Chain mode

The scaling results above all pertain to local segmental relaxation, with the exception of the viscosity data in Figure 24.5. Higher temperature and lower times involve the chain dynamics, described, for example, by Rouse and reptation models [22,89]. These chain modes, as discussed above, have different T- and P-dependences than local segmental relaxation. 

The experimental data also show that the crossover to the many-chain regime does not appear in the Q-window accessible to the method. Owing to this lack, the direct experimental evidence that the upturn has to be assigned to a single chain mode and does not result from a collective mode, is still missing. Nevertheless, assuming Dc c, and expressing Dg by DC/(Q/), from a simultaneous fit (c)/A = (6.0 0.5)c-1 and //A = 7.4 + 0.6 are derived. 

The majority of cyclic peptides synthesized on solid support are cyclized in the head-to-side-chain or side-chain-to-side-chain mode. For this purpose the amino acids involved in cyclization must be side-chain protected in a manner that allows for an additional level of orthogonal deprotection. Thus, upon assembly of the fully protected linear precursor on-resin, deprotection of the functionalities involved in the lactam ring formation is performed, followed by regio-selective cyclization by amide bond formation, and finally by the resin-cleavage/deprotection step as outlined in Scheme 16. In Table 8, examples of syntheses of such cyclic peptides are listed with the relevant information regarding protection scheme, resin anchor, and mode of cyclization. 

Table 10.1 Some Examples of Mode 2 At Mode 2 LUMO Antisymmetric HOMO Symmetric sd Mode 0 Chains Mode 0 LUMO Symmetric HOMO Antisymmetric...

To achieve low radical concentrations, most radical reactions are traditionally performed as chain reactions. Atom or group transfer reactions are one of the two basic chain modes. In this process the atom or group X is the chain carrier. A metal complex can promote such chain reactions in two ways. On one hand, the catalyst acts only to initiate the chain process by generating the initial radical 29A from substrate 29 (Fig. 10). This intermediate undergoes the typical radical reactions, such as additions or cyclizations leading to radical 29B, which stabilizes to product 30 by abstracting the group X from 29. A typical example is the use of catalytic amounts of cobalt(II) salts in oxidative radical reactions catalyzed by /V-hydroxyphthalimide (NHPI), which is the chain carrier [102]. 

FWl] H. I. Freedman and P. Waltman (1977), Mathematical analysis of some three-species food chain mode s," Mathematical Bioscience 33 257-76. 

Consider a molecule made out of two /-arm stars with Kuhn segments per arm with junction points connected by a central linear strand of Abb Kuhn monomers. This molecule is called a pom-pom polymer. If/= 1, this molecule is linear, while the H-polymer corresponds to /=2. Estimate the /-dependence of relaxation time and diffusion coefficient of a melt of monodisperse pom-pom polymers for /> 1. Consider only single-chain modes and assume that the coordination number of an entanglement network is z. 

The eigenvectors of polypeptide chain modes, as in the case of NMA, can be described by PEDs in terms of symmetry coordinates, which in turn are related to internal coordinates. A list of the internal coordinates for (Ala) is given in Table IV, and the local symmetry coordinates are given in Table V (Moore and Krimm, 1976b). These serve as the general local symmetry coordinates for most polypeptide chain structures [for the particular set for (Gly) I, see Dwivedi and Krimm (1982a)]. 

Another problem that must be faced if we concentrate only on polypeptide chain vibrations is the contribution of side-chain modes to the spectrum. At the very least, we must be able to identify characteristic frequencies associated with side-chain groups and S-S bridges. We first review below what is known about these structures. 

Amino acid side chains, particularly those with aromatic groups, exhibit characteristic frequencies that often are very useful in probing the local environment of the group in the protein (Spiro and Gaber, 1977). From our present point of view, however, we are interested in characterizing spectral features of backbone chain conformation. It is therefore important to know the locations of such bands so that their contribution to the spectrum is not confused with amide and backbone vibrations. We discuss below some features (in the nonstretching region) of such side-chain modes these are summarized in Table XL. 

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