Molecular Potential and Free Rotation

Thus we pass gradually from the sharp high frequency vibrations of the primary valence bonds by way of the break vibrations into the region 

Valence Forces, Deformation Forces and Nuclear Distances for Tetrahedral Molecules 

It will be convenient to discuss first the conditions obtaining in the simplest appropriate compound—ethane—passing on to more complex conditions and finally to the behavior of high polymeric substances in so far as this is possible. 

Conditions change if the three valences of the two atoms hitherto assumed free are saturated by substituents—perhaps by H atoms— because these can exert forces of attraction and repulsion on one another, whose potential depends upon the angle of inclination, , which the two methyl groups make with each other. Molecular mechanics does not allow of an exact calculation but only of a more or less rough estimate of this potential. Eyring has summarized the results of his studies in a diagram reproduced in Fig. 8, in which the total internal potential of the ethane molecule is expressed as a function of the azimuth p of the methyl groups capable 

It seemed, at first, as if these purely theoretical findings would be confirmed experimentally by some researches of Eucken and his collaborators  

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The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

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