Length-dependent thermal conductivity of single extended polymer chains

The low thermal conductivity of polymers will be one of the major roadblocks for the polymer-based microelectronics and macroelectronics due to the limited heat spreading capability. Despite that the thermal conductivity of bulk polymers is usually low, a single extended polymer chain could have very high thermal conductivity. In this paper we present atomistic simulation studies on the phonon transport in single extended polymer chains of various polymers as a function of polymer chain length. The thermal conductivity of single extended polymer chains can be 1–2 orders of magnitude higher than their bulk counterparts. The thermal conductivity of single extended polymer chains is a strong function of monomer type. For example, the thermal conductivity of the extended polymer chains with aromatic backbone can be up to 5 times as that of a polyethylene chain, while the thermal conductivity of the extended polymer chains with bond-strength or mass disorder can be only 1/25 as that of a polyethylene chain. We analyze the phonon transport mechanisms in single extended polymer chains of various polymers and find that the competition between ballistic phonon transport and diffusive phonon transport in a polymer chain leads to a diverging length-dependent thermal conductivity.

Figure 1

(a) Schematic drawing of a randomly coiled polyethylene chain. The random orientation of the chain segments is one of the main reasons for the low thermal conductivity of bulk polymers. (b) Schematic drawing of a single extended polyethylene chain. A single extended polymer chain with well-aligned polymer segments might have high thermal conductivity. (c) Upper panel: a typical NEMD simulation system for the thermal conductivity of a single extended polymer chain. The simulation system was divided into several slabs (20 to 50 slabs, depending on the total length), each with a thickness δ. At each end, the atoms in one slab were fixed to act as a heat-insulating wall. A small amount of heat Δ$E$ (∼10 J/mol) was added into the slab adjacent to the fixed slab (hot region) at each time step; the same amount of heat was removed from the slab adjacent to the fixed slab at the other end (cold region). Lower panel: a typical temperature profile in the simulation domain. The linear temperature region was fitted using the least-square method to obtain the temperature gradient $dT/dx$ for the calculation of the effective thermal conductivity using the Fourier's law of heat conduction.

Figure 2

The thermal conductivity of single extended polymer chains of various polymers as a function of the number of segments: (a) effect of aromatic backbone; (b) effect of double bonds and bond-strength disorder compared to polyethylene; (c) effect of bond-strength disorder/mass disorder by incorporation of oxygen atoms in polyethylene; and (d) the thermal conductivity of single extended polymer chains of five polymers as a function of chain length.

Figure 3

The averaged phonon boundary relaxation time ${\tau }_1$ and the averaged intrinsic phonon relaxation time ${\tau }_2$ of polyethylene, poly($p$-phenylene), and polybutadiene chains as a function of the number of segments.

Figure 4

Schematic drawing shows the normal vector of planar aromatic rings ${\mathbf{n}}_1$ and ${\mathbf{n}}_2$ and the backbone vector ${\mathit{e}}_1$ and ${\mathit{e}}_2$ in the aromatic backbone structure.