Attractive energy,

Fig. 3 a Scheme of a bundle (Model A [8,9]). Chain repeating units are evidenced as black dots, crystalline packed stems are shown as thickened straight portions of the chain, dashed lines stand for crystal-like attractions, b A bundle comprising 4 stems, 3 loops (see Appendix). Dashed lines stand for energy attraction between crystal-like stems with a chain atoms n, 7 2, 3 are numbers of chain atoms in the loops... 

The fact that the nuclei do not get closer together does not mean that the forces of attraction and repulsion are equal. The minimum distance is that distance where the total energy (attraction and repulsion) is most favorable. Because the molecule has some vibrational energy, the internuclear distance is not constant, but the equilibrium distance is Ra. Figure 3.2 shows how the energy of interaction between two hydrogen atoms varies with internuclear distance. 

The differences observed in the adsorption isotherm are also qualitatively and quantitatively significant for the entropy. It has been recently shown that the isotherm of adsorption of an ideal adsorbate on a heterogeneous surface can be appreciably improved by taking into account the exact form of S from Eq. (7) instead of the approximate one arising from F-H theory [22], Results for the coverage dependence of the chemical potential (adsorption isotherm) and entropy per site are shown in figs. 1-2 for various fc-mer s sizes and interaction energies [attractive (w<0) as well as repulsive (w>0)]. 

Alternative Energy Attracts Significant Venture Capital... 

Figure 12-15 A molecular interpretation of deviations from ideal behavior, (a) A sample of gas at a low temperature. Each sphere represents a molecule. Because of their low kinetic energies, attractive forces between molecules can now cause a few molecules to stick together. (b) A sample of gas under high pressure. The molecules are quite close together. The free volume is now a much smaller fraction of the total volume.

Fig. 5.2 Schematic representation of functional polymer chains configured on a cubic lattice. The darker cubes indicate a lattice site occupied by a functional end group, and the lighter cubes are occupied by polymer chain segments (a) illustrates a chain with a low-energy attractive end group, (b) depicts a nonfunctional polymer with neutral end groups. Reproduced with permission from [54]...

The result is to have the total ir-electron energy (attraction and repulsion) of a configuration set up on the basis of one-electron molecular orbitals that were obtained without consideration of interelectronic repulsion. It would, of course, be only a coincidence if this energy were to represent the minimum possible calculated energy. The energies of a number of "excited" configurations with one, two, or several electrons in normally unoccupied molecular orbitals are also calculated. These excited states may have more or less interelectronic repulsion than the presumed lowest state. 

A sam pie of gas at a low temperature. Each sphere represents a molecule. Because of their low kinetic energies, attractive forces between molecules can now cause a few molecules to stick together. ... 

Thus, we suppose that each molecule moves through a uniform field of potential, the lattice energy, (- ) (attractive) which will be determined by the mean number of near neighbors at a given distance from the molecule, and will essentially be a function of the number of molecules per imit volume, i.e. a function of the volume per molecule v. The contribution of the interactions to the canonical function can thus be written by supplementing it with the exponential term corresponding to that imiform potential. Thus, we obtain ... 

For the generation of electricity from renewable sources (biofuels), the subsidy received is assumed at 57.7/MW h. In the ease of municipal waste incineration it is assumed that 50% of the composition of the components is biodegradable, and therefore it was assumed that only half of the energy attracts subsidies (Table 5.21). 

If the orientation of the two dipoles were completely random, the average force would be zero, since attractive and repulsive orientations would occur equally. As the top of the Figure 4.5 shows, however, molecular dipoles in gases and liquids are free to rotate. This movement allows the energetically favored lower-energy attractive interactions to occur more frequently, as the dipoles tend to rotate to align. On the other hand, thermal energy leads to a randomization of orientation. 

Note that this interaction energy scales with the magnitude of the misfit between the impurity and the matrix, is strongest directly above or below the core of the dislocation, and increases in strength as 1/r as the atom approaches the dislocation line. Also note that if a dislocation core collects a large number of impurity atoms by this mechanism, its future movement is inhibited as it must break free from these impurities (and overcome the energy attracting them to the dislocation core). 

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