Eduard Muslimov
email: eduard.muslimov@lam.fr

Emmanuel Hugot

Xin Wang

David Valls Gabaud

Pascal Vola

Gérard R Lemaitre

The MESSIER path finder: a high performance, wide field, fast and distortion free telescope using a curved detector

come   L'archive ouverte pluridisciplinaire

Introduction

In the present work we study optical design for a MESSIER mission pathfinder. The scientific goals pursued by the mission require a survey of extended objects with very low surface brightness [1]. Such a goal requires a fast telescope to get the highest SNR in surface brightness, with the highest optical quality and smoothness for homogeneity of the PSF over the field of view, as well as a distortion as low as possible for scan-drift purposes. We propose to build a pathfinder telescope in order to demonstrate that the target performances are reached and also to test the technology readiness for a full-scale mission. Thus, on the one hand it is necessary to use novel design concepts and technologies to fulfill the challenging requirements, and on the other hand, the design can actually be manufactured within the next few years. We use the bi-folded reflective Schmidt scheme proposed in [START_REF] Hugot | A freeform-based, fast, wide-field, and distortionfree camera for ultralow surface brightness surveys[END_REF] as the baseline design with an entrance pupil diameter of 360 mm. The rest of the specifications are as follows: focal length 879 mm, field of view 1.6°x2.6°, working wavelengths 200-1000 nm, spatial resolution 12 µm in RMS, and distortion <0.5% in the scanning direction [START_REF] Hugot | A freeform-based, fast, wide-field, and distortionfree camera for ultralow surface brightness surveys[END_REF].

Optical design

The optical scheme represents a reflective Schmidt system with an additional folding mirror. Some mitigation in size and F-number are made for the pathfinder to get in-plane configuration with a relatively small angle of inclination of the primary mirror. Even then, for the chosen angle value of 11° it is impossible to use an axisymmetric profile of the aspherical mirror, and hence an anamorphic asphere should be used. The baseline design then implies the use of a curved detector [START_REF] Hugot | Flexible focal plane arrays for UVOIR wide field instrumentation[END_REF], though a field flattener option is considered as well. It should also be noted that the optical scheme has a central obscuration, though it is only about 9% of the area and affects minimally the performance of the telescope. Fig. 1a represents the general view of the optical system, which was preliminary investigated in [START_REF] Lemaitre | Reflective Schmidt Designs for Extended Object Detection in Space Astronomy -Active Optics Methods[END_REF]. Spot diagrams RMS radii change from 1.5 to 2.8 µm across the field of view. The spatial resolution calculated from the MTF (see Fig. 1b) is 105-193 lines/mm, i.e. 1.2-2.2" in angular units. The maximum distortion is approximately 0.04 % and in both X and Y directions.

Tolerances and manufacturability estimations

The proposed design consists in relatively simple elements. The secondary and tertiary mirrors have simple shapes (flat and spherical) and do not raise any concerns. The detector parameters are within technologically realizable boundaries: the linear field of view is 40.3 x 24.8 mm with a radius of curvature of 886 mm. The aspherical primary has a maximum sag of 34.7 µm and is described by 4 th order polynomials, so it can be manufactured by means of stress polishing [START_REF] Lemaître | Astronomical Optics and Elasticity Theory[END_REF]. The tolerancing was performed with the image quality criterion specified above. Assuming that the detector has an accurate 4-coordinate alignment, we obtained the following tolerance boundaries: the elements relative positions 0.1-0.2 mm, decenters 0.1-0.2 mm, tilts 1.8-12', surface irregularity 0.05-0.1µm i.e. λ/5-λ/10. If a lens field flattener is used these values remain almost unchanged, but the compensation parameters change increases several times.

Conclusions

An optical scheme of a wide-angle fast telescope prototype is developed to meet all the requirements for the optical quality, while the optical elements are as simple as possible. Thanks to the high nominal image quality and the use of a curved detector it becomes possible to guarantee a high performance with high tolerance and limited alignments, so that in principle this optical design can be manufactured without problems. The details of the primary mirror fabrication by stress polishing and optical testing issues will be considered elsewhere.


Luisa Arrabito
email: arrabito@in2p3.fr

Konrad Bernlöhr

Johan Bregeon

Gernot Maier

Philippe Langlois

David Parello

Guillaume Revy

Performance optimization of the air shower simulation program for the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA), currently under construction, is the next-generation instrument in the field of very high energy gammaray astronomy. The first data are expected by the end of 2018, while the scientific operations will start in 2022 for a duration of about 30 years. In order to characterize the instrument response to the Cherenkov light emitted when cosmic ray showers develop in the atmosphere, detailed Monte Carlo simulations will be regularly performed in parallel to CTA operation. The estimated CPU time associated to these simulations is very high, of the order of 200 millions HS06 hours per year. Reducing the CPU time devoted to simulations would allow either to reduce infrastructure cost or to better cover the large phase space. In this paper, we focus on the main computing step (70% of the whole CPU time) implemented in the CORSIKA program, and specifically on the module responsible for the propagation of Cherenkov photons in the atmosphere. We present our preliminary studies about different options of code optimization, with a particular focus on vectorization facilities (SIMD instructions). Our proposals take care, as automatically as possible, of the hardware portability constraints introduced by the grid computing environment that hosts these simulations. Performance evaluation in terms of running-time and accuracy is provided.

Introduction

The Cherenkov Telescope Array Observatory [START_REF] Actis | Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy[END_REF] aims at building and operating the world largest instrument to observe the very high energy gamma-ray sky. The instrument is being built as two arrays of telescopes (one per Earth hemisphere) exploiting the imaging Cherenkov technique to reconstruct the nature, direction and energy of cosmic-ray particles interacting in the atmosphere. High energy gamma-rays from the cosmos interact with the atoms of the atmosphere and convert into electron-positron pairs that then generate a large electromagnetic shower. Electrons and positrons, that go faster than light in the air, cause the emission of Cherenkov light (mostly optical blue light), which propagates through the atmosphere to the ground, where it is collected by CTA telescopes. Images of the showers, produced through the Cherenkov light cones, and acquired in the telescope camera are used to reconstruct the properties of the incident particle.

The instrument response functions (IRFs) are then used to go from a list of events to the estimation of the properties of gamma-ray sources. In this scheme, IRFs are produced through Monte Carlo simulations of the whole process: atmospheric air shower, production and propagation of the Cherenkov light, optical telescope response and camera image acquisition. Given the size of the CTA arrays (several km 2 ), the energy range (tens of GeV up to 300 TeV) and the very large parameter phase space, producing accurate IRFs requires large volume of simulations. These simulations are, as of today, mostly run on the EGI (European Grid Initiative) grid resources, that are gracefully made available to the CTA Consortium [START_REF] Arrabito | The Cherenkov Telescope Array production system for Monte Carlo simulations and analysis[END_REF]. Up to 10000 CPU cores can be available at a time, and more than 100 millions HS06 CPU hours have been consumed each year in the past 5 years. In this context, the optimization of the simulation software has multiple purposes: faster production, higher statistics, better coverage of the phase space and eventually cost reductions when CTA is in production phase. Given the large amount of CPU consumed every year for CTA simulations, even a modest improvement of the code performances would allow to save several millions of CPU hours. In this paper we present our first performance optimization of the air shower simulation software used in CTA, called CORSIKA, which is described in Section 2. In Section 3, we present the results of the program profiling and in Section 4 the work on the optimization.

Corsika, an air shower simulation program

CORSIKA [START_REF] Heck | CORSIKA: a Monte Carlo code to simulate extensive air showers[END_REF], for COsmic Ray SImulations for KAscade, is a program for detailed simulation of extensive air showers initiated by high energy cosmic ray particles. Originally developed at KIT (Karlsruhe Institute for Technology) in the early 90's for the KASCADE experiment, CORSIKA has been rapidly adapted by other experiments for their specific use case. Nowadays, it is the reference air shower simulation software for all cosmic-ray, gammaray and neutrino astronomy experiments (e.g. Auger, CTA, IceCube, etc.). For a given event, basically, the program tracks the initial particle until its first interaction in the atmosphere, then handles the development of the electromagnetic and hadronic cascades, particle energy losses, interaction processes and the production of the multiple secondary particles that are then propagated until they decay/interact or go below a given energy threshold, or reach the ground.

CORSIKA consists of a single main source code, written in Fortran 77, handling the description of the atmosphere, the stack of particles to propagate and the so-called particle transport. Physics interactions are handled in customized external packages. For the case of Cherenkov astronomy, an additional IACT/atmo package [START_REF] Bernlöhr | Simulation of imaging atmospheric Cherenkov telescopes with CORSIKA and sim_telarray[END_REF], written in C, implements the geometry of 3D arrays of Cherenkov telescopes, an improved description of the atmosphere (allowing the use of external atmospheric models) and the photon propagation through the atmosphere. In total CORSIKA consists of more than 10 5 lines of code. The description and response of the detectors are usually implemented in a separated software package.

The CTA use case

As explained in the introduction, in CTA we are interested in measuring the Cherenkov light produced within electromagnetic air showers. Two steps must then be considered: first the generation of Cherenkov photons, second the propagation of these photons to the ground.

The generation of Cherenkov photons is described by equation 1:

d 2 N dxdλ = 2παz 2 λ 2 1 - 1 β 2 n 2 (λ) (1)
where N is the number of photons per unit length of particle path and per unit of wavelength λ, ze the charge of the particle, α the fine structure constant, n the refraction index and βc the particle speed. While the energy loss of electrons and positrons is both small and smooth in the atmosphere, the production of Cherenkov light changes rapidly with the refraction index. This implies that to get a good description of the Cherenkov light production, small enough steps in the atmosphere are mandatory. At high energies air showers are composed of hundred of thousands of particles, and even more Cherenkov photons are produced at each step, each of which must be propagated to the ground. The propagation of light through the atmosphere is a very intensive computationally process, indeed for each photon the air refraction index profile must be computed and applied through an interpolation process of external atmospheric tables.

Cherenkov production is implemented in a dedicated subroutine (cerenk) of the COR-SIKA main program, while the photon propagation is handled in the raybnd function of the IACT/atmo package. Particle tracks are subdivided into several steps and for each step, the number of emitted Cherenkov photons is calculated from equation 1 within the cerenk subroutine. In order to reduce the computing time of photon propagation, all the computations are applied to bunches of typically 5 photons rather than to individual photons. Particle steps are further subdivided into sub-steps so that a single photon bunch is emitted at each sub-step. At each sub-step iteration the raybnd function is called to calculate the bending of the photon bunch due to the refraction in the atmosphere and its propagation toward the ground. Finally, the coordinates of the photon bunches intersecting the telescope geometry are recorded and saved in the CORSIKA output (telout function in IACT/atmo).

Corsika profiling

Before starting any optimization work on CORSIKA performances, we have performed a code profiling to identify which parts of the program are the most computationally intensive, using the Linux perf tool1 . The profiling was executed on a dedicated server (running Cen-tOS 7.4.1708 on a x86_64 Intel Xeon E5-2650 at 2.20 GHz) using a set of standard input parameters, as those used in the official CTA productions. The program execution duration is controlled by varying the number of generated showers. After having checked the stability of the profiling results for different run durations, we have set to 1000 the number of simulated showers, which for the chosen set of input parameters takes about 5 minutes.

Linux perf is an a event-based sampling tool. As sampling event, we have used the cycles event with a sampling frequency of 99 Hz. In order to easily visualize the profiling results, we have processed the sampled data with the Flame Graph tool2 . The obtained profile is shown in Fig. 1, where each box corresponds to a particular function or subroutine. The width of the boxes is proportional to the CPU spent in that function. The hierarchy of the function calls is also represented, each box having its parent function just below.

Analysing the graph in Fig. 1, we observe that 82% of the total CPU is consumed by the cerenk subroutine, of which about 50% is spent in the raybnd function, which we recall is responsible of the photon propagation through the atmosphere. These results confirm that photon propagation is one the most CPU intensive parts of CORSIKA. As explained in Section 2.1, raybnd is called once per photon bunch. Given that each shower produces on average hundreds of thousands of photon bunches (in the energy range relevant for CTA), in our reference run raybnd is called hundreds of millions times. Looking then at the CPU consumption within raybnd, we see that a large fraction (65%) is spent in mathematical functions (with the following sharing: 32% exp, 19% asin and 14% sincos), while another fraction (21%) is due to the atmospheric interpolation process, employing a binary search algorithm (rpol function). Finally, compatible results have also been obtained using different profiling tools, such as Callgrind3 and a gdb based profiler 4 [5].

Optimization strategy

Given the size and the complexity of CORSIKA, it seems difficult to achieve a significant optimization by means of optimization options provided by the compiler5 . Even if compiler has been greatly improved in the last decade, whole program optimization is still a difficult task. Inter procedural analysis (IPA) is often limited by pointer aliasing and compiler heuristics. Nevertheless, in order to get eventual hints for further manual optimization, we have performed extensive tests, measuring the execution times for many different combinations of compilation options. The results of these tests are presented in Section 4.1.

The next step consisted in applying some manual transformations, focusing on the hot parts of the program identified by the profiling. As presented in the previous section, about 40% of the overall CPU time is consumed for the photon propagation through the atmosphere. Since photon bunches propagate independently one from each other, the corresponding code might benefit from the application of vectorization techniques. The basic idea is to group photon bunches by 4 (or 8 according to the available instruction set on the target machine) into vectors and treat them all at once. In this context, we have also considered the use of highperformance (vectorized) mathematical libraries in specific parts of the program. Indeed, we have measured that 50% of the total CPU is consumed by calls to the libm. In Section 4.2, we present the first transformations that we have performed in this sense.

The vectorization approach is very promising, since it would bring a speed-up of about a factor 4 (or 8) for the concerned parts of the program, with relatively little code rewriting. Also, this approach is particularly interesting in the context of CTA, since vector instruction sets are widely available on the grid computing resources currently used for the CTA productions.

Finally, since Monte Carlo showers simulation is a massively parallel process, we did not consider the parallelization approach as beneficial in our case. However, the parallelization at the shower level may be interesting for experiments working at very high energies, for which the simulation of a single shower may take several days on a single core.

Automated optimization

In order to explore the compiler optimization capabilities, we have prepared a test framework to easily compile and execute CORSIKA by varying the optimization options. First of all, we have run a reference version of the program, compiled with gcc 4.8.1. Secondly, we have chosen a list of compiler optimization options, subdivided in the following four categories: 1) standard optimization: O1, O2, O3; 2) loop optimization: ftree-loop-if-convert, ftree-loop-distribution, ftree-loop-distribute-patterns, ftree-loop-im, ftree-vectorize, funrollloops, funroll-all-loops, floop-nest-optimize; 3) advanced instruction sets enabling: mavx, mavx2; 4) link-time optimization: flto. Then, we have compiled CORSIKA with all possible combinations of these options, obtaining in total more than 3000 program versions. Finally, each version was executed in exactly the same conditions, i.e. on the same host and with the same input parameters. The execution time has been measured with the Linux perf tool and compared to the reference version. Moreover, since CORSIKA is a stochastic simulation program, in order to ensure reproducible results, we have fixed the seed for the random number generators and checked that the output physics quantities (spatial coordinates and arrival time of the photon bunches) were identical to the reference version. The result of this test campaign is that we could achieve at most 1.03 of speed-up for some specific set of options [5]. Finally, we have also tried out the ffast-math flag, which optimizes the arithmetic expressions, without preserving however strict IEEE compliance. Even in this case, we did not observe any significant improvement (maximum speed-up of 1.06) [5]. Moreover, as expected, the numerical values of the output physics quantities were slightly different from the reference version, so that their validity should be carefully checked.

The whole test campaign took about 10 days of CPU, so that repeating the experience several times was not easily affordable. Nevertheless, by repeating our measurements several times for a few selected program versions, we have observed fluctuations of the order of a few percents. These results confirm that the optimization of a complex and large software, as CORSIKA, is beyond the compiler capabilities, while any eventual improvement necessarily go through manual transformations.

Manual optimization through vectorization

Before starting the actual vectorization work, we have identified simple transformations requiring little code rewriting and focusing only on the photon propagation module, which is one of the most costly parts of the program (cf. Section 3). In a first phase, we identified and removed a few redundant calls to functions performing the atmospheric tables interpolation. This first transformation improved performances by a factor 1.09 which is already higher than what was obtained through compiler optimizations (cf. Section 4.1). In addition, the transformed code exposes some vectorization possibilities for calls to the exp function, which is one of the most frequently called mathematical functions as shown by the profiling (cf. Section 3). Our second transformation thus consisted in applying a vectorized exp to a selected portion of the program, where 2 or 3 subsequent calls to exp could be easily grouped into vectors.

For this purpose, we have relied on external vectorized mathematical libraries. Among the various available, we have tested the SIMD vector libm [START_REF] Lauter | A new open-source SIMD vector libm fully implemented with high-level scalar[END_REF] and the CERN's VDT [START_REF] Piparo | Speeding up hep experiment software with a library of fast and autovectorisable mathematical functions[END_REF] library. The main advantage of these two libraries with respect to others (i.e. Intel's SVML6 , AMD's libm7 ), is that they are open source, fully written in high-level languages (C and C++) and hence portable across systems. Another library we may consider in future is the libmvec8 recently added to GNU glibc to support auto-vectorization in gcc. It is also open source, even if not portable on all architectures.

The speed-up achievable with the two tested libraries depends on the considered function. In the case of exp, the SIMD vector libm announces a speed-up of a factor 4, while VDT library reports an interesting 77 speed-up factor (for SIMD vectors of length 4). These differences may be explained by the fact that the SIMD vector libm certifies a certain level of accuracy, while there is no guarantee for VDT. Since performance and accuracy are intimately related, we plan to carry out a detailed study to determine the minimum required accuracy in air shower simulations. A similar study [START_REF] Piparo | Speeding up hep experiment software with a library of fast and autovectorisable mathematical functions[END_REF] has proven that typical High Energy Physics (HEP) applications do not require the high degree of accuracy of standard mathematical libraries which commonly provide correct rounding [8]. The performance result obtained after our second transformation is an overall speed-up of 1.16 for both the tested libraries. Regarding the accuracy, we did not observe any numerical difference on the output physics quantities with respect to the reference version.

Encouraged by these results, we have then extended the vectorization to other mathematical functions within the IACT/atmo module. This, however required a slightly larger code rewriting, such as the unrolling of the loop over the particle sub-steps (cf. Section 2.1) in the cerenk subroutine. This third transformation allowed us to apply mathematical vector libraries also to trigonometric functions (sin, cos and asin) mainly used for the refraction angle calculation and the photon trajectory projection. The obtained speed-up thus increased to a value of 1.20. More details about the three transformations just discussed can be found in [5].

Finally, in order to apply vector operations also to arithmetic expressions, we have tested different high-level libraries, which provide an abstraction of low level SIMD instructions. Among them we mention: bSIMD 9 , Vc [START_REF] Kretz | Extending C++ for Explicit Data-Parallel Programming via SIMD Vector Types[END_REF], UME (Unified Multicore Environment) [START_REF] Karpinski | An Embedded Domain Specific Language for General Purpose Vectorization[END_REF], xsimd 10 . In our preliminary non-exhaustive evaluation, we have considered the portability, the support of the most common vector types and operations for different instruction sets (SSE4, AVX, AVX2, AVX-512) as well as the support of vectorized mathematical functions. We found that bSIMD proposes a proprietary and a public version, however it is not clear which functionalities will be supported in the public version. Vc is an open source project widely used within the HEP community. It is the backend of the VecCore library 11 , but it does not support mathematical functions. UME is a similar project developed at CERN. It has the advantage over Vc to support AVX-512 instruction set, but with apparently lower overall performances [START_REF] Moneta | Vectorization of ROOT Mathematical Libraries[END_REF]. Finally, we did not test yet xsimd, an open source project, which seems to cover all the desired functionalities. Our future plan is to conduct a more detailed evaluation of all these products for their later application to CORSIKA.

Perspectives

In the optimization work presented in Section 4.2, we have restricted ourselves to the Cherenkov propagation module, where we have applied vectorized mathematical functions only to a few selected instructions. The next step will consist in extending the vectorization to a number of arithmetic expressions we have already identified both in the Cherenkov propagation and in the Cherenkov production modules. Moreover, the implementation of some conditional expressions is non optimal with respect to compiler branch prediction. However, since the Cherenkov production module is written in Fortran (cerenk subroutine), it is not possible to rely on one of the above mentioned high-level libraries for vectorization (cf. Section 4.2), so that we envisage to fully reimplement it as an external C++ module. A detailed study of the memory access patterns will most likely give us additional hints about further optimization opportunities. At a longer term, we plan to consider a complementary approach for optimization, which consists in reducing the format of certain variables (i.e. from double precision to single precision), still preserving the desired numerical accuracy of the output physics quantities. Indeed, format reduction can improve the overall performances of a program and has an even more direct impact on the vectorized portions. For this purpose, we will test one or more of the available tools for the identification of the candidate variables for reduction [START_REF] Rubio-Gonzalez | Precimonious: tuning assistant for floating-point precision[END_REF] [START_REF] Rubio-Gonzalez | Floating-point precision tuning using Blame analysis[END_REF].

Finally, another area of improvement concerns the algorithm used for the atmospheric tables interpolation applied in several places (cf. Section 2.1). Atmospheric tables contain the values of various physics quantities (air density, thickness, refraction index, etc.) at given altitudes. The goal of the interpolation procedure is to calculate the values of these quantities at intermediate altitudes (along the particle propagation path). Since the atmospheric profiles are almost exponential, a linear interpolation is performed between log values. The drawback of this simple approach is that it implies massive calls to exp to later retrieve the interpolated values. In order to dramatically reduce the number of calls to exp, we plan to evaluate ad-hoc interpolation schemes that replace linear interpolation of the log values.

Conclusions

In this work, we have demonstrated that vectorization techniques can be successfully employed in the CORSIKA air shower simulation program. Focusing on one of the most CPU consuming parts of the program, i.e. the Cherenkov propagation module, we have identified, applied and evaluated successive manual transformations summarized in Table 1. The highest speed-up (1.20) has been obtained by grouping photon bunches by 4 in the Cherenkov production module and applying vectorized mathematical functions in the photon propagation module. If we consider that a typical Monte Carlo campaign takes about 100 millions of CPU hours, a performance gain of 1.20 potentially allows a reduction of 17 millions CPU hours. Given the limited scope of the program transformations performed so far, we think that further optimizations should be achievable. In Section 5, we have presented several optimization options, mostly based on vectorization, precision reduction and optimization of the interpolation algorithm. Finally this work will serve as a basis for the application of vectorization techniques in the context of the recently started project of Next Generation Corsika [14].

Figure 1 .

 1 Figure 1. Corsika profile produced with Linux perf and the FlameGraph tool.

Table 1 .

 1 Speed-up obtained with automatic and manual transformations of CORSIKA. For each version of the program, the accuracy has been checked by comparing the output numerical values with those obtained with a CORSIKA reference version.

	Transformation	Speed-up Comments
	Automatic transformation with gcc 1.03	Using special optimization options
	Manual refactoring	1.09	Eliminating redundant calls to binary
			search in interpolation process
	First manual vectorization	1.14	Using vectorized exp
	Extended manual vectorization	1.20	Grouping photon bunches by 4 and using
			vectorized mathematical functions

https://perf.wiki.kernel.org/index.php/Main_Page

http://www.brendangregg.com/flamegraphs.html

http://valgrind.org/docs/manual/cl-manual.html

https://poormansprofiler.org/

https://gcc.gnu.org

https://software.intel.com/en-us/node/583201

http://developer.amd.com/tools-and-sdks/archive/libm/

https://sourceware.org/glibc/wiki/

https://developer.numscale.com/bsimd/documentation/v1.17.6.0/

https://github.com/QuantStack/xsimd

https://github.com/root-project/veccore

Acknowledgments

We gratefully acknowledge financial support from the agencies and organizations listed here: http://www.cta-observatory.org/consortium_acknowledgments.


Emeline Prandato

Michel Melas

Françoise Etienne Fleury

Françoise Méchin

Françoise Mechin
email: francoise.mechin@insa-lyon.fr

Structure-scratch properties relationships of acrylate photo-polymerizable protective coatings for thermoplastic substrates

Keywords: photo-polymerization, micro-scratch, bio-based monomers, nanoparticles, acrylates, polymer network

published or not. The documents may come

Structure-scratch properties relationships of acrylate photo-polymerizable protective coatings for thermoplastic substrates

Introduction

In a view to save weight and thus to lower polluting emissions, many automotive pieces are made of plastic. Headlights made of polycarbonate are a good example. An important drawback of this thermoplastic is however its low resistance to damage. And yet everyone knows that during its life, an automotive headlight is strongly subjected to scratches, impacts, abrasion… That is why the use of a protective coating is required. To go further into a sustainable development approach, such coatings can be photo-cured [1][2][3][4][5][6][7][8][9]. Indeed, photopolymerization is an environmentally-friendly technique, since it allows to work with mixtures containing no solvents, curing them at a very high rate, and it is an energetically economic process.

In the literature, many authors assess the efficiency of their coatings by hardness measurements [7][8][9][10][11], abrasion [1][2][3]7,10], indentation [8][9] or scratch tests [6,[10][11][12][13][14],

amongst other experiments evaluating the damage resistance [8][9]11]. However, all these techniques are closely related. For instance, numerous hardness measurements exist, which are all based upon the scratching or the indentation of the sample [15]. But Caro et al. [12] demonstrated that hardness is not directly linked to the abrasion resistance of ophthalmic coatings on organic lenses as evaluated by usual standardized tests. On the other hand these authors managed to correlate the results of microscratch testing, provided that they were carried out under well-defined conditions, to the abrasion resistance of their coatings.

More precisely, scratch hardness and residual depth proved to be especially relevant parameters to foresee the behavior of any ophthalmic coating submitted to abrasion.

The important characteristics which allow to evaluate the efficiency of a coating are indeed its resistance to indentation and its ability to recover its initial shape (elastic recovery). The load at which the first crack appears during the scratch is also a relevant parameter to assess the scratch resistance, since cracks constitute severe damaging that can worsen during the service life of the coating. It is easy to understand that a simple mechanical analysis cannot provide enough information to evaluate the damage resistance of coatings.

On the contrary, micro-or nano-scratch experiments, often used in the literature to assess the scratch resistance of coatings [6,[11][12][13][14], allow to evaluate all these characteristics when performed on well-defined samples, and thus provide a more comprehensive information about the resistance to damage. Thus, these tests are attractive to evaluate and compare protective coatings. Nano-scratch tests were used for example by Noh et al. [11] in order to determine the best curing sequence of UV-thermal dual-cure coatings; whereas Bautista et al. [13] used these tests to compare different nanocomposite coatings containing alumina or silica nano-fillers dispersed in various polymer matrices. These micro-or nano-scratch tests consist in applying a constant or increasing load on an indenter in contact with the surface of the sample while the latter moves. The indented depth is monitored in real time, whereas a pre-scan and post-scan allow to determine the initial relief and residual depth and to calculate the elastic recovery. An observation of the scratch, with an optical microscope for instance, allows to determine the critical load at which the first crack appears; this load is expected to be as high as possible. What is more, from an applicative point of view, the less visible the scratch is, the better. Of course, the scratch resistance of a material is related to its mechanical properties such as its modulus or its tensile behavior [16,[START_REF] Wong | Wiley, Properties and Behavior of Polymers[END_REF]. Nevertheless, because of the viscoelastic behavior of polymer materials, the scratch resistance also depends on the temperature, on the strain rate, and on the time elapsed between the test and the observation of the result. Even though these last two technical points can be controlled using the same protocol for each sample, the variation with temperature depends on the tested materials. Indeed, a material does not behave in the same way when it is in the glassy or in the rubbery state.

UV-curable coatings are mainly composed of multifunctional compounds, whose polymerization leads to the formation of a polymer network. The chemical structure between the crosslinks and their density play an important part in the properties of the resulting material. In particular, a lower crosslinking density is often associated with a lower elastic modulus at the rubbery plateau. Nevertheless, the damage resistance of UV-curable, 100% solids organic coatings is often not sufficient and many studies in the literature report the incorporation of nanoparticles in the systems. Nano-silica and nano-alumina are commonly used to improve the scratch or abrasion resistance of coatings [1,[3][4][5][7][8][9][START_REF] Roscher | [END_REF], since they are high hardness materials (respectively 7 and 9 on the Mohs' scale).

From an environmental point of view, the use of petro-based acrylate monomers is not representative of a sustainable chemistry, because of the depletion of fossil resources. Some authors published works concerning the use of bio-based acrylate compounds in UV-curable coatings. Nevertheless, these compounds were mainly obtained from triglycerides [19][20][21][22][23] and thus feature long fatty chains. This characteristic does not seem to be compatible with a protective efficiency. Nevertheless, there exist some commercially available bio-based acrylate compounds which are small molecules similar to their petro-based counterparts.

Their evaluation as monomers for protective coatings could be of great interest.

The aim of this work was to study the influence of different raw materials on the scratch resistance of 100% solids polyacrylate photo-polymerizable coatings designed for thermoplastic substrates and more specifically polycarbonate. The formulation was varied in order to study its influence on the scratch resistance of the material, in relation with its thermomechanical properties.

First, the influence of a multicyclic monomer was studied, varying its percentage in the polymer matrix of the coating. Then, alumina and silica nanoparticles were incorporated in the coatings, to observe the efficiency of these fillers. Finally, in order to go further into a sustainable development approach, some petro-based monomers were substituted by commercially available bio-based equivalents and the consequences on the scratch behavior of the coatings were examined.

Materials and methods

Materials

U6A (proprietary hexafunctional aliphatic urethane acrylate, CN9010EU), MPDDA (3-methyl-1,5-pentanediol diacrylate, SR341), TPGDA (tripropylene glycol diacrylate, SR306) and TCDDA (tricyclodecane dimethanol diacrylate, SR833S) are petro-based oligomer and monomers provided by Arkema. DiPEPHA (mix of dipentaerythritol pentaacrylate and dipentaerythritol hexaacrylate, 15%BBC), PETA (pentaerythritol tetraacrylate, 10% BBC) and DDA (1,10-decanediol diacrylate, 60%BBC), are commercial partially bio-based acrylate oligomers and monomers also provided by Arkema. The structure of these compounds is detailed in Fig. 1. The percentage of bio-based carbon (%BBC) is calculated following Eq.

(1):

100 ) ( %             based petro based bio based bio C C C BBC ( 1
)
The used nanofillers were Nanocryl ® C145 (silica nanoparticles dispersed in TPGDA)

provided by Evonik Industries, and NanoArc ® AL-2260 (alumina nanoparticles dispersed in TPGDA) provided by Nanophase, respectively. According to the suppliers' data both types of nanoparticles, 20 nm in diameter, are surface modified.

Irgacure 184 (1-hydroxycyclohexyl phenyl ketone) and Lucirin TPO-L (ethyl-2,4,6trimethylbenzoylphenylphosphinate) were used as photo-initiators; both were provided by BASF.

3,4,5-trichloropyridine (purity 99%) was purchased from Aldrich. DMSO-d 6 (deuterated dimethylsulfoxide) and tetramethylsilane (TMS) were purchased from Euriso-Top.

Methods

Preparation of the coatings

The mixtures (compositions specified in Tables 1 to 3), were prepared with the help of a Rayneri mixer. The used nano-filled additives consist of nanoparticles dispersed in TPGDA.

Thus, the addition of nanofillers to the formulations also implies the incorporation of this new monomer into the polymer matrix. Therefore in order to rigorously study the influence of nanoparticles on the scratch resistance of the coatings, nano-filled coatings were compared to unfilled reference coatings having the same polymer matrix.

(320-290 nm): 3837 mJ.cm -2 , 1747 mW.cm -2 ; UVB (280-320 nm): 3997 mJ.cm -2 , 1822 mW.cm -2 ; UVC (250-260 nm): 683 mJ.cm -2 , 321 mW.cm -2 . 150 µm-thick films on glass panels were also prepared under the same conditions, in order to peel them off to get free standing films that could be analyzed through mechanical experiments.

U6A

Determination of the acrylate double bond density of the mixtures

As the used monomers might contain some impurities and as the chemical composition of oligomer U6A was not precisely known, it was first necessary to determine the acrylate double bond density (d ac ) for each monomer and oligomer. This was achieved by 1 H NMR, using 3,4,5-trichloropyridine as an internal standard [24]. In a NMR tube were placed a weighed mass of standard (m s ) of known molar mass (M s ) and purity (p), and a weighed mass of acrylate compound (m ac ). The spectra were acquired at 300K in DMSO-d 6 (+TMS), with a Bruker Avance III 400 US+ (400 Hz), 8 scans, a relaxation delay of 90 s and a sampling of 128.10 3 points. The integration of the signals related to the acrylate protons and to the protons of the standard (respectively I ac and I s ) allowed to calculate d ac (Eq. ( 3)):

) . . . 3 ( ) . . . 2 ( ac s s s ac ac m M I p m I d 
Then, the acrylate double bond density of each mixture was calculated using d ac and taking into account the weight percentage for each of its components.

Determination of the acrylate double bond conversion by Fourier Transform

Infra-Red spectroscopy (FTIR)

The acrylate double bond conversion of the cured samples was determined by FTIR [8,11], using an Attenuated Total Reflectance (ATR) device equipped with a diamond crystal. For this purpose, the area of the acrylate band at 810 cm -1 was preferentially used. To avoid any bias related to an incorrect contact between the sample and the crystal, this area was normalized using the carbonyl band at 1720 cm -1 (constant throughout polymerization) as a reference. The comparison of the ratio of these areas for both the cured and uncured samples allowed to calculate the conversion degree after polymerization (Eq. 2). In order not to damage the device with a possible polymerization during the analysis, the uncured mixture was used without photo-initiator, after checking that this slight change did not have any influence on the results.

                                     cm cm cured cm cm uncured A A Conversion (%) A A (2)
The analyses were carried out with a Nicolet TM iS10 spectrometer (ThermoScientific), equipped with a Smart iTR ATR unit. The spectra were acquired after 32 scans with a resolution of 4 cm -1 . If the conversion could be determined for each side of the free standing films, it could obviously only be determined on the side in contact with air during the polymerization of films deposited on PC.

Dynamic Mechanical Thermal Analysis (DMTA)

DMTA measurements were carried out with a TRITON apparatus, in tension mode, using the following experimental conditions: temperature ramp: 3°C/min from -90°C to 300°C, frequency: 1 Hz, deformation: 0.1%, spacing between clamps: 2.5 mm. 150 µm-thick free standing films were analyzed, and at least three consistent analyses were carried out for each sample.

In all the graphics presented in this paper, tanδ curves have been vertically shifted in order to make the comparison easier; the absolute values should therefore not be taken into account.

Micro-scratch tests

Micro-scratch tests were carried out at 23°C and 50% relative humidity, with a CSM Micro-Scratch Tester equipped with a diamond Rockwell indentor featuring a 120° angle and a 100 µm-radius sphere. First, a pre-scan with a constant load of 0.03 N allowed to determine the initial topography on the path of the indentor before scratching the sample. Then, the 4 mm-long scratch was implemented at a speed of 8 mm.min -1 , applying on the indentor a progressive increasing load from 0.03 N to 10 N; the rate of the load increase was constant.

During the scratch test, the indented depth (P d ) was followed in real-time. Finally, a post-scan was run in the same conditions as the pre-scan, which allowed to measure the residual depth (R d ) of the scratch. The elastic recovery (R e ) that expresses the ability of the material to recover its initial shape could be calculated following Eq. 3.

100 ) (          d d d e P R P R (3)
After the test, the observation of the scratch with an optical microscope allowed to determine the critical load (L c ), i.e. the load at which the first crack appears. At least 5 micro-scratch tests were carried out for each sample. As the results (P d , R d , R e and L c ) could not be statistically studied for each load between 0.03 and 10 N, we chose to focus on particular normal loads: for 15 µm-thick coatings: 0.3 N and 1.5 N; for 150 µm-thick coatings: 1.5 N, 3.5 N and 9 N. The errors are given for a probability of 95%.

Transmission electron microscopy (TEM)

Transmission electron microscopy observations were carried out at the ''Centre Technologique des Microstructures de l'Université Claude Bernard Lyon1" on a Philips CM120 microscope operating at 80 kV. The samples were cut up in their thickness into thin slices (50-60 nm) by ultra-microtomy performed at room temperature.

Results and Discussion

The photo-polymerization of the liquid mixtures (compositions given in Tables 1 to 3) led to clear, tack-free coatings. In every case, the mean acrylate conversion was about 95%, i.e. a rather high value. Considering the structure of the monomers and oligomers, it can be inferred that all the polymer networks have a high crosslinking density. Note that the real acrylate conversion of the coatings containing nano-silica could not be precisely determined because of a partial overlapping of the acrylate band at 810 cm -1 and the SiO 2 band at 820 cm -1 . Nevertheless, taking into account the high value of the received UV dose, this sample was considered to have a conversion degree similar to the others.

As can been noticed Fig. 2, which illustrates in particular the case of the coating A3, the damage of polycarbonate is higher without coating, since the indented and residual depths are more important than for the coated PC. Nevertheless, the latter features cracks contrary to the uncoated substrate. This evidences the fact that if a coating is indeed necessary, there are also drawbacks.

Influence of the amount of a multicyclic monomer

The amount of monomer TCDDA was varied while maintaining the weight ratio between U6A and MPDDA constant; this percentage was increased from A1 to A7 respectively from 0 mol% to 100 mol%. The composition of all the studied coatings is summarized in Table 1.

Considering the polymer network, the increase in the TCDDA proportion gets along with a decrease in the proportion of oligomer U6A and in the overall density of acrylate double bonds in the mixture, determined by NMR (Fig. 3). But since all the components are multifunctional, a higher density of acrylate double bonds increases the crosslinking density; the presence of increasing amounts of the oligomer as well, because of its high functionality.

Since all the studied materials feature a similar conversion degree (95%), it comes out that the increase in the TCDDA proportion causes a decrease in the crosslinking density. From a thermomechanical point of view, all the samples feature a high elastic modulus E', higher than 10 8 Pa at the rubbery plateau (see Fig. 4). More precisely, sample A1 (the most highly crosslinked) indeed displays the highest value (E' ≈ 6.9. Figure 5 shows that the maximum of the mechanical relaxation regularly shifts toward higher temperatures as the TCDDA percentage increases, due to the multicyclic structure of this monomer. The observed values go from 143°C (A1) to 218°C (A7), in agreement with the values found by Ye et al. for a TCDDA sample cured isothermally at 100°C (189°C for 85% conversion, at least 205°C estimated for 100 % conversion) [25]. Indeed, in order for such a rigid structure to move, it is necessary to provide it with a high amount of energy. Thus, the higher its proportion, the higher the temperature at which the mechanical relaxation occurs.

However, it can be noticed that all the samples, even that without TCDDA (A1), are in the glassy state and have a rather similar elastic modulus at 23°C, temperature at which the micro-scratch experiments were carried out. The results of the micro-scratch experiments are summarized in Figure 6. The percentage of TCDDA does not influence the initially indented depth. In contrast, the elastic recovery decreases as this percentage of TCDDA increases. Consequently, the residual depth increases along with the latter. Finally an increase in the critical load with the proportion of TCDDA is also observed. Following the literature [12,16], this critical load is related to the ductile-brittle transition of the material. Indeed, Jardret et al. [16] suggested the following mechanism for the formation of the partial cone cracks such as those observed in this work (see Fig. 2): as the scratch is performed, tensile stresses are created at the rear of the indenter. These stresses increase until they reach the ultimate tensile strength; then a crack is formed. The tensile stresses are partially released but as the indenter keeps on ploughing the sample, they increase again, until reaching the ultimate tensile strength once more. A new crack is formed, etc… Consequently, the results of the micro-scratch tests suggest that the ductile-brittle transition is delayed when increasing the amount of diacrylate monomer TCDDA in the polymer matrix.

At the same time, the evolutions of the elastic recovery and of the critical load are opposite.

Yet both characteristics are equally important concerning the protective efficiency of the coatings, since a high elastic recovery decreases the visibility of the scratch, while the cracks are expected to appear at the highest possible load. Thus, a compromise must be found, and A3 could be suggested as a suitable coating.

The evolution of the elastic recovery, the residual depth and the critical load with the variation of the percentage of TCDDA is particularly remarkable for the extreme coatings A1 and A7 containing respectively 0 and 100 mol% of this monomer in their acrylate mixture. The evolution of these parameters between A2 and A6 is slightly less noticeable, but is nevertheless emphasized as the normal load increases. As stated before, as the TCDDA proportion increases, the network becomes less densely crosslinked. Moreover at the temperature at which the experiments were carried out, all the materials were in the same thermomechanical state. Thus, two points are underlined: first, the evolution of the scratch resistance with the percentage of TCDDA should be related to the evolution of the crosslinking density, but an influence of the specific rigid structure of this monomer must not be excluded. Secondly, the micro-scratch experiments allow a better differentiation of the samples comparing to DMTA.

Influence of nanoparticles

As the introduction of the fillers gets along with the introduction of a new monomer in the mixture, in order to rigorously study the effect of the nanoparticles, the filled coatings must be compared to references having the same polymer matrix. Thus, C1 will be compared to C1ref and C2 will be compared to C2ref (see Table 2). Here the studied coatings contained 5wt% nano-alumina or nano-silica (respectively C1 and C2); this percentage is given considering the mixture without photo-initiators. C1 and C1ref contain 12.6 wt% TPGDA in their polymer matrix, whereas C2 and C2ref contain 6.1 wt% TPGDA. The respective mass ratio between the other acrylate compounds (U6A, TCDA and MPDDA) is the same as in A3.

The filled coatings were compared with their respective reference, but also these references with A3, in order to observe the effect of the addition of TPGDA to the polymer matrix.

Before studying the properties of the coatings, the nanoparticles were first observed by TEM.

The nano-alumina particles are more or less agglomerated, and have a broad size distribution, with diameters from 10 nm to 100 nm. The nano-silica particles are rather agglomerated and have a mean particle size of 25 nm. It appears in Figure 7 that both types of nanoparticles display a special organization within the thickness of the polymer matrix, which can be divided into four main zones: i) an enrichment in particles in a thin layer (1-2 It can be assumed that during the processing of the coating, the nanoparticles migrate because of surface energy differences. The particle enrichment at the surface could also be related to the inhibition due to O 2 . Indeed, this phenomenon can cause the existence of a conversion gradient within the thickness, with a lower polymerization kinetics at the surface of the coating [26,27]. In this layer, the viscosity increases more slowly than in the bulk and the nanoparticles could have consequently more time to migrate toward the surface. The existence of the depletion zones is more intricate to explain, since many factors can act in addition to the oxygen inhibition; for instance, differences in polymerization kinetics within the thickness of the sample. Note that despite these observations, and consistently with the rather low amounts of incorporated nanoparticles, the coatings are perfectly clear. No change related to the presence of TPGDA in the polymer matrix can be noticed on the mechanical relaxation or on the elastic modulus (coatings C1ref and C2ref, Fig. 8). The small amount of flexible oxypropylene units incorporated in the polymer network through the addition of TPGDA is not sufficient to noticeably change the thermomechanical properties of the material.

PC PC air air

As seen in Figure 8, the incorporation of 5wt% nano-silica or nano-alumina in the coatings does not modify the mechanical relaxation or the elastic modulus of the materials. The relaxation remains broad whereas E' is always higher than 10 8 Pa at the rubbery plateau.

The presence of nanoparticles could have been expected to increase the elastic modulus.

Nevertheless, the unfilled materials already have a high modulus, thus maybe the small amount of particles cannot increase it anymore. In addition, these particles must have an influence on the relaxation times of the polymer chains, since they modify their environment.

As there is no noticeable change in the mechanical relaxation after the incorporation of nanoparticles, it is likely that some relaxation times are modified but still remain in the existing range. Thus, DMTA does not allow to distinguish differences between the mechanical properties of the different studied materials, filled or unfilled, containing TPGDA or not. As shown in Figure 9a to c, the indented depth does not change because of the addition of TPGDA in the polymer matrix, or because of the addition of nanoparticles. Having a closer look at the indented depth at the very surface of the samples (Fig. 10), no difference can be noticed between the unfilled and the filled coatings, despite the enrichment in nanoparticles in this particular zone for the filled samples.

Taking into account the statistical error, there is also no remarkable evolution of the elastic recovery or of the residual depth. The changes in the polymer network induced by the incorporation of TPGDA only have an influence on the critical load. Indeed, as can be seen in Figure 9d, all the coatings containing TPGDA feature a higher critical load (>2.5 N) than the

A3 C1 C1ref C2 C2ref 0,06 -0,02 0,02 0,06 0,10 0,14 0,18 Tan (δ)
coating A3 (<2.5 N). In the same way as for previous results (3.1.), this suggests that the presence of TPGDA delays the ductile-brittle transition. The incorporation of TPGDA in the polymer matrix is thus beneficial, since the later the first crack appears in terms of load, the better. Comparing these results with those concerning the variation of the TCDDA proportion (3.1.), it seems that increasing the weight percentage of diacrylate monomers (whatever their structure, soft or hard) in the polymer matrix leads to an increase in the critical load. This may be related to the decrease in the crosslinking density, which delays the ductile-brittle transition.

The only noticeable effect of nanoparticles is the increase in the critical load for a filler content of 5% nano-alumina. Following the explanations from Caro et al. [12], this may be related to a better adhesion between the nanoparticles and the matrix, and/or to a lower stress concentration around the fillers. Excepting this point, nanoparticles do not enhance the scratch properties of the coating; this could be due to the already good performances of the unfilled coatings.

As a more global conclusion, it can be put forward that the micro-scratch experiments bring additional information in comparison with DMTA, since coatings containing TPGDA feature a better scratch resistance in terms of critical load. 3). As seen in Figure 11, both bio-based coatings have the same thermomechanical properties. Their mechanical relaxation has a maximum at lower temperature than A3; this is attributed to the presence of DDA, featuring a long alkyl chain. The latter is supposed to favor long relaxation times and thus, according to the timetemperature equivalence, could shift the mechanical relaxation toward lower temperatures.

B1 and B2, but also A3, also feature a similar elastic modulus.

An overall observation is that at the temperature of the micro-scratch experiments (23°C), all these 3 samples are in the same thermomechanical state and have a similar elastic modulus. The intrinsic scratch resistance of the materials was first considered, studying 150 µm-thick coatings deposited on PC. As the layer thickness is important, the effect of the substrate could be neglected. What is more, even if the indented depth was higher than the tenth of the total thickness at high load [6], no change was noticed in the scratch behavior of the samples. For these thick samples, no crack was generated along the scratch.

Both bio-based coatings (B1 and B2) feature a similar scratch resistance (see Fig. 12). Their oligomers (respectively DiPEPHA and PETA) both have a structure based upon pentaerythritol (see Fig. 1); thus, the structure of the polymer networks in the coatings B1 and B2 is supposed to be rather similar. This could explain that the change of oligomer has no effect on the intrinsic scratch resistance of the studied bio-based materials.

Comparing B1, B2 and A3, it appears that the indented depth as well as the elastic recovery are higher for the bio-based coatings (see Fig. 12 a andc); as a result, the residual depth is lower (see Fig. 12 b). The coatings B1 and B2 thus feature a better intrinsic scratch resistance than the petro-based coating A3. From these results, it can be inferred that the indentation depth is not directly related to the elastic modulus of the materials. Indeed, even if A3, B1 and B2 feature a similar elastic modulus at the temperature of the micro-scratch tests, the indented depth is not similar for these three samples. The case of 15 µm-thick coatings was finally addressed. In Figure 13 a, a similar indented depth is observed for B1 and B2. The latter has a slightly higher elastic recovery (Fig. 13 c), and its residual depth (Fig. 13 b) is also a very little lower. Comparing these bio-based coatings with A3, no great difference can be noticed in the scratch resistance, contrary to what is observed for 150 µm-thick coatings. This evidences the significance of the thickness of the samples on the results of the micro-scratch experiments. However, it appears in Figure 13 d that the critical loads are higher for the bio-based coatings (>2.5 N) than for the petrobased A3 (<2.5 N). This is clearly noticeable in Figure 14. This suggests that the ductilebrittle transition in the bio-based materials is delayed comparing to the petro-based matrix.

Thus, the bio-based coatings feature a better scratch resistance than the petro-based reference.

The micro-scratch experiments allow a finer differentiation of the samples comparing to the DMTA analysis.

Conclusion

This work studied the influence of different raw materials on the scratch resistance of polyacrylate clear photo-polymerizable coatings, dedicated to the protection of polycarbonate substrates. Dynamic thermomechanical analysis evidenced that all the studied materials displayed similar thermomechanical behaviors at room temperature (23°C). Micro-scratch tests were then carried out at this temperature. They first allowed a better differentiation of samples containing different amounts of a multicyclic diacrylate monomer, TCDDA: although the use of increasing amounts of this monomer increased the maximum temperature of the mechanical relaxation, it also decreased the overall crosslinking density and consequently increased the residual depth while decreasing the elastic recovery. However for the thinnest coatings this was accompanied by an increase in the critical loads, i.e. a rather beneficial effect; therefore a compromise can be found by using a medium proportion of TCDDA as it seems to delay the ductile-brittle transition.

The incorporation of nano-fillers in the coating did not improve its scratch resistance.

Nevertheless, a study of the mechanisms which control the organization of the nanoparticles in the polymer matrix could complete this work, since the dispersion of the fillers in the whole sample has an impact on its properties. Finally, thin protective coatings featuring a good scratch resistance were obtained using bio-based monomers, with increased critical loads and a probably delayed ductile-brittle transition which could possibly be ascribed to their slightly different distribution of relaxation times observed by DMTA, and/or to their particular chemical structure. It can be noticed that contrary to the petro-based formulation the used bio-based monomers contain no urethane moiety, and therefore no hydrogen bonds; whether this could be of significant importance should be considered in future studies. This result is nevertheless promising concerning the development of totally bio-based coatings.

Figure 1 .

 1 Figure 1. Structure of the monomers and oligomers: TCDDA (a), MPDDA (b), TPGDA (c), DDA (d), DiPEPHA (e), PETA (f)

Figure 2 :

 2 Figure 2: Evolution of the indented and residual depths for the uncoated PC and for the PC coated with A3; observation of the scratches with an optical microscope

Figure 3 :

 3 Figure 3: Evolution of the density of acrylate double bonds in the uncured coatings with the TCDDA weight proportion in the formulation

10 8

 10 Pa at 280°C) while sample A7 (the less densely crosslinked) shows the lowest value (E' ≈ 2.8.10 8 Pa at 280°C). Ranking the intermediate samples according to their rubbery moduli is less easy, because the sensitivity of the used rheometer was apparently not sufficient to perfectly highlight such phenomenon; however, for this set of experiments the observed values are almost in the expected order: at 280°C, for A2 and A4: E' ≈ 5.4.10 8 Pa; for A3 and A5, E' ≈ 4.8.10 8 Pa; and for A6, E' ≈ 4.4.10 8 Pa.

Figure 4 .Figure 5 .

 45 Figure 4. Evolution of the elastic modulus E' during dynamic thermomechanical analysis at 1 Hz, for materials containing increasing amounts of TCDDA

Figure 6 :

 6 Figure 6: Micro-scratch tests carried out on 15 µm-thick coatings containing varying amounts of TCDDA, deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d)

  to the surface (air side) of the coating, ii) a depletion zone; iii) in the middle of the film, a thicker layer where the concentration of the nanoparticles is medium; and iv) a layer in contact with the PC substrate, without any particle.

Figure 7 :

 7 Figure 7: Distribution of the nanoparticles throughout the thickness of the photopolymerized polymer matrix: nano-alumina (a), nano-silica (b)

Figure 8 :

 8 Figure 8: Evolution of tanδ and of the elastic modulus during dynamic thermomechanical analysis at 1 Hz, for nano-filled materials and their references

Figure 9 :Figure 10 :

 910 Figure 9: Results of the micro-scratch tests run on the nano-filled 15 µm-thick coatings and their references, deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d)

Figure 11 :

 11 Figure 11: Evolution of tanδ and of the elastic modulus E' during dynamic thermomechanical analysis at 1 Hz, for materials containing bio-based monomers (B1 and B2) or the corresponding petro-based monomers (A3)

Figure 12 :

 12 Figure 12: Results of the micro-scratch tests for the bio-based (B1 and B2) and the petrobased (A3) 150 µm-thick coatings deposited on PC: indented depth (a), residual depth (b), elastic recovery (c)

Figure 13 :Figure 14 :

 1314 Figure 13: Results of the micro-scratch tests for the bio-based (B1 and B2) and the petrobased (A3) 15µm-thick coatings deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d)

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 .Figure 12 .Figure 13 .Figure 14 :

 1234567891011121314 Figure 1. Structure of the monomers and oligomers: TCDDA (a), MPDDA (b), TPGDA (c), DDA (d), DiPEPHA (e), PETA (f) Figure 2. Evolution of the indented and residual depths for the uncoated PC and for the PC coated with A3; observation of the scratches with an optical microscope Figure 3. Evolution of the density of acrylate double bonds in the uncured coatings with the TCDDA weight proportion in the formulationFigure 4. Evolution of the elastic modulus E' during dynamic thermomechanical analysis at 1 Hz, for materials containing increasing amounts of TCDDA Figure 5. Evolution of tanδ during dynamic thermomechanical analysis at 1 Hz, for materials containing increasing amounts of TCDDA Figure 6. Micro-scratch tests carried out on 15 µm-thick coatings containing varying amounts of TCDDA, deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d) Figure 7. Distribution of the nanoparticles throughout the thickness of the photopolymerized polymer matrix: nano-alumina (a), nano-silica (b) Figure 8. Evolution of tanδ and of the elastic modulus during dynamic thermomechanical analysis at 1 Hz, for nano-filled materials and their references Figure 9. Results of the micro-scratch tests run on the nano-filled 15 µm-thick coatings and their references, deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d) Figure 10. Evolution of the indented depth close to the surface of the nano-filled coatings and of their unfilled references Figure 11. Evolution of tanδ and of the elastic modulus E' during dynamic thermomechanical analysis at 1 Hz, for materials containing bio-based monomers (B1 and B2) or the corresponding petro-based monomers (A3) Figure 12. Results of the micro-scratch tests for the bio-based (B1 and B2) and the petrobased (A3) 150 µm-thick coatings deposited on PC: indented depth (a), residual depth (b), elastic recovery (c) Figure 13. Results of the micro-scratch tests for the bio-based (B1 and B2) and the petrobased (A3) 15µm-thick coatings deposited on PC: indented depth (a), residual depth (b), elastic recovery (c), critical load (d)

Table 3 :

 3 Composition of the coatings containing bio-based materials (wt%)

				MPDDA	TCDDA	Irgacure 184	Lucirin TPO-L
		A1	37.4	58.8	0.0		1.5	2.3
		A2	26.0	40.8	29.4		1.5	2.3
		A3	23.2	36.5	36.5		1.5	2.3
		A4	20.5	32.1	43.6		1.5	2.3
		A5	17.6	27.7	50.9		1.5	2.3
		A6	13.9	21.8	60.5		1.5	2.3
		A7	0.0	0.0	96.2		1.5	2.3
	Table 1. Composition of the coatings with varied percentages of TCDDA (wt%)
		U6A	MPDDA TCDDA	Nanocryl ® C145	NanoArc ® AL-2260	TPGDA	Irgacure 184	Lucirin TPO-L
	C1	20.7	32.5	32.5	10.4			-	1.5	2.3
	C1ref	21.8	34.2	34.2	-		-		5.9	1.5	2.3
	C2	19.3	30.3	30.3			16.3	-	1.5	2.3
	C2ref	20.3	31.9	31.9	-		-		12.1	1.5	2.3
	Table 2: Composition of the coatings containing nanoparticles (named Cx) and their
	respective references (named Cxref) (wt%)
			DiPEPHA PETA DDA TCDDA	Irgacure 184	Lucirin TPO-L
		B1	23.2	-	36.5	36.5	1.5	2.3
		B2	-	23.2	36.5	36.5	1.5	2.3

Table 1 . Composition of the coatings with varied percentages of TCDDA (wt%)

 1

		U6A	MPDDA	TCDDA	Irgacure 184	Lucirin TPO-L
	A1	37.4	58.8	0.0	1.5	2.3
	A2	26.0	40.8	29.4	1.5	2.3
	A3	23.2	36.5	36.5	1.5	2.3
	A4	20.5	32.1	43.6	1.5	2.3
	A5	17.6	27.7	50.9	1.5	2.3
	A6	13.9	21.8	60.5	1.5	2.3
	A7	0.0	0.0	96.2	1.5	2.3

Table 2 : Composition of the coatings containing nanoparticles (named Cx) and their respective references (named Cxref) (wt%)

 2

		U6A	MPDDA TCDDA	Nanocryl ® C145	NanoArc ® AL-2260	TPGDA	Irgacure 184	Lucirin TPO-L
	C1	20.7	32.5	32.5	10.4		-	1.5	2.3
	C1ref	21.8	34.2	34.2	-	-	5.9	1.5	2.3
	C2	19.3	30.3	30.3		16.3	-	1.5	2.3
	C2ref	20.3	31.9	31.9	-	-	12.1	1.5	2.3

Table 3 : Composition of the coatings containing bio-based materials (wt%)

 3 Micro-scratch tests enable a finer differentiation of the coatings than DMTA  The crosslinking density plays a part in the scratch resistance  Nanoparticles did not modify the properties of the coating  Bio-based coatings show a better scratch resistance than petro-based counterparts

		DiPEPHA PETA DDA TCDDA	Irgacure 184	Lucirin TPO-L
	B1	23.2	-	36.5	36.5	1.5	2.3
	B2	-	23.2	36.5	36.5	1.5	2.3

µm-and 150 µm-thick coatings on polycarbonate panels (PC; Makrolon AL 2447) were prepared for micro-scratch experiments, with a motorized film applicator Elcometer K4340 equipped with a spiral bar coater. They were polymerized through three passes under a Fusion F300S UV-lamp equipped with a conveyor belt. The mean total UV doses and irradiance peaks, measured with a Power Puck II (EIT), were respectively the following: UVA

Acknowledgements

Authors express their thanks to Pierre Alcouffe (IMP@LYON1) and to the ''Centre Technologique des Microstructures de l'Université Claude Bernard Lyon1" for the TEM micrographs. All the partners from the "3V" Project (Vernis Verts à très longue durée de Vie; FUI project) are also gratefully acknowledged.