Scattering interchain/intrachain

In principle, intrachain contraction should occur before interchain association as long as the solution is sufficiently dilute. The limitation is the sensitivity of our detection in laser fight scattering. Note that in Fig. 27,... 

The transverse charge motion is incoherent for a quasi-one-dimensional conductor as long as the condition h hiT is fulfilled (where the intrachain scattering time provides a broadening to the quasi-one-dimensional Fermi surface). This situation is encountered at high temperature. The interchain hopping rate is thus determined by the one-dimensional Fermi golden rule [60] ... 

The nearest-neighbor interchain interactions we shall consider are shown in Fig. (4). The interactions a°d are interchain forward scattering interactions, and these do not give rise to a phase transition of any type, but serve only to renormalize the effective intrachain interactions. In Fig. (5), we have shown the regions in 9 /92 space for g2=g, v2=v, aRd lv2l =... 

Thus, an electron on the inverted band TTF chain corresponds to a hole with a normal band structure, and vice-versa. The interactions are shown in Fig. (1). The intrachain interactions g and gare backward and forward scattering Interactions, as in the single chain problem, and are assumed to be the same on both chains. The interchain interactions are w and These interactions... 

Usually, Hi k) and H2(k) are called the intrachain interference factor and the interchain interference factor, respectively. At infinite dilution, the former reduces to the particle scattering factor P(k) that appeared in Part I. Further we note the following ... 

The scattering patterns of monodomain liquid crystalline polymers represent those from oriented liquid crystalline polymers. Such orientation can be achieved either in the solid state by quenching the oriented polymers or in the melt state by shearing the melt at the mesophase temperatures. Under a force field, such as a tensile force, shear force, or magnetic field, all the domains are aligned in the direction of the external field so that the polydomain liquid crystalline polymers can effectively become monodomain liquid crystalline polymers. For oriented main-chain liquid crystalline polymers, the scattering on the equator is due to interchain correlation and the scatterings on meridian raised from intrachain correlation. 

This example serves to illustrate the lengthy nature of the analysis of the intrachain scattering to give orientational parameters. However, it must be accepted that the final product, that of orientational parameters for a defined and evaluated structure, is of considerable value. It provides a sound route to the measurement of orientation using X-ray scattering, in contrast to the methods employing the interchain... 

For polymer chains in a crystal lattice, however, acoustic vibrations of polymer chains are subject to interchain interactions, yielding the crystal vibrations of the acoustic and optical branches. Accordingly, for vibrational analyses of neutron-scattering spedra in the low-frequency region, it is required to treat the normal vibrations of the crystal, on the basis of the interchain force field as well as the intrachain force field. Treatments of crystal vibrations are also necessary for the theoretical study of specific heat, zero-point energy and temperature factor of x-ray diffraction. 

A framework is introduced, within which we may begin to discuss usefully the local molecular arrangements of noncrystalline polymers. The statistical structure is partitioned into intrachain or conformational, orientational, and spatial interchain parameters. The procedures which initially employ the comparison of the experimental intensity data with scattering functions derived from molecular models, are described with reference to natural rubber. This is seen as a "typical" polymer system. More complex chemical configurations are considered. Both poly(a-methylstyrene) and the phenylene range of polymers appear to exhibit distinct and additional local correlations. The role of these special correlations within the general framework of noncrystalline polymers is discussed. 

We shall now introduce a partition of the intensity function into intrachain and interchain scattering components, justifying this partition later. The intense peak at f > 1.4 A may be... 

The structural analysis described above and in more detail elsewhere, shows the x-ray scattering functions to be sensitive to intrachain correlations. In fact, a more "random chain model (with a delocalized rotation state for one bond) than the "random coil" chain model is required to give a satisfactory match between the experimental and model si (s) functions. A model in which the interchain correlations are minimal with no orientational correlations provides a scattering function which is in good agreement with the observed scattering. Thus there seems to be no evidence to require more local order than inherent in a dense molecular system. This is perhaps not suprising. The polyisoprene molecule has a compact cross section, almost cylindrical in nature and corresponds to the "typical molecule drawn in schematic views of the noncrystalline state. 

The peaks at s = 2.0 and.3.0 A" in the scattering pattern (Fig. 16) from ar-PMMA are intrachain in nature and may be related to the unequal valence bond angles of the PMMA chain. The chain conformation is nearly all trans The peak at i = 1.0 A is interchain in origin. Thus the scattering pattern from ar-PMMA may be tackled in a similar manner to that outlined above for... 

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