Finite-Angle Scattering

In this section a brief survey over the results achieved so far by small-angle scattering studies is given. The discussion is done in two parts. First data obtained at vanishing concentration are presented that allow one to assess the density distribution inside the dissolved dendrimers. Then data measured at finite concentration are shown which give highly interesting information on the mutual interaction of dendrimers in solution. 

Small-angle scattering intensity in the high angle (q) region can be analysed to provide information on interface thickness (e.g. the lamellar interface thickness block in copolymer melts or core-corona interface widths in micelles). For a perfectly sharp interface, the scattered intensity in the POrod regime falls as q A (Porod 1951). For an interface of finite width this is modified to... 

The intensity of scattering at finite q, on the other hand, reflects the concentration fluctuations that exist on a more local scale. In the case of a single-component system, as discussed in Section 4.1, the finite-angle intensity data can be converted, through an inverse Fourier transform, to a radial distribution function g(r). With a two-component system a comparable general procedure is not available, and information on the structure is derived usually by comparing the observed intensity data, on the q plane, with expressions derived from theoretical models. 

It must be noted that classical geometric optics does not provide scattering matrix elements at discrete directions but only for finite-sized scattering-angle bins. The backscattering phase matrix elements shown in Fig. 9 have been calculated for the angular bin [179.95°, 180°]. i.e. for a bin size of 0.05°. 

I he effect of low-angle scattering leads to a decrease in the turbidity being measured when some of the scattered light is received by the colorimeter s detector due to the finite aperture value. The bigger particles and relative refractive index, the more pronounced is this effect. 

Fig, 32, Small angle scattering of X-rays by particles of finite dimeiisions... 

The form factor f takes the directional dependence of scattering horn a spherical body of finite size into account. The reciprocal distance s depends on the scattering angle and the wavelength A as given by Eq. (23). 

The curve labeled geometry illustrates the kinematic energy spread due to the finite acceptance angle of the detector. The multiple scattering contribution arises from the spread in ion energies introduced by secondaiy scattering events. 

By combining eq. (5) with eq. (11), we can imply a relation between the molecular weight, M, and the characteristic linewidth, T, at a finite scattering angle and a finite concentration... 

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