Clément Coquery

Federico Carosio

Claire Negrell

Nicolas Caussé

Nadine Pébère

Ghislain David
email: ghislain.david@enscm.fr

New bio-based phosphorylated chitosan/alginate protective coatings on aluminum alloy obtained by the LbL technique

Keywords: Phosphorylated chit osan, Layer -by-layer assembly, Coat ing, Al uminum alloy, El ectrochemical impedance spectroscopy

Bio -based coat ings were obtained by t he layer -by-layer (LbL) t echnique from a nat ive chit osan (M w 30,000 g mol -1 ) or from t wo synthesized phosphorylat ed chit osan of differ ent mol ecular weight s (M w 30,000 g mol -1 and M w 250,000 g mol -1 ) combined wit h alginat e and used for corrosion pr ot ect ion of an aluminum alloy (AA) 3003. Fir st , t he LbL gr owth was monit or ed by Four ier transfor m infrared spectroscopy on sil icon wafer s. Cr oss-sect ions of Si wafer s wer e exa mined by scanning el ectron microscopy allowing t he fil ms t hickness t o be measur ed. Wit h t he nat ive chit osan and in t he pr esence of 10 bilayer s, t he LbL t hickness was about 200 n m, wher eas it was about 300 n m wit h t he phosphorylated chit osan of l ow mol ecular weight and about 500 n m wit h t he phosphorylat ed chit osan of high mol ecular weight . Then, t he bio -based coat ings wer e deposit ed on t he AA3003 by the LbL t echnique and t heir pr ot ect ive pr opert ies wer e evaluat ed by el ectrochemical impedance spectroscopy (EIS) dur ing immer sion in a 0.1 M Na 2 SO 4 sol ut ion. It was shown t hat t he t hr ee LbL coat ings impr oved t he corrosion resistance of t he AA3003. The r esistance values, extract ed at low fr equency on t he impedance diagrams wer e attr ibut ed t o t he r esistance of t he aluminum oxide layer (R ox ). The R ox values wer e at l east t wo order s of magnit ude higher for t he coat ed sa mpl es (10 8 Ω c m 2 ) compar ed t o t he uncoat ed one (5 10 5 Ω c m 2 ). There was no significant differ ence bet ween t he differ ent LbL coat ings, which ma inl y act ed by decr easing t he act ive surface ar ea and have a l imit ed barr ier effect .

Introduction

The Layer-by-Layer (LbL) deposition represents an innovative and interesting alternative for the development of coatings for several applications such as flame retardants [START_REF] David | Biomacromol ecul es as novel gr een flame r etardant syst ems for t ext i l es: an overview[END_REF][START_REF]Layer -by-Layer nanostructured assembl ies for t he fir e pr ot ect ion of fabr ics[END_REF], electrochromic [START_REF] Cor Doba De Torr Esi | El ectrochromic Mat er ial s and Devices, Layer -by-layer assembl y of el ectrochromic mat er ial s: on t he efficient met hod for immobil isat ion of nanomat er ial s[END_REF] applications, medical and bioapplications [START_REF] Gunjkar | St imul i r esponsive layer by l ayer selfassembl y a novel a ppr oachs in current drug del ivery: r eview[END_REF][START_REF] Vol Odkin | Bioa ppl icat ions of l ight -sensit ive pol ymer fil ms and ca psul es assembl ed using t he layer -by-layer t echnique[END_REF] but also nanoengineering [START_REF] Est Illor E | Ionic Interact ions in Nat ural and Synt het ic Macromol ecul es., 2012, 17, Funct ional layer -by-layer pol yel ectrolyt es: assembl y strat egies, charact er izat ion, and sel ect ed a ppl icat ions[END_REF][START_REF] Andr Eeva | Mult i-layer smart coat ings for corrosion prot ect ion of aluminium alloys and st eel[END_REF]. The LbL technique is attractive mainly due to an easy integration of functional materials, treatment under ambient conditions (room temperature and atmospheric pressure) and ecological characteristics (solvent is mainly water and concentrations of solutions/dispersions are less than 1 wt. %). LbL coatings are elaborated on a substrate by the sequential adsorption of chemical species based on one or more functional interactions. The most common interaction is provided by the electrostatic attraction [START_REF] Decher | Fuzzy Nanoassembl ies: Toward Layer ed Pol ymer ic Mult icomposit es[END_REF][START_REF] Il Er | Mult i layer s of colloidal part icl es[END_REF]; indeed, the alternative adsorption of opposites charged polyelectrolytes allows the accumulation of structured laminated or strongly interpenetrated coatings [START_REF] Ber Ndt | Adsor pt ion of pol y(st yr enesulfonate) onto an ammonium monolayer on mica : a surface forces st udy[END_REF]. Among available polyelectrolytes, polysaccharides can be rather good candidates to perform fully bio-based LbL systems, due to their low toxicity, biodegradability and natural availability [START_REF] Umor En | Appl icat ion of car bohydrat e pol ymer s as corrosion inhibit or s for metal substrates in differ ent media : A r eview[END_REF]. Chitosan is the second most abundant bio-based polysaccharide on the earth, after cellulose, and is the major component in crustaceans, exoskeletons, fungi or insects [START_REF] Kim | Ch it in, Ch itosan, Ol igosacchar ides and Their Der ivat ives: Biol ogical Act ivit ies and Appl icat ions[END_REF]. Chitosan is a linear copolymer of glucosamine and N-acetyl-glucosamine, obtained from chitin by alkaline deacetylation [START_REF] Muzzar | Ch it in[END_REF] or from enzymatic pathway [START_REF] Tsigos | Chit in deacetylases: new, ver sat i l e t ool s in biot echnology[END_REF]. It is biocompatible [START_REF] Vandevord | Evaluat ion of t he biocompat ibil it y of a chit osan scaffold in mice[END_REF], non-toxic [START_REF] Rinaudo | Ch it in and chit osan: pr opert ies and a ppl icat ions[END_REF],

antibacterial [START_REF] Tokura | Mol ecular Weight Dependent Ant imicrobial Act ivit y by Ch it osan[END_REF] and can be used to form films [START_REF] Dutta | Tr ipat hi, Ch it in and chit osan: Chemistry, pr opert ies and a ppl icat ions[END_REF][START_REF] Nunt Hanid | Physical pr opert ies and mol ecular behavior of chit osan fil ms[END_REF]. Alginate is a linear polysaccharide formed from two monomers in different proportions bound in β-(1-4): mannuronate and guluronate [START_REF] En | High-fiel d, 1H-NMR spectroscopy of alginat e: sequent ial structure and l inkage confor mat ions[END_REF]. Alginate-chitosan system has already been used for various applications such as, membrane manufacturing [START_REF] Car Idade | Fr ee-Standing Pol yel ectrolyt e Membranes Made of Chit osan and Al ginat e[END_REF], biomedical [START_REF] Gao | In vitro and in vivo degradat ion and mechanical pr opert ies of ZEK100 magnesium alloy coat ed wit h alginat e, chit osan and mechano-growth factor[END_REF] and drug delivery [START_REF] George | Pol yionic hydrocolloids for t he int est inal del ivery of pr ot ein drugs: al ginat e and chit osan--a r eview[END_REF]. Lawrie et al. studied the interactions between alginate and chitosan using FTIR and XPS analyses [START_REF] Lawr Ie | Int eract ions bet ween Al ginat e and Ch it osan Bio pol ymer s Character ized Using FTIR and XPS[END_REF]. The interest to prepare LbL coatings for corrosion protection purpose is to build a physical barrier with strong interactions between each layer, thus preventing the penetration of aggressive species through the coating towards the metal substrate. To our knowledge, only Gao et al. reported the use of chitosan and alginate as component for a LbL coating for the protection of a magnesium implant in a biological fluid [START_REF] Gao | In vitro and in vivo degradat ion and mechanical pr opert ies of ZEK100 magnesium alloy coat ed wit h alginat e, chit osan and mechano-growth factor[END_REF]. In their study, the coating was elaborated by spin-coating including forty cycles, each containing four layers: the first layer was the anionic alginate (ALG), the second one was the cationic mechano-growth factor MGF (i.e. a cationic polypeptide polymer), the third one was again the anionic ALG and the fourth one was the cationic chitosan. The resulting multi-layer coating was 18 µm thick. The authors found that the corrosion rate of the coated Mg alloy was slightly decreased by comparison with the uncoated sample, despite the substantial LbL coating thickness.

Phosphonic acid-containing polymers have numerous potential applications as they exhibit attractive properties in term of adhesion [START_REF] Br Ondino | J. Schrynemacker s, Adhesive pr opert ies ont o galvanized st eel plat es of graft ed pol y(vinyl idene fl uor ide) powder s wit h phosphonat ed acrylates[END_REF] and are of interest in corrosion inhibition [START_REF] Kál Mán | Inhibit ion efficiency of N-containing car boxyl ic and carboxy-phosphonic acids[END_REF][START_REF] To | A corrosion-pr ot ect ive fil m for med on a car bon st eel by an organic phosphonat e[END_REF].

Furthermore, the phosphorous-containing molecules or polymers can act as adhesion promoters for different substrates such as aluminum, zinc and steel [START_REF] Ma Ege | Sel fassembl ing adhesion pr omot er s for corrosion resistant metal pol ymer int erfaces[END_REF][START_REF] Mill | Improvement of corrosion pr ot ect ion of steel by incor porat ion of a new phosphonat ed fatty acid in a phosphorus-containing polymer coat ing obtained by UV cur ing[END_REF]. In our previous work, it was shown that the use of chitosan bearing phosphonic acid groups decreased the corrosion rate of a carbon steel by comparison with native chitosan [START_REF] Coquery | Synt hesis of new high mol ecular weight phosphorylat ed chit osans for impr oving corrosion pr otect ion[END_REF]. Some LbL systems, based on phosphorylated chitosan have already been published, aiming at providing new protective coatings for fireproof applications [START_REF] Liu | Layer -by-Layer Assembl y of Hy po phosphorous Acid-Modified Chit osan Based Coat ing for Fla me-Retardant Pol yest er -Cotton Bl ends[END_REF]. To our knowledge, no alginatephosphorylated chitosan system was so far developed through the LbL technique in order to develop protective coatings.

In the present work, elaboration and characterization of LbL coatings from alginate and native or phosphorylated chitosan of two different molecular weights (30,000 g mol -1 and 250,000 g mol -1 ) were first investigated on Si wafers, commonly used as model surfaces for the LbL characterization, in particular to follow the LbL growth. In this study, the LbL growth was monitored by Fourier transform infrared (FTIR) spectroscopy and the films thickness was determined by scanning electron microscopy (SEM). Then, the LbL coatings were deposited on aluminum (AA3003) plates and characterized by electrochemical impedance spectroscopy (EIS). The impedance of the coated samples was measured as a function of the exposure time to a 0.1 M Na 2 SO 4 solution.

Experimental

Materials

Native chitosan, high molecular weight (M w ≈ 250,000 g mol -1 , degree of deacetylation: 92 %, henceforth called Nchitosan250) and medium molecular weight (M w ≈ 30,000 g mol -1 , degree of deacetylation: 92 %, henceforth called Nchitosan30) were purchased from Glentham Life Sciences society. Phosphorylated chitosan from Nchitosan30 (henceforth called Pchitosan30)

and from Nchitosan250 (henceforth called Pchitosan250) were synthesized according to our previous study [START_REF] Coquery | Synt hesis of new high mol ecular weight phosphorylat ed chit osans for impr oving corrosion pr otect ion[END_REF]. Sodium alginate (from brown algae, M w = 140,000 g.mol -1 ) was purchased from Aldrich. Acetic acid (> 99.7 %, Aldrich) was used as received. Deionized water was obtained from a Millipore Milli-Q purification system. The LbL coatings were deposited onto an aluminum alloy 3003 (AA3003). Its chemical composition in weight percent was: Cu = 0.05; Fe = 0.7; Mn = 1.5; Si = 0.6; Zn = 0.1 and Al to balance. The specimens consisted of 127 mm x 76 mm x 0.8 mm plates, purchased from Labomat. Before the deposition of the LbL coatings, the AA3003 samples were successively cleaned with acetone and ethanol and dried for 10 min at 80°C.

LbL assembly

The pr ocedur e for obtaining t he LbL f il ms was independent of t he substrates (Si wafer and AA3003

Analytical characterizations

Zeta potentials (ZP) were measured for 2 g L -1 of Nchitosan30 and Pchitosan30 using a Coating growth was monitored using a Frontier Perkin-Elmer FTIR spectrophotometer ( 16scans and 4 cm -1 resolution) equipped with a Ge/Ge crystal (depth of penetration 0.65 µm).

Cross-sections of the deposited coatings on Si wafers were imaged using a field-emission scanning electron microscope (FE-SEM, Zeiss Merlin 4248). Prior to FE-SEM observations Si cross-sections were chromium coated. A FEI Quanta 450 scanning electron microscope (SEM) was used for the surface characterization of the AA3003. Semi-quantitative analysis was performed by energy dispersive X-ray spectroscopy (EDX) with a Ge detector (EDS Bruker Quantax SDD). EDX analyses were performed over different locations on the AA3003 surface before and after exposure to the Na 2 SO 4 solution.

Electrochemical characterizations

Electrochemical impedance measurements were performed in a classical three-electrode cell in which the coated LbL sample served as working electrode. A cylindrical glass tube was clamped onto the coated AA3003 plate, exposing a surface area of 14.9 cm 2 and filled with 60 mL of a 0.1 M Na 2 SO 4 solution. A platinum electrode with a large surface area and a mercury sulfate electrode (MSE) in a saturated potassium sulfate solution with E MSE = 0.64 V/SHE were used as counter and reference electrodes, respectively. They were placed on the top of the glass tube by means of an electrode holder. The impedance diagrams were obtained for various immersion times (from 1 h to 48 h) to the Na 2 SO 4 solution. It is generally accepted that SO 4 2-are less aggressive than Cl -. In the present study, a less aggressive electrolyte was chosen to minimize the corrosion of the AA3003 substrate, thus allowing the LbL films to be compared according to their composition and thickness.

Electrochemical impedance measurements were carried out using a Biologic VSP apparatus.

The diagrams were obtained under potentiostatic conditions, at the open circuit potential, over a frequency range of 65 kHz to 10 mHz with 8 points per decade, using a 30 mV peak-to-peak sinusoidal voltage perturbation. The experiments were performed at room temperature (22 ± 3 °C). The linearity of the system was checked by varying the signal amplitude. 30 mV was a good compromise to obtain the impedance diagrams without any dispersion.

Results and discussion

Determination of phosphorylated chitosan global charge vs pH

In our previous study 30 , native chitosan, high molecular weight (M w ≈ 250,000 g mol -1 , called Nchitosan250) and medium molecular weight (M w ≈ 30,000 g mol -1 , called Nchitosan30)

were modified by grafting phosphonic acid functions onto primary amines. About 20% of the primary amines were modified for each chitosan. In the present study, high and medium Mw phosphorylated chitosan (Pchitosan250 and Pchitosan30, respectively) were used to build the LbL coatings. According to the pH value, phosphonic acid moieties can be anionic whereas amine groups can be cationic. Thus, due to the partial grafting of phosphonic moieties onto amine functions, the global charge of the functionalized chitosan must be evaluated. Zeta For the Nchitosan30, it can be seen that the ZP values are always positive in the pH range from 2 to 6.5, confirming that it is a cationic polymer. The ionic charge of the polymer is due to the amine protonation for pH values lower than 6.5 [START_REF] Va Ssil Eva | Dealkylat ion of phosphorus-containing alkylammonium salt s for med by t he int eract ion of phosphonic, met hanephosphonic and phosphor ic acid est er s wit h dia mines, Phosphorus, Sulfur Sil[END_REF]. For pH > 6.5, the Nchitosan is no longer soluble and precipitates in the solution.

In the case of Pchitosan30, the ZP values are positive for pH < 6 and negative for pH > 6.

Unlike Nchitosan30, Pchitosan30 remains soluble over the entire pH range due to the presence of phosphonic acid functions. At pH < 6, Pchitosan30 is a polymer with a global cationic behavior because most of the amine functions are protonated (Fig. 2), like Nchitosan.

For Pchitosan30, about 20-25% of the amine functions carry a bisphosphonic acid moieties.

At pH = 5, only one P-OH group is deprotonated to form P-O-(pKa 1 = 2.6 and pKa 2 = 6.7 [START_REF] Fal Ir Eas | Synt hesis and Aqueous Sol ut ion Pr opert ies of an Amino Bisphosphonat e Met hacrylat e Homo polymer via RAFT Polymer izat ion[END_REF]), which thus decreases the ZP (ZP = 20 ± 2 mV) as compared to Nchitosan (ZP = 39 ± 2 mV) but still remains positive. For pH > 6, Pchitosan is anionic. It is to be noted that Pchitosan250 solution showed a similar cationic behavior than that of the Pchitosan30 (not shown here). In the present study, the pH of the Nchitosan and Pchitosan solutions was fixed at 5 to ensure a cationic behavior for both solutions, even for the alginate solution since carboxylic acid groups are deprotonated at this pH (pKa = 3.5 [START_REF] Draget | Smidsr ød, Al gin ic acid gel s: t he effect of alginat e chemical composit ion and mol ecular weight[END_REF]). Moreover, the same pH value was used for all the solutions to avoid modification of the AA3003 surface during the formation of the LbL coatings [START_REF] Laufer | Clay-Chit osan Nanobr ick Wall s: Co mpl et ely Renewabl e Ga s Barr ier and Fla me-Retardant Nanocoat ings[END_REF].

Development of the LbL coatings on silicon wafers

Three LbL systems were investigated: alginate/Nchitosan30, alginate/Pchitosan30 and alginate/Pchitosan250. FTIR spectrum was recorded for each bilayer and for each system. Fig. 3 shows, as an example, the evolution of absorbance for the alginate/Pchitosan30 system, according to the bilayers number up to10 bilayers. Fr om Fig . LbL syst ems (Fig . 4). A l inear incr ease of t he absor bance is observed for t he t hr ee syst ems.

For 10 bilayer s, t he absorbance r ecorded for t he alginat e/Pchit osan250 coat ing is t he highest .

The absor bance for t he al ginat e/Pchit osan30 is sl ightly higher t han t hat of alginat e/Nchit osan30. Fr om t his r esult , it can be concluded t hat t he phosphorylat ion of nat ive chit osan sl ightly incr eased t he a mount of deposit ed chit osan. FE-SEM cr oss-sect ion observat ions of t he wafer /chit osan fil ms wer e perfor med for t he t hr ee LbL coat ings (Fig . 5). The micr ographs show t hat the t hr ee coat ings have a unifor m t hickness.

The al ginat e/Nchit osan30 and t he alginat e/Pchit osan30 LBL coat ings have r elat ively similar thickness values, i.e. 200 n m and 300 n m, r espectivel y. A h igher t hickness was measured for the alginat e-Pchit osan250 coat ing, around 500 nm, in good agr eement with t he FTIR r esult s. Thus, it can be concluded t hat t he use of phosphorylat ed chit osan wit h a high mol ecular weight l ed t o a higher t hickness for t he LbL coatings. At pH = 5, Nchit osan30 is a cat ionic pol ymer , which will show l inear confor mat ion when assembl ed wit h the anionic alginat e layer . On t he ot her way, we showed t hat at pH = 5, Pchit osan30 was zwitt er ionic (i.e. wit h maximum 20-25% of anionic charge and maximum 68-73% of cat ionic charge), which might lead t o some coil for ms due t o intramol ecular int eract ions bet ween cat ionic and anionic charges. Consequently, when associat ed t o t he anionic al ginat e layer , a h igher a mount of Pchit osan30 was deposit ed compar ed t o Nchit osan30. Mor eover , an incr ease of chit osan Mw, i.e. from 30 t o 250 kg mol -1 , has an influence on the LbL gr owth. The t hickening of t he layer for Pchit osan250 can be ex pla ined by a gr eat er entangl ement of t he polymer cha ins. As a consequence, a higher amount of Pchit osan250 was deposit ed, as compared t o Nchit osan or Pchit osan30.

Evaluation of corrosion protection of the AA3003 by the LbL coatings

EIS measurements were performed for the AA3003 LbL coated samples as well as for the uncoated AA3003 sample. For each system, the impedance diagrams were obtained consecutively for various immersion times (3 h, 12 h, 24 h and 48 h) in a 0.1 M Na 2 SO 4 solution. As an example, Fig. 6 shows the impedance diagrams obtained for the AA3003 coated with alginate/Nchitosan30 (10 BL). Independently of the immersion time, the diagrams are almost identical. They show a capacitive behavior and it can be observed that the impedance modulus and the phase angle slightly decrease at low frequency when the immersion time increases (more noticeable on the phase angle). Then, for comparison, the impedance diagrams obtained after 48 h of immersion for the three LBL coatings and for the uncoated sample are presented in Fig. 7.

The diagrams for t he t hree LbL coat ings ar e quit e comparabl e indicat ing similar corrosion pr ot ect ion perfor mance for t he differ ent syst ems. It can be underl ined t hat t he open circuit pot ent ial (OCP) for t he differ ent LbL syst ems deposit ed on t he AA3003 was r elat ivel y similar (-0.90 ± 0.5 V/MSE) in agr eement wit h t he impedance r esult s. The OCP was sl ightly shift ed towards mor e negat ive value by compar ison wit h the uncoat ed AA3003 sampl e (OCP = -0.85

± 0.2 V/MSE).
Despit e t he pr esence of the LbL f il ms, v isual ized on t he Si wafer s (Fig . 5), t he impedance diagrams ar e const it ut ed by a singl e t ime constant . The pr esence of an addit ional t ime constant in t he high fr equency range, charact er izing a fil m effect is not observed, as might be expect ed and as already observed for very t hin organic fil ms (20 n m) for med on a car bon st eel surface [START_REF] Baux | Impedance analysis of fil m-for ming a mines for the corrosion pr ot ect ion of a carbon st eel , El ectrochim[END_REF]. The impedance r esponse of t he LbL coat ings point ed out t hat t he barr ier pr opert ies wer e l ow, pr obably due t o a por ous structur e of t he coat ings. Thus, wit h and wit hout t he LbL coat ings, t he impedance diagrams charact er ize t he aluminum oxide fil m on the AA3003 surface. As can be seen in Fig. 6 and Fig. 7, the phase angle is always lower than -90° (maximum value around -87°) which indicates a non-ideal behavior of the AA3003 / LbL coating interface. From the impedance diagrams, some parameters can be extracted: the oxide film resistance (R ox ) and a constant phase element (CPE), which accounts for the nonideal behavior of the interface. The impedance of the CPE is given by Eq. 1:

= 1 ( ) Eq. (1)
With ω = 2πf and where α is related to the angle of rotation of a purely capacitive line on the complex plane plots and Q is a constant expressed in α -1 cm -2 s α .

In the present work, equivalent electrical circuits were not used to extract impedance parameters because all the parameters can be graphically determined [START_REF] Orazema | Enhanced Gra phical Repr esentat ion of El ectrochemical Impedance Data[END_REF]. The R ox values were obtained from the extrapolation at low frequency of the impedance modulus (when the phase angle decreases towards 0). The α parameter can be determined by plotting the logarithm of the imaginary part of the impedance (Z j ) with respect to the logarithm of the frequency (Eq. 2). Q is expressed as a function of and impedance data (Eq. 3):

= (-) ( )
Eq. ( 2)

= sin 2 -1 ( )(2 )
Eq. ( 3)

The and Q values are reported in Table 1 for t he differ ent syst ems and for var ious immer sion t imes. SEM on t he Si wafer s (Fig. 5).

SEM-EDX analysis was perfor med wit h a l ow energy (5 keV) t o compar e t he layer composit ion befor e (Fig . 9a and 9a ') and aft er 48 h of immer sion in t he Na 2 SO 4 sol ut ion (Fig . 9b and 9b'). The analysis was showed her e for t he alginat e-Pchit osan250 LbL coat ing. Befor e immer sion (Fig . 9a EIS data and EDX analysis revealed that chitosan/alginate LBL coatings allowed the AA3003 surface to be protected through a barrier effect, which decreased the active surface area in contact with the electrolyte. Nevertheless, during exposure to the Na 2 SO 4 solution, the barrier effect was limited, as shown from the impedance results, despite the presence of the coating, as proved by the EDX analysis. The limited barrier effect could be attributed to a swelling of the LBL coating, and to a partial solubility of the Nchitosan and Pchitosan in the aqueous solution.

Further mor e, t he phosphonic acid moiet ies graft ed onto chit osan allowed higher coat ing thicknesses t o be r eached compar ed t o nat ive chit osan (Fig . 5), but simil ar el ectrochemical behavior s wer e observed (Fig . 8 and Tabl e 1). One way t o impr ove t he barr ier pr opert ies of such coat ings might be t o perfor m an addit ional cross-l inking, aft er t he LbL deposit ion. Or , the bilayer should be more hydrophobic. In t his case, chit osan chemical modificat ion should be done pr ior t o perfor m the LbL deposit ion.

Conclusions

  Zetasizer 2000 system (Malvern Instruments LtD). The pH of the Nchitosan solution was adjusted at pH = 2 by adding acetic acid solution (1 M). The increase of pH was controlled by addition of NaOH (1 M). The applied voltage for driving electrodes of the capillary electrophoresis cell was 10 V. The Zetasizer 2000 cell was rinsed with deionized water before each experiment. All experiments were conducted at 25 °C.

  potential (ZP) measurements of the Nchitosan and Pchitosan solutions were performed to determine the global charge of the polymers. The ZP values of the Nchitosan30 and Pchitosan30, obtained at different pH values ranging from 2 to 10, are reported in Fig. 1.

Figure 1 .

 1 Figure 1. ZP of Nchitosan30 and Pchitosan30 as a function of pH.

Figure 2 .

 2 Figure 2. Structur e of stat ist ical Pchit osan30 at pH = 5, containing 8 % of acetylated mo iet ies, 68-73 % of a mine moiet ies and 20-25 % of a mino-bisphonic acid mo iet ies.

Figure 3 .

 3 Figure 3. FTIR spectra as a function of the bilayers (BL) number for the alginate/Pchitosan30 system.

Figure 4 .

 4 Figure 4. Absor bance at 1090 c m -1 as a funct ion of t he number of bilayer s for t he t hr ee LbL syst ems.

Figure 5 .

 5 Figure 5. FE-SEM micr ogra phs of t he cross-sect ions of Si wafer s coat ed with 10 bilayer s for : (a ) al ginat e/Nchit osan30, (b) al ginat e/Pchit osan30 and (c ) al ginat e/Pchit osan250.

Figure 6 .

 6 Figure 6. Electrochemical impedance diagrams obtained at E corr for the AA3003 coated with the alginate-Nchitosan30 (10 bilayers) for different immersion times in 0.1 M Na 2 SO 4 solution in Bode (impedance modulus (a) and phase angle (b)) and Nyquist (c) coordinate.

Figure 7 .

 7 Figure 7. Electrochemical impedance diagrams obtained at E corr after 48 h of immersion in 0.1 M Na 2 SO 4 solution for the uncoated AA3003 and the three LbL coatings (10 BL) in Bode (impedance modulus (a) and phase angle (b)) and Nyquist (c) coordinates.

Figure 9 .

 9 Figure 9. EDX analysis and SEM observations for the alginate-Pchitosan250 LbL coating: (a) and (a') before immersion and (b) and (b') after 48 h of immersion in the Na 2 SO 4 0.1 M solution.

  he viscosit y of t he sol ut ion, part icularly for t he Nchit osan[START_REF] Carosio | Ultra-Fast Layer -by-Layer Appr oach for Deposit ing Fla me Retardant Coat ings on Fl exibl e PU Foa ms wit hin Seconds[END_REF]. The differ ent chit osans wer e dissol ved in deionised wat er and t he pH was adjust ed t o 5 by addit ion of eit her acet ic acid for t he Nchitosan or Na OH for t he Pchit osan. Bot h substrat es (Si wafer and AA3003) were first dipped in a 0.1 wt. % BPEI (Branched PolyEthyleneImine) solution, leading to cationic charges onto their surfaces[START_REF] Carosio | Ca mino, All -pol ymer Layer by Layer coat ing as efficient solut ion t o pol yur ethane foa m flame r etardancy[END_REF]. The layer s wer e then deposit ed by alternat ing immer sion of t he sa mpl e dur ing 1 min in t he sol ut ion containing t he anionic pol ymer (alginat e) and then, dur ing 1 min in t he sol ut ion containing t he cat ionic pol ymer .Aft er each immer sion st ep, t he sa mpl e was washed wit h deionised wat er and dr ied wit h war m

	incr eased t
	). The negat ively charged sol ut ion was prepar ed wit h sodium al ginat e (1 wt . %, pH =
	5), whil e t he posit ivel y charged solut ion was pr epared from eit her Nchit osan30, Pchit osan30
	or Pchit osan250 (1 wt . %). Incr easing t he concentrat ion of chit osan in solut ion should r educe
	the t ime per deposit ion st ep but , in t he pr esent work, concentrat ion higher t han 1 wt . %

air . Up t o 10 l ayer s (BL) wer e deposit ed. Onl y Nchit osan30 was used to devel op t he LbL coat ing because t he Nchitosan250 was t oo viscous (even at l ow concentration) t o enabl e LbL assembl y. Thus, onl y t hr ee LbL syst ems wer e invest igat ed: alginat e/Nchit osan30, alginat e/Pchit osan30 and al ginat e/Pchit osan250.

  of phosphonic est er s t o phosphonic acids dur ing t he synthesis of Pchit osan30. Fr om Fig.3, t he absor bance at 1090 c m -1 (i.e. maximum wavel ength corresponding t o C-O-C bonds for bot h t he alginate and t he chit osan) was used t o follow t he fil m growth. The absor bance was pl otted as a funct ion of t he bilayer s number for t he t hree

	el ongat ion at 1594 c m -1 and symmetr ical el ongat ion at 1408 c m -1 , r espect ivel y. For t he
	Pchit osan30, t he t wo vibrat ions at 1656 and 1589 c m -1 ar e attr ibut ed t o amide I and t o N-H
	bending[38] of NH

3, it is possibl e t o depict vibrat ions of bot h alginat e and Pchit osan 30. For t he alginat e, t he vibrat ions of t he COO -car boxylate group

[START_REF] Lawr Ie | Int eract ions bet ween Al ginat e and Ch it osan Bio pol ymer s Character ized Using FTIR and XPS[END_REF]

ar e cl early visibl e: asymmetr ic 2 , r espect ivel y. The ma in phosphonat e band is al so observed at 1190 c m -1 due t o t he el ongat ion of t he P=O doubl e bond

[START_REF] Illy | New prospect s for the synthesis of N-al kyl phosphonat e/phosphonic acid-bear ing ol igo-chitosan[END_REF]

. The pr esence of t his peak is due t o t he part ial hydrolysis

Table 1 .

 1 Parameters obtained from the impedance data for the uncoated AA3003 and the three LbL coatings(10 BL) after different exposure times to 0.1 M Na 2 SO 4 solution.The var iat ion of R ox as a funct ion of t he exposur e t ime t o t he Na 2 SO 4 sol ut ion is shown in Fig .This assumpt ion is in agr eement wit h t he var iat ion of Q vs t he immer sion t ime (Table1). The Q value, related to the oxide film capacitance, increases with time indicating a decrease of the oxide film thickness.For t he t hr ee LbL coat ings, R ox sl ightly decr eases dur ing t he fir st hour s of exposur e t o t he el ectrolyt e and t hen r emains constant . Aft er 48 h of immer sion, t he R ox values ar e similar for the t hr ee syst ems and t hey ar e at l east t wo order s of magnit ude higher for the coat ed sa mpl es (10 8 Ω c m 2 ) by compar ison wit h t he uncoat ed sampl e (5 10 5 Ω c m 2 ), suggest ing a decr ease of the act ive surface ar ea by t he coat ings, since t her e is no modificat ion of t he α and Q paramet er s. Th is last r esult indicat es t hat t he chitosan phosphorylat ion did not impr ove t he corrosion pr ot ect ion of the AA3003 by compar ison wit h t he nat ive chit osan although t he LbL coat ings t hickness was higher , in part icular for t he alginat e-Pchit osan250, as observed by

		Immersion time	α	Q
	Sample	(h)
				(MΩ -1 cm -2 s α )
		3	0.94	3.2 ± 0.1
	Uncoated AA3003	12 24	0.94 0.94	3.6 ± 0.2 4.2 ± 0.2
		48	0.94	4.3 ± 0.2
		3	0.94	4.2 ± 0.2
	AA3003/Alginate-	12	0.94	4.3 ± 0.2
	Nchitosan30	24	0.94	4.3 ± 0.1
		48	0.94	4.5 ± 0.1
		3	0.93	3.7 ± 0.1
	AA3003/Alginate-	12	0.94	4.3 ± 0.1
	Pchitosan30	24	0.93	4.5 ± 0.1
		48	0.94	4.8 ± 0.2
		3	0.94	3.7 ± 0.1
	AA3003/Alginate-	12	0.94	3.9 ± 0.1
	Pchitosan250	24	0.94	4.0 ± 0.1
		48	0.94	4.2 ± 0.1

8.

Figure

8

. R ox as a funct ion of t he immer sion t ime in 0.1 M Na 2 SO 4 sol ut ion for t he uncoat ed AA3003 and for t he t hr ee LbL coat ings (10 BL).

For t he uncoat ed AA3003, t he R ox values decr eases wit h incr easing immer sion t ime. Th is might be attr ibut ed t o the corrosion pr ocess which induces a l ocal pH incr ease on t he aluminum surface due t o t he cathodic r eact ion (oxygen r educt ion)

[START_REF] Jorcin | Gal vanic Coupl ing Bet ween Pur e Co pper and Pur e Aluminum : Ex per imental Appr oach and Mat hematical Model[END_REF]

. As a consequence, t he nat ive aluminum oxide t ends t o dissolve (chemical r eact ion) when t he immer sion t ime incr eases.

  and 9a '), t he analysis reveal s t he pr esence of C, N, O and P peaks confir ming t he pr esence of t he alginat e and t he Pchit osan on t he AA3003 surface. It is worthy to not e t hat t he Al peak is not det ect ed, which might indicat e t he pr esence of a unifor m LbL coat ing, as shown by t he SEM observat ions on t he Si wafer s (Fig .5). Aft er immer sion in t he Na 2 SO 4 sol ut ion (Fig .9band 9b'), t he C, N, O and P peaks ar e st ill visibl e, showing t hat t he LbL coat ing is al ways pr esent on t he AA3003 surface. Aft er immer sion, Al is det ect ed which suggest s t hat t he LbL coat ing was da maged dur ing t he immer sion. In addit ion, t he Na and S peaks ar e observed, indicat ing t he pr esence of sodium sulfat e (from t he el ectrolyt e) in t he LbL coat ing. The EDX analyses confir med t hat a LBL coat ing was for med on t he AA3003 surface but t he barr ier effect was l imit ed (penetrat ion of t he el ectrolyt e and pr esence of t he Al peak).

Funding Sources

This work financially supported by the Direction Générale de l'Armement (DGA). The authors gratefully acknowledge the DGA for this support.

Layer-by-Layer coatings comprising alginate and either unmodified or phosphorylated chitosan at different molecular weights were evaluated for their potential to reduce the corrosion of an aluminum alloy 3003. First, the growing rate of the LbL coatings was determined on Si wafers by measuring the IR absorbance according to the bilayers number.

The system containing phosphorylated chitosan appeared to grow faster than that with the unmodified chitosan. FE-SEM observations revealed coating thicknesses between 200 nm and 500 nm according to the type of chitosan. It was found that the use of phosphorylated chitosan at 1 wt. % and high molecular weight (250,000 g mol -1 ) promoted the deposition of thicker coatings. The corrosion protection of the AA3003 was assessed by electrochemical impedance spectroscopy in a Na 2 SO 4 0.1 M solution. It was shown that the three LbL systems afforded similar corrosion protection by reducing the active surface area by comparison with the uncoated sample. Even if the EDX analysis has confirmed the presence of the coating on the metal surface, the EIS measurements revealed a limited barrier effect.

AUTHOR INFORMATION

Corresponding Author

*Gh islain DAVID: Gh islain.david@enscm.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally.


Céline Badouard

Fanny Traon

Clément Denoual

Claire Mayer-Laigle

Gabriel Paës

Alain Bourmaud

Exploring mechanical properties of fully compostable flax reinforced composite filaments for 3D printing applications

Keywords: Fused Deposition Modelling, Biocomposites, Flax fibres, Flax shives, Mechanical properties

Plant fibres are increasingly used for composite reinforcement, but valorization of by-products such as flax shives still needs to be developed. Also, additive manufacturing, such as Fused Deposition Modelling (FDM), is strongly progressing and can be of great interest to implement biocomposite solutions. The present work focuses on the development of innovative and fully biodegradable filaments for FDM. Three polymer matrices were tested: PLLA, PLLA/PBS 50/50 %-wt and PBAT. A filler content of 30-wt% has been achieved using flax shives with PBAT. Flax fibres and shives reinforced 3D printed parts exhibit promising performances and printability, highlighting their potential to successfully develop fully compostable filaments.

Introduction

Reinforcement of thermoplastic polymers with plant fibres is constantly increasing due to their high mechanical or environmental potential [START_REF] Bourmaud | Towards the design of high-performance plant fibre composites[END_REF]. Biocomposites can be implemented by injection moulding, compression and the promising concept of 3D printing [START_REF] Bourmaud | Towards the design of high-performance plant fibre composites[END_REF]. Their mechanical properties mainly depend on plant fibre type, aspect ratio (length/diameter) and quality of interface between the reinforcement and the polymer matrix. An important drawback of plant fibres is their moderate thermal resistance, potentially responsible for a decrease of the composite properties due to the thermo-mechanical shear rate occurring during the process [START_REF] Bourmaud | Towards the design of high-performance plant fibre composites[END_REF]. The choice of the polymer matrix is a key point for obtaining high quality manufactured final product, which will strongly determine the quality of the interface with fibres and the process temperature, which must remain moderate (between 100-160 °C) in order to preserve the properties of the plant walls.

Fused Deposition Modelling (FDM), is a 3D printing technique enabling the manufacture of objects from digital 3D model data, usually layer-by-layer. 3D printing and especially FDM has attracted attention in the last years due to its high speed technique to produce parts with complex shape and geometry. Moreover, it is currently the most commonly used additive manufacturing technique due to the wide range of materials possibly used, from neat thermoplastics to composites and even biocomposites [START_REF] Wang | Preparation of 3D printable micro/nanocellulose-polylactic acid (MNC/PLA) composite wire rods with high MNC constitution[END_REF]. One of the restricting factors for biocomposites manufacturing, and especially for 3D printing, is the incorporation of plant fibres.

Recently, the possibility to use milled biobased products (such as miscanthus, seashell or rice husk) was demonstrated, using 3D printing machines with inkjet print heads. In this case, morphology and preparation of powder are the main key points to obtain performing composites [START_REF] Zeidler | 3D printing of biodegradable parts using renewable biobased materials[END_REF]. For FDM applications, size of particles is also a technological bottleneck regarding 3D printer nozzle size (generally between 0.4 and 1.0 mm) which implies an intense milling step. Indeed, grinding processes can lead to high heterogeneity and a loss in the mechanical properties of the composite [START_REF] Berthet | Sorting natural fibres: A way to better understand the role of fibre size polydispersity on the mechanical properties of biocomposites[END_REF] mainly due to the decrease of the fibre aspect ratio. Specific techniques were developed to adapt the mechanical stress generated by the milling machines to the properties of the raw materials and hence to modulate the properties of the obtained powders [START_REF] Motte | Elastic properties of packing of granulated cork: Effect of particle size[END_REF]. Moreover, dry separation techniques, such as electrostatic or triboelectric separation enable to regulate the particle properties such as particle size and shape distribution, spreading of these distributions, composition and surface properties of the particles [START_REF] Mayer-Laigle | DRY biorefineries: Multiscale modeling studies and innovative processing[END_REF]. Finally, the filler dispersion and the crystallinity must be controlled to ensure a good-quality printing, especially regarding the shrinkage behaviour during the cooling step. In this context, most of the polymers used for FDM are amorphous or display a reduced crystallinity index [START_REF] Benwood | Improving the Impact Strength and Heat Resistance of 3D Printed Models: Structure, Property, and Processing Correlationships during Fused Deposition Modeling (FDM) of Poly(Lactic Acid)[END_REF] to limit shrinkage and preserve polymer properties, inter-layer deposition and final part homogeneity. Finally, for biocomposites, the fibre volume fraction is also an important parameter. Impact of wood fibre content on PLA-wood filaments was studied and showed a decrease in tensile strength of the filaments due to the presence of higher void quantities and fibre clusters [START_REF] Kariz | Effect of wood content in FDM filament on properties of 3D printed parts[END_REF].

The purpose of the present study is to investigate the development of 3D printable biocomposites reinforced with flax fibre and shives by comparing the mechanical properties of injected and 3D printed tensile specimens prepared with different matrices (PLLA for the reference, PBS and PBAT). The impact of the volume fraction and nature of the reinforcement, fibre or shive is also discussed.

Materials and methods

Materials

The flax fibre (Linum usitassisimum L.) used in this study is from the Alize variety (harvested in 2014) and was cultivated in Normandy (France). After dew retting and industrial scutching, flax fibres were cut at 1 mm length; the tensile Young's modulus, strength and elongation at break of the elementary scutched flax fibres were 53.8 ± 14.3 GPa, 1215 ± 500 MPa and 2.24 ± 0.59, respectively. Shives were first precrushed using a SM 300 knife mill with a 0.5 mm grid (Retsch, France) then fine milled with an UPZ impact mill with a 0.3 mm grid (Hosokawa Alpine®, Germany). The particle size distribution of shives and fibres was determined by laser diffraction using a laser diffraction particle size analyser Hydro 2000S (Malvern Instruments Ltd., United Kingdom) with liquid ethanol (ethylic alcohol: 96% v/v) carrier to avoid particle swelling. Three biodegradable polymers were used as matrices: Poly-(lactid) PLLA (7001D, Nature Works), Poly-(butyl-adipate-terephthalate) PBAT (Ecoflex® F Blend C1200, BASF) and Poly-(butylene-succinate) PBS (Bionolle 1020 MD, Showa Denko).

Processing

All raw materials were dried 15 hrs at 50 °C prior to the extrusion step to remove water. The formulated compounds were PLLA-10%-wt flax fibres (PLLA-10-F), PLLA/PBS 50/50-10%-wt flax fibres (PLLA-PBS-10-F), PLLA/PBS 50/50-10%-wt flax shives (PLLA-PBS-10-S) and PBAT-flax fibres at 10, 20 and 30%-wt (PBAT-10-F, PBAT-20-F and PBAT-30-F). All batches were compounded with a Bradender twin screw extruder at 20 rpm and 190 °C for PLLA composites and 150 °C for PBAT composites. The extruded composites were then granulated to obtain pellets, which were also dried at 50 °C and then injected to produce tensile specimens with a Battenfeld HM 80/210 injection press. Pellets were then extruded using a single-screw Scamex extruder (L/D = 20 and die diameter = 4 mm) to produce the filament. Filament thickness was adjusted to 2.85 ± 0.1 mm with a controlled diameter using a Zumbach 18 XY dual axis laser measuring head. 3D Printing was made using a Prusa i3 Rework 3D printer with Simplify 3D software and equipped with a 1.0 mm nozzle and an extrusion temperature of 190°C and 150°C for PLLA and PBAT composites, respectively. For all blends, printing speed and Z amplitude varied from 0.8-1.5 m.min -1 and 0.6-1.0 mm, respectively. All blends with 10 wt% flax were quite simple to process, by both extrusion or printing step. Due to higher fibre fraction used with PBAT matrix, appearance of a shark skin phenomenon was noticed during filament manufacturing for 20%-wt and 30%-wt flax fibre loadings. In addition, for PBAT-30-F-I3D, some variations in extrusion flow rate were observed during 3D printing due to the increase of viscosity induced by higher fibre content. Then, tensile specimens were printed with a rectilinear filling pattern (100%) oriented at 0° with respect to the tensile direction. During all the printings, the printing surface temperature was maintained at 70°C.

Characterization

Tensile specimens were conditioned at room temperature (23°C and 48% relative humidity) for thermal and hygroscopic stability and characterized using MTS Synergie RT/1000 tensile machine with a 10 kN sensor according to the ISO 527 standard. These tests were performed using an extensometer (gauge length = 25 mm) and at crosshead speed of 1 mm/min and 50 mm/min for PLLA and PBAT matrices, respectively. Five dog bone specimens (180 x 10 x 4 mm) were analysed for each batch and average values of Young's modulus, stress at yield and elongation at break were determined. Raw fibres and shives were characterized by scanning electron microscopy (SEM) using a JEOL JSM 6460LV microscope at 20 kV. In addition, morphology of composites was examined. Tensile specimens were cut using an automatic saw and carefully polished to a 1µm particle size finish solution. All samples were metallised with gold before being observed.

Results and discussions

Investigation of flax fibres and fines morphology

Figure 1 shows the particle size distribution of cut fibres and milled shives obtained by laser granulometry as well as SEM images of both reinforcements. Shives and fibres exhibit significant differences in size. Shives have a mono dispersed distribution with a peak at 220 µm and a median diameter value d(0.5) of 162 µm.

Differing from results obtained with shives, size distribution of fibres evidences the presence of three peaks, with maximum values around 20 µm, 125 µm and 650 µm (Fig 1 .A). This three-modal distribution was attributed to the response of the mathematical model of the particle size analyser applied to the diffraction image of flax elongated fibre. In addition, when a flax fibre batch is cut to produce short fibres, it was shown that (1) the main fibre fraction reached the targeted cut length and (2) the cutting process induces the production of the so-called fines particles, having a maximum length of 200 µm as defined by [START_REF] Le Moigne | A statistical analysis of fibre size and shape distribution after compounding in composites reinforced by natural fibres[END_REF]. Figure 1.A confirms this specific behaviour of plant fibres, mainly due to destructuration of cell walls or to fibre length reduction induced by the presence of defects such as kink bands along the fibre length. Regarding SEM images, fibres seem to present homogenous lengths, which confirms that the distribution profile is an artefact due to the assumption of spherical particle made by the model used during laser particle size analysis. One can note that several fibres display a larger diameter. Indeed, within the flax stem, fibres are assembled into bundles which could remain cohesive after scutching, depending of the retting degree of the batch [START_REF] Bourmaud | Towards the design of high-performance plant fibre composites[END_REF].

Choice of the relevant polymer matrix

Table 1 gathers the measured mechanical properties for different injected and 3D printed samples. When flax fibres were added as reinforcements, all composite samples exhibited an increase in Young's modulus, regardless of the considered matrix and the processing tools used (injection or 3D printing). As previously described [START_REF] Tymrak | Mechanical properties of components fabricated with opensource 3-D printers under realistic environmental conditions[END_REF], 3D printed mechanical properties of specimens are generally lower than those of injected ones due to presence of pores. Figure 2 shows cross sections of PLLA-10-F, PLLA-PBS-10-F and PBAT-10-F 3D printed specimens. Interestingly, whatever the considered matrix, inter-strand porosity is limited and the interface between printed layers are not clearly visible. However, porosities exist and are more numerous for PLLA-10-F sample which exhibits the highest tensile strength drop. Regarding the tensile strength of 3D printed or injected samples, values measured are always lower as compared to raw polymers except for PBAT matrix. Because of the important strain of this composites, these strength values are not representative of a common use of the material, these latter being generally used in a reduced range of elongation. For other formulations, injected composites exhibit tensile strength similar to raw polymers but a significant decrease was noticed for 3D printed parts with a loss of 35.7% and 18.5% for PLLA and PLLA-PBS blends, respectively. Tensile strength is dependent on the homogeneity and cohesion of composites and, even if printed materials had been subjected to a second extrusion step (for the implementation of the filament), this single screw melt could not be considered as an influencing compounding and homogenization step. Tensile strength is directly impacted by the presence of fibres bundles and also by large pores as observed on the PLLA-10-F sample. In the case of 3D printed composites, the reduced elongation at break, in comparison to the injected samples (Table 1), highlighted the presence of important defects such as porosities due to the printing step. Figure 4 confirms this statement by showing the important porosity fraction observed on 3D printed PLLA-10-F sample as compared to the injected ones, attributed to the specific layer-by-layer process and the filament manufacturing.

In addition to the clear correlation existing between strength values and presence of porosities within the samples, Young's modulus was also impacted. Indeed, a drop of 16.7%, 6.1% and 20.2% is observed for 3D printed PLLA-10-F, PLLA-PBS-10-F and PBAT-10-F, respectively, as compared to injection moulded samples.

These differences are mainly due to the ability of the composites to be 3D printed and material parameters since stiffness, thermal properties and viscosity are of great interest for an efficient printability. Regarding pure PLLA, its high stiffness, improved when plant fibres are added, induces processing problems such as filament breakage or extrusion feeding instability. Low fibre contents may also be a drawback when flexible PBAT matrix is used, leading to irregularities in filament extrusion process, driving force or diameter control inducing instabilities during filament deposition. These difficulties during processing and printing favour the presence of porosities that have a clear effect on the mechanical performance of the printed parts. Mechanical performances are impacted by the mechanical properties of fibres and matrix and also by the orientation of the fibres and by the quality of the stress transfer between matrix and fibres; in case of high porosity content, the stress transfer is reduced and values of strength or stiffness greatly impacted.

Impact of the volume fraction and nature of the reinforcement

Finally, the influence of the fibre content was studied. PBAT material was selected due to its flexible behaviour , enabling higher loadings, with a relatively low melting temperature (about 115°C). Ideally, for 3D printing, obtaining a semi-rigid material is a need to favour winding and printing steps. PBAT was filled with 10, 20 and 30 wt% flax fibres. As the filler content increased in PBAT blends, the Young's modulus (Fig. 3A) and stress at yield (Fig. 3B) increased for both processes (FDM and injection moulding). The printed tensile specimens showed lower Young's modulus and stress at yield than those injected but remained significantly higher than the native material. These results demonstrated that it is possible to reinforce a flexible matrix up to 30%-wt flax fibres for 3D printing application. It only requires an increase of the printing temperature to fit the viscosity of the materials. As explain in the Materials and Methods section, a 1 mm nozzle was selected to print the specimen to avoid the formation of clusters formed for high fibre fractions. A 0.4 or 0.6 mm nozzle might possibly be used in future work through the optimization of both fibre dispersion and granulometry.

Finally, an alternative solution, using flax shives was explored. For these experiments, a PLLA-PBS matrix was chosen for its good compatibility with flax and its high elongation at break which makes it well suitable for 3D printing process. Length of shives is significantly smaller than fibres (Fig. 1) and has consequently a reduced aspect ratio. Thus, Young's modulus of composite reinforced with shives was reduced as compared to those of PLLA-PBS-Flax fibres (Table 1). Interestingly, this latter was significantly higher than neat PLLA/PBS. As for the previous blends, Young's modulus of shives reinforced printed specimens was lower than injected ones but tensile strength values were in the same order for both injected and 3D printed samples. The smaller size of shives, as compared to fibres, is probably a significant advantage to improve the quality of 3D printed parts, due to a better dispersion of the reinforcement induced by the important shear rate occurring during the extrusion cycle needed to produce the filaments.

Conclusion

This work explored the use of flax fibers and shives to develop biodegradable filaments for 3D printing. It was shown that the choice of matrix is an important parameter to control the mechanical performance of the materials produced. Depending on their initial elongation, the considered polymers may accept more or less fibre volume fractions. Interestingly, PBAT appears to be a suitable candidate due to its flexibility. Finally, the crushed flax shives demonstrated their potential in reinforcing, providing high stiffness and strength when incorporated into a PLLA-PBS matrix and opening the way for a possible valorisation of these co-products of flax cultivation. Table 1. Tensile properties of raw polymers and flax fibres or shives reinforced composites with several of biodegradable matrices. Elongation at break of native PBAT cannot be obtained due to its excessive elongation. INJ = injected; 3DP = 3D printed; F = fibres and S = shives.

Sample

Young's Modulus (MPa)

Strength at max (MPa)

Elongation at break (%)

Figure caption Figure 1 .

 caption1 Figure caption Figure 1. Size distribution (A) and SEM images of flax shives (B) and fibres (C). Scale bar is 500 µm.

Figure 2 .

 2 Figure 2. SEM observation of composite cross section for 3D printed PLLA-PBS-10-F, PLLA-10-F and PBAT-10-F. Scale bar is 500 µm.

Figure 3 .

 3 Figure 3. SEM observation on composite cross section for injected (A) and 3D printed PLLA-10-F (B) sample. Scale bar is 500 µm.

Figure 4 .

 4 Figure 4. Evolution of tensile modulus (A) and strength (B) for injected and 3D printed PBAT-flax fibres composites.

Figure 1 .

 1 Figure 1. Size distribution (A) and SEM images of flax shives (B) and fibres (C). Scale bar is 500 µm.

Figure 2 .

 2 Figure 2. SEM observation of composite cross section for 3D printed PBAT-10-F, PLLA-10-F and PLLA-PBS-10-F samples. Scale bar is 500 µm.

Figure 3 .

 3 Figure 3. SEM observation of composite cross section for injected (A) and 3D printed PLLA-10-F (B) sample. Scale bar is 500 µm.

Figure 4 .

 4 Figure 4. Evolution of tensile modulus (A) and strength (B) for injected and 3D printed PBAT-flax fibres composites.

Acknowledgements

The authors want to acknowledge the French National Institute for Agricultural Research (INRA) for funding this work through the collaborative project FLUOFLAX4D.


Chang Xu

Jiayuan Liu

Chuong Nguyen
email: chuong.nguyen@csiro.au

Benoit Fabien Casten
email: fabien.castan@technicolor.com

Simone Gasparini
email: simone.gasparini@irit.fr

3D reconstruction of insects: an improved multifocus stacking and an evaluation of learning-based MVS approaches

3D reconstruction of insects from photographs is a challenging task as it requires to tackle several problems such as strong out-of-focus areas in macro-photography, thin structures (insect legs and hairs), flat-colored surfaces (insects shells), non-Lambertian (shells specularities) and even translucent surfaces (wings). In this work, we first present a new lens-based image registration technique for accurate multi-focus stacking suitable for 3D reconstruction purposes while other methods create in-focus images for viewing purpose only. We then evaluate and compare the classical Multi-View-Stereo (MVS) reconstruction pipeline for small and complex objects with recent deep learningbased reconstruction methods such as the Neural Radiance Fields (NeRF) and the Neural Sparse Voxel Fields (NSVF). We present an assessment of different sources of errors for the considered methods. The results are compared both quantitatively and qualitatively across the different methods. From this analysis we present a series of practical guidelines for addressing the common issues of the reconstruction of small objects under challenging conditions.

Introduction

Traditional multiview stereo (MVS) reconstruction [21] has become a popular tool for image-based 3D reconstruction and readily available as in a number of open-source and commercial software [20,[START_REF] Griwodz | AliceVision Meshroom: An open-source 3D reconstruction pipeline[END_REF]2,[START_REF] Agisoft | Agisoft -Metashape (Photoscan)[END_REF][START_REF]Realitycapture: Mapping and 3d modelling photogrammetry[END_REF][START_REF]3Dflow. 3DF Zephyry -photogrametry software -3d models from photos[END_REF]. MVS by itself has shown to be sufficiently accurate for large scale scenes and objects [START_REF] Frahm | Building rome on a cloudless day[END_REF]12]. However, 3D reconstruction of insects and biological specimens is challenging due to * These authors contributed equally to the work. small sizes, fine features, complex surface properties, and transparency. These problems have been tackled by multiple works [17,22,[START_REF] Plum | scAnt -an open-source platform for the creation of 3d models of arthropods (and other small objects)[END_REF] by extending MVS to work with multifocus images. Multifocus multiview stereo (MMVS) has been developed and applied with significant success to create true-color 3D models of challenging specimens: • Small size (a few mm to a few cm long) is overcome by using a high magnification lens. As such lens has narrow depth of focus, a set of multiple partially-focus images are captured with a focal plane moving across the whole depth of the object as shown in Fig. 1. These images are then registered and "stacked" to produce a synthetically in-focus image for a single view. Repeating the same process for multiple views [17] to be used for 3D reconstruction. Careful camera calibration for multifocus image registration improved the accuracy of 3D reconstruction [22]. The issue of perspective inconsistency was discovered and solved by a fixed lens setup [START_REF] Li | Perspective-consistent multifocus multiview 3D reconstruction of small objects[END_REF][START_REF] Shah Ariful | Fixed-lens camera setup and calibrated image registration for multifocus multiview 3d reconstruction[END_REF]. • Specular reflection interferes with stereo matching and cause significant error. It could be reduced by dome illumination [22] or polarisation filter. • Fine and thin structure is another challenge for pose and depth estimation of MVS. Backlight illumination and automatic masking and Visibility-Consistent Meshing (Agisoft Photoscan [START_REF] Agisoft | Agisoft -Metashape (Photoscan)[END_REF]) were used to improve depth estimation to some extent [22]. Hair-like structures and surfaces are still a challenge. • Transparency is the most challenging problem, often leading to incomplete 3D reconstructed models. Such 3D models need to be fixed manually with postprocessing using 3D editing software [START_REF] Plum | scAnt -an open-source platform for the creation of 3d models of arthropods (and other small objects)[END_REF].

These issues remain partially and continue to be an obstacle to more realistic 3D modeling of objects. "Out-ofthe-box" solutions could open to new possibilities including a) ground-truth or prior information for camera poses and image registration, b) deep-learning based 3D reconstruction. Using accurate motorised control could provide known poses for captured images, therefore potentially removing a major source of error. Recent progress in deep-learning based 3D modeling including NeRF [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF] and NSVF [START_REF] Liu | Neural sparse voxel fields[END_REF] also leads to better modeling complex geometries and surfaces.

The paper proposes three main contributions. We present (i) a new lens-based image registration technique (c.f . Section 2) for accurate multifocus stacking (c.f . Section 3.2) suitable for 3D reconstruction while other methods create in-focus images for viewing purpose only. We then present (ii) an extensive assessment of different sources of errors (c.f . Section 3) for the 3 selected methods, MVS, NeRF and NSVF. The results are compared and validated both quantitatively and qualitatively across the different methods. From this analysis, we present (iii) a series of guidelines (c.f . Section 4) for tackling the major challenges that arise when reconstructing small object under challenging conditions. Code and data used in this paper are released in open source 1 .

Methodology

Multi-focus capture and stacking

Image capturing with fixed lens. For conventional multi-focus image capturing, the lens and camera moves 1 https://github.com/chuong/3d_insect_recon_validation together, so as the lens move, the distance and scale of different parts of the object changes differently, leading to perspective distortion. To overcome this issue, fixed-lens [START_REF] Li | Perspective-consistent multifocus multiview 3D reconstruction of small objects[END_REF][START_REF] Shah Ariful | Fixed-lens camera setup and calibrated image registration for multifocus multiview 3d reconstruction[END_REF] is used where the camera lens is fixed, only the image sensor moves step by step when capturing images as shown by Fig. 1. The image formation follows the lens equation d 2 = d1f d1-f , where d 2 represents distance from camera lens to image sensor, d 1 represents distance from camera lens to focal plane, and f represents focal length.

The camera needs to change the position of its focal plane such that the overlap of multiple depth of fields (DOF), i.e. the distance range at which parts of the object are in focus, covers the full depth of the specimen. It is determined by the circle of confusion with diameter φ COC which describes the point spread of a light source directed onto the focal plane by the lens. An image is considered in focus as long as the size of the point formed on the image plane is smaller than φ COC (usually chosen to be 0.1% of the image width). The relation between DOF and φ COC is illustrated by Fig. 1 and given by DOF = 2 d1f φ COC (d1-f )φa , where φ a is the diameter of lens aperture. By moving image sensor, d 2 changes and so does d 1 without changing perspective projection. For a specimen with max depth length D, the number of images to capture is N = D DOF with the moving step ∆d 2 = d 2 -(d1+DOF )f (d1+DOF )-f . Image alignment. Before focus stacking, the images are aligned by homography transformation between one image to a reference image. Homography transformation can be computed using directly matching the images of the specimen. To improve the estimation accuracy of homography transformation, a calibration target could be used. A dual calibration target forming an angle of 90°(c.f . Supplementary material) was used to allow larger depth range.

Focus stacking. To stack the multi-focus images, they were firstly aligned to a reference image in the stack by using the computed homography matrices. Once the images were aligned, their in-focus regions were fused by computing the weight using Laplacian of Gaussian Pyramid [24].

Background removal. The image capturing process was done in frontlight and backlight environment. The backlight images served as the masks to remove the background noise in frontlight images. The background removal was done by firstly converting the backlight images to binary images that outlines the object's silhouette, and performing bit-wise operations with the frontlight images.

Image alignment method using lens equation

For fixed-lens image capturing, the image sensor only translates back and forth, so captured images only experience scaling changes:

S(i) = d 2 (ref ) d 2 (i) (1)
where d 2 (ref ) and d 2 (i) are the distances from the lens to the image sensor for a reference image and an arbitrary image i.

To account for the optical centre in the middle of the image, an offset from the top-left corner to the middle is also included. The homography for fixed-lens setup becomes:

H(i) =   S(i) 0 1 2 w(-S(i) + 1) 0 S(i) 1 2 h(-S(i) + 1) 0 0 1   (2)
where w and h are the image width and height.

The affine homography transformation given by Eq. (2) for focus stacking for fixed lens camera setup is a special case of the one described in [START_REF] Shah Ariful | Fixed-lens camera setup and calibrated image registration for multifocus multiview 3d reconstruction[END_REF]. Equation ( 2) is a simpler and more practical solution with the assumption that camera sensor is aligned well enough with the macro rail.

Image-based reconstruction methods

Multiview stereo reconstruction (MVS). MVS was performed using the open-source 3D reconstruction software Meshroom [START_REF] Griwodz | AliceVision Meshroom: An open-source 3D reconstruction pipeline[END_REF]. It provides a graphic interface that enables the user to customise a reconstruction pipeline, execute the reconstruction, and visualize estimated camera poses, dense point cloud and resulting 3D models. The 3D reconstruction pipeline for Meshroom can be summarized as follows: structure from motion to estimate camera poses and sparse point cloud, depth map estimation to generate dense point cloud, and meshing the dense point cloud and texturing the mesh.

Neural Radiance Fields (NeRF). NeRF is a multilayer perceptron (MLP) deep network [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF] that trains on a set of multiview input images to synthesise new realistic view or extract 3D shape model. For each view, NeRF takes as input a 5D vector including the spatial location coordinate x, y, z, and viewing azimuthal angle θ and polar angle φ relative to the reconstructed volume. NeRF requires images, camera poses and camera intrinsics as inputs. Camera poses can be estimated using traditional structure from motion.

Neural Sparse Voxel Fields (NSVF). NSVF is an MLPbased reconstruction approach similar to NeRF, but it incorporates sparse voxel octree for efficient rendering training and rendering [START_REF] Liu | Neural sparse voxel fields[END_REF]. While NeRF allocates a fixed computational budget for every ray, NSVF only calculates the ray through only the sparse voxels. Therefore, NSVF can compute faster and more efficient than NeRF, theoretically over ten times faster. NSVF takes images, camera poses, camera intrinsics, and bounding box as inputs.

Validation strategies

In this paper, we examine the impact of all important sources of errors to the final 3D reconstruction quality of challenging objects. We also validate MVS, NeRF and NVSF approaches against each other.

Effect of different image registrations for multi focus stacking. This is important when dealing with small objects and multifocus stacking before performing 3D reconstruction. The alignment could rely on the information contained in the object images, calibration images, or image formation via lens equation.

Effect of distribution of camera poses when taking multiview images. As a pan-tilt motorised stage is often used to rotate the object or move the camera on a spherical surface, the distribution of the camera poses around the object is often non-uniform. Three strategies of pose distribution are examined in this paper.

Effect of image resolutions. Low-cost lenses often yield low optical resolution and this could put a constraint the effective image resolution and therefore the quality of the final 3D reconstructed models. This paper aims at investigating how critical image resolution is to different 3D reconstruction approaches.

Effect of prior pose estimation. All 3D reconstruction approaches require camera poses of the input images to perform. The camera poses could be estimated by structure from motion, or prior-calibrated pose by a pan-tilt motorised stage. This paper aims to find out how much ground truth poses improve the 3D reconstruction as compared to using estimated poses.

Effect of different object geometries and materials, including transparency and reflection. These are known to be challenging for MVS, studies of NeRF and NSVF suggest that they could handle these challenging problems.

To validate the accuracy of different alignment methods for focus stacking, Structure Similarity Index (SSIM) [25] was used. This metrics quantifies the difference between an image and a reference ground-truth image. The closer the score is to 1, the more similar the two images are.

Validations of 3D reconstruction accuracy are also performed by computing the Hausdorff distance (using Mesh-Lab [START_REF] Cignoni | MeshLab: an Open-Source Mesh Processing Tool[END_REF]) of 3D reconstructed meshes relative to the groundtruth 3D meshes. Hausdorff distance is defined as the largest distance between two meshes. So when comparing two meshes, large Hausdorff distances indicate missing features in the reconstruction results. Once Hausdorff distance was computed and normalised by the diagonal distance of the 3D mesh bounding box, it is visualised as heatmap on the ground truth meshes.

Results

Data generation and preprocessing

3D rendering and ground truth poses. The experiment used synthetic images of realistic 3D scanned models from [22,[START_REF]disc3D. Digital archive of natural history (DiNArDa)[END_REF] rendered in Blender so that the 3D models could serve as the ground truth meshes to validate the effect of using different parameters in the 3D reconstruction pipeline.

The image capturing environment was modelled using an open-source Blender add-on for photogrammetry partially based on [START_REF] Alicevision | ScanRig: Multi-Cameras/Lighting Acquisition Setup for Photogrammetry[END_REF]. The Blender add-on generates a vertical array of cameras using the settings user provided. Each camera rotates around the object and render a stack of multifocus images using fixed-lens setup at multiple views. Unless mentioned elsewhere, the azimuth angle is modified such that the camera poses are approximately uniformly distributed around a sphere, with the centre being the object. The add-on was also modified to save the camera poses and convert to Meshroom format.

The image capturing process was applied to object in frontlight and backlight environment, where the backlight images could serve as masks to remove background noise from the frontlight images as in [22].

Image stacking and background removal. Focus stacking involve aligning the multi-focus images using their homography matrices, then fusing their in-focused regions. In the experiment, the multi-focus images of calibration target were stacked first to provide the calibrated homography matrices. The homography matrices were computed using different methods such as Enhanced Correlation Coefficient (ECC [START_REF] Evangelidis | Parametric image alignment using enhanced correlation coefficient maximization[END_REF]) homography, ECC affine, etc., to study the effect of homography transformation on the reconstruction result. Once the images for the calibration target were stacked, the front-light and back-light images for the object were stacked using the same calibrated homography matrices.

The stacked back-light images were then used as masks to remove the background noises from the stacked frontlight images. The background removal was achieved by firstly converting the stacked back-light images to binary images using a threshold, then bit-wise operation between the binary images and the stacked front-light images was performed to remove the background.

Pose estimation. In this paper, Meshroom [START_REF] Griwodz | AliceVision Meshroom: An open-source 3D reconstruction pipeline[END_REF] is chosen to perform structure from motion for pose estimation and multiview stereo reconstruction (MVS). As a result, from now on the term MVS will be used to refer to the reconstruction results produced by Meshroom.

Effect of homography transformations for image stacking

We tested 2 alignment methods for focus stacking, ECC affine homography (OpenCV [5]'s findTransformECC function based on [START_REF] Evangelidis | Parametric image alignment using enhanced correlation coefficient maximization[END_REF]) and the theoretical transformation from lens equation. For methods using ECC affine homography, we also tested them under different conditions such as with and without calibration, and with and without linear fitting.

ECC affine homography was able to compute the transformation matrices. However, they produce distortions in stacking results, as shown by Fig. 3. The distribution of the scaling and shifting factor in ECC affine homography with and without calibration target shows that this method is unreliable near the two extrema of the image stack due to the large areas out of focus. To improve the result of standard ECC affine homography methods, linear fitting is applied to the middle portion of the data point. To quantify the accuracy of all alignment methods, the SSIM algorithm was applied to the output images and the ground truth image rendered without the out of focus effect. The results are shown in Fig. 3 and Table 1. It could be noted that while linear fitting was able to eliminate the distortions in standard calibrated ECC affine homography methods, it was not applicable to non-calibrated ECC affine homography methods since its scaling and shifting components were highly different to the theoretical trend. This difference is found to vary from one view to another. Without using a calibration target for focus stacking, subsequent MVS reconstruction failed to produce reasonable results and therefore this case is ignored from now.

Focus

To validate the significance of different image alignments, reconstruction was performed using stacked images from ECC affine, linearly fitted ECC affine, and theoretical calculation. The results and their comparison to the ground truth model are shown by Fig. 4 and Table 2. As the results shown, the reconstruction result using stacked images from linearly fitted ECC affine was not significantly different to the reconstruction result using stacked images from theoretical calculation. On the other hand, the reconstruction result using stacked images from standard ECC affine was much worse, which suggests that distortions in focus stacking contribute significantly to the reconstruction result. Therefore, in practice, if theoretical calculation could not be achieved, it is recommended to linearly fit the standard ECC affine homography matrices.

Alignment methods

Normalised HD ECC Affine with calibration target 0.00922 Linearly fitted ECC Affine w.c.t. 0.00241 Our lens equation (Eq. ( 2)) 0.00154

Effect of image pose distribution to MVS

The conventional way to capture images is to keep the camera pointing to the object, and apply constant step for pan (azimuth) and tilt rotation (polar angle) leading to denser camera pose distribution at the poles than at the equator region. To reduce the non-uniform distribution, two new simple strategies are proposed: one with linear varia- tion of number of poses from 36 to 1 along z rotation axis, another with linear variation of the number of poses with tilt angle. Figure 5 shows the 3 different pose distributions and the resulting reconstructed meshes using high resolution and low resolution images. While all pose distribution methods were able to reconstruct the complete mesh using high resolution images, their impact on reconstruction results using low resolution images was much more significant, with the pose distribution method using linear variation with title angle provides the most complete mesh. Table 3 shows the quantification comparison, and the results for low resolution images proves that the linear variation of the title angle give the lowest Hausdorff distance values, while the slight differences in high resolution images were likely caused by slight misalignment when comparing to the ground truth.

Pose distributions

HD-12MP HD-2MP Constant pan-tilt rot. steps 0.001025 0.02628 Linear variation along z axis 0.000702 0.01734 Linear variation w. tilt angle 0.000821 0.01652 Table 3: Normalised Hausdorff distance (HD) by bounding box diagonal for reconstruction results using different pose distributions for two image resolutions 4320×2880 pixels and 1920×1080 pixels.

Effect of image resolutions

We performed the reconstruction with MVS, NeRF and NSVF using 4 different image resolutions: 4320 × 2880, 3024 × 2016, 1920 × 1080 and 960 × 540 pixels. However, in order to speed up the training convergence of NeRF and NSVF, the input images were cropped to a square size, from 1920 × 1080 pixels to 1080 × 1080 pixels, and from 960×540 pixels to 540×540 pixels. As shown by Fig. 6 and Table 4, MVS was able to achieve high quality reconstruction results using high resolution images, but its accuracy significantly decreases when using low resolution images, since the camera pose estimation significantly depends on the number of interest points that are extracted and matched.

Unlike MVS, NeRF and NSVF both were able to reconstruct high quality mesh even with low resolution images. In particular NSVF was able to achieve better accuracy using low resolution images than the high resolution result for MVS. Furthermore, it was shown that NSVF is not sensitive to image resolution variation as its results using 2 Mpx and 0.5 Mpx images are approximately the same. For the same set of 334 input images of 1920×1080 pixels, MSV took from 1 to 2 hours to run, NeRF from 8 to 12 hours, NSVF from 20 to 24 hours on the same on Nvidia 3.5. Effect of estimated poses vs ground truth poses MVS. For this validation, we use a number of objects of different shapes and material from [22,[START_REF]disc3D. Digital archive of natural history (DiNArDa)[END_REF] including: Agrilus Anxius (AA), Anoplophora Chinensis (AC), Fagus Sylvatica (FS), and Melitaea britomartis (MB)2 .

Reconstruction using MVS technique relies on the accuracy of the estimated poses to generate an accurate point cloud for meshing. However, in cases where image resolution is low, or where the object itself has a complex structure, pose estimation could be less accurate. Therefore, we compared the reconstruction results obtained using the estimated poses and the ground truth poses with 4 different specimens.

As shown by Fig. 7 and Table 5, for most specimens, pose estimation was accurate enough to reconstruct a sufficiently accurate meshes, and using ground truth poses leads to a small improvement. However, in the case of the butterfly, as shown by the last column of Fig. 8, where pose estimation was inaccurate as Meshroom to match correct image features the thin symmetric wings. Providing ground truth poses fixes the problem and produce highly accurate reconstructed mesh.

NeRF and NSVF. NeRF with estimated posed failed to generate a 3D model. NSVF however works to some extent and produced a 3D mesh shown in Fig. 9. Compared to NSVF reconstructed mesh using ground-truth poses shown in Fig. 6(e), NSVF reconstructed mesh using estimated posed is quite distorted leading to more than 4 times larger Hausdorff distance.

Effect of different types of object geometries

Reconstruction results using ground truth poses by MVS, NeRF and NSVF are shown in Fig. 10. Accuracy comparison in terms of Hausdorff distance is given by Table 6. Despite using image resolution of 1920 × 1080 pixels, NeRF and NSVF produce 3D reconstructed meshes equivalent or better than MVS using image resolution of 4320×2880 pixels. MVS reconstructed meshes tend to have broken thin parts including legs, wings and spikes. NeRF reconstructed meshes are complete, but they are thicker than ground truth meshes (bottom row of Fig. 7) and lose details. NSVF reconstructed meshes are closest to ground truth meshes, although the butterfly has incomplete antennae.

Specimen

Transparent structure and reflective surface

A set of 334 images of 1080×1080 pixels were rendered at uniform poses around the dragonfly model from [START_REF] Mrjeong | Bend swap -dragonfly[END_REF]. Again, Table 6 shows that NSVF produces a more accurate reconstructed mesh than MVS, although NSVF has some errors near the edges of the wings.

For more validation, the Supplementary material also includes the NeRF and NSVF reconstructed results of a spaceship 3D model with transparent cockpit dome and reflective metal surface [23]. Particularly, the surface of glass cockpit and its visible internal structure are successfully reconstructed.

Conclusion

Our study has led to several important practical guidelines for image-based 3D reconstruction of small objects such as insects. To deal with out-of-focus effect, homog-raphy transformation for image registration based on lens equation leads to accurate focus-stacked images that allows precise 3D reconstructions. If the lens focal length and magnification are unknown and therefore cannot use the lens equation, the next choice is using a 3D calibration target. Focus stacking without using either of the methods [START_REF] Li | Perspective-consistent multifocus multiview 3D reconstruction of small objects[END_REF][START_REF] Shah Ariful | Fixed-lens camera setup and calibrated image registration for multifocus multiview 3d reconstruction[END_REF] is not recommended, as this likely leads to incomplete and/or inaccurate 3D reconstructed meshes.

Capturing images with a uniform pose distribution around the object results in more complete and accurate 3D reconstructed meshes than the conventional constant rotation step around pan and tilt axis. Relatively uniform pose distribution could be achieved by adjusting the number of rotation steps linearly with tilt angle.

Pose estimated by structure from motion is significantly affected by low image resolutions and objects with flat geometry, reflective surfaces and transparent structures. Using pre-calibrated poses consistently improves the results and the impact can be dramatic for challenging objects, as shown with the butterfly dataset. As a result, using a good motorised stage to obtain ground truth poses is highly recommended.

While high image resolution (above 5 Mpx) is crucial for MVS to produce good pose and depth estimations for an accurate 3D model, image resolution could be as low as 0.5 Mpx for NSVF to still produce an accurate 3D model as long as camera poses are accurate enough. This suggests that a low-cost 3D reconstruction solution is achievable using NSVF using a good pan-tilt-rail stage (for prior calibrated poses) with a low resolution camera and low-cost macro lens.

The higher resolution meshes are reconstructed by NSVF, however this approach loses very thin structures. On the other hand, NeRF does not achieve the same accuracy but will maintain the thin structures while making them thicker than the ground truth. Even if MVS cannot achieve the quality reached by deep learning algorithms on low-resolution images, it is the only one capable of doing a reconstruction from images at very high resolution. Generally, NSVF and NERF require, respectively, ten and five times more computation and memory resources than MVS.

As the study focuses on using ray-tracing rendered images, it lacks some realistic conditions like image noise, non-uniform background, non-uniform illumination, lens distortion, and misalignment of camera sensor. However, these conditions variations should not change the findings of this study.

Figure 1 :

 1 Figure 1: Top: lens image formation and circle of confusion. Middle: multi-focus capture with fixed lens setup. Bottom: example images from one stack of 61 images.

Figure 2 :

 2 Figure 2: Distributions of the scale and shift in homography matrices estimated using different alignment methods.

Figure 3 :

 3 Figure 3: Focus stacked images and error maps. (a) ECC affine w/o calibration target. (b) & (c) ECC affine with calibration target and its linear fitting. (d) Lens equation.

Figure 4 :

 4 Figure 4: Reconstruction result using stacked images (top row) from different alignment methods and their Hausdorff distance to ground truth model (bottom row). (a) ECC affine with calibration target. (b) Linearly fitted ECC affine with calibration target. (c) Lens equation. Using estimated poses.

Figure 5 :

 5 Figure 5: Effect of different pose distributions for image capture: a) constant pan-tilt rotation steps (217 poses), b) linear variation along z axis (189 poses), and c) linear variation with tilt angle (217 poses). From top row to bottom row: camera control diagram, estimated camera poses, corresponding MVS reconstructed meshes using 4320×2880 pixel and 1920×1080 pixel images.

Figure 6 :

 6 Figure 6: 3D reconstructed meshes of Cicindela Campestris (green tiger beetle) [22, 8] for different image resolutions using ground-truth poses.

  Normalised Hausdorff distance (HD) for MVS reconstruction results using estimated poses versus ground truth poses.

Figure 7 :

 7 Figure 7: MVS reconstruction results using 4320×2880 pixel images with ground truth poses (top 2 rows), and estimated poses (mid 2 rows) as compared to ground truth meshes (bottom row).

Figure 8 :

 8 Figure 8: Estimated poses versus ground truth poses for 3D reconstruction of butterfly.

Figure 9 :

 9 Figure 9: NSVF reconstruction using estimated poses with image resolution of 1920 × 1080 pixels. Normalise Hausdorff is 0.006963.

Figure 10 :

 10 Figure 10: Ground-truth-poses reconstruction results of fine structure dataset by MVS (top rows), NeRF (middle rows) and NSVF (bottom rows). Image resolution for MVS is 4320×2880 pixels, for NeRF and NSVF 1080×1080 pixels.

Figure 11 :

 11 Figure 11: Reconstructed results of dragonfly. Left: ground-truth mesh. Middle: MVS. Right: NSVF.

Table 1 :

 1 SSIM score for focus stacking methods.

	Stacking Methods	SSIM Score
	ECC Affine w/o calibration target	0.938
	ECC Affine with calibration target	0.971
	Linearly Fitted ECC Affine w.c.t.	0.976
	Our lens equation (Eq. (2))	0.983

Table 2 :

 2 Hausdorff distance (HD) normalised by bounding box diagonal for reconstruction results using different focus stacking methods.

Table 4 :

 4 Normalised Hausdorff distance (HD) by bounding box diagonal for different image resolutions using groundtruth poses. Higher resolution for NeRF and NSVF is not possible due to constraints on GPU memory. P100 GPU. NSVF needs at least 16 GB of GPU RAM to perform the training while NeRF and MVS need much less RAM.

	Reconst. method	Image resolution	Normalised HD
		4320×2880 (12MP)	0.00197
	MVS [11]	3024×2016 (6MP) 1920×1080 (2MP)	0.00293 0.01220
		960×540 (0.5MP)	NA
	NeRF [15]	1920×1080 (2MP) 960×540 (0.5MP)	0.00264 NA
	NSVF [14]	1920×1080 (2MP) 960×540 (0.5MP)	0.00159 0.00139

Table 6 :

 6 Normalised Hausdorff distance (HD) for different reconstruction methods using ground truth poses.

		Normalised HD
		MVS	NeRF	NSVF
	AA	0.00173 0.00363 0.00175
	AC	0.00201 0.00295 0.00099
	FS	0.00315 0.00767 0.00225
	MB	0.00144 0.00309 0.00186
	Dragonfly	0.01790	NA	0.007963

The

3D models are available at https://skfb.ly/o7rRX

Acknowledgment

Chuong Nguyen would like to acknowledge the support of CSIRO Julius Career Award.