The efficient management of heat is crucial for numerous applications, ranging from advanced electronics to energy storage devices. Low-dimensional materials like carbon nanotubes (CNTs) possess high thermal conductivity, making them promising candidates for thermal management applications. However, the interfaces between these nanomaterials introduce significant thermal resistance, known as thermal contact resistance (TCR), which often dominates the overall thermal resistance. Understanding and controlling TCR at nanoscale contacts is therefore critical for optimizing the performance of these materials. Previous studies using molecular dynamics (MD) simulations have explored the influence of contact configurations (parallel vs. cross-contact, spacing, angle) and surface modifications on TCR. These studies showed significant variations in TCR depending on these factors. However, experimental studies directly measuring TCR at single CNT contacts have been limited due to experimental challenges. While previous experimental techniques like the micro-thermal bridge method have been used, they suffer from limitations such as difficulty in individual sample thermal conductivity measurement, inability to dynamically adjust contact morphology, and uncertainties caused by inherent variations in nanoscale samples. This study addresses these limitations by integrating a novel in-situ measurement approach to comprehensively investigate the effects of contact morphology on TCR at single CNT junctions.

Existing literature extensively utilizes molecular dynamics (MD) simulations to investigate the impact of contact configuration on thermal transport across CNT junctions. Zhong and Lukes demonstrated a four-order-of-magnitude increase in TCR per unit area as nanotube spacing increased. Hu et al. and Chen et al. showed that TCR decreases with decreasing crossing angle in cross-contacted CNTs. Studies also explored the impact of surface modifications, such as polymer wrapping or metal coatings, showing significant TCR reduction. However, direct experimental measurements of TCR at single CNT contacts have been scarce, with limitations arising from the difficulty of precisely controlling contact conditions at the nanoscale and the need to measure the thermal conductivity of each CNT individually. While methods such as micro-thermal bridge and micro-Raman-based temperature mapping have been used, they face difficulties such as fixing the samples, which hinder the ability to systematically study the effects of contact morphology. The lack of a comprehensive study on the morphology effect on TCR remains a gap in the literature.

This research employs a novel in-situ measurement technique integrating a movable nano-manipulator within a scanning electron microscope (SEM) with a nanofabricated thermal sensor. Two CNTs are attached to the manipulator and the sensor, respectively, using electron-beam induced deposition (EBID). The Pt nanofilm sensor acts as both a Joule heater and resistance thermometer. By manipulating the probe, the researchers precisely control the contact morphology (contact position, crossing angle, overlapping length) between the same pair of CNTs in real-time while simultaneously measuring the TCR. The SEM provides high-resolution images of the contact morphology, enabling a direct correlation between structure and thermal properties. Before contact, the thermal conductivity of the Pt film is calibrated using a parabolic temperature profile established along the film by applying a direct current. The temperature rise of the nanofilm is measured before and after contact to determine the total thermal resistance. After measuring the total thermal resistance for various morphologies, the CNTs are separated, and the thermal resistance of each CNT is measured individually using the same method. TCR is then calculated by subtracting the individual CNT resistances from the total resistance. The methodology employs a well-defined heat diffusion model to calculate the interfacial thermal conductance per unit length and the contact area for both cross-contact and aligned-contact morphologies. A novel method is used to estimate the van der Waals (vdW) contact area, considering the 3D interaction between CNT layers. The equilibrium distance between CNTs (0.24 nm) and a cutoff distance for vdW interaction (1 nm) are used to determine the contact area.

The study revealed significant variations in TCR across different contact morphologies, even for the same pair of CNTs. The TCR spanned two orders of magnitude, emphasizing the strong influence of morphology. Contact-through-contamination morphologies showed TCR 2-4 times higher than aligned or cross-contact morphologies. For aligned-contact morphologies, a heat diffusion model was developed, resulting in an interfacial thermal conductance per unit length of approximately 0.02 W m⁻¹ K⁻¹. A unified definition of the vdW contact area was proposed for both cross-contact and aligned-contact morphologies, with the aligned-contact area significantly larger than the cross-contact area. The TCR per unit vdW contact area was approximately 3.60 × 10⁻⁷ m² K W⁻¹ for aligned contacts, two orders of magnitude higher than cross contacts. This difference is attributed to non-uniform contact quality along the aligned contact segment. The study also found a weaker dependence of TCR on crossing angle than predicted by simulations, attributable to the inevitable presence of defects in real samples. The thermal conductivity of each individual CNT was also measured, revealing a significant difference between the two CNTs due to structural differences observed through TEM imaging (594.8 ± 94.1 W m⁻¹ K⁻¹ for MWCNT-1 and 14.5 ± 1.3 W m⁻¹ K⁻¹ for MWCNT-2).

This study's findings directly address the need for a better understanding of TCR in CNT-based thermal management applications. The observed significant variation in TCR with morphology directly impacts the design and optimization of such applications. The development of a heat diffusion model for aligned-contact morphologies and a unified definition for vdW contact area provide valuable tools for future studies and modeling efforts. The discrepancy between the experimental findings and simulation predictions highlight the importance of considering the realistic structural imperfections and surface contamination prevalent in experimental samples. The two-order-of-magnitude difference in TCR per unit area between aligned and cross-contact morphologies emphasizes the critical role of contact quality and geometry in determining overall thermal performance. This underscores the need for precise control over CNT contact conditions during fabrication to optimize thermal transport. The in-situ measurement approach provides a powerful platform for studying nanoscale heat transfer mechanisms. Future work could focus on extending the methodology to other 1D and 2D materials and exploring the effects of different surface treatments and external stimuli on TCR.

This research presents a novel in-situ SEM-based approach for measuring and analyzing thermal transport across CNT contacts. The study highlights the significant influence of contact morphology on TCR, emphasizing the need for precise control over contact conditions. The development of a heat diffusion model for aligned contacts and a unified vdW contact area definition provide valuable tools for future research. This work advances the understanding of nanoscale heat transfer, providing valuable guidance for developing high-performance thermally conductive materials. Future work could explore the impact of different surface modifications and external forces on TCR, and extend the methodology to other nanomaterials.

While this study provides a significant advancement in understanding thermal transport at CNT contacts, some limitations exist. The sample size is relatively small, limiting the statistical robustness of some findings. The estimation of the vdW contact area relies on several assumptions, which might introduce uncertainties. The study primarily focuses on multiwalled CNTs; applying the findings to single-walled CNTs or other nanomaterials requires further investigation. The effects of long-term stability and potential changes in contact morphology during measurement are not fully explored.