Molecular volumes, scattering lengths

Table I. Molecular volumes, scattering lengths and scattering length densities of polymer and solvent... 

As the variation of f and f" is of the same magnitude we have replaced f by f". This should be kept in mind whenever a more detailed consideration becomes necessary. For instance, with proteins the contrast is about 0.1 e /A. Assuming a molecular volume of 10000 A, which compares to those of small proteins with M = 10000, we obtain gV = 2.8 10 °cm 10 10 cm = 2.8 10 ° cm. This corresponds to the excess scattering length of 1000 electrons. Eq. (60) then yields... 

In most cases, it appears possible to interpret the critical behavior of microemulsion mixtures as a liquid/gas-like critical point [113-116]. Several light- and neutron-scattering studies on oil-rich ternary and quaternary microemulsions have clearly demonstrated that the structure of these media can be described as a solution of interacting water-in-oil droplets. As first shown by Calje et al. [117], the droplets may behave essentially as hard spheres. However, in many systems an attractive contribution to the interactions exists. It has been established that the strength of attractions between W/0 micelles is strongly dependent on the micellar size and on the chain lengths of both the alcohol and oil molecules. In particular, attractions have been found to increase when the micellar radius increases or the alcohol chain length decreases and the molecular volume of the oil increases [114, 115, 118-120]. 

This equation shows that the apparent mean square radius of gyration of a copolymer when plotted as a function of Y (i.e. measured in solvent of different scattering length draisity), should have a parabolic shape with downward curvature. lonescu et al. showed that this curve should be little altered in the presence of excluded volume, they also demonstrated that the curve can become severely distorted if the copolymers are polydispo-sed in molecular weight. Figure 19 shows the schematic variation in... 

Scattering techniques probe stmctural correlations on molecular or supermolecular length scales in a macroscopically large sample volume. Most polymer systems do not form highly ordered crystals, so that the correlations between the stmctural... 

The radial distance distribution in simple atomic and molecular fluids is determined essentially by the exclusion volume of the particles. Zemike and Prins [12] have used this fact to construct a one-dimensional fluid model and calculated its radial distance correlation function and its scattering function. The only interaction between the particles is given by their exclusion volume (which is, of course, an exclusion length in the one-dimensional case) making the particles impenetrable. The statistical properties of these one-dimensional fluids are completely determined by their free volume fraction which facilitates the configurational fluctuations. 

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