Lennard-Jones Devonshire

Detonation pressure may be computed theoretically or measured exptly. Both approaches are beset with formidable obstacles. Theoretical computations depend strongly on the choice of the equation of state (EOS) for the detonation products. Many forms of the EOS have been proposed (see Vol 4, D269—98). So.far none has proved to be unequivocally acceptable. Probably the EOS most commonly, used for pressure calcns are the polytropic EOS (Vol 4, D290-91) and the BKW EOS (Vol 4, D272-74 Ref 1). A modern variant of the Lennard Jones-Devonshire EOS, called JCZ-3, is now gaining some popularity (Refs -11. 14). Since there is uncertainty about the correct form of the detonation product EOS there is obviously uncertainty in the pressures computed via the various types of EOS ... 

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]. 

Fur die Berechnung des Detonationsdruckes, sowie der Geschwindig-keit der ebenen Detonationswelle nach der - Chapman-Jouget Theo-rie, wurden wahrend der letzten funfzig Jahre hauptsachlich die Becker-Kistiakowsky-Wilson (BKW)-, die Lennard-Jones-Devonshire (LJD)- und die Jacobs-Cowperthwaite-Zwisler (JCZ)-Zustandsglei-chung verwendet. 

When we consider a van der Waals system, we can start with the pair interaction as shown in Figure 2.2. The equation giving the pair potential is the 6-12 or Lennard-Jones-Devonshire equation ... 

Figure 2.2 Illustrative plot of the Lennard-Jones-Devonshire interatomic potential showing the force and the modulus curve for the pair interaction. Positive values indicate repulsion and negative values indicate attraction...

MSE.9. 1. Prigogine et P. Janssens, Une generalisation de la methode de Lennard-Jones-Devonshire pour le calcul de I integrale de configuration (A generalization of the Lennard-Jones and Devonshire method foir the calculation of the configuration integral), Physica 16, 895-906 (1950). 

Equation of state discussed in these papers is given in this Volume under Detonation (and Explosion), Equations of State", as Lennard-Jones Devonshire Equation of State"... 

Lennard-Jones Devonshire (LJD) Equations of State. For gases of low density, the following equation of LJD (Ref lb, p 55) applies ... 

Other virial equations are those of Kihara Hikita (item k2) and of Lennard-Jones Devonshire (item I4)... 

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... 

CA 55, 24011(1961) (Equation of state of the products in. RDX detonation) Mj) W. Fickett, "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermo-lecular Potentials , Los Alamos Scientific Laboratory Report LA-2712(1962), Los Alamos, New Mexico, pp 9-10 (Model of von Neumann-Zel dovich), pp 153-66 [Comparison of KW (Kistiakowsky-Wilson) equation of state with those of LJD (Lennard-Jones-Devonshire) and Constant-/ ] M2) C.L. 

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

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

Since the Eq must describe states ranging from the ideal gas to the dense compressed state, the G factor must reduce to the virial expansion at low density and must approach the value determined by the repulsive potential at the high density limit. Dr. Jacobs took a semiempirical approach to this problem and used the results of Monte Carlo (MC) and Lennard-Jones Devonshire (LJD) calculations to determine unknown parameters in theoretical expressions for p0(v) and G(v,T). ... 

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. 

There are substantially fewer MC studies of hydrates than there areMD studies. The initial MC study of hydrates was by Tester et al. (1972), followed by Tse and Davidson (1982), who checked the Lennard-Jones-Devonshire spherical cell approximation for interaction of guest with the cavity. Lund (1990) and Kvamme et al. (1993) studied guest-guest interactions within the lattice. More recently Natarajan and Bishnoi (1995) have studied the technique for calculation of the Langmuir coefficients. 

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... 

Except for oxygen-balanced expls, the computation of detonation products depends strongly on the choice of the equation of state (EOS) for these products. In the US the BKW EOS (see Vol 4, D272-R) has been favored and most of the computed product compns below will be based on it. Some of these will be compared with the relatively few calcns based on a Lennard-Jones-Devonshire (UD) EOS (see Vol 4, D287-L) CJ state product compns calcd via the BKW EOS are compared with compns computed with LJD types of EOS in Tables 2—4. For PETN (Table 2) an early variant of the LJD EOS (Ref 1) shows no solid C in the products and somewhat more CO than the BKW computation. Note that for PETN both EOS give product compn that show relatively little variation with p q, the initial density of the expl. This is not the case for RDX and TNT (Tables 3 4) where a change in Pq results in substantial changes in product compn. 

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]. 

Note that both models yield satisfactory results on this point. However, it is important to apply the comparison to several types of results. For example. Figure 1.11 shows that, for the representation of the distribution function, Lennard-Jones and Devonshire s model, Eyring s model and the calculations performed by numerical simulation are very similar. Meanwhile, Figure 1.12, which gives the variation of the compressibility coefficient as a function of a reduced volume, illustrates the significant behavioral difference between the molecular dynamics simulation and Eyring s model, on the one hand, and Lennard-Jones/Devonshire s, Guggenheim s (see section 1.3.1)... 

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