Models of the liquid state

MSE.6. 1. Prigogine et G. Garikian, Sur le modele de I etat liquide de Eennard-Jones et Devonshire (On the Lennard-Jones and Devonshire model of the liquid state), J. Chim. Phys., 45, 273-289 (1948). 

Thus our stochastic model predicts a monotonic decay of D(t) and Dj t). This may be valid for gases, but it is incorrect for liquids. From our computer experiments we saw that there are negative regions in both D(t) and Djit) in liquids. Thus we must search for better models of the liquid state. 

Liquid-Phase Models. Theoretical models of the liquid state are not as well established as those for gases consequently, the development of general equations for the description of liquid-phase equilibrium behavior is not far advanced. Cubic equations of state give a qualitative description of liquid-phase equilibrium behavior, but do not generally yield good quantitative results (3). For engineering calculations, equations and estimation techniques developed specifically for liquids must normally be used. 

Inspection of Eq. 7 reveals that the molecular interference function, s(x), can be derived from the ratio of the total cross-section to the fitted IAM function, when the first square bracketed factor has been accounted for. A widely used model of the liquid state assumes that the molecules in liquids and amorphous materials may be described by a hard-sphere (HS) radial distribution function (RDF). This correctly predicts the exclusion property of the intermolecular force at intermolecular separations below some critical dimension, identified with the sphere diameter in the HS model. The packing fraction, 17, is proportional for a monatomic species to the bulk density, p. The variation of r(x) on 17 is reproduced in Fig. 14, taken from the work of Pavlyukhin [29],... 

Why give these liquids special consideration Are not the concepts developed for understanding molten salts adequate for understanding molten oxides The essential features of fused salts ema-ge from models of the liquid state. Tha-e is no doubt that the fluidity of molten salts demands a model with plenty of free space, and a model based on density fluctuations that are constantly occurring in all parts of the liquid seems about the best way to think of the inside of a molten liquid. Is the same dependence on the opening up of temporary vacancies an adequate basis for explaining the behavior of the fused oxides ... 

Itinerant Oscillator. The itinerant oscillator model of dielectric response was introduced by Hill." It has considerable attraction as a model of the liquid state, and the name has become well known since Sears " used... 

The regular solution model provides no explanation of this excess entropy, nor can it account for a volume change on mixing. To study these problems we need a more detailed model of the liquid state which will enable us to relate these excess quantities to intermolecular forces. 

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 liquids28 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. 

The van der Waals equation of state can be replaced by better models of the liquid state, for example, the gas of hard spheres with intermolecular attractions superimposed (78), or the Lennard-Jones and Devonshire (19) theory of liquids. 

Since the laws of regular solutions closely approximate those derived by statistical mechanics for lattice models of the liquid state in which the partial molal volume of component i in the mixture is equal to the molal volume of pure liquid /, it is sometimes assumed that Vt =... 

Although the lattice model of the liquid state, upon which equations (26) and (27) are based, is open to criticism the treatment does describe a well-defined procedure for dividing a molecule into segments, counting the segment interactions of various kinds, and relating these to the thermodynamic properties of the mixture. The lattice model has frequently been applied at any one of three... 

Fig. 9.9. Two-dimensional model of the liquid state, showing long-range disorder. 

Supposing the potential function to be more or less constant, an initial model of the liquid state was proposed. 

This time referring to the local order in a liquid similar to that of a solid, the potential function is given a form very similar to that of a harmonic oscillator. Thus, a second model of the liquid state [MIE 03] was put forward. Beginning with the quasi-crystalline model of a liquid, we suppose that each molecule is in a field of potential whose minimum is (v ,), and that the molecule moves through that field corresponding to a three-dimensional harmonic oscillator of frequency v, which is also a fimction of the volume per molecule v . We use the symbol r to denote the distance from the center of the molecule to the center of the cavity where the minimum potential is in force. At that distanee, the molecule would have a... 

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