Coulombic forces, stabilization

Now lei us turn to the problem of how the composition of a nucleus affects its stability. The forces that exist between the particles in the nucleus are very large. The most familiar of ihe intranuclear forces is the coulomb force of repulsion which the protons must exert on one another. In order to appreciate the magnitude of this repulsive force, let us compare the force between two protons when they are separated by 10 8 cm, as they are in the hydrogen molecule, with the force between two protons separated by 10-18 cm, as they are in a helium nucleus. In the first case we have... 

As long as we only assume coulomb forces and repulsive forces of the type discussed, this contraction leads to the surprising result that the CsCl lattice can never be formed. It can only exist if the lattice energy of the CsCl lattice is smaller, or at least equal to that of the NaCl lattice. The conditions for the stability of the CsCl lattice are... 

In Figure 2.3, we compare the positions of the known stable nuclides of odd A with those of even A in the chart of the nuclides. Note that as Z increases, the line of stability moves from N = Z to N/Z 1.5 due to the influence of the Coulomb force. For odd A nuclei, only one stable isobar is found while for even A nuclei there are, in general, no stable odd-odd nuclei. This is further demonstrated by the data of Table 2.1 showing the distribution of stable isotopes. 

Enzymes are a class of macromolecules with the ability both to bind small molecules and to effect reaction. Stabilizing forces such as hydrophobic effects only slightly dominate destabilizing forces such as Coulombic forces of equal polarity thus the Gibbs free enthalpy of formation of proteins, AGformation, is only weakly negative. 

We have now seen how the attraction of charges and the interaction of frontier orbitals combine to make a reaction between two such species as the allyl anion and allyl cation both fast and highly regioselective. We should remind ourselves that this is not the whole story another reason for both observations is that the reaction is very exothermic the energy of a full a bond is released with cancellation of charge, which would not be the case if reaction took place at C-2 on either component. Thus we are in the situation of Fig. 3.1a—the Coulombic forces and the frontier orbital interaction on one side, and the stability of the product on the other, combine to lower the energy of the transition structure. 

Structurally, HMX exhibits conformational polymorphism, as demonstrated in Fig. 9.1. Brill and Reese (1980) analysed the relative stabilities of the a, p and 8 forms in terms of coulombic forces to interpret the thermophysical behaviour of the three forms. They concluded that the chair conformation found in the p modification is more stable than the chair-chair conformation in the other two forms. The relative stability to pyrolysis could also be accounted for by the analysis of the coulombic attractions and repulsions around the molecule in each of the modifications. More recently, Henson et al. (1999) have followed the change in second harmonic generation response during the jS -> 5 phase change, which has long been implicated in the thermal decomposition of HMX (Karpowicz and Brill 1982). 

In order to account for the stability of ionic crystals it is necessary to introduce repulsive forces between the ions in addition to the ordinary coulombic forces. Bom and Lande (20), in their original treatment of the problem, represented these forces as varying as the inverse nth power of the distance and treated the potential energy of the crystal as the sum of two terms, given by the expression... 

The arrows in Figure 19.1 show the directions of the types of decay discussed so far. Nuclei whose values of N/Z are too great move toward the line of stability by beta emission, whereas those whose values are too small undergo positron emission or electron capture. Nuclei that are simply too massive can move to lower values of both N and Z by alpha emission. The range of stable nuclides is limited by the interplay of attractive nuclear forces and repulsive Coulomb forces between protons in the nucleus. Scientists believe that it is unlikely that additional stable elements will be found, although long-lived radioactive nuclides may well exist at still higher Z. 

These interactions are frequently ionic in character. The coulombic forces of interaction between macroions and lower molecular weight ionic species are central to the life processes of the cell. For example, intermolecular interactions of nucleic acids with proteins and small ions, of proteins with anionic lipids and surfactants and with the ionic substrates of enzyme catalyzed reactions, and of ionic polysaccharides with a variety of inorganic cations are all improtant natural processes. Intramolecular coulombic interactions are also important for determining the shape and stability of biopolymer structures, the biological function of which frequently depends intimately on the conformational features of the molecule. 

Complex formation between drugs and excipients often leads to stabilization of drugs. The forces involved in complex formation include van der Waals forces, dipole-dipole interactions, hydrogen bonding, Coulomb forces, and hydrophobic interactions. 

Current research on nuclei, their properties, and the forces that hold them together focuses on studying nuclei at the limits of stability. The basic idea is that when one studies nuclei under extreme conditions, one then has a unique ability to test theories and models that were designed to describe the normal properties of nuclei. One limit of nuclear stability is that of high Z, that is, as the atomic number of the nucleus increases, the repulsion between the nuclear protons becomes so large as to cause the nucleus to spontaneously fission. The competition between this repulsive Coulomb force and the cohesive nuclear force is what defines the size of the Periodic Table and the number of chemical elements. At present there are 112 known chemical elements, and evidence for the successful synthesis of elements having the atomic numbers 114 and 116 has been presented. 

We can imderstand why the N Z ratio must increase with atomic number in order to have nuclear stability when we consider that the protons in the nucleus must experience a repulsive Coulomb force. The fact that stable nuclei exist means that there must be an attractive force tending to hold the neutrons and protons together. This attractive nuclear force must be sufficient in stable nuclei to overcome the disruptive Coulomb force. Conversely, in unstable nuclei there is a net imbalance between the attractive nuclear force and the disruptive Coulomb force. As the number of protons increases, the total r ulsive Coulomb force must increase. Therefore, to provide sufficient attractive force for stability the number of neutrons increases more rapidly than that of the protons. 

Electron transfers and the formation of stable ions depend upon the Coulomb forces, and upon the regulating character of the Pauli principle. The nature of atomic stability has already been discussed, and it can be said that an ion is simply a more stable form of atom. The problem of how it disposes itself with other ions to achieve an overall electrical neutrality is, from the point of view of the theory of atomic structure, a secondary matter but from another point of view it presents us with a quite fundamental question. Prom what has been said so far it cannot be concluded that the nature of the metallic state is at all obvious, and yet this is one of the commonest conditions which matter assumes. The constitution of the metallic state therefore calls for special consideration. 

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