Random-mass disorder

The growth of films via SCBD can be viewed as a random stacking of particles as for ballistic deposition [33,34]. The resulting material is characterized by a low density compared to that of the films assembled atom by atom and it shows different degrees of order depending on the scale of observation. The characteristic length scales are determined by cluster dimensions and by their fate after deposition. Carbon cluster beams are characterized by the presence of a finite mass distribution and by the presence of different isomers with different stabilities and relativities. Due to the low kinetic energy of clusters in the supersonic expansion stable clusters can survive to the deposition, while reactive isomers can coalesce to form a more disordered phase [35]. 

One of the most exciting developments of the past decade in the study of colloidal silica is the application of the fractal approach to the study of sols and gels. Fractals are disordered systems for which disorder can be described in terms of nonintegral dimension. The concept of fractal geometry, developed by Mandelbrot (II) in the early 1980s, provides a means of quantitatively describing the average structure of certain random objects. The fractal dimension of an object of mass M and radius r is defined by the relation... 

The amorphous state is associated with polymers that are unable to crystallize and form a disordered state. The surface of an amorphous polymer can therefore be pietured as an entangled mass of random coil, pseudo-spherical structures (Figure 10.1). 

It is now possible unambiguously to measure the partition of comonomer units between crystaUine and amorphous phases in polymers. By combining SANS and SAXS studies in the q range 0.01 to 0.2 A, measurements can be made of the difference Ap between the mass densities of the crystalline and disordered regions as well as the concentration fluctuations of the comonomer units. One example studied was that of randomly chlorinated linear polyethylene in which the partition (y) of CHQ units between phases was measured at different concrai-trations of CHCl units, Xf- At xp = 1-0 mole per cent, y = 1, showing that most of the non-crystallizable co-imits are excluded from the crystalline regions. 

Is there any order at all in liquid structure X-ray examination shows some limited regularity — but much less than the sharp patterns obtained from crystalline solids. One way to regard the liquid state is as a crystallinelike mass interspersed with molecular-sized spaces or holes whose arrangements are entirely random (Fig, 9.9). Molecules may enter or leave these holes this interchange produces overall disorder and ffuidity. 

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