Paired interactions model

Entropy on the pair interaction model. The entropy of the system in a pair... 

The third factor, ZR, in Eq. (5.1) is called the residual contribution in the chemical engineering notation and it arises from all kinds of non-steric interactions between molecules, i.e., usually from vdW, electrostatic, and hydrogen bond interactions. Despite its name, it is the most important contribution in most liquids. The basic assumption of surface-pair interaction models is that residual—i.e., non-steric—interactions can be described as local pairwise interactions of surface segments. The residual contribution is just the partition sum of an ensemble of pairwise interacting surface segments. 

Kneller E, Puschert W (1966) Pair interaction models for fine particle assemblies. IEEE Trans Magnetics MAG-2 250... 

Box based his explanation (8, 14) of the reverse anomeric effect on the lone-pair interaction model analogous to that presented earlier by Finch and Nagpurkar vide supra). The observed conformational behavior is a result of an interplay of stabilizing and destabilizing interactions. The former consist of attractive, stabilizing interactions between the lone pairs of the 0(1) oxygen and the electron deficient r, or n, orbitals of a substituent, which are favorable in 76e, as shown in Figure 9. The normal steric requirements of... 

If coi is the ensemble of positional coordinates (xi, x 2, x 3), of particle /, between two particles i and j there is an interaction energy % and we assume that the interaction energy only contains terms such as Eij even if several molecules are in mutual interaction. This hypothesis is known as the paired interaction model. The confrgirration integral (see relation [6.28]) has the following form ... 

The pair interaction model, (j)y, depends on the distance between sites i and j and also depends on the types of amino acids, a and The latter are defined by the alignment, because certain amino acid residues a 5 are placed in sites i and j, respectively. 

Luo, H. Hoheisel, C. (1992). Computation of transport coefficients of liquid benzene and cyclohexane using rigid pair interaction models. J. Chem. Phys., 96, 3173-3176. 

Contents Historical Development (up to 1961). Continuum Models. Pair Interaction Models. Other Experimental Proton Data on Qw. The Physical Nature of the Field F and of the Associated Excitation Energy. The Site Factor. The Repulsion Effect The Effect of Higher Order Dispersion Terms. The Parameters B. Ow in Dense Media. The Temperature Dependence of ow. Factor Analysis. 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

In the theory of the liquid state, the hard-sphere model plays an important role. For hard spheres, the pair interaction potential V r) = qo for r < J, where d is the particle diameter, whereas V(r) = 0 for r s d. The stmcture of a simple fluid, such as argon, is very similar to that of a hard-sphere fluid. Hard-sphere atoms do, of course, not exist. Certain model colloids, however, come very close to hard-sphere behaviour. These systems have been studied in much detail and some results will be quoted below. 

One of the major ingredient for the understanding of alloy phase stability is the configurational energy. Models have been proposed to represent the configurational energies in terms of effective multisite interactions, in particular effective pair interactions (EPls). 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

According to Table 3, the pair interactions converge to their bulk values, but the differences between their surface and bulk values are quite pronounced, larger than in the non-selfconsistent theory. In the model I, the surface value of the first nearest neighbor pair interaction is -0.34 mRy, to be compared with 6.28 mRy found for model... 

The modeler controls which redox reactions should be in equilibrium by interactively coupling or decoupling the redox pairs. For each coupled pair, the model uses the corresponding coupling reaction to eliminate redox species from the reactions in the database. For example, if the pair Fe+++-Fe++ is coupled, the model adds the coupling reaction to the reaction for hematite,... 

The regular model for an ionic solution is similarly analogous to the regular solution derived in Section 9.1. Recall that the energy of the regular solution model was calculated as a sum of pairwise interactions. With two sub-lattices, pair interactions between species in one sub-lattice with species in the other sub-lattice (nearest neighbour interactions) and pair interactions within each sub-lattice (next nearest neighbour interactions), must be accounted for. 

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