Interatomic and Inter molecular Forces and Elastic behaviour of Solid

Elasticity

Elasticity is a property of matter due to which it regains its original configuration when the deforming force is removed. All the three states of matter i.e. solid, liquid and gas exhibit elasticity. If the object perfectly regains its original shape and size after removal of a deforming force, it is said to possess perfect elasticity. If it does not end its original configuration after removal of the deforming force, it is said to have perfect plasticity.

There is no perfect elastic or perfect plastic body. Quartz fibre is supposed as the perfect elastic body.

Deforming Force

The force applied on a body which produces an only change in shape and size of the body and neither causes transitional or rotational motion on it is called deforming force.

Restoring Force

When a body is deformed from its original configuration, a force is developed in the system that tends to bring the body into its original configuration. This opposing force is called restoring force. At equilibrium condition, the magnitude of restoring force is called restoring force. At equilibrium condition, the magnitude of restoring force is equal to applied force. (i.e. deforming force)

Interatomic Forces

The inter-atomic forces are electrical in nature.When two atoms are brought near to each other, then the charges on each atom are distributed. As a result of this, attractive inter-atomic force is produced between them. This inter-atomic force increases as the distance between the atoms decreases. When the distance between two atoms is very small, then the electron clouds of two start overlapping and the inter-atomic force becomes repulsive.

An object is an arrangement of atoms or molecules in three dimension. The variation of Potential Energy (U) with intermolecular distance (r) is as shown in the figure. At equilibrium distance 'r_o' the potential energy is minimum. So, it is the stable state.The variation of inter-atomic force with the distance between atoms is shown in the figure. The inter-atomic force is equal to the negative gradient of the corresponding potential energy function

$$F = -\frac {dU (r)}{dr}$$

Intermolecular Forces

The force which is responsible for holding together the atoms or molecules of a matter is called intermolecular force. When two molecules are far from each other, the force between them is attractive in nature and negligible. As these molecules are brought closer to each other, the force of attraction between them increases. It has been found that the intermolecular force of attraction is inversely proportional to the seventh power of the distance between the molecules

$$\text {i.e.} F_a \propto \frac {1}{r^7}$$

$$\text {or,} F_a =- \frac {A}{r^7}\dots (i)$$

where As constant related to the nature of the molecules.The negative sign indicates that the force is attractive in nature.

As the distance between the molecules is decreased and made equal to the order of the dimension of the molecule, they begin to repel each other. The force changes rapidly than the attractive force. The force varies inversely as the ninth power of the intermolecular separation.

$$\text {i.e.} F_r = \frac {1}{r^9}$$

$$\text {or,} F_r =- \frac {B}{r^9}\dots (ii)$$

where B is constant related to the nature of the molecule.

Thus, the net force acting on a molecule is given by

$$ F =- \frac {A}{r^7} +\frac {B}{r^9}$$

There is a definite distance r_o between the molecules at which the force of attraction and repulsion balance each other and hence the resultant force acting is zero. That is F = 0 at r = r_o.

$$\text {or,}\frac {A}{r_o^7} =\frac {B}{r_o^9}$$

$$\text {or,} r_o = \sqrt {\frac BA} $$

At this stage, the molecules are in the state of stable equilibrium. As the intermolecular separation, r is decreased (i.e. r<r_o) the repulsion component given by equation (ii) dominates the attractive component of the force given by equation (i).

Elastic behaviour of Solid

In a solid , atoms and molecules are arranged in such a way that each molecule is acted upon by the forces due to the neighbouring molecules. The forces area known as intermolecular forces. These forces are known as intermolecular forces. When no external force is applied on the body, each molecule of the solid are maximum.

When a spring is slightly stretched by pulling its ends, the length of spring increases. In other words, the spring is deformed. The force acting on the spring to deform it is known as deforming force.

When the deforming force is applied on a body so that its length increases, then the molecules of the body go far apart. As, a result of this, the spring is slightly stretched and the intermolecular forces get changes which is shown in figure (b).