Thomas Bouvarel

Nathalie Delaunay

Valérie Pichon
email: valerie.pichon@espci.fr

Selective extraction of cocaine from biological samples with a miniaturized monolithic molecularly imprinted polymer and on-line analysis in nano-liquid chromatography

Keywords: Molecularly Imprinted Polymer, Monolith, on-line coupling, Cocaine, Human plasma, Saliva ACN, Acetonitrile, AIBN, Azo-N,N'-diisobutyronitrile, BZE, Benzoylecgonine, CEC, Capillary electrochromatography, CL, Cross-linking agent, COC, Cocaine, EGDMA, Ethylene glycol dimethacrylate, i.d., internal diameter, IF, Imprinting factor, LOD, Limit of detection, LOQ, Limit of quantification, MAA, Methacrylic acid, γ-MAPS, 3-(trimethoxysilyl) nanoLC, Nano-liquid chromatography, NIP, Non-imprinted polymer, P, porogen, RSD, Relative standard deviation, SEM, Scanning electron microscopy, SPE, Solid phase extraction, T, cocaine template, TRIM, Trimethylolpropane trimethacrylate, UV, Ultraviolet

We report the on-line coupling of a monolithic molecularly imprinted polymer to nano-liquid chromatography for the selective analysis of cocaine and its main metabolite, benzoylecgonine, in complex biological samples. After the screening of different synthesis conditions, a monolithic molecularly imprinted polymer was in situ synthesized into a 100 µm internal diameter fused-silica capillary using cocaine as template, methacrylic acid as functional monomer, and trimethylolpropane trimethacrylate as cross-linker. Scanning electron microscopy was used to assess the homogeneous morphology of the molecularly imprinted polymer and its permeability was measured. Its selectivity was evaluated by nanoliquid chromatography-ultraviolet, leading to imprinting factors of 3.2 ± 0.5 and 2.2 ± 0.3 for cocaine and benzoylecgonine, respectively, on polymers resulting from three independent syntheses, showing the high selectivity and the repeatability of the synthesis. After optimizing the extraction protocol to promote selectivity, the monolithic molecularly imprinted polymer was successfully on-line coupled with nano-liquid chromatographyultraviolet for the direct extraction and analysis of cocaine present in spiked human plasma and saliva samples. The repeatability of the obtained extraction recovery, between 85.4-98.7% for a plasma sample spiked at 100 ng.mL -1 , was high with relative standard deviation values lower than 5.8% for triplicate analyses on each of the three independently synthesized molecularly imprinted polymers. A linear calibration range was achieved between 100 and 2000 ng mL -1 (R 2 = 0.999). Limits of quantification of 14.5 ng mL -1 and 6.1 ng mL -1 were achieved in plasma and urine samples, respectively. The very clean-baseline of the resulting chromatogram illustrated the high selectivity brought by the monolithic molecularly imprinted polymer that allows the removal of a huge peak corresponding to the elution of interfering compounds and the easy determination of the target analyte in these complex biological samples.

Introduction

Miniaturized analytical devices have matured considerably since the initial lab-on-a chip concept proposed by Manz in 1990 [START_REF] Manz | Miniaturized total chemical analysis systems: A novel concept for chemical sensing[END_REF]. The potential benefits of miniaturization are enormous, following the principle that small-scale processes consume less time, samples, and reagents [2]. However, the miniaturization of the analytical system may result in loss of the separation power by the reduction of the separation lengths. This represents a serious limitation when target analytes are at trace levels in complex matrices. To overcome this problem, a selective sample pre-treatment step can be integrated into the miniaturized devices.

Solid-phase extraction (SPE) is a powerful method for the extraction and the purification of compounds contained in complex samples. However, the majority of the available sorbents mainly promotes the development of non specific interactions during the extraction procedure that leads to the co-extraction of a huge amount of interfering compounds. This lack of selectivity has been at the origin of the development of molecular imprinted polymers (MIPs). MIPS are synthetic and selective sorbents that possess specific cavities designed for a target analyte, with a retention mechanism based on molecular recognition, similarly to immunosorbents [START_REF] Brothier | Immobilized antibody on a hybrid organic-inorganic monolith: Capillary immunoextraction coupled on-line to nanoLC-UV for the analysis of microcystin-LR[END_REF][START_REF] Faure | Optimization of in-situ monolithic synthesis for immunopreconcentration in capillary[END_REF] or oligo-sorbents [START_REF] Brothier | Miniaturized DNA aptamer-based monolithic sorbent for selective extraction of a target analyte coupled on-line to nanoLC[END_REF][START_REF] Deng | Aptamer Modified Organic-Inorganic Hybrid Silica Monolithic Capillary Columns for Highly Selective Recognition of Thrombin[END_REF]. They are used in several fields, such as sensors, catalysis, enantiomeric separations, and extraction [START_REF] Pichon | Affinity Separations on Molecularly Imprinted Polymers with Special Emphasis on Solid-Phase Extraction[END_REF].

The analysis of various organic compounds from complex samples assisted by MIP extraction and clean-up has been largely described in literature [START_REF] Pichon | Selective sample treatment using molecularly imprinted polymers[END_REF][START_REF] Tan | Molecularly-imprinted monoliths for sample treatment and separation[END_REF]. As for conventional SPE sorbents, MIPs have been mainly used off-line by packing MIPs particles into a cartridge between frits.

For their on-line-coupling with conventional LC systems, some monolithic MIPs have been prepared in 4.6 mm internal diameter (i.d.) columns [START_REF] Li | Preparation of clenbuterol imprinted monolithic polymer with hydrophilic outer layers by reversible addition-fragmentation chain transfer radical polymerization and its application in the clenbuterol determination from human serum by on-line solid-phase extraction/HPLC analysis[END_REF][START_REF] Lv | Preparation and evaluation of a novel molecularly imprinted hybrid composite monolithic column for on-line solid-phase extraction coupled with HPLC to detect trace fluoroquinolone residues in milk[END_REF]. This approach was used to prepare a MIP column for HPLC separation [START_REF] Chen | In situ synthesis of monolithic molecularly imprinted stationary phases for liquid chromatographic enantioseparation of dibenzoyl tartaric acid enantiomers[END_REF][START_REF] Baykara | Synthesis of monolithic HPLC stationary phase with self-assembled molecular recognition sites for 4-aminophenol[END_REF] and did not require the covalent attachment of the MIP to the inner surface of the column since frits were used to maintain the sorbent in the column.

The miniaturization of MIPs for extraction is particularly attractive from a general point of view, and even more when templates or monomers are expensive or difficult to synthesize.

For devices base on partition, MIPs can be nanoparticles, mainly used in dispersive SPE [START_REF] Turiel | Molecularly imprinted polymers-based microextraction techniques[END_REF], a coating of a fiber or a thin film on the inner wall of a capillary for in-tube solid phase microextraction [START_REF] Sarafraz-Yazdi | Application of molecularly-imprinted polymers in solidphase microextraction techniques[END_REF][START_REF] Ansari | Recent progress, challenges and trends in trace determination of drug analysis using molecularly imprinted solid-phase microextraction technology[END_REF]. Concerning exhaustive extraction in SPE, MIP particles can be packed in a specially designed chip [START_REF] Lei | Preparation of Z-l-Phe-OH-NBD imprinted microchannel and its molecular recognition study[END_REF][START_REF] He | Micro flow sensor on a chip for the determination of terbutaline in human serum based on chemiluminescence and a molecularly imprinted polymer[END_REF] or the surface of a core monolith can be grafted by MIP [START_REF] Wei | Preparation and characterization of grafted imprinted monolith for capillary electrochromatography: CE and CEC[END_REF][START_REF] Szumski | Monolithic molecularly imprinted polymeric capillary columns for isolation of aflatoxins[END_REF][START_REF] Wen | Smart" molecularly imprinted monoliths for the selective capture and easy release of proteins: Other Techniques[END_REF]. The in situ synthesis of a monolithic MIP filling the entire section and wellanchored at the capillary or chip channel surface can lead to higher capacity than the opentubular approach to be applied to trace enrichment purposes. Monolithic MIPs were first synthesized for capillary electrochromatography (CEC) [START_REF] Spégel | Molecularly imprinted polymers in capillary electrochromatography: Recent developments and future trends[END_REF][START_REF] Zheng | Recent developments and applications of molecularly imprinted monolithic column for HPLC and CEC[END_REF][START_REF] Mu | Current trends in the development of molecularly imprinted polymers in CEC: CE and CEC[END_REF], especially for chiral separations [START_REF] Iacob | Recent advances in capillary electrochromatography using molecularly imprinted polymers: CE and CEC[END_REF][START_REF] Rutkowska | Application of molecularly imprinted polymers in analytical chiral separations and analysis[END_REF]. Recently, monolithic MIPs were also developed for off-line extractions in miniaturized devices, such as pipet-tips [START_REF] Li | Preparation of Cholecystokinin Molecularly Imprinted Polymer Monolith and its Application in Solid Phase Microextraction and HPLC Analysis[END_REF][START_REF] Zhu | A dummy molecularly imprinted monolith for selective solid-phase microextraction of vanillin and methyl vanillin prior to their determination by HPLC[END_REF], hollow-fiber membrane [START_REF] Chen | Hollow-fiber membrane tube embedded with a molecularly imprinted monolithic bar for the microextraction of triazine pesticides[END_REF], or 75 µm to 530 µm i.d. capillaries [START_REF] Zhang | Molecularly imprinted monolith in-tube solidphase microextraction coupled with HPLC/UV detection for determination of 8hydroxy-2′-deoxyguanosine in urine[END_REF][START_REF] Su | Molecularly imprinted solid-phase extraction monolithic capillary column for selective extraction and sensitive determination of safranine T in wolfberry[END_REF][START_REF] Zheng | Selective sample pretreatment by molecularly imprinted polymer monolith for the analysis of fluoroquinolones from milk samples[END_REF][START_REF] Lin | One-pot preparation of a molecularly imprinted hybrid monolithic capillary column for selective recognition and capture of lysozyme[END_REF][START_REF] Zhang | Determination of urinary 8-hydroxy-2′deoxyguanosine by a combination of on-line molecularly imprinted monolithic solid phase microextraction with high performance liquid chromatography-ultraviolet detection: Sample Preparation[END_REF][START_REF] Zhang | Porous molecularly imprinted monolithic capillary column for on-line extraction coupled to high-performance liquid chromatography for trace analysis of antimicrobials in food samples[END_REF][START_REF] Yuan | Sensitive determination of rose bengal in brown sugar by a molecularly imprinted solid-phase extraction monolithic capillary column coupled with capillary electrophoresis[END_REF][START_REF] Bi | Preparation of a POSS-hybridized molecularly imprinted monolith for the analysis of baicalin and its analogues in a microwave-assisted extract from Scutellaria baicalensis by means of online SPME-HPLC and off-line LC-MS/MS[END_REF][START_REF] Liang | Synthesis of carbon quantum dots-doped dummy molecularly imprinted polymer monolithic column for selective enrichment and analysis of aflatoxin B1 in peanut[END_REF][START_REF] Zhai | Novel coordination imprinted polymer monolithic column applied to the solid-phase extraction of flumequine from fish samples[END_REF]. If the repeatability of the extraction was sometimes mentioned, the repeatability of the MIP synthesis has almost never been described. Besides, to our knowledge, only one work is related to the on-line coupling of a capillary containing a MIP (100 µm i.d.) with a capillary column (300 µm x 25 cm) [START_REF] Szumski | Monolithic molecularly imprinted polymeric capillary columns for isolation of aflatoxins[END_REF]. The MIP was produced by a two-step process since it was synthesized at the surface of a monolith. The feasibility of the on-line coupling was demonstrated for the analysis of several aflatoxins. However, there is no application with real samples, no mention of synthesis repeatability, and the two-step synthesis procedure should give rise to a sorbent with a lower capacity than a direct in situ polymerization of a monolithic MIP.

The aim of the present work was the direct in situ synthesis of a monolithic MIP into a 100 µm i.d. capillary and its on-line coupling with nano-liquid chromatography (nanoLC) for the selective extraction of a target analyte from a biological fluid. For this proof-of-concept, cocaine was taken as a model molecule. Indeed, our group already synthesized MIPs in bulk for the selective extraction of cocaine and its metabolites, benzoylecgonine (BZE) and ecgonine methyl ester [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF][START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF]. In these studies, cocaine was chosen as template molecule and various monomers, cross-linking agents, porogens, and initiation modes were evaluated.

The most promising MIP was obtained with methacrylic acid (MAA) as monomer, ethylene glycol dimethacrylate (EGDMA) as cross-linker, and acetonitrile (ACN) as porogen. The bulk polymerization was initiated under UV using Azo-N,N'-diisobutyronitrile (AIBN) as initiator [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF]. The resulting MIP monolith was grinded and resulting MIP particles were packed into SPE cartridges to selectively extract the target analytes from hair extracts [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF] and urine samples [START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF] with high extraction recoveries of 89 ± 7% and 92 ± 15%, respectively, for cocaine. Another group synthesized a MIP with the same pathway to extract cocaine from saliva samples and quantify it by ion mobility spectrometry [START_REF] Sorribes-Soriano | Cocaine abuse determination by ion mobility spectrometry using molecular imprinting[END_REF]. In all cases, MIPs exhibited good selectivity and high capacity.

The success of the in situ synthesis of a monolithic MIP relies on the presence of large pores to provide convective flow-through and of highly selective binding sites. The synthesis conditions must therefore be adapted to satisfy these two parameters. In this work, different synthesis conditions were screened and the resulting monoliths were first characterized by permeability measurements and by scanning electron microscopy (SEM).

The most promising MIPs were then evaluated by studying their selectivity, comparing their retention factors with the ones of a non-imprinted polymer (NIP), i.e. a control polymer prepared in the same conditions but in absence of the template. After checking the repeatability of the synthesis, the extraction on the monolithic MIP was coupled on-line with nanoLC-UV analysis. The volume and the composition of the solution ensuring both the transfer of the target analytes from the injection loop to the MIP and the removal of nonspecific interactions were optimized using NIP. Finally, analyses of cocaine present in spiked plasma and saliva samples were carried out.

Experimental

Chemicals and reagents

Cocaine base and stock solutions of 1 mg mL -1 of BZE in MeOH were provided by Sigma-Aldrich (Saint-Quentin-Fallavier, France). The working solutions at 1 µg mL -1 were obtained by dilution of the stock solution (1 mg mL -1 ) in HPLC-grade ACN (Carlo Erba, Val-de-Reuil, France). These solutions were stored at -20°C. MeOH, EtOH, and isooctane were purchased from Carlo Erba. Acetic acid and anhydrous ACN were provided by Sigma-Aldrich. 1 M NaOH and 0.1 M HCl were obtained using deionized water (Milli-Q purification system, Millipore, Molsheim, France) and Titrisol solution from Merck (Darmstadt, Germany). MAA, EGDMA, trimethylolpropane trimethacrylate (TRIM), and 3-(trimethoxysilyl)propyl methacrylate (γ-MAPS) were purchased from Sigma-Aldrich. EGDMA was washed twice with an equal volume of a solution of 10% NaOH in deionized water, and then washed twice with an equal volume of water. Afterwards, it was dried using an equal volume of saturated NaCl solution and next over Na 2 SO 4 . Purified EGDMA and MAA were distilled under vacuum in order to remove inhibitors and stored at -20°C. AIBN was purchased from Acros Organics (Noisy-le-Grand, France). AIBN, TRIM, and γ-MAPS were of satisfactory purity so they were used without further purification. Fused-silica capillaries with a UV transparent protecting fluorocarbon polymer coating (PTFE-coated silica capillaries, 100 µm i.d. x 375 µm o.d.) were purchased from Polymicro Technologies (Photon Lines, Saint Germain-en-Laye, France).

In situ preparation of the monolithic polymers

The monolithic polymers were prepared in situ by a thermally initiated polymerization within fused-silica capillaries. Prior to polymerization, the inner wall of the capillaries was activated to anchor the monolith with γ-MAPS according to a procedure adapted from Hjertén [START_REF] Hjertén | High-performance electrophoresis : Elimination of electroendosmosis and solute adsorption[END_REF].

Briefly, the capillaries were first rinsed with water, then activated by flushing 1 M NaOH for 30 min. After a washing step with water, 0.1 M HCl was flushed for 30 min. The silanization was then achieved with 250 µL of γ-MAPS in 1 mL of EtOH, with a pH adjusted to 3.5 by acetic acid, for at least 1 h at room temperature. The capillaries were washed with EtOH and finally dried with nitrogen.

The template molecule (T: cocaine, 10 mg), functional monomer (M: MAA), cross-linking agent (CL: TRIM or EGDMA), and radical initiator (AIBN, 1.5% M+CL, %w/w) were dissolved in porogen (P: ACN containing 10% of isooctane) with a molar ratio T/M/CL of 1/4/20. Then the polymerization mixture was purged with nitrogen for 5 min to get rid of oxygen and introduced in the 15 cm-long capillaries. After sealing both ends of the capillaries with rubber septum, they were immersed in a thermostated water bath at 60°C. The thermal polymerization was allowed to proceed during 24 h. After polymerization, the capillary containing the monolithic MIP was connected to a nano-pump and rinsed at a flow rate of 200 nL min -1 with a volume of ACN/acetic acid (98/2, v/v) corresponding to ten volumes of the empty capillary to remove the template molecules and other residual reagents. Before using a new monolithic MIP, in order to confirm the removal of the template, blanks were made to verify that the potential leaching of cocaine led to a concentration level below the LOD. The monolithic NIPs were obtained by performing the same procedure in the absence of the template. The resulting capillaries were cut to obtain 5 cm-long capillaries.

Characterization of the monolithic MIP by SEM and nanoLC

The cross section of the capillaries containing the polymer was observed by SEM, with a FEI MAGELLAN 400 scanning electron microscope that operates with a beam energy comprised between 3 keV and 5 keV. Considering the support at our disposal to carry out the SEM observations, it was not possible to set the lens just above our capillaries, which means that the pictures were taken with a small angle, but it does not interfere with the observations we wanted to make concerning the monoliths. Permeability measurements were carried out with an Ultimate TM RSLCnano 3000 system (ThermoFisher Scientific, Le Pecq, France), composed of a nano-pump delivering 100% ACN (η = 0.316 mPa s at 35°C) at a constant temperature of 35°C with different flow rates and allowing to record the generated backpressure. The permeability was calculated using Darcy's law which expresses the permeability as a function of the applied flow rate: K is the permeability (m²), F the applied flow rate (m 3 s -1 ), η the viscosity of the solvent (Pa s), L the length of the capillary (m), ∆P the measured back-pressure (Pa), and d i the capillary inner diameter (m).

For retention studies, cocaine (25 µg mL -1 ) and BZE (25 µg mL -1 ) were injected on a nanoLC system composed of a six-port switching nano-valve (Cheminert nanovolume 6 ports 2 pos where t R and t 0 are the retention times of cocaine or BZE and of acetone, respectively; k MIP and k NIP the retention factors obtained on the MIP and the NIP monolithic columns, respectively.

NanoLC-UV analysis of cocaine and benzoylecgonine

The nanoLC analyses of standards of cocaine and BZE were achieved using the same device as the one described in Part 2.3, replacing the MIP/NIP capillaries by the nanoLC column (Acclaim TM PepMap TM 100 C18, 150 x 0.075 mm, 3 µm, ThermoFisher Scientific) and using an home-made injection loop of 50 nL. The separation was achieved at a flow-rate of 200 nL min -1 and a gradient based on ammonium formate 10 mM pH 3.1 adjusted with formic acid (A) and ACN (B). The gradient started with 10% B, increased to 25% B in 1.5 min, then reached 40% B in 5.6 min, increased to 80% B in 0.8 min, and remained for 2.4 min.

Finally, the mobile phase composition was set back to 10% B to let the system equilibrate.

Solutions composing the mobile phase were filtered by 0.45 µm nylon membrane filters purchased from Whatman (Maidstone, England) before using. The UV detection of cocaine and BZE was carried out at 233 nm.

On-line coupling of MIP or NIP extraction with nanoLC-UV analysis

The on-line set-up allowing the coupling of monolithic MIP/NIP to the nanoLC-UV device is In the first step of the extraction procedure, sample was loaded onto the loop (valve 1). In parallel, the analytical column was conditioned with mobile phase. In a second step, the valve 1 was switched in order to transfer the sample to the monolithic MIP/NIP extraction capillary (50 mm x 100 µm) using a washing solvent, a H 2 O/ACN mixture with optimized volume and composition as mentioned in section 3.4, delivered by the syringe pump through the sample loop at a flow rate of 200 nL min -1 . At the last step, the valve 2 was switched allowing thus the transfer of the trapped compounds from the monolithic MIP/NIP to the nanoLC analytical column by the mobile phase delivered by the nanoLC pump. After each analysis, the MIP/NIP capillaries were subsequently re-equilibrated with the initial H 2 O/ACN mixture (70/30, ν/ν), that was used for the extraction step, delivered at 200 nL min -1 by the syringe pump before being re-used. In order to confirm the complete elution of the analytes from the monolithic MIP/NIP, blanks were regularly perform to verify that the potential analyte residues led to concentrations level below the detection limit.

Preparation of plasma and saliva samples

Human plasma was provided by the French Blood Establishment (Ivry-sur-Seine, France). 500 µL of plasma sample were first mixed with ACN (50%, %v/v) for protein precipitation.

After vortex mixing, samples were centrifuged during 5 min at 6000 x g at 4°C. The supernatant was then recovered, filtered, and stored at 4°C until need. This treated plasma samples were either analyzed directly or spiked with cocaine to obtain a concentration of 50 ng mL -1 in the supernatant, which corresponds to 100 ng mL -1 in plasma equivalent. A volume of 50 nL was analyzed by SPE on MIP or NIP and nanoLC-UV. Saliva samples were collected using Salivettes from Sarstedt (Numbrecht, Germany) designed with cotton swab without preparation from healthy individual and were free of cocaine and BZE. Saliva was filtered with 0.45 µm pore size Millex® Syringe filters from Merck (Darmstadt, Germany) and stored at -20°C until use. The treated saliva samples were either analyzed directly or spiked with cocaine to obtain a concentration of 50 ng mL -1 and a volume of 50 nL was analyzed by SPE on MIP or NIP and nanoLC-UV.

Results and discussion

Preliminary studies for the choice of the reagents

In the present study, cocaine was chosen as model molecule to evaluate the possibility to synthesize a monolithic MIP in a capillary and to couple it on-line to nanoLC for the selective extraction of this compound from complex biological samples. For this, it was necessary to produce a MIP that was sufficiently permeable to allow the percolation of solutions, including the nanoLC mobile phase, without generating a high back-pressure. The MIP must also possess specific cavities to provide a high selectivity for the extraction procedure. As previously mentioned, MIP showing a high selectivity towards cocaine and its metabolites, BZE and ecgonine methyl ester, was synthesized by our group in ACN using MAA as monomer, EGDMA as CL, and AIBN as radical initiator [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF][START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF]. The acidic MAA was also here selected as monomer because of its strong interaction with the template that possesses a basic amino group. However, even if EGDMA was previously used, TRIM, a tri-functional monomer so-called "three arm cross-linker", was also considered as CL in this work. Indeed, TRIM has been reported to give rise to macroporous polymers under some conditions [START_REF] Reinholdsson | Preparation and properties of porous particles from trimethylolpropane trimethacrylate[END_REF][START_REF] Rosenberg | Macroporous gels. 2. Polymerization of trimethylolpropane trimethacrylate in various solvents[END_REF] and this is particularly important for the imprinted monoliths since they should present good flow-through pores. The use of TRIM may also lead to monoliths with welldefined recognition sites, favoring a high selectivity and a high loading capacity [START_REF] Kempe | Antibody-Mimicking Polymers as Chiral Stationary Phases in HPLC[END_REF]. Therefore, the first step of this work focused on the comparison of the impact of EGDMA and TRIM on the monolithic structure.

Sorbent porosity also depends on the careful tuning of some parameters such as the nature of the porogenic solvent. Depending on whether a good or a poor solvent is used as porogen, a large difference of the monolith porosity can be observed, since the porogen affects the polymer chain solvation in the reaction medium during the early stage of the polymerization [START_REF] Santora | Porogen and Cross-Linking Effects on the Surface Area, Pore Volume Distribution, and Morphology of Macroporous Polymers Obtained by Bulk Polymerization[END_REF][START_REF] Viklund | Molded", Porous Materials with High Flow Characteristics for Separations, Catalysis, or Solid-Phase Chemistry: Control of Porous Properties during Polymerization[END_REF]. Thus, the porogen composition is a key factor that may enable the tuning of the monolith porosity without changing its final chemical composition. A solvent is good when its solubility parameter is the same as the polymer's one [START_REF] Sellergren | ,+B.+Molecularly+Imprinted+Polymers:+Man-made+mimics+antibodies+and+their+applications+in+analytical+chemistry%3B+Livre% 3B+Elsevier[END_REF]. In such a solvent, the polymer exhibits low pore volume and high swelling, whereas a polymer prepared in a poor solvent exhibits permanent porosity and low swelling. To promote pore formation in the case of organic monoliths [START_REF] Švec | Monolithic Materials: Preparation, Properties and Applications[END_REF], common solvents are cyclohexanol/dodecanol mixtures.

However, these solvents are forbidden for the synthesis of MAA-based imprinted monoliths because they inhibit hydrogen bonds between this monomer and the template. This is why the most common solvents used in molecular imprinting are dichloromethane, chloroform, ACN, and toluene. In the present study ACN was selected because of the high selectivity previously obtained when preparing a MIP with it by bulk polymerization for cocaine [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF].

Reinholdssom et al. [START_REF] Reinholdsson | Preparation and properties of porous particles from trimethylolpropane trimethacrylate[END_REF] and Schweitz et al. [START_REF] Schweitz | Capillary electrochromatography with molecular imprint-based selectivity for enantiomer separation of local anaesthetics[END_REF][START_REF] Schweitz | Rapid electrochromatographic enantiomer separations on short molecularly imprinted polymer monoliths[END_REF] suggested the addition of a low amount of isooctane, a solvent of low dissolving capacity, to the porogen in order to tune the porosity of the resulting monolith. The effect of the addition of 10% of isooctane was then evaluated. At last, the thermal initiation has shown its potential for the bulk polymerization of a MIP for cocaine [START_REF] Thibert | Synthesis and characterization of molecularly imprinted polymers for the selective extraction of cocaine and its metabolite benzoylecgonine from hair extract before LC-MS analysis[END_REF] and is easier to set up than UV polymerization for this type of format. This is why, a thermal initiation of the reaction at 60°C was used.

To limit the template consumption, these preliminary evaluations were carried out by synthesizing only non-imprinted monoliths. Therefore, they were prepared using a polymerization mixture containing MAA as monomer (M) and EGDMA or TRIM as CL with a M+CL/P ratio of 20/80 or 15/85 (v/v, with a M/CL ratio of 1/5, mol/mol) introduced in a 15 cm-long capillary. The capillary was next cut in 5 cm-long capillaries and their permeability was measured by determining the back-pressure (ΔP) they generate while pumping ACN (200 nL min -1 ). A back-pressure close to 4 bars, exhibited by the nanoLC system itself when a 5 cm-long empty capillary is connected, was subtracted from the back pressure measured with the capillary containing the monolith.

For a 20/80 ratio and EGDMA, a back-pressure of 46 bars was measured, demonstrating that this monolith was not enough permeable. The use of a larger amount of porogen to favor macropores (M+CL/P of 15/85 instead of 20/80), gave rise to a higher permeability (ΔP = 7 bars). When using TRIM, the back-pressure was 8 and 2 bars for the 20/80 and 15/85 ratio, respectively, thus showing a very satisfactory permeability whatever the ratio. TRIM was therefore selected. These preliminary experiments were followed by three independent syntheses of monolithic MIPs and NIPs with TRIM and using the two M+CL/P ratios. The back-pressure generated and the permeability of each monolith were measured by applying various flow rates of ACN, as shown in Figure S1. With the 20/80 ratio, the permeability K of the MIP, determined following the equation given in section 2.3, was 1.2 x 10 -15 m 2 (RSD = 10%, n = 3) and 9.1 x 10 -15 m 2 (RSD = 7%, n = 3) for the NIP. For the 15/85 ratio, K values of 3.3 x 10 -15 m 2 (RSD = 3%, n = 3) for the MIP and of 3.7 x 10 -14 m 2 (RSD = 17%, n = 3) for the NIP were obtained. First of all, the permeability of NIP is always higher than the permeability of MIP thus showing the effect of the template molecules on the structure of the monolith. Finally, a higher permeability was obtained for both monolithic MIPs and NIPs with the 15/85 ratio.

These more permeable supports are thus more suitable for on-line coupling with nanoLC column in order to limit the back-pressure that could damage the monolith. To confirm these results, the inter-day permeability was studied by synthesizing three independent monolithic MIPs and NIPs each day for three days. The inter-day permeability was 2.8 x 10 - 15 m 2 (RSD = 17%, n = 3) for the MIP and 2.6 x 10 -15 m 2 (RSD = 37%, n = 3) for the NIP. These monolithic MIPs and NIPs were also observed by SEM to obtain complementary information related to the homogeneity of the monolith and its attachment to the capillary wall (Figure 2). As shown by these pictures, monolithic MIP and NIP occupied the whole section of the capillary and were well anchored to its surface. It is worthwhile to notice that identical SEM observations were made for the monolith synthesized with the 20/80 ratio (data not shown).

Evaluation of the selectivity studying retention properties in nanoLC

The selectivity of the monoliths obtained with both M+CL/P ratios was next characterized by studying the retention of cocaine and BZE injected on each MIP and its corresponding NIP in nanoLC with capillary length of 5 cm and a flow rate of 200 nL min -1 . The injection of acetone on each monolith allowed the determination of the t 0 value and then the calculation of the retention and imprinted factors. The evaluation was carried out in ACN because, as often mentioned in the literature related to MIP, the selectivity should be optimal when the solvent used is close to the porogen, i.e. ACN containing 10% isooctane here [START_REF] Pichon | Selective sample treatment using molecularly imprinted polymers[END_REF]. Moreover, the MIP previously prepared by bulk polymerization using cocaine, MAA, and EGDMA instead of TRIM was very selective towards cocaine and BZE in this solvent with recoveries higher than 80% on the MIP and lower than 10% on the NIP [START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF]. Retention factors and IFs measured on MIPs and their corresponding NIPs from three independent syntheses for the two different synthesis ratios are reported in Table 1 and the chromatograms are provided as supplementary material (Figure S2). First, RSD values of retention factor for cocaine measured on three independent MIPs lower than 19% confirm the repeatability of the synthesis procedure already demonstrated by the permeability measurements. This repeatability is highly satisfactory because it implies both the repeatability of the activation step and of the polymer synthesis itself. It is also important to notice that the broad shape of the peaks has a strong impact on measurement accuracy.

Moreover, cocaine is significantly more retained on MIPs than on the corresponding NIPs, thus attesting the presence of cavities specific to cocaine on MIP. In addition, these cavities are also able to selectively retain BZE, since it has a higher retention on MIP than on NIP too.

This first evaluation of the selectivity confirmed that TRIM can be associated to MAA to generate specific cavities.

By focusing on IFs, both MIPs obtained either with a M+CL/P ratio of 20/80 or 15/85 are selective towards the template molecule, i.e. cocaine, as shown by values higher than 1. The MIP obtained with the 20/80 ratio exhibits the best selectivity for cocaine (IF = 3.9 ± 0.2, n = 3), but the one obtained with the 15/85 ratio seems more selective towards BZE (IF = 2.2 ± 0.3, n = 3) while maintaining a very good selectivity for cocaine (IF = 3.2 ± 0.5, n = 3). Finally, the monolith synthesized with a ratio of 15/85 seems to correspond to the best compromise between permeability (K) and selectivity (IF) for cocaine and its main metabolite. It was therefore selected for further studies.

On-line coupling of the capillary containing the monolithic MIP and the nanoLC-UV system

Before evaluating the possibility to couple on-line the monolithic MIP with nanoLC-UV analysis, the performance of the nanoLC-UV analysis was first studied. For this, aqueous solutions of BZE and cocaine with five concentrations between 50 and 500 ng mL -1 for each compound were injected (V inj = 50 nL) on the nanoLC column (Acclaim TM PepMap TM 100 C18). The calibration lines and the chromatogram corresponding to the separation of cocaine and BZE at 500 ng mL -1 are presented in Figure S3. The response was linear in the range of studied concentration with R 2 of 0.97 and 0.99 for cocaine and BZE, respectively.

The limits of detection (corresponding to a signal-to-noise ratio of 3) and quantification (signal-to-noise ratio of 10) were estimated to 10 and 34 ng mL -1 for BZE, respectively, and 2 and 8 ng mL -1 for cocaine, respectively.

The MIP capillary (5 cm x 100 µm i.d.) was then coupled on-line with nanoLC. For this, it was coupling is performant. If we now compare the chromatograms obtained with the MIP and its corresponding NIP (Figure 3B and C, respectively) under the same conditions, the selectivity contribution of the monolithic MIP is not obvious, especially for cocaine, since the recovery yields are similar on both supports. Moreover, comparing the chromatogram obtained with the direct injection and the one after preconcentration on MIP, similar peak heights were obtained for cocaine whereas there is an injected amount ratio of 2, which indicates an extraction recovery of about 50%. This highlights the necessity to optimize the extraction protocol on the monolithic MIP in order to enhance the selectivity for cocaine and BZE and their extraction recoveries.

Optimization of the on-line MIP extraction and nanoLC-UV analysis protocol

The optimization of the extraction procedure consisted in studying the effect of the composition and volume of the solution that ensures the transfer of the sample from the loop to the monolithic MIP or NIP and the washing step, promoting cocaine retention on the MIP while decreasing its retention on the NIP in order to obtain an optimal selectivity. The water sample was spiked at 1 µg mL -1 with cocaine. Three different compositions for the transfer/washing solution were studied: 10%, 20%, and 30% of ACN in H 2 O. The resulting histograms, reported in Figure 4, show first an increase of the extraction recoveries of cocaine with an increase in the volume of the solution, whatever its ACN content, indicating that the presence of a void volume in the set-up (mainly due to connecting capillaries)

necessitates the use of a volume of solution higher than 1000 nL to ensure the whole transfer of the sample from the loop to the MIP or NIP. For a solution containing 10% of ACN (Figure 4A), the elution strength is too weak to remove cocaine from the NIP. With a higher elution strength using 20% of ACN, cocaine is gradually eluted from the NIP with a washing volume of more than 2200 nL while it is still retained on the MIP, highlighting the selective contribution of the MIP cavities in the retention process (Figure 4B). The optimal washing volume for cocaine is between 3000 and 4000 nL, since it is possible to observe an almost total loss of cocaine from the NIP (recovery of only 3-13%) keeping a recovery of about 100% on the MIP. In addition, when the elution strength is still increased up to 30% of ACN, a recovery close to 100% is still obtained on the MIP while it is reduced to 9% on the NIP for a volume of 1800 nL (Figure 4C). With a volume higher than 1800 nL, the breakthrough volume of cocaine is exceeded on both sorbents. Finally, a washing volume of 1800 nL with H 2 O/ACN mixture (70/30, v/v), was selected for extraction of cocaine from biological matrices corresponding to the condition giving rise to an optimal selectivity with a minimal washing volume. Similar experiments were next carried out with BZE. Results reported on Figure 5 show that the retained conditions of washing for cocaine extraction (1800 nL, H 2 O/ACN mixture (70/30, v/v)) caused the breakthrough of BZE on both sorbents. It was therefore imperative to reduce the elution strength of the washing solution and the best results were obtained with a solution containing 10% of ACN and a volume of 1000 nL. Indeed, in that case, the retention of BZE on the MIP is total while the recovery is only 23% on the NIP. This difference confirms the selectivity of the monolithic MIP for this metabolite, already demonstrated by the imprinted factor value. It is also worthwhile to notice that the MIP made with cocaine as template molecule has a lower affinity for BZE than for cocaine. This confirms previous results obtained using conventional cocaine-based MIP particles packed in a SPE cartridge [START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF]. The optimal selective extraction of BZE is then achieved with a solution whose volume and elution strength are much lower than those of cocaine, making the protocols for each analyte incompatible.

Applications to biological samples

The potential of the monolithic MIP coupled on-line to nanoLC-UV analysis was first evaluated for the extraction of cocaine from human plasma sample. The plasma was treated with ACN (50%, v/v) for protein precipitation and centrifuged. This treated plasma sample was either analyzed directly or after spiking with cocaine to obtain a concentration of 50 ng mL -1 in the supernatant, which corresponds to 100 ng mL -1 in plasma equivalent. A volume of 50 nL was injected and transferred to the monolithic MIP with 1800 nL of a To evaluate the potential of this on-line coupling, the extraction recoveries were determined by injecting the spiked plasma sample in triplicate on the monolithic MIPs and NIPs resulting from three independent syntheses. The recoveries are reported in Table 2. For MIPs, they are similar to those obtained with pure spiked water (96.9 ± 4.6%, n = 3), thus showing no matrix effects. In the case of the NIPs, recoveries were not reported in Table 2 as peak heights of cocaine were below the LOQ value previously determined (8 ng mL -1 ), which corresponds to recoveries lower than 16%. The difference between the recovery values obtained for MIP and NIP demonstrates that the high selectivity of the MIP for cocaine, already demonstrated in pure media, is preserved in this biological fluid and allows the removal of interfering compounds. This removal is definitely a strong advantage for the possible future coupling of this nanoLC device to mass spectrometry. Indeed, despite its high sensitivity, this detection mode suffers from matrix effects. The use of a MIP will reduce the risk of ion suppression often observed while applying such a detection device to trace analysis of a compound in a complex sample. It is important to confront the performance of our miniaturized analytical method with the concentration levels of cocaine commonly found in consumer samples. Gameiro et al.

conducted a study on blood samples obtained in vivo or post-mortem and cocaine concentrations ranged from 14 to 12,111 ng mL -1 (31 cases) [START_REF] Gameiro | Toxicological analysis of cocaine adulterants in blood samples[END_REF]. For Fiorentin et al., the average concentration in salivary, urinary or plasma samples was 144.7 ng mL -1 with an amplitude of 19,272 ng mL -1 (93 cases) [START_REF] Fiorentin | Simultaneous determination of cocaine/crack and its metabolites in oral fluid, urine and plasma by liquid chromatography-mass spectrometry and its application in drug users[END_REF]. In addition, a French decree defines a positivity threshold of 10 ng mL -1 for the screening of cocaine in saliva and blood matrices [START_REF]fixant les modalités du dépistage des substances témoignant de l'usage de stupéfiants, et des analyses et examens prévus par le code de la route et abrogeant l'arrêté du 5 septembre 2001 modifié fixant les modalités du dépistage des substances témoignant de l'usage de stupéfiants, et des analyses et examens prévus par le code de la route[END_REF]. It is therefore necessary to target cocaine in low concentrations to comply with the current legislation but with a wide linear range. In this sense, the optimized protocol based on a miniaturized monolithic MIP was evaluated by injecting in triplicate the plasma sample spiked with different concentrations of cocaine ranging from 10 to 1,000 ng mL -1 , corresponding to 20-2,000 ng mL -1 in plasma equivalent. Obtained recoveries and RSD values are reported in Table 3. The plotting of the concentration determined as a function of the injected concentration from 100 to 2,000 ng mL -1 (not shown) had a linear shape with a R 2 of 0.999, thus indicating that the MIP capacity was not reached for these injected amounts. The LOD and LOQ were estimated for cocaine at 7.7 and 25.5 ng mL -1 in plasma equivalent, respectively. These limits can be improved by increasing the injection volume up to 100 nL of plasma sample. In that case, LOD and LOQ values of 4.3 and 14.5 ng mL -1 were obtained, respectively. Therefore, it is possible to conclude that the developed approach fulfills the application requirements.

To further evaluate the potential of the monolithic MIP, another biological matrix, saliva, was studied. Injections were carried out with filtered saliva samples, spiked at 10 and 50 ng mL -1 with cocaine. The same transfer/washing procedure as for plasma was applied.

Chromatogram obtained for an injection of 50 nL of saliva spiked at 50 ng mL -1 with cocaine is available in Figure 6D. Cocaine peak can be clearly identified by comparison with the blank saliva performed with the same conditions (Figure 6F). Once again, the baseline of the resulting chromatogram is cleaned of the majority of the interfering components from the biological matrix. In addition, selectivity is demonstrated by the extraction of the same spiked saliva sample on the NIP (Figure 6E). The peak corresponding to cocaine is much less intense on the NIP than on the MIP, reflecting coherent results with those obtained previously. LOD and LOQ for MIP of 1.8 and 6.1 ng mL -1 , respectively, were obtained for cocaine in saliva sample for an injected volume of 100 nL. Recovery values achieved for cocaine at two spiking levels and injected volumes are available in Table 3. Similar performances as for plasma samples were obtained in terms of recovery and of repeatability, demonstrating the high potential brought by this approach for the selective extraction of cocaine from saliva too. A one-factor variance analysis (nature of the matrix, i.e. water, plasma, or saliva) was performed and revealed no significant difference between the three matrices (ANOVA, p value = 0.08 > 0.05), confirming the absence of matrix effect.

However, for the future of the project and more particularly the analysis of samples from consumers, it should be necessary to apply a corrective factor taking into account the recovery yields obtained in this work. But before that, it will be interesting to transfer the developed device to a microchip format in order to fully exploit the potential of this work.

Conclusions

The objective of this work was to demonstrate the possibility to couple on-line a selective extraction on a monolithic MIP prepared in a 100 µm i.d. capillary with nanoLC for the analysis of a targeted compound at trace level in a complex sample. For this, cocaine was taken as model molecule for the in situ synthesis of the monolithic MIP in a capillary. The most promising monolithic MIP resulting from the use of MAA, TRIM, and ACN containing 10% isooctane for its synthesis, demonstrated a high selectivity in pure media for the retention of cocaine and its main metabolite, BZE. Furthermore, particular care has been taken to evaluate the repeatability of permeability and selectivity for independent syntheses.

To optimize the selectivity of the extraction on the MIP coupled on-line with nanoLC-UV, various compositions and volumes of the washing solution were studied to transfer samples spiked with both targeted analytes to the MIP while reducing the contribution of nonspecific interactions (controlled by the use of the NIP in parallel). The optimized conditions were further applied to the on-line analysis of cocaine from 50 or 100 nL of spiked plasma or saliva samples and the resulting chromatograms showed very clean baselines.

This study has showed the important contribution of the monolithic MIP for the on-line selective extraction and nanoLC separation of cocaine and its main metabolite. Some limitations were encountered in aqueous media for the extraction of BZE, but further investigations will be carried out for the synthesis of a MIP with BZE as template molecule in order to obtain stronger retention of this analyte in plasma and saliva but also in urine samples. Finally, the successful miniaturized coupling of the monolithic MIP to nanoLC paves the way for the integration of this technology into a microfluidic chip for the development of a lab-on-chip with a possible UV, fluorescent, or electrochemical detection to provide a miniaturized and portable device. In addition, this miniaturized approach could target other applications and analytes, by modifying the nature of the molecular template used for the synthesis of the monolithic MIP.

1/ 32 "

 32 , manual CN2-4346, Vici Valco Instruments Inc. Co., Houston, TX, USA) connected to a home-made injection loop (50 nL), to a nano-pump (NCP-3200RS Nano Pump, ThermoFisher Scientific Dionex, controlled by Chromeleon 6.80 SR12), and to the MIP or NIP capillaries maintained at 35°C with a column oven (TCC 3000SD column compartment, ThermoFisher Scientific Dionex) connected to a diode array detector (VWD 3100 Detector, ThermoFisher Scientific Dionex) with a flow cell of 3 nL. Compounds were detected at 233 nm. The flow rate of ACN was set at 200 nL min -1 . The marker used to determine the dead volume was acetone. Retention factors k and imprinting factors (IF) were calculated using the following equations:

presented in Figure 1 .

 1 It consisted in a syringe pump (Standard Infuse/Withdraw PHD ULTRA TM 4400 Programmable Syringe Pump, Harvard apparatus, Les Ulis, France, Pump 1) connected to a six-port switching nano-valve. This valve, valve 1, was connected to a homemade injection loop (50 nL) and to another 6-port switching nano-valve. This second valve, valve 2, was connected to a nanoLC pump (Ultimate TM NanoFlow RSLC system, ThermoFisher Scientific Dionex, Pump 2), to the MIP or the NIP capillaries, and to the analytical column. All the connections were achieved with 26 µm i.d. fused-silica capillaries (Polymicro Technologies, 360 µm o.d.) and microtight unions PEEK (Upchurch Scientific).

Figure 1 .

 1 Figure 1. Set-up of the on-line coupling of the monolithic MIP/NIP (50 mm x 100 µm i.d.) with nanoLC-UV.

Figure 2 .

 2 Figure 2. Scanning electron micrographs of the cross section of a 100 µm i.d. capillary containing a monolithic (A, C) MIP or (B, D) NIP synthesized with the M+CL/P ratio of 15/85.

Figure 1 .

 1 placed at the loop position of a six-port switching valve and connected between a first valve having the injection loop, the nanoLC pump, and the nanoLC column as shown by the set-up presented in This set-up allows a back-flush elution of the compounds trapped on the MIP to nanoLC-UV system by the mobile-phase thus limiting some band broadening effects. The sample is first loaded in the loop (50 nL) present on valve 1 and next transferred by 1 µL of a hydro-organic solution (H 2 O/ACN, 90/10) to the MIP connected to valve 2. The composition of the transfer media was selected according to previous studies achieved on the MIP synthesized with cocaine, MAA, and EGDMA, showing that it should ensure the retention of cocaine and BZE on the MIP[START_REF] Thibert | Molecularly imprinted polymer for the selective extraction of cocaine and its metabolites, benzoylecgonine and ecgonine methyl ester, from biological fluids before LC-MS analysis[END_REF].

Figure 3 .

 3 Figure 3. Chromatograms obtained by direct injection of cocaine and BZE (500 ng mL -1 each) (A) and by on-line coupling of the extraction of water spiked at 1 µg mL -1 with cocaine and BZE on monolithic MIP (B) and NIP (C) synthesized with M+CL/P ratio of 15/85. V inj = 50 nL, UV detection at 233 nm, V washing = 1000 nL (H 2 O/ACN, 90/10, v/v) for on-line extraction.

Figure 4 .

 4 Figure 4. Effect of the volume and the composition of the transfer and washing solution, a H 2 O/ACN mixture with a ratio (A) 90/10, (B) 80/20, or (C) 70/30 (v/v), on the extraction recovery of cocaine on MIP and on NIP, synthesized with a M+CL/P ratio of 15/85, after the injection of 50 nL of water spiked with cocaine (1 µg mL -1 ).

Figure 5 .

 5 Figure 5. Effect of the volume and of the composition of the transfer and washing solution, a H 2 O/ACN mixture with a ratio 90/10, 80/20 or 70/30 (v/v), on the extraction recovery of BZE on MIP and on NIP, synthesized with a M+CL/P ratio of 15/85, after the injection of 50 nL of water spiked with BZE (1 µg mL -1 ).

H 2 O

 2 /ACN mixture (70/30, v/v), that was further eluted by the mobile phase to the nanoLC column. The resulting chromatogram is presented Figure6A. By comparing it with the chromatogram obtained for a blank plasma (Figure6C) under the same conditions, it appears that cocaine is extracted from the plasma sample and can be easily quantified.Moreover, the selectivity of the monolithic MIP allows the removal of the interfering compounds present in plasma, as both chromatograms have a clean baseline. The selectivity is further demonstrated with the extraction of the same spiked plasma sample on the NIP (Figure6B). The peak corresponding to cocaine is much less intense on the NIP than on the MIP, reflecting results consistent with those obtained previously in spiked water.

Figure 6 .

 6 Figure 6. Chromatograms obtained after the extraction on MIP (A) and NIP (B) of 50 nL of plasma spiked with cocaine (equivalent to 100 ng mL -1 in plasma) compared to the blank plasma (C) on MIP and chromatograms obtained after the extraction on MIP (D) and NIP (E) of 50 nL of saliva spiked at 50 ng mL -1 with cocaine compared to the blank saliva (F) on MIP. Transfer and washing step: 1800 nL of H 2 O/ACN (70/30, v/v).

Table 1 .

 1 Retention factors and imprinted factors of cocaine and BZE measured on three independentMIPs and NIPs synthesis for two different M+CL/P ratios. Injections of 50 nL of acetone, cocaine (COC, 25 µg mL -1 ), and BZE (25 µg mL -1 ) on 5 cm long capillary filled with the monolithic MIP or NIP. Mobile phase: ACN.

	Compound	Ratio 20/80 (M+CL/P)	Ratio 15/85 (M+CL/P)
		k MIP	k NIP	IF	k MIP	k NIP	IF
		(RSD, n=3)	(RSD, n=3)	(RSD, n=3)	(RSD, n=3)	(RSD, n=3)	(RSD, n=3)
	Cocaine	1.5 (4%)	0.4 (6%)	3.9 (5%)	1.0 (2%)	0.3 (19%)	3.2 (17%)
	BZE	2.3 (4%)	1.3 (1%)	1.7 (3%)	1.7 (21%)	0.8 (9%)	2.2 (13%)

Table 2 .

 2 Repeatability and intermediate reproducibility of the extraction recoveries of cocaineobtained for the analysis in triplicate of 50 nL of the spiked plasma sample (equivalent to 100 ng mL -1 in plasma).

	MIP synthesis	Repeatability of the extraction	Intermediate reproducibility of the
	number	recoveries	extraction recoveries
		Average extraction recovery (%)	RSD, n = 3 (%)	Average extraction recovery (%)	RSD, n = 3 (%)
	1	98.7	4.9
	2	85.4	5.8	92.3	7.5
	3	92.8	3.8
	Focusing on repeatability, the recoveries have low RSD values, between 3.8 and 5.8%, for
	three extractions on one given monolithic MIP, and 7.5% for the intermediate
	reproducibility. Therefore, the repeatability of the synthesis of this miniaturized sorbent and
	of the SPE procedure is fully satisfactory.

Table 3 .

 3 Determination of cocaine in spiked plasma or saliva samples by selective extraction on the monolithic MIP coupled on-line to nanoLC-UV

	Nature of matrix	V inj (nL)	Spiked concentration (ng mL -1 )	Average recovery (%)	RSD n=3 (%)	LOD (ng mL -1 )	LOQ (ng mL -1 )
	Water	50	1000	96.9	4.7	3.6	12.0
	Plasma	100	20*	89.8	5.2	4.3	14.5
		50	100*	98.7	4.9	7.7	25.5
			200*	96.4	3.1
			400*	98.8	1.6
			2000*	100.4	1.2
	Saliva	100	10	88.6	11.1	1.8	6.1
		50	50	92.6	4.7	4.2	13.9
	* Concentration in plasma equivalent

Supplementary materials


A Maurel-Pantel

M Voisin

Q Bui

N Cocheteau

F Lebon

C Hochard

A cohesive zone model for fracture initiation and propagation of fused silica direct bonding interface

Keywords:

Fused silica direct bonding is of particular interest for optical system manufacturing for spatial applications. However, in order to validate the European Space Agency standards, a better understanding of the assemblies mechanical behavior is required. Therefore, it is important to develop some predictive tools to determine numerically mechanical strength of complex assemblies. In this paper, a cohesive zone model is proposed to model the direct bonding interface behavior. In order to determine the mechanical strength of the interface, a propagation test, and an initiation test on a free edge the cleavage test have been performed on direct bonded fused silica samples. The FIT test (Flexible Initiation Test) is also used to identify the properties of the direct bonding joint. At the end, a comparative analyses is proposed between experimental results and finite elements models of the propagation and initiation tests.

Introduction

Direct bonding consists in joining two surfaces without using any adhesive or additional materials [START_REF] Tong | Semiconductor wafer bonding: recent developments[END_REF][START_REF] Kendall | Molecular adhesion and its applications[END_REF]. The first step of the direct bonding process is a polishing of surfaces to be bonded. Indeed, a high level of roughness results in a weak contacted zone and thus in the occurrence of defects at the interface during bonding (Fig. 1(a)) [START_REF] Tang | Modeling the formation of spontaneous wafer direct bonding under low temperature[END_REF][START_REF] Johnson | The adhesion of two elastic bodies with slightly wavy surfaces[END_REF][START_REF] Galanov | Models of adhesive contact between rough elastic solids[END_REF]. If the roughness is too high, bonding is impossible. In a second step, surfaces undergo a surface cleaning treatment. During this last step, contamination particles are removed from the surfaces [START_REF] Lai | Effect of surface treatment on wafer direct bonding process[END_REF][START_REF] Klier | Water at interfaces: molecular structure and dynamics[END_REF]. As described in Fig. 1(b), by reacting with ambient atmospheric water, the free silicon surfaces are recovered by silanol groups according to the following equation:

-+ → - Si O H O Si OH 2 (1)
Then surfaces will be recovered by clusters of water [START_REF] Stengl | A model for the silicon wafer bonding process[END_REF][START_REF] Kissinger | Void-free silicon-wafer-bond strengthening in the 200-400 °C range[END_REF]. The silanol groups are the precursor of the bonding [START_REF] Stengl | A model for the silicon wafer bonding process[END_REF] (Fig. 1(c)). They will generate bonds responsible of the adhesion during the room temperature bonding. In this case, adhesion is performed via clusters of waters. Direct wafer bonding emerged as a technology for Silicon based microelectronic systems [START_REF] Ventosa | Hydrophilic low-temperature direct wafer bonding[END_REF][START_REF] Nakanishi | Studies on SiO 2 -SiO 2 bonding with hydrofluoric acid. room temperature and low stress bonding technique for MEMS[END_REF][START_REF] Berthold | IC-compatible silicon wafer-to-wafer bonding[END_REF]. Now, this bonding process is also used in the manufacturing of high performance optical systems for terrestrial applications. For instance, Fig. 2 shows 1152 slices bonded together to give form to the larger optical slicer ever used for the MUSE project [START_REF] Laurent | MUSE image slicer: test results on largest slicer ever manufactured[END_REF]. Nowadays, they are of particular interest for spatial instruments applications. Indeed, this is a high-precision production process. The assemblies obtained by this process exhibit a dimensional stability because no mechanical parts or polymer adhesive are required. Moreover, since no adhesive materials are used in these processes, the risks of contamination associated with degassing are avoided, which is a big benefit in spatial applications. A first prototype has successfully completed the mechanical and thermal environment tests for space applications [START_REF] Pamplona | Three bipods slicer prototype: tests and finite element calculations[END_REF] where constraints involved (thermal fatigue, accelerations, vibrations, etc.) are different from those encountered on Earth. However, a better understanding of the assemblies mechanical behavior is required to validate the system life expectancy and to meet the European Space Agency standards.

In order to comply with these standards mechanical experiments: double shear tests, cleavage tests and wedge tests were performed in previous investigations in our laboratory to investigate the influence on the interface mechanical strength of some process parameters, such as annealing time and temperature [START_REF] Cocheteau | Process parameters influence on mechanical strength of direct bonded surfaces for both materials: silica and zerodurglasses[END_REF], roughness [START_REF] Cocheteau | Influence of roughness on mechanical strength of direct bonded silica and zerodur glasses[END_REF]. Now, there is a need to develop some numerical predictive tools to determine mechanical strength of spatial complex assemblies as slicer or cube corner.

In literature, some authors developed theoretical and numerical models for direct bonding [START_REF] Tang | Modeling the formation of spontaneous wafer direct bonding under low temperature[END_REF][START_REF] Johnson | The adhesion of two elastic bodies with slightly wavy surfaces[END_REF][START_REF] Scheerschmidt | Molecular dynamics modelling of silicon wafer bonding[END_REF][START_REF] Yu | A model of wafer bonding by elastic accommodation[END_REF][START_REF] Turner | Mechanics of direct wafer bonding[END_REF][START_REF] Kubair | Cohesive zone model for direct silicon wafer bonding[END_REF][START_REF] Liao | Effect of surface characteristic on room-temperature silicon direct bonding[END_REF]. Usually, these models are dedicated to nanometrical and micrometrical elements [START_REF] Scheerschmidt | Molecular dynamics modelling of silicon wafer bonding[END_REF][START_REF] Kubair | Cohesive zone model for direct silicon wafer bonding[END_REF][START_REF] Alfano | Cohesive zone modeling of mode i fracture in adhesive bonded joints[END_REF]. As seen above, direct bonding is described at the interface by chemical bonds at the nanometric scale. Lot of models using multiscale approaches were developed during the last years to described bonded interface mechanical behavior on wafer structures in microelectronical field.

Turner et al. have performed wafer bonding experiments and numerical analysis [START_REF] Turner | Mechanics of direct wafer bonding[END_REF][START_REF] Turner | Accurate characterization of wafer bond toughness with the double cantilever specimen[END_REF] and have shown that a fracture mechanics-based formalism (as VCCT method), using a single value work of adhesion, is suitable for modeling the fracture propagation of direct silicon wafer bonding.

In previous research studies, it has been shown that a phenomenological traction separation law (cohesive zone model (CZM)) can be introduced to model smaller scale phenomena such as surface roughness and patterning. Due to the complexity of the interface made up of the layer of hydrogen-bonded water molecules with a nanoscopic surface roughness, it is necessary to take into account the non continuous interaction between both molecular layers. The authors proposed a CZM in which the overall form and Fig. 2. Slicer made with direct bonding method developed for the Multi Unit Spectroscopic Explorer (MUSE) in the Very Large Telescope (VLT) [START_REF] Laurent | MUSE image slicer: test results on largest slicer ever manufactured[END_REF].

parameters are obtained from molecular dynamics (MD) simulations [START_REF] Kubair | Cohesive zone model for direct silicon wafer bonding[END_REF][START_REF] Kubair | Multiscale mechanics modeling of direct silicon wafer bonding[END_REF].

But these previous works are limited to wafer applications in the field of microelectronics and only concerns fracture propagation modelling. The cohesive zone models, proposed in literature, are not validated with implementation in a finite elements code to model the mechanical strength of a complex assembly. In this paper the considered optical assemblies are large structures from one to many millimeters as described in Fig. 2. To help engineers in designing the strength and durability of these optical assemblies, a new approach seems to be necessary to model the mechanical behavior (fracture propagation and initiation) of the direct bonded interface.

To provide a solution, we choose in this investigation as Kubair et al. [START_REF] Kubair | Multiscale mechanics modeling of direct silicon wafer bonding[END_REF] to develop a cohesive zone model (CZM). Indeed, according to Khoramishad et al. [START_REF] Khoramishad | A generalised damage model for constant amplitude fatigue loading of adhesively bonded joints[END_REF] the CZM have the advantage of:

• considering finite strains and stresses at the adhesive crack tip, • indicating both damage initiation and propagation as direct outputs of the model, • advancing the crack tip as soon as the local energy release rate reaches its critical value with no need of complex moving mesh techniques.

Based on Continuum Damage Mechanics and Fracture Mechanics, the CZM enables a diagnostic of the current state of the adhesive interface damage along the overlap. The damage, associated to micro-cracks and/or voids coalescence, results in a progressive degradation of the material stiffness before failure. An idealization of a CZM bilinear stress-strain relationship or CZM bilinear traction separation law is a well-established interface behavior that first assumes a linearly dependency relationship between the interface separation (deformation) and the resulting traction (stress) as related in Fig. 3. Once a prescribed value of separation is reached by the adhesive, the damage initiation is described in the shape of a linearly decreasing resulting traction stress. Finally, the propagation of the damage is described by voluntarily fixing the resulting traction stress to zero, hence modeling the creation of two traction-free surfaces (i.e.: physical cracking). Both damage initiation and damage propagation phases are addressed in the model with no need of assuming any initial crack in the material.

In this paper, we develop a phenomenological cohesive zone model whose the parameters are identified on experimental results to model the fracture propagation and fracture initiation of elementary direct bonded assemblies. The first section presents three mechanical tests performed to characterize fracture propagation and initiation on a free edge: the wedge test [START_REF] Maszara | Bonding of silicon wafers for silicon-on-insulator[END_REF], the flexible initiation test [START_REF] Bui | The flexible initiation test (FIT): a new experimental test to characterize fracture initiation in mode i at the free edge of bonded assemblies[END_REF] and the cleavage test. For all samples tested, the confidential industrial bonding process is considered. Meaning that all surfaces underwent several specific polishing and a chemical treatment, followed by a room temperature bonding without any thermal treatment. The second section introduced the atomistically motivated macroscopic cohesive zone model and values of model parameters identified on experimental tests. The last section describes the cohesive zone model implemented in the finite elements commercial code Abaqus, and compared prediction capability on fracture initiation and propagation simulations face to cleavage and wedge tests experimental results.

Mechanical experiments

In this section, we present three experimental tests performed on direct bonding samples to determine the following properties: the critical strain energy release rate, the critical stress in the joint on a straight free edge, and the critical initiation load on a chamfered free edge (i.e. first load drop in the load-displacement curve).

Wedge test to characterize propagation

The bonding energy W is classically used to characterize adhesion [START_REF] Maszara | Bonding of silicon wafers for silicon-on-insulator[END_REF]. The bonding energy can be related to the critical strain energy release rate [START_REF] Plßl | Wafer direct bonding: tailoring adhesion between brittle materials[END_REF]. The crack propagation method or wedge test is the most popular method to measure the bonding energy. As related in Fig. 4, a razor blade is inserted at the interface between two slices bonded together. Then a crack appears and propagates along the bonded interface until the establishment of the equilibrium between the elasticity of slices and the chemical bonds responsible for the adhesion (hydrogen bonds in this case). The length of the crack L is measured with a camera using interference fringes due to the small thickness of air trapped at the open interface. At the equilibrium, the critical strain energy release rate G C is equal to W and related to the crack length using linear elastic fracture mechanics [START_REF] Cognard | The mechanics of the wedge test[END_REF]. When both surfaces are identical, we can write in mode I:

= = G W γ 2 C ( 2
)
where γ is the surface energy. Moreover, the critical strain energy release rate, thus the bonding energy W can be approximately related to the length L using the following equation [START_REF] Cognard | The mechanics of the wedge test[END_REF]:

= G Et y L 3 16 C 3 2 4 ( 3
)
where E is the Young modulus of slices (in the case of fused silica glass, = E 72700 MPa), t the slice thickness; y the razor blade thickness and L the length of the crack. The wedge tests sample is composed with two slices of fused silica glass with 500 μm of thickness t, 10 mm of width and 80 mm of length bonded together. The razor blade 100 μm of thickness y is always inserted by the same length using a micrometric mobile plate and the insertion is controlled with a camera above the slices as shown in Fig. 4. Table 1 summarizes the wedge test results.

FIT Tests to identify properties of the joint

In previous investigations on direct bonding interface, we proposed the Flexible Initiation Test (FIT) to reduce the scattering of critical fracture initiation load measurements [START_REF] Bui | The flexible initiation test (FIT): a new experimental test to characterize fracture initiation in mode i at the free edge of bonded assemblies[END_REF]. The FIT test uses deformable support beams bonded to sample (the sample includes the substrate and the adhesive). The load is symmetrically imposed at the tip of support beams, and load and displacement are measured as related in Fig. 5. Results show that a long support beam allows to reduce the scattering of critical fracture initiation load measurements, in particular for the adhesives with a brittle mechanical behavior (Araldite, Cyanoacrylate and Direct Bonding). Therefore, we propose to use this test on direct bonded samples having a specific edge geometry in order to measure the critical fracture initiation load and to determine the critical stress of the direct bonding interface in mode I. The tests are carried out on fused silica glass samples. They are made up of two glass slices, adhered by molecular bonding, dimension 50 mm × 20 mm × 1 mm. One slice configuration is considered: a straight edge °90 as described in Fig. 6.

Samples preparation

In these tests, the deformable support beams are made of 2017A aluminum and the beam geometry is described in Fig. 7. To bond the direct bonded silica glass sample to support beams, we use the Scotch-WeldTM Epoxy Adhesive 2216 B/A. For sample preparation, the following protocol is used:

• In a first step, the beam supports are cleaned with acetone.

• Then the glue is spread on the beam supports. Fluorocarbon fishing lines with a diameter of 0.1 mm are used to calibrate the thickness of the joint. It is necessary to control very well the quantity of glue to avoid polluting the direct-bonded samples.

• In the last step, the direct-bonded sample is placed on the beam support. The beam supports and direct-bonded sample are placed in a specific device to ensure their positioning. Identical weights are used to create pressure between the beam support and the specimen to reach the calibrated thickness.

Results

Fig. 8 reports force-displacement curves measured with the FIT test for both edge configurations. According to the protocol, we obtain the critical initiation load value with a low dispersion of about 13% for these samples. We can also notice that the direct bonding interface exhibits a very brittle mechanical behavior. An accurate mean value of the critical initiation load F c can be identified. The F c average value is 2.568 N. We have now an experimental result with a straight edge configuration. With the F c average value measured, the critical stress of the direct bonded interface in mode I can be identified. We need to have the stress field along the interface for the homogeneous stress concentration and the corresponding load equal to the critical initiation load. Finite Fig. 5. Drawing of the Flexible Initiation Test (FIT) device [START_REF] Bui | The flexible initiation test (FIT): a new experimental test to characterize fracture initiation in mode i at the free edge of bonded assemblies[END_REF]. Fig. 6. Optical microscope image of the direct bonded fused silica glass sample tested with the FIT test with a straigth edge. element simulations in Abaqus are performed to obtain the stress field at the interface for straight edge configuration. The calculated stress fields are reported in Fig. 9. With the homogeneous stress concentration, the normal stress is constant along the interface. We are able to determine the mechanical strength of the interface and to identify the following fracture parameters: the critical stress σ c of the direct bonding interface in mode I is equal to 5.143 MPa.

Cleavage test to characterize fracture initiation on a free edge

The cleavage test on a free edge is used to measure the breaking strength of the elementary assembly close to those used in optical systems. Five samples constituted with two slices of 12.5 mm of thickness, 40 mm of width and 40 mm of length bonded together using the industrial bonding process's are considered. On these fused silica glass samples, two aluminum rigid handles are bonded with classical ductile epoxy glue (3 M 2216) as related in Fig. 10. A displacement is applied on these handles in order to characterize the fracture initiation on a free edge. The test campaign is led to obtain a mean value of the critical initiation load F c . Tests are performed at room temperature and constant humidity. The load F c is measured. Results obtained are presented in Table 2. Thus, the Fig. 7. Picture of FIT sample geometry. Device to adhere direct bonded fused silica samples on deformable aluminum support beams.

Cohesive zone model proposed

Cohesive zone models (CZMs) have been used to model adhesive mechanical behavior. The CZMs approach is one of the most commonly numerical methods used to investigate the failure of adhesive joints [START_REF] Elices | The cohesive zone model: advantages, limitations and challenges[END_REF][START_REF] Khoramishad | A generalised damage model for constant amplitude fatigue loading of adhesively bonded joints[END_REF]. The model is based on the assumption that a cohesive damage zone (or process zone) develops near the initiation zone generally at the crack tip. This zone can model the initiation of a micro crack. The cohesive zone model links cohesive stress to the relative displacement. Damage initiation occurs when the stress reaches the critical strength. During the crack opening process, energy is dissipated, when total energy dissipated corresponds to the critical energy release rate G c , the interface elements fail and the crack propagates. In literature, many CZMs with damage law have been proposed (trapezoidal law, bilinear law, power law, exponential law, etc.). A phenomenological model based on a bilinear law is proposed here. The bilinear traction separation law proposed in this work to model direct bonding interface is described in Fig. 3. This law allows to link the parameters together with the following expression:

= δ G σ 2 f c max (4)
The critical separation distance δ 0 is chosen equal to 0.2 nm based on atomistic considerations (the characteristic distance of hydrogen bond) as in our previous works [START_REF] Cocheteau | Influence of roughness on mechanical strength of direct bonded silica and zerodur glasses[END_REF] and highlighted by Kubair in molecular dynamics simulations [START_REF] Kubair | Multiscale mechanics modeling of direct silicon wafer bonding[END_REF]. The both parameters G c and σ max are determined with the wedge test and the FIT test as described in previous section. We could have identified the model by inverse identification, but in this case the uniqueness of the solution would not have been guaranteed. We choose here to use the FIT test applied on a sample with an homogeneous stress concentration to determine one of the parameters of the bilinear model. We can then build the model based on our observations of the interface behavior. The model is therefore identified on two experimental tests, an homogeneous test and an atomic analogy. Then, Eq. ( 4) gives us directly the value of δ f . The parameter δ f is equal to 9.92 nm.

Validation with numerical simulation of the experimental tests

In this section, 2D numerical simulations of experimental tests are performed with the commercial finite element code ABAQUS in order to validate the phenomenological model of direct bonding in mode I. In these simulations, the bilinear law related in Fig. 3 is implemented. The simulations are carried out in 2D for the sake of simplicity. Samples are modeled with plane strain elements (CPE4R) and the interface is modeled using cohesive elements with thickness equal to zero (COH2D4).

Mesh and material parameters

In case of direct bonding characterization, the direct bonded slices are made in fused silica glass and supports of slices are made in aluminum-alloy 2017-T4. We choose to model both material with a linear isotropic elastic behavior. Fused silicate and Aluminum have the same elastic mechanical properties, and the parameters used in simulation are related in Table 3. We need to choose the finite elements models mesh of experimental tests. We need a cohesive zone mesh in order to be sure to have convergence of the numerical scheme. The element size of the cohesive elements can be linked to the value of the critical strain energy release rate G C . Indeed, Turon et al. [START_REF] Turon | An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models[END_REF] propose two equations (Eqs. ( 5) and ( 6)) to calculate optimal cohesive zone length L cz and cohesive element size L e .

= L M G E σ cz c max 2 (5) = L L N e cz ( 6
)
where L cz is the cohesive zone length, L e the cohesive element size in the cohesive zone, based on the previous experimental results, we obtain < < M 0.21 1 and < < N 3 1 0 . After calculation with Turon et al. formula, the cohesive element sizes for the model is between 0.0234 mm and 0.0015 mm. Note that these dimensions are too small to perform calculations. Thus, a mesh sensitivity analysis is made for model tested to determine the optimal elements length. Four lengths are chosen (0.1 mm, 0.05 mm, 0.01 mm and 0.008 mm) to satisfy the compromise between computational time and accuracy. These element sizes are respected for the cohesive elements and the neighbouring elements of the bulk. For other mesh elements, an increasing element size is used in order to reduce calculation time.

Results of wedge test simulation

The total number of elements for the wedge test simulation with the highest = L 0. 11 shows the mesh used for the wedge test simulation with the smallest mesh size L e . Concerning the mesh of the wedge test, a pre crack is inserted at the interface between the two substrates as described in Fig. 11. A zone without cohesive element is necessary to introduce a pre-crack and to perform a propagation test. Table 4 presents the results obtained for the simulation of this test. L num represents the length of the crack calculated with the simulation and L exp is the length of the crack measured during the experience. Fig. 12 represents the wedge test simulation results with the stress field for the smallest mesh (0.008 mm). An error between numerical and experimental results close to 3.2% is observed for the phenomenological model. The phenomenological model allows to describe the behavior of fused silica direct bonding for a propagation test.

Results of cleavage test simulation

Simulations of the cleavage test are performed with the four different mesh sizes. The total number of elements for the cleavage mm it is about 769, 488 elements. Fig. 13 shows the mesh used for the cleavage test simulation with the smallest mesh size L e .

The numerical results are sumed up in Table 5. with the stress field for the largest mesh. When the mesh is refined, a decrease of the critical load at fracture initiation F c num is observed. Concerning the phenomenological model proposed the relative difference is close to 1.6%. The phenomenological model allows to describe the behavior of fused silica direct bonding for an initiation test.

Conclusions

In this paper, a phenomenological model based on a bilinear law of cohesive zone model describing the fused silica direct bonding is proposed. The CZM is implemented in a finite elements software to simulate an initiation test (cleavage test) and a propagation test (wedge test). The phenomenological model well describes the normal behavior of the interface for the initiation and propagation test. These first results give us an available tool to simulate the behavior of fused silica direct bonding assemblies. The final aim consists in designing large optical direct bonded structures as related in Fig. 2. However, it is important to note the fineness of the mesh size required for simulation results convergence. It will be necessary to try to optimize the mesh sizes of complex assemblies to limit computation times. But this calculation issue remains a limitation of the cohesive element modeling approach.

In order to improve the model, it could be possible to take into account more precisely the nanometric characteristic size of the direct bonding phenomenon and to insure a better change scale scheme in order to avoid a loss of information such as roughness [START_REF] Cocheteau | Influence of roughness on mechanical strength of direct bonded silica and zerodur glasses[END_REF], defects, nature of bonds. As prospects, multiscale methods could be developed and compared with experiments. These approaches could be based as Kubair et al. [START_REF] Kubair | Multiscale mechanics modeling of direct silicon wafer bonding[END_REF] on small-scale molecular dynamic calculations to describe the presence of different chemical bonds at the interface. On the other hand, more sophisticated numerical methods -such as multi grid methods [START_REF] Barbié | An automatic multilevel refinement technique based on nested local meshes for nonlinear mechanics[END_REF][START_REF] Lebon | Two-grid method for regularized frictional elastostatics problems[END_REF] or local defect correction method [START_REF] Barbié | Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems[END_REF] -could be studied and implemented to predict initiation at the direct bonded interface in order to reduce the time of calculation.

Fig. 1 .

 1 Fig. 1. (a) The free SieO bonds react with ambient atmospheric water to produce silanol bonds (SieOH), (b) the silanol bonds react with ambient water to form clusters of water on surface, (c) state of the interface after bonding depending on the number of clusters before adhesion.

Fig. 3 .

 3 Fig. 3. CZM bilinear traction separation law used to model normal behavior of the direct bonding interface with the confidential initial Winlight process.

Fig. 4 .

 4 Fig. 4. Principe of Wedge test for direct bonding interface.

Fig. 8 .

 8 Fig. 8. Experimental force-displacement curves measured with the FIT test for samples with a straight edge °90 .

Fig. 9 .

 9 Fig.9. Finite element simulation in Abaqus performed to obtain the normal stress distribution for the straight edge in order to identify the critical stress of the direct bonding interface in mode I.

Fig. 10 .

 10 Fig. 10. CAD and picture of the Cleavage test used to characterize direct bonding interface.

  F c num represents the critical load at fracture initiation calculated with the simulation and F c exp the critical load at fracture initiation measured during experiments. Fig. 14 represents the cleavage test simulation

Fig. 12 .

 12 Fig. 12. Wedge test simulation results: the von Mises stress field with the opening of cohesive element ( = L 0.01 e

Fig. 13 .

 13 Fig. 13. Mesh for the cleavage test modelling ( L 0.008 e

Table 1

 1 Wedge test results for fused silicate direct bonding interface.

		C	2
	28.6	0.0255

L (mm) exp -G (J m )

Table 2

 2 Cleavage tests results for fused silica direct bonding interface.

	Test	Room Temperature (°C)	Air humidity of bonding room (%)	Critical Initiation load F c (N)
	1	20.2	52	371
	2	20	55	310
	3	20.3	57	266
	4	20.5	55	250
	5	20.2	54	355

  [START_REF] Tong | Semiconductor wafer bonding: recent developments[END_REF]

			e	mm is about 10, 382 elements, with = L e	0.05
	mm it is about 25, 780 elements, with = L e	0.01	mm it is about 308, 437 elements and with = L	0.008

e

mm it is about 473, 569 elements. Fig.

Table 3

 3 Fused silicate and aluminum-alloy 2017-T4 elastic mechanical properties used in simulation.

	E (GPa)	ν
	70	0.33

Fig. 11. Mesh for the wedge test modelling ( = L 0.008 e mm). test simulation with the highest = L 0.1 e mm is about 39, 367 elements, with = L 0.05 e mm it is about 170, 889 elements, with = L 0.01 e mm it is about 426, 507 elements and with = L 0.008 e

Table 4

 4 Prediction of crack length with the wedge test simulation in function of the cohesive element size L e .

	L e (mm)	L exp	L num	Error (%)	Calculation time (h)
	0.1	28.6	16,7	41.6	1.8
	0.05	28.6	21	26.5	13.8
	0.01	28.6	27,5	3.8	53.3
	0.008	28.6	27,7	3.2	75.3

Acknowledgement

This work took place in the MATIOMA (Modelling and Technological improvement of Molecular Adhesion) project and has been carried out thanks to the support of the A*MIDEX project (n ANR-11-IDEX-0001-02) funded by the Investissements d Avenir French Government program, managed by the French National Research Agency (ANR). We would also like to thank the WinLight Optics Company for technical and financial support in these investigations.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.engfracmech. 2019.106649.