(Color online) Dielectric spectra of (a) propylene glycol (full symbols: present work, open symbols: courtesy of Lunkenheimer, cf. also Ref. 22, (b) 4-tertbutyl pyridine, and (c) -tricresyl phosphate (-TCP) fitted (solid line) by applying the GGE distribution of correlation times, Eq. (1). In the case of -TCP we included the conductivity contribution at two temperatures in order to demonstrate that conductivity and process show virtually the same temperature dependence. Numbers indicate temperatures in kelvins.
(Color online) Dielectric spectra of propylene carbonate as measured by Lunkenheimer et al. Ref. 21. (a) Solid lines are interpolations using Eq. (1) together with an additional power law to take account of the fast dynamics contribution. (b) Same data set represented as a function of rescaled frequency . While at the shape of the peak is approximately temperature independent (red points) and is well described by a CD function (dashed line); below the excess wing appears and the FTS principle is violated (blue lines).
(Color online) The double logarithmic derivative of glycerol and propylene carbonate (present work) and of the fits by the GGE distribution at selected temperatures.
(Color online) The parameters and of the excess wing in type A glass formers as a function of . Whereas the data of glycerol (GLY), PC, 2-picoline (2-PIC), 4-tertbutyl pyridine (4-TBP), trimethyl phosphate (TMP), and propylene glycol (PG) fall on a master curve, the parameters for -fluoroaniline (FAN), methyl tetrahydrofuran (MTHF), ethylene glycol (EG), and -tricresyl phosphate (-TCP) show small but systematic deviations. The solid lines show an interpolation by Eqs. (6) and (7), respectively. Note that for GLY, PC, and PG not only the data of the Bayreuth group (BT) but also data from Lunkenheimer and co-workers (Augsburg, A) (Refs. 21 and 22) were included in the analysis.
(Color online) The temperature dependence of the parameters and of the GGE distribution of correlation times, Eq. (1). a) and are shown for glycerol (GLY) and propylene carbonate (PC). In addition, (crosses) demonstrates that holds in good approximation. For clarity we do not distinguish between the data sets of the Augsburg and Bayreuth groups in this figure. b) (open symbols) and (full symbols) for 2-picoline (2-PIC), trimethyl phosphate (TMP), propylene glycol (PG), 3-fluoroaniline (3-FAN), methyl tetrahydrofuran (MTHF), -tricresyl phosphate (-TCP), and ethylene glycol (EG); .
(Color online) The exponent parameter of the peak as a function of the excess wing exponent . Solid line represents ; dashed lines show and , respectively. The dotted line represents for the case of glycerol the slightly more accurate linear relation .
(Color online) The onset parameter as a function of the exponent of the excess wing for ten different glass formers. The solid line represents Eq. (8).
(Color online) The exponent and onset parameter of the excess wing for ten different glass formers, rescaled by so that also the systems FAN, MTHF, EG, and -TCP coincide on the master curve. The respective values of are given in Table I. The solid lines represent Eqs. (9) and (10), respectively, whereas the dashed lines show the interpolations from Fig. 4 for comparison.
(Color online) The average -relaxation times of all the systems studied in the present work. (a) Basically the systems differ by a different slope of at . (b) By plotting as a function of the effect of an individual fragility is removed and a master curve is obtained for systems with similar . Solid line represents Eq. (11) with . Note that the data sets of -TCP and 2-picoline also contain time constants as obtained by conductivity and light scattering measurements, respectively.
(Color online) The master curve for for all systems under consideration according to Eq. (12). Upper part: The solid line represents Eq. (12). Deviations indicate the break down of the VFT equation. Lower part: The ratio shows deviations from VFT behavior most clearly. refers to as given by Eq. (12). Dashed lines: guide for the eye.
(Color online) The relative amplitude of the excess wing as defined by Eq. (15). The symbols refer to the systems GLY, PC, 2-PIC, TMP, 4-TBP, 3-FAN, MTHF, -TCP, PG, and EG as indicated in previous figures. In the case of glycerol is also shown for temperatures above in both, main figure and inset. The solid lines results from Eq. (15) with the interpolation of the temperature dependence of the parameters inserted. For details see text.
The characteristic parameters of the glass formers under study in the present work. The glass transition temperature was obtained by evaluating , the fragility by , and by rescaling in Fig. 8(a).
Article metrics loading...
Full text loading...