Lennard-Jones, generally mixture

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Figure 3. Generalized thermodynamic quantities calculated for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right) the generalized dilatation 6(k) the generalized linear thermal expansion coefficient ckt (fc) the generalized specific heat at constant volume Cy (fc) (the filled boxes at k = 0 correspond to the values obtained directly in MD simulations) and the generalized ratio of specific heats 7(k).

Figure 7. Generalized fc-dependent thermal conductivity obtained for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right).

Both types of functions are commonly used. Several sets of a, b, c, and d, coefficients are available [1-3]. Equally good results can be obtained using Lennard-Jones-type functions alone or Buckingham-type functions alone or mixtures of Lennard-Jones and Buckingham functions [4]. The attraction coefficients in these expressions are generally but not always calculated with the formula of Slater and Kirkwood [5] ... 

Droplets. - Liquid droplets and curved hquid surfaces in general have been the subject of some attention by MD and MC for about 30 years. A recent example of a simulation in this category was carried out by Ikoshoji et al They gradually cooled binary Lennard-Jones mixtures until they crystallised into icosahedrons or fee structures, depending on the system size. 

I - general interaction coefficient in the enhancement factor equations K = dummy constant used to write general mixture rules L-J = Lennard-Jones... 

In general, there are two methods that can be applied in order to describe Bx(T) (x = T], X) The most up-to-date theory, proposed by Friend Rainwater (1984 Rainwater Friend 1987), models the moderately dense gas as a mixture of monomers and dimers which interact according to the Lennard-Jones (12-6) potential. Besides the fact that this potential is only a rough approximation of the real physical situation, this model has the disadvantage that it has not yet been extended to describe the internal contribution to the initial density dependence of thermal conductivity. 

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