Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review

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Abstract

Thermally conductive polymer composites offer new possibilities for replacing metal parts in several applications, including power electronics, electric motors and generators, heat exchangers, etc., thanks to the polymer advantages such as light weight, corrosion resistance and ease of processing. Current interest to improve the thermal conductivity of polymers is focused on the selective addition of nanofillers with high thermal conductivity. Unusually high thermal conductivity makes carbon nanotube (CNT) the best promising candidate material for thermally conductive composites. However, the thermal conductivities of polymer/CNT nanocomposites are relatively low compared with expectations from the intrinsic thermal conductivity of CNTs. The challenge primarily comes from the large interfacial thermal resistance between the CNT and the surrounding polymer matrix, which hinders the transfer of phonon dominating heat conduction in polymer and CNT.

This article reviews the status of worldwide research in the thermal conductivity of CNTs and their polymer nanocomposites. The dependence of thermal conductivity of nanotubes on the atomic structure, the tube size, the morphology, the defect and the purification is reviewed. The roles of particle/polymer and particle/particle interfaces on the thermal conductivity of polymer/CNT nanocomposites are discussed in detail, as well as the relationship between the thermal conductivity and the micro- and nano-structure of the composites.

Introduction

Heat transfer involves the transport of energy from one place to another by energy carriers. In a gas phase, gas molecules carry energy either by random molecular motion (diffusion) or by an overall drift of the molecules in a certain direction (advection). In liquids, energy can be transported by diffusion and advection of molecules. In solids, phonons, electrons, or photons transport energy. Phonons, quantized modes of vibration occurring in a rigid crystal lattice, are the primary mechanism of heat conduction in most polymers since free movement of electrons is not possible [1]. In view of theoretical prediction, the Debye equation is usually used to calculate the thermal conductivity of polymers.λ=Cpνl3where Cp is the specific heat capacity per unit volume; v is the average phonon velocity; and l is the phonon mean free path.

For amorphous polymers, l is an extremely small constant (i.e. a few angstroms) due to phonon scattering from numerous defects, leading to a very low thermal conductivity of polymers [2]. Table 1 displays the thermal conductivities of some polymers [3], [4], [5].

Polymer crystallinity strongly affects their thermal conductivity, which roughly varies from 0.2 W/m K for amorphous polymers such as polymethylmethacrylate (PMMA) or polystyrene (PS), to 0.5 W/m K for highly crystalline polymers as high-density polyethylene (HDPE) [4]. The thermal conductivity of semi-crystalline polymers is reported to increase with crystallinity. As an example, the thermal conductivity of polytetrafluoroethylene (PTFE) was found to increase linearly with crystallinity at 232 °C [6].

However, there is a large scatter in the reported experimental data of thermal conductivity of crystalline polymers, even including some contradictory results. It should be noticed that the thermal conductivities of polymers depend on many factors, such as chemical constituents, bond strength, structure type, side group molecular weight, molecular density distribution, type and strength of defects or structural faults, size of intermediate range order, processing conditions and temperature. Furthermore, due to the phonon scattering at the interface between the amorphous and crystalline phase and complex factors on crystallinity of polymer, the prediction of the thermal conductivity vs. crystallinity presents a significant degree of complexity.

Semicrystalline and amorphous polymers also vary considerably in the temperature dependence of the thermal conductivity. At low temperature, semicrystalline polymers display a temperature dependence similar to that obtained from highly imperfect crystals, having a maximum in the temperature range near 100 K, shifting to lower temperatures and higher thermal conductivities as the crystallinity increases [7], [8], while amorphous polymers display temperature dependence similar to that obtained for inorganic glasses with no maximum, but a significant plateau region at low temperature range [9]. The thermal conductivity of an amorphous polymer increases with increasing temperature to the glass transition temperature (Tg), while it decreases above Tg [10], [11]. The study of the thermal conductivity of some amorphous and partially crystalline polymers (PE, PS, PTFE and epoxy resin) as a function of temperature in a common-use range (273–373 K) indicates that the conductivity of amorphous polymers increases with temperature and that the conductivity is significantly higher in crystalline than amorphous regions [12].

From the general overview given in the preceding, it appears that very limited thermal conductivity is usually characteristic of polymers. On the other hand, there are many reasons to increase thermal conductivity of polymer-based materials in various industrial applications including circuit boards in power electronics, heat exchangers, electronics appliances and machinery. This justifies the recent significant research efforts on thermally conductive composite materials to overcome the limitations of traditional polymers.

Many applications would benefit from the use of polymers with enhanced thermal conductivity. For example, when used as heat sinks in electric or electronic systems, composites with a thermal conductivity approximately from 1 to 30 W/m K are required [13]. The thermal conductivity of polymers has been traditionally enhanced by the addition of thermally conductive fillers, including graphite, carbon black, carbon fibers, ceramic or metal particles (see Table 2) [14], [15], [16], [17], [18]. It is worth noticing that significant scatter of data are typically reported for thermal conductivity of fillers. This is caused by several factors, including filler purity, crystallinity, particle size and measurement method. It is also important to point out that some materials, typically fibers and layers, are highly anisotropic and can show much higher conductivity along a main axis or on a plane, compared to perpendicular direction.

High filler loadings (>30 vol.%) are typically necessary to achieve the appropriate level of thermal conductivity in thermally conductive polymer composites, which represents a significant processing challenge. Indeed, the processing requirements, such as possibility to be extruded and injection molded, often limit the amount of fillers in the formulation and, consequently, the thermal conductivity performance [19]. Moreover, high inorganic filler loading dramatically alters the polymer mechanical behavior and density. For these reasons, obtaining composites having thermal conductivities higher than 4 W/m K and usual polymer processability is very challenging at present.

Carbon-based fillers appear to be the best promising fillers, coupling high thermal conductivity and lightweight. Graphite, carbon fiber and carbon black are well-known traditional carbon-based fillers. Graphite is usually recognized as the best conductive filler because of its good thermal conductivity, low cost and fair dispersability in polymer matrix [20], [21]. Single graphene sheets constituting graphite show intrinsically high thermal conductivity of about 800 W/m K [22] or higher (theoretically estimated to be as high as 5300 W/m K [23], [24]), this determining the high thermal conductivity of graphite, usually reported in the range from 100 to 400 W/m K. Expanded graphite (EG), an exfoliated form of graphite with layers of 20–100 nm thickness, has also been used in polymer composites [25], for which the thermal conductivity depends on the exfoliation degree [26], its dispersion in matrix [27] and the aspect ratio of the EG [28].

Carbon fiber, typically vapor grown carbon fiber (VGCF), is another important carbon-based filler. Polymer/VGCF composites have been reviewed by Tibbetts et al. [29]. Since VGCF is composed of an annular geometry parallel to the fiber axis, thermal conductive properties along the fiber axis are very different from the transverse direction (estimated up to 2000 W/m K in the axial direction vs. 10–110 W/m K in the transverse direction [30], [31]), directly affecting the thermal conductivity of aligned composites [32], [33].

Carbon black particles are aggregates of graphite microcrystals and characteristic of their particle size (10–500 nm) and surface area (25–150 m2/g) [14]. Carbon black is reported to contribute to electrical conductivity rather than thermal conductivity [34], [35], [36].

The filling of a polymer with metallic particles may result in both increase of thermal conductivity and electrical conductivity in the composites. However, a density increase is also obtained when adding significant metal loadings to the polymer matrix, thus limiting applications when lightweight is required. Metallic particles used for thermal conductivity improvement include powders of aluminum, silver, copper and nickel. Polymers modified with the inclusion of metallic particles include polyethylene [37], polypropylene [38], polyamide [39], polyvinylchloride and epoxy resins [40], showing thermal conductivity performance depending on the thermal conductivity of the metallic fillers, the particle shape and size, the volume fraction and spatial arrangement in the polymer matrix.

Ceramic powder reinforced polymer materials have been used extensively as electronic materials. Being aware of the high electrical conductivity of metallic particles, several ceramic materials such as aluminum nitride (AlN), boron nitride (BN), silicon carbide (SiC) and beryllium oxide (BeO) gained more attention as thermally conductive fillers due to their high thermal conductivity and electrical resistivity [41], [42]. Thermal conductivities of composites with ceramic filler are influenced by filler packing density [43], particle size and size distribution [44], [45], surface treatment [46] and mixing methods [47].

Several methods, as reviewed elsewhere [48], [49], have been proposed and used for measurement of the thermal conductivity of polymers and composites. Classical steady-state methods measure the temperature difference across the specimens in response to an applied heating power, either as an absolute value or by comparison with a reference material put in series or in parallel to the sample to be measured. However, these methods are often time consuming and require relatively bulky specimens.

Several non steady-state methods have also been developed, including hot wire and hot plate methods, temperature wave method and laser flash techniques [49]. Among these, laser-flash thermal diffusivity measurement is widely used, being a relatively fast method, using small specimens [50], [51], [52]. In this method, the sample surface is irradiated with a very short laser pulse and the temperature rise is measured on the opposite side of the specimen, permitting calculation of the thermal diffusivity of the material, after proper mathematical elaboration. The thermal conductivity k is then calculated according to Eq. (2):k=αCpρwhere α, Cp and ρ are the thermal diffusivity, heat capacity and density, respectively.

Differential scanning calorimetry (DSC) methods may also be used, applying an oscillary [53] or step temperature profile [54] and analyzing the dynamic response.

Significant experimental error may be involved in thermal conductivity measurements, due to difficulties in controlling the test conditions, such as the thermal contact resistance with the sample, leading to accuracy of thermal conductivity measurements typically in the range of 5–10%. In indirect methods, such as those calculating the thermal conductivity from the thermal diffusivity, experimental errors on density and heat capacity values will also contribute to the experimental error in the thermal conductivity.

Several different models developed to predict the thermal conductivity of traditional polymer composites are reviewed elsewhere [55], [56], [57], [58]. The fundamentals are recalled in this section.

The two basic models representing the upper bound and the lower bound for thermal conductivity of composites are the rule of mixture and the so-called series model, respectively. In the rule of mixture model, also referred to as the parallel model, each phase is assumed to contribute independently to the overall conductivity, proportionally to its volume fraction (Eq. (3)):kc=kpΦp+kmΦmwhere kc, kp, km are the thermal conductivity of the composite, particle, matrix, respectively, and Φp, Φm volume fractions of particles and matrix, respectively. The parallel model maximizes the contribution of the conductive phase and implicitly assumes perfect contact between particles in a fully percolating network. This model has some relevance to the case of continuous fiber composites in the direction parallel to fibers, but generally results in very large overestimation for other types of composites.

On the other hand, the basic series model assumes no contact between particles and thus the contribution of particles is confined to the region of matrix embedding the particle. The conductivity of composites accordingly with the series model is predicted by Eq. (4):kc=1((Φm/km)+(Φp/kp))

Most of the experimental results were found to fall in between the two models. However, the lower bound model is usually closer to the experimental data compared to the rule of mixture [55], which brought to a number of different models derived from the basic series model, generally introducing some more complex weighted averages on thermal conductivities and volume fractions of particles and matrix. These so-called second-order models including equations by Hashin and Shtrikman, Hamilton and Crosser, Hatta and Taya, Agari, Cheng and Vachon as well as by Nielsen [55], [56], [59], appear to reasonably fit most of the experimental data for composites based on isotropic particles as well as short fibers and flakes with limited aspect ratio, up to loadings of about 30% in volume. For higher loadings, the Nielsen's model appear to best fit the rapid increase of thermal conductivity above 30 vol.%, thanks for the introduction of the maximum packing factor into the fitting equation, despite the evaluation of maximum packing factor in real composites may present difficulties due to particle size distribution and particle dispersion in the matrix. However, the basic assumption of separated particles in the effective medium approach is not valid in principle for highly filled composites, where contacts are likely to occur, possibly leading to thermally conductive paths [60]. In order to take into account fluctuations in thermal conductivity in the composites, Zhou et al. [56] proposed the concept of heat-transfer passages, to model the conduction in regions where interparticle distance is low, applying the series model to “packed-belt” of conductive particles.

Even though these macroscopic approaches may be of interest from the engineering point of view, they deliver little or no information about the physical background of the observed behavior. As an example, very limited interpretation is given to the rapidly increasing conductivity with filler content above a certain filler loading (typically above 30 vol.%), or why the experimental results are so far away from the upper bound conductivity, even for highly percolated systems.

Attempts to model thermal conductivity taking into account the interfacial thermal resistance between conductive particles and matrix have been reported by several research groups [61], [62], [63], [64], [65] and applied particles with different geometries and topologies, including aligned continuous fibers, laminated flat plates, spheres, as well as misoriented ellipsoidal particles. In general, these models provided an improved fit with experimental data for ceramic based composites than models not accounting for interface thermal resistance. These approaches generally assume conductive particles to be isolated in the matrix and take into account the thermal resistance in heat transfer between conductive particle and matrix, also known as Kapitza resistance, from the name of the discoverer of the temperature discontinuity at the metal–liquid interface. A very simple proof of thermal interfacial resistance is the fact that a thermal conductivity lower than the reference matrix was experimentally found with some composites containing particles with thermal conductivity higher than the matrix [61], [62]. This phenomenon is explained by the very low efficiency of heat transfer between particles and matrix, so that the higher thermal conductivity of the filler cannot be taken into advantage and the composite behaves like a hollow material, thus reducing its conductivity compared to the dense reference matrix.

Recently, nanotechnology has gained much attention in research to develop materials with unique properties. Nanotechnology can be broadly defined as the creation, processing, characterization and use of materials, devices, and systems with dimensions in the range 0.1–100 nm, exhibiting novel or significantly enhanced physical, chemical, and biological properties, functions, phenomena, and processes due to their nanoscale size [66]. Nanocomposites, i.e., composites containing dispersed particles in the nanometer range, are a significant part of nanotechnology and one of the fastest growing areas in materials science and engineering.

Polymer based nanocomposites can be obtained by the addition of nanoscale particles which are classified into three categories depending on their dimensions: nanoparticles, nanotubes and nanolayers. The interest in using nanoscaled fillers in polymer matrices is the potential for unique properties deriving from the nanoscopic dimensions and inherent extreme aspect ratios of the nanofillers. Kumar et al. [67] summarized six interrelated characteristics of nanocomposites over conventional micro-composites: (1) low-percolation threshold (about 0.1–2 vol.%), (2) particle–particle correlation (orientation and position) arising at low-volume fractions (less than 0.001), (3) large number density of particles per particle volume (106 to 108 particles/μm3), (4) extensive interfacial area per volume of particles (103 to 104 m2/ml), (5) short distances between particles (10–50 nm at 1–8 vol.%) and (6) comparable size scales among the rigid nanoparticles inclusion, distance between particles, and the relaxation volume of polymer chains.

Different nanoparticles have been used to improve thermal conductivity of polymers. As a few examples, HDPE filled with 7 vol.% nanometer size expanded graphite has a thermal conductivity of 1.59 W/m K, twice that of microcomposites (0.78 W/m K) at the same volume content [68]. Poly(vinyl butyral) (PVB), PS, PMMA and poly(ethylene vinyl alcohol) (PEVA) based nanocomposites with 24 wt.% boron nitride nanotubes (BNNT) have thermal conductivities of 1.80, 3.61, 3.16 and 2.50 W/m K, respectively [69]. Carbon nanofiber was also reported to improve the thermal conductivity of polymer composites [70], [71]. However, the most widely used and studied nanoparticles for thermal conductivity are certainly carbon nanotubes (either single wall-SWCNT or multiwall-MWCNT), which have attracted growing research interest. Indeed, CNT couples very high thermal conductivity with outstanding aspect ratio, thus forming percolating network at very low loadings.

As the bulk properties of composite materials strictly depend on the structure formed during the processing step [72], a brief review on CNT-based composites preparation methods is given here, including solution mixing, melt blending, and in situ polymerization. Detailed information may be found in reviews on this topic [73], [74], [75], [76].

Solution mixing is one of the most commonly used techniques for preparing CNT based polymer–matrix composites. Solution mixing generally involves three major steps: dispersing CNTs in a suitable solvent, mixing with a polymer solution, and recovering the composite by precipitating or casting a film [77]. The difficulties in dispersing the pristine CNTs in a solvent by simple stirring, often require the use of high-power ultrasonication to make metastable suspensions of CNT or CNT/polymer mixtures [78]. Heat-treated [79], acid-treated [80] or functionalized CNTs [81], [82], [83] are often used to improve the dispersion of CNTs. Many polymer/CNT composites have been successfully prepared by the solution mixing method, including polyacrylonitrile/SWCNT [84], poly(methyl methacrylate)/SWCNT [85], poly(ethylene oxide)/MWCNT [86], poly(l-lactic acid)/MWCNT [87], chitosan/MWCNT [88]. However, the solution mixing approach is limited to polymers that freely dissolve in solvents suitable that also lead to stable suspension of CNTs.

In situ polymerization involves dispersion of nanotubes in a monomer followed by polymerization [89]. As in solution mixing, functionalized CNTs can improve the initial dispersion of the nanotubes in the liquid (monomer, solvent) and consequently in the composites. Furthermore, in situ polymerization methods enable covalent bonding between functionalized nanotubes and the polymer matrix using various chemical reactions. A few examples are mentioned here: composites of polyimides/MWCNTs were obtained by the reaction of 4,4′-oxydianiline (ODA) and pyromellitic dianhydride (PMDA) [90]; composites of polyaniline/MWCNT (acid treated) were synthesized by chemical oxidative polymerization [91]; and composites of polypyrrole/MWCNT were prepared by in situ inverse microemulsion [92] and in situ chemical polymerization [93].

Melt blending is a convenient method to produce CNT based nanocomposites owing to its cost effectiveness, fast production and environmental benefits, being a solvent-free process. Melt blending uses high temperature and high shear forces to disperse nanotubes in a thermoplastic polymer matrix, using conventional equipment for industrial polymer processing. Compatibilizers such as end-grafted macromolecules and coupling agents are often used to enhance dispersion of CNTs [94], [95]. Melt-blending approach has been reported for all the main polymer types, including polyolefines (PE, PP), polyamides, polyesters (PET, PBT and others), polyurethane, polystyrene, etc. However, compared with solution mixing, melt blending is generally less effective at dispersing nanotubes in polymers, and limited to lower concentrations due to the high viscosity of the composites at higher nanotubes loadings [96].

Masterbatches, i.e., thermoplastic polymers containing high loading of CNTs (typically 15–20 wt.%), have recently become widely used in the melt preparation of CNT based polymer nanocomposites. For industrial applications of the melt mixing extrusion technique, the masterbatch dilution seems to be favorable compared to the direct nanotube incorporation since it reduces dispersion difficulties, offers a dust-free environment and reduced safety-risk concerns, and easy handling [97], [98]. The state of CNT dispersion in the diluted composites is influenced by the state of the CNT dispersion in the masterbatches [99], processing conditions [100] and compatibility between the CNTs and polymer matrix [101]. Instead of the thermal conductivity of CNT based nanocomposites prepared from CNT masterbatch, the rheological and electrical properties have been given considerable attention [102], [103].

CNTs exhibit longitudinal thermal conductivity of 2800–6000 W/m K for a single nanotube at room temperature [16], [104], [105], comparable to diamond and higher than graphite and carbon fibers, as well as aspect ratio usually in the order 103 [106]. Based on these two properties, several authors claimed CNT suitable to obtain a breakthrough in thermal conductivity by the formation of a thermally conductive percolating network, similar to electrical conductivity [107], [108], [109], [110], [111]. However, the literature on the thermal conductivity of traditional composites summarized in Section 1.3.2 is most often neglected, even though very similar scenario may apply to nanocomposites.

Indeed, the reported experimental results for thermal conductivities of polymer/CNT composites are much lower than the values estimated from the intrinsic thermal conductivity of CNTs and the simple rule of mixing model [112], [113]. Very large scatter in the experimental data was also found; ranging from a remarkable enhancement of thermal conductivity by a small amount of CNT [111] to a decrease in the conductivity by CNT loading [114], evidencing the complexity of the problems and the difficulties in providing general rules for the thermal conductivity in polymer/CNTs nanocomposites.

Recent research revealed two main critical issues associated with the use of CNTs as thermally conductive fillers in polymer composites [115]: (1) CNTs tend to aggregate into ropes or bundles when dispersed in polymers due to the strong intrinsic Van der Waals forces and the inert graphite-like surface, causing poor dispersion and making it a challenging task to disperse CNTs properly to realize their full potential in improvement of thermal conductivities of composites; (2) the other is related to interfacial thermal resistance caused by the phonon mismatch at the interface of the CNTs and the polymer results in a high interface thermal resistance, leading to severe phonon scattering at the interface and a drastic reduction of thermal transport properties. In addition, the thermal transport through CNT network by phonons will be strongly hindered by the gaps between adjacent tubes. The attainment of polymer/CNT nanocomposites with high thermal conductivity is challenged to address these two critical issues and build effective conductive networks for heat transfer.

This review aims at the identification and discussion of the several parameters affecting the thermal conductivity of CNT-based polymer composites. The thermal conductivity of CNTs is first reviewed on the base of the dependence of thermal conductivity of nanotubes on the atomic structure, the tube size, the morphology, the defect, the purification and the functionalization. Then, the thermal conductivity of polymer/CNT nanocomposites is discussed, summarizing factors such as interfacial resistance, dispersion and alignment of CNTs and polymer crystallization.

Section snippets

Thermal conductivity of CNTs

Since their first observation nearly two decades ago by Iijima [116], CNTs have been the focus of considerable research efforts. Numerous investigators have reported remarkable physical and mechanical properties for this new form of carbon, among which the thermal conductivity of CNTs has received considerable attention [16], [117]. Recent measurements of the conductivity of a single CNTs confirmed conductivities of about 3000 W/m K for multi-walled carbon nanotubes (MWCNTs) [104] and above 2000 

Thermal conductivity of polymer/CNTs nanocomposites

Most of the published results present a disappointing message, indicating that the enhancement in the thermal conductivity of polymer/CNT composites failed to match the theoretical prediction. Also, the concentration dependence of the thermal conductivity of polymer/CNT composites does not reveal percolation behavior in the vicinity of electrical percolation concentration [243].

A summary of thermal conductivity performances for CNT-based nanocomposites reported in literature is given in Fig. 9.

Concluding remarks

As electronic devices tend to become slimmer and more integrated, heat management become a central task for device design and application. Similar issues are faced in several other applications, including electric motors and generators, heat exchangers in power generation, automotive, etc. Metallic materials are widely used as heat dissipation materials, but there have been many attempts to replace the metallic materials with highly thermally conductive polymer based composites due to their

Acknowledgements

The authors are grateful to Prof. Giovanni Camino and Prof. Guido Saracco at Politecnico di Torino for discussion and support during the preparation of this work. A. Fina also thanks Dr. Donald R. Paul at the University of Texas at Austin for the useful discussion on thermal conductivity modeling in polymer composites.

The research leading to this results has received funding from the European Community's Seventh Framework Programme (FP7 2007-2013) under grant agreement n° 227407 - Thermonano.

Z.

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