Thermal Percolation Threshold Research Articles

Cryogenic characteristics of graphene composites—evolution from thermal conductors to thermal insulators

The development of cryogenic semiconductor electronics and superconducting quantum computing requires composite materials that can provide both thermal conduction and thermal insulation. We demonstrated that at cryogenic temperatures, the thermal conductivity of graphene composites can be both higher and lower than that of the reference pristine epoxy, depending on the graphene filler loading and temperature. There exists a well-defined cross-over temperature—above it, the thermal conductivity of composites increases with the addition of graphene; below it, the thermal conductivity decreases with the addition of graphene. The counter-intuitive trend was explained by the specificity of heat conduction at low temperatures: graphene fillers can serve as, both, the scattering centers for phonons in the matrix material and as the conduits of heat. We offer a physical model that explains the experimental trends by the increasing effect of the thermal boundary resistance at cryogenic temperatures and the anomalous thermal percolation threshold, which becomes temperature dependent. The obtained results suggest the possibility of using graphene composites for, both, removing the heat and thermally insulating components at cryogenic temperatures—a capability important for quantum computing and cryogenically cooled conventional electronics.

High-Thermal-Conductivity and High-Fluidity Heat Transfer Emulsion with 89 wt % Suspended Liquid Metal Microdroplets.

Colloidal suspensions of thermally conductive particles in a carrier fluid are considered promising heat transfer fluids for various thermal energy transfer applications, such as transportation, plants, electronics, and renewable energy systems. The thermal conductivity (k) of the particle-suspended fluids can be improved substantially by increasing the concentration of conductive particles above a "thermal percolation threshold," which is limited because of the vitrification of the resulting fluid at the high particle loadings. In this study, eutectic Ga-In liquid metal (LM) was employed as a soft high-k filler dispersed as microdroplets at high loadings in paraffin oil (as a carrier fluid) to produce an emulsion-type heat transfer fluid with the combined advantages of high thermal conductivity and high fluidity. Two types of the LM-in-oil emulsions, which were produced via the probe-sonication and rotor-stator homogenization (RSH) methods, demonstrated significant improvements in k, i.e., Δk ∼409 and ∼261%, respectively, at the maximum investigated LM loading of 50 vol % (∼89 wt %), attributed to the enhanced heat transport via high-k LM fillers above the percolation threshold. Despite the high filler loading, the RSH-produced emulsion retained remarkably high fluidity, with a relatively low viscosity increase and no yield stress, demonstrating its potential as a circulatable heat transfer fluid.

Thermal and dielectric multiple percolation in α‐Si3N4 whiskers/silicone rubber

Currently, thermal interfacial materials (TIMs) play a great role to electronic and semiconductor devices working at high voltage, power and frequency. The urgent need for electrical insulating TIMs and relevant theory are not addressed yet. This study adopted an electrical insulating α-Si3N4 whisker as a filler to prepare Si3N4w/silicone rubber. The results show that the elongation at break and thermal conductivity of silicone rubber are promoted from 91.6% and 0.343 to 402.9% and 1.011 W m−1 K−1, respectively, at a filler fraction of 8.0 vol%. It reveals a multiple percolation phenomenon which has not been previously observed in an electrical insulating TIMs. The thermal percolation threshold is decreased to 4.0 vol% with increasing aspect ratio of the whisker. The behavior of the dielectric strength is explained by a double percolation model. A phonon quasi-ballistic transportation mechanism based on Coulomb interactions is proposed for the TIMs.

Highly enhanced thermal conductivity from boron nitride nanosheets and MXene phonon resonance in 3D PMMA spheres composites

Efficient thermal management materials are important for the proper operation of integrated circuits. In this work, the high-yield preparation of hydroxylated boron nitride nanosheets (BNNSs) was achieved by high-temperature ablation followed by ultrasonic exfoliation without the use of highly toxic solvents. The small-sized BNNSs have similar phonon vibration properties as the large-sized MXene, and they self-assemble by electrostatic adsorption on PMMA particles to form hybrid spheres. The appearance of thermal percolation threshold indicates the successful construction of thermal conductivity pathway. The exclusion effect is more pronounced for PMMA microspheres with a larger radius, and the best thermal conductivity of 4.13 W/m·K was achieved for the composite with 20 wt% nanosheet filling. The composite exhibited good thermal performance both in the finite element model and when used as an LED heat sink. Furthermore, the incorporation of fillers can also effectively improve the thermal stability and mechanical properties of the composite. Our study provides a facile and environmental exfoliation approach of h-BN and a new strategy for the preparation of high thermal conductivity electronic packaging materials.

Unified modeling and experimental realization of electrical and thermal percolation in polymer composites

Correlations between electrical and thermal conduction in polymer composites are blurred due to the complex contribution of charge and heat carriers at the nanoscale junctions of filler particles. Conflicting reports on the lack or existence of thermal percolation in polymer composites have made it the subject of great controversy for decades. Here, we develop a generalized percolation framework that describes both electrical and thermal conductivity within a remarkably wide range of filler-to-matrix conductivity ratios (Yf/Ym), covering 20 orders of magnitude. Our unified theory provides a genuine classification of electrical conductivity with typical Yf/Ym≥1010 as insulator–conductor percolation with the standard power-law behavior and of thermal conductivity with 102≤Yf/Ym≤104 as poor–good conductor percolation characterized by two universal critical exponents. Experimental verification of the universal and unified features of our theoretical framework is conducted by constructing a 3D segregated and well-extended network of multiwalled carbon nanotubes in polypropylene as a model polymer matrix under a carefully designed fabrication method. We study the evolution of the electrical and thermal conductivity in our fabricated composites at different loading levels up to 5 vol. %. Significantly, we find an ultralow electrical percolation threshold at 0.02 vol. % and a record-low thermal percolation threshold at 1.5 vol. %. We also apply our theoretical model to a number of 23 independent experimental and numerical datasets reported in the literature, including more than 350 data points, for systems with different microscopic details, and show that all collapse onto our proposed universal scaling function, which depends only on dimensionality.

Paraffin/polyacrylonitrile hybrid nanofibers for thermal hysteresis enhancement of paraffin actuators

Fast and facile one-step preparation of paraffin/polyacrylonitrile hybrid nanofibers via single needle (uniaxial) electrospinning system was studied. As-spun paraffin/polyacrylonitrile nanofibers were used for thermal hysteresis enhancement of paraffin actuators. Solid paraffin with the melting point of 32, 58, 89 and 114°C were employed for the preparation of the paraffin/polyacrylonitrile nanofibers. Differential scanning calorimetry measurements revealed that the melting point of the paraffin in paraffin/polyacrylonitrile hybrid nanofiber was clearly detectable and the melting entalpy coming from the paraffin part gradually increased from 9.6 to 101.5 J/g with the increase in the melting points of the added same amount of paraffins in paraffin/polyacrylonitrile nanofibers. When both calorimetric and weight loss measurements were considered, the paraffin which has the melting point of 32°C was found to be suitable to produce hybrid nanofibers paraffin actuator. Therefore, this hybrid nanofiber was selected for the application in paraffin actuators for e-vehicle battery cooling systems where the battery temperature must be kept between 15 and 35°C. Paraffin compound of the paraffin actuators was prepared with a mixture of pure paraffin and paraffin/polyacrylonitrile nanofiber with the wt.% of 2.5, 5, 7.5 and 10. In the hysteresis measurements, the hysteresis value at 3 mm stroke was successfully enhanced as 1.7, 3.4, 11.9 and 15.3% sequentially for the samples produced with the above ratios. Beyond hysteresis enhancement, the phenomena of thermal percolation threshold effect and thermal conductivity contrast ratio effect in nano scale were emprically exposed on opening and closing behavior of the paraffin actuator.

Thermal percolation in mixtures of monodisperse spheres

The connectivity of individual species in a locally heterogeneous granular mixture strongly influences assembly-scale behavior. A behavioral transition is observed at the percolation threshold for a given constituent; that is, the mixing fraction at which the constituent has statistical connectivity between two opposing boundaries. This behavior is particularly evident in conductivity phenomena, e.g., the percolation of conductive particles (thermal, electric) or the relative degree of connectivity of the void space (hydraulic). Hard-core (first nearest-neighbor or lattice) percolation has been extensively studied experimentally, theoretically, and numerically. That hard-core percolation occurs in dense randomly packed bi-phasic mixtures of monodisperse spheres occurs at a mixing fraction of 0.15 v/v is well-accepted. Radiant conduction (e.g., heat), however, is influenced by hard-core “soft-shell” percolation, which is an nth-nearest neighbor problem and less well-studied. In the current work, we use discrete element method simulations coupled with a thermal network model that leverages a robust domain decomposition algorithm to simulate large assemblies of spheres to investigate soft-shell percolation numerically. Our results show that the thermal conductivity of a randomly packed assembly obeys a power law with respect to volume fraction of conductive particles while percolation threshold follows a power law with respect to coordination number. The ability of the pore fluid to transmit heat over a longer distance results in an increase of thermal conductivity and a decrease in thermal percolation threshold. Moreover, we observe that, contrary to previous findings, critical percolation density is not a dimensional invariant and depends on the microstructure of the assembly.

Experimental Investigation of the Melt Shear Viscosity, Specific Volume and Thermal Conductivity of Low-Density Polyethylene/Multi-Walled Carbon Nanotube Composites Using Capillary Flow.

Understanding the flow behavior of polymer/carbon nanotube composites prior to melt processing is important for optimizing the processing conditions and final product properties. In this study, the melt shear viscosity, specific volume and thermal conductivity of low-density polyethylene (LDPE) filled with multi-walled carbon nanotubes (MWCNTs) were investigated for representative processing conditions using capillary rheometry. The experimental results show a significant increase in the melt shear viscosity of the LDPE/MWCNT composite with nanotube loadings higher than 1 wt.%. Upon increasing shear rates, the composites flow like a power-law fluid, with a shear-thinning index less than 0.4. The specific volume decreases with increasing pressure and nanotube loading, while the pVT transition temperature increases linearly with increasing pressure. The thermal conductivity of the LDPE/MWCNT composite is nearly independent of nanotube loading up to the thermal percolation threshold of 1 wt.% and increases linearly with further increases in nanotube loading, reaching 0.35 W/m·K at 5 wt.%. The Carreau–Winter and Cross viscosity models and Tait equation, respectively, are able to predict the shear viscosity and specific volume with a high level of accuracy. These results can be used not only to optimize processing conditions through simulation but also to establish structure–property relationships for the LDPE/MWCNT composites.

Noncuring Graphene Thermal Interface Materials for Advanced Electronics

AbstractDevelopment of next‐generation thermal interface materials (TIMs) with high thermal conductivity is important for thermal management and packaging of electronic devices. The synthesis and thermal conductivity measurements of noncuring thermal paste, i.e., grease, based on mineral oil with a mixture of graphene and few‐layer graphene flakes as the fillers, is reported. The graphene thermal paste exhibits a distinctive thermal percolation threshold with the thermal conductivity revealing a sublinear dependence on the filler loading. This behavior contrasts with the thermal conductivity of curing graphene TIMs, based on epoxy, where superlinear dependence on the filler loading is observed. The performance of the thermal paste is benchmarked against top‐of‐the‐line commercial thermal pastes. The obtained results show that noncuring graphene TIMs outperforms the best commercial pastes in terms of thermal conductivity, at substantially lower filler concentration of φ = 27 vol%. The obtained results shed light on thermal percolation mechanism in noncuring polymeric matrices laden with quasi‐two‐dimensional fillers. Considering recent progress in graphene production via liquid phase exfoliation and oxide reduction, the results open a pathway for large‐scale industrial application of graphene in thermal management of electronics.

Enhanced thermal conductivity of epoxy composites using boron nitride nanoplatelets prepared by Fe3O4 assisted liquid-phase exfoliation

Liquid-phase exfoliation was employed to fabricate BN nanoplatelets (BNNPs) with the assistance of an additional shear force from Fe3O4 nanoparticles. Iron-oxide nanoparticles vibrated between BN layers and bulk BN particles were exfoliated into nanoplatelets. A thermally conductive composite was fabricated by the incorporation of the resultant BNNP into an epoxy matrix. After exfoliation, BNNP exhibited better dispersion in the polymer composite compared to bulk BN due to the reduced mean interparticle distances. Thus, the introduction of BNNP enables the decrease in the thermal percolation threshold via the formation of heat flow paths and enhancement of the thermal conductivity by 480% with the addition of a filler content of 30 wt%.

Thermal Percolation Threshold and Thermal Properties of Composites with High Loading of Graphene and Boron Nitride Fillers.

We investigated thermal properties of the epoxy-based composites with the high loading fraction-up to f ≈ 45 vol %-of the randomly oriented electrically conductive graphene fillers and electrically insulating boron nitride fillers. It was found that both types of the composites revealed a distinctive thermal percolation threshold at the loading fraction fT > 20 vol %. The graphene loading required for achieving thermal percolation, fT, was substantially higher than the loading, fE, for electrical percolation. Graphene fillers outperformed boron nitride fillers in the thermal conductivity enhancement. It was established that thermal transport in composites with high filler loadings, f ≥ fT, is dominated by heat conduction via the network of percolating fillers. Unexpectedly, we determined that the thermal transport properties of the high loading composites were influenced strongly by the cross-plane thermal conductivity of the quasi-two-dimensional fillers. The obtained results shed light on the debated mechanism of the thermal percolation, and facilitate the development of the next generation of the efficient thermal interface materials for electronic applications.

Carbonization temperature controlled thermal conductivity of graphitic carbon nanoparticles and their polymer composites

Carbon materials as versatile fillers have drawn increasing attention in thermal conductive polymer composites, however, the thermal conductivity (TC) regulation of them remains challenging. Herein, the tunable lattice thermal conductivity is reported for glucose derived graphitic carbon nanoparticles (GCPs) and their polymer composites. Both the in-plane (La) and out-of-plane (Lc) coherence lengths of GCPs increase with carbonization temperature in the range of 700 °C to 1300 °C. The intrinsic TC of GCPs film is directly extracted from the dependence of the Raman G peak frequency on the excitation laser power and the first order temperature coefficient. It is found that the in-plane lattice TC increases exponentially with both of the increasing La and decreasing defect concentration. The GCPs are then used as highly processible fillers to fabricate thermoset composites based on reactive benzoxazine (BA-a). The total TC of the poly(BA-a)/GCPs are found increase monotonically from 0.27 W·m-1·K-1 to 0.34 W·m-1·K-1 with the increasing graphitization levels of GCPs, and a clear signature of thermal percolation threshold at 6 vol% GCPs loadings is also observed.

Temperature-Dependent Thermal Conductivity Study of MAPbI3: Using Mild Aging To Reach a Thermal Percolation Threshold for Greatly Improved Heat Transport

We report the thermal conductivity in the range from 7 to 300 K for methylammonium lead triiodide (MAPbI3) perovskite in different stages of environmental degradation. The results showed that thermal conductivity of the degraded perovskite pellet quickly approached that of lead iodide rather than pure MAPbI3, even while X-ray diffraction data of the degraded perovskite showed mostly peaks of the perovskite phase, alongside minor peaks from impurity phases belonging to the precursors and to an intermediate phase. For reference, a sample of pure lead iodide was also prepared and analyzed in the same way, and to our knowledge, thermal conductivity for lead iodide in the 7–300 K temperature range has not yet been published. The combination of thermal conductivity and materials characterization provides more detailed knowledge of the composition and structural changes of aged MAPbI3 perovskite. Moreover, we demonstrate that a thermal percolation threshold can be achieved through mild aging while preserving mos...

Massive enhancement in the thermal conductivity of polymer composites by trapping graphene at the interface of a polymer blend

Trapping graphene at the interface of a poly(ε-caprolactone) (PCL)/poly(lactic acid) (PLA) blend is achieved through the adsorption-desorption of polymer chains on the graphene surface. The resulting composite exhibits remarkably high thermal conductivity due to the graphene sheets being controlled at the interface of the polymer blend. At 0.53 vol%, when a good co-continuous structure is formed, the thermal conductivity of the graphene composite is nearly 4 times higher than that of the pure PCL/PLA blend with co-continuous structure. Moreover, the blend achieves an extremely low thermal percolation threshold (0.11 vol%), the lowest to date, because most of the graphene sheets are selectively located at the interface of the blend with co-continuous structure.

Highly conductive Poly(L-lactic acid) composites obtained via in situ expansion of graphite

In this work, highly electrically and thermally conductive biopolymer composites were prepared by low-temperature expandable graphite (EG) filling Poly(L-lactic acid) (PLLA) via an in situ exfoliation melt blending process. The electrical conductivity of the composites with various graphite contents was measured by a four-point probe resistivity determiner and a high value of 0.37 S/cm was obtained at 70 wt.% EG content. A hot-disk method was used to evaluate the thermal conductivity of the composites. At EG loading fraction of 70%, thermal conductivity of PLLA/EG composites reached to the highest 26.87 W/mK, which is 100 times higher than neat PLLA. The electrical percolation was observed in the vicinity of the thermal percolation threshold concentration. The expansion of EG was crucial to the overall conductivity of the blends, which was confirmed by X-ray diffraction (XRD) analysis and scanning electron microscope (SEM). Dynamic rheology analysis was applied to study the structural change by the interconnection of the exfoliated graphite flakes and the formation of the networks in the blends. Thermogravimetric analysis (TGA) was employed to determine the thermal properties of the investigated PLLA/EG composites.

Thermally Conductive Graphene-Polymer Composites: Size, Percolation, and Synergy Effects

The rapidly increasing device densities in electronics dictate the need for efficient thermal management. If successfully exploited, graphene, which possesses extraordinary thermal properties, can be commercially utilized in polymer composites with ultrahigh thermal conductivity (TC). The total potential of graphene to enhance TC, however, is restricted by the large interfacial thermal resistance between the polymer mediated graphene boundaries. We report a facile and scalable dispersion of commercially available graphene nanoplatelets (GnPs) in a polymer matrix, which formed composite with an ultrahigh TC of 12.4 W/m K (vs 0.2 W/m K for neat polymer). This ultrahigh TC was achieved by applying high compression forces during the dispersion that resulted in the closure of gaps between adjacent GnPs with large lateral dimensions and low defect densities. We also found strong evidence for the existence of a thermal percolation threshold. Finally, the addition of electrically insulating boron-nitride nanopart...

Combined photothermal and photoacoustic characterization of silicon–epoxy composites and the existence of a particle thermal percolation threshold

Photoacoustic (PA) and photothermal radiometric (PTR) detection were used to characterize thermal properties of silicon–epoxy composite materials in the volume range 0%< x<32 vol% ( 50 μm ). PA detection was used to study the variation of the thermal diffusivity as a function of Si volume fraction, and PTR was used to determine the influence of the electronic carrier contribution to the thermal transport with the optical properties taken into consideration. The combined PA and PTR measurements show that there exists no linear relation between thermal diffusivity and silicon volume fraction. Thermal diffusivity and optical absorption coefficient measurements can be obtained by means of combined PA and PTR measurements. Both parameters exhibit anomalous behavior in the 16% Si volume fraction range, corroborating the existence of a particle percolation threshold for three-dimensional random close packed (rcp) solids.