M C B Lira-Nogueira

V P Gilson

Valérie Nicolas

N S Santos-Magalhães

Dr Christine Vauthier
email: christine.vauthier@universite-paris-saclay.fr

Defining endocytic pathways of fucoidan-coated PIBCA nanoparticles from the design of their surface architecture

Keywords: Nanoparticles, PIBCA, fucoidan, cellular uptake, endocytic pathway Anionic emulsion polymerization, AMP: Actin mediated pathway, CLRs: C-type lectin receptors, Cm: Nanoparticle concentration in the dispersion expressed in g.mL -1, CME: Clathrin mediated endocytosis, CvME Caveolae mediated endocytosis, CCIP: Clathrincaveolae independant pathways, DH: Hydrodynamic diameter, FACS: Fluorescence activated cell sorting, FBS: Fetal bovine serum, IBCA: Isobutylcyanoacrylate, LRMP: Lipid raft mediated pathways, MeßCD: Methyl-ß-cyclodextrin, MTP: Microtubule mediated pathways, MWCO: Molecular weight cutoff, MR: Mannose receptor, NLRs Nanoparticles, PIBCA: Poly(isobutylcyanoacrylate), PRRs: Pattern recognition receptors, PDI: Polydispersity index, RREP: Redox radical emulsion polymerization, SR-A: Scavenger receptor type A, SRs: Scavenger receptors, TLRs: Toll-like receptors, ρ: volumetric mass of the nanoparticles

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Introduction

New-generation drugs, including peptides, proteins and nucleic acids such as DNA and RNA, need sophisticated delivery systems that can transport them to a specific intracellular compartment to exert their desirable therapeutic effect [START_REF] Kou | The endocytosis and intracellular fate of nanomedicines: Implication for rational design[END_REF][START_REF] Song | Plasmid DNA Delivery: Nanotopography Matters[END_REF][START_REF] Watson | Intracellular trafficking pathways and drug delivery: fluorescence imaging of living and fixed cells[END_REF][START_REF] Wu | Nanoparticle-Mediated Cytoplasmic Delivery of Messenger RNA Vaccines: Challenges and Future Perspectives[END_REF][START_REF] Zhao | Entry of nanoparticles into cells: the importance of nanoparticle properties[END_REF]. A recent example is that of the mRNA vaccines developed in the context of the COVID-19 pandemic which require cytoplasmic delivery of the mRNA in order for it to be effective [START_REF] Wu | Nanoparticle-Mediated Cytoplasmic Delivery of Messenger RNA Vaccines: Challenges and Future Perspectives[END_REF]. The use of nanosystems was essential for the success of these vaccines, demonstrating the formidable capacity of these carriers to achieve cytoplasmic delivery of active ingredients, including in clinical settings. As well as the lipid nanoparticles used in the design of the COVID-19 mRNA vaccines, nanoparticles prepared from polymers can also be used to deliver drugs to the cell cytoplasm. For example, nanoparticles composed of poly(isobutylcyanoacrylate) (PIBCA) have long been recognised as being able to allow cytoplasmic delivery of drugs, including anticancer molecules and nucleic acids, thereby opening the way to a wide range of therapeutic perspectives [START_REF] Chavany | Polyalkylcyanoacrylate nanoparticles as polymeric carriers for antisense oligonucleotides[END_REF][START_REF] Cavalcanti | Fucoidan-coated PIBCA nanoparticles containing oncocalyxone A: Activity against metastatic breast cancer cells[END_REF][START_REF] Couvreur | Polycyanoacrylate nanocapsules as potential lysosomotropic carriers: preparation, morphological and sorptive properties[END_REF][START_REF] Lambert | Polyisobutylcyanoacrylate nanocapsules containing an aqueous core as a novel colloidal carrier for the delivery of oligonucleotides[END_REF][START_REF] De Martimprey | Polymer nanocarriers for the delivery of small fragments of nucleic acids: oligonucleotides and siRNA[END_REF][START_REF] Merle | Safety and efficacy of intra-arterial hepatic chemotherapy with doxorubicin-loaded nanoparticles in hepatocellular carcinoma[END_REF][START_REF] Schwab | Antisense oligonucleotides adsorbed to polyalkylcyanoacrylate nanoparticles specifically inhibit mutated Ha-ras-mediated cell proliferation and tumorigenicity in nude mice[END_REF][START_REF] Soma | A clinically relevant case study: the development of Livatag ® for the treatment of advanced hepatocellular carcinoma[END_REF].

However, better control of the delivery of new drug candidates within cells that allows them to reach a well-defined intracellular compartment would be a great advantage for their activity. This could be achieved by controlling the intracellular trafficking of the nanoparticulate drug carrier by directing the carrier to a particular endocytic pathway for entering the cell [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF]. At present, incomplete understanding of the influence of the nanoparticle properties on their interactions with cells is a bottleneck to improving the design of carriers so that they can deliver their cargo to the desired intracellular compartment. Although this is a challenging subject, a better understanding on how the endocytic pathways of a nanomaterial can be manipulated by its properties would certainly open up tremendous perspectives towards achieving more efficient and precise intracellular delivery of drugs [START_REF] Watson | Intracellular trafficking pathways and drug delivery: fluorescence imaging of living and fixed cells[END_REF][START_REF] Zhao | Entry of nanoparticles into cells: the importance of nanoparticle properties[END_REF][START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Andrade | Modulation of Macrophages M1/M2 Polarization Using Carbohydrate-Functionalized Polymeric Nanoparticles[END_REF].

According to the literature, the intracellular destination of nanocarriers is affected by their physicochemical properties [START_REF] Kou | The endocytosis and intracellular fate of nanomedicines: Implication for rational design[END_REF][START_REF] Zhao | Entry of nanoparticles into cells: the importance of nanoparticle properties[END_REF][START_REF] Forest | Preferential binding of positive nanoparticles on cell membranes is due to electrostatic interactions: A too simplistic explanation that does not take into account the nanoparticle protein corona[END_REF][START_REF] Ghofrani | Development of Octreotide-loaded chitosan and heparin nanoparticles: evaluation of surface modification effect on physicochemical properties and macrophage uptake[END_REF]. The nanoparticle properties that alter internalization pathway are their surface chemistry, their chemical composition, their size, their surface charge expressed as the zeta potential, and their shape, but the endocytic pathway taken by the nanoparticles also depends on the cell type [START_REF] Zhao | Entry of nanoparticles into cells: the importance of nanoparticle properties[END_REF][START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Iversen | Endocytosis and intracellular transport of nanoparticles: Present knowledge and need for future studies[END_REF][START_REF] Souza De Almeida | Understanding nanoparticles endocytosis to improve targeting strategies in nanomedicine[END_REF]. As far as the nanoparticle surface design is concerned, the influence of the topography and the molecular architecture of the nanoparticle surface on interactions with biological systems remains poorly documented. However, clear effects have been observed in studies evaluating the in-vivo biodistribution [START_REF] Alhareth | Conformation of surface-decorating dextran chains affects the pharmacokinetics and biodistribution of doxorubicin-loaded nanoparticles[END_REF], the activation of the complement system by nanoparticles [START_REF] Coty | Tuning complement activation and pathway through controlled molecular architecture of dextran chains in nanoparticle corona[END_REF][START_REF] Hamad | Distinct polymer architecture mediates switching of complement activation pathways at the nanosphereserum interface: implications for stealth nanoparticles engineering[END_REF][START_REF] Peracchia | Complement consumption by poly(ethylene glycol) in different conformations chemically coupled to poly(isobutyl 2cyanoacrylate) nanoparticles[END_REF] and the entry of nanomedicines into cells [START_REF] Song | Plasmid DNA Delivery: Nanotopography Matters[END_REF]. An improvement of our knowledge about the influence of the nanomaterial surface properties at a molecular level on the cell entry pathway has become central to optimizing intracellular delivery of drugs [START_REF] Kou | The endocytosis and intracellular fate of nanomedicines: Implication for rational design[END_REF][START_REF] Souza De Almeida | Understanding nanoparticles endocytosis to improve targeting strategies in nanomedicine[END_REF][START_REF] Muro | Alterations in Cellular Processes Involving Vesicular Trafficking and Implications in Drug Delivery[END_REF][START_REF] Oh | Endocytosis and exocytosis of nanoparticles in mammalian cells[END_REF][START_REF] Sahay | Endocytosis of nanomedicines[END_REF].

In a previous work, we described differences in cytoplasmic accumulation within J774A.1 macrophage-like cells of a series of nanoparticles made of PIBCA differing by their surface content in fucoidan, a sulfated polysaccharide [START_REF] Zhao | Fucoidan reduces lipid accumulation by promoting foam cell autophagy via TFEB[END_REF], and also by the molecular architecture of the polysaccharide chains on the nanoparticle surface [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. Fucoidan was chosen because this polysaccharide is recognized by macrophage scavenger receptors (MSR). Based on the results, it was postulated that entry into cells of these fucoidan-coated nanoparticles might be increased compared with uncoated nanoparticles and occurred through different internalization pathways according to the nature of the nanoparticle surface. The present work was aimed at deciphering the internalization pathways taken by these nanoparticles in J774A.1 macrophages, a cell line commonly used to study various aspects of nanoparticle uptake [START_REF] Wang | Scavenger receptor mediated endocytosis of silver nanoparticles into J774A.1 macrophages is heterogeneous[END_REF]. It was designed to improve our understanding on the intracellular entry mechanisms and how this could be controlled by the surface design of the nanoparticles. Experiments were carried out in the presence of proteins contained in the fetal bovine serum (FBS) routinely added to the cell culture medium. It investigated the energy dependency of the intracellular uptake mechanisms, the uptake after a short contact time of the nanoparticles with the cells and the endocytosis of the nanoparticles in presence of inhibitors of different endocytic pathways. The internalization of fucoidan-coated nanoparticles by the cells was monitored using confocal microscopy and fluorescence activated cell sorting (FACS) as described previously [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Souza De Almeida | Understanding nanoparticles endocytosis to improve targeting strategies in nanomedicine[END_REF].

Materials and Methods

Materials

Isobutylcyanoacrylate (IBCA) was a gift from Henkel Biomedical (Dublin, Ireland). Dextran (Mw 66900) was purchased from Sigma (Saint Quentin Fallavier, France). Cerium (IV) from cerium (IV) ammonium nitrate was purchased from Fluka (Saint Quentin Fallavier, France). Polyfluor ® 570 (methacryloxyethyl thiocarbamoyl rhodamine B) was supplied from Polyscience (Biovalley, Marne la Vallee, France). Fucoidan was extracted and purified from Fucus vesiculosus according to the method described by Lira et al., 2011 (28). Endocytic pathway inhibitors (cytochalasin D, genistein, chlorpromazine and nocodazol) were purchased from Sigma Aldrich, and methyl-ß-cyclodextrin (MeßCD) was provided by Wacker Chemical.

Methods

Preparation of the PIBCA nanoparticles

Nanoparticles bearing a coating layer of dextran and/or fucoidan were prepared by anionic or redox radical emulsion polymerization [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. To synthesize the nanoparticles by anionic emulsion polymerization (AEP), the polysaccharides in various proportions (dextran 100%, fucoidan/dextran 25/75, fucoidan 100%) (50 mg) were dissolved in 10 mL Milli-Q ® water the pH of which was adjusted to 2.5 with 0.1 M HCl. The solution was placed under magnetic stirring (1000 rpm, at room temperature) and subsequently, 100 µL of monomer IBCA were added. A solution of Polyfluor ® 570 (100 µL, 5 mg.mL -1 in acetonitrile:water, 1:1) was added 5 min after the addition of IBCA. The system was left to polymerize for a total of 3 hours to obtain a dispersion of PIBCA nanoparticles. To prepare nanoparticles by redox radical emulsion polymerization (RREP), the polysaccharides in various proportions (dextran 100%, fucoidan/dextran 25/75) (135.6 mg) were dissolved in 9.3 mL of nitric acid and maintained at 40 °C under stirring with nitrogen bubbling for 10 minutes. Then, under strong magnetic stirring (1500 rpm), 0.7 mL of cerium (IV) ammonium nitrate (0.08 M in 0.2 M nitric acid) and immediately after 0.5 mL of monomer IBCA were added. One mL of a solution of Polyfluor ® 570 (2 mg.mL -1 , acetonitrile:water, 1:1) was added 2 minutes after the addition of IBCA. The system was left to polymerize at 40 °C for 1 hour. The PIBCA nanoparticle dispersion obtained was cooled to room temperature using an ice bath.

Nanoparticles were designated Ax and Rx depending on the preparation method, AEP and RREP respectively, where x was the percentage of fucoidan introduced into the formulation.

Purification of the nanoparticles

Nanoparticles were purified by dialysis using a membrane with a molecular weight cut off (MWCO) of 100,000 g.mol -1 (Spectrapor ® membrane, width: 16 mm; diameter: 10 mm; Biovalley, Marne la Vallee, France). The dialysis was performed against distilled water to eliminate all unused reagents and also to neutralize the formulation. The distilled water (1 L) was changed twice after 30 minutes and once before overnight dialysis. Purified nanoparticles were stored at 4 o C until use.

PIBCA nanoparticle characterization

All nanoparticles were characterized by evaluating their size, expressed as the mean hydrodynamic diameter (DH), their polydispersity index (PDI), their zeta potential and the nanoparticle concentration. The diameter and zeta potential were determined using a Zetasizer (Malvern Instrument, UK), after diluting the nanoparticles in water and KCl (1 mM), respectively. Nanoparticle concentration was determined by evaluating the weight of the dried residue obtained after lyophilization of a sample of 200 µL of nanoparticle dispersion. To perform the lyophilization, the sample was frozen at -20°C and the lyophilization was carried out under vaccuum (10 -4 Bar) for 24 hours using an Alpha 1-2 LD plus freeze dryer apparatus (Bioblock Scientific). The concentration in nanoparticles, Cm, obtained from this determination was given in mg.mL -1 . Equation 1 was used to convert Cm in a concentration in number of nanoparticles per mL, N.

𝑁

Equation 1

In which, DH was the mean hydrodynamic diameter of the nanoparticles determined by DLS and ρ the volumetric mass of the nanoparticles (ρ = 1.14 g.cm -3 (30)).

Cell culture experiments

The macrophage-like J774A.1 cell line (ATCC® TIB-67™) supplied by ATCC (Manassas, USA) was used in this work. Cells were grown in a 5 % CO2 atmosphere at 37 o C in complete RPMI medium (RPMI medium (Gibco, Cergy-Pontoise, France) supplemented with 10% FBS (Gibco, Cergy-Pontoise, France), Penicillin 50 IU/mL, Streptomycin 50 UI/mL). Experiments were performed between the eighth and the fourteenth passages. Viable cells were counted in a hemocytometer (Glasstic ® slide) to adjust the cell concentration to 1 x 10 5 viable cells/well for use in further experiments. To evaluate the uptake of PIBCA nanoparticles by the J774A.1 macrophages, the nanoparticles were added at a concentration of 3 x 10 10 NP/well in wells containing 1 x 10 5 cells. The nanoparticle concentration used in this work was considered as non cytotoxic as being below the IC50 (approximately 10 μg.mL -1 ) reported by Lira et al. [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. Incubation conditions depended on the type of evaluation and are explained in sections 2.2.4.1. and 2.2.4.2.

Energetic dependency of nanoparticle uptake and influence of the duration of the incubation.

The cells were seeded in a TPP 6-well plate (1 x 10 5 cells/well) and incubated at 37 o C and 5% CO2 for 24 hours in complete RPMI medium (as described above). Then, the culture medium was changed and the plates was placed at 37 o C. Pre-equilibrated nanoparticles (1 x10 3 NP.mL -1 ) at 37 °C were then added to each well and maintained at the predefined temperature for 1 hour. Similar experiments were carried out in parallel by incubating the cells with the nanoparticles at +4 °C to evaluate the influence of the energy-dependent mechanisms on the uptake of nanoparticles. The uptake of nanoparticles after a short-term incubation was evaluated after 10 minutes of incubation with the cells at 37 °C, using flow cytometry and confocal microscopy. All assays were performed and analyzed in duplicate.

Investigation of endocytic pathways of PIBCA nanoparticles using endocytic pathway inhibitors

Five pharmacological inhibitors of endocytic pathways and their concentrations to be used in our experiments were chosen from a litterature review (Table S1 -Supplementary material). They were used at the following concentrations in the present experiments: chlorpromazine, an inhibitor of the clathrin-dependent pathway (28 µM), genistein, an inhibitor of the caveolae-dependent pathway (200 µM), cytochalasin D, an inhibitor of the macropinocytosis and actin-mediated endocytosis pathways (40 µM), MeßCD known for depleting lipid rafts (3000 µM) and nocodazole, an inhibitor of the microtubule-mediated pathway (10 µM). For these experiments, the cells were seeded in a TPP 6-well plate (1 x 10 5 cells/well) and incubated at 37 o C and 5 % CO2 for 24 hours in complete RPMI medium. Then, 250 µL of one of the endocytic pathway inhibitor solutions was added to the wells and the cells were incubated for a further 30 min at 37 °C. Thereafter, nanoparticles at a final concentration of 3 x 10 10 NP.mL -1 in culture medium were added and the cells were incubated for another 1 hour at 37 °C. After incubation, the uptake of the nanoparticles by the cells was evaluated by flow cytometry and confocal microscopy. Results were expressed as relative fluorescence comparing the fluorescence due to the nanoparticles taken up by the cells incubated in the presence of endocytic pathway inhibitors with that of cells incubated in the same conditions but without the endocytic pathway inhibitor. All experiments were performed in duplicate.

Evaluation of the uptake of nanoparticles by the cells 2.2.5.1. Flow cytometry

After incubation with the nanoparticles under the different conditions, the cells were washed three times with culture medium and detached using a scrapper. The cell suspension obtained was transferred to Eppendorf ® type microtubes (300 µL) and analyzed by flow cytometry (MoFlo XDP (Beckman Coulter) driven by the Summit software). Each analysis considered 10,000 cells measured in each sampling gate.

Live cell confocal microscopy

For live cell confocal microscopy, J774A.1 macrophages (1 x 10 5 cells/well) were grown on a 25 mm glass coverslip placed in a 6-well plate for 48 hours at 37 o C and 5% CO2. All incubation condition were as those explained above in section 2.2.4.

To test cell viability, calcein AM (Life Technologies) was used. Calcein AM is a non fluorescent compound but when it penetrates into living cells, it is hydrolysed by intracellular esterases producing a strongly fluorescent calcein species in the cytoplasm of the cells. To highlight living cells during the confocal microscopy observations, 200 µL of calcein AM (3 µM) (Life Technologies) were added directly to cells and incubated for 5 minutes at room temperature, protected from light. Then, the glass coverslip was transferred into an Attofluor ® cell chamber for visualization. A sample of 100 µL of each type of nanoparticles and 1 mL of fresh culture medium were added, achieving a final concentration of 3 x 10 10 NP.mL -1 . The cells were observed for 1 hour. The assay was performed twice for each nanoparticle, and the image analysis was performed with Image J (version 1.49o) software (NIH, USA) at 10 different positions on each sample (up to 100 cells/sample). The images were acquired using an inverted confocal laser-scanning microscope LSM 510-Meta (Carl Zeiss, Germany) using a Plan-Apochromat 63X/1.4 objective lens, equipped with an argon (488 nm excitation wavelength) and a helium-neon laser (543 nm excitation wavelength).

The green and the red fluorescence emissions were collected with a 505-550 nm bandpass and a 560 nm long-pass emission filter respectively, under a sequential mode. DIC (Differential Interferential Contrast) images were obtained simultaneously with the green channel. The pinhole was set at 1.0 Airy unit. 12-bit numerical images were acquired with LSM 510 software version 3.2. For each condition, a 1-hour time lapse was applied and for each time point, a z-stack of images was collected every 4 µm along the z-axis from the up level (1 st zstack) to bottom (40 th z-stack). The 19 th z-stack corresponds to the z-stack in the middle of the cells. All observations were made with same settings of the camera to allow fluorescence analysis in comparable conditions.

Statistical Analysis

Data were plotted in Prism Software (GraphPad Software 7, La Jolla, CA, USA) and statistical significance was calculated by Student t-test and expressed as: ** (p < 0.05), or **** (p < 0.0001).

Results and discussion

In a previous work, we reported differences in the intracellular accumulation of a series of PIBCA nanoparticles in the well-known J774A.1 macrophage cell line [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. These PIBCA nanoparticles differed by the ratio between fucoidan and dextran at their surface and by the molecular architecture of the polysaccharides grafted on the surface depending on the method of polymerization used to prepare the nanoparticles [START_REF] Bertholon | Characterization of Dextran-poly(isobutylcyanocrilate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF][START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanocrylate) nanoparticles: influences if surface morphology, length and type of polysaccharide[END_REF][START_REF] Zandanel | Poly(isobutylcyanoacrylate) nanoparticles decorated with chitosan: effect of conformation of chitosan chains at the surface on complement activation properties[END_REF]. Differences in the intracellular distribution of these nanoparticles in the J774A.1 macrophage cell line have been reported, suggesting that they might enter cells by different endocytic pathways. Unraveling the mechanisms involved in the internalization of nanoparticles by cells would be of great value in designing drug carriers that could enter cells by a specific pathway and improve drug delivery to the desired intracellular compartment, such as the cell cytoplasm. Thus, the present work was aimed to study nanoparticle internalization and decipher the mechanisms by which each type of nanoparticles in this series were endocytosed in the J774A.1 macrophage cell line.

Properties of the PIBCA nanoparticles

As shown in Table 1, the properties of the nanoparticles synthesized for this work were consistent with those described in our previous work [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF] as a result of the high reproducibility generally observed with the methods of nanoparticle synthesis employed. The hydrodynamic diameter (nm) of the nanoparticles increased when the amount of fucoidan used in the polysaccharide mixture increased. In contrast, the zeta potential decreased with increasing fucoidan content. This could be explained by the negative charges carried by the fucoidan chains. This increase of the absolute value of the zeta potential reflects an increase of the charge density around the nanoparticles and this could explain the increase in size of the nanoparticles due to an increase in the repulsion between polysaccharide chains grafted on the nanoparticle surface. This effect could contribute to an expansion of the polysaccharide corona surrounding the nanoparticle core and hence the nanoparticle size, as suggested in a previous work considering PIBCA nanoparticle prepared with other charged polysaccharides [START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanocrylate) nanoparticles: influences if surface morphology, length and type of polysaccharide[END_REF]. As shown previously, the nanoparticles presented a spherical shape with core-corona structure [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. The nanoparticle surface design is illustrated on the Figure 1 based on previous results [START_REF] Bertholon | Characterization of Dextran-poly(isobutylcyanocrilate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF][START_REF] Zandanel | Poly(isobutylcyanoacrylate) nanoparticles decorated with chitosan: effect of conformation of chitosan chains at the surface on complement activation properties[END_REF]. With exception of R100, which formed aggregates and was therefore discarded, all the other preparations produced dispersions of nanoparticles with hydrodynamic diameters above 200 nm. According to the literature [START_REF] Zhao | Entry of nanoparticles into cells: the importance of nanoparticle properties[END_REF][START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Souza De Almeida | Understanding nanoparticles endocytosis to improve targeting strategies in nanomedicine[END_REF], nanoparticles in this size range would be taken up by cells by macropinocytosis or phagocytosis pathways. However, as well as size, other physicochemical properties of nanoparticles, such as shape, surface composition and charge density, can influence their cell internalization [START_REF] Verma | Effect of surface properties on nanoparticle-cell interactions[END_REF][START_REF] Wang | The impact of nanoparticle shape on cellular internalisation and transport: what do the different analysis methods tell us?[END_REF], emphasizing the importance of analyzing the whole picture. Several cell membrane proteins like clathrin and dynamin can play a crucial role in the endocytic pathways but, due to the nanoparticle size, pathways involving caveolae would not be expected to be involved based on the current understanding of this mechanism. The zeta potential of the fucoidan-bearing nanoparticles was negative, varying in magnitude depending on the fucoidan composition at the nanoparticle surface. It is noteworthy that the zeta potential of the nanoparticles A25 and R25 was quite different although these nanoparticles had the same fucoidan content in the corona (25%). A more negative value was observed with A25, about 2-fold lower (ζ(A25) = -33.2 ± 0.4, ζ(R25) = -14.0 ± 0.3), in which the fucoidan chains were expected to adopt a loop and train configuration which would expose a high proportion of the negative charges of the fucoidan chains to the dispersing media (Figure 1). In contrast, on the surface of the nanoparticle R25, the fucoidan and dextran chains grafted by one end to the nanoparticle core would form a dense brush in which the negative charges of the fucoidan might be hidden, resulting in a lower absolute value of zeta potential. The configuration in loops or brush of polysaccharide chains grafted on PIBCA nanoparticle surfaces prepared by the AEP and RREP methods respectively was demonstrated in previous studies considering dextran-coated and chitosan-coated nanoparticles [START_REF] Bertholon | Characterization of Dextran-poly(isobutylcyanocrilate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF][START_REF] Zandanel | Poly(isobutylcyanoacrylate) nanoparticles decorated with chitosan: effect of conformation of chitosan chains at the surface on complement activation properties[END_REF].

Evaluation of the uptake of the different PIBCA nanoparticles by the J774A.1 macrophage cell line

Preliminary experiments performed to evaluate the uptake of the nanoparticles by the J774A.1 macrophage cell line used the same incubation conditions as in previous work (37 °C, 1 hour) [START_REF] Lira | Cytotoxicity and cellular uptake of newly synthesized fucoidan-coated nanoparticles[END_REF]. Differences in the uptake of the nanoparticles by the cells were observed when comparing nanoparticles with different content of fucoidan within the series A and R as well as nanoparticles from series A and R with the same fucoidan content (Figure 2B). Living cell confocal microscopy showed that all types of PIBCA nanoparticles considered in this work were internalized by J774A.1 macrophages. The fluorescence was spread throughout the cell thickness, indicating that nanoparticles were able to penetrate cells and be distributed within them (Figure 2B and Figure 3). Image analysis of the confocal micrographs highlighted marked differences in the uptake of nanoparticles by the cells depending on their content in fucoidan, as seen in Figure 2A and B (10 and 60 minutes of incubation, respectively) and their type A or R at identical fucoidan content (Figure 4). The results from these sets of experiments were consistent with those of our previous work. They also supported the hypothesis that the uptake of the nanoparticles by the cells occurred through different pathways depending on the composition and molecular architecture of their surface. While conclusions from the two works were consistent, we could not compare the data on a quantitative basis due to slight changes introduced into the experimental protocols in the present study. Indeed, in our previous work, the uptake of nanoparticles by cells was evaluated from confocal microscopy images of cells fixed with paraformaldehyde while this was carried out on living cells in the present study. Another difference between the two studies was the expression of the concentration in nanoparticles to which cells were exposed.

Figure 4 shows the cellular uptake of the different nanoparticles. In Figure 4A confocal images show the nanoparticle internalization in a qualitative way and the differences in fluorescence intensity are clearly illustrated in the 3D graph (Figure 4B). The differences were confirmed after quantification measuring the fluorescence of at least 100 cells from 10 different places in each sample (Figure 4C).

Marked differences in the fluorescence of the J774A.1 macrophages was revealed depending on the type of nanoparticles with which they were incubated. When incubated with nanoparticles without fucoidan prepared by AEP method (A0), the cells showed lower fluorescent intensity per cell when compared with those incubated with R0, prepared by the RREP method (74 ± 10 and 401 ± 86 fluorescent arbitrary unit/cell, respectively), although both presented low uptake when compared with fucoidan-coated nanoparticles. Indeed, the fluorescence intensity increased by 48-and 47-fold when comparing the uptake of A25 and A100, respectively with that of nanoparticles without fucoidan (i.e. A0) and 3-folds when R25 was compared with R0 nanoparticles. Additionally, for A25 and A100 nanoparticles, the fluorescence was mainly observed homogeneously distributed in the cytoplasm of the cells. However, a punctuate fluorescence was also observed in both calcein and merged images (Figure 4A) suggesting that nanoparticles were sequestered within endosomal/lysosomal compartments [START_REF] Teo | Unravelling cytosolic delivery of cell penetrating peptides with a quantitative endosomal escape assay[END_REF][START_REF] Wong | Self-assembling dual component nanoparticles with endosomal escape capability[END_REF]. Although the fluorescence intensity was lower, the nanoparticles R0 and R25 also presented punctuated fluorescence inside the cells. Generally, no fluorescence was observed at the cell surface, except with the nanoparticles R25. The decrease in the fluorescence intensity of calcein observed while the fluorescence intensity of rhodamine increased was probably due to the fluorescence resonance energy transfer (FRET) phenomenon in which rhodamine and calcein can be considered as acceptor and donor, respectively [START_REF] Thompson | Fluorescence Sensors and Biosensors[END_REF]. The marked difference of intracellular uptake found between nanoparticles without fucoidan and those with fucoidan could be related to their zeta potential. As shown in Figure 5, nanoparticles that are close to neutrality, A0 and R0, (zeta potential -5.5 ± 0.3 and -5.2 ± 0.4 mV, respectively) seem to undergo lower cellular uptake than the negatively charged nanoparticles. The difference in the fluorescence intensity between these cells indicates that the nanoparticles A0 and R0 were not equivalent despite their similar size, surface composition and charge (Table 1). The difference in the cellular uptake can be explained by the distinct molecular arrangement of the polysaccharide chains at the surface of these two nanoparticle formulations as illustrated in Figure 1 as determined in previous work [START_REF] Bertholon | Characterization of Dextran-poly(isobutylcyanocrilate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF].

It was also observed in Figure 5A that cells incubated with the most negatively charged nanoparticles (A25 and A100 zeta potential -33.2 ± 0.4 mV and -55 ± 1 mV, respectively) presented the highest fluorescence intensity. Despite divergent studies concerning the influence of surface charge on nanoparticle internalization, the literature suggests that positively charged nanoparticles are the most internalized [START_REF] Souza De Almeida | Understanding nanoparticles endocytosis to improve targeting strategies in nanomedicine[END_REF][START_REF] Foroozandeh | Insight into cellular uptake and intracellular trafficking of nanoparticles[END_REF]. This is in contrast with our result, but the charge is not the only factor that influences nanoparticle internalization by cells; it may also be influenced by their composition [START_REF] Jeon | Surface Charge-Dependent Cellular Uptake of Polystyrene Nanoparticles[END_REF]. In this respect, the use of fucoidan as a coating molecule in these experiments, in addition to its arrangement on the surface of nanoparticles, markedly influenced the uptake by J774A.1 macrophages.

Figure 5. Comparison between nanoparticle uptake as a function of zeta potential (A) and particle size (B). Squares represent R nanoparticles with fucoidan (red square) and without fucoidan (red open square). Circles represent A nanoparticles with fucoidan (full circles) and without fucoidan (open circle).

Observations of fluorescence differences between cells incubated with A25 and R25 provided further evidence that the molecular arrangement of the polysaccharide on the surface of nanoparticles influenced the internalization of the nanoparticles by the cells (Figure 5). This was new additional evidence that the architectural disposition of polysaccharide on the surface of nanoparticles can promote different biological behavior, as suggested by other reports in the literature [START_REF] Alhareth | Conformation of surface-decorating dextran chains affects the pharmacokinetics and biodistribution of doxorubicin-loaded nanoparticles[END_REF][START_REF] Coty | Tuning complement activation and pathway through controlled molecular architecture of dextran chains in nanoparticle corona[END_REF][START_REF] Hamad | Distinct polymer architecture mediates switching of complement activation pathways at the nanosphereserum interface: implications for stealth nanoparticles engineering[END_REF]. The nanoparticles A25 were internalized 3-fold more than R25 (fluorescence intensity per cell 3,6 x 10 3 and 1,2 x 10 3 , respectively) although they were of similar size. Both nanoparticles contained 25% fucoidan in their corona but, because of the spatial configuration of the polysaccharide chains at the nanoparticle surface, the negative charges of fucoidan were largely exposed on A25, while on the surface of R25 nanoparticles they may be hidden (Figure 1). The difference in the exposure of the negative charge of fucoidan at the surface of the nanoparticles could be one reason explaining the differences in intracellular uptake observed between these nanoparticles. Furthermore, it is noteworthy that fucoidan is a known substrate of the Scavengers Receptors (SR), especially type A (SR-A) found on macrophages. These types of receptors are present on the J774A.1 cell line [START_REF] Wang | Scavenger receptor mediated endocytosis of silver nanoparticles into J774A.1 macrophages is heterogeneous[END_REF][START_REF] Yu | Scavenger receptor A (SR-A) is required for LPS-induced TLR4 mediated NF-κB activation in macrophages[END_REF]. These are primary endocytic receptors internalizing a number of substances including fucoidan as a sulfonated polysaccharide [START_REF] Hamasaki | Effects of scavenger receptors-1 class A stimulation on macrophage morphology and highly modified advanced glycation end product-protein phagocytosis[END_REF][START_REF] Verma | Surfacestructure-regulated cell-membrane penetration by monolayer-protected nanoparticles[END_REF]. These receptors could be involved in the uptake of fucoidan-coated nanoparticles by the J774A.1 macrophage cell line with a different uptake efficiency depending on the conformation of the fucoidan chains that could affect the accessibility of the fucoidan chain to the active site of the receptor. The relationship between the cell fluorescence and the volume of nanoparticles (v = 1/6 × π × DH 3 ) was examined as detailed in Figure 6. Differences were observed in the normalized uptake, again suggesting that each type of nanoparticles presented a distinct internalization mechanism. These results are consistent with the profile in Figure 4C. The size influenced cell uptake as discussed previously (Figure 5), and it can be noted that, once again, the results indicated that the disposition of fucoidan on nanoparticle surface influenced cell internalization. 1).

Evaluation of the energetic dependency of the internalization mechanisms of PIBCA nanoparticles by the cells.

Based on the results of the confocal microscopy presented above, the fluorescence of the cells measured by flow cytometry was interpreted as due to the cellular uptake of the nanoparticles. Variation of cell fluorescence measured by flow cytometry with the different nanoparticles shown on Figure 7 (data at 37°C) were consistent with those observed from image analysis of confocal micrographs (Figure 4). The possibility of an energy-dependent internalization mechanism was evaluated by reducing the temperature of the incubation of the cells to 4 °C, thereby cellular metabolism. As shown in Figure 7A, the median fluorescence intensity of cells incubated with A0 and R0 at 4° C was considerably reduced compared with the fluorescence of cells incubated with the same nanoparticles at 37 °C. These reductions were 8-and 4-fold for A0 and R0 nanoparticles respectively, giving evidence of the participation of energy-dependent endocytic mechanisms for their uptake by J774A.1 macrophages. In contrast, the association of nanoparticles A100 with J774A.1 macrophages did not appear to be different in cells incubated at the two temperatures, indicating that cells internalized these nanoparticles through energy-independent mechanisms. The results with nanoparticles A25 and R25 were intermediate. The fluorescence of the cells was reduced 0.5-and 1.5-fold respectively when the fluorescence of cells incubated at 4 °C was compared with those incubated at 37°C, suggesting that both energy-dependent and independent mechanisms were involved in their internalization by J774A.1 macrophages. Previously, Verma and Stellacci (34) described similar temperature-sensitive behavior for nanoparticles coated with a shell of hydrophobic and anionic ligands arranged in ribbonlike domains. The same authors reported that an organized, rather than random, arrangement of molecules on the surface of nanosystems provided unexpected surface properties [START_REF] Verma | Surfacestructure-regulated cell-membrane penetration by monolayer-protected nanoparticles[END_REF]. They observed that nanoparticles penetrated cell membranes both at 37 o C and 4 o C but at different levels, with higher internalization at 37 o C, and they suggested that the structural organization of nanoparticle surfaces influenced cell-membrane penetration [START_REF] Verma | Effect of surface properties on nanoparticle-cell interactions[END_REF]. In this study, differences between nanoparticle types (A and R) and also between nanoparticles of same type but with (A25 and R25) and without fucoidan (A0 and R0) were observed. Based on the energy dependency of the R0 and A0 internalization process by macrophages we can infer that an endocytic mechanism could be the dominant route of internalization of these nanoparticles. Concerning R25 and A25, which showed only a partial reduction of the fluorescence of the cells at 4 °C, other mechanisms that are not dependent on energy were involved, as well as energydependent endocytic mechanisms. The fact that A100 entered cells by an energy-independent mechanism suggested that the uptake mechanism differed from the usually observed endocytosis pathways that are energy-dependent. The results were consistent with mechanisms which involve receptors, as was assumed earlier with respect to nanoparticles decorated with fucoidan (see section 4.2.1).

Influence of reducing the incubation time on the uptake of the PIBCA nanoparticles by the cells.

According to the literature, nanoparticles can be internalized by cells through different pathways that proceed at different rates [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF]. Watanabe and Boucrot [START_REF] Watanabe | Fast and ultrafast endocytosis[END_REF] have focused their review paper on clathrin-independent endocytic process that are fast endocytic pathways in comparison with clathrin-mediated endocytosis processes which are considered too slow to internalize proteins from the cell surface during some physiological processes. To evaluate the rapidity at which the nanoparticles were internalized by cells, complementary experiments were performed using a shorter incubation time (10 min vs 1 hour at 37 °C) (Figure 7C,D). Results from confocal microscopy (Figure 2A) and flow cytometry (Figure 7C,D) showed that all types of nanoparticles can be observed to have been taken up by J774A.1 macrophages after 10 min of incubation (Figure 2A,7A,C). For nanoparticles A0, A25 and R0, the amount of fluorescence associated with the cells after 10 min and 1 hour was quite similar (Figure 2 and Figure 7A,C). In contrast, the fluorescence increased between 10 min and 1 hour with A100 nanoparticles and decreased dramatically for R25 nanoparticles. The differences noted between these groups of nanoparticles indicated marked differences in their rate of endocytosis. The dramatic reduction of fluorescence observed when cells were incubated with R25 nanoparticles suggested an internalization by cells through a fast process. However, after having been internalized by the cells, the nanoparticles were rapidly eliminated from the cells. In contrast, the steady-state level of fluorescence shown by the cells incubated with A0, A25 and R0 nanoparticles indicated that these nanoparticles were taken up by cells through a rapid mechanism and largely remained in the cells after having been captured. However, it cannot be excluded that the constant level of cell fluorescence observed between 10 min and 1 hour was the reflection of a state of equilibrium between efflux and capture mechanisms compensating each other. Only the fluorescence of the cells incubated with A100 nanoparticles increased between 10 min and 1 hour incubation indicating that their uptake by J774A.1 macrophages occurred by a slow process. The result observed with the nanoparticles R25 was intriguing, suggesting that the nanoparticles could be internalized well by the cells but followed an intracellular pathway which finally led to their elimination from the cells; that is, favoring nanoparticle efflux from the cells.

Elucidation of the endocytic pathways using endocytic pathway inhibitors

All the results reported above support our previous observation that the different types of nanoparticles were taken up by the J774A.1 macrophages by different routes. This last part of the work was designed to elucidate the different pathways by which nanoparticles penetrated cells in more detail. Different internalization pathways were investigated by incubating cells with pharmacological inhibitors known to block specific endocytic pathways. However, there are several limitations to this approach [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF]. For example, when a given endocytic pathway is blocked, another can be activated to compensate. Furthermore, some pharmacological inhibitors are not very specific, making it impossible to identify the endocytosis pathway precisely. Despite these challenges, this approach remains the most frequently used for this type of study.

The fluorescence associated with the cells incubated with the nanoparticles in the presence of inhibitors of endocytic pathways was monitored by both flow cytometry (Figure 8) and confocal microscopy (Figure 9), and compared with the signal obtained when cells were incubated in similar conditions without the inhibitors. It was assumed that the blockage of the preferred routes of entry of the nanoparticles would significantly reduce their accumulation in the cells hence the fluorescence of the cells. The uptake of each nanoparticle type was affected in a different fashion by the endocytic pathway inhibitors. The internalization of the nanoparticles A0 , those prepared without fucoidan, was almost completely inhibited by chlorpromazine (6.3 ± 0.7%), genistein (7.0 ± 1.0%) and MeßCD (5.5 ± 0.4%) while cytochalasin D (34 ± 9%) and nocodazole (56 ± 2%) only partially inhibited their uptake by the cells. Inhibition of the uptake of the nanoparticles R0 followed the same general pattern but with lower levels of inhibition. These results suggested that the preferred route of endocytosis of the A0 nanoparticles was the clathrin-mediated pathway (CME). These nanoparticles could also penetrate cells by caveolin (CvME) and clathrin-caveolae independent pathways but at a lower extent than by CME. This is consistent with previous observations that an endocytic pathway involving caveolae is taken by small-sized nanoparticles [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Iversen | Endocytosis and intracellular transport of nanoparticles: Present knowledge and need for future studies[END_REF]. Clathrin and clathrin-caveolae independent pathways, in that order, were the preferred routes for the internalization of R0 nanoparticles. The endocytic pathways identified for A0 and R0 are energy-dependent, which is coherent with the conclusion of the experiments described above when cells were incubated with the nanoparticles at 4 °C (Figure 7A andB). In contrast, the uptake of fucoidan-coated nanoparticles A25 and R25 was less affected by the presence of endocytic pathway inhibitors and, in the case of A100 nanoparticles, not affected at all. The general lower effect of the inhibitors meant that the nanoparticles were able to bypass, at least in part, endocytic pathways, entering J774A.1 macrophages by other energyindependent mechanisms, in accordance with the results reported above (Figure 8). The partial inhibition of the endocytic pathways recorded with A25 and R25 nanoparticles indicated that these nanoparticles were taken up by the J774A.1 macrophages by endocytic and non-endocytic pathways working concomitantly but at different extents. In contrast, since no endocytic pathway inhibitors prevented the uptake of the A100 nanoparticles, it can be assumed that they were taken up almost exclusively through non-endocytic pathways. Given that the particle diameter of A100 is around 500 nm, phagocytic routes could be involved [START_REF] Rennick | Key principles and methods for studying the endocytosis of biological and nanoparticle therapeutics[END_REF][START_REF] Iversen | Endocytosis and intracellular transport of nanoparticles: Present knowledge and need for future studies[END_REF], during which non-opsonic receptors interact with the surface of nanoparticles. These are known as pattern recognition receptor-mediated pathways (PRRs). According to the literature, these include scavenger receptors (SRs), Toll-like receptors (TLRs) and nucleotide-binding domain leucinerich repeat-containing receptors (NLRs) [START_REF] Hirota | Endocytosis of Particle Formulations by Macrophages and Its Application to Clinical Treatment[END_REF]. PRRs are functional in the J774A.1 cell line with some of these receptors recognizing carbohydrate patterns. For example, the macrophage scavenger receptors A (SR-A) can internalize polyanionic compounds like negatively charged carbohydrates such as fucoidan [START_REF] Verbij | The class I scavenger receptor CD163 promotes internalization of ADAMTS13 by macrophages[END_REF]. Through this pathway, nanoparticles are expected to accumulate in the cytoplasm, in agreement with what was observed in the Figure 4A [START_REF] Shannahan | Implications of scavenger receptors in the safe development of nanotherapeutics[END_REF]. Other receptors, including the C-type lectin receptors (CLRs) and the mannose receptor (MR), can bind the fucose moieties of which fucoidan is composed. Binding to these receptors depends on both the negative charge of the molecule and the density of charge. It can be assumed that the nanoparticles containing fucoidan in their corona could be taken up by the J774A.1 macrophages as a result of interactions with such PRRs. However, the extent by which these nanoparticles were taken up by different entry routes also depended on other properties of the nanoparticles. All the endocytic pathways studied in this manuscript (CME, CvME, CCIP, etc) can direct nanoparticles to endosomes [START_REF] Manzanares | Endocytosis: The Nanoparticle and Submicron Nanocompounds Gateway into the Cell[END_REF]. This was evident from the punctuate fluorescence observed on the confocal fluorescence microscopy images shown in Figures 3 and4A.

For this series of nanoparticles, the balance of their uptake by endocytic and nonendocytic pathways clearly depended on the properties of the nanoparticles. An increase of the internalization of the nanoparticles through non endocytic routes was linked to (i) an increase in size of the nanoparticles, (ii) an increase of the absolute value of the negative zeta potential indicating an increase of the negative charge density at the surface of the nanoparticles, (iii) an increase in the fucoidan content in the composition of the nanoparticle outmost and (iv) the exposure of fucoidan in the configuration in loops and trains at the nanoparticle surface. As shown in Figure 10, a clear hierarchy defining the predominant mechanism by which nanoparticles were taken up by cells could be established, going from one extreme to the other of each of these parameters. It should be noted that, from a quantitative point of view, the types of nanoparticles taken up by endocytic mechanisms appeared, by far, to be the least internalized by the J774A.1 cells. In contrast, those penetrating cells by a non-endocytic pathway, phagocytic routes assumed to involve a pattern recognition receptor recognizing fucoidan, were taken up by the cells to a much higher extent. This superior uptake ability would be advantageous for intracellular delivery of drugs. This is in accordance with the paper of Mosaia and co-workers [START_REF] Mosaia | Carbohydrate-based nanocarriers and their application to target macrophages and deliver antimicrobial agents[END_REF] suggesting that nanoparticles exposing glycans on their surface could be suitable carriers to deliver drug inside macrophages thanks to their interaction with specific PRRs.

Conclusion

The present work has shown that the internalization pathways taken by polysaccharide-coated PIBCA nanoparticles to penetrate J774A.1 macrophages can be determined by the surface composition in fucoidan and dextran and from the configuration given to the polysaccharide chains. The privileged routes of internalization of the PIBCA nanoparticles by the cells included non-endocytic pathways which appeared 3.3-fold more efficient than endocytic pathways when the extend of internalization of A100 nanoparticles (coated with 100% fucoidan) and A0 nanoparticles (coated with dextran only) were compared. Non-endocytic pathways providing high intracellular uptake were favored by a large size of the fucoidan-coated PIBCA nanoparticles (495 ± 18 nm), a high density of negative charge on the nanoparticle surface (zeta potential -55 ± 1 mV) and by the presence of fucoidan exposed in the loop and train conformation at the nanoparticle surface. In contrast, endocytosis through energy-dependent routes (endocytic pathways) were favored by a smaller size of the nanoparticles (254 ± 5 nm) and a composition of their corona made of dextran only. The general increased uptake of fucoidan-coated nanoparticles (A25, A100 and R25) by J774A.1 macrophages was attributed to a privileged interaction of the nanoparticles with carbohydrate recognition receptors, as part of macrophage scavenger receptors, but this deserves to be elucidated further. The difference in the intracellular distribution observed between nanoparticles of type A (A25, A100), accumulating in the cell cytoplasm, and nanoparticles of type R (R0, R25,) accumulating in intracellular compartments also deserves attention. Pursuing this work by deciphering the intracellular trafficking arising from the different routes by which nanoparticles were taken up by J774A.1 macrophages could improve the design efficacy of nanoparticles able to achieve efficient cytoplasmic drug delivery.

Table 1 .Figure 1 .

 11 Figure 1. Schematic structures of nanoparticles obtained in this work by anionic emulsion polymerization with different amount of fucoidan 0, 25 and 100 % (A0, A25 and A100, respectively) in the dextran-fucoidan mixture and by redox radical emulsion polymerization with 0 and 25 % of fucoidan in the dextran-fucoidan mixture (R0 and R25 respectively). Orange lines indicate fucoidan and purple lines indicate dextran.

Figure 2 .

 2 Figure 2. Fluorescence at different thickness of cells, from 1 to 40 z-stack with 4µm each, incubated with different nanoparticles for 10 (A) and 60 (B) minutes. The enlarged zone shown on the 19 th z-stack, which corresponds to the middle of the cells, was just above that marked on the 16th z-stack with the white rectangle. Scale bars correspond to 22 μm.

Figure 3 .

 3 Figure 3. Fluorescence images of A0 (A), A25 (B), A100 (C), R0 (D) and R25 (E) nanoparticles. The images shown z-stack that corresponds to the middle of the cells after 1 hour incubation. Insert shows fluorescence of calcein. Scale bars correspond to 22 μm.

1

 1

Figure 4 .

 4 Figure 4. Uptake of nanoparticles by macrophages (J774A.1) after 1 hour of incubation 37 o C. (A) Confocal images of nanoparticle internalization. (B) 3D fluorescence intensity view obtained from the confocal images shown in (A), the scale bar of fluorescence intensity is from red to pink (0 -4.000). (C) Data are indicated as fluorescence per cell, obtained after fluorescence quantification using confocal images. At least 100 individual cells from 10 different places were used for quantification and expressed as statistically different as ** (p < 0.05), and **** (p < 0.0001).

Figure 6 .

 6 Figure 6. Comparison of the fluorescence signal due to the nanoparticles captured by the cells normalized by the nanoparticle volume. The fluorescence of the cells determined in the Figure 4 was divided by the volume of the corresponding nanoparticles calculated from their DH (Table1).

Figure 7 .

 7 Figure 7. Influence of incubation temperature on cell uptake of different PIBCA nanoparticles by macrophages (J774A.1) during (A and B) a long incubation or (C and D) a short incubation (10 min). (A) The median fluorescent intensity (MFI) of the cells after 1 hour incubation with the nanoparticles at 37 o C (black column) and 4 o C (light grey column). (B) Histograms of flow cytometry at 37 o C: cells without nanoparticles (red); Cells with nanoparticles A0, A25 and A100 (blue line); R0 and R100 (yellow line). Data were obtained by flow cytometry, in duplicate, analyzing 10.000 cells measured in each sample gate and expressed as statistically different as ** (p<0.05) and **** (p<0.0001). (C) Data expressed as mean fluorescence intensity (%) were obtained by flow cytometry, in duplicate, analyzing 10.000 cells measured in each sample gate. (D) Histograms of flow cytometry: cells without nanoparticles (red); Cells with A0, A25 and A100 nanoparticles (blue); cells with R0 and R100 nanoparticles (yellow). Samples were analyzed in duplicate and expressed as statistically different as ** (p<0.05) and **** (p<0.0001).

Figure 8 :

 8 Figure 8: Percentage (%) of fluorescence of the cells grown in the presence of the pharmacological inhibitors of endocytic pathways compared to the fluorescence of cells grown in the absence of endocytic pathway inhibitors.

Figure 9 .

 9 Figure 9. Evaluation of endocytic pathways using endocytic pathway inhibitors by confocal microscopy.

Figure 10 .

 10 Figure 10. Summary figure indicating the predominant mechanism by which nanoparticles were taken up by cells. In bold, the predominant pathway. Abbreviations: CME: Clathrinmediated endocytosis, CvME: Caveolae-mediated endocytosis, CCIP: Clathrin-caveolae independant pathways, AMP: Actin-mediated pathway that can apply to macropinocytosis and phagocytosis, MTP: Microtubule-mediated pathways, LRMP: Lipid raft-mediated pathways, other: none of the above-mentioned pathways. The number of negative charges in the cloud represents the relative values shown by the zeta potential of the nanoparticles. The size shown by the nanoparticles represents their relative size.

Ethical Compliance

Not applicable

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgements

The authors would like to thank Dr Gillian Barratt for her careful reading of our manuscript and help in improving the English language. The authors gratefully acknowledge the support by Conselho Nacional de Pesquisa Científica -CNPq (#249904/2013-06), CNPq Universal (#427243/2016-5) Auxílio Pesquisador 065880/2020-93 and Qualis A (23076.054228/2020-29). CAPES-COFECUB project 721/11. CAPES Print (#2761/2018). They also thank the Région Ile-de-France and the Université Paris-Saclay for financial support to MIPSIT core facility confocal microscopy was performed.


Vipul Vijigiri
email: vipul.vijigiri@enise.fr

Cedric Courbon
email: cedric.courbon@enise.fr

Guillaume Kermouche
email: kermouche@emse.fr

Juliette Cayer-Barrioz
email: juliette.cayer-barrioz@ec-lyon.fr

Juliette Cayer

Finite element modelling and investigation of the interaction between an ultrasonic wave and a discontinuous interface

Keywords: Ultrasonic wave propagation, transmission coefficient, Interfacial stiffness, Contact ratio, multiple asperities, finite element analysis

When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact. Getting insight on the real behavior of these junctions is a challenging task. Theory states that contacts and asperities are continuously altered in two bodies due to applied pressure, which increases the number of active contacts. To addresses such altering interface conditions, wave propagation through tribological interface by means of the development of a numerical model is proposed. The proposed method is used to study and relate crucial parameters like stiffness, contact width, number of asperities that form a basis for an interface.

Introduction

Contact theory had been of great importance past few years to study the interface changes with respect to the crucial tribological aspects i.e., temperature changes, wear and material transfers etc. [START_REF] Wen | Principles of Tribology[END_REF]. Non-destructive testing of such tribological contacts has always been growing research with use of innovative methods like ultrasound. In-situ accessing cracks, defects using ultrasound wave propagation through the contacting bodies is an efficient method characterized by reflection and transmission wave through a crack or a tribological interface. Although, such measurements are sensitive to frequency, amplitude of the wave, type of contact and its properties. In general, Tribological contacts are formed when two bodies are pressured on to one another creating an imperfect contact interface which is never perfectly coupled. Microscopically, they have peaks and valleys due to the surface roughness as seen in figure 1. The points at which the surfaces in the contact intersect, they contribute to the real contact area. This real contact area is pretty small compared to the apparent contact area in magnitude. Real contact area is calculated from the interface based on the number of contact points and diameter of all the asperities in contact. Although, the real contact area is never consistent. To access this real contact area, several analytical models were proposed that built the relationship between the wave propagation parameters to contact area, but it is still a challenging procedure to work on rough contacts. The real contact area is very difficult to access or measure due to being small. Few methods like a) thermal b) ultrasonic, c) optical, d) resistive etc. are previously researched in reference to the contact theory [START_REF] Slade | Electrical Contacts: Principles and Applications, Second Edition[END_REF], [START_REF] Sahli | Evolution of real contact area under shear and the value of static friction of soft materials[END_REF], [4], [5],

[6], [7] but fall short due to their disadvantages. Ultrasound on the other hand is popular method like optical but it could also be applied and as well could propagate through any material. However, the existing literature on ultrasound in tribology focus more on the theoretical validation and experimental analysis of wave propagation which have their limitations in-terms of either geometry or complexity in analyzing micro scale contacts. There is also lack of literature on finite element modelling of wave propagating through such contacts and reviewing the contact theory. Use of ultrasound transmission in the evaluation of dry contacts initially was developed by [Kracter,1958] who investigated the performance of wave transmission through an interface with varying load which was later validated in detail by [START_REF] Greenwood | Contact of nominally flat surfaces[END_REF] [8], [START_REF] Kendall | An ultrasonic study of the area of contact between stationary and sliding surfaces[END_REF] [9], Yoshihisa MINAKUCHI [START_REF] Yoshihisa | Contact pressure measurements by means of ultrasonic waves : On a method of quantitative measurement[END_REF] etc. Work done by Kendall and Tabor gives an interesting insight about ultrasonic use in accessing contacts. They conducted various studies on wave propagation through a soft material when pressed between two solids, through a continuous and discontinuous interface, through single and multiple contacts and through stationary and sliding contacts. They conducted series of experiments initially on cylindrical disks pressed onto one another and in between are the asperities of soft rubber (0.1 mm in size each). These disks are then distanced (0 to 3 diameters) apart for each experimentally to study the change in stiffness (calculated based on the radius of the embracing contact). Finally, the relation of stiffness was built to the number of asperities on two conditions as seen in figure 2. Later, transmission coefficient was related to change in diameter of a constriction and a disk, a disk was placed, and its width is increased (1-10 mm scale) between two compressing steel bodies for every simulation and resulting transmission coefficient was compared. In both the cases, the analysis is very promising with a few limitations that, in the first case, the asperity is limited to rubber and in the scale of mm, In the second case, transmission coefficient was compared to one single soft disk with a growing diameter and concluded up on that, transmission coefficient is proportional to diameter of the disk and then to the stiffness (Stiffness is then proportional to the diameter of the asperity). The main question would then be, if is the hypothesis still applicable to asperities with different materials and sizes (in microns or below), also a standard explanation or result was not given or concluded relating

Contact Interface

Close look of two solids in contact

Rough surface with multiple contact points Solid B Solid A transmission coefficient to stiffness. [START_REF] Polijaniuk | Novel stage for ultrasonic measurement of real contact area between rough and flat parts under quasi-static load[END_REF] [11] assumed that real contact area is equal to the square times the reflection coefficient. Baik, 1984 [12] dealt majority on ultrasonic scattering from imperfect Interfaces using A Quasi-Static model, His work covers interfaces consisting of strip, circular, elliptical cracks and random distribution of contacts. He further commented on Kendall and Tabor's work that there is a lack of observations concerning measuring real contact area based on stiffness and number of asperities proving the point of further study. N.F. [START_REF] Haines | The reflection of ultrasonic pulses from surfaces[END_REF] [START_REF] Haines | The reflection of ultrasonic pulses from surfaces[END_REF] worked on wave transmission and reflection through contacting surfaces and also on the wave scattering from the contacting surfaces and cracks. [START_REF] Drinkwater | A study of the transmission of ultrasound across real rough solid-solid interfaces[END_REF] [14], Nagy (1992) [START_REF] Peter | Ultrasonic classification of imperfect interfaces[END_REF], S. [START_REF] Biwa | Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces[END_REF] [16] dealt majority on the wave propagation parameters and stiffness considering theoretical assumptions based on spring theory. Other researchers, Rober Dwyer Joyce (2005) [17], Bushan (1998) [START_REF] Bhushan | Contact mechanics of rough surfaces in tribology: multiple asperity contact[END_REF], Krolikowskiand Szczepek 1991 [19], worked exclusively on the experimental or analytical investigation of the interface or the real contact area, developed theory on stiffness Based on the spring model using quasi static approach. It is to be noted that there is an interesting disagreement in the literature on how the wave propagation parameters are related to either stiffness or real contact area. Models or theories that are developed previously have limitations interns of the either the type of interface they considered with fewer contact points and conditions. Also, theory of stiffness and true area of contact stands true in certain conditions but as we increase the no of contact points, effect of the wave propagation in the asperities changes drastically. This could attribute due to change in contact interface in factor of microns.

The goal of this paper is to FE model and study the relationship between contact interface to try to answer few aspects that are not covered previously by the researchers [9]. Lot of work has been done on the finite element modelling of either the surface topology or the asperities in contacts [20] [21] but not using ultrasonic wave propagation through contacts. In this paper, finite element modelling (in micro scale) on the use of ultrasound pulsed on to a solid-solid interface is proposed. Contact interface is altered accordingly to evaluate the parameters that effect the wave propagating through. A detailed study is conducted on the interface configuration and its dependency on crucial parameters (stiffness, contact ratio, contact width, number of asperities) relating stiffness to the ultrasonic transmission coefficient and to interface configuration.

Theoretical Literature

Generally, in tribological contacts tested using ultrasound, the quality of the contact is accessed through the reflection coefficient and transmission coefficient respectively, which is relatively dependent on real contact area. Real contact area is very small compared to the apparent contact area. It is due to existing surface roughness and small asperities that form due to friction and sliding. Assessing such contacts is not always easy as the smaller they get, visible area per contact reduces. Theoretical assumptions of asperity as a spring were made and finite element models were developed concerning the on-line measurement of such contacts. FE modeling and mathematical formulation of the propagation of ultrasonic waves was first formulated by [22], [17] and later by [START_REF] Quinn | The measurement of contact pressure in machine elements using ultrasound[END_REF]. The authors considered an incomplete interface and characterized it as a spring layer as seen in figure 3a. As stated by Baik, 1984 [12] before, real contact could be considered as a spring as seen in figure 3b. The quasi-static model that theoretically relates the reflection coefficient to impedance of the two bodies in contacts is given as

R = (Z1 -Z2 + iω(Z1Z2/K)) c (Z1 + Z2 + iω(Z1Z2/K)) (1)
Rc is the reflection coefficient, z1, z2 are the impedances of two interfacing bodies, 𝜔 the wave angular frequency and k is the stiffness. The equation can take a simpler form if the contacting solids are made of the same materials, i.e., same acoustic impedance (z1=z2=z), equation 4.

Cs (4)

The relationship between reflection coefficient and stiffness forms the basis for much interesting analysis as an interface can be accessed for different loading conditions based on the amount of reflection recorded for each amount of load applied. The reflection and transmission of waves at the interface of two bodies is dependent not only on their characteristic acoustic impedance, stiffness of the interface but also on the frequency of the pulse. In a real contact, the wave propagation occurs in micro scale. Each single contact in the model exhibits the reflection and transmission phenomena. All these interact with one another resulting in change of the characteristics of wave propagation. Their model is quite simple with series of circularly identical contacts are placed in between two compressing bodies. The stiffness, K for such interface can be given as,

K = N b .K0 (5)
k0 is the stiffness for each single asperity and b is a numerical variable that varies between 1 for when the N contacts are spaced so far to have negligible effect and 1/2 when N contacts are closely or tightly placed such that one has considerable effect on other. Perfect match or a perfectly closed interface has impedance close to zero or high stiffness allowing complete transmission and as if the air gaps are increased in the interface, transmission coefficient will reduce to zero. In both [9] and [22] research works, stiffness of the whole interface separating two solid bars was proved to be dominant parameter that controls the wave reflection and transmission. Young's modulus, Poisson's ratio, density, impedance is shown in the table below.

Table 1. Properties of the material (Aluminum) used in the FE model

The simulations were conducted with different contact or interface configurations characterized by the contact width (Cw) (20-100 microns), Contact space (Cs) (20-100 microns), and number of asperities (N). For number of asperities (N) from 20-100, corresponding contact ratio (Cr) is indicated as seen in figure 4. The geometry consists of quadrilateral mesh on a displacement element type. The mesh value is fixed to 20 microns in all simulations to maintain the mesh stability and to make sure the simulations are consistent. The solver employed for the simulations is explicit time dependent, dynamic temperature-displacement solver. The evolution of displacement along time of the global pressures is analyzed, relating it to the local interaction phenomena at the interface and global behavior of the solid-solid interface. Ultrasonic tone burst with 10 MHz frequency, 6 cycles and 1E+7 amplitude is applied as a load boundary to the element and then the output is measured on both side of the element. The tone burst is formulated as, Cw 5 mm

t A = A0(1 -cos(2πf N )) * (sin(2πft) (6)
A0 here is the amplitude. Input is a hanning windowed tone burst applied along the blue line in figure 5a. The excitation waveform and its first harmonic reflection and transmission are observed in the figure 5b. The time signal is Fourier transformed with in a time frame to extract the amplitude of Excitation, reflected and transmitted signals as seen in figure 5c. The level of accuracy of a wave propagation model is greatly influenced by the mesh density and time step. This section will project upon the influence of 2 mesh distributions with the aim of quantitatively defining a suitable mesh distribution that will be further used in later simulations. The mesh distribution is scaled from a coarse 200 to a fine 20 microns mesh in this sensitivity analysis. For the complex micro scale structures the mesh density must be very high as in time domain wave propagation, for each node, displacements are calculated and averaged.

Although time consumed to process is very high, wave propagation within the solid is depicted in precise detail. The quadratic element mesh distribution was used considering its advantage of meshing small scale structures (Abaqus manual, 2014). The effect of the mesh distribution/quality was first investigated by applying a tone burst on one side of the solid, whereas displacement amplitudes were extracted on both the sides. Following figure shows the wave propagation modes for two mesh types. From the results shown in figure 6, the propagated wave is seriously affected by the mesh distribution as it reaches the right end of the solid, whereas the scale for the 2 simulations is similar. There are two obvious observations, one is that the wave itself, as it starts propagating, has different displacement patterns. On the other hand, as it propagates through, the wave energy when using the coarse mesh is completely lost with almost zero transmission along the field. When using the fine 20-micron mesh, in the figure 6(2d), the peak amplitude is almost maintained until the end of the solid despite the slight beam spreading and scattering on the side walls. On the contrary, the figure 6 (1c) proves that the wave pattern is rapidly lost leading to a strong decrease in the wave amplitude. In practice, this will not be the case as based on the length of the solid, there could be a clear wave travelling along and reflecting unless altered due to attenuation or scattering. Figure 6 (a) presents the total displacement recorded in the propagation direction on both sides of the solid. In figure 6 (b), it can be noticed that the wave is almost fully transmitted to the right end of the solid whereas the first echo recorded on the left at 5 s is weaker in amplitude. When using a coarse mesh distribution, the whole signal intensity is lost over the few propagation steps which is noticeable. Based on the meshing rule, these simulations prove that smallest mesh size are necessary to reach an accurate performance of model and vice versa. This concludes that change in mesh density does affect the wave propagation efficiency and also introduce numerical inaccuracies. From multiple analyses on different mesh distributions, an efficiency curve versus mesh size was drawn as seen in figure 7. Based on the resulting curve, it clearly shows that when increasing the mesh size, the efficiency of the output reduces to nearly 10 percent. This concludes that 20 microns is a very good mesh size than can be adapted to the present model. Usually, the mesh size has to be 1/10 elements per wave length to simulate the wave propagation and in this case, the mesh size is 1/25 elements per wavelength.

Wave propagation mode shapes at different time intervals

The wave propagation through the contacting bodies is always interesting to show and it gives a clear overview of the wave propagating over time. Figure 23 show all the color plots of the wave when it is first initiated, propagated through the interface and as it reached the end. Within the interface, the part of the wave can be seen reflecting and part being transmitted through. The time plot is also seen in figure 24 which shows the first initial pulse that is fed to the solid and the second transmitted and reflected pulses. Harmonics are periodically seen until the amplitude is reduced near to zero (The plot corresponds to one contact / width-60 microns and number of asperities-33). In the previous section, a rectangular shaped asperity with a varying size was uniformly distributed to assess the effect of a change in the number of contact spot only. The question now could be, how does the wave behave for a given number of contact asperity but with a variable spatial distribution? In this modelling part, the size of solids remains same as specified in previous section, but the interface configuration is designed with a constant N=50 number of asperities with spacing of 60 microns and 20 microns in combination as seen in figure 8. All the cases result in the same contact ratio, Cr of 0.5 Figure 9 shows the FFT plots for four type of irregular interface distributions types. It can be observed that in all the cases, the amplitude remains almost unaltered with slight difference in levels. This tends to show that the interface at such a scale will not have a drastic effect on what is measured at the transmission end. This concludes that change in interface configuration for a given contact ratio will have minimal impact on the simulation capacity.

Random contact distribution

Effect on the wave transmission with change in width of the asperity

Considering a configuration with a 10-micron thick asperity, the study is focused on assessing the evolution of the reflection coefficient to change in width of a single asperity. Geometry in this case is similar to the previously defined model as seen in 4, except that the width of single asperity is changed from 0.1 to 3 mm. Figure 10 shows the corresponding images of wave as it partially reflects and transmits at the asperity. It is noticed that as the width of the asperity increases, amount of wave that is reflected reduces to near zero (once the asperity reaches 5 mm) and transmission increases gradually. In such cases with increased width, the fronts cannot interact with free spaces between the two contacting bodies which results in increased propagating wave. Figure 11 shows the relationship between the width of the asperity and the transmission coefficient being proportional to the width of the asperity. This appears to be in agreement with the work presented by [9] confirming the consistency of the modelling approach and the potential use for further analyses.

Relationship with the stiffness of the interface

It was stated in [9], that transmission is in fact proportional to the stiffness of the interface resulting from the increase of the asperity width. In order to verify this relationship, numerical simulations were carried out to assess the stiffness of each asperity size configurations. A simple 2D Axi-symmetric single asperity punch model is developed and studied in terms of changing contact width. The model is simulated in static, general and the element type is a 4-node bilinear plane stress. A short displacement of -0.1 is applied on the top boundary x and a symmetry boundary condition is applied in both x and y directions. Reaction Force is measured as output over time. A sketch of the geometry is shown in figure 12 with the corresponding input data in table 2. Figure 14 shows the reaction force plotted versus the punch displacement. The stiffness, slope of this force-displacement curve, can then be easily extracted, whereas one can also observe the increase of the stiffness with the increase of the asperity width. Stiffness is later plotted along the asperity or contact width (figure 15) and proportionality is confirmed above a critical value 0f 2 mm contact width but there is deviation below that level. The stiffness approaches close to zero with reduced contact width i.e., lowest 0.01 where the nonlinearity is observed. This is in perfect agreement with the literature from Kendall and Tabor 1971 [36] for value above 2 mm (or close to above 1.5 mm) and gives a valid reason for the assumption that stiffness is proportional to the contact changes. Indeed, it can be concluded that the transmission coefficient is proportional to the contact stiffness in the case of this single asperity where the condition is valid for values above 2 mm (or close to above 1.5 mm) and differs below. This 0.2 0.4 0.6 0.8 1

Normalized Displacement

could be due to the fact that although the transmission coefficient is linear to the diameter of the asperity, it cannot be true with stiffness in the lower asperity width regime. To assess the real contact area based on the stiffness, one should know the contact regions and the number of asperities in contact which in reality is difficult. The conclusion from Kendall and Tabor [36] that transmission only depends on the contact stiffness cannot be supported only by a single asperity configuration due to the fact that in the lower stiffness region and lower contact widths, there is a problem of linearity that need to be further studied. Thus, the present work proposes to address this by simulating the wave propagation with multi-asperity contact configurations.

Establishing the relationship between Wave propagation and interfacial parameters with multiple asperity model

To study the transmission change in the interface, different contact values for given contact width are simulated. In all the changing asperity case the contact width is constant. Thus 25 simulations are performed in covering different interface configurations. As seen in figure 16 from left to right, when the width of the asperity is increased, the resulting number of asperities is reduced too, causing the wave to propagate through asperities of the interface. As observed from top to bottom, contact space remains consistent for contact width of 20 microns but as the width is increased to 60 microns, reflection increases but with an overall reduced magnitude compared to when contact width is 20 microns. It further reduces to have high transmission in the end. This shows the double dependency of number of asperities and contact width in an interface. To evaluate this dependency, the transmission coefficient is calculated for different interface geometries and comparison plot is drawn for change in number of asperities for all the contact width and contact space configurations. Transmission coefficient is seen monotonically increasing as a function of number of asperities. Figure 17a shows Transmission coefficient plotted along number of asperities; N. linear proportionality can be observed between two parameters until the transmission reaches 0.8 and it is no longer proportional beyond. Individually, Transmission coefficient increases with increases in the asperity number for different contact widths, Cw. This is caused due to change in the interface size and reduction in the air gaps. The results agree with the important hypothesis explained by [9] that, Transmission coefficient, Tc is proportional to number and diameter of the contact. Figure 17b shows the transmission coefficient results obtained by varying the contact width between 20-100 µm of the asperity for different values of N. Transmission coefficient increases with increase in the contact width showing a strong linear proportionality. The relationship between the two parameters can be given as, Tc ∝ Cw. The proportionality is maintained for all the values of N concluding that as the contact width changes, transmission coefficient changes keeping the linear proportionality constant. But each parameter is individually investigated, whereas, the phenomena happen convolved with in the interface. Technically, it's the contact ratio, Cr that acts as the crucial parameter that need to be studied and is defined as,

Real contact area C r = apparent contact area = ENC w /L ( 10
)
E is young's modulus, L is the length of the apparent contact area, 4 mm in this case and N.Cw are the interface parameters. First thing to be noted in the figure 18 is that transmission coefficient increases with contact ratio, but it is no longer linearly proportional. This is because, for every change in N there is a simultaneous change in Cw. Important thing to be notes is that, for Cr=0.5, there is an increase in the transmission coefficient. Constant contact ratio internally has change in N, Cw. The important aspect that arises in this analysis is, how contact ratio or the interface parameters related to stiffness. Various analytical model was proposed previously to build the relation between interface and wave transmission or reflection. This analysis is in good agreement with the Kendall and Tabor (1971) hypothesis that real contact area is a function of number, size of the asperities in the interface. Most of the research carried out conclude on the theory that stiffness is the sole parameter used in evaluating the real contact area. Although, Dwyer Joyce [17] [START_REF] Baik | Ultrasonic scattering from imperfect interfaces: A quasi-static model[END_REF] put focus on the disagreement concluding that real contact area does not just depend on stiffness but also on the other parameters with in the interface

Relationship between contact stiffness and transmission coefficient

Now that the relationship between the transmission coefficient and other contact parameters is established, it is important to relate the transmission coefficient to the interface stiffness. To do so, a simple stiffness analysis has been performed for each contact configuration previously described in the figure 19. Moreover, complementary contact configurations using the same contact widths but fewer asperities were added in order to extend the range of contact ratios, especially towards the lower values. The contact space has been increased up to 2mm for some configuration. The selected model is similar in terms of mesh density, material type and interface distribution. However, the study is carried out in static analysis and no wave propagation is implemented. Instead, a small displacement is applied at a reference point and the values of the interface stiffness in each case is extracted based on the reactive force.

Various new boundaries and constraints are involved which are shown in figure 19. RP to the right is the reference point at which a 1E-11 amplitude displacement is applied in the negative x direction. A rigid body constraint is applied to both the interface and the solid B making it a combined solid indenting the solid A defined as deformable. Solid A is encastre on the left side ensuring zero displacement. The whole simulation is carried out in ABAQUS/static general case. The simulated reactive force versus displacement curve is extracted and the stiffness value calculated based on the equation:

Stiffness, k = (Reactiveforce)/Input displacement amplitude (11)
The figure 20 summarizes the evolution of the interface stiffness with the number of asperities for the different contact configurations. It is important to remind that the absolute value of the stiffness has to be carefully considered as it is extracted based on a 2D plane strain model. The observed trends appear to be in agreement with the contact mechanics exposed by [9]: for a given contact width, the stiffness linearly increases with the number of asperities up to a certain point beyond which they start to interact with each other, leading to a slow increase of the stiffness when further increasing N. When focusing on the stiffness computed beyond N = 20, one can still see that a short variation of stiffness from 2 to 4% can occur when increasing the number of asperities or the same order of magnitude when increasing the contact width for a given number of asperities. To conclude, a further relationship is built between stiffness and contact ratio as seen in figure 21. When combining this analysis to the wave propagation one, the transmission coefficient can now be plotted versus the interface stiffness (figure 22). It can be noticed that it follows a relatively unique bi-linear evolution with a slope change around the stiffness value of 0.95. Over the lower stiffness value range, i.e., for contact ratios from 0.09 to 0.33, the transmission coefficient is not highly sensitive to a change in stiffness. However, beyond this point, a slight change in stiffness induces a larger variation in terms of transmission coefficient. This could be because at that point, the space between asperities decreases twice to 10 times the value of the previously defined configurations which results in the sudden growth of the transmission curve. It should be important to state that interface stiffness is internally dependent on local interfacial parameters (size, shape and asperity distribution). But also, stiffness could be the same for different Interface configurations. In an interface the asperities even if they initially are far apart, they tend to be very close once new contact points are created, around the existing contacts due to increase in load. This will affect the wave propagation and the influence of local contact parameters. Also, it was previously noted that the transmission coefficient is proportional to the diameter of asperity which was limited to a single asperity. In that analysis, for a single asperity, it was noticed that above 0.5 mm change in diameter is independent it is contact ratio that has to be assessed. But, as the interface deals with multiple asperities, diameter and number are intrinsically dependent, it can in terms of contact ratio be said that above 0.5 different contact ratio combinations will lead to the same stiffness which means the same transmission value. It can be concluded from above analysis that stiffness is partially proportional to transmission coefficient and contact ratio and deviates due to change in internal geometrical parameters that are complex to study. Based on the above-mentioned results, following conclusions are drawn.

Conclusions

In the paper, a novel numerical approach based on a 2D finite element model was developed to study the interaction between the interface parameters and ultrasonic wave propagation. The transmission coefficient was measured for different model contact configurations and related to the corresponding contact stiffness. This study showed that, when investigating rough contact using a single element transducer, no unique relationship between the interface parameters such as contact width (Cw) or number of asperities (N) and the transmission coefficient could be extracted. Within mind to assess the real contact area in such contacts, it was shown that the contact ratio is also not a unique interface parameter that could be measured using this ultrasonic technique. However, a relationship has been identified when comparing the transmission coefficient to the contact stiffness. If this appears to agree with the literature suggesting a proportionality, it was shown that this seems to depend on the nature of the contact interface, i.e., to depend on the contact ratio. Although being able to measure in-situ the contact stiffness of a given contact is of interest, it was shown that characterizing precisely its morphology, i.e., number of contact spot and their size, required another approach rather to imagine a mapping strategy. Tx part of future study, the transmission coefficient recorded when using a single element transducer could be related to the contact stiffness. However, a sudden change was observed when reaching the largest contact ratio range, i.e., beyond 0.33, where transmission experienced a strong increase. As this phenomenon has not been explained, it would be relevant to develop further analyses to clearly point out the governing mechanisms

Fig. 1 .

 1 Fig. 1. Tribological contact representation

Fig. 2 .

 2 Fig. 2. Asperity distribution types in a contact when they are far apart and when they are closely placed

Fig. 3 .

 3 Fig. 3. (a) Tribological contact representation (b) Spring model representation

  Fig. 4. (a) Tribological contact representation (b)Table of contact width, contact space and asperity combination of the interface FE modelling is realized using ABAQUS/Explicit. Element type used is a first order 4 node bilinear solid element (CPE4R). In the model, aluminum has a 15 mm length/Height and 5 mm width geometry seen in the figure 4. Young's modulus, Poisson's ratio, density, impedance is shown in the table below.

Fig. 5 .4

 5 Fig. 5. (a) Solid-Solid interface (b) Time domain representation of input, reflected and transmitted waves (c) FFT or frequency domain representation of input, reflected and transmitted waves.Reflection and transmission coefficients as seen in equation 7 are calculated from ratio of the maximum displacement amplitudes extracted from the figure 5c. In the above figure S1(t) is the time signal representing input pulse and S2(t) is the time signal representation of the reflecting and transmitting parts. Also, ai, at, ar are amplitudes of the input, transmitted, reflected signals that are recoded. In general, the sum of both the coefficients equate to unity. The transmission coefficient is extracted from the 80 nodes on the right boundary of the solid and summed, resulting an estimate. Reflection coefficient is extracted from 45 nodes on the left side of the boundary.

Fig. 6 .

 6 Fig. 6. Time lapse of wave travelling as it reaches the right end of the solid for (1) coarse mesh distribution (2) Fine mesh distribution Displacement magnitude (a) plotted for the coarse mesh distribution (b) plotted for the fine mesh

Fig. 7 .

 7 Fig. 7. Mesh distribution size and its efficiency curve

Fig. 8

 8 Fig. 8. a) Solid-solid contact interface with the interface shown in black strip (b) (c) (d) (e) four different contact distribution types

Fig. 9 .

 9 Fig. 9. FFT plot (Transmission) of the four-time domain plots corresponding to irregular interfaces

Fig. 10 .

 10 Fig. 10. Wave propagating through different asperity width (a) 0.1 mm where all the wave is reflected back (b) 1.5 mm where part of the wave is transmitted and part reflected (c) 3 mm where most of the wave is transmitted (results are extracted at same time frame)

Fig. 11 .

 11 Fig. 11. Relationship between width of the asperity to transmission coefficient

Fig. 12 .

 12 Fig. 12. Schematic representation of the model assumed with load and the boundary conditions defined

Fig. 14 .

 14 Fig. 14. Reaction force versus displacement for different asperity width configurations

Fig. 15 .

 15 Fig. 15. Resulting contact stiffness versus the asperity/contact width

Fig. 16 .

 16 Fig. 16. Compilation of frequency domain plots showing difference in the transmission and reflection coefficients with their respective configuration changes.

Fig. 18 .

 18 Fig. 18. Transmission coefficient plotted in comparison to contact ratio for different contact width configurations and number of asperities, Tc /∝ Cr.

Fig. 19 .

 19 Fig. 19. Geometry corresponding to the model used in determining the interface stiffness.

Fig. 20 .

 20 Fig. 20. Relationship between the interface stiffness and the number of asperities.

Fig. 21 .

 21 Fig. 21. Relationship between stiffness to contact ratio Included contact ratios in the range of 0.09-0.33.

Fig. 22 .

 22 Fig. 22. Transmission coefficient versus the interface stiffness for different contact widths.

Fig. 23 .Fig. 24 .

 2324 Fig. 23. Wave propagation mode shapes in a solid (10mm) different time intervals showing the propagating and reflected signals.

Table 2 .

 2 Table corresponding to the load, boundary conditions, mashing rules implemented in this section

Acknowledgement

This work was supported by the LABEX MANUTECH-SISE (ANR-10 LABX-0075) of Universit de Lyon, within the program" Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).