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.

Untersuchung der Ordnung und Diffusion von Polymerdispersionen bei ihrer Verfilmung

Im Rahmen dieser Arbeit wurde die, für industrielle Applikationen sehr wichtige, Trocknung und Verfilmung von Latexdispersionen untersucht. Unter der Verfilmung wird in diesem Zusammenhang allgemein der Übergang einer Polymerdispersion in einen transparenten, mechanisch stabilen Polymerfilm während ihrer Trocknung verstanden. Für die Untersuchungen wurden schwerpunktmäßig Streumethoden verwendet. Die Untersuchungen haben gezeigt, daß die Streuung eine besonders geeignete Methode zur Untersuchung der Verfilmung ist, die in Abhängigkeit des beobachteten Streuvektorbereichs, der verwendeten Strahlung, der Probenpräparation und des resultierenden Kontrasts eine Vielzahl unterschiedlicher Informationen über die Verfilmung in ihren verschiedenen Phasen liefert. Von besonderem Interesse war es, den prinzipiellen Verlauf der Verfilmung bei den heterogen trocknenden Reinacrylatlatices zu untersuchen. Dazu wurde mit Hilfe der Röntgenultrakleinwinkelstreuung gezielt der Zustand der Partikel in den einzelnen Phasen der heterogen trocknenden Proben beobachtet. Mit Hilfe der Neutronenkleinwinkelstreuung konnte das Verhalten des Emulgators während der Verfilmung und dessen Verteilung im resultierenden Film genauer untersucht werden. Die Röntgenkleinwinkelstreuung erlaubte eine eingehende Untersuchung der Kristallisation des Emulgators im trockenen Film. Geeignete Kontrastierung durch gezielte Deuterierung ermöglichte die Untersuchung des Comonomereinflusses auf die Interdiffusion von Latexpartikeln mit Neutronenkleinwinkelstreuung. Aus den Meßergebnissen wurde ein Modell zur heterogenen Trocknung von Latexdispersionen entwickelt, das den Ablauf der Verfilmung in einem konsistenten Bild zusammenfaßt.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Fluidodinamica biomedica computazionale del flusso sanguigno in presenza di affezioni strumentali e/o patologiche

La tesi di Dottorato studia il flusso sanguigno tramite un codice agli elementi finiti (COMSOL Multiphysics). Nell’arteria è presente un catetere Doppler (in posizione concentrica o decentrata rispetto all’asse di simmetria) o di stenosi di varia forma ed estensione. Le arterie sono solidi cilindrici rigidi, elastici o iperelastici. Le arterie hanno diametri di 6 mm, 5 mm, 4 mm e 2 mm. Il flusso ematico è in regime laminare stazionario e transitorio, ed il sangue è un fluido non-Newtoniano di Casson, modificato secondo la formulazione di Gonzales & Moraga. Le analisi numeriche sono realizzate in domini tridimensionali e bidimensionali, in quest’ultimo caso analizzando l’interazione fluido-strutturale. Nei casi tridimensionali, le arterie (simulazioni fluidodinamiche) sono infinitamente rigide: ricavato il campo di pressione si procede quindi all’analisi strutturale, per determinare le variazioni di sezione e la permanenza del disturbo sul flusso. La portata sanguigna è determinata nei casi tridimensionali con catetere individuando tre valori (massimo, minimo e medio); mentre per i casi 2D e tridimensionali con arterie stenotiche la legge di pressione riproduce l’impulso ematico. La mesh è triangolare (2D) o tetraedrica (3D), infittita alla parete ed a valle dell’ostacolo, per catturare le ricircolazioni. Alla tesi sono allegate due appendici, che studiano con codici CFD la trasmissione del calore in microcanali e l’ evaporazione di gocce d’acqua in sistemi non confinati. La fluidodinamica nei microcanali è analoga all’emodinamica nei capillari. Il metodo Euleriano-Lagrangiano (simulazioni dell’evaporazione) schematizza la natura mista del sangue. La parte inerente ai microcanali analizza il transitorio a seguito dell’applicazione di un flusso termico variabile nel tempo, variando velocità in ingresso e dimensioni del microcanale. L’indagine sull’evaporazione di gocce è un’analisi parametrica in 3D, che esamina il peso del singolo parametro (temperatura esterna, diametro iniziale, umidità relativa, velocità iniziale, coefficiente di diffusione) per individuare quello che influenza maggiormente il fenomeno.

Structuring of polymer surface by evaporation of sessile microdrops

In this thesis, we investigated the evaporation of sessile microdroplets on different solid substrates. Three major aspects were studied: the influence of surface hydrophilicity and heterogeneity on the evaporation dynamics for an insoluble solid substrate, the influence of external process parameters and intrinsic material properties on microstructuring of soluble polymer substrates and the influence of an increased area to volume ratio in a microfluidic capillary, when evaporation is hindered. In the first part, the evaporation dynamics of pure sessile water drops on smooth self-assembled monolayers (SAMs) of thiols or disulfides on gold on mica was studied. With increasing surface hydrophilicity the drop stayed pinned longer. Thus, the total evaporation time of a given initial drop volume was shorter, since the drop surface, through which the evaporation occurs, stays longer large. Usually, for a single drop the volume decreased linearly with t1.5, t being the evaporation time, for a diffusion-controlled evaporation process. However, when we measured the total evaporation time, ttot, for multiple droplets with different initial volumes, V0, we found a scaling of the form V0 = attotb. The more hydrophilic the substrate was, the more showed the scaling exponent a tendency to an increased value up to 1.6. This can be attributed to an increasing evaporation rate through a thin water layer in the vicinity of the drop. Under the assumption of a constant temperature at the substrate surface a cooling of the droplet and thus a decreased evaporation rate could be excluded as a reason for the different scaling exponent by simulations performed by F. Schönfeld at the IMM, Mainz. In contrast, for a hairy surface, made of dialkyldisulfide SAMs with different chain lengths and a 1:1 mixture of hydrophilic and hydrophobic end groups (hydroxy versus methyl group), the scaling exponent was found to be ~ 1.4. It increased to ~ 1.5 with increasing hydrophilicity. A reason for this observation can only be speculated: in the case of longer hydrophobic alkyl chains the formation of an air layer between substrate and surface might be favorable. Thus, the heat transport to the substrate might be reduced, leading to a stronger cooling and thus decreased evaporation rate. In the second part, the microstructuring of polystyrene surfaces by drops of toluene, a good solvent, was investigated. For this a novel deposition technique was developed, with which the drop can be deposited with a syringe. The polymer substrate is lying on a motorized table, which picks up the pendant drop by an upward motion until a liquid bridge is formed. A consecutive downward motion of the table after a variable delay, i.e. the contact time between drop and polymer, leads to the deposition of the droplet, which can evaporate. The resulting microstructure is investigated in dependence of the processes parameters, i.e. the approach and the retraction speed of the substrate and the delay between them, and in dependence of the intrinsic material properties, i.e. the molar mass and the type of the polymer/solvent system. The principal equivalence with the microstructuring by the ink-jet technique was demonstrated. For a high approach and retraction speed of 9 mm/s and no delay between them, a concave microtopology was observed. In agreement with the literature, this can be explained by a flow of solvent and the dissolved polymer to the rim of the pinned droplet, where polymer is accumulated. This effect is analogue to the well-known formation of ring-like stains after the evaporation of coffee drops (coffee-stain effect). With decreasing retraction speed down to 10 µm/s the resulting surface topology changes from concave to convex. This can be explained with the increasing dissolution of polymer into the solvent drop prior to the evaporation. If the polymer concentration is high enough, gelation occurs instead of a flow to the rim and the shape of the convex droplet is received. With increasing delay time from below 0 ms to 1s the depth of the concave microwells decreases from 4.6 µm to 3.2 µm. However, a convex surface topology could not be obtained, since for longer delay times the polymer sticks to the tip of the syringe. Thus, by changing the delay time a fine-tuning of the concave structure is accomplished, while by changing the retraction speed a principal change of the microtopolgy can be achieved. We attribute this to an additional flow inside the liquid bridge, which enhanced polymer dissolution. Even if the pendant drop is evaporating about 30 µm above the polymer surface without any contact (non-contact mode), concave structures were observed. Rim heights as high as 33 µm could be generated for exposure times of 20 min. The concave structure exclusively lay above the flat polymer surface outside the structure even after drying. This shows that toluene is taken up permanently. The increasing rim height, rh, with increasing exposure time to the solvent vapor obeys a diffusion law of rh = rh0  tn, with n in the range of 0.46 ~ 0.65. This hints at a non-Fickian swelling process. A detailed analysis showed that the rim height of the concave structure is modulated, unlike for the drop deposition. This is due to the local stress relaxation, which was initiated by the increasing toluene concentration in the extruded polymer surface. By altering the intrinsic material parameters i.e. the polymer molar mass and the polymer/solvent combination, several types of microstructures could be formed. With increasing molar mass from 20.9 kDa to 1.44 MDa the resulting microstructure changed from convex, to a structure with a dimple in the center, to concave, to finally an irregular structure. This observation can be explained if one assumes that the microstructuring is dominated by two opposing effects, a decreasing solubility with increasing polymer molar mass, but an increasing surface tension gradient leading to instabilities of Marangoni-type. Thus, a polymer with a low molar mass close or below the entanglement limit is subject to a high dissolution rate, which leads to fast gelation compared to the evaporation rate. This way a coffee-rim like effect is eliminated early and a convex structure results. For high molar masses the low dissolution rate and the low polymer diffusion might lead to increased surface tension gradients and a typical local pile-up of polymer is found. For intermediate polymer masses around 200 kDa, the dissolution and evaporation rate are comparable and the typical concave microtopology is found. This interpretation was supported by a quantitative estimation of the diffusion coefficient and the evaporation rate. For a different polymer/solvent system, polyethylmethacrylate (PEMA)/ethylacetate (EA), exclusively concave structures were found. Following the statements above this can be interpreted with a lower dissolution rate. At low molar masses the concentration of PEMA in EA most likely never reaches the gelation point. Thus, a concave instead of a convex structure occurs. At the end of this section, the optically properties of such microstructures for a potential application as microlenses are studied with laser scanning confocal microscopy. In the third part, the droplet was confined into a glass microcapillary to avoid evaporation. Since here, due to an increased area to volume ratio, the surface properties of the liquid and the solid walls became important, the influence of the surface hydrophilicity of the wall on the interfacial tension between two immiscible liquid slugs was investigated. For this a novel method for measuring the interfacial tension between the two liquids within the capillary was developed. This technique was demonstrated by measuring the interfacial tensions between slugs of pure water and standard solvents. For toluene, n-hexane and chloroform 36.2, 50.9 and 34.2 mN/m were measured at 20°C, which is in a good agreement with data from the literature. For a slug of hexane in contact with a slug of pure water containing ethanol in a concentration range between 0 and 70 (v/v %), a difference of up to 6 mN/m was found, when compared to commercial ring tensiometry. This discrepancy is still under debate.

Modeling of complex chemical reactions and macromolecular orientation phenomena in confined geometries

The cooperative motion algorithm was applied on the molecular simulation of complex chemical reactions and macromolecular orientation phenomena in confined geometries. First, we investigated the case of equilibrium step-growth polymerization in lamellae, pores and droplets. In such systems, confinement was quantified as the area/volume ratio. Results showed that, as confinement increases, polymerization becomes slower and the average molecular weight (MW) at equilibrium decreases. This is caused by the sterical hindrance imposed by the walls since chain growth reactions in their close vicinity have less realization possibilities. For reactions inside droplets at surfaces, contact angles usually increased after polymerization to compensate conformation restrictions imposed by confinement upon growing chains. In a second investigation, we considered monodisperse and chemically inert chains and focused on the effect of confinement on chain orientation. Simulations of thin polymer films showed that chains are preferably oriented parallel to the surface. Orientation increases as MW increases or as film thickness d decreases, in qualitative agreement with experiments with low MW polystyrene. It is demonstrated that the orientation of simulated chains results from a size effect, being a function of the ratio between chain end-to-end distance and d. This study was complemented by experiments with thin films of pi-conjugated polymers like MEH-PPV. Anisotropic refractive index measurements were used to analyze chain orientation. With increasing MW, orientation is enhanced. However, for MEH-PPV, orientation does not depend on d even at thicknesses much larger than the chain contour length. This contradiction with simulations was discussed by considering additional causes for orientation, for instance the appearance of nematic-like ordering in polymer films. In another investigation, we simulated droplet evaporation at soluble surfaces and reproduced the formation of wells surrounded by ringlike deposits at the surface, as observed experimentally. In our simulations, swollen substrate particles migrate to the border of the droplet to minimize the contact between solvent and vacuum, which costs the most energy. Deposit formation in the beginning of evaporation results in pinning of the droplet. When polymer chains at the substrate surface have strong uniaxial orientation, the resulting pattern is no longer similar to a ring but to a pair of half-moons. In a final stage, as an extension for the model developed for polymerization in nanoreactors, we studied the effect of geometrical confinement on a hypothetical oscillating reaction following the mechanism of the so called periodically forced Brusselator. It was shown that a reaction which is chaotic in the bulk may be driven to periodicity by confinement and vice-versa, opening new perspectives for chaos control.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Diffusion in polymer systems studied by fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful technique to determine the diffusion of fluorescence molecules in various environments. The technique is based on detecting and analyzing the fluctuation of fluorescence light emitted by fluorescence species diffusing through a small and fixed observation volume, formed by a laser focused into the sample. Because of its great potential and high versatility in addressing the diffusion and transport properties in complex systems, FCS has been successfully applied to a great variety of systems. In my thesis, I focused on the application of FCS to study the diffusion of fluorescence molecules in organic environments, especially in polymer melts. In order to examine our FCS setup and a developed measurement protocol, I first utilized FCS to measure tracer diffusion in polystyrene (PS) solutions, for which abundance data exist in the literature. I studied molecular and polymeric tracer diffusion in polystyrene solutions over a broad range of concentrations and different tracer and matrix molecular weights (Mw). Then FCS was further established to study tracer dynamics in polymer melts. In this part I investigated the diffusion of molecular tracers in linear flexible polymer melts [polydimethylsiloxane (PDMS), polyisoprene (PI)], a miscible polymer blend [PI and poly vinyl ethylene (PVE)], and star-shaped polymer [3-arm star polyisoprene (SPI)]. The effects of tracer sizes, polymer Mw, polymer types, and temperature on the diffusion coefficients of small tracers were discussed. The distinct topology of the host polymer, i.e. star polymer melt, revealed the notably different motion of the small tracer, as compared to its linear counterpart. Finally, I emphasized the advantage of the small observation volume which allowed FCS to investigate the tracer diffusions in heterogeneous systems; a swollen cross-linked PS bead and silica inverse opals, where high spatial resolution technique was required.