Cell theory of liquids

Because of the high symmetry of the main cavities of sieve A, it might seem reasonable, in the spirit of the cell theory of liquids (5), to assume that the various charged species of the zeolite are distributed with complete spherical symmetry about the center of each cavity. This, of course, leads to zero electric field throughout the cavity and hence to zero contribution from ion-induced dipole and similar forces. The remaining terms, dispersion and repulsion, are assumed to be of the Lennard-Jones form and are taken to be additive. This theory then becomes essentially the same as the cell theory of liquids, except that we permit several molecules per cell. The total P.E. is given as = 299(fi) +... 

In view of the failure of the rigid sphere model to yield the correct isochoric temperature coefficient of the viscosity, the investigation of other less approximate models of the liquid state becomes desirable. In particular, a study making use of the Lennard-Jones and Devonshire cell theory of liquids would be of interest because it makes use of a realistic intermolecular potential function while retaining the essential simplicity of a single particle theory. The main task is to calculate the probability density of the molecule within its cell as perturbed by the steady-state transport process. 

Note that the combination of solid-like and gas-like components is an alternative way to obtain the reduction in the entropy value from that in the gas state. In the cell theory of liquids, one uses an excluded volume to capture the constraint of the molecules. Here the reduction is obtained by giving a lower-than-unity value to the gas component. 

Recently an approach to obtain the entropy of water If om the well-known cell theory of liquids has been developed by Henchman [13] and provides not only quantitative accuracy but also valuable insight into the origin of the entropy of liquid water. We shall briefly discuss the theory in the following. 

Cell or lattice models. Cell theories of liquids, such as the Lennard-Jones-Devonshire theory [177] have been applied to adsorption phenomena. For example, cell models including lateral interactions [178] permit the interpretation of experimental isosteric heats in multilayer adsorption [179,180]. 

Tn recent years, developing interests in surface energetics and adhesion of liquid-like polymers, or polymer liquids, have prompted both theoretical and experimental work on surface tension. Unlike low molecular weight liquids, polymer liquids have not been extensively studied. Bondi and Simkin (1) mentioned surface tension in their study on high molecular weight liquids. Roe (28) applied both the cell theory of polymer liquids and the hole theory of surface tension of simple liquids to develop an approximate theory of surface tensions of polymer liquids. His approach has met some degree of success. Notably, both Bondi s and Roes work are somewhat related to the cell theory introduced by Prigogine and... 

Thus surface tensions or surface energies of some simple liquids have already been calculated in terms of intermolecular forces from theories which are based on some simplifying assumptions such as the cell model of liquid structure. The results are in good agreement with observed values. 

If valid, such a crude theory of metals should in a certain sense be analogous to the cell theory of ordinary liquids, which also involves two molecular parameters e and cr. It would then be possible to develop along the same lines a theory of metallic solutions. The excess thermodynamic properties of a mixture of two metals A and B would then depend on the differences ( a b) 3-nd (ZoA — > ob)- That this theory is very rough for pure metals is not a limitation for its applicability to mixtures it is indeed well known from the theory of non-electrolyte solutions that the properties of mixtures may be reasonably analyzed from rather crude statistical models. 

The modeling of the formation of solutions that we have described assumes that there is no change in volume in mixing. Theories of liquids that consider cell models... 

Simha, R., and Hadden, S. T., Application of cell theory to liquid hydrocarbons, J. Chem. Phys., 25, 702-709 (1956). 

G. Meyer and S. W. J. Smith pointed out that Planck s theory of liquid contact potentials (see p. 705), since the ions of KCl and KI have practically equal mobilities, shows that there should be no contact potential between their solutions, and hence a cell formed from dropping electrodes in each should have practically no e.m.f. But Meyer found 0 284 volt and Smith 0 256 to 0 262 volt. Hence part of the potential difference at the electrode depends on the anion and is not eliminated. 

Theories of Liquid Mixtures 2.5.1 Lattice, Cell, and Hole Theories... 

The hole theory of liquids may be considered as a special case of the cell theory including multiple cell occupations corresponding to the restriction... 

In fact the hole theory of liquids was developed before the multiple cell occupation model (Cernuschi and Eyeing [1939], Ono [1947], Peek and Hill [1950], Rowlinson and Curtiss [1951], Mayer and Careri [1952], De Boer [1952]). 

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