By S. Hyde, Z. Blum, T. Landh, S. Lidin, B.W. Ninham, S. Andersson, K. Larsson
This e-book develops the thesis that constitution and serve as in various condensed structures - from the atomic assemblies in inorganic frameworks and natural molecules, via molecular self-assemblies to proteins - may be unified whilst curvature and floor geometry are taken including molecular form and forces. An spectacular number of man made and organic assemblies may be adequately modelled and understood when it comes to hyperbolic surfaces, whose richness and wonder are just now being printed via utilized mathematicians, physicists, chemists and crystallographers. those surfaces, frequently as regards to periodic minimum surfaces, weave and twist via house, carving out interconnected labyrinths whose diversity of topologies and symmetries problem the imaginitive powers.
The publication deals an summary of those constructions and structural ameliorations, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and toxins regulate to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases shaped by way of surfactants, detergents and lipids, man made block copolymer and protein networks, in addition to organic telephone assemblies, from muscle tissue to membranes in prokaryotic and eukaryotic cells. The relation among constitution and serve as is analysed by way of the formerly ignored
hidden variables of curvature and topology. hence, the catalytic task of zeolites and enzymes, some of the best fabric houses of interpenetrating networks in microstructured polymer composites, the delivery requisites in cells, the transmission of nerve indications and the folding of DNA may be extra simply understood within the mild of this.
The textual content is liberally sprinkled with figures and color plates, making it obtainable to either the start graduate scholar and researchers in condensed subject physics and chemistry, mineralogists, crystallographers and biologists.
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Extra resources for The Language of Shape - The Role of Curvature in Condensed Matter, Physics, Chemistry and Biology
Naturally all these operations are idealisations. Often we find small deviations from this ideal behaviour in a natural crystal. The properties of a crystalline material are heavily dependent on those deviations, which operate to produce non-ideal behaviour. 44 Chapter 2 Let us start by analysing the plane. There is an infinite number of ways to fill the plane with irregular tiles, but if we restrict ourselves to regular polygons, whose edge lengths and angles are all equal we find that only triangles, squares and hexagons will do the job.
P. 137. All of these are recommended introductions to differential geometry. M. Spivak, "A Comprehensive Introduction to Differential Geometry". Vol. IV, chapter 9. (1979), Berkeley: Publish or Perish, Inc. Spivak gives a modern technical account of all aspects of differential geometry in five volumes, including a good historical section, covering in some detail the original work of Gauss and Riemann (vol 2). C. Nitsche, "Vorlesungen fiber Minimalfli~chen". (1975), Berlin: Springer Verlag. C. Nitsche, "Lectures on Minimal Surfaces".
The fact that the atomic arrangement was clearly not ordered in the classical sense, but still exhibited a perfectly regular diffraction pattern could be explained as an ordering in higherdimensional space, as for the so-called "incommensurate structures". Ordering in "higher" space means that the positions of the atoms in space cannot be labelled by the three cartesian indices, but require extra labels. What is learnt from this goes beyond the statement that geometry is important. Crystallography is by necessity ruled by geometry and its rules are universally valid.