Thermal resistance network model for heat conduction of amorphous polymers

The thermal conductivities (TCs) of the vast majority of amorphous polymers are in a very narrow range, 0.1–0.5 W ${\mathrm{m}}^{-1}$ ${\mathrm{K}}^{-1}$, although single polymer chains possess TCs of orders of magnitude higher. The chemical structure of polymer chains plays an important role in determining the TC of bulk polymers. We propose a thermal resistance network (TRN) model for the TC in amorphous polymers taking into account the chemical structure of molecular chains. Our model elucidates the physical origin of the low TC universally observed in amorphous polymers with various chemical structures. The empirical formulas of the pressure and temperature dependence of TC can be successfully reproduced not only in solid polymers but also in polymer melts. We further quantitatively explain the anisotropic TC in oriented polymers.

Figure 1

(a) Illustration of a representative unit of an amorphous polymer. Molecular chains are entangled, forming a network structure. The dominant heat flow trajectory is marked by solid lines where different colors are used for distinguishing chains. Contact points are labeled from 1 to 5 in the trajectory. (b) Topologically equivalent 2D TRN corresponding to the trajectory from 1 to 5 shown in (a). Rectangles, circles, and ellipses denote the intrinsic resistance of segments, intrachain resistance at the contact points, and interchain resistance, respectively.

Figure 2

(a) Calculated TCs vs $4/\xi$ using Eq. (4) with three different values of $R_{\mathrm{inter}}$ are plotted in comparison with the measured TCs of various isotropic polymers and oriented polymers. $R_{\mathrm{inter}}$ calculated from MD of PE and PP are shown as a function of (b) interchain spacing and (c) temperature. The interchain spacings of PE and PP are 3.55 and 3.6 Å in (c), respectively.

Figure 3

Temperature dependence of ${\kappa }_{\parallel }$ of oriented (a) PT [12], (b) PI [14], and (c) N11 [11] with different diameters. Dots are experimental data and dashed lines are fitted by Eq. (9).

Figure 4

The values of $r_1$ and $r_2$ vs the diameter of polymer nanofibers. ${\gamma }_{\parallel }$ and $\lambda$ extracted from $r_1$ and $r_2$ are plotted in arbitrary units to the right $y$ axis.