Article Transverse Thermal Conductivity of Epoxy Carbon Fiber Prepreg Laminates with a Graphite Filled Matrix

Simon Bard * , Martin Demleitner, Marius Radtke and Volker Altstädt Department of Polymer Engineering, University of Bayreuth, Universitätsstr. 30, 95444 Bayreuth, Germany; [email protected] (M.D.); [email protected] (M.R.); [email protected] (V.A.) * Correspondence: [email protected]



Received: 26 March 2019; Accepted: 24 April 2019; Published: 1 May 2019


Abstract: The thermal conductivity of carbon fiber reinforced polymers is crucial for new technologies and is used in cutting-edge technologies such as sensors, heated rollers and anti-icing of airplane wings. Researchers so far focused on coating conventional prepregs with thermally conductive materials to enhance the transversal conductivity. Another strategy is followed in this study: Thermally conductive matrices filled with graphite platelets were processed by a laboratory prepreg line. Laminates produced from this type of prepregs show an enhancement in thermal conductivity by 3.3 times with a 20 vol% filler content relative to the matrix, and a 55 vol% fiber volume content in the laminate. The research shows that the incorporation of conductive particles in the matrix is more effective for increasing the conductivity than previous methods.

Keywords: thermal conductivity; prepreg; carbon fiber; graphite

1. Introduction In the aerospace industry, where lightweight is an important topic to reduce the life-cycle costs of airplanes, metals are increasingly replaced by carbon fiber reinforced polymers (CFRP) [1]. CFRP offer a very high strength to weight ratio, but lack the properties of high thermal and electrical conductivity, which are crucial for some applications. The thermal conductivity is needed to diffuse heat faster, in order to avoid substantial overheating at one side of the part that could lead to microcracking and mechanical defects. Furthermore, the material should conduct the heat from hotspots to a cooling fluid. As explained by Rolfes and Hammerschmidt, the thermal conductivity also influences the mechanical properties, and the calculation of the temperature fields in a part is therefore important for a safe design with CFRP [2]. Only few researchers have so far focused on the thermal conductivity of carbon fiber reinforced laminates. Some publications about the influence of fiber volume content on the thermal conductivity can be found. Rolfes and Hammerschmidt simulated the thermal conductivity with different fiber morphologies, i.e., Polyacrylonitrile (PAN) and pitch based carbon fibers, but the experimental data measured by steady-state guarded hot plate (GHP) only show transverse thermal conductivities for two different fiber volume contents [2]. Pilling et al. prepared laminates with four different fiber volume contents of PAN-based fiber and measured them via transient hot-strip (THS) [3]. The results from Rolfes and Pilling differ significantly, which can be attributed to the different measurement methods used in their work. Very interesting results could also be found by Shim et al., who showed the influence of the fiber shape on the thermal conductivity for pitch-based fiber [4]. One simple strategy to enhance the thermal conductivity is the coating of conventional prepregs with conductive materials. Han and Chung used carbon black, Carbon Nanotubes (CNT) and chopped carbon fiber as a conductive coating. However, the used filler content of up to 0.8 vol% is rather

J. Compos. Sci. 2019, 3, 44; doi:10.3390/jcs3020044 www.mdpi.com/journal/jcs J. Compos. Sci. 2019, 3, 44 2 of 11 small. With the guarded hot plate method, they measured an increase in thermal conductivity from 1.091 W/mK to 1.453 W/mK, which is about 33%, with the coating with CNT and a fiber volume content of 65% [5]. Remarkably, the measured conductivity of the unmodified laminate differs from the experimental value of Rolfes, although the fiber volume content is at a comparable level. This can be either attributed to the use of different carbon fiber, voids in the laminates or the different measurement techniques. To compare the results from different researchers, the enhancement in the thermal conductivity in Table1 is shown in relative values. The most common approach to enhance the conductivity in epoxy resins without fiber reinforcement is the incorporation of a conductive filler. Carbon-based fillers (graphite [6], carbon nanotubes [7], carbon black [8], and graphene [9]), metallic fillers (Ag, Cu [10], Al [11], and TiO2), ceramic fillers (BN [12], AlN [13], Si [14,15], and ZrB2 [16]) and vegetal fibers [17] can be distinguished. Promising results could be found with graphene, e.g., a conductivity of 2 W/mK was found in an epoxy matrix with 15 vol% graphene [18]. As known from the literature, the incorporation of nanotubes leads to very high viscosity, which reduces the processability of polymer/nanotube composites [19]. In an elaborative review, Burger et al. concluded that nanofillers may not be suitable to achieve high thermal conductivity, not only because of the difficulty to incorporate higher loadings of filler, but also due to the ineffective heat transport in the matrix [20]. The high number of polymer/nanotube interfaces leads to phonon scattering, reducing the thermal conductivity of the composite material. Only a single publication dealing with the approach to use conductive epoxy matrices was identified [21]. The authors used boron-nitride as a filler and a mesophase pitch fiber as reinforcement. However, the fiber volume content of the specific samples is not mentioned. The approach of the underlying research is to improve the thermal conductivity of carbon fiber reinforced composites by the incorporation of filler in the epoxy matrix. First, the effect of graphite as a conductive filler in an epoxy matrix is studied. From the conductive matrix, a carbon fiber reinforced prepreg is produced and processed into laminates.

Table 1. Transverse conductivities of samples from the literature and their fiber volume content (FVC) and measurement methods as Laser Flash Analysis (LFA).

Thermal Measuring Enhancement Sample FVC Conductivity Method Method Enhancement (%) Epoxy/Carbon Coating of prepreg: 65.0 proprietary 33.2% Fiber [5] 0.4% SWNT Epoxy/Mesophase Matrix n.a. LFA 78.9% Pitch Fiber [21] modification Underlying Conductive matrix: 55 LFA 330% research 20 vol% graphite

2. Production and Characterization Methods

2.1. Materials The resin Tetraglycidylmethylenedianiline (TGMDA, EpikoteTM RESIN 496, Hexion Inc., Columbus, OH, USA) is tetra-functional with an epoxy equivalent of 115 g/eq and was cured with Diethyltoluenediamine (XB3473TM, DETDA, hydrogen equivalent weight 43 g/eq). Graphite (Imerys Graphite & Carbon, Bodio, Switzerland) with the trade name Graphit Timrex® KS6 and KS44 was used as conductive filler. The filler is characterized by a platelet-shape and an average particle 3 size of 3.6 µm (D50) and 18.4 µm (D50), according to the manufacturer. The density is 2.255 g/cm . The particle size distribution was measured and can be found in Figure1. The data measured in our lab slightly differs from the manufacturer’s data. A PAN based fiber 12K A-49 (DowAksa, Atlanta, GA, J. Compos. Sci. 2019, 3, 44 3 of 11 J. Compos. Sci. 2019, 3, x 3 of 12

USA) with a tensile strength of around 4900 MPa and a Young’s modulus of 250 GPa has been used for the prepregJ. Compos. production.Sci. 2019, 3, x 3 of 12

Figure 1. Particle size distribution of the used graphite types. FigureFigure 1. 1.Particle Particle size size distributiondistribution of of the the used used graphite graphite types. types. 2.2. Resin Preparation and Curing 2.2. Resin2.2. Resin Preparation Preparation and and Curing Curing Resin and hardener were stirred at a stoichiometric ratio of 72:28. The mixture was degassed at ResinResin and and hardener hardener were were stirred stirred at at a a stoichiometric stoichiometric ratio ratio of of 72:28. 72:28. The The mixture mixture was was degassed degassed at at 10–2010–20 mbar. mbar. The Themass mass ratio ratio of ofgraphite graphite is is related related to to the volumevolume of of the the whole whole mixture, mixture, i.e., i.e., to achieve to achieve 3 3 3 100 cm1003 ofcm the3 of samplethe sample with with aa1515 a15 vol% vol% vol% graphite graphite content, content, 8585 cm cm3 3resin/hardener resin/hardenerresin/hardener and and 15 cm 153 cmgraphite3 graphite were weremixed. mixed. Densities Densities Densities of of 2.225of 2.225 2.225 g/cm³ g /g/cm³cm3 forfor for the thethe graphi graphitegraphite andand and 1.2 1.2 1.2 g/cm³ g/cm³ g/cm for3 forfor the the the resin resin resin were were were used used used for the for for the calculations,calculations, in in order order in order to to measure to measure the the relevant relevant mass mass of of thethe resinresin and and filler. filler. filler. A three-rollA three-roll mill mill (EXAKT (EXAKT 120EH-450, Norderstedt, Germany) was used to homogeneously disperse the filler in the matrix with 120EH-450, Norderstedt, Germany) was used to homoge homogeneouslyneously disperse the filler filler in the matrix with opening gaps of 63 and 21 μm. The samples were cured under pressure in a laboratory press at 120, opening gaps gaps of of 63 63 and 21 μµm. The The samples samples were were cured cured under under pressure pressure in in a a laboratory laboratory press press at at 120, 120, 160 and160 200and °C,200 at°C, each at each temperature temperature for for 1 1 h h with with a heating rate rate of of 10 10 K/min. K/min. A postcuringA postcuring at 220 at °C220 °C 160 andfor 2002 h followed,◦C, at each before temperature cooling down for 1at h a withrate of a heating5 K/min. rate of 10 K/min. A postcuring at 220 ◦C for for2 h 2 followed, h followed, before before cooling cooling down down at a at rate a rate of 5 of K /5min. K/min. 2.3. Prepreg Production 2.3. Prepreg Prepreg Production Production The unidirectional prepregs were produced via hot-melt processing at the laboratory scale Theprepreg unidirectionalunidirectional impregnation prepregs prepregs machinery were were of producedthe produced University via hot-meltviaof Bayreuth. hot-melt processing processing at the laboratoryat the laboratory scale prepreg scale prepregimpregnation impregnationFirst of machinery all, the machineryunidirectional of the University of rovingsthe University of of Bayreuth.12K carbon of Bayreuth. fibers are pre-spread on the pre-spreading Firstunit, ofas all,shown the in unidirectional Figure 2. The resinrovings film of was 12K coated carbon at 25fibers fibers °C on are a siliconizedpre-spread carrier on the paper pre-spreading in the coating unit of the prepreg machinery. Finally, the resin film and pre-spread fibers were impregnated unit, as shown in Figure 22.. TheThe resinresin filmfilm waswas coatedcoated atat 2525 °C◦C on a siliconized carrier paper in the coatingto the unit final of of the theprepreg prepreg prepreg with machinery. machinery. a calendar (25Finally, Finally, °C). The the producedresin resin film film prepregs and and pre-spread pre-spread were then fibers fibers hand-lain were were upimpregnated impregnated to the final unidirectional prepreg laminates and cured with the same parameter as the neat and filled resin toto the final final prepreg with a calendar (25 °C).C). The produced prepregs were then hand-lain up to the samples. The aimed fiber volume content◦ was set to 55 vol% to ensure the comparability of the final unidirectional prepreg laminates and cured with the same parameter as the neat and filled resin final unidirectionalprepreg laminates. prepreg laminates and cured with the same parameter as the neat and filled resin samples. The The aimed aimed fiber fiber volume volume content content was was set set to to 55 55 vol% vol% to to ensure ensure the comparability of the prepreg laminates.

Figure 2. Single unidirectional-rovings, pre-fiber spreading unit, resin coating unit and final prepreg, respectively. Figure2.4. Morphological 2. 2. SingleSingle unidirectional-rovings, Characterization unidirectional-rovings, pre-fiber pre-fiber spreadin spreadingg unit, resin unit, coating resin coatingunit and unit final and prepreg, final respectively.prepreg, respectively.

2.4. Morphological Characterization

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2.4. Morphological Characterization All samples were scanned with Skyscan 1072 Micro-CT (Bruker, Artselaar, Belgium), with a linear resolution of 3.50 µm at a magnification of 80 with an accelerating voltage of 80 kV and tube current of 122 µA. The projection images were acquired over 180◦ at angular increments of 0.23◦ with an exposure time of 2.57 seconds per frame, averaged over six frames. The three-dimensional images were reconstructed using the reconstruction software provided by the manufacturer (NRecon Version 1.6.4.1, Kontich, Belgium), where the ring artifact reduction was applied as needed. The samples were sputtered by a Cressington 108 Auto Sputter Coater (Watford, UK) with an Au coating thickness of 13 nm, and they were studied in a Jeol JSM 6510 Scanning Electron Microscope (Tokyo, Japan).

2.5. Thermal Conductivity Measurements The thermal conductivity was measured by the laser flash method (LFA) with LFA447 (Netzsch GmbH, Selb, Germany). Five shots were used with a duration of 30 ms each, and the signal was fitted with the Proteus Analysis Software (Netzsch GmbH, Selb, Germany), using the Cape-Lehman algorithm. The tested samples had a diameter of 12.7 mm. The laser flash analysis is the standard instrument for the determination of thermal transport properties of carbon fiber reinforced polymers because of its convenience, short experiment times and large measurement range [2,22]. The density was measured with AG245 (Mettler-Toledo International Inc., Columbus, OH, USA), using Archimedes’ principle. The thermal heat capacity was measured by DSC 1 (Mettler-Toledo International Inc., USA) according to ASTM E1269–11 with a heating rate of 20 K/min.

3. Results and Discussions

3.1. Neat and Filled Resin Conductivity For a thorough investigation, first the effects of the filler on the thermal conductivity should be evaluated. This section focuses only on the effects in composites of resin and filler, whereas the next sections focus on the fiber-reinforced composites. The thermal conductivity values of the composites versus the filler content are shown in Figure3. At lower filler concentrations of up to 10 vol%, the increase in the thermal conductivity is almost linear. At higher filler concentrations, the thermal conductivity increases exponentially. This behavior has already been described by several researchers [20,23,24]. At higher filler concentrations, a remarkable difference in the thermal conductivity can be found between the composites with small and larger particles. In the literature, contradicting influences of the particle size on the thermal conductivity have been reported. Boudenne et al. reported higher thermal conductivities for small copper particles of 12 µm in average in a Polypropylene matrix than for larger particles of 200 µm [25]. Zhu et al. reported contradictory results with boron-nitride of 70 nm and 7 µm in an epoxy matrix. [26] In both studies, it seems that the morphology and shape of the filler was not taken into account. In this study, the shape of the particles is very similar, as can be observed in Figure4. The aspect ratio was calculated from 60 measurements of the particles observed in Scanning Electron Microscope (SEM) and is at 36 4 for the smaller and ± 32 5 for the larger particles. The higher thermal conductivity for composites with larger particles ± can be explained from a thermo-mechanical point of view. Heat is conducted by phonons in polymer composites. It seems that for the thermal conductivity, the interfaces between the conducting parts of the composite are fundamental. As elaborated by Burger et al., the phonons are scattered at the interfaces, which lowers the thermal conductivity [20]. As a result, we can evaluate the resin-filler interfaces and the filler-filler interfaces, in case the particles are in contact with each other. The larger the particle size, the lower the number of interfaces at a given volume fraction of the filler. As already explained by Zhu, the lower number of contacts between particles can explain the better conductivity of larger sized particles [26]. The particle-matrix interaction seems to be more significant than the particle-particle interaction. As explained, the former leads to phonon scattering at the interface. J. Compos. Sci. 2019, 3, x 44 55 of of 1112

Smaller particles therefore lead to more interfaces, which result in an increase in phonon scattering and thereforeJ. Compos.a Sci. higher 2019, 3, x thermal resistance. 5 of 12

Figure 3. Thermal conductivity of epoxy/filler composites depending on the filler content, fitted with Figure 3. Thermal conductivity of epoxy/filler composites depending on the filler content, fitted with equationsFigure from 3. ThermalLewis/Nielsen. conductivity of epoxy/filler composites depending on the filler content, fitted with equationsequations from Lewisfrom Lewis/Nielsen./Nielsen.

Figure 4. Records from scanning electron microscope of small (3.6 μm) and large (18.4 μm) graphitic Figure 4.particles.Records from scanning electron microscope of small (3.6 µm) and large (18.4 µm) graphitic particles. Figure 4. Records from scanning electron microscope of small (3.6 μm) and large (18.4 μm) graphitic particles.Besides the size of the filler shown in Figure 4, the morphology of the samples is crucial for the Besides the size of the filler shown in Figure4, the morphology of the samples is crucial for the evaluation of the results from the thermal conductivity. Several methods have been used to study the evaluation of the results from the thermal conductivity. Several methods have been used to study the Besidesmorphology, the size from of whichthe filler μCT shown and SEM in seem Figure the most4, the promising. morphology The μ CTof scansthe samples of composites is crucial with for the morphology, from which µCT and SEM seem the most promising. The µCT scans of composites with evaluationparticles of the of results3.6 and 18.4from μm the are thermal shown in conducti Figure 5. vity.One can Several clearly methods see that no have voids been can beused found to instudy the particlesthe of material. 3.6 and 18.4The µdistributionm are shown of the in filler Figure seems5. One very can homogenous. clearly see The that voxel-size no voids of can the be μ foundCT is in the morphology, from which μCT and SEM seem the most promising. The μCT scans of composites with material.~2.5 The μm, distribution so agglomerations of the fillerof the seemsmicro-sized very homogenous.graphite particles The can voxel-size be excluded. of theFor µa CTdeeper is ~2.5 µm, particles of 3.6 and 18.4 μm are shown in Figure 5. One can clearly see that no voids can be found in so agglomerationsinvestigation of of the the morphologies, micro-sized several graphite SEMparticles pictures have can been be excluded.taken. Figure For 6 shows a deeper two fracture investigation the material.surfaces The of compositesdistribution with of 3.6 the and filler 18.4 seemsμm graphitic very homogenous.platelets. Both confirmThe voxel-size the homogenous of the μCT is of the morphologies, several SEM pictures have been taken. Figure6 shows two fracture surfaces ~2.5 μm,distribution so agglomerations in the matrix. of the micro-sized graphite particles can be excluded. For a deeper of composites with 3.6 and 18.4 µm graphitic platelets. Both confirm the homogenous distribution investigation of the morphologies, several SEM pictures have been taken. Figure 6 shows two fracture in the matrix. surfaces of composites with 3.6 and 18.4 μm graphitic platelets. Both confirm the homogenous distribution in the matrix.

J. Compos. Sci. 2019, 3, x 6 of 12 J. Compos. Sci. 2019, 3, 44 6 of 11 J. Compos. Sci. 2019, 3, x 6 of 12

Figure 5.5. μµCT scans cut from LFA samplessamples with small (left) and large (right)(right) particles with a fillerfiller contentFigurecontent 5. ofof μ 1515CT vol.%.vol.%. scans cut from LFA samples with small (left) and large (right) particles with a filler content of 15 vol.%.

Figure 6.6. SEM of small (3.6 μµm) and large (18.4 μµm) graphitic particles at a magnification magnification of 2 K. SamplesFigureSamples 6. fromfrom SEM LFALFA of small havehave been(3.6been μ brokenbrokenm) and manually.manually. large (18.4 μm) graphitic particles at a magnification of 2 K. Samples from LFA have been broken manually. 3.2. Laminate Characterization 3.2. Laminate Characterization 3.2. LaminateAs shown Characterization by Rolfes, the fiber volume content has an influence on the thermal conductivity [2]. As shown by Rolfes, the fiber volume content has an influence on the thermal conductivity [2]. To verify the comparability of the samples, the fiber volume content has been measured and calculated To verifyAs shown the comparabilityby Rolfes, the fiberof the volume samples, content the hasfiber an volume influence content on the hasthermal been conductivity measured and[2]. by thermogravimetry. The method has been described and verified by Monkiewitsch [27]. As shown Tocalculated verify bythe thermogravimetry. comparability of theThe samples,method has th ebe fiberen described volume andcontent verified has by been Monkiewitsch measured [27].and in Table2, the fiber volume content varies only slightly between the samples, so we can expect them to calculatedAs shown byin Tablethermogravimetry. 2, the fiber volume The method content has vari beesen only described slightly and between verified the by samples,Monkiewitsch so we [27]. can be comparable. Asexpect shown them in toTable be comparable. 2, the fiber volume content varies only slightly between the samples, so we can expect them to be comparable. Table 2. Fiber volume content of the produced laminates. Table 2. Fiber volume content of the produced laminates. Table 2. Fiber volume content of the produced laminates. PrepregPrepreg Laminate Laminate Fiber Fiber Volume Volume Content Content Prepregunfilled Laminate Fiber Volume 48 vol% Content Graphite ø 18.4unfilledµm–10 vol%48 55 vol% vol% unfilled 48 vol% GraphiteGraphite ø ø 18.4 18.4µ m–15μm–10 vol% vol% 55 53 vol% vol% GraphiteGraphite ø ø 18.4 18.4µ μm–20m–10 vol% vol% 55 57 vol% vol% GraphiteGraphite ø ø 3.6 18.4µm–15 μm–15 vol% vol% 53 56 vol% vol% Graphite ø 18.4 μm–15 vol% 53 vol% Graphite ø 18.4 μm–20 vol% 57 vol% Graphite ø 18.4 μm–20 vol% 57 vol% Figure7 shows the thermalGraphite conductivities ø 3.6 μm–15 of vol% the prepreg laminates 56 vol% measured by LFA. The unfilled resin has a thermal conductivityGraphite of ø 0.23 3.6 Wμm–15/mK, vol% which is increased 56 vol% to 0.36 W/mK by the incorporation of carbonFigure fibers. 7 shows The valuesthe thermal are lower conductivities than those of of otherthe prepreg researchers. laminates Rolfes measured and Hammerschmidt by LFA. The usedunfilledFigure fibers resin with 7 showshas a transverse a thermalthe thermal thermal conductivity conductivities conductivity of 0.23 ofof W/mK, 2the W/ mKprepreg which with roundlaminatesis increased carbon measured to fibers; 0.36 they W/mKby measuredLFA. by Thethe aunfilledincorporation transverse resin thermal hasof carbon a conductivitythermal fibers. conductivity The of 0.708 values W of/ mKare 0.23 withlo W/mK,wer 64.3 than vol%which those of is fiber ofincreased other with theresearchers. to steady-state 0.36 W/mK Rolfes guarded by andthe hotincorporationHammerschmidt plate (GHP) of setup. carbonused Forfibers fibers. the with cross-section The a transversevaluestype are ther usedlowermal in than conductivity this study,those Shimof ofother 2 et W/mK al. researchers. showed with around significantly Rolfes carbon and lowerHammerschmidtfibers; thermal they measured conductivity used a fibers transverse [4 ].with The athermal values transverse are conductivi also ther notmal comparable,ty conductivity of 0.708 W/mK as diofff 2erentwith W/mK 64.3 measurement with vol% round of fiber methods carbon with fibers; they measured a transverse thermal conductivity of 0.708 W/mK with 64.3 vol% of fiber with

J. Compos. Sci. 2019, 3, x 7 of 12 the steady-state guarded hot plate (GHP) setup. For the cross-section type used in this study, Shim J. Compos. Sci. 2019, 3, 44 7 of 11 et al. showed a significantly lower thermal conductivity [4]. The values are also not comparable, as different measurement methods have been used, and given that Rolfes and Hammerschmidt already showedhave been that used, there and is a given strong that variation Rolfes in and the Hammerschmidt measured thermal already conductivity showed with that the there GHP is aand strong the THSvariation methods. in the [2] measured When the thermal conductive conductivity graphite fille withd theresin GHP with and a thermal the THS conductivity methods [2 of]. 0.7 When W/mK the isconductive used for the graphite prepreg filled production, resin with the a conductivity thermal conductivity in the laminate of 0.7 increases W/mK is to used 0.91 for W/mK the prepreg for the largeproduction, particles. the conductivity in the laminate increases to 0.91 W/mK for the large particles.

FigureFigure 7. 7. ThermalThermal conductivity conductivity of of prepre prepregg laminates laminates measured by LFA.

Although the results from the graphite filled resins without carbon fibers indicate that larger Although the results from the graphite filled resins without carbon fibers indicate that larger particles lead to higher conductivities in the composite, the effect could not be repeated with carbon particles lead to higher conductivities in the composite, the effect could not be repeated with carbon fiber reinforced composites. Figure7 shows a strong e ffect of the filler volume content of the laminates fiber reinforced composites. Figure 7 shows a strong effect of the filler volume content of the on the thermal conductivity, as the conductivity of the laminate significantly increases when the filler laminates on the thermal conductivity, as the conductivity of the laminate significantly increases content is varied from 10 to 15 and to 20 vol%. when the filler content is varied from 10 to 15 and to 20 vol%. Figure8 shows records from µCT of the prepreg laminates. The images show that the samples Figure 8 shows records from μCT of the prepreg laminates. The images show that the samples are very homogenous. From the pictures that have been evaluated, no voids could be found in the are very homogenous. From the pictures that have been evaluated, no voids could be found in the prepreg laminates. For a deeper understanding of the morphology of the prepreg laminates, optical microscopy has been used to produce andand analyzeanalyze polishedpolished micrographmicrograph sections.sections. In In the unfilled unfilled laminate,laminate, thethe fibersfibers areare well well distributed. distributed. They They are ar note not absolute absolute homogenously homogenously distributed, distributed, as resin-richas resin- richareas areas can becan detected be detected in the in cross-section. the cross-section. The laminates The laminates with filled with matrices filled matrices have a layered have a structure layered structurewith layers with of resinlayers and of resin layers and of la fiber.yers Asof fiber. can be As seen can inbe Figureseen in9 ,Figure the distance 9, the distance between between the carbon the µ carbonfiber layer fiber varies layer between varies between 80 and 200 80 andm. From200 μ them. evaluatedFrom the images,evaluated no directimages, contact no direct between contact the J. Compos. Sci. 2019, 3, x 8 of 12 betweencarbon fiber the layerscarbon could fiber layers be found. could be found.

Figure 8. µCT scans of prepreg laminates, from left to right: unfilled, 10, 15, 20 vol% of large particles, Figure 8. μCT scans of prepreg laminates, from left to right: unfilled, 10, 15, 20 vol% of large particles, 15 vol% of small particles. 15 vol% of small particles.

Figure 9. Optical microscopy records of prepreg laminates, from left to right: unfilled, 15 vol% of small particles, 15 vol% of large particles.

The smaller particles of graphite had been chosen to test the assumption that particles with a smaller diameter than the fibers could be adsorbed between the fiber layer. As shown in Figure 10, only very few particles of the graphite with 3.6 μm will be pushed between the carbon fiber layers during the prepreg production and the curing process. Most particles stay in the matrix between the layers. Almost no larger particles of 18.4 μm could be found between the carbon fibers in the laminate. It seems that the layer of carbon-fiber is very dense and hence particles are not able to be infiltrated. Also, the very high viscosity of the graphite filled epoxy resin might reduce the movability of the graphite particles.

Figure 10. SEM records of the prepreg laminates, left: with small particles of 3.6 μm; and right: with particles of 18.4 μm.

4. Micromechanical Calculations The Lewis and Nielsen’s formula is used in various publications to calculate the thermal conductivity of composites [2,22,28,29]. It is formulated as follows:

J. Compos. Sci. 2019, 3, x 8 of 12 J. Compos. Sci. 2019, 3, x 8 of 12

Figure 8. μCT scans of prepreg laminates, from left to right: unfilled, 10, 15, 20 vol% of large particles, Figure 8. μCT scans of prepreg laminates, from left to right: unfilled, 10, 15, 20 vol% of large particles, J. Compos.15 vol% Sci. 2019of small, 3, 44 particles. 8 of 11 15 vol% of small particles.

Figure 9. Optical microscopy records of prepreg laminates, from left to right: unfilled, 15 vol% of FigureFigure 9.9. OpticalOptical microscopy microscopy records records of of prepreg prepreg laminates, laminates, from from left toleft right: to right: unfilled, unfilled, 15 vol% 15 ofvol% small of small particles, 15 vol% of large particles. particles,small particles, 15 vol% 15 of vol% large of particles. large particles.

TheThe smaller smaller particles particles of of graphite graphite had had been been chosen chosen to to test test the the assumption assumption that that particles particles with with a a The smaller particles of graphite had been chosen to test the assumption that particles with a smallersmaller diameter diameter than than the the fibers fibers could could be be adsorbed adsorbed between between the the fiber fiber layer. layer. As As shown shown in in Figure Figure 10, 10 , smaller diameter than the fibers could be adsorbed between the fiber layer. As shown in Figure 10, onlyonly very very few few particles particles of of the the graphite graphite with with 3.6 3.6 μµmm will will be be pushed pushed between between the the carbon carbon fiber fiber layers layers only very few particles of the graphite with 3.6 μm will be pushed between the carbon fiber layers duringduring the the prepreg prepreg production production and and the the curing curing proce process.ss. Most Most particles particles stay stay in in the the matrix matrix between between the the during the prepreg production and the curing process. Most particles stay in the matrix between the layers.layers. Almost Almost no no larger larger particles particles of of 18.4 18.4 μµmm could could be be found found between between the the carbon carbon fibers fibers in in the the laminate. laminate. layers. Almost no larger particles of 18.4 μm could be found between the carbon fibers in the laminate. ItIt seems seems that that the the layer layer of of carbon-fiber carbon-fiber is is very very dense dense and and hence hence particles particles are are not not able able to to be be infiltrated. infiltrated. It seems that the layer of carbon-fiber is very dense and hence particles are not able to be infiltrated. Also,Also, the the very very high high viscosity viscosity of of the the graphite graphite fill filleded epoxy epoxy resin resin might might reduce reduce the the movability movability of of the the Also, the very high viscosity of the graphite filled epoxy resin might reduce the movability of the graphitegraphite particles. particles. graphite particles.

Figure 10. SEM records of the prepreg laminates, left: with small particles of 3.6 µm; and right: with Figure 10. SEM records of the prepreg laminates, left: with small particles of 3.6 μm; and right: with particlesFigure 10. of SEM 18.4 µrecordsm. of the prepreg laminates, left: with small particles of 3.6 μm; and right: with particles of 18.4 μm. 4. Micromechanicalparticles of 18.4 μ Calculationsm. 4. Micromechanical Calculations 4. MicromechanicalThe Lewis and Calculations Nielsen’s formula is used in various publications to calculate the thermal conductivityThe Lewis of compositesand Nielsen’s [2,22 formula,28,29]. Itis is used formulated in various as follows: publications to calculate the thermal The Lewis and Nielsen’s formula is used in various publications to calculate the thermal conductivity of composites [2,22,28,29]. It is formulated as follows: conductivity of composites [2,22,28,29]. It is formulated1 + AB asφ follows: λ = λ (1) k M 1 B φ C − where φ is defined as the filler content and λM as the conductivity of the matrix. The factors A, B and C reflect the filler geometry, orientation and thermal conductivity. According to Guth [30], A can be calculated with the aspect ratio p of the filler: p A = + 1 (2) [2 ln(2p)] 3 − B is not an independent variable, since it also reflects the conductivity of the filler and matrix, and C reflects the maximal packing density φmax:

(λF) (λ ) 1 B = M − (3) ( ) λF + A (λM) J. Compos. Sci. 2019, 3, x 9 of 12

1 + 𝐴 𝐵 𝜙 𝜆 =𝜆 (1) 1−𝐵 𝜙 𝐶

where 𝜙 is defined as the filler content and 𝜆 as the conductivity of the matrix. The factors 𝐴, 𝐵 and C reflect the filler geometry, orientation and thermal conductivity. According to Guth [30], A can be calculated with the aspect ratio 𝑝 of the filler: 𝑝 𝐴 = +1 2ln(2𝑝) −3 (2) B is not an independent variable, since it also reflects the conductivity of the filler and matrix, and C

reflects the maximal packing density 𝜙: J. Compos. Sci. 2019, 3, 44 9 of 11 (𝜆 ) −1 (𝜆 ) 𝐵= (3) (𝜆 ) (1 φ+max𝐴 ) C = 1 + (𝜆−) φ (4) 2 φmax (1 − 𝜙) 𝐶=1+ 𝜙 (4) The maximal packing density of the fibers in the𝜙 composite is 78%, with the thermal conductivity of the matrixThe given maximal above packing and the density transverse of the thermalfibers in the conductivity composite is of 78%, the fiberwith ofthe 1.1 thermal W/mK. conductivity The transverse thermalof the conductivity matrix given of above the fiber and canthe onlytransverse be estimated thermal conductivity as no method of tothe measure fiber of 1.1 a single W/mK. fiber The could be identifiedtransverse in thermal the literature. conductivity Rolfes of the and fiber Hammerschmidt can only be estimated [2] calculated as no method a transverse to measure conductivity a single of 2 W/mKfiber fromcould their be identified experimental in the dataliterature. for round-type Rolfes and Hammerschmidt PAN fiber. For the[2] calculated cross-section a transverse type used in this study,conductivity Shim of et 2 al. W/mK showed from a their significantly experimental lower data thermal for round-type conductivity, PAN fiber. so For a thermal the cross-section conductivity of 1.1type W/ mKused seems in this reasonablestudy, Shim foret al. this showed study a [si4gnificantly]. A is calculated lower thermal to 0.83 conductivity, with an aspect so a thermal ratio of 0.5, as suggestedconductivity in the of 1.1 literature W/mK seems [2]. reasonable for this study [4]. A is calculated to 0.83 with an aspect ratio of 0.5, as suggested in the literature [2]. Figure 11 shows the experimental data and calculations with the above equation of transverse Figure 11 shows the experimental data and calculations with the above equation of transverse thermal conductivities of the laminates. For the unfilled laminate and the laminate with 10 vol% thermal conductivities of the laminates. For the unfilled laminate and the laminate with 10 vol% of of graphiticgraphitic filler, filler, the the Lewis Lewis/Nielsen/Nielsen calculation over overestimatesestimates the the transverse transverse thermal thermal conductivities. conductivities. For theFor laminates the laminates of 15 vol%of 15 ofvol% graphite of graphite and 20 vol%and 20 of graphite,vol% of graphite, the calculations the calculations with the Lewiswith /theNielsen formulaLewis/Nielsen seem very formula accurate. seem very accurate.

FigureFigure 11. Thermal 11. Thermal conductivity conductivity of of the the laminates laminates from from th thee experimental experimental data data and and calculated calculated according according to Lewisto Lewis/Nielsen/Nielsen equations. equations. 5. Conclusions

The aim of this work was to explore the influence of a graphitic filler on the thermal conductivity of an epoxy-based carbon-fiber reinforced polymer. The following conclusions can be drawn from the analysis of the results:

In the epoxy resin, a non-linear dependence of the thermal conductivity from the filler volume • content could be found. Larger particles showed a higher conductivity, most probably due to lower phonon scattering. In the carbon fiber reinforced composites, the thermal conductivity was enhanced by a factor of 4 • with 20 vol% of graphitic particles. The fiber reinforced laminate showed a different behavior compared to the epoxy graphite composites: Small and large particles showed very similar transverse thermal conductivities.

Further developments are needed to understand the influence of the fiber on the thermal conductivity. As stated above, no measurement method has been developed so far to measure the conductivity of carbon fibers, which makes simulations almost impossible. For a further increase in J. Compos. Sci. 2019, 3, 44 10 of 11 the thermal conductivity, conductive fibers might be used. Furthermore, a deeper understanding of the mechanical properties of CFRP is crucial for the application of the materials in the industry.

Author Contributions: Conceptualization, S.B.; Methodology, S.B.; Validation, S.B., M.R. and V.A.; Formal Analysis, S.B. and M.R.; Investigation, M.R.; Resources, V.A.; Data Curation, S.B. and M.R.; Writing-Original Draft Preparation, S.B.; Writing-Review & Editing, M.D.; Visualization, S.B.; Supervision, S.B.; Project Administration, S.B. Funding: Authors kindly thank to the German Ministry of Economy and Energy (BMWi) for the funding of the Lufo Project TELOS (FKZ 20Y1516D). Conflicts of Interest: There are no conflicts of interest associated with this publication.

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