7.4b.2 Van der Waals Equation of State for Monolayers

We noted above that the applicability of Equation (14) to insoluble monolayers is severely restricted to very low values of *π*. Figure 7.10 shows that the deviations from Equation (14) with increases in *π* are very similar to what is observed for nonideal gases. Specifically, the positive deviations associated with excluded volume effects in bulk gases and the negative deviations associated with intermolecular attractions are observed. It is tempting to try to correct Equation (14) for these two causes of nonideality in a manner analogous to that used in the van der Waals equation:

$\left(\pi +\frac{a}{{\sigma}^{2}}\right)(\sigma -b)={k}_{B}T$ |
(15) |

where *a* and *b* are the two-dimensional analogs of the van der Waals constants. Note that ...

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