Noncrystalline Systems

In the absence of molecular dynamics investigations of ion transport in noncrystalline phases of polymers, we describe investigations of the motion of small neutral molecules in amorphous polymers. The success of these studies in providing a description of the motion of (albeit) neutral diffusants encourages their extension to similar investigations of the transport of dopant ions through polymer materials. 

More recently Takeuchi reported details of a jump mechanism of a small diffusant molecule in a system of endless polymer chains that is quenched at the glassy state (T T ). For most diffusant species (simulating O2 molecules) trapped in rigid cages formed by strands of the glassy polymer, the time evolution of the 

FIGURE 5.25. A comparison of the mean square displacement ir(r)i of a (a) trapped and (b) migrating oxygen diffusant in a glassy polymer, obtained by a molecular dynamics simulation. (Takeuchi, by permission of the author and of the American Institute of Physics.) 

Recently Sok et simulated the transport of He and of CH4 through a polydimethylsiloxane (PDMS) membrane. The polymer was selected because of the almost invariably amorphous condition of its samples. Thus the interpretation of experimental diffusion data is uncomplicated by the presence of crystallites. The PDMS chains were represented by oligomers consisting of 30 monomer units, and the MD simulation was based on a fine-grained representation of polymer and diffusant, i.e., all atoms were included explicitly. Like the mechanism described by Takeuchi here, too, transport occurred by a jump mechanism. Facilitated by fluctuations in the polymer chains, the hole surrounding the diffusant was observed to expand just prior to the jump, and a transient channel was opened, thus enabling the transition to occur. Diffusion coefficients derived for He and CH4 (respectively, 18 X 10 and 2.1 x 1(T cm s ) are consistent with at least the magnitudes of experimental measurement (10 x 1(T and 2.0 x 10 cm  

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The description of the atomic distribution in noncrystalline materials employs a distribution function, (r), which corresponds to the probability of finding another atom at a distance r from the origin atom taken as the point r = 0. In a system having an average number density p = N/V, the probability of finding another atom at a distance r from an origin atom corresponds to Pq ( ). Whereas the information given by (r), which is called the pair distribution function, is only one-dimensional, it is quantitative information on the noncrystalline systems and as such is one of the most important pieces of information in the study of noncrystalline materials. The interatomic distances cannot be smaller than the atomic core diameters, so = 0. 

Powerful w/o emulsifiers such as polyglycerol polyricineolate gives stability in noncrystalline systems, such as warm emulsions, which are important in low fat spread production particularly for very low fat spreads of 20 to 25% fat content. 

A morphological term used in noncrystalline systems, such as block copolymers, in which the chemically different sections of the chain separate, generating amorphous phases. 

An empirical relation between the correlation length, r, in real space and the peak position, Q, in the intensity profile, Qr = 2.5n is known in various noncrystalline systems of liquids and amorphous alloys (Waseda 1980). By applying this empirical relation to the prepeak in the intensity profile, the correlation length causing the prepeak at 14 run was estimated to be 0.561 nm. Since this value is comparable to the distance between the... 

The otiier type of noncrystalline solid was discovered in the 1980s in certain rapidly cooled alloy systems. D Shechtman and coworkers [15] observed electron diffraction patterns with sharp spots with fivefold rotational synnnetry, a syimnetry that had been, until that time, assumed to be impossible. It is easy to show that it is impossible to fill two- or tliree-dimensional space with identical objects that have rotational symmetries of orders other than two, tliree, four or six, and it had been assumed that the long-range periodicity necessary to produce a diffraction pattern with sharp spots could only exist in materials made by the stacking of identical unit cells. The materials that produced these diffraction patterns, but clearly could not be crystals, became known as quasicrystals. 

Several other catalyst systems have been suggested, including boron fluoride and both crystalline and noncrystalline siUcas and alurninosihcates. Although no commercial faciUty exists, the concept of using a crystalline siUca or alurninosihcate catalyst in an integral reaction and distillation apparatus has been proposed (9). 

Some organic contaminants are volatilized and escape from the soil surface and must be collected by a vacuum system. Inorganics and some organics are trapped in the melt, which, as it cools, becomes a form of obsidian or very strong glass. When the melt is cooled, it forms a stable noncrystalline solid. 

The development of the internal orientation in formation in the fiber of a specific directional system, arranged relative to the fiber axis, of structural elements takes place as a result of fiber stretching in the production process. The orientation system of structural elements being formed is characterized by a rotational symmetry of the spatial location of structural elements in relation to the fiber axis. Depending on the type of structural elements being taken into account, we can speak of crystalline, amorphous, or overall orientation. The first case has to do with the orientation of crystallites, the second—with the orientation of segments of molecules occurring in the noncrystalline material, and the third—with all kinds of structural constitutive elements. 

There are two major experimental techniques that can be used to analyze hydrogen bonding in noncrystalline polymer systems. The first is based on thermodynamic measurements which can be related to molecular properties by using statistical mechanics. The second, and much more powerful, way to elucidate the presence and nature of hydrogen bonds in amorphous polymers is by using spectroscopy (Coleman et al., 1991). From the present repertoire of spectroscopic techniques which includes IR, Raman, electronic absorption, fluorescence, and magnetic resonance spectroscopy, the IR is by far the most sensitive to the presence of hydrogen bonds (Coleman et al., 1991). 

Microscopic and mechanistic aspects of diffusion are treated in Chapters 7-10. An expression for the basic jump rate of an atom (or molecule) in a condensed system is obtained and various aspects of the displacements of migrating particles are described (Chapter 7). Discussions are then given of atomistic models for diffusivities and diffusion in bulk crystalline materials (Chapter 8), along line and planar imperfections in crystalline materials (Chapter 9), and in bulk noncrystalline materials (Chapter 10). 

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