Los resultados del trabajo de investigación que se presentan en esta tesis representan un aporte al entendimiento de la relación entre estructura y propiedades de polímeros. En este sentido, el objetivo principal del presente trabajo ha sido contribuir al entendimiento de la reología no-lineal de polímeros de diferentes arquitecturas moleculares analizando su comportamiento en flujos de corte, lineales y no-lineales, a la luz de algunos modelos reológicos seleccionados, derivados a partir de diferentes teorías. Con este objetivo, se sintetizaron polibutadienos lineales y en estrella modelo mediante la técnica de polimerización aniónica. En todos ellos se mantuvo constante la microestructura (proporción de isómeros que constituyen las macromoléculas) variándose el peso molecular entre aproximadamente 10 y 100 kg/mol. El estudio reológico incluye la medición de funciones materiales de corte en flujos en estado estacionario y transitorios, en un rango amplio de temperaturas, y siempre dentro del régimen de materiales altamente entrelazados. Tanto las funciones materiales medidas como los parámetros calculados a partir de ellas fueron analizados en función de las características estructurales de los polímeros, la temperatura y las variables de flujo (deformación, velocidad de deformación, etc.). El comportamiento viscoelástico lineal, caracterizado por los módulos dinámicos, se ajustó con el modelo de Maxwell multimodal que permite determinar los coeficientes {ηi λi} que componen el espectro de relajación discreto de cada material en el rango de caracterización experimental. El comportamiento no-lineal se analizó con el modelo de White y Metzner (que es una generalización empírica del modelo de Maxwell Convectivo proveniente de los modelos llamados cuasi-lineales), el modelo de Giesekus (proveniente de teorías cinéticas de soluciones diluidas), y los modelos de Wagner y de Phan-Thien y Tanner, ambos provenientes de la teoría de redes para polímeros en estado fundido. Los coeficientes particulares de estos modelos fueron calculados por ajuste de las funciones viscométricas. Las predicciones que los distintos modelos hacen de las funciones materiales correspondientes a los flujos transitorios de inserción de flujo de corte y de relajación de tensiones después de un desplazamiento súbita fueron entonces comparadas con las mediciones experimentales. La dependencia de los parámetros de ajuste de los modelos con las características moleculares de los polímeros sintetizados muestra que todos los polímeros, lineales y en estrella, presentan comportamiento reológico no-lineal muy similar, a pesar de las notables diferencias en el comportamiento viscoelástico lineal entre estas dos arquitecturas moleculares. Complementariamente, se analizó la estructura y el comportamiento reológico de los materiales resultantes de la hidrogenación parcial del polibutadieno. Los resultados demuestran que este proceso se produce de forma que durante la adsorción de las moléculas en la superficie del catalizador, éstas hidrogenan ~89% de sus dobles enlaces. Es por esto que en la hidrogenación parcial se generan mezclas inmiscibles de polímero ~89% saturado y polibutadieno no hidrogenado. Los materiales resultaron ser termo-reológicamente complejos y presentaron módulos elásticos relativamente altos a baja frecuencia, como suele ocurrir en mezclas inmiscibles debido a la presencia de la interfase. El cálculo de los espectros de relajación discretos de estas mezclas permitió determinar el modo de relajación lento correspondiente a la dinámica de la interfase. / The results of the research work presented in this thesis represent a contribution to the comprehension of the relationship between the structure and properties of polymers. In that sense, the main objective of the present work has been to contribute to the understanding of the non-linear rheological behavior of polymers of different molecular architectures analyzing their behavior in shear flows, linear and non-linear, at the light of selected rheological models that have been derived from different theories. At the light of this objective, linear and star model polybutadienes were synthesized using anionic polymerization technique with molecular weights were in the range between approximately 10 and 100 kg/mol. All the materials have the same microstructure (proportion of isomers that constitute the macromolecules). The rheological study includes the determination of the shear materials functions associated to steady-state and transient flows, in a large range of temperatures, and always in the regime of highly entangled materials. The material functions, as well as the parameters determined from them, were analyzed as a function of the structural characteristics of the polymers, temperature and flow variables (like deformation, shear rate, etc.). The linear viscoelastic behavior of the polymers, characterized through the dynamic moduli, was modeled with the multimode Maxwel model, determining the {ηi , λi} coefficients that constitute the discrete relaxation spectrum of each material in the experimental range covered. The non-linear behavior was analyzed with the White Metzner model (which is an empiric generalization of the Convective Maxwell model that comes from de so called quasi-linear models), the Giesekus model (originated in kinetic theories of dilute solutions), and the Wagner and Phan-Thien and Tanner models, both derived from the network theory for molten polymers. The coefficients of these models were calculated adjusting the viscometric functions to their predictions. The materials functions predicted by the different models, corresponding to start-up and step-strain transient shear flows, were then compared to the experimental data. The dependency of the adjusted parameters of the different models to the molecular characteristics of the synthesized polymers shows that all the polymers, linear and stars, present very similar rheological behavior, even thought the linear viscoelastic behavior of these two different molecular architectures are very different. As a complement, the structure and rheological behavior of partially hydrogenated polybutadienes were analyzed. The results show that the hydrogenation proceeds in such a way that during the adsorption of the molecules to the catalyst surface, ~89% of their double bonds hydrogenate. For this reason, the partial hydrogenation of polybutadiene generates un immiscible blend of a ~89% saturated polymer and non-hydrogenated polybutadiene. These materials turn out to be thermo-rheologically complex and displayed dynamic moduli relatively large at low frequencies, as it is frequently found in immiscible polymer blends due to the presence of the interphase. The calculation of the discrete relaxation spectra of these blends allowed the evaluation of the relatively large relaxation time that corresponds to the dynamic of the interphase.

A literatura corrente possui informações limitadas sobre o projeto da área de troca térmica de tanques com jaqueta, serpentina helicoidal, serpentina espiral e chicana tubular vertical, em operação com fluidos não-Newtonianos. A presente tese teve por objetivo principal analisar a transferência de calor, potência consumida e ampliação de escala em tanques com impulsores mecânicos na agitação de fluidos não-Newtonianos com duas superfícies de transmissão de calor, chicana tubular vertical e serpentina em espiral. O trabalho também visou fornecer métodos de ampliação de escala de tanques com agitação para fluidos não-Newtonianos que sigam o modelo reológico da lei das potências. A unidade experimental contemplou dois tanques de acrílico, com volume de 10 litros e 50 litros, respectivamente, chicanas tubulares verticais e serpentina em espiral. Os impulsores mecânicos utilizados foram o axial com 4 pás inclinadas a 45° e o radial turbina com 6 pás planas. Como fluidos utilizaram-se soluções aquosas de carboximetilcelulose (0,5%, 1,0% e 1,5%), solução aquosa de carbopol 940 (1,5%), solução aquosa de sacarose (50%) e água. Todos os experimentos foram conduzidos em batelada. Com os dados obtidos, empregou-se o uso de regressões para a obtenção da Equação de Nusselt, as quais forneceram valores de coeficiente de determinação ajustados entre 0,83 e 0,89 com Reynolds no intervalo de 20 a 405000, Prandtl na faixa de 4 a 6400 e índice reológico do modelo da lei das potências entre 0,45 e 1,00. Observou-se que no aquecimento realizado com a chicana tubular vertical, o impulsor radial forneceu coeficientes de convecção 20% acima quando comparado com o impulsor axial, entretanto o consumo de potência foi cerca de 66% maior em relação ao impulsor axial. No caso da serpentina espiral, o impulsor axial promoveu coeficientes de convecção por volta de 15% superiores em relação ao impulsor radial com um consumo de potência 65% menor. Desse modo, em processos em que não é necessária uma elevada turbulência, recomenda-se o uso do impulsor axial com a serpentina espiral, porém, se o processo demandar uma turbulência significativa, deve-se usar o impulsor radial com a chicana tubular vertical. Em uma última análise, os modelos não-lineares obtidos para ampliação de escala forneceram erros entre 11% e 20% na predição da rotação no tanque industrial, os quais são válidos para Reynolds modificados de Metzner e Otto (1957) na faixa de 20 a 4000 e para fluidos não-Newtonianos pseudoplásticos com índices reológicos entre 0,45 e 1,00. / Current literature has limited information on the design of the thermal exchange area of tanks with jacket, helical coil, spiral coil and vertical tuber baffle, in operation with non-Newtonian fluids. The main purpose of this thesis was to analyze heat transfer, power consumption and scale-up in tanks with mechanical impellers in the agitation of non-Newtonian fluids with two heat transfer surfaces, vertical tube baffle and spiral coil. The work also aimed to provide methods of scale-up tank scale with agitation for non-Newtonian fluids that follow the rheology model of the law of powers. The experimental unit included two acrylic tanks, with a volume of 10 liters and 50 liters, respectively, vertical tube baffles and spiral coil. The mechanical impellers used were the 45° pitched blade turbine (PBT) and the Rushton turbine (RT). Aqueous solutions of carboxymethylcellulose (0.5%, 1.0% and 1.5%), aqueous solution of carbopol 940 (1.5%), aqueous solution of sucrose (50%) and water were used as fluids. All the experiments were conducted in batch. With the obtained data, we used the regressions to obtain the Nusselt Equation, which provided coefficient of determination values adjusted between 0.83 and 0.89 with Reynolds in the range of 20 to 405000, Prandtl in the range of 4 to 6400 and rheological index of the power law model between 0.45 and 1.00. It was observed that in the heating performed with the vertical tube baffle, the RT provided convection coefficients 20% higher when compared to the axial impeller, however the power consumption was about 66% higher in relation to the PBT. In the case of the spiral coil, the PBT promoted convection coefficients around 15% higher than the RT with 65% lower power consumption. Thus, in processes where high turbulence is not required, it is recommended to use the PBT with the spiral coil, but if the process requires significant turbulence, the RT must be used with the vertical tubular chassis. In a final analysis, the nonlinear models obtained for scaling provided errors between 11% and 20% in the prediction of rotation in the industrial tank, which are valid for Metzner and Otto (1957) modified Reynolds in the range of 20 to 4000 and for non-Newtonian pseudoplastic fluids with rheological indexes between 0.45 and 1.00.

A literatura corrente possui informações limitadas sobre o projeto da área de troca térmica de tanques com jaqueta, serpentina helicoidal, serpentina espiral e chicana tubular vertical, em operação com fluidos não-Newtonianos. A presente tese teve por objetivo principal analisar a transferência de calor, potência consumida e ampliação de escala em tanques com impulsores mecânicos na agitação de fluidos não-Newtonianos com duas superfícies de transmissão de calor, chicana tubular vertical e serpentina em espiral. O trabalho também visou fornecer métodos de ampliação de escala de tanques com agitação para fluidos não-Newtonianos que sigam o modelo reológico da lei das potências. A unidade experimental contemplou dois tanques de acrílico, com volume de 10 litros e 50 litros, respectivamente, chicanas tubulares verticais e serpentina em espiral. Os impulsores mecânicos utilizados foram o axial com 4 pás inclinadas a 45° e o radial turbina com 6 pás planas. Como fluidos utilizaram-se soluções aquosas de carboximetilcelulose (0,5%, 1,0% e 1,5%), solução aquosa de carbopol 940 (1,5%), solução aquosa de sacarose (50%) e água. Todos os experimentos foram conduzidos em batelada. Com os dados obtidos, empregou-se o uso de regressões para a obtenção da Equação de Nusselt, as quais forneceram valores de coeficiente de determinação ajustados entre 0,83 e 0,89 com Reynolds no intervalo de 20 a 405000, Prandtl na faixa de 4 a 6400 e índice reológico do modelo da lei das potências entre 0,45 e 1,00. Observou-se que no aquecimento realizado com a chicana tubular vertical, o impulsor radial forneceu coeficientes de convecção 20% acima quando comparado com o impulsor axial, entretanto o consumo de potência foi cerca de 66% maior em relação ao impulsor axial. No caso da serpentina espiral, o impulsor axial promoveu coeficientes de convecção por volta de 15% superiores em relação ao impulsor radial com um consumo de potência 65% menor. Desse modo, em processos em que não é necessária uma elevada turbulência, recomenda-se o uso do impulsor axial com a serpentina espiral, porém, se o processo demandar uma turbulência significativa, deve-se usar o impulsor radial com a chicana tubular vertical. Em uma última análise, os modelos não-lineares obtidos para ampliação de escala forneceram erros entre 11% e 20% na predição da rotação no tanque industrial, os quais são válidos para Reynolds modificados de Metzner e Otto (1957) na faixa de 20 a 4000 e para fluidos não-Newtonianos pseudoplásticos com índices reológicos entre 0,45 e 1,00. / Current literature has limited information on the design of the thermal exchange area of tanks with jacket, helical coil, spiral coil and vertical tuber baffle, in operation with non-Newtonian fluids. The main purpose of this thesis was to analyze heat transfer, power consumption and scale-up in tanks with mechanical impellers in the agitation of non-Newtonian fluids with two heat transfer surfaces, vertical tube baffle and spiral coil. The work also aimed to provide methods of scale-up tank scale with agitation for non-Newtonian fluids that follow the rheology model of the law of powers. The experimental unit included two acrylic tanks, with a volume of 10 liters and 50 liters, respectively, vertical tube baffles and spiral coil. The mechanical impellers used were the 45° pitched blade turbine (PBT) and the Rushton turbine (RT). Aqueous solutions of carboxymethylcellulose (0.5%, 1.0% and 1.5%), aqueous solution of carbopol 940 (1.5%), aqueous solution of sucrose (50%) and water were used as fluids. All the experiments were conducted in batch. With the obtained data, we used the regressions to obtain the Nusselt Equation, which provided coefficient of determination values adjusted between 0.83 and 0.89 with Reynolds in the range of 20 to 405000, Prandtl in the range of 4 to 6400 and rheological index of the power law model between 0.45 and 1.00. It was observed that in the heating performed with the vertical tube baffle, the RT provided convection coefficients 20% higher when compared to the axial impeller, however the power consumption was about 66% higher in relation to the PBT. In the case of the spiral coil, the PBT promoted convection coefficients around 15% higher than the RT with 65% lower power consumption. Thus, in processes where high turbulence is not required, it is recommended to use the PBT with the spiral coil, but if the process requires significant turbulence, the RT must be used with the vertical tubular chassis. In a final analysis, the nonlinear models obtained for scaling provided errors between 11% and 20% in the prediction of rotation in the industrial tank, which are valid for Metzner and Otto (1957) modified Reynolds in the range of 20 to 4000 and for non-Newtonian pseudoplastic fluids with rheological indexes between 0.45 and 1.00.

When calculating scattering amplitudes in gauge and gravitational theories one encounters infrared (IR) divergences associated with massless fields. These are known to be artifacts of constructing a quantum field theory starting with free fields, and the assumption that in the asymptotic limit (i.e. well before and after a scattering event) the incoming and outgoing states are non-interacting. In 1937, Bloch and Nordsieck provided a technical procedure eliminating the IR divergences in the cross-sections. However, this did not address the source of the problem: A detailed analysis reveals that, in quantum electrodynamics (QED) and in perturbative quantum gravity (PQG), the interactions cannot be ignored even in the asymptotic limit. This is due to the infinite range of the massless force-carrying bosons. By taking these asymptotic interactions into account, one can find a picture changing operator that transforms the free Fock states into asymptotically interacting Faddeev- Kulish (FK) states. These FK states are charged (massive) particles surrounded by a “cloud” of soft photons (gravitons) and will render all scattering processes infrared finite already at an S-matrix level. Recently it has been found that the FK states are closely related to asymptotic symmetries. In the case of QED the FK states are eigenstates of the large gauge transformations – U(1) transformations with a non-vanishing transformation parameter at infinity. For PQG the FK states are eigenstates of the Bondi-Metzner-Sachs (BMS) transformations – the asymptotic symmetry group of an asymptotically flat spacetime. It also appears that the FK states are related the Wilson lines in the Mandelstam quantization scheme. This would allow one to obtain the physical FK states through geometrical or symmetry arguments. We attempt to clarify this relation and present a derivation of the FK states in PQG from the gravitational Wilson line in the eikonal approximation, a result that is novel to this thesis.