Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

Computer simulation of ordering and dynamics in liquid crystals in the bulk and close to the surface

The aim of this PhD thesis is to investigate the orientational and dynamical properties of liquid crystalline systems, at molecular level and using atomistic computer simulations, to reach a better understanding of material behavior from a microscopic point view. In perspective this should allow to clarify the relation between the micro and macroscopic properties with the objective of predicting or confirming experimental results on these systems. In this context, we developed four different lines of work in the thesis. The first one concerns the orientational order and alignment mechanism of rigid solutes of small dimensions dissolved in a nematic phase formed by the 4-pentyl,4 cyanobiphenyl (5CB) nematic liquid crystal. The orientational distribution of solutes have been obtained with Molecular Dynamics Simulation (MD) and have been compared with experimental data reported in literature. we have also verified the agreement between order parameters and dipolar coupling values measured in NMR experiments. The MD determined effective orientational potentials have been compared with the predictions of Maier­Saupe and Surface tensor models. The second line concerns the development of a correct parametrization able to reproduce the phase transition properties of a prototype of the oligothiophene semiconductor family: sexithiophene (T6). T6 forms two crystalline polymorphs largely studied, and possesses liquid crystalline phases still not well characterized, From simulations we detected a phase transition from crystal to liquid crystal at about 580 K, in agreement with available experiments, and in particular we found two LC phases, smectic and nematic. The crystal­smectic transition is associated to a relevant density variation and to strong conformational changes of T6, namely the molecules in the liquid crystal phase easily assume a bent shape, deviating from the planar structure typical of the crystal. The third line explores a new approach for calculating the viscosity in a nematic through a virtual exper- iment resembling the classical falling sphere experiment. The falling sphere is replaced by an hydrogenated silicon nanoparticle of spherical shape suspended in 5CB, and gravity effects are replaced by a constant force applied to the nanoparticle in a selected direction. Once the nanoparticle reaches a constant velocity, the viscosity of the medium can be evaluated using Stokes' law. With this method we successfully reproduced experimental viscosities and viscosity anisotropy for the solvent 5CB. The last line deals with the study of order induction on nematic molecules by an hydrogenated silicon surface. Gaining predicting power for the anchoring behavior of liquid crystals at surfaces will be a very desirable capability, as many properties related to devices depend on molecular organization close to surfaces. Here we studied, by means of atomistic MD simulations, the flat interface between an hydrogenated (001) silicon surface in contact with a sample of 5CB molecules. We found a planar anchoring of the first layers of 5CB where surface interactions are dominating with respect to the mesogen intermolecular interactions. We also analyzed the interface 5CB­vacuum, finding a homeotropic orientation of the nematic at this interface.

Aspetti innovativi per la valutazione e la misura della porosità nei materiali dell'edilizia antica e moderna. La geometria frattale della porosità

New concepts on porosity appraisal in ancient and modern construction materials. The role of Fractal Geometry on porosity characterization and transport phenomena. This work studied the potential of Fractal Geometry to the characterization of porous materials. Besides the descriptive aspects of the pore size distribution, the fractal dimensions have led to the development of rational relations for the prediction of permeability coefficients to fluid and heat transfer. The research considered natural materials used in historical buildings (rock and earth) as well as currently employed materials as hydraulic cement and technologically advanced materials such as silicon carbide or YSZ ceramics. The experimental results of porosity derived from the techniques of mercury intrusion and from the image analysis. Data elaboration was carried out according to established procedures of Fractal Geometry. It was found that certain classes of materials are clearly fractal and respond to simple patterns such as Sierpinski and Menger models. In several cases, however, the fractal character is not recognised because the microstructure of the material is based on different phases at different dimensional scales, and in consequence the “fractal dimensions” calculated from porosimetric data do not come within the standard range (less than 3). Using different type and numbers of fractal units is possible, however, to obtain “virtual” microstructures that have the fraction of voids and pore size distribution equivalent with the experimental ones for almost any material. Thus it was possible to take the expressions for the permeability and the thermal conduction which does not require empirical “constants”, these expressions have also provided values that are generally in agreement with the experimental available data. More problematic has been the fractal discussion of the geometry of the rupture of the material subjected to mechanical stress both external and internal applied. The results achieved on these issues are qualitative and prone to future studies. Keywords: Materials, Microstructure, Porosity, Fractal Geometry, Permeability, Thermal conduction, Mechanical strength.

Sistemi liquido cristallini complessi: simulazioni al calcolatore e studi ESR

The aim of this PhD thesis was to study at a microscopic level different liquid crystal (LC) systems, in order to determine their physical properties, resorting to two distinct methodologies, one involving computer simulations, and the other spectroscopic techniques, in particular electron spin resonance (ESR) spectroscopy. By means of the computer simulation approach we tried to demonstrate this tool effectiveness for calculating anisotropic static properties of a LC material, as well as for predicting its behaviour and features. This required the development and adoption of suitable molecular models based on a convenient intermolecular potentials reflecting the essential molecular features of the investigated system. In particular, concerning the simulation approach, we have set up models for discotic liquid crystal dimers and we have studied, by means of Monte Carlo simulations, their phase behaviour and self­-assembling properties, with respect to the simple monomer case. Each discotic dimer is described by two oblate Gay­Berne ellipsoids connected by a flexible spacer, modelled by a harmonic "spring" of three different lengths. In particular we investigated the effects of dimerization on the transition temperatures, as well as on the characteristics of molecular aggregation displayed and the relative orientational order. Moving to the experimental results, among the many experimental techniques that are typically employed to evaluate LC system distinctive features, ESR has proved to be a powerful tool in microscopic scale investigation of the properties, structure, order and dynamics of these materials. We have taken advantage of the high sensitivity of the ESR spin probe technique to investigate increasingly complex LC systems ranging from devices constituted by a polymer matrix in which LC molecules are confined in shape of nano- droplets, as well as biaxial liquid crystalline elastomers, and dimers whose monomeric units or lateral groups are constituted by rod-like mesogens (11BCB). Reflection-mode holographic-polymer dispersed liquid crystals (H-PDLCs) are devices in which LCs are confined into nanosized (50­-300 nm) droplets, arranged in layers which alternate with polymer layers, forming a diffraction grating. We have determined the configuration of the LC local director and we have derived a model of the nanodroplet organization inside the layers. Resorting also to additional information on the nanodroplet size and shape distribution provided by SEM images of the H-PDLC cross-section, the observed director configuration has been modeled as a bidimensional distribution of elongated nanodroplets whose long axis is, on the average, parallel to the layers and whose internal director configuration is a uniaxial quasi- monodomain aligned along the nanodroplet long axis. The results suggest that the molecular organization is dictated mainly by the confinement, explaining, at least in part, the need for switching voltages significantly higher and the observed faster turn-off times in H-PDLCs compared to standard PDLC devices. Liquid crystal elastomers consist in cross-linked polymers, in which mesogens represent the monomers constituting the main chain or the laterally attached side groups. They bring together three important aspects: orientational order in amorphous soft materials, responsive molecular shape and quenched topological constraints. In biaxial nematic liquid crystalline elastomers (BLCEs), two orthogonal directions, rather than the one of normal uniaxial nematic, can be controlled, greatly enhancing their potential value for applications as novel actuators. Two versions of a side-chain BLCEs were characterized: side­-on and end­-on. Many tests have been carried out on both types of LCE, the main features detected being the lack of a significant dynamical behaviour, together with a strong permanent alignment along the principal director, and the confirmation of the transition temperatures already determined by DSC measurements. The end­-on sample demonstrates a less hindered rotation of the side group mesogenic units and a greater freedom of alignment to the magnetic field, as already shown by previous NMR studies. Biaxial nematic ESR static spectra were also obtained on the basis of Molecular Dynamics generated biaxial configurations, to be compared to the experimentally determined ones, as a mean to establish a possible relation between biaxiality and the spectral features. This provides a concrete example of the advantages of combining the computer simulation and spectroscopic approaches. Finally, the dimer α,ω-bis(4'-cyanobiphenyl-4-yl)undecane (11BCB), synthesized in the "quest" for the biaxial nematic phase has been analysed. Its importance lies in the dimer significance as building blocks in the development of new materials to be employed in innovative technological applications, such as faster switching displays, resorting to the easier aligning ability of the secondary director in biaxial phases. A preliminary series of tests were performed revealing the population of mesogenic molecules as divided into two groups: one of elongated straightened conformers sharing a common director, and one of bent molecules, which display no order, being equally distributed in the three dimensions. Employing this model, the calculated values show a consistent trend, confirming at the same time the transition temperatures indicated by the DSC measurements, together with rotational diffusion tensor values that follow closely those of the constituting monomer 5CB.

Numerical simulation of ion transport through ion channels and solid-state nanopores

Ion channels are pore-forming proteins that regulate the flow of ions across biological cell membranes. Ion channels are fundamental in generating and regulating the electrical activity of cells in the nervous system and the contraction of muscolar cells. Solid-state nanopores are nanometer-scale pores located in electrically insulating membranes. They can be adopted as detectors of specific molecules in electrolytic solutions. Permeation of ions from one electrolytic solution to another, through a protein channel or a synthetic pore is a process of considerable importance and realistic analysis of the main dependencies of ion current on the geometrical and compositional characteristics of these structures are highly required. The project described by this thesis is an effort to improve the understanding of ion channels by devising methods for computer simulation that can predict channel conductance from channel structure. This project describes theory, algorithms and implementation techniques used to develop a novel 3-D numerical simulator of ion channels and synthetic nanopores based on the Brownian Dynamics technique. This numerical simulator could represent a valid tool for the study of protein ion channel and synthetic nanopores, allowing to investigate at the atomic-level the complex electrostatic interactions that determine channel conductance and ion selectivity. Moreover it will provide insights on how parameters like temperature, applied voltage, and pore shape could influence ion translocation dynamics. Furthermore it will help making predictions of conductance of given channel structures and it will add information like electrostatic potential or ionic concentrations throughout the simulation domain helping the understanding of ion flow through membrane pores.