Relaxation dynamics of glasses along a wide stability and temperature range

While lots of measurements describe the relaxation dynamics of the liquid state, experimental data of the glass dynamics at high temperatures are much scarcer. We use ultrafast scanning calorimetry to expand the timescales of the glass to much shorter values than previously achieved. Our data show that the relaxation time of glasses follows a super-Arrhenius behaviour in the high-temperature regime above the conventional devitrification temperature heating at 10 K/min. The liquid and glass states can be described by a common VFT-like expression that solely depends on temperature and limiting fictive temperature. We apply this common description to nearly-isotropic glasses of indomethacin, toluene and to recent data on metallic glasses. We also show that the dynamics of indomethacin glasses obey density scaling laws originally derived for the liquid. This work provides a strong connection between the dynamics of the equilibrium supercooled liquid and non-equilibrium glassy states.

to obtain the value of glass relaxation time from the heating rate of the experiment, assigning this value to the onset temperature. b) in the second approach, we calculate the transformation time from the width of the transformation peak and the midpoint value of the heating rate, assigning it to the temperature at the maximum of the transformation peak.

Comparison between procedures to determine relaxation and transformation times
In the supplementary Fig. 2 we show the comparison among different methods to infer the value of relaxation time of a glass with a particular stability and heated at a given rate.
In the Supplementary Fig. 2a, we compare the transformation time calculated, on one hand, using the expression referred in the main text, t trans (T max ) = ΔT β ⁄ , and, on the other, the transformation time directly measured from an isotherm measure at the same temperature performed in a conventional DSC. The transformation time is considered to be the time elapsed from the beginning of the isotherm process to the moment at which the power output of the DSC is constant. The transformation time obtained from the two methods, 182 and 150 seconds respectively, are fairly comparable.
On the other hand, we can derive the relaxation time of a glass at the onset of the transformation measured at a given rate from the well-known expression τ 1 β 1 = τ 2 β 2 , taking as reference values τ 1 = 100 and β 1 = 0.167 / . In particular, for an ultrastable glass measured at β 2 = 0.033 / , τ 2 = 506 . We can compare this value to the one obtained by performing an isothermal measurement at the same temperature (T on = 332 ), 550 s, in fair agreement with the previous result ( Supplementary Fig. 2b). Comparison between procedures to determine relaxation times. a) DSC scan of an IMC glass deposited at Tdep = 266 K, heated at 0.033 K/s. From the width of the peak and the heating rate, the transformation time is inferred as indicated and assigned to the temperature where the maximum of the peak appears. In the inset, a DSC isotherm on an equivalent sample performed at the temperature of the maximum of the peak is shown. From that measurement, we find the transformation time of the sample at that temperature. From the two measurements, we find that both methodologies are approximately equivalent. b) a DSC isotherm on an equivalent sample performed at the onset temperature of the transformation is shown. The transformation time is fairly equivalent to the relaxation time inferred using the expression = , as explained in the text.
In Supplementary Fig. 3 we plot the relaxation time (a) and transformation time (b) calculated for glasses with different stability and measured at different heating rates, together with the structural relaxation time published for IMC supercooled liquid. The fitting of these data using equation (2) yields similar curves, as seen in Supplementary table 1. Also, the limiting fictive temperature values obtained by fitting the experimental points shown in Supplementary Fig. 3 a and b, and also obtained from the combined data shown in Fig. 1a, yields similar results, as seen in Supplementary Table 2. From these observations, we can infer that: i) the relaxation time of glasses, calculated using the expression, τ 1 β 1 = τ 2 β 2 , and that of the supercooled liquid can be described using the same empirical relationship, and ii) the similitude between the fitting parameters obtained using the expression above for the relaxation times and those determined from the transformation times, is indicative of the similarity between the two concepts, at least in the experimental conditions under which our experiments were performed. For all this, we consider both measurements as representative of the same magnitude, the relaxation time of the glass.
The agreement between the nominal limiting fictive temperature of the measured glasses and T f ′ obtained by fitting the experimental data using equation (5) can also be seen from the data shown in Supplementary

Derivation of and from equation (2)
In supercooled liquid, T f = T at all the temperatures. In this case, equation (1) and (2) should coincide. Therefore, Taking natural logarithms and isolating, ξ(T), we obtain that, Assuming the expression, ξ = AT f + B, we see that, From where we obtain the equations (3) and (4) for D and τ 0 . In the left axis, data is represented with respect to the density of a glass cooled at 1 K/min ( ′ = 309 K), as shown in the reference. Right axis has been stablished after the consideration that, for ′ = 315 K (conventional glass), the density is 1.31 g/cm 3 . Transformation from Tdep data to ′ has been performed according to the relationship between the two quantities, as shown in ref 3 .

Supplementary table 3.
Values of density and thermal expansion coefficients used for each glass and for the supercooled liquid in equation (5)   , where and refer to the temperature and specific volume of the system at the transition from liquid to glass. All experimental data have been extracted from reported results 1,4 .

Alternative calculation of scaling parameter from glass relaxation time data
From the relaxation data plotted in Figure 2b in the main text, we obtain T g as the temperature at which the relaxation time of the glass equals 100 s. At this temperature, the specific volume of the glass is . From the slope of the representation shown in Supplementary figure 7, we can calculate the scaling factor, according to We note the similitude between the scaling parameter found from the fitting of the relaxation time using equation 5 in the main text (γ glass = 6.53) and using the approach in Supplementary figure 7 (γ glass = 7).