Helical macromolecules

Good agreement with experimental viscoelastic measurements on several helical polymers has been obtained with an empirical hybrid relaxation spectrum in which a separate rotational mode (relaxation time tq) has been added to a set of mechanisms attributed to internal motions and spaced in accordance with the Zimm spectrum (tj, T2,. . The appropriate equations for [(/ ] and are as follows  

Here the terms in tq are taken from equations 8 and 9, and the functions Z and 

garithmic plots of (C ]/ and [C ]/ against h [rj ti,M/RT for poly(7-benzyl-L-glu-tamate) with My, = 57 X 1(H in dimethyl formamidc (open circles) and n-cresol (black circles). The different solvent viscosities extend the effective frequency range. Curves drawn from equations 46 and 47 with mi = 0.555, m2 = 0, ti/to = 0.211, and z = 1. Reproduced, by permission, from Biopolymers. 

For several samples of poly(7-benzyl-L-glutamate) with molecular weights between 6.4 X 10 and 57 X 10, Wada and collaborators showed by combining data from two laboratories that tq (or its equivalent in a somewhat different analysis) conformed to equation 14 with the correct, very strong dependence on molecular length so this relaxation time clearly represents end-over-end rotation. The others (tj, T2.) might be attributed either flexural or accordionlike elon-gational modes. For the former, the fundamental relaxation time has been calculated as 

From the observed ratio tq and r and equations 14 and 49, the flexural rigidity B can be calculated and from it the Young s modulus of the helix considered as a uniform rod. ° This is about 0.2 X 10 ° dynes/cm for poly(7-benzyl-L-gluta-mate) and 1.2 X 10 ° dynes/cm for paramyosin. However, the relation between rotational and internal motions represented by the empirical hybrid spectrum should be modified to conform to improved theory. -  

---

Several natural and synthetic helical macromolecules such as DNA, polypeptides, and polyisocyanates form, in the appropriate solvent, cholesteric meso-phases. Also self-assembled supramolecular systems formed by guanosine derivatives 2 and 3 (G-wires), which are essentially four-stranded helices (Figure 7.8), behave in a similar way.35... 

A large number of chromophoric, helical macromolecules and oligomers, and supramolecular helical assemblies have been constructed by utilizing vari-... 

On the other hand, globular and helical macromolecules can be intentionally denaturated so that the samples are analyzed in the random coil conformation. The transition into random coil conformation can be caused by the elevation of temperature or by addition of structure-breaking substances to the eluent (cf.. Section... 

A simplified determination of amylose in milled rice has involved an initial dispersion in dilute alkali.The amylose-iodine complex at pH 7.5 was estimated from the absorption at 630 nm. Ultrafiltration was considered to be a suitable method for a hydrodynamic study of the amylose-iodine complex formation. No partially complexed amylose molecules were present in the permeate and so it was considered that complex formation took place instantaneously in a whole molecule and not successively in different zones of the molecule. The conformation of amylose in aqueous solution is entirely that of loose and extended helices. The formation of the iodine complex is visualized as a trapping of iodine atoms by the contraction of the loose helical macromolecule into tight and stiff helices. 

Poly(3-hydroxybutyrate) is a linear polyester with helical macromolecules. The secondary stracture of PHB is specified as left-hand 2j helix in a g g tt conformation, while the structure of oligolides consists of right-hand 3i helices [99]. The surface of the 3i(-l-) helix is covered by methyl groups, leading to the lipophilic nature of the macromolecule. The carbonyl bonds in the 2i(—) helix are placed perpendicularly, while in the 3i(-l-) counterpart, they are parallel to the helix axis. The latter is the reason for ability to form ionic complexes. 

For an introduction to the physics of helical macromolecules see T. Birshtein, O. Ptitsyn, Cottformations of Macromolecules, Interscience Publishers, New York, 1966. 

When anisotropy is present in the fluid state, the phenomenon described in Chapter 3 becomes more complex. We attempt to illustrate this complexity with a few aspects of viscoelastic behavior taken from the literature on lyotropic polypeptide LCPs (rod-like o -helical macromolecules in helicogenic solvents). For example, when c < ci, conventional viscosity-versus-shear-rate behavior is observed (see Chapter 3). Contrary to intuition, however, Fig. 5.29 shows that, at any given shear rate, the viscosity decreases with increasing concentration of polymer when the polypeptide concentration c exceeds that required for uniform LC formation. 

Kornyshev, A. A. and Leikin, S. 2000. Electrostatic interaction between long, rigid helical macromolecules at all interaxial angles., 62(2), 2576. 

Various kinds of experimental data (solubility, viscosity X-ray-diagrams) suggest that polyisocyanides with bulky substituents exist in the form of rod-like helical macromolecules, and contain long sequences of monomeric units of the seane configuration (either syn or anti). In the case of poly-tert-butyl-isocyanide,... 

Caron, L., 8c Sanche, L. (2003). Low-energy electron diffraction and resonances in DNA and other helical macromolecules. Physical Review Letters, 91,113201. 

Moreover, even in the case of regular constitution, configuration, and conformation, disorder may be present in the crystals because of the presence of defects in the mode of packing. Disorder in the packing may occur while some structural feature, for instance, some atoms or the axes of helical macromolecules, maintain periodic positions [137], The degree of disorder in the... 

---