The structural regularity of monomer molecules affects the packing structure and compactness of molecular chains, and affects the thermal conductivity of polymers^[1]. The presence of asymmetric side groups in the monomer results in low thermal conductivity due to the reduction of the packing density of the polymer molecules, for example, polyethylene (PE) without side groups has a greater thermal conductivity than polypropylene (PP). The number of polar groups and the dipole moment in the monomer molecule affect the intermolecular interaction force (dipole interaction) and the phonon transfer along the molecule. For example, the thermal conductivity of polar polyimide is about 0.37 W/ (m · K), which is higher than that of nonpolar polytetrafluoroethylene (0.25 W/ (m · K))^[1,5]. Molecular dynamics simulation (MDS) shows that there is a negative correlation between the atomic mass in the monomer molecule and the thermal conduction of the polymer. The C-C main chain has the largest contribution to the thermal conduction, accounting for about 80%. When the heavy atoms such as O, S and P replace C atoms in the main chain, the low thermal conduction is caused by the reduction of the phonon group velocity.For example, the thermal conductivity of PE is about 0. 3 W/ (m · K), which is greater than that of organosilicon (0. 15 W/ (m · K)).The thermal conductivity of C-C chain is inversely proportional to the number of substituted atoms, and the thermal conductivity of the system decreases by about 75% when 3% of H atoms are replaced by heavy atoms^[1][15].

The structure of liquid crystal (LC) molecules includes the chemical structure and spatial distribution of crystallogenic units, the structure and length of flexible chains, etc. Reactive liquid crystal molecules containing biphenyl, methylene arylamine, aryl ester and other crystallogenic units, such as liquid crystal epoxy (Figure 2) and organosilicon monomers, are self-assembled into liquid crystal Domains with nematic and smectic ordered structures by π-π interaction between crystallogenic units in the liquid crystal temperature range, providing a fast path for phonon transmission. According to the spatial position of the crystallogenic units, liquid crystals can be divided into main chain, side chain and discotic types. The structure of the crystallogenic units and the type of liquid crystals affect the thermal conductivity of liquid crystal polymers^[8,16⇓~18]. For cross-linked liquid crystal molecules, the chemical structure of the curing agent affects the self-assembly behavior of liquid crystal units, the spatial distribution and topology of oriented liquid crystal domains in the cross-linked network, and the construction and distribution of three-dimensional phonon pathways. Therefore, the design and synthesis of different structures and types of liquid crystal molecules, based on the induced self-assembly of liquid crystal molecules and the optimization of the spatial distribution of liquid crystal domains, can effectively control and improve the thermal conductivity of liquid crystalline polymers^[13].

Some organic molecules with two-dimensional structural characteristics, such as metal-organic frameworks (MOF) and covalent organic frameworks (COF), form one-dimensional ordered orientation structures by means of π-π stacking effect between organic frameworks, and the molecular structure of MOF/COF and the radius of central ions affect the ordered structure of stacking self-assembly. The active functional groups outside the framework can lock the ordered structure of the stack orientation based on the chemical reaction, which constructs an ordered channel with low thermal resistance for phonon transfer and improves the heat conduction of the system^[20,21]. For example, by adjusting the radius of the substituent ions (Ni, Cu, Zn, H) at the center of the porphyrin-based MOF/COF (Figure 2) molecule and the planar structure of the organic framework, it is found that the thermal conductivity of the MOF polymer is up to 1.2 W/ (m · K) when the central ion is Zn^[20]. The microporous structure of MOF/COF organic framework can effectively reduce the dielectric constant and loss of the system, which is a kind of organic thermal conductive material with very low dielectric constant and loss, and has extremely important industrial application value in the field of electronic packaging.

When there are substituents in the monomer molecule, the structural type, size, length and spatial distribution of the substituents or side chains affect the molecular chain structure, interchain forces and aggregation structure, resulting in different phonon scattering and thermal resistance, and affecting the thermal conductivity of the polymer^[12⇓~14].

The presence of substituents and side chains first reduces the packing density of the molecular chain, and scatters the phonons transmitted along the main chain direction to reduce the thermal conductivity, so polymers without substituents or with few side chains often have higher thermal conductivity. Secondly, the chemical structure, size, bonding mode and position of the side chain and substituent will induce different degrees of defects in the monomer and polymer structure, resulting in different degrees of phonon scattering. Substituents with symmetric structure have relatively weak phonon scattering, while polar substituents and side chains with asymmetric structure weaken the ordered arrangement between molecular chains and reduce the effective packing density in space, resulting in significant phonon scattering and reducing the thermal conductivity of polymers^[22]. Compared with short side chains, long side chains produce more disordered structures, which lead to phonon scattering, and the degree of scattering increases with the increase of chain length, resulting in the phase state of long side chain polymers between crystalline and amorphous phases, such as the thermal conductivity of comb polymers decreases to the lowest value with the increase of side chain length^[23]. The branched chain structure reduces the thermal conductivity of the polymer by strongly scattering phonons compared to the linear side chain, for example, the linear side chain exhibits 160% higher thermal conductivity than the polymer with a bulky branched chain structure^[22]. The branched chain structure, length and branching degree all affect the thermal conductivity of the molecular chain, and the thermal conductivity decreases significantly with the increase of the branching degree. As shown in Figure 3, different branched structures lead to different degrees of thermal conductivity decrease, and the introduction of heavy atoms in the branched structure reduces the thermal conductivity of the system more than light atoms^[13][22].

The substituent and side chain structure of the monomer also affect the intermolecular force and the efficiency of intermolecular heat exchange^[19]. With the help of the strong non-covalent force between substituents, it is easy to form more physical connection structures between molecules, which can effectively inhibit phonon scattering and reduce thermal resistance as phonon transfer pathways. However, the weak intermolecular interaction can not build a path for phonon transfer, the phonon scattering is significant, and the interfacial thermal resistance increases. Therefore, the thermal conductivity of polymers can be controlled by changing the non-covalent bonding forces (van der Waals force, hydrogen bonding and electrostatic interaction) between substituents.

The weak van der Waals force between nonpolar C and H atoms of PS (polystyrene) makes the thermal conduction only 0.15 W/ (m · K), while the thermal conduction of PMMA (polymethyl methacrylate) increases to 0.19 W/ (m · K) due to the strong induced dipole force between substituent atoms. The thermal conduction of these amorphous polymers with only van der Waals force between monomer molecules is in the range of about 0.15 ~ 0.21 W/ (mK). Some polymers containing hydrogen bonds, such as PVA (polyvinyl alcohol), PAA (polyacrylic acid) and PVPA (polyvinylphosphoric acid), have formed a multi-scale three-dimensional physical connection structure between chains due to the hydrogen bonds of different sizes between substituents, which creates a low thermal resistance channel for phonon transfer, so the thermal conductivity is increased to 0. 3-0. 5 W/ (m · K). Some polyelectrolytes, such as PACa (calcium polyacrylate) and PAPLi (lithium polyphosphate) (shown in Figure 2), have the strongest intermolecular force due to the electrostatic force between monomer substituents, and the electrostatic force plays a physical crosslinking role between molecules, which greatly inhibits phonon scattering and reduces interfacial thermal resistance.The thermal conductivity is as high as 0.5 ~ 0.7 W/ (m · K). For example, the thermal conductivity of PAPCa, a polymer salt with electrostatic interaction between chains, is as high as 0.7 W/ (m · K), which is the highest thermal conductivity of amorphous polymers^[19][16]. Therefore, the enhanced monomer intermolecular force enhances the thermal conduction of the polymer by strengthening and promoting the interchain phonon heat transfer effect. In addition, the intermolecular force also increases the hardness and modulus of the polymer. The calculation and simulation show that the strong intermolecular ionic bonding is equivalent to the structural and thermal conduction effect of adding about 20 GPa external pressure to the polymer with only van der Waals interaction^[19].

Certain monomeric molecules containing cage structures (Fig. 2) such as buckyballs, silsesquioxanes, adamantanes, etc.,A large number of atoms on the large and loose cage structure are in the local thermal vibration mode, which significantly reduces the number of atoms participating in the phonon thermal vibration in the molecular chain direction, that is, the localization effect of phonon vibration. Although the cage structure contributes to the molecular heat capacity,However, the atoms on them can not effectively participate in the phonon heat transfer along the main chain direction of the polymer, and the mismatch effect between the huge cage structure and the main chain of the fat in the phonon vibration density state obviously hinders the phonon heat transfer along the main chain direction.Therefore, the monomer with cage structure shows very low thermal conductivity, for example, the thermal conductivity of PC71BM cage structure molecule is as low as 0. 067 W/ (m · K), which is the lowest value of amorphous polymer thermal conductivity at present^[19][19].

The molecular chain is limited and affected by the chemical crosslinking point and the degree of crosslinking, and can not form an ordered structure or crystal, and the disordered crosslinking structure leads to very low thermal conductivity of the crosslinked polymer^[13]. The thermal conductivity of traditional cured epoxy E-51 is about ~ 0.2 W/ (m · K), while the thermal conductivity of PE decreases gradually with the increase of crosslinking degree^[24]. MDS studies show that if the epoxy and curing agent molecules are connected in a parallel arrangement, the thermal conductivity of the cured product is as high as 0.8 W/ (m · K), and when oriented by stretching, it soars to 6.5 W/ (m · K)^[25]. However, in fact, epoxy resins with high curing degree can not improve the structural order by external force orientation like thermoplastics. The current strategies to improve the thermal conductivity of crosslinked polymers mainly include: 1) introducing liquid crystal units and controlling the spatial distribution of self-assembled liquid crystal domains, 2) using the structure of crosslinking agents and increasing the non-covalent forces between crosslinking points^[13]. The main factors affecting the thermal conductivity of thermosetting resin are the chemical structure of prepolymer and crosslinking agent, the degree of crosslinking, and the non-covalent force between crosslinking points. The influence mechanism of crosslinking structure on the thermal conductivity of polymers is described from the above three aspects.

(A) chemical structure of prepolymer

The chemical structure of the prepolymer affects the thermal conductivity of the cured product^[1,5]. The liquid crystal monomer preferentially forms a liquid crystal self-assembly structure under the control condition of the crosslinking process, and can form a cured product with micro order and macro disorder after curing, and the heat conduction of the system can be improved by regulating the spatial distribution of liquid crystal domains in the crosslinking network^[8,16⇓~18]. Liquid crystal unit structure, including the chemical structure and spatial distribution of crystallogenic units, and the length of flexible chain, affects the clearing point, melting point, self-assembly behavior, mechanical and electrical properties of cured liquid crystal molecules^[13]. The structure of curing agent affects the spatial distribution of liquid crystal domains in the cured network, so the curing of liquid crystal units with different structures needs to consider the appropriate curing agent, such as cationic curing agent, which can anchor the self-assembled liquid crystal domains in the crosslinked network in an orderly manner based on the chain propagation reaction, and maintain a high spatial order to increase the thermal conductivity of the system^{[26⇓~28][28]}. The synergistic effect of aromatic amine or multiple hydrogen bond curing agent containing liquid crystal units and liquid crystal epoxy in the construction of multiple and multi-scale phonon transfer pathways is often used to improve the structural order of liquid crystal cured products and simultaneously improve thermal conductivity and electrical insulation^[29].

(B) structure and crosslink degree of crosslinking agent

For the same reaction monomer, the change of the chemical structure of the crosslinking agent will cause the change of the crosslinking network structure, which has a certain impact on the thermal conductivity of the cured product^[25,30]. For example, phenolic and amine cured epoxies are slightly more thermally conductive than anhydride cured systems. With the increase of the amount of curing agent, the curing degree of epoxy increases, and more uniform molecular thermal bridges connected by covalent bonds are formed, resulting in a slight increase in thermal conductivity. For crystalline polymers, with the increase of crosslinking degree, the crystalline region of the ordered structure decreases, and the radius of gyration (R_g) and thermal conductivity of the molecular chain decrease^[24]. The thermal conductivity of rubber-like amorphous polymer is related to the uniformity of the network structure. With the increase of the crosslinking degree, the thermal conductivity of the system increases, and the space network structure formed by crosslinking shortens the length of heat transfer along the molecular chain^[31]. In addition, under the same crosslinking degree, the crosslinking position has little effect on the thermal conductivity, and the end and middle crosslinking have little effect on the thermal conductivity of the system, but the increase of the crosslinking active point interval is beneficial to the increase of the thermal conductivity of the system^[32]. For thermoplastic crosslinked polymers such as PE, uniaxial stretching can improve thermal conductivity, but the vertical direction of thermal conductivity is reduced^[33].

(C) non-covalent interaction between crosslink point

The physical connection structure established by non-covalent interactions (hydrogen bonds, electrostatic forces, van der Waals forces) between chemical crosslinking points can construct multiple and multi-scale phonon transmission paths, thus enhancing thermal conduction. The distance between crosslinks, the type of noncovalent interaction, the structure and type of groups affect the degree of noncovalent interaction between chains^[13]. It has been reported that when adjacent molecules are closely linked by a short enough length of crosslinking agent, the multiple multi-scale phonon channels constructed between the crosslinking points by non-covalent interaction can promote phonon transmission compared with a single covalent bond^[34]. The short-chain crosslinking agent has higher thermal conductivity than the long-chain system, and the phonons are transmitted not only along the covalent bond, but also along the multi-scale phonon path constructed by the multiple physical connection structures constructed by different non-covalent interactions between the crosslinking points to realize fast phonon transmission.In the crosslinked network, the sound velocity caused by the non-covalent interaction between chemical crosslinks is significantly higher than that of the system with only a single covalent bond, indicating that the type, kind and number of the non-covalent interaction between chemical crosslinks have different effects and contributions on phonon transfer^[34][24].

The effect of phonon heat transfer along the chemical bonds of the main chain is much greater than that between molecules, and the morphological and conformational changes of the main chain can significantly affect the phonon heat transfer. The activation energy of segmental motion of the main chain or melting of the crystalline region is reduced by the increase of temperature, which causes the change of chain aggregation structure and chain conformation, and significantly affects the phonon transfer along the main chain, which is an important reason for the change of polymer thermal conductivity with temperature^{[1,5,12⇓~14]}. When the temperature reaches the glass transition temperature (T_g) of amorphous polymers or the melting point (T_m) of crystalline polymers, the huge number of conformational changes of chain segments due to violent internal rotation and bending will significantly intensify phonon scattering, reduce the phonon group velocity and the MFP of phonons, and produce very low thermal conduction^[1,12⇓~14]. As shown in Fig. 4, the experiment and molecular simulation show that the melting of the crystalline part of PE in the temperature range of 380 ~ 400 K leads to the slip motion of the molecular chain, and the strong conformational change of the chain has a significant scattering effect on the phonon transfer, and the thermal conductivity of the molecular chain decreases sharply^[14]. Therefore, increasing the rigidity of the main chain and enhancing the interaction between chains can increase the energy barrier required for the motion of the chain segments, effectively suppress the motion of the main chain such as internal rotation, kink and slip, and thus effectively weaken the phonon scattering and enhance the intrinsic thermal conductivity of the polymer^[35].

Compared with C-C single bond polymers such as polyolefin, when the main chain contains benzene ring, biphenyl, pentadiene, conjugated double bond and other structures,As well as strong non-covalent interactions such as hydrogen bonding and π-π stacking between chains, can effectively improve the rigidity of the main chain and inhibit the internal rotation of the chain unit, thereby improving the phonon group velocity and preventing the occurrence of temperature-induced phase transition, and synchronously improving the heat resistance and heat conduction of the polymer^{[36⇓⇓~39][1,35]}. High modulus (E) polymer fibers containing π-π conjugated and biphenyl rigid skeletons often have high thermal conductivity. According to the k∝ρC_pE^1/2, the π-π conjugated rigid skeletons on the main chain of high thermal conductivity greatly improve the modulus of fibers in the orientation direction, effectively inhibit the conformational changes of the main chain such as kinking and bending, and induce extremely high phonon group velocity^[1]. For example, amorphous polythiophene (PT) fibers conduct heat up to 4 W/ (m · K), which is derived from the fact that the rigid backbone structure maintains the long-range linear state of the PT backbone, significantly increasing the phonon MFP^[40]. The π-π interaction does not directly enhance the interchain heat conduction, but plays a role in stretching the main chain and strengthening the phonon transfer along the main chain direction^[41]. However, the rigid backbone does not necessarily produce high thermal conductivity, for example, the well-known Kevlar fiber is significantly more rigid than PE fiber, but its thermal conductivity (1 ~ 2 W/ (m · K)) is lower than PE fiber (3 ~ 6 W/ (m · K)).There is a very low energy dihedral rotation mode in the Kevlar-derived chain segment, which can easily overcome the low energy barrier and rotate, causing significant phonon scattering and reducing heat conduction. If the highly oriented structure formed after full stretching effectively eliminates the phonon scattering caused by segment rotation, the thermal conductivity of Kevlar fiber can be increased by about 10 times, which is much greater than that of PE^[42]. Therefore, the rigid structure of the main chain and its effective suppression effect on the phonon scattering caused by the kinking and rotation of the chain segments are the fundamental reasons for the production of high thermal conductivity polymer fibers.

The effect of heat transfer along the main chain covalent bond is closely related to the R_g and persistence length (L), which characterize the conformation and rigidity of the main chain. The molecular chain with high R_g and large L tends to adopt a more relaxed extended state.This provides a long-range spiral thermal conduction channel for phonon transfer, which is conducive to long-range phonon transfer. This relationship between K and R_g and L is often reflected in binary and ternary copolymers^[14][40]. In addition, the one-dimensional rigid backbone with high L is easy to crystallize spontaneously to form an ordered aggregation state, and the phonons in the extended chain transfer rapidly in an approximately ballistic manner^[12][40].

The effect of polymer phase structure on thermal conduction is related to its molecular chain length (CL), which has different effects on the heat transfer mechanism. The competition between ballistic and diffusive heat transfer makes the phonon transfer of a single molecular chain have obvious chain length dependence^[14,43,44]. The phonon transfer along the main chain of a short chain may be ballistic, and the chain end and interface scattering are the main phonon scattering. For long chains, it may be phonon to phonon scattering and structural defect scattering^[1,13]. Naghizadeh et al. Proposed a :k∝CL^0.44 for the relationship between K and CL of amorphous PE, which is consistent with the MDS prediction considering the density, chain conformation and rigidity^[45]. Based on the non-equilibrium MDS, it is found that the effect of the chain length of amorphous PE on the thermal conduction at room temperature increases to a certain value and then tends to be slow with the increase of the chain length, and the polymer experiences different phases and two competing phonon transfer mechanisms with the increase of the chain size.When CL ≤ 7 and CL > 140, the combined interatomic collision and phonon vibration mechanisms play a role, respectively, while when CL < 12 < 140, the two mechanisms compete with each other^[23][46].

After decomposing the contributions of different forces to the heat flux, it is found that phonons are mainly transmitted along the main chain of the molecule, and the thermal conduction of polyacrylic acid (PAA) increases with the chain length, and to a certain extent, the conformation of the coiled chain increases, which leads to phonon scattering, so K shows a saturation trend with the increase of the chain length^[47]. By comparing the thermal conductivity of linear polyethanols and polyalkanes with different chain lengths, it is found that the thermal conductivity of linear polyethanols is greater than that of polyalkanes at the same chain length, and the difference in thermal conductivity decreases with the increase of chain length, which is attributed to the fact that the terminal hydroxyl groups of polyethanols strengthen the intermolecular interaction, but the interaction between terminal hydroxyl groups decreases with the increase of chain length^[48]. The study on the effect of chain length on thermal conductivity shows that the chemical structure, density, chain conformation and chain length of the structural unit synergistically affect the thermal conductivity of the polymer.

The chain end is an important phonon boundary scattering point, which has a significant impact on the phonon scattering, including intrachain and interchain scattering, structure scattering and boundary scattering^[43,49]. For PE, PMMA and PS with short chain structure, there is a :k∝M^1/2 when the molecular weight is M<10⁵, and the thermal conductivity decreases at low M due to the existence of more chain-end structural defects, while with the increase of M to a sufficient value, the influence of chain-end defects weakens, so K does not change much, which is similar to the influence of chain length on thermal conductivity^[49]. It has also been shown that M has only a slight effect on K before the molecular chain is entangled, and then has no effect^[50]. At present, there is no unified understanding of the mechanism of the effect of molecular weight on the thermal conductivity of polymers, and the deep understanding of the relationship between them is still very simple.

The conformational change caused by chain rotation significantly reduces the thermal conductivity of the molecular chain due to a large number of phonon scattering, which is the key factor for the reduction of thermal conductivity of the single chain. The chain rotation factor (CRF) quantitatively represents the degree of internal rotation of the single chain. Based on the theoretical calculation of phonon properties, it is found that the CRF with enlarged molecular chain significantly reduces the group velocity and MFP of phonons, resulting in low thermal conductivity^[51]. For example, as the CRF increases, the sound velocity of several molecular chains studied almost decreases from 4000 m/s to less than 2500 m/s^[51].

When the energy obtained by a molecular segment is not enough for chain rotation, it will cause local kink motion of the segment. Like chain rotation, kink also significantly causes chain conformational changes, increases the number of main chain conformations, and thus causes strong phonon scattering to hinder phonon transmission. Compared with the single chain without kink, the effect of the kink on the phonon transfer along the single chain is mainly reflected in two aspects: 1) the kink increases the conformational change, intensifies the phonon scattering and increases the additional thermal resistance; 2) the kinking process kinks the whole single chain into many small segments, and the phonon scattering reduces the thermal conduction of each segment^[52]. Fig. 5 theoretically shows the results of the effect of kinks on the thermal conduction of aliphatic single chains, and it is found that the thermal conduction of molecular chains decreases rapidly with the increase of the number of kinks^[52].

The chain orientation can significantly reduce the CRF of the molecular chain and increase the MFP of the phonon, and the rigid skeleton containing conjugated double bonds, benzene rings, biphenyl and fused benzene rings can effectively inhibit the kinking and free rotation of the single chain and reduce the influence of chain conformational changes on phonon scattering. In addition, non-covalent interactions such as π-π stacking, hydrogen bonding, and electrostatic interactions between molecular chains can strengthen the interaction between chains, inhibit chain rotation and kinking, reduce the CRF of single chains, and improve the thermal conductivity^[53].

The phonon transfer and the MFP of phonons in low-dimensional nanomaterials are limited by the size of the system. When the sample size is lower than the MFP of phonons, the phonon transfer is mainly affected by the boundary scattering, resulting in an obvious size effect, which shows that the thermal conductivity increases with the increase of the sample size^[3]. Size-dependent thermal conduction has been found in quasi-one-dimensional nanowires, nanorods and nanotubes, as well as in two-dimensional materials^[3]. In low-dimensional materials, molecular chains originally freely distributed in three-dimensional space are constrained by the dimensionality and size of the sample, and are forced to preferentially distribute along the sample size direction, which increases the L and R_g of molecular chains in this direction, allowing phonon transmission along the main chain to reach longer distances until it is disturbed and interrupted by chain-end defects^[54]. The confinement effect of the molecular chain changes the conformation and distribution of the chain segments, thus affecting the phonon heat transfer. When the molecular chains of small diameter polymer fibers are forced to orient along the radial direction of the fiber due to the confinement effect in other directions, a highly oriented structure can be formed, which promotes the transmission of phonons along the main chain. However, the molecular chains of large diameter fibers are easy to form a staggered structure of random orientation and radial orientation due to their large free distribution space, showing almost isotropic phonon transfer characteristics, which hinders the phonon transfer along the radial direction of the fiber and leads to low thermal conductivity^[18,55]. For example, when the diameter of amorphous polyimide fiber increases from 20 nm to 160 nm, K decreases rapidly from 3. 6 W/ (m · K) to 0. 5 W/ (m · K)^[55]. Chain confinement has different effects on polymer fibers and amorphous polymers. The thermal conductivity of amorphous PS films increases with the h/R_g factor when the thickness is h<R_g, that is, the thermal conductivity of the films decreases due to the formation of fewer thermal conduction pathways due to the interdigitating structure between the chains in the case of stronger confinement or less entanglement^[56].

Allen divided the heat carriers in the amorphous region into three types according to their essential characteristics: phonon-like propagons with size-dependent long-range delocalization, diffusons without size-dependent short-range delocalization, and highly localized modes (locons)^[57]. According to the calculation, diffusons are the main heat transfer carriers at room temperature, not propagons with high wavelength, and the transfer modes of diffusons and propagons are essentially different^[58]. At present, it is not clear what the similarities and differences are between the heat carriers of amorphous polymers and amorphous inorganics, but relevant studies have shown that the contribution of propagons to the thermal conduction of polymers at room temperature is basically zero. Therefore, combined with temperature, phase state and material structure, these three modes have different contributions to thermal conduction, and the latter two occupy a major position in amorphous polymers^[59].

Amorphous disorder is more prominent than phonon scattering, and even in the pure amorphous state, the molecular chain conformation is still the key factor affecting thermal conduction^[1,14]. Not only does the overall amorphous phase significantly affect the thermal conduction, but even the local amorphous phase has an important impact on the thermal conduction. The loose packing of highly coiled and randomly entangled molecular chains results in internal voids and low density, which causes scattering and inhibits phonon transfer. In addition, the weak interaction between chains makes heat transfer no longer a lattice wave mode in crystals.It is a very slow diffusion transfer mode, which causes the disordered vibration and rotation of all atoms around the equilibrium position and scatters to the adjacent molecular chains, so the phonon MFP of amorphous polymers is often less than 10 nm^{[1,5,12,13][14]}. Amorphous inorganic materials have only pure chemical bonding, while amorphous polymers include covalent bonds and non-covalent bonds such as Van der Waals force, hydrogen bonding and electrostatic interaction, showing a local anisotropic bonding environment, which makes the influence of the actual structure of amorphous polymers on thermal conductivity more complex.

Compared with the amorphous structure, the long-range ordered structure in the crystalline region increases the MFP of phonons and promotes the thermal conduction of phonons. According to the k=k_aw_a+k_cw_c, the thermal conduction of polymers at room temperature has a linear relationship with the thermal conductivity k_c in the crystalline region and the mass fraction w_c, and also has a positive relationship with the crystallinity^[1][60]. In general, a high degree of crystallinity is beneficial for producing high thermal conductivity, but only if the grains are oriented. If the grains are randomly distributed and not well oriented, the amorphous disordered region between the crystalline regions becomes a phonon scattering concentration point due to the high interfacial thermal resistance, resulting in a low thermal conductivity of the crystalline polymer^[14]. As shown in Fig. 6B, the thermal conductivity of polytrifluoroethylene is almost linear with the crystallinity, but the thermal conductivity of the system is only 0.24 W/ (m · K) at 90% crystallinity. In order to reasonably explain the thermal conduction of polymers with high crystallinity (e.g. > 83%), the factors such as the orientation of crystalline regions, the interface between crystalline regions and amorphous regions, and the distribution of phase regions must be carefully considered.

When stretching/shearing is applied to the thermoplastic polymer at a certain temperature, as shown in the schematic diagram of fig. 6a, a low stretching ratio (λ) causes the wafer to be aligned in the direction of the applied force, while a higher stretching causes the tie molecules between the crystal regions to be pulled apart and aligned; If λ continues to increase, the molecules in the crystalline region and the amorphous band will further orient and crystallize along the external force. At high crystallinity, the band molecules act as a bridge between the crystal regions to form an anisotropic crystal, resulting in high thermal conductivity along the stretching direction. The number and orientation of the band molecules between the crystal regions significantly affect the thermal conductivity of the system. As shown in Fig. 6C, the crystallinity and thermal conductivity of the PE film reach 90% and 2 W/ (m · K), respectively, at λ < 5. With a continuous increase of λ = 100, the crystallinity increases slightly, but the thermal conductivity soars to 60 W/ (m · K)^[58]. The thermal conductivity of some ultra-drawn polymers such as PE fibers is even as high as ~ 100 W/ (m · K), indicating that the thermal conductivity continues to increase after a certain λ, although there is little room for the crystallinity to increase because the crystalline orientation along the external force is saturated at low λ^[35]. At low λ, the proportion of amorphous region decreases, while at high λ, the disordered structure of the amorphous region is changed, and the tie molecules connecting the crystalline region begin to orient along the main chain direction, resulting in an increase in the partial thermal conductivity of the amorphous region. Fig. 6d shows the theoretical thermal conductivity of PE at different λ^[15]. The results show that at λ = 110, the random frenulum molecules in the amorphous region are oriented, and the thermal conductivity of the amorphous region with low thermal conductivity is as high as 15 W/ (m · K), which is the fundamental reason for the sharp increase of the thermal conductivity of the stretched PE film after high λ^[61]. Therefore, the ladder-like metal-like thermal conductivity of the oriented polymer after a certain λ is caused by the formation of ordered molecular chains with oriented structure in the amorphous region^[1].

Orientation refers to the arrangement of molecular main chains and chain units along the direction of external force when polymers are stretched and sheared during processing. Orientation is the most effective means to improve the crystal distribution of polymers and the order of disordered long chain structure. The long-range ordered structure produced by the optimal orientation of molecular chains along the direction of external force can significantly suppress the interfacial thermal resistance and increase the phonon MFP, making the thermal conductivity in this direction much higher than that in other directions^{[1,5,14][39,40]}. In the amorphous region of the polymer fiber, there is a random structure which is exactly the same as the bulk structure but has a certain degree of orientation, and the external force makes the amorphous molecules orient to obtain a higher degree of order.Because the main contribution of domain interface scattering is thermal resistance, rather than phonon-phonon scattering and phonon-defect scattering, the amorphous structure of polymer can only transmit low-energy phonons^[63][64]. The orientation facilitates phonon transmission between crystalline regions, enabling phonons to traverse domain interfaces, for example, phonon transmission with MFPs up to 200 nm is often found within oriented PE fiber structures^[14]. In addition, the orientation significantly improves the modulus of the material in the tensile direction, improves the degree of interconnection and density within the material, reduces and eliminates porosity and various structural defects, so the thermal conductivity of the system is greatly improved.

The orientation process of the crystalline polymer undergoes two stages of structural changes: 1) the microfibril structure is formed in the amorphous region, and the crystal plate in the crystalline region splits into several crystal segments intercalated by amorphous microfibers.2) The tie molecules between the wafers are pulled out from the crystal block and further oriented at higher λ. The random molecular chain orientation in the amorphous region during the orientation process is the key to determine the thermal conductivity improvement of the nanofiber or film^[14][14,65]. When an amorphous elastomer or glassy polymer is stretched, the molecular chains are rearranged along the external force, and the orientation-induced crystallization further improves the structural order, as shown in 6a^[13,66,67]. Orientation effectively changes the orientation, distribution and phase state of molecules, chain segments, crystalline regions and amorphous regions, and the stretching rate and λ determine the thermal conductivity of the fiber. High λ and slow stretching can simultaneously improve the chain orientation of nanofibers, resulting in ultra-high thermal conductivity, which can be increased by two orders of magnitude when λ > 400^[68]. Slow stretching allows enough time for structural adjustment and orientation of the chain segments, reducing the distance between the molecular chains and the structural disorder of the amorphous region. Heat-stretching give that segments sufficient time to develop a high degree of orientation, further enhancing the thermal conductivity of the polymer fiber. With the increase of strain in the tensile process, the contribution from covalent bonding is huge, while the contribution from non-covalent bonding to thermal conduction becomes negligible. High λ makes the molecular backbone fully oriented along the direction of the external force, and maximizes the advantage of heat transfer along the chemical bonds of the backbone^[14][14].

Various methods are often used to improve the orientation of molecular chains. After the ultra-high molecular weight PE (UHMWPE) powder is dissolved and extruded by Couette method, the random molecular chains in the amorphous region obtain obvious orientation after high drawing orientation, and the K is as high as 60 W/ (m · K)^[69]. The Shish-kebab structure formed in the vertical in-plane direction of the PE film during the biaxial orientation process can connect multiple Shish straight chain crystals, and multiple phonon transfer paths are constructed in the vertical and horizontal directions, which synchronously improves the in-plane and thickness heat conduction of the film^[70].

The efficiency of intramolecular heat transfer by covalent bonds along the main chain is much higher than that by noncovalent bonds between molecules. The Ohara model decomposes the contribution to heat conduction into three terms: covalent and noncovalent interactions between atoms, and molecular advection^[71]. With the increase of chain length, the contribution of intrachain covalent bonding to thermal conduction increases monotonously, which is significantly greater than that of non-covalent bonding. The simulation shows that the contribution of covalent interaction to heat conduction in C₂₄H₅₀ alkanes is about ~ 50%, non-covalent interaction is ~ 30%, and molecular advection is ~ 20%, indicating the important contribution of covalent bonds along the main chain to heat transfer^[14]. The non-covalent interaction also contributes to the heat transfer between molecular chains, which is the fundamental difference between amorphous polymers and simple fluids with almost no intramolecular interaction and amorphous inorganics with pure covalent interaction in heat transfer carrier and heat transport mechanism^[14].

Intermolecular noncovalent forces include electrostatic forces, hydrogen bonds, van der Waals forces, etc. The molecular chain conformation and space structure can be effectively regulated based on the intermolecular non-covalent interaction, and the increase of the intermolecular non-covalent interaction is beneficial to the formation of an intermolecular physical connection structure, the construction of a long-range ordered structure, the promotion of phonon transfer between chains, and the realization of the purpose of regulating heat conduction^[1,5,13]. The effects of interchain and intrachain interactions on the thermal conductivity of the blends were studied. It was found that increasing the interchain interactions could effectively stretch the molecular chains and increase the R_g and heat flux, so the thermal conductivity of the blends increased^[72].

(A) Electrostatic force

Coulombic electrostatic interactions between charged or highly polarized atoms add to the heat transfer complexity of polymer electrolytes. The Coulomb electrostatic interaction between chain functional groups can be used to change the R_g and aggregation structure of molecular chains^[14]. For example, in PAA and poly (methacrylic acid) (PMAA), after partial carboxyl groups are ionized in aqueous solution, the counter ions are clustered around the ionized ions, and after part of the counter ion H⁺ is neutralized by alkali,Due to the repulsion effect between the same charges, the charged ions cause the molecular chain to stretch out from the random coil curve, forming a mutual entanglement and interpenetration structure, and the L and R_g increase, which promotes the heat transfer of phonons along the main chain^[73]. The different positions of substituents and ions in polymer electrolytes lead to molecular chain conformations such as isotactic, syndiotactic, and atactic, which affect thermal conductivity. For example, the thermal conductivities of syndiotactic and isotactic PAA ionized at high pH are 1.2 and 0.55 W/ (m · K), respectively, and the thermal conductivities of syndiotactic and isotactic PMAA are 0.69 and 0.48 W/ (m · K), respectively, which are attributed to the strong electrostatic interaction between the side groups in the same main chain stretching the main chain, increasing the molecular chain R_g and enhancing the phonon transfer along the main chain^[74].

The Coulomb electrostatic interaction between molecular chains does not directly contribute to the thermal conduction of the polymer, but only makes the atoms of opposite charges closer and increases the Lennard-Jones (LJ) interaction. From the molecular scale, the Coulomb force between ions makes them closer, and the LJ interaction transits from attraction to repulsion, and the LJ interaction potential changes from positive to negative with the increase of ionization degree, which greatly improves the thermal conductivity of polymer electrolytes in the repulsive region of the interaction potential^[14]. The ionic charge and ionic radius affect the counterion-counterion, counterion-polymer, polymer-polymer interaction and heat conduction. The effect of ionic radius on heat conduction is the most obvious. With the increase of ionic radius, the force between ionic pairs decreases, and the heat conduction decreases^[14]. The factors affecting the thermal conductivity of polyelectrolytes include chain conformation, pH, ions, backbone type, counterion type, water content, etc. Many factors do not affect the thermal conductivity alone, but are intertwined with each other^[14]. With the help of MDS and machine learning, it is expected to reveal the thermal conduction mechanism of polyelectrolytes.

(B) Hydrogen bond

The soft handle effect of hydrogen bonding between the side groups of polymer chains can effectively inhibit the internal rotation and kinking of chain units, reduce chain conformation and increase R_g, and improve the regularity and crystallinity of molecular chains^[1,14]. For example, the hydrogen bond network between nylon chains induces the regular arrangement of molecular chains, resulting in high crystallinity, so the thermal conductivity of polymer nanofibers can be increased by 1 to 2 orders of magnitude by using hydrogen bonds^[72].

For a single polymer, the hydrogen bonding between bifunctional small molecules such as amino acids and the functional groups on the side groups of the main chain can be used to construct a small molecule hydrogen bond thermal bridge network between molecular chains to promote the heat transfer of phonons between adjacent molecular chains^[75]. The structure and functional group of small molecule thermal bridge affect the strength and number of hydrogen bonds^[76]. For PVA or PAA, small molecules with different functional groups at both ends can construct more effective and dense phonon thermal conduction networks than small molecules with the same functional groups^[13]. The length of the thermal bridge molecule has an effect on the phonon transport between the molecular chains, and the shorter the length, the higher the thermal conductivity of the polymer^[1]. Therefore, the thermal bridge effect based on interchain hydrogen bonding can effectively regulate the thermal conduction of a single polymer by designing a suitable structure of bridging small molecules^[77]. In addition, the hydrogen bonding between the chain functional groups can increase the R_g of the molecular chain, change the aggregation structure, and improve the structural regularity of the polymer^[78]. For example, PAA, polyacrylamide, and polystyrene sulfonate have relatively high thermal conductivity due to a large number of hydrogen bonds between the chains^[78].

For polymer blends, the interpenetration and physical entanglement of the chain structure of hydrogen-bonded ligands due to the interaction of hydrogen bonds with each other lead to changes in T_g and thermal conductivity^[79]. For example, the thermal conductivity of PVA/PAA follows the simple mixture rule, while the thermal conductivity of PS/PMMA reaches the highest value near the T_g^[80]. Rigid short chain poly (N-allylpiperidine) (PAP) is inserted into the R_g of long chain PAA and PVA due to hydrogen bonding. After orientation, the coiled molecular chain is forced to spread out, and L and R_g become larger. The multiple hydrogen bonding network constructed between the chains enhances the thermal conductivity of the system. The highest thermal conductivity of PAA/PAP and PAP/PVA systems is 1.1 W/ (m · K) and 0.4 W/ (m · K), respectively^[79]. It is difficult to effectively improve the thermal conductivity by hydrogen bonding alone between the blend chains, and the coordinated orientation is necessary to enhance the ordered structure of the multi-scale molecular chains and form a multi-scale physical connection network to enhance the thermal conductivity^[79⇓~81]. For example, the thermal conductivity of PVDF/PVA sol after electrospinning orientation is as high as 2. 4 W/ (m · K) based on the hydrogen bonding between molecular chains^[82]. The molecular weight of the blend components and the blend ratio have a significant effect on the number and strength of hydrogen bonds and the final thermal conductivity.

(C) Van der Waals force

On the one hand, the interchain van der Waals force can restrict the free rotation and twisting motion of the chain units and segments, increase the dihedral angle energy and reduce the thermal resistance, and on the other hand, the intrachain van der Waals force can make the chain units curl and scatter phonons, and these two competitive effects exist at the same time^[1,13,14]. The theoretical study shows that the intramolecular van der Waals force changes the chain conformation of the minor component in the binary mixture, but does not change the thermal conductivity, while the increase of the intermolecular van der Waals force increases the chain R_g of the major and minor components, promotes the phonon heat transfer along the main chain direction, and increases the thermal conductivity of the blend^[83].

The defects and impurities in the polymer act as phonon scattering sources, which is one of the main reasons for the decrease of thermal conductivity. From the point of view of phonon transfer, defects include molecular-level defects such as molecular chain ends, chain twists, chain entanglements, and random orientations. For example, backbone kinks twist the molecular chain and sharply reduce heat conduction. External defects include voids, various interfaces, amorphous-crystalline interfaces, etc^[14]. All external and internal defects can cause significant phonon scattering, and the long-range structural order of the molecular chain is continuously improved with the increase of the orientation degree during the orientation process of the polymer.Internal and external defects are greatly eliminated. For example, the core reason why polymer fibers have ultra-high thermal conductivity compared with bulk polymers is that the orientation process eliminates various defects^[1,13]. The simulation results show that the theoretical thermal conductivity of PE molecular chain without defects is as high as 1400 W/ (m · K), while that of PE fiber with structural defects is more than 300 W/ (m · K), but the experimental thermal conductivity of ultra-drawn PE fiber is as high as 104 W/ (M · K)^[41,42]. The gap between that theoretical prediction and the actual value imply a great potential for eliminating structural defect to provide thermal conduction.

Impurities introduced by raw materials and processing, such as foreign particles, liquid molecules and bubbles, can cause strong phonon scattering and reduce heat conduction, just like defects. For example, the introduction of bubbles can significantly reduce the thermal conductivity of the polymer.

Stretching orientation is the most widely used method, which can effectively improve the orientation and crystallinity of polymers. For example, PE forms a needle-like crystal-crystal bridge structure composed of extended molecular chains along the stretching direction at λ = 200, and the thermal conductivity is as high as 37 W/ (m · K)^[1,5,93,94]. At λ = 400, the highly oriented structure causes phonons to transport in a ballistic-like manner, and the thermal conductivity soars to 104 W/ (m · K), which is comparable to the thermal conductivity of some metals^[35]. In the process of injection, extrusion, molding, centrifugation, spin coating and other different ways of polymer processing, the shear force makes the molecular chain oriented along the direction of the external force, and the anisotropic structure affects the mechanical, thermal, electrical and other properties of the polymer^[1,5,13]. For example, the UHMWPE bulk sample prepared by Li et al. Using a solid-state extrusion process formed a variety of crystal structures along the orientation direction, including cylindrical crystals, monoclinic crystals, and highly oriented wafers, showing high modulus and strength, and high thermal conductivity (3.3 W/ (m · K))^[95]. Poly (3-hexylthiophene) films prepared by spin-coating method exhibit anisotropic orientation induced by shear flow, and the maximum thermal conductivity is 3. 8 W/ (m · K) with the increase of orientation degree^[96]. The amorphous disordered structure of crystalline polymer induces crystallization during orientation, which improves the orientation and crystallinity of the original disordered region, which is the main reason for the sharp increase of thermal conductivity of highly drawn fibers and films.

Spinning methods include electrospinning, melt spinning, gel spinning, wet spinning and dry spinning. Electrospinning is the most widely used because of its advantages of relatively small batch performance changes and easy control^[14]. The directional stretching and shearing effect induced by high voltage electric field induced molecular chain orientation, which reduced the fiber diameter and increased the crystal orientation, and greatly improved the thermal conductivity of the fiber^[97,98]. For example, the folded molecular chain of UHMWPE is highly oriented and almost composed of extended chains during gel spinning, which increases the axial mechanical strength, modulus and thermal conductivity. At λ = 125, the crystallinity and thermal conductivity of the fiber are as high as 99% and 16. 4 W/ (m · K), respectively^[99]. The oriented amorphous polyimide fibers obtained by electrospinning were hot-pressed into films, and the thermal conductivity of the PI films was significantly improved by the axial chain orientation induced by spinning and the ordered structure maintained by π-π interaction between chains^[100].

Phonon engineering focuses on the control of heat transfer at the atomic scale, and the sensitive polarization response of ferroelectric polymers such as PVDF to external electric field can be used to change the force between molecular chains to achieve the purpose of modulating heat conduction. The strong polarization of ferroelectric polymer under high voltage electric field can enhance the interaction between molecular chains and improve the order of lattice between chains, thus increasing the phonon group velocity and inhibiting the phonon scattering between chains to enhance thermal conduction. As shown in fig. 8, the thermal conductivity of the unpoled P (VDF-TrFE) film is about 0.16 W/ (m · K), which is independent of temperature, while the thermal conductivity of the poled P (VDF-TrFE) film along the polarization direction increases to 0.52 W/ (m · K) at 80 MV/m, which is about 225% higher, and the thermal conductivity has a negative temperature coefficient^[101]. The main advantage of the thermal conduction strategy based on electric field control of ferroelectric polymers is that the thermal conduction of polymers can be changed in all directions, which has the advantages of simple and rapid operation and low cost.

The thermal conductivity of polymers can be improved by self-assembled domains of organic small molecular crystals and liquid crystal molecular motifs, and the physical bridging effect of organic molecules based on double-ended functional groups between molecular chains based on hydrogen bonding can significantly enhance the interchain interaction and improve the thermal conductivity of polymers^[1].

Succinic acid, glutaric acid, adipic acid and other small organic molecules are mixed and dissolved in PVA solution, and the small organic molecules begin to form molecular crystals with different shapes during the volatilization of the solvent,With the help of hydrogen bonding between organic molecular crystals and PVA chains, phonon pathways constructed by long-range ordered organic molecular crystals distributed along oriented PVA chains can be obtained by blade coating and spin coating, which can improve the thermal conductivity of PVA films^[13,102].

The introduction of organic liquid crystal units into PVA and PAA solutions can control the spatial distribution of liquid crystal domains in PVA by means of centrifugal orientation and the non-covalent force between the self-assembled liquid crystal domains of liquid crystal units and PVA molecular chains in the process of polymer film formation, which can enhance the thermal conductivity and other properties of the film^[77].

A physical thermal bridge network based on small molecular hydrogen bonds can be constructed between molecular chains by using the hydrogen bonding interaction between dibasic organic acids and alcohols with the same/different bifunctional groups at both ends and the functional groups of the main chains and side groups of molecules such as PVA and PAA, so as to promote the heat transfer of phonons between adjacent molecular chains^[75]. The chemical structure and the type of functional groups of bifunctional small molecules affect the strength and number of hydrogen bonds, and have a regulatory effect on the thermal conductivity of polymers.

Polymerization based on the template-assisted orientation function is an effective method to prepare structurally controlled polymers. Based on the template-assisted orientation function, the polymerized molecular chains produce an ordered structure, thus improving the thermal conductivity. For example, the axial thermal conductivity of amorphous polythiophene fibers obtained by nano-template-assisted polymerization is as high as 4. 4 W/ (m · K), which is the highest thermal conductivity of amorphous polymers at present^[40]. With the help of the special template and the fast initiation of ultraviolet light, the molecular chain of the polymerized acryl liquid crystal monomer shows an obvious orientation structure, and the thermal conductivity along the main chain orientation direction is up to 0. 69 W/ (m · K)^[103].

Oxidative chemical vapor deposition (oCVD) polymerization does not use solvents, and can realize the gradual growth polymerization of gas-phase monomers on any substrate such as glass and Si surface under the catalysis, which is beneficial to controlling the structure and performance of molecular chains. Chen et al. Used FeCl₃ as a catalyst to realize vapor phase stereospecific polymerization of thiophene on glass and Si substrates by oCVD, and constructed a multi-phonon thermal conduction network within and between chains by virtue of the ordered rigid main chain structure induced by oCVD polymerization and the π-π stacking effect of interchain thiophene groups. The thermal conduction of the obtained amorphous polythiophene was as high as 2.2 W/ (m · K)^[37].

Monomer molecules such as liquid crystalline epoxy and organosilicon are self-assembled into high-order smectic or nematic supramolecular structures with oriented arrangement by means of the π-π packing effect among their crystallogenic units, that is, liquid crystalline domains, and the reactive functional groups of the self-assembled supramolecules are cured by curing agent gel to introduce ordered liquid crystalline domain structures into the crosslinked network.O as to improve the structural order of the original random curing network; and based on the spatial distribution of liquid crystal domains in the crosslinking network, the phonon scattering can be effectively inhibited, and the phonon transmission and MFP can be increased, so that the macroscopic isotropic heat conduction is presented^[1,13]. As shown in fig. 9, the epoxy containing biphenylcyanide crystallogenic units in the side chain can improve the thermal conductivity of the cured epoxy by relying on the ordered crystal domains formed by the self-assembly of the crystallogenic units as phonon pathways^[104]. Liquid crystal molecules containing crystallogenic units do not necessarily have high thermal conductivity after polymerization, and the core of improving thermal conductivity is to preferentially complete the self-assembly of liquid crystal molecules.The liquid crystal domains are then anchored in the network by a chemical crosslinking reaction. The competition between the ordered physical self-assembly process and the disordered chemical crosslinking reaction depends on the liquid crystal temperature and the gelation temperature of the curing agent.

An external magnetic field and an electric field are used to induce the alignment of self-assembled liquid crystal domains along the external field to produce anisotropic thermal conduction behavior, and a micro-scale ordered structure is constructed in the cured network through a crosslinking reaction to enhance the thermal conduction as a phonon transfer path, so the external field induced alignment of liquid crystal domains is a current research hotspot of thermally conductive crosslinked polymers^[1,8,13]. For example, the liquid crystal molecules with diphenylacetylene as the core and flexible thiol aliphatic chain as the tail were first self-assembled, and the thermal conductivity of the film after orientation and polymerization under external electric field was 3. 56 W/ (m · K)^[105]. By using the induction effect of the magnetic field, the self-assembled liquid crystal domains are easier to form a smectic liquid crystal structure which is more regular than a nematic structure in the absence of a magnetic field, and the heat conduction of the cured liquid crystal epoxy is further improved^[13].