Thermal Percolation Research Articles

Sorption kinetics of salt-in-porous-matrix composites: The effect of expanded natural graphite on cooling power

Sorption heat transformers and thermal energy storage systems are emerging technologies that utilize and store low-grade waste heat for heating and cooling applications. The performance of sorption systems is not only affected by systems’ operating conditions, and overall systems’ design but also by sorption material or composite parameters such as thermal diffusivity, composition, and pore structure, among others. In this study, CaCl2-based salt-in-porous-matrix composites of different compositions and coating thicknesses were synthesized. During synthesis, salt to silica gel and polyvinyl alcohol to silica gel ratios were fixed and the thermal additive (expanded natural graphite) to silica gel ratio was varied with care from 0 to 0.26 (or 0 to 20.5 wt.%, additive to silica gel ratio). The thickness of samples varied from 2.3 to 8.3 ± 0.1 mm. The composites were characterized by a transient plane source (thermal conductivity and thermal diffusivity), nitrogen adsorption porosimetry (specific surface area and total pore volume), and thermogravimetric sorption analysis (water sorption equilibrium) methods. A custom-built gravimetric large pressure jump (G-LPJ) testbed was used to study water sorption kinetics (water uptake vs. time) for selected samples. The thermal conductivity and diffusivity of the studied composite samples have shown significant enhancements, e.g., 240% (0.11 W/(m·K) vs. 0.37 W/(m·K)) and 310% (0.21 mm2/s vs. 0.87 mm2/s), respectively, by adding 12.5 wt.% expanded natural graphite (additive to silica gel ratio is 0.14) as a thermally conductive additive (additive to silica gel ratio) because of thermal percolation effect. This ratio of expanded natural graphite to silica gel was found to be optimal for studied composition. The results indicate that sorption composites with higher thermal diffusivity offer notably higher specific cooling power and improved sorption kinetics, compared to the composites without expanded natural graphite of the same thickness (850 W/kg vs. 480 W/kg at 70% water conversion for samples with thickness of 5.3 mm).

Metal ion-crosslinked thermoconductive sugar-functionalized graphene fluoride-based cellulose papers with enhanced mechanical properties and electrical insulation

Thermally conductive papers with electrical insulation and mechanical robustness are essential for efficient thermal management in modern electronics. In this study, we introduced a metal ion-assisted interfacial crosslinking strategy to strengthen sugar-functionalized graphene fluoride (SGF) and cellulose nanofibers (CNF) by hydrogen bonding and metal ion crosslinking that leads to simultaneous enhancements in thermal conductivity and mechanical properties. The facile sugar-assisted ball-milling exfoliation method was developed to achieve the exfoliation of graphite fluoride and hydroxyl group functionalization on the surface of graphene fluoride. Thanks to the good dispersibility of the SGF sheets in water, the flexible SGF/CNF composite papers with hydrogen bonding were prepared via vacuum-assisted filtration. We introduced hydrogen bonding and metal ion crosslinking into SGF/CNF papers to obtain densely packed composite papers. Ca2+ or Al3+ ion-crosslinked SGF/ CNF papers exhibited superior thermal and mechanical properties owing to hydrogen bonding and metal ion crosslinking. SGF/CNF-Ca2+ and SGF/CNF-Al3+ papers at 50 wt% of SGF yield in-plane thermal conductivities of 72.93 and 75.02 W m–1 K–1, and tensile strengths of 121.5 and 135.7 MPa, respectively. A thermal percolation value was observed at 12.6 vol% of SGF filler content. In addition, the SGF/CNF papers exhibited electrical insulation properties. These remarkable characteristics of the metal ion-crosslinked SGF/CNF papers are attributed to the densely packed structures caused by the strong interfacial interactions from hydrogen bonding as well as metal ion-crosslinking that could promote phonon transport. High-performance metal ion-crosslinked SGF/CNF papers with these fascinating advantages offer great potential for the thermal management of flexible electronics.

Significantly Enhanced Thermal Conductivity of hBN/PTFE Composites: A Comprehensive Study of Filler Size and Dispersion.

High-temperature polymers are attractive for applications in extreme temperatures, where they maintain their mechanical flexibility and electrical insulating properties. However, their heat dissipation capability is limited due to their intrinsically low thermal conductivities. Hexagonal boron nitride (hBN) is a chemically inert, thermally stable, and electrically insulative compound with a high thermal conductivity, making it an ideal candidate as a filler within a high-temperature polymer matrix to increase the thermal conductivity. This study evaluates the effect of filler size and dispersion on thermal conductivity by producing homogeneous composite samples using a combination of solvent mixing and resonant acoustic mixing (RAM). We carefully characterized our samples, including the spread of the size distribution, and observed that the smaller sized hBN centered around 5 μm was able to integrate more seamlessly into the polytetrafluoroethylene (PTFE) matrix with particle size in the 15 μm range and hence outperformed 30 μm, in contrast to the conventional wisdom, which asserts that larger fillers universally perform better than smaller ones. Our thermal conductivity of hBN/PTFE composites at 30 wt % is 2× higher than the literature values. Notably, we reached the record-high value of 3.5 W/m K at 40 wt % with an onset of percolation at 20 wt %, attributed to optimized hBN dispersion that facilitates the formation of thermal percolation. Our findings provide general guidelines to enhance the thermal conductivity of polymer composites for thermal management, ranging from power transmission to microelectronics cooling.

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

AbstractCurrently, 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.

Thermal percolation in a magnetic field responsive composite

The effect of thermal percolation in a magnetic fluid composite was found when changing the content of conducting microparticles in a low-conducting medium. It is shown that the effect of the magnetic field on the thermal conductivity of the composite material is significant at the concentration of conducting microparticles above the percolation threshold and much less pronounced otherwise. The relative increase in thermal conductivity can exceed 600% under the influence of a magnetic field parallel to the heat flux and is achieved in fields of intensity <10 kA/m at a volume concentration of conducting microparticles of 0.25.

Thermal percolation network in alumina based thermal conductive polymer

Polymers incorporated with high thermal conductivity fillers have numerous applications in thermal interface materials. Plenty of efforts have been made to improve the thermal conductivity of polymer composite. A possible method is to choose fillers with different morphologies, which can combine the advantages of various fillers. However, owing to the limitations of the effective medium theory as well as lack of researches of thermal percolation, there is still little understanding of the synergistic mechanism of fillers with different morphologies. In order to avoid the coupling effect of different materials, this work uses the same kind of alumina but with different morphologies to prepare different kinds of epoxy composites incorporated with spherical alumina, plate-like alumina and fillers mixed of 1:1 ratio. The thermal conductivity of each sample is measured by the steady state method. With the fitting of the thermal percolation theory, the synergistic effect of plate-like fillers and that of spherical fillers are verified to promote the formation of thermal percolation network. In addition, by observing the microscopic distribution of fillers, we try to explain the mechanism of this synergistic effect.

Thermal percolation network in Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; based thermal conductive polymer

Polymers incorporated with high thermal conductivity fillers have numerous applications in thermal interface materials. Plenty of efforts have been made to improve the thermal conductivity of polymer composite. A possible method is to choose fillers with different morphologies, which can combine the advantages of various fillers. However, owing to the limitations of the effective medium theory as well as lack of researches of thermal percolation, there is still little understanding of the synergistic mechanism of fillers with different morphologies. In order to avoid the coupling effect of different materials, this work uses the same kind of Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; but with different morphologies to prepare different kinds of epoxy composites incorporated with spherical Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;, plate-like Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; and fillers mixed of 1∶1 ratio. The thermal conductivity of each sample is measured by the steady state method. With the fitting of the thermal percolation theory, the synergistic effect of plate-like fillers and that of spherical fillers are verified to promote the formation of thermal percolation network. In addition, by observing the microscopic distribution of fillers, we try to explain the mechanism of this synergistic effect.

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.

Enhancement of thermal percolation in composites: A two-dimensional case study

We investigated the thermal conductivity (TC) of a two-dimensional composite consisting of matrices with low TC and nanowire fillers with high TC using the Monte Carlo method and the finite element method. Compared to the electrical percolation that requires direct contact between fillers, an additional thermal transport channel through non-contact fillers is found to be important for the thermal percolation in composites. This additional channel can lead to an effective expansion of thermal percolation network by including extra fillers into the network. Thus, it can be utilized to enhance the TC of the composite that is helpful to improve the performance of thermal interface materials.

Thermal Percolation of Antiperovskite Superionic Conductor into Porous MXene Scaffold for High-Capacity and Stable Lithium Metal Battery.

Lithium metal battery is considered an emerging energy storage technology due to its high theoretical capacity and low electrochemical potential. However, the practical exploitations of lithium metal batteries are not realized because of uncontrollable lithium deposition and severe dendrite formation. Herein, a thermal percolation strategy is developed to fabricate a dual-conductive framework using electronically conductive Ti3 C2 Tx MXene aerogels (MXAs) and Li2 OHCl antiperovskite superionic conductor. By melting Li2 OHCl at a low temperature, the molten antiperovskite phase can penetrate the MXA scaffold, resulting in percolative electron/ion pathways. Through density functional theory calculations and electrochemical characterizations, the hybridized lithiophilic (MXA)-lithiophobic (antiperovskite) interfaces can spatially guide the deposition of lithium metals and suppress the growth of lithium dendrites. The symmetric cell with MXA-antiperovskite electrodes exhibits superior cycling stability at high areal capacities of 4 mAh cm-2 over 1000 h. Moreover, the full cell with MXA-antiperovskite anode and high-loading LiFePO4 cathode demonstrates high energy and power densities (415.7Wh kgcell -1 and 231.0W kgcell -1 ) with ultralong lifespans. The thermal percolation of lithium superionic conductor into electronically conductive scaffolds promises an efficient strategy to fabricate dual-conductive electrodes, which benefits the development of dendrite-free lithium metal anodes with high energy/power densities.

Multiscale modeling of thermal conductivity of hierarchical CNT-polymer nanocomposite system with progressive agglomeration

Agglomeration of carbon nanotubes (CNTs) is a key phenomenon that affects the effective thermal conductivity of CNT-polymer nanocomposites. This issue needs to be adequately studied especially in the practice of prediction of the effective thermal properties of CNT nanocomposites. In this study, we developed a multiscale model within the framework of effective medium theory to predict the effect of CNT agglomeration on the overall thermal conductivity of the hierarchical CNT-polymer nanocomposite system over a wide range of CNT loading. With an introduced Cauchy cumulative probability function, we developed a new model of CNT agglomeration wherein the CNT volume fraction progressively evolves with the total loading of the CNT fillers in the composite. This model is self-consistent and it leads to a very good agreement with experimental observations. The entire multiscale approach consists of the newly developed model of the progressive agglomeration as well as models that altogether take into account the effect of two types of CNT interfacial thermal resistance and the unique feature of the CNT nanostructure. We highlighted this multiscale approach with its implementation in the prediction of the overall thermal conductivity. Good agreement was confirmed between the prediction and the experimental data. The study shows that the existence of CNT agglomerates downgrades the thermal percolation networks and it can cause a decrease up to 50% in the overall thermal conductivity of the nanocomposite. Two important parameters for the progressive agglomeration model were identified and their influences to the predicted results were examined.

Electrical and thermal percolation in two-phase materials: A perspective

Electrical percolation in two-phase materials involves a very singular behavior, manifested as a huge change in the electrical conductivity, for a given volume or mass fraction of the phase with higher conductivity. In contrast, in the case of heat transfer, in two-phase composite systems, analogous percolative phenomena are far more elusive and have been rather difficult to observe in various physical systems. In this Perspective, we present a critical analysis of experimental results and the application of theoretical models aimed to study the effects of percolation phenomena on the thermal and electrical properties of two-phase materials. Our attention will be focused on composites made of high conductivity particles in a polymeric matrix. The effect of several factors, such as the geometrical and physical characteristics of fillers and their connectivity with the matrix, the proportion between the conductivity of filler and the matrix, as well as the crucial role of interfacial thermal resistance, is considered. In particular, the differences between the thermal and electrical thresholds and the physical and geometrical conditions that should be fulfilled to observe thermal percolation are discussed. Future trends, to be followed in the development of new materials, in order to enhance the thermal conductivity as well as in making the thermal percolative effects notable, based on including additional phases and 2D fillers, are also discussed.

High-Temperature Thermal Transport Properties of Multifunctional PTFE/PEEK-Matrix Composite With Short Carbon Fibers and Graphite Flakes

Abstract A combined experimental and theoretical investigation is conducted on elevated-temperature thermal transport properties of a multifunctional polytetrafluoroethylene (PTFE)/polyetheretherketone (PEEK) matrix composite containing short carbon fibers and graphite flakes. In experiments, X-ray diffraction (XRD), scanning electron microscope (SEM), and optical microscopy are used to determine morphologies and microstructure of neat PTFE and PEEK polymers, PTFE/PEEK blend, and individual PTFE and PEEK phases in the carbon fiber (CF)Gr/PTFE/PEEK composite. Microstructure parameters determined are used in subsequent analytical modeling and predictions. Effective heat capacity and thermal conductivities of the composite and its polymer matrix are determined by a modulated differential scanning calorimetry (MDSC) method with temperature up to 225 °C. The results show that thermal transport properties of the composite are significantly affected by temperature and polymer transitions. The carbon fibers and graphite in the composite improve its mechanical and tribological performance and also enhances heat conduction. Thermal diffusivity of the composite, however, is governed by the PTFE/PEEK matrix due to its high thermal capacity. In the theoretical/analytical study, thermodynamic considerations are made at both molecular and micromechanical levels. Theoretical models and micromechanics analyses are used to determine effective thermal transport properties of the composite. The results clarify the roles of individual constituents and temperature effects on the composite thermal transport. Thermal percolation predictions compare well with experimental data; they also reveal that 10% (by volume) graphite lubricant in the carbon fiber-reinforced PTFE/PEEK composite leads to formation of effective thermal conductive networks, which rapidly increases thermal percolation due to their high efficiency of thermal transport.

Thermal Percolation in Well-Defined Nanocomposite Thin Films.

Thermal percolation in polymer nanocomposites─the rapid increase in thermal transport due to the formation of networks among fillers─is the subject of great interest in thermal management ranging from general utility in multifunctional nanocomposites to high-conductivity applications such as thermal interface materials. However, It remains a challenging subject encompassing both experimental and modeling hurdles. Successful reports of thermal percolation are exclusively found in high-aspect-ratio, conductive fillers such as graphene, albeit at filler loadings significantly higher than the electrical percolation threshold. This anomaly was attributed to the lower filler-matrix thermal conductivity contrast ratio kf/km ∼104 compared to electrical conductivity ∼1012-1016. In a randomly dispersed composite, the effect of a low contrast ratio is further accentuated by uncertainties in the morphology of the percolating network and presence of other phases such as disconnected aggregates and colloidal dispersions. Thus, the general properties of percolating networks are convoluted as they lack a defined structure. In contrast, a prototypical system with controllable nanofiller placement enables the elucidation of structure-property relations such as filler size, loading, and assembly. Using self-assembled nanocomposites with a controlled 1,2,3-dimension nanoparticle (NP) arrangement, we demonstrate that thermal percolation can be achieved in spite of using spherical, nonconductive fillers (kf/km ∼60) at a low volume fraction (9 vol %). We observe that the effects of volume fraction, interfacial thermal resistance, and filler conductivity on thermal conductivity depart from effective medium approximations. Most notably, contrast ratio plays a minor role in thermal percolation above kf/km ∼60─a common range for semiconducting nanoparticles/polymer ratios. Our findings bring new perspectives and insights to thermal percolation in nanocomposites, where the limits in contrast ratio, interfacial thermal conductance, and filler size are established.

Enhanced thermal conductivity of graphene nanoplatelet filled polymer composite based on thermal percolation behavior

The demand for lightweight heat-dissipating composites has increased interest in strategies to improve the thermal conductivity of polymer composites by incorporating nanocarbon fillers. In this study, composite incorporating uniformly dispersed high content (∼50 wt%) of graphene nanoplatelet was fabricated with low-viscosity polyamide 6 (PA6) resin. The measured thermal conductivity of the composite exhibited thermal percolation when GNP content exceeded 30 wt%, and the in-plane thermal conductivity improved to 19.39 W/m·K (1315% increase compared to neat PA6) at the filler content of 50 wt%. In addition, thermal conductivity of the prepared composites was in good agreement with theoretical results based on Nan's model (filler content of 0–30 wt%) considering interfacial thermal resistance and the percolation equation (filler content of 40–50 wt%) considering a connected filler network. It was confirmed that thermal percolation was generated due to contacts and network formation between fillers in the fabricated composites using an internal structure analysis. Potential insights on the design, manufacture, and application of nanocomposites exhibiting heat dissipation performance can be provided by composite systems using low-viscosity resin and theoretical evaluation methods.

Thermal Percolation Behavior in Thermal Conductivity of Polymer Nanocomposite with Lateral Size of Graphene Nanoplatelet.

In this study, the thermal percolation behavior for the thermal conductivity of nanocomposites according to the lateral size of graphene nanoplatelets (GNPs) was studied. When the amount of GNPs reached the critical concentration, a rapid increase in thermal conductivity and thermal percolation behavior of the nanocomposites were induced by the GNP network. Interestingly, as the size of GNPs increased, higher thermal conductivity and a lower percolation threshold were observed. The in-plane thermal conductivity of the nanocomposite containing 30 wt.% M25 GNP (the largest size) was 8.094 W/m·K, and it was improved by 1518.8% compared to the polymer matrix. These experimentally obtained thermal conductivity results for below and above the critical content were theoretically explained by applying Nan’s model and the percolation model, respectively, in relation to the GNP size. The thermal percolation behavior according to the GNP size identified in this study can provide insight into the design of nanocomposite materials with excellent heat dissipation properties.

Cluster approach to ferromagnetic Ising-type model for spin-crossover systems

A cluster approach to ferromagnetic Ising-type model for spin-crossover systems is developed via the ghost bonds method, and exact relations between some thermal quantities and percolation variables are obtained. Simulations by the Swendsen-Wang cluster MC dynamics for 2D systems show an agreement between the clusters properties and the thermal quantities.