We investigated thermal properties of the epoxy-based composites with a high loading fractionup to ≈ 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 > 20 vol. %. The graphene loading required for achieving the thermal percolation, , was substantially higher than the loading, , for the electrical percolation. Graphene fillers outperformed boron nitride fillers in the thermal conductivity enhancement. It was established that thermal transport in composites with the high filler loading, ≥ , 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-twodimensional fillers. The obtained results shed light on the debated mechanism of the thermal × Contributed equally to the work. * Corresponding author (A.A.B.): balandin@ece.ucr.edu ; web-site: http://balandingroup.ucr.edu/ Thermal Percolation Threshold and Thermal Properties of Composites with Graphene and Boron Nitride Fillers, UCR (2018) 2 | P a g e percolation, and facilitate the development of the next generation of the efficient thermal interface materials for electronic applications. Main TextThe discovery of unique heat conduction properties of graphene 1-7 motivated numerous practically oriented studies of the use of graphene and few-layer graphene (FLG) in various composites, thermal interface materials and coatings [8][9][10][11][12][13][14][15] . The intrinsic thermal conductivity of large graphene layers exceeds that of the high-quality bulk graphite, which by itself is very high -2000 Wm −1 K −1 at room temperature (RT) 1,11,16,17 . The first studies of graphene composites found that even a small loading fractions of randomly oriented graphene fillers -up to = 10 vol. %can increase the thermal conductivity of epoxy composites by up to a factor of ×25 [Ref. 11]. These results have been independently confirmed by different research groups 18,19 . The variations in the reported thermal data for graphene composites can be explained by the differences in the methods of preparation, matrix materials, quality of graphene, lateral sizes and thickness of graphene fillers and other factors 3,20-25 . Most of the studies of thermal composites with graphene were limited to the relatively low loading fractions, ≤ 10 vol. %. The latter was due to difficulties in preparation of high-loading fraction composites with a uniform dispersion of graphene flakes. The changes in viscosity and graphene flake agglomeration complicated synthesis of the consistent set of samples with the loading substantially above = 10 vol. %.Investigation of thermal properties of composites with the high loading fraction of graphene or FLG fillers is interesting from both fundamental science and practical applicat...

and environment. [12][13][14] The current industrial and safety standards require blocking of more than 99% of the EM radiation from any electronic devices. [1,[15][16][17] From the other side, the operation of the electronic devices can be disrupted by the outside EM waves. The heat and EM radiation have an inherent connection-absorption of EM waves by any material results in its heating. The energy from EM wave transfers to electrons and then to phonons-quanta of crystal lattice vibrations. The conventional approach for handling the heat and EM radiation problems is based on utilization of the thermal interface materials (TIM), which can spread the heat, and electromagnetic interference (EMI) shielding materials, which can protect from EM waves. These two types of materials have different, and, often, opposite characteristics, e.g., excellent EMI material can be a poor heat conductor, while efficient TIM can utilize electrically nonconductive fillers, resulting in its transparency for EM waves. Here, we propose a concept of the "dual-functional" EMI shielding-TIM materials, and demonstrate it on the example of graphene composites.It is well known that EMI shielding requires interaction of the EM waves with the charge carriers inside the material so that EM radiation is reflected or absorbed. For this reason, the EMI shielding material must be electrically conductive or contain electrically conductive fillers, although a high electrical conductivity is not required. The bulk electrical resistivity on the order of 1 Ω cm is sufficient for most of EMI shielding applications. [1,3,15] Most of the polymer-based materials widely used as TIMs in electronic packaging are electrically insulating and, therefore, transmit EM waves. Conventionally, metal particles are added as fillers in high volume fractions to the base polymer matrix in order to increase the electrical conductivity and prevent EM wave propagation from the device to the environment and vice versa. [1,[18][19][20][21] However, the polymer-metal composites suffer from high weight, cost, and corrosion, which make them an undesirable choice for the state-of-the-art downscaled electronics. Several studies reported the use of carbon fibers, [22][23][24][25][26][27][28][29] carbon black, [30,31] bulk graphite, [32][33][34] carbon nanotubes (CNT), [16,17,[35][36][37][38][39] reduced graphene oxide (rGO), [2,6,[40][41][42][43][44][45][46][47][48][49][50] graphene, [51][52][53][54] and combination of carbon allotropes with orThe synthesis and characterization of epoxy-based composites with few-layer graphene fillers, which are capable of dual-functional applications, are reported. It is found that composites with certain types of few-layer graphene fillers reveal an efficient total electromagnetic interference shielding, SE tot ≈ 45 dB, in the important X-band frequency range, f = 8.2 −12.4 GHz, while simultaneously providing high thermal conductivity, K ≈ 8 W m −1 K −1 , which is a factor of ×35 larger than that of the base matrix material. The efficiency of the d...

We report on the thermal and electrical properties of hybrid epoxy composites with graphene and boron nitride fillers. The thicknesses, lateral dimensions, and aspect ratios of each filler material were intentionally selected for geometric similarity to one another, in contrast to prior studies that utilized dissimilar filler geometries to achieve a "synergistic" effect. We demonstrate that the electrically-conductive graphene and electrically-insulating boron nitride fillers allow one to effectively engineer the thermal and electrical conductivities of their resulting composites. By varying the constituent fraction of boron nitride to graphene in a composite with ~44% total filler loading, one can tune the thermal conductivity enhancement from a factor of ×15 to ×35 and increase the electrical conductivity by many orders of magnitude. The obtained results are important for the development of next-generation thermal interface materials with controllable electrical properties necessary for applications requiring either electrical grounding or insulation.

We review the current state-of-the-art graphene-enhanced thermal interface materials for the management of heat in the next generation of electronics. Increased integration densities, speed and power of electronic and optoelectronic devices require thermal interface materials with substantially higher thermal conductivity, improved reliability, and lower cost. Graphene has emerged as a promising filler material that can meet the demands of future high-speed and high-powered electronics. This review describes the use of graphene as a filler in curing and non-curing polymer matrices. Special attention is given to strategies for achieving the thermal percolation threshold with its corresponding characteristic increase in the overall thermal conductivity. Many applications require high thermal conductivity of composites, while simultaneously preserving electrical insulation. A hybrid filler approach, using graphene and boron nitride, is presented as a possible technology providing for the independent control of electrical and thermal conduction. The reliability and lifespan performance of thermal interface materials is an important consideration towards the determination of appropriate practical applications. The present review addresses these issues in detail, demonstrating the promise of graphene-enhanced thermal interface materials compared to alternative technologies.

We show that every Picard rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration. The fibers of these Landau-Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau-Ginzburg model coming from a toric degeneration.