Understanding Divergent Thermal Conductivity in Single Polythiophene Chains Using Green–Kubo Modal Analysis and Sonification

Abstract

Abstract:We used molecular dynamics simulations, the Green-Kubo Modal Analysis (GKMA) method and sonification to study the modal contributions to thermal conductivity in individual polythiophene chains. The simulations suggest that it is possible to achieve divergent thermal conductivity and the GKMA method allowed for exact pinpointing of the modes responsible for the anomalous behavior. The analysis showed that transverse vibrations in the plane of the aromatic rings at low frequencies ~ 0.05 THz are primarily responsible. Further investigation showed that the divergence arises from persistent correlation between the three lowest frequency modes on chains. Sonification of the mode heat fluxes revealed regions where the heat flux amplitude yields a somewhat sinusoidal envelope with a long period similar to the relaxation time. This characteristic in the divergent mode heat fluxes gives rise to the overall thermal conductivity divergence, which strongly supports earlier hypotheses that attribute the divergence to correlated phonon-phonon scattering/interactions. Main text:In all substances, energy/heat is transferred through atomic motions. In electrically conductive materials, electrons can become the primary heat carriers, but in all phases of matter, atomic motions are always present and contribute to the thermal conductivity of every object. Here, we use the term "object" instead of "material" to emphasize that thermal conductivity is highly dependent on the actual structure of an object, that is, its internal atomic level structure and its larger nanoscale or microscale geometry [1][2][3][4][5][6] . In studying the physics of thermal conductivity, tremendous progress has been made over the last 20 years toward understanding various mechanisms that allow one to reduce thermal conductivity in solids 1,7 . This reduction is generally measured relative to a theoretical upper limiting maximum value that arises solely from the intrinsic anharmonicity within the interactions between atoms.In the limiting case, where the atomic interactions are perfectly harmonic, thermal conductivity tends to infinity because the normal modes of vibration do not interact, thus yielding effectively infinite phonon mean free paths and thermal conductivity. As a result, the notion of anharmonicity is critical, and perfectly harmonic interactions between atoms are physically unreasonable. This is because an asymmetry in the energetic well between atoms is an inherent consequence of finite bonding energy (e.g., at some point, the potential energy surface must become concave down). Although one can approach the harmonic limit at cryogenic temperatures, the notion that divergent thermal conductivity (e.g., anomalous thermal conductivity) might be realizable in a real material at room temperature seems theoretically impossible. However, in 1955 Fermi, Pasta, and Ulam (FPU) 8 made a "shocking little discovery" that even an anharmonic system can exhibit infinite thermal conductivity.FPU conducted a numerical experiment with a one-dimensio...

Assessing the anomalous superdiffusive heat transport in a single one-dimensional PEDOT chain

“…Depending on the assigned initial velocities, we observed that the Green-Kubo integral differently evolved in time: therefore, for some trajectories (actually 6 out of 10) the Green-Kubo integral was eventually found to reach a constant value, while for the remaining ones we observe an overall divergence. The diverging behavior and its chaotic dependence on the initial conditions was previously observed in different single polymer chains [12][13][14]. A similar behavior has been also observed in 2D graphene subjected to a uniaxial strain [35].…”

“…In particular, the nonintensive character of κ has been experimentally observed in 1D-like carbon and boron-nitride nanotubes [3,4] as well as in SiGe nanowires [5], while a similarly characterized anomalous heat conduction has been theoretically shown to occur in 1D Fermi-Pasta-Ulam [6] and diatomic Toda lattices [7]. Atomistic simulations as well predict anomalous heat conduction in different 1D-like materials, such as carbon nanotubes [8,9], silicon nanowires [10], and polymer chains [11][12][13][14].…”

Thermal Transport in Conductive Polymer–Based Materials

“…Besides, Lv and Henry derived a new method, Green–Kubo modal analysis (GKMA), which combines the lattice dynamics with the Green–Kubo formula for the direct calculation of the thermal conductivity contributions from different types of modes. Using GKMA method, Lv et al observed the divergent thermal conductivity in a single PT chain. The anomalous heat conduction phenomenon originates from the transverse vibrations in the plane of the aromatic rings at low frequencies around 0.05 THz, which can be determined by the sonification of the modal heat flux.…”

“…In recent years, thermal conductivity of conductive polymers has been investigated by both experimental and theoretical studies . Table 1 lists the thermal conductivity value for some typical conductive polymers, which are two to three orders of magnitude lower than that of conventional semiconducting crystals.…”

“…Mode‐coupling theory proposed that there are long tails in the heat‐flux correlation function and slow decay toward equipartition. In this case, the phonon gas model based on the Boltzmann transport equation is invalid . However, the divergent phenomenon will disappear when the system includes disorder or consists of many chains, as the disorder or the interchain interaction could cause the attenuation of intrachain correlation.…”