Bond occupation probability

The procedure for the calculation of connectivities c, following closely Seaton [8], can be summarized as follows The bond occupation probability / was obtained as a function of percolation probability F from the adsorption isotherms (Figure 1) using the pore size distribution as follows ... 

The conventional symbols for the bond occupation probability and the percolation probability are p and P, respectively, rather than q and 9 these symbols are not used in the present review to avoid confusion with the symbol for the pressure. 

Here jUe is the electron field-effect mobility, c is the fullerene site occupation probability (c = Cl Co), p is the bond occupation probability, pc is the threshold bond occupation probability for percolation, a is the wavefunction overlap parameter of the fullerene molecules, and a is given by the following function ... 

P—>0 as d—>°o is obvious, and one recovers Eq. (75) in the asymptotic limit. By virtue of the 1/ d = 0 expansion, Eq. (114) is exact in high dimensions. Eq. (114) states that the bond percolation threshold, Dc, should go up inversely in proportion to the site-occupation probability, ps, in accord with the observations by Agrawal, Redner and Stanley [60], and by Stauffer [58]. 

In our above simple square lattice, we have considered only nearest neighbors and the bonding between them. Let us consider now the case where we also include occupied second nearest neighbors [11]. In that case, under the same site occupation probability p, where farther (second nearest) neighbors are also considered, the percolation onset will be achieved at a p for which no percolation existed in the nearest neighbors-only case. Let us define now the critical pc values for the two... 

Fracture of the weld occurs by disentanglement of the minor chains, or bond rupture. In the VP theory, many properties follow scaling laws dependent on the difference between p, the occupational probability of the lattice and the percolation threshold Pc, the minimum concentration (occupational probability) at which connectivity could occur in an infinite lattice. In particular, the fracture toughness, which depends on this percolation term, Gic [p - Pc], determines the number of bonds to be broken, or disentangled. 

The reason for preferential axial site occupancy by mono-dentate ligands is probably related to results of recent CNDO calculations on [Co CO) ] (15) which show that the axial carbonyls are least involved in back-bonding. Extrapolation to Rh - and Ir -derivatives seems reasonable and finds some support from n.m.r. measurements, which show that the n.m.r. chemical shift of the axial carbonyl is always at higher field than the radial carbonyl in both rhodium (16) and iridium derivatives. (12)... 

To date, chemical properties have been reported mainly for 59 and 61. Occupancy of the silicon 3p orbital by electrons from nitrogen greatly reduces the electrophilicity of these silylenes. This, together with probable aromatic stabilization, significantly mutes the behavior of 59 and 61 as silylenes. For example, 59 does not insert into Si—H bonds, or react with alkynes such as PhC=CPh367, Moreover, 59 shows no Lewis acidic behavior, even toward bases as strong as pyridine. 

The first rule is the movement probability Pm. This rule involves the probability that an occupant in an unbound cell, i, will move to one of four adjacent cells, /, if that space is unoccupied. An example is cell i in Figure 6 that may move (in its turn) to any unoccupied cell, /. If it moves to a cell whose neighbor is an occupied cell, k, then a bond will form between cells i and k. As... 

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