Lennard-Jones Devonshire theory

Detonation, Lennard-Jones-Devonshire Theory. See Detonation, Free Volume Theory of LJD (Lennard-Jones-Devonshire)... 

The Lennard-Jones-Devonshire theory (as summarized by Fowler and Guggenheim, 1952, pp. 336ff) averaged the pair potentials of Equation 5.24a and b between the solute and each water, for Zi molecules in the surface of the spherical cavity to obtain a cell potential r) of... 

The experimentally fitted hydrate guest Kihara parameters in the cavity potential uj (r) of Equation 5.25 are not the same as those found from second virial coefficients or viscosity data for several reasons, two of which are listed here. First, the Kihara potential itself does not adequately fit pure water virials over a wide range of temperature and pressure, and thus will not be adequate for water-hydrocarbon mixtures. Second, with the spherical Lennard-Jones-Devonshire theory the point-wise potential of water molecules is smeared to yield an averaged spherical shell potential, which causes the water parameters to become indistinct. As a result, the Kihara parameters for the guest within the cavity are fitted to hydrate formation properties for each component. 

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]. 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

Detonation, Free Volume Theory of the Liquid State Developed by Eyring et al and by Lennard-Jones-Devonshire. The free volume theory of the liquid state developed by Eyring Hirshfelder (Ref 1) and by Lennard-Jones Devonshire (Ref 2) has provided a useful approximate description of the thermodynamic props of liquids in terms of intermolecular forces... 

Detonation, free volume theory of the liquid state developed by Eyring et al and by Lennard-Jones-Devonshire 4 D349... 

Next to the - Chapman-Jouget theory, during the last 50 years, the principal methods of calculating detonation pressure and the velocity of flat detonation waves have been the Becker-Kistiakowsky-Wilson (BKW), the Lennard-Jones-Devonshire (LJD) and the Jacobs-Cow-perthwaite-Zwisler (JCZ) equations of state. 

The other cause, the density effect, is especially important at high densities, where molecules are more or less confined to cells formed by their neighbors. In analogy to the well-known quantum mechanical problem of a particle in a box, the translational energies of such molecules are quantized, and this has an effect on the thermodynamic properties. In 1960 Levelt Sengers and Hurst [3] tried to describe the density quantum effect in term of the Lennard-Jones-Devonshire cell model, and in 1980 Hooper and Nordholm proposed a generalized van der Waals theory [4]. The disadvantage of both approaches is that, in the classical limit, they reduce to rather unsatisfactory equations of state. 

Free Volume Theory of the Liquid Stote Developed by Eyring et ol and by Lennard-Jones Devonshire. See Vol 4, pp D349-L R... 

Lennard-Jones, J., and A. Devonshire. 1939. Critical and Co-operative Phenomena IV. A Theory of Disorder in Solids and Liquids and the Process of Melting. Proc. R. Soc. London, Ser. A, Vol. 170, 464. 

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. 

A. The cell model theoiy. The cell model theory was first introduced by Lennard-Jones and Devonshire to calculate the bulk properties of molecular fluids (Barker, 1%3). In this approach, the array of particles is replaced by an array of hypothetical cells inside which the movement of each particle is confined. 

The most successful equation of state for semicrystalline polymers such as PE and PA stems from two unlikely sources (1) calculation of 5 = a of polymeric glasses at T< 80K [Simha et al., 1972] and (2) the Lennard-Jones and Devonshire (L-JD) cell model developed originally for gases and then liquids. Midha and Nanda [1977] (M-N) adopted the L-JD model for their quantum-mechanical version of crystalline polymers, taking into account harmonic and anharmonic contributions to the interaction energy. Simha and Jain (S-J) subsequently refined their model and incorporated the characteristic vibration frequency at T= 0 K from the low-Tglass theory [Simha and Jain, 1978 Jain and Simha, 1979a,b] ... 

Using the theory of Lennard-Jones and Devonshire for the description of the liquid state, De Boer and Lunbeck have calculated Pci and Pj at various values of v and T. Their expression of the reduced equation of state differs from (V-21) only by the fact that Aes is replaced by A. 

A theoretical treatment of order-disorder phenomena in molecular crystals has been developed by Pople and Karasz. The theory considered disorder in both the positions and orientations of the molecules and it was assumed that each molecule could take up one or two orientations on the normal, a-, and the interstitial, ]8-, sites of the two-lattice model proposed by Lennard-Jones and Devonshire in their treatment of the melting of inert gas crystals. The theory introduced a single non-dimensional parameter, v- related to the relative energy barriers for the... 

Reuter, J. Buesing, D. Tamarit, J. L. Wiirflinger, A. High-pressure differential thermal analysis of the phase behavior in some rm-butyl compounds, J. Mater. Chem. 1997,7,41 6. This paper also discusses some phenomenological theories of crystal melting (like the Pople-Karasz theory, 1961) that take into account orientational disorder in the solid, based on ideas presented in 1939 by Lennard-Jones and Devonshire. The essential parameter of such a theory is the ratio of the barriers to reorientation and to diffusion, which is also a measure for the anisotropy in molecular shape. 

Once the mean potential to r) is known, we may use the general relations (7.1.3)-(7.1.6) to compute the thermod3mamic functions. This can imfortunately not be done in closed form because of the complicated analytical form of the mean potential. However, tables of the cell partition function W and its derivatives with respect to volume and temperature now exist (Lennard-Jones and Devonshire [1937, 1938], Hill [1947], Prigogine and Garikian [1948], Wentorf, Buehler, Hirschfelder and Curtiss [1950], Hirschfelder, Curtiss and Bird [1954]), which permit to compare the Lennard-Jones and Devonshire theory with experimental data. 

The main progress in the theory of concentrated solutions came from two somewhat complementary directions of approach. A decisive step toward the understanding of the liquid state was made in 1937 by Lennard-Jones and Devonshire using a free volume theory (or cell model). Before Lennard-Jones and Devonshire, the cell model had been used by many authors (mainly by E3rring and his coworkers) to correlate the thermodynamic properties of liquids. However, Lennard-Jones and Devonshire were the first to use it to express the thermodynamic properties in terms of intermolecular forces (as deduced for example, from drial measurements). 

Simple Cell Model of Prigogine et al. The cell model by Frigogine et al. (10-12) is an extension of the cell model for small molecules by Lennard-Jones and Devonshire (68) to polymers. Each monomer in the system is considered to be trapped in the cell created by the surroimdings. The general cell potential, generated by the smroimdings, is simplified to be athermal. This turns the simple cell model into a free volmne theory. The mean potential between the centers of different cells are described by the Lennard-Jones 6-12 potential. The dimensionless equation of state has the following form ... 

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