Persistence length unperturbed

Fig. 38. Correlation between the unperturbed Benoit-Doty persistence length and the persistence length q L 671 A, cellulose/cadoxen A cellulose/FeTNa O CA(2.92)/DMAc (J) CA(2.46)/DMAc —O CA(2.46)/acetone <> CA(2.46)/THF CA(0.49)/DMAc O ...

Experimental Assessment, The most direct experimental assessment of the persistence length may be obtained from the root-mean-square radius of gyration measured by light scattering. The analytical expression for the unperturbed Rq of a. wormlike chain has been given by Benoit and Doty (5) ... 

The persistence length model therefore describes the whole spectrum from the more rodlike oligomers (small j) to the well-developed coils (large y). However, the model ignores the finite thickness of the chain, and so it only holds strictly for unperturbed coils. The error due to the finite thickness may be neglected when the persistence length is much greater than the chain thickness. 

Chain stiffness prevents the monomer units of a polymer molecule from having contact with one another. Thus, we may expect that there exists for a semi-flexible polymer a certain contour length Lc below which the excluded-volume effect on the chain dimensions disappears (in a statisitical sense). This prediction is borne out by the data of Figure 5-3, which show that (5 )/M follows the curve for an unperturbed wormlike chain until Mw reaches 3 x 10 (L 4 X 10 ). Obviously, Lc ought to be larger for a stiffer polymer, i.e., one with larger persistence length q. 

Statistical properties of an unperturbed HW chain in equilibrium are determined with five parameters chain length L, ao,l3o,Ko, and tq (the latter four characterize U s) of the chain). This should be contrasted to the fact that only two parameters L and q are needed for the description of these properties of an unperturbed wormlike chain. In adapting the HW chain to actual polymers, the shift factor Ml(= M/L), instead of L, may be chosen as a parameter since M can be determined experimentally. Thanks to eq 2.10 the stiffness parameter (2A) may be used for ao. For HW chains we have no equation corresponding to eq 2.2. Hence (2A) may not be equated to q according to eq 2.14. It should be noted that the persistence length q is the concept associated only with wormlike chains. The Poisson ratio ao of the HW chain is expressed in terms of o and j3o as... 

The definition of a segment stiffness depends on its nature. If a long stiff segment can be described as a worm-like chain, characterized by a particular smooth and uniform curvature, then the chain persistence length is a good initial descriptor. For a hypothetical worm-like chain of contour length L and statistical mechanical average square of the unperturbed end-to-end distance o, it was shown by Porod and Kratky [49,50], that in the limit of L -> oo,... 

---