{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:1808"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:1808","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Anomalous diffusion in anisotropic media","abstract":"The structure and dynamics of three 'soft-matter' systems was investigated by pulsed field gradient diffusion NMR and complementary deuterium line shape analysis. Restricted diffusion was studied in two lyotropic lamellar systems, the first consisting of crosslinked flat lamellae in anisotropic hydrogels and the second consisting of spherically bent lamellae in multilamellar vesicles. In the third system, a swollen PDMS network, obstructed diffusion was investigated in the fractal topology.
Anisotropic Hydrogels: The structure and ordering of macroscopically oriented anisotropic hydrogels was investigated on different length scales. Diffusion NMR proved the existence of defects in the lamellae on a mesoscopic scale and gave an estimate of the minimal extension of homogeneous domains. Temperature dependent obstruction factors for diffusion parallel to the layer normal showed an anomalous step at around 312 - 314 K. This was interpreted as the generation of further defects and microscopic cracks due to elastic forces from the network. The network tends to restore its original shape of a coil and becomes the dominating factor in the coupled system of mesophase and polymer network above this temperature range. The anisotropy of diffusion for D2O on the mesoscopic level was determined to be 10 : 1. For the diffusion of a dye the anisotropy decreased to 5.3 : 1 on the macroscopic level. The comparison of two hydrogels with different content of water showed higher order and fewer structural defects in the system with lower content of water.
Multilamellar Vesicles: The dynamics of D2O in the shear-induced multilamellar vesicle (MLV) phase was investigated using the system C10E3/D2O as an example. An empirical relationship between vesicle size and the D2O single pulse line shape was established. Deuterium line shapes of the solid and stimulated echo showed a splitting at long evolution delays, which was identified as the 90° singularity of the motionally averaged Pake spectrum of the normal, macroscopically disordered lamellar phase. The stimulated echo line shape is dominated by rotational motions with correlation times in the order of the evolution delays. Pulsed gradient diffusion measurements showed a strong dependence of the echo decay on the diffusion time. This was attributed to the restricted diffusion along the spherical lamellae in the MLVs. A theoretical model for diffusion in an idealized MLV structure was tested for its ability to describe the measured echo decay. The observed differences in comparison to the measured data were mainly attributed to three factors: first the incomplete description of the line shape in the stimulated echo, second the neglect of diffusion during the finite gradient duration and third the diffusion through the layers.
PDMS Model Networks: PDMS model networks were investigated by pulsed gradient diffusion NMR in order to detect anomalous diffusional behavior as a test for recently developed theories on inhomogeneous network swelling. Diffusion time dependent measurements were carried out on different samples. No evidence for inhomogeneous swelling of the networks was found. Neither the shape of the echo decay, which is Gaussian, nor diffusion time dependencies nor variation of the degree of swelling showed a significant effect from which obstructed diffusion could have been deduced. Even in a deliberately inhomogeneously synthesized bimodal networks, where heterogeneities were expected, no such evidence was found.","abstract_html":"The structure and dynamics of three 'soft-matter' systems was investigated by pulsed field gradient diffusion NMR and complementary deuterium line shape analysis. Restricted diffusion was studied in two lyotropic lamellar systems, the first consisting of crosslinked flat lamellae in anisotropic hydrogels and the second consisting of spherically bent lamellae in multilamellar vesicles. In the third system, a swollen PDMS network, obstructed diffusion was investigated in the fractal topology. <br> <br>Anisotropic Hydrogels: The structure and ordering of macroscopically oriented anisotropic hydrogels was investigated on different length scales. Diffusion NMR proved the existence of defects in the lamellae on a mesoscopic scale and gave an estimate of the minimal extension of homogeneous domains. Temperature dependent obstruction factors for diffusion parallel to the layer normal showed an anomalous step at around 312 - 314 K. This was interpreted as the generation of further defects and microscopic cracks due to elastic forces from the network. The network tends to restore its original shape of a coil and becomes the dominating factor in the coupled system of mesophase and polymer network above this temperature range. The anisotropy of diffusion for D2O on the mesoscopic level was determined to be 10 : 1. For the diffusion of a dye the anisotropy decreased to 5.3 : 1 on the macroscopic level. The comparison of two hydrogels with different content of water showed higher order and fewer structural defects in the system with lower content of water. <br> <br>Multilamellar Vesicles: The dynamics of D2O in the shear-induced multilamellar vesicle (MLV) phase was investigated using the system C10E3/D2O as an example. An empirical relationship between vesicle size and the D2O single pulse line shape was established. Deuterium line shapes of the solid and stimulated echo showed a splitting at long evolution delays, which was identified as the 90° singularity of the motionally averaged Pake spectrum of the normal, macroscopically disordered lamellar phase. The stimulated echo line shape is dominated by rotational motions with correlation times in the order of the evolution delays. Pulsed gradient diffusion measurements showed a strong dependence of the echo decay on the diffusion time. This was attributed to the restricted diffusion along the spherical lamellae in the MLVs. A theoretical model for diffusion in an idealized MLV structure was tested for its ability to describe the measured echo decay. The observed differences in comparison to the measured data were mainly attributed to three factors: first the incomplete description of the line shape in the stimulated echo, second the neglect of diffusion during the finite gradient duration and third the diffusion through the layers. <br> <br>PDMS Model Networks: PDMS model networks were investigated by pulsed gradient diffusion NMR in order to detect anomalous diffusional behavior as a test for recently developed theories on inhomogeneous network swelling. Diffusion time dependent measurements were carried out on different samples. No evidence for inhomogeneous swelling of the networks was found. Neither the shape of the echo decay, which is Gaussian, nor diffusion time dependencies nor variation of the degree of swelling showed a significant effect from which obstructed diffusion could have been deduced. Even in a deliberately inhomogeneously synthesized bimodal networks, where heterogeneities were expected, no such evidence was found.","abstract_has_math":false,"creators":["Kleinschmidt, Felix"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Schmidt, Claudia"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:28Z","subjects":["multilamellare Vesikel","heterogenes PDMS Netzwerk","scherinduzierte Struktur","Scherung","Anomale Diffusion","multilamellar vesicle","hydrogel","heterogeneous network","pulsed field gradient","deuterium NMR"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/1808","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schmidt, Claudia"]},{"key":"dc:creator","label":"Author","values":["Kleinschmidt, Felix"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["multilamellare Vesikel","heterogenes PDMS Netzwerk","scherinduzierte Struktur","Scherung","Anomale Diffusion","multilamellar vesicle","hydrogel","heterogeneous network","pulsed field gradient","deuterium NMR"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The structure and dynamics of three 'soft-matter' systems was investigated by pulsed field gradient diffusion NMR and complementary deuterium line shape analysis. Restricted diffusion was studied in two lyotropic lamellar systems, the first consisting of crosslinked flat lamellae in anisotropic hydrogels and the second consisting of spherically bent lamellae in multilamellar vesicles. In the third system, a swollen PDMS network, obstructed diffusion was investigated in the fractal topology.
Anisotropic Hydrogels: The structure and ordering of macroscopically oriented anisotropic hydrogels was investigated on different length scales. Diffusion NMR proved the existence of defects in the lamellae on a mesoscopic scale and gave an estimate of the minimal extension of homogeneous domains. Temperature dependent obstruction factors for diffusion parallel to the layer normal showed an anomalous step at around 312 - 314 K. This was interpreted as the generation of further defects and microscopic cracks due to elastic forces from the network. The network tends to restore its original shape of a coil and becomes the dominating factor in the coupled system of mesophase and polymer network above this temperature range. The anisotropy of diffusion for D2O on the mesoscopic level was determined to be 10 : 1. For the diffusion of a dye the anisotropy decreased to 5.3 : 1 on the macroscopic level. The comparison of two hydrogels with different content of water showed higher order and fewer structural defects in the system with lower content of water.
Multilamellar Vesicles: The dynamics of D2O in the shear-induced multilamellar vesicle (MLV) phase was investigated using the system C10E3/D2O as an example. An empirical relationship between vesicle size and the D2O single pulse line shape was established. Deuterium line shapes of the solid and stimulated echo showed a splitting at long evolution delays, which was identified as the 90° singularity of the motionally averaged Pake spectrum of the normal, macroscopically disordered lamellar phase. The stimulated echo line shape is dominated by rotational motions with correlation times in the order of the evolution delays. Pulsed gradient diffusion measurements showed a strong dependence of the echo decay on the diffusion time. This was attributed to the restricted diffusion along the spherical lamellae in the MLVs. A theoretical model for diffusion in an idealized MLV structure was tested for its ability to describe the measured echo decay. The observed differences in comparison to the measured data were mainly attributed to three factors: first the incomplete description of the line shape in the stimulated echo, second the neglect of diffusion during the finite gradient duration and third the diffusion through the layers.
PDMS Model Networks: PDMS model networks were investigated by pulsed gradient diffusion NMR in order to detect anomalous diffusional behavior as a test for recently developed theories on inhomogeneous network swelling. Diffusion time dependent measurements were carried out on different samples. No evidence for inhomogeneous swelling of the networks was found. Neither the shape of the echo decay, which is Gaussian, nor diffusion time dependencies nor variation of the degree of swelling showed a significant effect from which obstructed diffusion could have been deduced. Even in a deliberately inhomogeneously synthesized bimodal networks, where heterogeneities were expected, no such evidence was found.","Die Struktur und Dynamik von drei 'soft matter'-Systemen wurde durch NMR-Diffusionsmessungen mit gepulsten Feldgradienten und Deuterium-Linienformanalyse untersucht. Die eingeschränkte Diffusion in lyotrop flüssigkristallinen Systemen wurde anhand von zwei Beispielen analysiert: zum einen an einem anisotropen Hydrogel mit makroskopisch einheitlich orientierten lamellaren Schichten, zum anderen an kugelförmigen Lamellen multilamellarer Vesikel. Am dritten System, einem gequollenen PDMS-Netzwerk, wurde gehinderte Diffusion in einer fraktalen Topologie betrachtet.
Anisotrope Hydrogele: Die Struktur und Ordnung von makroskopisch einheitlich orientierten Hydrogelen in lamellarer Phase wurde auf verschiedenen Längenskalen untersucht. NMR-Diffusionsmessungen zeigten auf mesoskopischer Skala Defekte in den Lamellen und ermöglichten eine Abschätzung der minimalen Ausdehnung einer homogenen Domäne. Temperaturabhängige Messungen des Obstruktionsfaktors der Diffusion zeigten eine anomale Stufe bei etwa 312 - 314 K für die Diffusion durch die Lamellen. Dies wurde durch die Entstehung weiterer Defekte und mikroskopischer Risse erklärt, die durch elastische Rückstellkräfte des Netzwerks hervorgerufen werden. Das Netzwerk neigt dazu, seine ursprüngliche Knäuelkonformation wieder herzustellen, und wird oberhalb dieses Temperaturbereichs zum dominierenden Faktor im gekoppelten System aus Mesophase und Netzwerk. Die Anisotropie der Diffusion von Wasser auf mesoskopischer Ebene wurde zu 10 : 1 bestimmt. Für die Diffusion eines Farbstoffes auf makroskopischer Längenskala nahm die Anisotropie auf 5.3 : 1 ab. Der Vergleich zweier Hydrogele, die mit unterschiedlichem Wassergehalt hergestellt wurden, zeigte geringere Defekte und höhere Ordnung für das Hydrogel mit geringerem Wassergehalt.
Multilamellare Vesikel: Die Dynamik von D2O in durch Scherung hergestellten multilamellaren Vesikeln (MLV) wurde am System C10E3/D2O untersucht. Eine empirische Beziehung zwischen der Vesikelgröße und der D2O-Linienform wurde aufgestellt. Die Deuterium-Linienformen im quadrupolaren und stimulierten Echo zeigten eine Aufspaltung bei langen Evolutionszeiten, die mit der 90°-Singularität des bewegungsgemittelten Pake-Spektrums der normalen, makroskopisch ungeordneten lamellaren Phase identifiziert wurde. Die Linienform im stimulierten Echo ist dabei dominiert von Rotationsbewegungen mit Korrelationszeiten in der Größenordnung der Evolutionszeiten. Diffusionsmessungen mit gepulsten Feldgradienten zeigten ein starke Abhängigkeit von der Diffusionszeit. Dies wurde mit der eingeschränkten Diffusion entlang der kugelförmigen Lamellen erklärt. Ein theoretisches Modell für eine idealisierte MLV-Struktur wurde auf seine Fähigkeit hin getestet, den Echoabfall im Diffusionsexperiment erklären zu können. Die beobachteten Unterschiede zu den Messdaten wurden auf drei mögliche Faktoren zurückgeführt: erstens auf eine unvollständige Beschreibung der Linienform im stimulierten Echo, zweitens auf die Nichtberücksichtigung von Diffusion während der Dauer der Gradienten und drittens auf Diffusion durch die Schichten hindurch.
PDMS-Modellnetzwerke: Als Test für neuere Theorien zur inhomogenen Quellung von Netzwerken wurden PDMS-Modellnetzwerke mit gepulsten Feldgradienten im Hinblick auf anomale Diffusion untersucht. Zeitabhängige Diffusionsexperimente wurden an verschiedenen Proben durchgeführt. Es wurde kein Beweis für ein inhomogenes Quellen der Netzwerke gefunden. Weder in der Form des Echoabfalls, der gaussförmig ist, noch in der Zeitabhängigkeit des Diffusionskoeffzienten noch durch die Variation des Quellgrades zeigte sich ein Effekt, der auf gehinderte Diffusion hätte schließen lassen. Auch in einem gezielt inhomogen synthetisierten bimodalen Netzwerk, in dem Heterogenitäten zu erwarten waren, wurden diese nicht beobachtet."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Anomalous diffusion in anisotropic media","Anomale Diffusion in anisotropen Medien"]}]}],"canonical_facts":{"dc:contributor":["Schmidt, Claudia"],"dc:creator":["Kleinschmidt, Felix"],"dc:description.abstract":["The structure and dynamics of three 'soft-matter' systems was investigated by pulsed field gradient diffusion NMR and complementary deuterium line shape analysis. Restricted diffusion was studied in two lyotropic lamellar systems, the first consisting of crosslinked flat lamellae in anisotropic hydrogels and the second consisting of spherically bent lamellae in multilamellar vesicles. In the third system, a swollen PDMS network, obstructed diffusion was investigated in the fractal topology.
Anisotropic Hydrogels: The structure and ordering of macroscopically oriented anisotropic hydrogels was investigated on different length scales. Diffusion NMR proved the existence of defects in the lamellae on a mesoscopic scale and gave an estimate of the minimal extension of homogeneous domains. Temperature dependent obstruction factors for diffusion parallel to the layer normal showed an anomalous step at around 312 - 314 K. This was interpreted as the generation of further defects and microscopic cracks due to elastic forces from the network. The network tends to restore its original shape of a coil and becomes the dominating factor in the coupled system of mesophase and polymer network above this temperature range. The anisotropy of diffusion for D2O on the mesoscopic level was determined to be 10 : 1. For the diffusion of a dye the anisotropy decreased to 5.3 : 1 on the macroscopic level. The comparison of two hydrogels with different content of water showed higher order and fewer structural defects in the system with lower content of water.
Multilamellar Vesicles: The dynamics of D2O in the shear-induced multilamellar vesicle (MLV) phase was investigated using the system C10E3/D2O as an example. An empirical relationship between vesicle size and the D2O single pulse line shape was established. Deuterium line shapes of the solid and stimulated echo showed a splitting at long evolution delays, which was identified as the 90° singularity of the motionally averaged Pake spectrum of the normal, macroscopically disordered lamellar phase. The stimulated echo line shape is dominated by rotational motions with correlation times in the order of the evolution delays. Pulsed gradient diffusion measurements showed a strong dependence of the echo decay on the diffusion time. This was attributed to the restricted diffusion along the spherical lamellae in the MLVs. A theoretical model for diffusion in an idealized MLV structure was tested for its ability to describe the measured echo decay. The observed differences in comparison to the measured data were mainly attributed to three factors: first the incomplete description of the line shape in the stimulated echo, second the neglect of diffusion during the finite gradient duration and third the diffusion through the layers.
PDMS Model Networks: PDMS model networks were investigated by pulsed gradient diffusion NMR in order to detect anomalous diffusional behavior as a test for recently developed theories on inhomogeneous network swelling. Diffusion time dependent measurements were carried out on different samples. No evidence for inhomogeneous swelling of the networks was found. Neither the shape of the echo decay, which is Gaussian, nor diffusion time dependencies nor variation of the degree of swelling showed a significant effect from which obstructed diffusion could have been deduced. Even in a deliberately inhomogeneously synthesized bimodal networks, where heterogeneities were expected, no such evidence was found.","Die Struktur und Dynamik von drei 'soft matter'-Systemen wurde durch NMR-Diffusionsmessungen mit gepulsten Feldgradienten und Deuterium-Linienformanalyse untersucht. Die eingeschränkte Diffusion in lyotrop flüssigkristallinen Systemen wurde anhand von zwei Beispielen analysiert: zum einen an einem anisotropen Hydrogel mit makroskopisch einheitlich orientierten lamellaren Schichten, zum anderen an kugelförmigen Lamellen multilamellarer Vesikel. Am dritten System, einem gequollenen PDMS-Netzwerk, wurde gehinderte Diffusion in einer fraktalen Topologie betrachtet.
Anisotrope Hydrogele: Die Struktur und Ordnung von makroskopisch einheitlich orientierten Hydrogelen in lamellarer Phase wurde auf verschiedenen Längenskalen untersucht. NMR-Diffusionsmessungen zeigten auf mesoskopischer Skala Defekte in den Lamellen und ermöglichten eine Abschätzung der minimalen Ausdehnung einer homogenen Domäne. Temperaturabhängige Messungen des Obstruktionsfaktors der Diffusion zeigten eine anomale Stufe bei etwa 312 - 314 K für die Diffusion durch die Lamellen. Dies wurde durch die Entstehung weiterer Defekte und mikroskopischer Risse erklärt, die durch elastische Rückstellkräfte des Netzwerks hervorgerufen werden. Das Netzwerk neigt dazu, seine ursprüngliche Knäuelkonformation wieder herzustellen, und wird oberhalb dieses Temperaturbereichs zum dominierenden Faktor im gekoppelten System aus Mesophase und Netzwerk. Die Anisotropie der Diffusion von Wasser auf mesoskopischer Ebene wurde zu 10 : 1 bestimmt. Für die Diffusion eines Farbstoffes auf makroskopischer Längenskala nahm die Anisotropie auf 5.3 : 1 ab. Der Vergleich zweier Hydrogele, die mit unterschiedlichem Wassergehalt hergestellt wurden, zeigte geringere Defekte und höhere Ordnung für das Hydrogel mit geringerem Wassergehalt.
Multilamellare Vesikel: Die Dynamik von D2O in durch Scherung hergestellten multilamellaren Vesikeln (MLV) wurde am System C10E3/D2O untersucht. Eine empirische Beziehung zwischen der Vesikelgröße und der D2O-Linienform wurde aufgestellt. Die Deuterium-Linienformen im quadrupolaren und stimulierten Echo zeigten eine Aufspaltung bei langen Evolutionszeiten, die mit der 90°-Singularität des bewegungsgemittelten Pake-Spektrums der normalen, makroskopisch ungeordneten lamellaren Phase identifiziert wurde. Die Linienform im stimulierten Echo ist dabei dominiert von Rotationsbewegungen mit Korrelationszeiten in der Größenordnung der Evolutionszeiten. Diffusionsmessungen mit gepulsten Feldgradienten zeigten ein starke Abhängigkeit von der Diffusionszeit. Dies wurde mit der eingeschränkten Diffusion entlang der kugelförmigen Lamellen erklärt. Ein theoretisches Modell für eine idealisierte MLV-Struktur wurde auf seine Fähigkeit hin getestet, den Echoabfall im Diffusionsexperiment erklären zu können. Die beobachteten Unterschiede zu den Messdaten wurden auf drei mögliche Faktoren zurückgeführt: erstens auf eine unvollständige Beschreibung der Linienform im stimulierten Echo, zweitens auf die Nichtberücksichtigung von Diffusion während der Dauer der Gradienten und drittens auf Diffusion durch die Schichten hindurch.
PDMS-Modellnetzwerke: Als Test für neuere Theorien zur inhomogenen Quellung von Netzwerken wurden PDMS-Modellnetzwerke mit gepulsten Feldgradienten im Hinblick auf anomale Diffusion untersucht. Zeitabhängige Diffusionsexperimente wurden an verschiedenen Proben durchgeführt. Es wurde kein Beweis für ein inhomogenes Quellen der Netzwerke gefunden. Weder in der Form des Echoabfalls, der gaussförmig ist, noch in der Zeitabhängigkeit des Diffusionskoeffzienten noch durch die Variation des Quellgrades zeigte sich ein Effekt, der auf gehinderte Diffusion hätte schließen lassen. Auch in einem gezielt inhomogen synthetisierten bimodalen Netzwerk, in dem Heterogenitäten zu erwarten waren, wurden diese nicht beobachtet."],"dc:format.medium":["application/pdf"],"dc:subject":["multilamellare Vesikel","heterogenes PDMS Netzwerk","scherinduzierte Struktur","Scherung","Anomale Diffusion","multilamellar vesicle","hydrogel","heterogeneous network","pulsed field gradient","deuterium NMR"],"dc:title":["Anomalous diffusion in anisotropic media","Anomale Diffusion in anisotropen Medien"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:28Z"}