1 Introduction

Polymers have advantages of lightweight, low cost, corrosion resistance, and easy processing, so they have received great attention in electronics, engineering, energy, and aerospace fields for heat dissipation [1,2,3,4,5]. Since most polymers are thermal insulators, to date, special attention has been focused on the thermally conductive polymer composites (TCPCs), where thermally conductive fillers are often introduced to form special paths to transport thermal energy [6,7,8,9]. For the samples requiring both thermal conductivity (TC) and electrical conductivity, metallic fillers (e.g., copper nanowires (CuNWs), silver nanoparticles (AgNPs)) and carbon-based fillers (e.g., graphite, carbon fibers (CFs), carbon nanotubes (CNTs), graphene) are often utilized; for the samples, only requiring TC, ceramic fillers (e.g., aluminum oxide (Al2O3), aluminum nitride (AlN), boron nitride (BN), silicon nitride (Si3N4), and silicon carbide (SiC)) are often used.

Over the past few decades, researchers have come up with various approaches to enhance the TC of TCPCs, for instance, to enhance the intrinsic TC of polymer, modify polymer/filler interfaces, search novel fillers with high intrinsic TC, and design and construct spatially continuous filler networks in TCPCs [10,11,12,13,14]. Herein, studies have indicated that forming continuous networks is one of the most effective and promising methods to achieve a high TC for TCPCs [15,16,17]. It has been concluded that filler content, filler aspect ratio, and filler size greatly affect the network. Generally, high filler content has already been widely reported to successfully form the networks, but it always deteriorates the mechanical and processing properties of TCPCs. A non-monotonous change in the TCs induced as the filler content increase also has been reported, since the failed network was always caused by the agglomeration of fillers. Fiber-like or platelet-like fillers are preferred than spherical fillers to build the networks due to their high aspect ratio, while they often trigger anisotropic TCs of TCPCs, which may not be needed in some TCPCs requiring isotropic TCs. Spherical fillers offer a high level of viscosity percolation threshold because they point contact in polymer matrices. This is benefit for the filler networks and the processing ability of TCPCs. So, nowadays, novel methods, such as spray-drying and spray-freeze-drying, have been developed to prepare the spherical fillers from other two shapes. Fillers can present different effects on the filler network since they often have a size from nanometers to millimeters. So, factors of filler-specific surface area, filler surface energy, filler–polymer interfacial thermal resistance, filler/filler contact areas, etc., have already been comprehensively studied in the literature. In addition, the filler networks greatly depend on the constructing methods without more filler content. Up to date, methods of 3D self-assembled network, double continuous network, segregated filler network, hybrid fillers, filler orientation, and other novel methods, such as forming method and ice-templated method, have already been proposed. In this review, we firstly focused on the affecting factors of filler network. After that, a critical review of the latest developments in the approaches to tailor filler networks is presented. Finally, the challenges and prospects of TCPCs are discussed. We hope that this review is helpful for the researchers to make TCPCs with high TC, yet light weight.

2 Influencing factors of the filler network

Both the theoretical and experimental results indicate that the formation of the continuous filler network is significant as it can greatly allow phonons or electrons to transport within the TCPCs. The filler content, filler aspect ratio, and filler size are the main parameters that largely influence the building of filler network. Thus, it is necessary for us to take a comprehensive view on these factors.

2.1 Filler content

Generally, theoretical and most experimental results have shown that a monotonous increase in TCs (Fig. 1a) was expected because the stable networks were gradually formed as fillers were employed with a increasing content [18,19,20,21,22]. Fillers are difficult to form a continuous path or network as the filler content is low, so a large loading level (often higher than 30 vol%) is always introduced into the polymer matrix [3], but the percolation threshold similar to electrical conductivity was seldom reported in TC as filler content increasing, except for only some fillers with extremely high TC, such as graphdiyne [23] and grapheme [24,25,26]. Also, it should be noted that the excessively high filler content is not always desired because it always deteriorates the mechanical and processing properties of TCPCs [27, 28]. For example, Kim et al. [29] reported a TC value of 2.92 W/(mK) after incorporating 70 wt% of BN into the ETDS matrix. For this extent of TC enhancement, very high filler loadings are required. This can result in increased density of ETDS composites, loss in mechanical properties, processing difficulties, and increased cost. Meanwhile, the content of fillers has a limitation; for example, the theoretical maximum addition volume fraction is 0.637 [30] as the spherical fillers dispersed randomly in polymer matrix.

Fig. 1
figure 1

(a) A monotonous increasing [18] and (b) non-monotonous change [31] in TC as increasing the filler content (Images reprinted with permission from [16] and [27].)

Full size image

Some experimental results have reported a non-monotonous change in the TCs as increasing the filler content, especially in the TCPCs with the nanoscale fillers (Fig. 1b), which attributes to the failed network caused by the agglomeration of fillers [31, 32]. Patti and co-workers [31] studied the TC of polypropylene/MWCNT composites. It was concluded that TCs changed in a non-linear trend via varying the amount of MWCNTs because the dispersion of MWCNTs often leads to uneven filler distribution, characterized by dispersed and agglomerated areas. Similar results also happened in the modified BN/polyvinylidene fluoride composites [33] and BN/poly(lactic-co-glycolic acid) composites [34].

2.2 Filler shape

Fillers can be catalogued as fiber-like fillers or quasi-1D fillers (e.g., CF, CNT, and CuNW), platelet-like fillers or quasi-2D fillers (e.g., graphene, graphite, BN, and AlN) and spherical fillers (e.g., AlN, Al2O3) based on the aspect ratio.

Generally, fiber-like and platelet-like fillers are preferred to build the filler networks due to their high aspect ratio [35,36,37,38,39]. For example, Kim et al. [40] studied the effect of AlN shape on the TCs of TCPCs. It was found that AlN platelets triggered a TC almost 1.5 times higher than AlN spheres in the polyvinyl alcohol matrix with the same filler content of 50 vol%. Fiber-like or platelet-like fillers afford anisotropic TC, characterized by a much higher TC along the longitudinal (fiber-like fillers) or the in-plane direction (platelet-like fillers) than that along the perpendicular direction. So far, these fillers, such as BN [41,42,43] and grapheme [44,45,46], have already been widely used to prepare anisotropic TCPCs. The methods to prepare these TCPCs were discussed in the following part.

Spherical fillers often offer a fairly high level of viscosity percolation threshold because these fillers are point contact in polymer matrices, which is benefit for the filler networks and the processing ability of TCPCs [47]. Some researchers even developed methods (e.g., spray-drying [48, 49], spray-freeze-drying [50]) to prepare the spherical fillers from other fillers with intrinsic high TC. Su et al. [51] used the spray-drying technique to prepare the spherical BN particles from plate-like h-BN particles. The TC of spherical BN/PU composite was improved to 7.302 W/mK due to the well continuous networks, higher than that of platelet-like BN/PDMS composite with the same filler content of 40 wt%. Ren et al. [52] came up with a spray-assisted self-assembly approach to fabricate spherical BNs from plate-like BNs. The TC of spherical BN/PDMS composite was improved to 2.30 W/mK, almost fourfold higher than that of platelet-like BN/PDMS composite with the same filler content of 50 wt%, but with a much lower viscosity.

2.3 Filler size

Generally, thermally conductive fillers have a size from nanometers to millimeters, which presents different effects on the TCs of TCPCs. On the one hand, it has been reported that the TCs of TCPCs decrease as the filler size decreases. For example, Shin et al. [53] investigated the TCs of the BN/HDPE composite with different BN sizes. It was concluded that the TCs of the BN/HDPE composite decreased by 1.18 times from 4.5 W/(mK) to 3.8 W/(mK) as BN size decreases from 20 to 3 μm at filler content of 50 vol%. Similar results have also been reported in PVDF-HFP composites with graphene flake [54] and epoxy composites with BN [55]. This phenomenon can be explained by the following reasons. Firstly, fillers with smaller size often have larger specific surface areas, and this easily creates more filler–polymer interfacial thermal resistance, i.e., it easily causes phonon scattering and hinders phonon transporting; secondly, fillers with a larger size easily create more stable paths or networks because of the formed larger contact area [56]. In addition, agglomeration often occurs as the filler size decreases due to the differences of surface energies and surface chemistries between fillers and polymer matrices, which significantly restrict the formation of filler network [57, 58].

On the other hand, some contradictory results have also been reported, i.e., smaller particles were easier to trigger a higher TC. For example, Zhou et al. [59] investigated the TCs of BN/HDPE composites as particle sizes decreasing from 15 to 0.5 μm. It was concluded that the TCs of BN/HDPE composite increased by 1.12 times from 1.05 W/(mK) to 1.18 W/(mK). This phenomenon was explained that since the absorption energy between smaller size fillers and HDPE particles was much higher compared with the larger size fillers, more stable filler paths were easily formed by the former. Zhang et al. [60] described relatively similar results in HDPE/Al2O3 composites, where Al2O3 with 4 different sizes from 0.1 to 10.0 μm were mixed with HDPE. The results indicated that the HDPE composites with smaller size fillers had the larger TC than larger ones at the same filler content because the smaller size particles can form filler pathways or networks more easily due to the large specific surface area and high surface energy.

In summary, it is important to consider the mechanical and processing properties of TCPCs simultaneously, when high content fillers are used to construct the networks. Although the fillers with high aspect ratio are efficient to build the networks, the anisotropic TCs are always obtained, which may not be needed in some polymer composites requiring isotropic TCs. Spherical fillers are also significant to the network since they offer a high level of viscosity percolation threshold. Nowadays, this triggers the tendency to explore spherical fillers from other shapes. Due to the size of fillers ranging from nanometers to millimeters, fillers present different effects on the filler network, so it is necessary for us to comprehensively consider the affecting factors of specific surface area, surface energy, filler–polymer interfacial thermal resistance, filler-filler contact area, etc.

2.4 Filler network tailoring method

The filler network also greatly depends on the preparing methods. Nowadays, scholars have proposed several types of methods to control the formation of filler network. Many methods to tailor filler network have been summarized here.

2.4.1 3D self-assembly network

The self-assembly network usually takes place as increasing the filler content above the percolation threshold, where the possible aggregation forces of the fillers, including van der Waals force, electrostatic force, liquid bridge, and hydrogen bonding, are larger enough than the resistant forces of steric repulsion and electrostatic repulsion; thereby, the fillers agglomerate with the adjacent fillers to form a self-assembled network [61, 62]. According to this theory, for electrically conductive polymer composites, a filler content above the percolation threshold was always reported to trigger 2–3 orders of enhancement in electrical conductivity [63], but for TCPCs, a much higher filler content (often larger than 30 vol%) was required to allow the fillers to directly contact to transport phonons [64, 65]. Embedding a high filler content, however, always leads to poor processing ability, poor mechanical properties and high cost. Thus, artificially controlled 3D self-assembled filler networks have been created without further filler content, such as forming method and ice-templated method.

Foaming method

Foaming method is a promising route to construct filler network without so much filler content. This method is always combined with infiltration to prepare polymer composites. Up to date, 3D protein forming, commercial sponge, and cotton candy-templating have already been developed to prepare the foam structure. For example, Xiao et al. [66] used the egg white protein to fabricate a honeycomb-like Al2O3 network (Fig. 2a(i and ii)). The TC of epoxy composite reached to 2.56 W/(mK) at 23.32 vol%, 3.6-fold higher than epoxy composite with random dispersion of Al2O3 (Fig. 2(a–iii)). Yin et al. [67] used the protein forming method to prepare the continuous sintered Si3N4 network (Fig. 2b(i)). The epoxy solution was then infiltrated into the Si3N4 foams by using a vacuum-assisted resin impregnation method (Fig. 2b(ii)). The TC of epoxy composite reached 3.89 W/(mK) at 22.2 vol%, 17-fold higher than neat epoxy (Fig. 2b(iii)). Liu et al. [68] obtained a 3D graphene foam (GF) based on the commercial PU sponge, followed by infusing the homogeneous epoxy solution cured at temperature of 165 °C for 14 h (Fig. 2c(i and ii)). The GF/polymer composites exhibited a TC up to 1.52 W/(mK) at a filler content of 5.0 wt% (Fig. 2c(iii)). Later on, Liu et al. [69] further developed the GF via sacrificial commercial polyurethane sponge template. The epoxy composite with a TC of 8.04 W/(mK) at a filler content of 6.8 wt% was obtained.

Fig. 2
figure 2

(a) (i) Diagram of the preparation of filler network via egg white protein; (ii) SEM image of continuous filler network; and (iii) TCs of TCPCs as a function of filler content [66]. (b) (i) and (ii) SEM images of continuous filler network and polymer composite; (iii) TCs of TCPCs as a function of filler content [67]. (c) (i) (a) Diagram of the preparation of the filler network via commercial PU sponge; (ii) SEM image of continuous PU framework; (iii) TCs of TCPCs as a function of filler content[68]. (Images reprinted with permission from [61,62,63].)

Full size image

Inspired by the cotton candy, Wu et al. [70] constructed a facile and eco-friendly Al2O3 network by the cotton candy-templating method. In brief, the cotton candy was firstly fabricated through centrifugal spinning via cotton-candy-machine; then, the continuous cotton candy fibers were dissolved in the water, leaving hollow channels inside the polymer matrix; the hollow channels were replaced by the fillers via vacuum-assisted impregnation and high-pressure treatment (Fig. 3a). The fabricated Al2O3/epoxy composites had a continuous filler network (Fig. 3b) and a 15-fold enhancement in TC at 36.2 vol% compared with pristine epoxy (Fig. 3c).

Fig. 3
figure 3

(a) Schematic illustration of the preparation of TCPCs by the cotton candy-templating method. (b) SEM image of TCPCs with continuous pathway. (c) TCs of the TCPCs as a function of filler content [65]. (Images reprinted with permission from [65].)

Full size image

Ice-templated method

Ice-templated method is also a novel method to construct the filler network, and it always combines with infiltrating method to prepare polymer composites. For example, Chen et al. [71] constructed the cellulose nanofiber-supported 3D interconnected BNNS (3D-C-BNNS) aerogels via sol–gel and freeze-drying method based on self-assembled BNNSs on a 3D cellulose skeleton (Fig. 4a). The epoxy matrix was introduced into the space among filler network by infiltration. The epoxy composites exhibited a continuous filler network (Fig. 4b), and an ultrahigh TC of 3.13 W/(mK) was achieved at a low BNNS content of 9.6 vol% (Fig. 4c). Besides, the TC could be easily enhanced by tailoring the BNNS loading in the interconnected 3D network.

Fig. 4
figure 4

(a) Preparation of epoxy composites. (b) The cross-sectional SEM image of epoxy composites with 9.6 vol% BNNS. (c) TCs of epoxy composites as a function of filler content. [71] (Images reprinted with permission from [66].)

Full size image

The ice-templated method is always employed to orient the filler for an enhanced TC in the special direction of polymer composites. So far, fillers of CNTs, BN [72,73,74,75,76], and SiC [77] have been oriented well by the ice-templating method. For example, Zeng et al. [75] studied the ice-templating approach to successfully construct the oriented 3D BN nanosheets (3D-BNNS) network (Fig. 5a). The obtained polymer composites exhibited an oriented 3D-BNNS aerogel path for phonons (Fig. 5b). The TC of products reached 2.85 W/mK at a relatively low BNNS content of 9.29 vol% (Fig. 5c). Later, Yao et al. [74] introduced the reduced graphene oxide (r-Go) into the above 3D-BNNS network. An ultrahigh through-plane TC of 5.05 W/(mK) was obtained. Hu et al. [73] combined the ice-templating method and infiltration method to fabricate the ordered 3D-BN networks. It was found that the TCPC possessed a TC up to 4.42 W/mK at a filler content of 34 vol%, much higher than that of the counterpart with random 3D-BN (1.81 W/mK) and counterpart with random BN (1.16 W/(mK)).

Fig. 5
figure 5

(a) Diagram of the prepared 3D-BNNS aerogels. (b) Hierarchical structures of the free-standing 3D-BNNS aerogel: (i) SEM image of 3D-BNNS aerogel in the perpendicular direction to ice growth; (ii) photograph of a 3D-BNNS aerogel. (c) TCs of products as a function of BNNS content. (Images reprinted with permission from [70].)

Full size image

Generally, in a word, these artificially controlled methods are efficient to construct the filler networks, but they normally need multiple processes and they are often time consuming, so it is difficult for mass fabrication.

2.4.2 Double continuous network

A double continuous networking system typically contains fillers and two immiscible polymers. With appropriate fractions of two immiscible polymers and appropriate temperature and enthalpy, a double continuous structure with selected location of fillers in one polymer could be obtained, and the one containing fillers acts as continual conductive network [78]. Each double continuous structure has its best volume ratio [79,80,81,82]. For instance, the two immiscible polymers of PBT and PC were mixed together with GNPs, and a continual conductive network of PBT/GNPs was constructed well when the volume ratio of PBT to PC was 50:50 [79], as illustrated in Fig. 6.

Fig. 6
figure 6

Schematic diagram of PBT/PC/GNP composites with various volume ratio of PBT to PC: (a) 70/30, (b) 50/50, and (c) 30/70 [79]. (Images reprinted with permission from [74].)

Full size image

Generally, the location of fillers in immiscible polymer matrices commonly lies on the interfacial energies between components and the viscosity of polymers. In theory, once the thermodynamic equilibrium was achieved, the localization of fillers was determined by the interfacial energy. The thermodynamic equilibrium for the localization of fillers can be estimated from wetting coefficient (\({w}_{a}\)) based on Young’s equation [80].

$${w}_{a}=\frac{{\gamma }_{f-PA}-{\gamma }_{f-PB}}{{\gamma }_{PA-PB}}$$
(1)

where \(\gamma\) is the interfacial energy between components. When \({w}_{a}\)< − 1, the filler is preferentially located in phase A; when − 1 < \({w}_{a}\)  < 1, the filler is located at the interface between phases A and B; when \({w}_{a}\) > 1, the filler is preferentially located in phase B.

The interfacial energy \(\gamma\) was calculated by the harmonic mean Eq. (2) and geometric mean Eq. (3) [83].

$${\gamma }_{1-2}={\gamma }_{1}+{\gamma }_{2}-4\left[\frac{{\gamma }_{1}^{d}{\gamma }_{2}^{d}}{{\gamma }_{1}^{d}{+\gamma }_{2}^{d}}+\frac{{\gamma }_{1}^{p}{\gamma }_{2}^{p}}{{\gamma }_{1}^{p}+{\gamma }_{2}^{p}}\right]$$
(2)
$${\gamma }_{1-2}={\gamma }_{1}+{\gamma }_{2}-2\left[\sqrt{\left({\gamma }_{1}^{d}{\gamma }_{2}^{d}\right)}+\sqrt{\left({\gamma }_{1}^{p}{\gamma }_{2}^{p}\right)}\right]$$
(3)

where \({\gamma }^{d}\) and \({\gamma }^{p}\) are the disperse component and polar component of the surface energy of the component, respectively.

Over the past decades, it has already been proved that the double continuous networking method is effective to enhance the electrical conductivity and low down the percolation threshold of electrical conductivity [84, 85]. In these years, this method is becoming popular to enhance the TCs of TCPCs with two immiscible polymers, such as HDPE/PMMA, PBT/PC, PP/PS, LDPE/PS, and PC/PA66, as shown in Table 1.

Table 1 TCs of polymer composites with double continuous network
Full size table

Obviously, the results (in Table 1) show that the double continuous networking method plays an important role in the greater enhancement of TCs, compared with the traditional self-assembled network at the same or a lower filler content. The double continuous network can also be constructed by selecting polymers with different melt temperatures. For example, Zhou et al. [97] prepared a double continuous network in Elvaloy and PBT matrices based on the different melting temperature between Elvaloy and PBT. A TC up to 7.8 W/(mK) was obtained as LTED was introduced into Elvaloy/PBT matrices. Briefly, the LTEG and Elvaloy were firstly mixed by an internal mixer at a temperature of 170 ℃. After that, the PBT was introduced into Elvaloy-LTEG mixtures and mixed together by the internal mixer at a temperature of 170 ℃. Finally, the samples for different measurements were fabricated with thickness of approximately 4 mm using a hot pressing method at 10 MPa and 240 °C to keep the network architecture intact (Fig. 7).

Fig. 7
figure 7

(a) Fabrication process of Elvaloy-LTEG/PBT composites with the segregated network. (b) SEM pictures of segregated network in Elvaloy-LTEG/PBT composites. (c) TC of Elvaloy-LTEG/PBT composites as a function of LTEG content and PBT particles size [97]. (Images reprinted with permission from [92].)

Full size image

2.4.3 Segregated filler network

In order to maximize the utilization efficiency of the fillers, forming the segregated structures in the TCPCs has becoming a promising method, where the fillers are selectively located at the interfaces of polymer particles by drying or solution mixing.

In the last decade, numbers of researchers have devoted to the design and develop the segregated 3D architectures. For example, Hu et al. [98] reported a 3D-segregated network of AlN in the PP matrix to improve the TCs of TCPCs (Fig. 8a). The AlN was selectively located at the PP particles by the mechanical grinding method, and a TC of 0.81 W/(mK) was obtained at 30 vol% AlN. A segregated structure of graphite constructed in UHMPE matrix by the binder-mixing method and solvent-mixing method (Fig. 8b), respectively, was reported by Feng et al. [99]. The TCs of UHMPE composites were improved to 2.276 and 1.883 W/(mK) with the graphite content of 18.83 vol%, respectively. Jiang et al. [100] reported a TC of 4.15 W/(mK) for a segregated filler network of BN in PPS matrix by chemical cross-linking (Fig. 8c). The TC of 2.45 W/(mK) exhibited 1.69 times higher than PPS/BN composite at the same BN content. Ding et al. [101] reported a 3D-segregated network of BN in the PI matrix by a hot pressing method. Herein, the BN was firstly coated on the surface of PI granules via the PI adhesive to form a core–shell structure; after that, the BN-PI granules were transformed to the segregated network by hot embossing. The TC of BN/PI composites reached up to 4.47 W/(mK) at 20 vol%.

Fig. 8
figure 8

Mechanism of segregated filler network by (a) mechanical grinding [98], (b) solution method [99], and (c) chemical cross-linking [100]. (Images reprinted with permission from [93,94,95].)

Full size image

Segregated structures with hybrid filler system were also reported. A TC of 7.1 W/(m/K) in UHMWPE composite with hybrid segregated structure of AlN/BN was reported by Wang et al. [102]. Herein, AlN and BN were firstly mechanically wrapped upon UHMWPE granules, and after that they were consolidated with high-pressure to form segregated structure. Wu et al. [103] reported a TC of 1.08 W/(mK) in polystyrene composites with a unique hybrid segregated filler network of GNPs/MWCNT (3.5/1.5 wt%). A segregated structure with a hybrid filler system was further studied to balance the TC and electrical insulation performance for thermal management applications. Zhang et al. [104] reported a TC up to 2.69 W/(m K) in PA 6 composites with a hybrid segregated filler network of graphene nanoplatelets (GNPs)/BN, almost tenfold improvement in TC of pure PA6, and an electrical conductivity as low as 4.13 × 10 − 9 S/m. Wang et al. [105] constructed a segregated filler network with hybrid filler of BN and CNT. The PVDF composites exhibited a TC of up to 1.8 W/(mK), much higher than PVDF composites with BN/CNT random structure or segregated BN structure.

2.4.4 Hybrid fillers

A combination of two or more fillers mixed as hybrid fillers can generate synergistic effects to enhance the TC, which is superior to that achievable with any TCPCs consisting of either filler alone. The synergistic effects always occur when each filler is dissimilar to the other in size and aspect ratio. In one aspect, smaller fillers locating between larger fillers can provide a path between the two larger fillers in which heat may flow between the larger fillers with no or less distance traversed through the highly insulating matrix. In another aspect, fillers with a higher aspect ratio can efficiently connect fillers with smaller aspect ratio even when the content of the former is relatively low. Figure 9 illustrates the common hybrid fillers designed with different aspect ratios and sizes in the TCPCs.

Fig. 9
figure 9

Illustration of different strategies for the used hybrid fillers in TCPCs. Hybrid fillers of (a) quasi-1D fibers and spherical fillers, (b) quasi-1D fibers with different size, (c) spherical fillers with different radii, (d) quasi-2D fillers and quasi-1D, (e) quasi-2D fillers and spherical particles, and (f) quasi-2D fillers with different material or size

Full size image

A hybrid filler system consisting of quasi-1D fibers and spherical fillers is shown in Fig. 9a. CFs, CNTs, and AlN whiskers, as the typical quasi-1D fillers, were always combined with spherical fillers of Al2O3 [106, 107], spherical AlN [93, 108], and SiO2 [109]. For example, Dang et al. [110] investigated PVDF composites filled with anisotropic AlN whiskers and isotropic spheres AlN. A maximum TC of 4.321 W/(mK) at 60 vol% (volume ratios of former to latter is 1:1) was achieved because the AlN spheres successfully served as wedges between AlN whiskers to promote the construction of the 3D filler network. Oh et al. [109] studied TC of epoxy composites filled with CNT and spherical SiO2. A maximum TC value of 0.340 W/(mK) at 0.6 wt% CNT and SiO2 was achieved, higher than composites only with SiO2.

The hybrid filler system that consisted of quasi-1D fillers with different sizes is shown in Fig. 9b. CNTs and CFs were always combined together, as the CNTs can serve as wedges between CFs to promote the formation of filler network [27, 111,112,113,114,115,116,117]. The hybrid filler of CNTs and CFs could also induce a three-dimensional hierarchical network for the enhanced TC in and through thickness of samples even though the TCs of CNT and CF are anisotropic. Ji and co-workers [111] employed the chemical vapor deposition (CVD) method and electrostatic flocking device to align the CNT and CF respectively in and through thickness of silastic composites. The TCs up to 7.51 and 3.72 W/mK through and in-plane of samples were achieved.

A hybrid filler system that consisted of spherical fillers with different radii is shown in Fig. 9c. So far, the hybrid spherical filler systems of Al2O3/AlN [118] and Al2O3/SiC [119] have already been reported. It was concluded that the hybrid spherical filler systems were important in the high TC of TCPCS because as the spherical fillers with different sizes were mixed, small particle fillers easily entered the gap between large particle fillers, so the porosity between fillers was easily reduced and the packing density was easily increased, and more heat chains were formed for the heat flow.

Figure 9d shows a hybrid filler system that consisted of quasi-2D fillers and quasi-1D particles. Herein, graphene, graphite, and BN, as the typical quasi-2D particles, have attracted growing attention in recent years to build a hybrid filler system because the adjacent quasi-2D fillers can be easily bridged by the quasi-1D fillers, which simultaneously strengthens the interfacial connection and forms a highly conducting network for heat flow. So far, the hybrid filler systems of BN/CNT [105, 120,121,122,123,124,125], BN/CF [126,127,128], graphene/CuNWs [129], BN/SiC [130], graphene/SiC [45], and graphene/CNTs [131,132,133], have already been reported in the literature. The results all indicated that the presence of synergistic effect in hybrid polymer composites contributed to the high TC, not the utilization of single fillers.

Figure 9e shows a hybrid filler system consisted of quasi-2D fillers and spherical fillers. Synergetic enhancement of TC was reported in this hybrid filler system because hybrid fillers can create more pathways for phonon transport. The hybrid filler systems of BN/spherical AlN [134, 135], graphene/AlN [136], graphene/Al2O3 [137,138,139], BN/Al2O3 [140,141,142,143], BN/SiO2 [144], and BN/AgNPs [145] were widely reported. In addition, since the quasi-2D fillers afford strong anisotropic TC, TCPCs generally exhibit high in-plane TC while low through-plane TC. In order to improve the through-plane TC, spherical fillers were introduced to disrupt the alignment of quasi-2D fillers along the lateral direction during processing. For example, Pan et al. [146] used the h-BN platelets and AlN particles as hybrid fillers to improve the through-plane TC of PTFE. It was concluded that AlN particles effectively disrupt the alignment of h-BN platelets along the lateral direction during the compression processing and a high through-plane TC up to 1.04 W/mK was achieved at 30 vol% filler content, 3.8 times that of neat PTFE.

Quasi-2D filler and quasi-2D fillers with different sizes or materials were often investigated as a hybrid filler system, as shown in Fig. 9f. BN, graphene, and graphite nanoplate were always used to form a hybrid filler system to improve the TC [104, 147,148,149]. Zhang et al. [104] fabricated a core–shell structures by GNPs and BN to form a continuous filler network. A TC up to 2.69 W/(mK) in nylon 6 composites was achieved, almost tenfold improvement in TC of pure PA6. Due to the conductive network of GNPs cut off by the BN segregated layer, an electrical conductivity as low as 4.13 × 10 − 9 S/m was obtained. Lewis et al. [148] also presented similar results in the epoxy composites with hybrid fillers of graphene and BN fillers (21.8 vol% in total). Herein, the hybrid fillers of graphene and BN were intentionally chosen with similar thickness, lateral dimensions, and aspect ratios. A TC up to 6.5 W/(mK) was obtained in epoxy composites. Xing et al. [150] introduced hybrid fillers of graphite nanoplates with small size around 1–5 μm and large size around 20 μm into the epoxy matrix. A TC of 1.33 W/(mK) was achieved at 20 wt% (weight ratios of large particles to small particles is 17:3).

2.4.5 Filler orientation

Many thermally conductive fillers have anisotropic TC. These fillers always have a non-spherical shape, such as quasi-2D fillers (BN, graphene, graphite flakes) and quasi-1D fillers (CF, CNT). These fillers can be oriented during processing to achieve a high TC in the direction of orientation, but a low TC perpendicular to the direction of orientation. Shear or stretching forces, external fields, ice-templating, 3D printing, and CVD are the methods often used to orient the fillers, as shown in Fig. 10.

Fig. 10
figure 10

Illustration of methods to orient fillers in the polymer. (a) Shear or stretching forces, e.g., (i) drawing process [151], (ii) electrostatic spinning [152], and (iii) compression [153]. (b) External fields, e.g., (i) electrical field [154] and (ii) magnetic field [155]. (c) Ice-templating [72]. (d) 3D printing [140]. (e) Chemical vapor deposition (CVD) [156]. (Images reprinted with permission from [67, 134, 145,146,147,148,149,150].)

Full size image

Shear or stretching forces can make the fillers arrange along the shear or stretching direction to form a conductive path. Shear or stretching forces are from processing of drawing process [151], electrostatic spinning [152, 157, 158], compression [19, 153, 159,160,161,162,163,164], 3D printing [140, 165], milling [41, 166,167,168], injection [169,170,171], and casting [172]. Some processes are shown in Fig. 10a.

The magnetic field is often utilized to orient the fillers (Fig. 10b). The magnetic substances, such as Fe3O4 and FeCo, are often coated on the surface of fillers for the magnetic property of fillers. Yuan et al. [155] used the magnetic field to orient the BN platelets coated with super-paramagnetic iron oxide nanoparticles. The TC of TCPCs with oriented BN, parallel to the heat flux direction, was 44.5% higher than that of composites with unaligned BN at filler content of 9.14 vol%. Shi et al. [44] used the external magnetic field to align multilayer graphene (MG) modified by Fe3O4 in the silicon rubber (SR) matrix. The Fe3O4@MG/SR composites possessed a high TC of 0.64 W/(mK) in the alignment direction. Yan et al. [173] used the magnetic field to align graphene nanosheets (GNSs) coated with Fe3O4. The epoxy composites possessed a high TC in the direction of heat flow at low Fe3O4@GNS loadings, much higher than the composites with randomly dispersed bare GNSs. Kim et al. [174] used the magnetic field to orient the BN in the polymer matrix. An enhancement of 1.96-fold (at filler content of 30 vol%) in TC was obtained for the synthesized vertically aligned composites. Other scholars [175,176,177] have also studied the external magnetic field to orient the BN to improve the TC in the direction of heat flow.

The electric field with alternating current (AC) or directing current (DC) voltage has already been applied to orient the fillers, as shown in Fig. 10b. The substances, such as TiO2, are often coated on the surface of fillers to enhance the dielectric property. Guo et al. [154] induced the graphene orientation in PVDF via DC electrical field. A TC up to 0.587 W/(mK) at 20 wt% was achieved, 4.5% higher than that before aligning graphene. The coated BN with TiO2 used to prepare TiO2@BN/polyurethane acrylate composite via external electric field with 500–700 kHZ and 600 V AC voltage was reported by Kim et al. [178]. The TC reached to 1.54 W/(mK), 1.9-fold (at filler content of 20 vol%) higher than the counterpart with randomly oriented BN (0.78 W/(mK)). Liu et al. [179] introduced an AC electrical field to align the clay nanoparticles along the thickness direction in the PDMS matrix. The obtained TC up to 0.316 W/(mK) in through-plane of composites was around 1.6 times higher than the counterpart with nonaligned clay nanoparticles at 5 wt%.

Recently, the ice-templated method was widely used to orient fillers, as shown in Fig. 10c, and many examples have been introduced in part 2.4.1. Other methods of 3D printing and CVD have also been used to prepare the oriented filler network (Fig. 10d, e). For example, Shao et al. [156] induced the vertically aligned CNT arrays (VACNT) by the CVD method in the epoxy matrix. The longitudinal TC of 1.85 W/(mK) was obtained due to the contracted vertical heat transfer channels in the film, as shown in Fig. 10e.

3 Conclusions and outlook

The continuous filler network plays a significant role to enhance the thermal conductivity of polymer composite. The formation of the filler network is a function of filler aspect ratio, content, and size. It is a must for us to take a holistic approach when designing the filler network. In this review, we mainly discussed these main affecting factors of the filler network. The preparing methods also greatly affect the formation of the network. Herein, the methods of 3D self-assembled networking, double continuous networking, segregated filler networking, hybrid fillers, and filler orientation, to deal with the filler network, have been summarized.

Although some successes of polymer composites have already been obtained by scholars, there are still many challenges for thermally conductive polymer composites. More studies are expected in the following aspects. First, most reported methods to construct the continuous filler network are time consuming, costly, and relatively complicated. Thus, they still needed further studies for simple and mass production. Other novel and simple methods also need to be further explored to prepare polymer composites. Second, a significant amount of fillers is often required to achieve a high thermal conductivity in polymer composite. However, the high filler loading often fails to achieve the expected high thermal conductivity, and often results in the deterioration of mechanical and processing properties, as well as a high cost. So, further studies should be conducted to balance the above properties of polymer composites. Finally, even though a great enhancement in thermal conductivity was reported in some literature, the thermal conductivity of polymer composites was still much less than the instinct thermal conductivity of filler; thus, the mechanism of this phenomena needs to be further studied, excluding the theory of the thermally conductive path theory, the thermal percolation theory, and the thermoelastic coefficient.