Mixed pair interaction energies

Fig. 1. The mixing energies agree rather well with the results of Pasturel et al. and those of Abrikosov et al. . The pair interaction i> (c) is In a very good agreement with the locally relaxed quantity given by Carlsson, and also it is rather similar to the effective pair interaction found by Pasturel et al., although it is smaller approximately by a factor 0.7. The pair interaction u (c) differs from the corresponding quantity reported by Abrikosov et al. , which can be probably attributed to different computational schemes, as we assume neutral spheres, while Abrikosov et al. suppose equal sphere radii. The pair interaction (c) closely follows u (c) for Ni-rich alloys and v (c) for Al-rich alloys, at intermediate concentrations all three quantities...

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

The various factors affecting the entropies of mixing and rotation of the dimethylcyclohexanes are collected in Table 1. For computation of equilibria in such a complex system it is convenient to define an equilibrium constant, as being the ratio of two isomers that differ by only one, gauche interaction. Then for a pair of isomers that differ in energy by n interactions,... 

Mixing rules are available to extend the models to multicomponent systems, with the use of adjustable binary parameters. In the absence of associating sites, we will consider only the binary interaction parameter which enters the mixing mle for the characteristic interaction energy between pairs of unlike segments i and j ... 

In ideal solutions it is assumed for the pair interactions that no energy is released on replacing a unit of group 1 by a unit of group 2, that is, Ae in Equation (6-11) equals zero. Consequently, the enthalpy of mixing of an ideal solution is also equal to zero. 

At the right-hand side of (10.8), the first five terms come from Floiy s semiflexibility treatment (8.55), the sixth term comes from the mean-field estimation for the pair interactions of parallel bonds (10.7), and the last term comes from the mean-field estimation for the mixing interactions between the chain units and the solvent molecules (8.21). According to the Boltzmann s relation F = —kTlnZ, the free energy of the solution system can be obtained as... 

The same positive AH, which arises from interactions between different species, usually prevails in polymer mixtures and most polymer pairs are mutually immiscible. The strengths of the interactions between components is usually expressed in terms of an interaction parameter Xab (Eq- 3), which originates from Flory-Huggins theory of polymer solutions. The enthalpy of mixing, or interaction energy term, arises in a van Laar type expression of heats of mixing and is of the form... 

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