Secondary minimum aggregation

Chin, C.J. et al.. Secondary minimum aggregation of superparamagnetic colloidal particles, Langmuir, 16, 3641, 2000. 

At larger particle separation, a second minimum may occur in tire potential energy. In many cases, tliis minimum is too shallow to be of much significance. For larger particles, however, tire minimum may become of order kT. Aggregation in tliis minimum is referred to as secondary minimum flocculation. 

Flocculation a relatively reversible aggregation often associated with the secondary minimum of a potential energy diagram. Particles are held together loosely with considerable surface separations. 

As two particles approach in a liquid their charge fields may interact and form two minima as depicted in Figure 6.8. If the particles approach to a distance Li, known as the primary minimum they aggregate to form a configuration with minimum energy - and rapid coagulation is said to take place. On the other hand, if the particles remain separated at a distance L2, the secondary minimum, loose clusters form which do not touch. This is known as slow coagulation and is the more easily reversed. 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

Fig. 31 Overall interaction energy between two DNA-coated colloids, (a) Sketch of the interacting surfaces of two spheres of radius R0 separated by d. The maximum length of hybridized strands is 2L. (b) Total interaction energy as a function of d. It is the sum of the attractive I/DNA from the binding of accessible DNA strands, the repulsive I/rep from electrostatics and/or polymer steric effect, and the van der Waals attraction t/vdw. (c) For weak, short-range I/rep, particles which are unbound at high temperatures are irreversibly trapped in the van der Waals well after DNA hybridization at low temperatures, (d) For strong, medium-range I/rep, DNA binding produces a secondary minimum of reversible aggregation. Reproduced with permission from [138]...

With this size of latex particle it becomes possibfe to make direct observations on particles over a perind of time and record them with a high-speed camera. Using this technique Cornell et al (1975)) discovered that particles in an associated unit could be quite mobile. It was observed that as well as some particles leaving the aggregated unit as single particles and returning to the disperse phase there was a continued rearrangement of the particles. This was also observed with floccules at salt concentrations well above the ccc. These observations clearly support the contention that association can occur in a secondary minimum and that in this situation a liquid film is maintained between the particles. 

Occurrence of flocculation may be explained if secondary minima aggregation is assumed. This is confirmed by the V/KT vs (H (A)) curves, which indicate that at higher values of H, repulsion becomes negligible and attraction predominates and emulsion flocculates. It is also observed that the depth of secondary minimum is more at higher concentration, 5-20 KT, which is deep enough for reversible aggregation, while at low concentrations, the depth of the secondary minima is too shallow to trap the particles. 

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