Dynamics of Hydrogen Bonded Systems
Vibrational Echo Dynamics in Ethylene Glycol
Figure 1: Arrhenius plot of the pure dephasing linewidth as a function of inverse temperature. The linear inverse temperature dependence at low temperature indicated an activated dephasing process. The activation energy of ~200 cm-1 strongly implicates the excitation of hydrogen bond vibrations as the source of this low temperature dephasing. For inhomogeneously broadened absorptions, the intrinsic dynamics of a system are masked by the effectively static distribution of local solvent configurations. Echo spectroscopies provide a powerful range of techniques for the investigation of the intrinsic dynamics of the system. A review of echo spectroscopies can be found in at (link). We have utilized the two-pulse echo technique to investigate the dynamics the echo decay in partially deuterated ethylene glycol as a function of temperature. A semi-log plot of the pure dephasing homogeneous linewidth as a function of inverse temperature can be found in figure 1. Well below the glass transition temperature of Tg = 153 K for ethylene glycol, the echo linewidth increases exponentially with temperature indicative of an activated dephasing mechanism:
where G is the dephasing rate, A is the attempt rate, Ea is the activation energy, kB is Boltzmann’s constant , and T is the temperature. The slope of the temperature dependent rate of dephasing on a semilog plot gives an activation energy of ~200 cm-1. This strongly suggests that at low temperature the excitation of a hydrogen bond vibration, generally believed to have a frequency of ~200 cm-1, leads to vibrational dephasing.
However, as the glass transition temperature is approached the rate of dephasing exhibits a marked increase. The temperature dependence of this feature can be seen in figure 2. This rate has been fit with the Vogel-Tammann-Fulcher equation, an empirical fitting function used to describe the onset of diffusion in molecular glasses,
Figure 2: Onset of orientational dynamics near the glass transition. The low temperature activated contribution to the linewidth has been subtracted, with the residual rate of dephasing fit to the Vogel-Tammann-Fulcher equation with a transition temperature T0 = 123 K. This temperature coincides with the ideal glass transition temperature predicted in thermodynamics heat capacity measurements.
where G is the dephasing rate and T0 represents the onset temperature for diffusion. The fit in figure 2 has a T0 = 123 ± 5 K, roughly 30 K below the Tg. T0 has been associated with an ideal glass transition temperature where the heat capacity of the liquid and crystal become the same. This ideal glass transition temperature has been measured to be ~120 K in ethylene glycol, consistent with our transition temperature of 123 K. For more information on the dynamics of glasses and supercooled liquids, see (link).
