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Three-dimensional magnetic fields: from coils to reconnection
This thesis is a work divided into two parts on aspects of three-dimensional (3D) magnetic fields: (I) magnetic reconnection treated from a strictly 3D viewpoint and (II) the design of coils for producing the 3D magnetic fields of optimized stellarators.
In astrophysical settings, magnetic fields are generically 3D. 3D divergence-free fields have rich topological structures such as magnetic nulls and chaotic field line structures. Standard reconnection literature identifies magnetic nulls as locations of magnetic reconnection, and that intense currents will build up around them. This idea is explored with a key realization that by placing a vanishingly small sphere around the null, boundary conditions on field lines passing through the sphere may be sorted out. The main result here is (1) the dismissal of the notion that nulls are crucial places for magnetic reconnection and current accumulation, instead identifying separatrices of topological type on the boundaries of null-passing field lines to be crucial. Standard reconnection literature dismisses chaotic flows yet 3D fields generically have chaotic flows. An inherent property of chaotic flows is exponentiation. The main result here is (2) the identification of exponentiation as a natural mechanism for magnetic reconnection and that the associated current builds up linearly in time in contradiction to standard results requiring the formation of high-density current sheets.
The magnetic fields of optimized stellarators are intricate, producing complex 3D magnetic surfaces. These fields are conventionally generated by non-planar electromagnetic coils, though these coils are costly to manufacture, slow device assembly, and hinder stellarator maintenance. Part II of this thesis explores methods of stellarator coil simplification that do not involve modular coils. All of this work uses current potentials, which are stream functions of the current sheets that produce magnetic surfaces. We begin with a result found using analytic methods on current potentials that (1) there may be an inherent limitation in the ability of modular coils to produce fields at a distance. This result is not surprising, though further analysis is necessary to work out some complexities of the result.
Next, (2) a novel method to produce localized patches of current potential, representative of patches of current sheets, is developed and used to identify crucial locations of current placement for shaping magnetic surfaces. Most notably, these current sheet patches are able to produce much of the surface shaping while occupying a small fraction of the winding surface, resulting in good open-access stellarator coil configurations. Continuing the trend away from modular coils, (3) helical coils are optimized to support stellarator magnetic fields.
This work agrees with related work on the optimization of helical coils, finding them unsuitable to the precise production of equilibria generated by modular coils. To improve this result, we use coil sets of mixed-type: helical coils with windowpane coils or permanent magnets, to mitigate field error left behind by the helical coils. Finally, (4) the development of a generalized method to cut modular, helical, and windowpane coils out of current potentials and to identify the associated coil currents is developed and used in coil optimization
Routing schemes for hybrid communication networks
We consider the problem of computing routing schemes in the HYBRID model of distributed computing where nodes have access to two fundamentally different communication modes. In this problem nodes have to compute small labels and routing tables that allow for efficient routing of messages in the local network, which typically offers the majority of the throughput. Recent work has shown that using the HYBRID model admits a significant speed-up compared to what would be possible if either communication mode were used in isolation. Nonetheless, if general graphs are used as the input graph the computation of routing schemes still takes polynomial rounds in the HYBRID model. We bypass this lower bound by restricting the local graph to unit-disc-graphs and solve the problem deterministically with running time O(|H|2+logâĄn), label size O(logâĄn), and size of routing tables O(|H|2â
logâĄn) where |H| is the number of âradio holesâ in the network. Our work builds on recent work by Coy et al., who obtain this result in the much simpler setting where the input graph has no radio holes. We develop new techniques to achieve this, including a decomposition of the local graph into path-convex regions, where each region contains a shortest path for any pair of nodes in it
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Inoculation strategies for bounded degree graphs
We analyze a game-theoretic abstraction of epidemic containment played on an
undirected graph : each player is associated with a node in and can
either acquire protection from a contagious process or risk infection. After
decisions are made, an infection starts at a random node and propagates
through all unprotected nodes reachable from . It is known that the price of
anarchy (PoA) in -node graphs can be as large as . Our main
result is a tight bound of order on the PoA, where is
the maximum degree of the graph. We also study additional factors that can
reduce the PoA, such as higher thresholds for contagion and varying the costs
of becoming infected vs. acquiring protection
Synthesis and Characterization of Nanoporous Resin Particles for Water Purification
Through progressive industrialization and the relentless consumption of natural raw materials, man is exerting a negative influence on his habitat. In particular, water as the basis of life and almost all processes of our economy is contaminated by various pollutants due to excessive use and insufficient purification. Here, oxyanions, heavy metal ions and organic pollutants pose a high risk to aquatic habitats and ultimately to humans. Due to insufficient removal, they also contribute to the loss of non-renewable raw materials for industrial cycles. Due to a mostly low effect concentration and potential interactions with diverse living organisms, the removal of many contaminants is extremely important to avoid further altering existing ecosystems.
Adsorption represents an energy-efficient method of removal using adsorbents suitable for this purpose. Highly cross-linked resin polymers such as poly(melamine-co-formaldehyde) (PMF) with its excellent chemical resistance, high number of functional groups and ease of preparation, represent promising starting points for adsorbents.
This dissertation describes the colloidal aqueous synthesis of nanoporous resin particles (e.g. PMF) by templating with SiO2 nanoparticles (SiO2 NPs), which are subsequently used to adsorb water pollutants. An overall goal of this work consists of elucidating the mechanism for particle and pore formation by systematically varying various synthesis parameters. Electron microscopy, N2-soprtion and particle size measurement are used to analyze the morphology, size and pore structure of the particles. Comprehensive investigations thus allow to determine the influence of each tested synthesis parameter on these properties.
A very important goal, especially for future large-scale applicability, is the colloidal production of uniform particles, which have both a high ordered porosity and particle diameters in the range of a few micrometers. This enables an application as a fixed-bed adsorber that can be flowed through. This goal is closely linked to the mechanistic elucidation of pore and particle formation in the synthesis.
The prepared nanoporous PMF particles were tested for various adsorption applications after their characterization. In order to obtain a comprehensive picture of the applicability of PMF particles, experiments with oxyanions, with pharmaceuticals as representatives of organic pollutants and with heavy metal ions will be carried out respectively. On the one hand, these experiments will focus on investigating the adsorption performance and mechanism of PMF with the respective pollutant. On the other hand, the influence of the changed porosity on the adsorption mechanism is investigated by using different particles of a varied synthesis parameter.
Sulfate and phosphate ions were investigated in the oxyanion class. Extremely high separation rates were demonstrated for both ions, significantly outperforming previous commercially available materials. In experiments concerning a potential selective adsorption and thus separation of both species, the PMF/SiO2 hybrid particles, in which the template had not yet been removed, showed a selective sulfate adsorption.
The immobilization of heavy metal ions was analyzed with special focus on the simultaneous separation of the Cu2+ ions and respective anions used here. Investigations of the adsorbent after the adsorption experiments by means of electron microscopy, X-ray scattering and electron spin resonance spectroscopy elucidated the adsorption mechanism, which had been insufficiently analyzed so far. Here, adsorption and surface-induced precipitation were identified as partially separate subprocesses, both of which are responsible for the separation of both metal and anions from solution. In adsorption experiments with the monovalent ions nitrate and chloride, a two-step uptake process was identified, which was mathematically described for the first time via a new adsorption isotherm.
In the scope of organic water pollutants, the separation of the pharmaceutical diclofenac is being tested. In particular, the adsorption of pharmaceuticals is an urgent issue due to their low effect concentration and ubiquity in surface and tap waters. Pharmaceutical separation using PMF has hardly been investigated worldwide despite its promising properties. In these experiments, particles templated with SiO2 NPs of different sizes and stabilized in different ways were tested. This resulted in pore systems that varied from each other especially in their accessibility of the pore system and in the diameter of the connecting channels between the main cavities. These characteristics significantly affected the adsorption capacity and separation rates in low concentration range.
A final goal is to synthesize a resin network that uses an equally highly functional triazine-based monomer instead of melamine. The monomer 2,4,6-tris(2,4,6-trihydroxyphenyl)-1,3,5-triazine (3PT) possesses nine hydroxyl groups each, whereby a polymer based on it should exhibit strongly modified adsorption properties compared to PMF. This monomer was used in an aqueous polymerization analogous to PMF to produce a previously unknown polymer network, which was designated P(3PT-F). Here, templating was omitted because the newly prepared material already exhibited intrinsic nanoporosity due to the size of the 3PT monomer. In subsequent adsorption experiments, very high separation rates were demonstrated for the toxic metal ions Pb2+, Cd2+ and Ni2+. In realistic initial concentrations, the contamination was reduced to drinking water quality in each case. P(3PT-F) also showed highly selective removal of Pb2+ over the common ions Ca2+, Mg2+, K+ and Fe2+. As fundamental evidence, reusability was also demonstrated by complete desorption with dilute HCl and subsequent re-adsorption without significant reduction in capacity.
Overall, starting from the fundamental study of PMF particle synthesis, a more general understanding of aqueous dispersion polymerization of hydrophobic resins was first derived and templating with hydrophilic SiO2 NPs was implemented. With the help of understanding the particle growth processes and interactions responsible for templating, the properties of the resulting particles could be controlled. Subsequently, the influence of the changed porosity in particular on the separation performance could be investigated in the adsorption studies. In addition, it was possible to analyze which interactions PMF enters into with the respective pollutant types. By replacing the monomer melamine with a hydroxyl-containing monomer, a novel resin polymer could be produced. With its altered porosity and reactivity, this can now serve as a new starting point for adsorption experiments with strongly altered adsorption performance, e.g. towards heavy metal ions.:Abstract 1
Kurzfassung 5
List of Publications 9
First-Author Publications 9
Co-Author Publications 10
Patent 12
Conference Proceedings 12
Oral Presentations 12
Poster 12
List of Figures 13
Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal: 14
Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal: 15
Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles: 16
SiO2 Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles: 18
Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions: 19
List of Tables 21
Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal: 21
Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal: 21
Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles: 22
SiO2 Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles: 22
Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions: 23
Abbreviations 25
Symbols 26
1. Introduction 1
2. Objectives and Experimental Design 5
3. Scientific Background 11
3.1. Poly(melamine-co-formaldehyde) 11
3.1.1. Polymerization Mechanism 11
3.1.2. Synthesis Strategies for the Preparation of Porous PMF Particles. 13
3.1.3. Fields of Application of PMF 13
3.2. Adsorption 15
3.2.1. Adsorption Isotherms and Mathematical Modeling 16
3.3. Surface Precipitation 20
4. Fundamentals of Instrumental Analytics 23
4.1. Gas Sorption Measurements 23
4.1.1. Determination of Pore Sizes 26
4.1.2. Determination of Specific Surface Area 27
4.2. Transmission Electron Microscopy 29
4.3. Inductively Coupled Plasma Optical Emission Spectroscopy 31
Results and Discussion 33
Chapter Overview 33
5. Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal 37
Graphical Abstract 37
Abstract 37
1. Introduction 38
2. Results and Discussion 39
2.1. Synthesis and Characterization of the PMF Particles 40
2.2. Sorption Experiments 47
3. Materials and Methods 54
3.1. Materials 54
3.2. Methods 54
3.3. Synthesis of the PMF Particles 56
3.4. Water Treatment Experiments 57
4. Conclusions 59
6. Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal 65
Graphical Abstract 65
Abstract 65
1. Introduction 66
2. Materials 68
3. Methods 68
3.1. Synthesis of the PMF particles 70
3.2. Water treatment experiments with diclofenac solution 72
3.3. Theoretical model 72
3. Results and Discussion 73
3.1. Synthesis and characterization of the PMF particles 74
3.2. Adsorption of Pharmaceutics 80
4. Conclusion 84
7. Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles 89
Graphical Abstract 89
Abstract 89
1. Introduction 90
2. Materials and methods 91
2.1. Materials 91
2.2. Synthesis of the Poly(melamine-co-formaldehyde) particles 92
2.3. Methods 93
2.4. Water treatment experiments 96
3. Results and discussion 97
3.1. Synthesis and characterization of the PMF particles 98
3.2. Cu2+ uptake experiments 102
3.3. Mechanism for Cu2+ and Anion Removal 115
3.4. Investigation of other heavy metal salts 116
4. Conclusions 117
8. SiOâ Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles 121
Graphical Abstract 121
Abstract 121
1. Introduction 122
2. Materials and methods 123
2.1. Materials 123
2.2. Methods 124
2.3. Synthesis of the PMF particles 125
2.4. Water treatment experiments 128
2.5. Theoretical model 129
3. Results and Discussion 132
3.1. PMF-Std 133
3.2. Influence of the reaction mixture composition 136
3.3. Variation of the process parameters 140
3.4. Conclusion on the templating mechanism for PMF-Std 146
3.5. Acquiring ”m-sized porous PMF particles for adsorption application 149
3.6. Adsorption experiments with K2Cr2O7 solution 151
4. Conclusion 155
9. Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions 161
Graphical Abstract 161
Abstract 161
1. Introduction 162
2. Materials and methods 163
2.1. Materials 163
2.2. Synthesis 164
2.3. Characterization 166
2.4. Batch adsorption experiments 169
2.5. Calculation and theoretical models 170
3. Results and discussion 172
3.1. Synthesis and characterization of the polymer particles 172
3.2. Adsorption experiments with Ni2+, Cd2+, and Pb2+ onto P(3PT-F)-3L 178
4. Conclusions 184
10. Conclusion and Outlook 191
Contribution to Publications 197
Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal 197
Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal 198
Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles 199
SiOâ Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles 200
Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions 201
Danksagung 203
Appendix 205
References 207
Eidesstattliche Versicherung 217Durch fortschreitende Industrialisierung und den schonungslosen Verbrauch natĂŒrlicher Rohstoffe ĂŒbt der Mensch negativen Einfluss auf seinen Lebensraum aus. Insbesondere Wasser als Grundlage des Lebens und fast aller Prozesse unserer Wirtschaft wird durch eine ĂŒbermĂ€Ăige Nutzung und unzureichende Reinigung mit diversen Schadstoffen kontaminiert. Hierbei stellen Oxyanionen, Schwermetallionen und organische Schadstoffe ein hohes Risiko fĂŒr aquatische LebensrĂ€ume und letztendlich auch den Menschen dar. Durch unzureichende Entfernung tragen sie auĂerdem zum Verlust nicht-erneuerbarer Rohstoffe fĂŒr industrielle KreislĂ€ufe bei. Durch eine meist geringe Effektkonzentration und potentielle Wechselwirkungen mit diversen Lebewesen ist die Entfernung vieler Verunreinigungen extrem wichtig, um bestehende Ăkosysteme nicht weiter zu verĂ€ndern.
Adsorption stellt eine energieeffiziente Methode zur Entfernung dieser Schadstoffe durch hierfĂŒr geeignete Adsorbentien dar. Hochgradig vernetzte Harzpolymere wie Poly(melamin-co-formaldehyd) (PMF) stellen mit ihrer sehr hohen chemischen BestĂ€ndigkeit, einer hohen Zahl funktioneller Gruppen und einfachen Herstellbarkeit einen vielversprechenden Ausgangspunkt fĂŒr Adsorbentien dar.
Diese Dissertation beschreibt die kolloidale, wĂ€ssrige Synthese nanoporöser Harzpartikel (z. B. PMF) durch eine Templatierung mit SiO2 Nanopartikeln (SiO2 NPs), welche anschlieĂend zur Adsorption von Wasserschadstoffen eingesetzt werden. Ein ĂŒbergeordnetes Ziel dieser Arbeit besteht aus der AufklĂ€rung des Mechanismus zur Partikel- und Porenbildung durch systematische Variation verschiedener Syntheseparameter. Mittels Elektronenmikroskopie, N2-Sorption und PartikelgröĂenmessung wird die Morphologie, GröĂe und Porenstruktur der Partikel analysiert. Umfassende Untersuchungen ermöglichen somit, den Einfluss der einzelnen getesteten Syntheseparameter auf diese Eigenschaften zu bestimmen.
Ein sehr wichtiges Ziel, besonders fĂŒr eine zukĂŒnftige groĂtechnische Anwendbarkeit, ist dabei die kolloidale Herstellung uniformer Partikel, welche sowohl eine hohe geordnete PorositĂ€t als auch Partikeldurchmesser im Bereich einiger Mikrometer aufweisen. Dies ermöglicht einen Einsatz als durchströmbaren Festbett-Adsorber. Dieses Ziel ist eng mit der mechanistischen AufklĂ€rung der Poren- und Partikelbildung in der Synthese verknĂŒpft.
Die hergestellten nanoporösen PMF-Partikel wurden nach ihrer Charakterisierung fĂŒr verschiedene Adsorptionsanwendungen getestet. Um ein umfassendes Bild ĂŒber die Einsetzbarkeit von PMF-Partikeln zu erhalten, sollen jeweils Versuche mit Oxyanionen, mit Schwermetallionen und mit Pharmazeutika als Vertreter organischer Schadstoffe durchgefĂŒhrt werden. Bei diesen Versuchen steht zum einen die Untersuchung der Adsorptionsleistung und des Adsorptionsmechanismus des jeweiligen Schadstoffes an PMF im Vordergrund. Zum anderen wird durch die Verwendung verschiedener Partikel, bei welchen ein einzelner Syntheseparameter variiert wurde, der Einfluss der verĂ€nderten PorositĂ€t auf den Adsorptionsmechanismus untersucht.
Sulfat- und Phosphationen wurden in der Klasse der Oxyanionen untersucht. FĂŒr beide Ionen wurden extrem hohe Abtrennraten nachgewiesen, welche bisherige kommerziell erhĂ€ltliche Materialien signifikant ĂŒbertraf. In Versuchen hinsichtlich einer potentiellen selektiven Adsorption und somit Trennung beider Spezies, zeigten die PMF/SiO2-Hybridpartikel, bei welchen das Templat noch nicht entfernt wurde, eine selektive Sulfatadsorption.
Die Immobilisierung von Schwermetallionen wurde mit besonderem Fokus auf die gleichzeitig auftretende Abtrennung der dafĂŒr verwendeten Cu2+-Ionen und jeweiliger Anionen analysiert. Durch Untersuchungen des Adsorbens nach den Adsorptionsversuchen mittels Elektronenmikroskopie, Röntgenstreuung und Elektronenspinresonanz-Spektroskopie wurde der bisher unzureichend analysierte Adsorptionsmechanismus aufgeklĂ€rt. Hierbei wurden Adsorption und oberflĂ€cheninduzierte FĂ€llung als separate Teilprozesse identifiziert, welche beide jeweils fĂŒr die Abscheidung von sowohl Metall- als auch Anionen aus der Lösung verantwortlich sind. Bei Adsorptionsversuchen mit den einwertigen Ionen Nitrat und Chlorid wurde ein zweistufiger Prozess identifiziert, welcher erstmals ĂŒber eine neue Adsorptionsisotherme mathematisch beschrieben wurde.
Im Bereich organischer Wasserschadstoffe wird die Abtrennung des Pharmazeutikums Diclofenac getestet. Insbesondere die Adsorption von Pharmazeutika stellt aufgrund von deren geringen Effektkonzentration und AllgegenwĂ€rtigkeit in OberflĂ€chen- und LeitungswĂ€ssern ein dringliches Thema dar. Die Pharmazeutika-Abtrennung mittels PMF wurde trotz seiner vielversprechenden Eigenschaften weltweit bisher kaum untersucht. Im Rahmen dieser Versuche wurden Partikel getestet, welche mit unterschiedlich groĂen und unterschiedlich stabilisierten SiO2 NPs templatiert wurden. Dadurch entstanden Porensysteme, die besonders in derer ZugĂ€nglichkeit ihres Porensystems und in dem Durchmesser der VerbindungskanĂ€le zwischen den HauptkavitĂ€ten voneinander variierten. Diese Eigenschaften wirkten sich signifikant auf die AdsorptionskapazitĂ€t und die Abtrennraten im niedrigen Konzentrationsbereich aus.
Ein abschlieĂendes Ziel ist die Synthese eines Harznetzwerkes, welches statt Melamin auf einem ebenso hochfunktionellen, triazinbasierten Monomer basiert. Das Monomer 2,4,6-Tris(2,4,6-trihydroxyphenyl)-1,3,5-triazin (3PT) besitzt jeweils neun Hydroxylgruppen, wodurch ein darauf basierendes Polymer stark verĂ€nderte Adsorptionseigenschaften gegenĂŒber PMF aufweisen soll. Mit diesem Monomer wurde in einer analog zu PMF durchgefĂŒhrten wĂ€ssrigen Polymerisation ein bisher unbekanntes Polymernetzwerk hergestellt, welches als P(3PT-F) bezeichnet wurde. Hierbei wurde auf Templatierung verzichtet, da das neu hergestellte Material bereits intrinsische NanoporositĂ€t durch die GröĂe des verwendeten 3PT-Monomers aufwies. In anschlieĂenden Adsorptionsversuchen wurden sehr hohe Abtrennraten fĂŒr die toxischen Metallion Pb2+, Cd2+ und Ni2+ nachgewiesen. In realistischen Ausgangskonzentrationen wurde die Kontamination mit diesen Ionen jeweils auf TrinkwasserqualitĂ€t reduziert. P(3PT-F) zeigte auĂerdem eine sehr selektive Abtrennung von Pb2+ gegenĂŒber den hĂ€ufig vorkommenden Ionen Ca2+, Mg2+, K+ und Fe2+. Als grundlegender Beweis konnte eine Wiederverwendbarkeit durch die vollstĂ€ndige Desorption mit verdĂŒnnter HCl gezeigt werden und eine anschlieĂende erneute Adsorption ohne signifikante Verringerung der KapazitĂ€t.
Insgesamt wurde ausgehend von der grundlegenden Untersuchung der PMF-Partikelsynthese erst ein generelleres VerstĂ€ndnis der wĂ€ssrigen Dispersionspolymerisation hydrophober Harze abgeleitet und die Templatierung mit hydrophilen SiO2 NPs implementiert. Mithilfe des VerstĂ€ndnisses der Partikelwachstumsprozesse und der Wechselwirkungen, welche fĂŒr die Templatierung verantwortlich sind, konnten die Eigenschaften der entstehenden Partikel gesteuert werden. Im Rahmen der Adsorptionsuntersuchungen konnte anschlieĂend der Einfluss insbesondere der verĂ€nderten PorositĂ€t auf die Abtrennleistung untersucht werden. AuĂerdem konnte analysiert werden, welche Wechselwirkungen PMF mit den jeweiligen Schadstoffarten eingeht. Durch den Austausch des Monomers Melamin gegen das hydroxylhaltiges Monomer 3PT konnte ein neuartiges Harzpolymer hergestellt werden. Dieses kann mit seiner verĂ€nderten PorositĂ€t und ReaktivitĂ€t nun als neuer Ausgangspunkt fĂŒr Adsorptionsexperimente mit stark verĂ€nderter Adsorptionsleistung z. B. gegenĂŒber Schwermetallionen dienen.:Abstract 1
Kurzfassung 5
List of Publications 9
First-Author Publications 9
Co-Author Publications 10
Patent 12
Conference Proceedings 12
Oral Presentations 12
Poster 12
List of Figures 13
Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal: 14
Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal: 15
Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles: 16
SiO2 Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles: 18
Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions: 19
List of Tables 21
Mesoporous Poly(Melamine-co-Formaldehyde) Particles for Efficient and Selective Phosphate and Sulfate Removal: 21
Tuning the Pore Structure of Templated Mesoporous Poly(melamine-co-formaldehyde) Particles toward Diclofenac Removal: 21
Adsorption vs. Surface Precipitation of CuÂČ+ onto Porous Poly(melamine-co-formaldehyde) Particles: 22
SiO2 Nanospheres as Surfactant and Template in Aqueous Dispersion Polymerizations Yielding Nanoporous Resin Particles: 22
Waterborne Phenolic, Triazine-Based Porous Polymer Particles for the Removal of Nickel, Cadmium, and Lead Ions: 23
Abbreviations 25
Symbols 26
1. Introduction 1
2. Objectives and Experimental Design 5
3. Scientific Background 11
3.1. Poly(melamine-co-formaldehyde) 11
3.1.1. Polymerization Mechanism 11
3.1.2. Synthesis Strategies for the Preparation of Porous PMF Particles. 13
3.1.3. Fields of Application of PMF 13
3.2. Adsorption 15
3.2.1. Adsorption Isotherms and Mathematical Modeling 16
3.3. Surface Precipitation 20
4. Fundamentals of Instrumental Analytics 23
4.1. Gas Sorption Measurements 23
4.1.1. Determination of
The Complexity of Recognizing Geometric Hypergraphs
As set systems, hypergraphs are omnipresent and have various representations
ranging from Euler and Venn diagrams to contact representations. In a geometric
representation of a hypergraph , each vertex is associated
with a point and each hyperedge is associated
with a connected set such that for all . We say that a given
hypergraph is representable by some (infinite) family of sets in
, if there exist and such
that is a geometric representation of . For a family F, we define
RECOGNITION(F) as the problem to determine if a given hypergraph is
representable by F. It is known that the RECOGNITION problem is
-hard for halfspaces in . We study the
families of translates of balls and ellipsoids in , as well as of
other convex sets, and show that their RECOGNITION problems are also
-complete. This means that these recognition problems are
equivalent to deciding whether a multivariate system of polynomial equations
with integer coefficients has a real solution.Comment: Appears in the Proceedings of the 31st International Symposium on
Graph Drawing and Network Visualization (GD 2023) 17 pages, 11 figure
A critical review on latest innovations and future challenges of electrochemical technology for the abatement of organics in water
Updated water directives and ambitious targets like the United Nationsâ Sustainable Development Goals (SDGs) have emerged in the last decade to tackle water scarcity and contamination. Although numerous strategies have been developed to remove water pollutants, it is still necessary to enhance their effectiveness against toxic and biorefractory organic molecules. Comprehensive reviews have highlighted the appealing features of the electrochemical technologies, but much progress has been made in recent years. In this timely review, a critical discussion on latest innovations and perspectives of the most promising electrochemical tools for wastewater treatment is presented. The work describes the performance of electrocatalytic anodes for direct electrochemical oxidation, the oxidation mediated by electrogenerated active chlorine, the electrocatalytic reduction as well as coupled approaches for synchronous anodic and cathodic processes combined with homogeneous and heterogeneous catalysis. The last section is devoted to the assessment of scale-up issues and the increase in the technology readiness level
Fundamental mechanics : newtonian mechanics for engineering
TraducciĂł de: MecĂ nica fonamental : mecĂ nica newtoniana per a l'enginyeriaDescripciĂł del recurs: 31 gener 2023This book is addressed at a first course in engineering mechanics. Newtonian mechanics is studied, a non-relativistic classical mechanics and, therefore, applied to objects that are neither extremely small nor excessively fast. The newtonian mechanics affects a good part of the world around us. It is the mechanics of the everyday world. The book includes the basic concepts of mechanics with theoretical demonstrations. You will also find issues and problems, some resolved. The text includes graphs, figures, and diagrams for facilitate understanding. Mainly the foundations of mechanics are studied, but you will also find an introduction to wave phenomena and a small foray into analytical mechanics.First editio
Studies and Cooling of Highly Charged Ion Ensembles in the ARTEMIS Trap and High-Precision Mass Measurements of 221Fr, 219Rn, 213Bi, 211Pb, 209Pb, 207Tl and 207Pb at SHIPTRAP
Penning traps open up unique experimental possibilities for mass spectrometry and spectroscopy of atomic ions with high precision. Two such experiments based on Penning traps are SHIPTRAP and ARTEMIS at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt.
The ARTEMIS experiment is designed to measure the magnetic moment (g-factor) of an electron in heavy, highly charged ions at the 10â9 level, by the means of laser-microwave double-resonance spectroscopy. Such measurements represent highly stringent tests of QED in extreme fields. The ion of choice for the demonstration and development of the experimental methods is 40Ar13+, which can be produced internally in the trap, for later measurements 209Bi82+ is foreseen. For each of the measurements, the preparation of a cleaned and cooled cloud of ions in the spectroscopy trap
is necessary. In this work, the system is optimised for non-destructive detection and cooling of the ions, and production, transport, cooling, selection and storage of the
Ar13+ ions are systematically demonstrated.
Precision mass measurements of the long-lived decay products of 225Ac and 223Ra are carried out at SHIPTRAP, using the phase-imaging ion-cyclotron-resonance technique. The masses of 221Fr, 219Rn, 213Bi, 211Pb, 209Pb, 207Tl and 207Pb are measured with a relative precision of 10â9, allowing an increase in the accuracy of other masses in this region. Some of these masses find direct input into the g-factor measurements, such as in the case of 209Bi, which is of interest to ARTEMIS. Furthermore, the doublet 205Tl / 205Pb, which is of great significance in nuclear astrophysics, is also linked to the measured masses
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