Excluded-volume effects of molecular vibrations in a one-dimensional gas

Some thermodynamic properties are found for a system composed of N rod-like molecules in one dimension (1D), where a molecule's length oscillates with an amplitude determined by its (quantized) vibrational energy. Evaluation of the partition function requires integrations over the internal phases describing the oscillations, as well as the molecular positions and momenta. For N > 1 and large system length L, the average energy of the system is increased compared to that for a system of rigid rods as are the entropy and compressibility; the pressure, however, is decreased, and there is a variable effect on the heat capacity. These changes can be traced to an effective increase in the 1D volume available to the molecules, the increase being larger for higher energy states. This behavior is collective: a system composed of a single oscillating molecule mixed with fixed-length rods shows similar alterations in its properties, whereas a single oscillating molecule alone does not (as long as L is greater than the molecule's maximum length). For small N, the oscillations have minimal influence when L is large compared to the combined length of all molecules, but dominate when the two become comparable.