Persistence length defined

As cylindrical micelles grow, their total length can eventually exceed their persistence length (defined in Section 2.2.4), and they then become semiflexible wormy micelles. 

There is one more essential difference between the flexibility of 2-dimensional membranes and that of giant 1-dimensional micelles. In the present case, the moduli K, K have dimensions of energy. There is therefore no equivalent for the idea of persistence length defined in the 1-dimensional case. Once again, this can be related to common experience. The effort required to curve a square plate through a given angle does not depend on its size, provided the thickness remains the same, of course. 

The combination of parameters lj9 enters in the expressions of the persistence length /p and the Kuhn length b. The worm-like chain is defined as the limit 0 and 6 0 at constant persistence length /p (constant Ij ) and constant chain contour length = nlcos 9j2) = nl. 

Another striking experimental feature is that the attractions do not appear to lead to macroscopic phase separation. In this sense, the counterion-mediated attraction between the chains appears to have a different character from ordinary attractions that lead simply to phase separation at sufficiently high concentrations. Instead, the chains tend to form dense bundles of a fairly well-defined thickness [8,11]. The precise morphology of the bundles appears to depend sensitively on the persistence length of the polyelectrolyte, the chain length, and the concentration. In the case of dilute DNA, the bundles tend to be toroidal or rod-shaped. Other stiff polyelectrolytes tend to form rodlike bundles or networks of bundles. In each case, however, there is a well-defined cross-sectional thickness for the bundles. We will concentrate on the question of why there is a characteristic cross-sectional bundle diameter, rather than on the specific morphology of the bundles. 

Chain stiffness can be quantitatively characterized by the persistence length a, defined as... 

A simple descriptor of chains is the end-to-end distance = ri — r l, defined also from geometry and connectivity. For a wormlike chain, the configurationally averaged end-to-end chain is related to the persistence length as follows ... 

---