Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Copper(I) phenanthroline complexes and supramolecular systems containing fullerenes: Photophysics, photochemistry and potential applications in sustainable energy technologies.

Chemistry can contribute, in many different ways to solve the challenges we are facing to modify our inefficient and fossil-fuel based energy system. The present work was motivated by the search for efficient photoactive materials to be employed in the context of the energy problem: materials to be utilized in energy efficient devices and in the production of renewable electricity and fuels. We presented a new class of copper complexes, that could find application in lighting techhnologies, by serving as luminescent materials in LEC, OLED, WOLED devices. These technologies may provide substantial energy savings in the lighting sector. Moreover, recently, copper complexes have been used as light harvesting compounds in dye sensitized photoelectrochemical solar cells, which offer a viable alternative to silicon-based photovoltaic technologies. We presented also a few supramolecular systems containing fullerene, e.g. dendrimers, dyads and triads.The most complex among these arrays, which contain porphyrin moieties, are presented in the final chapter. They undergo photoinduced energy- and electron transfer processes also with long-lived charge separated states, i.e. the fundamental processes to power artificial photosynthetic systems.

Development and characterization of non-oxide ceramic composites for mechanical and tribological applications

The main reasons for the attention focused on ceramics as possible structural materials are their wear resistance and the ability to operate with limited oxidation and ablation at temperatures above 2000°C. Hence, this work is devoted to the study of two classes of materials which can satisfy these requirements: silicon carbide -based ceramics (SiC) for wear applications and borides and carbides of transition metals for ultra-high temperatures applications (UHTCs). SiC-based materials: Silicon carbide is a hard ceramic, which finds applications in many industrial sectors, from heat production, to automotive engineering and metals processing. In view of new fields of uses, SiC-based ceramics were produced with addition of 10-30 vol% of MoSi2, in order to obtain electro conductive ceramics. MoSi2, indeed, is an intermetallic compound which possesses high temperature oxidation resistance, high electrical conductivity (21·10-6 Ω·cm), relatively low density (6.31 g/cm3), high melting point (2030°C) and high stiffness (440 GPa). The SiC-based ceramics were hot pressed at 1900°C with addition of Al2O3-Y2O3 or Y2O3-AlN as sintering additives. The microstructure of the composites and of the reference materials, SiC and MoSi2, were studied by means of conventional analytical techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (SEM-EDS). The composites showed a homogeneous microstructure, with good dispersion of the secondary phases and low residual porosity. The following thermo-mechanical properties of the SiC-based materials were measured: Vickers hardness (HV), Young’s modulus (E), fracture toughness (KIc) and room to high temperature flexural strength (σ). The mechanical properties of the composites were compared to those of two monolithic SiC and MoSi2 materials and resulted in a higher stiffness, fracture toughness and slightly higher flexural resistance. Tribological tests were also performed in two configurations disco-on-pin and slideron cylinder, aiming at studying the wear behaviour of SiC-MoSi2 composites with Al2O3 as counterfacing materials. The tests pointed out that the addition of MoSi2 was detrimental owing to a lower hardness in comparison with the pure SiC matrix. On the contrary, electrical measurements revealed that the addition of 30 vol% of MoSi2, rendered the composite electroconductive, lowering the electrical resistance of three orders of magnitude. Ultra High Temperature Ceramics: Carbides, borides and nitrides of transition metals (Ti, Zr, Hf, Ta, Nb, Mo) possess very high melting points and interesting engineering properties, such as high hardness (20-25 GPa), high stiffness (400-500 GPa), flexural strengths which remain unaltered from room temperature to 1500°C and excellent corrosion resistance in aggressive environment. All these properties place the UHTCs as potential candidates for the development of manoeuvrable hypersonic flight vehicles with sharp leading edges. To this scope Zr- and Hf- carbide and boride materials were produced with addition of 5-20 vol% of MoSi2. This secondary phase enabled the achievement of full dense composites at temperature lower than 2000°C and without the application of pressure. Besides the conventional microstructure analyses XRD and SEM-EDS, transmission electron microscopy (TEM) was employed to explore the microstructure on a small length scale to disclose the effective densification mechanisms. A thorough literature analysis revealed that neither detailed TEM work nor reports on densification mechanisms are available for this class of materials, which however are essential to optimize the sintering aids utilized and the processing parameters applied. Microstructural analyses, along with thermodynamics and crystallographic considerations, led to disclose of the effective role of MoSi2 during sintering of Zrand Hf- carbides and borides. Among the investigated mechanical properties (HV, E, KIc, σ from room temperature to 1500°C), the high temperature flexural strength was improved due to the protective and sealing effect of a silica-based glassy phase, especially for the borides. Nanoindentation tests were also performed on HfC-MoSi2 composites in order to extract hardness and elastic modulus of the single phases. Finally, arc jet tests on HfC- and HfB2-based composites confirmed the excellent oxidation behaviour of these materials under temperature exceeding 2000°C; no cracking or spallation occurred and the modified layer was only 80-90 μm thick.

In situ real-time investigation of Organic Ultra-Thin-Film transistors: growth, electrical properties and biosensing applications

Organic electronics has grown enormously during the last decades driven by the encouraging results and the potentiality of these materials for allowing innovative applications, such as flexible-large-area displays, low-cost printable circuits, plastic solar cells and lab-on-a-chip devices. Moreover, their possible field of applications reaches from medicine, biotechnology, process control and environmental monitoring to defense and security requirements. However, a large number of questions regarding the mechanism of device operation remain unanswered. Along the most significant is the charge carrier transport in organic semiconductors, which is not yet well understood. Other example is the correlation between the morphology and the electrical response. Even if it is recognized that growth mode plays a crucial role into the performance of devices, it has not been exhaustively investigated. The main goal of this thesis was the finding of a correlation between growth modes, electrical properties and morphology in organic thin-film transistors (OTFTs). In order to study the thickness dependence of electrical performance in organic ultra-thin-film transistors, we have designed and developed a home-built experimental setup for performing real-time electrical monitoring and post-growth in situ electrical characterization techniques. We have grown pentacene TFTs under high vacuum conditions, varying systematically the deposition rate at a fixed room temperature. The drain source current IDS and the gate source current IGS were monitored in real-time; while a complete post-growth in situ electrical characterization was carried out. At the end, an ex situ morphological investigation was performed by using the atomic force microscope (AFM). In this work, we present the correlation for pentacene TFTs between growth conditions, Debye length and morphology (through the correlation length parameter). We have demonstrated that there is a layered charge carriers distribution, which is strongly dependent of the growth mode (i.e. rate deposition for a fixed temperature), leading to a variation of the conduction channel from 2 to 7 monolayers (MLs). We conciliate earlier reported results that were apparently contradictory. Our results made evident the necessity of reconsidering the concept of Debye length in a layered low-dimensional device. Additionally, we introduce by the first time a breakthrough technique. This technique makes evident the percolation of the first MLs on pentacene TFTs by monitoring the IGS in real-time, correlating morphological phenomena with the device electrical response. The present thesis is organized in the following five chapters. Chapter 1 makes an introduction to the organic electronics, illustrating the operation principle of TFTs. Chapter 2 presents the organic growth from theoretical and experimental points of view. The second part of this chapter presents the electrical characterization of OTFTs and the typical performance of pentacene devices is shown. In addition, we introduce a correcting technique for the reconstruction of measurements hampered by leakage current. In chapter 3, we describe in details the design and operation of our innovative home-built experimental setup for performing real-time and in situ electrical measurements. Some preliminary results and the breakthrough technique for correlating morphological and electrical changes are presented. Chapter 4 meets the most important results obtained in real-time and in situ conditions, which correlate growth conditions, electrical properties and morphology of pentacene TFTs. In chapter 5 we describe applicative experiments where the electrical performance of pentacene TFTs has been investigated in ambient conditions, in contact to water or aqueous solutions and, finally, in the detection of DNA concentration as label-free sensor, within the biosensing framework.

Supramolecular approaches to organized luminescent nanostructures for sensing, labeling and imaging applications

The common thread of this thesis is the will of investigating properties and behavior of assemblies. Groups of objects display peculiar properties, which can be very far from the simple sum of respective components’ properties. This is truer, the smaller is inter-objects distance, i.e. the higher is their density, and the smaller is the container size. “Confinement” is in fact a key concept in many topics explored and here reported. It can be conceived as a spatial limitation, that yet gives origin to unexpected processes and phenomena based on inter-objects communication. Such phenomena eventually result in “non-linear properties”, responsible for the low predictability of large assemblies. Chapter 1 provides two insights on surface chemistry, namely (i) on a supramolecular assembly based on orthogonal forces, and (ii) on selective and sensitive fluorescent sensing in thin polymeric film. In chapters 2 to 4 confinement of molecules plays a major role. Most of the work focuses on FRET within core-shell nanoparticles, investigated both through a simulation model and through experiments. Exciting results of great applicative interest are drawn, such as a method of tuning emission wavelength at constant excitation, and a way of overcoming self-quenching processes by setting up a competitive deactivation channel. We envisage applications of these materials as labels for multiplexing analysis, and in all fields of fluorescence imaging, where brightness coupled with biocompatibility and water solubility is required. Adducts of nanoparticles and molecular photoswitches are investigated in the context of superresolution techniques for fluorescence microscopy. In chapter 5 a method is proposed to prepare a library of functionalized Pluronic F127, which gives access to a twofold “smart” nanomaterial, namely both (i)luminescent and (ii)surface-functionalized SCSSNPs. Focus shifts in chapter 6 to confinement effects in an upper size scale. Moving from nanometers to micrometers, we investigate the interplay between microparticles flowing in microchannels where a constriction affects at very long ranges structure and dynamics of the colloidal paste.

Sustainable inorganic Binders and Their Applications in Building Engineering: A Green Alternative to Ordinary Portland Cement

In the last decades, the building materials and construction industry has been contributing to a great extent to generate a high impact on our environment. As it has been considered one of the key areas in which to operate to significantly reduce our footprint on environment, there has been widespread belief that particular attention now has to be paid and specific measures have to be taken to limit the use of non-renewable resources.The aim of this thesis is therefore to study and evaluate sustainable alternatives to commonly used building materials, mainly based on ordinary Portland Cement, and find a supportable path to reduce CO2 emissions and promote the re-use of waste materials. More specifically, this research explores different solutions for replacing cementitious binders in distinct application fields, particularly where special and more restricting requirements are needed, such as restoration and conservation of architectural heritage. Emphasis was thus placed on aspects and implications more closely related to the concept of non-invasivity and environmental sustainability. A first part of the research was addressed to the study and development of sustainable inorganic matrices, based on lime putty, for the pre-impregnation and on-site binding of continuous carbon fiber fabrics for structural rehabilitation and heritage restoration. Moreover, with the aim to further limit the exploitation of non-renewable resources, the synthesis of chemically activated silico-aluminate materials, as metakaolin, ladle slag or fly ash, was thus successfully achieved. New sustainable binders were hence proposed as novel building materials, suitable to be used as primary component for construction and repair mortars, as bulk materials in high-temperature applications or as matrices for high-toughness fiber reinforced composites.

Chemical Production and Microelectronic Applications of Graphene and Nano-Graphene Derivatives

Graphene and graphenic derivatives have rapidly emerged as an extremely promising system for electronic, optical, thermal, and electromechanical applications. Several approaches have been developed to produce these materials (i.e. scotch tape, CVD, chemical and solvent exfoliation). In this work we report a chemical approach to produce graphene by reducing graphene oxide (GO) via thermal or electrical methods. A morphological and electrical characterization of these systems has been performed using different techniques such as SPM, SEM, TEM, Raman and XPS. Moreover, we studied the interaction between graphene derivates and organic molecules focusing on the following aspects: - improvement of optical contrast of graphene on different substrates for rapid monolayer identification1 - supramolecular interaction with organic molecules (i.e. thiophene, pyrene etc.)4 - covalent functionalization with optically active molecules2 - preparation and characterization of organic/graphene Field Effect Transistors3-5 Graphene chemistry can potentially allow seamless integration of graphene technology in organic electronics devices to improve device performance and develop new applications for graphene-based materials. [1] E. Treossi, M. Melucci, A. Liscio, M. Gazzano, P. Samorì, and V. Palermo, J. Am. Chem. Soc., 2009, 131, 15576. [2] M. Melucci, E. Treossi, L. Ortolani, G. Giambastiani, V. Morandi, P. Klar, C. Casiraghi, P. Samorì, and V. Palermo, J. Mater. Chem., 2010, 20, 9052. [3] J.M. Mativetsky, E. Treossi, E. Orgiu, M. Melucci, G.P. Veronese, P. Samorì, and V. Palermo, J. Am. Chem. Soc., 2010, 132, 14130. [4] A. Liscio, G.P. Veronese, E. Treossi, F. Suriano, F. Rossella, V. Bellani, R. Rizzoli, P. Samorì and V. Palermo, J. Mater. Chem., 2011, 21, 2924. [5] J.M. Mativetsky, A. Liscio, E. Treossi, E. Orgiu, A. Zanelli, P. Samorì , V. Palermo, J. Am. Chem. Soc., 2011, 133, 14320

Pyrolysis of peptides and proteins. Analytical study and environmental applications

Analytical pyrolysis was used to investigate the formation of diketopiperazines (DKPs) which are cyclic dipeptides formed from the thermal degradation of proteins. A quali/quantitative procedure was developed combining microscale flash pyrolysis at 500 °C with gas chromatography-mass spectrometry (GC-MS) of DKPs trapped onto an adsorbent phase. Polar DKPs were silylated prior to GC-MS. Particular attention was paid to the identification of proline (Pro) containing DKPs due to their greater facility of formation. The GC-MS characteristics of more than 80 original and silylated DKPs were collected from the pyrolysis of sixteen linear dipeptides and four model proteins (e.g. bovine serum albumin, BSA). The structure of a novel DKP, cyclo(pyroglutamic-Pro) was established by NMR and ESI-MS analysis, while the structures of other novel DKPs remained tentative. DKPs resulted rather specific markers of amino acid sequence in proteins, even though the thermal degradation of DKPs should be taken into account. Structural information of DKPs gathered from the pyrolysis of model compounds was employed to the identification of these compounds in the pyrolysate of proteinaceous samples, including intrinsecally unfolded protein (IUP). Analysis of the liquid fraction (bio-oil) obtained from the pyrolysis of microalgae Nannochloropsis gaditana, Scenedesmus spp with a bench scale reactor showed that DKPs constituted an important pool of nitrogen-containing compounds. Conversely, the level of DKPs was rather low in the bio-oil of Botryococcus braunii. The developed micropyrolysis procedure was applied in combination with thermogravimetry (TGA) and infrared spectroscopy (FT-IR) to investigate surface interaction between BSA and synthetic chrysotile. The results showed that the thermal behavior of BSA (e.g. DKPs formation) was affected by the different form of doped synthetic chrysotile. The typical DKPs evolved from collagen were quantified in the pyrolysates of archaeological bones from Vicenne Necropolis in order to evaluate their conservation status in combination with TGA, FTIR and XRD analysis.

Numerical Modelling of Graphene Nanoribbon-fets for Analog and Digital Applications

Graphene, that is a monolayer of carbon atoms arranged in a honeycomb lattice, has been isolated only recently from graphite. This material shows very attractive physical properties, like superior carrier mobility, current carrying capability and thermal conductivity. In consideration of that, graphene has been the object of large investigation as a promising candidate to be used in nanometer-scale devices for electronic applications. In this work, graphene nanoribbons (GNRs), that are narrow strips of graphene, for which a band-gap is induced by the quantum confinement of carriers in the transverse direction, have been studied. As experimental GNR-FETs are still far from being ideal, mainly due to the large width and edge roughness, an accurate description of the physical phenomena occurring in these devices is required to have valuable predictions about the performance of these novel structures. A code has been developed to this purpose and used to investigate the performance of 1 to 15-nm wide GNR-FETs. Due to the importance of an accurate description of the quantum effects in the operation of graphene devices, a full-quantum transport model has been adopted: the electron dynamics has been described by a tight-binding (TB) Hamiltonian model and transport has been solved within the formalism of the non-equilibrium Green's functions (NEGF). Both ballistic and dissipative transport are considered. The inclusion of the electron-phonon interaction has been taken into account in the self-consistent Born approximation. In consideration of their different energy band-gap, narrow GNRs are expected to be suitable for logic applications, while wider ones could be promising candidates as channel material for radio-frequency applications.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

Novel etheroatom containing aliphatic polyesters for biomedical and environmental applications

Biodegradable polymers for short time applications have attracted much interest all over the world. The reason behind this growing interest is the incompatibility of the polymeric wastes with the environment where they are disposed after usage. Synthetic aliphatic polyesters represent one of the most economically competitive biodegradable polymers. In addition, they gained considerable attention as they combine biodegradability and biocompatibility with interesting physical and chemical properties. In this framework, the present research work focused on the modification by reactive blending and polycondensation of two different aliphatic polyesters, namely poly(butylene succinate) (PBS) and poly(butylene 1,4-cyclohexanedicarboxylate) (PBCE). Both are characterized by good thermal properties, but their mechanical characteristics do not fit the requirements for applications in which high flexibility is requested and, moreover, both show slow biodegradation rate. With the aim of developing new materials with improved characteristics with respect to the parent homopolymers, novel etheroatom containing PBS and PBCE-based fully aliphatic polyesters and copolyesters have been therefore synthesized and carefully characterized. The introduction of oxygen or sulphur atoms along the polymer chains, by acting on chemical composition or molecular architecture, tailored solid-state properties and biodegradation rate: type and amount of comonomeric units and sequence distribution deeply affected the material final properties owing, among all, to the hydrophobic/hydrophilic ratio and to the different ability of the polymer to crystallize. The versatility of the synthesized copolymers has been well proved: as a matter of fact these polymers can be exploited both for biomedical and ecological applications. Feasibility of 3D electrospun scaffolds has been investigated, biocompatibility studies and controlled release of a model molecule showed good responses. As regards ecological applications, barrier properties and eco-toxicological assessments have been conducted with outstanding results. Finally, the ability of the novel polyesters to undergo both hydrolytic and enzymatic degradation has been demonstrated under physiological and environmental conditions.

Development of an X-ray spectrometric system and feasibility tests of Silicon Drift Detector for medical and space applications

The thesis work concerns X-ray spectrometry for both medical and space applications and is divided into two sections. The first section addresses an X-ray spectrometric system designed to study radiological beams and is devoted to the optimization of diagnostic procedures in medicine. A parametric semi-empirical model capable of efficiently reconstructing diagnostic X-ray spectra in 'middle power' computers was developed and tested. In addition, different silicon diode detectors were tested as real-time detectors in order to provide a real-time evaluation of the spectrum during diagnostic procedures. This project contributes to the field by presenting an improved simulation of a realistic X-ray beam emerging from a common X-ray tube with a complete and detailed spectrum that lends itself to further studies of added filtration, thus providing an optimized beam for different diagnostic applications in medicine. The second section describes the preliminary tests that have been carried out on the first version of an Application Specific Integrated Circuit (ASIC), integrated with large area position-sensitive Silicon Drift Detector (SDD) to be used on board future space missions. This technology has been developed for the ESA project: LOFT (Large Observatory for X-ray Timing), a new medium-class space mission that the European Space Agency has been assessing since February of 2011. The LOFT project was proposed as part of the Cosmic Vision Program (2015-2025).

Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.