par Prigogine, Ilya 
;Bingen, Roald ;Bellemans, André
Référence Physica, 20, page (633-654)
Publication Publié, 1954
;Bingen, Roald ;Bellemans, André Référence Physica, 20, page (633-654)
Publication Publié, 1954
Article révisé par les pairs
| Résumé : | In the two preceding papers we have discussed the zero-point energy of isotopic mixtures as compared with its value for pure isotopes. Their difference has been shown to be much smaller than the experimental value of the free energy of mixing for isotopic liquid mixtures of light molecules such as H2-D2 and 3He-4He. If the effects of the change in the zero-point energy are completely neglected, it is possible to relate quite easily the properties of the isotopic mixture to those of the pure components. On account of the quantum effects, the volume of the isotopic mixture and that of the pure isotopes are different (for given pressure and temperature values). However if the pure isotopes are first brought to the same volume as they have in the mixture (by compressing one and by applying a “negative” pressure to the other) and then united together, no appreciable change in the free energy should occur (except for the entropy of the mixture). The basic assumption of this paper is therefore introduced in the following form: the free energy of an isotopic mixture is, for given values of volume per particle and temperature, the sum of the free energy of the pure isotopes and of a term due to the entropy of mixing. This assumption is automatically satisfied in simple statistical models of condensed phases like the cell model or an assembly of anharmonic oscillators, the change on mixing of the zero-point energy not being taken into account. It thus constitutes a satisfactory method of approach for the understanding of the thermodynamic properties of isotopic mixtures.From this hypothesis the free energy of mixing, the excess volume and the heat of mixing can be expressed in terms of properties of the pure isotopes only. Striking agreement is reached with the experimental material published up to date on thermodynamic properties of isotopic mixtures (H2-D2, H2-HD, T2-D2, 3He-4He). The present lack of sufficient experimental data unfortunately prevents the testing of many of the predictions of the model.This theory predicts for isotopic mixtures heat absorption and positive deviations from Raoult's law (positive excess free energy and thus phase separation at sufficiently low temperature). On the contrary the sign of the excess volume is more complex: dilatation on mixing is found for cases like H2-D2, H2-HD or D2-T2, but contraction on mixing for 3He-4He. Our method does not, however take account of the influence of quantum statistics and does not permit the study of phenomena such as the effect of the concentration of 3He on the λ point of 4He. The treatment of such effects requires a generalisation of our additivity hypothesis and will be treated separately.Some simple statistical models are considered in some detail in order to understand the thermodynamic properties of the pure isotopes. By applying the fundamental assumption of this paper, the qualitative features of the mixtures can then easily be discussed. The effects calculated in this paper and the change in zero-point energy on mixing are compared; for sufficiently light molecules, the second effect is shown to be indeed negligible in comparison with the first. |
