A generalization of the Adam–Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam–Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.
A Raman spectroscopic analysis of the room temperature ionic liquid 1-ethyl-3-methlimidazolium thiocyanate, [EMIM][SCN], has revealed that certain stretching vibrations associated with both the anion and cation shift to higher energy (or blue-shift) as water is introduced to the system (by up to 15 cm–1 for a CH stretching mode associated with EMIM+ and up to 12 cm–1 for the CS stretch of SCN–). Density functional theory was employed to gain molecular level insight into the origins of these spectral perturbations by computing changes in the structures, energetics, and harmonic vibrational frequencies of the [EMIM][SCN] ion pair as a single explicit water molecule was added to the system. The computed harmonic vibrational frequency shifts for the low-energy structures of the ion pair and the corresponding monohydrated complex reproduce the experimentally observed trends. These results indicate that the donation of a hydrogen bond from water to the N atom of SCN– produces the blue-shifts associated with the CN and CS stretching modes. In contrast, the vibrational frequency shifts associated with CH stretches of EMIM+ do not appear to require a direct interaction with the water molecule.