By Klaus Strenge Hans Sonntag
ISBN-10: 1475706170
ISBN-13: 9781475706178
ISBN-10: 1475706197
ISBN-13: 9781475706192
Colloidal dispersions play a vital position in nature, undefined, and everyday life. occasionally, long term balance is saw or wanted as in ferrotluids (composed of very small magnetic debris with radii of ~ 10 nm), which needs to be solid even in exterior fields. however, in simple terms non permanent reliable dispersions will be important in the course of genuine processing operations, for instance, dispersions of magnetite debris in the course of tape manufacture. the steadiness of dispersions and plenty of in their actual houses are regarding the interplay among the debris within the dispersion medium, which can include surfactants or macromolecular species. If the internet interparticle interplay forces are beautiful, then aggregation may well happen. common different types of aggregation habit will be distinct: coagulation and flocculation. those phrases are often used synonymously yet IUPAC has suggested the next definitions: Coagulation implies formation of compact aggregates, resulting in the macroscopic separation. Flocculation implies the formation of a unfastened or open community, floc, that may or won't separate macroscopically. Flocculation caused via the simultaneous coadsorption of polymer molecules on (or extra) debris is often called bridging flocculation. If coagulation leads to the merging of 2 debris into one, as may well ensue with liquid droplets in emulsions, this strategy is known as coalescence.
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As with gold particles, the primary minimum is supressed by introducing a distance of closest approach and coagulation should not occur. However, this is not in accord with experimental results. 4. Superposition of the Interparticle Forces 37 ducing a distance of closest approach. 14. l5b interaction energy-distance curves are shown for spherical particles with a Hamaker constant of 5 · l o- 21 J. This value is typical for latex particles. With particles of radii of 200 nm or greater a secondary minimum of sufficient depth for flocculation is formed.
57 the the the an 3. 1. 1) This equation corresponds to a bimolecular chemical reaction 1 ). 2) k. = 27tR11 D11 is referred to as the Smoluchowski rate constant [equ. 30)]. ). Therefore the total change in singlet concentration is given by I dz - -1 = -R 11 D11 z 21 - .. 47t dt R 12 D12 z 1 z 2 - R 13 D13 z 1z 3 ... , L i= I 1) R 3 ;D 3;Z; In every collision two single particles will disappear. 1) by a factor of 2. ). 1. k:. 6) i=l The following, simplifying assumptions were made by von Smoluchowski: I.
Dx d. • dt However, this expression cannot be used directly to find the mean displacement in the x direction. For mathematical reasons we have to consider the square of the velocity and the acceleration. This is because the probabilities that particles have velocity + (~;)and- (~;)and acceleration +(~::)and- (~:n are equal in both cases. 8) 40 2. 11) Up to this point we have only made mathematical steps. 12) The product of the driving force F and the displacement x is zero, on average. since there is an equal probability of collisions with solvent molecules occurring in any directions.
Coagulation Kinetics and Structure Formation by Klaus Strenge Hans Sonntag
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