Radial excess electron density

Consideration of the chemical nature of zero-valent lanthanide metals raises some intriguing questions. The stability of zero oxidation state transition metal complexes depends in large part on the capacity of the metal to transfer its excess electron density back to the ligands via backbonding. Given the limited radial extension of the 4/orbitals (8, 9),... 

Figure 2 displays the SAXS-intensities Io(q) calculated for the radial electron density shown in Fig. 1. Parameter of the curves is the contrast p - Pm expressed as the number of excess electrons per nm. The isoscattering points are clearly visible. Furthermore, the calculation shows that forward scattering for a mono-disperse particle will vanish at zero contrast in accordance with the above deductions. As a consequence of this, the radius of gyration will increase or decrease rapidly as function of contrast in the vicinity of the match point (see below).

The scattering data thus corrected are solely due to the radial excess electron density of the particles. Fig. 14 displays the measured intensity (filled circles) of the polystyrene latex discussed in conjunction with Fig. 10. The solid line is the fit of the experimental data by a core-shell model and a slightly asymmetric size distribution ([46] see below) taken from the analysis by ultracentrifugation [87]. In terms of a Gaussian size distribution the polydispersity corresponds to a standard deviation of 4.2%. The thin shell having a higher electron density stems from the adsorbed surfactant used in the synthesis of the latex. This effect and its detection by SAXS will be discussed further below (see Sect. 4.4). 

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