Polymer Lattice Structures

Other methods of determining chain structure in polymers include tunneling electron microscopy,which has been used to reveal the presence of helical chains, and extended X-ray absorption fine structure (EXAFS), which when applied to metal-ion-doped polymers can reveal the immediate atomic environment of the dopant ion. 

Morse Parameters for the Bond Stretching Potentials Defined by Eq. (3) 

The interaction between nonbonded molecular systems can be expressed as a power expansion involving separation vectors and products of their electric multipole moments. Much effort has gone into calculating intermolecular potentials. 

If the dopant species are monatomic ions, the derivation of their mutual interactions fall into two classes. Using quantum chemical electron gas theory, electronic charge distributions derived from Hartree-Fock calculations on the ions are allowed to interact at various intemuclear distances. In another method lattice simulation calculations are performed to fit the constants in Eqs. (7) or (8) to measured bulk data, such as elasticity tensor components, dielectric constants and/or lattice structures, thereby providing empirically derived potentials. 

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Keywords High pressure Fullerene polymers Lattice structures Raman spectroscopy Intermolecular bonding... 

In three dimensions, Ohta and Kurokawa [32] reported that a BCC arrangement was only slightly more favored than the FCC arrangement. In fact, many BCC structures have been reported for AB type block copolymers and the blends of homopolymer-block copolymer systems [27,33-35]. However, the lattice structure of the core-shell type polymer microspheres was FCC. This FCC formation resulted in the lower viscosity of... 

The first section involves a general description of the mechanics and geometry of indentation with regard to prevailing mechanisms. The experimental details of the hardness measurement are outlined. The tendency of polymers to creep under the indenter during hardness measurement is commented. Hardness predicitions of model polymer lattices are discussed. The deformation mechanism of lamellar structures are discussed in the light of current models of plastic deformation. Calculations... 

On the other hand, one strength of the approach is the availability of algorithms (such as the slithering snake algorithm) by which undercooled polymer melts can be equilibrated at relatively low temperatures. This allows the static properties of the model to be established over a particularly wide parameter range. Furthermore, the lattice structure allows many questions to be answered in a well-defined, unique way, and conceptional problems of the approach can be identified and eliminated. Last but not least, the lattice structure allows the formulation of very efficient algorithms for many properties. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

We will confine ourselves to those applications concerned with chemical analysis, although the Raman microprobe also enables the stress and strain imposed in a sample to be examined. Externally applied stress-induced changes in intramolecular distances of the lattice structures are reflected in changes in the Raman spectrum, so that the technique may be used, for example, to study the local stresses and strains in polymer fibre and ceramic fibre composite materials. 

Mark, in the five years he worked at the Institute, established himself as an expert crystallographer. Between 1923 and 1927 more than fifty papers were (co)authored on the lattice structure of metals, simple organic and inorganic compounds, and polymers. The laboratory became known as an efficient, smoothly functioning research organization which attracted all kinds of visitors. Max von Laue was a frequent visitor as was P. P. Ewald, the author of the first book on X-ray diffraction. Others who visited Dahlem were J. R. 

There are two classes of materials which may be used as electrolytes in all-solid-state cells polymer electrolytes, materials in which metal salts are dissolved in high molar mass coordinating macromolecules or are incorporated in a polymer gel, and ceramic crystalline or vitreous phases which have an electrical conductance wholly due to ionic motion within a lattice structure. The former were described in Chapter 7 in this... 

EPITAXY. An oriented crystalline growth between two crystalline solid surfaces of different chemical composition, in which the surface of one crystal provides, through its lattice structure, preferred positions lor the deposition of the second crystal. This behavior is characteristic of some types of high polymers. 

Crystallinity. Crystals are an ordered, regular arrangement of units in a repeating, three-dimensional lattice structure. Small molecules, which in the liquid state have three-dimensional mobility, crystallize readily when cooled. It is not so easy for polymers, because a repeating unit cannot move independently of its neighbors in the chain. Nevertheless, some polymers can and do crystallize, though never completely. 

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