Hyperverzweigte Polyphenylene und redoxaktive Dendrimere

Die Doktorarbeit gliedert sich in zwei Abschnitte. Das erste Kapitel beschäftigt sich mit den hyperverzweigten Polyphenylenen. Es wurden Untersuchungen des Molekulargewichts in Abhängigkeit von der Monomerkonzentration und der Reaktionszeit durchgeführt. Die synthetisierten Polymere haben große Polydispersitäten, die durch fraktioniertes Fällen herabgesetzt werden können. Die Funktionalisierung der hyperverzweigten Polyphenylene mit unterschiedlichen Methoden führt zu verschiedenen Funktionen auf der Oberfläche der Polymere. Die chlormethylierten hyperverzweigen Polymere können als Makroinitiator für den Aufbau von Kern-Schale-Systemen genutzt werden. Mit Hilfe der ATRP-Polymerisation wurde Methylmethacrylat anpolymerisiert. Als Charakterisierungsmethode zur Bestimmung des freien Volumens findet die Positronenauslöschungsspektroskopie Anwendung. Im zweiten Teil der Arbeit stehen die Synthese und Charakterisierung von redoxaktiven Dendrimeren mit Triphenylamin- bzw. Naphthalinkern im Mittelpunkt. Den Einfluß der Dendrimerhülle auf die Redoxaktivität zeigen cyclovoltammetrische Untersuchungen. Die Zunahme der dendritischen Hülle führt zu einer Abschirmung des Redoxzentrums gegen die Elektrode und damit zu einer Inhibierung des Elektronentransfers. Das spiegelt sich in der Abnahme der Geschwindigkeitskonstanten sowie in der Ausdehnung der cyclovoltammetrischen Kurve wieder. Die Funktionalisierung der Triphenylamin-Dendrimere mit Chromophoren auf der Oberfläche führt zu einer Änderung der optische Eigenschaften, die mit Hilfe von Absorptions- und Emissionsmessungen untersucht wurden.

Festkörper-NMR-Spektroskopie

Die innerhalb dieser Arbeit mittels moderner Festkörper-NMR-Methoden untersuchte molekulare Dynamik in Poly(methacrylat)-Schmelzen und Polyphenylen-Dendrimeren ist durch eine bemerkenswerte Anisotropie gekennzeichnet.Die Anisotropie der molekularen Dynamik zeigt sich in geschmolzenen, ataktischen und isotaktischen Poly(ethylmethacrylaten) (PEMA) durch die Zeitskalenseparation der segmentellen alpha-Relaxation von einem etwa zwei Größenordnungen langsameren Relaxationsprozeß, welcher die Isotropisierung der Polymerhauptkette wiedergibt. Die Isotropisierungsdynamik der Polymerhauptkette wird - mit Ausnahme von PMMA - durch eine universelle, nicht-korrelationszeitenverteilte Relaxationsmode der Poly(methacrylate) quantifiziert, deren Temperaturabhängigkeit durch einen einheitlichen WLF-Parametersatz beschrieben werden kann. Geometrisch läßt sich die Isotropisierung der Hauptkette durch Sprungprozesse beliebiger Amplitude von Kettenstücken mit gestreckter all-trans-Konformation interpretieren. Die Kette zeigt eine außergewöhnliche konformative Stabilität. WAXS-Messungen deuten für PEMA und seine höheren Homologen die Existenz einer Schichtstruktur an, in der sich die steifen, polaren Hauptketten lokal in Monolagen anordnen, welche durch Bereiche zusammengelagerter Seitengruppen getrennt sind. Die Festkörper-NMR-Untersuchungen an Polyphenylen-Dendrimeren bringen zwei zentrale Aspekte in der wechselseitigen Beziehung von Struktur und Dynamik hervor. Zum einen ist die beobachtete molekulare Dynamik auf lokale Reorientierungen einzelner, terminaler Phenylringe um definierte Achsen beschränkt. Polyphenylen-Dendrimermoleküle sind unter diesen Bewegungen formstabil. Zum anderen können sowohl schnelle, als auch langsame Phenylreorientierungen nachgewiesen werden, wobei jeweils die intramolekulare Packungsdichte der Phenylringe das dynamische Verhalten der Polyphenylen-Dendrimere kontrolliert.

Sphärische Blockcopolymer Mizellen in Homopolymerschmelze als weiche Modellkolloide

Zusammenfassung: Im Rahmen dieser Arbeit wurde die Dynamik in Blockcopolymer-Homopolymerblends mit sphärischen Mikrophasen untersucht.Anhand eines PI-PS-Blockcopolymers in drei verschiedenen PI-Homopolymeren wurde der Einfluss des Molekulargewichts des Homopolymers betrachtet. Die Ergebnisse aus Forcierter Rayleigh Streuung (Diffusion) und Rheologie (Relaxation) zeigen, dass sich die PS-PI-Mizellen in allen drei Homopolymeren kolloid-ähnlich verhalten. Die Analyse nach der Theorie des freien Volumens ergab, dass es sich bei den Mizellen um weiche Partikel handelt, deren Größe und Deformierbarkeit mit sinkendem Matrix-Molekulargewicht zunimmt.Der Einfluss des Blocklängenverhältnisses wurde an zwei PB-PS- Blockcopolymeren mit unterschiedlich langen PS-Blöcken (Kern) untersucht. Diese unterschieden sich jedoch in ihrem dynamischen Verhalten nicht maßgeblich. Es wurde jedoch ein deutlicher Unterschied zum PI-PS- System (s.o.) gefunden. Der zuvor gefundene Partikelcharakter wird für die PB-PS-Copolymere nicht mehr beobachtet. Dies wird auf den im Vergleich zum PI-PS-Copolymer deutlich längeren Coronablock zurückgeführt.

Mixtures of colloidal rods and spheres in bulk and in confinement

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. Monte Carlo simulations were performed to study the phase diagram of such rod-polymer mixtures. The colloidal rods were modelled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while overlap of polymers and rods is forbidden. In this thesis the emphasis was on the depletion effects caused by the addition of spheres on the isotropic phase of rod-like particles. Although most of the present experimental studies consider systems close to or beyond the isotropic-nematic transition, the isotropic phase with depletion interactions turns out to be a not less interesting topic. First, the percolation problem was studied in canonical simulations of a system of hard rods and soft spheres, where the amount of depletant was kept low to prevent phase separation of the mixture. The lowering of the percolation threshold seen in experiment is confirmed to be due to the depletion interactions. The local changes in the structure of the fluid of rods, which were measured in the simulations, indicated that the depletion forces enhance local alignment and aggregation of the rods. Then, the phase diagram of isotropic-isotropic demixing of short spherocylinders was calculated using grand canonical ensemble simulations with successive umbrella sampling. Finite size scaling analysis allowed to estimate the location of the critical point. Also, estimates for the interfacial tension between the coexisting isotropic phases and analyses of its power-law behaviour on approach of the critical point are presented. The obtained phase diagram was compared to the predictions of the free volume theory. After an analysis of the bulk, the phase behaviour in confinement was studied. The critical point of gas-liquid demixing is shifted to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surface film. If the separation between the walls becomes very small, the critical point is shifted back to smaller concentrations of rods because the surface film breaks up. A method to calculate the contact angle of the liquid-gas interface with the wall is introduced and the wetting behaviour on the approach to the critical point is analysed.

Ionenleitfähigkeit in polymeren Matrizes – Synthese, Charakterisierung und Untersuchung dynamischer Prozesse von neuen Lithium- und Protonenleitern

Die vorliegende Dissertation befasst sich mit der Synthese, physikochemischen und polymerspezifischen Charakterisierung und insbesondere der impedanzspektroskopischen Untersuchung von sowohl neuartigen, solvensfreien lithiumionen- als auch protonenleitfähigen Polymermaterialien für potentielle Anwendungen in sekundären Lithiumionenbatterien bzw. in Hochtemperatur-Protonenaustauschmembran-Brennstoffzellen (engl.: proton exchange membrane fuel cell, auch: polymer electrolyte membrane fuel cell, PEMFC). Beiden Typen von ionenleitfähigen Membranen liegt das gängige Prinzip der chemischen Anbindung einer für den Ionentransport verantwortlichen Seitengruppe an eine geeignete Polymerhauptkette zugrunde („Entkopplung“; auch Immobilisierung), welcher hinsichtlich Glasübergangstemperatur (Tg), elektrochemischer und thermischer Stabilität (Td) eine dynamisch entkoppelte, aber nicht minder bedeutsame Rolle zukommt. Die Transportaktivierung erfolgt in beiden Fällen thermisch. Im Falle der Protonenleiter liegt die zusätzliche Intention darin, eine Alternative aufzuzeigen, in der die Polymerhauptkette gekoppelt direkt am Protonentransportmechanismus beteiligt ist, d.h., dass der translatorisch diffusive Ionentransport entlang der Hauptkette stattfindet und nicht zwischen benachbarten Seitenketten. Ein Hauptaugenmerk der Untersuchungen liegt sowohl bei den lithiumionen- als auch den protonenleitfähigen Polymermembranen auf temperaturabhängigen dynamischen Prozessen der jeweiligen Ionenspezies in der polymeren Matrix, was die Ionenleitfähigkeit selbst, Relaxationsphänomene, die translatorische Ionendiffusion und im Falle der Protonenleiter etwaige mesomere Grenzstrukturübergänge umfasst. Lithiumionenleiter: Poly(meth)acrylate mit (2-Oxo-1,3-dioxolan)resten (Cyclocarbonat-) in der Seitenkette unterschiedlicher Spacerlänge wurden synthetisiert und charakterisiert. Die Leitfähigkeit s(,T) erreicht bei Poly(2-oxo-[1,3]dioxolan-4-yl)methylacrylat (PDOA): Lithium-bis-trifluormethansulfonimid (LiTFSI) (10:3) ca. 10^-3,5 S cm^-1 bei 150 °C. Weichmachen (Dotieren) mit äquimolaren Mengen an Propylencarbonat (PC) bewirkt in allen Fällen einen enormen Anstieg der Leitfähigkeit. Die höchsten Leitfähigkeiten von Mischungen dieser Polymere mit LiTFSI (und LiBOB) werden nicht beim System mit der niedrigsten Tg gefunden. Auch dient Tg nicht als Referenztemperatur (Tref) nach Williams-Landel-Ferry (WLF), so dass eine WLF-Anpassung der Leitfähigkeitsdaten nur über einen modifizierten WLF-Algorithmus gelingt. Die ermittelten Tref liegen deutlich unterhalb von Tg bei Temperaturen, die charakteristisch für die Seitenkettenrelaxation sind („Einfrieren“). Dies legt nahe, dass der Relaxation der Seitenketten eine entscheidende Rolle im Li^+-Leitfähigkeitsmechanismus zukommt. Die Li^+-Überführungszahlen tLi^+ in diesen Systemen schwanken zwischen 0,13 (40 °C) und 0,55 (160 °C). Protonenleiter: Polymere mit Barbitursäure- bzw. Hypoxanthinresten in der Seitenkette und Polyalkylenbiguanide unterschiedlicher Spacerlänge wurden synthetisiert und charakterisiert. Die Leitfähigkeit s(,T) erreicht bei Poly(2,4,6(1H,3H,5H)-trioxopyrimidin-5-yl)methacrylat (PTPMA) maximal ca. 10^-4,4 S cm^-1 bei 140 °C. Höhere Leitfähigkeiten sind nur durch Mischen mit aprotischen Lösungsmitteln erreichbar. Die höchste Leitfähigkeit wird im Falle der Polyalkylenbiguanide bei Polyethylenbiguanid (PEB) erzielt. Sie erreicht 10^-2,4 S cm^-1 bei 190 °C. Die Aktivierungsenergien EA der Polyalkylenbiguanide liegen (jeweils unterhalb von Tg) zwischen ca. 3 – 6 kJ mol^-1. In allen beobachteten Fällen dient Tg als Tref, so dass eine konventionelle WLF-Behandlung möglich ist und davon auszugehen ist, dass die Leitfähigkeit mit dem freien Volumen Vf korreliert.

Polymeric membranes for CO2 separation: effect of aging, humidity and facilitated transport

Polymeric membranes represent a promising technology for gas separation processes, thanks to low costs, reduced energy consumption and limited waste production. The present thesis aims at studying the transport properties of two membrane materials, suitable for CO2 purification applications. In the first part, a polyimide, Matrimid 5218, has been throughout investigated, with particular reference to the effect of thermal treatment, aging and the presence of water vapor in the gas transport process. Permeability measurements showed that thermal history affects relevantly the diffusion of gas molecules across the membrane, influencing also the stability of the separation performances. Subsequently, the effect of water on Matrimid transport properties has been characterized for a wide set of incondensable penetrants. A monotonous reduction of permeability took place at increasing the water concentration within the polymer matrix, affecting the investigated gaseous species to the same extent, despite the different thermodynamic and kinetic features. In this view, a novel empirical model, based on the Free Volume Theory, has been proposed to qualitatively describe the phenomenon. Moreover, according to the accurate representation of the experimental data, the suggested approach has been combined with a more rigorous thermodynamic tool (NELF Model), allowing an exhaustive description of water influence on the single parameters contributing to the gas permeation across the membrane. In the second part, the study has focused on the synthesis and characterization of facilitated transport membranes, able to achieving outstanding separation performances thanks to the chemical enhancement of CO2 permeability. In particular, the transport properties have been investigated for high pressure CO2 separation applications and specific solutions have been proposed to solve stability issues, frequently arising under such severe conditions. Finally, the effect of different process parameters have been investigated, aiming at the identification of the optimal conditions capable to maximize the separation performance.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Estudo da microestrutura e dinâmica molecular do Poly(3-(2\'-ethylhexyl)thiophene)(P3EHT) via ressonância magnética nuclear

O estudo da microestrutura e dinâmica molecular de polímeros conjugados é de grande importância para o entendimento das propriedades físicas desta classe de materiais. No presente trabalho utilizou-se técnicas de ressonância magnética nuclear em baixo e alto campo para elucidar os processos de dinâmica molecular e cristalização do polímero Poly(3-(2’-ethylhexyl)thiophene) - P3EHT. O P3EHT é um polímero modelo para tal estudo, pois apresenta temperatura de fusão bem inferior a sua temperatura de degradação. Esta característica permite acompanhar os processos de cristalização in situ utilizando RMN. Além disso, sua similaridade ao já popular P3HT o torna um importante candidato a camada ativa em dispositivos eletrônicos orgânicos. O completo assinalamento do espectro de 13C para o P3EHT foi realizado utilizando as técnicas de defasamento dipolar e HETCOR. Os processos de dinâmica molecular, por sua vez, foram sondados utilizando DIPSHIFT. Observou-se um gradiente de mobilidade na cadeia lateral do polímero. Além disso, os baixos valores de parametros de ordem obtidos em comparação a experimentos similares realizados no P3HT na literatura indicam um aparente aumento no volume livre entre cadeias consecutivas na fase cristalina. Isso indica que a presença do grupo etil adicional no P3EHT causa um completo rearranjo das moléculas e dificulta seu empacotamento. Constatou-se ainda pouca variação das curvas de DIPSHIFT para os carbonos da cadeia lateral como função do método de excitação utilizado, o que aponta para um polímero que apresenta cadeia lateral móvel mesmo em sua fase cristalina. Os dados de dinâmica molecular foram corroborados por medidas de T1, T1ρ e TCH. Utilizando filtros dipolares em baixo campo observou-se três temperaturas de transição para o P3EHT: 250 K, 325 K e 350 K. A cristalização desse material é um processo lento. Verificou-se que o mesmo pode se estender por até até 24h a temperatura ambiente. Mudanças no espectro de 13C utilizando CPMAS em alto campo indicam um ordenamento dos anéis tiofeno (empacotamento π – π) como o principal processo de cristalização para o P3EHT.

Thin-layer isothermal drying of fructose, maltodextrin, and their mixture solutions

Solutions of fructose, maltodextrin (DE 5), and their mixtures at the ratios of 20:80, 40:60, 50:50, 60:40, and 80:20 were gelled with 1% agar-agar and dried under convective-conductive drying conditions. The thin slabs were maintained at isothermal drying condition of 30 and 50 degrees C. Yamamoto's simplified method based on regular regime approach was used to calculate the (effective) moisture diffusivity. Both the drying rates and the moisture diffusivity exhibited strong concentration dependence. The concentration dependence was stronger in the case of fructose and fructose rich solutions. Both the moisture diffusivity and drying rates of the mixture solutions were enhanced due to plasticization of fructose on maltodextrin, which is explained through free volume theory.

Transport phenomena in hydrogel membranes

In this thesis the factors surrounding the permeation of alkali and alkaline earth metal salts through hydrogel membranes are investigated. Although of relevance to aqueous separations in general, it was with their potential application in sensors that this work was particularly concerned. In order to study the effect that the nature of the solute has on the transport process, a single polymer matrix, poly (2-hydroxyethyl methacrylate), was initially studied. The influence of cation variation in the presence of a fixed anion was looked at, followed by the effect of the anion in the presence of a fixed cation. The anion was found to possess the dominant influence and tended to subsume any influence by the cation. This is explained in terms of the structure-making and structure-breaking characteristics of the ions in their solute-water interactions. Analogies in the transport behaviour of the salts are made with the Hofmeister series. The effect of the chemical composition of the polymer backbone on the water structuring in the hydrogel and, consequently, transport through the membrane, was investigated by preparing a series of poly (2-hydroxyethyl methacrylate) copolymer membranes and determining the permeability coefficient of salts with a fixed anion. The results were discussed in terms of the `free-volume' model of permeation and the water structuring of the polymer backbone. The ability of ionophores to selectively modulate the permeation of salts through hydrogel membranes was also examined. The results indicated that a dualsorption model was in operation. Finally, hydrogels were used as membrane overlays on coated wire ion-selective electrodes that employed conventional plasticised-PVC-valinomycin based sensing membranes. The hydrogel overlays were found to affect the access of the analyte but not the underlying electrochemistry.

Characterization of New Carbosilane Liquid Crystalline Monomers and Dimers

‘De Vries-like’ smectic liquid crystals exhibit low layer contraction of approximately 1% on transitions from the SmA to the SmC phase. These materials have received considerable attention as potential solutions for problems affecting liquid crystal displays using surface-stabilized ferroelectric liquid crystals (SSFLC). In SSFLCs, layer contraction of 710% is normally observed during the SmA to SmC phase transition. A study by the Lemieux group has shown that liquid crystals with nanosegregating carbosilane segments exhibit enhanced ‘de Vries-like’ properties through the formation of smectic layers and by lengthening the nanosegregating carbosilane end-groups from monocarbosilane to tricarbosilane. This observed enhancement is assumed to be due to an increase in the cross-section of the free volume in the hydrocarbon sub-layer. To test this hypothesis, it is assumed that dimers with a tricarbosilane linking group have smaller cross-sections on time average. In his thesis, this hypothesis is tested through the characterization of new liquid crystalline monomers (QL39-n) and dimers (QL40-n) with 2-phenylpyrimidine cores and tricarbosilane end-groups and spacers, respectively. The thesis describes the synthesis of two homologous series of liquid crystals and their characterization using a variety of techniques, including polarized optical microscopy, differential scanning calorimetry and X-ray diffraction. The results show that the monomers QL39-n form a tilted SmC phase only, whereas the dimers QL40-n form an orthogonal SmA phase. These results are discussed in the context of our hypothesis.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Free-breathing inner-volume black-blood imaging of the human heart using two-dimensionally selective local excitation at 3 T.

Black-blood fast spin-echo imaging is a powerful technique for the evaluation of cardiac anatomy. To avoid fold-over artifacts, using a sufficiently large field of view in phase-encoding direction is mandatory. The related oversampling affects scanning time and respiratory chest motion artifacts are commonly observed. The excitation of a volume that exclusively includes the heart without its surrounding structures may help to improve scan efficiency and minimize motion artifacts. Therefore, and by building on previously reported inner-volume approach, the combination of a black-blood fast spin-echo sequence with a two-dimensionally selective radiofrequency pulse is proposed for selective "local excitation" small field of view imaging of the heart. This local excitation technique has been developed, implemented, and tested in phantoms and in vivo. With this method, small field of view imaging of a user-specified region in the human thorax is feasible, scanning becomes more time efficient, motion artifacts can be minimized, and additional flexibility in the choice of imaging parameters can be exploited.