Lennard-Jones potential parameters

Table B1 Lennard-Jones (6-12) potential parameters and critical properties...

Table B1 Lennard—Jones (6—12) Potential Parameters and Critical Properties...

Table 3.2 Lennard-Jones potential parameters found from viscosities (Cussler, 1997)...

Lennard-Jones potential parameters ([Pg.612]

Table 7.2 Lennard-Jones potential parameters used in the simulations for assembling D4R units. Reproduced with permission of John Wiley Sons, Ltd and the American Chemical Society...

There exist several linkages of the SBUs which should be avoided, for example, the short separation of two metal atoms (M Mj), one ligand atom and one bridging atom (Lj Bj), and L Mj in SBUs unlinked. To prevent these undesirable linkages, other potential functions have to be considered, including the repulsive potential between Mj Mj pairs, the attractive potential between L, - - - Mj pairs, and the repulsive potential between Lj Bj pairs. A repulsive potential between Mr Mj pairs prevents SBUs from overlapping with each other. The distance between the Mr Mj pair is limited to 3.4 A for D4R. The Lennard-Jones potential parameters used in assembling the D4R are provided in Table 7.2. 

Table 7.3 Lennard-Jones potential parameters used in the simulations for assembling ML4 units...

The above description has illustrated the computational design of new inorganic frameworks constmcted from D4R units. Other types of SBUs are also allowed in this method. If ML4 (M—L = 1.65 A) is used as the SBU (Lennard-Jones potential parameters are given in Table 7.3), the potential function of SBU in the unit cell is calculated by Equation (7.3) [35]... 

By use of these formulas accurate calculations of the transport coefficients can thus be performed provided that the Lennard-Jones potential parameters like i and ci are known. Extensive lists of these parameters are given for many substances by Hirschfelder et al [39] and Bird et al [5], among others. 

The Lennard-Jones potential parameters a, p, Gap are chosen [20] to agree with diffraction experiments [17]. The charge q has been computed with the help of a linear combination of plane orbitals (LCPO) [37] or of Gaussian orbitals (LCGO). In both cases, q is significantly less than le qp = 0.1c in TeFe (LCPO) qp = 0.25e in TeFe (LCGO) [38]. 

Figure 4 Time-dependence of temperature, uniaxial stress in the shock propagation direction, and volume calculated for an elastic-plastic shock in the [111] direction of a perfect Lennard-Jones crystal. After initial elastic compression, pltistic deformation occurs around 2 picoseconds into the simulation. Lennard-Jones potential parameters have been chosen for Argon. See text for details.

Lennard-Jones Potential Parameters for the Reacting Quaternary Mixture... 

The collision diameter o g is determined from the Lennard-Jones potential parameters for the two molecules... 

Table 15-2. Lennard-Jones potential parameters and values of the collision integral for ideal Fickian gas diffusivity calculation with Chapman-Enskog equation (15-221 (Cussler. 2009 Hirshfelder et aL,...

Assuming the validity of the corresponding states principle, the eos is expressed in reduced variable form, where the reducing parameters, P, T, and V, depend on the two Lennard-Jones potential parameters e and v ... 

Lennard-Jones potential parameters such as collision diameter. Gay and energy of interaction, e y for nonpolar and nonreacting molecule pairs can be computed from the corresponding values of pure component species based on the following rules ... 

First, estimate the Lennard-Jones potential parameters from Equation 6.110... 

Use of this potential can then provide a quantitative measure of cohesion in these solids. One measure of the strength of these potentials is the vibrational frequency that would correspond to a harmonic oscillator potential with the same curvature at the minimum this is indicative of the stiffness of the bond between atoms. In Table 1.1 we present the frequencies corresponding to the Lennard-Jones potentials of the common noble gas elements (see following discussion and Table 1.2 for the relation between this frequency and the Lennard-Jones potential parameters). For comparison, the vibrational frequency of the H2 molecule, the simplest type of covalent bond between two atoms, is about 500 meV, more than two orders of magnitude larger the Lennard-Jones potentials for the noble gases correspond to very soft bonds indeed ... 

Fig. 5.3 Density as a function of temperature at 1 bar pressure, averaged over five sampies of polyethylene model PE I, with a degree of polymerization of 1000. The cooling rate was about K ps but at each temperature the samples were relaxed for about a further 1 ns. The Lennard-Jones potential parameters for the van der Waals interactions were adjusted to give a density at SOO K which agreed with a linear extrapolation of experimental data (see text for further details). Also shown are data reported for a sample of model PE III polyethylene cooled at a comparable rate. ...

In the Yukawa potential, A is an inverse range parameter. The value A = 1.8 is appropriate for the inert gases. Each of the above potentials has a hard core. Real molecules are hard but not infinitely so. A slightly softer core is more desirable. The Lennard-Jones potential... 

Figure 2.10. Part of the better description of the Morse and Exp.-6 potentials may be due to the fact that they have three parameters, while the Lennard-Jones potential only employs two. Since the equilibrium distance and the well depth fix two constants, there is no additional flexibility in the Lennard-Jones function to fit the form of the repulsive interaction.

In these equations, a and e are parameters in the Lennard-Jones potential function for interactions between unlike molecules, the customary mixing rules were used ... 

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