Random coil chain model

The structural analysis described above and in more detail elsewhere, shows the x-ray scattering functions to be sensitive to intrachain correlations. In fact, a more "random chain model (with a delocalized rotation state for one bond) than the "random coil" chain model is required to give a satisfactory match between the experimental and model si (s) functions. A model in which the interchain correlations are minimal with no orientational correlations provides a scattering function which is in good agreement with the observed scattering. Thus there seems to be no evidence to require more local order than inherent in a dense molecular system. This is perhaps not suprising. The polyisoprene molecule has a compact cross section, almost cylindrical in nature and corresponds to the "typical molecule drawn in schematic views of the noncrystalline state. 

Finally we mention the Kratky plot which also may help to detect branching. Here ((S2) q2) Pz (q2) is plotted against q. Figures 26 and 27 show the Kratky plots for regular star-molecules and for the soft sphere model. Linear randomly coiled chains result in... 

Expressions for the spectral density can be developed from models for local motion in randomly coiled chains. Two general types of local motion will be considered, and they are segmental motion and anisotropic rotation. Segmental motion itself will be... 

Fig. 6.11 The randomly coiled chain. A photograph of a model of a polymethylene chain containing 1000 links made by setting the links at the correct valence angle and choosing the position of each successive link in the circle of rotation as one of the six equally spaced positions obtained by throwing a die. (Reproduced by permission of Oxford University Press.)...

Self-diffusion of random coiled chains in the bulk was studied by Edwards [32] and de Gennes [33], who developed a reptation model of a chain confined to a tube. As shown in Figure 8.2, a single chain of TP with a contour length of L is diffused in a tube, which represents the topological constraints on its motion imposed by the matrix and by other chains in the bulk. At the same time, the tube contour represents another random walk. At a given time the... 

Our single-chain model may be roughly described in these terms one end of an (admittedly short) random coil chain is anchored near the surface of the amphiphilic aggregate and the probabilities of the chain conformations are changed as little as possible consistent with setting up a state of constant density in the aggregate interior. 

Two remarks about the model are in order here. In the first place, this description implies that a solvent site affects the folding equilibrium of an adjacent site exactly as an adjacent unfolded site does. This is not unreasonable, since the randomly coiled chain occupies a considerable volume of solution, and hence contacts with a space occupied by a random chain, are largely contacts with solvent. 

As for further analysis, curve fitting against the worm-like chain (WLC) model was conducted and indicated as a solid line in Figure 21.4. The model describes single polymer chain mechanics ranging from random-coil to fully extended forms, as follows ... 

Before discussing details of their model and others, it is useful to review the two main techniques used to infer the characteristics of chain conformation in unordered polypeptides. One line of evidence came from hydrodynamic experiments—viscosity and sedimentation—from which a statistical end-to-end distance could be estimated and compared with values derived from calculations on polymer chain models (Flory, 1969). The second is based on spectroscopic experiments, in particular CD spectroscopy, from which information is obtained about the local chain conformation rather than global properties such as those derived from hydrodynamics. It is entirely possible for a polypeptide chain to adopt some particular local structure while retaining characteristics of random coils derived from hydrodynamic measurements this was pointed out by Krimm and Tiffany (1974). In support of their proposal, Tiffany and Krimm noted the following points ... 

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