Range Interaction Model

In his thesis, Chen suggested using the Debye-Hilckel model  

As shown by Robinson and Stokes (C6), the mole fraction based activity coefficient, f, is related to the mean molal activity coefficient, y, by the following relationship  

This relationship is presented for the sake of uniformity as the other methods outlined in this chapter are presented on a molality basis. 

---

Multilayer Adsorption of Water. As the amount of water in the clay increases over that needed for a one- or two-layer hydrate, the study of the properties of the water becomes experimentally more difficult. This is important because it is only at water contents in excess of the two-layer hydrate that a conflict arises between the short-range and long-range interaction models. In support of the short-range model, two studies are noteworthy. A small angle... 

It is difficult to reconcile these very different views of the interaction of water and clay surfaces. Sposito (8.) has attempted this. He points out that the thermodynamic properties have an essentially infinite time scale, whereas the spectroscopic measurements look at some variant of the vibrational or a predecessor of the diffusional structure of water. It is possible that the thermodynamic properties reflect a number of cooperative interactions which can be seen only on a very long time scale. Still, the X-ray diffraction studies seemingly also operate on as long a time scale as the thermodynamic properties. There is still not a clear choice between the short-range and long-range interaction models. 

Raghu, C., Anusooya Pati, Y., Ramasesha, S. Structural and electronic instabilities in polyacenes density-matrix renormalization group study of a long-range interacting model. Phys. Rev. B 2002, 65(15), 155204. 

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

Chemi-ionization reactions of the resonant states appear to form the simplest general category because of the applicability of near-resonance, long-range interaction models, in which the dipole transition moments of the noble gas A A( .9) radiative transition and the reagent photoionization transition determine the reaction cross section. The impact-parameter, linear trajectory form of this model of Watanabe and Katsuura has been applied jq chemi-ionization... 

The gradient model for interfacial tension described in Eqs. III-42 and III-43 is limited to interaction potentials that decay more rapidly than r. Thus it can be applied to the Lennard-Jones potential but not to a longer range interaction such as dipole-dipole interaction. Where does this limitation come from, and what does it imply for interfacial tensions of various liquids ... 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

B. Bergersen, Z. Racz. Dynamical generation of long-range interactions Random Levy flights in the kinetic Ising and spherical models. Phys Rev Lett 67 3047-3050, 1991. 

We have assumed so far, implicitly, that the interactions are strictly local between neighboring atoms and that long-ranged forces are unimportant. Of course the atom-atom interaction is based on quantum mechanics and is mediated by the electron as a Fermi particle. Therefore the assumption of short-range interaction is in principle a simplification. For many relevant questions on crystal growth it turns out to be a good and reasonable approximation but nevertheless it is not always permissible. For example, the surface of a crystal shows a superstructure which cannot be explained with our simple lattice models. 

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

---