In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

Este trabalho teve por objetivo investigar a obtenção de espinélio MgAl2O4 nanoestruturado através da síntese contínua por combustão em solução e sua caracterização por diferentes técnicas. Incluso neste estudo a influência do tipo de combustível e a razão combustível-oxidante no tamanho do cristalito. As partículas de espinélio MgAl2O4 foram sintetizadas utilizando-se os precursores químicos nitrato de alumínio e nitrato de magnésio como fonte dos cátions metálicos. Uréia, glicina e sacarose foram empregadas como agentes redutores, com diferentes valores da razão combustível-oxidante para a sacarose. Estes parâmetros foram relacionados com sua influência no tamanho de cristalito, tamanho de partícula e área superficial. Na caracterização do pó obtido, foram utilizadas técnicas como análise termodiferencial (ATD) e termogravimétrica (ATG), granulometria por difração de laser (GDL), análise de área superficial (BET), análise cristalográfica por difração de raios X (DRX), morfologia por microscopia eletrônica de varredura (MEV). As reações químicas da síntese contínua por combustão em solução resultaram na formação in situ de fases cristalinas para reações estequiométricas de uréia, glicina e sacarose e as deficientes de sacarose. Preponderância de fase amorfa ocorreu nas reações com excesso de sacarose para o pó como-sintetizado. A totalidade de fase cristalina foi obtida após um tratamento térmico a 900°C do pó como-sintetizado. Os pós de espinélio MgAl2O4 obtidos apresentaram-se como constituídos de cristalitos nanométricos, dispostos na forma de agregados de tamanho micrométrico. O tamanho de cristalito médio, calculado pelo método Single Line, a partir de dados de análises por DRX, foi de 13 nm. A área superficial média dos pós calcinados medida pelo método BET foi de 54 g/m2 Por análise granulométrica constatou-se um Tamanho de partícula médio de 17 μm para o pó como-sintetizado e 17,1 μm para o calcinado a 900ºC. As análises por MEV confirmaram a agregação das partículas do pó sintetizado, a partir de partículas preponderantemente esféricas e algumas com morfologia irregular. / This study has investigated a continuous solution combustion synthesis technique to obtain the nanostructured MgAl2O4 spinel powder and their characterize them by different tecniques. This study has also included the investigation of the influence of different kinds of fuel and fuel-to-oxidant ratio on crystallite size. The MgAl2O4 spinel powder was performed using aluminum nitrate and magnesium nitrate to obtain the metallic ions. Urea, glycine and sucrose were used like fuel, with several fuel-to-oxidant ratio. These parameters were correlating with powders characteristics, like crystallite size, particle size and superficial area. The techniques used for powder characterization included differential thermal analyzer (DTA), thermogravimetric analyzer (TGA), particles size analyzer (PSA), surface area by BET analysis, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The chemical reactions of solution combustion resulted on crystalline phase to the reactions with urea, glycine and sucrose (to desabilites on fuel and stoichiometric) and amorphous phase formation of MgAl2O4 in situ for as-synthesized powder. The crystalline phase formation of spinel MgAl2O4 was only succeeded obtained after a thermal treatment of as-synthesized powder under 900°C.The spinel MgAl2O4 powders obtained were composed of nano-size crystallites, but in micrometer-sized aggregates. The mean particle size calculated, via Single Line method, using XRD was 13 nm. PSA indicated that the synthesized powders contain a mean aggregates size with a tri mode distribution of around 17.1 μm. SEM analyses confirmed that the as-synthesized powders are composed of particles aggregation. They have an irregular morphology and nano-size crystallites.

Este trabalho teve por objetivo investigar a obtenção de espinélio MgAl2O4 nanoestruturado através da síntese contínua por combustão em solução e sua caracterização por diferentes técnicas. Incluso neste estudo a influência do tipo de combustível e a razão combustível-oxidante no tamanho do cristalito. As partículas de espinélio MgAl2O4 foram sintetizadas utilizando-se os precursores químicos nitrato de alumínio e nitrato de magnésio como fonte dos cátions metálicos. Uréia, glicina e sacarose foram empregadas como agentes redutores, com diferentes valores da razão combustível-oxidante para a sacarose. Estes parâmetros foram relacionados com sua influência no tamanho de cristalito, tamanho de partícula e área superficial. Na caracterização do pó obtido, foram utilizadas técnicas como análise termodiferencial (ATD) e termogravimétrica (ATG), granulometria por difração de laser (GDL), análise de área superficial (BET), análise cristalográfica por difração de raios X (DRX), morfologia por microscopia eletrônica de varredura (MEV). As reações químicas da síntese contínua por combustão em solução resultaram na formação in situ de fases cristalinas para reações estequiométricas de uréia, glicina e sacarose e as deficientes de sacarose. Preponderância de fase amorfa ocorreu nas reações com excesso de sacarose para o pó como-sintetizado. A totalidade de fase cristalina foi obtida após um tratamento térmico a 900°C do pó como-sintetizado. Os pós de espinélio MgAl2O4 obtidos apresentaram-se como constituídos de cristalitos nanométricos, dispostos na forma de agregados de tamanho micrométrico. O tamanho de cristalito médio, calculado pelo método Single Line, a partir de dados de análises por DRX, foi de 13 nm. A área superficial média dos pós calcinados medida pelo método BET foi de 54 g/m2 Por análise granulométrica constatou-se um Tamanho de partícula médio de 17 μm para o pó como-sintetizado e 17,1 μm para o calcinado a 900ºC. As análises por MEV confirmaram a agregação das partículas do pó sintetizado, a partir de partículas preponderantemente esféricas e algumas com morfologia irregular. / This study has investigated a continuous solution combustion synthesis technique to obtain the nanostructured MgAl2O4 spinel powder and their characterize them by different tecniques. This study has also included the investigation of the influence of different kinds of fuel and fuel-to-oxidant ratio on crystallite size. The MgAl2O4 spinel powder was performed using aluminum nitrate and magnesium nitrate to obtain the metallic ions. Urea, glycine and sucrose were used like fuel, with several fuel-to-oxidant ratio. These parameters were correlating with powders characteristics, like crystallite size, particle size and superficial area. The techniques used for powder characterization included differential thermal analyzer (DTA), thermogravimetric analyzer (TGA), particles size analyzer (PSA), surface area by BET analysis, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The chemical reactions of solution combustion resulted on crystalline phase to the reactions with urea, glycine and sucrose (to desabilites on fuel and stoichiometric) and amorphous phase formation of MgAl2O4 in situ for as-synthesized powder. The crystalline phase formation of spinel MgAl2O4 was only succeeded obtained after a thermal treatment of as-synthesized powder under 900°C.The spinel MgAl2O4 powders obtained were composed of nano-size crystallites, but in micrometer-sized aggregates. The mean particle size calculated, via Single Line method, using XRD was 13 nm. PSA indicated that the synthesized powders contain a mean aggregates size with a tri mode distribution of around 17.1 μm. SEM analyses confirmed that the as-synthesized powders are composed of particles aggregation. They have an irregular morphology and nano-size crystallites.

Este trabalho teve por objetivo investigar a obtenção de espinélio MgAl2O4 nanoestruturado através da síntese contínua por combustão em solução e sua caracterização por diferentes técnicas. Incluso neste estudo a influência do tipo de combustível e a razão combustível-oxidante no tamanho do cristalito. As partículas de espinélio MgAl2O4 foram sintetizadas utilizando-se os precursores químicos nitrato de alumínio e nitrato de magnésio como fonte dos cátions metálicos. Uréia, glicina e sacarose foram empregadas como agentes redutores, com diferentes valores da razão combustível-oxidante para a sacarose. Estes parâmetros foram relacionados com sua influência no tamanho de cristalito, tamanho de partícula e área superficial. Na caracterização do pó obtido, foram utilizadas técnicas como análise termodiferencial (ATD) e termogravimétrica (ATG), granulometria por difração de laser (GDL), análise de área superficial (BET), análise cristalográfica por difração de raios X (DRX), morfologia por microscopia eletrônica de varredura (MEV). As reações químicas da síntese contínua por combustão em solução resultaram na formação in situ de fases cristalinas para reações estequiométricas de uréia, glicina e sacarose e as deficientes de sacarose. Preponderância de fase amorfa ocorreu nas reações com excesso de sacarose para o pó como-sintetizado. A totalidade de fase cristalina foi obtida após um tratamento térmico a 900°C do pó como-sintetizado. Os pós de espinélio MgAl2O4 obtidos apresentaram-se como constituídos de cristalitos nanométricos, dispostos na forma de agregados de tamanho micrométrico. O tamanho de cristalito médio, calculado pelo método Single Line, a partir de dados de análises por DRX, foi de 13 nm. A área superficial média dos pós calcinados medida pelo método BET foi de 54 g/m2 Por análise granulométrica constatou-se um Tamanho de partícula médio de 17 μm para o pó como-sintetizado e 17,1 μm para o calcinado a 900ºC. As análises por MEV confirmaram a agregação das partículas do pó sintetizado, a partir de partículas preponderantemente esféricas e algumas com morfologia irregular. / This study has investigated a continuous solution combustion synthesis technique to obtain the nanostructured MgAl2O4 spinel powder and their characterize them by different tecniques. This study has also included the investigation of the influence of different kinds of fuel and fuel-to-oxidant ratio on crystallite size. The MgAl2O4 spinel powder was performed using aluminum nitrate and magnesium nitrate to obtain the metallic ions. Urea, glycine and sucrose were used like fuel, with several fuel-to-oxidant ratio. These parameters were correlating with powders characteristics, like crystallite size, particle size and superficial area. The techniques used for powder characterization included differential thermal analyzer (DTA), thermogravimetric analyzer (TGA), particles size analyzer (PSA), surface area by BET analysis, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The chemical reactions of solution combustion resulted on crystalline phase to the reactions with urea, glycine and sucrose (to desabilites on fuel and stoichiometric) and amorphous phase formation of MgAl2O4 in situ for as-synthesized powder. The crystalline phase formation of spinel MgAl2O4 was only succeeded obtained after a thermal treatment of as-synthesized powder under 900°C.The spinel MgAl2O4 powders obtained were composed of nano-size crystallites, but in micrometer-sized aggregates. The mean particle size calculated, via Single Line method, using XRD was 13 nm. PSA indicated that the synthesized powders contain a mean aggregates size with a tri mode distribution of around 17.1 μm. SEM analyses confirmed that the as-synthesized powders are composed of particles aggregation. They have an irregular morphology and nano-size crystallites.

In this thesis, new all-printed capacitors are developed for the applications of energy storage, filter, and resonant circuits by using new dielectric material and an advanced technology. The innovative devices provide satisficing electrical performances with high breakdown voltages and capacitance densities. The main body of this thesis is divided in three parts. The first part is to introduce the fundamental background of printing technologies, electrical capacitors and printable materials. Among all the printing technologies, direct writing family is the most advantageous in the small-scale and fast production of printed electronics due to the properties of masterless processing, digital control, and print-on-demand. Both inkjet printing and ultrasonic fluid dispensing applied in this work are grouped into the direct writing family. A cross-linkable dielectric material poly(methyl methacrylate)84/(4-benzoylphenyl methacrylate)16 [P(MMA84/BPMA16)] exhibits the optimized chemical and mechanical stabilities in comparison with uncross-linked poly(methyl methacrylate) (PMMA). Poly(vinylidene fluoride-co-trifluoro ethylene) [P(VDF-TrFE)] exhibits a high dielectric constant of 16. The great advantages of both polymeric dielectrics make them ideal for printed electronics. The second part is devoted to the preparation of printed thin-film capacitors by providing four different layouts and architectures for multiple electronic applications. The printing setup, process setting and steps are summarized in detail. The following part which is the major content of this thesis is divided into two aspects: in the first aspect, the intriguing new form of continuous solution dispensing technology, ultrasonic fluid dispensing, is demonstrated as an alternative printing technology for the commonly applied ones. In comparison with the widely-used inkjet printing, continuous solution dispensing is the most advantageous in thin-film capacitor processing with metal nanoparticle and polymer dielectric inks. It enables precise pattern transfers with low surface roughness, small feature size (as small as 5 μm), and accurate positioning (5 μm resolution). Most importantly, problems due to discrete droplets and nozzle clogging in inkjet printing are avoided in continuous solution dispensing. All the inks applied for printed capacitors in this work are printed successfully with this innovating technology. Direct printing on demand and rapid switching among different inks are some other attributes of this printing technology that enable high throughput. The second aspect of this part is to characterize and evaluate the fabricated capacitors. The measured values include capacitor dimension, dielectric strength, capacitance density, energy density, charge/discharge behavior and so on. In summary, this work provides not only the use of the advantageous materials P(MMA84/BPMA16) and P(VDF-TrFE) in high-performance capacitors, but also paves the way of developing thin-film capacitors with a new continuous solution dispensing technology which makes the low-cost and high-quality manufacture of printed devices possible.

In this thesis, new all-printed capacitors are developed for the applications of energy storage, filter, and resonant circuits by using new dielectric material and an advanced technology. The innovative devices provide satisficing electrical performances with high breakdown voltages and capacitance densities. The main body of this thesis is divided in three parts. The first part is to introduce the fundamental background of printing technologies, electrical capacitors and printable materials. Among all the printing technologies, direct writing family is the most advantageous in the small-scale and fast production of printed electronics due to the properties of masterless processing, digital control, and print-on-demand. Both inkjet printing and ultrasonic fluid dispensing applied in this work are grouped into the direct writing family. A cross-linkable dielectric material poly(methyl methacrylate)84/(4-benzoylphenyl methacrylate)16 [P(MMA84/BPMA16)] exhibits the optimized chemical and mechanical stabilities in comparison with uncross-linked poly(methyl methacrylate) (PMMA). Poly(vinylidene fluoride-co-trifluoro ethylene) [P(VDF-TrFE)] exhibits a high dielectric constant of 16. The great advantages of both polymeric dielectrics make them ideal for printed electronics. The second part is devoted to the preparation of printed thin-film capacitors by providing four different layouts and architectures for multiple electronic applications. The printing setup, process setting and steps are summarized in detail. The following part which is the major content of this thesis is divided into two aspects: in the first aspect, the intriguing new form of continuous solution dispensing technology, ultrasonic fluid dispensing, is demonstrated as an alternative printing technology for the commonly applied ones. In comparison with the widely-used inkjet printing, continuous solution dispensing is the most advantageous in thin-film capacitor processing with metal nanoparticle and polymer dielectric inks. It enables precise pattern transfers with low surface roughness, small feature size (as small as 5 μm), and accurate positioning (5 μm resolution). Most importantly, problems due to discrete droplets and nozzle clogging in inkjet printing are avoided in continuous solution dispensing. All the inks applied for printed capacitors in this work are printed successfully with this innovating technology. Direct printing on demand and rapid switching among different inks are some other attributes of this printing technology that enable high throughput. The second aspect of this part is to characterize and evaluate the fabricated capacitors. The measured values include capacitor dimension, dielectric strength, capacitance density, energy density, charge/discharge behavior and so on. In summary, this work provides not only the use of the advantageous materials P(MMA84/BPMA16) and P(VDF-TrFE) in high-performance capacitors, but also paves the way of developing thin-film capacitors with a new continuous solution dispensing technology which makes the low-cost and high-quality manufacture of printed devices possible.