Helical wormlike coil model

Yamakawa and co-workers developed the quasi-two-parameter (QTP) theory from the earlier two-parameter (TP) theory, to incorporate chain stiffness into the model. Specifically, the QTP theory computes C o via the helical wormlike coil model (HW),... 

Yoshizaki, T., Nitta, L, and Yamakawa, H., Transport coefficients of helical wormlike coils 4. Intrinsic viscosity of the touched-bead model. Macromolecules, 21, 165-171 (1988). 

A consideration of the molecular conformation using the wormlike chain model suggests that the curdlan molecule may contain helical portions but, as a whole, takes a random-coil conformation ( ) ... 

In the range of y where the helical and wormlike models display their absolute maxima in Figure 1, the presumably more realistic random coil model R has a much lower and broader... 

Figure 1. F(ii) = NiJP(ii) vi. ii = (4t/ K) sin (e/2) for helical amylosic chain nwdels A, B, and C, wormlike amylosic chain model W, jointed helical model J, and realistic random coil model R. Details of the models are described in the text.

A perfect helical main chain conformation always leads to a rodlike or cylindrical external shape. But each monomeric unit in such a rod contributes a certain flexibility. So, the flexibility of the rod, as a whole, must increase with increasing degree of polymerization, even when the flexibility per monomeric unit remains constant. A macroscopic example of this would be the flexibility of steel wires of equal diameter but different lengths. Thus, even a perfect helix will adopt coil shape if the molecular mass is very high. Because of this, helically occurring macromolecules, and other stiff macromolecules, can often be well represented by what is known as the wormlike screw model for macromolecular chains at low molecular masses, the chains behave like a stiff rod, but for high molecular masses, the behavior is more coil-like. Examples are nucleic acids, many poly(a-amino acids), and highly tactic poly(a-olefins). 

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