Thermal Conductance across Phosphonic Acid Molecules and Interfaces: Ballistic versus Diffusive Vibrational Transport in Molecular Monolayers

Abstract

The influence of planar organic linkers on thermal boundary conductance across hybrid interfaces has focused on the organic/inorganic interaction energy, rather than on vibrational mechanisms in the molecule. As a result, research into interfacial transport at planar organic monolayer junctions has treated molecular systems as thermally ballistic. We show that thermal conductance in phosphonic acid (PA) molecules is ballistic, and the thermal boundary conductance across metal/PA/sapphire interfaces is driven by the same phononic processes as those across metal/sapphire interfaces without PAs, with one exception. We find a more than 40% reduction in conductance across Henicosafluorododecyl phosphonic acid (F21PA) interfaces, independent of metal contact, despite similarities in structure, composition and terminal group to the variety of other PAs studied. Our results suggest diffusive scattering of thermal vibrations in F21PA, demonstrating a clear path toward modification of interfacial thermal transport based on knowledge of ballistic and diffusive scattering in single monolayer molecular interfacial films.

Molecules and the Eigenstate Thermalization Hypothesis

“…The Landauer formalism, introduced to quantify electrical conductance in mesoscopic systems [100,101], can be applied to thermal transport through molecules between two leads at different temperature. We find that this approach yields results for the thermal conductance through alkane chains and fluorinated alkane chains bridging gold and sapphire that are in good agreement with experiment [56], as shown in Fig. 4.…”

“…For these systems, separate calculations indicate that thermalization is expected to be quite rapid, and we expect thermal conductance to rise more rapidly with temperature than the Landauer model predicts. Which of these trends actually occurs can be settled by the kind of experiments [56] that were carried out on alkane and perfluoroalkane chains, which produced the results plotted in Fig. 4.…”

“…On molecular scales of ~ 1 nm, the energy diffusion picture and Fourier's heat law break down, as revealed by numerous experimental measurements probing vibrational energy and thermal transport in molecules, which indicate absence of thermalization and often ballistic heat transport [50,51,56,[94][95][96]. Of course, a molecule at a junction, such as the alkane chain illustrated in Fig.…”

The influence of titanium adhesion layer oxygen stoichiometry on thermal boundary conductance at gold contacts

“…[2][3][4][5][6] Historically, understanding of the phonon transport mechanisms driving the thermal boundary conductance across interfaces has relied on the concept of energy transmission driven by the relative dissimilarities of the acoustic properties 7,8 or phonon densities of states 2 intrinsic to the bulk of the two materials comprising the interface. More recently, defects and atomic disorder in the form of substrate roughness, 9,10 dislocations, 11 atomic diffusion, 12 nanoscale or molecular defects, 13,14 and structurally disordered thin films (with thicknesses d ( l K ) 9,[15][16][17][18] at and near the interface have been shown to decrease h K as compared to the corresponding "perfect" interface. 4 Under certain conditions, the inclusion of additional interfacial moieties in the form of point defects or thin films can be used to increase the thermal boundary conductance (decrease the thermal boundary resistance).…”

“…For example, when molecules have been used to increase the bonding at film/substrate interfaces, and thus increase h K , the intrinsic thermal resistance of the interfacial molecule at the junction is assumed negligible 24,25 (i.e., heat flow through the molecule is ballistic). 29,30 A large enough molecule at a film/substrate interface that exhibits diffusive thermal transport can lead to reductions in h K , 13,31 thus counteracting any benefit of increased adhesion on thermal boundary conductance. This interplay is poorly understood and has pronounced impacts on our understanding of the intertwined role of defects and adhesion layers on the thermal boundary conductance across interfaces, along with the ability to assess and validate concepts and theories of thermal boundary conductance at strongly bonded interfaces.…”