The Two Parameter Model of Atomic Forces

The idea that there were two terms in the expression for the force between atoms and molecules was recognized by Newton, but really began to take shape this century when a number of theorists, like Mie for example, started to formulate mathematical equations to describe both an attractive term and a repulsive term, as shown in Fig. 5.2. 

In this diagram, the potential energy between two atoms is plotted on the vertical axis as the atoms are separated a certain distance, shown horizontally. Conventionally, the attraction is viewed as a negative potential given by the first term of the theory, and the repulsion is seen as positive, i.e. the second term. The two terms added together gave the total picture of the energy as shown in Fig. 5.2. 

From this energy, the force F between the atoms can readily be calculated by taking the gradient of the curve at any point, as shown on the top curve. Thus the force is zero at the minimum of the energy curve. The minimum of the force curve is where the bond breaks as the atoms are pulled apart. This is the maximum tension which can be supported by the attraction. 

The top curve shows that there is a minimum in the energy e at a separation r, . This is the equilibrium point, that is the point at which the repulsion and attraction balance. It is an energy well by analogy with a water well. Thus the atoms sit at the bottom of the energy well. 

Professor of Chemistiy at Cambridge. At the atomic bond level, there is no difference between physics and chemistry. Lennaid-Jones, with his colleagues Taylor and Dent, realized that all known intermolecular forces are electromagnetic in nature. They range from the Coulombic forces between ions, to dipole forces between polar molecules, to the weak van der Waals forces which act between all atoms and which are responsible for adhesion. These adhesive forces, sometimes called London, London-van der Waals or dispersion forces, are always attractive because they result from instantaneous dipoles in one atom and their induced dipoles in a neighboring atom. The Lennard-Jones equation can be written 

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