Structural properties of the melt

1 Mean-squared bond length and radius of gyration 

In addition to the scale of a bond, another important length scale for a polymer is that of the radius of gyration. This quantity is defined by  

Presumably it would be possible to verify the result, presented in Fig. 6.9, in a neutron scattering experiment if one measured the structure factor of a chain in the vicinity of the glass transition for various cooling rates. From the behavior of the structure factor at small wave numbers q one could determine / Q(r,rQ), whereas the end of the scaling regime, where the structure factor is proportional to if, would yield the temperature- and cooling-rate-dependence of the persistence length . Since a monomer 

The collective static structure factor for an isotropic system can be defined in the following way  

In addition to the behavior of the structure factor at large -values, also the small -limit of S q) is interesting because it is related to the isothermal compressibility Moreover, the isothermal compressibility can also be calculated from the density fluctuations in subsystems, using the so-called block-analysis , by virtue of the fluctuation-dissipation theorem. Therefore there are two independent ways to determine kt in the simulation, which should coincide  

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