Next-nearest neighbors

This region has been divided into two subphases, L and S. The L phase differs from the L2 phase in the direction of tilt. Molecules tilt toward their nearest neighbors in L2 and toward next nearest neighbors in L (a smectic F phase). The S phase comprises the higher-ir and lower-T part of L2. This phase is characterized by smectic H or a tilted herringbone structure and there are two molecules (of different orientation) in the unit cell. Another phase having a different tilt direction, L, can appear between the L2 and L 2 phases. A new phase has been identified in the L 2 domain. It is probably a smectic L structure of different azimuthal tilt than L2 [185]. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

The fact that there are no characteristic length scales immediately implies a similar lack of any characteristic time scales for the fluctuations. Consider the effect of a single perturbation of a random site of a system in the critical state. The perturbation will spread to the neighbors of the site, to the next nearest neighbors, and so on, until, after a time r and a total of / sand slides, the effects will die out. The distribution of the life-times of the avalanches, D t), obeys the power law... 

All next-nearest neighbors i and j , linking them only if the 2-tuple (q,/ ) = (1,3). By next-nearest neighbor we mean those pairs which are themselves unlinked but which share at least one other linked neighbor a,g), h,r) and w,y), for example, are all next-nearest neighbors at t = l. For c and g we find... 

Ii89] Li, W., Complex patterns generated by next nearest neighbor cellular automata, Computers and Graphics 13 (1989). 

In water at room temperature some molecules have more than four nearest neighbors, but at any moment the majority have four neighbors, as in ice. If the molecules tend to have a tetrahedral arrangement like that of ice, the average distance between next-nearest neighbors would be... 

Fig. 20. The structure of ice Molecules numbered 8, 7, 6 are in contact with 5, while molecules 5, 4, 3, 2 arc in contact with 1. Molecules 2, 3, 4 are among the next-nearest neighbors of 5, while molecules 0, 7, 8 are among the next-nearest neighbors of 1. [Diagram taken from E. J. W. Verivey, Rec. trav. chim. 60, 893 (1941).]...

In Chapter 3, in discussing water near its freezing point, we took the point of view that at any moment the liquid contains many groups of molecules that have a local order similar to that of ice. In Fig. 20 the molecules numbered 2, 3, 4, 5 are nearest neighbors of molecule 1, while molecules 6, 7, 8 are neighbors of 5, and consequently arc next-nearest neighbors of 1. To be definite, let us identify the molecules 2, 3, 4, 5 with the outer tetrahedra of Fig. 19, and let us suppose that the protons... 

Table 2. Surface density (0 ), direct band gap energy (Egd), and number of next nearest neighbors (N ) on WO -ZrOi calcined at 1073 K.

A simple way of treating the local intrachain structure on the 2nnd lattice is to focus on the distance between next-nearest neighbor beads. In this approximation, the 2nnd lattice can only accept information from a 9 x 9 statistical... 

In the previous section, the adaptation of the RIS model was based on the distance between next-nearest neighbor beads. This approach is obviously inadequate for CH3-CHX-CH2-CHX-CH3, because it necessarily abandons the ability to attribute different conformational characteristics to the meso and racemo stereoisomers. Therefore a more robust adaption of the RIS model to the 2nnd lattice is necessary if one wants to investigate the influence of stereochemical composition and stereochemical sequence on vinyl polymers [156]. Here we describe a method that has this capability. Of course, this method retains the ability to treat chains such as PE in which the bonds are subject to symmetric torsion potential energy functions. 

The method based on the orientation of pairs of vectors of length L produces slower dynamics than the method based on next-nearest neighbor distances. Since the acceptance rates for single-bead moves differ very little in the two methods, it appears that the probability for immediate reversal of a successful move is higher in the method based on the orientation of the pairs of vectors, such that the chain shivers rapidly, but moves its center of mass slowly. This problem is more severe in PP melts than in PE melts. Significant diffusion of the center of mass of the chains in PP melts is achieved when reptation, as well as single-bead moves, is allowed [158, 158A]. 

The next-nearest-neighbor-orbital resonance integrals, /JI3, also remain unaffected by the pure twisting motion. We conclude that a pure twisting motion can therefore represent at best only a relatively small perturbation of the electronic structure of the polysilane chain, suitable for treatment by first-order perturbation theory. The perturbation is represented by changes in the resonance integrals between more distant hybrid orbitals, among which / 14 clearly is the most important. 

The second digit gives the number of next-nearest neighbors. 

Nanoparticles of dilute magnetic semiconductors have also been studied by NMR. Here one important question is whether the magnetic ion is incorporated into the NC or resides on the surface. The 113Cd MAS-NMR of NCs of Cd0.991Co0.009S with diameters from 3.5 to 29.5 nm showed peaks shifted by electron hyperfine interactions from next-nearest neighbor Co2+ ions, and by comparison with results from bulk samples that were discussed in Sect. 3.5 it was concluded that Co2+ ions occupied Cd2+ sites and were distributed homogeneously ... 

Recently the 29Si hyperfine interaction from the nearest and next-nearest neighbors has been studied (Kiefl et al., 1988b). The experiments are difficult because of the low natural isotopic abundance (4.7%) of 29Si... 

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