Intermolecular potential, effect second virial coefficient

In dilute solution, all macromolecular chains undergo interactions with each other resulting in the so-called intermolecular excluded volume effect, corresponding to the intermolecular potential. This effect is also observed if one does not assume particular cohesive forces to occur between the macromolecular chains. Under these conditions, the second virial coefficient is calculated from the equation1,2) ... 

It is important to note that most treatments using the matrix method for the lattice dynamical treatment of molecular solids adjust the parameters of the potential model to fit observed frequencies. In this case, the formal error in the treatment is minimized in its importance. It may be of importance only inasmuch as the same potential model is assumed to be useful to interpret other physical properties such as gas phase second virial coefficients. It may also be important when one attempts to determine parameters for intermolecular potentials in terms of atom-atom interactions which are general to a class of molecules rather than specific to one substance. It is also evident that the error will be very serious in every case involving low-frequency librations (as for a-Ng). The reason for the small effect of the first derivative term in many cases is as follows. Both repulsive and attractive terms of the potential usually contribute significantly to the first derivative but their contributions have opposite sign and cancel. By comparison, the contribution to the second derivative of the potential is usually much larger for the repulsive potential term than for the attractive term (Shimanouchi, 1970),... 

The second and third virial coefficients in the equation of state of rare gases calculated by the use of Eq. (49) with s = 12 agree with observed values when the nonadditivity of the intermolecular potential is taken into account. If we assume additivity, on the other hand, then we must use an effective intermolecular potential with a wider bowl in order to explain the temperature dependence of the third virial coefficient.In other words, the influence of nonadditivity of the intermolecular potential can, to some extent, be eliminated by using an effective (additive) intermolecular potential with a wider bowl. An appropriate choice seems to be not far from Eq. (50) with a = 8.675, for which the two structures of close packing have exactly equal cohesive energies. 

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