Synergistic Effects of Various Ceramic Fillers on Thermally Conductive Polyimide Composite Films and Their Model Predictions

Article Synergistic Effects of Various Ceramic Fillers on Thermally Conductive Polyimide Composite Films and Their Model Predictions

Heeseok Song 1,2, Byoung Gak Kim 1,3, Yong Seok Kim 1,3, Youn-Sang Bae 2, Jooheon Kim 4,* and Youngjae Yoo 1,3,*

1 Division of Advanced Materials, Korea Research Institute of Chemical Technology, Daejeon 34114, Korea; [email protected] (H.S.); [email protected] (B.G.K.); [email protected] (Y.S.K.) 2 Department of Chemical and Biomolecular Engineering, Yonsei University, Seoul 03722, Korea; [email protected] 3 Department of Chemical Convergence Materials, University of Science and Technology, Daejeon 34113, Korea 4 School of Chemical Engineering & Materials Science, Chung-Ang University, Seoul 156-756, Korea * Correspondence: [email protected] (J.K.); [email protected] (Y.Y.); Tel.: +82-2-820-5763 (J.K.); +82-42-860-7216 (Y.Y.); Fax: +82-2-824-3495 (J.K.); +82-42-861-4151 (Y.Y.) Received: 14 January 2019; Accepted: 4 March 2019; Published: 13 March 2019

Abstract: In this study, thermally conductive composite films were fabricated using an anisotropic boron nitride (BN) and hybrid filler system mixed with spherical aluminum nitride (AlN) or aluminum oxide (Al2O3) particles in a polyimide matrix. The hybrid system yielded a decrease in the through-plane thermal conductivity, however an increase in the in-plane thermal conductivity of the BN composite, resulting from the horizontal alignment and anisotropy of BN. The behavior of the in-plane thermal conductivity was theoretically treated using the Lewis–Nielsen and modified Lewis–Nielsen theoretical prediction models. A single-filler system using BN exhibited a relatively good fit with the theoretical model. Moreover, a hybrid system was developed based on two-population approaches, the additive and multiplicative. This development represented the first ever implementation of two different ceramic conducting fillers. The multiplicative-approach model yielded overestimated thermal conductivity values, whereas the additive approach exhibited better agreement for the prediction of the thermal conductivity of a binary-filler system.

Keywords: thermal conductivity; binary ﬁller; modeling; polymer composite

1. Introduction Heat generation in electronic devices has a significant effect on the performance of these devices; thus, various methods of thermal control have recently attracted considerable attention. To solve the heat dissipation problem in electronic devices, polymeric hybrid materials, such as alumina (Al2O3)[1–3] silicon carbide (SiC) [4], aluminum nitride (AlN) [5], and hexagonal boron nitride (BN) [6,7], have been used as thermally conductive ceramic fillers in polymer matrices. Also, graphene is used to improve the thermal conductivity of composites. Zhaid et al. reported the graphene supported thermal interface material (TIM), which has outstanding thermal and electrical conductivity by a simple fabrication process [8]. Among these materials, BN seems the most promising, owing to its high thermal conductivity (up to 400 W/m·K) and relatively low dielectric constant (approximately four), compared with those of other ceramic fillers. Moreover, the thermal conductivity of BN depends on the orientation direction (i.e., is anisotropic), thereby leading to a high versatility of BN in product design [9,10]. Thermally

Polymers 2019, 11, 484; doi:10.3390/polym11030484 www.mdpi.com/journal/polymers Polymers 2019, 11, 484 2 of 9 conductive composites containing ceramic fillers in epoxy [2], high-density polyethylene (HDPE) [11], linear low-density polyethylene (LLDPE) [12], polystyrene (PS) [13], and polyamide (PA) [6] have been previously reported. Recently, polyimide (PI)-based composite materials with outstanding properties (high chemical resistance, high mechanical strength, high thermal stability, and low dielectric constants) have been widely applied to packaging and insulating materials in the microelectronics and aerospace industries. Unfortunately, high concentrations of conducting filler in these materials hinder the use of the composites in various applications, owing to the loss of polymeric material [6,7]. Several studies have considered binary filler systems for polymer composites. Che et al. fabricated high-density polyethylene/boron nitride/carbon nanotubes (CNTs) via melt-mixing and subsequent hot rolling and reported that as the content of BN increases, BN forms an effective network with CNTs in the matrix [14]. Bian et al. prepared dopamine modified binary filler, micro-sized BN, and nano-sized Al2O3 for epoxy composites. They confirmed that BN mainly built the heat conduction network and Al2O3 formed a bridge between the BN particles [14]. Chen et al. [15] fabricated epoxy composites with two types of spherical Al2O3 to control the viscosity and thereby improve the processability; these composites exhibited high thermal conductivity. Furthermore, Choi et al. [16] prepared Al2O3 and AlN of different sizes with the aim of improving the packaging loading of fillers, and the resulting composites yielded high thermal conductivity. As an extension of a previous study based on carbon fillers [17], the present work represents a systematic investigation of the morphology and properties characterizing composite films based on ceramic fillers. The effects of individual and multiple fillers on the morphology and thermal conductivity are discussed. Furthermore, a detailed model prediction for the composites is presented and used for the incorporation of two fillers.

2. Experimental

2.1. Materials Analytical grade pyromellitic dianhydride (PMDA) and 4,40-oxydianiline (ODA) were obtained from Daicel Chemical (Osaka, Japan) and Wakayama Seika Kogyo Co. Ltd. (Wakayama, Japan). N,N-dimethylacetamide (DMAc) solvent was purchased from J.T. Baker (Phillipsburg, NJ, USA). Preferentially, PMDA was puriﬁed by vacuum sublimation. The BN powder (with an average particle size of approximately 5 µm) was purchased from ChangSung (Seoul, Korea), while the Al2O3 (average particle size > 10 µm) and AlN (average particle size of approximately 10 µm) powders were acquired from Sigma Aldrich (St. Louis, MO, USA).

2.2. Preparation of Polyimide-Filler Composite Films The PMDA powder was first purified by vacuum sublimation. First, a specified amount of 4,40-oxydianiline (ODA) was stirred with N,N-dimethylacetamide (DMAc) solvent. Then, a pyromellitic dianhydride (PMDA) of the same molar ratio as 4,40-oxydianiline (ODA) was added. Therefore, a PMDA-ODA (polyamic acide, PAA) precursor of 20 wt % was prepared. A specified amount of the BN filler mixture with 3.3 mL of DMAc was added with 10 g of prepared PAA under N2 atmosphere and was agitated overnight using magnetic stirring. The weight ratios of the hybrid BN + AlN and BN + Al2O3 fillers that were utilized in this study were equal to 1:1. The filler contents were manufactured with 10, 20, and 30 wt %. The prepared samples were first cast on a 230 × 85 × 3 mm glass plate using a doctor blade and were then dried at 40 ◦C in a vacuum oven for 4 h to remove solvent traces as well as any micro- or nano-sized bubbles. After that, the samples were polyamic acid, PAA subjected to imidization in a convection oven at 120, 180, and 250 ◦C for 30 min and then at 350 ◦C for 1 h. The fabrication procedure of PI composites is illustrated in Scheme1. Polymers 2018, 10, x FOR PEER REVIEW 3 of 9

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Scheme 1. Illustration of the PI (polyimide) composite fabrication procedure.

2.3. Characterization The cross-sectionalScheme 1. fracture Illustration surfaces of the PI of (polyimide the film were) composite polished fabrication using procedure. an ion polishing system (Ilion II model 697, Thomson Scientific Instruments, Box hill, Victoria, Australia). To investigate the2.3. morphologyCharacterization of the fillers and PI matrices, the cross-sectional fracture surfaces of the films wereThe observed cross-sectional by using fieldfracture emission surfaces scanning of the film electron were microscopy polished using (FE-SEM, an ion Merlin, polishing Carl system Zeiss, Oberkochen,(Ilion II model Germany) 697, Thomson at the Scientific Korea Basic Instruments, Science Institute, Box hill, DaejeonVictoria, centerAustralia). (KBSI). To investigate Also, thermal the diffusivitymorphology was of measuredthe fillers and at room PI matrices, temperature the cross-sectional using a laser flashfracture analyzer surfaces (LFA of the 447, films Netzsch, were Waldkraiburg,observed by using Germany). field Then,emission the densitiesscanning and electron specific microscopy heats of the (FE-SEM, film were Merlin, measured Carl by Zeiss, a gas pycnometerOberkochen, (AccuPyc Germany) II 1340, at the Micromeritics, Korea Basic Norcross,Science Institute, GA, USA) Daejeon and differential center (KBSI). scanning Also, calorimeter thermal k (DSCdiffusivity Q200, TAwas instruments), measured at respectively. room temperature The thermal using conductivity a laser flash ( ) valuesanalyzer were (LFA calculated 447, Netzsch, using a heatWaldkraiburg, conduction Germany). equation that Then, describes the densities the relationship and specific between heats of thermal the film diffusivity were measured (α), density by a (gasρ), and specific heat (Cp) of the polymer (k = α·ρ·Cp). pycnometer (AccuPyc Ⅱ 1340, Micromeritics, Norcross, GA, USA) and differential scanning 3.calorimeter Results and (DSC Discussion Q200, TA instruments), respectively. The thermal conductivity (k) values were calculated using a heat conduction equation that describes the relationship between thermal 3.1.diffusivity Morphology (α), density (ρ), and specific heat (Cp) of the polymer (k = α∙ρ∙Cp). All samples that were used in this study exhibited a high degree of flexibility, up to 30 wt % 3. Results and Discussion concentration of the filler, regardless of the filler type. The morphology of the cross-sectional fracture surfaces was investigated via FE-SEM. Figure1a shows a FE-SEM image of the PI composite film 3.1. Morphology containing 30 wt % BN. The BN filler consists of plate-shaped particles which are aligned primarily alongAll the samples horizontal that direction were used of the in film.this study Images exhibited of the films a high containing degree 30of wtflexibility, % AlN, 30 up wt to % 30Al wt2O %3, 30concentration wt % BN + AlNof the (1:1), filler, and regardless 30 wt % of BN the + filler Al2O type.3 (1:1) The fillers morphology (Figure1 b–e,of the respectively) cross-sectional indicate fracture a significantsurfaces was degree investigated of interaction via FE-SEM. between Figure different 1a fillershows particles. a FE-SEM At smallimage filler of the amounts, PI composite alignment film ofcontaining the plate-shaped 30 wt % BN. BN The particles BN filler primarily consists along of plate-shaped the horizontal particles direction which of are the aligned composite primarily films preparedalong the via horizontal casting isdirection difficult, of owing the film. to theImages relatively of the lowfilms shear containing force applied 30 wt % to AlN, the films. 30 wt However,% Al2O3, the30 wt morphology % BN+AlN shown (1:1), and in Figure 30 wt1 d,e% BN+Al2O3 reveals that (1:1) the fillers filler (Figure particles 1b–e, will respectively) probably interact indicate in a thesignificant horizontal degree direction. of interaction Therefore, between the different in-plane filler thermal particles. conductivity At small increased,filler amounts, owing alignment to the well-connectedof the plate-shaped horizontal BN particles heat flow primarily path generated along bythe the horizontal binary filler direction system. of the composite films prepared via casting is difficult, owing to the relatively low shear force applied to the films. However, the morphology shown in Figure 1d and e reveals that the filler particles will probably interact in the horizontal direction. Therefore, the in-plane thermal conductivity increased, owing to the well- connected horizontal heat flow path generated by the binary filler system.

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Figure 1. 1. FE-SEMFE-SEM (field (field emission emission scanning scanning electron electron microscopy) microscopy) images images of of the the cross-sectional cross-sectional fracture fracture surfacessurfaces of the composite filmsfilms containingcontaining ((aa)) 3030 wtwt %% ofof PI/BNPI/BN (boron nitride); ((b)) 3030 wtwt %% ofof PI/AlNPI/AlN (aluminum nitride); ( c) 3030 wtwt %% ofof PI/AlPI/Al22O3;;( (d)) 30 wtwt %% ofof PI/BNPI/BN+AlN + AlN (1:1); (1:1); and and (e (e) )30 30 wt wt % % of of PI/BN+AlPI/BN +2 AlO32 O(1:1)3 (1:1) (the (the arrow arrow mark mark meaning meaning the the effect effectiveive thermal thermal pathway pathway originated originated from from the connectionconnection of thermal conductive fillers). fillers).

3.2. Thermal Thermal Conductivity Conductivity Figure 22a,ba,b show show the the values values of ofthermal thermal conducti conductivityvity calculated calculated along along the through-plane the through-plane and in- planeand in-plane directions, directions, respectively, respectively, of the of theobtained obtained films. films. Figure Figure 3a,b3a,b show show the correspondingcorresponding enhancements ofof thethe conductivityconductivity along along these these orientations, orientations, with with the the highest highes valuest values occurring occurring along along the · thein-plane in-plane direction direction of the of films the containingfilms containi hybridng fillers.hybrid The fillers. maximum The maximum (4.091 W/m (4.091K) andW/m minimum∙K) and · minimum(2.404 W/m (2.404K) values W/m∙K) of thevalues thermal of the conductivity thermal conductivity along the in-plane along the direction in-plane were direction observed were for observedthe samples for withthe samples 30 wt % with PI/BN 30 wt + AlN% PI/BN+AlN and the sample and the with sample 30 wt with % AlN, 30 wt respectively. % AlN, respectively. However, However,the conductivities the conductivities along the through-planealong the through-plan direction weree direction larger were for the larger films for containing the films only containing the BN · onlyfiller the than BN for filler the than composites for the composites with hybrid with fillers. hybrid A maximum fillers. A valuemaximum of 0.719 value W/m of 0.719K was W/m observed∙K was · observedfor the sample for the with sample 30 wtwith % 30 of wt BN % and of BN a minimum and a minimum value ofvalue 0.368 of W/m0.368 W/mK occurred∙K occurred for the for filmthe containing a mixture of BN and Al O . The through-plane thermal conductivity results show that BN film containing a mixture of BN and2 Al3 2O3. The through-plane thermal conductivity results show that is a better thermally conductive filler than Al O and AlN for the PI-based composite film. Therefore, BN is a better thermally conductive filler than2 3 Al2O3 and AlN for the PI-based composite film. Therefore,the reduction the inreduction the BN content in the BN and content addition and of otheraddition filler of leads other to filler thermal leads conductivity to thermal conductivity degradation. However, compared with the Al O and AlN composites, the hybrid filler system exhibited lower degradation. However, compared2 with3 the Al2O3 and AlN composites, the hybrid filler system exhibitedthrough-plane lower thermal through-plane conductivity, thermal however conductivity higher, however in-plane thermalhigher in-plane conductivity. thermal These conductivity. behaviors Thesecan be behaviors attributed can to thebe attributed interaction to between the interaction the filler between particles the described filler particles in the previousdescribed section.in the previousThe hybrid section. fillers The lead hybrid to increased fillers fillerlead alignmentto increased along filler the alignment in-plane direction,along the therebyin-plane obstructing direction, the through-plane thermal pathways. As a result, added Al O or AlN leads to increased interaction thereby obstructing the through-plane thermal pathways. As2 3a result, added Al2O3 or AlN leads to increasedbetween the interaction filler and between an extra the thermal filler pathwayand an ex alongtra thermal the in-plane pathway direction. along the in-plane direction.

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PolymersPolymers 2018 2018, 10, ,10 x ,FOR x FOR PEER PEER REVIEW REVIEW 5 of5 9of 9

FigureFigure 2. 2.Thermal Thermal conductivity conductivity along along along the the the ( a ))( a through-planethrough-plane) through-plane and and and (b )( b in-planein-plane) in-plane directionsdirections directions ofof of thethe the composite compositeﬁlmscomposite plotted films films as plotted functions plotted as asfunc offunctions thetions ﬁller of ofthe content.the filler filler content. content.

FigureFigure 3. 3. Thermal3.Thermal Thermal conductivity conductivity enhancements enhancements enhancements along along alongthe the (a) the( through-planea) through-plane (a) through-plane and and (b )( bin-plane and) in-plane (b) directions in-plane directions directions of the composite films plotted as functions of the filler content. ofof the the composite composite ﬁlmsfilms plotted as as functions functions of ofthe the filler ﬁller content. content.

3.3.3.3.3.3. Modeling Modeling Various model equations describing the relations among the aspect ratio, density, filler shape VariousVarious model model equationsequations describing describing the the relations relations among among the aspect the aspect ratio, ratio,density, density, filler shape filler shape and type, modulus, orientation, thermal conductivity, and weight fraction have been proposed for andand type, type, modulus, modulus, orientation,orientation, thermal thermal conductivi conductivity,ty, and and weight weight fraction fraction have been have proposed been proposed for for predictingpredicting the the effective effective thermal thermal conductivity conductivity of ofpolymer polymer composites composites [18–23]. [18–23]. The The regular regular and and predicting the effective thermal conductivity of polymer composites [18–23]. The regular and modified modifiedmodified Lewis–Nielsen Lewis–Nielsen models models are are generally generally used used for for this this prediction. prediction. In Inthis this work, work, the the results results Lewis–Nielsencalculatedcalculated by by using using models these these aremodels models generally were were compared used compared for thiswith with prediction. the the obtained obtained In experimental thisexperimental work, thedata. data. results The The main calculated main by usingequationequation these governing governing models these were these models compared models ma may withbey be expressed theexpressed obtained as asfollows follows experimental [24–27]: [24–27]: data. The main equation governing these models may be expressed as follows [24–27]: 𝟏+𝟏+𝑨 ∙𝑩∙𝝓𝑨 ∙𝑩∙𝝓𝒇 𝑲=𝒌 ∙ 𝒇 (1) 𝑲=𝒌𝒎 𝒎 𝟏−𝑩∙𝝓∙ ∙𝜳 (1) 𝟏−𝑩∙𝝓" 𝒇 𝒇 ∙𝜳 # 1 + A·B·φf 𝒌𝒇⁄𝒌𝒌𝒎⁄𝒌𝟏𝟏 K = k · (1) where 𝑨=𝒌 −𝟏 and 𝑩= 𝒇 𝒎 ; 𝒌 , 𝒌 , 𝒌m , and 𝝓 are the Einstein coefficient, thermal where 𝑨=𝒌𝑬 𝑬 −𝟏 and 𝑩=𝒌 ⁄𝒌 𝑨 ; 𝑬𝒌𝑬 , 𝒎𝒌𝒎 , 𝒇𝒌𝒇 1, −andB ·𝒇φ𝝓f𝒇· Ψare the Einstein coefficient, thermal 𝒇 𝒌𝒇𝒎⁄𝒌𝒎𝑨 conductivityconductivity of ofa polymera polymer matrix, matrix, thermal thermal conducti conductivityvity of ofa composite,a composite, and and packing packing fraction fraction of ofa a 𝟏𝝓 − 𝝓 k𝟏𝝓f/𝒎𝒂𝒙km𝒎𝒂𝒙1 𝒎𝝓𝒎 wherefiller, respectively.A = k − 1 𝜳=𝟏+and B = 𝟐 ∙𝝓𝒇; k for, kthe, Lewis–Nielsenk , and φ are model the Einstein and 𝜳=𝟏+ coefficient,𝝓 thermal𝒎𝒂𝒙 ∙𝝓𝒇 conductivity+ filler, respectively.E 𝜳=𝟏+𝝓k /k +𝟐 A∙𝝓𝒇E form the fLewis–Nielsenf model and 𝜳=𝟏+𝝓𝒎𝒂𝒙 𝝓𝒎𝒂𝒙 ∙𝝓𝒇 + 𝒎𝒂𝒙f𝝓𝒎𝒂𝒙m 𝝓𝒎𝒂𝒙 𝟏−𝝓 ∙𝝓 𝝓 𝝓 of a𝟏−𝝓 polymer𝒎𝒂𝒙𝒎𝒂𝒙 ∙𝝓 matrix,𝒎 𝒎 (here, (here, thermal 𝒎𝝓: 𝒎packing: packing conductivity fraction fraction of of ofthe a the composite, matrix matrix and and and 𝒎𝒂𝒙𝝓𝒎𝒂𝒙 packing: maximum: maximum fraction packing packing of afraction filler,fraction respectively.of of 1−φmax φm Ψthethe= filler)1 filler)+ for for the the modified·φ modifiedfor the Lewis–Nielsen Lewis–Nielsen model. model. model and Ψ = 1 + φ ·φ + (1 − φ )·φ (here, φ 2 f φmax max f max m Figure max4 shows the theoretical prediction and experimental thermal conductivity data for the φm: packingFigure fraction4 shows ofthe the theoretical matrix andpredictionφmax: maximumand experimental packing thermal fraction conductivity of the filler) data for for the the modified PI/BN, PI/Al2O3, and PI/AlN composites. Good fitting between the experimental and theoretical data Lewis–NielsenPI/BN, PI/Al2O model.3, and PI/AlN composites. Good fitting between the experimental and theoretical data in both models was realized only for the PI/BN composite. The other composites were considerably in bothFigure models4 shows was therealized theoretical only for predictionthe PI/BN composite. and experimental The other composites thermal conductivity were considerably data for the underestimated.underestimated. The The theoretical theoretical models models described described ab aboveove are are valid valid for for systems systems consisting consisting of ofsingle single PI/BN, PI/Al2O3, and PI/AlN composites. Good fitting between the experimental and theoretical data in both models was realized only for the PI/BN composite. The other composites were considerably underestimated. The theoretical models described above are valid for systems consisting of single Polymers 2019, 11, 484 6 of 9

Polymers 2018, 10, x FOR PEER REVIEW 6 of 9 fillers inside a polymer matrix. However, the hybrid filler systems utilized in this study were composed fillers inside a polymer matrix. However, the hybrid filler systems utilized in this study were of mixtures containing two different fillers, namely BN and Al2O3 or AlN particles. Therefore, a model that considerscomposed twoof mixtures filler types containing is required two fordifferent accurate fillers, prediction namely ofBN the and experimental Al2O3 or AlN results particles. [18,28 –30]. Therefore, a model that considers two filler types is required for accurate prediction of the Two population models involving additive and multiplicative approaches are often utilized for this experimental results [18,28–30]. Two population models involving additive and multiplicative purpose.approaches The additive are often approach utilized for method this purpose. can be The described additive by approach the following method equation: can be described by the following equation: K kf1 kf2 add = + − 1 𝑲𝒂𝒅𝒅 𝒌𝒇𝟏 𝒌𝒇𝟐 (2) km = km + km−𝟏 (2) 𝒌𝒎 𝒌𝒎 𝒌𝒎

FigureFigure 4. Experimental 4. Experimental and and theoretical theoretical thermalthermal conductivi conductivityty obtained obtained using using the theregular regular and modified and modiﬁed

Lewis–NielsenLewis–Nielsen models models for for the the (a ()a PI/BN;) PI/BN; (b) PI/Al PI/Al2O23O; and3; and (c) PI/AlN (c) PI/AlN composite composite films. ﬁlms.

Here, 𝑲 is the predicted thermal conductivity of a hybrid filler composite, whereas 𝒌 and Here, Kadd is𝒂𝒅𝒅 the predicted thermal conductivity of a hybrid filler composite, whereas𝒇𝟏 kf1 and 𝒌 are the thermal conductivities of the composites with only the BN- and Al-containing fillers, kf2 are𝒇𝟐 the thermal conductivities of the composites with only the BN- and Al-containing fillers, respectively.respectively. The The experimental experimental results results correspond correspond closely closely to to the the theoreticaltheoretical predictions obtained obtained via via the the additive approach method applied to the regular and modified Lewis–Nielsen models (see Figure additive approach method applied to the regular and modified Lewis–Nielsen models (see Figure5). 5). In the multiplicative approach method, the contribution of the BN filler to the thermal conductivity In the multiplicative approach method, the contribution of the BN filler to the thermal conductivity of a composite is calculated first and the obtained BN-containing composite is considered the matrix of a composite is calculated first and the obtained BN-containing composite is considered the matrix for the second Al2O3 or AlN filler. In other words, the contribution of the second filler to the thermal for theconductivity second Al is2O calculated3 or AlN by filler. using In the other PI/BN words, composite the contribution matrix (𝒌𝑪) ofrather the secondthan the filler neat toPI thematrix thermal conductivity(𝒌𝒎). The isobtained calculated contributions by using of the both PI/BN fillers are composite multiplied matrix as follows (kC) [18,28], rather than the neat PI matrix (km). The obtained contributions of both fillers are multiplied as follows [18,28], 𝑲𝒎𝒖𝒍𝒕 𝒌𝒇𝟐 𝒌𝒇𝟏 = ∙ (3) 𝒌𝒎 𝒌𝑪 𝒌𝒎 K kf2 kf1 mult = · (3) where Kmult is the predicted thermal conductivitykm kofC the composite.km The additive and multiplicative models are commonly used to predict synergetic filler effects on thermal conductivity. However, where Kmult is the predicted thermal conductivity of the composite. The additive and multiplicative models are commonly used to predict synergetic filler effects on thermal conductivity. However, when the filler content is relatively high, a greater improvement in the conductivity is often better predicted Polymers 2019, 11, 484 7 of 9

Polymers 2018, 10, x FOR PEER REVIEW 7 of 9 Polymers 2018, 10, x FOR PEER REVIEW 7 of 9 by usingwhen thethe filler multiplicative content is relatively approach high, method a grea ratherter improvement than the additivein the conductivity approach. is often Figure better6 shows thewhen thermal the conductivityfiller content is data relatively predicted high, bya grea theter multiplicative improvement in approach the conductivity method is for often the better composite predictedpredicted by by using using the the multiplicative multiplicative approach approach meth methodod rather rather than than the the additive additive approach. approach. Figure Figure 6 6 films and the corresponding experimental values. As Figure5 indicates, the hybrid-filler thermal showsshows thethe thermalthermal conductivityconductivity datadata predictedpredicted byby thethe multiplicativemultiplicative approachapproach methodmethod forfor thethe conductivitycompositecomposite films datafilms and measuredand the the corresponding corresponding in this study experimental experimental concur more values. values. closely As As Figure Figure with 5 the5 indicates, indicates, additive the the approachhybrid-filler hybrid-filler applied to thethermalthermal regular conductivity conductivity and modified data data measured Lewis–Nielsenmeasured in in this this modelsstudy study concur concur than more withmore closely theclosely multiplicative with with the the additive additive model approach approach presented in Figureappliedapplied6. The toto measured thethe regularregular conductivity andand modifiedmodified and Lewis–NielsenLewis–Nielsen the conductivity modelsmodels predicted thanthan withwith from thethe multiplicative themultiplicative additional modelmodel approach increasepresentedpresented in a similarin in Figure Figure manner, 6. 6. The The measured measured whereas, conductivity conductivity in the multiplicative and and the the conductivity conductivity approach predicted predicted model, thefrom from predicted the the additional additional values are approach increase in a similar manner, whereas, in the multiplicative approach model, the predicted overestimatedapproach increase compared in a similar with themanner, experimental whereas, in results. the multiplicative Therefore, approach compared model, with the the predicted multiplicative values are overestimated compared with the experimental results. Therefore, compared with the approach,values are the overestimated additive approach compared is morewith the suitable experimental for hybrid results. filler Therefore, systems. compared The aforementioned with the multiplicativemultiplicative approach,approach, thethe additiveadditive approachapproach isis moremore suitablesuitable forfor hybridhybrid fillerfiller systems.systems. TheThe modelaforementioned prediction is model based prediction on the following is based on assumptions: the following the assumptions: polymer isthe unaffected polymer is byunaffected the presence of theaforementioned filler (e.g., no model change prediction in polymer is based crystallinity on the following and noassumptions: change in the filler polymer orientation), is unaffected the matrix byby thethe presencepresence ofof thethe fillerfiller (e.g.,(e.g., nono changechange inin polymerpolymer crystallinitycrystallinity andand nono changechange inin fillerfiller and the filler are isotropic and strongly bonded, and no filler–filler interactions or agglomerations orientation),orientation), thethe matrixmatrix andand thethe fillerfiller areare isotropicisotropic andand stronglystrongly bonded,bonded, andand nono filler–fillerfiller–filler occurinteractionsinteractions [31]. The or morphologyor agglomerations agglomerations of the occur occur composite [31]. [31]. The The films mo morphology inrphology this work of of the the is, composite nevertheless,composite films films far in in more this this work complexwork is, is, than morphologiesnevertheless,nevertheless, based farfar more onmore these complexcomplex assumptions. thanthan morphologimorphologi Moreover,eses based thebased distribution onon thesethese assumptions.assumptions. of fillers in the Moreover,Moreover, surface ofthethe casting filmsdistributiondistribution usually differs of of fillers fillers from in in the the surface surface distribution of of casting casting at thefilm film center.ss usually usually However, differs differs from from the the simplifiedthe distribution distribution model at at the the presented center. center. here enablesHowever,However, the behavioral the the simplified simplified prediction model model presented presented of an ideal here here structure enable enabless the the and behavioral behavioral filler distribution prediction prediction of andof an an ideal elucidates ideal structure structure the basic and filler distribution and elucidates the basic role of the fillers in thermally conductive polymer roleand of thefiller fillers distribution in thermally and elucid conductiveates the polymerbasic role composite of the fillers films. in thermally conductive polymer compositecomposite films. films.

Figure 5. Experimental and theoretical thermal conductivity obtained for the (a) PI/BN+Al2O3 and (b) FigureFigure 5. Experimental5. Experimental and and theoreticaltheoretical thermal thermal conductivity conductivity obtained obtained for the for (a the) PI/BN+Al (a) PI/BN2O3 and + Al (b2)O 3 and PI/BN+AlN composites by using the additive approach model. (b) PI/BNPI/BN+AlN + AlN composites composites by using by using the additive the additive approach approach model. model.

Figure 6. Experimental and theoretical thermal conductivity obtained for the (a) PI/BN+Al2O3 and (b) FigureFigure 6. Experimental6. Experimental and and theoreticaltheoretical thermal thermal conductivity conductivity obtained obtained for the for (a the) PI/BN+Al (a) PI/BN2O3 and + Al (b)O and PI/BN+AlN composites by using the multiplicative approach model. 2 3 (b) PI/BNPI/BN+AlN + AlN composites composites by using by using the multiplicative the multiplicative approach approach model. model. 4. Conclusions 4. Conclusions4. Conclusions

PI-based thermally conductive composite materials were fabricated using anisotropic BN, spherical AlN, and Al2O3 particles. Among them, the PI/BN composite had outstanding thermal Polymers 2019, 11, 484 8 of 9

conductivity in the through- and in-plane directions. In this composite, some amount of Al2O3 and AlN were added to the binary filler. In the case of the through-plane direction, the hybrid filler system shows lower thermal conductivity than the PI/BN composite, whereas in-plane thermal conductivity was enhanced because the BN particles were horizontally aligned via the binary filler. The maximum thermal conductivity value along the in-plane direction was 4.091 W/m·K for the film containing 30 wt % of PI/BN + AlN filler, whereas the value of the PI/ BN composite was 3.371 W/m·K. These experimental results were compared with the Lewis–Nielsen and modified Lewis–Nielsen theoretical prediction models. The PI/BN composite corresponded better with the theoretical model than with the Al2O3 and AlN composites. However, these theoretical predictions are only applicable to the single-filler system. Therefore, the additive and multiplicative approaches were applied to PI/BN + Al2O3 and PI/BN + AlN composites. This has not been reported previously for the prediction of a binary filler system. As a result, the additive approach shows a better fit with experimental results, whereas the multiplicative approach overestimates, especially for a high filler concentration.

Author Contributions: Investigation, Y.S.K.; Supervision, Y.Y. and J.K.; Writing–original draft, H.S.; Writing–review & editing, H.S.; Conceptualization, B.G.K.; Resources, Y.-S.B. Funding: This research received no external funding. Acknowledgments: This work was supported by a grant from the KRICT General Research Program (SI1803-03) funded by the Ministry of Trade, Industry & Energy of Korea and also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017R1A2A2A05069858). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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