(553a) Key Signatures of the Linear Relaxation Behavior of Glass Forming Polymers and Small Molecules

The linear relaxation behavior of glass forming polymers and small molecules is probed by the combination of linear viscoelastic, dielectric and other spectroscopic experiments as well as by molecular simulations. The key features of the relaxation response are (i) the super-Arrhenian dependence of the mobility and (ii) the non-symmetric shape of the relaxation spectra. Using a combination of experimental data and molecular simulations, it recently has been shown that for the small molecule glass former ortho-terphenyl (OTP) the logarithm of the mobility is a linear function of 1/U_x, where U_x is the molar excess internal energy defined as the difference between the liquid and crystalline internal energies. The 1/U_x model describes the temperature and pressures of the OTP mobility over 16 orders-of-magnitude for all available temperatures and pressures in both the super-Arrhenian region and well as in the Arrhenian regions at higher temperatures, albeit with a different proportionality constant. The 1/U_x model quantitatively describes the super-Arrhenian for all 21 glass forming small molecules where there is sufficient data for analysis, and a related configurational internal energy model describes the mobility for all 12 polymers where there is sufficient data.

With respect to linear viscoelastic data, the relaxation spectra is typically determined from master curves developed via time-temperature superposition of isotherms with a limited frequency/time range, where time-temperature superposition implicitly implies that the material is thermo-rheologically simple. determined from the master curve. In contrast, broadband dielectric data covers a much wider frequency range where it is clear that glass forming materials are thermo-rheologically complex. The individual dielectric isotherms are typically fit by a combination of empirical spectral functions, e.g. KWW, Cole-Cole, etc., where the parameters in these empirical functions change with temperature, sometimes nonmonotonically, indicating that this procedure is a curve fit. The traditional determination of the spectra from relaxation data implicitly assumes a constant spectral density, i.e. a uniform spacing for discrete spectra, where the intensity of the individual spectral elements change by orders-of-magnitude in order to describe the relaxation data. Alternatively, it is mathematically equivalent to assume that the individual spectral elements have constant intensity, where the spectral density changes by orders-of-magnitude in order to describe the data. Using this second method, thermo-rheological complexity is readily accommodated, since there is no requirement that all spectra elements have the same temperature dependence as required in time-temperature superposition. This new spectral analysis method has been applied to both polymers and small molecules, where the features of the alpha, excess wing and the sub-Tg gamma processes are exposed. The implications of this new, more physically realistic way of looking at the linear relaxation in glass forming materials will be discussed.