Erika Páez
email: erika_paezv@hotmail.com

Janne K Valkonen

Keith R Willmott3

Pável Matos-Maraví4

Marianne Elias1

Johanna Mappes

Hard to catch: Experimental evidence supports evasive mimicry

Keywords:

Most research on aposematism has focused on chemically defended prey but signalling difficulty of capture remains poorly explored. Similar to classical Batesian and Müllerian mimicry related to distastefulness, such "evasive aposematism" may also lead to convergence in warning colours, known as evasive mimicry. A prime candidate group for evasive mimicry are Adelpha butterflies, which are agile insects and show remarkable colour pattern convergence. We tested the ability of naïve blue tits to learn to avoid and generalise Adelpha wing patterns associated with difficulty of capture, and compared their response to that of birds that learned to associate the same wing patterns with distastefulness. Birds learned to avoid all wing patterns tested, and generalised their aversion to other prey to some extent, but learning was faster with evasive prey compared to distasteful prey. Our results on generalisation agree with longstanding observations of striking convergence in wing colour patterns among Adelpha species since, in our experiments, perfect mimics of evasive and distasteful models were always protected during generalisation and suffered the lowest attack rate. Moreover, generalisation on evasive prey was broader compared to that on distasteful prey. Our results suggest that being hard to catch may deter predators at least as effectively as distastefulness. This study provides empirical evidence for evasive mimicry, a potentially widespread but poorly understood form of morphological convergence driven by predator selection.

BACKGROUND

Many organisms with chemical, morphological or behavioural defences often display a conspicuous signal, such as a colour pattern, that warns predators of the potential cost of attacks [1]. Possession of such warning signals is known as aposematism [1,[START_REF] Cott | Adaptive coloration in animals[END_REF]. In many cases, the effectiveness of aposematism in terms of prey avoidance depends on the ability of predators to associate the signal with an unpleasant experience (i.e. learning and lasting memory), and to attribute signal properties to different prey individuals (i.e. generalisation, reviewed in [START_REF] Mappes | The complex business of survival by aposematism[END_REF]; [START_REF] Exnerová | Avoidance of aposematic prey in European tits (Paridae): learned or innate?[END_REF][START_REF] Skelhorn | Learning about aposematic prey[END_REF][START_REF] Ruxton | Avoiding attack: the evolutionary ecology of crypsis, warning signals, and mimicry[END_REF]). Aposematic prey are under positive frequency-dependent selection, which can result in convergence of warning signals among co-occurring defended species, known as Müllerian mimicry [START_REF] Muller | Ituna and Thyridia; a remarkable case of mimicry in butterflies[END_REF]. Aposematism and Müllerian mimicry associated with distastefulness have been extensively studied in many taxa [START_REF] Symula | Molecular phylogenetic evidence for a mimetic radiation in Peruvian poison frogs supports a Müllerian mimicry hypothesis[END_REF][START_REF] Saporito | Experimental Evidence for Aposematism in the Dendrobatid Poison Frog Oophaga pumilio[END_REF][START_REF] Marek | A Mullerian mimicry ring in Appalachian millipedes[END_REF][START_REF] Wilson | North American velvet ants form one of the world's largest known Müllerian mimicry complexes[END_REF], and especially so in Lepidoptera [START_REF] Devries | The Butterflies of Costa Rica and Their Natural History[END_REF][START_REF] Brown | Mimicry, aposematism and crypsis in neotropical Lepidoptera: the importance of dual signals[END_REF][START_REF] Beccaloni | Ecology, natural history and behaviour of Ithomiine butterflies and their mimics in Ecuador (Lepidoptera: Nymphalidae: Ithomiine)[END_REF][START_REF] Mallet | Mimicry and warning colour at the boundary between races and species[END_REF][START_REF] Willmott | Maintaining mimicry diversity: optimal warning colour patterns differ among microhabitats in Amazonian clearwing butterflies[END_REF]. However, there is increasing evidence that aposematism may also be associated with an alternative defence, namely evasiveness ( [START_REF] Pinheiro | Both Palatable and Unpalatable Butterflies Use Bright Colors to Signal Difficulty of Capture to Predators[END_REF][START_REF] Guerra | Evasive mimicry: too beetle, or not too beetle?[END_REF]; reviewed in [START_REF] Ruxton | Evasive mimicry: when (if ever) could mimicry based on difficulty of capture evolve?[END_REF]). Theoretically, predators should avoid attacking evasive prey since unsuccessful attacks likely represent a significant cost in time and energy [START_REF] Ruxton | Evasive mimicry: when (if ever) could mimicry based on difficulty of capture evolve?[END_REF][START_REF] Hasson | Pursuit-deterrent signals: communication between prey and predator[END_REF][START_REF] Srygley | Incorporating motion into investigations of mimicry[END_REF], similar to that described for prey that signal long handling times [START_REF] Cyriac | Don't waste your time: predators avoid prey with conspicuous colors that signal long handling time[END_REF]. Selection exerted by predators is thus expected to drive convergence in signals that they associate with the evasiveness of their prey [START_REF] Guerra | Evasive mimicry: too beetle, or not too beetle?[END_REF][START_REF] Brower | Experimental studies of mimicry in some North American butterflies[END_REF][START_REF] Van Someren | Some comments on protective resemblance amongst African lepidoptera (Rhopalocera)[END_REF][START_REF] Pinheiro | Palatability and escaping ability in Neotropical butterflies: tests with wild kingbirds (Tyrannus melancholicus, Tyrannidae)[END_REF][START_REF] Pinheiro | Some Possible Cases of Escape Mimicry in Neotropical Butterflies[END_REF][START_REF] Pinheiro | The responses of wild jacamars (Galbula ruficauda , Galbulidae) to aposematic, aposematic and cryptic, and cryptic butterflies in central Brazil[END_REF], in a process known as escape mimicry or evasive mimicry (hereafter we use the latter term).

Previous experiments have shown that bird predators can use visual cues to identify evasive prey [START_REF] Gibson | Batesian mimicry without distastefulness?[END_REF][START_REF] Gibson | The role of escape in mimicry and polymorphism: I. The response of captive birds to artificial prey[END_REF][START_REF] Hancox | A simulation of evasive mimicry in the wild[END_REF], but more empirical work is needed to test whether outstanding potential examples of evasive mimicry could indeed be the result of selection for such signals related to evasiveness. One such example is the diverse Neotropical butterfly genus Adelpha, where repeated convergence of their apparently conspicuous and contrasting wing patterns among distantly related sympatric species has been interpreted as evidence for mimicry [START_REF] Willmott | The Genus Adelpha: Its Systematics, Biology and Biogeography (Lepidoptera: Nymphalidae: Limenitidini)[END_REF][START_REF] Willmott | Cladistic analysis of the Neotropical butterfly genus Adelpha (Lepidoptera: Nymphalidae), with comments on the subtribal classification of Limenitidini[END_REF][START_REF] Ebel | Rapid diversification associated with ecological specialization in Neotropical Adelpha butterflies[END_REF].

Putative aposematic displays occur in Adelpha butterflies when they are at rest (not perching) with the wings open, and during flight as well, which involves short bursts of wing beats and longer periods of gliding i.e., with the wings open and horizontal).

Mimicry in Adelpha has been hypothesized to be at least partly driven by chemical defences in some species [START_REF] Aiello | Adelpha (Nymphalidae): deception on the wing[END_REF][START_REF] Finkbeiner | Frequency dependence shapes the adaptive landscape of imperfect Batesian mimicry[END_REF][START_REF] Hill | Adult Feeding as a Potential Mechanism for Unprofitability in Neotropical Adelpha (Limenitidini, Limenitidinae, Nymphalidae)[END_REF], but there is currently limited, conflicting evidence for distastefulness [START_REF] Pinheiro | Palatability and escaping ability in Neotropical butterflies: tests with wild kingbirds (Tyrannus melancholicus, Tyrannidae)[END_REF][START_REF] Finkbeiner | Frequency dependence shapes the adaptive landscape of imperfect Batesian mimicry[END_REF][START_REF] Chai | Predation and the Flight, Morphology, and Temperature of Neotropical Rain-Forest Butterflies[END_REF][START_REF] Finkbeiner | Complex dynamics underlie the evolution of imperfect wing pattern convergence in butterflies[END_REF]. In contrast to most classic groups of chemically defended butterflies, Adelpha butterflies have short and stout thoraxes which are favourable traits for strong flight [START_REF] Chai | Predation and the Flight, Morphology, and Temperature of Neotropical Rain-Forest Butterflies[END_REF][START_REF] Srygley | Correlations of the Position of Center of Body Mass With Butterfly Escape Tactics[END_REF], and exhibit an irregular flight with sharp turns and powered dives when pursued by avian predators (K.W., personal observations, [START_REF] Srygley | Incorporating motion into investigations of mimicry[END_REF]), making the genus a prime candidate for evasive mimicry [START_REF] Mallet | Individual selection, kin selection, and the shifting balance in the evolution of warning colours: the evidence from butterflies[END_REF]. Moreover, species resembling Adelpha exist in distantly related lineages (e.g., females from the genus Doxocopa, belonging to a different subfamily [START_REF] Srygley | Incorporating motion into investigations of mimicry[END_REF][START_REF] Willmott | The Genus Adelpha: Its Systematics, Biology and Biogeography (Lepidoptera: Nymphalidae: Limenitidini)[END_REF]), whereas closely related, allopatric Adelpha species may harbour different wing colour patterns, suggesting convergence rather than inheritance from a shared ancestor [START_REF] Willmott | Cladistic analysis of the Neotropical butterfly genus Adelpha (Lepidoptera: Nymphalidae), with comments on the subtribal classification of Limenitidini[END_REF][START_REF] Ebel | Rapid diversification associated with ecological specialization in Neotropical Adelpha butterflies[END_REF][START_REF] Mullen | Rapid diversification and not clade age explains high diversity in neotropical Adelpha butterflies[END_REF].

In this study, we use artificial prey models based on common Adelpha wing patterns and wild blue tits as naïve bird predators to address the following questions: 1. Can birds learn to associate wing colours and patterns with evasiveness of prey? 2. Can such a signal be generalised across putative mimetic species? 3. What type of defence drives faster learning by predators, evasiveness or distastefulness?

MATERIALS AND METHODS

We used wild blue tits (Cyanistes caeruleus) to examine whether birds learn to avoid Adelpha colour patterns associated with evasive (escaping) behaviour, and whether birds generalise the learned avoidance across similar, naturally occurring wing patterns. In addition, we conducted parallel experiments with distasteful prey having the same colour pattern but not evasiveness. European blue tits were chosen as predators because: 1) they have no previous experience with wing colour patterns displayed by Neotropical Adelpha butterflies, 2) they have been used extensively in learning experiments as naïve (and experienced) predators with various types of prey [START_REF] Exnerová | Avoidance of aposematic prey in European tits (Paridae): learned or innate?[END_REF][START_REF] Kikuchi | Selection for multicomponent mimicry: equal feature salience and variation in preferred traits[END_REF][START_REF] Rönkä | Colour alone matters: no predator generalization among morphs of an aposematic moth[END_REF][START_REF] Rojas | Multiple modalities in insect warning displays have additive effects against wild avian predators[END_REF], 3) they are visual foragers and their visual capabilities are well understood [START_REF] Hart | Visual pigments, oil droplets, ocular media and cone photoreceptor distribution in two species of passerine bird: The blue tit (Parus caeruleus L.) and the blackbird (Turdus merula L.)[END_REF][START_REF] Hart | Modelling oil droplet absorption spectra and spectral sensitivities of bird cone photoreceptors[END_REF], and 4) they eagerly catch both stationary prey as well as moving prey (e.g., flying butterflies, JM personal observations). Potential unwanted behaviours of naïve predators (e.g., startling, fleeing prey sooner or no motivation to attack) were controlled first during the pretraining phase in their home aviaries the day before the experiment, and then in the experimental aviaries; an approximate 2-3-hour habituation period was needed until startling, or no motivation to attack disappeared (See electronic supplementary material S1).

Experiments were conducted from January to March 2019 at Konnevesi Research Station in Central Finland, which provided the infrastructure, wildlife research and collection permits, and expertise needed to conduct experiments with wild birds in captivity. Blue tits were captured from feeding sites around the station and were maintained in captivity for a maximum of 10 days. During captivity, they were kept singly in illuminated plywood cages (daily light period of 12 h 30 min) with food and fresh water available ad libitum. After experiments, each bird's sex and age were determined, birds were ringed and released into the site of capture. Our sample comprised individuals of both sexes (51 males and 36 females) and was composed mainly by juveniles (65 out of 87), which likely reflects natural variation in the composition of blue tit winter flocks (JM personal observations, see [START_REF] Smith | Intraspecific Variation in Migratory Pattern of a Partial Migrant, the Blue Tit (Parus caeruleus): An Evaluation of Different Hypotheses[END_REF]). We performed preliminary generalized linear mixed models (GLMMs) to test the effects of sex and age on learning. We did not find any significant effect of sex on learning (Z=0.55; p value= 0.58; CI= 0.82 -1.42), therefore, we excluded the sex factor from further analyses. Although juveniles tended to learn slightly faster than adults (mean±SD number of attacks until learning criterion is achieved: adults 53.1±21.4; juveniles 49.4±20.7), the effect of age on learning was not significant either (Z=1.906; p value= 0.06; CI 0.99 -1.93), in agreement with studies that have not detected a strong age effect in blue tits' learning of novel prey (e.g., [START_REF] Hämäläinen | Social learning within and across predator species reduces attacks on novel aposematic prey[END_REF]). We therefore also excluded the age factor from further analyses.

Artificial prey

Artificial defended prey (4.1 x 2.5 cm) were constructed by printing images (HP Color Laserjet CP2025, regular printer paper) of different wing colour patterns displayed by the species Adelpha salmoneus (orange forewing band), A. cocala (orange and white transverse band), and A. epione (white forewing band; figure 1). These species represent three putatively distinct mimicry rings [START_REF] Willmott | The Genus Adelpha: Its Systematics, Biology and Biogeography (Lepidoptera: Nymphalidae: Limenitidini)[END_REF][START_REF] Ebel | Rapid diversification associated with ecological specialization in Neotropical Adelpha butterflies[END_REF] and were chosen because they differ in colour and pattern. We used these to test if apparently distinct signals may provide protection from predation in evasive mimicry. An entirely dark brown model of a non-defended prey was constructed as a control. To make prey attractive for birds, a piece of almond (reward) was glued to the underside of prey. For distasteful models (see below), almonds were soaked in chloroquine phosphate solution (7%) to give them a bitter taste (following e.g., [START_REF] Ihalainen | Prey community structure affects how predators select for Müllerian mimicry[END_REF]).

Experimental procedures

The experiments took place in experimental aviaries of 49 x 48 x 67 cm. To mimic daylight conditions, aviaries were illuminated with a TRUE-LIGHT Daylight 6000 20W (960 lm) fluorescent light bulbs (these lamps do not emit enough amount of UV to be reflected by our paper models). Each aviary contained a perch and a water bowl. Birds were observed through a one-way glass situated on the front of the aviary. Two plastic prey holders gliding on aluminium profile rails (fixed on both sides of the aviary's floor) allowed simulation of the artificial prey's escaping (see electronic supplementary material, S1-figure 2 and a video is available in S4).

Avoidance learning

We used 87 birds, trained to attack artificial butterflies (see the electronic supplementary material, S1 for details of the training procedure), divided into 3 treatment groups (figure 1). The first two groups were trained to avoid evasive prey and a third group was trained to avoid distasteful prey with the same wing colour pattern as group 2. Before initiating the experiment, birds were habituated to the experimental aviary for at least an hour. In the treatment group where birds were trained to avoid escaping prey, the learning experiments consisted of presenting simultaneously two prey items to the bird, one control and one displaying an Adelpha wing colour pattern. Birds had one opportunity of attack per trial. If they approached the control prey, they were allowed to capture and eat the almond of that prey; if they approached the evasive prey, it was rapidly pulled out of reach (i.e., escaping) when the bird was less than 5 cm from the prey and displaying a clear intention to attack (see electronic supplementary material S1 and video S4). In the treatment group where birds were trained to avoid distasteful prey they were allowed to consume the attacked prey (i.e., distasteful prey and control prey). Training presentations continued for at maximum 80 trials or until the bird attacked an evasive or distasteful prey no more than twice over ten consecutive trials. This learning criterion was important for two reasons: 1) it allowed us to test if some treatments were associated with a faster learning than others; and 2) it ensured that all birds, i.e., "quick" and "slow" learners, reached the same level of knowledge despite encountering different numbers of preys ("quick" learners encountered fewer preys than "slow" learners) which is important for generalisation.

Birds that finished the experiment earlier and were able to continue with the generalisation experiment the same day received a break of at least 2 hours with 3 sunflower seeds offered every 30 minutes before starting the next experiment.

Otherwise, those birds that finished the experiment late in the afternoon were placed back in their home cages and continued with the generalisation experiment the next day. Birds that finished the experiment but did not achieve the learning criterion were not included in the generalisation test.

Generalisation of learned avoidance to other prey (imperfect mimics)

We used only birds that achieved the learning criterion in the previous phase (group 1 n=23 out of 28, group 2 n=25 out of 31, group 3 n=18 out of 28) to test whether and to what extent the previously learned avoidance of warning colouration associated with evasiveness (group 1 and 2) or distastefulness (group 3) can be remembered and generalised to novel wing colour patterns that shared similar features (i.e., either colour or pattern, figure 1). Those novel colour patterns are referred to as imperfect mimics. This phase consisted of a single trial where birds encountered simultaneously four types of prey: a (i) control prey, (ii) the model they have previously learned (which can be regarded as a perfect mimic) and (iii) two imperfect mimics (figure 1). The experiment was finished after the first choice of attack was registered (see electronic supplementary material, S1 for detailed description).

Before starting the experiment, each bird received, on average, a 15-minute habituation period to the new mechanism for presenting prey (see electronic supplemental material, S1 for details), during which three pre-training prey with one sunflower seed were offered. When the three pre-training prey and the sunflower seeds were consumed, the bird was considered ready to start the test.

Statistical analyses

Avoidance learning

We examined whether wing colour pattern affected learning of birds from group 1 (n=28) and group 2 (n=31) by assessing the probability of prey survival within trials. Learning curves and their confidence intervals (figure 2A) were estimated as a function of the interaction between treatments (i.e., groups) and trial ("ggeffects" package version 4.0.3 in RStudio). We performed a generalized linear mixed model (GLMM) ("lme4" package v.1.1.23 in RStudio version v.4.0.2) with a logit link function and binomial distribution. Survival probability of prey within trial was explained by the wing colour pattern (explanatory variable). To account for repeated measurements, bird ID nested within trial was added as random factor. Additionally, we calculated the odds ratio (OR) based on GLMM estimates and its confidence interval (CI) to assess the strength of the effect of different wing patterns.

Comparison of avoidance learning between evasive and distasteful prey

To compare avoidance learning among birds facing aposematic prey signalling for evasiveness and birds facing aposematic prey signalling for distastefulness with the same colour pattern (group 2 and 3, respectively; figure 1), we performed another GLMM following the method above. Survival of prey within trial was explained by the type of prey defence (i.e. evasiveness or distastefulness). Bird ID nested within trial was defined as random factor. Odds ratio based on GLMM estimates and confidence intervals were calculated as well to assess the strength of the effect of type of defence.

Generalisation of learned avoidance to other prey (imperfect mimics)

For each experimental group, to test for differences in attack probabilities between the different types of prey (the control, the model and the two imperfect mimics, figure 1), we calculated the log-likelihood of observing the number of attacks that were recorded on each prey type compared to others in the group as follows (calculation details are in electronic supplementary material, S3.1).

log10(L) = Σi[ai log10(Pi)+ (N-ai) log10(1-Pi)] + K
Where i is one of the four prey types; N is the total number of trials; ai is the number of times a butterfly of type i was attacked; Pi is the attack rate of butterflies of type i and K is a constant term that disappears in model comparisons. This maximum-likelihood method has been used in previous studies to estimate differences in probabilities of attack [START_REF] Willmott | Maintaining mimicry diversity: optimal warning colour patterns differ among microhabitats in Amazonian clearwing butterflies[END_REF] and to investigate mate preference [START_REF] Mérot | Beyond magic traits: Multimodal mating cues in Heliconius butterflies[END_REF].

We explored several scenarios where attack rates of different types of prey could be equal or not (see figure 3 and electronic supplementary material S3.2 for a list of all those scenarios) and calculated the log-likelihood functions of those scenarios. As an example, a scenario where the attack rate on the control is equal to those on the imperfect mimics and higher than that on the perfect mimic means that birds only generalises the learned avoidance to the perfect mimic, and not to the imperfect mimics; a scenario where the attack rate on the perfect mimic is equal to those on the imperfect mimics and lower than that on the control means that birds have fully generalised the learned avoidance to the perfect and imperfect mimics; and a scenario where the attack rate on the imperfect mimics is lower than that on the control but higher than that on the perfect mimic means that birds have partially generalised the learned avoidance to the imperfect mimics, compared to the perfect mimic. Models were selected on the basis of their AICc, which accounts for the number of parameters and the sample size. For each group, the model with the lowest AICc was considered the best. We considered that models within a 2-unit AICc interval from the best model could not be rejected.

RESULTS

Avoidance learning

According to the learning criterion, most birds learned to avoid their evasive prey model: 23 out of 28 birds from group 1 (i.e., orange forewing band) and 29 out of 31 birds from group 2 (i.e., orange/white transverse band). Additionally, 18 out of 28 birds (group 3) learned to avoid the distasteful prey model.

The generalized linear mixed model detected no significant effect of treatments on predicted survival probabilities within trials (Z=0.01; P=0.992) (OR=1.002; CI 0.736 -1.362) for group 1 and group 2, i.e., birds that learned to avoid different wing patterns of evasive prey. For group 2 and 3, (birds that learned to avoid evasive or distasteful prey that harboured the same pattern) a significant effect of treatment on predicted survival probabilities within trials was detected (Z=3.60; P=0.0003). Birds were 1.6 times more likely to attack distasteful prey than evasive prey (OR=1.640; CI=1.248 -2.159) (figure 2B).

Generalisation of learned avoidance to other prey (perfect and imperfect mimics)

Bird attack frequencies on mimics differed within and among groups (figure 4, electronic supplementary material S2). For group 1 (prey with orange forewing band as evasive model, figure 4A, table 1), in the best scenario (s5) learned avoidance was fully generalised to the imperfect mimic that shared the orange colour with the model (orange/white transverse band), while the other imperfect mimic (white forewing band, which shares the pattern but no colour with the model) was attacked as much as the control. Two additional scenarios could be considered as similarly plausible based on their AICc. One scenario (s7) was similar to the previous, except that the orange/white imperfect mimic was attacked more often than the perfect mimic (but still less than the control), indicating partial generalisation. In the other scenario (s4), only the perfect mimic was attacked less than the control, implying generalisation only to the perfect mimic.

Regarding group 2, (orange/white as evasive model) (figure 4B, table 1), in the best scenario (s3) avoidance was fully generalised to both imperfect mimics, which both shared a colour with the model. Another scenario (s6), where generalisation to the mimics was partial, was within a 2-unit AICc interval with that of the best scenario. In group 3 (orange/white as distasteful model) (figure 4C, table 1), a single scenario stood out as best, in which avoidance was fully generalised to the orange imperfect mimic (s5). See results from all the explored scenarios in electronic supplementary material S3.3.

DISCUSSION

Learning and generalisation of signals associated with an effective escaping ability

The idea that some butterflies have evolved signalling of evasiveness as an antipredator defence has a long history [START_REF] Srygley | Incorporating motion into investigations of mimicry[END_REF][START_REF] Van Someren | Some comments on protective resemblance amongst African lepidoptera (Rhopalocera)[END_REF][START_REF] Lindroth | Disappearance as a Protective Factor. A supposed case of Batesian mimicry among beetles (Coleoptera: Carabidae and Chrysomelidae)[END_REF][START_REF] Holm | Pre-adaptation and speed mimicry among Namib Desert scarabaeids with orange elytra[END_REF][START_REF] Srygley | Locomotor mimicry in butterflies? 1994 The associations of positions of centres of mass among groups of mimetic, unprofitable prey[END_REF]. Still, surprisingly few experiments to date have tested the idea of evasive mimicry [START_REF] Pinheiro | Palatability and escaping ability in Neotropical butterflies: tests with wild kingbirds (Tyrannus melancholicus, Tyrannidae)[END_REF][START_REF] Gibson | Batesian mimicry without distastefulness?[END_REF][START_REF] Gibson | The role of escape in mimicry and polymorphism: I. The response of captive birds to artificial prey[END_REF][START_REF] Hancox | A simulation of evasive mimicry in the wild[END_REF]. It is therefore unclear whether predators can learn, memorize and generalise naturally occurring signals associated with evasiveness, which is crucial for the evolution of evasive mimicry. Gibson [START_REF] Gibson | Batesian mimicry without distastefulness?[END_REF][START_REF] Gibson | The role of escape in mimicry and polymorphism: I. The response of captive birds to artificial prey[END_REF] and Hancox & Allen [START_REF] Hancox | A simulation of evasive mimicry in the wild[END_REF] presented wild avian predators with artificial prey (i.e. dyed millet seeds, coloured mealworms or pastry models) that disappeared from sight when attacked. After extensive training (approx. 20 days), they observed that birds reduced their attacks on such hard-to-catch prey. We showed that wild birds, with no experience of Adelpha butterflies, were able to associate both orange and orange/white patterns with evasiveness within a day of training. Unlike previous experiments [START_REF] Gibson | Batesian mimicry without distastefulness?[END_REF][START_REF] Gibson | The role of escape in mimicry and polymorphism: I. The response of captive birds to artificial prey[END_REF][START_REF] Hancox | A simulation of evasive mimicry in the wild[END_REF], our birds faced a "simpler" prey scenario [START_REF] Ihalainen | Prey community structure affects how predators select for Müllerian mimicry[END_REF], with a warningly coloured prey that could be easily discriminated from the non-defended prey, which may explain the reported faster avoidance learning compared to previous studies. In our experiment, birds were more likely to attack the control prey than the aposematic prey in the first trial of the learning phase. This is not surprising since wild birds often avoid colourful prey [START_REF] Ham | Does colour matter? The importance of colour in avoidance learning, memorability and generalisation[END_REF] and part of this bias seems to have a genetic basis [START_REF] Lindstrom | Reactions of hand-reared and wild-caught predators toward warningly colored, gregarious, and conspicuous prey[END_REF]. However, our data provide evidence for additional learning on the top of this initial preference since our learning criterion (no more than two attacks in ten consecutive trials) implies that birds that fulfilled this criterion were at least four times more likely to attack control over aposematic butterflies, which is much more than the initial bias (see electronic supplementary material S5).

Our results showed that birds were often able to generalise their learned avoidance to somewhat similar prey that shared either a colour or the pattern with the learned model. Perfect mimics were always strongly avoided but often at a level that could not be distinguished from those of the imperfect mimics. Previous work on distasteful prey found that learning and generalisation of aposematic visual signals by avian predators are primarily driven by colour rather than pattern [START_REF] Rönkä | Colour alone matters: no predator generalization among morphs of an aposematic moth[END_REF][START_REF] Aronsson | Domestic chicks primarily attend to colour, not pattern, when learning an aposematic coloration[END_REF][START_REF] Chittka | Cognitive dimensions of predator responses to imperfect mimicry[END_REF][START_REF] Arias | Crossing fitness valleys: empirical estimation of a fitness landscape associated with polymorphic mimicry[END_REF][START_REF] Finkbeiner | Warning signals are seductive: relative contributions of color and pattern to predator avoidance and mate attraction in Heliconius butterflies[END_REF] and wing shape [START_REF] Kazemi | Stimulus Salience as an Explanation for Imperfect Mimicry[END_REF]. Our findings are consistent with these studies for group 2 and partially for group 3 because birds generalised their avoidance to prey that presented a colour in common with the formerly learned model (orange imperfect mimic and white imperfect mimic for group 2; only to orange imperfect mimic for group 3), despite harbouring different wing patterns. Generalisation to imperfect mimics is supported with prey models from groups 2 and 3

(generalisation to only one imperfect mimic in the latter case). Generalisation to imperfect mimics was unclear for group 1 as results were mixed, possibly due to relatively low sample size and reduced statistical power. The different plausible scenarios for group 1 showed that avoidance was always generalised to the perfect mimic, was never generalised to the white imperfect mimic, and was sometimes generalised to the orange/white imperfect mimic, depending on the scenario. Overall, we showed that birds generalised their learnt association to evasive preys, although the cues used in generalisation remain unclear. Further experiments comparing models with different colours could shed light on whether some colours are better learned and/or generalised than others. The three Adelpha species we studied are not regarded as strongly co-mimetic, since a number of other species show much more similar (practically identical) colour patterns, concordant geographic variation and broader sympatry [START_REF] Willmott | The Genus Adelpha: Its Systematics, Biology and Biogeography (Lepidoptera: Nymphalidae: Limenitidini)[END_REF]. Preliminary trials from a pilot test suggested that our predators were incapable of distinguishing among the most closely resembling co-mimics of Adelpha cocala (e.g., Adelpha thesprotia, see electronic supplementary material S1-figure 4), so we expanded our experiment to include more dissimilar species to examine the significance of mimetic accuracy. Our mixed generalisation results do not allow us to assess the extent of selection on mimetic fidelity in Adelpha. However, we

show that perfect mimicry is at least as good as imperfect mimicry when providing protection to co-mimics since the model (perfect mimic) was always less attacked than the other mimics, although not always significantly so. Future work might include other aspects such as prey community structure, or the predator's level of hunger, that might affect prey mimetic fidelity, as has been studied in classical aposematism based on chemically defended prey [START_REF] Ihalainen | Prey community structure affects how predators select for Müllerian mimicry[END_REF][START_REF] Hetz | Predation pressure on an imperfect Batesian mimicry complex in the presence of alternative prey[END_REF][START_REF] Beatty | The evolution of müllerian mimicry in multispecies communities[END_REF][START_REF] Arias | Inter-species variation in unpalatability does not explain polymorphism in a mimetic species[END_REF].

In the case of Adelpha, it would be especially insightful to assess avoidance learning associated with evasiveness in the wild by their natural predators.

Neotropical passerine birds tend to live longer than higher-latitude birds [START_REF] Muñoz | Age effects on survival of Amazon forest birds and the latitudinal gradient in bird survival[END_REF],

which potentially means that they can learn more effectively and pay attention to finer signal details, and thus generalise less broadly to other similar prey. It is also important to keep in mind that not only the community structure of predators (see e.g., [START_REF] Rönkä | Geographic mosaic of selection by avian predators on hindwing warning colour in a polymorphic aposematic moth[END_REF]), but also prey communities influence the outcome of avoidance learning and generalisation of distasteful prey [START_REF] Ihalainen | Prey community structure affects how predators select for Müllerian mimicry[END_REF].

Evasiveness versus distastefulness as deterrents to predators

Learning about distastefulness is thought to be generally quicker and easier than evasiveness because prey unprofitability can be determined, unambiguously, from a single experience when prey is ingested. By contrast, a prey individual might escape capture because of better escaping ability, or just because of chance [START_REF] Ruxton | Evasive mimicry: when (if ever) could mimicry based on difficulty of capture evolve?[END_REF]. There is thus some disagreement about the circumstances under which evasive aposematism and mimicry might occur and the extent to which its evolution might be different from that of aposematism and mimicry based on distastefulness [START_REF] Ruxton | Avoiding attack: the evolutionary ecology of crypsis, warning signals, and mimicry[END_REF].

In our experiments, in contrast to expectations [START_REF] Ruxton | Evasive mimicry: when (if ever) could mimicry based on difficulty of capture evolve?[END_REF], birds learned to avoid evasive prey faster than distasteful prey, and learning seemed to be easier as a higher proportion of birds achieved the learning criterion with evasive prey (94%) compared to distasteful prey (63%). It is well known that distastefulness of aposematic prey widely varies within and between populations [START_REF] Ritland | Comparative unpalatability of mimetic viceroy butterflies (Limenitis archippus) from four south-eastern United States populations[END_REF][START_REF] Brower | Ecological Chemistry and the Palatability Spectrum[END_REF], and that there is intra-and interspecific variation in predator's tolerance to distastefulness [START_REF] Arias | Inter-species variation in unpalatability does not explain polymorphism in a mimetic species[END_REF][START_REF] Pinheiro | Does Müllerian Mimicry Work in Nature? Experiments with Butterflies and Birds (Tyrannidae)[END_REF][START_REF] Terhune | Components of a visual stimulus used by scrub jays to discriminate a batesian model[END_REF][START_REF] Endler | Predator Mixes and the Conspicuousness of Aposematic Signals[END_REF][START_REF] Hämäläinen | Social information use about novel aposematic prey is not influenced by a predator's previous experience with toxins[END_REF]. Signals associated with prey evasiveness may actually provide a more reliable message to birds about unprofitability than does aposematic signalling related to distastefulness. Moreover, catching a prey, even if distasteful, can be more rewarding for a predator than missing a prey completely.

It is thus possible that the learning curve for avoiding evasive prey also depends on the physiological needs of a predator (e.g. its hungriness), the costs of pursuing and consuming a prey (i.e., the likelihood to catch, toxicity) and the nutritional benefits associated with a consumed prey. Although capturing an evasive butterfly prey might represent a rich source of nutrients compared to a distasteful prey (i.e., larger thoracic muscles that allow a powerful flight), there might also be a palatability spectrum, which likely affects the cost-benefit ratio.

Future experiments should simulate different scenarios to assess the importance of nutritional value of evasive versus a non-evasive prey in learning to avoid prey.

We also found a wider generalisation to imperfect mimics of the evasive prey when it was compared to that of the distasteful prey (i.e., group 2 versus group 3, where blue tits were trained on the same wing colour pattern). In group 2 (evasive treatment), in two out of three best scenarios birds generalised to some extent their learned avoidance toward the prey sharing any of the wing colours with the model, and both imperfect mimics were attacked less than the control.

By contrast, in group 3 (distasteful treatment), birds only avoided the orange imperfect mimic, as the white imperfect mimic was highly attacked, despite the fact that the white colour was also present in the model. It has been suggested

that selection for accurate mimicry can be affected by different factors [START_REF] Ruxton | Avoiding attack: the evolutionary ecology of crypsis, warning signals, and mimicry[END_REF] such as level of prey distastefulness or unpleasantness [START_REF] Duncan | Sensory discrimination and its role in the evolution of batesian mimicry[END_REF][START_REF] Goodale | The effect of distastefulness of the model on the predation of artificial batesian mimics[END_REF]. Although broad generalisation to imperfect mimics probably occurs when the model is highly distasteful or unpleasant (see in [START_REF] Lindstrom | Imperfect Batesian mimicrythe effects of the frequency and the distastefulness of the model[END_REF]), our results suggest that evasiveness is another powerful dimension of defence that affects a predator's decision whether to attack warningly coloured prey. Given that a wider generalisation was supported with some prey models, more experiments with different types of predators and signals are needed to examine whether generalisation tends to be broader across mimics where the model is defended by evasiveness rather than distastefulness or toxicity. In addition, a follow-up study to assess the memorability of naturally occurring signals of evasive prey (see [START_REF] Brower | Locomotor Mimicry in butterflies? A critical review of the evidence[END_REF]) and compare it to that associated to distasteful prey would be very insightful.

CONCLUSION

Although distastefulness has been considered a prime adaptive defence mechanism against predation in aposematic butterflies, evasiveness is also likely to be important in many groups. Our results give a strong experimental support for the hypothesis, mostly based on field observations, that predators can learn and generalise to some extent naturally occurring colour pattern signals that are associated with the escaping ability of prey. We therefore suggest that evasive mimicry could be a plausible explanation for colour pattern convergence in fast moving prey, such as Adelpha butterflies.

Ethics.

Figure 1 .

 1 Figure 1. Schematic illustration of the experimental design that consisted of 3 phases: pretraining, learning and generalisation. A forewing orange-banded prey (A. salmoneus) was presented as a model and perfect mimic for group 1, and as an imperfect mimic during generalisation for group 2 and 3. A transverse forewing orange/hindwing white-banded prey (A. cocala) was the model and perfect mimic for group 2 and 3, and an imperfect mimic during generalisation for group 1. The forewing white-banded prey (A. epione) was presented as an imperfect mimic during generalisation for all groups.

Figure 2 .

 2 Figure 2. Predicted probability of prey survival among trials. Each curve illustrates predicted values with their 95% confidence intervals (bands) for birds attacks on prey per group and among trials. Each plot shows the comparison between (A) group 1 versus group 2; and (B) group 2 (evasiveness) versus group 3 (distastefulness). The plotted data were derived from the generalized linear mixed models.

Figure 3 .

 3 Figure 3. Scenarios investigated based on attack rates from the generalisation experiment (group 1 is used as an example).

Figure 4 .

 4 Figure 4. Comparison among observed attack rates during generalisation tests. Bars illustrate proportion of attacks within groups on the control (black coloured bar), different putative mimics (grey coloured bars) and the perfect mimic (orange coloured bar) after birds learned to avoid the model pattern. Number of attacks are indicated inside the bars (at the top of the bars), as well as standard error bars. Birds from group 1 (A) learned evasive orange prey as the model; group 2 (B) learned orange/white as the model; and group 3 (C) learned distasteful orange/white as the model.

Table 1 .

 1 Best scenarios from generalisation based on the AICc value. Scenarios within a 2-unit AICc interval with that of the best scenario are considered plausible as well.

	Best scenario	Alternative scenarios

  The Southwest Finland Centre for Economic Development, Transport and Environment (VARELY/294/2015) and National Animal Experimental Board (ESAVI/9114/04.10.07/2014) provided permission to capture and keep wild blue tits (Cyanistes caeruleus) in captivity and to use them in behavioural studies.

Acknowledgments. We acknowledge Helinä Nisu for taking loving care of birds and Konnevesi Research Station for facilities to conduct this experiment. EPV and ME thank Christine Calvas from the Center of Ecology and Conservation Sciences for kindly handling the funding that allowed EPV to travel to Konnevesi.

EPV thanks to Sebastián Mena for designing figure 2 (electronic supplementary material). PMM thank the support of the Department of Ecology (Biology Centre, CAS) and its head, Vojtěch Novotný, for partly covering travel expenses to carry out the behavioural experiments. We thank the organizers of the 8th International Conference on the Biology of Butterflies, held in Bangalore, India, in 2018, where the idea of this project emerged.

Footnotes. Electronic supplementary material is available online in Figshare:

Funding. This study was funded by The Academy of Finland (project no.

319124), and additionally supported by the Doctoral School 227 Muséum

National d'Histoire Naturelle -Sorbonne Université (TRANSHUMANCE mobility grant for EPV), and Secretaría de Educación Superior, Ciencia, Tecnología e Innovación Senescyt (graduate fellowship to EPV). PMM. was funded by the Czech Science Foundation (Junior GAČR grant GJ20-18566Y) and the PPLZ program of the Czech Academy of Sciences (fellowship grant L200961951)

Data accessibility

The dataset and coding necessary to reproduce the results of this study are available in the Dryad Digital Repository (doi:10.5061/dryad.vq83bk3rj).

Author's contribution. JM, KRW, ME and PMM conceived the project. JM, EPV, JV, designed the experimental setup, with input from KRW and ME. EPV, JV, PMM and JM ran the experiments. EPV, JV and ME performed statistical analyses. All authors discussed the protocol and results throughout the study.

EPV wrote the paper with contributions from all authors. All authors gave final approval for publication and agree to be held accountable for the work performed therein.

Competing interests. We declare we have no competing interests


F Cervantes-Alvarez

J A Ramirez-Rincon

J D Macias

N W Pech-May

Jose Ordonez-Miranda

J J Alvarado-Gil

I Y Forero-Sandoval

Percolation threshold of the thermal, electrical and optical properties of carbonyl-iron microcomposites

Keywords: Thermal conductivity, Electrical conductivity, Emissivity, Thermal percolation threshold, Electrical percolation threshold

Introduction

The incorporation of metallic or semiconductor fillers in a polymeric matrix enhance its mechanical, thermal, electric and optical performance. Additionally, the ability of such composites, to be molded and adapted has rapidly increased their use over the last decades, having applications in compact electronic devices [START_REF] Zweben | Advances in composite materials for thermal management in electronic packaging[END_REF], conducting adhesives [START_REF] Kim | The effects of functionalized graphene nanosheets on the thermal and mechanical properties of epoxy composites for anisotropic conductive adhesives (ACAs)[END_REF], anti-static materials [START_REF] Li | Improving the antistatic ability of polypropylene fibers by inner antistatic agent filled with carbon nanotubes[END_REF], electromagnetic interference shielding [START_REF] Zhang | High dielectric constant and low dielectric loss hybrid nanocomposites fabricated with ferroelectric polymer matrix and BaTiO 3 nanofibers modified with perfluoroalkylsilane[END_REF][START_REF] Wang | Effects of interfaces between adjacent layers on breakdown strength and energy density in sandwich-structured polymer composites[END_REF], among many others [START_REF] Huang | Aligned Carbon Nanotube Composite Films for Thermal Management[END_REF][START_REF] Vadivelu | Polymer composites for thermal management: a review[END_REF][START_REF] Prasher | Thermal Interface Materials: Historical Perspective, Status, and Future Directions[END_REF]. Also, it is possible to produce light-weight and high-strength composite foams with an excellent electrical conductivity and EMI shielding properties [START_REF] Fei | Highstrength, flexible and cycling-stable piezo-resistive polymeric foams derived from thermoplastic polyurethane and multi-wall carbon nanotubes[END_REF][START_REF] Ju | Lightweight multifunctional polypropylene/carbon nanotubes/carbon black nanocomposite foams with segregated structure, ultralow percolation threshold and enhanced electromagnetic interference shielding performance[END_REF][START_REF] Kuang | Facile preparation of lightweight high-strength biodegradable polymer/multi-walled carbon nanotubes nanocomposite foams for electromagnetic interference shielding[END_REF]. On the other hand, heat and electronic transport in these systems is a complex phenomena, that depends on many factors, such as the thermal and electrical properties of the matrix and fillers, their concentration, distribution, orientation, size, shape, as well as on the matrix-filler interface thermal and electrical resistance [START_REF] Lebovka | Scaling in percolation behaviour in conductive-insulating composites with particles of different size[END_REF][START_REF] Lee | Enhanced thermal conductivity of polymer composites filled with hybrid filler[END_REF].

In this kind of composites as the concentration of fillers increases, some of these physical properties changes smoothly, but as soon as a percolation threshold (v p ) is reached, those physical properties exhibit significant changes due to the formation of conducting networks [START_REF] Clerc | La percolation[END_REF]. This connectivity of the composite fillers is described as percolation, which usually shows up for sizeable differences between the physical properties of the matrix and fillers [START_REF] Vigolo | An Experimental Approach to the Percolation of Sticky Nanotubes[END_REF]. For instance, when a composite, formed by an electrically insulating matrix is progressively filled with metallic fillers, there will be a certain volume fraction of them, known as percolation threshold, for which the composite will become electrically conductive [START_REF] Kargar | Thermal Percolation Threshold and Thermal Properties of Composites with High Loading of Graphene and Boron Nitride Fillers[END_REF], as is presented in Fig. 1.

Several studies have focused on the thermal and electrical properties of composites, to establish the percolation threshold dependence [START_REF] Kargar | Thermal Percolation Threshold and Thermal Properties of Composites with High Loading of Graphene and Boron Nitride Fillers[END_REF][START_REF] Kim | The experimental determination of the onset of electrical and thermal conductivity percolation thresholds in carbon nanotubepolymer composites[END_REF][START_REF] Yin | Graphene platelets/aluminium nitride metacomposites with double percolation property of thermal and electrical conductivity[END_REF][START_REF] Kwon | A large increase in the thermal conductivity of carbon nanotube/polymer composites produced by percolation phenomena[END_REF][START_REF] Sun | Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites[END_REF]. The electric percolation threshold (v pE ) is more easily found compared with the thermal counterpart (v pT ), because of the difference of thermal conductivities, between the matrix and the fillers is usually not as high as it is for the electrical ones. This is reasonable due to the marked differences in the mechanisms of charge and heat transport [START_REF] Shenogina | On the lack of thermal percolation in carbon nanotube composites[END_REF][START_REF] Biercuk | Carbon nanotube composites for thermal management[END_REF].

Geometrical percolation is reached when the fillers randomly added to a matrix results in a geometrically connected phase [START_REF] Garboczi | Geometrical percolation threshold of overlapping ellipsoids[END_REF] and its concentration v p threshold can be estimated using the excluded volume percolation theory [START_REF] Kim | The experimental determination of the onset of electrical and thermal conductivity percolation thresholds in carbon nanotubepolymer composites[END_REF][START_REF] Balberg | Excluded volume and its relation to the onset of percolation[END_REF], as follows:

()aaaa

where D is a constant related with the excluded volume and AR is the aspect ratio of fillers [START_REF] Kim | The experimental determination of the onset of electrical and thermal conductivity percolation thresholds in carbon nanotubepolymer composites[END_REF]. In the case of spheres D = 2.8, AR = 1 and v p (AR) = 0.30.

Experimentally, however, it is found that the percolation threshold in some cases does not take the same value for the electrical and thermal conductivity, as predicted by Eq. ( 1). [START_REF] Sun | Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites[END_REF]. This work presents a simultaneous experimental characterization of the direct current (DC) electrical conductivity, thermal properties, and infrared emissivity of composites made up of carbonyl-iron spherical particles. These particles are randomly dispersed in a polyester resin matrix, which allows studying the effect of geometric percolation. We find that the percolative behavior of the electrical and thermal conductivities generates increments of 6 orders of magnitude and 9 times, respectively. By contrast, the infrared emissivity exhibits a significant decay of 0.8 times. Our experimental results show shifts of 53% and 26% for the electrical and thermal percolation thresholds, with reference to the ones predicted by Eq. ( 1). On the other hand, the emissivity displays a shift of 38%. These facts indicate that the geometric percolation threshold is a reference point, but the low contrast of the thermal transport between the matrix and the fillers, compared with the electrical one, the interfacial resistance between interfaces, and the phonon scattering produces a deviation from the expected value.

Materials and samples preparation

Materials

A low-cost commercial polyester resin (Poliformas plásticas de México, SA de CV) was used as matrix and a carbonyl-iron particles CIP (Sigma-Aldrich), with an average diameter of 1.67 mm, density of 7.8 gcm -3 , and a thermal conductivity of 80.2 Wm -1 K -1 was used as filler. Micrometric CIP were used due to the high contrast between the thermal and electrical conductivities with respect to the matrix ones. With respect to the emissivity, the carbonyl coating reduces the contrast, nevertheless, it is enough to notice the filling effect. The carbonyl shell avoids oxidation. On the other hand, it is a material widely used in composites due to its narrow size distribution, low-cost, and capability of interaction with external magnetic fields.

Samples preparation

The composites were prepared dispersing carbonyl-iron particles (CIP) in a polyester resin matrix. The liquid composite was mechanically mixed for 15 minutes, until obtaining a homogeneous mixture and later sonicated with an ultrasonic tip (Sonics Vibra-Cell at 65 W, 20 KHz) for 2 minutes. To accelerate the polymerization, a catalyst was added and mixed slowly for 30 seconds, and finally, the sample was deposited in a cylindrical plastic cast. After polymerization, the samples were cut in plates and polished until their diameters and thicknesses were reduced to about 2 cm and 1 mm, respectively. For the thermal characterization, each sample was painted with a thin layer (around 50 µm) of matte black paint, to improve the light absorption and the IR emissivity.

Twelve different samples were prepared and tested with 0, 0.05, 0.12. 0.27, 0.30. 0.33, 0.36, 0.38, 0.41, 0.45, 0.50 and 0.55 vf of CIP. Figures 2a-e show SEM images of some structures formed by the CIP particles, along with a representative histogram of their size distribution. In Figures 2a and2b, it is possible to see that there is a tendency to form clusters of few particles, which are evenly distributed in the matrix. It is reported that during the polymerization process, the dispersion of fillers is strongly dependent on the crystallization, and the fillers and other impurities are rejected from the crystal phase to the amorphous region [START_REF] Tjong | Electrical properties of low-density polyethylene/ZnO nanocomposites: The effect of thermal treatments[END_REF]. However, the employed matrix is an amorphous polyester resin and during polymerization, the fillers keep uniformly dispersed. For the SEM analysis the surfaces were covered by an Au-Pd layer of less than 8 nm of thickness to avoid charge accumulation and correspond to a cut parallel to the symmetry axis of the sample. Note that the particles exhibit a random spatial distribution inside the matrix and an average diameter of 1.67 ± 0.87 µm. 3 Theoretical framework for thermal characterization

Figure 3 shows the two configurations employed to determine the thermal properties of our composites. In both cases, the sample of thickness L is heated by a homogeneous light pulse of intensity Q at z = 0, whose temperature evolution is recorded as a function of time. The thermal diffusivity and thermal effusivity are obtained through the cooling curves recorded for the first (Fig. 3a) and second (Fig. 3b) configurations, respectively. The use of the fluid allows to have a proper contrast between the thermal effusivities of the samples and their backing fluid, for low vf. As thermal effusivity of the polyester resin matrix (550 Ws 1/2 m -2 K -1 [START_REF] Pech-May | Study of the thermal properties of polyester composites loaded with oriented carbon nanofibers using the front-face flash method[END_REF]) increases along with the CIP concentration, it is expected a contrast reduction for high concentrations, which will not allow the simultaneous determination of the thermal diffusivity and thermal effusivity of our samples, as shown by Pech-May et al. [START_REF] Pech-May | Simultaneous measurement of thermal diffusivity and effusivity of solids using the flash technique in the front-face configuration[END_REF]. This is why both thermal properties were measured separately.

Measurement of the thermal diffusivity

Considering that an opaque sample of thickness L, thermal diffusivity α and thermal effusivity e s is uniformly illuminated by a heating pulse of intensity Q during a short time (∼20 ms), as shown in Fig. 3a, the temperature profile at the surface z = 0 can be derived by solving the one-dimensional heat diffusion equation. The Laplace transform of this temperature is given by [START_REF] Pech-May | Study of the thermal properties of polyester composites loaded with oriented carbon nanofibers using the front-face flash method[END_REF]

θ(0) = Q e s √ sτ + h p tanh( √ sτ ) 2h p √ sτ + (sτ + h 2 p ) tanh( √ sτ ) . ( 2
)
where s is the Laplace parameter, τ = L 2 /α, h p = h √ τ /e s and h is the heat transfer coefficient by convection from the solid surfaces in contact with air. Equation (2) depends on the three parameters Q/e s , τ and h p , which can be determined by numerically fitting the obtained inverse Laplace transform of Eq. ( 2) to its corresponding experimental data. The thermal diffusivity α = L 2 /τ is then calculated for a sample of known thickness L and diffusion time τ . Fig. 3 Schemes of the two configurations used for performing the full thermal characterization of the composites with a backing of (a) air and (b) semi-infinite fluid. In both cases, the composite of thickness L is subjected to a short pulse of light with intensity Q, at z = 0, whose temperature evolution in time is recorded. The factor h represents the heat losses by convection.

Measurement of the thermal effusivity

In order to derive an appropriate model to extract the thermal effusivity, it is consider that the opaque samples are in contact with a semi-infinite fluid backing of thermal effusivity e f . The surface at z = 0 is uniformly heated up by a light pulse of intensity Q, for a short time (∼20 ms), as shown in Fig. 3b. Under this condition, the heat conduction in the sample is along the z axis mainly, and the Laplace transform of the temperature at z = 0 is given by [START_REF] Pech-May | Simultaneous measurement of thermal diffusivity and effusivity of solids using the flash technique in the front-face configuration[END_REF]

θ(0) = Q e s √ s 1 + b 21 tanh( √ sτ ) b 21 + hp √ sτ + 1 + hpb21 √ sτ tanh( √ sτ ) (3)
where b 21 = e f /e s and h is the heat transfer coefficient by convection from the illuminated surface to air. Considering into account that τ is a known parameter, the values of the other three unknown ones, Q/e s , b 21 and h p in Eq. ( 3) can be extracted by fitting the inverse Laplace transform of Eq. ( 3) to the corresponding experimental data. The sample thermal effusivity e s = e f /b 21 is then determined, provided that the thermal effusivity of the backing fluid is known. Note that Eq. ( 3) does not reduce to Eq. ( 2) when the fluid backing is replaced by air, because of the different convection contributions shown in Figs. 3a and3b. The inverse Laplace transforms of Eqs. ( 2) and

(3) were numerically calculated by means of the well-known Euler algorithm and fitted to the measured experimental data [START_REF] Abate | A Unified Framework for Numerically Inverting Laplace Transforms[END_REF]. The fittings were done by using the least-squares fitting procedure based on the Levenberg-Marquardt algorithm [START_REF] Marquardt | An Algorithm for Least-Squares Estimation of Nonlinear Parameters[END_REF]. A capacitor (0.2 µF) in parallel with the voltmeter is placed, to filter out any interference that may affect the high impedance of the voltmeter. b) Scheme of the experimental setup used to obtain the thermal conductivity. Samples are heated up by a flash lamp and the temporal evolution of the temperature is recorded by means of an infrared camera. An infrared filter is placed between the flash lamp and the sample to prevent that the IR radiation of the lamp reaches the sample surface. Furthermore, the camera lens is protected with a Ge window placed in front of the camera.

Experimental setups

Electrical conductivity

The experimental setup used to measure the electrical conductivity of our composites is shown in Fig. 4a. On each composite, of resistance R, a pair of electrodes are attached by means of colloidal silver paint (SPI Supplies), to obtain proper electric contact. Then the composite is placed in series with a multimeter (Fluke 79 series III), which must be connected as a voltmeter mode. The DC applied voltage (Keithley 2231A-30-3) V f drops in the internal resistance R m =11.11 MΩ of the multimeter and in the sample of resistance R. The voltage V m , resulting from the drop produced by the circuit resistance, is read at the voltmeter display, the electrical resistance R of the sample is:

R = R m V f -V m V m . (4)
The DC source voltage (V f ) was operated in a range from 30 to 40 V and a capacitor of 0.2 µF was used. The value of the electrical conductivity is determined using the size of the sample and the resistivity measured, namely σ = L/(RA), where L is the thickness of the sample and A is the cross-sectional area.

Thermal properties

The experimental setup used to measure the thermal properties of our composites is shown in Fig. 4b. The sample is heated up by a flash lamp (Speedotron 206VF) working at 4.8 kJ per pulse. The pulse duration extends up to 20 ms with a temporal shape previously discussed [START_REF] Forero-Sandoval | Measurement of the thermal transport properties of liquids using the front-face flash method[END_REF]. An infrared (IR) filter is placed in front of the flash lamp to prevent that its IR radiation reaches the sample surface. The time evolution of the illuminated surface temperature of the sample is recorded with an IR camera (InfraTec 8320) working in the spectral range from 3 to 5 µm. Each pixel in the detector averages the IR emission coming from a square with dimensions of 0.165 × 0.165 mm 2 in the sample surface. Images were recorded at a rate of 250 frames per second. To prevent that the flash lamp radiation reaches the camera lens a Ge window transparent to mid infrared wavelengths is employed, as shown in Fig. 4b.

Results and discussion

Electrical conductivity

Figure 5 shows the electrical conductivity as a function of vf. Each experimental point has been obtained from the average of five measurements and are represented by a gray point. The red line represents the second derivative of the electrical conductivity σ and its maximum represents the electrical percolation threshold v pE at vf = 0.46, which is shown by a green dashed line. A trend line corresponds to the fitting of a statistical-thermodynamic model (sigmoidal-Boltzmann curve) in accordance with the fitting proposed by Rahaman [START_REF] Rahaman | A New Insight in Determining the Percolation Threshold of Electrical Conductivity for Extrinsically Conducting Polymer Composites through Different Sigmoidal Models[END_REF] and Merzouki [START_REF] Merzouki | Electrical Conductivity Modeling of Polypropylene Composites Filled with Carbon Black and Acetylene Black[END_REF]. Fig. 5 Electrical conductivity σ and its second derivative as functions of vf. The gray points are the experimental data. The maximum of the second derivative stands for the electrical percolation threshold of σ.

σ = σ 1 -σ 2 1 + exp[(vf -σ 0 )/(∆σ)] + σ 2 . (5)
The parameters σ 1 = 5.26 × 10 -11 Sm -1 , σ 2 = 8.09 × 10 -5 Sm -1 , ∆σ = 0.012 and σ 0 = 0.46 are obtained by means of curve fitting. An inset in the Fig. 5 is added to highlight the changes on the electrical conductivity for all the concentrations. For volumetric fractions between 0 and 0.27 no appreciable changes were observed on the electrical conductivity. The average value for the electrical conductivity in this region was 8.2×10 -11 Sm -1 , which is a typical value for polyester resin [START_REF] Yaman | Thermal and Electrical Conductivity of Unsaturated Polyester Resin Filled with Copper Filler Composites[END_REF]. On the other hand, the electrical conductivity has a rapid increase for volumetric fractions above 0.27, reaching a value of 8×10 -5 Sm -1 for a 0.5 vf, corresponding to an increase of 6 orders of magnitude respect to the matrix. Similar increments have been reported by Merzouki for polypropylene matrices with carbon black and acetylene black particles [START_REF] Merzouki | Electrical Conductivity Modeling of Polypropylene Composites Filled with Carbon Black and Acetylene Black[END_REF] and Genetti et al. for microparticles of nickel dispersed on low-density polyethylene (LDPE) [START_REF] Genetti | Polymer matrix composites: Conductivity enhancement through polypyrrole coating of nickel flake[END_REF]. The behavior of the electrical conductivity shows the characteristic s-shape, presenting the three characteristic regimes [START_REF] Marsden | Electrical percolation in graphene-polymer composites[END_REF][START_REF] Ukshe | Percolation model for conductivity of composites with segregation of small conductive particles on the grain boundaries[END_REF]: the insulator (0 to 0.27 vf), percolative (0.30 to 0.50 vf) and conductive (above 0.5 vf).

Thermal diffusivity

Figure 6a shows the experimental cooling curves of three representative samples along with their corresponding fitting curves obtained by Eq. ( 2). One out of ten experimental data points is plotted. The residuals obtained from the fitting of the parameters Q 0 /e s , τ = L 2 /α and h p = h/e s are smaller than 2%, indicating high accuracy, as confirmed by the good agreement between the experimental and theoretical results. The time evolution of temperature exhibits a clear change of the slope at earlier times for higher volume fractions. The time at which this "characteristic elbow" occurs represents the time required by the heat flux to propagate through the whole sample of thickness L and is given by τ 0 = τ /π [START_REF] Parker | Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity[END_REF]. Since the thickness of all measured samples is equal, the reduction in τ indicates that α increases with the CIP content. Figure 6b shows the experimental values of the thermal diffusivity as a function of vf. Each experimental data point is obtained from the average of five measurements. For low concentrations of CIP (vf < 0.35), the expected increase of α agrees with the reported by Sofian et al. [START_REF] Sofian | Metal Powder-Filled Polyethylene Composites[END_REF] and Rusu et al. [START_REF] Rusu | Properties of Iron Powder Filled High Density Polyethylene[END_REF], such as an increase of 1.2 times is reached with a 0.12 vf. For high concentrations (vf > 0.35), on the other hand, the values of α are smaller than those reported by these authors, due to the differences in the particles sizes, whose impact on α is expected to strengthen as vf increases. The maximum thermal diffusivity value measured at the highest concentration considered in this work (0.55 vf) is 4.8 times that of the matrix. Moreover, the rate of change of α for vf > 0.35 is higher than for vf < 0.35, indicating that the thermal percolation threshold is expected to appear near to vf = 0.35.

Thermal effusivity

The typical cooling curves obtained of samples in contact with a semi-infinite fluid backing are shown in Fig. 7a, from three representative vf of 0.05, 0.36 and 0.50. One out of ten experimental data points are plotted along with their fitting curves. The residuals obtained for the fitting of the parameters Q 0 /e s , b 21 = e f /e s and h p = h/e s are smaller than 2%, which indicates that retrieved values are highly accurate. The backing fluid was ethylene-glycol with a thermal effusivity of 858 Ws 1/2 m -2 K -1 [START_REF] Forero-Sandoval | Measurement of the thermal transport properties of liquids using the front-face flash method[END_REF]. For times smaller than the diffusion one (t < τ 0 = L 2 /(πα)), the logarithmic plot of the surface temperature evolution exhibits a slope m ≈ -0.5, in agreement with previous reported works [START_REF] Pech-May | Simultaneous measurement of thermal diffusivity and effusivity of solids using the flash technique in the front-face configuration[END_REF][START_REF] Parker | Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity[END_REF]. For long times (t > τ 0 = L 2 /(πα)), on the other hand, the temperature behavior becomes sensitive to the interface between the sample and backing, and therefore its slope is driven by the ratio of their thermal effusivities. The surface temperature decreases (increases) smoothly until the slope -0.5 is reached, such that no change is appreciable for e s = e f . This fact along with Fig. 7a indicate that the sample with 0.05 vf (0.50 vf) has a thermal effusivity smaller (greater) than that of ethylene glycol, while the sample with 0.36 vf has an intermediate thermal effusivity, as expected.

Figure 7b shows the experimental values of the thermal effusivity as a function of vf. Each experimental point is obtained from the average of five measurements. The increase of the thermal effusivity with the fillers concentration is fairly linear and there is no significant change in the slope for the entire range of volume fractions studied. The maximum enhancement of the thermal effusivity reached in this work was 4.1 times that of the matrix, at the maximum concentration consider (0.55 vf). Given that the thermal effusivity indicates the amount of heat that the polymeric composite transfers to the environment, the obtained results could be paramount in the design and operation of heat exchanges.

Volumetric heat capacity

The [START_REF] Pech-May | Heat transport in epoxy and polyester carbonyl iron microcomposites: The effect of concentration and temperature[END_REF]. The uncertainty of C v was properly determined by using the error propagation theory [START_REF] Bevington | Data Reduction and Error Analysis for the Physical Sciences[END_REF]. Note that the values of C v increases rapidly at low concentrations and saturate for high enough ones. The maximum enhancement of C v was around 1.9 times that of the matrix, for vf > 0.30. On the other hand, C decreases as the fillers concentration increases, as was reported for similar fillers [START_REF] Sofian | Metal Powder-Filled Polyethylene Composites[END_REF][START_REF] Rusu | Properties of Iron Powder Filled High Density Polyethylene[END_REF]. The maximum reduction of C found in this work was about 0.42 times the one of the matrix at 0.55 vf.

Thermal conductivity

Figure 9a shows the thermal conductivity k = e √ α (gray points) of our composites as a function of concentration of CIP. The red line represents the second derivative of k and its maximum determine the thermal percolation threshold v pT = 0.38, which is represented by the green dashed line and very close to the inferred for α in Fig. 6b. For vf > v pT , k increases faster than for vf < v pT , due to the formation of heat conduction networks among the particles, at high S p e c i f i c h e a t c a p a c i t y , C ( k J k g -1 K -1 )

Fig. 8 Volumetric heat capacity (gray dots) and the specific heat capacity (red squares) versus volume fraction concentration of filler. In both cases, the continuous lines are only a visual guide.

concentrations, as shown in Fig. 2. Note that the experimental values are well predicted by the Zhang model [START_REF] Zhang | A Percolation Model of Thermal Conductivity for Filled Polymer Composites[END_REF], which establishes that the effective thermal conductivity of composites with a percolation threshold v pT is given by

k = k f k p k f 1-vf 1-v pT n , (6)
where k p = k(v pT ), k f is the thermal conductivity of the fillers, which in our case is k f = 80.2 Wm -1 K -1 [44], and n = 0.54 is a percolation exponent determined by fitting, this parameter depends on the filler size, shape, and distribution on the composites and the range studied and is expected to be in the range of 0.3 to 0.8. The maximum enhancement of k was 9.1 times that of the matrix, for a 0.55 vf.

In contrast to the behavior of C (Fig. 8), the experimental values of k showed in Fig. 9a do not display a saturation, as was reported by Elimat et al. [START_REF] Elimat | Effect of Iron Particle Size and Concentration on Thermal Conductivity of Iron/Polystyrene Composites[END_REF], but rather it tends to increase exponentially after crossing the percolation threshold, which is consistent with the data reported by Sofian et al. [START_REF] Sofian | Metal Powder-Filled Polyethylene Composites[END_REF] and Rusu et al. [START_REF] Rusu | Properties of Iron Powder Filled High Density Polyethylene[END_REF]. For a concentration of 0.12 vf, the thermal conductivity increases 1.9 times that of the matrix. Although greater increments of k would be expected for fillers with a thermal conductivity higher than the CIP used in this work, the effects of their shape and size should also be taken into account. For instance, by using aluminum fillers with a thermal conductivity 3 times greater than iron and an average diameter of 44 µm, Boudenne et al. [START_REF] Boudenne | Thermophysical properties of polypropylene/aluminum composites[END_REF] obtained similar increments than the ones reported in this work, involving CIP with a mean diameter of 1.67 µm.

The ratio between the thermal conductivity and the electrical conductivity (k/σ) as a function of volume fraction are shown in Fig. 9b. The experimental points are derived from the values of k and σ, and is represented by gray 5) and [START_REF] Huang | Aligned Carbon Nanotube Composite Films for Thermal Management[END_REF].

points. The red line is obtained by means of Eqs. ( 5) and ( 6), with the parameters previously obtained. The behavior of the curve is mostly determined by the electrical conductivity, due to its high changes with respect to thermal conductivity.

Infrared emissivity

In order to obtain the emissivity of each sample, an FTIR (Perkin Elmer Spectrometer, model frontier NIR-MED), equipped with an integrating sphere of 76.2 mm, with the interior surface coated with gold (Mid-IR integratIR of pike technologies) was used to obtain the total reflectance from 2-12 µm. Due to the samples are optically opaques, the emissivity can be calculated by means [START_REF] Ramírez-Rincón | On the use of photothermal techniques for the characterization of solar-selective coatings[END_REF]:

ε = λ2 λ1 [1 -R(λ)]P (λ)dλ λ2 λ1 P (λ)dλ , (7)
where R(λ) is the infrared reflectance of the surface and P (λ) is the black body emissive power given by Planck's law:

P (λ) = C 1 λ 5 (exp(C 2 /λT ) -1) , (8)
where C 1 = 1.498 × 10 -15 Wm 2 , C 2 = 1.4385 × 10 -2 mK and T is the room temperature. Figure 10 shows the emissivity as a function of the concentration of CIP at room temperature. A trend line corresponds to the fitting of a sigmoidal-Boltzmann curve,

ε = ε 1 -ε 2 1 + exp[(vf -ε 0 )/(∆ε)] + ε 2 . (9)
The parameters ε 1 = 0.85, ε 2 = 0.75, ∆ε = 0.063 and ε 0 = 0.33 are obtained by means of curve fitting. The red line represents the second derivative of the emissivity ε and its maximum represents the maximum decrease rate at 0.41, which is indicated by a green dashed line. The emissivity of the composite has a slight decrease (10%) as the concentration increases, this is due to the increase of metallic particles on the surface increases the optical reflectance. Our results are consistent with the reported for epoxy filled with CIP, in which the emissivity decreases monotonically from 0.87 to 0.76 for concentrations between 0 and 50% [START_REF] Houtz | A Measurement Technique for Infrared Emissivity of Epoxy-Based Microwave Absorbing Materials[END_REF]. Using low emissivity fillers like Al or Cu, is possible to obtain large reductions in emissivity (more than 0.5) of composites as a function of concentration [START_REF] Hu | The epoxy-siloxane/Al composite coatings with low infrared emissivity for high temperature applications[END_REF][START_REF] Wu | Preparation and characterization of a new low infrared-emissivity coating based on modified aluminum[END_REF][START_REF] Yu | Low infrared emissivity of polyurethane/Cu composite coatings[END_REF]. However, increases in concentration are not the only factor that influences changes in emissivity. for example, Wu, G. et al. showed that the emissivity increases as the thickness of the polymer increases as well, their studies were performed in organic coatings based on polyethylene wax filled with aluminum flakes on a steel substrate [START_REF] Wu | Preparation and characterization of a new low infrared-emissivity coating based on modified aluminum[END_REF] and Yu, H. et al. showed that the increase of the temperature reduces the emissivity, their studies were made on samples of polyurethane filled with copper [START_REF] Yu | Low infrared emissivity of polyurethane/Cu composite coatings[END_REF].

Discussion

An important aspect, is the shift between the thermal (v pT = 0.38) and electrical percolation threshold (v pE = 0.46). This difference is around of 20%, and these values differ from the value estimated by Eq. ( 1). This shift can be explained due to the differences in the transport mechanisms involved in the electrical and thermal conduction. In the case of the electrical conductivity, the electron transport occurs principally through three mechanisms: resistive, quantum tunneling and percolative [START_REF] Sherman | Electron transport processes in conductor-filled polymers[END_REF][START_REF] Albers | Effects of Compression and Filler Particle Coating on the Electrical Conductivity of Thermoplastic Elastomer Composites[END_REF]. For low concentrations, the electrical conductivity of the polymer is controlled only by the high resistivity of the matrix. As the volume fraction increases, the distance between the conductive particles becomes smaller, and for separations less than 10 nm, the electrons can be transported between conductive particles by means of a mechanical quantum tunnel effect, which in combination with the resistive mechanism increase the electrical conductivity [START_REF] Balberg | Tunneling and nonuniversal conductivity in composite materials[END_REF]. Finally, at high concentrations the percolative transport dominates. Macroscopic chains of conductive material are formed, facilitating the transport of electrons. When this mechanism occurs, the largest changes in electrical conductivity occur.

On the other hand, heat transfer in the polymer matrix is due to quantized vibrational modes within a rigid lattice of molecules (phonons), which are the heat carriers in this kind of polymer materials [START_REF] Huang | Thermal conductivity of polymers and polymer nanocomposites[END_REF], where the length of a phonon mean free path is closely related to the size of crystal regions in the polymer. Phonons transport is strongly limited by scattering between amorphous and crystal regions in polymers and structural defects that induce the lowering the thermal conductivity [START_REF] Huang | Thermal conductivity of polymers and polymer nanocomposites[END_REF][START_REF] Hida | Thermal resistance and phonon scattering at the interface between carbon nanotube and amorphous polyethylene[END_REF]. By contrast in the carbonyl iron particles, the heat is mostly carried by electrons which have mean free paths substantially larger [START_REF] Sun | Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites[END_REF]. At the interface polymer/filler particle, additional phonon scattering due to the mismatch between both mechanisms of heat transfer is present. This phenomenon can be considered as a thermal interface resistance, that limits heat transfer in this kind of composites. In the composite, as the concentration of particles increases and the formation of networks occurs, the electronic contribution becomes important, due to the possibility of the electrons to move through these paths.

The difference between the thermal and electrical percolation threshold is expected because in the case of heat transfer, heat carriers are electrons and phonons, and in the electrical transport only electrons. Heat conduction by phonons is always present in the composite and even at low volume fractions it is affected by the scattering. In contrast, the electrical conductivity is very small in the matrix and only grows substantially, until the percolation threshold is achieved. On the other hand, the interfacial resistance between the fillers and matrix is another factor that produce a shift between the thermal and the electrical percolation thresholds, from the predicted values by the Bruggeman's effective medium approximation [START_REF] Wang | A continuum model with a percolation threshold and tunneling-assisted interfacial conductivity for carbon nanotube-based nanocomposites[END_REF][START_REF] Wang | Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling[END_REF].

Interestingly, the effects of the growing volume fraction on the emissivity appear from higher concentrations, reaching a maximum decrease at 0.41. Considering that the microparticles (with lower reflectance than the polymer matrix) are randomly distributed in the composite, the above-mentioned dependence on the volume fraction can be explained by the increase (decrease) of the contributions on the infrared reflectance of the fillers (matrix) with regard to the total surface reflectance. This behavior produces a reduction of emissivity because the surface will be "more metallic". This is a surface rather than bulk phenomena, as it is in the case of thermal and electronic conductivities.

Variations on the percolation thresholds of different physical properties, as the reported in this work, has been previously observed by Shi et al. [START_REF] Shi | Percolation behavior of electromagnetic interference shielding in polymer/multi-walled carbon nanotube nanocomposites[END_REF] they reported differences between the percolation threshold of electromagnetic interference shielding and the percolation threshold of electrical conduction.

The results reported in this work indicate that in the design of polymer micro composites, by varying the volume fraction of inclusions, it is possible to adjust different physical properties at will, choosing the best conditions to satisfy different needs. For example, a composite which at a given concentration presents a relatively high thermal conductivity, but with a low electrical conductivity, would be very useful in dissipating heat from a circuit avoiding a electrical short circuit.

Conclusions

We have measured the thermal and electrical conductivities along with the infrared emissivity of composites composed of carbonyl iron microparticles randomly distributed in a polyester resin matrix, for volume fractions ranging from 0 to 0.55. The obtained results show that both the thermal and electrical conductivities increases with the particles' concentration, such that their percolation threshold appears at volume fractions of 0.46 and 0.38, respectively, which can be explained due to the contrast of properties between fillers and matrix, and the transport mechanism. The emissivity, on the other hand, decreases as the fillers' concentration increases, such that it exhibits a substantial decay at a volume fraction of 0.41, that is produced by the increase of the contributions on the infrared reflectance of the fillers as the concentration increases. The percolation threshold of the emissivity is thus higher than that of the thermal conductivity, but lower than the one of the electrical conductivity. This dispersion on the percolation concentration can be justified taking into a account the different physical mechanisms required to activate the electrical, thermal and optical responses of the considered composites. The obtained results show that the percolation phenomenon can be efficiently used to enhance or reduce the value of specific physical properties of particulate composites.

Fig. 1

 1 Fig. 1 Schematic diagram showing the percolation behavior in an insulating matrix conductive filler composite. (a) Isolated clusters. (b) Percolation threshold and (c) Conductive network.

Fig. 2

 2 Fig. 2 SEM images of a composite with a particles concentration of (a) 0.05 (b) 0.12, (c) 0.27, (d) 0.41, and (e) 0.50 vf. All the SEM images were presented at 500X. f) Histogram showing the size distributions of particles.

Fig. 4

 4 Fig.4Experimental setups. a) Scheme of the experimental setup used to obtain the electrical conductivity. Samples are placed in series with a voltmeter of high impedance. A capacitor (0.2 µF) in parallel with the voltmeter is placed, to filter out any interference that may affect the high impedance of the voltmeter. b) Scheme of the experimental setup used to obtain the thermal conductivity. Samples are heated up by a flash lamp and the temporal evolution of the temperature is recorded by means of an infrared camera. An infrared filter is placed between the flash lamp and the sample to prevent that the IR radiation of the lamp reaches the sample surface. Furthermore, the camera lens is protected with a Ge window placed in front of the camera.

2 P

 2 e r i m e n t a l d a t a S i g m o i d a l -B o l t z m a n n d 2 σ/ d ( v f ) e r c o l a t i o n t h r e s h o l d V o l u m e f r a c t i o n , v f E l e c t r i c a l c o n d u c t i v i t y ,

Fig. 6 a

 6 Fig. 6 a) Experimental and fitted cooling curves used to measure the thermal diffusivity of three representative samples. Symbols represent the experimental data and continuous lines the best fittings (left Y-axis). The corresponding residuals are plotted too (right Yaxis). b) Thermal diffusivity of polyester resin/CIP composites as a function of the fillers volume fraction. Dots represent the experimental data, the dashed line is a visual guide and the vertical line at vf = 0.35 stands for the increase in the rate of change of the thermal diffusivity.

Fig. 7 a

 7 Fig. 7 a) Cooling curves used to measure the thermal effusivity of composites with concentrations of 0.05, 0.36 and 0.50. Symbols represent the experimental data and continuous lines the best fittings. The corresponding residuals are also plotted. b) Thermal effusivity of polyester resin/CIP composites as a function of the vf. Dots represent the experimental data, the dashed line is a visual guide.

  dependence of the volumetric heat capacity C v and the specific heat capacity C as a function of vf are shown in Fig 8. The values of C v (represented by gray dots) were determined by means of the experimental data of e and α and the relationship C v = e/ √ α. The values of C (represented by red squares) were obtained from the values of C v and the density ρ of the composite and using relationship C = C v /ρ. The composite density was determined through the additions rules ρ = ρ m (1 -vf) + ρ p vf, with ρ m = 1160 kgm -3 and ρ f = 7870 kgm -3

  u m e f r a c t i o n , v f V o l u m e t r i c h e a t c a p a c i t y S p e c i f i c h e a t c a p a c i t y V o l u m e t r i c h e a t c a p a c i t y ,

Fig. 9 a

 9 Fig.9 a) Thermal conductivity k and its second derivate as functions of the volume fraction of fillers. The points represent the experimental data, while the predictions of Zhang model (Eq. (6)) are represented by the continuous line. The maximum of the second derivative stands for the thermal percolation threshold of k. b) Ratio between the thermal conductivity and the electrical conductivity as a function of volume fraction. The points represent the experimental data and the continuous line is obtained by means of the Eqs. (5) and (6).

2 P 2 Fig. 10

 2210 Fig. 10 Emissivity ε and its second derivative as function of the volume fraction of fillers. The gray points represent the experimental data. The maximum of the second derivative stands for the the maximum decrease rate.

Acknowledgements This work was partially supported by projects SRE-AMEXID-2016-1-278320 and Cinvestav Scientific Research and Technological Development Fund No. 98. F. C-A acknowledges the postdoctoral scholarship obtained from the project SEP-CB-2015-01-251882. N.W. P-M acknowledges support from the Adolf Martens fellowship at BAM Berlin. The FESEM analyzes were carried out by the M.C. Dora Huerta Quintanilla at the National Laboratory of Nano and Biomaterials, Cinvestav-IPN; financed by the projects FOMIX-Yucatán 2008-108160, CONACYT LAB-2009-01-123913, 292692, 294643, 188345 and 204822. The authors are grateful to J. Bante-Guerra for his technical assistance.

Conflict of interest

The authors declare that they have no conflict of interest.