A transmissão de conceitos matemáticos para Portugal: integrais e funções elípticas

Esta tese considera a transmissão de conceitos matemáticos para Portugal no século XIX, particularmente no campo dos Integrais Elípticos e das Funções Elípticas, tal como foi realizado no trabalho de António Zeferino Cândido. Depois de uma introdução histórica geral ao assunto no capítulo 1, o capítulo 2 estuda a vida de António Zeferino Cândido da Piedade. Ele foi, talvez, o primeiro matemático português a publicar uma tese sobre este assunto. A parte principal, isto é, o capítulo 3, é dedicada à análise do seu trabalho “Integraes e Funcções Ellipticas”. Mostra detalhes da sua abordagem baseada, não só, no livro dos autores Franceses Briot e Bouquet, mas também do autor alemão Schloemilch, o que reflecte as mudanças que ocorreram naquela época na liderança matemática na Europa.

Quantum criptography in optical fibers

As comunicações quânticas aplicam as leis fundamentais da física quântica para codificar, transmitir, guardar e processar informação. A mais importante e bem-sucedida aplicação é a distribuição de chaves quânticas (QKD). Os sistemas de QKD são suportados por tecnologias capazes de processar fotões únicos. Nesta tese analisamos a geração, transmissão e deteção de fotões únicos e entrelaçados em fibras óticas. É proposta uma fonte de fotões única baseada no processo clássico de mistura de quatro ondas (FWM) em fibras óticas num regime de baixas potências. Implementamos essa fonte no laboratório, e desenvolvemos um modelo teórico capaz de descrever corretamente o processo de geração de fotões únicos. O modelo teórico considera o papel das nãolinearidades da fibra e os efeitos da polarização na geração de fotões através do processo de FWM. Analisamos a estatística da fonte de fotões baseada no processo clássico de FWM em fibras óticas. Derivamos um modelo teórico capaz de descrever a estatística dessa fonte de fotões. Mostramos que a estatística da fonte de fotões evolui de térmica num regime de baixas potências óticas, para Poissoniana num regime de potências óticas moderadas. Validamos experimentalmente o modelo teórico, através do uso de fotodetetores de avalanche, do método estimativo da máxima verossimilhança e do algoritmo de maximização de expectativa. Estudamos o processo espontâneo de FWM como uma fonte condicional de fotões únicos. Analisamos a estatística dessa fonte em termos da função condicional de coerência de segunda ordem, considerando o espalhamento de Raman na geração de pares de fotões, e a perda durante a propagação de fotões numa fibra ótica padrão. Identificamos regimes apropriados onde a fonte é quase ideal. Fontes de pares de fotões implementadas em fibras óticas fornecem uma solução prática ao problema de acoplamento que surge quando os pares de fotões são gerados fora da fibra. Exploramos a geração de pares de fotões através do processo espontâneo de FWM no interior de guias de onda com suceptibilidade elétrica de terceira ordem. Descrevemos a geração de pares de fotões em meios com elevado coeficiente de absorção, e identificamos regimes ótimos para o rácio contagens coincidentes/acidentais (CAR) e para a desigualdade de Clauser, Horne, Shimony, and Holt (CHSH), para o qual o compromisso entre perda do guia de onda e não-linearidades maximiza esses parâmetros.

Compósitos CNTs/biocerâmico para a estimulação elétrica óssea in situ

The present thesis aims to develop a biocompatible and electroconductor bone graft containing carbon nanotubes (CNTs) that allows the in situ regeneration of bone cells by applying pulsed external electrical stimuli. The CNTs were produced by chemical vapor deposition (CVD) by a semi-continuous method with a yield of ~500 mg/day. The deposition parameters were optimised to obtain high pure CNTs ~99.96% with controlled morphologies, fundamental requisites for the biomedical application under study. The chemical functionalisation of CNTs was also optimised to maximise their processability and biocompatibility. The CNTs were functionalised by the Diels-Alder cycloaddition of 1,3-butadiene. The biological behaviour of the functionalised CNTs was evaluated in vitro with the osteoblastic cells line MG63 and in vivo, by subcutaneous implantation in rats. The materials did not induce an expressed inflammatory response, but the functionalised CNTs showed a superior in vitro and in vivo biocompatibility than the non-functionalised ones. Composites of ceramic matrix, of bioglass (Glass) and hydroxyapatite (HA), reinforced with carbon nanotubes (CNT/Glass/HA) were processed by a wet approach. The incorporation of just 4.4 vol% of CNTs allowed the increase of 10 orders of magnitude of the electrical conductivity of the matrix. In vitro studies with MG63 cells show that the CNT/Glass/HA composites guarantee the adhesion and proliferation of bone cells, and stimulate their phenotype expression, namely the alkaline phosphate (ALP). The interactions between the composite materials and the culture medium (α-MEM), under an applied electrical external field, were studied by scanning vibrating electrode technique. An increase of the culture medium electrical conductivity and the electrical field confinement in the presence of the conductive samples submerged in the medium was demonstrated. The in vitro electrical stimulation of MG63 cells on the conductive composites promotes the increase of the cell metabolic activity and DNA content by 130% and 60%, relatively to the non-stimulated condition, after only 3 days of daily stimulation of 15 μA for 15 min. Moreover, the osteoblastic gene expression for Runx2, osteocalcin (OC) and ALP was enhanced by 80%, 50% and 25%, after 5 days of stimulation. Instead, for dielectric materials, the stimulus delivering was less efficient, giving an equal or lower cellular response than the non-stimulated condition. The proposed electroconductive bone grafts offer exciting possibilities in bone regeneration strategies by delivering in situ electrical stimulus to cells and consequent control of the new bone tissue formation rate. It is expected that conductive smart biomaterials might turn the selective bone electrotherapy of clinical relevance by decreasing the postoperative healing times.

Ferroelectric : CNTs structures fabrication for advanced functional nano devices

This work is about the combination of functional ferroelectric oxides with Multiwall Carbon Nanotubes for microelectronic applications, as for example potential 3 Dimensional (3D) Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Miniaturized electronics are ubiquitous now. The drive to downsize electronics has been spurred by needs of more performance into smaller packages at lower costs. But the trend of electronics miniaturization challenges board assembly materials, processes, and reliability. Semiconductor device and integrated circuit technology, coupled with its associated electronic packaging, forms the backbone of high-performance miniaturized electronic systems. However, as size decreases and functionalization increases in the modern electronics further size reduction is getting difficult; below a size limit the signal reliability and device performance deteriorate. Hence miniaturization of siliconbased electronics has limitations. On this background the Road Map for Semiconductor Industry (ITRS) suggests since 2011 alternative technologies, designated as More than Moore; being one of them based on carbon (carbon nanotubes (CNTs) and graphene) [1]. CNTs with their unique performance and three dimensionality at the nano-scale have been regarded as promising elements for miniaturized electronics [2]. CNTs are tubular in geometry and possess a unique set of properties, including ballistic electron transportation and a huge current caring capacity, which make them of great interest for future microelectronics [2]. Indeed CNTs might have a key role in the miniaturization of Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Moving from a traditional two dimensional (2D) design (as is the case of thin films) to a 3D structure (based on a tridimensional arrangement of unidimensional structures) will result in the high reliability and sensing of the signals due to the large contribution from the bottom electrode. One way to achieve this 3D design is by using CNTs. Ferroelectrics (FE) are spontaneously polarized and can have high dielectric constants and interesting pyroelectric, piezoelectric, and electrooptic properties, being a key application of FE electronic memories. However, combining CNTs with FE functional oxides is challenging. It starts with materials compatibility, since crystallization temperature of FE and oxidation temperature of CNTs may overlap. In this case low temperature processing of FE is fundamental. Within this context in this work a systematic study on the fabrication of CNTs - FE structures using low cost low temperature methods was carried out. The FE under study are comprised of lead zirconate titanate (Pb1-xZrxTiO3, PZT), barium titanate (BaTiO3, BT) and bismuth ferrite (BiFeO3, BFO). The various aspects related to the fabrication, such as effect on thermal stability of MWCNTs, FE phase formation in presence of MWCNTs and interfaces between the CNTs/FE are addressed in this work. The ferroelectric response locally measured by Piezoresponse Force Microscopy (PFM) clearly evidenced that even at low processing temperatures FE on CNTs retain its ferroelectric nature. The work started by verifying the thermal decomposition behavior under different conditions of the multiwall CNTs (MWCNTs) used in this work. It was verified that purified MWCNTs are stable up to 420 ºC in air, as no weight loss occurs under non isothermal conditions, but morphology changes were observed for isothermal conditions at 400 ºC by Raman spectroscopy and Transmission Electron Microscopy (TEM). In oxygen-rich atmosphere MWCNTs started to oxidized at 200 ºC. However in argon-rich one and under a high heating rate MWCNTs remain stable up to 1300 ºC with a minimum sublimation. The activation energy for the decomposition of MWCNTs in air was calculated to lie between 80 and 108 kJ/mol. These results are relevant for the fabrication of MWCNTs – FE structures. Indeed we demonstrate that PZT can be deposited by sol gel at low temperatures on MWCNTs. And particularly interesting we prove that MWCNTs decrease the temperature and time for formation of PZT by ~100 ºC commensurate with a decrease in activation energy from 68±15 kJ/mol to 27±2 kJ/mol. As a consequence, monophasic PZT was obtained at 575 ºC for MWCNTs - PZT whereas for pure PZT traces of pyrochlore were still present at 650 ºC, where PZT phase formed due to homogeneous nucleation. The piezoelectric nature of MWCNTs - PZT synthesised at 500 ºC for 1 h was proved by PFM. In the continuation of this work we developed a low cost methodology of coating MWCNTs using a hybrid sol-gel / hydrothermal method. In this case the FE used as a proof of concept was BT. BT is a well-known lead free perovskite used in many microelectronic applications. However, synthesis by solid state reaction is typically performed around 1100 to 1300 ºC what jeopardizes the combination with MWCNTs. We also illustrate the ineffectiveness of conventional hydrothermal synthesis in this process due the formation of carbonates, namely BaCO3. The grown MWCNTs - BT structures are ferroelectric and exhibit an electromechanical response (15 pm/V). These results have broad implications since this strategy can also be extended to other compounds of materials with high crystallization temperatures. In addition the coverage of MWCNTs with FE can be optimized, in this case with non covalent functionalization of the tubes, namely with sodium dodecyl sulfate (SDS). MWCNTs were used as templates to grow, in this case single phase multiferroic BFO nanorods. This work shows that the use of nitric solvent results in severe damages of the MWCNTs layers that results in the early oxidation of the tubes during the annealing treatment. It was also observed that the use of nitric solvent results in the partial filling of MWCNTs with BFO due to the low surface tension (<119 mN/m) of the nitric solution. The opening of the caps and filling of the tubes occurs simultaneously during the refluxing step. Furthermore we verified that MWCNTs have a critical role in the fabrication of monophasic BFO; i.e. the oxidation of CNTs during the annealing process causes an oxygen deficient atmosphere that restrains the formation of Bi2O3 and monophasic BFO can be obtained. The morphology of the obtained BFO nano structures indicates that MWCNTs act as template to grow 1D structure of BFO. Magnetic measurements on these BFO nanostructures revealed a week ferromagnetic hysteresis loop with a coercive field of 956 Oe at 5 K. We also exploited the possible use of vertically-aligned multiwall carbon nanotubes (VA-MWCNTs) as bottom electrodes for microelectronics, for example for memory applications. As a proof of concept BiFeO3 (BFO) films were in-situ deposited on the surface of VA-MWCNTs by RF (Radio Frequency) magnetron sputtering. For in situ deposition temperature of 400 ºC and deposition time up to 2 h, BFO films cover the VA-MWCNTs and no damage occurs either in the film or MWCNTs. In spite of the macroscopic lossy polarization behaviour, the ferroelectric nature, domain structure and switching of these conformal BFO films was verified by PFM. A week ferromagnetic ordering loop was proved for BFO films on VA-MWCNTs having a coercive field of 700 Oe. Our systematic work is a significant step forward in the development of 3D memory cells; it clearly demonstrates that CNTs can be combined with FE oxides and can be used, for example, as the next 3D generation of FERAMs, not excluding however other different applications in microelectronics.