Secondary relaxation processes in neat and binary glass formers studied by 2H NMR spectroscopy
- The present study employs various solid state 2H NMR techniques to elucidate glassy dynamics in plastic crystals and binary mixtures of glass forming substances. We focus on the Johari-Goldstein beta-process, which not only plays a key role for the understanding of glassy dynamics in neat systems, but also in binary mixtures thereof.
The first part is devoted to the plastic crystalline (PC) phase of cyanocyclohexane. A 2D 2H NMR assessment regarding the alpha-process demonstrated that dynamics is not governed by the symmetry of the lattice, rather molecular reorientation in cyanocyclohexane can be modelled via the same distribution of small and large angular jumps as reported for many structural glass formers. Although the stimulated echo technique yields a strong temperature dependence of the latter fractions, it was shown that this effect can be rationalized via the time-window of the experiment and the inherent decoupling of jump-times within the distribution of angles. This analysis also holds in case of previously studied structural glass formers and questions the arise of a dynamical crossover at temperatures somewhat above Tg.
The beta-process of cyanocyclohexane below Tg is well described by models developed for the structural glass former toluene, where the C-2H bond is confined to the base circle of a cone, i.e. also the secondary relaxation is not significantly affected by the translational symmetry of the PC phase. As alpha- and beta-process do not merge in cyanocyclohexane, pronounced effects were observed at high temperatures: for the first time an additional minimum in the spin-lattice relaxation T1 reflecting the beta-process was found. Furthermore the solid-echo spectra at T>Tg exhibit an articulate and characteristic deviation from a Pake pattern over a broad temperature range. These fast motion limit line-shape effects allow for a direct determination of the spatial restriction: a model based on a Gaussian distribution of cone opening angles proved adequate for a detailed modelling of the spectral evolution. T1 was modelled by means of the spectral density from dielectric spectroscopy, the results in terms of the relaxation strength 1-S are in agreement with the line shape analysis. Hence the pronounced NMR effects naturally arise due to the non-merging beta-process in cyanocyclohexane and are in full agreement with an extension of previous models for the beta-process in structural glass formers at T<Tg. Furthermore the present study emphasizes the important role of the beta-process for glassy dynamics, as it demonstrates that a substantial fraction of correlation is lost via the beta-process at high temperatures in the absence of merging.
The second part addresses the dynamics of the glass former toluene in binary mixtures. Below Tg of neat toluene a pronounced concentration dependence of the beta-process was observed in mixtures of toluene and a polychlorinated biphenyl (PCB54). Whereas the distribution of correlation times remains unaltered, the relaxation strength of the process significantly decreases below a threshold toluene concentration of x=0.7. Stimulated echo experiments demonstrated that this attenuation arises from a fraction of toluene molecules, 1-fb, which do no longer exhibit a beta-process. This finding is in accordance with bi-exponential magnetization curves observed around Tg of the mixture. Hence the "islands of mobility" concept for the beta-process, refuted in the case of neat glass formers, was introduced in binary mixtures thereof.
A model was developed that links the fraction 1-fb to toluene molecules in a local PCB54 rich environment, which only exhibit the alpha-process of the latter, whereas the remainder of molecules reorient on a faster time scale (alpha'-process) and show a beta-process. This bimodal approach with two distinct toluene sub-ensembles was shown to explain the observed behaviour in virtually all NMR experiments, whereas an adaptation via a single broad distribution for the toluene motion was infeasible. The relative weight of the fractions is a function of concentration and temperature, as 2D NMR spectra demonstrated that exchange between the sub-ensembles exists. 2D NMR experiments furthermore show that toluene molecules in the mixtures reorient via the same mechanism as in the neat system - both sub-ensembles are governed by typical glassy dynamics.
To widen the validity of the present study, previous results from other binary mixtures containing toluene were reassessed: all features regarding the beta-process were recovered and its concentration dependence below Tg in diverse mixtures was successfully described within a simple lattice model. This dependence of the beta-process on the local toluene concentration provides strong arguments for a cooperativeness of the process, in contrast to the general perception.
Influence of side walls and undulated topography on viscous gravity-driven film flow
- While a gravity-driven viscous film flow down an inclined flat plane of infinite extent can be described by an easy analytical solution, flow problems in nature, like glacier movements or the liquid film on the human eye are much more complex.
Also to optimize a large number of technical applications, like coating applications or heat exchanger devices, one has to investigate and understand how different influencing factors, like topological features on the substrate or a finite width of the system, influence the flow and its stability isolated from each other.
By introducing a wavy structure to the underlying topography, which could be for example a model for roughness, new effects emerge in the flow, which cannot be observed in flows over a flat incline.
Eddies can separate from the main flow at the lee side of the undulation for kinematic reasons, or induced by inertial effects.
In biological systems these eddies are dead water areas, which are cut off from nutrient supply, in heat exchanger applications their appearance has a strong impact on the convective heat transport within the liquid.
Furthermore, the amplitude of free surface of the liquid can be amplified immensely when the liquid is in resonance with the undulation of the underlying topography.
In this work we study experimentally as well as numerically the complex interaction of this resonance phenomenon with the appearing of eddy structures in the valleys of the undulation and show, that one can suppress flow separation selectively even at rather high Reynolds numbers when one exploits the resonance phenomenon specifically.
Another part of this work deals with the question how the presence of side walls and the contact angle of the liquid there influences the free surface shape of the liquid, the velocity field and the globally transported volume flux.
While an additional no--slip condition at the wall causes additional friction and leads thus to a lower volume flux, capillary elevation at the side walls can generate a velocity overshoot in the vicinity of the walls, depending on the film thickness and the wetting properties of the liquid, which counteracts the additional friction coming from the walls.
An extensive theoretical parameter study, which is supplemented with experimental data, provides criteria for the first onset of the velocity overshoot and gives answer to the question when the counteracting influences on the global volume flux just cancel each other.
An experimental study of the free surface shape of a draining flow shows that this configuration cannot be described by a series of quasi-steady states, even when a dynamic contact angle is taken into consideration, although the flow changes only very slowly in time.
Additional time dependent numerical simulations of the draining flow reveal an indentation of the free surface in the vicinity of the side wall, which could promote film rupture in technical thin film applications.
Furthermore, side wall effects play an important role for the physical stability of the flow.
Waves develop at the free surface of a gravity--driven flow and grow while they are traveling downstream, when a critical volume flux is exceeded.
It is shown by experimental variation of the contact angle, the film thickness and the side wall distance, that the presence of side walls generates different effects which have competing influences on the stability of the flow.
Capillary elevation leads to a pretensioning of the free surface, which tends to stabilize the free surface, just as the additional no-slip condition at the wall does.
The emerging of a velocity overshoot in the capillary elevation on the other hand leads to a destabilization of the flow.
In the system studied here the stabilizing influence of the side walls dominates over the destabilizing influence which is of comparatively short range, which means that this flow configuration is more stable than the corresponding flow of infinite extent.
However, the results suggest that the destabilizing influences should dominate over the stabilizing influences in similar flow configurations when the film would become even thinner.
While free surface film flows typically form long waves at first, we find for this flow configuration, that the type of instability changes from a long-wave type in the middle of the channel to a short-wave type instability, as it is well known for boundary layer flows, as the side wall distance is reduced.