Primitive path length

L average primitive path length mo occupying pnmitive segments, Z ]... 

The primitive path length L of a dtmn which has m path segments... 

The reptation model assumes the contour length of the primitive path is fixed at its average value (L). In reality, the primitive path length... 

L fluctuates in time as the chain (or snake) moves. A full description of chain dynamics requires knowledge of the probability distribution of the primitive path lengths. This problem has been solved exactly by Helfand and Pearson in 1983 for a lattice model of a chain in a regular array of... 

The contribution to the free energy is not strictly linear because for each primitive path length L, the entropy of not only the ends, but of the rest of the chain in an entanglement network needs to be considered. 

Average primitive path length Half thickness of thin polymer slab Critical molecular weight of polymer... 

Khaliulhn, R.N. and Schieber, J.D. (2008) Analytic expressions for the statistics of the primitive-path length in entangled polymers. Php. Rev. Lett., 100, 188302. 

Each of the processes for moving ends past entanglements - reptation as a whole, primitive path length fluctuations, contraction in stretched tubes - contributes to tube renewal. The different time scales for each, as well as the distribution of time scales arising in a polydispersed sample, introduce new features in the relaxation modulus. 

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