Origins of molar volume isotope effects in hydrocarbon systems

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Abstract
Lattice dynamics calculations are carried out on the hydrogenated and deuterated forms of crystalline polyethylene to elucidate the origins of the molar volume isotope effect. These calculations focus on the consequences of molecular packing on the vibrational free energy, rather than the differences between the C–H and C–D bond lengths arising from differences in the vibrational amplitudes which has been the standard theory for the molar volume isotope effects. It is found that a significant molar volume isotope effect occurs even in the absence of C–H and C–D bond length differences, and is due to differences in intermolecular separations (i.e., H...H or D...D nonbonded distances) rather than intramolecular bond lengths. This effect arises primarily from the volume dependence of the C–H/D stretching frequencies. The total molar volume isotope effect will include both the intermolecular effects described here, plus the intramolecular C–H/D bond length effects described previously. These results show that the standard theory for the molar volume isotope effect, based on the differences in the C–H and C–D bond lengths, is not complete.