Calculation of Suspension Peptization Page: 23
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In making the integration Hamaker assumed that the spheres are far enough
apart to allow integration on a volume basis in place of a summation over
each possible atom pair. He also showed that the interaction of particles
is attractive even when they are suspended in a liquid. The above formula
indicates that the attractive energy depends on the ratio of the common
radii of the particles to their separation. However, when the absolute
dimensions approach 50 or 100 A, the apparent attractive energy tends to
be too high because the integration does not correct for the phase shift
mentioned above.
The value of the attraction constant, A, of eq. 46 is a major con-
sideration in the theory of attractive forces. This constant depends on
the number of atoms per unit volume and on the interaction of two atoms
separated by unit distance. The theoretical interaction is not precisely
defined, and the approximate formulation involves experimental quantities
not readily available for all materials. In the practical situation where
solids such as Th02 are suspended in an aqueous medium, the value of A is
even much less certain because in this case the overall effect includes
solid-to-solid, solid-to-liquid, and liquid-to-liquid interactions. As a
result of the uncertainty in fixing A by theory, its value here will be re-
garded as a more-or-less arbitrary parameter. It will be assumed to be
1 x 10-12 erg, a value which Verwey and Overbeek (p. 104) have thought to
be in the neighborhood of a correct value. This is the same order as the
0.6 x 10-12 value for water-water interaction calculated by Verwey and
Overbeek (p. 104) by a method of Slater and Kirkwood (see reference list).
Equation 46 can be written in a form similar to that of eq. 41,
l A 1 2a2 2a2 R2 - 4a2
=2 + n (47)
kT T T 2 2 2 2
- 4a R R
Combined Potential Energy. The overall potential energy function for
the interaction of two spheres is the sum of eqs. 41 and 47,
v v + VA (48)
kT kT kT
where V = total potential energy of interaction for two charged spheres.
The sketch below shows the general relation of V, VR, and VA as a function
of the distance between the spheres:23
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Sweeton, F. H. Calculation of Suspension Peptization, report, 1960; Oak Ridge, Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc100288/m1/25/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.