Thermodynamic and Kinetic Fragility of Freon 113: The Most Fragile Plastic Crystal

We present a dynamic and thermodynamic study of the orientational glass former Freon 113 (1,1,2-trichloro-1,2,2-trifluoroethane, ${\mathrm{CCl}}_2\mathrm{F}\text{−}{\mathrm{CClF}}_2$) in order to analyze its kinetic and thermodynamic fragilities. Freon 113 displays internal molecular degrees of freedom that promote a complex energy landscape. Experimental specific heat and its microscopic origin, the vibrational density of states from inelastic neutron scattering, together with the orientational dynamics obtained by means of dielectric spectroscopy have revealed the highest fragility value, both thermodynamic and kinetic, found for this orientational glass former. The excess in both Debye-reduced specific heat and density of states (boson peak) evidences the existence of glassy low-energy excitations. We demonstrate that early proposed correlations between the boson peak and the Debye specific heat value are elusive as revealed by the clear counterexample of the studied case.

Figure 1

Specific heat of Freon 113 [35] around the glasslike transition, $T_g=72\mathrm{K}$.

Figure 2

Debye-reduced vibrational density of states divided by ${\omega }^2$ for Freon 112 (red squares) and for Freon 113 (black circles) determined at 5 K by means of inelastic neutron scattering at the MARI spectrometer. Inset: Molar heat capacity divided by $T^3$ for Freon 112 and Freon 113 [35], the calculated Debye values, and the fits (dashed lines) corresponding to the soft potential model in a semilogarithmic plot.

Figure 3

Relaxation time as a function of reciprocal temperature for both $\alpha$ (red circles) and slower (green diamonds and black squares) relaxations. Top left inset shows obtained dielectric spectra for several temperatures ranging from 70 to 90 K. Solid lines are examples of the fits using Havriliak-Negami and Cole-Cole functions (dashed lines for the spectrum at 88 K) for the main $\alpha$ relaxation and the slower processes, respectively. Bottom right inset collects the ${\beta }^{\mathrm{KWW}}$ exponent as a function of temperature.

Figure 4

(Top panel) ${\tau }_{\alpha }$ as a function of $T_g/T$ (Angell plot). VFT parameters for Freon 113 are $T_0=58.9\pm 0.6\mathrm{K}$, ${\tau }_0=(2.9\pm 1.6)\times {10}^{-12}\text{s}$, $D=(6.4\pm 0.5)$. Fragility index is $m=127$. (Bottom panel) Reciprocal of the excess entropy—normalized by the excess entropy at $T_g$—as a function of $T_g/T$. Inset: Entropy for the plastic and glassy crystal phases (red solid line), for the stable crystal II and the liquid (blue points, from Ref. [38]) as a function of temperature. The green dashed line indicates the extrapolation of the crystal II as a reference for higher temperatures. In both (top panel) and (bottom panel), the dashed lines drawn at the $½$ and $¾$ marks are used to obtain either kinetic (top panel) or thermodynamic (bottom panel) fragilities $F_{1/2}$ and $F_{3/4}$, respectively.

Figure 5

Excess heat capacity $C_{p,\mathrm{exc}}=C_p-C_D$, at the boson-peak maximum in $C_p/T^3$ scaled to $C_D$, as a function of the fragility index $m$ in a semilogarithmic scale. Black circles correspond to canonical glasses, taken from the original figure from Ref. [37]. We have added some data (red triangles) from this (Freon 113) and earlier works: adamantanone (2O-Ada) [39], cyclohexanol (${\mathrm{C}}_6-\mathrm{ol}$) [40], Freon 112 [31], and ethanol both as orientational (Eth-OG) and structural (Eth-SG) glass [41, 42]. Solid symbols indicate structural glasses and open symbols indicate orientational glasses.