Low Interfacial Thermal Resistance Between Crossed Ultra-Thin Carbon Nanothreads

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Zhan, Haifei, Zhang, Gang, Zhuang, Xiaoying, Timon, Rabczuk, & Gu, Yuantong (2020) Low interfacial thermal resistance between crossed ultra-thin carbon nanothreads. Carbon, 165, pp. 216-224.

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Notice: Please note that this document may not be the Version of Record (i.e. published version) of the work. Author manuscript versions (as Sub- mitted for peer review or as Accepted for publication after peer review) can be identiﬁed by an absence of publisher branding and/or typeset appear- ance. If there is any doubt, please refer to the published source. https://doi.org/10.1016/j.carbon.2020.04.065 Low Interfacial Thermal Resistance Between Crossed Ultra-thin Carbon Nanothreads Haifei Zhan1,2, Gang Zhang3,*, Xiaoying Zhuang4, Rabczuk Timon5, and Yuantong Gu1,2,**

1School of Mechanical, Medical, and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia 2Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia 3Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, Singapore 138632, Singapore 4Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstraße 11, 30157 Hannover, Germany 5Institute of Structural Mech. Bauhaus-Universität Weimar, Marienstraße 15, 99423 Weimar, Germany

Abstract

To ensure reliable performance and lifetime of electronics, effective and efficient heat removal is essential, which relies heavily on the high thermal conductivity of the packaging substrates and thermal interface materials (TIMs). Highly conductive fillers have been commonly applied to enhance the thermal conductivity of TIMs, while the enhancement effect has been significantly impeded by the interfacial thermal resistance. This work reveals that the new type of ultra-thin carbon nanomaterial – carbon nanothreads, possess a much smaller interfacial thermal resistance (3.1±0.4´10-9 Km2/W) between each other compared with that of the (4,0) carbon nanotubes (8.8±4.6´10-9 Km2/W). Similar as found for carbon nanotubes, the interfacial thermal resistance decreases when the interfacial crossing angle decreases or the contact area increases. Surprisingly, both compressive and stretching interfacial distance are found to enhance the interfacial thermal conductance. It is found that different carbon nanothreads exhibit an interfacial thermal conductance between 60 and 110 pW/K, which can be remarkably enhanced by introducing interfacial cross-linkers. Combining with the ultra-thin nature of carbon nanothreads, our work suggests that carbon nanothreads can be an excellent alternative nanofillers for polymer composites with enhanced thermal conductivity.

Keywords: carbon nanothread, kapitza resistance, density of states, carbon nanotube, molecular dynamics simulation

*Corresponding author. Email: [email protected] (Gang Zhang) **Corresponding author. Email: [email protected] (Yuantong Gu)

1 Introduction Nanotechnology has continuously minimized the electronic devices/systems, which drastically increases their power density and results in significant heat generation [1]. To ensure reliable performance and lifetime, effective and efficient heat removal is desired, which relies heavily on the high thermal conductivity of the packaging substrates and thermal interface materials (TIMs) [2-4]. Polymer composite is one of the common TIMs in the electronic packing industry, which have received extensive interests from both scientific and engineering communities [5, 6]. They also have broad applications as underfill materials, organic substrate materials, and in flexible electronic devices. The intrinsic thermal conductivity of polymer is very low about 0.2-0.5 Wm-1K-1, due to the strong inherent phonon scattering between chain ends, entanglements and impurities [7]. In this regard, extensive works have been devoted to promote the heat transfer in polymer composites by adding different types fillers with high thermal conductivity. Owing to their high thermal conductivity, carbon-based nanomaterials are one type of the frequently used thermally conductive fillers for polymer composites, such as one-dimensional (1D) carbon nanotube or nanowire [8-10], two-dimensional (2D) graphene, and three-dimensional (3D) nanoarchitectures like carbon foams. For instance, CNTs are shown with a thermal conductivity as high as ~ 3,000-3,500 W/mK at room temperature [11, 12]. It is believed that to enable an efficient heat transfer while not deteriorating other properties (such as mechanical and electrical insulation characteristics) of the polymer, a percolation network is desired, within which the nanofillers are interconnected with each other. However, studies shown that even at high loading fillers well above the geometric percolation – only a minor enhancement in the overall thermal conductivity is observed for the composite system, which is well below the prediction based on the rule of mixture [13]. For illustration, most of the reported polymer composites with CNT fillers are still well below 5 W/mK [7]. In theory, many factors can constrain the enhancement from the CNT, such as the thermal resistance at the CNT/CNT and CNT/matrix interfaces, the dispersion and alignment of CNTs, and the geometrical parameters of CNTs (e.g., size and shape) [14]. Among these factors, the thermal resistance at the filler/filler and filler/matrix interfaces are the two main constraints that restrict effective heat transfer [15]. Different strategies have been proposed to enhance the heat transfer at the CNT/CNT interface or contacts that is influenced by several factors, including the CNT diameter, aspect ratio,

2 deformation, number of walls, external force, and others [16-22]. The most effective way is to introduce covalent bonds to the interface, which however will remarkably suppress the intrinsic thermal conductivity of CNTs. Recently, a new class of one-dimensional (1D) carbon nanostructure – carbon nanothread, has been reported [23-25], which provides a novel thermally conductive filler for polymer nanocomposites. Unlike the sp2 bonding in CNT, carbon nanothreads have an ultra-thin sp3-bonded carbon structure with a fully hydrogenated surface. Their hydrogenated surface allows for the introduction of covalent bonds between carbon nanothreads, or the attachment of functional groups to the nanothreads, while retaining the threadlike morphology and their excellent mechanical properties [26]. According to our previous work, the nanothread-based bundles exhibit an order of magnitude higher interfacial shear strength than CNT bundles due to the irregular surface-induced stick-slip motion [27], and they also show a good load transfer efficiency with the polymer matrix they are embedded in [28]. Apart from that, preliminary studies have shown that carbon nanothreads possess a tailorable thermal conductivity [8, 29]. Combining its intriguing features (including ultrathin diameter, good thermal conductivity, hydrogenated surface, and high interfacial load transfer efficient), it is expected that the carbon nanothreads can be a new filler for polymer composites with a high mechanical and thermal transport performance. To this end, this work assesses the thermal resistance at the interface of two carbon nanothreads mimicking the nanothread junctions or percolated nanothread networks in the polymer composites. Our results establish for the first time a comprehensive understanding of the heat transfer at the nanothread junction with varying parameters (such as nanothread types, crossing angle, inter-thread distance, interface linkers), which will pave the way for its application in polymer nanocomposites.

Methods Nonequilibrium molecular dynamics (NEMD) simulations were employed to acquire the thermal resistance between carbon nanothreads at 300 K. Such simulation scheme has been widely utilized to investigate the thermal conductivity of CNTs or interfacial thermal resistance between CNTs [30, 31], which show good agreement with the experimental measurements [32, 33]. The model was configurated by two carbon nanothreads that cross over each other, which was firstly optimized by the conjugate gradient minimization method and then equilibrated using Nosé-

3 Hoover thermostat [34, 35] for 400 ps. During the energy minimization, both nanothreads were not constrained. While, both two ends of the two nanothreads were fixed during the relaxation process and thermal transport simulation. The temperatures of the heat source (320 K) and sink (280 K) were controlled by the Langevin thermostat [36], with a temperature difference of 40 K. The system was firstly simulated for 4 ns to reach a steady state, and continued to another 6 ns for the thermal resistance calculation. To ensure reliable calculations, the thermal resistance is calculated at a time interval of 2 ns and averaged over 6 ns. A small time step of 0.5 fs was used for all calculations with all MD simulations being performed under the software package LAMMPS [37]. Non-periodic boundary conditions were applied in all directions. For all simulations, the widely-used adaptive intermolecular reactive empirical bond order (AIREBO) potential was employed to describe the C-C and C-H atomic interactions [38, 39]. This potential includes short-range interactions and long range vdW interactions, which has been shown to well represent the binding energy and elastic properties of carbon materials. It adopts Lennard- Jones term to describe the van der Waals (vdW) interactions, which has been reported to reasonably capture the vdW interactions in multi-layer graphene [40], multi-wall CNTs [41], CNT bundles [42], and hybrid carbon structure [43].

Results and Discussions Figure 1a shows the settings for the NEMD simulation, where two carbon nanothreads cross over each other with a right angle. Initially, we select the tube(3,0) nanothread (as it has a same tubular structure as that of CNTs), which is named as 123456 following the convention developed by the theoretical work [44]. There are three different regions in each nanothread, including the boundary region, the thermal control region, and the free region. Specifically, one unit of atoms (with a length of 0.43 nm) at the two ends of each nanothread are taken as fixed boundaries. Three units of atoms (with a length of 1.30 nm) adjacent to the two boundaries are the heat sink or heat source. The rest region of the nanothread is the free region with no thermal control. Such scheme has also been previously used to probe the thermal resistance between CNTs [16, 45,

46]. The temperature of each unit cell is calculated using equipartition � = ∑ �� , where ! each unit cell has n atoms and the ith atom has a mass of � and a velocity of � ; � is the Boltzmann’s constant.

4 To note that there may exist different interfacial morphologies between nanothreads. Inset in Figure 1a shows the initial interfacial configuration between the two carbon nanothreads. To exploit this issue, we consider the relaxation of the system with different initial perturbations, including adjusting the initial distance (from -0.5 Å to 1.5 Å) between the two nanothreads in the stacking direction (x-axis) and cross direction (y-axis), and rotating the upper carbon nanothread along its axis from 0 to 60°. Adopting high convergence tolerance criteria, i.e., a potential energy change rate less than 1.0×10-10 and a force change less than 1.0×10-10 eV/Å, a uniform interfacial configuration is obtained as illustrated in Figure 1b. The potential energy change rate is calculated from Δ�/� where Δ� and � are the potential energy change and the initial potential energy of the system.

Figure 1. Atomic configuration of the model. (a) Schematic view of the simulation settings. Inset shows the initial configuration at the cross region. Each nanothread has three regions, including the edges, thermal control regions, and the free region. (b) Different views of the interfacial morphology with the lowest potential energy. Cyan and white solid spheres represent C and H atoms, respectively.

The interfacial thermal conductance (G, in the unit of W/K) is calculated from � = �/∆� (1) Here ∆� is the temperature jump at the interface; � is the heating power or heat flow rate across the interface or junction (in the unit of W). The heating power in the heat source or sink is in the order of 10-9 W to maintain the temperature difference of 40 K. Besides, the interfacial thermal resistance (R, in the unit of Km2/W) that accounts for the influence from the contact area is also calculated based on

5 � = �∆�/� (2) Here � is the interface area. Note that Eq. 2 is usually applied to systems with planar interface where � is well defined and the heat flow is one-dimensional. For the junction configuration in Figure 1, the interface contact area � is not well defined geometrically. In this regard, the effective contact area � is calculated based on the interfacial potential energy � , i.e., � = ��/� . Here, � is the interfacial potential energy between two layers of diamane sheets with a contact area of �. The 2D diamane is considered as the referencing system as it has the similar carbonization status as that in carbon nanothreads. Previous studies have shown that the AIREBO potential is able to well reproduce the properties of diamane compared with that obtained from first principle calculations [47-51]. The calculation scheme for the effective contact area has been widely used while investigating the interfacial thermal resistance between CNTs (with a referencing system of graphene layers) [16, 52].

Interfacial thermal conductance

Figure 2a compares the time history of the accumulated heat � added in the heat source and removed from the heat sink for tube(3,0) nanothread. As it is seen, the accumulated thermal energy exhibits a very good linear relationship with time, indicating a stable heat transfer in the system. Figure 2b illustrates the temperature profile in the upper and lower nanothreads at the time of 6 ns, from which an evident temperature jump around 35.2 K is observed at the crossing region or junction. Based on these results, the interfacial thermal conductance G is estimated as 79.2 ± 12.7 pW/K, and the corresponding interfacial thermal resistance R is 3.1±0.4´10-9 Km2/W.

It is interesting to compare the interfacial thermal resistance of carbon nanothreads with that of CNTs. In literature, MD simulations have predicated a very scattered G in the range of ~ 10 pW/K to 1000 pW/K for CNTs, as induced by different simulation methods, contact-area estimation methods, CNT parameters, and other factors [53]. For the frequently studied (10,10) single-walled CNT, whose diameter is much larger than that of the nanothread, the thermal conductance at a 90° crossing angle contact or interface is found less than 100 pW/K at 300 K. For fair purpose, we calculate the interfacial thermal resistance of the ultrathin (4,0) CNT whose diameter is similar to that of the tube(3,0) nanothread. As compared in Figure 2a, the accumulated heat added in the heat source or removed from the heat sink for (4,0) CNT is around 1.0´10-17 J at

6 the simulation time of 10 ns, which is much lower than that of the tube(3,0) nanothread (about 2.8´10-17 J). Compared with tube(3,0) nanothread, (4,0) CNT exhibits a much smaller G of 28.1 ± 7.7 pW/K, and its R is 8.8±4.6´10-9 Km2/W, more than two times larger than that of tube(3,0) nanothread. These results suggest that the heat transfer at the carbon naonthread junctions is more efficient than that at the (4,0) CNT junctions.

Figure 2. NEMD simulation for crossed tube(3,0) nanothread with a 90° crossing angle. (a) The accumulated heat as a function of the simulation time; and (b) The temperature profile at the simulation time of 6 ns.

Theoretically, the heat transfer at the interface is determined by the coupling strength and the matching of phonon spectra or the vibrational density of states (VDOS, �(�)) between the upper and lower nanothreads or CNTs. Here, �(�) is calculated from the Fourier transformation of the averaged velocity auto-correlation function (VACF) [54], and it is normalized such that �(�)�� = 1. A small portion (with a length of about 1 nm) of the lower and upper nanothreads ∫ or CNTs at the crossing interface is selected for the VACF calculation. The profiles of the VDOS for the lower and the upper nanothreads and CNTs are shown in Supporting Information S1, respectively. The relationships with the overlap of the phonon bands of the upper and lower nanothread or CNT can be measured by [55]

7 ( ( ) ∫) "#$ %#&'() � = ( ( (3) ( ) ∫) "#$() ∫) %#&'

Here, �(�) and �(�) represent the VDOS of the hot (upper) and cold (lower) nanothread or CNT, respectively. It is found that the tube(3,0) nanothread shows a larger � (about 0.08) than that of the (4,0) CNT (about 0.06), indicating a higher phonon overlap ratio at the interface. To further exploit the difference between nanothread and (4,0) CNT, we calculate the phonon population variation (∆�) from the VDOS profile, which is defined as the ratio between phonon occupations as [56],

- ∫) *+,() ∆�(�) = - − 1 (4) ∫) .*+()

Here, �(�′) and �(�′) represent the VDOS of the nanothread and CNT, respectively. Based on the VDOS profile, ∆� can be calculated for the hot (upper) or cold (lower) regions, separately. As illustrated in Figure 3, ∆� is positive for both cold and hot regions, signifying that there are more phonon populations in the tube(3,0) nanothread compared with (4,0) CNT. Overall, the VDOS results indicate that there are more phonon populations and higher phonon overlap ratio at the interface of tube(3,0) nanothread, which explains the smaller interfacial thermal resistance between tube(3,0) nanothread compared with that of (4,0) CNT.

Figure 3. Phonon occupation variation of cold and hot regions between tube(3,0) nanothread and (4,0) CNT. The profile is truncated at the phonon frequency of 60 THz.

Impact from the sample length and the crossing angle

Next, influences from several factors such as the sample length and the crossing angle are explored to approach the practical condition, due to the randomness of the percolation network in

8 the polymer matrix. To examine the length impact, we investigate the interfacial heat transfer for the tube(3,0) nanothread with a varying sample length from 6.5 nm to 20.4 nm (while maintaining a 90° crossing angle).

As illustrated in Figure 4a, the interfacial thermal conductance shows an initial slight increase when the sample length increases, which fluctuates around 81.5 pW/K when the sample length is over 10 nm. Compared with that observed for (10,10) CNT [15, 52, 57], the thermal conductance of the nanothread exhibits a weak length dependence (presumably due to its much smaller effective contact area). The relationship between � and � has been explained by considering the whole junction as two thermal resistors in series [52], i.e., 1/� = 1/� + 1/�.

Here, � is the sample length, and 1⁄� and 1⁄� represent the external junction thermal resistance and internal thermal resistance, respectively. For comparison purpose, we also examine the interfacial thermal conductance of the (4,0) CNTs with varying sample length. As plotted in Figure 4a, (4,0) CNTs share a similar changing pattern of � as that of the tube(3,0) nanothread. It is expected that more low-frequency phonon modes exist in longer samples, which enhances the coupling at the junction and reduces the thermal resistance [58]. Of interest, we compare the phonon population variation in the hot and cold regions separately between the nanothreads with a longer (�~10 nm) and shorter (�~6.5 nm) sample length. As illustrated in Figure 4b, the longer nanothread exhibits higher phonon populations for both hot and cold regions (with ∆� > 0 for most frequencies in the interval of 5 – 30 THz).

Figure 4. The influence of sample length. (a) The boxplot of the thermal interfacial conductance (�) of tube(3,0) nanothread as a function of the sample length; and (b) the phonon occupation variation of cold/hot regions between long ( �~10 nm) and short ( �~6.5 nm) tube(3,0) nanothreads.

With above understanding, another important factor that influences the interfacial thermal resistance is the crossing angle between nanothreads. For the percolation network in the composite, the crossing angles between two nanothreads can assume random values. Therefore, we construct different atomic configurations by rotating the upper nanothreads with a certain angle based on the relaxed structure with a crossing angle of 90°. Geometrically, the effective contact area between the bottom and the top nanothreads increases when the crossing angle decreases, in line with that reported for CNT [59]. As compared in Figure 5a, the effective contact area for the configuration with a 15° crossing angle is around five times of that with a 90° crossing angle.

From Figure 5a, the interfacial thermal resistance decreases (or the thermal conductance increases) when the contact area at the interface increases, which agrees with that observed in crossing CNTs [31, 57, 58]. For instance, at the crossing angle of 15°, R is around 24.1±3.0´10-10 Km2/W and G is around 456 ± 62 pW/K, which is over 20% smaller and 450% larger than those of the configuration with 90° crossing angle, respectively. It is noticed that the inverse of thermal conductance generally follows a linear relationship with the inverse of the contact area (1/�) (see

10 Supporting Information S2), which agrees with that observed from the (10,10) CNTs [52]. Such observation also agrees with the analytical model developed in literature [59], i.e., an inverse proportional relationship between the inverse of the thermal conductance and the contact area. According to the phonon occupation variations between small and large crossing angle scenarios (Figure 5b), the model with 15° crossing angle (or larger contact area) has a slightly larger population for phonons at ~ 1 THz at both cold and hot regions compared with the counterpart with a 90°crossing angle, which is expected as resulted from the enhanced inter-thread vdW interactions. Interestingly, although the model with 15° crossing angle contains more higher frequency modes (between ~15 to ~50 THz) in the cold region compared with the 90° case, it exhibits less higher frequency modes between ~2 to 40 THz in the hot region (i.e., ∆� < 0). To be noted that, the magnitude of R experiences a relatively large fluctuation, which is expected due to the variations of the interfacial distance as resulted from the thermal fluctuations (same as that in Figure 4a for G, see Supporting Information S2 for more details). Additionally, R for model with 45° crossing angle appears slightly larger than the model with 30° or 60° crossing angle in Figure 5a, which is presumably due to assumptions adopted for the models, i.e., the models with different crossing angle are assumed to have a same inter-thread distance and a same thread length.

Figure 5. The influence of crossing angle. (a) The boxplot of the thermal interfacial resistance (�) and the effective contact area (�) of tube(3,0) nanothread as a function of the crossing angle;

11 and (b) the phonon occupation variation of the hot/cold regions between the model with a crossing angle of 15° and 90°.

Impact from the interface distance The interfacial heat transfer is largely determined by the inter-thread vdW interactions, in this regard, we examine how the interfacial thermal resistance will change with varying inter- thread distances. For such purpose, the hot (or top) nanothread of the equilibrated sample with a crossing angle of 90° is displaced by a distance of -1.0 Å, -0.5 Å, 0.5 Å, 1.0 Å and 1.5 Å, respectively, along the stacking direction (x-axis in Figure 1), which introduces a compression or stretching effect at the interface. Due to its relatively small flexural rigidity, the nanothread experiences a slight bending deformation under both stretched and compressed scenarios (see Supporting Information S3). Such fact leads to a much smaller actual interface distance change than the prescribed displacement after structural relaxation. For discussion convenience, we define the interface strain as � = (� − �)/� , where � and � represent the initial and shifted inter-thread distance between the crossing nanothreads after structural relaxation (i.e., the distance between the two axes of the crossing nanothreads). The initial inter-thread distance between tube(3.0) nanothreads is about 6.44 Å. As expected, the effective contact area at the interface decreases with the continuous increase of the interfacial strain (Figure 6a). Figure 6a compares the interfacial thermal resistance of the crossing tube(3,0) nanothreads with different interfacial strain. Strikingly, R exhibits a decreasing tendency either under compressive or stretching strain. Such observation is different from that reported for CNT(10,10) [45], where the thermal resistance increases continuously with increasing inter-tube distance. The apparent inconsistent observation between CNT(10,10) and the carbon nanothread is attributed to their distinct geometry. As discussed above, carbon nanothread experiences a slight bending deformation under both stretched and compressed scenarios as resulted from the interface vdW interactions, which remarkably reduces the prescribed interfacial strain. For instance, an initial 1.5 Å shift only yields to a stretching interface strain of around 0.19% (corresponding an actual distance change of ~ 0.012 Å after structural relaxation). Such minor interfacial distance change results in a slight change to the total potential energy of the system (less than 0.25 eV). Despite the minor interfacial distance change (or strain), the thermal resistance magnitude receives a much

12 larger change. For instance, � is about 20% smaller at the stretching strain of 0.19% than that without strain. Compared with the non-strained configuration, the phonon population increases in the cold regions but decreases in the hot regions under either external compressive or stretching interfacial strain (Figure 6b). It is expected that the increased low frequency modes in the cold regions enhance the heat transfer at the interface and reduce the thermal resistance.

Figure 6. The influence of interfacial strain. (a) The boxplot of the thermal interfacial resistance

(�) and the effective contact area (�) of tube(3,0) nanothread as a function of the interfacial strain. Red markers are the mean values; and (b) the phonon occupation variations of the hot (top) and cold (bottom) regions between the configuration with and without interfacial strain.

Morphology influence As aforementioned, there are many carbon nanothreads being theoretically predicted [44]. To obtain an overall understanding of the thermal interfacial resistance of carbon nanothreads, we selected 12 different fully-saturated nanothread morphologies that belong to the chiral and achiral groups. Similar simulation settings and a sample length around 10 nm are adopted for all different nanothreads. Figure 7a shows the thermal conductance for all examined carbon nanothreads. As is seen, all examined nanothreads exhibit a thermal conductance between 60 and 110 pW/K, which is much

13 larger than the (4,0) CNT (around 28 pW/K), suggesting better heat transfer efficiency at the interface. Following the previous calculation approach for the effective contact area, a generally higher � is observed for the nanothreads with a larger � or interfacial energy (see Supporting Information S4). While, the magnitudes of � for almost all nanothreads exhibit a relevant large fluctuation due to its high flexibility.

Figure 7. Thermal conductance of carbon nanothreads. (a) Comparisons of thermal conductance (�) of different carbon nanothreads. NT represents carbon nanothreads. The six-digital number is the nomenclature of nanothreads, which indicates the topology information [44]; (b) The phonon occupation variation between a chiral (145263) and an achiral (123456) carbon nanothreads for the hot and cold regions, respectively.

Figure 7b compares the phonon occupation variation in the hot and cold regions between a chiral nanothread (145263) and an achiral nanothread (123456). Figure 7a shows that the chiral nanothread 145263 has a much higher � (~ 106±12 pW/K) than the achiral 123456 nanothread (~63±5 pW/K). It is found that the chiral nanothread contains slightly higher phonon populations than the achiral nanothread in both hot and cold regions at the low-frequency regime between 1 to

14 3 THz. It also exhibits more phonon populations in the frequency between 10 and 30 THz in the cold regions, but less phonon populations in the frequency between 3 to 20 THz in the hot regions. These results indicate that there are more low-frequency phonon modes in the chiral nanothread, and thus enhance the heat transfer as the interface.

The interface linkers

One advantage of carbon nanothreads over CNTs is their hydrogenated surface, which makes it ready to introduce interfacial covalent bonds between carbon nanothreads [60, 61] (while retaining their threadlike morphology and excellent mechanical properties) [26]. Experiments have already demonstrated the possibility of functionalizing nanothreads with -NH2 groups [61], and DFT calculations [60] show the possibility of introducing various functional groups, such as, –

CH3, –NH2, –OH, and –F). An earlier work discussed the interfacial thermal resistance between

(10,10) CNTs with –(CH2)n–, EPON-862 (epoxy resin), –(C6H4)n–, and aromatic links [62].

According to literature, –(C6H4)n– cross-linkers can be introduced to CNTs by aryl cross-linking reaction [63, 64]. Based on these preliminary works, we examine how the thermal interfacial resistance will change for carbon nanothreads by introducing interfacial covalent bonds. For illustration, we consider the tube(3,0) carbon nanothreads (123456) with a crossing angle of 90°, and the –(C6H4)n– molecules are employed to build the cross-linking between top and bottom nanothreads (see inset in Figure 8a).

Due to the ambiguity in defining the effective contact area for the cross-linkers, we focus on the thermal conductance (G) of the crossing nanothreads with different number (or length) of cross-linkers. As shown in Figure 8a, the introduction of covalent cross-linkers significantly enhances the thermal conductance at the interface. For instance, the configuration with one –

(C6H4)– cross-linker exhibits a G of 692 ± 49 pW/K, which is more than one order higher than the configuration without cross-linker. From the phonon occupation variation (Figure 8b), we can see that the cross-linker has remarkably increased the overlapping of VDOS between the hot and cold nanothreads (see Supporting Information S4 for the detail VDOS), which explains the significantly enhanced thermal conductance at the interface. The interfacial cross-linkers are found to exert different influences on the phonon modes in the cold and hot regions (Figure 8c). In the hot region, the cross-linked models exhibit high phonon population than the non-linked models in

15 the frequency range between ~ 1 and 30 THz. In comparison, the cross-linker seems to reduce the phonon modes between ~ 1 and 15 THz in the cold regions, while increase the high-frequency phonon modes (between ~ 15 THz and 30 THz).

Figure 8. Thermal conductance of carbon nanothreads with covalent linkers. (a) Comparisons of thermal conductance (G) of carbon nanothreads with different cross-linkers. Inset shows the configuration with a –(C6H4)– linker; (b) The phonon occupation variation between hot and cold nanothreads for the model with none, –(C6H4)– and –(C6H4)5– covalent linkers, respectively; (c) The phonon occupation variation between the model with and without cross-linkers in the hot and cold regions, respectively.

It is further found that by increasing the length of the cross-linker, the enhancement to the thermal conductance will be suppressed. As illustrated in Figure 8a, the thermal conductance at the interface decreases continuously when the length of the cross-linker increases, which exhibits a convergence tendency with longer cross-linkers. Such result is expected as resulted from the stronger phonon scattering for longer cross-linkers [62]. It is noteworthy that the configuration with –(C6H4)2– cross-linker shows a thermal conductance of 402 ± 33 pW/K, which is more than

40% smaller than the counterpart with –(C6H4)– cross-linker. However, comparing with the case with –(C6H4)3– cross-linker (G = 350 ± 17 pW/K), it is only 13% higher. The relatively larger reduction of G for the configuration with –(C6H4)2– cross-linker is actually originated from the interfacial vdW interactions. Ideally, the length of a –(C6H4)– cross-linker is around 6 Å. In comparison, the cut-off radius for the vdW interactions is chosen as 10.2 Å between the two nanothreads in this work. In other words, there are two heat transfer channels at the interface for the configuration with –(C6H4)– cross-linker, i.e., the interfacial covalent linkers and the interfacial vdW interactions, which thus leads to a much higher thermal conductance at the interface

16 compared with other configurations with longer cross-linkers. Such fact is also well reflected by the phonon occupation variation between the nanothreads with shorter and longer cross-linkers, where the model with –(C6H4)– cross-linker exhibits more low-frequency phonon populations

(between ~ 1 and 10 THz) than the scenario with –(C6H4)5– cross-linker (see Supporting Information S5). Despite the decreasing tendency, the structure with five cross-linkers still exhibits a G of 285±16 pW/K, which is more than three times larger than the structure without cross-linkers. These results suggest that the thermal interfacial resistance can be effectively improved through the covalent cross-linkers.

Conclusions Based on the large-scale molecular dynamics simulations, we find that the novel 1D ultrathin carbon nanothreads possess a much smaller interfacial thermal resistance (3.1±0.4´10-9 Km2/W) between each other compared with that of the (4,0) CNTs (8.8±4.6´10-9 Km2/W). The interfacial thermal conductance is found to increase slightly with the sample length, which exhibits a converged fashion when the sample length is over 10 nm. Similar as reported for CNTs, the interfacial thermal resistance decreases when the interfacial crossing angle decreases. However, both compressive and stretching interfacial distance are found to reduce the interfacial thermal resistance or enhance the interfacial thermal conductance, which is supposed as resulted from the increased low-frequency phonon populations in the cold regions. With varying morphologies, carbon nanothreads are found to exhibit an interfacial thermal conductance between 60 and 110 pW/K that is much larger than the (4,0) CNT (around 28 pW/K). Further investigations show that the interfacial thermal conductance can be remarkably enhanced by introducing interfacial cross- linkers, and a shorter cross-linkers with a length less than the vdW interaction cutoff distance induces the strongest enhancement.

In summary, this work suggests that the new ultrathin carbon nanothreads possess higher interfacial thermal conductance, which makes them ideal thermally conductive nanofillers for polymer composites. Particularly, carbon nanothreads have a hydrogenated surface that is ready to introduce covalent linkers in polymer matrix, which could remarkably enhance the interfacial thermal conductance. The current work has focused on the interfacial thermal conductance between two carbon nanothreads, it is worthwhile to probe the interfacial thermal conductance

17 between multiple nanothreads, and between nanothreads and polymer matrix. For instance, studies reveal that the contact thermal conductance decreases when the contact number increases [65, 66]. To be noted that in application of carbon nanothreads as fillers, its overall impact depends on many other key factors, including polymer chain structure, dimensions and dispersion state, flow- induced orientation, and interfacial thermal resistance between nanothreads is only one of these key factors. Since the present work only focuses on the interfacial thermal resistance, a comprehensive investigation of the overall impact of the filler in an application will be assessed in our following work. Additionally, literature shows that the interfacial thermal conductance increases monotonically with the increase of temperature, reported in theoretical simulations [67- 69] and experiments [70-72]. This is because with the increase of temperature, anharmonicity of the interatomic interaction increases. Therefore, phonon transmission across the interface is enhanced facilitated by inelastic scattering.

Supporting Information The Supporting Information is available free of charge, including: the vibrational density of states of tube(3,0) nanothreads and (4,0) CNT; the interfacial thermal conductance as a function of the effective contact area; deformation of the nanothread due to the interfacial strain; the interfacial thermal conductance of different carbon nanothreads; and phonon occupation variation between the nanothreads with a shorter and longer cross-linkers.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]

Author Contributions

HZ carried out the simulations. HZ, GZ, JB, VT, and YG conducted the analysis and discussion.

Notes

The authors declare no competing financial interests.

ACKNOWLEDGEMENT

18 Support from the ARC Discovery Project (DP170102861) and the High-Performance Computing (HPC) resources provided by the Queensland University of Technology (QUT) are gratefully acknowledged (HZ, YG, JB). This research was undertaken with the assistance of resource and services from Intersect Australia Ltd, and the National Computational Infrastructure (NCI), which is supported by Australian Government. HZ would also like to acknowledge the support from the Start-up Fund from Queensland University of Technology.

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