2.2 REDLS-Setup
3.1.12 Other relaxations found
not enhanced in comparison to bulk material, since bulk values were used to theoretically calculate the free-surface dynamics. On the other hand, films that could not be thoroughly annealed due to their intrinsic thermal instability, such as some oligomeric films, presented enhanced free-surface mobility, as can be seen in the PS 1821 g/mol, h = 45, 60, and 130 nm, Figure 3.14 and 3.15. Thinner films, submitted to better annealing conditions as the PS 1821 g/mol, h = 17 and 25 nm, were well in agreement with the theory within the experimental error, Figures 3.14 and 3.15. If the enhanced mobility was a real physical change, it should be seen in the thinner films as well, having even a stronger effect than in thick ones. The reason for a better agreement with the theory for higher molecular weight polymers, as in Figure 3.16, is that these films show higher temperature stability and therefore they could be annealed under better conditions (Tg+50 ○C, under vacuum –p<1 mbar–, for about 36 hours).
A highly mobile free-surface, which expands its mobility to the central region of the film, decreasing Tg can be therefore discarded. On the other hand, the existence of a free-surface with a little higher mobility, without impacting on the filmsTg, cannot be completely excluded on the basis of the statistical accuracy of REDLS and the mathematical model used to describe the experimental data. In case of existence of a more mobile free-surface in polymer ultrathin films, this region cannot exceed the very last molecular layers (monomers), considering the length scale of capillary waves and the good agreement of theory and experiments. This enhanced mobility cannot also be completely discrepant in comparison to the capillary waves dynamics.
At temperatures much lower than Tg, the viscosity is infinitely high and, therefore, all capillary waves are expected to be overdamped, cf. Chapter 1.
Propagating waves are expected to appear in the q-range accessible to the REDLS experiment when the viscosity becomes too low, i.e., by increasing temperature aboveTg, they should first manifest as overdamped waves, and when the viscosity becomes small enough, then propagating capillary waves may appear, cf. section 1.2.3.2.
1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 3
0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5
G 1 x 10-3
L a g t i m e ( s )
Figure 3.29: Black curve: relaxation observed in PS 4 389 g/mol, h = 45 nm at T = 24 ○C, θs = 60○. The red line is a fit function with the type of equation 1.50.
In contrast to capillary waves, surface waves such as sound waves, become slower by increasing temperature, due to diminishing stiffness, as predicted by the Newton-Laplace equation [158]:
cL=
¿ ÁÁ
À E(1−ψ)
ρ(1+ψ)(1−2ψ) (3.22) where, cL is the longitudinal velocity of propagation of sound waves in a medium of Young modulus (or stiffness) E, density ρ, and ψ the Poisson’s ratio. The transversal velocity component is given by:
cT =
√ G
ρ (3.23)
whereGis the shear modulus. By substituting the glassy modulus of polystyrene
(G′g≈ 1.5 GPa) and the density ρ= 1050 kg/m3, ones finds [159]:
cT ≈
√ 1.5GP a
1.05×103 kg/m3 ≈1200 m/s (3.24) Withc=λf, where f is frequency in the range of GHz, the wavelength of such elastic waves should be in the nm range. Considering the low apparent propagating frequency, f = 0.019 Hz, one gets a wavelengthcT/f =λ≈63 km ! Therefore, it is not possible that this type of relaxation observed is the mani-festation of such elastic waves. A conclusive answer about the nature of such waves cannot be driven so far, as the full characterization of this mode was not possible.
Another type of relaxation that is found in some REDLS spectra is shown in the right side of the dashed line in Figure 3.30. The q-dependence of this mode revealed to be non-systematic. This relaxation seems to appear often in high viscous and relatively stiff materials, as it can be observed in PS 189 680 g/mol and 350 000 g/mol and not often in PS 1821 g/mol. The shape of the curves cannot be fitted by a stretched exponential. The slow-mode appears in these polymers at longer times than this mode shows, i.e., this undefined mode, from now on labeled as “x-mode”, has in general relaxation times between the fast and the slow-mode, but at high temperatures the slow-mode can overlap with the x-mode, cf. 3.31. The x-mode is temperature independent, and it should not be confused with the α-relaxation just due to the apparent q-independence of the relaxation times, because it does not fulfill the features of the α-relaxation, as for example the VFT temperature-dependence of the relaxation times, and to show relaxations described by a stretched exponential with βKW W = 0.4, cf. section 3.1.13.
As the x-mode seems to behave similarly in different molecular weight polystyrene samples, different thicknesses, temperatures and scattering vec-tors, one can imagine that the x-mode is not a polymer film mode, but some external excitations that are not absorbed by the insulation system. An ex-planation why it appears in high viscous systems, and not in low viscous ones, is possibly because low viscosity systems are able to absorb and damp these external excitations, while high viscous materials couple with the ex-ternal fluctuations. The x-mode relaxes at about τ ≈ 1 s, which is likely to be due to vibrations of the building or laboratory. The x-mode is not due to the intrinsic self-correlation generated by single-mode optical fibers, due to the Fabry-Perot effect, cf. Chapter 2.2.2.2. Throughout this entire work, multi-mode fibers were used to avoid this effect, and the base-line for this configuration is shown in Figure 2.20.
1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 0 . 0
0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
G 1
L a g t im e ( s )
θs = 3 5 ° θs = 5 0 ° θs = 7 0 ° θs = 8 0 ° θs = 9 0 ° θs = 1 0 0 °
Figure 3.30: This relaxation appears in higher times-scales than the fast-mode. For non-annealed films of PS 189 680 g/mol, h = 50 nm, T = 63○C, the fast-mode appears in the left side of the dashed line.
All these low frequency relaxations are possibly originated by external sources, which cannot be absorbed by the active anti-vibration table as this insulation system starts its insulation activity at frequencies around 1 Hz and higher, cf. Chapter 2.2.2.1.
1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 2 . 7 6
2 . 8 8 3 . 0 0 3 . 1 2
x - m o d e
s lo w - m o d e f a s t - m o d e
1 0 5 ° C 1 4 2 ° C
G 1 x 10-2
L a g t im e ( s )
Figure 3.31: PS 350 000 g/mol, h = 28 nm,θs= 60○. Between the fast and the slow-mode, one can observe the x-mode, which is temperature independent.
The slow-mode becomes faster in higher temperatures and overlaps with the x-mode in high temperatures. The slow-mode in PS 350 000 g/mol could not be fully resolved even in high temperatures due to the high viscosity of this polymer.
1 0 - 2 1 0 - 1 1 0 0 1 0 1
- 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5
P S 3 5 0 0 0 0 g / m o l, T = 1 0 5 ° C , h = 2 8 n m θs = 6 0 °
G 1
L a g t im e ( s )
P S 1 8 9 6 8 0 g / m o l, T = 6 3 ° C , h = 5 0 n m θs = 1 0 0 °
x - m o d e
Figure 3.32: Here the x-mode is compared in two polymers at completely different physical conditions. Even though, in both cases this mode behaves similarly, being independent of q, thickness, molecular weight and tempera-ture.