Intermolecular interference

The partition of molecular distance correlations into intra- and intermolecular contributions allows us to interpret these correlations in terms of a simple geometrical model. By this means, we are able to elicit structural units as for example segment-clusters that include intermolecular interference phenomena. These clusters are the primary structure units which we call monodomains . These natural units characterize the basic symmetry of the whole structure. If we keep in mind this basic symmetry, we can construct our structure model from a molecular level up to the level of the monodomain treating intra- and intermolecular correlations independently. If we do so, every X-ray pattern can be represented by accounting for the orientation distribution of these monodomains. 

In order to extract information on the single chain structure from SLS data, it is necessary to fulfill the condition of a single mode scattering, similarly to the extraction of molecular weight and second virial coefficient from SLS data (see Sec. VII). A further condition is that the scattering from polyions should not be influenced by intermolecular interference due to intermolecular interactions, i.e., the solution structure factor S(0) = 1. In this case the total... 

Thus, in dealing with large molecules, it is necessary to extrapolate data to = 0 to correct for this intermolecular interference effect. To get the proper molecular weight from a HcjR(q plot, one must carry out a double extrapolation , both to c - 0 and q- Q. One way of doing this is by a Zimm Plot . 

Separating the angular dependence found earlier for small particles by dividing the Rayleigh ratio by (1 + cos 0), one obtains AR90, which is still ( -dependent because of the intermolecular interference. As expected, there is no reduction in the... 

From all these results it may be assumed that synthetic high polymers, because of the non-uniformities unavoidable in their preparation, are usually poorly susceptible to x-ray analysis with regard to very long periods, but that the natural products, which are usually formed much more slowly, display a considerably higher internal molecular order with greater sharpness and definition. As in the case of the above substances they throw much light on intermolecular interferences. 

The derivations given in Section 9.5.2 refer to small, isotropic, randomly distributed molecules that move independently of one another, e.g., in a vacuum. The total intensity of scattered light is here given as the sum of the intensities scattered by the individual molecules. In liquids, the Brownian motions of the molecules are not independent of each other. Because of intermolecular interference, the measured total intensity of scattered light is less than the sum of the individual intensities. 

SANS measurements of polymers in dilute solution (i.e. below the overlap concentration, at which molecules start to interpenetrate) offer basically the same information as that from LS light and X-ray-scattering techniques, which permit the elucidation of chain dimensions via the electron-density contrast between a macromolecule and solvent. A greater signal-to-noise ratio may be obtained with the neutron technique since it is less sensitive to dust particles [44] and also because of the larger contrast possible with a deuterated polymer (or solvent). However, the main impact of SANS has been in the area of semidilute and concentrated systems. The technique has provided a wealth of new information previously unobtainable by LS or SAXS, for which intermolecular interference effects had restricted... 

At the limit of very low added salt concentration, the strong electrostatic forces lead to the formation of surprisingly stable intermolecular structures which are most easily detected experimentally by scattering methods as intermolecular interference (structure peaks). These intermolecular structure peaks are observed at very low added salt concentrations with an even lower polyion concentration (X, < 1) and for high polyion concentration with low added salt (A, > 1). It is this intermolecular interaction which obscures experimental results on the conformation of single polyions at low ionic strength, even in the comparatively simple regime X 1. And it is this intermolecular interaction which makes the already complex behaviour of polyelectrolytes for X, > 1 even less transparent. 

When the macromolecules of the solute are small (< X,/20) compared to the wavelength of the incident light, each macromolecule can be viewed as a unique scattering center. In absence of intermolecular interferences, no dissymmetry is observed at 45° and 135° and the scattering intensity can be measured only at one angle, generally 90°. 

Thus, when characterizing large molecules, it is necessary to extrapolate data to g = 0 so as to avoid the effects due to intermolecular interferences. 

FIGURE 5 Low-to-medium-Q scattering pattern of a nematic side-chain polymer aligned in the magnetic field (field axis vertical). The pattern features a strong diffuse equatorial arc and a weak diffuse meridional streak, both attributed to intermolecular interference. 

Scattering intermolecular interference function Gas constant C illary radius... 

In a next step, eqn [22] is decomposed into intramolecular and intermolecular interference terms P(Q) und W(Q) according to... 

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