Non-metallic crystalline materials conduct heat by the transport of quantized atomic lattice vibrations called phonons. Thermal conductivity depends on how far phonons travel between scattering events-their mean free paths. Due to the breadth of the phonon mean free path spectrum, nanostructuring materials can reduce thermal conductivity from bulk by scattering long mean free path phonons, whereas short mean free path phonons are unaffected. Here we use a breakdown in diffusive phonon transport generated by high-frequency surface temperature modulation to identify the mean free path-dependent contributions of phonons to thermal conductivity in crystalline and amorphous silicon. Our measurements probe a broad range of mean free paths in crystalline silicon spanning 0.3-8.0 mm at a temperature of 311 K and show that 40±5% of its thermal conductivity comes from phonons with mean free path 41 mm. In a 500 nm thick amorphous silicon film, despite atomic disorder, we identify propagating phonon-like modes that contribute 435±7% to thermal conductivity at a temperature of 306 K.

Soft dielectric materials typically exhibit poor heat transfer properties due to the dynamics of phonon transport, which constrain thermal conductivity (k) to decrease monotonically with decreasing elastic modulus (E). This thermal−mechanical trade-off is limiting for wearable computing, soft robotics, and other emerging applications that require materials with both high thermal conductivity and low mechanical stiffness. Here, we overcome this constraint with an electrically insulating composite that exhibits an unprecedented combination of metal-like thermal conductivity, an elastic compliance similar to soft biological tissue (Young's modulus < 100 kPa), and the capability to undergo extreme deformations (>600% strain). By incorporating liquid metal (LM) microdroplets into a soft elastomer, we achieve a ∼25× increase in thermal conductivity (4.7 ± 0.2 W·m ) under stress-free conditions and a ∼50× increase (9.8 ± 0.8 W·m) when strained. This exceptional combination of thermal and mechanical properties is enabled by a unique thermal−mechanical coupling that exploits the deformability of the LM inclusions to create thermally conductive pathways in situ. Moreover, these materials offer possibilities for passive heat exchange in stretchable electronics and bioinspired robotics, which we demonstrate through the rapid heat dissipation of an elastomer-mounted extreme high-power LED lamp and a swimming soft robot.liquid metal | thermal conductivity | soft materials | soft robotics | stretchable electronics

Thermopower measurements offer an alternative transport measurement that can characterize the dominant transport orbital and is independent of the number of molecules in the junction. This method is now used to explore the effect of chemical structure on the electronic structure and charge transport. We interrogate junctions, using a modified scanning tunneling microscope break junction technique, where: (i) the 1,4-benzenedithiol (BDT) molecule has been modified by the addition of electron-withdrawing or -donating groups such as fluorine, chlorine, and methyl on the benzene ring; and (ii) the thiol end groups on BDT have been replaced by the cyanide end groups. Cyanide end groups were found to radically change transport relative to BDT such that transport is dominated by the lowest unoccupied molecular orbital in 1,4-benzenedicyanide, while substituents on BDT generated small and predictable changes in transmission.

Transport in metal-molecule-metal junctions is defined by the alignment and coupling of molecular orbitals with continuum electronic states in the metal contacts. Length-dependent changes in molecular orbital alignment and coupling with contact states were probed via measurements and comparisons of thermopower (S) of a series of phenylenes and alkanes with varying binding groups. S increases linearly with length for phenylenediames and phenylenedithiols while it decreases linearly in alkanedithiols. Comparison of these data suggests that the molecular backbone determines the length dependence of S, while the binding group determines the zero length or contact S. Transport in phenylenes was dominated by the highest occupied molecular orbital (HOMO), which aligns closer to the Fermi energy of the contacts as approximately L(-1), but becomes more decoupled from them as approximately e(-L). In contrast, the decreasing trend in S for alkanedithiols suggests that transmission is largely affected by gold-sulfur metal induced gap states residing between the HOMO and lowest unoccupied molecular orbital.