Network chain density

FIGURE 18.2 Tensile strength of styrene-butadiene rubber (SBR) as a function of network chain density. (From Bueche, F. and Dudek, T.J., Rubber Chem. Tech., 36, 1, 1963.)... 

The equilibrium stress-strain isotherms in elongation, and the swelling ratios in benzene, were measured at 25°C for these networks. Network chain densities calculated from these measurements exceeded the values predicted from stoichiometry. 

A3 is the ratio of network chain density calculated from the affine network equililbrium swelling theory (inside the [ ]) to that obtained from stoichiometry ... 

The physical network chain density (nent) was estimated from the comparison of the NMR and swelling results. A linear relationship of the nent in the NR system as a function of carbon black content exists. This result suggests that the physical adsorption plays a major role in the polymer-filler interactions. 

Figure 9.11 Physical network chain densities of NR cure to t9() with a variety of carbon black as a function of carbon-black content...

It is demonstrated that the quasi-static stress-strain cycles of carbon black as well as silica filled rubbers can be well described in the scope of the theoretic model of stress softening and filler-induced hysteresis up to large strain. The obtained microscopic material parameter appear reasonable, providing information on the mean size and distribution width of filler clusters, the tensile strength of filler-filler bonds, and the polymer network chain density. In particular it is shown that the model fulfils a plausibility criterion important for FE applications. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. 

Table 17. Network chain density data obtained at different curing times for (V)-EPTM and ENB-EPDM... 

If the objective of the experiment is to estimate the network chain density by the statistical theory, and if swelling is resorted to as a means for alleviating the above experimental difficulties, then the measurement of stresses becomes redundant the theory of equilibrium swelling of Flory and Rehner (127,128) makes an estimate of the desired network chain density possible with only the knowledge of the equilibrium swelling volume. The usual procedure is to calculate the volume fraction of polymer in the swollen rubber (ar) under the assumption that the filler does not swell. The Flory-Rehner theory then yields, for a network containing no sol fraction ... 

Since vr0jvT varies only slowly with vr0, while v is a rather sensitive function of the inverse swelling ratio, the result of substituting vr into the Flory-Rehner equation is a vapp which is too large, but which still reflects rather faithfully any changes in vr0 brought about by varying the network chain density. Thus we may write as an approximation... 

Thus, the Tg-value difference increases according to equation 7.4 linearly with the network chain density. This relation was checked for two vulcanised rubber systems an experimental solution SBR (SSBR) and an commercial emulsion SBR (ESBR,... 

The Tg increase of SSBR due to vulcanisation versus the network chain density... 

The Tg-value increase plotted as a function of the network chain density in Figure 7.5, shows indeed a linear relation which nearly crosses the origin for the non-crossiinked, pure rubber. Hence, equation 7.2 decribes the Tg-value increase of an experimental SSBR system due to vulcanisation satisfactorily. 

Vapp is essentially the network chain density in the rubber phase, the number of filler-contributed linkages being much smaller than the number of cross-links, v,. 

Figure 3.1 3 Comparison of measured rubber shear modulus with that calculated from the network chain density (from Treloar, L. G. R., Introduaion to Polymer Science, Wykeham, 1970).

Torsional creep measurements were made on the urethane-crosslinked polybutadiene elastomers at temperatures between -68 and 25°C.The average molecular weight of a networks chain. Me, is 3400, 5200, and 8300 for TB-1, TB-2, and TB-3 respectively. The reduced shear creep compliance Jp(t/ar) curves obtained for the three samples are shown in Fig. 18. The reference temperatures are chosen to be 7.4,0.0, and 17.0°C for TB-1, TB-2, and TB-3 respectively so that superposition is achieved at shorter times in the primary softening dispersion. The most loosely urethane-crosslinked TB-3 has the largest 7e = 2.5 x lO Pa There is a plateau intermediate between the glassy compliance 7g (not reached in these measurements) and /e, and its level is about 2.0 X 10 Pa in all three samples. The network chain density does not affect the form of the time-dependent response up to and including the intermediate plateau in the Jp(t) curves. Only the terminal dispersion, i.e., the approach to /e, is influenced. The shift factors, Uj, that were used to obtain the... 

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