Core multiplicity

Developments. A variety of process modifications aimed at improving surface finish or weld line integrity have been described. They include gas assisted, co-injection, fusible core, multiple Hve feed, and push—pull injection mol ding (46,47). An important development includes computer-aided design (CAD) methods, wherein a proposed mold design is simulated by a computer and the melt flow through it is analy2ed (48). 

Where Nc = initiator core multiplicity Nb = branch cell multiplicity NcNbM = number of covalent bonds formed/step... 

It is apparent that both the core multiplicity (Nc) and branch cell multiplicity (Nh) determine the precise number of terminal groups (Z) and mass amplification as a function of generation (G). One may view those generation sequences as quantized polymerization events. The assembly of reactive monomers [48, 78], branch cells [48, 83, 89] or dendrons [85, 90] around atomic or molecular cores... 

As a consequence of the excluded volume associated with the core, interior and surface branch cells, steric congestion is expected to occur due to tethered connectivity to the core. Furthermore, the number of dendrimer surface groups, Z, amplifies with each subsequent generation (G). This occurs according to geometric branching laws, which are related to core multiplicity (iVc) and branch cell multiplicity (iVb). These values are defined by the following equation ... 

Figure 1.21 Periodic properties for poly(amidoamine) (PAMAM) dendrimers as a function of generation G = 0-10 (I) flexible scaffolding (G = 0-3) (II) container properties (G = 4-6) and (III) rigid surface scaffolding (G = 7-10) various chemo/ physical dendrimer surfaces amplified according to Z = NCN where Nc = core multiplicity, Nb = branch cell multiplicity, G = generation...

For the heavier noble gases, the core multiplicity of the metastable states give rise to eight potential curves (six for 3P2 and two for 2P0). The Ne2 potentials have been calculated by Schneider and Cohen,87 who have also performed scattering calculations for this system. Theoretical and experimental data exist for Ar2,88 whereas only qualitative estimates of the potentials are available for Kr2 and Xe2. These excited states play a prominent role in the rare-gas excimer lasers.89,90 ... 

This equation ultimately expresses no more than the fact that the number of terminal groups increases as a function of the number of (former) functional groups of the core (core multiplicity) and that of the branching units (branching multiplicity) rises exponentially with the number of generations. 

The cascade name for Figure 3.5 is derived by the process described above, except that the attachments to the adamantane core (i. e., 1,3,5,7) must be noted after the core multiplicity. The repeat units are readily named via replacement nomenclature, thus ... 

Control and development of branch cell multiplicities (Nb) and core multiplicities (Ne). 

A variety of mono-, di-, tetra-, and polydendron PAMAMs have been synthesized from simple amines as well as linear polyamine cores [2, 83, 124]. Linear poly(ethylenimines) with core multiplicities (Nc of ca. 300-400) have been shown to produce high-aspect ratio, rod-like dendrimers at generation 3 or 4 [2]. Their length is determined by the degree of polymerization (n) of the initiator core and their diameter is derived from the number of generations (see Scheme 3). 

Thompson and Gdanski (34) also performed dual-core experiments to determine the best diversion method using foam, and the maximum permeability difference needed to achieve an equal flow rate through the core. Multiple diversion techniques were used, including foamed acid, multiple stages of foamed add, and various qualities of foamed brine. The tests showed that foamed brine reduced flow rates better than foamed add. Also, higher quality foamed brines were most effective. In order to effectively use foamed diversion fluids, the permeabilities of the zones of interest must be relatively similar. The limit on permeability differences is approximately a factor of 10. Otherwise, the more permeable zone will accept both the diversion and treatment fluids. 

The stfucture of dendrimer depends on the core multiplicity (N ), the branch-cell multiplicity (N ), and the critical molecular design parameters (CMDPs) [30]. A typical branching structure is given below [31],... 

Figure 11.5 Two-dimensional projections of Starburst dendrimers with initiator core multiplicity (N = 3) and branch-ceU multiplicity N = 2).

The initiator-core multiplicity (N and the branch-ceU multiplicity (N directly affect the number of terminal groups, the number of repeating units (branch cells), and the molar mass of the dendrimers. The percolation threshold for a Cayley tree having z branches is = 1/(Z- 1) [32]. 

FIGURE 42.9. Mathematical expressions for calculating the theoretical number of surface groups (Z), branch cells (BC) and molecular weights (MW) as a function of generation, A/o = core multiplicities and A/b = branch cell multiplicity. 

In the case where the size of the buffer tube is small and several are located within the same cable core, multiple buffer tubes are stranded in a concentric, helical pattern that reverses direction periodically. The reason for this is to improve the performance of the cable under temperature and tensile load extremes, as well as in relatively tight bends, and to improve mid-span fiber accessibility. For cables with a large number of buffer tubes, the tubes maybe arranged in two or more layers using the same type of stranding process for each. 

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