Chain-tension relaxation

Consider a single chain having N entanglement strands with the slip-link positions at Rq, Ri,. .., Rat. Let the number of Rouse segments on the th entanglement strand be denoted by AT. Then the total number of Rouse segments of the chain is 

Letting the index n represent the nth Rouse segment in the entanglement strand between Rj i and R, Doi assumes for t r (see Eq. (9.B.26)) 

Let Sn be the point on the primitive-chain contour corresponding to the nth Rouse segment. Denote the positions of Sn in three-dimensional space before and after a step deformation E is applied as R°(S ) and R(S (t)), respectively. Then, before the application of E, the length vector /()v° along the primitive chain corresponding to the nth Rouse segment is given by 

And at time t following the initial application of E, the length vector corresponding to the nth Rouse segment is given by 

Equation (12.5) contains two relaxation processes (v (t)v (t)) is to be randomized or relaxed by the chain reptational motion, and the change in with time represents the chain-tension relaxation. The former is much slower than the latter if the molecular weight is large. At t T q, the chain-tension relaxation process ends and ln t)) returns to its equihbrium value / the stress tensor T(t Teg) becomes 

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The reinforcement induces important changes of the elastomer network, due to the formation of strong and weak bonds between the chain segments and reticulation centres located on the surface of active charge particles [1199]. The Mullins effect or the tension relaxation in networks is ascribed to the splitting of weak bonds. 

The mechanism proposed by F. Bueche comprises the following fundamental steps 1) the splitting of the chain fragments located between two particles of filler 2) recovering to a statistical distribution of tensions, after 3) tensions relaxation and 4) stress redistribution on the network chains. 

Attempts of photo-dilatation and contraction of polyamide and polyimide containing stilbene in the aromatic chain backbone were made in water. It was found that poly-imide-poly(iininoisophthaloylimino-l, 3-phenylenevinylene-1,4-phenylene), if stretched under constant tension, relaxed on irradiating with UV light, and recovered to initial stress when the irradiation was stopped This type of polyimide is stable in the dark in the trans conformation which is more stretched, and transforms to the cis form which is the more coiled conformation under irradiation. Therefore, the relaxation by photoirradiation should be associated with an increase in polarity of the polymer film. 

Very frequent are the cases of stress-induced crystallizations. A typical case is that of slightly vulcanized natural rubber (1,4-m-polyisoprene) which, under tension producing a sufficient chain orientation, is able to crystallize, while it reverts to its original amorphous phase by relaxation [75],... 

First approaches to approximating the relaxation time on the basis of molecular parameters can be traced back to Rouse [33]. The model is based on a number of boundary assumptions (1) the solution is ideally dilute, i.e. intermolecular interactions are negligible (2) hydrodynamic interactions due to disturbance of the medium velocity by segments of the same chain are negligible and (3) the connector tension F(r) obeys an ideal Hookean force law. 

If the PEP-PEE triblock chains are arranged in microdomains separated by well-defined interfaces, then the additional fast relaxation process observed by NSE would result from the undulation motions of the interface. The thermal motions of the interface are driven by the surface tension and overdamped. With an effective viscosity r eff in the interfacial region, the relaxation rate if Q) ... 

RoLe has to be calculated for a chain with one end fixed to a surface). Fig-ure 6.15 displays a fit of the measured spectra at both temperatures with the complete dynamic structure factor where the Rouse relaxation rate was taken from an earlier experiment. Fit parameters were the surface tension and the effective local viscosity of the short labelled PEP segments. The data are well... 

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