Rubber networks, relaxing

Approximative Methods for the Evaluation of Equilibrium Moduli of Relaxing Rubber Networks... 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

When a rubber network is stretched only those chain sections extending between crosslinking points are permanently oriented by the external stress and contribute to the elastic equilibrium modulus. Dangling chains are temporarily oriented by a deformation, but they can relax, reptating from the free ends towards their permanent... 

In the present poblem of telechelic polymers, the A-state corresponds to the bridge chain connecting the micellar junctions, while the B-state is the dangling chain. In affine network theory, va = ( X ) r as in (9.3), and vb = 0. But vb may also be affine if the B-state is another type of the elastically effective state, such as helical conformation or globular conformation of the same chain. We can study the stress relaxation in rubber networks in which chains change their conformation by deformation [30]. 

Consider next a network that is initially in the completely amorphous state as represented by point B in Fig. 8.4. If the temperature is lowered while the length is held consistent, a path vertically downward from point B is traversed. As the two-phase region is entered, oriented crystallinity will develop and the equilibrium stress will concomitantly decrease. At 303.2 K the stress will have decreased about tenfold. A formal basis is thus provided for the experimental results of Smith and Saylor,( 18) Tobolsky and Brown,(19) and Gent (20) who observed a relaxation of the stress during the oriented crystallization of natural rubber networks held at fixed length. 

Thermodynamic Analysis. As reported previously, the storage modulus G of PDMS networks with tetrafunctional crosslinks is independent of frequency between 10 3 and 1 Hz (21). This behaviour which is entirely different from that of vulcanized natural rubber or synthetic polyisoprene networks, was attributed to the lack of entanglements, both trapped and untrapped, in these PDMS networks. Figure 4 shows that G of a network with comb-like crosslinks is also frequency independent within an error of 0.5%. For comparison, two curves for PDMS having tetrafunctional crosslinks are also shown. The flat curves imply that slower relaxations are highly unlikely. Hence a thermodynamic analysis of the G data below 1 Hz can be made as they equal equilibrium moduli. 

From a theoretical point of view, the equilibrium modulus very probably gives the best characterization of a cured rubber. This is due to the relationship between this macroscopic quantity and the molecular structure of the network. Therefore, the determination of the equilibrium modulus has been the subject of many investigations (e.g. 1-9). For just a few specific rubbers, the determination of the equilibrium modulus is relatively easy. The best example is provided by polydimethylsiloxane vulcanizates, which exhibit practically no prolonged relaxations (8, 9). However, the networks of most synthetic rubbers, including natural rubber, usually show very persistent relaxations which impede a close approach to the equilibrium condition (1-8). 

An effect of network morphology is illustrated by the work of Shen and Tobolsky (ISO). They cross-linked rubbers in the presence of inert diluents such polymerizations tend to promote intramolecular chain loops rather than interchain cross-links. Their polymers had very low stress-relaxation... 

The reduction in stress which takes place in a test strip of rubber held at constant elongation. Stress relaxation measurements are used in the study of the ageing of rubber vulcanisates, the degradation of the network structure resulting in a reduction of the tension. 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

Knibbe, D. E. Diffusion-controlled stress relaxation of swollen rubber-like networks, Rotterdam University Press 1968. 

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