Secondary minimum effects

Deuterium Substitution. The a and P secondary isotope effects affect the rate in various ways (p. 298). The measurement of a secondary isotope effects provides a means of distinguishing between SnI and Sn2 mechanisms, since for Sn2 reactions the values range from 0.95 to 1.06 per a D, while for S l reactions the values are higher. This method is especially good because it provides the minimum of perturbation of the system under study changing from a H to a D hardly affects the reaction, while other probes, such as changing a substituent or the polarity of the solvent, may have a much more complex effect. 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

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.

The presence of polymers or polyelectrolytes have important effects on the Van der Waal interaction and on the electrostatic interaction. Bacterial adhesion, as discussed in Chapter 7.9 may be interpreted in terms of DLVO theory. Since the interaction in bacterial adhesion occurs at larger distances, this interaction may be looked at as occurring in the secondary minimum of the net interaction energy (Fig. 7.4). Particle Size. The DLVO theory predicts an increase of the total interaction energy with an increase in particle size. This effect cannot be verified in coagulation studies. 

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. 

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]...

By splitting the quasi-steady-state assumption of diffusion of particles under the action of the interaction force field into two parts, kinetic equations which account for accumulation at both the primary and secondary minimum are formulated. Conditions are established under which, after a short transient, reversible adsorption or coagulation can be treated by neglecting accumulation at the secondary minimum. The effect of tangential velocity of particles on the rate of reversible adsorption is analyzed and a criterion established when the effect... 

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