Hyde / Blum / Landh The Language of Shape

The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology
1. Auflage 1996
ISBN: 978-0-08-054254-6
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 383 Seiten

This book develops the thesis that structure and function in a variety of condensed systems - from the atomic assemblies in inorganic frameworks and organic molecules, through molecular self-assemblies to proteins - can be unified when curvature and surface geometry are taken together with molecular shape and forces. An astonishing variety of synthetic and biological assemblies can be accurately modelled and understood in terms of hyperbolic surfaces, whose richness and beauty are only now being revealed by applied mathematicians, physicists, chemists and crystallographers. These surfaces, often close to periodic minimal surfaces, weave and twist through space, carving out interconnected labyrinths whose range of topologies and symmetries challenge the imaginative powers.The book offers an overview of these structures and structural transformations, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and pollution control to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases formed by surfactants, detergents and lipids, synthetic block copolymer and protein networks, as well as biological cell assemblies, from muscles to membranes in prokaryotic and eukaryotic cells. The relation between structure and function is analysed in terms of the previously neglected hidden variables of curvature and topology. Thus, the catalytic activity of zeolites and enzymes, the superior material properties of interpenetrating networks in microstructured polymer composites, the transport requirements in cells, the transmission of nerve signals and the folding of DNA can be more easily understood in the light of this.The text is liberally sprinkled with figures and colour plates, making it accessible to both the beginning graduate student and researchers in condensed matter physics and chemistry, mineralogists, crystallographers and biologists.

Kare Larsson, Camurus Lipid Research Foundation, Lund, Sweden.

Autoren/Hrsg.

Hyde, S.

Blum, Z.

Landh, T.

Lidin, S.

Ninham, B. W.

Andersson, S.

Larsson, K.

Inhaltsverzeichnis

1;Front Cover;1
2;The Language of Shape: The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology;4
3;Copyright Page;5
4;Table of Contents;10
5;Chapter 1. The Mathematics of Curvature;14
5.1;1.1. Introductory remarks;14
5.2;1.2 Curvature;15
5.3;1.3 Differential geometry of surfaces;17
5.4;1.4 The Gauss map;19
5.5;1.5 Geodesic curvature and geodesics;20
5.6;1.6 Torsion;21
5.7;1.7 The Gauss-Bonnet theorem;23
5.8;1.8 Topology;24
5.9;1.9 A provisional catalogue of surface forms;27
5.10;1.10 A historical perspective;31
5.11;1.11 Periodic minimal surfaces;34
5.12;1.12 The Bonnet transformation: the P-surface, the D-surface and the gyroid;40
5.13;1.13 Parallel surfaces;45
5.14;1.14 Future directions;45
5.15;Appendix: A catalogue of some minimal surfaces;46
5.16;Mathematical Bibliography;53
5.17;References;54
6;Chapter 2. The Lessons of Chemistry;56
6.1;Inorganic Chemistry: From the discrete lattice of crystal symmetry to the continuous manifolds of differential geometry;56
6.2;2.1 The background;56
6.3;2.2 The unravelling of complex structures;57
6.4;2.3 Defects;59
6.5;2.4 The intrinsic curvature of solids;62
6.6;2.5 Hydrophobic zeolites and adsorption;65
6.7;2.6 Phase transitions, order and disorder;68
6.8;2.7 Quantitative analysis of hyperbolic frameworks: silicate densities;71
6.9;2.8 Tetrahedral frameworks: Three- or two-dimensional structures?;76
6.10;2.9 Quasicrystals;79
6.11;Organic Chemistry-The Shape of Molecules;86
6.12;2.10 The hyperbolic nature of sp3 orbitals;86
6.13;2.11 Organic sculptures: carcerands, crowns, etc.;88
6.14;2.12 Beyond graphite: fullerenes and schwarzites;91
6.15;Appendix: The Problem of Quasicrystals;93
6.16;References;97
7;Chapter 3. Molecular Forces and Self-Assembly;100
7.1;3.1 The background;100
7.2;3.3 The background to surface forces;109
7.3;3.4 Molecular forces in detail;111
7.4;3.5 A gallimaufry of forces;118
7.5;3.6 Self-organisation in surfactant solutions;126
7.6;Appendix A: Evolution of concepts on long range molecular forces responsible for organisation and interactions in colloidal systems;137
7.7;Appendix B: Modern concepts of self-assembly;141
7.8;Appendix C: Remarks on the nature of the hydrophobic interaction and water structure;142
7.9;References;150
8;Chapter 4. Beyond Flatland: The Geometric Forms due to Self-Assembly;154
8.1;4.1 Introduction: molecular dimensions and curvature;154
8.2;4.2 The local geometry of aggregates;156
8.3;4.3 The composition of surfactant mixtures: the global constraint;159
8.4;4.4 Bilayers in surfactant-water mixtures;162
8.5;4.5 Monolayers in surfactant-water mixtures;167
8.6;4.6 Geometrical physics: bending energy;170
8.7;4.7 The mesophase behaviour of surfactant- and lipid-water mixtures;173
8.8;4.8 The hyperbolic realm: cubic and intermediate phases;176
8.9;4.9 Mesostructure in ternary surfactant-water-oil systems: microemulsions;183
8.10;4.10 Block copolymer melts: an introduction;189
8.11;4.11 Copolymer self-assembly;190
8.12;4.12 Relation between material properties and structure;198
8.13;4.13 Protein assemblies in bacteria: a mesh phase;199
8.14;4.14 Self-assembly of chiral molecules;200
8.15;References;207
9;Chapter 5. Lipid Self-Assembly and Function In Biological Systems;212
9.1;5.1 Self-association of lipids in an aqueous environment;212
9.2;5.2 Cell membranes;226
9.3;References;245
10;Chapter 6. Folding and Function In Proteins and DNA;250
10.1;6.1 Overall features of protein structure;250
10.2;6.2 a-helix domains;252
10.3;6.3 a-helix / ß--sheet domains;252
10.4;6.4 ß-sheet domains;254
10.5;6.5 Membrane proteins;255
10.6;6.6 Enzymatic action;256
10.7;6.7 Protein function and dioxin poisoning;260
10.8;6.8 Geometry in hormone-receptor interactions;261
10.9;6.9 Self / non-self recognition;263
10.10;6.10 DNA folding;264
10.11;6.11 Self-assembly and crystallisation of proteins;266
10.12;References;269
11;Chapter 7. Cytomembranes and Cubic Membrane Systems Revisited;270
11.1;7.1 Membrane organisation;270
11.2;7.2 Recognition of hyperbolic periodic cytomembrane morphologies in electron microscopic sections;272
11.3;7.3 The structure and occurrence of cubic membranes;279
11.4;7.4 Cubic membranes in unicellular organisms: prokaryotes and protozoa;285
11.5;7.5 Cubic membranes in plants;288
11.6;7.6 Cubic membranes in fungi;297
11.7;7.7 Cubic membranes in metazoa;299
11.8;7.8 Relationships between tubuloreticular structures, annulate lamellae, and cubic membranes;327
11.9;7.9 Biogenesis of cubic membranes;330
11.10;7.10 Relationships between cubic membranes and cubic phases;334
11.11;7.11 Functionalities of cubic membranes;336
11.12;7.12 Cell space organisation and topology;337
11.13;7.13 Specific structure-function relations;340
11.14;Abbreviations;343
11.15;References;344
12;Chapter 8. Some Miscellaneous Speculations;352
12.1;Templating;352
12.2;8.2 Supra Self-Assembly;361
12.3;8.3 The origin of life: a role for cubosomes?;372
12.4;8.4 A final word;375
12.5;References;376
13;Index;378