Polymer-Based Thermally Conductive Materials by Fused Filament Fabrication

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This entry is adapted from the peer-reviewed paper 10.3390/polym14204297

With the miniaturization and integration of electronic products, the heat dissipation efficiency of electronic equipment needs to be further improved. Notably, polymer materials are a choice for electronic equipment matrices because of their advantages of low cost and wide application availability. Intelligent electronic devices are currently being researched to meet people’s pursuit of a high-quality life through integration and miniaturization. In order to ensure product safety and operational efficiency, it is imperative to improve the thermal conductivity of electronic devices. Polymers are frequently used in preparing heat dissipation materials because of their low price, light weight, ease of processing, and wide applications.

additive manufacturing fused filament fabrication polymer-based thermally conductive material thermal conductivity

1. Three-Dimensional Printing in Thermally Conductive Composites

The molding processes of traditional polymer matrix composites include contact molding, compression molding, extrusion molding, and injection molding, all of which require the aid of model-assisted molding without exception, so the mold constrains the part’s shape. The most significant benefit of 3D printing is that it can create prints with intricate shapes without the need for molds, which brings down production costs. The 3D printing process used for molding thermally conductive materials mainly includes FFF, SLA, DIW, and so on ^[1]. The principles of these techniques and their research progress on thermally conductive composites are briefly introduced in the following.

1.1. SLA

The 3D system was founded in 1986 by inventor Charles and entrepreneur Raymond S. Freed, who launched the first SLA printer in 1988, paving the way for commercialization. Consequently, SLA can be regarded as the progenitor of 3D printing. The liquid photopolymer is first added to the resin tank, and the build platform is lowered to a level slightly below the liquid surface of the resin. The laser beam is selectively focused on the surface of the liquid photopolymer to achieve the transition from liquid to solid state. Afterward, the build platform rises to a specific height, and the liquid resin covers the previous print again by laser curing. The resin is stacked layer-by-layer until the printing process is completed. Finally, the finished product is removed from the resin tank for cleaning ^[2]^[3]^[4]. SLA has the benefits of a high level of automation and the ability to make high-resolution prints, so it is frequently employed to produce complicated models.

The printing material of SLA, also known as photosensitive resin, usually consists of oligomers, reactive diluents, photoinitiators, etc. Oligomers are low-molecular-weight monomers or prepolymers that serve as the photosensitive resin’s main components and determine the printed part’s performance after curing. Choosing oligomers requires consideration of the physical and chemical properties of the cured product on the one hand, and the feasibility of production—such as system viscosity and cost—on the other hand, so there are relatively few options. The most used oligomer in SLA is epoxy acrylate, followed by urethane acrylate. Other oligomers, such as polyester acrylate and polyether acrylate, can also be used as raw materials for photosensitive resins. Active diluents reduce the viscosity of oligomers and accelerate the reaction of resins. The photoinitiator generates reactive intermediates by absorbing radiation energy to activate oligomers and diluent monomers for cross-linking reactions. Since the research on SLA technology is late, the research on photosensitive resin is mainly concentrated in universities and research institutes. As the prints made by SLA have poor mechanical properties and toughness, the researchers used nanoparticles to modify the resin. It can improve the compatibility between the polymer and the filler and further enhance the prints’ performance ^[5]. Due to the advantages of high precision and rapid prototyping, SLA is regarded as one of the manufacturing technologies of thermal management materials by researchers. In terms of materials, achieving better thermal management starts with designing the cooling structure, including thermal interface materials and packaging materials. In order to dissipate heat without dielectric breakdown, these materials are usually composed of fillers with excellent thermal conductivity and insulation. The most prevalent are alumina ^[6]^[7]^[8]^[9], silicon carbide ^[10]^[11], titania ^[12]^[13], etc., which are applied in thermal management materials frequently because of their low price and extensive availability. Azarmi et al. ^[14] prepared ceramic materials by adding Al₂O₃ to a photosensitive polymer resin and tested their thermal properties. After sintering, the porosity of the material decreased from 19.01 ± 1.12% to 8.14 ± 0.85%, while the thermal conductivity showed an increasing trend. The actual measured thermal conductivity increases from 5.17 ± 1.05 W∙m⁻¹∙K⁻¹ to 26.81 ± 3.5 W∙m⁻¹∙K⁻¹, confirming that porosity plays a negative role in the heat transfer.

Ceramic fillers with better thermal conductivity, such as boron nitride (BN), aluminum nitride (AIN), and silicon nitride (SIN), have attracted widespread attention. Gurijala et al. ^[15] made superparamagnetic nanoparticles (SPIONs) lose electrons and bind to negatively charged hBN particles to produce magnetized hBN that low magnetic fields can control (<10 mT).

Mubarak et al. ^[12] modified Ag on the TiO₂ surface with the help of the sol–gel method. The obtained Ag-TNP was added to the resin as a filler, which induced photopolymerization of the resin under UV irradiation. Under the influence of ultraviolet light, the nanoparticles will generate valence band holes and conduction band electrons on their surface, which facilitates the formation of monomer radicals, thereby initiating free-radical photopolymerization and enhancing the thermal conductivity and mechanical properties of the polymer. The tensile strength and flexural strength of SLR/Ag-TNP nanocomposites were enhanced with the increase in Ag-TNP content, which were improved by 60.8% and 71.8%, respectively, at a loading of 1.0%. The highest thermal conductivity was achieved at a filler concentration of 1%, with a value of 0.3456 W∙m⁻¹∙K⁻¹. However, the thermal conductivity showed a decreasing trend with the increase in filler concentration. Therefore, solving the problem of uneven heat dissipation from the polymer matrix caused by the agglomeration phenomenon at high filler content is still a problem that needs further research. The limited availability of raw materials that can be applied to SLA and the significant odor and toxicity of liquid resins have hindered its development to some extent.

1.2. DIW

The raw material for DIW is ink with a specific viscosity, usually containing an organic matrix, thickeners, filler particles, and so on. The ink must have both the appropriate shear-thinning rheological behavior to ensure the extrusion process’s smoothness and that the extruded ink can maintain structural stability when in contact with the substrate ^[16]. DIW works by the three-dimensional movement of the printhead according to the shape of the designed print part, stacked layer by layer to form the initial sample. The curing reaction is then completed under UV light or heat conditions to form the final part. Since the preparation of DIW relies on an extrusion process, the researchers took advantage of this feature to make anisotropic thermally conductive fillers oriented under high shear forces to produce thermally conductive composites.

When the viscosity of the ink is sufficiently high, direct printing in the vertical direction can be accomplished in addition to layer-by-layer printing in the horizontal direction. Liang et al. ^[17] dispersed BN in the F-127 solution, where F-127 was used as a binder to improve the mechanical strength of the printing ink to ensure that the extruded filaments are self-supporting and will not bend or collapse. Due to the anisotropy of the BN shape and the shear force generated when the ink is extruded from the nozzle during printing, the BN nanosheets are tightly packed along the Z-axis to form a continuous thermal conduction path. In order to test the thermal conductivity of the material, they encapsulated a vertical BN-rod array in a polydimethylsiloxane matrix (PDMS) to create a bulk material. The thermal conductivity of the BN-array/PDMS was measured to be 1.50 W∙m⁻¹∙K⁻¹, whereas the theoretically calculated thermal conductivity of the BN rod is as high as 5.65 W∙m⁻¹∙K⁻¹. Even though the thermal conductivity of BN-array/PDMS cannot approach the theoretically predicted thermal conductivity, the thermal conductivity of polymer matrix composites can be increased by changing the number of BN rods within the same volume.

The work has apparent advantages, such as the possibility of obtaining a vertically aligned layered structure directly, moving away from the traditional horizontal stack molding. Moreover, the finished product is directly dried overnight without curing post-treatment, providing an avenue for the design of thermal conductivity pathways for the rest of the two-dimensional fillers. However, the disadvantage is also obvious. In order to achieve the purpose of printing ink vertically, the range of the window in which the BN content can be changed is tiny. The extruded ink filament is insufficient to support the molding when the content is less than 50 wt%. The nozzle will be blocked due to excessive ink viscosity when it exceeds 55.6 wt%. Hence, the preparation of vertical printing inks is relatively demanding and challenging.

1.3. FFF

Scott Crump pioneered FFF technology in 1988, which was commercialized by Stratasys the following year, and the first FFF 3D printing machine was sold in 1992. The working principle is to feed the plastic filament into the gear, throat, and nozzle in sequence. The solid filament is heated by the nozzle to a molten state and deposited on the platform after extrusion. After setting the slicing parameters and generating the g-code format file according to the requirements of the desired part, the nozzle is controlled by the program to move in the X and Y axes. Each time a layer of thickness is deposited, the nozzle is raised upwards by one layer of thickness to form the final printed part ^[18]^[19]^[20]^[21]^[22].

FFF has various advantages over other 3D printing technologies: First, FFF printing equipment is inexpensive, but equipment for other printing technologies, such as photocuring and laser sintering, is costly and complicated. Second, the printing material is simple to create, does not have a complex formula design, and the printing process is environmentally friendly and free of pollution. Lastly, the prints produced by FFF can be formed quickly, eliminating the need for lengthy and complex postprocessing for prints that do not require a support structure. In light of these benefits, researchers feel that using FFF 3D printing technology to make polymer-based thermally conductive materials has some practical potential; consequently, several studies have been carried out. The following section briefly introduces the thermal conduction mechanism and then a summary of the literature on FFF thermally conductive materials.

2. Thermally Conductive Fillers in FFF 3D Printing

Polymer thermally conductive materials can be separated into intrinsic and filler types based on their ingredients ^[23]. Intrinsically thermally conductive materials reduce the resistance to heat transfer by improving the disorderly arrangement of polymer chains through chemical reactions or mechanical action, thereby reducing the entanglement of molecular chains ^[24]^[25]. Xu et al. ^[26] dissolved semicrystalline polyethylene powder in decalin to make the polymer chains undergo preliminary untwisting. The solution is sent to the Couette flow system, where the shear force during the extrusion process will further reduce the tangling of the molecular chain before the solution flows to the liquid nitrogen-cooled substrate to form a film that will maintain the disentangled structure. As the draw ratio increases, the diameter of the fibers in the film decreases, and the density increases. When the draw ratio reaches 110 times, the polyethylene film is as high as 62 W∙m⁻¹∙K⁻¹ in the stretching direction, which is higher than many metals and ceramics. Nevertheless, the preparation process for this intrinsic thermal polymer is typically quite complex. In contrast, filler-type thermally conductive polymers are easier to prepare. According to the shape, the thermally conductive fillers can be divided into anisotropic and isotropic fillers. Based on electrical conductivity, they can be classified as insulating and conductive fillers, and different types of fillers can be chosen depending on the application area.

The FFF thermally conductive fillers mainly include graphene, expandable graphite, carbon fiber, carbon nanotubes, BN, AIN, Cu, Fe, SiC, etc. Expandable graphite can be used as a precursor for preparing graphene, as opposed to researchers who are more interested in using graphene to improve the thermal conductivity of printed parts. Carbon fibers and nanotubes are one-dimensional carbon fiber materials with similar properties, so the more-used carbon fiber was chosen as a representative. Cu and Fe are metal fillers, and both have similar thermal conductivity mechanisms, so Cu, which has more relevant studies and is more representative, was chosen for the introduction. The fillers with similar properties are no longer described in detail. They are divided into two main categories according to the electrical properties of thermally conductive fillers in the following part.

2.1. Electrically and Thermally Conductive Fillers

The addition of thermally conductive fillers will not only improve the overall thermal conductivity of the polymer but will also impart the electrical properties of the filler itself to the composite. Commonly used electrically and thermally conductive fillers in FFF include graphene, metal particles, carbon fibers, diamond, graphite, etc. A brief description of these fillers and their research progress in FFF is presented next.

2.1.1. Graphene

Graphene is a material with a monolayer honeycomb lattice structure formed by tightly packed carbon atoms connected by SP² hybridization ^[27]. As a kind of anisotropic thermally conductive filler, graphene possesses excellent in-plane thermal conductivity (IPTC) of about 2000–5000 W∙m⁻¹∙K⁻¹ ^[28], while its through-plane thermal conductivity (TPTC) is only 5–20 W∙m⁻¹∙K⁻¹ ^[29]. Due to the vast difference between TPTC and IPTC, maximizing the use of IPTC in thermally conductive composites has become an important issue. In order to maximize the thermal conductivity of the composite, the graphene sheets need to be maximally exfoliated and highly oriented.

However, the typical layered structure of graphene tends to cause folds in the lamellar layers during the compounding process. Moreover, the van der Waals forces between single graphene layers are large, which makes it challenging to achieve exfoliation ^[30]. In early work, most researchers simply melt-mixed graphene with polymers, thus often resulting in graphene sheet stacks that did not achieve the desired modification.

Meanwhile, graphene’s degree of dispersion and exfoliation determines whether the thermal conductivity channels can be established most efficiently, dramatically affecting the composite’s thermal conductivity. As a result, the researchers increased the degree of graphene dispersion in the matrix and further exfoliated graphene sheets by combining solution or mechanical mixing with melt mixing. For instance, solid-state shear milling can reduce the number of graphene stacks by repeatedly milling graphene powder and polymer powder ^[31]. During mechanical mixing, graphene and polymers undergo mechanochemical reactions due to the generation of free radicals ^[32]. The filler transitions from physical mixing to chemical grafting, which enhances the compatibility between the filler and the polymer matrix, reduce the interfacial thermal resistance and therefore accomplish the goal of enhancing thermal conductivity ^[29]. Solution mixing here refers to dissolving the polymer in an organic solvent to untwist it, adding graphene powder and stirring to disperse it, and then removing the organic solvent where the polymer improves its dispersion by trapping the graphene and limiting its restacking ^[33]. The double-mixing method is an excellent way to ensure that graphene is evenly distributed in the polymer matrix and reduces agglomeration.

In addition, the filler’s orientation is crucial for the formation of the thermal transfer network due to the anisotropy of graphene. The researchers believe that most graphene will be horizontally in the X-Y printing plane. In order to take maximum advantage of the IPTC of graphene, the print structure can be designed so that the heat flux direction is aligned with the orientation direction of graphene. By using FFF, it can achieve a higher degree of graphene sheet orientation. However, few researchers have conducted in-depth research on the orientation process. Guo et al. ^[33] thought that the orientation of graphene sheets would occur via the following process: Initially, the graphene would be oriented along the direction of rotation of the twin screw, and then the 1.75 mm filament would be melted and compressed into 0.4 mm microfilament, during which the graphene would change into a vortex morphology protruding from the cross-section. During the printing process, the bottom holds its vortex structure due to the rapid cooling rate, while the top has a certain fluidity due to the relatively slow cooling rate. The compressive effect caused by the deposition process aligns the top graphene sheet horizontally, resulting in asymmetric top and bottom structures.

2.1.2. Cu

Metals have a vast number of electrons that are not constrained, and the interaction or collision that occurs between these electrons can result in the rapid transfer of heat. Therefore, the metal particles are usually added to the polymer to increase the thermal conductivity of the composite material. Among them, copper has become one of the most commonly used fillers to improve the thermal conductivity of polymers due to its low price, abundant reserves, high thermal conductivity, and low coefficient of thermal expansion. The thermal conductivity of copper is 397 W∙m⁻¹∙K⁻¹, second only to silver, which can achieve excellent results in the heat transfer of composites. However, one of the disadvantages of utilizing copper as a filler is that it is susceptible to oxidation, and the high hardness of copper tends to induce machine wear.

Hwang et al. ^[34] mixed ABS with copper and iron particles to make a new metal/polymer composite wire that can be used for FFF. When the amount of copper is 50 wt%, the thermal conductivity increases to 0.912 W∙m⁻¹∙K⁻¹, which is only 41% improved compared with pure ABS (0.646 W∙m⁻¹∙K⁻¹) and has not improved significantly. Vu et al. ^[35] made Cu particles form a separated structure by adding PMMA, which promoted the dispersion of Cu particles and facilitated the phonon transfer in the PLA matrix. The addition of PMMA beads plays a synergistic role in the Cu particles, which is conducive to the formation of the thermal channel of the Cu particles. Following the addition of 20 wt% PMMA beads and 50 wt% Cu particles, the thermal conductivity of the composite material is 317% greater than that of the pure PLA. However, the composites became brittle after the addition of fillers, leading to a decrease in tensile strength and elongation at break, which showed the same trend as the research results of Hwang et al. Therefore, how to ensure the improvement of thermal conductivity without damaging the mechanical properties is also a significant direction to be explored in the future.

2.1.3. Carbon Fiber (CF)

Carbon fibers are composed of incomplete graphite crystals arranged axially along the fiber. The basic structural unit is a hexagonal network plane, and the atomic levels of carbon fibers are subject to irregular translation and rotation, so carbon fibers belong to the turbostratic graphite structure ^[36]^[37]^[38]. Inheriting the anisotropy of graphite lamellar structure, some physical properties of carbon fibers also show significant differences in axial and radial directions, especially the mechanical properties. According to length, carbon fiber may be separated into long, short, and short-cut fibers, all of which have superior corrosion resistance, thermal conductivity, coefficient of thermal expansion, axial strength, and modulus. As mentioned above, the addition of thermal conducting particles often sacrifices the mechanical properties of composites. To solve this problem, the researchers took advantage of the excellent mechanical properties of short-cut fibers in the axial direction to achieve simultaneous improvement in thermal conductivity and mechanical properties. In the process of FFF 3D printing, shear stress will occur between the melt and the inner wall of the nozzle. In order to reduce the flow resistance, the carbon fibers are forced to arrange along the flow direction, thus forming a phenomenon of orientation along the printing direction. Due to the shape and orientation of carbon fibers, when the material is stressed, the crack growth direction is perpendicular to the fiber orientation, which limits the crack growth while converting part of the stress, thus improving the mechanical properties of the composite.

2.2. Insulating Thermally Conductive Fillers

Research on polymer-based materials with excellent thermal conductivity and insulating properties is a hot topic for further development in electrical and electronic fields. Insulating thermally conductive materials can protect electronic components on the one hand and export the heat generated by integrated circuits in time to ensure the safe operation of electronic devices on the other. Insulation and thermal conductivity fillers mainly include metal oxides (Al₂O₃ ^[39], SiO₂ ^[40], etc.) and metal nitrides (AIN ^[41], BN ^[42], etc.).

2.2.1. BN

In the crystalline structure of BN, B and N atoms form a densely connected hexagonal ring network within each layer due to strong covalent bonds and dipole moment forces, whereas the layers are connected by van der Waals forces and electrostatics ^[43]. The crystal structure can be divided into hexagonal and cubic crystal types by stacking heterogeneous atoms between layers ^[44]^[45]. Under high temperature and high pressure, hexagonal crystal form can be transformed into cubic crystal form, including four variants: hexagonal boron nitride (hBN), rhombic boron nitride (RBN), cubic boron nitride (CBN), and wurtzite boron nitride (WBN). Among them, hBN is referred to as “white graphite” since it is white and has a similar lamellar structure to graphene ^[46]. Similar to graphene, hBN has a high thermal conductivity of 600 W∙m⁻¹∙K⁻¹ in the in-plane direction, yet only 30 W∙m⁻¹∙K⁻¹ in the through-plane direction ^[47]. Due to its low dielectric constant, low dielectric loss, and high volume resistance, hBN is not only an excellent conductor of heat but also an excellent insulator of electricity. It is very suitable for electronic packaging materials, which can not only provide mechanical support for electronic chips but also achieve the purpose of heat dissipation.

Studies have shown that the thermal conductivity of hBN/polymer composites is influenced by various factors, including the orientation of the hBN, the quantity of filling, and the interfacial bonding between the hBN and the matrix. To increase the thermal conductivity of TPU composites, Liu et al. ^[48] used the shear force generated by the nozzle during the FFF process to promote the alignment of hBN along the printing direction. The thermal conductivity of the printed sample prepared by Tyler et al. ^[49] by adding 35 wt% BN was only 0.93 W∙m⁻¹∙K⁻¹, which was improved but still failed to meet the requirements of thermal conductivity materials in engineering applications (>1 W∙m⁻¹∙K⁻¹). In this regard, the authors propose that this is due to the poor adhesion of BN to the ABS substrate, and that the thermal conductivity can be further improved by the subsequent surface modification of BN.

2.2.2. SiC

Si atoms and C atoms are covalently bonded by SP³ to form a tetrahedron, which constitutes the basic constituent unit of the SiC crystal. SiC has the advantages of broad band gaps and high electronic saturation rates, so its development prospects in the semiconductor industry are promising. In addition, SiC has high thermal stability and corrosion resistance ^[50], and its theoretical thermal conductivity can reach 490 W∙m⁻¹∙K⁻¹ ^[51]. As the development of the electronics industry has progressed, SiC has solved the problem of heat dissipation under high heat densities, thereby prolonging the device’s service life. Liu et al. ^[52] used SiC and C as the fillers of PLA to make the shape memory polymer, placed the composite material in hot water to trigger the shape recovery, and evaluated the shape recovery properties of materials with different filler contents by recovery speed and recovery time. With the addition of thermal conductivity filler, the maximum deformation recovery time of the composites is significantly reduced from 1.9 s to 0.25 s with the addition of 50 wt% C and 10 wt% SiC, which is mainly attributed to the high thermal conductivity of 4.777 W∙m⁻¹∙K⁻¹. This work shortens the response time of shape-memory polymers by regulating the thermal conductivity of the materials, which can be used to design the structures of shape-memory materials activated at different rates.

2.2.3. Diamond

The fundamental structural particles of diamonds are carbon atoms, where each carbon atom is linked to four carbon atoms in sp3 hybrid orbitals to form a tetrahedron. Each carbon atom is located at the center of the tetrahedron, and the surrounding four carbon atoms are at the vertices. Because of the high bond energy of the C-C bond makes diamond the most rigid solid in nature ^[53]. Since the valence electrons of carbon atoms are used to form covalent bonds, resulting in no free electrons in diamond, its volume resistivity is as high as 5 × 10¹⁴ Ω cm, which is an insulating material. In terms of heat conduction, diamond mainly transfers heat through lattice vibration, and phonon scattering is small, so the thermal conductivity is as high as 2000 W∙m⁻¹∙K⁻¹ ^[54]^[55], and the coefficient of thermal expansion is only (0.86 ± 0.1) × 10⁻⁵/K, which makes it an excellent choice of thermal conductivity material. In addition, diamond has excellent optical and mechanical properties and chemical corrosion resistance, so it has great potential for heat dissipation.

Waheed et al. ^[56] dissolved the diamond and ABS in acetone and underwent six extrusions, ensuring the diamond’s uniformity and making the wire more dimensionally stable. After several times of mixing, the upper limit of the thermally conductive filler quantity is increased, thereby considerably enhancing the heat dissipation performance of the print. The disadvantage is that even with a high content of excellent thermal conductivity fillers, the greatest thermal conductivity of the composite is only 0.94 W∙m⁻¹∙K⁻¹, leaving a great deal of space for improvement. In this work, diamond and ABS are only physically combined and not chemically bonded, which may be a significant factor in the composites’ low thermal conductivity. Su et al. ^[57] utilized octadecyl amine (ODA) as the surfactant of diamond to form a hydrogen bond between the -NH₂ group of ODA and the -OH group of diamond, thereby enhancing the interface compatibility between filler and matrix and promoting phonon transfer between diamond and PLA. The maximum thermal conductivity attained in this work is 2.22 W∙m⁻¹∙K⁻¹, which can guide the future research of FFF thermally conductive materials.

3. FFF Thermally Conductive Composites Process Parameters

For conventional FFF printing materials, extensive theoretical research and practical experience have produced a relatively comprehensive data model. However, to maximize the composite’s thermal conductivity after the addition of thermally conductive fillers, optimization of parameters in each process is essential. In every work, parameter optimization is often used to prepare for subsequent work, as the change in parameters directly determines the internal structure of the printed part and thus affects the thermal conductivity. The most common printing parameters and their intrinsic relationship to thermal conductivity are listed below.

3.1. Nozzle Temperature

As the nozzle is in direct contact with the polymer, the nozzle’s temperature will determine the fluid’s melt state ^[58]. The polymer is not entirely molten when the nozzle temperature is too low. When the temperature is increased appropriately, the flow of the polymer improves. At this point, the diffusion of interlayer polymer chains increases, and the filament extruded from the nozzle will transport heat to the deposited part, forcing it to remelt, ensuring better interlayer adhesion, and enhancing thermal conduction throughout the entire print ^[59]. When the temperature rises, it provides a longer time for the crystallization process of the polymer so that the crystallinity will increase. The orderliness of the molecular chains in the crystalline region increases, the resistance decreases when phonons diffuse, and the propagation velocity from one end to the other becomes faster, manifested as an increase in thermal conductivity. However, high nozzle temperatures may lead to polymer degradation or deformation of the filament during deposition due to the inability to reduce the temperature quickly, making the printed part less accurate. Therefore, the proper nozzle temperature should ensure the complete melting of the filament and maintain the extruded filament without deformation.

3.2. Nozzle Diameter

The diameter of the nozzle has an effect on the shear force in the nozzle, with the following formula ^[48]:

τ = \frac{32 {η ρ Q}_{v}}{{π d}^{3}}

where η is the viscosity of the melt, ρ is the density of the filament, d is the diameter of the nozzle, and Q_v is the flow rate. η, ρ, and d can be regarded as constants for the same material under the same experimental conditions. As shown in the formula, nozzle diameter and shear force are inversely related, and as the diameter rises, the shear force falls. As previously noted, the shear force produced during the printing process causes anisotropic fillers to align along the printing direction, resulting in the formation of a thermally conductive network. As a result, the filler’s degree of orientation is determined by the shear force, which impacts thermal conductivity.

3.3. The Printing Speed

Print speed affects the mechanical properties and accuracy in the printed part, and in the case of thermal conductivity, improper print speed can create more voids that affect thermal conductivity. When the printing speed is too slow, on the one hand, it makes printing inefficient, and on the other hand, the extruded melt will be stacked together, making the accuracy decrease. If the printing speed is too fast, the filament will be sent out before it is completely melted, and the extrusion speed of the melt cannot keep up with the printing speed, which will cause an uneven diameter of the filament, resulting in voids inside the parts. Therefore, a suitable printing speed should ensure a specific printing efficiency and the preparation of printed parts with a dense internal structure.

3.4. Platform Temperature

The platform temperature refers to the temperature of the print filament deposition plane, which directly affects the mechanical properties and molding quality of the printed part. If the platform temperature is too low, the extruded filaments will not deposit appropriately on the platform, resulting in warping and delamination of the print. After the temperature of the platform is moderately increased, the bottom layer will conduct the temperature to the middle layer. After a while, the temperature of the middle layer decreases to a more stable temperature. After incorporating the thermally conductive filler, the heat transfer between the layers is enhanced, thus increasing the stable temperature of the middle layer. If the temperature of the interlayer can be kept above Tg for a longer time, the diffusion of the polymer chains between the layers can be increased, thus improving the adhesion of the layers ^[60]. Simultaneously, the cooling time of the print following an increase in platform temperature is lengthened, which facilitates the remelting and recrystallization of the deposited filaments, thereby strengthening interlayer bonding and decreasing heat conduction resistance. However, the temperature of the platform must not be too high, or the natural cooling and shaping of the print would be affected.

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