### Intermolecular forces and potentials

So far, we have discussed attractive portion of potentials. The
simplest way to include the idea of excluded volume is to assume a
"hard sphere" repulsion when the molecules approach too closely.
That is, we assume an impenetrable molecule radius, $\sigma$.

$\Gamma = 0$ for $r > \sigma$

$\Gamma = \infty$ for $r \le \sigma$

##### DEFINITION

The simplest total model of intermolecular potential available
is the **Sutherland Potential** which simply adds van
der Waals potential(s) to the hard sphere potential.

$\Gamma = \frac{-(C_6)}{r^6}$ for $r > \sigma$

$\Gamma = \infty$ for $r \le \sigma$

##### DEFINITION

A more "realistic" model of intermolecular potential is the
**Lennard-Jones Potential** which includes van dew
Waals-like attraction and a strong (but not hard sphere)
repulsion.

$\Gamma = 4\epsilon \left [ \left (\frac{\sigma}{r}
\right )^{12} - \left ( \frac{\sigma}{r}\right )^6 \right
]$

##### Outcome

Define a potential function

##### Outcome

Write equations for ideal gas, hard sphere, Sutherland, and
Lennard-Jones potentials and relate them to intermolecular
interactions