# EoS: Intermolecular Potentials

### 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