Page 313 - Instant notes

Weak intermolecular interactions 299

These dispersion forces are always attractive, and are independent of temperature. At
sufficiently low temperatures, therefore, all molecular and atomic substances must
condense to either the liquid or solid phase when kT is less than the dispersion energy.

Repulsion energy

At small intermolecular distances, the electron clouds of the molecules begin to
interpenetrate, and a very strong repulsion energy becomes important. It is possible to
express this repulsion term in two forms:

or U(r)=+βexp(−r/ρ)
where b, β, n and ρ are empirical factors whose value is chosen to best fit the data. The
exponential expression is both theoretically and experimentally preferred, but the
differences are minimal. In the former expression, the radius is generally raised to its
twelfth power (i.e. n=12), making the repulsive force insignificant at high r, yet dominant
at low r.

The total intermolecular interaction energy

For the case of dipolar, polarizable, molecules in the gas phase, the total intermolecular
interaction energy is approximately given by the sum of the attractive and repulsive
interaction energies:

where A is a constant. The total interaction simplifies considerably to the expression:

where the constant, C, is the sum of the coefficients in the expressions for the attractive
potentials. The resulting curve is known as the Lennard-Jones potential (Fig. 2). This
plot also enables definition of a collision diameter, σ, which corresponds to the
intermolecular distance at which U(r)=0.