Camelia Matei Ghimbeu

Loïc Vidal

Luc Delmotte

Jean-Marc Le Meins

Cathie Vix-Guterl

Catalyst-free soft-template synthesis of ordered mesoporous carbon tailored using phloroglucinol/ glyoxylic acid environmentally friendly precursors †

Carbon porous materials with a periodically ordered pore structure, controlled pore size and geometry and high thermal stability are synthesized using self-assembly of environmentally friendly phloroglucinol/ glyoxylic acid precursors with an amphiphilic triblock copolymer template. Glyoxylic acid, a plant-derived compound, is used for the first time as a substituent of carcinogen formaldehyde usually employed in such a synthesis. Thanks to the double functionality, i.e., aldehyde and carboxylic acid, glyoxylic acid plays not only the role of a cross-linker for the formation of the resin but also the role of a catalyst by creation of H-bonding or specific reactions between the precursors. Hence, no extra catalyst such as strong acids (HCl) or bases (NaOH) is any longer required. Carbon films and powders were successfully prepared with high surface areas (up to 800 m 2 g -1 ), high porous volume (up to 1 cm 3 g -1 ), tunable pore size (0.6 nm to 7 nm) and various pore architectures (hexagonal, cubic, and ink-bottle) by tuning the precursor ratio and by applying different manufacturing engineering strategies. Insights on the synthesis mechanism of the phenolic resin and carbon mesostructures were obtained using several analysis techniques, i.e., nuclear magnetic resonance ( 13 C NMR) and FTIR spectroscopy, temperature programmed desorption coupled with mass spectrometry (TPD-MS) and thermo-gravimetric analysis (TGA).

Introduction

Since their discovery, [1][2][3] ordered carbon materials have attracted tremendous attention due to their outstanding properties including a high surface area, uniform and interconnected pores, tunable pore size and shape, good electronic conductivity and chemical inertness. [4][5][6][7] Undoubtedly, these features make them ubiquitous and indispensable for a wide range of applications in the field of catalysis, 8 energy conversion and storage, 7,9 sensors, 10 adsorption and separation, 11,12 controlled drug release, 13,14 etc. Moreover, the ordered carbons can be also considered as model materials for establishing a comprehensive understanding of physical-chemical phenomena occurring during the applications. 4,9,10,15,16 The design of such interesting materials was first achieved by the so-called hard-template or nanocasting approach. [1][2][3] In this approach, an ordered inert template (zeolite, silica) is infiltrated with a carbon precursor ( propylene, sucrose, furfuryl alcohol, etc.), followed by confined carbonization and then removal of the template by harsh acidic or basic conditions (HF, NaOH). Despite the large variety of ordered carbon materials that can be obtained, 4,6,17 this multistep, expensive and hazardous pathway limits to some extent its large scale utilization. To overcome these drawbacks, more recently, [18][19][20][21] the softtemplate approach has been developed and has received much greater attention due to the limited synthesis steps, easy production of large quantities 22 and moreover the possibility of designing various kinds of carbon materials such as films, powders and monoliths. 5,6 Generally this method is based on the self-assembling of carbon precursors with a soft block copolymer via hydrogen bonding and/or covalent bonding under basic or acidic conditions. 5,18 A further thermopolymerization (∼100 °C) and carbonization and/or graphitization step (600-2500 °C) allows the obtainment of ordered carbon structures. The most commonly employed phenolic monomers are phenol, resorcinol and phloroglucinol, and are used in most cases together with formaldehyde as a cross-linker. The latter one is well known to be a carcinogen which represents an important drawback. It is worth mentioning that very little recent effort has been made by our group 23 or other groups 24,25 to overcome this major problem. However, even if more environmental precursors were explored (tannin, fructose, etc.), high acidic conditions and high temperatures and pressures were still required to obtain the ordered carbons. These parameters are well known to affect the reactivity, the polymerization rate, the self-assembly process and finally the carbon features. In addition, they have a direct negative impact from the environmental point of view and for industrial applications where non-corrosive reagents and low cost procedures are strongly required. The necessity to find other catalysts than the commonly used NaOH and HCl was recently pointed out in a recent review devoted to the synthesis of ordered mesoporous carbon by the soft-template approach. 5 In the present work, we propose as an alternative to the already existing precursors and catalysts the environmental friendly glyoxylic acid, which thanks to its bi-functionality (aldehyde and carboxylic acid groups) plays a double role in carbon synthesis, i.e., as a cross-linker for the formation of phenolic resin and as a catalyst as it can promote polymerization of phenolic resin. This compound is a colorless solid that occurs as a natural constituent of plants and its release in air, water and soil is biodegradable which makes it very attractive.

Therefore, we report in this work a green, simple and efficient approach for the synthesis of ordered carbon materials by means of self-assembly of environmentally friendly phloroglucinol/glyoxylic acid carbon precursors and a structure directing agent at room temperature and without a catalyst. The phenolic resol solution obtained with these precursors is suitable for the synthesis of ordered carbon films as well as carbon powders by both evaporation induced selfassembly (EISA) and macroscopic phase separation routes. 5 The proposed green precursors allow obtaining ordered carbon materials with tunable textural characteristics (surface area, pore size, pore geometries) and high thermal stability by simply adjusting the molar ratio between the precursors as highlighted by several analysis techniques.

Materials and methods

Chemicals

Triblock copolymer Pluronic F127 ( poly(ethylene oxide)-blockpoly( propylene oxide)-block-poly(ethylene oxide, PEO 106 PPO 70 -PEO 106 , M w = 12 600 Da), phloroglucinol (1,3,5-benzentriol, C 6 H 6 O 3 ), glyoxylic acid monohydrate (C 2 H 2 O 3 •H 2 O) and absolute ethanol (C 2 H 6 O) were purchased from Sigma-Aldrich and used as received without any further purification.

Synthesis

The carbon materials were synthesized by the evaporationinduced self-assembly pathway and macroscopic phase separation.

Powders by EISA. In a typical EISA synthesis, phloroglucinol (0.82 g), glyoxylic acid monohydrate (0.61 g) and Pluronic F127 (1.61 g) were dissolved under stirring at room temperature in absolute ethanol (40 ml). The obtained clear solution was transferred into smooth glass dishes and left at room temperature for about 6 hours in order to evaporate the ethanol solution, and subsequently a thermal treatment at 80 °C for one night was performed to cross-link the phenolic resin framework in the material. The obtained materials were scraped from the dishes and pyrolysed at 600 °C under inert atmosphere (Ar) for 2 hours. The influence of glyoxylic acid amount in the reaction mixture was studied by varying its quantity while keeping the other parameters constant. Thus, different molar ratios between phloroglucinol and glyoxylic acid (1 : 1; 1 : 1.25 and 1 : 1.5) were defined (see Table 1).

The obtained materials are denoted CGY-x, where x denotes the molar ratio of phloroglucinol/glyoxylic acid (CGY-1, CGY-1.25 and CGY-1.5). The influence of surfactant on the CGY-1 material was studied by decreasing the amount of template (sample CGY-1S, where S means surfactant, Table 1).

Films by EISA. Thin films were also prepared by dip-coating on a quartz plane substrate. The substrate was first cleaned with ethanol and acetone and after drying was immersed five times in the solution with a speed of 1.2 mm s -1 , a distance of 30 mm and an immersion time of 10 s. Drying, curing and carbonization were performed as described before.

Powders by phase separation. Carbon powders were also obtained by phase separation which occurs after a certain time period, typically between 1.5 and 5 days of aging the solution at room temperature. The required time to achieve the phase separation depends on the molar ratio between phloroglucinol and glyoxylic acid. Once the phase separation occurred, the upper layer solution was discarded while the rich polymer-gel was recovered and then dried, thermopolymerized and pyrolysed in a similar way as already mentioned. The obtained sample is denoted CGY-1P (P meaning powder).

Characterisation

Carbon material characterization. The textural properties of the materials were investigated with a Micromeritics ASAP 2020 instrument using N 2 adsorbate at -196 °C. Prior to the analysis, the samples were out-gassed overnight in a vacuum at 300 °C on the degassing port followed by 4 h out-gassing on the analyse port. The BET (Brunauer-Emmett-Teller) surface area (S BET ) was calculated from the linear plot in the relative pressure range of 0.05-0.3 while the micropore volume (V micro ) was determined using the Dubinin-Radushkevich (DR) equation. The mesopore volume (V meso ) was obtained by subtracting the micropore volume from the total pore volume of N 2 adsorbed at a relative pressure P/P 0 of 0.95. The average mesopore size was determined with the BJH (Barrett-Joyner-Halenda) model on the adsorption branch. The micropore size distribution was determined using the N 2 DFT model for slit pores. X-Ray powder diffraction (XRD) data were collected with a Philips X'Pert MPD diffractometer with a Cu Kα 1,2 doublet and a flat-plate Bragg-Brentano theta-theta geometry.

The long-range ordering of the materials was studied by small angle X-Ray scattering (SAXS) analysis using a Rigaku SMax 3000 equipped with a rotating Cu anode Micromax-007HF (40 kV, 30 mA) and OSMIC CMF optics. ImageJ 26 software was used for SAXS treatment of different images collected with the X-ray 2D detector. The unit cell parameter, a 0 , was calculated using the formulas 2d 100 /√3 for hexagonal structures and (√2)d 110 for cubic structures, respectively, 27 where d 100 and d 110 represent the d spacing values of the 100 and 110 diffraction planes.

The carbon material morphology was evaluated by transmission electron microscopy (TEM) with a Philips CM200 instrument working at 200 kV. For film analysis a small quantity was mechanically removed from the substrate.

Phenolic resin characterization. A JASCO Fourier transform infrared spectrometer 4100 was used to characterize the chemical surface of the phenolic resin before carbonization. First, a background spectrum was run, and then the spectra of the phenolic resin samples were collected against the background spectrum. A total of 60 scans at a resolution of 16 cm -1 (in the IR region of 4000-600 cm -1 ) were performed to achieve a good signal-to-noise ratio.

Proton and 13 C solid-state CPMAS NMR experiments have been performed on a Bruker Avance 750 MHz spectrometer using 3.2 mm zirconia rotors spinning at a MAS frequency of 18 kHz.

Recycle delay for all CP experiments was 4 s and spinal-64 decoupling was applied during signal acquisition. Cross-polarization transfers were performed using adiabatic tangential ramps to enhance the transfer efficiency, and the contact time was 1 ms. Single-pulse MAS experiments were used for 1 H spectra.

Thermo-gravimetric analysis (TGA) was used to study the mass loss during phenolic resin carbonization by heating with 2 °C min -1 up to 950 °C under nitrogen (METTLER-TOLEDO TGA 851e). The type of species evolved during the carbonization of phenolic resin was analyzed by temperature programmed desorption coupled with mass spectrometry. 28,29 A small quantity of cured phenolic resin/F127 (∼2 mg) was introduced into a quartz tube place inside a furnace and heattreated in a vacuum with a linear heating rate of 2 °C min -1 up to 950 °C. The gases evolved during the heating process were continuously detected using a mass spectrometer.

Results and discussion

Carbon characterization

The nitrogen adsorption/desorption isotherms of carbon materials synthesized using different mass ratios between the precursors (see Table 1) are shown in Fig. 1a. For CGY-1S and CGY-1 the mass ratio between the carbon precursors ( phloroglucinol-glyoxylic acid) and the template is 0.6 and 1.2, respectively. The two carbons exhibit a type IV isotherm characteristic of mesoporous materials. A high increase of nitrogen uptake in the low relative pressure (P/P 0 ) region corresponds to the volume adsorbed by micropores and the formation of nitrogen multilayers on the pore walls. This adsorbed volume is higher in the case of CGY-1, maybe due to the higher quantity of Pluronic which by decomposition favors, besides mesopore formation, also the creation of micropores. The DFT micropore size distribution (Fig. S1 †) reveals for all materials pores with average diameter 0.6 nm but also some pores with higher diameter (∼1.2 nm).

Moreover, in both cases a hysteresis loop of H 2 -type (CGY-1S) or H 1 -type (CGY-1) is observed, respectively, when the mass ratio between the precursors and the template is increased from 0.6 to 1.2. H 2 hysteresis indicates a delayed condensation and in addition pore blocking percolation or cavitation effects are present. [30][31][32] This type of hysteresis is specific to materials having complex pore structure, namely ink-bottle or cage-like pores.

The lower limit of the closure of the hysteresis loop occurs at a relative pressure comprised between 0.45 and 0.48, which suggests a cavitation mechanism [30][31][32] with pore entrance diameter to the main mesoporous cavities less than 6 nm. H1-like hysteresis is usually attributed to uniform mesopores with a cylindrical geometry. Therefore, the difference in the features of the hysteresis loops can be correlated to different pore topologies. The average pore size of CGY-1S and CGY-1 is 8.3 nm and 6.5 nm, respectively (Table 2). Particularly in the Fig. 1 Nitrogen adsorption/desorption isotherms (a) and SAXS patterns (b) of carbon materials synthesized using different experimental conditions as listed in Table 1.

case of CGY-1S the pore size determined by the BJH adsorption is underestimated by about 45%, in good agreement with previous reports for this type of complex pore morphology. 34 This can be sustained by the TEM pictures (Fig. 2a) showing pores with an average size of about 14 nm as determined by ImageJ software. The surface area and the total pore volume (Table 2) are higher for the CGY-1 (679 m 2 g -1 and 0.83 cm 3 g -1 ) compared to CGY-1S material (493 m 2 g -1 and 0.4 cm 3 g -1 ).

The influence of glyoxylic acid amount on the carbon textural properties was also studied. With increasing the quantity of glyoxylic acid (CGY-1.25 and CGY-1.5) the obtained material still exhibits an isotherm of type IV but the hysteresis is no longer visible. Previous studies have shown the absence of a hysteresis loop for pore sizes in the range of small mesopores. 35 The surface area and the total porous volume decrease with the increase of the glyoxylic acid amount. A significant decrease in the mesoporous volume can be noticed which is accompanied by a decrease in the pore size from 7.3 nm (for CGY-1) to 2.9 and 2.7 nm for CGY-1.25 and CGY-1.5, respectively.

The SAXS patterns from Fig. 1b show no diffraction peak for CGY-1S indicating no ordering at long range distances. For all the other materials, the SAXS patterns reveal one resolved peak. For CGY-1 the peak is placed at q ∼ 0.5 nm -1 and can be indexed to the 10 diffraction planes of an ordered 2D hexagonal p6m mesostructure. 27,33 In the case of CGY-1.25 and CGY-1.5 the SAXS maximum peak position is shifted towards higher q values ∼0.7 and 0.75 nm -1 , respectively, corresponding to the 110 diffraction planes of an ordered body-centered cubic mesostructure with a space group Im3 ˉm. 27,33 The values of the cell lattice parameter, a 0 (Table 2), calculated from the SAXS parameters are 15.8 nm for CGY-1 material and 12.4 nm and 12.0 nm for CGY-1.25 and CGY-1.5 carbons, respectively. Hence, a shrinkage in the carbon framework is noticed besides the mesostructure pore structure modification when the molar ratio between glyoxylic acid and phloroglucinol increases in the reaction mixture from 1 to 1.25. Further increase in this ratio to 1.5 or 2 (data not shown) does not induce significant morphology or structure modifications.

The wall thickness calculated based on the SAXS peak position and textural parameters is listed in Table 2. The wall thickness decreases from 9.3 nm (CGY-1) to 8.0 nm (CGY-1.5) when decreasing the ratio of F127/resin from 1.2 to 0.9. This is not surprising since the wall thickness is related to the domain sizes of phenolic resins structured by the soft-templates and the ratio of F127 templates to phenolic resin. 33 The morphology of the carbons was studied by TEM. As depicted in Fig. 2a, the CGY-1S carbon presents spherical mesopores with average size of about 14 nm. When increasing the quantity of Pluronic (CGY-1, Fig. 2b) the material presents stripe-like and parallel channels specific to a 2D hexagonal structure in good agreement with the SAXS results. When, in addition, the glyoxylic acid amount increases (CGY-1.25 and CGY-1.5) the materials exhibit ordered cubic mesopores interconnected through smaller windows. The 2D and 3D interconnected porosity makes these materials interesting for a wide range of potential applications, i.e., separation, sensing, energy storage and catalysis.

It is worth mentioning that besides the synthesis of powder by the EISA method, thin films can also be obtained by this method using a simple dip-coating method which is suitable for large surface coatings as well. A typical film cast on a quartz substrate is shown in Fig. 3a together with its morphology. We can observe, by TEM pictures, spherical pores oriented perpendicular to the substrate (Fig. 3a). The mesoporous film is continuous over a large domain without visible cracks, and its thickness evaluated by AFM was found to be around 120 nm.

The average centre-to-centre distance between the two adjacent mesochannels is about 16 nm while the pore size is roughly estimated at 11 nm. As can be noticed, the morphology of the film is not the same as that of the powder (Fig. 3b) even if identical chemical conditions were used. Changes in the material structure induced by the experimental casting procedure, i.e., powders or thin films, were already reported and very nicely described by Song et al. 36 Table 2 Textural and structural properties of carbon materials synthesized under different conditions

Material name

S BET (m 2 g -1 )

V t (cm 3 g -1 )

V micro (cm 3 g -1 )

V meso (cm 3 S BETthe total surface area determined by the BET method. V T , V meso and V microthe total pore volume, mesopore volume and micropore volume. D Pmesopore diameter calculated by the BJH method from the isotherm adsorption branch. a 0unit cell parameter calculated by SAXS. t wallthe wall thickness is calculated using the equation a 0 -D P for hexagonal structure and [(√3/2)](a -D) for cubic structure. 27,33 Fig. 2 TEM pictures of CGY-1S (a), CGY-1 (b), CGY-1.25 (c) and CGY-1.5 (d) carbon materials obtained using different experimental conditions (Table 1).

This can be explained by the fact that in the case of films, its interfaces impose geometric constraints of self-assembly which are absent in bulk powder.

The powders obtained by EISA (CGY-1, Fig. 3b) were compared with those obtained by the phase separation method (CGY-1P, Fig. 3c). The advantage of the phase separation method is mainly related to the higher quantity that can be synthesized than that reported for the EISA method. Typically, for the precursor solution volume used in this work (40 ml) about 0.5 g of carbon is obtained. This quantity can be easily scaled-up using bigger size synthesis flasks. It should be mentioned that by this method the complete phase separation occurs in about 5 days for CGY-1P (Fig. 3c,up) and this time decreases as the glyoxylic acid quantity increases (one day for phloroglucinol : glyoxylic acid molar ratio, 1 : 2). The reaction is slow mainly due to the mild pH synthesis conditions employed (∼5) and the absence of a catalyst.

It should be remarked that these carbon powders present quite a similar morphology but are less ordered for the second synthesis method (Fig. 3b andc). The textural properties are also slightly different (Fig. S2 and Table S1, ESI †), the CGY-1 having higher surface area and porous volume, and a narrower and more defined pore size than the CGY-1P. Moreover, it can be mentioned that the morphology and the structure of the powders obtained by tuning the molar ratio between the precursors may differ from those obtained by the EISA method (data not shown). This can be related to the different self-assembly mechanism when these two different approaches are used. The evaporation induced self-assembly involves the self-assembly of phloroglucinol/glyoxylic acid phenolic resins (resols) with the triblock polymer through organic-organic interactions occurring during the evaporation of the solvent.

This method is very suitable for the synthesis of carbon films and monoliths but, however, for the synthesis of large powder quantities the macroscopic phase separation approach is more convenient. Contrary to the EISA method, in the phase separation approach the self-assembly of resols around the template with the formation of ordered mesostructures occurs via a macroscopic phase separation. Firstly, the triblock copolymer self-assembles in micelles and the carbon precursor ( phloroglucinol) interacts with the PEO block of the template via hydrogen or columbic interactions to form a self-assembly structure, while glyoxylic acid cross-links with phloroglucinol and a phase separation containing a rich polymer phase and a liquid solvent occurs. Further separation and isolation of this rich polymer phase followed by thermopolymerization and carbonization gives the ordered carbon powders 5,37 .

The thermal stability of ordered carbon materials is an important issue for designing materials for various applications where graphitic carbons possessing good conductivity and controlled textural properties (high surface area and controlled pore size) are required. The structure of the as-synthesized carbon materials at 80 °C was investigated by the XRD technique (Fig. S3, ESI † and Fig. 4a-c) and the influence of further thermal annealing at higher temperature (380 °C, 600 °C and 1500 °C) on the structural and textural properties was evaluated. At 80 °C (Fig. S3, ESI †) the XRD patterns are characterized mainly by one peak placed around ∼23°which corresponds to the (002) reflection of graphite. The peak is very broad suggesting a material with a low degree of graphitization. A second less intense peak appears at ∼44°when the resin is heat treated above 380 °C (Fig. S3, ESI † and Fig. 4a) which is related to the (101) and/or (100) reflections. When the material is thermally treated at 1500 °C the (002) and (101) peaks become narrower and sharper and a supplementary small peak (∼80°) corresponding to the (110) reflection of a graphitic structure gives indications of the improvement of the graphitization level in the material. At this high temperature the material does not notably modify its textural features (Fig. 4b). The mesoporous volume and the mesopore size remain unchanged while a decrease in the microporous volume is observed (Fig. 4b and Table S1, ESI †). This is also sustained by the TEM pictures (Fig. 4c) showing that the porous morphology and structure organization are conserved. Hence, it is worth highlighting the remarkably high thermal stability of these materials compared to other ordered carbon materials synthesized by the soft-template method under 1). neutral or basic conditions where significant structural age upon treatment was reported along with the modification of textural properties. 19,21,38

Phenolic resin and carbon formation

Carbon materials are synthesized by self-assembly of phloroglucinol/glyoxylic acid with Pluronic surfactant in ethanol organic medium. The pH of the solution is around 5 independently of the precursor ratio of phloroglucinol/glyoxylic acid. Due to its double functionality (aldehyde and carboxylic acid) the glyoxilic acid plays an important role in the self-assembly reaction of resol precursors and the triblock copolymer. The aldehyde group induces the cross-linking resulting in the formation of phloroglucinol/glyoxylic acid resol oligomers which further interact with the PEO segments of the self-assembled copolymer block via hydrogen bonding. The carboxyl group was reported to act as a catalyst as it can promote polymerization of phenolic resin by H-bond formation. 39,40 However, the formation mechanism of mesoporous carbons derived from reosorcinol-formaldehyde resins catalyzed by organic carboxylic acid was not investigated in these reports. In the present work, as glyoxylic acid is used for the first time together with phloroglucinol and in the absence of a catalyst, the phenolic resin and carbon formation mechanism is worth investigating.

Thus, the FT-IR was used to access more details of the chemical surface of phenolic resin synthesized using different quantities of glyoxylic acid. The FT-IR spectra of CGY-1 and CGY-1.5 phenolic resin/F127 composites are shown in Fig. 5.

For both samples, a strong and broad peak is observed around 3450 cm -1 which is related to the -OH stretching indicating the presence of a large amount of phenolic -OH groups.

The peak placed at 2935 cm -1 along with the peak at 1157 cm -1 correspond to the C-H and C-O-C asymmetric stretching vibration of the F127 surfactant. 33,41 At the same time the band between 2800 and 3000 cm -1 can also corres-pond to the stretching of the CH saturated bonds of the resin bridges. 42 Three other peaks are observed between 1900 and 1500 cm -1 . The absorption peaks at 1828 cm -1 and 1732 cm -1 are due to the CvO groups in cyclic lactones or anhydrides. [START_REF] Socrates | Infrared and Raman Characteristic Group Frequencies: Tables and Charts[END_REF] The peak seen around 1643 cm -1 is specific to deformation vibration of lattice water. [START_REF] Socrates | Infrared and Raman Characteristic Group Frequencies: Tables and Charts[END_REF] Several other peaks can also be noticed between 1500 and 1100 cm -1 . The peak placed at 1465 cm -1 can be assigned to C-H deformation while the peak at 1377 cm -1 belongs to the OH group in plane in phloroglucinol. [START_REF] Marcovich | [END_REF]45 The peak from 1045 cm -1 belongs to the single bond C-O stretching vibration of resin ester or lactone bridges. 42 The peaks shown in the interval range 600-900 cm -1 are characteristic of the number of adjacent hydrogen atoms on the aromatic ring, due to the C-H vibrations out of the plane of the aromatic ring. The peak from 953 cm -1 is specific to aromatic vC-H out-of-plane deformation vibrations in the 1,2,3 trisubstituted benzene ring. [START_REF] Socrates | Infrared and Raman Characteristic Group Frequencies: Tables and Charts[END_REF] The other peaks placed at 841-849 cm -1 can be related to the 1,2,3,5 tetrasubstituted benzenes. [START_REF] Socrates | Infrared and Raman Characteristic Group Frequencies: Tables and Charts[END_REF] Comparing the two phenolic resins IR spectra, the presence of similar vibration bands can be noticed, but the bands are slightly shifted towards higher frequency for CGY-1.5. In addition, it can also be seen that for CGY-1.5 the peak placed at 953 cm -1 is absent.

It should be remembered that this band corresponds to the vC-H vibrations in the 1,2,3 trisubstituted benzene ring, suggesting a different and more advanced cross-linking process in this case where only tetra-substituted benzenes are seen (841 cm -1 peak).

The phenolic resins were also analyzed by 13 C and 1 H NMR and representative spectra are given in Fig. 6. For 13 The intensity of the first peak (175.1 ppm) is slightly higher for CGY-1.5 to the higher quantity of glyoxylic acid in the resin compared to CGY-1 (see Table 1). The 105.7 ppm and 98.7 ppm signals can be related to the unsaturated aromatic carbon bonded with the C atom in trihydroxy phenylacetic acid and saturated carbon atoms in phloroglucinol, respectively. This indicates the cross-linking of phloroglucinol which is much advanced for CGY-1.5 taking into account the lower intensity of the latest peak compared to CGY-1. The stronger observed chemical shifts around 73.3 ppm are related to the carbon atoms (-CH-; -CH 2 -) bonded with O atoms in the triblock copolymer Pluronic F127. 27 The resonance peak placed at 39.1 ppm can be assigned to the carbon from lactone bridges between the phloroglucinol rings, characteristic of phenolic resins. 27,46 The much intense peak for the CGY-1.5 resin suggests once again its higher degree of polymerization induced certainly by the greater amount of glyoxylic acid used. In addition to the already observed chemical shifts the CGY-1.5 exhibits an extra peak at 24.7 ppm which is absent for CGY-1 resin. This corresponds to carbon atom bonded to carbon in anhydride or ester bridges suggesting a condensation reaction between two carboxylic groups and/or between a carboxylic group and a hydroxyl group.

Further insights on the chemical structure of these two phenolic resins were obtained by 1 H NMR (Fig. 6b). For both samples three NMR signals are noticed at 4.73 ppm, 4.57 ppm and 3.32 ppm, respectively, corresponding to protons in the propylene oxide (PPO) and ethylene oxide (PEO) moiety of the F127 surfactant. As can be seen, these two spectra reveal differences mainly in terms of peak intensity and width. The CGY-1.5 exhibits lower and narrow peak intensity reported to CGY-1 implying a certain difference in the rigidity and/or organization of the mesostructure of phenolic resin/template composites. This results in good agreement with the observed different textural and structural characteristics of these materials ( pore size and geometry, structure symmetry).

Based on these results a synthesis mechanism for the formation of the phenolic resin/pluronic can be proposed. First, it should be considered that glyoxylic acid is an aldehyde with electron-withdrawing substituents which often exist mainly as a hydrate. Thus, the formula for glyoxylic acid can be expressed as (HO) 2 -CH-COOH (eqn (1)).

In the first step, phloroglucinol can react with the glyoxylic acid hydrate, (HO) 2 -CH-COOH, by an electrophilic aromatic substitution with the formation of a trihydroxy phenylacetic acid compound. In the next step, the trihydroxy phenylacetic acid further reacts with another phloroglucinol molecule by two possible mechanisms. The first mechanism (eqn (2)) involves an electrophilic aromatic substitution giving rise to carboxylic acid bridges between the benzene rings.

Further elimination of H 2 O by condensation of the carboxylic group with the hydroxyl group induces the creation of lactone bridges (eqn (3)). This was shown by IR and 13 C NMR analysis (39.1 ppm).

The second mechanism is based on condensation reactions by the nucleophilic addition-elimination approach (eqn (4)). Taking into consideration the 13 C NMR results, the second mechanism seems to occur only in the case of CGY-1.5 resin taking into consideration the presence of 24.7 ppm chemical shift. As the quantity of glyoxylic acid in the reaction mixture is higher for CGY-1.5, the carboxylic groups of trihydroxy phenylacetic acid can condense directly with a hydroxyl group of phloroglucinol with the formation of ester bridges (eqn (4)). The compounds formed can further condensate and longer polymer chains can be formed. It should be mentioned that various possibilities of substitution/condensation reactions in different positions on the phenol ring are possible as a function of experimental conditions. In addition, H-interaction between the functional groups of resols (-OH, -COOH) and the block polymer ether bridges are also present, favoring the self-assembly of ordered mesostructures. Considering these results, it is evident that the present synthesis mechanism is much more complex than in the case of phenol/ formaldehyde systems where no carboxylic groups are involved.

The IR and NMR results revealed several differences between the CGY-1 and CGY-1.5 resins which could explain partly the different textural and structural features of the derived carbons (Fig. 1 and2).

However, the thermal decomposition of the resins may also induce modification and this process was studied in detail. The resulting phloroglucinol/glyoxylic acid thermopolymerized at 80 °C was further carbonized at 380 °C and 600 °C to decompose the template with the formation of the mesoporosity.

The as-made CGY-1 phenolic resin (80 °C) shows two SAXS peaks (Fig. 8a) at q around 0.45 and 0.7 nm -1 which can be indexed as 10 and 11 reflections of an ordered hexagonal mesostructure with a p6m symmetry. At this temperature as the template is still not removed, the ordered structure cannot be emphasized by TEM analysis (inset, Fig. 8a), a smooth and dense surface being observed instead.

The carbonization process of phenolic resins heat treated at 80 °C was followed in situ by TGA analysis performed in nitrogen by heating with a constant heating rate up to 950 °C (Fig. 7).

For a better understanding, the thermal decomposition of the carbon precursor is also shown. Glyoxylic acid decomposes with a temperature maximum at around 200 °C, phloroglucinol at 300 °C while the surfactant at ∼400 °C.

The phenolic resin CGY-1 decomposes mainly at a temperature similar to that of template removal (∼400 °C) while a significantly different decomposition behavior is noticed for CGY-1.5 (synthesized with a higher amount of glyoxylic acid) for which decomposition takes place in a lower temperature interval, comprised between 200 °C and 400 °C. This can suggest a strong interaction of glyoxylic acid with the template and the phloroglucinol carbon precursor as already emphasized by NMR and IR spectra.

Structural information on the phenolic resin at this stage of the thermal treatment (380 °C) was obtained by SAXS and TEM as shown by Fig. 8a. The hexagonal structure is clearly evidenced by the two techniques. In the case of CGY-1 resin, the lattice parameter of the as-prepared CGY-1 (a = 16.6 nm) decreases to 15.6 nm (6%) on heating at 380 °C.

This suggests a small framework shrinkage compared to CGY-1.5 phenolic resin (Fig. S4 and S5 †) where 25% shrinkage is noticed. This is in line with other reports 27 concerning phenol based resins; however, despite the large framework shrinkage the structural organization is well conserved (Fig. 8a and S4 †).

In addition, for CGY-1 resin, no further significant modification in the lattice parameter is observed when the temperature is increased to 600 °C, while for the CGY-1.5 the cell still contracts by about 15% (Fig. S5 †) during this heating step.

As can be observed, for glyoxylic acid and pluronic surfactant a noticeable mass loss occurs and almost no residue is left at the end of the thermal treatment, contrary to phloroglucinol where ∼15 wt% carbon is obtained at 900 °C. This quantity is similar to the one obtained by the decomposition of phenolic resins indicating that phloroglucinol is the carbonyielding component while the pluronic is the structure directing agent and the pore-forming component. Glyoxylic acid is the cross-linker which forms with phloroglucinol a highly cross-linked polymer resin around the template that serves to retain its nanostructure during the decomposition.

Details of the species evolved during the carbonization are provided by TPD-MS analysis. The phenolic resin comprising all these precursors decomposes by releasing several molecules as clearly seen in the TPD-MS spectra (Fig. 8).

The main gas desorption takes place in the same temperature range as observed by TGA analysis (Fig. 7). For CGY-1 (Fig. 8b), in a first step (<100 °C), mainly H 2 O (m/z = 18) and H 2 (m/z = 2) are desorbed.

At higher temperature (∼250 °C) desorption of CO 2 (m/z = 44) is noticed being probably related to the decomposition of carboxylic groups (-COO -) coming from glyoxylic acid. For temperatures higher than 400 °C, desorption of H 2 , H 2 O and CO occurs indicating the organization of the carbon by decomposition of oxygenated functional groups and C-H bond cleavage. As for the CGY-1.5 sample (Fig. 8c), desorption of CO (m/z = 28), H 2 (m/z = 2), H 2 O (m/z = 18) and ethyl species (m/z = 29) is predominant for temperatures inferior to 300 °C, but the presence of methyl and ethyl species (m/z = 15 respectively 43) and ethanol is also noticed. These species are related to the decomposition of pluronic surfactant chains. It should be noted that the decomposition of the pluronic takes place at a lower temperature than 373 °C suggesting its modification by strong interactions with glyoxylic acid, this behavior not being observed in the case of CGY-1 where smaller glyoxylic acid quantities are used. In addition, at higher temperatures comprised between 300 and 500 °C simultaneous desorption of CO, CO 2 and water is seen, which could be specific to anhydride decomposition. The presence of anhydrides can be explained by the reaction of two neighboring -COOH groups with elimination of water. For temperatures higher than 500 °C mainly H 2 desorption occurs due to the cleavage of C-H bonding.

Thus, taking into consideration the obtained results, a schematic representation of the ordered carbon synthesis pathway based on phloroglucinol/glyoxylic acid precursors can be illustrated as in Fig. 9.

Conclusions

A green, simple and efficient approach is demonstrated in this work for the synthesis of ordered carbon powders and films by self-assembly of environmentally friendly phloroglucinol/ glyoxylic acid precursors with a triblock copolymer template in organic medium and without a catalyst. The synthesized materials by tuning the experimental conditions exhibit high surface area and porous volume, defined pore size and architecture (hexagonal 2D, cubic 3D, cage-like) and high thermal stability. The formation mechanism of such structures studied by NMR, TPD-MS and IR proved that both glyoxylic acid functional groups (-OH, -COOH) are involved in the mesostructure formation and play an important role in the formation of various ordered carbons. In summary, the proposed herein synthesis pathway provides a significant step in the improvement of ordered carbon material eco-design by using environmentally friendly precursors, no catalyst, and moreover, a simple, rapid and scalable synthesis approach suitable for industrial applications.

Fig. 3 (

 3 Fig. 3 (bottom) TEM pictures of carbon (a), EISA thin films (b), EISA powders (CGY-1) and (c) powders by phase separation (CGY-1P); (top)the corresponding phenolic resin before thermal treatment. The molar ratio between the precursors corresponds to that of CGY-1 carbon (Table1).

Fig. 4

 4 Fig. 4 XRD patterns (a), nitrogen adsorption/desorption isotherms (b) (inset: pore size distribution) and TEM pictures (c) of CGY-1 carbon heat treated at 600 °C and subsequently at 1500 °C (CGY-1T).

Fig. 5

 5 Fig.5FT-IR spectra of CGY-1 and CGY-1.5 phenolic resin/F127 cured at 80 °C.

  ð4Þ

Fig. 6

 6 Fig.613 C and 1 H solid-state NMR spectra of CGY-1 and CGY-1.5 phenolic resin/F127 cured at 80 °C.

Fig. 8

 8 Fig. 8 SAXS patterns (inset: TEM pictures) (a) of the CGY-1 phenolic resin heated at 80 °C and 380 °C respectively and TPD-MS desorption curves of CGY-1 (b) and CGY-1.5 (c) phenolic resins/F127 surfactant.

Fig. 7

 7 Fig. 7 TGA weight loss and DTG derivative weight loss curves of (a) individual precursors used for the synthesis and (b) phenolic resin polymer CGY-1.0 and CGY-1.5.

Fig. 9

 9 Fig. 9 Schematic representation of the synthesis pathway of ordered carbon using phloroglucinol and glyoxylic acid precursors.

Table 1

 1 Synthesis conditions used for the preparation of carbon materials

			Molar ratio of	Mass ratio of
	Material		phloroglucinol :	phloroglucinol +
	name	Method	glyoxylic acid	glyoxylic acid : template
	CGY-1S	EISA	1 : 1	1 : 0.6
	CGY-1	EISA	1 : 1	1 : 1.2

  g -1 )

						D p	a 0	t wall
						(nm)	(nm)	(nm)
	CGY-1S	493	0.40	0.23	0.17	8.3	-	-
	CGY-1	679	0.83	0.34	0.49	6.5	15.8 9.3
	CGY-1.25 525	0.30	0.24	0.06	2.9	12.4 8.2
	CGY-1.5 582	0.31	0.27	0.04	2.7	12.0 8.0

Acknowledgements

We acknowledge Gautier Schrodj for performing the TGA analysis and Dr Joseph Dentzer for fruitful discussions concerning TPD-MS experiments.


Goulven Rochcongar

Hélène Pillet

Elena Bergamini

S Moreau

Patricia Thoreux

Wafa Skalli

Philippe Rouch

A new method for the

Keywords:

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

Introduction

The knee is one of the most studied joints with more than 110,000 occurrences in Pubmed. It is also probably the most complex one, characterised by a compromise between great stability and mobility. This is allowed by the interaction of different passive structures: femur, tibia, patella, ligaments, and menisci. Among them, the four major knee ligaments (anterior and posterior cruciate ligaments, ACL and PCL, medial and lateral collateral ligaments, MCL and LCL, respectively), together with the popliteal complex (comprising the femoral insertion of the popliteus tendon and the fibular insertions of the popliteo-fibular ligament [START_REF] Laprade | The anatomy of the posterior aspect of the knee. An anatomic study[END_REF]), play a crucial role in guiding the knee passive kinematics and stabilising this joint [START_REF] Southmayd | The forgotten popliteus muscle. Its usefulness in correction of anteromedial rotatory instability of the knee. A preliminary report[END_REF][START_REF] Wilson | Ligaments and articular contact guide passive knee flexion[END_REF]. The knowledge of the biomechanical behaviour of these elements is essential to understand the complex kinematics of the healthy joint, and is an important prerequisite to understand ligament injury mechanisms, predict the consequences of ligament disruption, and properly design surgical interventions.

The variation of the length (commonly defined as the geometric distance between the ligament origin and insertion and hereinafter referred to as "end-to-end distance") of the major knee ligaments has been widely dealt with in the literature. However, most studies considered each ligament individually, with particular attention to the ACL [START_REF] Amis | Functional anatomy of the anterior cruciate ligament. Fibre bundle actions related to ligament replacements and injuries[END_REF][START_REF] Iwahashi | Assessment of the "functional length" of the three bundles of the anterior cruciate ligament[END_REF][START_REF] Yoo | Changes in ACL length at different knee flexion angles: an in vivo biomechanical study[END_REF] or the PCL [START_REF] Boisgard | Study of the posterior cruciate ligament using a 3D computer model: ligament biometry during flexion, application to surgical replacement of the ligament[END_REF][START_REF] Jeong | An analysis of the posterior cruciate ligament isometric position using an in vivo 3-dimensional computed tomography-based knee joint model[END_REF][START_REF] King | In vivo open-bore MRI reveals region-and sub-arc-specific lengthening of the unloaded human posterior cruciate ligament[END_REF][START_REF] Nakagawa | The posterior cruciate ligament during flexion of the normal knee[END_REF] or, to a lesser extent, to the MCL [START_REF] Park | The change in length of the medial and lateral collateral ligaments during in vivo knee flexion[END_REF][START_REF] Victor | How isometric are the medial patellofemoral, superficial medial collateral, and lateral collateral ligaments of the knee?[END_REF] or the LCL [START_REF] Park | The change in length of the medial and lateral collateral ligaments during in vivo knee flexion[END_REF][START_REF] Sugita | Anatomic and biomechanical study of the lateral collateral and popliteofibular ligaments[END_REF][START_REF] Victor | How isometric are the medial patellofemoral, superficial medial collateral, and lateral collateral ligaments of the knee?[END_REF]. Few works studied the popliteal complex [START_REF] Sugita | Anatomic and biomechanical study of the lateral collateral and popliteofibular ligaments[END_REF], although it has a critical role in the control of the rotation of the knee joint, especially limiting the external rotation of the tibia with respect to the femur [START_REF] Pasque | The role of the popliteofibular ligament and the tendon of popliteus in providing stability in the human knee[END_REF]. Last but not least, methodological issues still exist related to the reliable identification of each ligament insertion [START_REF] Rachmat | Generating finite element models of the knee: how accurately can we determine ligament attachment sites from MRI scans?[END_REF] and, when ex-vivo studies are considered, to the reproduction of the knee passive kinematics, which are both crucial aspects when the accurate estimation of the ligament end-to-end distance is aimed.

To the authors' knowledge only two publications studied the end-toend distance variation of all the four major ligaments simultaneously during passive knee flexion ex-vivo, including the individual identification of the ligament attachment site locations [START_REF] Belvedere | Geometrical changes of knee ligaments and patellar tendon during passive flexion[END_REF][START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF]. In the first study, Belvedere et al. [START_REF] Belvedere | Geometrical changes of knee ligaments and patellar tendon during passive flexion[END_REF] used an optoelectronic system to identify the ligament attachment sites after minimal cadaver dissections and the position of each ligament insertion was digitised and expressed with respect to tibia and femur anatomical systems of reference by means of cluster of markers attached on a pointer and on the bones. However, although optoelectronic systems are considered as the gold-standard for the estimation of the knee kinematics, this is not the case for what concerns the ligament insertion identification. The above-mentioned procedure, in fact, apart from being time consuming, is affected by uncertainties due to difficulties for the surgeon to accurately palpate the ligament attachment sites without performing a complete dissection, particularly those of the medial and lateral collateral ligaments and of the PCL on the tibia. In the second study [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF], a virtual palpation procedure was carried out to identify the ligament insertions on generic digital bone models. Subject-specific insertion locations were then estimated by matching the generic models to low-dose stereoradiography images of knee specimens. However, the accuracy of the ligament insertion identification was not assessed and no bundle separation was performed for the ACL, PCL and MCL. Moreover, none of these studies provided information about the insertion locations of the popliteal complex as well as about its end-to-end distance variation during knee flexion.

In the light of the above-mentioned considerations, the aim of the present study is to propose an original and robust technique to identify the knee ligaments and popliteal complex attachment sites and to describe how the end-to-end distance of these structures vary over passive knee flexion-extension movement.

Methods

Specimens

Twelve fresh frozen lower limbs were used in this study, six left and six right knees harvested from subjects aged between 47 and 79 years. Each specimen included entire femur with femoral head, patella, fibula and tibia without the ankle. Absence of trauma was checked and integrity of cartilage, meniscus and ligaments was inspected at the end of the experimentation during specimen dissection. Limbs were thawed at room temperature for 24 h. Skin and muscles, except eight centimetres of quadriceps tendon and popliteus muscle, were removed before the study. Nine tantalum balls were placed into the metaphysis of each bone, three into the tibia, three into the femur and three into the patella.

Kinematic data acquisition

The specimens were set in motion using a device described and validated in previous literature [START_REF] Azmy | EOS orthopaedic imaging system to study patellofemoral kinematics: assessment of uncertainty[END_REF] (Figure 1). The femur was rigidly fixed to a rig and the tibia was free to move (Figure 1). As no constraints have to be applied to coupled movements between the femur and the tibia, the device was slightly modified to allow free varus/valgus movements and a flexion-extension range of movement of 0°-120°. A motor was connected to the tibial pilon by a rope and was used to pull the rope thus allowing the flexion-extension movement. A 10 N force was applied to the quadriceps tendon via a pulley hung in order to guide the patella. The direction of this force was as parallel as possible to the tendon itself. Clusters made of three retro-reflective markers each were screwed in the femur, the tibia and the patella (Figure 1). As different alignments between the femur and tibia could affect both the knee axial rotation and varus-valgus kinematics, special attention was paid to the correct alignment of the bones when mounting the specimens on the rig. The position and orientation of each cluster of markers were registered with an optoelectronic system previously used in motion analysis (Polaris, Northern Digital Inc., Canada, sampling frequency = 60 samples/s) [START_REF] Billuart | 3D kinematics of the glenohumeral joint during abduction motion: an ex vivo study[END_REF].

To obtain the three-dimensional (3D) tibio-femoral and patellofemoral kinematics, anatomical frames associated with each bone were defined. To this aim, two orthogonal digital radiographs of each knee specimen were simultaneously acquired using a low dosage X-ray system (EOS, EOS-imaging, France) and 3D digital models of the femur and tibia, with fibula and patella, were obtained through a reconstruction algorithm described in a previous study [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF]. Femoral, tibial and patellar anatomical frames were defined following the indications reported by Schlatterer et al. [START_REF] Schlatterer | Skeletal landmarks for TKR implantations: evaluation of their accuracy using EOS imaging acquisition system[END_REF]. The tantalum balls pierced in each bone, as well as the markers of each cluster, were also identified and the 3D coordinates of the centroid of each ball and marker with respect to the EOS system of reference were obtained. Technical frames associated with the marker clusters were defined allowing acquisition of a mathematical relation between anatomical and technical frames expected to be invariant due to the rigid body assumption. The bone models and the relevant anatomical axes were then registered with respect to the movement data obtained in the optoelectronic system of reference. The 3D kinematics of the tibio-femoral joint was estimated from the instantaneous position of the clusters of markers and flexion/extension, adduction/abduction and internal/external rotation angles were obtained using the Cardan convention and the sequence "ZXY". For each specimen and each angle, a similarity analysis was performed to investigate if significant differences existed in the kinematics obtained during the different cycles. To this aim, the Spearman correlation coefficient was calculated using IBM SPSS Statistics (IBM Corp., Armonk, NY, USA).

The kinematic variability during the six flexion-extension cycles was less than one degree and one millimetre with a high Spearman correlation (r = 0.98, p b 0.001 for each knee). Therefore, as no significant hysteresis was present among the cycles, the average curve was considered as representative of the individual kinematics of each specimen. This confirmed the good reliability of the tested rig, which was previously reported by Azmy et al. for the patello-femoral joint [START_REF] Azmy | EOS orthopaedic imaging system to study patellofemoral kinematics: assessment of uncertainty[END_REF], as well as the proper alignment of the bony segment during the kinematic acquisitions.

Ligament attachment site identification and registration

After kinematic data acquisition, knee specimens were fully dissected, according to anatomical references previously published [START_REF] Diamantopoulos | The posterolateral corner of the knee: evaluation under microsurgical dissection[END_REF][START_REF] Edwards | The attachments of the anteromedial and posterolateral fibre bundles of the anterior cruciate ligament[END_REF][START_REF] Laprade | The anatomy of the posterior aspect of the knee. An anatomic study[END_REF][START_REF] Siebold | Flat midsubstance of the anterior cruciate ligament with tibial "C"-shaped insertion site[END_REF] in order to identify and mark ligaments/tendon origins and insertions using radio opaque paint composed of barium sulphate (Figure 2). The following structures were taken into account: ACL, PCL, MCL (deep and superficial bundles, i.e. the two tibial insertions), LCL, and popliteal complex (going from the femoral insertion of the popliteus tendon to the fibular insertion of the popliteo-fibular ligament). For the sake of readability, the word "ligaments" will be used throughout the manuscript when referring to both the knee ligaments and the popliteal complex.

After the specimen was dissected and the attachment sites identified, the femoral and tibial epiphyses were scanned, using a computed tomography (CT) Scanner (Philips, Best, The Netherlands; thickness = 0.67 mm, distance = 0.33 mm). Digital models of each bone epiphysis, each ligament/tendon attachment site and each tantalum ball were obtained using Aviso® (Burlington, MA, US). The 3D coordinates of the tantalum balls with respect to the CT Scanner system of reference were then used to perform the registration between the CT Scan and the EOS systems of reference and, thus, to express the ligament attachment site coordinates with respect to the EOS frame. For those ligaments commonly separated into two bundles (ACL, PCL and MCL), the digital footprints obtained on each bone model were visually separated, using an ad hoc developed software, into two regions corresponding to the two bundles (antero-medial (AM) and postero-lateral (PL) for the ACL, antero-lateral (AL) and postero-medial (PM) for the PCL, superficial and deep for the femoral insertion of the MCL). This procedure was carried out by an expert surgeon as described in the literature [START_REF] Colombet | Morphology of anterior cruciate ligament attachments for anatomic reconstruction: a cadaveric dissection and radiographic study[END_REF][START_REF] Laprade | The anatomy of the medial part of the knee[END_REF][START_REF] Lorenz | Radiological evaluation of the anterolateral and posteromedial bundle insertion sites of the posterior cruciate ligament[END_REF]. The centroid of each ligament attachment site was finally calculated for the whole insertions as well as for each bundle. Concerning the ACL and the PCL, the centroids of the whole insertions were referred to as "intermediate".

Calculation of ligament end-to-end distance variations

Knowing the position of each ligament insertion in the EOS reference frame, it was possible to obtain the same information in the clusterbased technical frame of each bone and to track the insertion positions all along the flexion-extension cycle. For each ligament (and bundle when considered), the distance between the femoral and tibial/fibular insertions was then estimated and referred to end-to-end distance. According to the existing literature [START_REF] Hosseini | In vivo anterior cruciate ligament elongation in response to axial tibial loads[END_REF][START_REF] Hsieh | Knee kinematics and ligament lengths during physiologic levels of isometric quadriceps loads[END_REF][START_REF] Jordan | The in vivo kinematics of the anteromedial and posterolateral bundles of the anterior cruciate ligament during weightbearing knee flexion[END_REF][START_REF] Li | In vivo kinematics of the ACL during weightbearing knee flexion[END_REF][START_REF] Li | In vivo elongation of the anterior cruciate ligament and posterior cruciate ligament during knee flexion[END_REF][START_REF] Papannagari | Function of posterior cruciate ligament bundles during in vivo knee flexion[END_REF] and for the sake of readability, we referred to ligament lengthening when this distance increased and to ligament shortening when this distance decreased. The variation of the end-to-end distance of each ligament was then represented as a function of the tibio-femoral flexion-extension.

Results

For what concerns the knee kinematics, a tibio-femoral adduction of about 4°± 4°( mean ± 1 standard deviation (SD)) and an internal rotation of the tibia with respect to the femur of about 18°± 4°at 120°of flexion were observed (Figure 3).

The mean end-to-end distance of each ligament for a set of specific knee flexion angles is reported in Table 1. Figure 4 shows the ligament end-to-end distances expressed as a percentage of the maximal distance obtained during the knee movement (left panel) and the ligament end-to-end distance variations expressed in percentage with respect to the distance at knee maximal extension (right panel). During the knee flexion, the ACL (AM, PL and intermediary bundles), MCL (deep and superficial) and LCL shortened. The PCL lengthened of about 21%. The popliteus complex shortened until 30°of flexion and then lengthened.

Discussion

The present article is based on ex-vivo data and proposes a new methodology to identify the knee ligament attachment site locations in order to quantify the end-to-end distance variation patterns of the popliteal complex and of the main bundles of the four major knee ligaments (ACL, PCL, MCL, and LCL) during continuous passive knee flexion. The proposed method proved to be robust and reliable and allowed obtaining information about the synergic behaviour of the main knee ligaments and of the popliteal complex, as well as about the individual 3D tibio-femoral kinematics.

Specifically, for what concerns the tibio-femoral kinematics, an internal rotation of the tibia of about 18°at 120°of flexion was found. An internal rotation was also reported by many authors between eight degrees and 29°at 120°of flexion [START_REF] Li | Kinematics of the knee at high flexion angles: an in vitro investigation[END_REF][START_REF] Mcpherson | Imaging knee position using MRI, RSA/CT and 3D digitisation[END_REF][START_REF] Wilson | Ligaments and articular contact guide passive knee flexion[END_REF] and between 10°and 15°a t 90°of flexion [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF][START_REF] Myers | In vivo tibiofemoral kinematics during 4 functional tasks of increasing demand using biplane fluoroscopy[END_REF][START_REF] Wünschel | Differences in tibiofemoral kinematics between the unloaded robotic passive path and a weightbearing knee simulator[END_REF]. Similarly, results about varus displacement are in agreement with previous studies which reported less than five degrees of adduction [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF][START_REF] Wünschel | Differences in tibiofemoral kinematics between the unloaded robotic passive path and a weightbearing knee simulator[END_REF].

The results about the end-to-end distance of the ligaments in extended position are in general agreement with those reported in the existing literature. For what concerns the ACL, the end-to-end distances of the different bundles were found to be 35 mm (AM bundle), 32 mm (intermediate bundle), and 29 mm (PL bundle). Bicer et al. [START_REF] Bicer | Current knowledge in the anatomy of the human anterior cruciate ligament[END_REF] reported that the AM bundle is the longest with an end-to-end distance between 22 mm and 41 mm (mean value of about 32 mm), whereas the PL bundle was shorter measuring 27 mm. Regarding the PCL end-to-end distance, the results of the present study were 33 mm for the PM bundle, 29 mm for the intermediate bundle, and 27 mm for the AL bundle. Nakagawa et al. reported a PCL end-to-end distance up to 34 mm without considering bundle separation [START_REF] Nakagawa | The posterior cruciate ligament during flexion of the normal knee[END_REF]. As for the end-to-end distances of the superficial and deep bundles of the MCL, results were respectively 92 mm and 36 mm. These values are in agreement with a previous study of Liu et al. which reported an end-to-end distance of 95 mm for the superficial bundle of the MCL and 42 mm for the MCL deep bundle [START_REF] Liu | In vivo length patterns of the medial collateral ligament during the stance phase of gait[END_REF]. A very good concordance was observed for the LCL which was found to be 61 mm. The same result was reported indeed by Diamantopoulos et al. [START_REF] Diamantopoulos | The posterolateral corner of the knee: evaluation under microsurgical dissection[END_REF]. Finally, the distance between the femoral insertion of the popliteus tendon and the fibular insertion of the popliteo-fibular ligament was found to be 43 mm, in general agreement with a previous study published by Diamantopoulos et al. which reported a distance of about 35 mm.

Many articles dealt with the variation of the end-to-end distance of each individual knee ligament during knee flexion-extension, both invivo and ex-vivo. In the early 90s, Amis and Dawkins found that the anteromedial bundle of the ACL was lengthening after 30°of flexion, whereas the intermediary and posterolateral bundles were shortening [START_REF] Amis | Functional anatomy of the anterior cruciate ligament. Fibre bundle actions related to ligament replacements and injuries[END_REF]. Actually, recent in-vivo studies performed on unloaded knees concluded to a shortening of all bundles, the anteromedial bundle being the most isometric one [START_REF] Jordan | The in vivo kinematics of the anteromedial and posterolateral bundles of the anterior cruciate ligament during weightbearing knee flexion[END_REF][START_REF] Yoo | Changes in ACL length at different knee flexion angles: an in vivo biomechanical study[END_REF], as confirmed by the results of the present work. For what concerns the PCL, Nakagawa et al. and Jeong et al. reported a stretching over flexion for this ligament, especially for the anterolateral bundle [START_REF] Jeong | An analysis of the posterior cruciate ligament isometric position using an in vivo 3-dimensional computed tomography-based knee joint model[END_REF][START_REF] Nakagawa | The posterior cruciate ligament during flexion of the normal knee[END_REF]. This stretching, which was found to be about 20% with respect to the PCL end-to-end distance at knee full extension, is confirmed by the present results. As for the MCL, a shortening (six percent) of the deep bundle of the MCL was found in the present study, primarily during the first 40°of flexion. Similarly, a shortening (six percent) of the MCL superficial bundle was found, occurring during all the flexion-extension range of motion. These findings are in agreement with a study of Park et al. concluding to a shortening of the medial part of the MCL superficial bundle [START_REF] Park | The change in length of the medial and lateral collateral ligaments during in vivo knee flexion[END_REF]. Concerning the LCL, a shortening of 15% was found. This result confirms previous findings from Victor et al. [START_REF] Victor | How isometric are the medial patellofemoral, superficial medial collateral, and lateral collateral ligaments of the knee?[END_REF] and Sugita and Amis [START_REF] Sugita | Anatomic and biomechanical study of the lateral collateral and popliteofibular ligaments[END_REF] who reported that the LCL shortened by about 11%. According to the existing literature [START_REF] Laprade | The posterolateral attachments of the knee: a qualitative and quantitative morphologic analysis of the fibular collateral ligament, popliteus tendon, popliteofibular ligament, and lateral gastrocnemius tendon[END_REF][START_REF] Laprade | The anatomy of the posterior aspect of the knee. An anatomic study[END_REF][START_REF] Sugita | Anatomic and biomechanical study of the lateral collateral and popliteofibular ligaments[END_REF] in the present study the femoral insertion of the popliteal tendon and the fibular insertion of the popliteo-fibular ligament were considered. In this respect, the quantification of the end-to-end distance variation of the popliteal complex is particularly interesting in clinical practice because many surgical procedures reconstruct the popliteus tendon using the abovementioned insertions [START_REF] Arciero | Anatomic posterolateral corner knee reconstruction[END_REF][START_REF] Coobs | An in vitro analysis of an anatomical medial knee reconstruction[END_REF][START_REF] Zhang | Popliteofibular ligament reconstruction for posterolateral external rotation instability of the knee[END_REF][START_REF] Zorzi | Combined PCL and PLC reconstruction in chronic posterolateral instability[END_REF]. When observing the end-to-end distance variation of the popliteal complex, it is worth noting that the inversion of the curve occurs around 30°of knee flexion. A five percent shortening of the popliteal complex during the first 30°of knee flexion was found, followed by a lengthening of about two percent in deep flexion. Sugita and Amis [START_REF] Sugita | Anatomic and biomechanical study of the lateral collateral and popliteofibular ligaments[END_REF] found a lengthening of about 12%. The limited sample size and large standard deviations (10 mm corresponding to 25% of the global end-to-end distance of the complex) associated with the latter study could explain the difference in the reported results.

Only two papers described both the kinematics and the end-to-end distance variation of the knee ligaments considering all ligaments simultaneously [START_REF] Belvedere | Geometrical changes of knee ligaments and patellar tendon during passive flexion[END_REF][START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF]. However, these studies did not take the popliteal complex into account even if it plays a major role in controlling rotational stability of the knee. Moreover, minimal dissection together with an optoelectronic system [START_REF] Belvedere | Geometrical changes of knee ligaments and patellar tendon during passive flexion[END_REF] or virtual palpation procedures [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF] were used to identify and register the ligament attachment sites, and therefore neither methodology is able to guarantee the realism required in clinical applications. Conversely, the original technique to identify the ligament attachment sites proposed in the present study allowed for a reliable and robust identification and registration of the insertions of the popliteal complex and of all the four major knee ligaments. This allowed for overcoming the main limitations related both to the use of optoelectronic systems and minimal dissection procedures [START_REF] Belvedere | Geometrical changes of knee ligaments and patellar tendon during passive flexion[END_REF] which do not allow accurate palpation of all ligament attachment sites, and to virtual palpation procedures [START_REF] Bergamini | Tibiofemoral joint constraints for bone pose estimation during movement using multibody optimization[END_REF] which do not necessarily take into account the accuracy and the variability of the ligament/tendon attachment site location.

Among the limitations of the present study, there is the fact that ligament length was modelled as the end-to-end distance between the ligament femoral and tibial/fibular insertions. Some ligaments, as the ACL and the MCL, are tightened in extension whereas others such as the PCL are slackened. Moreover, ligament wrapping around bone prominences and periosteal tissues was not accounted for. As ligaments are incompressible structures, their length cannot be less than the tension free length. This is particularly true for the PCL for which the end-to-end distance increases during the full range of motion whereas the "true" fibre lengthening occurs after 50°of flexion [START_REF] Markolf | Changes in knee laxity and ligament force after sectioning the posteromedial bundle of the posterior cruciate ligament[END_REF]. It must be noted, however, that accurate modelling of the ligament path (and thus the quantification of the actual shortening and lengthening) is crucial when ligament forces/strains need to be assessed, which is not the case for the present study. Finally, the end-to-end distance approximation can be considered largely acceptable in most applications for which the data provided in the present paper could be useful for (i.e. subject-specific knee modelling for clinical or movement analysis purposes).

In this study, CT-scan was used to reconstruct only the accurate position of the ligament attachment sites, whereas the femur and tibia/fibula bone models were obtained using biplanar X-ray imaging. This is because the latter, being characterised by low-dosage irradiation and thus less risky for the subjects, can be used to obtain subject-specific information in-vivo even in routine clinical practice. Given the accuracy with which the bone models were obtained using the EOS system (on average lower than 1.3 mm as reported in Chaibi et al. [START_REF] Chaibi | Fast 3D reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar X-rays[END_REF] and Quijano et al. [START_REF] Quijano | Three-dimensional reconstruction of the lower limb from biplanar calibrated radiographs[END_REF]), we consider the reconstruction errors to have no impact on the end results.

Conclusion

In the present study, an original technique was used for a reliable and robust identification of the insertions of the popliteal complex, and of the cruciate and collateral ligaments on knee specimens. Detailed information regarding the 3D tibio-femoral kinematics as well as regarding the end-to-end distance variation pattern of the considered structures and of their sub-bundles was provided. This information represents an important contribution towards the understanding of ligament injury mechanisms, the prediction of the consequences of ligament disruption, and hopefully the design of effective surgical interventions.

Figure 1 .

 1 Figure 1. View of the device used to set in motion the knee specimens. The clusters of markers fixed to the femur, tibia and patella bones are also depicted.

Figure 2 .

 2 Figure 2. View of the proximal epiphysis of a randomly chosen tibia, showing the different ligament insertions marked with the radiopaque paint (white marks).

Figure 3 .

 3 Figure 3. Knee internal/external rotations (left panel) and abd/adduction (right panel) as a function of the flexion/extension range of motion. Mean (solid line) and ± one standard deviation (dotted line) are reported.

Figure 4 .

 4 Figure 4. Mean ligament/tendon (and bundles where indicated) length expressed as the percentage of the maximal length reached during flexion/extension (left panel) and mean length variation expressed as the percentage of the length reached at knee maximal extension (right panel). Both variables are depicted as a function of the knee flexion angle.

Table 1

 1 Mean ± 1 one standard deviation of each ligament/tendon (and bundles where indicated) length (mm) obtained at specific knee flexion angles.

		0°15°30°60°90°120°A
	CL
	AM	35 ± 5	35 ± 4	35 ± 4	34 ± 4	34 ± 4	33 ± 4
	PL	29 ± 5	28 ± 5	28 ± 5	26 ± 4	25 ± 3	25 ± 3
	Intermediate	32 ± 4	32 ± 4	32 ± 4	30 ± 4	29 ± 4	29 ± 3
	PCL
	AL	27 ± 3	28 ± 2	28 ± 3	32 ± 3	34 ± 3	35 ± 3
	PM	34 ± 5	32 ± 4	32 ± 3	34 ± 3	35 ± 3	35 ± 3
	Intermediate	29 ± 4	30 ± 3	30 ± 3	33 ± 3	34 ± 3	35 ± 3
	MCL
	Deep	36 ± 4	34 ± 4	34 ± 4	34 ± 4	34 ± 4	34 ± 3
	Superficial	92 ± 9	91 ± 8	91 ± 8	90 ± 8	89 ± 8	86 ± 8
	LCL	62 ± 6	60 ± 6	59 ± 6	57 ± 6	55 ± 5	53 ± 5
	Popliteus	44 ± 5	42 ± 6	41 ± 6	42 ± 7	44 ± 7	45 ± 6

Acknowledgements

Thanks to Ann-Laure Pollastri for her technical support and to Louis Dagneaux for helping during the experimental session. The authors also thank the ParisTech BiomecAM chair program on subject-specific musculoskeletal modelling.

This research was approved by the ethics committee of the human anatomy lab of the University of Caen (Basse Normandie, France).

Conflict of interest

The authors declare that they have no conflict of interest for this publication.