The overall thrust of this dissertation is to gain a comprehensive understanding over the factors that govern the performance and behavior of ultra-thin, cross-linked polymer films. Poly(NIPAAm) was used as a model polymer to study volume phase transition in surface tethered networks. Poly(NIPAAm) undergoes a reversible phase transition at approximately 32°C between a swollen hydrophilic random coil to a collapsed hydrophobic globule state, thought to be caused by increased hydrophobic attractions between the isopropyl groups at elevated temperatures. We present a simple photochemical technique for fabricating structured polymer networks, enabling the construction of responsive surfaces with unique properties. The approach is based on the photo-cross-linking of copolymers synthesized from N-isopropylacrylamide and methacroyloxybenzophenone (MaBP). In order correlate layer swelling to the MaBP content, we have studied the swelling behavior of such layers in contact with aqueous solutions with neutron reflection. The cross-linked networks provide a three-dimensional scaffold to host a variety of functionalities. These networks serve as a platform which can be used to amplify small local perturbations induced by various stimuli like temperature, pH, solvent, ionic strength and peptide modified hydrogels to bring about a macroscopic change. Neutron reflection experiments have shown that the volume-phase transition of a surface-tethered, cross-linked poly(NIPAAm) network coincided with the two-phase region of uncross-linked poly(NIPAAm) in solution. Parallel measurements with ATR-FTIR investigating the effect of temperature, pH and salts suggest that the discontinuous transition is the result of cooperative dehydration of the isopropyl groups, with water remaining confined between amide groups in the collapsed state as weakly hydrogen bonded bridges. Hybrid polymers with specific peptide sequences have shown specific response to external cues such as pH and metal ions exhibiting unique phase behavior.

In this thesis, we consider two models from physics, which are characterized by the interplay of thermodynamical and fluid mechanical phenomena: demixing (spinodal decomposition) and Rayleigh--Bénard convection. In both models, we investigate the dependencies of certain intrinsic quantities on the system parameters. The first model describes a thermodynamically driven demixing process of a binary viscous fluid. During the evolution, the two components of the mixture separate into two domains of the different equilibrium volume fractions. One observes a clear tendency: Larger domains grow at the expense of smaller ones, and thus, the average domain sizes increases --- a phenomenon called coarsening. It turns out that two mechanisms are relevant for the coarsening process. At an early stage of the evolution, material transport is essentially mediated by diffusion; at a later stage, when the typical domain size exceeds a certain value, due to the viscosity of the mixture, a fluid flow sets in and becomes the relevant transport mechanism. In both regimes, the growth rates of the typical domain size obey certain power laws. In this thesis, we rigorously establish one-sided bounds on these growth rates via a priori estimates. The second model, Rayleigh--Bénard convection, describes the behavior of a fluid between two rigid horizontal plates that is heated from below and cooled from above. There are two competing heat transfer mechanisms in the system: On the one hand, thermodynamics favors a state in which temperature variations are locally minimized. Thus, in our model, the thermodynamical equilibrium state is realized by a temperature with a linearly decreasing profile, corresponding to pure conduction. On the other hand, due to differences in the densities of hot and cold fluid parcels, buoyancy forces act on the fluid. This results in an upward motion of hot parcels and a downward motion of cold parcels. We study the dependence of the average upward heat flux, measured in the so-called Nusselt number, on the temperature forcing encoded by the container height. It turns out that the efficiency of the heat transport is independent of the height of the container, and thus, the Nusselt number is a constant function of height. Using a priori estimates, we prove an upper bound on the Nusselt number that displays this dependency --- up to logarithmic errors. Further investigations on the flow pattern in Rayleigh--Bénard convection show a clear separation of length scales: Along the horizontal top and bottom plates one observes thin boundary layers in which heat is essentially conducted, whereas the large bulk is characterized by a convective heat flow. We give first rigorous results in favor of linear temperature profiles in the boundary layers, which indicate that heat is indeed essentially conducted close to the boundaries.:1 Introduction 2 Coarsening rates in binary viscous fluids 2.1 Background from physics 2.2 Background from mathematics 2.3 The model 2.4 The gradient flow structure 2.5 Heuristics 2.6 Numerical simulations 2.7 Main results 2.8 Preliminaries 2.9 Proof of upper bounds on coarsening rates 2.10 Appendix: Well-posedness and regularity of solutions 3 Scaling of the Nusselt number 3.1 Background from physics 3.2 The model and the Nusselt number 3.3 Heuristics 3.4 Main results 3.5 Scaling law in the linear regime 3.6 Preliminaries and review 3.7 Upper bound using the background field method 3.8 Upper bound using the maximum principle 3.9 Appendix: Some elementary estimates 4 The laminar boundary layer 4.1 Background, model, and motivation 4.2 Main results 4.3 Preparation: Bounds on the velocity field 4.4 On the energy distribution 4.5 Bounds on the second order derivatives of the temperature field 4.6 Bounds on the third order derivatives of the temperature field

L'augmentation de la concentration de dioxyde de carbone (CO2) dans l'atmosphère depuis la révolution industrielle a conduit à l'augmentation de la température moyenne du globe. Pour limiter l’accroissement des températures atmosphériques moyennes, la quantité de dioxyde de carbone émise dans l'atmosphère doit être réduite. Une des solutions envisagée sur les sources fixes est le captage et le stockage du CO2. Ce procédé d’absorption/désorption, bien connu dans le traitement du gaz naturel, est onéreux et peu efficace pour le traitement du gaz des sources fixes et doit être optimisé. La solution proposée s’appuie sur l’utilisation de solvants démixants, présentant une séparation de phase équilibre liquide-liquide (LLE) en solution aqueuse en fonction de la température. Ce manuscrit présente une étude réalisée pour la famille des alkyl-pipéridines connues pour ses séparations de phase. Cette étude permettra d’évaluer l’influence de la taille, de la positionet du nombre de substituants sur les propriétés thermodynamiques d’intérêt pour le procédé. Pour étudier les LLE des solutions aqueuses démixantes, en particulier dans le cas des solutions chargées en gaz, deux instruments ont été mis au point. Il a été possible de démontrer que les changements opérés sur les diagrammes de phase des amines sont liés aux réactions chimiques mises en jeu lors de la dissolution du CO2. Pour les alkyl-pipéridines tertiaire on observe la température de démixtion diminue avec l’addition de CO2, allant avec la formation de carbonates. Avec les alkyl-pipéridines secondaires la température de démixtion augmente, ce qui est lié à la présence en solution de carbamates qui stabilisent la solution aqueuse. Le comportement des amines secondaires très encombrées, qui ne peuvent donc pas formées de carbamates, est similaire à celui des amines tertiaires, ce qui est cohérent avec les conclusions précédentes. Une étude approfondies des propriétés thermodynamiques d’excès (VE, CpE et HE) des alkyl-pipéridines en solution aqueuse a également permis de démontrer des relations structure - propriétés. La position du substituant sur le cycle pipéridine a une influence considérable et prévisible sur l’intensité des propriétés d’excès, alors que la nature de l’amine (secondaire ou tertiaire) va influencer la position de l’extremum de cette propriété. Enfin, une modélisation thermodynamique rigoureuses des solubilités et des enthalpies de dissolution du CO2 dans les solutions aqueuses de pipéridines a permis de déterminer les constantes de formation des carbamates dans les solutions aqueuses de 3- et 4-méthylpipéridines. / The increase of carbon dioxide (CO2) concentration in the atmosphere, since the industrial revolution has led to the rise in the average global climate temperature. To prevent the escalation of global climate temperatures the amount of CO2 emitted into the atmosphere must be reduced. One solution is carbon capture and sequestration which removes CO2 from fixed sources. The absorption/desorption cycle is well known for the treatment of acid gas, but is expensive and not as efficient for the treatment of gas from fixed/industrial sources. A solution to this problem is the use of aqueous demixing amine solvents which present a liquid-liquid phase equilibrium (LLE) as a function of temperature. This manuscript presents a study done to measure the LLE and thermodynamic properties of the alkyl piperidine family, which can be used for carbon capture processes. This work evaluates the effect of the size, position and number of alkyl substituents on the thermodynamic properties of interest in the carbon capture process. To study the LLE of aqueous demixing solutions, particularly gas loaded solutions, two novel apparatuses were developed. The results demonstrate that the changes in the amine phase diagrams are related to the chemical reactions involved with dissolution of CO2. The tertiary alkyl piperidines displayed reduced demixing temperature with the addition of CO2 due to the formation of carbonate species. The secondary alkyl piperidines display an increasing demixing temperature which is related to the formation of carbamate species which stabilizes the solution. Secondary alkyl piperidines that are severely sterically hindered, which cannot produce carbamates, behave similarly to the tertiary amine which is coherent with the preceding conclusion. The structure property relationship concerning the excess thermodynamic properties (VE, CpE et HE) of aqueous solutions were studied in depth. This revealed that the position of the substituents on the cyclic ring has a considerable and obvious influence on the intensity of the excess properties, along with the class of the amine, whether secondary or tertiary, will influence the positions of the extrema of the excess property. To conclude, a rigorous thermodynamic model based on the CO2 solubility and the enthalpy of solution for CO2 in aqueous solutions of alkyl piperidine, allowed for the determination of the carbamate formation constants of 3- and 4-methylpiperidine.

No description available.