High and low thermal conductivity of amorphous macromolecules

We measure the thermal conductivity, heat capacity and sound velocity of thin films of five polymers, nine polymer salts, and four caged molecules to advance the fundamental understanding of the lower and upper limits to heat conduction in amorphous macromolecules. The thermal conductivities vary by more than one order of magnitude, from $0.06\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ for [6,6]-phenyl-C71-butyric acid methyl ester to $0.67\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ for poly(vinylphosphonic acid calcium salt). Minimum thermal conductivity calculated from the measured sound velocity and effective atomic density is in good agreement with the thermal conductivity of macromolecules with various molecular structures and intermolecular bonding strength.

Figure 1

Chemical structures of six types of polyelectrolytes studied for thermal conductivity, heat capacity, and sound velocity. Polystyrene (PS) is included as a reference.

Figure 2

Contour plot of thermal conductivity and heat capacity for the thin films of polyelectrolytes in a two-dimensional parameter space. The area enclosed by the contour lines indicates the 95% confidence interval of the measured values. Data of PAA are from Ref. [5].

Figure 3

(a) Measured thermal conductivity as a function of average sound velocity for several polymers and polymer salts with the same backbone structures and varying interchain bonds: PS and PMMA (blue symbols) have van der Waals intermolecular interactions; PVA, PAA, and PVPA (red symbols) possess hydrogen bonds; PALi, PACa, PVPLi, and PVPCa (black symbols) are polymer salts with ionic interchain bonds. (b) Comparison between measured longitudinal elastic constant $C_{11}$ and transverse elastic constant $C_{44}$ for the macromolecules. The magenta and dark yellow dashed lines stand for a Poisson's ratio of 0.37 and 0.25, respectively. The data of PAA and PVA in (a) and (b) are from Ref. [5].

Figure 4

Chemical structures of four caged molecules we studied: ADP, GHSQ, DSQ, and PC71BM.

Figure 5

Contour plot of thermal conductivity and heat capacity for the caged molecules.

Figure 6

(a) Measured heat capacity as a function of calculated heat capacity using the Debye model. Red circles are reference data, including the water-soluble polymers by Xie et al. [5] and fullerene derivatives by Wang et al. [11]. Blue dashed line corresponds to a slope of 1. (b) Comparison of the measured thermal conductivity with the minimum thermal conductivity ${\mathrm{\Lambda }}_{\min }$ calculated based on Eq. (1) and the estimated atomic density $n_C$. Red squares and red circles are data of water-soluble polymers by Xie et al. [5] and fullerene derivatives by Wang et al. [11], respectively. Blue dashed line represents the perfect match, and dark yellow dashed line is the lower limit of minimum thermal conductivity set by CsI. (c) Measured thermal conductivity as a function of predicted minimum thermal conductivity considering the localization effect. The correction factor $\alpha$ equals ${(n_{\mathrm{eff}}/n_C)}^{2/3}.$