Distance between aggregates

In the case of carbon black, the aggregates are distributed in the matrix rather than individual particles, it is therefore important in some applications (e.g., conductive plastics) to evaluate the distance between these aggregates. It is now possible to measure these distances by atomic force microscopy coupled with straining device. There is a linear relationship between the parallel distance between aggregates dispersed in SBR and strain value. For 10 phr of N 234, the mean distance between aggregates varied in a range from 1.85 to 3.42 jm. For practical purposes, a modified equation [5.4] is used to determine the interaggregate distance ... 

The distance between aggregates, 5aa, can be obtained from the following equation ... 

The distance between aggregates is a value which correlates with many properties of filled rubber. Figure 7.35 gives an example of the correlation with tanb. " Other applications were made with these properties ball rebound, effect of graphitization on properties of carbon black and parameters of carbon black which characterize structure. 

Basic considerations on optimum dispersion allow estimating the most likely distance between aggregates. Let us indeed consider the most compact spatial disposition of spheres of equal diameter it corresponds to the face centered cubic lattice (Figure 5.1). One may consider that an aggregate occupies a spherical volume whose diameter is half the so-called Stokes... 

In order to avoid all points aggregating near the minima (reactant and product), constraints are imposed for keeping the distance between two neighbouring points close... 

FIGURE 19.6 Dependency on carbon black loading of perimeter distance between the nearest aggregates obtained from three-dimensional-transmission electron microscopic (3D-TEM) images (dp) and volume resistivity at room temperature (pv). (From Kohjiya, S., Kato, A., Suda, T., Shimanuki, J., and Ikeda, Y., Polymer, 47, 3298, 2006. With permission.)... 

Ion-pair formation (or the formation of triplets, etc.) is a very simple kind of interaction between ions of opposite charge. As the electrolyte concentration increases and the mean distance between ions decreases, electrostatic forces are no longer the only interaction forces. Aggregates within which the ions are held together by chemical forces have certain special features (i.e., shorter interatomic distances and a higher degree of desolvation than found in ion pairs) and can form a common solvation sheath instead of the individual sheaths. These aggregates are seen distinctly in spectra, and in a number of cases their concentrations can be measured spectroscopically. 

When we will discuss the effects of solvent collapse in solute-solvent interactions (section 8.11.2), we will mean local modifications of the water structure (degree of distortion of the oxygen bond distance between neighboring oxygen nuclei) induced by the presence of electrolytes in solution. We refer to the classical text of Eisemberg and Kauzmann (1969) for a more detailed discussion on the various aggregation states of the H2O compound. 

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