Flexible coil

Figure 1.6 A flexible coil attached at the origin at one end and (a) in a volume element dx dy dz at the other end and (b) in a spherical shell of volume 47rr dr. (Reprinted from Ref. 4, p. 116.)...

Semi-flexible coil cellulose derivatives, chitosans... 

The reason for the low intrinsic viscosities in solution is that dendrimers exist as tightly packed balls. This is by contrast with linear polymers, which tend to form flexible coils. The effect of this difference is that, whereas polymer solutions tend to be of high viscosity, dendrimer solutions are of very low viscosity. In fact, as dendrimers are prepared, their intrinsic viscosity increases as far as the addition of the fourth monomer unit to growing branches (the so-called fourth generation), but this is the maximum value that the viscosity reaches, and as the side chains grow beyond that, the viscosity decreases. 

Studies of the hydrodynamic properties and unperturbed dimensions of fractionated PCL have shown that it is a flexible coil (54,55). The following Mark-Houwink equations have been reported ... 

Fig. 45.—Ratio of observed to corrected intensity as a function of y/v = /2jZ /r / )2Tr sin (0/2) for flexible coils and (2ttL/ ) sin (6/2) for spheres of diameter L or rods of length L. (Doty and Edsall. )...

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

P.-G. de Gennes, Kinetics of collapse for a flexible coil, J. Phys. Lett. 46, L639 (1985). 

In order to estimate whether the true molar masses of the dendronized polymers are larger or smaller than the GPC molar masses reported in Table 1, it is useful to recall that the separation in a GPC experiment is based on the hydro-dynamic volume (Vn) of macromolecules. For flexible coils, Vn depends on the chain length (i. e. contour length) L = MxbxMo1 according to... 

The most widely accepted parameter defining the elution volume V in SEC is the hydrodynamic volume, (13) which for flexible coils of finite dilution is proportional to the product of the molecular weight M and the intrinsic viscosity [n] ( =... 

Alternative expressions linking Vc -t to Mr have been developed1239 for peptides, based on the relationship between the radius of gyration, Rg, and the molecular mass, Mr, i.e. Rg oc Mra where a = l for prolate or rod-like peptides, a =1/2 for flexible coiled-coil peptides, and a =1/3 for spherical peptides. For compact coiled-coil peptides, the hydrodynamic volume, Vh, can be calculated as follows ... 

More recently [79], a carboxy-terminated PBZT ([r ] = 4.8 dL/g) was reacted with m-phenoxybenzoic acid via a Friedel Craft procedure in a meth-anesulfonic acid/P2Os mixture. This provided an ABA block copolymer in which the outer blocks (A) are composed of flexible coil polyetherketone (PEK) and a center block (B) which contains the rigid-rod PBZT. Thermomechanical analysis showed that 20 PBZT/80 PEK and 10 PBZT/90 PEK compositions exhibited glass transition temperatures of 157 °C and 135°C respectively. Consolidation studies have not been investigated to date. 

While the processing and characterization of the graft copolymers have not been sufficiently pursued to this point to establish the viability of the concept, these research efforts have demonstrated that rigid-rod polymer fusibility could be substantially modified through the introduction of flexible coil side chains. Unfortunately, in spite of the careful processing and the attainment of excellent consolidation as well as minimal phase separation, the tensile properties are less than expected. 

As the results of Schwander and Cerf (188) and of Leray (180,181), which were obtained on samples of DNA from calf thymus, have been reproduced already in several review articles (1,3), the present discussion can be kept rather short. When the viscosity of the solvent (1.0 molar aquous solution of sodium chloride) is increased by replacing part of the water by glycerol, the behaviour of the initial slope of the extinction angle curve follows the qualitative pattern, as given by Fig. 5.10. At low solvent viscosities the molecules seem to behave like frozen molecules, at high solvent viscosities they seem to become flexible coils exhibiting internal friction. These results have been considered to prove the correctness of Cerf s theoretical model. 

Stockmayer and Casassa163 realized that for flexible coils this factor varies with the coil expansion but still the more general equation... 

These results show that the supramolecular structures of thin films of block copolymers can be manipulated by varying the rod-to-coil ratios. Variables such as the polydispersity, the nature of the structures, and their crystallinity can be controlled in this manner. The factors that govern the formation of ordered structures from these copolymers are, however, complex. Important factors include entropy effects associated with the flexible coil segments, crystallization of the rods, and steric considerations. Upon crystallization of the rods, the entropies of the coil blocks may be increasingly compromised as a result of increasing steric repulsion. This may effect the sizes of the aggregates that are formed. The organization of ordered structures can furthermore be controlled by non-specific interactions such... 

---