Deep Primitive Path Fluctuations

The simplest possible type of branched polymer is a monodisperse star. In some respects, monodisperse stars are actually easier to consider than linears, because for stars one can neglect reptation. This leaves only the relaxation mechanisms of primitive path fluctuations, constraint release, and high-frequency Rouse modes that need to be considered to describe the linear 

Because of the exponential dependence of relaxation time on the potential, the relaxation of star polymers is extremely sensitive to the strength of the potential and therefore to the value of V and of Mg, which sets the value of Z. The correct value of v has been controversial a discussion of this and of non-quadratic corrections to Eq. 9.2 can be found in McLeish [14]. Recent fine-scale simulations using lattice models and real-space pearl necklace models of entangled polymers provide some justification for the quadratic potential and for the value v= 3/2 [15, 16]. As mentioned in Section 6.3, the relationship between and is also open to revision [17]. Hence, adjustments of either or v might be needed to obtain quantitative predictions of the rheology of star polymers. 

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For linear chains, only the portions near the chain ends relax by primitive path fluctuations, and we will use the symbol Tgariy( ) in our development of a model for this fast relaxation. The interior parts of the chain, however, require quite deep fluctuations to reach them, and the time required to do this is slower than the time at which these portions of the chain will have already relaxed by reptation. We will later use the symbol in our discussion of this... 

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