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We review the current state of the art of graphene-enhanced thermal interface materials for the management of heat 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 the composites while simultaneously preserving electrical insulation. A hybrid filler -- graphene and boron nitride -- approach is presented as possible technology for independent control of electrical and thermal conduction. 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 the graphene-enhanced thermal interface materials as compared to alternative technologies., Comment: 56 pages, 16 figures, 1 large table with accompanying table explaining jargon

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 x15 to x35 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., Comment: 32 pages; 5 figures

We report on the synthesis and characterization of the epoxy-based composites with the few-layer graphene fillers, which are capable of the duel functional applications. It was found that composites with the certain types of few-layer graphene fillers reveal an efficient total electromagnetic interference shielding, SE~45 dB, in the important X-band frequency range, f=8.2 GHz - 12.4 GHz, while simultaneously providing the high thermal conductivity, K = 8 W/mK, which is a factor of x35 larger than that of the base matrix material. The efficiency of the dual functional application depends on the filler characteristics: thickness, lateral dimensions, aspect ratio and concentration. Graphene loading fractions above the percolation threshold allow for strong enhancement of both the electromagnetic interference shielding and heat conduction properties. Interestingly, graphene composites can block the electromagnetic energy even below the percolation threshold, remaining electrically insulating, which is an important feature for some types of thermal interface materials. The dual functionality of the graphene composites can substantially improve the electromagnetic shielding and thermal management of the airborne systems while simultaneously reducing their weight and cost., Comment: 24 pages; 4 figures

We investigated thermal properties of the epoxy-based composites with a 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 f>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, above the thermal percolation threshold, 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., Comment: 29 pages; 5 figures

We report results of Brillouin - Mandelstam spectroscopy of transparent alumina crystals with Nd dopants. The ionic radius and atomic mass of Nd atoms are distinctively different from those of the host Al atoms. Our results show that even a small concentration of Nd atoms incorporated into the alumina samples produces a profound change in the acoustic phonon spectrum. The velocity of the transverse acoustic phonons decreases by ~600 m/s at the Nd density of only ~0.1 %. Interestingly, the decrease in the phonon frequency and velocity with the doping concentration is non-monotonic. The obtained results, demonstrating that modification of the acoustic phonon spectrum can be achieved not only by nanostructuring but also by doping have important implications for thermal management as well as thermoelectric and optoelectronic devices., Comment: 16 pages, 4 figures

We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our attention to these families is motivated by the Doran-Morgan classification of variations of Hodge structure which can underlie families of Calabi-Yau threefolds with $h^{2,1} = 1$ over the thrice-punctured sphere. We explore their torically induced fibrations by $M$-polarized K3 surfaces and use these fibrations to construct an explicit geometric transition between an anticanonical hypersurface and a nef complete intersection through a singular subfamily of hypersurfaces. Moreover, we show that another singular subfamily provides a geometric realization of the missing "14th case" variation of Hodge structure from the Doran-Morgan list.

The largest group which occurs as the rotational symmetries of a three-dimensional reflexive polytope is the symmetric group on four elements. There are three pairs of three-dimensional reflexive polytopes with this symmetry group, up to isomorphism. We identify a natural one-parameter family of K3 surfaces corresponding to each of these pairs, show that the symmetric group on four elements acts symplectically on members of these families, and show that a general K3 surface in each family has Picard rank 19. The properties of two of these families have been analyzed in the literature using other methods. We compute the Picard-Fuchs equation for the third Picard rank 19 family by extending the Griffiths-Dwork technique for computing Picard-Fuchs equations to the case of semi-ample hypersurfaces in toric varieties. The holomorphic solutions to our Picard-Fuchs equation exhibit modularity properties known as "Mirror Moonshine"; we relate these properties to the geometric structure of our family., Comment: 13 pages, 2 figures. Updated references. Comments are welcome!

We show that every 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., Comment: v3: minor corrections for final version

A closed hyperbolic 3-manifold is exceptional if its shortest geodesic does not have an embedded tube of radius $\ln(3)/2$. D. Gabai, R. Meyerhoff and N. Thurston identified seven families of exceptional manifolds in their proof of the homotopy rigidity theorem. They identified the hyperbolic manifold known as Vol3 in the literature as the exceptional manifold associated to one of the families. It is conjectured that there are exactly 6 exceptional manifolds. We find hyperbolic 3-manifolds, some from the SnapPea's census of closed hyperbolic 3-manifolds, associated to 5 other families. Along with the hyperbolic 3-manifold found by Lipyanskiy associated to the seventh family we show that any exceptional manifold is covered by one of these manifolds. We also find their group coefficient fields and invariant trace fields., Comment: 19 pages, minor revisions, added appendix by Alan Reid, published by Experimental Mathematics