Wu | Wavelet Analysis of Laser-Generated Surface Waves in a Layered Structure With Unbond Regions[END_REF], [START_REF] Bruno | Optimisation des modes de Lamb à vitesse de groupe nulle engendrés par laser et évaluation de structures collées[END_REF]. In these studies, only optically opaque samples are considered.

To avoid these problems, a PolyEthylene Terephthalate (PET) film was deposited on an aluminum substrate. The variations in the thickness of this layer are very small in comparison with typical coatings and the film can be stuck to the substrate surface without any glue. Moreover, it is optically transparent at the laser wavelength ( 532), so Rayleigh modes can be generated directly on the substrate at the interface by focusing the laser pulse through the film. Consequently, the influence of the acoustic source position on the surface waves dispersion according to the variations in the degree of adhesion can be investigated.

In the first part, we investigate the influence of variations in thickness and adhesion on the Rayleigh mode dispersion curves. The Matrix Transfer method by Thomson-Haskell was used to establish the dispersion relation [START_REF] Thomson | Transmission of Elastic Waves through a Stratified Solid Medium[END_REF], [START_REF] Haskell | The dispersion of surface waves on multilayered media[END_REF]. The well known interfacial stiffness method was used to model the influence of adhesion on acoustic waves propagation [START_REF] Jones | Waves at a flexibly bonded interface[END_REF]- [START_REF] Rokhlin | Analysis of boundary conditions for elastic wave interaction with an interface between two solids[END_REF].

In the second part, Finite Element simulations taking the position of the source into account are presented.

Finally, the experimental results are discussed and compared to the theoretical predictions. Different degrees of adhesion were considered and their influence on acoustic wave propagation was analyzed using a laser source located at the interface.

Analytical study

SAW dispersion phenoma depends on the layer and substrate materials, which are assumed to be isotropic in this case. Depending on the shear wave velocities of the film and the substrate, it is possible to observe three types of dispersive behavior [START_REF] Farnell | Elastic wave propagation in thin layers[END_REF]. In our case, the ratio between the shear wave velocity in the film ′ and in the substrate is less than 1/√2, as shown in Table 1. In this situation, several Rayleigh modes, which the phase velocity decreases with the frequency, propagate in the structure. At low frequencies, the first mode tends to the Rayleigh wave velocity in the substrate, and higher order modes tend to the shear wave velocity in the substrate because the wavelength is long in relation to the film thickness. At high frequencies, the first mode tends to the Rayleigh wave velocity in the film and higher order modes tend to the shear wave velocity in the film. Indeed, for these frequencies, the acoustic wavelength is small compared to the film thickness [START_REF] Farnell | Elastic wave propagation in thin layers[END_REF].

These observations are only valid in the case of perfect contact, which is given by:

= = ( 1 )
where is the stress in the substrate at the boundary ( ′ is the stress in the film at the boundary) in the direction to the surface of normal and is the particle displacement in the substrate at the boundary ( ′ is the particle displacement in the film at the boundary) in the direction .

The most commonly used model in the literature represents the interface as a very thin layer compared to the acoustic wavelength. Adhesion depends on its mechanical characteristics [START_REF] Rokhlin | Analysis of boundary conditions for elastic wave interaction with an interface between two solids[END_REF]. In addition, considering that its mass is negligible, it is possible to approximate the interface with a normal and a tangential stiffness, denoted by and [START_REF] Rokhlin | Analysis of boundary conditions for elastic wave interaction with an interface between two solids[END_REF], respectively. The boundary conditions are then given as follows:

= = - ( 2 )
where = for the normal component to the interface (i.e. = ), and = for the tangential component to the interface (i.e.

). Table 1 summarizes the characteristics used to calculate the dispersion curves presented on Figure 1 to 3. These values were measured experimentally using bulk waves generated by piezoelectric transducers and the pulse-echo method. The film thickness ( = 132 1.5 %) was obtained using a high-precision comparator. 1: Characteristics of the materials used for the analytical calculations and the simulations.

PET film

Table 2 presents the stiffness values used to determine the dispersion curves. The higher and , the greater the adhesion is. Values higher or lower than quasi-perfect contact and quasi-total disbanding, respectively, were not considered. Indeed, values outside these limits no longer have a significant influence on the dispersion curves. These values were chosen arbitrarily.

Degree of adhesion

Normal stiffness * + ,/# ) Tangential stiffness Total disbonding 0 0 Table 2: Stiffness values used to model adhesion for the analytical calculations and the simulations.

* -,/# ) Perfect contact ∞ ∞ 1 (quasi-perfect contact) 2.10 /0 1.
Figure 1 shows the influence of adhesion on the dispersion curves of the Rayleigh modes for a PET film on an aluminum substrate structure, calculated using the matrix transfer method [START_REF] Thomson | Transmission of Elastic Waves through a Stratified Solid Medium[END_REF], [START_REF] Haskell | The dispersion of surface waves on multilayered media[END_REF]. The dispersion curves corresponding to the degrees of adhesion 1 and 5 overlap with those for perfect contact and total disbanding, respectively. The solid lines represent perfect contact (black) and total disbonding (green and red). In the latter situation, one curve corresponds to the Rayleigh wave propagating in the substrate (green) and the other one to Lamb waves propagating in the film (red). The dashed lines represent intermediate degrees of adhesion (2 cyan, 3 magenta and 4 blue). The weaker the adhesion is, the more the dispersion curves tend to those for the Rayleigh and Lamb waves in the substrate and the film, respectively. In this case, the first two Rayleigh modes clearly tend to the first two Lamb modes in the film. With weak degrees of adhesion, the third Rayleigh mode tends to the Rayleigh wave in the substrate for the low-frequency part. However, at high frequencies, this mode tends to the third Lamb mode in the film. The third and fourth Rayleigh modes exhibit the opposite behavior. This result is original because it brings an additional contribution to articles published concerning the evolution of Rayleigh modes towards Lamb waves in the film [START_REF] Du | Evaluation of film adhesion to substrates by means of surface acoustic wave dispersion[END_REF], [START_REF] Wu | Wavelet Analysis of Laser-Generated Surface Waves in a Layered Structure With Unbond Regions[END_REF]. The analytical calculation carried out does not consider the source position. Two types of Rayleigh mode behaviors were obtained for weak adhesion but only one of these was observed depending on the position of the source. In the case of poor adhesion, when the source is located in the film or at its surface, the dispersion curves tend to those of guided waves in the coating, whereas when the acoustic source is located on the substrate, the Rayleigh modes become a Rayleigh wave.

The film thickness also influences the dispersion curves depending on the quality of adhesion. Figure 3 presents the dispersion curves of the first two Rayleigh modes for different film thicknesses and contact conditions. As shown, the results obtained with small variations in adhesion are similar to those obtained with small variations in thickness. In order to avoid this problem, we have chosen a layer-substrate structure with a quasi-constant thickness.

Finite Element Modeling

To study the influence of the source position, Finite Element simulations were conducted using the COMSOL Multiphysics software [START_REF] Fourez | Non-contact thickness gauging of a thin film using surface waves and a void effect on their propagation[END_REF]. The quality of the adhesion between the film and the substrate was modeled by considering the interface as a thin layer 100 thick. Its mechanical characteristics were determined using the stiffness values given in Table 2 [START_REF] Rokhlin | Analysis of boundary conditions for elastic wave interaction with an interface between two solids[END_REF].

The source for generating the acoustic waves was modeled using a tangential forces dipole at the film surface or at the interface. The normal displacement of the acoustic waves was measured using 201 point probes with an interval of 50 . Two configurations were investigated. The source and the probes were placed at the filmsubstrate interface (on the substrate surface) in the first configuration (Figure 4 a) and on the film surface in the second case (Figure 4 b). For each configuration, simulations were carried out for the 5 degrees of adhesion summarized in Table 2. The elastic parameters used for the two materials are those given in Table 1. A 2D Fast Fourier Transform was applied to the probe signals to obtain the Rayleigh modes phase velocity dispersion curves. Figure 5 shows the results for the 5 degrees of adhesion in the first configuration. The results corresponding to the second configuration are presented in Figure 6. The colormap corresponds to the normalized modulus of the Fast Fourier Transform. The solid line represents the previous dispersion curves obtained from the analytical calculations. For the fifth degree of adhesion, the analytical curves correspond to the Rayleigh wave in the substrate (Figure 5) and Lamb modes in the film (Figure 6).

Figure 5 and 6 clearly highlight the influence of the source position on the modes generated. When the excitation is at the interface on the substrate side (Figure 5), the first four Rayleigh modes are clearly observed, as expected. The second mode only appears for very good adhesion and disappears for bad adhesion. The low-frequency part of the first mode is generated for all degrees of adhesion except total disbonding. When adhesion decreases, a shift in the dispersion curve to lowerfrequencies is observed. Only the low-frequency part of the third mode and the high-frequency part of the fourth mode exist for all the degrees of adhesion considered. Whatever the degree of adhesion, only the parts of the dispersion curves around the Rayleigh wave velocity in the substrate are generated. This also explains why the second mode is more difficult to excite when adhesion decreases. Indeed, its part around the Rayleigh wave velocity in the substrate is reduced due to a steeper slope.

When the acoustic source is placed on the film surface, the opposite phenomenon is observed. This time, the first and second modes are predominant and their excited parts correspond to phase velocities that are lower or higher than the Rayleigh wave velocity in the substrate. When adhesion decreases, these modes tend to the first two Lamb modes in the film. The third and fourth Rayleigh modes are weakly excited with good degrees of adhesion and only the high-frequency part of the third mode and the low-frequency part of the fourth mode are excited when adhesion is weak. These two modes merge together to form the third Lamb mode in the film.

These results show that each mode is composed of a combination of a Rayleigh wave part and a Lamb mode part. For a given source position, only one of these two parts is excited. When adhesion decreases, this part tends to Rayleigh wave in the substrate when the source is placed at the interface, or tends to Lamb modes in the film when the source is placed at the surface of the film. These simulations confirm our assumption stated previously following the analytical calculations. Only one of the two configurations is observed for a given source location when adhesion is very weak.

Experimental study a. Measurement setup

The samples used were composed of a PET film in direct contact with an aluminum substrate. It was possible to remove and replace the film several times before adhesion was no longer possible.

Figure 7 shows the experimental setup. A 10 5 Q-switched Nd:YAG laser pulse of 532 was focused as a line source on the aluminum substrate surface, through the PET film.

The normal displacement of the surface waves was detected by a Mach-Zehnder type interferometer with a power of 100 6 and a bandwidth of 200 789 -45 ;89. To improve sensitivity, a filter with a bandwidth of 200 789 -4 ;89 was used. To improve the signal-to-noise ratio, eight laser shots were performed for each measurement. Detection was achieved directly on the substrate surface, away from the film.

To vary the adhesion, Polytetrafluoroethylene (PTFE) particles were sprayed on the side of the film in contact with the substrate. These particles are known to be anti-adherent. The film was removed from the substrate between two experiments to add PTFE in order to progressively decrease the adhesion. In this way, the variations in surface wave propagation observed experimentally were mainly due to the contact conditions between the film and the substrate.

Four degrees of adhesion were achieved using different grids (see Figure 8) to protect the film to a lesser or greater extent when the PTFE was sprayed on. The greater the surface area covered with PTFE, the weaker the adhesion is.

The first degree of adhesion corresponds to good adhesion when there is no PTFE on the film. For the other degrees of adhesion, PTFE was sprayed on the film starting with the grid with the smallest holes and ending with the grid with the largest holes.

Figure 7: Laser-Ultrasonics setup.

A smoothed pseudo-Wigner-Ville distribution was applied to the signals obtained, which provides a good time-frequency representation of the latter [START_REF] Flandrin | Some features of time-frequency representations of multicomponent signals[END_REF]- [START_REF] Allard | Utilisation de la pseudo-distribution de Wigner-Ville lissée pour la détermination de l'instant de fermeture de la glotte[END_REF].

Only the generation and detection at the interface between the substrate and the film was investigated here. Indeed, the configuration of a source-probe position at the film surface has already been considered in other studies on opaque films [START_REF] Du | Evaluation of film adhesion to substrates by means of surface acoustic wave dispersion[END_REF]. 8), e: Considering substrate without film.

Conclusion

This work deals with the influence of the source position on SAW in film-substrate structures with varying degrees of adhesion. Analytical calculations, Finite Element simulations, and experiments were conducted to investigate this. Using a transparent PET film in combination with Laser-Ultrasonics, we were able to generate acoustic waves at the interface. Furthermore, the small variations in the thickness of the film made it possible to consider that the changes in Rayleigh modes behavior were mainly due to adhesion.

We have clearly shown that for different degrees of adhesion, the Rayleigh modes behavior depends on the source position. Two configurations were considered. The first one corresponded to an excitation located at the interface. In this case, the weaker the adhesion, the closer the Rayleigh mode behavior was to that of the Rayleigh wave in the substrate. For the second configuration, the source was placed on the surface of the film. In this case, the Rayleigh modes tended to the Lamb modes in the film as adhesion decreased.

To characterize adhesion, it would be interesting to combine interface excitation with generation at the surface of the film. This would be very useful to obtain more information and resolve the inverse problem with greater accuracy.

  Figure1shows the influence of adhesion on the dispersion curves of the Rayleigh modes for a PET film on an aluminum substrate structure, calculated using the matrix transfer method[START_REF] Thomson | Transmission of Elastic Waves through a Stratified Solid Medium[END_REF],[START_REF] Haskell | The dispersion of surface waves on multilayered media[END_REF]. The dispersion curves corresponding to the degrees of adhesion 1 and 5 overlap with those for perfect contact and total disbanding, respectively. The solid lines represent perfect contact (black) and total disbonding (green and red). In the latter situation, one curve corresponds to the Rayleigh wave propagating in the substrate (green) and the other one to Lamb waves propagating in the film (red). The dashed lines represent intermediate degrees of adhesion (2 cyan, 3 magenta and 4 blue). The weaker the adhesion is, the more the dispersion curves tend to those for the Rayleigh and Lamb waves in the substrate and the film, respectively. In this case, the first two Rayleigh modes clearly tend to the first two Lamb modes in the film. With weak degrees of adhesion, the third Rayleigh mode tends to the Rayleigh wave in the substrate for the low-frequency part. However, at high frequencies, this mode tends to the third Lamb mode in the film. The third and fourth Rayleigh modes exhibit the opposite behavior. Figure 2 clearly shows this evolution for the degrees of adhesion 3 (top figure) and 5 (middle figure), as well as the Lamb modes in a PET film and the Rayleigh wave in an aluminum substrate (bottom figure).

Figure 1 :

 1 Figure 1: Rayleigh modes dispersion curves in a PET-aluminum structure for different degrees of adhesion.

Figure 3 :

 3 Figure 3: Dispersion curves of first (top figure) and second (bottom figure) Rayleigh modes in PET-aluminum structure with different values of thickness for the PET film and different degrees of adhesion.

Figure 4 :

 4 Figure 4: Source and detection positions for the two configurations studied.

Figure 5 :

 5 Figure 5: Dispersion curves obtained from the FEM simulations with source and probes placed between the layer and the substrate at the interface. a) to e): Degrees of adhesion 1 to 5. Black curves correspond to analytical calculations.

Figure 6 :

 6 Figure 6: Dispersion curves obtained from the FEM simulations with source and probes placed on the film surface. a) to e): Degrees of adhesion 1 to 5. Black curves correspond to analytical calculations.

Figure 8 :

 8 Figure 8: Grids used to mask the film when the PTFE is sprayed. The left grid allows a weak PTFE covering of the surface and the right grid a large one. b. Experimental results Figure 9 presents the signals obtained for the different configurations.Figure 9 a corresponds to the signal obtained for the film with no PTFE. Figure 9 b to 9 d correspond to the signals obtained with PTFE sprayed through the three grids from left to right, respectively (Figure 8).Figure 9 e was obtained for the substrate alone to simulate a total disbonding.

  Figure 9 presents the signals obtained for the different configurations.Figure 9 a corresponds to the signal obtained for the film with no PTFE.Figure 9 b to 9 d correspond to the signals obtained with PTFE sprayed through the three grids from left to right, respectively (Figure 8).Figure 9 e was obtained for the substrate alone to simulate a total disbonding.

  Figure 9 presents the signals obtained for the different configurations.Figure 9 a corresponds to the signal obtained for the film with no PTFE.Figure 9 b to 9 d correspond to the signals obtained with PTFE sprayed through the three grids from left to right, respectively (Figure 8).Figure 9 e was obtained for the substrate alone to simulate a total disbonding.

Figure 9 :

 9 Figure 9: Signals corresponding to the five configurations. a: Without PTFE, b to d: With PTFE using grid from left to right (Figure 8), e: Considering substrate without film.

Figure 9

 9 Figure 9 clearly shows that the weaker the adhesion, the less dispersive the signal is. With complete disbonding the latter becomes a Rayleigh wave in the substrate (Figure 9 e).Figure 9 a and 9 b are similar due to the small holes in the grid used. The signal in Figure 9 d is very close to the Rayleigh wave signal despite the presence of the film over the substrate corresponding to very bad adhesion. These results are in good agreement with the simulation results provided previously.

  Figure 9 clearly shows that the weaker the adhesion, the less dispersive the signal is. With complete disbonding the latter becomes a Rayleigh wave in the substrate (Figure 9 e).Figure 9 a and 9 b are similar due to the small holes in the grid used. The signal in Figure 9 d is very close to the Rayleigh wave signal despite the presence of the film over the substrate corresponding to very bad adhesion. These results are in good agreement with the simulation results provided previously.

Figure 10

 10 Figure 10 presents the smoothed pseudo-Wigner-Ville distributions linked to the signals in Figure 9. The colormap corresponds to the normalized square modulus of the Wigner-Ville distribution. As mentioned before, Figures 10 a and 10 b are similar and clearly dispersive. The frequency band and the dispersive nature of the signals indicate that the first Rayleigh mode is observed, as shown in Figures 5 a, 5 b or 5 c.Figure 10 d and 10 e exhibit non-dispersive waves as expected from the simulation results in Figures 5 d or 5 e.Figure10c presents a slightly dispersive part at low frequency. Above 1.5 ;89, non-dispersive components appear at a velocity close to that of the Rayleigh wave. This behavior is similar to that observed in Figure5c.

Figure 10 d

 10 Figure 10 presents the smoothed pseudo-Wigner-Ville distributions linked to the signals in Figure 9. The colormap corresponds to the normalized square modulus of the Wigner-Ville distribution. As mentioned before, Figures 10 a and 10 b are similar and clearly dispersive. The frequency band and the dispersive nature of the signals indicate that the first Rayleigh mode is observed, as shown in Figures 5 a, 5 b or 5 c.Figure 10 d and 10 e exhibit non-dispersive waves as expected from the simulation results in Figures 5 d or 5 e.Figure10c presents a slightly dispersive part at low frequency. Above 1.5 ;89, non-dispersive components appear at a velocity close to that of the Rayleigh wave. This behavior is similar to that observed in Figure5c.

Figure 10 c

 10 Figure 10 presents the smoothed pseudo-Wigner-Ville distributions linked to the signals in Figure 9. The colormap corresponds to the normalized square modulus of the Wigner-Ville distribution. As mentioned before, Figures 10 a and 10 b are similar and clearly dispersive. The frequency band and the dispersive nature of the signals indicate that the first Rayleigh mode is observed, as shown in Figures 5 a, 5 b or 5 c.Figure 10 d and 10 e exhibit non-dispersive waves as expected from the simulation results in Figures 5 d or 5 e.Figure10c presents a slightly dispersive part at low frequency. Above 1.5 ;89, non-dispersive components appear at a velocity close to that of the Rayleigh wave. This behavior is similar to that observed in Figure5c.

Figure 10 :

 10 Figure 10: Normalized square modulus of the smoothed pseudo-Wigner-Ville distribution for the signals shown on Figure 9. a: Without PTFE, b to d: With PTFE using grid from left to right (Figure 8), e: Considering substrate without film.


Kevin Jacq
email: kevin.jacq@univ-smb.fr

Charline Giguet-Covex

Pierre Sabatier

Yves Perrette

Bernard Fanget

Didier Coquin

Maxime Debret

Fabien Arnaud

Kévin Jacq

Kévin Jacq

High-resolution grain size distribution of sediment core with hyperspectral imaging

Keywords: Grain size distribution, Hyperspectral Imaging, Chemometrics, Visible and Near-Infrared Spectroscopy, End-Members

Introduction

Particle size analysis is widely used in sediment studies. Several methods exist, such as gravimetric sedimentation, sieving or laser diffraction. The last one is the most used for fine lacustrine sediment.

Such laboratory analyses of sediment textures are time and material consuming, labor-intensive, destructive and have low spatial resolution (0.5-1 cm sampling-steps are typically run) and thus temporal resolution. Spectroscopic methods show great possibilities to estimate particle size fractions (clay, silt, sand) without any sampling [START_REF] Viscarra Rossel | A global spectral library to characterize the world's soil[END_REF][START_REF] De Santana | Visible and near infrared spectroscopy coupled to random forest to quantify some soil quality parameters[END_REF][START_REF] Nanni | Partial least squares regression (PLSR) associated with spectral response to predict soil attributes in transitional lithologies[END_REF]. The classically used coarser fractions, i.e., silt and sand, seem the most complicated to predict in several studies [START_REF] De Santana | Visible and near infrared spectroscopy coupled to random forest to quantify some soil quality parameters[END_REF][START_REF] Nanni | Partial least squares regression (PLSR) associated with spectral response to predict soil attributes in transitional lithologies[END_REF]. The physical properties of the sediment can be estimated with the spectra baseline that is affected by the grain size in the visible and near-infrared ranges [START_REF] Wetzel | Near-infrared reflectance analysis[END_REF]. It was also done in remote sensing with multispectral imaging [START_REF] Casa | A comparison of sensor resolution and calibration strategies for soil texture estimation from hyperspectral remote sensing[END_REF][START_REF] Demattê | Hyperspectral remote sensing as an alternative to estimate soil attributes[END_REF][START_REF] Nouri | Clay content mapping from airborne hyperspectral Vis-NIR data by transferring a laboratory regression model[END_REF]. Multi-and hyperspectral imaging are methods in the interface of spectroscopy and imaging with the acquisition of an image in which each pixel is characterized by a reflectance spectrum. Recently developed hyperspectral core loggers open new possibilities for the high-resolution prediction of organic matter [START_REF] Van Exem | Hyperspectral core logging for fire reconstruction studies[END_REF]Jacq et al., 2019b) and pigments [START_REF] Butz | Hyperspectral imaging of sedimentary bacterial pigments: a 1700-year history of meromixis from varved Lake Jaczno, northeast Poland[END_REF] and could thus be used also for the estimation of particle size.

The particle size distribution (PSD) is even more informative than the particle fractions. Some studies show the potential of visible and near spectroscopy to estimate the PSD [START_REF] Hermansen | Complete Soil Texture is Accurately Predicted by Visible Near-Infrared Spectroscopy[END_REF]. To go further, the PSD allows for differentiation and quantification of the different compounds of the sediment (deposition sources, processes), each of which is characterized by its PSD signature. Several algorithms have been proposed to estimate the relative contribution of these pure signatures in a sediment mixture [START_REF] Heslop | Using non-negative matrix factorization in the "unmixing" of diffuse reflectance spectra[END_REF][START_REF] Dietze | An end-member algorithm for deciphering modern detrital processes from lake sediments of Lake Donggi Cona, NE Tibetan Plateau, China[END_REF][START_REF] Paterson | New methods for unmixing sediment grain size data[END_REF][START_REF] Yu | BEMMA: A Hierarchical Bayesian End-Member Modeling Analysis of Sediment Grain-Size Distributions[END_REF][START_REF] Zhang | Unmixing grainsize distributions in lake sediments: a new method of endmember modeling using hierarchical clustering[END_REF]. [START_REF] Van Hateren | On the genetically meaningful decomposition of grain-size distributions: A comparison of different end-member modelling algorithms[END_REF] argued that only a statistical comparative study of these estimated end-members and or a geological background could validate these signatures. The particle size end-member analysis of annually deposited sediments permits discrimination of allochthonous and autochthonous compounds to study varve formation and seasonal deposit variations over time (Żarczyński et al., 2019). The estimated end-members also allow for characterization of their relative abundance in each sample and therefore through time. It is also interesting to study instantaneous events, such as floods, to estimate their intensity for example.

This study aims to use hyperspectral imaging to estimate particle size fractions and distribution, then to estimate and characterize end-members. Partial least squares regression (PLSR) is one of the most used multivariate methods for the development of a quantitative predictive model with spectroscopic and physical-chemical data. PLSR is used to estimate particle size fractions and distribution in the same way as for organic matter (Jacq et al., 2019b). Two hyperspectral imaging sensors were used to cover the spectroscopic ranges from visible to near-infrared light (Vis-NIR: 400-2500 nm). A laser grain-sizer was used to estimate the particle size distribution and then after statistic treatment, the main fractions and other variables (D50, D90, skewness, kurtosis). The AnalySize Matlab function was used to unmix the PSD end-members and to estimate their abundance along the core. The proposed methodology is applied to a Lake Bourget sediment core and is compared with previous studies [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF][START_REF] Jenny | A spatiotemporal investigation of varved sediments highlights the dynamics of hypolimnetic hypoxia in a large hard-water lake over the last 150 years[END_REF][START_REF] Jenny | A 4D sedimentological approach to reconstructing the flood frequency and intensity of the Rhône River (Lake Bourget, NW European Alps)[END_REF]. Then, the end-members were used to characterize the annual laminations (varves), to count them, to estimate their accumulation rate per year and their Vis-NIR signatures.

Site description

Lake Bourget is a hard-water lake, 18 km long and 2.8 km wide, located at an altitude of 231.5 m at the northwestern edge of the French Alps (Fig. 1). The rivers Leysse and Sierroz flow into Lake Bourget, which then flows into the Rhone River by the Saviere Channel under normal hydrological conditions. However, during major floods, water from the Rhone River flows into Lake Bourget with the reversal of the water-current of this channel. The sediment is mainly composed of river-borne silicate, between 10-40%, and carbonate, between 60-90%. The ratio between these two compounds varies depending on past climate conditions [START_REF] Arnaud | 7200 years of Rhône river flooding activity in Lake Le Bourget, France: a high-resolution sediment record of NW Alps hydrology[END_REF][START_REF] Arnaud | Lake Bourget regional erosion patterns reconstruction reveals Holocene NW European Alps soil evolution and paleohydrology[END_REF][START_REF] Debret | North western Alps Holocene paleohydrology recorded by flooding activity in Lake Le Bourget, France[END_REF][START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF][START_REF] Jenny | Réponses des grands lacs périalpins aux pressions anthropiques et climatiques récentes : reconstitutions spatio-temporelles à partir d'archives sédimentaires[END_REF][START_REF] Jenny | A 4D sedimentological approach to reconstructing the flood frequency and intensity of the Rhône River (Lake Bourget, NW European Alps)[END_REF].

The location of core LDB09-P101 (length = 54 cm, width = 9 cm) was selected in the northern basin of the lake (45°45'20.0"N 5°51'19.9"E, 145 m water depth). It was sampled for the IPER-RETRO program (ANR-08-VUL 005; [START_REF] Perga | High-resolution paleolimnology opens new management perspectives for lakes adaptation to climate warming[END_REF]). This site was selected because it contains both laminated sediments as well as interbedded deposits triggered by the Rhone River [START_REF] Jenny | Réponses des grands lacs périalpins aux pressions anthropiques et climatiques récentes : reconstitutions spatio-temporelles à partir d'archives sédimentaires[END_REF].

Materials and methods

Sample preparation and measurement

The core was divided into two halves, one that was used for PSD and several destructive analyses, the other used for non-destructive analysis such as the hyperspectral imaging. This LDB09-P101 core is correlated to dated reference cores sampled in this lake, thanks to radionuclides ( 210 Pb, 137 Cs, 241 Am), historically known instantaneous events and varve counting [START_REF] Jenny | Réponses des grands lacs périalpins aux pressions anthropiques et climatiques récentes : reconstitutions spatio-temporelles à partir d'archives sédimentaires[END_REF].

Particle size distribution

Particle size distribution (PSD) analyses were carried out on bulk sediments (5 mm thick, n = 18) using a Malvern Mastersizer 800S. This device uses the laser diffraction principle to estimate the particle diameter and estimate a distribution of them for 64 known classes between 0.06 μm and 800 μm.

Then statistics allowed to calculate the mean particle size, several percentiles (e.g., median, D90, D99), mode, sorting, and particle size fraction (clay, silt, sand).

Hyperspectral Imaging analyzes and registration

A hyperspectral image (HSI) is an image with high spatial resolution, in which each pixel contains a spectrum with a continuous spectral resolution.

The core was analyzed with two hyperspectral sensors (Specim Ltd., Finland) presented in Table 1 with the lens OLES22,5 at the M2C lab, University of Normandie-Rouen.

The sediment core must be as flat as possible for the analysis, so cleaning of the core was made, that also revealed the finest sediment structures. Spectral calibration of the camera was made with a spectralon reference to have reliable intensity. The spatial calibration was achieved by imaging a known object to obtain its true shape and thus obtain squared pixels. The calibration was checked at the end of the acquisition and no deviation was observed. More details about the acquisition protocol can be found in [START_REF] Butz | Hyperspectral imaging spectroscopy: a promising method for the biogeochemical analysis of lake sediments[END_REF].

A composite sensor was created by down-sampling the VNIR sensor at 200 μm and a spatial registration to fit spatially the two hyperspectral images. The registration was made with the moisture content that can be recovered in the two sensors at 970 nm for the VNIR and at 1200 nm for the SWIR (Ce [START_REF] Liu | SIFT Flow: Dense Correspondence across Scenes and Its Applications[END_REF]Jacq et al., 2019a). The SWIR image was registered on the VNIR one, because it has a lower resolution. Thus, a deformation model was estimated with these wavelengths and used on all the SWIR spectral planes. Then the two registered hyperspectral images were put together to create a composite sensor that covers the wavelengths between 400 nm and 2574 nm. It was not possible to up-sample the SWIR sensor at 50 μm because the spatial details cannot be estimated (Jacq et al., 2019a).

Data Analysis

ENVI 4.8 was used to perform the data acquisition. Then, MATLAB (R2018a, MathWorks) was used for advanced processing and analyzing these data. PLSR was used to establish a relationship between the HSI and the PSD of the core to create predictive models and then to estimate the PSD in each pixel. Then AnalySize Matlab function was used to unmix the predicted PSD to find pure sources [START_REF] Paterson | New methods for unmixing sediment grain size data[END_REF].

Predictive model estimation

A multivariate method was used to create quantitative predictive models with the particle size and the VNIR-SWIR spectra of the core. Several noisy bands due to the detector were removed on two sides of the spectra of each sensor; consequently 202 of 242 wavelengths were used. An autoscale spectral pre-processing was realized to reduce the matrix effect. Calibration spectra are median spectra of the particle size sampling areas.

PLSR was used to model the relation between the spectra and the reference particle size values. This method is based on the extraction of orthogonal predictor variables (also called latent variables, LV) corresponding to the maximum variability in the spectral bands used as predictors linked to one or several predicted variable(s) [START_REF] Wold | The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses[END_REF]. Two main algorithms exist, called PLS1 and PLS2, the difference is the number of dependent variables to predict. PLS1 is used when a single variable is predicted. When there are several variables to predict, several PLS1 can be realized, or a single PLS2 if variables to predict are dependent. PLS1 was used to predict particle size fractions, whereas PLS2 to predict the PSD because the fine particle fractions are highly correlated and co-dependent. The spectra register some biological-physical-chemical properties of the sample. For a specific proxy, all these spectral information were not mandatories, so we decided to use a variable selection algorithm (random frog, genetic algorithm) with the PLSR. This allowed to find the most relevant wavelengths, decrease redundancy and to interpret the model chemically. More details about this methodology can be found in Jacq et al. (2019b). Model accuracy was estimated with calibration and validation correlation coefficients and its uncertainty (Unc (%)). Another correlation is calculated between the median predictions of the sampling areas and the reference PSD to validate that the surface acquisition by hyperspectral methods contains the volume information of the particle size analyses (rV/S).

Sedimentary deposition sources discrimination

Each PSD is a mixture of pure sub-PSD, that can be related to some specific sediment source. The Matlab function AnalySize [START_REF] Paterson | New methods for unmixing sediment grain size data[END_REF] was used to unmixed each PSD and find these end-members. The assumption behind this function is a linear model equation (Eq. 1):

= × + (Eq. 1)
with X the reference PSD profile, A the estimated abundance, S T the estimated PSD of the pure components and E the residual matrix.

The intensity of the PSD and its abundance should not be negative. Thus, non-negative spectra and concentrations constraints were used. Another constraint was added to have the sum of abundance and the intensity of S T at 1.

AnalySize allows estimating end-members in two ways. One is called non-parametric end-member analysis (EMA) that estimates end-members empirically from the whole dataset. The other uses a parametric distribution (Weibull, skewed generalized Gaussian distribution) to fit the PSD. A parametric distribution was chosen to unmix the predicted PSD to overcome uncertainties of the model prediction that disturb the sum of Gaussian theoretical distributions.

Results

Lithology and particle size variations

The Lake Bourget sediment core presents three main units (Fig. 2b) that are mainly composed of clay and silt fractions [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF].

Unit I, between 0 and 18 cm depth, presents millimeter-thick biochemical varves and corresponds to perennial anoxic conditions at the lake-sediment interface, with a particle size mode near 22 μm [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF][START_REF] Jenny | Réponses des grands lacs périalpins aux pressions anthropiques et climatiques récentes : reconstitutions spatio-temporelles à partir d'archives sédimentaires[END_REF]. This facies is related to the development of human-triggered lake eutrophication. Unit II, between 18 cm and 26 cm depth, presents disturbed varves with a decreasing particle size mode from 22 μm to 6 μm. Unit III, between 26 cm and 54 cm, is characterized by fuzzy laminated structures and a particle size mode near 6 μm. In the two first units, there are also instantaneous event deposits mostly triggered by floods [START_REF] Jenny | A 4D sedimentological approach to reconstructing the flood frequency and intensity of the Rhône River (Lake Bourget, NW European Alps)[END_REF]. One major instantaneous event occurs between 13.5 cm and 14.5 cm (Fig. 2b).

Eighteen measurements of PSD were performed on the core with a range of the clay fraction between 14-68% with a mean of 40%, and a range for the silt fraction between 30-71% and a mean of 53%. Particle size fraction according to depth can be seen in Fig. 2c and the equivalent PSD in Fig. 3b.

Predictive models of particle size fraction and PSD

PLSR was used to generate quantitative models of the four main particle size fractions (clay, silt, very fine sand and fine sand) and also one to predict the 50 (out of 64) PSD classes from 0.15 μm to 259 μm of the core. The other classes do not have enough variabilities or spectral information to be modeled. Consequently, five models were created. The performance of each is presented in Table 2.

All the models are validated with correlation coefficients (rcal and rval) and rV/S above 0.9 except for five classes between 6 μm and 10 μm of the PSD model with correlations greater than 0.5 (Supplementary material 3) due to very low variability in these classes. A similar number of selected wavelengths and LV was found between these models. Except for the silt fraction (4.0-62.5 μm) with a higher number of LV that induces a more complex spectral modeling, this agrees with the five classes between 6-10 μm that present lower modeling performances.

The selected wavelengths of these models allow us to identify the structural information that are correlated with the particle size effect [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]Jacq et al., 2019b). The selected wavelengths for the grain size fractions and PSD predictions are consistent. This allows for identifying precisely the spectral areas of each particle size fraction. Nine spectral areas can be seen (Fig. 4):

• (1) Carotenoids and/or iron oxides compounds can be associated with wavelengths around 470 nm;

• (2,3) Two other areas can be linked to the presence of iron oxides presence (around 550 nm and 625 nm);

• (4) Chlorophyll pigments absorb around 700 nm;

• (5,7) The absorption wavelengths around 900 nm and 1450 nm can be due to water content, and this can be residual water that can be related to porosity;

• (6) Organic and hydroxyl bonds are associated with wavelengths around 1150 nm;

• (8) Mineralogical clay compounds wavelengths around 2200 nm are needed to predict physical clay fraction;

• (9) around 2400 nm are wavelengths associated with some mineral hydroxyl bonds.

Areas 1-5 and 7-8 are used for the prediction of fine fractions, such as clays and silts, whereas areas 5-6 and 9 are related to coarser fractions (very fine and fine sand).

Most of the selected wavelengths (34 over 44) are in the VNIR range, but that does not imply that the SWIR selected wavelengths are not relevant, because they contain relevant particle size information. Furthermore, the use of only one of the two sensors, independently of the other, does not allow to obtain a performant model. If only the VNIR is used, the performances of prediction are lower than 0.9, and the uncertainty is slightly higher. The same applies to the SWIR with performance lower than 0.9 and an inversion of the grain size of laminae (in which coarse grains are predicted as fine grains). This shows the importance of combining sensors of several spectral ranges to improve modeling performances with complementary information.

Prediction distribution

The predicted PSD in Fig. 3d evidence the same three units than the reference PSD in Fig. 3b (unit I:

22 μm, unit II: 22-6 μm and unit III: 6 μm). The down-sampling of the predicted PSD in Fig. 3c allows for surface and volume analysis to be linked together with a correlation of 0.96 (p<0.05) with the reference PSD. Two instantaneous deposits are quite visible at 14 cm and 16 cm depth through a marked drop in particle size.

The 50 models (one for each grain size class of PSD) allow estimation of the particle size fractions with the sum of the fine classes associated with the fractions according to the Wentworth scale [START_REF] Wentworth | A Scale of Grade and Class Terms for Clastic Sediments[END_REF]. The correlation between the prediction maps of a single or several models and the bias (difference of the predicted values) have been estimated (Table 3, Supplementary material 4). This shows that the coarser the particle size, the lower the correlation. Moreover, there is more bias for the silt fraction, which matches the observation of rV/S for the class between 6-10 μm. The rV/S is better for those estimated with a single model (Table 2), and the abundance maps (Supplementary material 4) seem to be smooth for those estimated from the predicted PSD.

Sediment sources

Five classes (EM) with their modes and abundances were estimated using the AnalySize function applied to the PSD prediction (Fig. 5a-c):

1. The first one (EM1) has a mode at 0.42 μm (width at half height: 0.2-0.9 μm) and shows a decreasing abundance trend from the bottom to the top of the core, from 25% to 10%.

The second (EM2

) is centered at 4.19 μm (width at half height: 1.44-12.21 μm). It has an upward decreasing trend from 62.5% to 5% and is mainly present below 25 cm depth and in instantaneous event deposits with values higher than 30%.

3. The third (EM3) has a mode at 9.00 μm (width at half height: 4.88-15.21 μm) and has an abundance quite stable at 10% except an increase at 15% in the instantaneous event.

4. The fourth (EM4) centered at 22.49 μm (width at half height: 12.21-45.51 μm) is mainly present in the first 25 cm (eutrophic part) with an increasing upward trend from 5% to 30%.

5. The fifth (EM5) has a mode at 65.51 μm (width at half height: 26.2-150.0 μm) and is mainly present in the first 25 cm (eutrophic part) with an increasing upward trend from 5% to 25%.

6. The residual part is mainly present in the two first units and has values lower than 2.5%.

The abundance maps in Fig. 6b-f show down and cross variations of the five pure classes. The two first (EM1-2) have the same variations and a high correlation of 0.99 (p < 0.05). They characterize unit III, i.e., the pre-eutrophication unit. Their trend along the core depth is the opposite of those of the two last (EM4-5) regardless of the proportions. EM4-5 are thus enriched in unit II and mostly unit I. The EM3 map is different with a quite homogeneous variation along the core except in specific lamina in the two first units. This end-member is also relatively abundant in the instantaneous event layer. The residual fraction (Fig. 6g) is more present in the laminated part of the core that might be explained by the presence of other sediment sources or a change in the size of previous sources.

Discussion

Interpretation of the sources based on the laminae succession

To interpret the end-members, we discuss a few laminae successions to see their compositions with the three main modes (EM2-3-4, Fig. 7) and to compare with previous descriptions of the laminae EM4 agrees with the size range for large calcite crystals (15-30 µm) and diatoms (30-45 µm). EM3

reflecting small calcite crystals were characterized by a mode between 4.5 μm and 8 μm by [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF]. EM2 fits well with the detrital particles previously defined with a mode between 6 μm and 9 μm. EM1, which is highly correlated to EM2 (0.99 (p < 0.05)), was also observed but not discussed in the previous study [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF]. This mode was only present in the carbonated PSD. We thus interpret it as representing micrite deposits. EM5 can be associated with a mix between diatom frustules and organic matter because it is highly correlated with EM4, which characterizes the spring lamina (i.e., the time of diatom bloom).

Due to the predicted PSD range (0.15 μm to 259 μm), two modes determined in the previous study cannot be estimated with hyperspectral data (OM: 150-350 µm and very large carbonate particles: 160-300 µm). The modes are not the same due to the data used for their estimations. In [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF], PSD from the carbonated and decarbonated fractions of the sediments were used. Whereas in our study, we use the complete PSD that corresponds to a mix between the two fractions.

Lamina counting

The small calcite crystals (EM3; Fig. 7c), are quite localized and can be discriminated from the others.

It is possible to enhance it with image processing. An abundance threshold is fixed at 40% to binarize the abundance map, in which upper values correspond to the EM3 deposit, and below this value to another one. A median filter is used to remove solitary points. Then, the lamina can be easily manually counted. They are correctly counted, until the year 1953, so 57 laminae can be discriminated. Before this, they are too fuzzy and thin. Also, the small calcite crystal abundance decreases lower than 40%, and even a linear decreasing threshold allows with difficulty to discriminate this deposit because of laminae thinness.

Estimation of the accumulation rate for each lamina

The accumulation rate of each lamina can be estimated if the first pixel of each year is determined.

The EM2-3-4 maps were reduced to a median signal along the depth, the EM4 trend shows fluctuations that can allow the beginning of the year to be identified. Unfortunately, it is too variable to use automatic detection, so manual selections were made. Then, each pixel is associated with one of the three laminae based on their EM percentage. Because the spring and summer laminae are related to the same compounds (EM3-4) that overlap spatially, a rule based on the EM3-4 values is proposed to separate them. If the value of the EM3 is greater than 40% of the EM4 one, then the corresponding lamina is summer, otherwise, it is the spring. There is not this kind of problem with the winter lamina (EM2). Finally, this classification signal is used to count the number of pixels of each season in a year to estimate accumulation rates for each lamina (Fig. 7f and8).

Fig. 8c shows an increase in diatom and large calcite crystal accumulations until 1982, followed by a decrease. These components reflect primary productivity. Consequently, a decrease after 1982

indicates an improvement in trophic status, which is in agreement with the decrease in phosphorus supplies presented in [START_REF] Jenny | A spatiotemporal investigation of varved sediments highlights the dynamics of hypolimnetic hypoxia in a large hard-water lake over the last 150 years[END_REF]. The small calcite crystal accumulation rate has an opposite trend relative to the large calcite crystals and diatoms (Fig. 8b). This can also be explained by changes in trophic status. Eutrophication favors the precipitation of large calcite crystals compared to smaller ones. The accumulation rate of detrital particles (Fig. 8a) represents annual inputs from the Rhône River floods to the lake. The peak in 1990 represents the large floods of February 1990 [START_REF] Jenny | A 4D sedimentological approach to reconstructing the flood frequency and intensity of the Rhône River (Lake Bourget, NW European Alps)[END_REF].

Visible and near-infrared spectra of each lamina

The three laminae, the instantaneous events and unit III were manually selected to find their pixels and then to extract their average spectral signatures (Fig. 9). The continuum removed [START_REF] Clark | Reflectance spectroscopy: Quantitative analysis techniques for remote sensing applications[END_REF] of the spectra allows for them to be normalized to compare the absorption spectra. It allows us to see five spectral ranges, which have different contributions in the different units and facies:

• The carotenoids and or iron oxides are mostly present in the laminated unit, in all the laminae.

• The chlorophyll pigments are mostly present in the spring and summer lamina and indicate the increase in lacustrine productivity due to eutrophication.

• The organic and hydroxyl compounds are higher in the summer and winter laminae as well as in the instantaneous events. This result is interpreted as reflecting lacustrine and terrestrial organic matter.

• The water content shows a gradient, from the lowest to the highest: non-eutrophic part, instantaneous event, winter, spring, summer laminae. This can be associated to residual water linked to porosity and compaction.

Detection of a sub-unit

The high resolution of analysis allows us to observe the trends with high precision and detect similar groups of trends for unit characterization. The Bourget core was divided into three units, but based on our evidence unit I was split into two sub-units, from 0 to 6 cm depth (2009( -1992, unit Ia) , unit Ia) and from 6 to 18 cm (1992( -1962, unit Ib), unit Ib). The main observed changes in unit I are:

• A decrease of particle size in the PSD (Fig. 3d) that corresponds to an increase in small bioinduced calcite crystals, a decrease of large calcite crystals and diatom frustules (Fig. 5c and 6d-e),

• An increase in the residual part (Fig. 6g) that can be induced by modification of the environment.

The changes in this sub-unit can reflect the response of the lake to restoration programs, especially the diversion of treated waste-waters into the Rhône river in the 1990s that improved water quality and changed the biochemistry of the lake [START_REF] Jacquet | The proliferation of the toxic cyanobacterium Planktothrix rubescens following restoration of the largest natural French lake (Lac du Bourget)[END_REF][START_REF] Berthon | Sensitivity and responses of diatoms to climate warming in lakes heavily influenced by humans[END_REF].

Possibilities of the hyperspectral analysis

The use of high-resolution analysis, such as hyperspectral imaging, to estimate PSD associated with unmixing methods shows great possibilities to infer the provenance of the material and their transport, as well as some deposition processes (floods, landslide, eruption). And also their variations across times, with changes in the population of diatoms or other organisms, changes in the physicalchemistry of the lake or the watershed or beyond.

Hyperspectral imaging is a very informative tool which can be used for more than particle size studies. This method has already proved useful for the prediction of organic matter [START_REF] Van Exem | Hyperspectral core logging for fire reconstruction studies[END_REF]Jacq et al., 2019b), pigments (Schneider et al., 2018), and to perform source to sink analysis (Van Exem et al., 2019). Some proxies can be estimated directly after HSI acquisition, and other proxies need to process the data with or without destructive analysis.

A Matlab toolbox was created for the study of particle size presented in this paper and for a previous study of organic matter (Jacq et al., 2019b), and also allows for the generation of models for organic matter (LOI550 and RockEval) and particle size on several lakes (unpublished works). This toolbox can be found at https://github.com/JacqKevin/HSI_PLSR, developed with Matlab R2018a (the Parallel Computing Toolbox can be used for faster calculations). It contains functions to create a PLSR model and to apply it to the data, and also spectral preprocessing and variable selection algorithms. The regular use of this toolbox allows for highlighting precautions and difficulties related to data. The destructive data used to calibrate the models need to be representative of the main variations observed in the sample. The creation of an optimal predictive model requires to have variability inside the destructive analysis values. Future works will focus on the determination of relevant sampling areas for a proxy using only hyperspectral data. There are also the sediment matrix effects with the presence of several different lithologies that can disturb the modeling.

Conclusions

Hyperspectral imaging, with its spatial and spectral dimensions, is a very informative analytical method. This method promises great possibilities because it offers high resolution (200 μm), is non-destructive and fast (15 min for a 1.5 m core for each sensor). In this study, HSI allows estimation of particle size distribution and size fraction in each point of the lake Bourget core. Then, with an unmixing method, five sediment sources were estimated and characterized in a previous study on this lake. The high spatial resolution allowed discrimination of three laminae. With image processing methods, they were discretized to estimate their spectral signatures and thus their chemistry. They were also manually counted, and that agreed with the age model. Therefore, hyperspectral imaging for the prediction of PSD and characterization of end-members, as well as their annual accumulation rates, is very useful for the study of sediment cores and environmental samples.

Some improvements are needed for the extraction of a relevant number of end-members in this data. Sequential extraction of end-members with the study of residuals seems to be relevant because the existing algorithms find only the main ones. Further works using the spatio-spectral approaches can improve the relevance of the estimated PSD, the fine particles can be estimated with the spectral dimension and the coarse ones with the spatial dimensions Tables Table 1. Hyperspectral sensor properties Table 2. Statistics of the reference data and models performances (number of latent variables (LV) and of selected wavelengths (wl), calibration and validation correlations (rcal and rval), uncertainty (Unc), volume-surface correlation (rV/S)) for the four particle size fractions and the averaged of the fifty classes of the PSD.

Table 3. Correlation and bias between the abundance maps of the particle size fractions estimated by their PLSR models or with the PSD prediction; volume-surface correlation of the map estimated with the PSD prediction.

(

  [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF] (Supplementary material 2). As presented in the lithological description, there are three different laminae, which are also well discriminated by the end-members (Fig.7; Supplementary material 2. Based on PSD from the carbonated and decarbonated fractions of the sediments,[START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF] defined six classes corresponding to different sediment components. Five of these classes can be associated with the end-members determined in this study.

Figures

  Figures

Fig. 1 .

 1 Fig. 1. (a) Location and the catchment area of Lake Bourget. (b) Bathymetry, tributaries and effluents

Fig. 2 .

 2 Fig. 2. (a) Image RGB of the core, (b) lithology (with three units and flood deposits), (c) particle size

Fig. 3 .

 3 Fig. 3. (a) Image RGB of the core, (b) PSD (in %) of the laser granulometer, (c) predicted PSD (in %)

Fig. 4 .

 4 Fig. 4. Selected wavelengths and associated compound areas for the five models (four fractions and

Fig. 5 .

 5 Fig. 5. (a) The five end-members estimated with the predicted PSD by HSI, (b) image RGB of the core,

Fig. 6 .

 6 Fig. 6. (a) Image RGB of the core, (b-f) the abundance maps of the five end-members estimated by

Fig. 7 .

 7 Fig. 7. (a) Image RGB of a laminated area, (b-d) the three main end-members abundance maps (EM4-

Fig. 8 .

 8 Fig. 8. Estimation of the annual lamina accumulation rates for (a) detrital particles, (b) small calcite

Fig. 9 .

 9 Fig. 9. (a) Visible and near-infrared signatures and (b) continuum removal with associated main

  It is characterized by a triplet of laminae made of different components (Giguet-

	Covex et al., 2010) (Supplementary materials 1, 2). The lowermost lamina (dark-brown after
	oxidation) is deposited in spring and is mainly composed of diatom frustules and large bio-induced

calcite crystals. The intermediate lamina (whitish to ochre after oxidation) is deposited in summer. It is composed of large and mostly small calcite crystals, micrite, few diatoms frustules and organic matter. The uppermost grey lamina corresponds to the winter deposit, which mainly contains organic matter and detrital particles. Some years a bloom of diatoms can occur in the fall. The presence of the large bio-induced calcite crystals and a high amount of diatoms is characteristic of the eutrophication period.

Acknowledgements

The Bourget core used in this study is stored in the EDYTEM laboratory that also performed the PSD analysis in 2009 during the IPER-RETRO program (ANR-08-VUL 005). The hyperspectral imaging acquisition was made at the University of Normandie-Rouen and was funded by the Region Normandie, which supports the scientific consortium SCALE UMR CNRS 3730. Furthermore, we thank the anonymous reviewer and Jasper Knight (Editor-in-Chief) for their helpful comments.

Supplementary materials

Supplementary material 1. Correlations of the sediment cores use for our (LDB09_P101) and Giguet (LDB06_P2) studies [START_REF] Giguet-Covex | Sedimentological and geochemical records of past trophic state and hypolimnetic anoxia in large, hard-water Lake Bourget, French Alps[END_REF] Supplementary material 2. Thin section of the LDB06_P2 core used for the Ca, Al and Si counts by micro-XRF. Supplementary material 3. Correlation coefficients of the PSD models in calibration, validation and for rV/S. Supplementary material 4. Abundance maps of the particle size fractions estimated with their models (single, a-c-e-g) or with the predicted PSD (multiple, b-d-f-h) (in %).

Name