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.
General
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