Philippe Louâpre

Cécile Le Lann

Thierry Hance

How parasitoids forage in a complex environment

Keywords: Aphidius rhopalosiphi, foraging behavior, parasitoid, sequential adjustment, Sitobion avenae, spatial distribution

Insect parasitoids developing inside hosts face a true challenge: hosts are scattered in the field and their localization and selection require the use of complex and sometime confusing information. It was assumed for a long time that small-brained organisms like parasitoids have evolved simple and efficient behavioral mechanisms, leading them to be adapted to a given ecological situation, e.g. the spatial distribution of hosts in the habitat. However, hosts are not static and their distribution may also vary through generations and within the life of parasitoid individuals. We investigated if and how parasitoids deal with such a spatial complexity in a mesocosm experiment. We used the Aphidius rhopalosiphi/Sitobion avenae parasitoid/host system to investigate if parasitoid females experiencing different host aggregation levels exhibit different foraging behaviors independently of the number of hosts in the environment. We showed that A. rhopalosiphi females exploited hosts more intensively both within and among patches at higher host aggregation levels. We discussed the adaptiveness of such behaviors in the light of evolution and biological control.

Introduction

Information and decision processes are key components of female parasitoid fitness because they allow them to maximize the number of hosts parasitized during their life [START_REF] Van Alphen | Information acquisition and time allocation in insect parasitoids[END_REF]. In order to optimize their fitness, female parasitoids need to locate and access host patches, select available hosts in the patches, and leave them at the appropriate depletion level [START_REF] Charnov | Optimal foraging, the marginal value theorem[END_REF][START_REF] Stephens | Foraging Theory[END_REF][START_REF] Godfray | Parasitoids: Behavioral and Evolutionary Ecology[END_REF]. As a consequence, the spatial distribution of hosts among . patches and how this patchiness is perceived are of fundamental importance for maximizing the host exploitation rate [START_REF] Iwasa | Prey distribution as a factor determining the choice of optimal foraging strategy[END_REF][START_REF] Rodrigues-Girones | Density-dependent patch exploitation and acquisition of environmental information[END_REF][START_REF] Pierre | A bayesian approach to optimal foraging in parasitoids[END_REF][START_REF] Pierre | Neuroeconomics in parasitoids: computing accurately with a minute brain[END_REF].

The host distribution (also later called field infestation distribution) is highly dynamic and can drastically complicate the foraging task for parasitoids, during their lifetime and/or from generation to generation. For example, the spatial distribution of herbivore hosts varies in space and time and it may be disrupted by many ecological factors, such as climate [START_REF] Andrade | Winter host exploitation influences fitness traits in a parasitoid[END_REF], local variation of the plant structure and quality [START_REF] Rincon | Generating within-plant spatial distributions of an insect herbivore based on aggregation patterns and per-node infestation probabilities[END_REF][START_REF] Riolo | Local variation in plant quality influences largescale population dynamics[END_REF], or the agricultural landscape complexity and the degree of fragmentation (Al [START_REF] Hassan | Relationship between landscape composition and the abundance of aphids and their natural enemies in crop fields[END_REF][START_REF] Banks | Aphid parasitoids respond to vegetation heterogeneity but not to fragmentation scale: An experimental field study[END_REF]. One key model of such host dynamic distribution is aphid feeding on plant sap: colonies can rapidly grow since females reproduced parthenogenetically during the main part of the year. In this system, the spatial distribution of individuals depends on both the rate at which winged forms are produced and leave the native colony to disperse in a new habitat [START_REF] Ben-Ari | Walking aphids can partake in within-field dispersal to distant plants[END_REF] and the movement of apterous forms that can be induced by the presence of natural enemies such as predators/parasitoids disturbing the colony [START_REF] Sloggett | Parasitoids induce production of the dispersal morph of the pea aphid, Acyrthosiphon pisum[END_REF], as well as abiotic factors acting at a local scale such as wind or rain [START_REF] Mann | Movement of apterous Sitobion avenae (Homoptera: Aphididae) in response to leaf disturbances caused by wind and rain[END_REF]. The spatial distribution of aphids also varies at a larger temporal scale, as aphids are scarce and distributed among few patches in winter, while in spring they are abundant and aggregated in large patches [START_REF] Legrand | Autumn, winter and spring dynamics of aphid Sitobion avenae and parasitoid Aphidius rhopalosiphi interactions[END_REF][START_REF] Stilmant | Host specialization in habitat specialists and generalists[END_REF][START_REF] Andrade | Winter host exploitation influences fitness traits in a parasitoid[END_REF][START_REF] Honek | Annual predictions of the peak numbers of Sitobion avenae infesting winter wheat[END_REF].

The variability of hosts in space and time may drastically modify the optimal decisions parasitoids should make in order to maximize their long-term fitness gain [START_REF] Spataro | Influence of environmental conditions on patch exploitation strategies of parasitoids[END_REF][START_REF] Calcagno | How optimal foragers should respond to habitat changes: a reanalysis of the Marginal Value Theorem[END_REF]. For example, [START_REF] Visser | Interference among insect parasitoids: a multi-patch experiment[END_REF] demonstrated by using an experimental arena with 5 host patches, that the habitat exploitation by the parasitoid Trybliographa rapae (Hymenoptera: Figitidae) depends in part on the host distribution. Such response to the host distribution that varies in space and time may involve spatial orientation and spatial memory [START_REF] Collett | Memory use in insect visual navigation[END_REF][START_REF] Dukas | Evolutionary biology of insect learning[END_REF][START_REF] Collett | Spatial memories in insects[END_REF], perception of the quality of patches previously visited [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF][START_REF] Le Lann | Do past experience and competitive ability influence foraging strategies of parasitoids under interspecific competition[END_REF][START_REF] Louâpre | Information gleaned and former patch quality determine foraging behavior of parasitic wasps[END_REF], and measurement of time linked to oviposition rate or patch encounter rate [START_REF] Charnov | Optimal foraging, the marginal value theorem[END_REF][START_REF] Marschall | Foraging in a patchy environment: preyencounter rate and residence time distributions[END_REF][START_REF] Adler | Departure time versus departure rate: How to forage optimally when you are stupid[END_REF][START_REF] Hills | Time's crooked arrow: optimal foraging and rate-biased time perception[END_REF][START_REF] Thiel | Knowing your habitat: linking patch-encounter rate and patch exploitation in parasitoids[END_REF][START_REF] Vásquez | On the value of information: studying changes in patch assessment abilities through learning[END_REF][START_REF] Collett | Spatial memories in insects[END_REF][START_REF] Thiel | How to measure patch encounter rate: decision-making mechanisms in the parasitic wasp Asobara tabida[END_REF]. Such a variability represents a selection pressure that probably determines the proximate mechanisms and the behaviors leading to the optimal choice selection for parasitoids [START_REF] Van Alphen | Information acquisition and time allocation in insect parasitoids[END_REF][START_REF] Van Alphen | Information acquisition, information processing, and patch time allocation in insect parasitoids[END_REF].

In this study, we compared the foraging behavior of Aphidius parasitoid females experiencing different host aggregation levels by manipulating both the number of patches (plant with at least one host) and the host patch density in mesocosms with the same number of hosts and the same number of plants. To date, the effect of the host distribution (simulated by the patch encounter rate or the quality of the visited patches) was often confounded with the whole quality of the explored environment (i.e. the total number of hosts within the set-up) in studies investigating the foraging behaviour of Aphidius species in complex environments (see for examples, [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF][START_REF] Muratori | The impact of patch encounter rate on patch residence time of female parasitoids increases with patch quality[END_REF][START_REF] Lanteigne | Patch experience changes host acceptance of the aphid parasitoid Aphidius ervi[END_REF]. However, the number of hosts in an environment and their distribution among patches are two different parameters characterizing the habitat for parasitoids. We thus monitored the foraging behavior of the aphid parasitoid Aphidius rhopalosiphi De Stefani-Perez (Hymenoptera: Aphidiinae) in a multi-patch environment consisting of different aggregation levels of its main host, the grain aphid Sitobion avenae Fabricius (Hemiptera: Aphididae). In their natural environment, A. rhopalosiphi females encounter very contrasted aphid aggregation levels during their life or through generations, as detailed above. Given that aphids move and develop rapidly, A. rhopalosiphi females must be able to respond to a highly ephemeral distribution of aphids [START_REF] Winder | Cereal aphid colony turnover and persistence in winter wheat[END_REF]. Aphidius rhopalosiphi females perceive host patch density within the environment through inter-patch travel time, and modify their response according to their previous acquired experience [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF][START_REF] Muratori | The impact of patch encounter rate on patch residence time of female parasitoids increases with patch quality[END_REF]. In consequence, we hypothesized that the foraging strategy of different .

5

A. rhopalosiphi females depends on the aggregation level of their hosts even if the environments contain the same number of hosts: The foraging effort (estimated, among others, by the patch residence time and the number of ovipositor contacts) in each visited patch should be high for females exposed to a high level of host aggregation while it should be lower for females exploring a more uniform distribution of these hosts. Moreover, as leaving a patch is risky when the hosts are highly aggregated in the environment (the lower the number of patches, the lower the probability to encounter another patch after leaving the current one), we also expected that parasitoids would sample more intensively the neighboring environment at a high host aggregation level in comparison with a low one, even if both environments contain the same number of hosts. Finally, the expected adaptive behavior expressed by A. rhopalosiphi should impact the aphid population of a given size depending on their aggregation among the wheat plants. We expected that the aphid population should suffer more importantly when individuals are clumped among some patches in comparison with a more uniform distribution.

Materials and methods

Parasitoids and hosts

The A. rhopalosiphi females used in the study originated from mummies collected from a mass rearing at the Plant Protection and Ecotoxicology Unit of the Walloon Agricultural Research Centre (Belgium). The parasitoid was maintained on a Sitobion avenae colony established in 2013 from individuals collected in corn crops at the Marbaix (UCL) experimental farm (50°06 N, 4°63 W). The parasitoids and their hosts were reared in nylon boxes (50 × 50 × 50 cm) on fresh winter wheat (Triticum aestivum) under controlled climatic conditions (21 ± 1°C, 60% ± 10% RH and 16 L : 8 D photoperiod). All experiments were conducted under the same conditions used for rearing, and involved only 2-4 days-old, mated and fed A. rhopalosiphi females. To eliminate females that were unable to oviposit, females were offered 5 healthy hosts for parasitism for 60 min prior to the commencement of experiments [START_REF] Le Lann | Do past experience and competitive ability influence foraging strategies of parasitoids under interspecific competition[END_REF]. Only second instar aphid nymphs were used, as this is the preferred instar of A. rhopalosiphi (Outreman et al., 2001a).

Experimental design

In order to analyze the influence of aphid spatial distribution on neighboring plants on the foraging behavior of parasitoids, each female was exposed in mesocosms to one host aggregation level (low, medium or high) while the number of hosts and plants remain the same among treatments. For this purpose, mesocosms were constituted by 16 wheat plants infested by 16 second instars S. avenae according to three levels of host aggregation: (i) low: one aphid per plant on all 16 plants; (ii) medium: 4 aphids per plant on the 4 central plants; and (iii) high: 8 aphids on each of the 2 central plants (Fig. 1). Each plant with at least one aphid was considered to be a patch, by contrast with plants without aphids. Wheat plants (h = 15 cm) planted 10 cm apart in a tray containing a 5 cm sand layer and covered by a thin layer of water to prevent aphid escapes were placed inside a Plexiglas cage (50 × 50 × 50 cm) having ventilation holes on each side. To prevent the accumulation of chemicals emitted by the plants or aphids, a fan located on the top of the cage removed the air from the cage at a rate of 20 cm 3 /s. One hour after the aphid infestation, a single 2-4 days-old mated and fed (with a drop of honey) A. rhopalosiphi female was deposited on the bottom of the wheat plants on which at least one aphid had been placed, and the cage was closed. The female parasitoid was observed continuously, and the following behaviors were noted: arrival to and departure from a plant, walking, resting, cleaning, host attack (antennal contact with an aphid, followed by ovipositor contact) or rejection (antennal contact with an aphid, not followed by ovipositor contact), departure behaviors (female standing still on the border of a leaf and rotating its antennae circularly in many directions) [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF]. To identify if parasitoids visited several times the same patches, the number of wheat plants visited by a female and their position in the mesocosm were noted. The experiment was stopped after 1 h or when the female rested or cleaned continuously for more than 15 min. A total of 31 females was tested in the experiment (11, 10, and 10 females experienced the low, medium, and high levels of host aggregation, respectively), for a total of 496 aphids (176, 120 and 120 aphids in the low, medium, and high levels of host aggregation, respectively).

Statistical analyses.

The number of hosts encountered in a mesocosm could be considered as a proxy of its quality and thus may inform about the optimal aphid density and distribution. In consequence, we analyzed the relationships between that number and factors such as the number of aphids on wheat plants, the rank of visit of the wheat plant, and the exploitation state of the wheat plant (never exploited or previously exploited) as explanatory fixed factors using a generalized linear mixed model with clustered data (Poisson distribution). The identity of each female was included in the model as random effect, enabling data concerning the same female to be correlated. In the same way, patch residence time (censored data for parasitoids still foraging inside a patch at the end of the experiment) was analyzed using a Cox's proportional hazard model [START_REF] Cox | Regression models and life-tables[END_REF]. This model determines a patch-leaving tendency associated with different fixed factors and time dependent covariates (Table 2), in terms of a hazard ratio. Thus, the tendency of a female to leave the current patch can decrease (hazard ratio < 1) or increase (hazard ratio > 1) depending on events occurring during the experiment or fixed by the experimenter. The duration of the departure behavior was analyzed by a linear mixed model including the number of aphids on the wheat plant and the exploitation state of these plants as fixed factors and the identity of the females as a random effect. The effect of host aggregation on the proportion of attacked hosts was analyzed with a generalized linear model with (Poisson distribution as error family). All analyses were carried out using R 3.4.0 software (R Development Core Team, 2017), with glmmML [START_REF] Broström | R Package. glmmML: Generalized linear models with clustering[END_REF], nlme [START_REF] Pinheiro | Temporal variability of aphid biological control in contrasting landscape contexts[END_REF] and survival [START_REF] Therneau | R package. Survival[END_REF] packages.

Results

Oviposition behaviour

The number of ovipositor contacts observed increased with the number of aphids on wheat plants (β = 0.29, z = 0.032, P < 0.001) but this effect was modulated by the patch exploitation state (never or already visited) (interaction terms; β = -0.843, z = -5.432, P < 0.001), and the and the rank of the visited patch (interaction term; β = -0.023, z = -2.1428, P = 0.032): The number of aphids on a patch had an effect only on wheat plants never visited previously and was close to zero on plants that had been visited at least twice (Fig. 2). In addition, the number of ovipositor contacts decreased on the second and subsequent wheat plants visited in comparison with the first visited wheat plant; this phenomenon occurred at all three host aggregation levels (Fig. 3).

The allocation of time in patches

Data fitted with a Cox proportional hazard model pointed out that several parameters significantly influenced the tendency of the parasitoids to leave the wheat plants they visited (Table 1). First, as expected, the patch-leaving tendency decreased as the host aggregation level increased (including wheat plants without aphids). In the same way, the number of aphids on the visited wheat plants (from 0 to 8) influenced the tendency of the parasitoids to stay on wheat plants: the higher the number of aphids on a wheat plant, the lesser the tendency of the parasitoid to leave it (Fig. 4). The tendency of parasitoids to leave a patch previously exploited did not depend on the numbers of aphids in it (Fig. 5).

The patch departure behavior

The duration of the patch departure behavior was longer when more aphids were present on the patch (F 3,213 = 5.318, P = 0.001), but did not depend on previous visits of the same patch (F 1,213 = 1.572, P = 0.211). Indeed, this duration was longer on wheat plants having 8 aphids (z = 3.371, P = 0.004) than on plants having zero or one aphid (z = 1.436, P = 0.006) (Fig. 6).

The proportion of attacked hosts

The proportion of aphids attacked by A. rhopalosiphi increased with the host aggregation level (GLMM: df = 2, χ 2 = 5.016, P < 0.017; Fig. 7): aphids were attacked in larger proportions in the environment with the high host aggregation level than in the medium and low ones.

Discussion

The aim of this study was to test the effect of the host aggregation level on the foraging strategies of aphid parasitoids. We showed that the tendency to leave a wheat plant as well as the number of ovipositor contacts in each of the visited patches differed between the treatments: the foraging intensity seems to be stronger for females experiencing a high host aggregation level than lower ones.

Moreover, the spatial distribution of hosts in mesocosms influenced the way parasitoids acquired information about the host availability as they spend more time to explore environments characterized with more aggregated hosts than with more uniformly distributed ones. We also demonstrated that the host attack rate by parasitoids increased when hosts were aggregated on few patches. Therefore, the way aphids are distributed among wheat plants influences their own survival as well as the foraging behavior of their parasitoids.

Parasitoids showed a low patch-leaving tendency when the host aggregation level was high compared to lower aggregation levels. Such response is consistent with the theoretical model of . optimal patch departure: the higher the host aggregation level, the lower the patch-leaving tendency [START_REF] Iwasa | Prey distribution as a factor determining the choice of optimal foraging strategy[END_REF]. Linked to the proximate mechanisms of foraging, parasitoids tend to concentrate their foraging effort in few patches when foraging on a highly-aggregated resource probably through a higher incremental mechanism [START_REF] Pierre | A bayesian approach to optimal foraging in parasitoids[END_REF][START_REF] Pierre | Neuroeconomics in parasitoids: computing accurately with a minute brain[END_REF]. This study provides the first empirical evidence that the host aggregation level is a key feature of the environment perceived by parasitoids, regardless of the average quality, although this may not be a general rule. Indeed, it was recently reported that the parasitoid Meteorus pulchricornis foraging on soybean plants does not respond to host aggregation level within a patch [START_REF] Sheng | Departure mechanisms for host search on highdensity patches by the Meteorus pulchricornis[END_REF]. It is possible that patches are perceived in different ways by parasitoids when foraging on plants varying in architectural complexity (e.g. wheat plants vs. soybean plants), and that the potential adaptive mechanism we observed on wheat plants in the present study occurs at a larger scale on soybeans. It is also possible that at the spatial scale of the mesocosm used in our study, parasitoid perceived the patchiness of their hosts while at the plant scale used in other studies, such distribution is not perceived. Based on the unambiguous definition of a patch [START_REF] Waage | Foraging for patchily-distributed hosts by the parasitoid, Nemeritis canescens[END_REF], the patchiness of the host distribution in the mesocosm we used here is likely to be perceived by the parasitoids, as A. rhopalosiphi expressed different arresting behaviors before leaving each wheat plants containing aphids, even once.

Different sources of information can be used by parasitoids in order to express their adaptive response to the host aggregation. They do not only perceive the average quality of their habitat, but also the way aphids are distributed among the patches. As previously shown, we showed that A. rhopalosiphi responds to cues acquired in the current patch and the neighboring ones (even when they were not visited), and combines this information with its previous patch exploitation experience to adjust its foraging behavior sequentially [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF]. It was generally assumed that parasitoids expressed such an adaptive behavior by an intra-patch information perception. Here we also showed that A. rhopalosiphi seems to perceive cues about the host aggregation level, such as the presence of neighboring wheat plants containing aphids, at a distance, as observed in other parasitoid species [START_REF] Corley | Patch time allocation by a parasitoid: The influence of con-specifics, host abundance and distance to the patch[END_REF][START_REF] Fischbein | Patch choice from a distance and use of habitat information during foraging by the parasitoid Ibalia leucospoides[END_REF]. In Aphidius species such as A. ervi, patches of aphids are located thorough the perception of the alarm pheromones (E)-β-farnesene emitted in large quantities when attacked [START_REF] Micha | Aphid alarm pheromone (E)-β-farnesene: A host finding kairomone for the aphid primary parasitoid Aphidius uzbekistanicus (Hymenoptera: Aphidiinae)[END_REF][START_REF] Hatano | Do aphid colonies amplify their emission of alarm pheromone[END_REF][START_REF] Vandermoten | Aphid alarm pheromone: An overview of current knowledge on biosynthesis and functions[END_REF]. As first mentioned by [START_REF] Outreman | Effects of within-and among-patch experiences on the patch-leaving decision rules in an insect parasitoid[END_REF], A. rhopalosiphi females circles their antennae in the air at the leaf border before leaving the visited plants. We interpret this patch leaving behavior as the need for the females to analyze cues coming from the neighboring patches and probably to compare them with previous experience or other cues to make a take-off decision. The patch departure behavior probably enables the parasitoids to detect such aphid kairomones derived from neighboring patches, or alarm pheromones emitted by parasitized aphids, and so to detect the presence and/or the quality of other nearby patches. Here we showed that the richer the visited patch, the longer the patch departure behavior. It is thus plausible that the high number of aphids in patches and therefore the quantity of alarm pheromones emitted in the current visited patch might disrupt the ability of parasitoids to detect cues from other patches in the environment [START_REF] Shaltiel | The use of kairomones for foraging decisions by an aphid parasitoid in small host aggregations[END_REF]). An alternative hypothesis is that kairomones emitted by attacked hosts are attractive for A. rhopalosiphi at a distance of the patch [START_REF] Micha | Aphid alarm pheromone (E)-β-farnesene: A host finding kairomone for the aphid primary parasitoid Aphidius uzbekistanicus (Hymenoptera: Aphidiinae)[END_REF], and repellent once upon the patch entrance (Outreman et al., 2001b). To specifically determine the effect of kairomones perceived at a distance or inside a patch is a key point requiring further investigations as field observations reported that alarm pheromone emitted at natural levels did not attract predators and parasitoids under field conditions [START_REF] Weisser | Does the aphid alarm pheromone (E)-β-farnesene act as a kairomone under field conditions[END_REF].

We demonstrated that the host aggregation levels influenced the foraging behavior of parasitoids regardless of the total number of hosts in the environment. Winder et al. (2013) showed that the spatial distribution of S. avenae and Metopolophium dirhodum, two main targets of the parasitoid A. rhopalosiphi, may be highly variable, even in winter, but depends on the scale at which the spatial process is considered. For example, aphid colonies are extremely ephemeral at the host plant scale, continuously redistributed though local dispersal, while aphid populations seem to be more stable at the field scale. At this scale, variation of the spatial pattern emerges from the season . considered [START_REF] Langer | Seasonal activity and distribution of cereal aphid parasitoids in Belgium[END_REF][START_REF] Legrand | Autumn, winter and spring dynamics of aphid Sitobion avenae and parasitoid Aphidius rhopalosiphi interactions[END_REF][START_REF] Honek | Annual predictions of the peak numbers of Sitobion avenae infesting winter wheat[END_REF]. As pointed out by several authors, optimization of biological control programs requires an understanding of the response of parasitoids to the distribution of their hosts at the relevant scales (ie. spatial scale: from the host plant to the field, temporal scale: from the individual lifespan to the season) [START_REF] Pinheiro | Temporal variability of aphid biological control in contrasting landscape contexts[END_REF][START_REF] Bosem Baillod | Landscape-scale interactions of spatial and temporal cropland heterogeneity drive biological control of cereal aphids[END_REF][START_REF] Morgan | Density dependence and environmental factors affect population stability of an agricultural pest and its specialist parasitoid[END_REF]. In our study, we showed that both the ovipositor contact rate was higher when aphids were aggregated on some wheat plants than homogeneously distributed among many wheat plants, and that A. rhopalosiphi disperse more and visit more wheat plants at a low aphid aggregation level. Aphid populations are thus likely to suffer more from a parasitoid attack when aggregated among a few number of patches, than when they are more uniformly distributed among the plants. While the host density is known to have a strong impact on the density, the distribution and the behavior of natural enemies [START_REF] Morgan | Density dependence and environmental factors affect population stability of an agricultural pest and its specialist parasitoid[END_REF], the host aggregation is not taken into account itself. For instance, in the beginning of the season when aphids are sparse and dispersed among the wheat plants, the ability of A. rhopalosiphi to perceive such a uniform distribution of cereal aphids may result on a high parasitism rate by dispersing parasitoids among the infested wheat plants [START_REF] Legrand | Autumn, winter and spring dynamics of aphid Sitobion avenae and parasitoid Aphidius rhopalosiphi interactions[END_REF]. Early releases of parasitoids in the season may thus slow down the initial growth rate of aphid populations by using natural enemies that adjust their foraging strategy to the aggregation of their hosts [START_REF] Chambers | Control of cereal aphids in winter wheat by natural enemies: aphid specific predators, parasitoids and pathogenic fungi[END_REF][START_REF] Sigsgaard | A survey of aphids and aphid parasitoids in cereal fields in Denmark, and the parasitoids' role in biological control[END_REF][START_REF] Legrand | Autumn, winter and spring dynamics of aphid Sitobion avenae and parasitoid Aphidius rhopalosiphi interactions[END_REF]. support. All applicable institutional and national guidelines for the care and use of animals were followed.

Winder, L., Alexander, C.J., Woolley, C., Perry, J.N. and Holland, J.M. ( 2013 Fig. 2 The number of ovipositior contacts by the parasitoid in patches as a function of the number of aphids on the wheat plant and revisits to the patches (black: first visit; grey: subsequent visit).

Different letters above bars indicate a significant difference, according to the Tukey HSD test.

Fig. 1

 1 Fig. 1 Experimental design, showing the three levels of aphid aggregation (low, medium and high)

Fig. 3

 3 Fig.3The number of ovipositior contacts in patches as a function of the number of aphids on the

Fig. 4

 4 Fig. 4 Probability of the parasitoid of staying on the patch (Kaplan-Meyer survival curves) during the

Fig. 5

 5 Fig. 5 Probability of the parasitoid of staying on wheat plants having one (grey) and four aphids

Fig. 6

 6 Fig.6The duration of the patch-leaving posture displayed by parasitoid females on wheat plants

Fig. 7

 7 Fig. 7 The proportion of attacked a total of 16) during the course of the experiment

  Figure 1.

  Figure 3.

  Figure 5.

  Figure 6.

Figure 7 .

 7 Figure 7.

Table 1

 1 ) The spatial distribution of canopy-resident and ground-resident cereal aphids (Sitobion avenae and Metopolophium dirhodum) in winter wheat. Arthropod-Plant Interactions, 7, 21-32. Estimated regression coefficients (β) and hazard ratios [exp(β)] for covariates included in the Cox proportional hazard model. The model described the patch-leaving tendency of Aphidius rhopalosiphi foraging in a multi-patch environment containing 16 wheat plants and 16 Sitobion avenae aphids distributed according to different levels of aggregation. χ 2 corresponds to the likelihood ratio tests. The overall significance of the fitting model: χ 2 = 308, df = 17.77, P value < 0.001.

	Manuscript received November 28, 2017
	Final version received January 30, 2018
	Accepted February 22, 2018
	Factors / Covariates	β	exp(β)	χ 2	df	P-value	Tendency to
							leave the patch
	Level of hosts
	aggregation	-0.062	0.939	8.38	1	0.004	
	Number of aphids on
	the wheat plant (1)	-0.518	0.595	32.79	1	>0.001	
	Number of wheat
	plants previously	0.184	1.202	16.20	1	>0.001	
	visited
	Revisit of the wheat
	plant (2)	1.225	3.406	7.07	1	0.008	

Acknowledgments

This research was supported by the OPTIFIELD program co-funded by the Académie Universitaire Louvain (AUL) and the Marie Curie Actions of the European Commission. We thank J. P. Jansen (Centre Wallon de Recherches Agronomiques) and G. Collignon (Ferme experimentale de Marbaix -UCL) for providing the parasitoid and aphid strains, and O. Lebbe and M. Pirnay for their technical .

Author contributions: PL, TH and CLL conceived and designed the experiments. PL performed the experiments. PL, TH and CLL analyzed the data and wrote the manuscript.

Disclosure

The authors declare that they have no conflict of interest.


Malo Robin

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Maria Amela-Cortes

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Direct Integration of Red-NIR Emissive Ceramic-like A n M 6 X i 8 X a 6 Metal Cluster Salts in Organic Copolymers Using Supramolecular Interactions

Hybrid nanomaterials made of inorganic nanocomponents dispersed in an organic host raise an increasing interest as low-cost solution-processable functional materials. However, preventing phase segregation while allowing a high inorganic doping content remains a major challenge, and usual methods require a functionalization step prior integration. Herein, we report a new approach to design such nanocomposite in which ceramic-like metallic nanocluster compounds are embedded at 10 wt % in organic copolymers, without any functionalization. Dispersion homogeneity and stability are ensured by weak interactions occurring between the copolymer lateral chains and the nanocluster compound. Hybrids could be ink-jet printed and casted on a blue LED. This proof-of-concept device emits in the Red-NIR area and generates singlet oxygen, O 2 ( 1 g), of particular interest for lightings, display, sensors or photodynamic based therapy applications.

Integrating inorganic nanocomponents in polymer matrices has become a pre-requisite to design easy to shape 3D functional nanomaterials dedicated to optoelectronic applications. [1] Indeed, technologies like dip-or spin-coating, drop casting or printing can be used to deposit them, lowering the devices production costs compared to technics involving high temperatures (400-1400°C) and/or high vacuum such as Chemical Vapor Deposition or Plasma induced Chemical Vapor Deposition. However, a key challenge remains for nanocomposite large-scale and costeffective production, meanwhile allowing high inorganic doping content: controlling the inorganic components dispersion within the organic host. This step is mandatory to prevent the nanocomponents self-aggregation responsible of the nanoscopic dimension benefits loss, light scattering and premature ageing. To do so, the interactions between the organic and inorganic phases have to be carefully considered. [2] Thus, several strategies have been developed, beside the simple blending technic that generally leads to phase segregation with ageing. An obvious approach is to modify the inorganic nanoobjects, via covalent grafting, with organic moieties able, either to act as compatibilizers with the organic host, [3] or to react with the host during a copolymerization. [4] A second strategy relies on designing hybrid building blocks in which tailor-made organic polymerizable ligands are interacting electrostatically with the inorganic component. It was used by e.g. L. Wu and co-workers [5] to integrate polyoxometalate polyanions in polyacrylate matrices. These integration approaches, although very efficient, imply to finely engineer the chemical nature of the organic ligands via multi-step organic synthesis and often lead to nanoobjects surface state modifications. Here, we describe a general method allowing the homogeneous integration of non-functionalized inorganic ionic nanocomponents in organic polymers. To illustrate our strategy, we base our demonstration on rare earth-free, lead -free and cadmium-free M 6 transition metal nanocluster compounds and a poly(methylmethacrylate) (PMMA) copolymer derivative. Considered as intermediates between transition metal complexes and nanoparticles, [6] octahedral metal cluster compounds of general formula A n M 6 X i 8 L a 6 (A: alkali cation; M: Mo, W, Re; X i : inner ligand; L a : apical ligand; Figure 1) are obtained as ternary salt ceramic-like powders by high temperature synthesis and emit very efficiently in the red NIR area when excited in the UV-blue region. Several groups including our, used the previously descibed ways to integrate these phosphorescent emitters in hybrid materials. [7] In all cases, a modification of the inorganic salt was necessary to maximize the interactions between components either by a covalent grafting on the clusters apical positions [8] or by exchanging its alkali cations with functional organic ones. [9] Such functionalization can have a strong impact on the native cluster emission properties, rendering the ones of resulting hybrids difficult to anticipate. [10] In this work, a metallic nanocluster compound is integrated without any chemical modifications in the host matrix, and keeps intact its intrinsic properties. Our strategy relies on weak supramolecular interactions occurring between oxygen atoms contained in polyethylenoxide (PEO) chains and the alkali ions of the inorganic salt. In fact, it is well known since the pioneering work of the 1987 Nobel Prize of Chemistry C. J. Pedersen that, when ethylene oxide fragments are organized in cyclic oligomers, they form crown ether macrocycles able to form stable complexes with alkali ions. [11] We recently demonstrated that these macrocycles could be used to design nanocluster containing liquid crystals. [12] Herein, we expect that using linear PEO chains instead of macrocycles would generate weak interactions, yet strong enough to maintain homogeneity and stability within the hybrid material. A similar approach was used by T. Mori et al. in Japan to develop Cs molecular sensors after the Fukushima Daiichi nuclear disaster. [13] Figure 1. Schematic representation of the nanocluster ternary salt and its integration in the PMMA-PEOMA copolymer.

At first sight, we suspected that, by controlling the amount of PEO chains in the copolymers, we would tailor the inorganic-organic interactions and, as a result, control the homogeneity of our hybrid material.

Hence, several poly(methylmethacrylatepolyethyleoxidemethacrylate) (PMMA-PEOMA) copolymers containing 1.2, 2 or 5 mol% of PEOMA (respectively referenced as P1, P2 and P5) were synthesized in solution by radical polymerization using azobisisobutyronitrile (AIBN) as radical intiator (see ESI for experimental details). Copolymers were characterized by 1 H NMR, differential scanning calorimetry (DSC) and FTIR spectroscopy (ESI, Figures S1-S7). Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 nanocluster salt based on the [Mo 6 I i 8 (OCOC 2 F 5 ) a 6 ] 2-dianionic cluster unit was chosen for its excellent ability to emit compared to fully halogenated salts. [14] Hybrids PiC samples (with i=1, 2 or 5) containing 10 wt% of inorganic emitter were easily obtained by blending solutions of both components in an adequate ratio, followed by solvent evaporation and drying (other doping concentration will be reported in due course). The interactions between the copolymer and the nanocluster could not be evidenced by IR spectroscopy as no shift of the absorption bands related to the inorganic moieties or the ethylenoxide chains is observed. Magic Angle Spinning (MAS) solid state 133 Cs NMR experiments are, among all available technics, the best illustrative ones to observe the interactions between the alkali cations and the polymer PEO lateral chains. Indeed, 133 Cs NMR spectra (see ESI Figure S8) contain two signals located at -4,97 ppm and -106,52 ppm either when they are recorded for Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 in its crystalline form (Cs + location is shared between two crystallographic positions) [9b] or when it is embedded in pure PMMA. This indicates that the inorganic salt crystallizes within the polymer matrix and therefore that the mixture is segregating. In PiC (i = 1-5) sample 133 Cs spectra, only one signal, located at -30.69 ppm, -36.56 ppm, and -37.92 ppm, for P 1 C, P 2 C and P 5 C respectively, are observed. The presence of only one signal reveals that Cs cations are equivalent when the cluster salt is interacting with the PEO lateral chains and that no crystallization occurs. The signal shift to higher field with the increase of PEO content characterizes the increase of the Cs + electronic density due to its interactions with the oxygen free electronic doublets contained in the PEO chains. It shows as expected, that these interactions become stronger with an increase of PEO content. These interactions are responsible of the hybrid homogeneity and physical stability. Increasing the PEOMA/MMA ratio has a strong plastisizing effect on the resulting pure copolymer. Indeed, DSC measurements show that the glass transition temperature decreases from 118°C for pure PMMA to 36°C for copolymer containing 5 mol% of PEOMA (see Table 1

.).

Table 1. Physical and photophysical parameters of hybrids and cluster precursor (A and B). Glass transition temperature (Tg), calculated absolute quantum yield values under air and N2 atmosphere (), emission maximum position, full width at half height of emission signal, and calculated phosphorescence lifetime decay (contribution in parenthesis) for doped copolymers.

Sample

Tg [a] values in parenthesis are given for non doped copolymer); [b] calculated value for a deaerated solution. A : Cs2Mo6I8(OCOC2F5)6 in crystalline powder; B : Cs2Mo6I8(OCOC2F5)6 in solution.

This behavior is related to the lateral PEO chains that increase the distance between polymer main chains. Introducing 10 wt% of nanoclusters in the organic matrix affects also the Tg value. While a plastisizing effect is observed for polymers with low PEOMA/MMA ratio, an increase of the glass transition is observed 10.1002/chem.201800860

Accepted Manuscript

Chemistry -A European Journal for P 5 C showing that, in this particular case, nanocluster-polymer interactions lead to a stiffness of the organic scaffold. Absorption measurements realized in acetonitrile solution for all samples show that pure copolymers have a very low absorption after 320 nm (see ESI, Figures S9-11). Thus, doped copolymers absorption spectra contain mainly the cluster absorption bands between 350 and 450 nm. Figures 2a and 2b present the excitation maps recorded in this wavelength range for a deaerated acetone solution of Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 .and P 1 C respectively. Similar results are obtained when hybrids are deposited on quartz substrate (see ESI Figure S12) for pictures of deposited films. The optimal excitation wavelength to observe the strong red-NIR emission of the ternary salt does not depend on the host matrix and is located at 400 nm. As depicted in Figure 2c, introducing the cluster in the copolymer does not change the general shape of its emission band as the full width at half height (FWHM) is nearly not modified (variation of less than 2%). However, a slight red shift of the emission maximum, increasing with the PEO polymer content is observed (Table 1).The ability of hybrids to emit light was characterized further with absolute quantum yield (AQY) measurements. A perfectly reversible enhancement of the AQY from 16 % up to 51% (table 1 and inset Figure 2c) for P 1 C was observed when passing from an air to a N 2 atmosphere in the integrating sphere. The same trend, even more pronounced, was observed when measurements were realized on a deaerated or aerated acetone solution of Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 with a variation from 49% to 1% respectively. Such change in the emission efficiency is due to the quenching of the nanocluster excited state by triplet oxygen and is known to generate the emissive O 2 ( 1  g ) (vide infra). [15] This phenomenon being a physical one, it does not imply any degradation of the emitter and is perfectly reversible. Oxygen strongly influences also the cluster phosphorescence emission decay. Indeed, a 269 µs phosphorescence lifetime decay could be determined for a deaerated acetone solution of Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 , value consistent with previously reported one for Mo 6 based nanocluster compounds. [16] This decay dropped down to 2 µs for the same solution, but aerated (see ESI, Figures S13-S15).

In the solid state or once Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 is embedded in the P i matrix, the emission decay profile could be fitted with a long and a short components as we previously observed when the same inorganic anion was integrated via ionic assembling in a polyurethane matrix. [17] Blowing N 2 on P i C samples during the measurements induces an increase of the longer component from 80 µs to around 200 µs that correlates well with the behavior of phosphorescent dyes dynamically quenched by molecular oxygen. [18] Hence, The integration method developed in this work does not affect the abilities of nanoclusters to strongly emit which pushes us forward to investigate the process ability of these new hybrids.

Accepted Manuscript

Following a procedure, we developed for a freshly doped epoxy based ink, P 1 C was inkjet printed on glass substrates. [19] Figure 2d shows printed drops (see ESI Figure S16, for printed film studies) under UV light excitation ( exc = 370 nm). Regarding morphological aspects, the patterns clearly shows the usual coffee stain effect responsible for the ring shape. [20] Emission light intensity profiles highlight this phenomenon and show that material amount varies along the drop. Thickness profile measured by mechanical profilometry shows a similar shape (see ESI, Figure S16). Thus, high AQY combined with high doping level with no phase segregation and printing-abilities make this hybrid copolymer an excellent candidate for optical applicationsTo demonstrate such potentialities, P 1 C was casted on top of a commercial 395 nm UV-blue LED. The emission spectra were recorded for the LED with and without copolymer coating and with different viewing angles (Figure 2e). The native UV-Blue LED emission spectrum possesses an intense band centered at 395 nm and its second diffraction order at 790 nm. Once coated with P 1 C, the emission spectra depends significantly on the orientation of the optical fiber used to record the signal compared to the normal of the LED plan. At 0°, the radiative energy transfer from blue to red is only partial because the copolymer layer is not thick enough to absorb all the UV light. As a result, the blue component of the emission is stronger than the red one. When the angle increases, the red emission becomes stronger compared to the blue LED emission. This well-known phenomenon is mainly due i) to the fact that increasing the angle of detection implies that the UV light passes through an increased polymer thickness and thus more clusters are excited, and ii) to the ability of polymers to guide the emitted light which has already been exploited to design active waveguides [21] or solar cell concentrators [22] with cluster based materials. Nonetheless, although very simple, this example shows the high potential of this red phosphorescent copolymer as external conversion layer for optical applications. Moreover, we investigated whether it was possible to generate O 2 ( 1  g ) with our simple device. As shown in the inset of figure 2e, an emission band centered on 1270 nm related to O 2 ( 1  g ) emission could be detected. Therefore, a simple device made of a UV-LED covered with our copolymer can act as a local O 2 ( 1  g ) generator, of particular interest for photodynamic therapy like in dermatology for e.g. melanoma treatments, [23] or for bactericidal photodynamic applications. [24] In summary, this work presents the first example of hybrid acrylate in which a metal nanocluster compound, namely Cs 2 Mo 6 I i 8 (OCOC 2 F 5 ) a 6 , is embedded homogeneously at 10 wt % by a simple solution blending. The softness of the integration method, based on weak interactions evidenced by 133 Cs NMR, allows the entire properties of the native inorganic salt to be transferred to the hybrid matrix. Compared to pure PMMA, the introduction of lateral PEO chains in the organic matrix insures the hybrid homogeneity and increases its gas permeability leading to highly O 2 sensitive materials. This high sensitivity is highlighted by the detection of O 2 ( 1  g ) emission when a hybrid thin layer is deposited on a blue LED. Finally, taking into account the wide potentialities offered by inorganic molecular or supermolecular polyanionic species in terms of applicative prospects (energy conversion, catalysis,…) and the ease of integration described herein, the presented strategy offers promising perspectives in the developments of new hybrid copolymers with enhanced functionalities.

Figure 2 .

 2 Figure 2. a) Excitation map of Cs2Mo6I i 8(OCOC2F5) a 6 in deaerated acetone solution; b) excitation map of P1C (the blue and red colors correspond to a weak and strong intensity respectively); c) emission spectra (exc = 370 nm) of crystalline Cs2Mo6I i 8(OCOC2F5) a 6 (black), P1C (red), P2C (green) and P5C (blue), inset: AQY variation of P1C depending on its atmosphere content; d) inkJet printed P1C patterns under UV light excitation and corresponding colorimetric profils for drops matrix; e) emission spectra recorded for 395 nm commercial blue-led (in blue) and P1C covered blue LED recorded at various angle, inset: NIR corrected emission spectrum generated with the covered blue led.

COMMUNICATION

  High content of red-NIR phosphorescent metal clusters are integrated in acrylate copolymers without preliminary functionalization. The hybrid homogeneity is ensured by weak interactions occurring between the cluster salt cations and the lateral chains of the host. The resulting hybrids can be processed by inkjet and, once deposited as a thin film on a blue LED, generates bright red-nir light and singlet oxygen. M. Robin, N. Dumait, M. Amela-Cortes, C. Roiland, M. Harnois, E. Jacques, H. Foliot, Y. Molard* Page No. -Page No.

Acknowledgements M. Robin thanks MENSR for financial support.. Keywords: Cluster compounds • Energy conversion • Organicinorganic hybrid composites • Self-assembly • Singlet oxygen


Christelle A Bernard

Nadia Bahlouli

Christiane Wagner-Kocher
email: christiane.wagner-kocher@umontpellier.fr

Jian Lin

Saïd Ahzi

Yves Rémond

Multiscale description and prediction of the thermomechanical behavior of multilayered plasticized PVC under a wide range of strain rate

Keywords: Plasticized PVC, Multiscale, Strain rate, Temperature

Introduction

Since the early 1970s, the part polymeric materials play in the automotive industry has strongly increased to reduce the mass of vehicles. Thus, the fuel consumption is lowered and performances are improved in terms of noise, shock absorption or lifetime. Among the polymers used in the automotive industry, poly(vinyl chloride) (PVC) is widely used for crashworthiness applications. At room temperature, PVC is a glassy polymer. Several works [START_REF] Wang | Characterization and Constitutive Modeling of a Plasticized Poly(vinyl Chloride) for a Broad Range of Strain Rates[END_REF][START_REF] Aubin | homme, Analysis of the glass transition temperature of miscible polymer blends[END_REF][START_REF] Lu | Relationship between the glass transition temperature and the interaction parameter of miscible binary polymer blends[END_REF] measured the glass transition of PVC around 82°C. However, Pezzin et al. [START_REF] Pezzin | The dependence of the glass transition temperature on molecular weight for polyvinylchloride[END_REF] showed that the glass transition of PVC is dependent on its molecular weight. This can be explained by the PVC chain stiffness and the free volume theory [START_REF] Gibbs | Nature of the Glass Transition and the Glassy State Nature of the Glass Transition and the Glassy State[END_REF][START_REF] Somcynsky | The glass transition and the reduced temperature of polymeric liquids[END_REF]. The conditions of polymerization are such that all samples have the same degree of syndiotacticity. Pezzin et al. [START_REF] Pezzin | The dependence of the glass transition temperature on molecular weight for polyvinylchloride[END_REF] found that the glass transition temperature increases rapidly and asymptotically reaches the limiting value T g ∞ = 78 °C.

The PVC used in the automotive industry is generally modified by plasticizing to obtain flexible PVC. This is the so-called plasticized PVC (PPVC), where the effects of weather, road and driving conditions are minimized. In PPVC, powdered resin is mixed with each of a stabilizer, plasticizer, lubricant and dioctyl phthalate that explain the thermal stability of PPVC at processing temperatures [START_REF] Varughese | Tensile and tear failure of plasticized poly (vinyl chloride)/epoxidized natural rubber miscible blends[END_REF][START_REF] Ha | Fracture toughness and properties of plasticized PVC and thermoplastic polyurethane blends[END_REF][START_REF] Roy | Asymmetric membranes based on poly(vinyl chloride): effect of molecular weight of additive and solvent power on the morphology and performance[END_REF].

Investigations of the mechanical response, plasticizer effect and morphology of PPVC have been of particular interest to academic researchers and industrialists because of the widespread use of PPVC in automotive crashworthiness. Many authors [START_REF] Kendall | Strain rate dependence in plasticized and un-plasticized PVC[END_REF][START_REF] Kendall | Rate dependence of poly(vinyl chloride), the effects of plasticizer and time-temperature superposition[END_REF][START_REF] Zhang | Dynamic rheological property and membrane formation of mechanochemically modified polyvinylchloride[END_REF][START_REF] Bernard | Impact behaviour of an innovative plasticized poly(vinyl chloride) for the automotive industry[END_REF] investigated the strain rate dependence of PVC and PPVC with a high-level of plasticizer, from quasi-static to dynamic loading at room temperature. They also investigated the temperature sensitivity of both materials for a strain rate of 10 -2 s -1 . For all strain rates tested, at room temperature PVC exhibits a glassy polymer behavior, whereas PPVC shows a change of behavior between the quasi-static and dynamic loading. Thus, at low strain rates, PPVC reveals a rubbery polymer behavior and at high strain rates, the mechanical response of PPVC is glassier. However, at room temperature strain softening of PPVC is not observed, unlike PVC.

Investigation of the temperature sensitivity clearly shows a change in the mechanical response of PPVC. For temperatures lower than -40°C, PPVC exhibits a glassy polymer response. The yield stress is clearly identified and is followed by strain softening. Between -20°C and 0°C, the mechanical response of PPVC is less glassy and a rubbery mechanical behavior is identified for temperatures above 21°C. These authors also showed that the yield stress is bi-linearly dependent on the log of the strain rate. Wang et al. [START_REF] Wang | Characterization and Constitutive Modeling of a Plasticized Poly(vinyl Chloride) for a Broad Range of Strain Rates[END_REF] investigated the strain rate dependence of PPVC. Loading-unloading compressive tests at constant strain rates highlight a viscoelastic behavior of PPVC. Mulliken et al. [START_REF] Mulliken | High-rate thermomechanical behavior of poly(vinyl chloride) and plasticized poly(vinyl chloride)[END_REF] performed dynamic mechanical analyses and quasi-static and dynamic uniaxial compressive tests on PVC and 20 % PPVC. They found that the addition of 20 % of plasticizers into the PVC blend decreased the glass transition temperature to 22°C. Moreover, for this level of plasticizer at room temperature, the PPVC exhibits a glassy behavior at high strain rates and the yield point is followed by strain softening. This is in contrast to the PPVC investigated by Kendall and Siviour [START_REF] Kendall | Strain rate dependence in plasticized and un-plasticized PVC[END_REF][START_REF] Kendall | Rate dependence of poly(vinyl chloride), the effects of plasticizer and time-temperature superposition[END_REF]. Thus, the percentage of plasticizer in the PPVC blend is of great importance for its mechanical properties. The effects of the plasticizer content on the material properties of PPVC have been investigated previously [START_REF] Matuana | The effect of low levels of plasticizer on the rheological and mechanical properties of polyvinyl chloride/newsprint-fiber composites[END_REF][START_REF] Marcilla | Effect of the plasticizer concentration and heating rate on the thermal decomposition behaviour of PVC plastisols. Kinetic analysis[END_REF] and several observations have been made. In addition to the previous observations, the addition of a plasticizer to the PPVC blend decreases the glass transition temperature [START_REF] Lu | Relationship between the glass transition temperature and the interaction parameter of miscible binary polymer blends[END_REF][START_REF] Altenhofen Da Silva | Polyvinylchloride (PVC) and natural rubber films plasticized with a natural polymeric plasticizer obtained through polyesterification of rice fatty acid[END_REF][START_REF] Ceccorulli | Composition dependence of the glass transition temperature of polymer-diluent systems: 1. Experimental evidence of a dual behaviour in plasticized PVC[END_REF]. Moreover, while the addition of a plasticizer improves the elongation at break and increases both the fracture energy and the Poisson's ratio, it decreases the elastic modulus, the yield stress and the hardness of the material [START_REF] Varughese | Tensile and tear failure of plasticized poly (vinyl chloride)/epoxidized natural rubber miscible blends[END_REF][START_REF] Ha | Fracture toughness and properties of plasticized PVC and thermoplastic polyurethane blends[END_REF][START_REF] Rehm | The compression set of plasticized PVC[END_REF][START_REF] Pita | Mechanical properties evaluation of PVC/plasticizers and PVC/thermoplastic polyurethane blends from extrusion processing[END_REF][START_REF] Elicegui | A study of plasticization effects in poly(vinyl chloride)[END_REF].

Thus, the mechanical behavior of PPVC exhibits a triple dependence on strain rate, temperature and plasticizer level. Thus, a literature review highlights strong differences depending on the PPVC and its plasticizer content. Varughese et al. [START_REF] Varughese | Tensile and tear failure of plasticized poly (vinyl chloride)/epoxidized natural rubber miscible blends[END_REF] and Thomas et al. [START_REF] Thomas | Scanning electron microscopy studies on tensile, tear and abrasion failure of plasticized poly (vinyl chloride) and copolyester thermoplastic elastomers[END_REF] investigated the tensile and tear fracture surfaces. Scanning electron microscopy observation on fractured surface after tensile tests showed ductile-type failure, mainly due to shear fracture with high plastic deformation, whereas the tear fractography brings out the presence of sine waves.

The purpose of this paper is to characterize and analyze the thermomechanical behavior and the deformation mechanisms of PPVC sheets obtained by a layered process. This process is not useful for the dynamic loading. Because the manufacturing process strongly influences the mechanical properties of a material, it is necessary to analyze the strain rate and temperature sensitivity of a layered PPVC at different scales. The studied PPVC is destined to components designed for the automotive industry. Thus, the PPVC structure will be submitted to high strain rates. The thermomechanical behavior of the material and its morphology were characterized: detailed thermal and mechanical analyses being performed over a wide range of strain rates and temperatures to . To improve the use of the layered PPVC, we propose a predictive modeling of the modulus and the threshold stress.

Materials and methods

Materials

The PPVC studied in this paper is composed of 50 % PVC, 40 % plasticizer and 10 % additives. The material was manufactured by Faurecia using an innovative layered process and provided as PPVC sheets of 1 mm thickness.

Morphology

Micrographs were taken before and after mechanical characterization, to observe modifications of the morphological aspects and defects of PPVC along its thickness. Chemical microanalyses of energy dispersive X-ray spectra (EDS) were registered and microstructure analysis was carried out using Energy Dispersive X-ray Microanalysis together with Scanning Electron Microscopy (SEM; JEOL 6700F). Sections were cut from the gauge length before and after tensile tests. The fractured surfaces were obtained by breaking PPVC specimens in liquid nitrogen to minimize the development of plastic deformation. The topology of the fracture surfaces was directly observed after iridium coating. The presence and the sizes of voids were analyzed using ImageJ and compared, before and after tensile tests for three specimens.

Thermal analysis

The thermal stability of PPVC was evaluated by thermogravimetric analysis (TGA) on a METTLER TOLEDO TGA/DSC1 machine, with the STAR system, operated in air from 40°C to 1000°C at a heating rate of 20°C/min. The mass of the specimens ranged between 15 and 25 mg. The mass loss and temperature during the test were recorded. The accuracy of the weighing machine is 1 µg.

Differential Scanning Calorimetry (DSC) tests were conducted on a METTLER TOLEDO DSC1 machine with the STAR System and a HSS8 sensor. These tests characterize the transition temperatures and analyze the phase miscibility of the material. The mass of the tested specimens was approximately 15 mg. The heating cycle was carried out for a temperature range from -150°C to 250°C with a heating rate of 10°C/min. A second scan was performed at the end of the first scan after quenching, to evaluate the polymer properties after removing the sample thermal history. This is erased when the material is heated above its glass transition temperature.

Dynamic mechanical analyses (DMA) were conducted under tensile loading at 1 Hz for a temperature range from -100°C to 120°C. The glass transition temperature range was first determined by testing the sample using a 2°C/min dynamic temperature sweep at 0.2% strain and 1 Hz [START_REF] Diani | Predicting thermal shape memory of crosslinked polymer networks from linear viscoelasticity[END_REF][START_REF] Dixit | Investigation of miscibility and mechanical properties of PMMA/PVC blends[END_REF]. The evolution of the storage modulus, loss modulus and tan δ (the ratio between the loss and storage moduli) were investigated over the range of temperature studied. The glass transition temperature measured by DSC and DMA were compared using different analysis methods to better understand the discrepancies that exist between these two thermal techniques.

Mechanical characterization

Quasi-static uniaxial tensile tests

For the quasi-static strain rate tests, uniaxial quasi-static tensile tests were conducted using an INSTRON 3384 universal testing machine equipped with a temperature chamber (500 Series Chambers ) to perform mechanical tests at different temperatures. Tests were carried out at constant displacement rates, at 50 and 500 mm/min for different constant temperatures (-30°C, 0°C, 23°C, 85°C). The stress-strain behavior of the samples was determined from the load-displacement data of the tensile device. At the yield point, identified on the stress-strain curves as the intersection point between the viscoelastic behavior slope and the viscoplastic behavior slope, these displacement rates lead to true strain rates of 0.03 s -1 and 0.3 s -1 respectively. The test specimens are cut from PPVC sheets by Faurecia. The specimen geometry follows the standard ASTM D412 classically used in international industries. For both temperature and strain rate, at least five samples were tested.

Dynamic uniaxial compressive tests

For the high strain rates, uniaxial compression tests were carried out on a homemade Split Hopkinson Pressure Bar (SHPB) [START_REF] Matadi | High strain rate behaviour of renewable biocomposites based on dimer fatty acid polyamides and cellulose fibres[END_REF][START_REF] Wang | Dynamic behavior and flame retardancy of HDPE/hemp short fiber composites: Effect of coupling agent and fiber loading[END_REF] at three temperatures (-30°C, 23°C, 85°C) and two ranges of strain rates. Two devices, one for low and one for high temperatures, were adapted on our SHPB. At high temperatures, the sides of the two bars in contact with the specimen were positioned in a homemade furnace containing two electrical resistances. For low temperatures, the specimen was sandwiched between the two bars inside a home-made temperature chamber. Then, the specimen and a short part of the bars were cooled to below -30°C by the addition of liquid nitrogen to the chamber. The addition of technical alcohol helps to maintain the thermal equilibrium during the tests. Four thermocouples inserted in the temperature chamber allow the temperature inside the oven to be controlled. To reach a thermal equilibrium, the samples were heated or cooled in the appropriate chamber and maintained at the target temperature for 15 min before testing [START_REF] Matadi | High strain rate behaviour of renewable biocomposites based on dimer fatty acid polyamides and cellulose fibres[END_REF][START_REF] Wang | Impact response of recycled polypropylene-based composites under a wide range of temperature: Effect of filler content and recycling[END_REF].

The test fixture is composed of three 22 mm diameter steel bars. The input and output bars are 3 m long and the strikers are 0.5 m and 1 m long, to reach a wider range of strain rates.

These strikers are launched with an air gun against the incident bar to generate the incident pressure pulse. On impacting the input bar, the striker generates an incident pulse εi (t). Once this pulse reaches the specimen, one part εr (t) is reflected into the incident bar, the other part εt (t) goes through the specimen and is transmitted to the output bar. According to the wave propagation theory, the stress and particle velocity can each be calculated at every section of the bars. In particular, they are shifted from the gauge location to both bar/specimen interfaces considering two superposed waves propagating in opposite directions at a velocity Cb, which is the speed of sound into the bars when dispersion is neglected. This velocity was measured during a conventional SHPB test without specimen [START_REF] Bahlouli | Recycling effects on the rheological and thermomechanical properties of polypropylene-based composites[END_REF][START_REF] Lee | Dynamic material property characterization by using split Hopkinson pressure bar (SHPB) technique[END_REF]. Thus, assuming that the bars are linear with a constant section and that the deformation and forces are homogenous within the sample, we can apply the classical elastic wave propagation theory. The nominal strain rate 𝜀̇𝑛, strain 𝜀 𝑛 and stress 𝜎 𝑛 are given by:

𝜀̇𝑛(𝑡) = - 2𝐶 𝑏 𝐿 𝑠 (0) 𝜀 𝑟 (𝑡) (1)
𝜀 𝑛 (𝑡) = - 2𝐶 𝑏 𝐿 𝑠 (0) ∫ 𝜀 𝑟 (𝜏) 𝑡 0 𝑑𝜏 (2)
𝜎 𝑛 (𝑡) = 2𝐸 𝑏 𝐴 𝑏 𝐴 𝑠 (𝜀 𝑖 (𝑡) + 𝜀 𝑟 (𝑡) + 𝜀 𝑡 (𝑡)) (3)
where 𝐸 𝑏 is the Young modulus of the bar, 𝐿 𝑠 (0) is the initial length of the sample, 𝐴 𝑏 and 𝐴 𝑠 are the cross-sectional area of the bar and the sample, respectively. According to ν, the polymer viscosity, the true strain and true stress are identified from the nominal measurement:

𝜀 𝑡 (𝑡) = -ln(1 + 𝜀 𝑛 (𝑡)) (4)
𝜎 𝑡 (𝑡) = 𝜎 𝑛 (𝑡)(1 -𝜀 𝑛 (𝑡)) 2𝜈 (5)
Cylindrical specimens with a diameter of 10 mm, cut from the PPVC sheets, were tested to investigate their dynamic thermomechanical behavior. For each condition (temperature, strain rate), at least five samples were tested.

Results and Discussion

Microstructural characterization

The fracture surface morphology was observed by scanning electron microscopy at different visualization scales. Figure 1 shows SEM micrographs of the fractured surfaces taken perpendicular to the loading direction before (Figure 1a) and after (Figure 1b) quasi-static tensile tests. Due to the cooling of samples in liquid nitrogen before breakage, the material exhibits brittle fracture. The fractured surfaces reveal the presence of voids. Before testing, the percentage of voids within the specimen is around 4% and increased to 6.7% after testing.

The number of small and middle size voids increase by 50% whereas the number of the larger voids is quite constant. However, it appears that their diameter highly increases (+150-200%) after testing.

For all the analyzed specimens, the voids are well distributed with the presence of the small and middle size voids mainly located at the bottom of the specimen and the larger size voids located in the specimen core. Because the voiding appears perfectly aligned along a line, their presence and position are probably related to degassing phenomena occurring at different time intervals of the manufacturing process of the PPVC sheets. Even though similar microstructures are observed before and after mechanical testing of the specimen, in terms of voids repartition, the fracture surface of the tested specimen (see Figure 1b) exhibits some irregularities unseen in the non-tested area (see Figure 1a). When we increase the magnification (see Figure 1c,d,e), voids with different shapes were observed.

At higher magnification, clusters of cubic particles appear (see Figure 1e). The size of the cubic particle is approximately 1 µm 3 .

Analysis by X-ray diffraction presented in Figure 2b will provide more information about sample constitution. The areas contained in the white squares shown in Figure 2a were analyzed. Sq1 corresponds to the fractured surface outside the cluster; Sq2 is taken from inside the cluster and S3 matches one cubic nodule. The results of X-ray patterns are presented in Figure 2b. SEM coupled with energy dispersive X-ray spectroscopy also allows highlighting of the chemical composition of the observed particles. Sq1 and Sq2 show similar chemical compositions while S3 demonstrates a higher oxygen peak and non-negligible representative peaks of Na, Al and Si. In the Sq2 zone, even if the presence of agglomerates is observed, the X-ray pattern shows very low contents of Na, Al and Si. These elements (O, Na, Al, Si) are proof of the presence of sodium aluminosilicate classically used as a stabilizing component of PVC melts [START_REF] Pessey | Polymer composites for the automotive industry: characterisation of the recycling effect on the strain rate sensitivity[END_REF].

Thermogravimetric analysis

The thermal degradation of PPVC, characterized by TGA, is shown in Figure 3, for three specimens to evaluate the discrepancy seen in the material. The thermogravimetry (TG) curves show the percentage of mass loss versus temperature. The DTG curves are superposed onto the TG curves and indicate the rate of mass loss used to evaluate the degradation temperature of the material. Similarly to pure PVC [START_REF] Altenhofen Da Silva | Polyvinylchloride (PVC) and natural rubber films plasticized with a natural polymeric plasticizer obtained through polyesterification of rice fatty acid[END_REF][START_REF] Gong | Thermal properties of poly(vinyl chloride)/montmorillonite nanocomposites[END_REF], the thermogravimetric curves of PPVC (see Figure 3a) show two degradation peaks around 330°C and 455°C. These correspond to a loss of 73.9%±2.1% and 15.4%±0.3% of the initial mass. This leads to a total mass loss of approximately 90 % for each tested specimen. The samples are thermally stable and the weight loss rate is almost equal to zero at temperatures below 250°C. Above this temperature, the decomposition rate falls and reaches a minimum of -13.97 (± 8%) %.min -1 at 329.8 (± 1.27%) °C. According to previous publications, [START_REF] Yao | Thermal degradation of PVC in the presence of polystyrene[END_REF][START_REF] Soudais | Coupled DTA-TGA-FT-IR investigation of pyrolytic decomposition of EVA, PVC and cellulose[END_REF][START_REF] Bacaloglu | Degradation and stabilization of poly(vinyl chloride). I. Kinetics of the thermal degradation of poly(vinyl chloride)[END_REF][START_REF] Marongiu | Thermal degradation of poly(vinyl chloride)[END_REF], the first degradation step matches the dehydrochlorination of PVC, with the formation of hydrochloric acid (HCl) and conjugated polyene sequences of 5-25 double bonds. The second step is characterized by the formation of alkyne aromatic hydrocarbons and char residues, due to the rearrangement of polyene structures through cyclization and cross-linking reactions. When PPVC samples are heated above 500°C, their mass is stable. The residual weight fraction is 10.8%±2.1% and this can be related to the cubic particles observed during characterization of morphology. The thermogravimetric curves obtained for each sample are plotted in Figure 3b. The two degradation steps are clearly identified. Between the three specimens studied, some discrepancies appear at the beginning of the second stage due to a difference of mass loss at the end of the first stage. This difference can be attributed to a variation in the quantity of HCl during the first step. Despite the difference of mass loss between the two degradation stages, the total degradation of the material is approximately the same at the end of the thermogravimetry analysis. According to the literature, the presence of plasticizers and additives in the PVC does not delay the first stage of deformation, however, it delays the second stage of the material degradation (from 454°C to 466°C for [START_REF] Altenhofen Da Silva | Polyvinylchloride (PVC) and natural rubber films plasticized with a natural polymeric plasticizer obtained through polyesterification of rice fatty acid[END_REF] and from 465°C to 515°C for [START_REF] Gong | Thermal properties of poly(vinyl chloride)/montmorillonite nanocomposites[END_REF]).

Differential Scanning Calorimetry (DSC)

Figure 4 shows the DSC thermograms of PPVC from -150°C to +250°C for three specimens, to evaluate the discrepancy in material properties induced by the layered process. The first heating run was carried out to remove the thermal history of the samples. The second heating run leads to the determination of the different thermal transitions of the studied polymer.

The glass transition temperature of PPVC is characterized by an endothermic deviation from the baseline in the DSC thermogram. From the DSC tests, we assume that the glass transition temperature is given the midpoint of the heat-capacity shift. In the first scan, an endothermic deviation appears at approximatively -41°C. In the second scan, the first deviation, which corresponds to the glass transition temperature, is close to -32°C. A third peak is detected on the first scan around +240°C, as shown in Figure 4. On the second scan, this peak is shifted to above +250°C. These are exothermic peaks. A comparison between the TGA thermogram and the DSC scan leads to the conclusion that this peak corresponds to the beginning of the material degradation, which occurs around +260°C.

Dynamic mechanical analysis

DMA tests have been performed at 1 Hz for temperatures ranging from -100°C to 120°C.

The results are presented in Figure 5 for storage modulus, loss modulus and tan delta (tan 𝛿)

curves. The tan 𝛿 curve is defined as the ratio between the loss modulus and the storage modulus.

According to the tan 𝛿 curve, the glass transition region, at 1 Hz, extends from -40°C to 80°C. Close to the beginning of the glass transition region, a peak is observed at around -30°C on the loss modulus curve, whereas another peak is observed on the tan 𝛿 curve, at around 0°C. In the literature [START_REF] Barton | Thermoanalytical study of an epoxy resin crosslinked with an aliphatic polyamine[END_REF][START_REF] Kumler | Detection of Tll in styrene-ethyl acrylate random copolymers by differential scanning calorimetry and dynamic mechanical analysis[END_REF][START_REF] Cassel | Glass transition determination by thermomechanical analysis, a dynamic mechanical analyzer, and a differential scanning calorimeter[END_REF], a large discrepancy is observed between DMA Tg given by the tan 𝛿 peak and DSC Tg. However, Achorn and Ferrillo [START_REF] Marongiu | Thermal degradation of poly(vinyl chloride)[END_REF] determine a DMA Tg in agreement with DSC Tg by considering the glass transition temperature as the average of the loss modulus and tan 𝛿 peak temperature measured at 1 rad/s (around 0.15 Hz). According to this procedure, T g is measured around -15°C at 1 Hz, higher than DSC T g due to relative higher frequency (supposedly around 0.15 Hz according to the work of Achorn and Ferrillo [START_REF] Achorn | Comparison of thermal techniques for glass transition measurements of polystyrene and cross-linked acrylic polyurethane films[END_REF]).

The discrepancy observed in the glass transition temperature between DSC and DMA can be explained by a) these two techniques involve different material states during the analysis, b) since the operating conditions between DSC and DMA differ, the thermal equilibrium within the material is not the same. Thus, because the glass transition is a thermally activated process, it is expected to observe such discrepancy between two different measures.

Moreover, DSC measurements are known to be more thermodynamically stable than DMA where thermal gradients can occur inside the sample whose geometry and weight are quite different from DSC.

Throughout the entire glass transition region, we observe a major drop in the storage modulus, from 3 GPa to around 2 MPa. Thus, for temperatures below -50°C, PPVC is in its glassy state, while for temperatures above 80°C, this material is in its rubbery state.

Thermomechanical characterization

The thermomechanical behavior of PPVC has been investigated at low and high strain rates, for temperatures ranging from -30°C to 85°C. This corresponds to the glass transition region according to Figure 5. During the lifetime of the structure, the temperature of the material can vary between -30°C and 85°C. Thus, this temperature range is classically used by the automotive industry to validate their materials. Tensile tests have been performed at low strain rates, until the failure of the material or the maximum displacement of the machine is achieved. Dynamic tests have been performed at high strain rates. The level of strain reached at the end of the dynamic test is not relevant. Thus, the level of strain reached under dynamic loading will not be analyzed, as we cannot link it to the failure. Equilibrium was reached for each test presented in this study.

Mechanical behavior of PPVC

Representative true stress-strain curves are plotted in Figure 6. The temperature sensitivity of PPVC at 0.03 s -1 is plotted in Figure 6a and its strain rate sensitivity is plotted in Figure 6b, Figure 6c and Figure 6d for three temperatures (-30°C, 23°C and 85°C). For low strain rates, specimens have been tested under tensile loading, whereas for high strain rates, specimens were tested under compressive loading. However, no barreling effect is observed in dynamic conditions due to the low thickness/diameter ratio. Evolution of the thermomechanical behavior of PPVC is observed: from a viscoelastic-viscoplastic behavior to a rubbery behavior.

The true stress-strain curves presented in Figure 6 show two stages: a short stage at the beginning of the curve corresponding to elastic, viscoelastic behavior and a second stage characterized by non-linearity of the stress-strain curves. The slope of the curves in the second phase decreases as temperature increases. The material properties, elastic modulus and yield stress, increase when the temperature decreases as shown in Figure 6a. For all specimens, no necking was observed during tensile tests. For the different tested strain rates and temperatures, all stress-strain curves show a major strain hardening. All specimens have been broken in the gauge length except those tested at 85°C, where no failure was observed, as

shown in Figure 6a.

The strain rate sensitivity of PPVC is presented in Figure 6b, Figure 6c and Figure 6d for three temperatures: firstly, -30°C, close to the glass transition region (see Figure 6b); secondly, at room temperature in the rubbery state (see Figure 6c); thirdly, at 85°C (see Figure 6d). For all temperatures, the elastic modulus and the yield stress increase when the strain rate increases.

At low temperatures exemplified by Figure 6b, a change of mechanical behavior is observed between dynamic and quasi-static loadings. At high strain rate, PPVC exhibits a glassy behavior, whereas at low strain rate, it exhibits a viscoelastic-viscoplastic behavior. Then, the material is in its glass transition region (𝑇 𝑔 = -32°C, see DSC curves in Figure 4). At high strain rates, PPVC demonstrates a classical mechanical behavior under compression loading; after a linear elastic response, a non-linear response appears before the yield point. After this point, the material exhibits a plastic behavior. The viscoplasticity of the material can be divided into two domains: an initial strain softening domain, followed by a strain hardening domain due to polymer chain alignment. At low strain rates, there is no strain softening. The viscoelastic stage is directly followed by the strain hardening domain, until specimen failure occurs. At room temperature, a change of behavior is also observed between high and low strain rates (see Figure 6c). The mechanical behavior at high strain rates is close to that observed at low strain rates and temperature (see Figure 6a). Thus, at room temperature and a high strain rate, PPVC exhibits a viscoelastic-viscoplastic behavior. At room temperature and low strain rate (see Figure 6c) and at 85°C at all strain rates (see Figure 6d), PPVC presents a rubbery behavior.

By comparing Figure 6b, Figure 6c and Figure 6d, the temperature sensitivity of PPVC at high strain rate is clearly identified on the evolution of the flow stress. Moreover, the behavior of PPVC gradually changes from an elastic-viscoplastic behavior to a viscoelastic-viscoplastic one, followed by a hyper-viscoelastic behavior [START_REF] Oshmyan | Simulation of small-strain deformations of semicrystalline polymer: Coupling of structural transformations with stress-strain response[END_REF][START_REF] Patlazhan | Structural mechanics of semicrystalline polymers prior to the yield point: a review[END_REF].

Temperature and strain rate sensitivity of material properties

Elastic modulus, yield strain, yield stress, strain at break-point and stress at break-point have been analyzed using the true stress-strain curves presented above. At low strain rates due to the low stiffness of the material, we use the nominal stress-strain curves to determine an accurate value for the elastic modulus and the onset of yield. Young's modulus is calculated from the initial slope of the true (or nominal) stress-strain curves. When the elasticviscoelastic behavior of PPVC is followed by strain softening, the yield stress is taken as the maximum between these two stages. In cases where the stress-strain curves do not show a local maximum, the yield stress is defined as the intersection of the elastic and the plastic slopes.

Temperature sensitivity of material properties at low strain rates

For a better understanding of the temperature sensitivity on the mechanical properties of PPVC, these are plotted in Figure 7. The elastic modulus (see Figure 7a), the yield stress, the stress at break-point (see Figure 7b), the yield strain and the elongation at break-point (see Figure 7c) were plotted. Two strain rates are investigated. Figure 7a shows a non-linear relationship between elastic modulus and temperature. At -30°C, a discrepancy is found for the elastic modulus, due to the proximity of this temperature to the glass transition temperature. Above this temperature, the material is in a rubbery state. A non-linear evolution was observed. At low temperature, and for a strain rate of 0.3 s -1 , the elastic modulus could not be measured due to limitations of the experimental setup. In the rubbery region, between 23°C and 85°C, the experimental data for the two strain rates are superimposed. This means that the strain rate sensitivity of PPVC is not significant in the rubbery region.

The temperature sensitivity of the yield stress and the stress at break-point is plotted in Figure 7b. The yield stress decreases non-linearly as the temperature increases and it increases with the strain rate. The stress at break-point increases when the temperature increases or when the strain rate decreases. At 85°C, the samples did not break and the maximum displacement of the testing machine is reached before material failure. The strain rate sensitivity of PPVC is considerable at low temperature.

In Figure 7c, the temperature sensitivity of the yield strain and the elongation at breakpoint are plotted for two strain rates: 0.03 s -1 and 0.3 s -1 . These properties increase with temperature. The yield strain exhibits a non-linear dependence on temperature, where a change of slope is observed at 0°C. Moreover, the yield strain increases when the strain rate increases. Contrary to the yield strain, the elongation at break-point does not seem to be influenced by the glass transition temperature. As for the stress at break-point, the elongation is linearly dependent on the inverse of the temperature.

The miscibility of plasticizers with PVC results in the formation of a physical network between the two materials. The plasticizer in this network [START_REF] Pitaae | Mechanical properties evaluation of PVC/plasticizers and PVC/thermoplastic polyurethane blends from extrusion processing[END_REF] causes chain slippage and consequently high elongation at break-point for plasticizer components in blends [START_REF] Varughese | Tensile and tear failure of plasticized poly (vinyl chloride)/epoxidized natural rubber miscible blends[END_REF].

All results presented in these sections comes from a set of data. Thus, all include standard deviation. However, it can appear, for some results, very small standard deviation which are not visible on the figures.

Strain rate sensitivity of material properties

The strain rate dependence of the elastic modulus, yield stress and yield strain at three temperatures (-30°C, 23°C, 85°C) are presented in Figure 8a, Figure 8b and Figure 8c, respectively. -30°C is close to the glass transition temperature, while 23°C and 85°C are in the rubbery region. At high strain rates and 85°C, these material properties are not reported due to the hyper-elastic behavior of the material for these coupled conditions.

In Figure 8a, we observe a major discrepancy of the elastic modulus at high strain rates.

This phenomenon is due to the strong strain rate sensitivity of the elastic modulus in the glass transition region and a non-optimal dynamic equilibrium. Between quasi-static and dynamic loadings, an increase of the elastic modulus is observed.

Figure 8b shows an increase of yield stress when the temperature decreases and the strain rate increases. At 23°C, the yield stress is bi-linearly dependent on the log of the strain rate. A drop in yield stress is observed between -30°C and 23°C due to the passage of the glass transition region.

In Figure 8c, the strain rate dependency of the yield strain is plotted for the three temperatures tested. At low strain rates, the yield strain increases when the temperature and strain rate increase. However, at high strain rates, for the two temperatures considered (-30°C and 23°C), the yield strain increases when the strain rate increases but decreases when the temperature increases. Two assumptions can be formulated to explain this change of yield strain mechanical behavior between low and high strain rates. Firstly, we can consider that the modification in behavior is due to the change of behavior between quasi-static and dynamic loading upon the glass transition to a glassy region at -30°C and from rubbery to a glass transition region at 23°C. Secondly, the change of behavior could be due to an increase of viscoelasticity at 23°C, as observed in Figure 6. The same level of yield strain is obtained for the couples (low strain rates, 30°C) and (high strain rates, 23°C), as shown in Figure 8c. At 85°C, in the rubbery region, a major discrepancy is observed due to the hyper-elastic behavior of the material at this temperature.

Modelling

Storage modulus

Several models described in the literature allow the evolution of the storage modulus from the glassy region to the rubbery region to be modelled [START_REF] Mahieux | Property modeling across transition temperatures in polymers: a robust stiffness-temperature model[END_REF][START_REF] Mahieux | Property modeling across transition temperatures in polymers: application to thermoplastic systems[END_REF][START_REF] Richeton | A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures[END_REF][START_REF] Dupaix | Constitutive modeling of the finite strain behavior of amorphous polymers in and above the glass transition[END_REF]. Among them, the model developed by Mahieux and Reifsnider [START_REF] Mahieux | Property modeling across transition temperatures in polymers: a robust stiffness-temperature model[END_REF][START_REF] Mahieux | Property modeling across transition temperatures in polymers: application to thermoplastic systems[END_REF] and improved by Richeton et al. [START_REF] Richeton | A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures[END_REF] has been validated for a large number of polymers (amorphous and semi-crystalline). The model is based on Weibull statistics to simulate the breakage of the secondary links:

𝐸(𝑇) = (𝐸 1 -𝐸 2 ) exp (-( 𝑇 𝑇 𝛽 ) 𝑚 1 ) + (𝐸 2 -𝐸 3 ) exp (-( 𝑇 𝑇 𝑔 ) 𝑚 2 ) + 𝐸 3 exp (-( 𝑇 𝑇 𝑚 ) 𝑚 3 ) (6)
where 𝐸 1 , 𝐸 2 and 𝐸 3 are the instantaneous moduli of the material at the beginning of each region (glassy, glass transition and rubbery). 𝑇 𝛽 , 𝑇 𝑔 and 𝑇 𝑚 are the temperatures of each transition (secondary relaxation, glass transition and melting temperature) and 𝑚 𝑖 are the Weibull moduli associated with the breakage of the secondary links.

This model is used to simulate the temperature sensitivity of the storage modulus observed at 1 Hz for the DMA test (see Figure 5). The comparison between the DMA experimental results and the numerical predictions are presented in Figure 9 for linear and logarithmic scales. A good agreement is observed between the experimental results and the numerical model calibrated with the parameters described in Table 1.

Yield stress

During recent decades, numerous models [START_REF] Richeton | A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures[END_REF][START_REF] Eyring | Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates[END_REF][START_REF] Robertson | Theory for the Plasticity of Glassy Polymers[END_REF][START_REF] Argon | A theory for the low-temperature plastic deformation of glassy polymers[END_REF][START_REF] Bowden | A molecular model for yield and flow in amorphous glassy polymers making use of a dislocation analogue[END_REF][START_REF] Ree | Theory of Non-Newtonian Flow. I. Solid Plastic System[END_REF] have been developed to model the strain rate and temperature dependencies of the yield stress. These models consider the yield stress as a thermally activated process. They allow modelling of the yield strength of glassy polymers over a wide range of strain rates and temperatures. However, few models allow reproduction of the yield stress in the glass transition and rubbery regions. Among those that do so, the cooperative model developed in our team by Richeton et al. [START_REF] Richeton | A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures[END_REF][START_REF] Richeton | Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress[END_REF] takes into account the drop of yield strength due to the glass transition temperature.

The cooperative model considers the cooperative jump motions of 𝑛 polymer chain segments. Lower than 𝑇 𝑔 , it takes on the existence of an internal stress 𝜎 𝑖 , structural parameter which depicts the thermal history of the material. Higher than 𝑇 𝑔 , the internal stress is null, allowing the flow of polymer chain segments. Thus, as a function of temperature, the internal stress is defined as [START_REF] Achorn | Comparison of thermal techniques for glass transition measurements of polystyrene and cross-linked acrylic polyurethane films[END_REF]:

𝜎 𝑖 (𝑇) = { 𝜎 𝑖 (0) -𝑚𝑇 𝑖𝑓 𝑇 < 𝑇 𝑔 0 𝑖𝑓 𝑇 ≥ 𝑇 𝑔 (7)
with 𝜎 𝑖 (0) the internal stress at 0K and 𝑚 a material parameter close to 𝜎_𝑖(0) 𝑇 𝑔 ⁄ . According to Fotheringham and Cherry [START_REF] Fotheringham | Comment on "the compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strainrates[END_REF][START_REF] Fotheringham | The role of recovery forces in the deformation of linear polyethylene[END_REF], the yield stress 𝜎 𝑦 is given by:

𝜎 𝑦 =
with Δ𝐻 𝛽 the 𝛽 activation energy, 𝑐 1 , 𝑐 2 the WLF parameters, 𝑅 the gas constant and 𝜀̇0 a preexponential constant.

To build the master curve for the yield stress, a referenced temperature 𝑇 𝑟𝑒𝑓 is chosen and the time/temperature superposition principle is applied. The horizontal and vertical shifts are

In Figure 10, the master curve is built at -30°C using the parameter presented in Table 2. An important dispersion of the experimental results is observed at high strain rates. However, a good agreement between experimental results and the numerical prediction can still be observed from quasi-static to dynamic strain rates. quasi-static tests and from glassy region to rubbery region for dynamic range, all the spectrum of behavior is analyzed. In the investigated range of temperature and strain rate, elastic modulus, yield stress and yield strain exhibit a non-linear behavior with a change of slope around 0°C (peak of the tan δ curve). In the case of the stress at break and elongation at breakpoint, linear evolution is observed in the studied temperature range. Modelling of the storage modulus and yield stress were also performed and a good agreement was found between the numerical prediction and the experimental results.

Figure 1 :

 1 Figure 1: SEM micrographs of a) the fractured surface of virgin material, and b) after quasi-static tensile tests and c, d, e) gradual magnification of b) highlighting the presence of cubic clusters near the porosity.

Figure 2 :

 2 Figure 2: a) Identification of three microstructures in the PPVC studied and b) X-ray patterns of these three zones.

Figure 3 :

 3 Figure 3: Thermogravimetric curves of the PPVC sheets for each thickness.

Figure 4 :

 4 Figure 4: DSC thermograms for the two courses and three samples.A second endothermic peak appears around +65°C on the first scan. According to the results of Wang et al.[START_REF] Wang | Characterization and Constitutive Modeling of a Plasticized Poly(vinyl Chloride) for a Broad Range of Strain Rates[END_REF], this value corresponds to the glass transition temperature of unplasticized PVC. This result is in agreement with the open literature[START_REF] Altenhofen Da Silva | Polyvinylchloride (PVC) and natural rubber films plasticized with a natural polymeric plasticizer obtained through polyesterification of rice fatty acid[END_REF][START_REF] Lindström | Environmentally friendly plasticizers for poly(vinyl chloride)-Improved mechanical properties and compatibility by using branched poly(butylene adipate) as a polymeric plasticizer[END_REF] Indeed, it is well-known that the type and percentage of plasticizer lead to a drop in the glass transition temperature. The second scan curve is straight, suggesting complete miscibility between PVC and plasticizers.

Figure 5 :

 5 Figure 5: DMA curve plotted at 1 Hz.

Figure 6 :

 6 Figure 6: Experimental true stress-true strain curves under uniaxial quasi-static tensile loading and dynamic compressive loadings. a) Temperature sensitivity at 0.03s -1 . Strain rate sensitivity at b) -30°C, c) 23°C and d) 85°C.

Figure 7 :

 7 Figure 7: Temperature sensitivity at 𝜺̇= 𝟎. 𝟎𝟑 𝒔 -𝟏 and at 𝜺̇= 𝟎. 𝟑 𝒔 -𝟏 a) elastic modulus, b) yield stress and stress at break and c) yield strain and elongation at break.

Figure 8 :

 8 Figure 8: Strain rate sensitivity at three temperatures (-30°C, 23°C, 85°C) a) elastic modulus, b) yield stress and c) yield strain.

Figure 9 :

 9 Figure 9: Numerical modelling of the storage modulus. Comparison between experimental results and numerical prediction in a) linear and b) logarithmic scale.

Figure 10 :Table 2 :

 102 Figure 10: Master curve built at -30°C for the PPVC tested in uniaxial tension for low strain rates and uniaxial compression for high strain rates. Table 2: Model parameters for the cooperative model used to build the master curve at -30°C. 𝚫𝑯 𝜷 (kJ/mol)

Table 1 : Model parameters for the storage modulus (eq. (1) 𝑬

 1

	𝒎 𝟏	𝒎 𝟐	𝒎 𝟑

𝟏 (MPa) 𝑬 𝟐 (MPa) 𝑬 𝟑 (MPa) 𝑻 𝜷 (K) 𝑻 𝒈 (K) 𝑻 𝒎 (K)

  with 𝑘 the Bolzmann constant, 𝑇 the absolute temperature, 𝜀̇ the strain rate, 𝑉 the activation volume, 𝜀̇ * the characteristic strain rate and 𝑛 describing the cooperative character of the yield process. The temperature sensitivity of the characteristic strain rate is defined by:

			𝜎 𝑖 (𝑇) +	2𝑘𝑇 𝑉	sinh -1 (	𝜀ε ̇ * (𝑇)	1/𝑛 )	(8)
	𝜀̇ * =	{	𝜀̇0 exp (-𝜀̇0 exp (-	𝛥𝐻 𝛽 𝑅𝑇 𝛥𝐻 𝛽 ) 𝑅𝑇 𝑔 ) exp (	ln 10 𝑐 1 (𝑇 -𝑇 𝑔 ) 𝑐 2 + 𝑇 -𝑇 𝑔	𝑖𝑓 𝑇 < 𝑇 𝑔 ) 𝑖𝑓 𝑇 ≥ 𝑇 𝑔

Acknowledgements

The authors thank Professor Christophe Fond and Assistant Professor Rigoberto Ibarra for their helpful discussions.