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.

Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Simulation of Smart Materials

The aim of this thesis is the elucidation of structure-properties relationship of molecular semiconductors for electronic devices. This involves the use of a comprehensive set of simulation techniques, ranging from quantum-mechanical to numerical stochastic methods, and also the development of ad-hoc computational tools. In more detail, the research activity regarded two main topics: the study of electronic properties and structural behaviour of liquid crystalline (LC) materials based on functionalised oligo(p-phenyleneethynylene) (OPE), and the investigation on the electric field effect associated to OFET operation on pentacene thin film stability. In this dissertation, a novel family of substituted OPE liquid crystals with applications in stimuli-responsive materials is presented. In more detail, simulations can not only provide evidence for the characterization of the liquid crystalline phases of different OPEs, but elucidate the role of charge transfer states in donor-acceptor LCs containing an endohedral metallofullerene moiety. Such systems can be regarded as promising candidates for organic photovoltaics. Furthermore, exciton dynamics simulations are performed as a way to obtain additional information about the degree of order in OPE columnar phases. Finally, ab initio and molecular mechanics simulations are used to investigate the influence of an applied electric field on pentacene reactivity and stability. The reaction path of pentacene thermal dimerization in the presence of an external electric field is investigated; the results can be related to the fatigue effect observed in OFETs, that show significant performance degradation even in the absence of external agents. In addition to this, the effect of the gate voltage on a pentacene monolayer are simulated, and the results are then compared to X-ray diffraction measurements performed for the first time on operating OFETs.

Reconstructing Quantum Field Theory from an Educational Perspective

The research work concerns the analysis of the foundations of Quantum Field Theory carried out from an educational perspective. The whole research has been driven by two questions: • How the concept of object changes when moving from classical to contemporary physics? • How are the concepts of field and interaction shaped and conceptualized within contemporary physics? What makes quantum field and interaction similar to and what makes them different from the classical ones? The whole work has been developed through several studies: 1. A study aimed to analyze the formal and conceptual structures characterizing the description of the continuous systems that remain invariant in the transition from classical to contemporary physics. 2. A study aimed to analyze the changes in the meanings of the concepts of field and interaction in the transition to quantum field theory. 3. A detailed study of the Klein-Gordon equation aimed at analyzing, in a case considered emblematic, some interpretative (conceptual and didactical) problems in the concept of field that the university textbooks do not address explicitly. 4. A study concerning the application of the “Discipline-Culture” Model elaborated by I. Galili to the analysis of the Klein-Gordon equation, in order to reconstruct the meanings of the equation from a cultural perspective. 5. A critical analysis, in the light of the results of the studies mentioned above, of the existing proposals for teaching basic concepts of Quantum Field Theory and particle physics at the secondary school level or in introductory physics university courses.