Backbone relaxation

if there are arms attached to the backbone, the drag that these arms add to that of the backbone is 

---

The torsional movement of the side chains is characterized by an activation energy that is strongly dependent on the type and size of the side chains. The bonds adjacent to the side groups belong to the backbone chain. At temperatures below Tg, the activation energy for backbone relaxation is very high (75 kcal/mol for poly(dimethylsiloxane) [PDMS i]). Whether local and limited relaxation occurs for the backbone at temperatures below Tg is uncertain. At temperatures above Tg, the activation energy for backbone relaxation is much lower. For PDMS, a value of 2.75 kcal/mol was determined experimentally (i). 

Dynamics of Conformational Transitions. The fastest backbone relaxations in polymers are conformational transitions. These must proceed along a reaction coordinate which is a localized mode. This frequently leads to cooperative, cranklike pairs of transitions and nonexponential correlation functions. Simulations of chains undergoing conformational transitions will be described. 

Notice that when the volume fraction of arms 0 approaches unity, Eq. 9.18 yields the expression for dynamically diluted star arms, while when 0 approaches zero, Eq. 9.18 reverts to the arm relaxation time in the absence of dynamic dilution. Eq. 9.18 should then be used in Eq. 9.13 to compute the backbone relaxation time. In Eq. 9.10 the number of entanglements Z should be taken to be the number of entanglements of the backbone with other backbones, because the arms have released all their constraints on the time scales over which the backbone is moving. Since the backbone volume fraction is 0, the number of backbone/backbone entanglements is 0(, where is the number of undiluted backbone entangle-... 

B.8 Predictions of the McLeish-Larson Constitutive Equation for Branched Polymers (McLeish and Larson, 1998). The stress tensor for a branched polymer, which is given in Table 3.7, is a function of the dynamic variable S, which describes the average backbone orientation, and A, which describes the average backbone stretch. The model described in the table is written for multiple relaxation modes and represents the simplest model for a branched polymer. Dynamic expressions for S and X for each relaxation mode are given in Eqs. 2 and 3 in Table 3.7. Tb is the /th mode of the backbone relaxation time and Ts, is the backbone stretch orientation time, v is taken as Hq, where q is the number of branch arms associated with a given Ts. 

---