Effect of attractive interactions

These ideas can be generalized to describe the effect of attractive interactions on vibrations. If the interaction couples to a highly correlated... 

The Lennard-Jones potential includes a strongly repelling term proportional to which represents the excluded volume by an atom, and a long attractive tail of the form — l/rif, which models the effect of attractive interactions between induced dipoles due to fluctuating charge distributions. This potential provides reasonable simulation results for the properties of liquid argon. The parameters dij and Sij, the effective diameter and the depth of the potential well between different atoms, can be calculated by using the combination rules since... 

We now consider the behavior of multicomponent mixtures where we add an A-C copolymer to a blend of A and B homopolymers. Our objective was to study the effect of attractive interactions between B and C monomers (i.e., X < 0) on interfacial properties and microphase separation. The complexity in these mixtures is the fact that their phase behavior is governed by three x parameters Xab XaC ... 

Although essentially all studies to date using PRISM and the molecular closures have involved macromolecules, it is conceivable such closures may be of value even for small or intermediate-sized flexible and/or rigid molecules. A careful documentation of the accuracy of the new molecular closures as a broad function of thermodynamic state and molecular fluid type remains an important future direction. In addition, recent interesting alternative approaches to liquid theory for polymer mixtures with attractions have been developed within the general PRISM framework by Melenkevitz and Curro based on the optimized RPA(ORPA) approach, and Donley et. ah " based on density functional theory and also from a field-theoretic perspective by Chandler. Application of these approaches to treat the effect of attractive interactions on fluid structure and phase transitions remains to be worked out. 

The existence of surface tension in solids composed of neutral molecules can be attributed to the effects of attractive interactions between other than nearest neighbours. These next-nearest-neighbour and more distant attractions ensure that a plane of molecules is more closely packed than a row of molecules, but less closely packed than a large three-dimensional array. If a layer of molecules is produced separately it has to contract to fit onto the bulk phase and must therefore be put into compression. The balancing tension in the bulk phase falls rapidly to zero over a few molecular diameters. 

Figure 7.9. Effect of lateral interactions on the distribution of a single adsorbate species A on the surface. The adsorption energy of each atom A is calculated using Eq. (20) and the interaction energies indicated underthe maps. Negative energies correspond to attraction,...

In this review, we focus on the effect of anisotropic interactions, in particular parallel attractions, and demonstrate that the inclusion of such interactions in a model leads to a great richness in possible polymer phase behavior. From a practical point of view, the model that we describe has the advantage that it is computationally very cheap—although this advantage comes at the price of sacrificing the greater realism of an off-lattice model. 

These results point to a significant effect of the configuration of the diol moiety on the intracomplex forces involved in the isomeric [C/j-M/j/j], [C/j-M/js], and [C/j-Mss] adducts. The OH- - -O hydrogen bonding in these complexes is responsible for the bathochromic shifts observed in the corresponding spectra. " Different spectral shifts for diastereomeric complexes are often due to the superimposing effects of attractive dispersive (polarization) and repulsive (steric) interactions. ... 

In addition to steric effects, which make use of repulsive interactions between a reactant molecule and the environment of the active site, it is also possible to make use of attractive interactions. An example of this is the selective terminal activation of hexane by Co-AlPO. The high selectivity in the oxidation of hexane to 1,6-hexanediacid over a Co-AlPO (Co/Al = 0.1) catalyst was attributed to the attractive interaction of the hexane molecule with the cage wall of AlPO, orienting the molecule in such a way that the two terminal carbons are in close proximity to the two Co atoms. 

Now, we examine the effect of attraction. Each atom is surrounded by (N - 1) atoms in the volume V. The number of atoms in a spherical shell of thickness dr at a distance r from any atom is 4ttr2(N/V)dr. Therefore, the interaction energy u experienced by any atom is given by... 

As it was mentioned above, up to now only the dynamic interaction of dissimilar particles was treated regularly in terms of the standard approach of the chemical kinetics. However, our generalized approach discussed above allow us for the first time to compare effects of dynamic interactions between similar and dissimilar particles. Let us assume that particles A and B attract each other according to the law U v(r) = — Ar-3, which is characterized by the elastic reaction radius re = (/3A)1/3. The attraction potential for BB pairs is the same at r > ro but as earlier it is cut-off, as r ro. Finally, pairs AA do not interact dynamically. Let us consider now again the symmetric and asymmetric cases. In the standard approach the relative diffusion coefficient D /D and the potential 1/bb (r) do not affect the reaction kinetics besides at long times the reaction rate tends to the steady-state value of K(oo) oc re. 

The effect of coordination number on the Madelung constant, A, and therefore on the lattice energy, is clearly demonstrated in Table 3.4 when same-formula types are compared the larger the coordination number, the larger the value of A. This is due, of course, to the larger number of attractive interactions that are possible. On the whole, though, this variation amounts to only a few per cent of the lattice energy. 

P. Meakin, The effects of attractive and repulsive interaction on three-dimensional reaction-limited aggregation, J. Colloid Interface Sci. 134 235 (1990). 

For the case of purely attractive forces (such as Lon-don-van der Waals forces) the length Sjr over which they act is a useful characteristic. An attractive force which acts over a distance which is much less than Sc will not contribute substantially to the overall rate. When repulsive forces (such as the electrostatic double-layer forces) are also present, they may effectively prevent particles from arriving at the collector, even when they act only over a very short distance. For this reason the decay length alone cannot characterize the relative importance of the joint effect of attractive and repulsive farces. Useful characteristics of their combined effect may be obtained by considering the total potential energy of interaction between the particle and the collector. 

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

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