Topology of Polymers (eBook)

Kai Ishihara, Koya Shimokawa, Yasuyuki Tezuka (Autoren)

eBook Download: PDF

2019 | 1st ed. 2019
VIII, 81 Seiten
Springer Japan (Verlag)
978-4-431-56888-9 (ISBN)

Infos

Plastics, films, and synthetic fibers are among typical examples of polymer materials fabricated industrially in massive quantities as the basis of modern social life. By comparison, polymers from biological resources, including proteins, DNAs, and cotton fibers, are essential in various processes in living systems. Such polymers are molecular substances, constituted by the linking of hundreds to tens of thousands of small chemical unit (monomer) components. Thus, the form of polymer molecules is frequently expressed by line geometries, and their linear and non-linear forms are believed to constitute the fundamental basis for their properties and functions. In the field of polymer chemistry and polymer materials science, the choice of macromolecules has continuously been extended from linear or randomly branched forms toward a variety of precisely controlled topologies by the introduction of intriguing synthetic techniques. Moreover, during the first decade of this century, a number of impressive breakthroughs have been achieved to produce an important class of polymers having a variety of cyclic and multicyclic topologies. 

These developments now offer unique opportunities in polymer materials design to create unique properties and functions based on the form, i.e., topology, of polymer molecules. The introduction and application of topological geometry (soft geometry) to polymer molecules is a crucial requirement to account for the basic geometrical properties of polymer chains uniquely flexible in nature, in contrast to small chemical compounds conceived upon Euclidian geometry (hard geometry) principles. Topological geometry and graph theory are introduced for the systematic classification and notation of the non-linear constructions of polymer molecules, including not only branched but also single cyclic and multicyclic polymer topologies. On that basis, the geometrical-topological relationship between different polymers having distinctive constructions is discussed. A unique conception of topological isomerism is thus formed, which contrasts with that of conventional constitutional and stereoisomerism occurring in small chemical compounds. 

Through the close collaboration of topology experts Shimokawa and Ishihara and the polymer chemist Tezuka, this monograph covers the fundamentals and selected current topics of topology applied in polymers and topological polymer chemistry. In particular, the aim is to provide novel insights jointly revealed through a unique interaction between mathematics (topology) and polymer materials science.

Inhalt

Preface 6
Contents 7
Chapter 1 Topology meets polymers: Introduction 9
1.1 Polymer constructions by topology insights 9
1.2 From topological analyses to constructing graph-structure polymers 11
References 12
Chapter 2 Graph theory analyses of polymers 14
2.1 Graphs 14
2.1.1 Definition of graphs 14
2.1.2 Graphs associated with molecules and polymers 16
2.1.3 Adjacency matrix 17
2.1.4 Complete graphs Kn and complete bipartite graphs Kn1,n2 18
2.2 Systematic notation of polymers 19
2.3 Enumeration of graphs associated with multicyclic polymers 20
2.4 Construction of graphs by folding 27
2.4.1 Eulerian and semi-Eulerian graphs 27
2.4.2 Construction of multicyclic polymers by folding linear polymers 27
References 30
Chapter 3 Classification of polymer topologies based on alkane molecular graphs 33
3.1 Polymer graph constructions and alkane molecular graphs 33
3.2 A nomenclature for alkane molecular graphs 34
3.3 Classification of branched polymer topologies 34
3.4 Classification of monocyclic polymer topologies 35
3.5 Classification of multicyclic polymer topologies 37
3.5.1 Dicyclic polymer topologies 37
3.5.2 Tricyclic polymer topologies 39
3.5.3 Tetra- and pentacyclic polymer topologies 40
3.6 Comparison of nomenclatures 41
References 41
Chapter 4 Types of graphs 43
4.1 Operations and decomposition of graphs 43
4.1.1 Operations of graphs 43
4.1.2 Blocks and types 46
4.2 Graph theory characterization of graph types 50
4.3 Types of graphs and adjacency matrix 52
References 55
Chapter 5 Knot theory analysis of polymers 56
5.1 Knots, links, and spatial graphs 56
5.1.1 Knots and links 56
5.1.2 Spatial graphs 58
5.2 Non-planarity 60
5.3 Chirality 60
References 62
Chapter 6 Topological operations and chemical isomerism of polymers 64
6.1 Constitutional, stereo, and topological isomerism in graph-structure polymers 64
6.2 Topological analysis of isomerism in monocyclic polymers 68
6.3 Topological analysis of isomerism in dicyclic polymers 70
6.4 Topological operation vs. chemical transformation of polymer molecules 72
References 74
Chapter 7 Topological polymer chemistry and graph-structure construction 76
7.1 A ring family tree 76
7.2 Synthesizing multicyclic polymers with spiro- and bridged- topologies 78
7.3 Synthesizing multicyclic polymers with fused- and hybrid-topologies 79
7.4 Constructing a macromolecular K3,3 graph topology 80
References 84
Chapter 8 Topology meets polymers: Conclusion and perspectives 85

Produkt-Details

• Erscheint lt. Verlag: 6.12.2019
• Reihe/Serie: SpringerBriefs in the Mathematics of Materials
• Reihe/Serie: SpringerBriefs in the Mathematics of Materials
• Zusatzinfo: VIII, 81 p.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Naturwissenschaften ► Chemie ► Organische Chemie
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Wirtschaft
• Schlagworte: graph theory • knot theory • Polymer (materials) science and engineering • Topological polymer chemistry • Topology (topological geometry)
• ISBN-10: 4-431-56888-3 / 4431568883
• ISBN-13: 978-4-431-56888-9 / 9784431568889