Staircase structures

The formation of such a staircase structure in the macromolecules of PAN in the process of thioamidation of PAN fibres with aqueous solutions of ammonium sulfide accounts for the significant increase of heat resistance of the modified fibres obtained. 

However, the constraints of the the 2S-MILP have a so-called staircase structure (see Figure 9.9). Although commercial MILP solvers partially exploit the structure of a MILP, they are not yet able to automatically detect and exploit the structure of the 2S-MILP [8],... 

One expects to observe a barrier resonance associated with each vibra-tionally adiabatic barrier for a given chemical reaction. Since the adiabatic theory of reactions is closely related to the rate of reaction, it is perhaps not surprising that Truhlar and coworkers [44, 55] have demonstrated that the cumulative reaction probability, NR(E), shows the influence barrier resonances. Specifically, dNR/dE shows peaks at each resonance energy and Nr(E) itself shows a staircase structure with a unit step at each QBS energy. It is a more unexpected result that the properties of the QBS seem to also imprint on other reaction observables such as the state-to-state cross sections [1,56] and even can even influence the helicity states of the products [57-59]. This more general influence of the QBS on scattering observables makes possible the direct verification of the existence of barrier-states based on molecular beam experiments. 

For example, the racemic tetrabromide 6 invariably forms inclusion compounds with a staircase structure. Each host molecule contributes one of its aromatic... 

The series of inclusion compounds formed by 6 differ in the details of their staircase construction and guest inclusion, but their common feature is the PHD interaction involving pairs of opposite enantiomers. Between these step pairs, however, there may be a twofold axis or no symmetry at all. In some examples, such as (6)4-(benzene), there are two independent molecules (A and B) in the asymmetric unit. The staircase structure now contains both A-A and B-B PHD interactions (where indicates the enantiomer of opposite handedness), as illustrated in Figure 4. 

Figure 4.3. To maintain a constant surface pressure during the deposition process, the area enclosed by the barrier is reduced systematically. This schematic Y-type dipping sequence for a diagram shows a staircase structure of 4, 8, 12, and 16 monolayers. Courtesy of Joyce-Loebl Company, Gateshead, England.)...

Cyclic ladder polysilanes with staircase structure 03MI75. 

Figure 2.4.2 Views of (a) a simple linear chain complex [Ag(4-pytz)]PF6 °° that contrasts with the helical staircase structure formed by [Ag(4-pytz)]N03 °° [29].

Zinc is not the only metal employed in the assembly of porphyrins via axial coordination. Among the metals that possess interesting photophysical behavior, gallium(III) offers the possibility of forming hexacoordinate complexes. In addition, the Ga(III) porphyrin is a cationic species which allows an additional electrostatic contribution to the driving force of the axial binding in the presence of anionic axial bases. This is illustrated by the staircase structure 85 prepared by Kobuke and represented in Figure 13.49. ... 

Figure 3.2 Cumulative reaction probability for the coUinear H+H2 reaction. The circles are the J —matrix propagation results (summed over final states) by Bondi et aL, and the line is the power series Green s function results. Excellent agreement is obtained over the entire energy range. The staircase structure is evident, with N E) = 1 when the is one open channel, and = 1.6 with two open channels. The non-monotonic increase indicates recrossing dynamics, and the peak at = 0.87 eV indicates a collision complex for H3.

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