Potential energy secondary minimum

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. 

The second type of quantum monodromy occurs in the computed bending-vibrational bands of LiCN/LiNC, in which the role of the isolated critical point is replaced by that of a finite folded region of the spectrum, where the vibrational states of the secondary isomer LiNC interpenetrate those of LiCN [9, 10]. The folded region is finite in this case, because the secondary minimum on the potential surface merges with the transition state as the angular momentum increases. However, the shape of the potential energy surface in HCN prevents any such angular momentum cut-off, so monodromy is forbidden [10]. 

In such systems the requirement of the electrostatic contribution to colloidal stability is quite different than when no steric barrier is present. In the latter case an energy barrier of about 30 kT is desirable, with a Debye length 1/k of not more than 1000 X. This is attainable in non-aqueous systems (5), but not by most dispersants. However when the steric barrier is present, the only requirement for the electrostatic repulsion is to eliminate the secondary minimum and this is easily achieved with zeta-potentials far below those required to operate entirely by the electrostatic mechanism. 

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.

Other structural analyses of crystals in which the bifluoride is present are listed in Table 7. One compound, p-toluidinium fluoride [C7H,oN ][HF2 ], is worthy of further comment. The first X-ray diffraction study reported a symmetrical anion (Denne and MacKay, 1971), but a later analysis showed that the proton was not centred between the two fluorines and 7 f h values were 102.5 and 123.5 pm (Williams and Schneemeyer, 1973). This can be explained not by a double minimum potential energy well but by asymmetry due to other forces, such as secondary hydrogen bonding between one end of the bifluoride anion and the N—H group of the cation. An alternative explanation attributes the asymmetry of the bifluoride hydrogen bond to an unsymmetrical crystal field caused by the cation (Ostlund and Bellenger, 1975). 

The identification of the primary ion which is responsible for the secondary product ion can usually be ascertained in simple systems by the coincidence of their appearance potentials. The appearance potential is the minimum energy of the bombarding electrons at which the ion appears. 

Nuclei can be trapped in the secondary minimum of the fission barrier. Such trapped nuclei will experience a significant hindrance of their y-ray decay back to the ground state (because of the large shape change involved) and an enhancement of their decay by spontaneous fission (due to the thinner barrier they would have to penetrate.) Such nuclei are called spontaneously fissioning isomers, and they were first observed in 1962 and are discussed below. They are members of a general class of nuclei, called superdeformed nuclei, that have shapes with axes ratios of 2 1. These nuclei are all trapped in a pocket in the potential energy surface due to a shell effect at this deformation. 

Another characteristic feature of these potential energy curves is the presence of a secondary minimum at relatively large interparticle... 

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