Kinetic theory, of liquids

J. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford, 1946. 

Born M and Green H S 1946 A general kinetic theory of liquids I. The molecular distribution functions Proc. R. Soc. A 188 10... 

Born M and Green H S 1949 A General Kinetic Theory of Liquids (Cambridge Cambridge University Press)... 

Frenkel, J. Kinetic theory of liquids, New York Dover Publ. 1955... 

A very much more detailed and illuminating theory for radical combination based on the kinetic theory of liquids was developed by Kapral et al. [285, 286]. This is considered in Chap. 12. 

By contrast, when both the reactive solute molecules are of a size similar to or smaller than the solvent molecules, reaction cannot be described satisfactorily by Langevin, Fokker—Planck or diffusion equation analysis. Recently, theories of chemical reaction in solution have been developed by several groups. Those of Kapral and co-workers [37, 285, 286] use the kinetic theory of liquids to treat solute and solvent molecules as hard spheres, but on an equal basis (see Chap. 12). While this approach in its simplest approximation leads to an identical result to that of Smoluchowski, it is relatively straightforward to include more details of molecular motion. Furthermore, re-encounter events can be discussed very much more satisfactorily because the motion of both reactants and also the surrounding solvent is followed. An unreactive collision between reactant molecules necessarily leads to a correlation in the motion of both reactants. Even after collision with solvent molecules, some correlation of motion between reactants remains. Subsequent encounters between reactants are more or less probable than predicted by a random walk model (loss of correlation on each jump) and so reaction rates may be expected to depart from those predicted by the Smoluchowski analysis. Furthermore, such analysis based on the kinetic theory of liquids leads to both an easy incorporation of competitive effects (see Sect. 2.3 and Chap. 9, Sect. 5) and back reaction (see Sect. 3.3). Cukier et al. have found that to include hydrodynamic repulsion in a kinetic theory analysis is a much more difficult task [454]. 

Finally, it may be noted that the analysis of homogeneous reaction and of escape/recombination probabilities using the kinetic theory of liquids is rather more complex, but can incorporate all these complications in a more natural and fundamental manner. Kapral and co-workers [37, 285, 286] have made considerable progress in this direction and their work is discussed in Chap. 12. 

Oiffusivity The kinetic theory of liquids is much less advanced than that of gases. Therefore, the correlation for diffusivities in liquids is not as reliable as that for gases. Among several correlations reported, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most widely used for dilute solutions of nonelectrolytes,... 

In terms of molecular theory the meaning of this test for molecular association is rather obscure, and it does not appear to be an independent method of determining molecular association, as it has been discovered as an empirical rule obtaining among compounds known from other evidence to behave normally. Until the kinetic theory of liquids is better understood it seems useless to look to the data of surface tension for information as to molecular complexity. 

Frenkel Yal (1959) Kinetic theory of liquids. USSR Moscow—Leningrad USSR Acad Sci... 

J.H. de Boer, The Dynamical Character of Adsorption. Clarendon Press. Oxford (1953). chapter 1 Ya.I. Frenkel, Kineticheskaya Teoriya Zhidkostei. Engl, transl. Kinetic Theory of Liquids, Dover (1955), p.5ff. 

J. Frenkel, Kinetic Theory of Liquids , University Press, Oxford, 1946 J. G. Kirkwood, Theory of Liquids , ed. B. J. Adler, Gordon and Breach, New York,... 

From kinetic theories of liquids, Milner deduced and Dieterici ... 

The question whether the dispersion bands observed with feebly damped waves by Colley, Obolensky, Romanoff, Potapenko, and others (Handbuch der Physiky 15, 514 et seq. (Berlin, 1927)) in the region of wave-lengths of a few decimetres correspond to intramolecular vibrations might be determined by comparison of the spectra of the vapours with those of the liquids. As is well known, the kinetic theory of liquids has recently exhibited a decided tendency to follow the theory of crystal lattices more closely in many respects for a comprehensive account of some of the most important papers on this subject see K. Jellinek, Lehrbuch der physikalischen ChemiCy 1, 824 et seq, especially pp. 828, 831 (Stuttgart, 1928). 

Frenkel 1.1., The Kinetic Theory of Liquids (in Russian), Ac. Sci. USSR, Moscow, 1945 (peKKen M. M., KHKeTHRecKaa TeopHH jKHAKOCTeii, AKan. HayK CCCP, Mockbr, 1945). Frohberg M. G. and Rohde W., Glastech, Ber, 37 (1964) 453. 

---