Ph.D. thesis (pdf) - dirac

124 Mean squared displacement
1.5
Int [arb uni]
1
0.5
0
0 100 200 300
T [K]
Figure 7.1: The raw data of cumene at ambient pressure in aluminum cell (diamonds)
and at 100 MPa in the high pressure clamb cell (triangles). The signal of the clamb
cell is also shown (circles). The signal of the aluminum cell is not shown, as it would
be almost invisible on this scale.
incoherent signal and it is consequently the incoherent intermediate scattering function
at ∼ 1 ns which is probed. The measured intensity at a fixed Q gives direct
information on the pressure and temperature dependence of the dynamics on the
nanosecond timescale.
Figure 7.2 shows the temperature dependence of the measured intensity of DBP at
atmospheric pressure and at 500 MPa at Q = 1.96 Å. The curves are in both cases
normalized, to start in Int=1 at T = 0 K, which corresponds to assume that the
molecules have no zero-point movement.
At both pressures we see the measured intensity decreasing to essentially zero in
the high temperature limit. This corresponds to a situation where the intermediate
scattering function is totally decayed, I inc (Q, t) = 0, at the nanosecond timescale.
The curve hence shows the transition from relaxed to non-relaxed dynamics on the
nanosecond timescale. It is clearly seen that this happens at a higher temperature
at elevated pressure, and also that I inc (Q, t) increases with increasing pressure at
all temperatures.
7.2.1 Calculating 〈u 2 〉
The mean square displacement is calculated from the measured intensities by assuming
the Gaussian approximation, such that equation 4.3.29 holds. This gives
ln(I) = A + −Q2 〈u 2 〉
3
(7.2.1)