Unusual thermal transport behavior in self-assembled fullerene nanorods

Abstract

In this work, fullerene (C₆₀) nanorods were prepared by a surfactant-assisted self-assembly method. Although the orientation of molecular alignment remains unchanged from one end to the other end in these C₆₀ nanorods, they cannot be rigorously treated as single crystals because of the existence of amorphous-like regions formed by a high density of defects such as stacking faults and vacancy clusters. The partially crystalline and partially amorphous structure results in unusual thermal transport behavior in C₆₀ nanorods, which cannot be classified into either typical crystalline-like or typical glass-like behavior. The thermal resistances of the C₆₀ nanorods decrease with increasing temperature and reach a plateau around 100 K, which can be attributed to the combined effect of Einstein localized vibration in C₆₀ molecules, intracluster vibration, and phonon-defect scattering. Accompanied with depositing Pt/C composites at two ends of a C₆₀ nanorod to improve thermal contact between Pt electrodes and the C₆₀ nanorod, tensile strain may be introduced in the C₆₀ nanorod due to contraction, which enhances thermal resistance, especially in the low temperature range. Ultralow thermal conductivity (less than 0.06 W m⁻¹ K⁻¹) is observed for self-assembled C₆₀ nanorods at room temperature, which is significantly lower than the thermal conductivity of bulk C₆₀ single crystals and polycrystalline C₆₀/C₇₀ compacts but on the same order of magnitude as the lower limit of thermal conductivity of amorphous carbon.

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Introduction

Recent years have seen a rapid growth of interest in tuning thermal transport properties of materials motivated by fundamental studies and practical needs.^1,2 The thermal transport property of a material is rooted in its atomic structure and can be tuned by changing atomic arrangement and bonding or introducing interfaces. Conventionally, low thermal conductivity is found in amorphous insulators, in which the majority of the vibrational energy modes demonstrate a random walk on the time and length scales of atomic vibrations.³ Recent reports show that heat conduction is strongly impeded by thermal interfaces in multilayer crystalline thin films and superlattices and thus ultralow thermal conductivity is observed in these materials, which is even lower than the minimum thermal conductivity of the homogeneous amorphous oxide.⁴ To date, the lowest thermal conductivity in a fully dense crystal is achieved in the cross-plane direction of the layered WSe₂ thin films.⁵

Carbon materials, which form a variety of allotropes and derivatives, are unique in terms of their ability to conduct heat with the room-temperature thermal conductivity spanning five orders of magnitude, i.e., about 4000–5000 W m⁻¹ K⁻¹ in free-standing graphene,^6,7 3000–3500 W m⁻¹ K⁻¹ in single-walled carbon nanotubes,^8,9 about 2000 W m⁻¹ K⁻¹ in diamond,¹⁰ and 0.02–0.2 W m⁻¹ K⁻¹ in amorphous carbon.¹¹ Fullerene (C₆₀) is discovered as the third stable allotrope of carbon after diamond and graphite, which is entirely composed of carbon atoms and has a ball-shaped structure with a diameter of about 0.7 to 1.0 nm.¹² Thermal conductivity of single C₆₀ molecules is still unknown since C₆₀ molecules are zero-dimensional materials and it is experimentally challenging to measure their thermal properties. Bulk single crystals of C₆₀ molecules have been prepared via a sublimation–recrystallization method and their thermal conductivity demonstrates typical crystalline-like behavior, which means that thermal conductivity decreases with increasing temperature from 30 K to 300 K due to phonon Umklapp scattering.¹³ By contrast, polycrystalline C₆₀/C₇₀ compacts, prepared by directly compacting C₆₀ and C₇₀ powders at 3000 atm, show the glass-like thermal transport behavior, which means that thermal conductivity shows no temperature dependence above 10 K since only localized vibrations of rigid molecules contribute to thermal transport.¹⁴

Recently, there is a great interest to synthesize one-dimensional C₆₀ nanorods via a surfactant-triggered self-assembly method for their potential applications in nanoelectronic and photoelectronic devices.^15,16 It is fundamentally important to understand thermal transport in C₆₀ nanorods in order to enhance the performance and stability of electronic devices. In this work, we prepared self-assembled C₆₀ nanorods and carried out mesoscopic thermal transport measurements of individual C₆₀ nanorods through a suspended thermal bridge method. Unusual thermal transport behavior is observed in self-assembled C₆₀ nanorods, which is different from those in bulk single crystals of C₆₀ molecules¹³ and polycrystalline C₆₀/C₇₀ compacts,¹⁴ due to their unique structures.

Experimental

C₆₀ nanorods are synthesized by a self-assembly method, similar to a previous report.¹⁷ C₆₀ (purity > 99.9%) and m-xylene (purity > 99.0%) were purchased from J&K Scientific Corporation, USA. Both materials were used without any further treatment. A 100 nm thick C₆₀ layer was deposited by a physical evaporation method on a silicon (Si) substrate. Then, the Si substrate with the C₆₀ seed layer was sealed in a glass bottle containing a saturated solution of C₆₀ dissolved in m-xylene (1.4 mg mL⁻¹) with the surface of the substrate just above the liquid level. Next, C₆₀ nanorods were formed on the substrate by evaporating the solution at about 35 °C for over 6 hours. The obtained product is thermally treated in a tubular furnace under the vacuum condition (10⁻³ Pa) with the temperature accurately controlled at 150 °C for 3 hours to eliminate organic contaminants. The final product was characterized by transmission electron microscopy (TEM) and Raman spectroscopy.

Thermal conductivity of individual C₆₀ nanorods was measured by using a suspended thermal bridge method in a cryostat from 20 K to 300 K. The details of the measurement technique can be found in the literature.¹⁸ In brief, a microfabricated device consisting of two suspended silicon nitride membranes is used for thermal conductivity characterization. The scanning electron microscopy (SEM) image of a suspended device is shown in Fig. S1 (ESI†). Two membranes are separated by several microns and serve as heat source and heat sink, respectively, in the measurement. A platinum (Pt) coil and a Pt electrode with a thickness of 50 nm are patterned on each membrane. The Pt coil serves as a heater to increase the temperature of the suspended membrane (heat source), as well as a resistance thermometer to measure the temperature of each suspended membrane (heat source or heat sink). The Pt electrode is designed to have a large width of 3 μm, which is beneficial for thermal conductivity measurement of one-dimensional nanostructures due to a large contact area between the nanostructure and the electrode. An individual C₆₀ nanorod was placed bridging two membranes by using a micromanipulator. Following a previous report,¹⁹ we introduced a Wheatstone bridge into the circuit at the sensing side to reduce the effect of temperature fluctuation of the cryostat on thermal conductivity measurement. The diameter of the C₆₀ nanorod and its suspended length between two Pt electrodes were measured from the SEM image.

Results and discussion

Structural characterization of C₆₀ nanorods

Fig. 1(a) shows a typical TEM image of self-assembled C₆₀ nanorods. It is clearly shown that the sample is rod-shaped with some porous structures formed along the length. High resolution TEM (HRTEM) images along with fast Fourier transform (FFT) patterns were obtained, as shown in Fig. 1(b)–(d) and their insets, to study structural details of the nanorod such as growth direction and defects. It is worth noting that HRTEM measurements were carried out from one end to the other end for the C₆₀ nanorod. The crystal lattice formed through alignment of C₆₀ molecules can be clearly detected with a face-centered cubic (fcc) structure. The orientation of molecular arrangement remains unchanged along the axial direction, which is a typical characteristic of single crystals. However, amorphous-like regions formed by intense aggregation of molecular misalignments and vacancies percolate throughout the whole nanorod as indicated by red circles in Fig. 1(b). Therefore, strictly speaking, the nanorod is partially crystalline and partly amorphous. It should be pointed out that even in crystalline regions, stacking faults or molecular vacancies may also exist but are relatively sparse compared to amorphous regions. Raman spectrum of self-assembled C₆₀ nanorods is also obtained and shown in Fig. 2. Ten Raman peaks at positions of 272, 431, 493, 709, 772, 1100, 1250, 1424, 1467, and 1574 cm⁻¹, have been observed, which is a characteristic of the pristine C₆₀. The high-frequency A_g-symmetry ‘pentagonal-pinch’ mode is located at 1467 cm⁻¹, indicating that C₆₀ nanorods consist of monomeric C₆₀. Otherwise, it should shift to a lower frequency around 1460 cm⁻¹ for polymerized C₆₀.²⁰ The HRTEM and Raman characterization indicates that, in C₆₀ nanorods, interfaces of building blocks are dominated by van der Waals interactions and stiff covalent bonds connect C atoms in each building block, i.e., a single C₆₀ molecule, which are the same as other C₆₀ solids previously reported.^13,14 The formation of high density of defects in C₆₀ nanorods is believed to be closely related to the preparation method. The process to eliminate organic contaminants may induce additional defects and form amorphous regions.

Fig. 1 (a) TEM image of a C₆₀ nanorod; (b) HRTEM and FFT images from region 1 in (a). Red circles refer to molecule misalignments and induced molecule vacancies. (c) HRTEM and FFT images from region 2 in (a); (d) HRTEM and FFT images from region 3 in (a).

Fig. 2 The Raman spectrum of C₆₀ nanorods.

Temperature dependence of thermal resistance

An individual C₆₀ nanorod (Sample 1) was placed onto a suspended device for thermal measurement as shown in Fig. 3(a). The diameter of Sample 1 is about 743 nm and the suspended length between two Pt electrodes is measured to be 6.40 μm. Thermal resistance of Sample 1 was measured in a temperature range from 20 K to 360 K. Results show that the measured thermal resistance decreases by half as temperature increases and reaches a plateau of around 9 × 10⁸ K W⁻¹ above 100 K, which is significantly different from those reported for bulk C₆₀ single crystals¹³ and polycrystalline C₆₀/C₇₀ compacts.¹⁴

Fig. 3 (a) The SEM image of a C₆₀ nanorod on a suspended device (Sample 1); (b) the SEM image of the same nanorod in (a) with Pt/C composites deposited at the contacts between the C₆₀ nanorod and Pt electrodes by EBID; (c) temperature-dependent thermal resistances of the C₆₀ nanorod before and after EBID.

It is well-known that thermal transport in hard solids is rooted in materials' structure and can be classified as crystalline-like or amorphous-like behavior. In crystalline solids, atoms vibrate collectively as elastic waves which dominate thermal transport.²¹ The bulk C₆₀ single crystals prepared by a sublimation–recrystallization method are believed to have a relatively high degree of order in the alignment of C₆₀ molecules, which is confirmed by their crystalline-like thermal transport behavior, i.e., thermal resistance showing increasing trend with the increase of temperature.¹³ However, in amorphous solids or disordered crystals, heat is transported in a random walk among harmonically coupled localized oscillators, which are assumed to vibrate with random phases.²² Previous studies on C₆₀ solids^13,14 have confirmed that from 10 K to 40 K, vibrational motions of rigid buckyball molecules (localized excitations) dominate thermal transport; while above 40 K, intracluster vibrations (surface modes) gradually appear and dominate thermal transport. The polycrystalline C₆₀/C₇₀ compacts, prepared by directly compacting C₆₀ and C₇₀ powders at 3000 atm, should have a low degree of order in the alignment of building blocks, which is confirmed by their glass-like thermal transport behavior, i.e., thermal resistance showing temperature independence above 10 K.¹⁴ Their thermal transport behavior indicates that only localized vibrations of rigid molecules contribute to thermal transport in C₆₀/C₇₀ compacts, while surface modes play insignificant role.

The measured thermal resistance of the C₆₀ nanorod (Sample 1) indicates that, vibrational motions of rigid buckyball molecules (localized excitations) contribute to thermal transport in the C₆₀ nanorod below 40 K, while intracluster vibrations (surface modes) contribute to thermal transport above 40 K. The unique thermal transport behavior results from the coexistence of amorphous and crystalline structures in the C₆₀ nanorod: (1) from 20 K to 40 K, thermal resistance mainly comes from Einstein localized oscillators in amorphous regions; (2) above 40 K, thermal resistance is mainly caused by intracluster scattering in crystalline regions; (3) the combination of these two features results in the absence of an obvious peak in the thermal resistance curve (Fig. 3(c)). The temperature independence of thermal resistance above 100 K results from the phonon-defect scattering, which dominates over phonon Umklapp scattering in the temperature range from 100 K to 360 K. The defects here refer to stacking faults and vacancies in crystalline regions, as well as interfaces between amorphous and crystalline regions. The abrupt change of thermal resistance associated with the transition from the torsional vibration to nearly free rotation in C₆₀ single crystals at 260 K (ref. 13) is not observed, which indicates that the degree of disorder in the nanorod is large enough to quench the transition.

It should be noted that the measured thermal resistance consists of two parts: the intrinsic thermal resistance of the C₆₀ nanorod and the contact thermal resistance between the nanorod and Pt electrodes. To minimize the contact thermal resistance, Pt/C composites are deposited at contacts between the nanorod and Pt electrodes by electron beam induced deposition (EBID) as shown in Fig. 3(b). As seen in Fig. 3(c), temperature dependence of thermal resistance shows a similar trend before and after the deposition of Pt/C composites. At 300 K, the total thermal resistance after EBID is reduced by 16% compared to the value before EBID.

It is also observed that two measured thermal resistance curves intersect with each other at 50 K and the thermal resistance measured after EBID at 20 K is 10% higher than the counterpart measured before EBID. A similar phenomenon is observed for the other nanorod (Sample 2) as shown in Fig. S2.† If the deposition of Pt/C composites only reduces contact thermal resistance, we would expect that the thermal resistance measured after EBID is lower than that measured before EBID for the whole measurement temperature range. The intersecting thermal resistances we observed indicate that the deposition of Pt/C composites might induce some other effects in the C₆₀ nanorod in addition to the reduction of contact thermal resistance. Since compositions of Pt/C composites are similar to Pt electrodes and the C₆₀ nanorod, it is reasonable to assume that Pt/C composites will not significantly change the nature of the contact interface. On the other hand, we notice that the measured suspended lengths before and after EBID are very close to each other (with less than 1% difference). We hypothesize that the higher thermal resistance after EBID at low temperature might be due to the effect of contraction. C₆₀ molecules will contract with the decrease of temperature,²³ which in turn will result in the contraction of the C₆₀ nanorod. Before EBID, two ends of the nanorod are loosely placed on the suspended device, so no strain will be introduced with the decrease of temperature. However, after EBID, two ends of the nanorod are fixed onto the suspended device by Pt/C composites, which will hinder contraction and induce tensile stress in the C₆₀ nanorod. The induced tensile stress will affect thermal transport in the C₆₀ nanorod since both stiffness and lattice anharmonicity will vary with strain and thus phonon velocity and mean free path will be changed.²⁴ The tensile strain could increase thermal resistance of the C₆₀ nanorod by: (1) softening phonon modes and reducing velocities of phonons for both Einstein localized oscillator modes (vibrational motions of rigid buckyball molecules) and surface modes (intracluster vibrations);^24–26 (2) decreasing the specific heat of each propagating phonon mode;^24–26 and (3) inducing defects to reduce phonon coupling. As an example, the van der Waals interactions between neighboring C₆₀ molecules could be broken and as a result thermal resistance will be enhanced.

Thermal conductivity of C₆₀ nanorods

In total, we have measured four self-assembled C₆₀ nanorods (Sample 1–4) and the obtained thermal conductivity is shown in Fig. 4. The diameter, suspended length, and thermal conductivity at 300 K for Sample 1–4 are listed in Table 1. For all the samples we measured, the relative uncertainty in thermal conductivity is estimated to be less than 8%. Ultralow thermal conductivity (<0.06 W m⁻¹ K⁻¹ at 300 K) is observed for all self-assembled C₆₀ nanorods, which is significantly lower than thermal conductivity of bulk C₆₀ single crystals (0.4 W m⁻¹ K⁻¹ at 300 K)¹³ and polycrystalline C₆₀/C₇₀ compacts (0.1 W m⁻¹ K⁻¹ at 300 K).¹⁴ However, it is on the same order of magnitude as the lower limit of thermal conductivity reported for amorphous carbon.¹¹ Thermal conductivity of C₆₀ nanorods is found to be widely distributed, e.g., from 0.019 W m⁻¹ K⁻¹ to 0.054 W m⁻¹ K⁻¹ at 300 K. The observed ultralow thermal conductivity indicates that phonon mean free path in the self-assembled C₆₀ nanorods is very short. On the other hand, as shown in Table 1, the widely distributed thermal conductivity observed for different C60 nanorods does not demonstrate any diameter dependence. Instead, imperfections in self-assembly such as stacking faults and vacancy clusters play an important role in thermal transport behavior in self-assembled C₆₀ nanorods. We believe the difference in thermal conductivity can be ascribed to different degrees of order in different samples. Thermal conductivity of Sample 1 is lower than 0.02 W m⁻¹ K⁻¹ at room temperature, which is even lower than the cross-plane thermal conductivity of disordered WSe₂ crystals.⁵

Fig. 4 Thermal conductivity of four self-assembled C₆₀ nanorods (Sample 1–4).

Table 1 The diameter, suspended length, and thermal conductivity at 300 K of C₆₀ nanorods measured in this work

Sample	Diameter (nm)	Suspended length (μm)	Thermal conductivity at 300 K (W m^−1 K^−1)
1	743	6.4	0.019
2	562	7.3	0.025
3	578	7.5	0.027
4	788	8.0	0.054

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Conclusions

In summary, we prepared self-assembled C₆₀ nanorods which have partially crystalline and partially amorphous structure. Thermal transport behavior of self-assembled C₆₀ nanorods is different from that of C₆₀ single crystals and polycrystalline C₆₀/C₇₀ compacts previously reported in the literature. Thermal resistance of the C₆₀ nanorod decreases with increasing temperature below 100 K and is independent of temperature above 100 K, which is due to the combined effect of Einstein localized vibration, intracluster vibration, and phonon-defect scattering. By depositing Pt/C composites on two ends of the C₆₀ nanorod, thermal resistance is reduced by 16% at 300 K but enhanced by 10% at 20 K. The enhanced thermal resistance observed at low temperatures after EBID might be due to the tensile stress induced by contraction. Ultralow thermal conductivity (<0.06 W m⁻¹ K⁻¹ at 300 K) is observed for self-assembled C₆₀ nanorods. Although self-assembled C₆₀ nanorods have been proposed to be used in nanoelectronic devices, their ultralow thermal conductivity might pose thermal management challenges for practical applications since poor heat dissipation will cause unstable performance and shorter lifespan. Our study also indicates that it is important to achieve high crystalline quality for self-assembled nanostructures, not only for improving carrier transport, but also for enhancing thermal stability of the nanoelectronic devices.

Acknowledgements

D. X. acknowledges the financial support from the National Natural Science Foundation of China (51276153) and the Research Grants Council of the Hong Kong Special Administrative Region, China, under Theme-based Research Scheme (Project No. T23-407/13-N). J. Y. acknowledges the financial support from the Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201413) and the Fundamental Research Funds for the Central Universities.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra14042d

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