Ph.D. thesis (pdf) - dirac

136 Mean squared displacement
as being due to the softening of the harmonic potential. The break in 〈u 2 〉 around T g
is in this frame understood as being due the change in temperature dependence of
the high frequency elastic constants (sound speeds) at T g (see sections 2.5 and 6.2).
The arguments behind the elastic model ignore/disregard any possible contributions
to 〈u 2 〉 from non-harmonic and relaxational movements.
In order to test the elastic model it is necessary to assume that there is no extra
relaxational motion contributing to 〈u 2 〉 around T g . However, it is not likely that
this assumption is fulfilled. We know from the time of flight spectra that DHIQ has
strong quasi-elastic scattering already at T g (section 8.3.3). The time of flight has a
broader resolution function, so this quasi-elastic scattering correspond to relaxation
at even shorter times than the 〈u 2 〉 we probe with backscattering. If the relaxational
contribution is larger for more fragile liquids, then it might explain that the prediction
of the elastic model appears to hold better for stronger systems. The alpha
relaxation itself also enters the experimental window at some time, maybe already
when τ α ≈ 1µs. This happens intrinsically faster for fragile liquids than for strong
liquids.
The fragility dependent difference in the temperature dependence of 〈u 2 〉 seen in
figure 7.13 is difficult to anticipate very close to T g but becomes significant only
above 1.1T g . This explains why differences that are apparent to the naked eye in
figure 7.13 correspond to relatively small differences in figure 7.14. The liquids are
already quite far from the glass transition at 1.1T g and the actual alpha relaxation
time depends intrinsically and strongly on the fragility of the liquid. In figure 7.15
we show the mean square displacement of the least fragile of the systems we study,
glycerol, and of the most fragile liquid, DHIQ. The mean square displacement is
scaled with its values at T g as a function of temperature scaled with T g (hence, it is
the same type of plot as the one depicted in figure 7.13, just with a different scale).
Glycerol has τ α ≈ 0.01 s while the very fragile DHIQ has an alpha relaxation time
of only τ α ∼ 1µs, meaning that their alpha relaxation time differ by four orders
of magnitude when compared at T = 1.1T g . The alpha relaxation time of glycerol
only becomes as fast as τ α ∼ 1µ s at a much higher temperature, namely around
T = 1.3T g , where the mean square displacement of glycerol also increases rapidly.
7.7 Summary
The mean square displacement at the nanosecond timescale has been studied as a
function of temperature in a set of molecular liquids which covers a large range of
fragilities.