Patterns in and kinetics of phase separation in binary mixtures

This work focused mainly on two aspects of kinetics of phase separation in binary mixtures. In the first part, we studied the interplay of hydrodynamics and the phase separation of binary mixtures. A considerably flat container (a laterally extended geometry), at an aspect ratio of 14:1 (diameter: height) was chosen, so that any hydrodynamic instabilities, if they arise, could be tracked. Two binary mixtures were studied. One was a mixture of methanol and hexane, doped with 5% ethanol, which phase separated under cooling. The second was a mixture of butoxyethanol and water, doped with 2% decane, which phase separated under heating. The dopants were added to bring down the phase transition temperature around room temperature.rnrnAlthough much work has been done already on classical hydrodynamic instabilities, not much has been done in the understanding of the coupling between phase separation and hydrodynamic instabilities. This work aimed at understanding the influence of phase separation in initiating any hydrodynamic instability, and also vice versa. Another aim was to understand the influence of the applied temperature protocol on the emergence of patterns characteristic to hydrodynamic instabilities. rnrnOn slowly cooling the system continuously, at specific cooling rates, patterns were observed in the first mixture, at the start of phase separation. They resembled the patterns observed in classical Rayleigh-Bénard instability, which arises when a liquid continuously is heated from below. To suppress this classical convection, the cooling setup was tuned such that the lower side of the sample always remained cooler by a few millikelvins, relative to the top. We found that the nature of patterns changed with different cooling rates, with stable patterns appearing for a specific cooling rate (1K/h). On the basis of the cooling protocol, we estimated a modified Rayleigh number for our system. We found that the estimated modified Rayleigh number is near the critical value for instability, for cooling rates between 0.5K/h and 1K/h. This is consistent with our experimental findings. rnrnThe origin of the patterns, in spite of the lower side being relatively colder with respect to the top, points to two possible reasons. 1) During phase separation droplets of either phases are formed, which releases a latent heat. Our microcalorimetry measurements show that the rise in temperature during the first phase separation is in the order of 10-20millikelvins, which in some cases is enough to reverse the applied temperature bias. Thus phase separation in itself initiates a hydrodynamic instability. 2) The second reason comes from the cooling protocol itself. The sample was cooled from above and below. At sufficiently high cooling rates, there are situations where the interior of the sample is relatively hotter than both top and bottom of the sample. This is sufficient to create an instability within the cell. Our experiments at higher cooling rates (5K/h and above) show complex patterns, which hints that there is enough convection even before phase separation occurs. Infact, theoretical work done by Dr.Hayase show that patterns could arise in a system without latent heat, with symmetrical cooling from top and bottom. The simulations also show that the patterns do not span the entire height of the sample cell. This is again consistent with the cell sizes measured in our experiment.rnrnThe second mixture also showed patterns at specific heating rates, when it was continuously heated inducing phase separation. In this case though, the sample was turbid for a long time until patterns appeared. A meniscus was most probably formed before the patterns emerged. We attribute the reason of patterns in this case to Marangoni convection, which is present in systems with an interface, where local differences in surface tension give rise to an instability. Our estimates for the Rayleigh number also show a significantly lower number than that's required for RB-type instability.rnrnIn the first part of the work, therefore, we identify two different kinds of hydrodynamic instabilities in two different mixtures. Both are observed during, or after the first phase separation. Our patterns compare with the classical convection patterns, but here the origins are from phase separation and the cooling protocol.rnrnIn the second part of the work, we focused on the kinetics of phase separation in a polymer solution (polystyrene and methylcyclohexane), which is cooled continuously far down into the two phase region. Oscillations in turbidity, denoting material exchange between the phases are seen. Three processes contribute to the phase separation: Nucleation of droplets, their growth and coalescence, and their subsequent sedimentation. Experiments in low molecular binary mixtures had led to models of oscillation [43] which considered sedimentation time scales much faster than the time scales of nucleation and growth. The size and shape of the sample therefore did not matter in such situations. The oscillations in turbidity were volume-dominated. The present work aimed at understanding the influence of sedimentation time scales for polymer mixtures. Three heights of the sample with same composition were studied side by side. We found that periods increased with the sample height, thus showing that sedimentation time determines the period of oscillations in the polymer solutions. We experimented with different cooling rates and different compositions of the mixture, and we found that periods are still determined by the sample height, and therefore by sedimentation time. rnrnWe also see that turbidity emerges in two ways; either from the interface, or throughout the sample. We suggest that oscillations starting from the interface are due to satellite droplets that are formed on droplet coalescence at the interface. These satellite droplets are then advected to the top of the sample, and they grow, coalesce and sediment. This type of an oscillation wouldn't require the system to pass the energy barrier required for homogenous nucleation throughout the sample. This mechanism would work best in sample where the droplets could be effectively advected throughout the sample. In our experiments, we see more interface dominated oscillations in the smaller cells and lower cooling rates, where droplet advection is favourable. In larger samples and higher cooling rates, we mostly see that the whole sample becomes turbid homogenously, which requires the system to pass the energy barrier for homogenous nucleation.rnrnOscillations, in principle, occur since the system needs to pass an energy barrier for nucleation. The height of the barrier decreases with increasing supersaturation, which in turn is from the temperature ramp applied. This gives rise to a period where the system is clear, in between the turbid periods. At certain specific cooling rates, the system can follow a path such that the start of a turbid period coincides with the vanishing of the last turbid period, thus eliminating the clear periods. This means suppressions of oscillations altogether. In fact we experimentally present a case where, at a certain cooling rate, oscillations indeed vanish. rnrnThus we find through this work that the kinetics of phase separation in polymer solution is different from that of a low molecular system; sedimentation time scales become relevant, and therefore so does the shape and size of the sample. The role of interface in initiating turbid periods also become much more prominent in this system compared to that in low molecular mixtures.rnrnIn summary, some fundamental properties in the kinetics of phase separation in binary mixtures were studied. While the first part of the work described the close interplay of the first phase separation with hydrodynamic instabilities, the second part investigated the nature and determining factors of oscillations, when the system was cooled deep into the two phase region. Both cases show how the geometry of the cell can affect the kinetics of phase separation. This study leads to further fundamental understandings of the factors contributing to the kinetics of phase separation, and to the understandings of what can be controlled and tuned in practical cases. rn

Synthesis and characterization of Poly(vinylphosphonic acid) for proton exchange membranes in fuel cells

Vinylphosphonic acid (VPA) was polymerized at 80 ºC by free radical polymerization to give polymers (PVPA) of different molecular weight depending on the initiator concentration. The highest molecular weight, Mw, achieved was 6.2 x 104 g/mol as determined by static light scattering. High resolution nuclear magnetic resonance (NMR) spectroscopy was used to gain microstructure information about the polymer chain. Information based on tetrad probabilities was utilized to deduce an almost atactic configuration. In addition, 13C-NMR gave evidence for the presence of head-head and tail-tail links. Refined analysis of the 1H NMR spectra allowed for the quantitative determination of the fraction of these links (23.5 percent of all links). Experimental evidence suggested that the polymerization proceeded via cyclopolymerization of the vinylphosphonic acid anhydride as an intermediate. Titration curves indicated that high molecular weight poly(vinylphosphonic acid) PVPA behaved as a monoprotic acid. Proton conductors with phosphonic acid moieties as protogenic groups are promising due to their high charge carrier concentration, thermal stability, and oxidation resistivity. Blends and copolymers of PVPA have already been reported, but PVPA has not been characterized sufficiently with respect to its polymer properties. Therefore, we also studied the proton conductivity behaviour of a well-characterized PVPA. PVPA is a conductor; however, the conductivity depends strongly on the water content of the material. The phosphonic acid functionality in the resulting polymer, PVPA, undergoes condensation leading to the formation of phosphonic anhydride groups at elevated temperature. Anhydride formation was found to be temperature dependent by solid state NMR. Anhydride formation affects the proton conductivity to a large extent because not only the number of charge carriers but also the mobility of the charge carriers seems to change.

Anwendung der geoelektrischen 3D-Tomographie für die Analyse thermisch induzierter Strömungen im Labor

Sowohl in der Natur als auch in der Industrie existieren thermisch induzierte Strömungen. Von Interesse für diese Forschungsarbeit sind dabei die Konvektionen im Erdmantel sowie in den Glasschmelzwannen. Der dort stattfindende Materialtransport resultiert aus Unterschieden in der Dichte, der Temperatur und der chemischen Konzentration innerhalb des konvektierenden Materials. Um das Verständnis für die ablaufenden Prozesse zu verbessern, werden von zahlreichen Forschergruppen numerische Modellierungen durchgeführt. Die Verifikation der dafür verwendeten Algorithmen erfolgt meist über die Analyse von Laborexperimenten. Im Vordergrund dieser Forschungsarbeit steht die Entwicklung einer Methode zur Bestimmung der dreidimensionalen Temperaturverteilung für die Untersuchung von thermisch induzierten Strömungen in einem Versuchsbecken. Eine direkte Temperaturmessung im Inneren des Versuchsmaterials bzw. der Glasschmelze beeinflusst allerdings das Strömungsverhalten. Deshalb wird die geodynamisch störungsfrei arbeitende Impedanztomographie verwendet. Die Grundlage dieser Methode bildet der erweiterte Arrhenius-Zusammenhang zwischen Temperatur und spezifischer elektrischer Leitfähigkeit. Während der Laborexperimente wird ein zähflüssiges Polyethylenglykol-Wasser-Gemisch in einem Becken von unten her erhitzt. Die auf diese Weise generierten Strömungen stellen unter Berücksichtigung der Skalierung ein Analogon sowohl zu dem Erdmantel als auch zu den Schmelzwannen dar. Über mehrere Elektroden, die an den Beckenwänden installiert sind, erfolgen die geoelektrischen Messungen. Nach der sich anschließenden dreidimensionalen Inversion der elektrischen Widerstände liegt das Modell mit der Verteilung der spezifischen elektrischen Leitfähigkeit im Inneren des Versuchsbeckens vor. Diese wird mittels der erweiterten Arrhenius-Formel in eine Temperaturverteilung umgerechnet. Zum Nachweis der Eignung dieser Methode für die nichtinvasive Bestimmung der dreidimensionalen Temperaturverteilung wurden mittels mehrerer Thermoelemente an den Beckenwänden zusätzlich direkte Temperaturmessungen durchgeführt und die Werte miteinander verglichen. Im Wesentlichen sind die Innentemperaturen gut rekonstruierbar, wobei die erreichte Messgenauigkeit von der räumlichen und zeitlichen Auflösung der Gleichstromgeoelektrik abhängt.