Intermolecular potential, characteristic value

Spherical nonpolar molecules obey an interaction potential which has the characteristic shape shown in Fig. 2. At large values of the separation r it is known that the potential curve has the shape — r 6, and at short distances the potential curve rises exponentially the exact shape of the bottom part of the curve is not very well known. Numerous empirical equations of the form of Eq. (78) have been suggested for describing the molecular interaction given pictorially in Fig. 2. The discussion here is restricted to the two most important empirical functions. A rather complete summary of the contributions to intermolecular potential energy and empirical intermolecular potential energy functions used in applied statistical mechanics may be found in (Hll, Sec. 1.3) ... 

Tbe basic scheme for modeling the phase behavior of binary mixtures is first to input the pure component characteristic parameters Tc, Pc, and to, and then determine the binary mixture parameters, kj. and iij., by fitting data such as pressure-composition isotherms. Normally k.. and tIj. are expected to be lie between 0.200. If the two species are close in chemical ize and intermolecular potential, the binary mixture parameters will have values very close to zero. In certain cases a small value of either of these two parameters can have a large influence on the calculated results. 

We have seen above that the 6-12 Lennard-Jones potential closely approximates intermolecular forces for many molecules. Equation (12) can be made dimensionless by dividing F by e. This results in a universal function in which the dimensionless poten-ial is a function of the dimensionless distance of separation between the molecules, r/a. The energy parameter e. and the distance parameter a. are characteristic values for a given molecule. This is a microscopic theory of corresponding states. It is related to the macroscopic theory through the critical properties of a fluid. Because the critical temperature is a measure of the kinetic energy of fluids in a common physical state, there should be a simple proportionality between the energy parameter e. and the critical temperature Tc. Because the critical volume reflects molecular size, there should also be a simple proportionality between a. and the cube root of Vc. For simple non-polar molecules which can be described by the 6-12 Lennard-Jones potential, the proportionalities have been found to be ... 

The O—H N hydrogen bond in the phenylazoresorcinol monoanion is strong, giving a large and positive value of A[S( H) — 8( H)], characteristic of a double minimum potential (Hibbert and Phillips, 1989). Two examples of intermolecularly hydrogen-bonded species for which the isotope effect on the chemical shift has been measured are also given in Table 5. 

Supercritical Fluid Extraction. The properties of cryogenic fluids under supercritical conditions give them considerable potential for regenerating spent adsorbents. The solution characteristics of the fluid should be compatible with the adsorbed components and, when the fluid is pumped through the adsorbent bed, it will dissolve the adsorbed spiU components. The supercritical fluid can be evaporated easily due to its volatility, and in some cases both the solvent and the contaminant from the spill can be recovered. The high solvation character of the supercritical fluids is due to low intermolecular distances between the solvent molecules. This novel process is expensive at present and therefore the spilled material should be high value added and recoverable, such as pharmaceutical products. 

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