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SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 17 (2008) 025011 (10pp)

doi:10.1088/0964-1726/17/2/025011

Conductive polymer composites with double percolated architecture of carbon nanoparticles and ceramic microparticles for high heat dissipation and sharp PTC switching G Droval1,2 , J F Feller1, P Salagnac2 and P Glouannec2 1 Laboratory of Polymers, Properties at Interfaces and Composites (L2PIC), University of South Brittany (UBS) Research Centre, F-56321 Lorient, France 2 Laboratory of Thermal, Energetic and Environment Studies (LET2E), University of South Brittany (UBS) Research Centre, F-56321 Lorient, France

Received 19 September 2007, in final form 15 January 2008 Published 11 February 2008 Online at stacks.iop.org/SMS/17/025011 Abstract In classical self-limiting heating devices where conductive polymer composites (CPC) are used, one of the main problems to solve is the stability of properties with time. Different strategies are proposed to stabilize the morphologies during the structuring of these heterogeneous materials. Some of them are well known in the use of co-continuous polymer blends or confinement but the interest of this work is to combine different structuring methods such as volume exclusion, adsorption and multiple percolations to achieve original properties. In fact the CPC developed exhibit enhanced heat dissipation and thermal stability (up to 180 ◦ C), independent adjustability of electrical and thermal conductivity, and a sharp and large amplitude PTC effect. These original results were obtained with a co-continuous structure associating a thermally conductive polymer phase (syndiotactic poly(styrene) (sPS) filled with aluminum oxide (Al2 O3 ) or boron nitride (BN)) with an electrically conductive polymer phase (high-density poly(ethylene)) (hdPE) filled with carbon nanoparticles (CNP) in appropriate proportions. (Some figures in this article are in colour only in the electronic version)

(relative to percolation threshold) make lots of applications possible. During the last decade the development of smart applications of CPC such as self-heating [4, 7, 15–18], pressure sensing [8, 19, 20] or solvent vapor sensing [6, 10, 13, 21, 22] has focused the attention of many researchers. Several technical problems such as CPC stability in thermal cycling and tension overshooting found satisfying answers in the use of reticulated polymer matrices [6, 19, 23] or co-continuous polymer structures [1–5, 7, 11, 24]. In this latter case the conducting phase is thermally protected by a second insulating polymer phase of higher melting temperature which prevents any negative temperature coefficient (NTC) effect. But if this strategy presents additional advantages like the decrease of the percolation threshold, the recyclability of

1. Introduction Conducting polymer nanocomposites (CPC) are obtained by the dispersion of electrically conducting fillers, such as carbon nanoparticles [1–6], metal particles [7, 8] or carbon nanotubes [9–12], into a large variety of insulating polymer matrices. In fact this simple operation of dispersion is a critical step as, depending on processing temperature [5], blending time [1] and particle/matrix interactions [13, 14], the resulting CPC can have very different electrical properties. Controlling the impact of all these parameters allows finding the right balance between dispersion and aggregation phenomena to prevent either formation of micro-agglomerates or conductive pathway breakage. The wide choice of polymers/filler combinations and the adjustment of conducting filler content 0964-1726/08/025011+10$30.00

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© 2008 IOP Publishing Ltd Printed in the UK

Smart Mater. Struct. 17 (2008) 025011

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Table 1. Main characteristics of the polymers studied. hdPE

hdPE-CNP

sPS

Producer

Arkema

Premix

Dow

Trade name

Finathene 5203

PRE-ELEC TP 5813

QA101 Questra

— 133.6 ± 0.5 111.5 ± 0.5 95/303 31 0.93 ± 0.05 23 35

99 275 — 28.9/53.2 51 1.05

◦

Tg ( C) Tm (◦ C) Tc,n (◦ C) Hm /H∞ (J g−1 ) X% crystallinity Density (g cm−3 at 25 ◦ C) % CNP v/v % CNP m/m

−30 133 107 95/303 31 0.95

Table 2. Filler properties. Filler

Aluminum oxide

Boron nitride

Vulcan XC72

Chemical formula/abbreviation Density, d (g cm−3 ) a Melting temperature, Tm (◦ C)a Thermal conductivity, k (W m−1 K−1 ) at 300 Ka Specific heat, C p (J kg−1 K−1 ) at 300 Ka Electrical resistivity, ρ ( cm) at 300 Ka Iodine number (mg g−1 ) Absorption DBP (ml/100 g) Particle diameter (μm) Shape factor [27]

Al2 O3 4.00 2054 36 776 1014 —

BN 2.30 3027 125 730 2 × 1014 —

CNP 1.8

11 5.6 [27]

8 79 [27]

a

6–175 [27] — — 254 174 30 × 10−3 —

From producer.

end of life heating elements and ease of processing, there are also some drawbacks limiting the applications such as the low thermal conductivity of such compounds and the difficulty in controlling the distribution of conducting nanofillers during the process within the two polymers. In this paper, we propose a new strategy to enhance heat dissipation in co-continuous CPC and stabilize the conducting nanoparticles structure by double particle percolation. The different materials of the CPC have been selected for their high level of thermal or conductive properties (cf tables 1 and 2):

2. Materials and techniques 2.1. Materials High density poly(ethylene) (hdPE) was provided by ArkemaFrance (Finathene 5203) and used to dilute a master batch from PREMIX-France (PRE-ELEC TP 5813) of highly filled hdPE matrix with 23%v/v of carbon nanoparticles (Vulcan XC 72 N472 from Cabot). This batch was selected because it showed in previous work [26] an ability to adsorb onto silicate nanoplatelets whereas at the same time it did not increase much the viscous modulus of the blend even at high carbon nanoparticle content. Two different types of ceramic microparticles, aluminum oxide (Al2 O3 ) from Sigma-Aldrich-France and boron nitride (BN) from MCSEFrance, were selected for their good thermal properties from previous work on thermal percolation [27]. The thermally conductive microfillers were dispersed in a Questra syndiotactic poly(styrene) (sPS) matrix from Dow ChemicalUSA. The main properties of the polymers are summarized in table 1 whereas some of the filler characteristics are recalled in table 2.

• syndiotactic poly(styrene) (sPS) has very good chemical and thermal stabilities due to its aromatic nature, high melting temperature (Tm = 270 ◦ C) and crystallinity ( X c = 51%), • high density poly(ethylene) (hdPE) was known for a long time to be the polymer leading to high PTC amplitude with sharp commutation [25], • carbon nanoparticles (CNP) XC72 are highly structured, and thus very conductive, • ceramic microparticles of boron nitride (BN) are one of the most thermally conductive microfillers, being at the same time electrically insulating.

2.2. Techniques 2.2.1. Blending. All components were dried during 12 h under vacuum at 90 ◦ C prior to use. The development of the triple percolated CPC was done in three steps:

The CPC resulting from the association of these compounds led to original multiple percolated structures with high self-heating capabilities.

(1) Adjustment of electrically conducting phase at appropriate conductivity by melt dilution of hdPE-23%CNP with pure 2


G Droval et al

hdPE in a contra-rotating twin screw Brabender extruder at 20 or 30 rpm. The temperature profile from feed to die was 190/195/205 ◦ C. (2) Formulation of the thermally conducting phase was done by melt mixing of sPS pellets with ceramic microfillers in a single-screw Fairex extruder. The mixing speed was 30 rpm and the temperature profile from feed to die was 275/277/280/280 ◦ C. (3) Final assembling of the two immiscible phases was done blending the electrical phase with the thermal phase in the contra-rotating Brabender twin-screw extruder. Compounds were blended at 275/280/280 ◦ C with a mixing speed of 20 rpm to obtain tapes from a 5 × 50 mm2 die.

0.1 mm diameter (in the core and at the surface all along the tape) as presented in figure 9 on a transversal cut. Tensions up to 100 V were applied between the two electrodes situated at the tape extremities as already described elsewhere [17]. 2.2.6. Simulation. The mathematical model describing the electrothermal behavior was developed with FEMLAB® . This software uses a finite element method. The domain has been discretized in triangular elements and quadratic interpolation was used for each parameter. In all configurations, networking was checked to reach the same solution with a minimum of elements. Thus the grid contains from hundreds to thousands of elements.

3. Results and discussion

2.2.2. Morphology. A scanning electronic microscopy (SEM) JEOL JSM-6031 was used to determine the composites’ morphologies after two weeks’ boiling xylene extraction of hdPE phase in a Kumagawa at 110 ◦ C. Observations were done after fracture of the sample in liquid nitrogen and spray deposition onto the surface of a thin gold layer.

The objectives of the following experiments were two: determine the intrinsic calorimetric and thermoelectric properties of the CPC developed but also to investigate their complex structures and morphologies. 3.1. Percolation

2.2.3. Thermal properties. Thermal stability and filler content was measured by a Setaram thermo-gravimetric analysis (TGA) apparatus under nitrogen flow. The sample initial weight was approximately 30 mg and the precision of measurements was estimated to be less than 0.5%. Calorimetric measurements were performed with a Mettler Toledo DSC 822. Calibration was done with indium and zinc prior to a set of experiments and the base line was checked every day. Aluminum pans with holes were used and the sample’s mass was approximately 15 mg. All samples were first heated up to 300 ◦ C during 5 min to get rid of their thermomechanical history. Nonisothermal crystallization and melting temperatures, respectively Tc,n and Tm , were determined from the peak extremum in experiments at ±10 ◦ C min−1 heating/cooling rates. To prevent sample degradation, experiments were carried out under nitrogen flow. Tc and Tm were determined at less than ±0.5 ◦ C and Tg at less than ±1 ◦ C.

Three different kinds of percolations are expected to take place in the optimized CPC formulation:

• the percolation of carbon nanoparticles (CNP) to constitute the electrically conducting pathways, • the percolation of ceramic microparticles (CMP) to constitute the thermal architecture, • the percolation between hdPE electrically conducting phase and sPS thermally conducting phase. Thus to better understand each phenomenon independently, a step by step investigation was used. First the classical percolation of conducting fillers, now rather well known [28, 29], was studied. But it is always very instructive to analyze percolation curves since they give plenty of indications on particle shape factor or dispersion, the level of interaction between particles and macromolecules of the matrix, volume exclusion or adsorption phenomena [3, 5, 26]. The evolution of electrical resistivity with CNP content was followed for three different kinds of blends:

2.2.4. Density. For conversion of mass into volume fraction, density measurements were carried out with a pycnometer at room temperature (27 ◦ C) in methanol.

• CNP dispersed in hdPE matrix, denoted ‘hdPE-(%)CNP’, give information on primary nanoparticle percolation into hdPE, • hdPE-23%CNP dispersed into sPS matrix, denoted ‘sPS(%)/(hdPE-23%CNP)’, • hdPE-CNP with different filler contents are dispersed in a fixed quantity of sPS, i.e. approximately 60% v/v (cf table 3), denoted ‘sPS60%/hdPE-CNP(%)’.

2.2.5. Conductivity. Percolation curves and thermoelectrical cycles (PTC effect, resistivity at room temperature ρRT , maximum resistivity ρmax , switching temperature upon heating Tdisc and cooling Tcon ) were determined by a four-point probe technique (with a digital multimeter, Keithley 2700) already described in previous work [3]. Samples of 2 × 10 × 80 mm3 dimension were introduced into a programmable Memmert oven (from 20 to 180 ◦ C at ±0.5 ◦ C min−1 ). Contact resistances were minimized using silver paint at the probe/sample interface. Electrothermal characteristics were determined using CPC tapes of about 100 × 50 × 5 mm3 dimensions, instrumented with six type K thermocouples of

Percolation curves are plotted in figure 1 and subsequently fitted using the percolation law (cf equation (1)) used by Kirkpatrick [28], in which ρc is the effective CPC resistivity and φ is the filler volume fraction:

ρc = ρ0 (φ − φc )−t . 3

(1)


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Table 5. Coefficients extracted from electrical percolation law (equation (1)).

hdPE (%)CNP sPS 60%/hdPE(%)CNP sPS (%)/hdPE 23% CNP

φc (%)

ρ0

t

11.0 4.5 2.6

0.01 0.01 0.02

2.2 2.8 2.3

Table 6. Coefficients of thermal percolation law (equation (2)) for BN and Al2 O3 .

◦

Figure 1. CPC percolation curves at 20 C of hdPE-CNP and diphasic sPS/hdPE-CNP.

φCNP (%)

sPS60%/(hdPE 11% CNP) sPS60%/(hdPE 13% CNP) sPS59%/(hdPE 16% CNP) sPS58%/(hdPE 20% CNP) sPS53%/(hdPE 23% CNP)

4.6 5.2 6.8 8.5 10.6

Table 4. CPC formulations for thermoelectrical studies. Name

Formulations

CPC1 CPC2 CPC3

sPS 53%/(hdPE-23% CNP) 47% (sPS 28% Al2 O3 ) 60%/(hdPE 23% CNP) 40% (sPS 33% BN) 63%/(hdPE 23% CNP) 37%

BN

Al2 O3

Measured shape factor D/λ φm (%) A

79 40 7.56

5.6 55 3.55

applications the preferred CNP content will be somewhat over the percolation threshold, not far from 10% v/v, to ensure easy disconnection upon temperature increase and prevent chaotic electrical behavior. For the same reason the value of 60% for sPS phase content was chosen because it is about 15% below the end of the sPS/hdPE-CNP co-continuity domain. The thermal conductivity range is only 2 decades whereas that of electrical conductivity is about 20. Thus it is not surprising to find that the same law cannot describe the two types of percolations. The Lewis and Nielsen model (cf equations (2)) follows quite well the evolution of thermal conductivity with filler content, i.e. what could be called by analogy the thermal percolation:

Table 3. CPC formulations for CNP percolation study in co-continuous sPS/hdPE-CNP systems. Formulations

Filler type

1+ Aβφ m 1 − β φ 1 + 1−φ φm2 φ kf −1 km β= kf +A km

kc = km

The three parameters that can be extracted from this law, ρ0 an adjustable coefficient, φc the filler volume fraction at which percolation takes place (percolation threshold) and the critical exponent t are collected in table 5 and commented in the following. Typical values for t are 2.0 and 1.3 for associations of spheres in 3D and 2D [29], respectively. However, in the case of multiple percolations or for particles with high shape factor such as fibers, values up to 4 are reported [2]. In fact, t depends also on the dimensions of the conductive architecture, rather complicated to determine accurately in our CPC. t values for our systems are all higher than 2. In the case of hDPE-CNP this can be due to the high structure of XC72 whose aggregates are more likely branched objects than spheres. Concerning the two co-continuous sPS/hdPECNT CPC the morphology of conducting pathways may be so complicated that any interpretation of t should require further modeling and morphological investigations to conclude. But, observing the evolution of φc with decreasing CNP content either directly or through the hdPE-CNT phase shows it is possible to decrease φc from 11% v/v to 2.6% v/v. Even the highest value is lower than that of 16.4% predicted by theory for conducting spheres randomly distributed in an insulating matrix [28]. This is a confirmation of the high structuring of CNP aggregates. Nevertheless for self-limiting heating

with

(2)

kc , km and k f are, respectively, the thermal conductivities of the composite, the matrix and the filler. A is a constant which depends on the filler shape and orientation. φm is the maximum packing volume fraction of the dispersed particles. A previous study [27] showed that, unlike for electrical percolation, no sharp increase of thermal conductivity can be expected under 20% v/v of filler. Values between 30 and 60%v/v are often found by extrapolation with models like that of equation (2) depending on the shape factor and intrinsic thermal conductivity of fillers. Thus, to achieve significant thermal conductivity enhancement in insulating polymer matrices it is necessary to add at least 20%v/v of thermal filler. In the present work the improvement of sPS thermal conductivity was obtained by addition of BN and Al2 O3 ceramic microparticles. From table 6 it can be concluded that BN is the most suitable filler for our purpose but, nevertheless, its platelet-like shape may also be a drawback (making it process-dependent) together with its high price. This is the reason why we have also compared its performance with alumina, a more common product with acceptable thermal characteristics and much lower price. 4


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Table 7. Calorimetrical characteristics of hdPE-CNP samples. hdPE composites (% CNP v/v) hdPE weight (mg) Melting temperature, Tm (◦ C) Crystallization temperature, Tc,n (◦ C) X c (%) calculated with Hm∞ = 303 J g−1

0% CNP 12.3 140.0 107.5 31%

10% CNP 5.5 140.0 111.5 30%

13% CNP 9.0 142.5 110.5 34%

20% CNP 6.0 141.0 110.5 32%

23% CNP 7.0 139.5 111.5 32%

Figure 4. DSC thermogram showing melting and crystallization of hdPE phase in co-continuous CPC from 90 to 150 ◦ C at 10 ◦ C min−1 .

Figure 2. DSC thermogram showing hdPE-CNP crystallization at 15 ◦ C min−1 .

CNP have a small nucleating effect (+4 ◦ C) shown by a slight increase of Tc,n and no effect on Tm and X c . This means that there are few interactions between CNP and hdPE macromolecules during the electrically conducting network structuring where particles are excluded from crystallizing areas. In contrast figure 3 shows that ceramic microparticles Al2 O3 and BN have a more important effect on sPS crystallization as shown by a Tc,n increase of respectively +5 ◦ C and +10 ◦ C. This rather important impact of microfillers was even found to be significant from 5% of fillers [27]. Consequently this Tc,n shift cannot be attributed only to any experimental artifact due to thermal conductivity increase (and sample inertia change) but also to a real nucleating effect. In figure 4 for co-continuous CPC considered as optimized (see table 4 for composition), although the melting temperature is quite unchanged whatever the composite, there are important modifications of hdPE crystallization. For CPC1 (without CMP) Tc,n = 112 ◦ C (equivalent to that of hdPE-23% CNP) and X c = 32%. But in the presence of Al2 O3 (CPC2), Tc,n increases up to 117 ◦ C and X c to 45%. This effect is even stronger with BN (CPC3) since Tc,n = 119 ◦ C and X c = 51%. At first sight, given the processing protocol it is surprising to assume that CMP could have so much influence on hdPE crystallization. During the first step of processing CNP are dispersed in hdPE and CMP in sPS, and only in a second step are hdPE macromolecules able to get into contact with CMP. Moreover the increase of X c suggests that CMP may have helped chains packing into crystals more than adsorbing at their surface (which would have caused their immobilization and prevented them from crystallizing). Thus a possible interpretation of these observations could be that CMP, due to their much higher thermal conductivity than the polymer (a hundred times more), create thermal bridges speeding up the

Figure 3. DSC thermogram showing sPS-CMP crystallization at 10 ◦ C min−1 .

3.2. Calorimetric study Studying highly filled polymer composites that will have to be melt processed makes it a must to investigate the influence of fillers on CPC structuring, i.e. on polymer crystallization. In fact it is during this cooling step that the different percolated networks are built through the CPC at the nano/mesoscale and will provide the macroscopic properties. The effects of either nano-or microparticles on the calorimetric characteristics of CPC are clearly visible in figure 2 for hdPE with CPN and in figure 3 for sPS with CMP. Table 7 recalls quantitative data from figure 2 after enthalpy corrections with respect to CNP mass. Surprisingly carbon nanoparticles are found to have a weak effect on hdPE calorimetric properties unlike what was observed with poly(ethylene-co-ethyl acrylate) (EEA) and poly(butylene terephthalate) (PBT) in previous work [24]. 5


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Table 8. Characteristics of PTC and NTC effects.

Tdis heating/Tcon cooling (◦ C)

IPTC a hdPE-CNP (%)

Monophasic

Diphasic

Monophasic

Diphasic

13 16.5 20.0 23

3.6 2.0 1.6 1.2

3.4 2.2 1.5 1.2

131/110 133/112 133/115 135/122

128/116 134/112 130/115 128/120

a

INTC Monophasic

−1.6 −0.5 −0.3 −0.1

Diphasic

−0.6 −0.1 −0.05 −0.02

IPTC and INTC are expressed in decades of resistivity.

Figure 5. SEM picture of (sPS-28%Al2 O3 )60/(hdPE-23%CNP)40.

Figure 6. SEM picture of (sPS-33%BN)63/(hdPE-23%CNP)37.

germination process locally and giving more time to hdPE to crystallize before chain freezing. Additional information can now be obtained looking into the CPC morphology.

than 2% [26]. Depending on the filler’s ratio and on mutual interactions a decrease or an increase of electrical conductivity can be observed. Here, given the high CMP content (#30%v/v) the driving parameters for electrical properties are expected to be volume exclusion and confinement of the electrically conductive phase (hdPE-NC) between the CMP. Concerning the filler’s orientation during processing, figures 5 and 6 confirm that, indeed, the shape factor of Al2 O3 being very different from BN (table 6), the former is less likely to orient during processing than the latter. This point must be looked after to keep the CMP network interconnectivity and consequently a high level of CPC thermal conductivity.

3.3. Morphology SEM observations have been carried out on CPC2 and CPC3 giving, respectively, the images of figures 5 and 6. The high crystallinity of hDPE and sPS made difficult any selective solvent extraction for precise investigation of the expected cocontinuous structure of the blend. A two week processing in boiling xylene at 110 ◦ C only resulted in superficial etching. The first point to note from these figures is that, due to the large size of CMP as compared to CNP (a thousand times) and unlike what could have been suggested by the processing protocol, there is no continuous thermally conducting phase composed of CMP well wrapped by an sPS matrix. During the blending the two polymers recombine in the melt although they are immiscible and create a new co-continuous blend between the CMP percolated network. Inside this co-continuous blend the hdPE-CNP phase allows current circulation, meaning it is not constituted of independent nodules. In figure 5, the remaining aggregates of CNP of about 200–600 nm are visible at the Al2 O3 particle surface; this suggests that a certain amount of electrically conductive phase could have been adsorbed there, increasing CPC conductivity. But the very clean BN particle surface tends to show that it is not the case in CPC3. When electrically conductive CNP adsorb onto ceramic nanofiller such as montmorillonite (whose thickness is nanometric but other dimensions are micron-sized) this can considerably affect the electrical properties even at low nanofiller content, i.e. less

3.4. Thermoelectric behavior of the CPC: PTC effect Studying thermoelectric properties of CPC mainly consists in determining the so-called ‘PTC effect’ characteristics. A positive temperature coefficient is characterized by a sharp resistivity increase with temperature when the conducting particles of the polymer coating go through a phase transition (Tm or Tg ). Its amplitude IPTC can rise up to 4 or 5 decades with a vertical slope. These features will determine the future properties of the self-limiting heating element. Thus classically PTC curves are analyzed determining the amplitude IPTC = log(ρmax ) − log(ρmin ), the disconnection/connection temperatures of the switching effect Tdis /Tcon and the room temperature resistivity ρRT (collected in tables 8 and 9). Figure 7 presents the thermoelectric signatures of two types of CPC, mono- and diphasic (corresponding to the second cycle of heating/cooling, the first one corresponding to erasing of the thermomechanical history of the sample) for two different CNP contents in the hdPE phase, 23% and 13% 6


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Figure 8. Thermoelectrical behavior of co-continuous sPS/hdPE 23% CNP CPC with and without 30%CMP (second cycle).

Figure 7. Thermoelectrical behavior of hdPE-CNP and sPS/hdPE-CNP CPC.

Table 9. Characteristics of PTC and NTC effects. CPC no.

IPTC a

Tdis heating/Tcon cooling (◦ C)

1 2 3

1.0 0.9 1.0

129/109 129/112 133/115

a

INTC a

Tsurface

+0.02 −0.03 −0.05

IPTC and INTC are expressed in decades of resistivity.

CPC

(close to the percolation threshold). The benefit expected from the use of diphasic CPC is generally to decrease the percolation threshold and also to increase the thermal stability preventing the appearance of too important an NTC effect (negative temperature coefficient) that may cause the destruction of the heating element. For CPC filled with 23%CNP no apparent difference in thermal stability can be seen between mono-and diphasic CPC in the temperature range scanned; but in practice important warping of the sample without sPS was noticed, meaning its forthcoming disintegration, so that the superior temperature was limited to 150 ◦ C for monophasic CPC. In contrast no warping was observed with diphasic CPC up to 180 ◦ C, the limiting temperature of our experimental device. ρRT is found to increase for the diphasic CPC compared to monophasic CPC, which results from the decrease of the current passage effective section as normally observed in such a case. The heating/cooling hysteresis observable due to classical undercooling (the difference between melting and crystallization temperatures) is found to be consistent with DSC thermograms (figures 2 and 3). Upon heating the beginning of the PTC jump corresponds to the beginning of hdPE melting and not to the endotherm extremum, meaning that conductive CNP chains are extremely sensitive to local changes inducing macromolecular mobility variations. In figure 7 for CPC filled with 13%CNP, an important increase of IPTC can be noticed compared to formulations with 23%CNP. In fact, according to table 8 decreasing CNP content leads to both larger PTC and NTC effects. Additionally no effect of filler content can be observed on Tdis except for high CNP content, i.e. over 20%v/v, whereas Tcon is shifted by more than 5 ◦ C. It can also be noticed that the area covered by the hysteresis is larger when the filler content gets closer to

Air

T

Figure 9. Simulation of thermal transfers between a CPC tape and its air environment.

the percolation threshold. The percolated architecture is more brittle (and also more sensitive), but remains reproducible upon cycling as ρRT is unchanged. But the most remarkable feature of figure 7 is the similarity of IPTC for both monophasic and diphasic CPC at the same CNP content in hdPE. This is very different from what was observed with another diphasic CPC, i.e. PBT60/(EEA-CNP)40, for which IPTC was reduced from 2 decades to only 0.5 for the diphasic CPC [3]. Low IPTC can be advantageous in heating devices requiring low starting power input, but can also be considered as a drawback if an important self-regulation capability is expected. With sPS60/(hdPE13%CNP)40 (cf table 8) it is possible to combine high thermal stability, large PTC amplitude (up to 3.4) and reasonable conductivity (ρ RT #2 × 103 cm). Figure 8 shows the second heating/cooling cycle that shows the influence of ceramic microparticles on the thermoelectric behavior of co-continuous CPC sPS/hdPE23%CNP (see table 4 for composition):

• Tcon is increased with Al2 O3 and BN as a consequence of the nucleating effect already noted in DSC experiments (figure 4), 7


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• Tdisc is slightly increased with BN, • ρRT is decreased and IPTC is increased with both microparticles. Unexpectedly the addition of 30%v/v thermally conductive microfiller improves the thermoelectric signature of cocontinuous CPC. All CPC present very good thermal stability and switching capabilities. The slight improvement of CPC room temperature conductivity is interpreted by a more important confinement of the hdPE-CNP phase due to volume exclusion induced by ceramic microparticles as already noticed by SEM pictures (figures 5 and 6). 3.5. Electrothermal behavior of CPC: power dissipation Figure 10. Thermal gradient evolution with self-generated flow for the different CPC.

Thermoelectric behavior is investigated with low currents (some V and several mA) to measure resistivity evolution when temperature variations are imposed on samples by a programmable oven. In the case of the study of electrothermal behavior, sample solicitations are closer to usage conditions, i.e. tension and intensity are large enough to make CPC tape (which is instrumented with thermocouples, cf figure 9) unable to self-generate heat by the Joule effect and increase its temperature. It is thus possible to follow the temperature increase with tension in both the center and surface of the sample depending on environmental characteristics (the standard is air at room temperature in natural convection). It is such experiments that have initiated the present study by showing a thermal gradient in several samples’ thickness and width due to insufficient thermal conductivity. In fact, depending on formulation, sample geometry and environmental conditions, the gradient could reach more than 15 ◦ C. The problem then is not necessarily that the element will not heat homogeneously, but that it will create internal stresses, reducing the element’s durability. To extend such an investigation to elements of any shape and composition we have developed a model using FEMLAB (for more details concerning the model see the appendix and also [18]), making it possible to simulate different conditions of thermal exchanges between the heating element and its environment. An example of such a calculation is given in figure 9 after input of a sample’s thermophysical properties (evaluated in a preliminary study [27]) into the software. Thus it is possible to obtain temperature and current distributions anywhere in the sample and to optimize the formulation. But prior to any systematic study it is necessary to validate the model comparing experimental to simulated data. This is exactly what has been done in figure 10 where points correspond to measured values and lines to simulated data. Results given in figure 10 show that the evolution of thermal gradient (per thickness unit, but could as well be estimated per width unit) is quite linear with dissipated power (and thus tension) which is not surprising; but more interesting is the influence of ceramic microparticles on this gradient, i.e. there is a constant ratio between the gradient increase with power of the three CPC. Adding 30%v/v BN or 30%v/vAl2 O3 into sPS matrix allows a reduction, respectively, of the thermal gradient of 62.5% and 30%. Finally one can say that at low self-generated power (under 200 W m−2 ) the use of any CMP is not judicious but

as soon as tension is raised the gain in thermal gradient is very significant. Moreover the use of CMP in CPC formulation will not only decrease the thermal gradient but also improve the efficiency of the heating device.

4. Conclusion The origin of the present study is the finding of an important thermal gradient in conductive polymer nanocomposites (CPC) used for self-limited heating elements’ development [17]. From a first set of experiments, two types of ceramic microparticles (CMP), BN and Al2 O3 , have been selected for their capability (taking into account their thermal conductivity and shape factor) to enhance the polymer’s thermal conductivity [27]. Thermoelectric and electrothermal behaviors of two optimized CPC formulations containing 30% of these CMP have been compared to the same kind of CPC but without CMP. Results are interpreted in the light of their calorimetrical and morphological properties. Carbon nanoparticles (CNP) initially dispersed into the hdPE phase appear to weakly modify the polymer calorimetric properties, since no major change in Tm , Tc,n or X c is noticed. This is not the case for CMP which, more than shifting the transition temperatures of sPS and hdPE up to 10 ◦ C, also increase the hdPE crystallinity notably (10%). Contrary to what processing conditions could have made us think, the final morphology of optimized CPC is not constituted of two co-continuous phases of 60% sPS-CMP and 40% hdPE-CNP but much more of two co-continuous phases of 50%sPS and 50%hdPE-CNP intercalated between a percolated network of CMP. Some amount of hdPE-CNP could also be adsorbed onto CMP preferentially but this point is difficult to check from SEM pictures as selective extraction is quite impossible with sPS/hdPE blends. Thermoelectrical properties of CPC show that the sPS structuring matrix does not reduce IPTC of hdPECNP, thus preserving its self-regulation ability together with increasing CPC thermal stability up to 180 ◦ C. Surprisingly introducing 30%v/v of CMP into CPC formulations does not change much its thermoelectric signature and even improves it. Electrothermal properties investigated by both experiment and simulations give results in good agreement and predict an 8


G Droval et al

where σs is the Stefan–Boltzmann constant, ε is the emissivity of the CPC, Ts is the surface temperature of the CPC and Twall is the experimental wall temperature. Boundary conditions At the walls, the velocity is set to zero and the temperature is changed to the experimental wall temperature. On the vertical symmetric axis, all the perpendicular gradients (temperature, velocity and pressure) are null.

appreciable reduction of the thermal gradient of CPC of 62.5% if 30% v/v of BN is added to the initial formulation.

Acknowledgments The authors would like to thank H Bellégou, H Guézénoc, F Péresse, J Costa and M Dumons for their contribution to this work and the French Ministry of Research and New Technology and Brittany Region for financial support.

References

Appendix

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The mathematical model of the electro-thermal behavior of the studied system has been developed with FEMLAB® . This software uses the finite element method. The domain is discretized in triangular elements and a quadratic interpolation is used for each variable. For the CPC, only the energy equation is used: · k ∇T (3) ∇ + σ E2 = 0 with T the temperature, k the thermal conductivity, σ the electrical conductivity and E the electrical field. The electrothermal coupling takes place in the term σ E 2 , which represents the internal heat source generated by the Joule effect. The thermophysical properties of CPC (σ, k ) are a function of temperature. The power generated by the Joule effect in the CPC is dissipated in the surroundings by free convection and far infrared radiation. The laminar flow around the CPC is governed by the continuity, Navier–Stokes and energy equations. The fluid is supposed incompressible and Newtonian. Continuity equation:

· U = 0. ∇

(4)

Navier–Stokes equations U − η∇ 2 U + ∇ p = F ρ U · ∇

(5)

with Fz = −ρgβ(T − Tair )Fy = 0. Energy equation · k ∇T − ρC p T U = 0. ∇

(6)

In these equations, U is the air velocity field, ρ is the density, η is the dynamic viscosity, p is the pressure, g is the gravitational acceleration, β is the coefficient of thermal expansion, T is the temperature of the fluid, Tair is the reference temperature, k is the thermal conductivity and C p is the specific heat capacity. The air thermo-physical properties are assumed as polynomial functions of temperature. At the CPC–fluid interface, the radiative flux density ϕ is taken into account in the model by 4 ϕ = εσs Twall − Ts4 (7) 9


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[15] Chung D D L 2004 Self-heating structural materials Smart Mater. Struct. 13 562–5 [16] Wan Y and Wen D 2004 Thermo-sensitive properties of carbon-black-loaded styrene butadiene rubber composite membranes Smart Mater. Struct. 13 983–9 [17] Feller J F, Chauvelon P, Linossier I and Glouannec P 2003 Characterization of electrical and thermal properties of extruded tapes of thermoplastic conductive polymer composites (CPC) Polym. Test. 22 831–7 [18] Droval G, Glouannec P, Feller J F and Salagnac P 2005 Simulation of electrical and thermal behavior of conductive polymer composites heating elements J. Thermophys. Heat Transfer 19 375–81 [19] Wang X and Chung D D L 1998 Short carbon fiber reinforced epoxy coating as a piezoresistive strain sensor for cement mortar Sensors Actuators A 71 208–12 [20] Cochrane C, Koncar V, Lewandowski M and Dufour C 2007 Design and development of a flexible strain sensor for textile structures based on a conductive polymer composite Sensors 7 473–92 [21] Feller J F, Guézénoc H, Bellégou H and Grohens Y 2005 Smart poly(styrene)/carbon black conductive polymer composites films for styrene vapour sensing Macromol. Symp. 222 273–80 [22] Zribi K, Feller J F, Elleuch K, Bourmaud A and Elleuch B 2006 Conductive polymer composites obtained from recycled

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