Constraint release mechanism

Newer rubber elasticity theories based on the tube model (35) consider special constraint release mechanisms which allow a physi-... 

For 100 < P < 1000, the measured diffusion coefficients for N = P no longer follow the N 2 reptation prediction. In the same range of N values, D remains proportional to N 2 if P N, i.e. if the motion of the chains surrounding the test chain are frozen down during the diffusion time of the test chain. The comparison of the data obtained with N = P and with N P clearly puts into evidence the acceleration of the dynamics associated with the matrix chains, similarly to what has yet been observed with other polymers [11, 12, 42 to 44] or in solutions [10]. This acceleration, by a factor close to three, can be attributed to the constraint release mechanism [7, 8, 13], the effects of fluctuations of the test chain inside its tube [9] being a priori the same in the two situations P = N and P N. 

Figure 3.27 Depiction of the constraint-release mechanism of relaxation. In (a), the topological constraint imposed on chain A by chain C is released, as the end of chain C crosses under chain A. Even if C eventually re-entangles with A, chain A has been given a chance to change its orientation, as illustrated in the two-dimensional depiction in (b) (From Doi and Edwards, copyright 1986 by Oxford University Press, Inc. Used by permission of Oxford University Press, Inc.)...

There are in fact two additional processes for relaxation which are quite natural to consider. One is the renewal of conformation by release of constraints which confine each chain, arising from diffusion of the surrounding chains which supply the con-straints This constraint release mechanism would operate in liquids, where the obstacles are themselves parts of reptating chains, but not in a network. 

Constraint release mechanism when chain B reptates away, it releases the constraint on chain A. Later, this constraint is replaced by chain C. which confines chain A in a displaced tube. 

Sawada, T., X. Qiao, and H. Watanabe. 2007. Viscoelastic relaxation of linear polyiso-prenes Examination of constraint release mechanism.. Soc. Rheol. Japan (Nihon Reoroji Gakkaishi) 35 11-20. 

Fig. 3.40. An illustration of the reptation, fluctuation, and constraint-release mechanisms for relaxation of entangled chains [56].

Again one finds, as for the melts, that Hess s form of the diffusion crossover, which considers an enhanced constraint release mechanism, fits the data well, giving iVe( ) 500(4 / ) ... 

Contour Length Fluctuation and Constraint Release Mechanism... 

Assuming that the constraint release mechanism is independent of the pure repta-tion mechanism, Graessley (1982) suggested the following expression for the stress relaxation modulus ... 

We will now include the contribution of constraint release in the reptation motion of the miscible polymer mixture considered previously. In so doing, we will apply the constraint release mechanism introduced in Chapter 4, and will assume a linear blending law for the stress relaxation modulus G ff) as... 

Dielectric properties reflect different averages of chain configuration and motion than viscoelastic properties and can thus be used to track features of chain dynamics that are different from those to which the stresses respond [27]. For example, the longest dielectric relaxation time is twice the longest Rouse stress relaxation time. Thus, this technique is useful for evaluating molecular models for relaxation processes, particularly constraint release mechanisms in the tube model as shown in Section 9.5.3.1. Cis-polyisoprene is particularly well suited for dielectric relaxation studies [28]. 

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