Ph.D. thesis (pdf) - dirac

18 Slow and fast dynamics
T > T 2
κ
ω T 2 > T > T 1
1
κ
ω 2
T 1 > T
T 1 T 2
ω 1 ω 2
Figure 2.3: The left figure shows an idealized illustration of the temperature dependence
of the compressibility measured at two different time scales, a high frequency
ω 2 and a low frequency ω 1 (with the latter corresponding to the timescale of the
cooling rate). The right figure shows the corresponding frequency dependent compressibility
at different temperatures. The jump in level is the signature of the
temperature dependent alpha relaxation. The probe frequencies are indicated with
vertical lines. The figure illustrates three domains. At temperatures above T 2 the
two probes measure the same low frequency compressibility - its value decreasing
with decreasing temperature. At temperatures lower than T 2 but higher than T 1 the
high frequency probe measures the high frequency value of the compressibility while
the low frequency probe measures the low frequency value. Both high frequency
and low frequency compressibility depend on temperature, but not a priori with
the same temperature dependence. At temperatures lower than T 1 both probes see
the high frequency compressibility. This is so because the alpha relaxation time
has become longer than the time scale of both probes. The alpha relaxation is also
longer than the characteristic time of cooling - meaning that liquid is frozen in its
glassy state. This freezing in also has the consequence that the measured compressibility
does not change significantly with decreasing temperature. The value of the
compressibility in the glass corresponds to the high frequency compressibility at T g
when the liquid is frozen in.