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and water will spread. If they are bulky, the functionalized molecules should be mixed with unfunctionalized ones to avoid packing defects. Mixtures
  with different chain lengths (e.g., X = C  and C ) give liquid-like SAMs. The biologically ubiquitous lipid bilayer membrane could be considered to
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  belong to this category. The component molecules are of type XR, where X is an alkyl chain as before, and R is a rather polar “head group”, the
  volume of which is typically roughly equal to that of X. Placing XR molecules in water and gently agitating the mixture will spontaneously lead to the
  formation of spherical bilayer shells RXXR called vesicles. The vesicles will coat a planar hydrophilic substratum with a lipid bilayer when brought
  into contact with it [38].
  SAMs can be patterned using photolithography, or “stamping” (microletterpress), to create patterns on substrata (e.g., gold and/or silica) to which
  the SAM precursor molecules will bind, leaving other zones free. In this procedure, the required pattern is the first created in relief on a silicon
  substrate, which is then used as a mould for the elastomeric polymer PDMS (polydimethylsiloxane). The SAM molecules can be used directly as
  ink to coat the projecting parts of the relief pattern, which is then stamped onto the substratum, or else the ink is some substance that passivates
  the substratum with respect to the SAM molecules, which then selectively bind as required.
  6.4. Crystallization and Supramolecular Chemistry
  It is a remarkable fact that many or even most organic molecules, despite their usually very complicated shapes, are able to spontaneously form
  close-packed crystals. Perhaps only familiarity with the process prevents it from occupying a more prominent place in the world of self-assembly. In
  seeking  to  understand  this  remarkable  phenomenon  better,  Kitaigorodskii  formulated  an Aufbau  principle [92],  according  to  which  the  self-
  assembly (cf. Section 8.2.1) of complicated structures takes place in a hierarchical fashion in the following sequence:

    Stage 0 a single molecule (or a finite number of independent molecules).
    Stage 1 single molecules join up to form linear chains.
    Stage 2 the linear chains are bundled to form two-dimensional monolayers.
    Stage 3 the two-dimensional monolayers are stacked to form the final three-dimensional crystal.
  Many natural structures are evidently hierarchically assembled. Wood, for example, derives its structural strength from glucose polymerized to form
  cellulose chains, which are bundled to form fibrils, which are in turn glued together using lignin to form robust fibers. Note that the interactions
  between the molecular components of the crystal may be significantly weaker than the covalent chemical bonds holding the atomic constituents of
  the molecules together. Such weakness enables defects to be annealed by locally melting the partially formed structure. There is an obvious
  analogy between “crystallization” in two dimensions and tiling a plane. Since tiling is connected to computation, self-assembly, which can perhaps
  be regarded as a kind of generalized crystallization, has in turn been linked to computation.
  Just as quantum dots containing several hundred atoms can in some sense (e.g., with regard to their discrete energy levels) be regarded as
  “superatoms” (Section 2.5), so can supramolecular assemblies (typically made up from very large and elaborate molecules) be considered as
  “supermolecules”. The obtainable hierarchically assembled structures—an enormous literature has accumulated—provide powerful demonstrations
  of the Kitaigorodskii Aufbau principle. The use of metal ions as organizing centers in these assemblies has been a particularly significant practical
  development.
  6.5. Composites
  Most of the materials around us are composites. Natural materials such as wood are highly structured and built upon sophisticated principles. The
  basic structural unit is cellulose, which is a polymer of the sugar glucose, but cellulose on its own makes a floppy fabric (think of cotton or rayon),
  hence to give it strength and rigidity it must be glued together into a rigid matrix. This is accomplished by the complex multi-ring aromatic molecule
  lignin. Another example is the shell of marine molluscs such as the abalone. They are composed of about 95% by volume of thin platelets, small
  enough to rank as nano-objects, of aragonite, a form of calcium carbonate and about 5% of protein. The toughness of the composite seashell
  exceeds by more than tenfold the toughness of pure calcium carbonate.
  A striking thing about these natural composites is the enormous increase in desirable properties, such as stiffness or toughness, through small (by
  volume or mass) inclusions of another material that would, by its nature, normally rank as the matrix in artificial composites. In contrast, the matrix in
  artificial composites is usually the majority component (in mass or volume or both). The principle of combining two or more pure substances with
  distinctly  different  properties  (which  might  be  mechanical,  electrical,  magnetic,  optical,  thermal,  chemical,  and  so  forth)  in  order  to  create  a
  composite  material  that  combines  the  desirable  properties  of  each  to  create  a  multifunctional  substance  has  been  refined  by  humans  over
  millennia, presumably mostly by trial and error. Typically, the results are, at least to a first approximation, merely additive. Thus we might write a sum
  of materials and their properties like







  Empirical knowledge is used to choose useful combinations, in which the desirable properties dominate—in principle one might have ended up
  with a weak and repellent material. The vast and always growing accumulation of empirical knowledge usually allows appropriate combinations to
  be chosen. Indeed, the motif of strong fibers embedded in a sticky matrix is very widely exploited, other examples being glass fiber- and carbon
  fiber-reinforced polymers.
  There are two principal motivations for creating composites. The first is to increase the toughness of the majority component (as in the seashell).
  This occurs by dividing up the monolithic material into nano-objects and gluing the objects together. The increase in toughness comes partly
  through the increased ductility of the comminuted objects (Sections 2.7 and 6.1.1 and partly through the fact that any fracture that does occur can
  only extend to the object boundary or, if it occurs in the matrix, to the nearest object lying in its path, a distance which might well be shorter than the
  object size. Particularly in this kind of composite the wetting of the principal phase by the glue is of extreme importance. Empirical knowledge is
  now backed up and extended by fundamental knowledge of the molecular-scale forces involved, but natural materials still far surpass artificial ones
  in this respect. Proteins in particular are very versatile glues because of the variety of chemical functionalities possessed by amino acids. The
  second motivation is the combination of properties—these composites might well be called composites to distinguish them from the other kind; for
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