Medium-range forces

To separate the non-bonded forces into near, medium, and far zones, pair distance separations are used for the van der Waals forces, and box separations are used for the electrostatic forces in the Fast Multipole Method,[24] since the box separation is a more convenient breakup in the Fast Multipole Method (FMM). Using these subdivisions of the force, the propagator can be factorized according to the different intrinsic time scales of the various components of the force. This approach can be used for other complex systems involving long range forces. 

In addition to these direct long-range forces there may also exist effective long-range forces, produced by some medium or substrate. An especially drastic effect is expected for epitaxial growth on a semiconductor. If adsorbate atoms are different from the substrate, the adsorbed layers have a lattice constant different from that of the substrate. In the case of thick adsorbate layers, an instability then appears on the surface of the crystal such that the surface undergoes wavy deformation, which might even lead to... 

This indicates that the polarity of a medium is a long-range property that goes much further than the first solvation shell and therefore involves the two adjacent bulk media properties. This result is, however, valid for compounds the solvation of which is not determined by specific interactions with the first solvent shell, but rather by long-range forces like dipole interactions. The solvation of DEPNA was determined by molecular dynamics too and similar conclusions were drawn [82]. 

In a homogeneous medium of an electrolyte solution, an ionic liquid or a solid electrolyte under conditions of constant pressure and temperature, mechanical, electrostatic and short-range forces act on the individual particles in solution, but these forces average out in time. The effect of these forces is reflected in the activity values of the individual components of the system. 

Medium-range interactions can be defined as those which dominate the dynamics when atoms interact with energies within a few eV of their molecular binding energies. These forces determine a majority of the physical and chemical properties of surface reactions which are of interest, and so their incorporation in computer simulations can be very important. Unfortunately, they are usually many-body in nature, and can require complicated functional forms to be adequately represented. This means that severe approximations are often required when one is interested in performing molecular dynamics simulations. Recently, several potentials have been semi-empirically developed which have proven to be sufficiently simple to be useful in computer simulations while still capturing the essentials of chemical bonding. 

Section IV is devoted to excitons in a disordered lattice. In the first subsection, restricted to the 2D radiant exciton, we study how the coherent emission is hampered by such disorder as thermal fluctuation, static disorder, or surface annihilation by surface-molecule photodimerization. A sharp transition is shown to take place between coherent emission at low temperature (or weak extended disorder) and incoherent emission of small excitonic coherence domains at high temperature (strong extended disorder). Whereas a mean-field theory correctly deals with the long-range forces involved in emission, these approximations are reviewed and tested on a simple model case the nondipolar triplet naphthalene exciton. The very strong disorder then makes the inclusion of aggregates in the theory compulsory. From all this study, our conclusion is that an effective-medium theory needs an effective interaction as well as an effective potential, as shown by the comparison of our theoretical results with exact numerical calculations, with very satisfactory agreement at all concentrations. Lastly, the 3D case of a dipolar exciton with disorder is discussed qualitatively. 

There are other major objections to Crocker and Grier s claim [13, 14], one of which we consider in Chapter 7. First, there is the timescale of the measurements. The laser tweezer experiments measure transient collisions, whereas equilibrium in these dispersions usually takes weeks or months to achieve [17], Inspection of Figure 3.8 reveals that any transient experiment is going to be dominated by the medium-range strong repulsion. The minimum is so shallow that the true equilibrium nature of the forces takes weeks to reveal itself against the background of the Brownian motion. We also observed that when an n-butylammonium vermiculite gel had been compressed... 

Nonbonded interactions have generally not been included in our force field, except where an unusually close contact is present, such as H - H in (Gly) I (Moore and Krimm, 1976a). The main reason is that they ordinarily have a small influence on the medium-range frequencies, and in particular no effect on amide I or amide II splittings (V. Naik and... 

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