Kilian Philippe
email: kilian.philippe@yahoo.fr

Thierry Paillard

Romain Dubois

Olivier Maurelli

Jacques Prioux

Key Performance Indicators in Tour de France Sailing. 1 2 3

Keywords: Sailing, Tour de France, Elite Athletes, Inshore sailing

This study aimed to determine the key performance indicators of inshore sailing during 32 the sailing Tour de France. Technical and physical parameters were investigated to 33 determine the discriminating factors between successful and less successful international 34 level sailors. Measurements from 21 sailors (mean ± SD; age = 23.81 ± 4.18 years) were 35 conducted prior to the sailing Tour de France. Global Positioning System data of all 36 participating teams (n=23) was analyzed. Sailors were divided in two groups (i.e. 37 successful and less successful) according to qualifying performance percentage. The 38 differences between successful and less successful sailors were explored by means of 39 independent t-tests. Results indicate that successful boats displayed higher maximal 40 speed, higher average speed and more efficient starting performance per race than less 41 successful boats. Successful sailors have stronger handgrip strength, higher isometric 42 maximal voluntary force relative to bodyweight (isometric mid-thigh pull) and more 43 powerful submaximal pulling (bench pull) actions than their less successful counterparts.

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The results of this study suggest that multiple sailing, physical and physiological variables 45 are related to sailing performance in inshore sailing. Therefore, we emphasize the 46 importance of integrating specific testing protocols to evaluate the performance potential 47 of inshore sailors participating in the sailing Tour de France.

Materials and methods

Germany) and a stadiometer (Seca®, Barcelona, Spain) were used to measure weight 157 and height respectively. Measurements for height (standing and sitting) and weight were 158 made with an accuracy of 0.5 cm and 0.1 kg respectively. Wingspan was measured to the 159 nearest 0.1 cm, from one middle fingertip to the other using a measuring tape (Seca®, 160 Barcelona, Spain). Three skinfolds were taken on the right side of each participant 161 (pectoral, abdominal and thigh) according to recommendations by Jackson and Pollock 162 (Jackson and Pollock, 1978). The skinfolds were measured with a Harpenden skinfold 163 caliper (Harpenden®, Burgess Hill, UK) with 10-g.mm -2 of constant pressure. Body density 164 was assessed (Jackson and Pollock, 1978) while body fat was calculated using Brozek's 165 equation [START_REF] Brozek | Densitometric analysis of body composition: 557 revision of some quantitative assumptions[END_REF]. A measuring tape (Seca®, Barcelona, Spain) was used to 166 measure the girth of relaxed arms, thighs and calves on left and right sides following 167 measuring recommendations of the international society for the advancement of 168 kinanthropometry (ISAK; Marfell-Jones et al., 2006). Rosedale, USA). Knee angle was measured with a goniometer, to ensure a range of 125-199 140° [START_REF] Haff | The reliability of isometric force-time 581 variables collected on a portable mid-thigh pull testing device[END_REF]. The bar height was adjusted to meet the testing criteria and to 200 accommodate to the athlete's size. Once the test had been thoroughly described and 201 testing parameters were set, a specific warm-up was conducted. Athletes were provided 202 with two warm-up pulls, 1 at 50 % and 1 at 75 % of perceived maximum effort, separated 203 by 1 min of rest. Once body position was stabilized (verified by observation and live force 204 measures), the subject was given a countdown of "3, 2, 1, pull." Minimal pre-tension was 205 allowed to ensure that there was no slack in the subject's body before initiation of the pull.

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Athletes performed 3 maximal IMTP with the instruction to pull the bar with maximal effort Ense-Parsit, Germany). V ̇O2max, expressed as ml.min -1 .kg -1 , measures were collected 238 through the use of a portable self-contained metabolic cart CardioCoach (Korr Medical 239 Technologies®, Salt Lake City, UT) and previously validated [START_REF] Dieli-Conwright | Validation of the CardioCoachCO2 for Submaximal and Maximal Metabolic 574 Exercise Testing[END_REF]. and57 races andaccumulated 474.3 ± 38.3 maneuvers (NS: 355.1 ± 37 Table 2 shows mean (± SD) for the age and anthropometric characteristics of professional 285 male TDF sailors. No significant differences were observed in anthropometric parameters 286 between crew positions (Table 2) and success attribute. The physical and physiological 287 profiles of sailors are reported in Table 3. Successful sailors had stronger HGSDom Hence, it can be assumed that the anaerobic energy system is significantly stressed 316 during TDF racing. However, the TDF competition also requires a good aerobic level to 317 endure the 15 days of sailing and to optimize recovery when racing (NS: 77 ± 14 318 min.stage -1 ; CR: 244 ± 35 min.stage -1 ). (Caimmi and Samprini, 2017). To the best of our 326 knowledge, this is the first study to analyse such parameters in fleet racing.

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With regards to our results, we observed variability in the distance covered and 328 time to finish a heat. Wind direction and wind speed influences the organisation committee 329 in course settings (Perez Turpin et al., 2009). Nevertheless, it should be noted that sailing 330 also relies on cognitive skills [START_REF] Araújo | Ecological dynamics of continuous and categorical decision-making: The regatta 531 start in sailing[END_REF] and that different racing strategies exist. Indeed, offshore sailors tended to be smaller and heavier (177 ± 7 cm and 78 ± 10 kg; 360 [START_REF] Hurdiel | Sleep restriction and degraded reaction-time performance in Figaro solo sailing 585 races[END_REF] whilst measures reported on the 2002 TDF outlined the smaller and 361 lighter profiles of sailors at the time (173 ± 6 cm and 62.6 ± 9.3 kg; Leger et al., 2008).

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The body fat of athletes in the study hereby (12.91 ± 4 %) was similar to previously 363 reported data of America's Cup sailors (13 ± 4 %; Neville et al., 2009), and seems within 364 the range (10-15%) of international and Olympic dinghy sailors (Vangelakoudi et al., 2007; 365 Bojsen-Moller et al., 2007). Anthropometric characteristics vary according to competitive 366 status, crew position, publishing date and sailing classification (Larsson et al., 1996).

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Surprisingly, there was no significant difference in anthropometric data in regards to crew 368 position (Table 2). This could be the result of the race organization's choice to set the

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The physical and physiological characteristics reported in the present study also 374 varied when compared to other sailing studies. V ̇O2max of our present study (53.4 ± 8.5 375 ml.mn -1 .kg -1 ), seems to be (i) lower than in elite laser sailors (58.2 ± 4.7 ml.mn -1 .kg -1 ; 376 Castagna and Brisswalter, 2006), (ii) higher than finn sailors (47.6 ± 3.5 ml.mn -1 .kg -1 ; 377 Bojsen-Moller et al., 2007) and (iii) similar to America's Cup grinders (52.2 ± 4.6 ml.mn - 378 1 .kg -1 ; [START_REF] Bernardi | Physiological characteristics of America's Cup sailors[END_REF]. The differences outlined in these studies could be related to [START_REF] Bourgois | Isometric 554 quadriceps strength determines sailing performance and neuromuscular fatigue during an 555 upwind sailing emulation[END_REF]. The sailors undertaking the MRWT-MPO test in this 388 study (565.9 ± 97.9 W) held similar anaerobic capacity than highly trained college level 389 rowers (548.97 ± 95.57 W;Shaharudin and Zanotto, 2014). This comforts our 390 understanding that TDF sailors rely significantly on anaerobic energy delivery during 391 racing.

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Lower body power was assessed using SJ and CMJ protocols. Few other studies 393 have analyzed such parameters on sailors. Indeed, only one has assessed national level 394 sailors for lower body power (Tan et al., 2006) and found similar results to the present 395 study (36.0 ± 6.2 vs 34.0 ± 4.0 cm) on the SJ. Nevertheless, it seems that no correlation 396 between jumping performance and hiking potential exists (Tan et al., 2006). Hiking is 397 characterized by strong isometric contractions and coactivation of the muscles involved: 398 quadriceps, hamstrings, abdominal and paravertebral muscles (Larsson et al., 1996;Tan 399 et al., 2006). Numerous studies have analyzed isokinetic muscle strength of knee, hip and 400 trunk flexors and extensors of elite level sailors [START_REF] Aagaard | Isokinetic muscle strength and hiking performance in elite sailors[END_REF]Chicoy and 401 Encarnacion-Martinez, 2015). These studies have highlighted the high demands of these Trimming and hoisting actions requires powerful and energetic movements on the 417 sheets [START_REF] Bay | Bay testen. En fysiologisk performance test for 49'er gaster 541[END_REF]. By doing so, sailors increase the amount of apparent 418 wind that covers the sail and, thus, increase boat speed. Indeed, it was thought that sailors 419 participating in the TDF would have high amounts of maximal strength due to the 420 predominance of pulling actions necessary when maneuvering the boat. Differences can 421 be outlined for the one repetition maximum between Americas Cup sailors (99.41 ± 5.4 422 kg; Pearson et al., 2009) and TDF sailors of this present study (77.5 ± 13.0 kg).

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Nevertheless, it should be noted that the America's cup sailors were heavier (97.8 ± 12.5 424 vs 74.8 ± 6.6 kg). Bar velocity at fixed loads was also evaluated and turned out to be Indeed, it has been linked to performance in many sports [START_REF] Cronin | A Brief Review of 567 Handgrip Strength and Sport Performance[END_REF]. Significant 434 decreases in grip strength between pre-and post-sailing training sessions have been 435 reported in junior male semi-elite sailors [START_REF] Bateup | The Influence of Training Load 536 on Markers of Fatigue in Junior Male Semi-Elite Sailors[END_REF]. The TDF sailors (61.1± 9.5 436 kg) reported stronger HGSDom than collegiate dinghy sailors (48.28 ± 5.31 kg;Pulur, 2011).

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These results outline the high mechanical stress placed on forearms when maneuvering 438 TDF boats. HGSDom was found to significantly discriminate between SA and LSA. It was 439 also correlated to racing outcome (NS and CR). These results could indicate more 440 efficiency to maneuver the D24 at higher speeds (i.e. optimized gripping ease against high 441 resistance in sheets and cranks). It would seem interesting to analyze the acute and 442 chronic load effects of sailing on handgrip strength.

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An interesting finding of this study was that no significant difference was found 444 between crew positions for physical and physiological parameters. This could indicate an 445 equal importance of overall fitness of TDF sailors to maneuver the boat. Indeed, it was higher training loads on-water and off-of SA [START_REF] Bateup | The Influence of Training Load 536 on Markers of Fatigue in Junior Male Semi-Elite Sailors[END_REF].

  inshore sailors (N = 21; mean ± SD; age = 23.81 ± 4.18 109 years; height = 179.32 ± 7.30 cm; body mass = 74.78 ± 6.56 kg) were assessed in the 110 final preparation phase leading up to the 2019 TDF. Subjects were informed of the testing 111 procedures, potential risks and the purpose of their participation. All subjects had already 112 competed in international competitions. Their collective experience included 59 TDF 113 campaigns. At the time of testing, the subjects had completed 6 months of sailing training 114 and had been actively participating in strength and conditioning programs for at least three 115 years. None of the participants reported injuries or diseases that would impair their 116 physical performance. The study protocol was approved by the ethics committee of 117 Rennes University. Written informed consent was obtained from all participants before the 118 start of the study. In this study, criteria used to qualify an athlete's performance was based A c c e p t e d m a n u s c r i p t of the daily finals. Less successful boats (LSB, n=16) qualified for half or less of the daily measured in the following order: weight, height, 155 sitting height, wingspan, skinfolds and body girths. A weighing scale (Seca®, Hamburg, 156

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  Session 2: Physical testing. 170 Physical and physiological characteristics were measured in randomized order. 171 Handgrip strength. Maximal isometric hand-grip strength (HGS) was assessed with a 172 Jamar® handgrip dynamometer (Sammons Preston Corp., Bolingbrook, Ill., USA). The 173 test positions were standardized (Svantesson et al., 2009). Three trials were performed 174 on each hand. The first three trials started with the right hand. Subjects were instructed to 175 squeeze the device as hard as possible for 3 s. The time between each trial was 15 s and 176 3 min of rest was allowed when changing hands. The maximal measure of the three trials 177 A c c e p t e d m a n u s c r i p t was retained in kilograms (Kg). Sum (HGSsum) of both hands and dominant hand (HGSdom) measures were assessed and included in the results. 179 Vertical jumps. Lower body power was tested on the squat jump (SJ) and 180 countermovement jump (CMJ) using a chronojump contact mat (Chronojump-181 Boscosystem™, Software, Spain). Each subject had three attempts per jump with 1 min 182 of rest between trials. Subjects started with SJ and, after a 3 min passive recovery, were 183 assessed on CMJ. Instructions for the jumps were explained and controlled with a 184 goniometer for the SJ. Subjects were instructed to descend to 90° knee flexion. Once 185 position was reached, a countdown of "3, 2, 1, jump" was indicated orally. A validated and 186 reliable smartphone application (Balsalobre-Fernandez et al., 2015) was used for lateral 187 video analysis. This allowed to track lateral kinematics and thus avoid collecting results 188 that involved a countermovement action. Both the SJ and CMJ were done with subjects 189 placing hands on their hips as to avoid arm movement. For the CMJ, athletes were 190 instructed to perform a rapid eccentric phase, immediately followed by a rapid concentric 191 phase with the intention to jump as high as possible. Height and peak power of the best 192 SJ (SJH and SJPP) and CMJ (CMJH and CMJPP) performances were reported for analysis. 193 Isometric mid-thigh pull. Testing for isometric mid-thigh pull (IMTP) was conducted on a 194 customized pulling rack apparatus specifically developed for data collection. IMTP was 195 performed using two portable force platforms sampling at 1000 Hz (Pasco™, Rosedale, 196 USA) and previously validated (Peterson Silveira et al., 2017). The force plates were 197 connected to a portable laptop running the Capstone Software Program (Pasco™, 198

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  possible and push the feet down into the force platform. The time between 208 each trial was 1 min. Each maximal isometric trial was performed for 5 s. The best trial 209 was used for data collection and was analyzed relatively to the athlete's body weight 210 (IMTPW).

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  Force-velocity pulling profile. Force-velocity curve testing on the bench-pull (BP) was 212 conducted on an elevated bench-pull device placed above a guided squat rack (Smith 213 machine). The Smith machine (Technogym®, Cesena, Italy) allowed for vertical 214 displacement through guided rods. A Chronojump linear position transducer 215 (Chronojump™, Barcelona, Spain) was placed below the bar and automatically calculated 216 the kinematic parameters of every repetition. Subjects were instructed to pull the bar with 217 maximum effort until the barbell hit the bench 8 cm below the subject's chest. The barbell 218 was then lowered and a brief pause of 1 s was observed to avoid the rebound effect or 219 any stretch-shortening cycle interference. The protocol followed Sanchez-Medina's 220 instructions (Sanchez-Medina et al., 2014). Initial load started at 20 kg and increased by 221 increments of 10 kg until mean propulsive velocity (BPMPV) was lower than 0.7 m.s -1 . Three 222 attempts were executed for light (< 50 % 1RM), 2 for medium (50-80 % 1RM) and only 1 223 for the heaviest (> 80 % 1RM) loads. Inter-set rest intervals were 3 min for the light and 224 medium loads and 5 min for the heaviest loads. The fastest bar speed for each load was 225 recorded. The maximum load that could be lifted once was considered the athlete's 1RM 226 (BP1RM). BPMPV was calculated for the loads that were completed by all subjects (BPMPV20, 227 BPMPV30, BPMPV40 and BPMPV50).

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  Anaerobic capacity. Anaerobic capacity was tested using a modified rowing Wingate test 229 (MRWT) on a rowing ergometer Concept II-D (Concept 2 INC™, Vermont, USA). The 230 flywheel was set at 130 drag factor. Subjects were allowed 3 min of warm-up at a rate of 231 perceived exertion of 5 out of 10. Athletes then completed the 30 s all-out test. Exercise 232 performance was expressed as mean power output (MPO) in watts (W) and was 233 calculated automatically by Concept II-D. The procedure has been described previously 234 (Riechman et al., 2002). 235 Maximal oxygen uptake. Maximal oxygen uptake (V ̇O2max) was assessed through a step 236 incremental test (MOUT25) on an electromagnetically braked cycle ergometer (Kettler® 237 A c c e p t e d m a n u s c r i p t

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  Subjects were given time to adjust seat and bar height before starting the test. MOUT25 241 started at 20 W and increased by 25 W.min -1 until voluntary exhaustion(Amann et al., 242 2004). A cadence of 90-100 RPM was standardized throughout the test. During the 243 MOUT25 the following variables were constantly registered: heart rate (HR), minute 244 ventilation (V ̇E) and oxygen uptake (V ̇O2). Prior to each test, the gas analyzer was 245 calibrated according to the manufacturer's specifications. V ̇O2max was determined when 246 physical signs suggestive of exhaustion were apparent and at least one of the following 247 two criteria were met; (1) HRmax was no less than 15 beats below the predicted maximum 248 [220 -(0.65 x age); Spiro 1977] and (2) a steady state of V ̇O2 despite an increase in 249 workload (Vehrs et al., 2007). 250 Statistics 251 Data was calculated through standard statistical methods and are presented as mean ± 252 standard deviation. All variables were considered normally distributed through analysis 253 with the Shapiro-Wilk test, histograms and skewness values prior to analysis. One-way 254 analysis of variance (ANOVA) was used to compare anthropometric, physiological and 255 physical measures for the different crew positions. Independent t-tests were performed to 256 determine if significant differences existed between physical profiles (SA vs. LSA) and 257 technical parameters (SB vs. LSB). When results were significantly different, an effect size 258 (ES) calculation was used. ES was evaluated using Cohen's d along with 95% confidence 259 intervals. ES of ≤0.2, 0.21-0.60, 0.61-1.20, 1.21-2.0, ≥2.0 were considered as trivial, small, 260 moderate, large and very large, respectively (Batterham and Hopkins 2006). Finally, 261 Spearman's Rank Order Correlation (r) was used to identify the relationship between 262 outcome (race and overall standings) and the key performance indicators identified as 263 significant in the independent t-tests. Statistical analyses were performed using the SPSS 264 package (15.0 version; SPSS, Inc., Chicago, IL, USA). The level of significance was set 265 at p<0.05. was 17 ± 2 min for NS and 244 ± 35 min for CR. Course distance was 269 2672.9 ± 610.3 m for NS and 59000 ± 17500 m for CR. Teams participated between 47 270

  281and average speed (r=0.81). All three of the highlighted performance parameters were 282 also significantly correlated to final rankings of the TDF.283Profiling and physical key performance indicators 284

288(

  ES=0.82) and IMTPW relatively to body weight (ES=0.93) and exerted faster BPMPV20 289 (ES=1.18) than their less successful counterparts. The differences between SA and LSA 290 were significant (p=0.001). HGSDom (r=0.54), IMTPW (r=0.41) and BPMPV20 (r=0.61) were 291 significantly correlated (p<0.01) to rank in NS heats. CR results were correlated to HGSDom 292 (r=0.37; p<0.05) and BPMPV20 (r=0.74; p<0.01). BPMPV20 showed strong correlation with 293 final TDF rankings (r=0.8; p<0.05).

  s c r i p t The aim of this present study was threefold. First, our objective was to analyze and 297 report the nature of sailing during the TDF. Second, we attempted to identify the key 298 performance indicators associated with racing outcome. Third, we directed a descriptive 299 analysis of anthropometric, physical and physiological profiles of elite level sailors 300 participating in the TDF. Most prominently, the analysis has indicated the capacity to 301 discriminate between SB/LSB and SA/LSA by considering technical and physical the first report on the nature of sailing during the TDF. Overall, sailors travelled 306 541300 ± 64900 m in 1792.3 ± 409.3 min during the 15 days of competition. Mean race 307 duration (SN: 17 min; CR: 244 min) and the number of maneuvers were highly variable 308 due to external parameters (e.g. race course and tactics, environmental condition). 309 Insights on the nature of energetic demands and work to rest ratio can nevertheless be 310 estimated. In sailing, particularly where sailors must hike, work to rest ratio should be re-311 evaluated as a dynamic to static effort ratio. Tacking maneuvers lasted around 8 s while 312 a gybe lasted around 12 s. High intensity efforts, linked to the demands of maneuvering 313 (Neville et al., 2009), occurred on a 1:14 ratio in NS and 1:50 in CR. Dynamic to static 314 ratio reached as high 1:10 when boats chose to sail a course close to shoreline (CR).

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  performance analysts to monitor external training load 322[START_REF] Cummins | Global Positioning Systems (GPS) 570 and Microtechnology Sensors in Team Sports: A Systematic Review[END_REF] and collect data to identify technical and tactical performance 323 indicators in sailing activities(Perez Turpin et al. 2009). Research has identified the key 324 technical performance indicators in windsurfing[START_REF] Anastasiou | Descriptive 522 analysis of Olympic class windsurfing competition during the 2017-2018 regatta 523 season[END_REF], match racing 325A c c e p t e d m a n u s c r i p t (Neville et al., 2009) and kiteboarding

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  Teams must regularly analyse weather and oceanographic reports to determine the most 332 appropriate course(Thill, 1982). Other external parameters (e.g., position in the fleet, 333 changes of racing conditions, placement of opponents on course) can provoke variations 334 and modifications in initial strategy(Araujo and Sepra, 1997; Ward, Williams and Bennett, 335 2002; Manzanares, Segado and Menayo, 2012).336Speed parameters have previously discriminated between successful and less 337 successful athletes in other sailing competitions[START_REF] Anastasiou | Descriptive 522 analysis of Olympic class windsurfing competition during the 2017-2018 regatta 523 season[END_REF] Caimmi and 338 Samprini, 2017). This comforts our findings in that both average speed and maximal 339 speed were significantly correlated to both race and TDF overall outcome. On the basis 340 of bio-informational data, one can assume that SB were more efficient in determining the 341 most favourable course to take in order to optimize boat speed. Pluijms et al. (2015) have 342 investigated the difference in visual fixation behaviour between top and bottom-ranked 343 sailors. On the one hand, bottom ranked sailors focus their centre of attention on the boat 344 and thus might discard important environmental information. On the other hand, top 345 ranked sailors, were capable of "feeling" the changes in boat speed and direction through 346 mechanical and proprioceptive feedback. SB also displayed better starting performance 347 (rank and time gap at first mark) than LSB. Starting performance was significantly 348 correlated with race outcome and overall TDF ranking. This could be due to sailors 349 changing their gaze to look for relevant environmental information that might enhance the 350 boat's performance (Pluijms et al., 2015). Indeed, if boats arrived first at the first mark they 351 would not have to account for other information concerning opposing team position.

  .e. Americas Cup and Olympic Games), none has analyzed the anthropometric, 356 physical and physiological demands for multihull fleet racing. Hence, we can only compare 357 our data to those of similar sailing events. The mean data for height and weight of the 21 358 subjects (179.3 ± 7.3 cm and 74.8 ± 6.6 kg) are different to those found in other studies.

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  minimal total crew weight to 210 kg and supports findings by Neville et al., 2009 that 370 highlights the modern sailors' strategy to reduce body fat of the whole crew as to maximize 371 lean muscle mass for roles demanding higher physical output. This outlines the complexity 372 when establishing normative data for sailing in general.

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  the effect induced by the various peculiar onboard activity and/or the use of various testing 380 methodologies. Nevertheless, research has outlined the low aerobic demands during a 381 dinghy regatta(Portier et al., 2003). Indeed, sailors participating on TDF engage in high 382 intensity hoisting and trimming actions when maneuvering. Between the different 383 maneuvers, the sailors are involved in quasi-isometric hiking. Previous studies showed a 384 significantly decreased oxygenation pattern in the m. Vastus Lateralis during hiking 385 A c c e p t e d m a n u s c r i p t (inherent to isometric contractions > 30% maximal voluntary contraction), indicating an 386 imbalance between oxygen supply and demand, and probably due to restricted muscle 387 blood flow

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  specific strengths on hiking performance. In the present study, to assess maximal 403 isometric strength of the lower body, an IMTP test was performed. To date, this is the first 404 study to use such a protocol in an elite sailing environment. Relative strength should be 405 considered when assessing sailors, or other sports, where body weight is regulated by 406 competition rules. Isometric maximal voluntary force, using the IMTP test, has been linked 407 to functional performance in sport (Ran-Wang et al. 2016). We aimed at analyzing 408 isometric strength at hip/knee angles like those of other sailing studies (Chicoy and 409 Encarnacion-Martinez, 2015) by using the IMTP. Interestingly, maximal IMTP 410 discriminated between SA and LSA when the results were compared relatively to 411 bodyweight (IMTPW). IMTPW performance was significantly correlated (r=0.41; p<0.01) 412 with rank on NS courses. These results suggest that a high level of relative strength is 413 necessary in TDF sailors, and supports the findings in other studies analyzing the 414 relationship between lower body strength and sailing performance (Blackburn and 415 Hubinger, 1995).

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  significantly different between SA and LSA at 20 kg loads.Neville and collaborators (2009) 426 reported that successful boats maneuvered faster than less successful boats. Faster bar 427 velocity at submaximal loads could be directly correlated to hoisting/trimming efficiency 428 and, thus, sailing performance through faster maneuvers. BPmpv20 was in fact significantly 429 correlated to racing outcome (NS and CR) and TDF final ranking (r=.80; p<0.05). Future 430 research should therefore aim at establishing associations between bar velocities at fixed 431 loads with hoisting actions. 432 Handgrip strength has received a considerable amount of interest in past research.

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  see sailors switch position when racing or during specific maneuvers 447 throughout the TDF. Comparison of physical and physiological parameters from 21 elite 448 sailors indicated that SA had greater strength (HGSDom), muscular voluntary contraction 449 (IMTPW) and power (BPmpv20) compared to LSA. Differences were most marked between 450 trimmers (IMTPW, BPmpv20, BPmpv30 and BPmpv40) and bowmen (BPmpv20) which are primarily 451 responsible for trimming and material handling (sails, ropes and cranks). A possible 452 explanation highlighting the difference in HGSDom found in this study could result from 453

  the present study have been identified during the analysis process.457First, the sample size of 21 elite level sailors accounted for 6 fully crewed boats out of 23.458Testing more crew members may have permitted to perform more significant correlational 459 analysis between crew characteristics, as a mean or sum, and ranking. Second, as 460 previously mentioned, sailing relies on bio-informational and strategic qualities to perform. 461 Indeed, overall and specific sailing experience was not accounted for and could have 462 influenced performance and account for discrimination of success. findings have identified multiple variables (technical and physical) that 466 discriminate between successful and less successful athletes/boats. The results can be 467 used as normative data to compare, detect and guide athletes in their preparation for 468 performance. The present study highlights successful sailors having stronger grip 469 strength, more powerful bench-pull and higher IMTP than their less successful 470 counterparts. Successful boats displayed a faster average speed, maximal speed and 471 more efficient starting performance. Nevertheless, these findings should be applied with 472 caution to other populations (i.e. youths, less experimented sailors and other sailing 473 categories).

  like to acknowledge the Sailing Federation (France) and 488 Georacing® for their continued collaboration.

Figure 1 .

 1 Figure 1. Side and top view of a DIAM24 One Design multihull. The figure shows the position and 504 roles of the 3 athletes on-board. In winds over 10 knots all three sailors are hiking on the same 505 hull. 506 A c c e p t e d m a n u s c r i p t

Figure 2 .

 2 Figure 2. A typical Tour de France nautical stadium course. (1) Represents the downwind portion 508 and (2) the upwind portion. (1) And (2) can be sailed up to three times according to race committee. 509 Teams must go through the gates and can chose to round either mark (3). (4) Represents the final 510 straight before gybing towards the finish line. 511 512 A c c e p t e d m a n u s c r i p t

  Sailing parameters collected during the TDF are analyzed in Table 1 for SB, LSB and all 278 boats. Race outcome for NS was significantly correlated (p<0.01) with starting 279 performance (r=.52), maximal speed (r=.33) and average speed (r=.76). Coastal raid 280 ranking was correlated (p<0.01) with starting performance (r=.58), maximal speed (r=.43)

	271	.8; CR: 119.1 ±
	272	6.6). Gybes (downwind maneuver; lasted ~12 s) were more recurrent than tacks (upwind
	273	maneuver; lasted ~8 s), respectively 259.3 ± 26.8 vs. 214.9 ± 26.1. Maneuver count per
	274	NS heat was 8.7 ± 0.9 and 23.8 ± 1.3 for CR. Sailing distance for NS heats was 4161.8 ±
	275	80.1 m and 78500 ± 34900 m for CR. Course coverage for NS was 158.5 ± 3.0 % and
		133.8 ± 4.9 % for CR.

276

Technical key performance indicators 277

Table 2 .

 2 Age and anthropometric characteristics (mean (SD)) of TDF sailors.

		n	TDF	Age	Weight	Height	Sitting	Arm	BMI	∑3	Body	LBM	Girth	Girth	Girth
			(campaigns)	(years)	(kg)	(cm)	Height	Span	(kg.m -²)	Skinfol	Fat	(kg)	Arm	Thigh	Calves
							(cm)	(cm)		d (mm)	(%)		(cm)	(cm)	(cm)
	Successful
	Helmsmen Bowmen Trimmers All Less-Successful Helmsmen Bowmen Trimmers All Total All	4 3 3 10 3 4 4 11 21	2.8 (0.5) 2.7 (0.6) 3.0 (0.0) 2.8 (0.4) 2.7 (1.2) 2.7 (1.3) 3.0 (0.0) 2.7 (0.4) 2.8 (0.9)	22.0 (1.4) 22.3 (2.1) 23.7 (1.2) 22.6 (1.6) 23.7 (4.5) 25.0 (5.9) 25.8 (6.9) 24.9 (5.5) 23.8 (4.2)	70.9 (5.9) 71.8 (6.1) 77.8 (4.2) 73.3 (5.8) 68.4 (3.9) 79.1 (8.0) 79.1 (3.8) 73.5 (7.6) 74.8 (6.6)	176.4 (9.4) 175.5 (5.3) 183.3 (6.0) 178.2 (7.5) 176.4 (14.2) 175.5 (1.9) 183.3 (6.2) 180.4 (7.3) 179.3 (7.3) m 93.1 181.3 (4.6) (7.5) 91.0 (2.6) 190.0 (2.1) 95.7 (3.3) 188.3 (10.4) 93.3 (3.8) 185.8 (7.7) 92.3 (4.6) 186.0 (12.5) 92.9 (1.6) 183.8 (4.2) 91.4 (4.3) 184.3 (3.8) 92.2 (3.4) 184.6 (6.5) 92.7 (3.5) 185.1 (6.9) a n u s c r i p t 22.8 29.6 13.2 61.5 30.4 (1.2) (11.0) (3.8) (5.3) (1.8) 23.3 (0.6) 22.0 (4.4) 10.7 (1.7) 64.1 (4.3) 30.8 (2.0) 23.1 (0.6) 26.0 (15.4) 12.0 (5.2) 68.4 (5.0) 32.7 (1.3) 23.0 (0.8) 26.3 (10.4) 12.1 (3.6) 64.4 (5.3) 31.2 (1.8) 21.4 (2.3) 29.1 (8.0) 13.2 (2.6) 59.4 (3.8) 29.1 (1.4) 24.3 (2.3) 20.1 (4.6) 10.1 (1.6) 71.0 (6.5) 32.3 (4.0) 24.2 (1.9) 42.0 (13.5) 17.5 (4.5) 65.1 (3.6) 31.1 (2.6) 23.5 (2.4) 30.5 (13.1) 13.65 (4.0) 65.7 (6.5) 31.0 (3.0) 23.3 (1.8) 28.5 (11.8) 12.91 (4.0) 65.0 (5.9) 31.1 (2.5)	53.0 (1.6) 54.3 (0.9) 55.3 (1.8) 54.1 (1.3) 52.2 (3.2) 53.1 (7.0) 55.4 (1.3) 53.7 (4.4) 53.9 (3.2)	34.8 (1.6) 36.0 (0.9) 34.5 (1.8) 35.1 (1.5) 33.8 (1.3) 39.8 (6.2) 35.9 (1.4) (4.4) 35.9 (3.3) 36.7
	Range TDF: Tour de France; BMI: Body Mass Index; LBM: Lean Body Mass; Note: Successful, sailors finishing in the top 7 teams; Less successful, sailors finishing 8 th to [1-4] [17-33] [65.5-88.8] [163.5-190.5] [85.5-100] [173.5-200] [19.3-26.8] [13-54.5] [7.6-22] [55.3 -78.9] [27.5 -37] [44.5-61.5] [32.5-41] 23 rd . * Significant difference with values of successful athletes; P ≤ 0.05 (**; P ≤0.01). † Significant difference with values of successful athletes at same position; P ≤ 0.05 ( † †; P ≤ 0.01) A c c e p t e d

Table 3 .

 3 Physical and physiological characteristics (mean (SD)) of TDF sailors. : Dominant Hand Grip Strength; HGSSum: Sum of Hand Grip Strength; SJH: Squat Jump Height; SJPP: Squat Jump Peak Power; CMJH: Countermovement Jump Height; CMJPP: Countermovement Jump Peak Power; IMTP: Isometric Mid-Thigh Pull; IMTPW: Isometric Mid-Thigh Pull relative to Weight; MRWT-MPO: Modified Rowing Wingate Test Mean Power Output; BP1RM: Bench Press 1RM; BPMPV20: Bench Press Velocity at 20 kg; BPMPV30: Bench Press Velocity at 30 kg; BPMPV40: Bench Press Velocity at 40 kg; BPMPV50: Bench Press Velocity at 50 kg; V ̇O2max: Maximal Oxygen Uptake. Note: Successful, sailors finishing in the top 7 teams; Less successful, sailors finishing 8 th to 23 rd ; * Significant difference with values of successful athletes; P ≤ 0.05 (**; P ≤0.01). † Significant difference with values of successful athletes at same position; P ≤ 0.05 ( † †; P ≤ 0.01)

		n	HGSDo	HGSSu	SJH	CMJH	IMTP	IMTPW	MRWT-	BP1R	BPMPV2	BPMPV3	BPMPV4	BPMPV5	V ̇O2max
			m (kg)	m (kg)	(cm)	(cm)	(N)	(N.kg -	MPO (W)	M (kg)	0 (m.s -	0 (m.s -	0 (m.s -	0 (m.s -	(ml.mn -
								1 )			1 )	1 )	1 )	1 )	1 .kg -1 )
	Successful
	Helmsmen Bowmen Trimmers All Less-Successful Helmsmen Bowmen Trimmers All Total	4 3 3 10 3 4 4 11	59.3 (5.6) 72.0 (6.9) 66.3 (8.5) 65.2 (8.3) 56.3 (15.4) 58.3 (9.9) 57.3 (5.9) 57.4 (9.4)*	113.5 (9.7) 138.0 (11.1) 127.3 (20.1) 125.0 (16.3) 110.3 (27.5) 114.3 (18.9) 110.8 (11.8) 111.9 (17.5)	32.7 (4.8) 42.8 (5.5) 35.6 (1.0) 35.6 (1.0) 39.3 (7.7) 36.8 (5.8) 31.0 (5.6) 35.4 (6.7)	37.6 (5.2) 37.6 (2.2) 39.0 (2.4) 37.9 (38.6) 36.5 (4.7) 38.7 (7.5) 35.8 (6.8) 37.1 (6.1)	2649.9 (397.6) 2894.1 (189.7) 2955.6 (144.9) 2814.9 (293.5) 2433.4 (776.7) 2723.2 (614.7) 2527.7 (377.5) 2573.1 (540.8) m 37.3 (3.4) 40.4 (1.1) 38.0 (2.2) 38.4 (2.7) 35.2 (9.8) 34.3 (5.7) 31.9 (3.4) † 33.7 (5.9)* a n u s c r i p t 501.3 (82.3) 73.8 (6.3) 1.5 (0.02) 1.2 (0.1) 1.1 (0.1) 623.7 (115.0) 83.3 (2.9) 1.7 (0.1) 1.4 (0.1) 1.2 (0.2) 632.7 (126.0) 81.7 (10.4) 1.7 (0.1) 1.5 (0.1) 1.3 (0.1) 577.4 (114.2) 79.0 (7.8) 1.6 (0.1) 1.3 (0.1) 1.2 (0.2) 488.7 (46.0) 67.5 (4.3) 1.3 (0.2) 1.1 (0.0) 1.0 (0.06) 586.0 (109.4) 88.8 (20.15) 1.5 (0.1) † 1.4 (0.2) 1.2 (0.2) 575.0 (66.4) 70.0 (13.5) 1.3 (0.1) † † 1.2 (0.1) † † 1.1 (0.1) † 555.5 (84.9) 76.1 (16.8) 1.3 (0.2)** 1.2 (0.2) 1.1 (0.1)	0.9 (0.1) 1.0 (0.1) 1.2 (0.1) 1.0 (0.1) 0.8 (0.06) 1.0 (0.2) 0.9 (0.3) 0.9 (0.2)	53.5 (6.4) 52.5 (14.0) 56.5 (2.2) 54.1 (7.8) 48.7 (13.6) 57.3 (13.6) 51.4 52.8 (9.4) (6.8)
	All Range	61.1 (9.5) [46-80] A c c e p t e d 118.1 (17.8) 36.0 (6.2) 38.6 (5.6) 2688.2 (447.5) 35.9 (5.1) [90-150] [24.1-49.1] [26.2-46.7] [1567. 5-3160] [24.5-43.7]	565.9 (97.9) [430-774]	77.5 (13.0) [50-105]	1.5 (0.2) [1.04-1.83]	1.3 (0.2) [1.06-1.63]	1.1 (0.2) [0.92-1.45]	1.0 (0.2) [0.77-1.29]	53.4 (8.5) [36.5-76.8]

HGSDom

Acknowledgements

This study may provide useful information to coaches, sports scientists and sailors Nutrition,40,[497][498][499][500][501][502][503][504] Larsson, B., Beyer, N., Bay, P., Blond, L., Aagaard, P. and Kjaer, M. (1996). Exercise


Céline Vicard
email: celine.vicard@mines-albi.fr

Olivier De Almeida
email: olivier.dealmeida@mines-albi.fr

Arthur Cantarel
email: arthur.cantarel@iut-tarbes.fr

Gérard Bernhart

TTT DIAGRAM OF THE ANIONIC POLYMERIZATION PA6 FROM -CAPROLACTAM

Keywords: liquid reactive process, thermoplastic composite, synthesis kinetics, coupling modeling

Adaptation of liquid reactive process for composite thermoplastic manufacturing has been studied through the polyamide 6 case. Its polymerization from ε-caprolactam monomer involves simultaneously the crystallization of the growing chains over the temperature range. In order to understand and predict the behavior of the coupling between both phenomena, an experimental study has been carried out by performing isothermal syntheses in DSC. Different curves morphology has been obtained, depending of the level of coupling between polymerization and crystallization. The final degree of conversion, characterized by TGA, has been recorded between 92 and 97 wt.%, indicating a high reaction yield. The crystalline phase obtained has been characterized by DSC and WAXS. The samples showed a high crystallinity and from α-type. This database has been used as input into phenomena modeling. Polymerization was described by Malkin's model and crystallization by JMA's model. The Hillier's coupling has been adapted in the polymerization/crystallization case by adding a diffusion factor, allowing a better understanding of mechanisms. Thank to this work, isothermal TTT diagrams of the PA6 synthesis have been established.

INTRODUCTION

Fiber reinforced thermoplastic composites offer an interesting compromise between mechanical performances, chemical resistance and recyclability that make them serious challengers of thermoset composites. However, the high melting temperature and viscosity of thermoplastic matrices still restrict their growth mainly because of the expensive and time-consuming manufacturing processes like autoclave or hot press. Impregnation of reinforcing yarns is therefore necessarily a slow process although complex semi-finished products (commingled, powdered), or fast processes allow reducing the consolidation time of thermoplastic composites.

To overcome these limitations, reactive systems leading to a thermoplastic polymer represent a promising alternative for the fabrication of thermoplastic composites and allow the adaptation of liquid molding processes (RTM, infusion) [START_REF] Van Rijswijk | Thermoplastic composite wind turbine blades -Vacuum infusion technology for anionic polyamide-6 composites[END_REF][START_REF] Teuwen | Thermoplastic composite wind turbine blades -Kinetics and processability[END_REF]. The thermoplastic matrix is obtained by in situ polymerization of its low-viscosity monomer after impregnation of the fibrous structure.

This study focuses on the semi-crystalline polyamide 6 (PA6) obtained by anionic ring-opening polymerization of ε-caprolactam monomer by means of an activator and a catalyst. The PA6 synthesis is particular in that both chain polymerization and polymer crystallization occur. This is due to the possible synthesis temperature range that coincides with the crystallization temperature of PA6. The consequence of these simultaneous mechanisms is a strong coupling between both phenomena: crystallization kinetics depends on the increasing amount of available polymer chains during polymerization.

Control of the synthesis kinetic is mandatory because the both phenomena induce an increase of the reactive mixture viscosity. A higher processing temperature moderates the crystallization, but it accelerates the polymerization and may limit the infusion time. Moreover, the polymerizationcrystallization coupling may affects the porosity of composites and the fiber-matrix adhesion. Its understanding and modeling is critical for predicting the reaction evolution whatever the thermal cycle applied in order to optimize the process.

The characterization of PA6 synthesis has been mainly performed at a bulk scale thanks to an adiabatic reactor [START_REF] Teuwen | Thermoplastic composite wind turbine blades -Kinetics and processability[END_REF][START_REF] Davé | Polyamides from lactams via anionic ringopening polymerization: 2, kinetics[END_REF]. This is an inverse approach that consists in monitoring the temperature of the reactive mixture at the core of an insulated reactor during polymerization and crystallization. The main advantage of this approach is that several hundred grams of polymer are synthesized which ensures reactive mixture homogeneity. However, as both phenomena are exothermic, the separation of their contribution to the temperature increase is hardly possible without the use of complex kinetic modeling. Another drawback of this method is that it does not allow for isothermal synthesis, the thermodependence of phenomena is thus difficult to characterize.

On the other hand, the Differential Scanning Calorimetry (DSC) is an interesting method to follow the in situ synthesis at a smaller scale. First studies have mainly been focused on the influence of the nature and concentration of catalysts on reaction kinetics [START_REF] Bolgov | Role of the functionality of activators during isothermal crystallization accompanying the activated anionic polymerization of e-caprolactam[END_REF][START_REF] Wilfong | Separation of polymerization and crystallization processes for nylon-6[END_REF]. Syntheses were performed under a few representative conditions in order to highlight the coupling or separation of polymerization and crystallization. But this is only recently by Khodabakhshi et al. [START_REF] Khodabakhshi | Anionic Polymerisation of caprolactam: an approach to optimising the polymerisation conditions to be used in a jetting process[END_REF] that PA6 reactive mixtures have been investigated by DSC over a wide range of isothermal and non-isothermal conditions. However, they focused on mixtures designed for 3D inkjet printing involving a very high concentration of catalysts for a rapid reaction. The literature then lacks kinetic data on reactive mixtures dedicated to composite manufacturing.

From the modeling point of view, first mechanistic models of the PA6 synthesis have been developed in the 60's [START_REF] Reimschuessel | Ring-Opening Polymerization, chapter 7[END_REF] and considered each step of the reaction (initiation, propagation, side-reactions like catalyst degradation, ramification, etc.) . They have been progressively replaced by semi-empirical global models which consider the reaction as a whole. The works of Malkin et al. [START_REF] Ya | General treatment of polymer crystallization kinetics -part 2, The kinetics of nonisothermal crystallization[END_REF] are the first to describe anionic PA6 polymerization, its associated crystallization and their coupling. The modified version of Camargo et al. [START_REF] Camargo | Bulk polymerization kinetics by the adiabatic reactor method[END_REF] remains the key reference to this day. It has been reused by many authors [START_REF] Teuwen | Thermoplastic composite wind turbine blades -Kinetics and processability[END_REF][START_REF] Davé | Polyamides from lactams via anionic ringopening polymerization: 2, kinetics[END_REF][START_REF] Kim | Mechanism and kinetics of adiabatic anionic polymerization of e-caprolactam in the presence of various activators[END_REF][START_REF] Lin | A kinetic study of the activated anionic polymerization of ε-caprolactam[END_REF][START_REF] Lee | Reaction-induced crystallization kinetics during the anionic polymerization of ε-caprolactam[END_REF] although several enhancements have been proposed in the literature: modification of the polymerization model by Lin et al. [START_REF] Lin | A kinetic study of the activated anionic polymerization of ε-caprolactam[END_REF], use of the Kamal-Sourour model by Teuwen [START_REF] Teuwen | Thermoplastic composite wind turbine blades -Kinetics and processability[END_REF] and Russo et al. [START_REF] Russo | Fast-activated anionic polymerization of εcaprolactam in the bulk under quasi-adiabatic conditions: Comparison of different kinetic models[END_REF] and modification of the crystallization model [START_REF] Kim | Mechanism and kinetics of adiabatic anionic polymerization of e-caprolactam in the presence of various activators[END_REF][START_REF] Lee | Reaction-induced crystallization kinetics during the anionic polymerization of ε-caprolactam[END_REF].

This study investigates and proposes a modeling of the coupled polymerization-crystallization of PA6 from ε-caprolactam under isothermal conditions based on a complete DSC campaign. The reactive mixture selected presents a polymerization kinetic that suits with liquid molding process. The final monomer conversion has been determined by TGA [START_REF] Zhang | Anionic polymerization of lactams: A comparative study on various methods of measuring the conversion of ε-caprolactam to polyamide 6[END_REF] based on evaporation of residual monomer after polymerization. DSC and WAXS have been used to characterize the degree of crystallinity and microstructure of synthesized semi-crystalline PA6. An original coupled model of polymerization and crystallization is presented and TTT diagrams are edited.

EXPERIMENTAL STUDY OF THE SYNTHESIS

Materials

All reactants have been kindly supplied by Brüggemann Chemical, Germany. The products used for the anionic ring opening polymerization of PA6 are the ε-caprolactam monomer "AP-NYLON®" (moisture content of < 150 ppm), caprolactam magnesium bromide as catalyst (MgBrCL -"Nyrim C1®" 1.4 mol.kg-1 in caprolactam) and difunctional hexamethylene-1,6-dicarbamoylcaprolactam as activator (HDCL -"Brüggolen C20P®" 2.0 mol.kg-1 in caprolactam). Since the reaction is sensitive to moisture [35], products were dried overnight at 35°C under vacuum prior to mixture preparation and all subsequent handling was performed in an inert atmosphere to prevent any moisture uptake.

The reactive mixture was prepared by molten reactants under stirring. The ratio MgBrCL/HDCL used was 0.79/1.10 mol.% of CL. Once homogeneous, batch was quenched in liquid nitrogen to prevent early reaction. The product was then stored in a sealed pot at -18°C before sampling.

Isothermal synthesis in DSC

Isothermal PA6 syntheses were performed with few milligrams of reactive mixture in a powercompensated DSC. Samples were heated at 300°C/min to different isothermal temperature Tiso between 130 and 200°C (every 10°C) and kept until the full conversion. Figure 1 shows one representative DSC curve of each condition. The morphology of DSC curves changes over the investigated temperature range. Syntheses at 200°C lead to one sharp exothermic peak, while at 180°C and 190°C two distinct peaks are obtained. Between 150 and 170°C, syntheses are characterized by one dissymmetric peak with a shoulder; and at 130°C and 140°C the DSC scans exhibit a double exothermic peak with a first maximum at the early stage of the reaction.

These exothermic peaks correspond to the polymerization and crystallization of PA6. The polymerization is necessary the first mechanism since the monomer cannot crystallize at those temperatures. On the curves at 180 and 190°C, the first maximum is due to polymerization and the second to crystallization. Separation of phenomena is a consequence of the slow crystallization kinetic at high temperature due to the low undercooling. In order to understand the synthesis process, the samples were cooled from Tiso to 0°C at -10°C/min at the end of isotherm and then heated at 10°C/min until 270°C. Representative DSC scans of the cooling phase are shown in Figure 2a for three different Tiso and Figure 2b shows a representative melting curve of PA6 after polymerization at 150°C. This later exhibits a sharp melting peak at around 220°C and is typical of all synthesis temperatures. Even if all polymers melt during this last heating scan, the exothermic peaks on curves in Figure 2a indicate that the crystalline structure was not systematically formed during the isothermal stage. In particular for a Tiso of 200°C, the sharp crystallization peak and the distinct baseline above the peak reveal that PA6 crystallization only occurs during the cooling step. The single exothermic peak observed during syntheses at 200°C then only corresponds to the polymerization (Figure 1a).

After the isotherm at 190°C, a smaller crystallization peak starts right at the beginning of the cooling phase (Figure 2a). Since two distinct peaks appear during the synthesis among which one is due to isothermal crystallization, the crystallization during cooling is thus partial and completes the crystalline structure previously formed.

For lower temperatures, i.e. between 130 and 180°C, no exothermic peak is observed during cooling, meaning that the crystallization is achieved during the isothermal stage. The single dissymmetric peak obtained between 130 and 170°C results of the simultaneous crystallization. Since the polymerization occurred at a low temperature, the high degree of undercooling involves a near-instantaneous crystallization of the growing chains. The polymerization kinetic slows down and determines the crystallization kinetic.

Total enthalpies ΔHtot of isothermal syntheses are summarized in Table 1. They include polymerization and crystallization contributions even when two distinct peaks were observed. The lowest enthalpy is obtained during synthesis at Tiso 200°C since only the polymerization occurs. This value is in good agreement with the enthalpy of polymerization reported in literature that is comprised between 130 and 147J/g depending on the reference used [START_REF] Bolgov | Role of the functionality of activators during isothermal crystallization accompanying the activated anionic polymerization of e-caprolactam[END_REF][START_REF] Wichterle | Alkalische polymerisation des 6-caprolactams xii. Ãoeber die polymerisation von 6-caprolactam und die kristallisation des gebildeten polymeren unter adiabatischen bedingungen[END_REF][START_REF] Bukac | Alkaline polymerization of 6caprolactam[END_REF] For the lowest temperatures, crystallization gives rise to a significant increase of ΔHtot, with a maximum at 150°C. However, it must be noticed that some variability is obtained at low temperature. It is thus considered that the reaction globally leads to a high enthalpy at any condition below Tiso 150°C.

Characterization of the synthesized PA6

In order to characterize the synthesized polymer, the final degree of conversion Xp∞ was measured by TGA by evaporating the residual amount of ε-caprolactam contained in samples. Results in table 1 show a degree of conversion between 92 and 97 wt.%, which means that the polymerization is almost complete regardless of the condition applied.

Degree of crystallinity are characterized by the melting enthalpy ΔHm obtained in DSC during the heating ramp at 10°C/min. For the sake of comparison, ΔHm in Table 1 are only given for samples which crystallization was fully achieved during the polymerization stage, i.e. from 130 to 180°C. The values obtained show that a low synthesis temperature favors the crystallization while above 160°C, the low degree of undercooling limits progressively the ability of PA6 to crystallize.

Samples were also analyzed by X-Ray Diffraction (WAXS) in order to characterize the crystalline structure formed during the synthesis. Two main peaks are distinguished at 2θ = 20° and 2θ = 24° correspond respectively to the diffraction planes (200) and (002)-(202) of the thermodynamically stable α-type crystalline structure [START_REF] Illers | Polymorphie, kristallinitat und schmelzwarme von poly(ε-caprolactam)[END_REF]. This phase is generally connected with the formation of high-order superstructures, like spherulites, and ensures high mechanical properties.

Study of the crystallization from the molten state of the synthesized PA6

In order to compare the crystallization process during synthesis to the one from the molten state, the isothermal crystallization kinetic of a sample synthesized at Tiso 150°C was characterized by DSC from the molten state. The sample was heated above the thermodynamic equilibrium temperature of the PA6 crystal, i.e. Tm O = 260°C, and cooled at -150°C/min to different isothermal temperatures between 180 and 190°C (every 2°C). The isothermal step was maintained until the complete crystallization, then the sample was cooled rapidly to 0°C. A heating ramp to 270°C at 10°C/min was performed to characterize the melting of the crystals formed. Figure 3a shows the crystallization obtained for each temperature.

It appears that the crystallization slows down when the temperature increases, which is in agreement with the influence of the degree of undercooling. The dissymmetry of the peaks also reflects a kinetic slowdown at the end of crystallization which suggests the existence of a secondary crystallization.

Figure 3b shows the superposition of the crystallization curve at 180°C from the molten state with the second peak of the synthesis curve at the same temperature (corresponding to the crystallization). It is found that when the crystallization occurs separately from the polymerization, its kinetics corresponds to the one obtained from the molten state. The same observation was made for the synthesis at 190°C, which suggests that the crystallization process is similar during synthesis and from the molten state. Modeling the exothermic reaction of synthesis amounts to modeling the overall reaction kinetic γ, which includes polymerization α and crystallization β. This normalized global kinetic is determined experimentally from the heat flux determined by DSC according to equation 1.

𝛾(𝑡) = 𝑞(𝑡) 𝑄 𝑡𝑜𝑡 = ∫ 𝑑 𝑑𝑡 𝐻(𝑡)𝑑𝑡 𝑡 0 ∫ 𝑑 𝑑𝑡 𝐻(𝑡)𝑑𝑡 ∞ 0
(1)

Decoupled polymerization kinetics

Polymerization kinetic is modeling with the Malkin's model, modified by Camargo et al. [START_REF] Camargo | Bulk polymerization kinetics by the adiabatic reactor method[END_REF] (Equation 2). It has four parameters: A0 [s -1 ], which is a constant representative of the number of collisions between molecules, B0 [-] an autocatalytic factor, np [-] the order of reaction and Ea [J.g -1 ] the activation energy of the reaction

𝑑𝛼 𝑑𝑡 = 𝐴 0 (1 -𝛼) 𝑛 𝑝 (1 + 𝐵 0 𝛼)𝑒𝑥𝑝 (- 𝐸 𝑎 𝑅𝑇 ) (2)

Decoupled crystallization kinetic

The experimental study of PA6 shows that crystallization processes during synthesis and occurring from the melting state are similar. Models specifically developed for PA6 synthesis by Malkin et al. [START_REF] Ya | General treatment of polymer crystallization kinetics -part 2, The kinetics of nonisothermal crystallization[END_REF][START_REF] Ya | General treatment of polymer crystallization kinetics -part 1, A new macrokinetic equation and its experimental verification[END_REF] have been abandoned in favor of conventional models describing the crystallization from the molten state of thermoplastic polymer. Among the different models of the literature, the Johnson-Mehl-Avrami model (JMA), based on the generalized form of Avrami, was chosen because it allows to simply model isothermal and non-isothermal kinetics thanks to single model (Eq. 3).

𝑑𝛽 𝑑𝑡 (𝑡 -𝑡 𝑐,0 ) = 𝑛 𝐾(𝑇)(1 -𝛽)𝑙𝑛 ( 1 1 -𝛽 ) 𝑛-1 𝑛 (3)
Where K [s -1 ] is a kinetic constant thermo-dependent which is described with a Hoffman-Lauritzen relation type [START_REF] Hoffman | Crystallization of bulk polymers with chain folding: theory of growth of lamellar spherulites[END_REF], n [-] the Avrami constant representing the type of nucleation/growth and tc,0 [s] initiation time of crystallization. Crystallization kinetic calculated with the JMA model is compared with experimental results on figure 4. The JMA model fits correctly experimental curves, except at the end of crystallization where a secondary crystallization appears.

Coupling model

In the literature, the only coupling used for the synthesis of reactive PA6 is the one proposed by Bolgov [START_REF] Bolgov | Role of the functionality of activators during isothermal crystallization accompanying the activated anionic polymerization of e-caprolactam[END_REF], which describes the overall heat flux q in two terms attributed to the two phenomena polymerization α and crystallization β (Eq. 4).

𝑑𝑞 𝑑𝑡 = 𝑄 𝑝 𝑑𝛼 𝑑𝑡 + 𝑄 𝑐 𝑑𝛽 𝑑𝑡 𝛼(𝑡) (4)
Qp and Qc [J.g -1 ] correspond respectively to total polymerization enthalpy and crystallization enthalpy, which are dependent of polymerization kinetic and crystallization kinetic. This coupling reflects the fact that at each new increment of polymerization, the formed phase is involved in the crystallization progress. However the use of the JMA crystallization model with the Bolgov coupling does not allow to correctly model the synthetic kinetics, in particular the shoulders observed during the syntheses at Tiso < 170°C.

In order to improve the coupling between the polymerization and crystallization, the equation 5 was used. It is based on the form proposed by Hillier for taking into account the secondary crystallization process during the crystallization of thermoplastic polymers [START_REF] Hillier | Modified Avrami equation for the bulk crystallization kinetics of spherulitic polymers[END_REF]. This coupling assumes that the polymerized phase at each increment follows its own crystallization kinetic with its initiation time and its growth kinetic. The results obtained for the syntheses at 150°C and 190°C (figure 5) show that this form of coupling correctly predicts the crystallization kinetic when it is separated from the polymerization, like at 180°C and 190°C. However this formulation does not allow the prediction of shoulders related to crystallization observed at 150°C and 170°C. Indeed the instantaneous crystallization starts at the same time then the polymerization, which totally attenuates the occurrence of shoulders. At the beginning of the polymerization, the growing chains are too short to be able to fold up on themselves. The crystallization takes place between chains, which must first diffuse in a medium composed mainly of monomer. To take this phenomenon into account, a diffusion factor was introduced into the coupling in a manner similar to the formulation used in the thermosetting crosslinking models [START_REF] Fournier | Changes in molecular dynamics during bulk polymerization of an epoxide-amine system as studied by dielectric relaxation spectroscopy[END_REF], which transcribes the diffusion of the monomer within a densely reticulated network (Eq. 6):

𝑓 𝑑 (𝛼) = 1 - 1 1 + 𝑒𝑥𝑝 (𝐶(𝑇)(𝛼 -1) + 𝐷(𝑇)) (6)
Injected in equation 5, this coupling becomes equation 7:

𝑄 𝑡𝑜𝑡 𝛾(𝑡) = 𝑄 𝑝 𝛼(𝑡) -𝑄 𝑐 𝑓 𝑑 (𝛼, 𝑇) ∫ 𝛼(𝜃) 𝑑 𝑑𝜃 𝛽(𝑡 -𝜃 -𝑡 𝑐,0 )𝑑𝜃, 𝑖𝑓 (𝑡 -𝜃 -𝑡 𝑐,0 ) > 0 0, 𝑖𝑓 (𝑡 -𝜃 -𝑡 𝑐,0 ) ≤ 0 𝑡 0 (7)
The superposition of the kinetics predicted by the model at 150°C with the experimental results in figure 6 demonstrates the advantage of this diffusion factor: a crystallization peak is superimposed on the wider polymerization peak, thereby generating shoulder observed on the experimental curve.

TTT diagram

Thanks to the complete modeling of the isothermal synthesis of reactive PA6, the isothermal TTT diagram was edited (figure 7) in isoconversion of the degree of conversion Xp and of crystallization Xc (with ΔHc100%=230 J/g). The very strong coupling existing for the lowest synthesis temperatures (130-150°C) between the two phenomena appears distinctly, since the crystallization is limited by the progress of the polymerization. The higher the temperature, the more the two phenomena separate (acceleration of polymerization, slowing of crystallization), until a limit temperature of 190°C is reached in crystallization beyond which the newly formed chains do not crystallize.

CONCLUSION

PA6 synthesis in the context of a reactive liquid molding for thermoplastic composites manufacturing has been studied experimentally and a synthesis kinetic model is proposed. DSC allows to carry out isothermal syntheses and to obtain a fine characterization of the kinetics of polymerization and crystallization as well as their temperature dependencies. The degree of conversion and the crystallinity obtained were characterized by ATG, DSC and WAXS. These analyzes revealed a high transformation efficiency, a very high crystallinity rate between 130 and 160°C and the formation of a main α-type crystal phase. In addition, a study of the kinetics of crystallization from the molten state has shown that the crystallization kinetic during synthesis was similar to the one occurring from the molten state.

A kinetic synthesis model is proposed in which the crystallization is based on a JMA model and on the Malkin polymerization model. A coupling based on the Hillier formulation and incorporating a thermo-dependent diffusion factor is proposed. This formulation is effective for predicting the various phenomena observable on the kinetic curves. The isothermal TTT diagram was published for the purpose of using PA6 for the reactive thermoplastic composite manufacturing.

PERSPECTIVES

An experimental study of the polymerization and crystallization of PA6 in a fibrous medium must be carried out to determine the influence of this confinement on the reaction kinetics. This influence will then be taken into account in our models.

These models of reactions will then be implemented in a multi-physics model of simulation, at the scale of process, of resin injection in a fibrous reinforcement [START_REF] Gantois | BEM-based models to simulate the resin flow at macroscale and microscale in LCM processes[END_REF]. These models take into account resin flows and heat transfers. The influence of these reactions, which will modify the viscosity of the polymer and the temperature of the system during the injection, is studied in reference cases that we have developed.

Figure 1 :

 1 Figure 1: DSC curves of isothermal syntheses of PA6

Figure 2 :

 2 Figure 2: DSC scans of the cooling step the cooling step (a), heating (b)

Figure 3 :

 3 Figure 3: DSC scans of crystallization from molten state (a) isothermal steps, (b) synthesis superposition at 180°C

Figure 4 :

 4 Figure 4: Crystallization modeling from molten state

  𝑄 𝑡𝑜𝑡 𝛾(𝑡) = 𝑄 𝑝 𝛼(𝑡) -𝑄 𝑐 ∫ 𝛼(𝜃) 𝑑 𝑑𝜃 𝛽(𝑡 -𝜃 -𝑡 𝑐,0 )𝑑𝜃, 𝑖𝑓 (𝑡 -𝜃 -𝑡 𝑐,0

Figure 5 :

 5 Figure 5: Modeling with equation 5 syntheses at (a) 150°C, (b) 190°C

Figure 6 :

 6 Figure 6: Modeling with equation 7 at 150°C

Figure 7 :

 7 Figure 7: TTT diagram (blue: degree of conversion Xp, green: degree of crystallization Xc)

Table 1 :

 1 Reaction enthalpies and degree of conversion obtained on isothermal synthesis

	Tiso	ΔHtot	ΔHm	Tm	Xp∞
	[°C]	[J/g]	[J/g]	[°C] [wt.%]
	130 196.3 ± 11.1 95.7 217.9	91.9
	140 205.6 ± 14.5 100.0 218.9	93.3
	150 219.8 ± 3.3 100.6 220.2	95.1
	160 211.9 ± 1.8	93.0 218.5	94.5
	170 198.4 ± 8.3	81.0 215.2	95.6
	180 194.7 ± 6.3	72.8 215.6	96.8
	190 142.3 ± 10.1	-	214.7	95.8
	200 121.7 ± 4.5	-	202.2	95.1

ACKNOWLEDGEMENTS

Brüggemann Chemical, Germany are acknowledged for kindly supplying reactants.