Effects of internal molecular degrees of freedom on the thermal conductivity of some glasses and disordered crystals

The thermal conductivity $\kappa \left(T\right)$ of the fully ordered stable phase II, the metastable phase III, the orientationally disordered (plastic) phase I, as well as the nonergodic orientational glass (OG) phase, of the glass former cyclohexanol (C${}_6$H${}_{11}$OH) has been measured under equilibrium vapor pressure within the 2–200 K temperature range. The main emphasis is here focused on the influence of the conformational disorder upon the thermal properties of this material. Comparison of results with those regarding cyanoclyclohexane (C${}_6$H${}_{11}$CN), a chemically related compound, serves to quantify the role played by the terminal groups -OH and -CN on the phonon scattering processes. The picture that emerges shows that motions of such groups do play a minor role as scattering centers, both within the low-temperature orientationally ordered phases as well as in the OG states. The results are analyzed within the Debye-Peierls relaxation time model for isotropic solids comprising mechanisms for long-wave phonon scattering within the OG and orientational ordered low-temperature phases, as well as others arising from localized short-wavelength vibrational modes as pictured by the Cahill-Pohl model. By means of complementary neutron and Raman scattering we show that in the OG state the energy landscapes for both compounds are very similar.

Figure 1

Log-log plot of the thermal conductivity as a function of temperature for crystalline phases II and III (circles and triangles, respectively) and OG (diamonds) of cyclohexanol (empty red symbols) and for crystalline phase II (full black circles) and OD and OG (full black diamonds) of cyanocyclohexane. Solid red lines correspond to data from Ref. 32 for phases II and III of cyclohexanol at 0.06 GPa.

Figure 2

Density of states as a function of energy for C${}_6$OH (empty red circles) and C${}_6$CN (filled black circles) OGs at 50 K as derived from inelastic neutron scattering measurements. Dotted-dashed lines indicate the effective Debye density of states [$g\left(\omega \right)=3{\omega }^2/{\omega }_D^3$] for $\omega$${}_D$ $=$ 9.9 (C${}_6$OH) and 8 meV (C${}_6$CN). The inset shows the density of states scaled by ${\omega }^2$ to better show the departure from the Debye behavior in the low-energy domain.

Figure 3

Low-frequency Raman spectra of C${}_6$OH measured on cooling from 306 down to 100 K (in cm${}^{-1}$, bottom axis, and meV, top axis): (a) liquid phase at 306 K; (b) OD phase I at 293 K; (c) OG state at 100 K. BP is attributed to the boson peak at 15.3 cm${}^{-1}$ (1.9 meV) on the spectrum of OG.

Figure 4

Thermal conductivity times temperature as a function of temperature for the orientationally ordered phases. Symbols as in Fig. 1.

Figure 5

Low-frequency Raman spectra (in cm${}^{-1}$, bottom axis, and meV, top axis) of the stable (II) (dotted blue line) and metastable (III) (red line) phases of C${}_6$OH at 100 K.

Figure 6

Thermal conductivity as a function of temperature for OGs C${}_6$OH (empty circles) and C${}_6$CN (full diamonds). Dash line (magenta color) is the fitted curve ${\kappa }_{\mathrm{ph}}\left(T\right)$ using the soft-potential model. Dotted line (blue color) is minimal thermal conductivity${\kappa }_{\min }\left(T\right)$ accordingly to Cahill-Pohl model. Solid line is $\kappa \left(T\right)={\kappa }_{\mathrm{ph}}\left(T\right)+{\kappa }_{\min }\left(T\right)$.

Figure 7

Phonon component [${\kappa }_{\mathrm{ph}}\left(T\right)$] of the thermal conductivity as a function of temperature for orientationally ordered phases of cyclohexanol (C${}_6$OH) and cyanocyclohexane (C${}_6$CN). Symbols as in Fig. 1. Continuous lines show the fits according to the Debye-Peierls model.

Figure 8

Temperature dependence of the low-frequency Raman and INS spectrum of solid cyclohexanol.