Shear moduli of two dimensional colloidal mixtures
| dc.contributor.author | Seyboldt, Rabea | |
| dc.date.accessioned | 2011-11-09T08:19:21Z | deu |
| dc.date.available | 2011-11-09T08:19:21Z | deu |
| dc.date.issued | 2011 | deu |
| dc.description.abstract | In this thesis a Mode Coupling Theory (MCT) equation is derived that calculates the shear modulus for multi-component colloidal mixtures in two-dimensional systems in linear approximation. With this equation, the plateau shear modulus G∞ is calculated for two two-dimensional systems at the glass transition: for a binary mixture of hard spheres and for a binary mixture of dipolar particles. The results for the shear modulus are compared with a three-dimensional system of hard spheres using data by Götze and Voigtmann. The plateau shear modulus has about the size G∞/(nkT) ≈ 20 and a variation of ±10 for all systems. Here n denotes the total number density. We find that for all systems (the dipolar, the two-dimensional and the three-dimensional hard sphere system) the critical surface (φc resp. Γc) and G∞ have maxima in the region of large differences in the size of the particles and large concentration of the smaller particles. We disagree with the common explanation of depletion attraction for this effect but show that the maxima in the plateau shear modulus are produced by the big particles and the force of the small ones on them. With exception of the region of these maxima, all systems show a lowering of G∞ through mixing. This can be compared to the effect of plasticizing for polymers. The glass transition surface shows that for all systems the liquid is stabilized, but for the hard sphere systems there exists a threshold for the size ratio of the particles. Above that the glass is stabilized. This threshold is lower for the two-dimensional system. For the dipolar system there exist experimental values for the system developed by König et al. A comparison shows a good agreement of the plateau shear modulus. The transition parameter Γc is overestimated by MCT by a factor two, as has been found for other systems. A perturbational method, where the shear moduli of the particles are calculated separately as would be done for a monodisperse system and then added up, shows good qualitative and mostly even quantitative agreements with the two-component calculation, although the maximum in the region of large differences in the size of the particles and large concentration of the smaller particles is overestimated. Overall MCT seems to yield good results for the systems studied here. Only close to the boundaries some small-scale crystallizing is visible in the particle plots of the dipolar system. | eng |
| dc.description.version | published | |
| dc.identifier.ppn | 352853549 | deu |
| dc.identifier.uri | http://kops.uni-konstanz.de/handle/123456789/14626 | |
| dc.language.iso | eng | deu |
| dc.legacy.dateIssued | 2011-11-09 | deu |
| dc.rights | terms-of-use | deu |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | deu |
| dc.subject | plateau shear modulus | deu |
| dc.subject | hard sphere | deu |
| dc.subject | dipolar particles | deu |
| dc.subject.ddc | 530 | deu |
| dc.subject.gnd | Modenkopplung | deu |
| dc.subject.gnd | Schubmodul | deu |
| dc.title | Shear moduli of two dimensional colloidal mixtures | eng |
| dc.type | BSC_THESIS | deu |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @mastersthesis{Seyboldt2011Shear-14626,
year={2011},
title={Shear moduli of two dimensional colloidal mixtures},
author={Seyboldt, Rabea}
} | |
| kops.citation.iso690 | SEYBOLDT, Rabea, 2011. Shear moduli of two dimensional colloidal mixtures [Bachelor thesis] | deu |
| kops.citation.iso690 | SEYBOLDT, Rabea, 2011. Shear moduli of two dimensional colloidal mixtures [Bachelor thesis] | eng |
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<dcterms:abstract xml:lang="eng">In this thesis a Mode Coupling Theory (MCT) equation is derived that calculates the shear<br />modulus for multi-component colloidal mixtures in two-dimensional systems in linear approximation.<br />With this equation, the plateau shear modulus G∞ is calculated for two two-dimensional<br />systems at the glass transition: for a binary mixture of hard spheres and for a binary mixture<br />of dipolar particles.<br /><br />The results for the shear modulus are compared with a three-dimensional system of hard<br />spheres using data by Götze and Voigtmann. The plateau shear modulus has about the size<br />G<sub>∞</sub>/(nkT) ≈ 20 and a variation of ±10 for all systems. Here n denotes the total number density.<br /><br />We find that for all systems (the dipolar, the two-dimensional and the three-dimensional<br />hard sphere system) the critical surface (φc resp. Γ<sub>c</sub>) and G<sub>∞</sub> have maxima in the region of<br />large differences in the size of the particles and large concentration of the smaller particles.<br /><br />We disagree with the common explanation of depletion attraction for this effect but show<br />that the maxima in the plateau shear modulus are produced by the big particles and the<br />force of the small ones on them.<br />With exception of the region of these maxima, all systems show a lowering of G∞ through<br />mixing. This can be compared to the effect of plasticizing for polymers.<br />The glass transition surface shows that for all systems the liquid is stabilized, but for the<br />hard sphere systems there exists a threshold for the size ratio of the particles. Above that<br />the glass is stabilized. This threshold is lower for the two-dimensional system.<br />For the dipolar system there exist experimental values for the system developed by König<br />et al. A comparison shows a good agreement of the plateau shear modulus. The transition<br />parameter Γc is overestimated by MCT by a factor two, as has been found for other systems.<br /><br />A perturbational method, where the shear moduli of the particles are calculated separately<br />as would be done for a monodisperse system and then added up, shows good qualitative<br />and mostly even quantitative agreements with the two-component calculation, although the<br />maximum in the region of large differences in the size of the particles and large concentration<br />of the smaller particles is overestimated.<br />Overall MCT seems to yield good results for the systems studied here. Only close to<br />the boundaries some small-scale crystallizing is visible in the particle plots of the dipolar<br />system.</dcterms:abstract>
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| kops.description.abstract | In dieser Arbeit wird mit Hilfe der Modenkopplungstheorie (MCT) eine Formel für das<br />Schermodul G(t) für binäre kolloidale Mischungen in zwei Dimensionen aus einer MCT-<br />Formel für drei Dimensionen abgeleitet.<br />Damit wird das Plateau-Schermodul G<sub>∞</sub> von binären Mischungen harter Kugeln und<br />dipolaren Punktteilchen für verschiedene Zusammensetzungen jeweils am Glasübergang be-<br />rechnet.<br /><br />Die Ergebnisse werden einem dreidimensionalen System harter Kugeln gegenübergestellt,<br />dafür werden Werte von Götze und Voigtmann herangezogen. Die Schermoduln<br />G<sub>∞</sub>/(nkT) der<br />drei Systeme haben etwa den selben Wert 20 mit Abweichungen von etwa ±10. Dabei ist n<br />die totale Anzahldichte.<br /><br />Ein Vergleich von zwei- und dreidimensionalem Hartkugel- und zweidimensionalem di-<br />polaren System zeigt, dass alle drei Systeme ihr Maximum des kritischen Parameters und<br />des Plateau-Schermoduls (abhängig vom Größenverhältnis δ und dem Anzahlverhältnis xs<br />der kleinen Teilchen relativ zu den großen) im Mischungsbereich vieler sehr kleiner Ku-<br />geln haben. Eine Analyse der Partikel-Koordinaten ergibt, dass dies zumindest für dipolare<br />Teilchen nicht durch eine Verarmungsattraktion zwischen den großen Kugeln entsteht. Aller-<br />dings scheint der Effekt durch ein Störungsfeld der kleinen Partikel auf die großen zustande<br />zu kommen.<br /><br />Mit Ausnahme dieser Maxima zeigen alle drei Systeme eine Verminderung des Plateau-<br />Schermoduls durch Mischen. Dies kann mit der Plastifizierung von Polymeren verglichen<br />werden.<br />Die Glasübergangsfläche des kritischen Parameters Γc bzw. φ<sub>c</sub> ergibt, dass in allen drei<br />Systemen der kritische Parameter durch Mischen erhöht, also die Flüssigkeit stabilisiert wird.<br />Für die Hartkugel-Systeme existiert ein Grenzwert für δ über dem das Glas stabilisiert wird.<br />Dieser Grenzwert ist niedriger für das zweidimensionale System.<br /><br />Für das dipolare System existiert eine experimentelle Realisierung von König et al. mit<br />dem die Ergebnisse verglichen werden können. Es ergibt sich eine gute Übereinstimmung<br />für das Plateau-Schermodul. Der kritische Parameter Γc zeigt eine von MCT-Rechnungen<br />bereits für andere Systeme bekannte Abweichung um den Faktor zwei.<br /><br />Eine Störungsrechnung, bei der das Schermodul als Summe der Schermoduln der einzelnen<br />Komponenten der Mischung berechnet wird, zeigt eine gute qualitative und teilweise sogar<br />quantitative Übereinstimmung mit der zwei-Komponenten Rechnung. Allerdings wird das<br />Maximum der Kurve in der Region mit vielen sehr kleinen Kugel überbewertet.<br />Insgesamt scheint die Modenkopplungstheorie bei den untersuchten Systemen in den be-<br />trachteten Bereichen gute Ergebnisse zu liefern. Nur bei sehr kleinen Mischungsverhältnissen<br />sieht man Abweichungen der Störungslösung von der anderen. Dies liegt vermutlich an be-<br />ginnender Kristallbildung. | deu |
| kops.description.openAccess | openaccessgreen | |
| kops.identifier.nbn | urn:nbn:de:bsz:352-146267 | deu |
| kops.submitter.email | rabea.seyboldt@uni-konstanz.de | deu |
| relation.isAuthorOfPublication | 3253dc97-d929-4915-8063-2c4389f6715e | |
| relation.isAuthorOfPublication.latestForDiscovery | 3253dc97-d929-4915-8063-2c4389f6715e |
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