Zhugen Yang

Yann Chevolot

Thomas Gehin

Vincent Dugas

Nicolas Xanthopoulos

Vincent Laporte

Thierry Delair

Yasemin Ataman-Oenal

Geneviève Choquet-Kastylevsky

Eliane Souteyrand

Thomas Géhin

Yasemin Ataman-Önal

Emmanuelle Laurenceau

Characterization of Three Amino-Functionalized Surfaces and Evaluation of Antibody Immobilization for the Multiplex Detection of Tumor Markers Involved in Colorectal Cancer

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

In the past decades, tumor markers have been routinely detected for cancer diagnosis in clinical oncology [START_REF] Luo | Taguchi Design-Based Optimization of Sandwich Immunoassay Microarrays for Detecting Breast Cancer Biomarkers[END_REF][START_REF] Wu | Biomedical and clinical applications of immunoassays and immunosensors for tumor markers. Trac-Trend[END_REF] . However, due to the diversity and variation in different cancers, no single tumor marker is sensitive and specific enough to meet strict diagnostic criteria. Therefore, a combination of tumor markers is required to increase sensitivity and to establish distinct patterns to increase specificity [START_REF] Sun | A protein chip system for parallel analysis of multi-tumor markers and its application in cancer detection[END_REF] . Owing to multiplex detection, antibody microarrays appear as powerful tools for screening and identifying tumor markers, with the advantages of high-throughput, minimal sample volume requirement and low-cost. The immobilization procedure of antibodies is a crucial step in the elaboration of efficient antibody microarrays. Many studies have reported that analytical performance of microarray mainly depends on surface chemistry and detection conditions to prevent loss of biological activity as well as achieving high signal-to-noise ratio [START_REF] Angenendt | Toward optimized antibody microarrays: a comparison of current microarray support materials[END_REF][START_REF] Bi | A protein microarray prepared with phage-displayed antibody clones[END_REF][START_REF] Kusnezow | Antibody microarrays: an evaluation of production parameters[END_REF][START_REF] Niemeyer | Semisynthetic DNA-Protein Conjugates for Biosensing and Nanofabrication[END_REF][START_REF] Seurynck-Servoss | Evaluation of surface chemistries for antibody microarrays[END_REF][START_REF] El Khoury | Development of miniaturized immunoassay: Influence of surface chemistry and comparison with enzyme-linked immunosorbent assay and Western blot[END_REF][START_REF] Yang | Cancer biomarkers detection using 3D microstructured protein chip: Implementation of customized multiplex immunoassay[END_REF] .

Methods for immobilizing probe proteins on solid support range from covalent binding and affinity ligand capture, to simple physical adsorption [START_REF] Zhu | Protein chip technology[END_REF] . Covalent binding gives a durable and stable linkage to the solid substrate, but can lead to partial loss of biological activity of the immobilized proteins [START_REF] Jonkheijm | Chemical Strategies for Generating Protein Biochips[END_REF][START_REF] Rusmini | Protein immobilization strategies for protein biochips[END_REF] . Proteins can be covalently grafted onto chemically reactive surfaces, like epoxide or succinimide ester functionnalized surfaces, via their amino groups. Sometimes it is required to activate proteins for coupling and this may reduce the affinity of probe proteins.

The pre-treatment of the probes burdens the preparation step and can limit the types of biomolecules that can be attached. Although the affinity capture retains the native conformation of immobilized proteins and should permit to control their orientation, it requires conjugation of the probe protein to be immobilized with an affinity tag (polyhistidine, biotin, etc) and surface modification of the substrate [START_REF] Zhou | Protein microarrays on hybrid polymeric thin films prepared by self-assembly of polyelectrolytes for multiple-protein immunoassays[END_REF] . Compared to covalent binding and affinity, physical adsorption offers the simplest process for immobilization with ample binding capacity in some cases [START_REF] Kusnezow | Antibody microarrays: an evaluation of production parameters[END_REF][START_REF] Zhu | Protein chip technology[END_REF] . Amino-functionalizations of the surface are convenient and popular methods for protein immobilization via adsorption. Kusnezow and co-workers [START_REF] Kusnezow | Antibody microarrays: an evaluation of production parameters[END_REF] modified the glass slide with (3aminopropyl)trimethoxy silane (APTES) and poly-L-lysine to physically adsorb proteins onto surface, and evaluated the performances of such protein microarrays in comparison with other commercial glass slides. Signal intensity, background and spot morphology on poly-L-lysine modified surfaces were of sufficient quality. In contrast, APTES glass surfaces showed high background signal, which was about 4-5 times more intense than the background on poly-Llysine slides. Various reactive molecules (like functional polymers) with amine functionality have also been used to modify glass surface resulting in more selective and sensitive protein microarrays. Compared to the monolayers, multilayer coated surfaces with sufficient steric space better maintain the native conformation of proteins and prevent the loss of biological activities [START_REF] Kusnezow | Antibody microarrays: an evaluation of production parameters[END_REF][START_REF] Seurynck-Servoss | Evaluation of surface chemistries for antibody microarrays[END_REF][START_REF] Kim | Effects of polymer grafting on a glass surface for protein chip applications[END_REF][START_REF] Prabhulkar | Amperometric micro-immunosensor for the detection of tumor biomarker[END_REF] . Kim et al [START_REF] Kim | Effects of polymer grafting on a glass surface for protein chip applications[END_REF] modified the glass slide surfaces with either monolayers produced by silanisation or with polymer layers for protein chip implementation. Covalent immobilization yield and non-specific adsorption were examined by quantifying IgG-peroxidase conjugates immobilized to polymer-grafted glass substrates. Polymer-grafted glass substrates showed that non-specific adsorption was reduced by 10-60 % as compared with 3-aminopropyltriethoxysilane (APTES)-treated substrate. In particular, chitosan-grafted substrates exhibited very low nonspecific protein adsorption. However, the proteins were covalently bound onto aminated surfaces through activation of glutaraldehyde, which made the process more complicated and probably reduced the affinity of probe proteins.

Our recent work [START_REF] Yang | Cancer biomarkers detection using 3D microstructured protein chip: Implementation of customized multiplex immunoassay[END_REF][START_REF] Yang | Improvement of protein immobilization for the elaboration of tumor-associated antigen microarrays: Application to the sensitive and specific detection of tumor markers from breast cancer sera[END_REF][START_REF] Laurenceau | Tumor antigens titration on novel miniaturized immunoassay: 3D-Protein chip performance evaluation[END_REF] demonstrated that immobilization of antibodies by physical adsorption onto chitosan functionalized surface could be better than covalent linking. Lower limit of detection and higher dynamic range were obtained depending on the tested antibody. In an effort to determine leading factors affecting performances of antibody microarray, different surface chemistries were investigated with respect to immobilization efficiency and biological activity of probe proteins. In this study, we evaluated the effect of three different chain-length aminofunctionalizations ((3-aminopropyl) dimethylethoxysilane (APDMES), Jeffamine, and chitosan) on the performances of antibody microarrays for the detection of tumor markers (CEA, HSP60, PDI and DEFA6) involved in colorectal cancer. APDMES, Jeffamine and chitosan are primary amine-bearing molecules. APDMES is small chain molecule with a monovalent silane that cannot polymerize. Thus it cannot form a multilayer on the surface. Jeffamine is a longer chain diamine. Its chain is composed of ethylene glycol and propylene glycol units increasing the distance between the amine group and the surface, as well as the chain mobility. Moreover, the presence of the propylene glycol units enhances the hydrophobic behaviour of the molecule.

Finally, chitosan is a long chain highly aminated biopolymer composed of glucosamine units which give it a hydrophilic behaviour. These three aminated surfaces should vary in terms of surface energy, surface hindrance and amine surface density. The immobilization efficiency of antibody and its biological activity were addressed as a function of these parameters. The spotting pH buffer was optimized for enhancing antibody immobilization while preserving biological recognition on the miniaturized system.

MATERIALS AND METHODS

Materials.

All chemicals were of reagent grade or the highest grade commercially available. They were used as received unless stated otherwise. Bovine serum albumin (BSA) lyophilized powder fraction IV, dimethyl sulfoxide (DMSO, anhydrous, 99.9 %), 0.01 M phosphate-buffered saline (PBS, pH 7.4) at 25 o C (0.0027 M potassium chloride and 0.138 M sodium chloride), sodium dodecyl sulfate (SDS), sodium acetate, sodium bicarbonate, sodium carbonate, N-Hydroxysuccinimide (NHS), Jeffamine M-600 (polyoxypropylenediamine, M w = 600 g/mol), N, N'-diisopropylcarbodiimide (DIC), tetrahydrofuran (THF) (purum grade), polyvinylalcohol (PVA), (3-aminopropyl)dimethylethoxysilane (APDMES) and Coomassie brilliant blue (CBB) ( >95% purified dye), all were obtained from Sigma-Aldrich (St. Quentin Fallavier, France).

Tween 20 was purchased from Roth-Sochiel (Lauterbourg, France). Chitosan (M w =470 000 g/mol) was modified to obtain 94 % of deacetylation degree (DD).

Borosilicate flat glass slide (76 x 26 x 1 mm) were purchased from Schott (Mainz, Germany).

Anti-tumor antibodies and tumor antigens were described in previous report [START_REF] Hamelin | Identification and verification of heat shock protein 60 as a potential serum marker for colorectal cancer[END_REF] for HSP60, in patent application WO2010/004214 for PDI and CEA [START_REF] Ataman-Onal | Method for assaying Prodefensin-A6 for the in vitro diagnosis of colorectal cancer[END_REF] and in patent application WO2010/112777 for DEFA6 [START_REF] Ataman-Onal | Protein Disulfide Isomerase assay method for the in vitro diagnosis of colorectal cancer[END_REF] . DL647 is a fluorescence dye (supplied by bioMérieux), used to conjugate with anti-CEA antibody for sandwich assay detection. Cy3-labeled goat anti-rabbit antibody immunoglobulin G (IgG) and Cy3-labeled streptavidin were purchased from Jackson ImmunoResearch and Sigma-Aldrich, respectively. Hydrogen peroxide (H 2 O 2 ) solution (30 vol.) was obtained from Gilbert Laboratories (Hérouville Saint-Claire, France). Ultrapure water (18.2 M) was delivered by an Elga water system. 0.01 M PBS or PBS 1X (pH 7.4) was prepared by dissolving the content of one pouch of dried powder in 1 L of ultrapure water. 0.02 M sodium carbonate buffers at pH 10.7 were prepared from 0.1 M NaHCO 3 and 0.1 M Na 2 CO 3 solutions in ultrapure water. Washing buffer contained PBS 1X and 0.1 % Tween 20 (PBS-T) at pH 7.4. Blocking solution was prepared by dissolving 10 g of BSA in 100 ml of PBS-T.

Surface functionalization of microstructured glass slide.

Flat microscope glass slides were microstructured as described previously [START_REF] Mazurczyk | Low-cost, fast prototyping method of fabrication of the microreactor devices in soda-lime glass[END_REF][START_REF] Vieillard | Application of microfluidic chip with integrated optics for electrophoretic separations of proteins[END_REF][START_REF] Zhang | Specific recognition of lectins by oligonucleotide glycoconjugates and sorting on a DNA microarray[END_REF] . In our microstructured glass slides, each well corresponds to independent microarray, which allows for multiplexed parameters detection (like buffer, tumor marker, surface chemistry etc) in one assay.

Then they were aminosilanized with (3-aminopropyl) dimethylethoxysilane (APDMES) as the following protocol: The slides were washed with fresh piranha (H 2 SO 4 / H 2 O 2 , 7:3, v/v) for 30 min in the ultrasonic bath and rinsed with DI water. The substrates were dried under nitrogen stream at 150 o C for 2h. APDMES in pentane (dried over molecular sieves) was added (APDMES from 0.06 % to 0.6 %, v/v) and allowed to react at room temperature under stirring for 1h.

Pentane was evaporated, and the reaction was allowed to proceed under nitrogen stream at 150 o C overnight. Aminosilanized slides were rinsed with pentane, THF and dichloromethane in ultrasonic bath for 10 min each.

Alternatively, microstructured glass slides were silanized with tert-butyl -11-(dimethylamino) silylundecanoate (TDSUM) and carboxylic acids were deprotected as described previously [START_REF] El Khoury | Development of miniaturized immunoassay: Influence of surface chemistry and comparison with enzyme-linked immunosorbent assay and Western blot[END_REF][START_REF] Chevolot | Multiplexed binding determination of seven glycoconjugates for Pseudomonas aeruginosa Lectin I (PA-IL) using a DNA-based carbohydrate microarray[END_REF][START_REF] Dugas | Immobilization of single-stranded DNA fragments to solid surfaces and their repeatable specific hybridization: covalent binding or adsorption? Sensor[END_REF][START_REF] Zhang | DNA-directed immobilisation of glycomimetics for glycoarrays application: Comparison with covalent immobilisation, and development of an on-chip IC50 measurement assay[END_REF] .

Activation of carboxylic acid was carried out with a mixture of NHS/DIC (molar ratio 1:1, 0.1 M in THF) overnight at room temperature to obtain NHS surface. Then slides were washed for 10 min in THF and 10 min in dichloromethane under ultrasound. NHS slides were substituted with Jeffamine (0.1 M, THF) overnight at room temperature to generate amino groups on the surface (Jeffamine surface). The slides were then washed for 30 min with 0.1% SDS at 70 o C and rinsed with ultrapure water. Chitosan surface was obtained by derivatization of the NHS surface with chitosan solution at 1 mg/mL dissolved in acetic acid/DI-H 2 O mixture. The concentration of acetic acid was determined by the degree of deacetylation (DD) of the chitosan and the expected concentration of chitosan. The structure formulas of the three amine reagents and surface modification steps are illustrated in Scheme 1.

APDMES Jeffamine

Chitosan

N H 2 O O O NH 2 CH 3 CH 3 C H 3 x y z Si NH 2 CH 3 CH 3 O NH 2 O O H O H OH O NH 2 O H OH O OH NH 2 O H O OH n
Scheme 1. Scheme of structure formula of APDMES, Jeffamine M-600 and chitosan; Successive surface modification steps with carboxysilane, aminosilane, jeffamine and chitosan derivatives.

Evaluation of amine grafting density on amino-functionalized surfaces.

The grafting density of amino groups on the surface was determined using the modified ADECA ((amino density estimation by colorimetric Assay) method [START_REF] Chamieh | Preparation and full characterization of a micro-immunoaffinity monolithic column and its inline coupling with capillary zone electrophoresis with Ochratoxin A as model solute[END_REF] developed by Coussot et al. [START_REF] Coussot | Aminated dendritic surfaces characterization: a rapid and versatile colorimetric assay for estimating the amine density and coating stability[END_REF][START_REF] Coussot | A rapid and reversible colorimetric assay for the characterization of aminated solid surfaces[END_REF] . ADECA method allows estimating from 0.03×10 14 to 40×10 14 N + /cm 2 . Solution S1 was prepared by mixing 100 ml methanol, 50 ml glacial acetic acid and 850 ml DI water. CBB solution (S2) was prepared by dissolving 50 mg of CBB in 50 mL methanol and 25 mL acetic acid under ultrasonic bath. Following complete dissolution, DI water was added to a final volume of 500 mL. The final composition was 0.1 mg/ml CBB in mixed solution of 10% (v/v) methanol, 5% (v/v) acetic acid and 85% (v/v) H 2 O. The detection solution (S3) was prepared by mixing 50 mL of 1 M ammonia buffer with 50 mL of methanol. Amino surfaces were protonated in solution S1 for 10 min, followed by immersion in solution S2 for 15 min for coloration of the surface, then washed with solution S1 for 3 x 10 min and DI water for 10 min under stirring. After drying by centrifugation, slides were transferred into solution S3 for 5 min under stirring for de-coloration, and this solution was collected for absorption measurement at 611 nm. Added volume of solution S1, S2 and S3 was set in order to fully immerse glass slide sample. The amine density of the sample was quantified by the amount of CBB released in solution S3. Each surface was tested at least for four times, and negative control was freshly pirhanized glass slide.

X-ray Photoelectron Spectroscopy (XPS).

The XPS analysis was performed using an imaging Kratos Axis Ultra (UK) X-ray photoelectron spectrometer equipped with a conventional hemispherical analyzer. A monochromatized Al Kα (1486.6 eV) operating at 150 W was employed. Spectrum acquisitions were performed under ultrahigh vacuum conditions (UHV, 10 -9 Torr). Sample analysis area were 0.21 mm 2 and take off was 90° relative to the substrate surface. The pass energies were 80 and 20 eV for wide-scan and high-resolution elemental scans, respectively. Charge compensation was performed with low-energy electrons (0.1 eV). The C-C, C-H contribution was adjusted to 285 eV. The data reduction (atomic concentration, shift, curve fitting,etc.) was performed with CasaXPS Version 2.

Contact angle measurement of amino-funtionalized surfaces

Amino-functionalized glass slides were characterized for surface energy by contact angle measurements (Digidrop Goniometer, GBX, France). De-ionized water, Ethylene-glycol and Diiodomethane were used as the probe liquid in all measurements. To minimize the experimental error, the contact angle was measured at five random locations for each sample and the average value was reported. The surface energies were determined according to Owens-Wendt model.

Protein microarray manufacturing and multiplex immunoassays

Anti-CEA, anti-HSP60, anti-PDI and anti-DEFA6 capture antibodies were spotted (Biorobotics, Scienon) at the bottom of microwells of functionalized microstructured glass slides (1 type of antibody per microwell) at 10 µM. Spotting buffers were composed of 0.1 M sodium acetate (pH=4.5), PBS 1X (pH=7.4) or 0.05 M sodium carbonate (pH=9.6) with 0.05 % (v/v) PVA as additive. Spotting buffers alone and goat anti-rabbit IgG-Cy3 at 0.6 µM were spotted at the meantime for negative control and reference protein, respectively. Antibodies were allowed to react with functionalized surfaces under water-saturated atmosphere overnight at 4 o C. Slides were then washed for 2 x 5 min with PBS and for 5 min with PBS-T, and then dried by centrifugation for 3 min at 1300 rpm. The slides were blocked with 10% BSA/PBS-T solution to limit further non specific adsorption (2 h at room temperature), washed for 3 x 5 min with PBS-T and then dried.

Microwells were then incubated with antigens (CEA, HSP60, PDI and DEFA6 diluted in 4% BSA/PBS 1X) at different concentration (one antigen concentration per microwell, CEA and HSP60: 0.001 nM, 0.01 nM 0.1 nM, 1 nM, 10 nM and 50 nM; PDI and DEFA6: 0.1 nM, 1 nM, 10 nM, 50 nM 100 nM and 500 nM). The slides were left to react for 1 h at room temperature in a water-saturated atmosphere, thoroughly rinsed for 3 x 5 min with PBS-T and then dried.

Microwells were then incubated with 0.5 µM labeled detection antibodies (anti-CEA-DL647, biotinylated anti-HSP60, biotinylated anti-PDI, biotinylated anti-DEFA6 diluted in 4% BSA/PBS-T), for 1 h at room temperature in a water-saturated atmosphere. After washing and drying, microwells were then incubated with 1 µM streptavidin-Cy3 for 1 h at room temperature in a water-saturated atmosphere, except for the wells incubated with anti-ACE-DL647. The slides were washed for 3 x 5 min with PBS-T and for 1 min with DI water, followed by drying.

Fluorescence scanning

Slides were scanned with the Microarray scanner, GenePix 4100A software package (Axon Instruments) at wavelengths of 532 nm with photomultiplier tube (PMT) 500. The fluorescence signal of each antibody was determined as the average of the median fluorescence signal of six spots, and the value was divided by the signal of background from surface to get the signal-tonoise ratio (SNR).

RESULTS AND DISCUSSION

Amine density of functionalized glass slides.

Organosilanes are widely used in the fields of biosensors and biochip technology. In previous studies we reported use of silanizations for effectively introducing carboxylic group on the surface of silicon/glass slides for biochip manufacturing [START_REF] Dugas | Immobilization of single-stranded DNA fragments to solid surfaces and their repeatable specific hybridization: covalent binding or adsorption? Sensor[END_REF][START_REF] Phaner-Goutorbe | Silanization of silica and glass slides for DNA microarrays by impregnation and gas phase protocols: A comparative study[END_REF] . The grafting reaction of a monofunctional silane (APDMES and TDSUM) was selected because it is simpler and more reproducible than those of multifunctional silanes. Indeed, compared to the grafting of multifunctional silanes (e.g. APTES), monofuncitonal silanes are less sensitive to experimental conditions like moisture for example. The grafting process (by impregnation) used in our experimental set-up allows to overcome the lower reactivity of such monofunctional silanes. As a follow-up of this work, microstructured glass slides were functionalized with APDMES at various concentrations and quantitative analysis of amine density was performed as described in references [START_REF] Coussot | Aminated dendritic surfaces characterization: a rapid and versatile colorimetric assay for estimating the amine density and coating stability[END_REF][START_REF] Coussot | A rapid and reversible colorimetric assay for the characterization of aminated solid surfaces[END_REF][START_REF] Coussot | Colorimetric quantification of amino groups in linear and dendritic structures[END_REF] . Indeed, Coussot et al. have developed a rapid method based on the adsorption/desorption of Coomassie Brillant Blue (CBB) for the estimation of available N + groups on surfaces of polymeric and silica-based materials.

As shown in Figure 1A, the amine density on aminosilanized glass slides reached a maximum around 1.3 x 10 14 amino groups/cm 2 and did not depend on the concentration of APDMES introduced in the reaction mixture, in the range tested. Our results are in agreement with Oh et al. [START_REF] Oh | Characteristics of DNA microarrays fabricated on various aminosilane layers[END_REF] who have prepared aminosilane layers on glass slides with APDMES and determined the amine density as being 10 14 amino groups/cm 2 . In another study [START_REF] Zhang | Chemical Vapor Deposition of Three Aminosilancs on Silicon Dioxide: Surface Characterization, Stability, Effects of Silane Concentration, and Cyanine Dye Adsorption[END_REF] , covalently bound monolayers of aminosilane were deposited on dehydrated silicon surface by chemical vapor deposition. The results showed that aminosilane concentrations over a wide range did not affect surface coverage because the number of reactive sites on the surface was limited. Dugas et al. have demonstrated the complete reaction of all surface accessible substrate silanols with monofunctional silane [START_REF] Dugas | Surface hydroxylation and silane grafting on fumed and thermal silica[END_REF] .

Similarly, in the present study, the limiting factor is most probably the number of reactive silanols on the substrate surface. Complete reaction is achieved with 0.05% of APDMES. Jeffamine and chitosan were grafted by reaction with NHS activated carboxylic groups from TDSUM modified surfaces (Scheme 1). The reaction leads to the formation of an amide bond.

Jeffamine is a diamine that can either react with only one NHS ester group leading to an aminated surface or react with two adjacent NHS ester groups leading to "bridge" formation with no available amine. Chitosan is a polyaminated polymer, whose amine density was also determined with the ADECA method (Figure 1B). Results indicated that functionalization with these two polymers led to about three time less amine density than with APDMES (Jeffamine:

4.5 x 10 13 amino groups/cm 2 , chitosan: 5.3 x 10 13 amino groups/cm 2 ).

The chitosan used in this study was of high molecular weight (Mw = 470 000 g/mol) with a high degree of deacetylation (94 %). These characteristics correspond to a long-chain structure bearing a large amount of amino groups. The lower amine density observed on chitosan surface suggests that, steric hindrance or electrostatic repulsion between chitosan molecules may occur leading to low amount of available amino groups on the surface. It is also possible that CBB could not reach all surface amino groups due to steric hindrance or diffusion limitations related to the long polymeric chains. However, the amine density of chitosan modified surfaces was similar to the one observed on Jeffamine surfaces.

XPS analysis of modified surfaces.

Tables 1a and1b summarize the XPS atomic percentage and contributions of C 1s, N 1s, Si 2p

and O 1s lines. Figure 2 shows the high-resolution XPS spectra of Si 2p and N 1s of piranha cleaned silica surface and mono-functional silane APMDES modified silica. The presence of nitrogen (Table 1)

on APMDES surface confirmed that APDMES was successfully introduced with our protocol.

Besides, two fit peaks were present on the high-resolution N 1s spectra (Figure 2 B2) revealing two contributions, which were associated with a free amine NH 2 -C (around 400 eV) and protonated amine NH + 3 -C (around 401.6 eV) [START_REF] Noel | Quantification of Primary Amine Groups Available for Subsequent Biofunctionalization of Polymer Surfaces[END_REF] , respectively. The protonated amine component peak is attributed to interactions between the APDMES amine groups and surface silanols on the silica substrate, resulting in proton transfer to the amine group [START_REF] White | Reaction of (3-Aminopropyl)dimethylethoxysilane with Amine Catalysts on Silica Surfaces[END_REF] . The presence of the monofunctional silane on APDMES surface is further supported by the peak at 101.6 eV on the Si 2p peak corresponding to Si(O-) 1 . Indeed, Alexander and co-workers [START_REF] Alexander | A study of HMDSO/O-2 plasma deposits using a high-sensitivity and -energy resolution XPS instrument: curve fitting of the Si 2p core level[END_REF] originated from the underlying silica. Therefore, this ratio is independent on subsequent surface layers as far as they do not contain silicon. On the contrary, due to the mean inelastic free path of electrons (constant probing depth), increased surface coverage results in decreased signal originating from the substrate and therefore the decrease of Si 2p atomic percentage. The percentages of Si(-O) 1 for APDMES and TDSUM modified silica were 4.9 % and 1.7 % respectively. The Si(-O) 1 for TDSUM was the mean of 1.1%, 1.4% and 2.8 % corresponding to TDSUM, Jeffamine and chitosan surfaces. A lower Si atomic percentage was observed on APDMES surface (27.7 %) compared to TDSUM surface (29.0 %). These results suggest that a slightly higher surface coverage was obtained with APDMES compared to TDSUM but remained in the same order of magnitude for both surfaces.

Upon reaction of TSDUM surface with either Jeffamine or chitosan, the N 1s AC% increased from 0 to 0.56 and 0.42 % respectively, whereas the Si 2p AC% decreased as expected.

According to the N 1s AC%, the amine surface densities are lower for these two surfaces confirming the results obtained from the amine colorimetric titration. surfaces. [START_REF] Kallury | Effect of Surface-Water and Base Catalysis on the Silanization of Silica by (Aminopropyl)Alkoxysilanes Studied by X-Ray Photoelectron-Spectroscopy and C-13 Cross-Polarization Magic-Angle-Spinning Nuclear-Magnetic-Resonance[END_REF][START_REF] Mclean | Method of immobilization of carboxymethyl-dextran affects resistance to tissue and cell colonization[END_REF] The contribution at 286.1 eV can be attributed to the polyoxypropylene backbone of Jeffamine or to the polysaccharide backbone of chitosan. On N 1s spectra of Jeffamine, two peaks are observed at 399.7 eV and 401.7 eV; These contributions can be assigned to NH 2 -C or N-C=O respectively. Alternatively, they can be attributed to N-C=O and + H 3 N-C or NH 2 -C and + H 3 N-C (Figure 3 A2). The reaction proceeds in tetrahydrofuran, an aprotic solvent. So most probably the contribution at 399.7 eV corresponds to NH 2 -C and the contribution at 401.7 eV to a nitrogen involved in an amide bond. In the case of chitosan, the contribution at 401.7 is not observed and would suggest that reaction between the NHS ester and the amine of the chitosan did not occur. This suggests that chitosan is mostly physisorbed on the TDSUM surface despite the washing step with 18.2 M water.

Surface energy of amino-functionalized glass slides.

The three amine surfaces were characterized by contact angle measurements to evaluate surface energy. The surface energies, viz., the total energy (E T ), the dispersive energy (E D ) and the polar energy (E P ) were calculated from the wetting angle (θ) accordingly to the Owens-Wendt equations. As is shown in Table 2, the total surface energy was higher for polymer functionalized surface than for aminosilane and Jeffamine functionalized surfaces. Although APDMES and Jeffamine displayed comparable polar energy 6.2 mJ/m² and 7.1 mJ/m², respectively, Jeffamine surface was more hydrophilic than APDMES surface as indicated its higher total surface energy.

This could be attributed to the polyoxyproplene backbone of Jeffamine compared to the alkyl chain of ADPMES. While Jeffamine and chitosan present comparable dispersive component of the surface energy, chitosan surface was the most hydrophilic surface due to its high polar energy which was about two times that of APDMES and Jeffamine surfaces. Indeed, chitosan is a natural polysaccharide with hydrophilic characteristic as already described [START_REF] Drogoz | Towards biocompatible vaccine delivery systems: Interactions of colloidal PECs based on polysaccharides with HIV-1 p24 antigen[END_REF][START_REF] Schatz | Static light scattering studies on chitosan solutions: From macromolecular chains to colloidal dispersions[END_REF] , and results obtained for APDMES surface is also in agreement with published data [START_REF] Zhang | Chemical Vapor Deposition of Three Aminosilancs on Silicon Dioxide: Surface Characterization, Stability, Effects of Silane Concentration, and Cyanine Dye Adsorption[END_REF][START_REF] Wu | Argon-Plasma-Treated Chitosan: Surface Characterization and Initial Attachment of Osteoblasts[END_REF] .

Characterization of antibody immobilization on amino-functionalized surfaces.

Antibody immobilization was characterized by fluorescence scanning using a goat anti-rabbit IgG labelled with cyanine 3 (Cy3). The labelled antibody was spotted at 0.6 µM in various pH buffers in order to evaluate the antibody immobilization capacity of the amino-functionalized surfaces. The results are expressed as signal to noise ratio (SNR) (Figure 4). For the three surfaces, the SNR increased with increasing pH values of buffer suggesting charge dependence for the antibody immobilization. The electrostatic interactions between positively charged amino groups on the surface and antibodies bearing negative charge, increased with increasing pH value of buffer (in the range of pH studied) except for chitosan functionalized surface. Moreover, considering one buffer, the immobilization yield of antibodies is 2 to 6 times higher on chitosan surface than on the other two amino-functionalized surfaces. Whereas Jeffamine surface displayed half lower amine density than APDMES (Figure 1B), its immobilization density for antibodies was slightly higher. Wetting properties of both surfaces suggested that Jeffamine surface developed more Van der Waals and non-site-specific interactions, relative to the dispersive energy of the surface, with antibodies than APDMES surface. Chitosan surface displayed the same amine density as Jeffamine surface, but three main physico-chemical differences could explain the higher antibody immobilization density of chitosan surfaces. First, the chitosan sample used has a high molecular weight, Mw = 470 000 g/mol, hence developing high immobilization surface area. Second, chitosan surface was shown to be more hydrophilic than the other two surfaces, with higher polar energy part. Third at pH 7.4 and above, chitosan is poorly charged and most probably the interactions developed with antibodies are hydrogen bonding. These low energy interactions do not block the protein at the outer surface of the polymer layer but allows, by successive H-bond breaking and forming steps, a penetration of the immunoglobulin within the polysaccharide layer. However, the immobilization capacity of a surface was not directly correlated to its ability to preserve the biological activity of the immobilized proteins. However, the most significant variations were obtained for the detection of DEFA6 with up to 7 times SNR on chitosan surface than on Jeffamine or APDMES surfaces (Figure 6D). For the other tumor markers, a maximum of 5 times SNR was obtained on chitosan surface compared to APDMES surface. These results confirmed that the binding capacity of chitosan surface for the immobilisation of antibodies is higher than that of Jeffamine and APDMES surfaces (Figure 4).

Moreover, chitosan surface allowed maintaining the biological activity of the immobilized antitumor marker antibodies in order to efficiently detect tumor markers. Additionally, SNR curves obtained for CEA and DEFA6 on chitosan surface showed saturation plateau from 10 nM and 100 nM of tumor marker, respectively. This result suggested that maximum binding efficiency of biologically active immobilized antibodies was reached. For HSP60 and PDI, the saturation plateau was not reached in the tested range indicating that the detection of these two tumor markers was less efficient than the detection of CEA and DEFA6.

On chitosan surface, the limit of detection for each tumor marker can reach their lowest tested concentration (CEA and Hsp60 1 pM, PDI and DEFA6 100 pM). Recently we reported that DEFA6 has the best analytical performance (a lowest limit of detection at 10 pM and a broad dynamic range of 4.7 log) on chitosan surface under the protein spotted in 20 % (v/v) glycerol/PBS (pH 7.4) [START_REF] Yang | Cancer biomarkers detection using 3D microstructured protein chip: Implementation of customized multiplex immunoassay[END_REF] . In this paper, the signal could be detected even in the case of CEA and Hsp60 at 1 pM or below under optimal condition on chitosan surface.

Although APDMES surface displayed 2 times more amine density than Jeffamine and chitosan surfaces, it showed the lowest antibody immobilization efficiency and maintenance of biological activity. This was attributed to its low surface energy leading to poor wettability properties and to the shortness of the amino chains reducing binding surface capacity. On the contrary, chitosan surface was demonstrated to be the most hydrophilic surface leading to more efficient immobilization of antibodies and better biological activity. According to our results, surface energy and chain length were the leading parameters for protein immobilization. However, it may well be that the amine density of chitosan surface was underestimated due to diffusion limitation (steric hindrance). Other researchers also indicated [START_REF] Kusnezow | Antibody microarrays: an evaluation of production parameters[END_REF]47 that the most hydrophilic and biocompatible surfaces were favourable for the immobilization of proteins and limiting nonspecific adsorption. Moreover, the high antibody immobilization efficiency of chitosan surface could be attributed to its long amino chains increasing specific surface. Finally, chitosan is a hydrosoluble biopolymer suitable to preserve the biological activity of adsorbed proteins.

CONCLUSION

We designed and developed three different aminated surfaces, APDMES, Jeffamine and chitosan, on 3D microstructured glass slide to implement antibody microarray for the detection of tumor markers involved in colorectal cancer. Influences of amino chain length and physicochemical characteristics (surface energy, amine density) on antibody immobilization and on the ability to maintain their biological activity were studied. The efficiency of antibody immobilization was evaluated using fluorescent-labeled antibody allowing to compare the relative surface density obtained with the three aminated surfaces. Similarly, the relative biological activity of immobilized antibody on each surface was addressed using a sandwich assay with secondary fluorescent-labeled detection antibody. For all tested antibody/antigen systems, significantly enhanced signal-to-noise ratio was obtained on chitosan surface. This surface displayed the highest surface energy and chain length. Furthermore, sodium carbonate buffer (pH 9.6) was found to be the optimal spotting buffer on the three amino-functionalized surfaces. Thus to improve the analytical performance of protein microarray it is required to optimize surface chemistry and immobilization conditions. In conclusion, antibody microarrays based on physical adsorption of proteins on aminated surfaces were successfully developed to supply simple and effective tools for the detection of tumor markers. Future work will focus on the detection of tumor markers from colorectal cancer sera using our optimized antibody microarray.

47 Ruckenstein, E.; Li, Z. F. Surface modification and functionalization through the selfassembled monolayer and graft polymerization. Adv. Colloid. Interfac. 2005, 113, 43-63.

TOC Graphic

  3.14 software. The operating software Vision 2, corrects for the transmission function. The relative sensitivity factors (RSF) were 0.278, 0.477, 0.780 and 0.339 for C 1s, N 1s, O 1s and Si 2p respectively, used for determining the atomic concentrations (%AC) of the surface composition. Background type was Shirley and Gaussian-Lorentzian peak shape (30%) was used for peak fitting. Full widths at half-maximum (FWHM) for the component peaks of Si 2p, C 1s, N 1s and O 1s were constrained to be 1.5 eV, 1.4 eV, 1.7 eV and 1.5 eV, respectively. Component peak positions of Si 2p were based on the results by Alexander et al. 31 who reported the binding energies of Si(-O) 1 , Si(-O) 2 , Si(-O) 3 , and Si(-O) 4 to be around 101.5, 102.1, 102.8, and 103.4 eV, respectively.

Figure 1 .

 1 Figure 1. Effect of APDMES concentration (v/v in pentane) on grafting density on glass slide

Figure 2 .

 2 Figure 2. High-resolution XPS spectra of piranha cleaned silica surface Si 2p (A) and of APDMES functionalized silica surface Si 2p (B1) and N 1s (B2).

Table 1

 1 gives the respective atomic concentration (AC %) of C, Si, N, O as well as the relative contribution of Si(-O) 1 in the Si 2p for APDMES, TDSUM, Jeffamine and chitosan modified surfaces. The relative contribution (%) of Si(-O) 1 was calculated as the contribution of the Si(-O) 1 determined by curve fitting over the total area of the Si 2p (Si(-O) 1 and Si(-O) 4 ). As mentioned above, Si(-O) 1 signal originated only from the silane molecule while the Si(-O) 4

Figure 3

 3 Figure3presents the spectra of N 1s and C 1s of Jeffamine and chitosan surfaces obtained after reaction with TDSUM modified surfaces (XPS spectra not shown)[START_REF] Dugas | Immobilization of single-stranded DNA fragments to solid surfaces and their repeatable specific hybridization: covalent binding or adsorption? Sensor[END_REF][START_REF] Dugas | Chemical Reactions in Dense Monolayers: In Situ Thermal Cleavage of Grafted Esters for Preparation of Solid Surfaces Functionalized with Carboxylic Acids[END_REF] leading to the

Figure 3 .

 3 Figure 3. High-resolution XPS spectra for Jeffamine (A) and chitosan (B) surfaces. A1, B1 are

Figure 4 .

 4 Figure 4. Signal to noise ratio from immobilization of IgG-Cy3 in different spotting buffer

3. 5 .

 5 Detection of tumor markers on antibody microarray.According to previous results[START_REF] Yang | Cancer biomarkers detection using 3D microstructured protein chip: Implementation of customized multiplex immunoassay[END_REF] , four monoclonal antibodies directed against tumor markers involved in colorectal cancer (anti-CEA, anti-HSP60, anti-PDI and anit-DEFA6) were spotted at 10 µM on the amino-functionalized surfaces in the different pH buffers (sodium acetate pH 4.5, PBS pH 7.4 and sodium carbonate pH 9.6). These capture antibodies were allowed to interact with corresponding tumor markers at various concentrations. Detection of the biological recognition was performed using biotinylated monoclonal antibodies directed against another epitope of the corresponding tumor marker, followed by incubation with Cy3-labeled streptavidin. Figure5presents the effects of the buffer pH on the biological activity of anti-CEA antibody immobilized on chitosan surface for the detection of CEA. The four anti-tumor marker antibody/tumor marker systems displayed the same behavior on each amino-functionalized surface (data not shown). Typically, SNR increased with the increasing tumor marker concentration and pH value of spotting buffer. The best immunoassay response was obtained with carbonate buffer (pH 9.6) in agreement with data obtained for IgG-Cy3 immobilized on the various amino-functionalized surfaces. This result demonstrated that carbonate buffer (pH 9.6) as the spotting buffer not only facilitated the immobilization of antibodies on aminated surfaces but also allowed to maintain their biological activity. Therefore, sodium carbonate buffer at pH 9.6 was chosen as spotting buffer in the following experiments.

Figure 5 .

 5 Figure 5. Signal to noise ratio (SNR) relative to biological recognition of anti-CEA antibody

Figure 6

 6 Figure 6 illustrates the results of multiplex immunoassays for the detection of the four tumor

Figure 6 .

 6 Figure 6. Detection of tumor markers in multiplex immunoassays on aminated surfaces. (a)

Table 1a .

 1a Atomic concentration calculated from XPS analysis, N/Si (-O) 1 : ratio between nitrogen and silicon atomic concentrations.

	Surfaces		Atomic concentration (AC%) C Si N	O		Si (-O) 1 (%)	N/Si (-O) 1
	APDMES		14.6	27.7		1.24	56.4		4.9		1.0
	TDSUM		10.6	29.0		-	60.4		1.1		-
	Jeffamine		22.1	25.0		0.56	52.4		1.4		-
	Chitosan		14.0	27.6		0.42	58.0		2.8		-
	Table 1b. XPS contributions of the C 1s, N 1s, Si 2p and O 1s lines for APDMES, Jeffamine
	and chitosan surfaces.
	Surfaces	C-C C-H BE (eV)	%	C-O C-N BE (eV)	%	C=O O-C-O BE (eV) %	N-C=O O-C=O BE (eV) % BE NH 2 -C (eV) %	N-C=O + H 3 N-C BE (eV) %	Si(-O) 1 Si(-O) 4 O-C BE (eV) % BE (eV) % BE (eV)	%	O=C BE (eV)	%
	APDMES 285 74.2 286.1 17.6 287.5 4.5 288.9 3.7 400 67.1 401.5 32.9 101.6 4.8 103.6 95.2 530.7 14 532.8 98.6
	Jeffamine 285 65.3 286.5 33.4 -	-288.2 1.4 399.7 39.9 401.7 60.1 101.6 1.4 103.5 98.6 532.6 99.2 533.8 0.8
	Chitosan 285 81.2 286.2 13.6 288 4.1 289.3 1.1 399.8 100 -	-102 2.8 103.6 97.2 532.7 98.6 534.1 1.4

Table 2 .

 2 Wetting properties of amino-functionalized surfaces determined with Owens-Wendt model; E T , E P and E D are relative to the total, polar and dispersive energy, respectively.

	Surfaces	E T (mJ/m²)	E P (mJ/m²)	E D (mJ/m²)	water	Contact angle (θ /°) Ethylene-Glycol	Diiodo-methane
	APDMES	31.6 ±2.1	6.2±0.7	25.4±1.9	79.5±0.2	64.6±0.4	59.6±0.5
	Jeffamine	38.4±3.2	7.1±0.5	31.3±2.8	74.1±0.2	50.5±0.5	51±0.4
	Chitosan	43.7±3.5	12.4±1.0	31.4±2.4	62.4±0.5	44.5±0.7	47.2±0.7

ACKNOWLEDGMENTS

China Scholarship Council is grateful to offer PhD fellowship to Z.G Yang. CNANO Rhône-Alpes and BQR Ecole Centrale de Lyon are acknowledged for financial support and thanks NanoLyon for its technical support.

AUTHOR INFORMATION


Christèle Beauvais

Xavier Guerrault

François-Xavier Coudert

Anne Boutin

Alain H Fuchs

Distribution of Sodium Cations in Faujasite-Type Zeolite: A Canonical Parallel Tempering Simulation Study

A Monte Carlo replica exchange (MCRE) algorithm was used to compute the sodium cation distribution in bare faujasite zeolite with a number of cations per unit cell ranging from zero (Si:Al → ∞) to 96 (Si:Al = 1). Eight independent realizations of the system were simulated simultaneously, in the temperature range 300-2325 K. The resulting distributions at room temperature were found to be in very good agreement with both available experiments and the analytical quasi-chemical model of Mortier and co-workers. A single canonical simulation at room temperature using site-to-site hopping yields identical results. The main advantage of the MCRE method is that no assumption is needed on the actual cation adsorption sites. One could thus, in principle, predict cation locations and distributions in a nanoporous solid for which the precise location of extraframework cations is not known.

Introduction

Aluminosilicate faujasite-type zeolites have been widely studied in the past few years, owing to their industrial importance in gas adsorption and separation. In these materials, the presence of aluminum atoms introduces charge defects that are compensated with some nonframework cations (sodium, potassium, barium, etc.). Adsorption properties in zeolites are closely related to the location of nonframework cations and to their accessibility to adsorbed molecules. However, the precise location and the distribution of monovalent cations in faujasite by conventional diffraction techniques is rendered especially difficult because of partial occupancy affecting low symmetry sites.

Since the initial diffraction work by Mortier, [START_REF] Mortier | Compilation of Extraframework Sites in Zeolites[END_REF] there have been a significant number of studies dedicated to the reinvestigation of cation location in dehydrated NaY and NaX, using powder or single-crystal diffraction refinements [START_REF] Eulenberger | [END_REF][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] or NMR studies. 15,[18][19][20][21] Theoretical models 10,[22][23][24][25][26][27] and computational approaches have also been used to predict cation location in this material 13,[28][29][30][31] as well as in other zeolites. [48][49][50] The cation distribution is usually described as follows (see Figure 1). Na + can occupy sites I, located in the hexagonal prisms which connect sodalite cages. Sites I' are inside the sodalite cages facing sites I. Sites II are in front of the 6-rings inside the supercages. Sites III are also in the supercages, near the 4-rings of the sodalite cages.

Site I has a multiplicity of 16 per unit cell, sites I' and II have a multiplicity of 32, and site III has a multiplicity of 48 per unit cell. Some cations have also been found (in the case of NaX) in the 12-ring windows. [12][13] These are called sites III'. Sites III and III' are believed to be of higher potential energy than sites I, I', and II. At low occupancy (Si:Al ≥ 2), cations are known to occupy sites I, I', and II only. Grand canonical Monte Carlo simulations, using statistical bias for studying large anisotropic molecules, have been shown to provide reasonably accurate predictions of adsorption data. 32 Molecular simulation is a method of choice for direct predictions of adsorption selectivity in mixtures, using experimentally obtained pure components data to fit some of the potential parameters. As pointed out by Talu 33 the pure component isotherm is the simplest measurement of adsorption equilibrium and it can be determined quite accurately. On the other hand, binary mixture measurements are at least an order of magnitude more complicated and time-consuming. It is thus suggested that a combination of experiments and simulations can be used to help in the rational design of adsorbents for mixture separations. To achieve this goal, there is a need for some refinements of the simulation models together with some progress in the simulation methods.

Here we describe a method that enables one to take into account in the Monte Carlo simulations the possible redistribution of extraframework cations upon adsorption of guest molecules. In most of the previously published computational studies of adsorption, cations were placed in the positions obtained experimentally for the dehydrated material and kept fixed throughout the simulations. 32 Only recently have the cation positions been taken into account in the simulation of alkane mixture adsorption in low aluminum content ZSM-5. 34 The need clearly exists for a method that could enable one to predict the way cations are distributed among the available sites in systems for which experiments are lacking and how cations redistribute upon adsorption of highly polar molecules. Some experimental evidence exists for cation redistribution upon HFC 35 and water 36 adsorption in faujasite. This was confirmed by a recent molecular dynamics study of some HFC (CF2H-CF2H and CH2F-CF3) in NaX. 37 In a previous paper, 31 we have shown that the extraframework sodium cations in faujasite experience an extremely rough potential energy landscape. Numerous metastable states were obtained either through standard Monte Carlo simulations or simulated annealing. In many cases, we have found it necessary to combine simulated annealing with long distance site-to-site hopping in order to reach the (supposedly) most stable state corresponding to the most probable cation distribution for a given Si:Al ratio.

Here we use the canonical replica-exchange Monte Carlo method [38][39][40][41][42] (also known as parallel tempering), to enhance the configuration sampling of low-energy states in the sodium-faujasite system. In this method, several independent realizations of the system are simulated simultaneously, each differing in temperature. As the simulation proceeds, systems at adjacent temperatures are allowed to interchange configurations from time to time, subject to a specific acceptance criteria. These swap moves considerably improve the sampling of configuration space. The higher temperatures are chosen in such a way that the system can easily overcome energy barriers and thus can provide the low-temperature systems with configurations that cover a broad range of configuration space. This method was used here to compute the stable distributions at room temperature for a number of cations per unit cell ranging from 0 (Si:Al → ∞) to 96 (Si:Al = 1).

The remainder of the paper is organized as follows. In section 2, we discuss the computational methodology.

In section 3, we present the results of the replica-exchange Monte Carlo simulations and we compare our results with both the available experimental data and the analytical model proposed by Mortier and co-workers. 10,[25][26][27] Concluding remarks are given in section 4.

∼

Computational Methodology

A. Simulation Model. The faujasite model, atomic charges, and the cation force field used have been described in details in a previous paper. 30 The framework structure of dehydrated faujasite was taken from the experimental neutron diffraction studies of Fitch et al. 4 The crystalline structure is described in the Fd3m space group, and the cubic lattice parameter is 24.8536 Å. The same framework structure was used throughout this work and was considered as rigid. One unit cell of faujasite was used as the simulation box, with periodic boundary conditions in all three directions. The different host framework-guest cations systems had a Si:Al ratio ranging from 1 to ∞. The corresponding number of sodium cations per unit cell ranged from 96 (Si: Al = 1) to 0 (Si:Al → ∞). For each system, an average tetrahedrally bonded (T) atom was used, for reasons detailed in ref 30. Partial charges on the oxygen and T atoms were adjusted in the way described in ref 30, using the electronic structure calculations of Mortier and co-workers, 43 and the number of cations was fixed accordingly. Sodium cations bear a charge of +1 au.

The cation force field has been adapted from the work of Jaramillo and Auerbach, 29 in the way described in ref 30. The cation-framework potential consists of an exp-6 repulsion-dispersion term that acts between the cation and the oxygen atoms of the faujasite and a Coulombic term that acts between the cation and both the oxygen and T atoms of the framework. Sodium cations interact with each other through a single Coulombic term. Different cation force fields have been tested in a previous work, and it turned out that the one proposed by Jaramillo and Auerbach was doing the best job in reproducing the cation positions in NaY. 44 Finally, Ewald sums were used to calculate the long-range Coulombic terms. The Ewald parameter α was equal to 0.19 Å -1 and the k vectors were such that k ∈ [-3, 3]. This allows us to reproduce the exact Coulombic energy with high precision (<1% error).

B. Monte Carlo Simulations.

We performed replica-exchange canonical Monte Carlo simulations of the sodium cations subjected to the external field imposed by the rigid faujasite framework host. For each system (corresponding to a given Si:Al ratio), eight independent realizations of the system were simulated simultaneously.

The chosen temperatures (in Kelvin) were 300, 410, 560, 780, 1050, 1380, 1805, and 2325. The highest temperature was chosen in such a way that the cations experienced a "liquid-like" behavior. The lowest temperature is room temperature, at which most of the adsorption experiments have been carried out. It was found that eight different temperatures were needed in order to ensure a reasonable degree of overlap between the potential energy distributions of neighboring state points (Figure 2). This number may seem quite large, but one has to remember that a unit cell of faujasite is made of 576 T and oxygen atoms, plus a variable number of cations (from 0 to 96). The number of realizations needed to ensure an effective simulation depends on the size of the system, since the width of the probability distribution function decreases with the system size. Adjacent temperatures are in a ratio of 1.3 for each temperature interval. It has been shown recently by Kofke 45 that the acceptance probability can be made uniform across the multireplica partition by selecting adjacent temperatures that are in a fixed ratio. Each simulation ranged between 10 7 and 3 10 7 Monte Carlo trials. In each trial, either a cation displacement or a replica exchange was attempted, selected at random, such that displacements were attempted 100 times more often than exchanges. To satisfy detailed balance, the displacement and exchange trials were accepted with probabilities

Pacc(i→j) = min[1, exp(-β (Uj -Ui))] Pacc(m→n) = min[1, exp(-(βm -βn) (Un -Um))]
for the displacement and exchange trial, respectively. In eq 1, i and j refer to two successive configurations in a canonical simulation for a given realization at a temperature T = 1/kB β (kB is the Boltzmann's constant). For the exchange trial, we consider a pair of systems (subscripts m and n) at temperature Tm = 1/kB βm and Tn = 1/kB βn respectively. In Figure 4a-d, the simulation data and the quasi-chemical model are compared with the available experimental data, in the range of 48-96 cations per unit cell. The overall agreement is quite satisfactory. Some experimental data can be found for cation numbers lower than 48. However, these experiments 10,26 have actually been performed on NaHY samples, in which sodium cations were progressively exchanged by H atoms, at a fixed Si:Al ratio. The corresponding cation distributions cannot be compared to our simulations.

Results and Discussion

The observed trends in the simulated site populations can be understood in terms of a competition between the individual cation-framework potential energy interaction and the Coulombic interaction between cations. In Above CN ~ 20, site I' is becoming (individually) more stable than site II. Some site I' occupancy is then observed in the range 20 < CN < 30 (Figure 3b), but the overall tendency is to keep filling sites II up to a complete occupancy of 32 cations per unit cell. It turns out that the Coulombic cation-cation interaction, while negligible in the limit of CN → 0, becomes progressively dominant with respect to the cation-framework interaction as CN increases. Thus, instead of filling sites I', cations will keep occupying sites II because the II-II distance is larger than the II-I' one (see Figure 1). By the time sites II are completely occupied (CN = 32), cations start to fill sites I. Again, the dominant term in the total interaction energy is now the cation-cation Coulombic energy. Thus, the system prefers to occupy sites I, which are further away from sites II than sites I' are from site II. This holds up to a complete occupancy of 16 sites I per unit cell.

Above CN = 48, which corresponds in our model to a complete occupancy of sites II and I, a further increase in CN can only be achieved by occupying sites I'. Because the distance between sites I and I' is extremely small (2.18 Å), a sodium cation can only occupy a site I' if the adjacent cation in site I is at the same time displaced toward the opposite site I', due to the strong repulsive Coulombic interionic energy (see Figure 1). This explains the simultaneous increase in the site I' population and decrease in site I occupancy. We note in passing that it has been supposed for long, and checked experimentally, that adjacent sites I and I' are not simultaneously occupied. 24 Above CN ∼ 56, a progressive occupation of sites III is observed. In much the same way as in our previous work, 30 the positions spontaneously reached by the cations after convergence of the replica-exchange MC runs at Mellot. 11 While site II location is unchanged, two extra locations are observed for sites I' and III, respectively. The extra site I' is located at 0.2 Å away from the initial site I' toward to hexagonal prism which leads to broaden the cation distribution around site I'. Two types of site III are observed in the simulations. The first one lies in the middle of a 4-ring. The second one is close to the 12-ring window. It corresponds quite well to the site III' location reported by Vitale et al. 13 The relative occupancy of sites III and III', however, is not satisfactorily reproduced in the simulations. A better agreement with experiments has been obtained recently by using a model in which silicon and aluminum atoms are explicitly distinguished, instead of using an average T-atom. 31 The reader is referred to ref 30 and 31 for more details on this issue.

B.

Comparison with the Analytical "Quasi-Chemical" Model. Mortier and co-workers 5,10,25,26 have developed an analytical model for cation distribution in faujasite-type zeolites, which was called the "quasichemical model" (QC). In this model, only interactions between cations in nearest neighbor sites (I and I') are taken into account. A cation in site II is considered to have no neighbor (or to behave ideally). A single potential energy of interaction (-w) is postulated for any nearest neighbor pair. The canonical partition function of the system is written in terms of the number of nearest neighbor pairs configurations, which van Dun et al., 25 given the assumptions of the model, have been able to explicitly enumerate. The site populations can then be expressed as a function of three parameters: the interaction energy w and the energy level differences (eI' -eI) and (eII -eI), where ei denotes the stabilization energy of the cation at site i relative to the ground-state energy at infinity.

Using the data of a NaxHY series of structures, a best fit for these three parameters was determined. 25 Furthermore, the energy differences were assumed to vary linearly with the aluminum content of the faujasite framework. 10 The values for the QC model parameters were then where NAl is the number of aluminum atoms per unit cell of faujasite, which is equal to the number of cations in NaY or NaX. The observed trends of the cation distributions in most X and Y faujasites were found to be well reproduced by the QC model. 10 In Figure 3, we have sketched the site populations as a function of the cation number CN, using the QC model with w = 50 kJ mol -1 , together with the results of the present parallel tempering simulations. We note in passing that the QC model takes explicitly into account three sites only (I, I', and II). The site III population shown in Figure 3 corresponds to cations which have been repelled from the I-I' configuration.

Once sites I' and II are fully occupied, all of the other cations (as CN increases) are accommodated in site III.

The overall agreement between the simulations and the QC model is quite good. The increase in site II population is steeper in the MC data. A sigmoid shape is observed in the QC model variation of site I' population in the range of CN ~ 45-55. It has no clear physical meaning. It is in this range of aluminum content that a reversal of site preferences is found in the QC model (see Figure 6). It is thus possible that this behavior is due to a numerical instability of the QC model equations.

The site energy differences (eI' -eI) and (eII -eI) as a function of CN are shown in Figure 6 for the QC model and for the model used in the present simulations. A linear variation of the energy differences with CN is found in our simulations, in agreement with the assumption of the QC model. The origin of this finding is simply that the partial charges on the framework atoms vary linearly with CN. Absolute values of the energy difference in both models are not strictly comparable, because only an effective I-I' interaction is taken into account in the QC model, through the w parameter, whereas in the simulation model, the Coulombic interaction between cations in sites I, I', II, and III is explicitly computed.

The individual site preference for low CN is, in both cases, II > I' > I. A reversal of site preference is found as CN increases. At high CN values, the cation site preference is I' > I > II for the MC model and I > II > I' for the QC model. The difference in site preference and in variation of the energy differences between the two models is quite large. However, as already pointed out by Mortier and co-workers, 25 the cation occupancy scheme is dominated by the Coulombic repulsive energy between cations, at least for a high enough cation number. This explains why the differences observed in Figure 6 between the two models have no profound effect on the cation site populations. Finally, it is interesting to note that both models predict that site II will be preferentially occupied as the cation number tends to zero. This means that residual cations in dealuminated faujasite would be located in sites II rather than in sites I', which is in contradiction with conventional wisdom, as pointed out earlier by Lievens et al. 5

Conclusion

We have used the Monte Carlo replica exchange (MCRE) algorithm to compute the sodium cation distribution in faujasite. The resulting distributions were found to be in very good agreement with both available experiments and the QC model of Mortier and co-workers.

The QC model has the advantage, over MC simulations, that it is simple and analytical. The assumptions of the model, however, are based on a preliminary knowledge of the cation site topology (the existence of I-I' nearest neighbor sites for instance). This is not the case for MC simulations, which could in principle be extended to any type of nanoporous materials, provided that the framework structure is known and that a decent cation force field is available.

The MCRE method is rather time-consuming. A drastic simplification of the method consists of using siteto-site hopping in a single (N,V,T) Monte Carlo simulation at room temperature. This enables one to jump over the potential energy barriers in the configuration space and leads to a rapid convergence of the MC simulations.

We have checked here that site-to-site hopping simulations yield essentially identical results as the more general MCRE method.

The main advantage of the MCRE method is that no assumption is needed on the actual cation adsorption sites. One could thus, in principle, predict cation locations and distributions in a zeolite for which the precise location of extraframework cations is not known.

We intend to implement this method into multicomponent adsorption calculations, in which at least one of the adsorbates is a polar molecule. Recently, Mellot and Cheetham 47 have carried out a neutron scattering study of CFCl3 adsorption in NaY. Cation redistribution was observed together with a new and previously unknown cation location. This is a typical situation in which the MCRE method could be useful, either for predicting cation distributions or for interpreting the experimental results.

Figure 1 .

 1 Figure 1. Schematic view of a faujasite supercage with the site I, I', II, and III locations.

Figure 2 .

 2 Figure 2. Potential energy distribution for the eight realizations of the system.

A

  . Cation Distributions from Parallel Tempering Simulations. Sodium cation occupancy of sites I, I', II, and III as a function of the cation number per unit cell at 300 K are shown in Figure 3a-d. The dotted line shows the prediction of the analytical "Quasi-Chemical" model of Mortier and co-workers, 10,25-27 which we will discuss in the next section.

Figure 3 .

 3 Figure 3. Sodium cation occupancy of sites I (a), sites I' (b), sites II (c), and sites III (d). Full line: parallel tempering simulations. Dotted line: QC model.

Figure 4 .

 4 Figure 4. Sodium cation occupancy of sites I (a), sites I' (b), sites II (c), and sites III (d) from CN = 48-96. Full line: parallel tempering simulations. Dotted line: QC model. Crosses: experiments. The letters correspond to the following references: m (ref 46), j (ref 3), e (ref 2), h (ref 7), z (ref 16), p (ref 17), v (ref 13), and o (ref 12).

∼Figure 5

 5 Figure 5 is shown the cation-framework potential energy in each site (regardless of the cation-cation interaction), as a function of the cation number. At low cation number (CN), site II is the most favorable adsorption site. This explains why cations preferentially occupy sites II from CN = 0 to approximately 20.

Figure 5 .

 5 Figure 5. Cation-framework potential energy as a function of the cation number CN for site I, I', II, and III.

  eI' -eI = -38.23 kJ mol -1 + 0.93 NAl eII -eI = -45.23 kJ mol -1 + 0.93 NAl w > 22 kJ mol -1

Figure 6 .

 6 Figure 6. Sites energy differences (eII -eI) and (eI' -eI) as a function of the cation number CN for the Monte Carlo simulations (MC) and the Quasi Chemical model (QC).

Acknowledgment. We acknowledge Florent Calvo, Wilfried Mortier, Juan de Pablo, and Pascal Pernot for fruitful discussions.