Branch cells structural parameters

Figure 1.8 Branch cell structural parameters (a) branching angles, (b) rotation angles, (/) repeat units lengths, (Z) terminal groups and dendritic subclasses derived from branches (IVa) random hyperbranched, (IVb) dendrigrafts and (IVc) dendrons/dendrimers...

Fig. 9 Branch cell structural parameters a branching angle, b rotation angle, I repeat unit length, Z terminal group, I molecular reference marker or core. Dendritic subclasses derived from branches IVa random hyperbranched, IVb dendrigrafts, and IVc dendrons/dendrimers [93]. Copyright Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission...

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],... 

In general, however, identification of the crystal cell is only part of the problem of characterizing the structure of crystalline polymers. Crystals are never perfect and the units cells do not infinitely duplicate through space even when they are grown very carefully from dilute solution using low molecular mass materials. As with the organic crystals considered in Chapter 3, a variety of defects can be observed and are associated with chain ends, kinks in the chain and jogs (defects where the chains do not lie exactly parallel). The presence of molecular (point) defects in polymer crystals is indicated by an expansion of the unit cell as has been shown by comparison of branched and linear chain polyethylene. The c parameter remains constant, but the a and b directions are expanded for the branched polymer crystals. Both methyl and... 

We will now discuss the density of states and the specific heat of 3 AgI as derived from observed and calculated phonon dispersions [3.15]. The hexagonal unit cell and the crystal structure of 3-AgI are shown in Fig.3.7a Fig.3.7b illustrates the corresponding Brillouin zone. The observed and calculated phonon dispersions are depicted in Fig.3.12. 3-AgI contains 4 ions in the unit cell which gives rise to 12 branches. A valence-shell model (Chap.4) has been used to calculate 03.(q) and the parameters of this model... 

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