Persistence length, fractal

Figure 37 Brush molecules change from (a) flexible to (b) rod-like conformation with the increase in the DP of side chains n. (c) Persistence length Ip is determined as the distance along the chain at which the fractal dimension changes from d= 1 to d= 1.33. (d) The persistence length increases with the side-chain length as Ip Reprinted from Sheiko, S. S. Sun, F. C. Randall, A. etal. /Vafwre 2006, 44( (7081), 191-194, with permission from Nature...

The object we have thus created is usually addressed as the Brownian chain , and it is characterized by just one parameter, namely the mean-squared end-to-end distance R ). Although being defined as a mathematical limiting structure, the Brownian chain may indeed serve as a representative of real polymer chains in a certain region which is well-defined, namely for length scales which are larger than the persistence length and smaller than the size i o of the chain. The Brownian chain represents correctly the fractal properties and differs from the real chain in that it extends these fractal properties down to zero distances. 

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