Three-contact addition

Theorem All benzenoids with h + 1 hexagons can be generated by (only) three types of additions to all benzenoids with h hexagons, viz. the (i) one-, (ii) two- and (iii) three-contact additions. All these three types are necessary. 

Fig. 8. Benzo[e]pyrene (C20H12) generated by the one-, two- and three-contact addition ( + C4H2, +C3H and +C2, respectively)...

Principle 6.2 states the sufficiency of one-, two— and three-contact additions in the building-up process. It is easy to prove that these three types also are necessary in general. That is for instance proved by examples where all free edges occur in (i) Lj—, (ii) or (iii) mode hexagons exclusivdy (see Fig. 4). It is dear that the last step in the building-up of the a ve systems had to employ a (i) one-contact—, (ii) two-contact— and (iii) three-contact addition. 

According to Principle 6.2 the (i) one—, (ii) two— and (iii) three-contact additions should be applied to those isomers which have one hexagon less than in and (i) the same number... 

Assume that at the isothermal temperature of interest the following stable condensed phases (solid or liquid) can be formed M, MO, MS, MSO4. From the Phase Rule it is clear that the maximum number of condensed phases in contact with each other can be three, in addition to the gaseous phase (SO2 and O2). Following the suggestion of Kellog and Basu , the... 

The outlined problems correspond to the most typical system where three phases, e.g. liquid, gas and solid, are brought in contact. Additional wetting geometries can occur when the liquid phase consists of two subphases, e.g. mixture of incompatible polymer liquids, and/or the substrate surface exhibits variations in chemical composition. In these cases, the interfacial interactions will strongly interfere with the phase separation inside the film. Laterally ordered polymer films might be formed due to the preferential wetting of the patterned substrate by one of the liquid phases. 

In order to inspect the first term on the right-hand side of Eq. (27) closer we ask ourselves first on which circular benzenoid the two-contact addition according to (a) should be executed. It is clear that the formula of this circular benzenoid is obtained by subtracting C3H from C HS. In terms of the three-parameter code it was found that ... 

Fig. 4. Muscle proteins. Positions of myosin heads (S-1), actin monomers (A) and troponin (circies) in active and relaxed states shown in relationship to a cross section of decorated actin. S-1 a, S-1 b and S-1 c indicate the domains of the HMM. Aa and Ab are the domains of the actin monomers. The circles labeled a" show troponin fibrils in the active position b" and "c are possible positions in the relaxed state. This drawing is not a helical projection but a schematic view of two actin monomers (the one on top is 27 A above the other one and rotated by about 167° around the filament axis) and their associated S1s. The SI on the left is therefore 27 A above the SI on the right hand side of the drawing. In three dimensions, additional S1s would be in contact with both of the actin subunits shown. Therefore it only appears in this two-dimensional drawing that the tropomyosin and SI do not make equivalent contacts with the two ac-tins. [Used with permission from E.H.Egelman J. Muse. Res. Cell. Moti7. 6(1985) 129-151]...

For the sake of clarity, the formula shifts which are implied in the above exposition, are illustrated in the below diagram they are exactly those associated with the (i) one—, (ii) two—, (iii) three—, (iv) four— and (v) five-contact additions. 

Shell Higher Olefins Process (SHOP). In the Shell ethylene oligomerization process (7), a nickel ligand catalyst is dissolved in a solvent such as 1,4-butanediol (Eig. 4). Ethylene is oligomerized on the catalyst to form a-olefins. Because a-olefins have low solubiUty in the solvent, they form a second Hquid phase. Once formed, olefins can have Htfle further reaction because most of them are no longer in contact with the catalyst. Three continuously stirred reactors operate at ca 120°C and ca 14 MPa (140 atm). Reactor conditions and catalyst addition rates allow Shell to vary the carbon distribution. 

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