The Relaxation Strength

A total applied stress a is given in terms of the initial unrelaxed strain e by adding the stresses in both springs. Thus 

The final relaxed strain C2 is given in terms of an applied stress a by 

All the relationships defined above are proportional to G — Gr, and hence to the relaxation strength, tan 5 iax and tan 5d(ln co) are closest to our original definition in being normalised to a dimensionless quantity. This provides some formal justification for the use of tan S rather than G2 for estimating the relaxation strength to correlate with structural parameters [8]. 

Boltzmann, L. (1876) Zur Theorie der elastischen Nachwirkung. Pogg. Ann. Phys. Chem., 7,624. 

(1960) Viscoelastic stress analysis in Proceedings of the First Symposium on Naval Structural Mechanics, (eds J.N. Goodier and J.F. Hoff), Pergamon Press, Oxford, p. 456. 

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It is apparent that there are a considerable number of parameters to be determined. According to equation (8) and equations (2-7) there are 6N+2 parameters where N is the number of relaxations present (it is not 8N because the relaxed modulus of one process is equal to the unrelaxed modulus of the next process in a sequence). In practice, it is found that with the large number of experimental points available in a scan (typically 50-100) the determinaton usually proceeds satisfactorily. However, in coitimon with many statistical fitting situations, it can happen that parameter determination is not unique. Our experience has shown that problems can arise when the relaxation strength is small or when only part of a peak is recorded. The problem with small relaxaton strength is associated with equation (1) where it is seen that the activation energy is related to the ratio of peak area and relaxation strength E(j- Ep. When the process is quite... 

The relaxation strengths are the difference between the instantaneous value and equilibrium value,... 

The site model appears to provide an adequate description of basic features of the dynamics of molecular motions in secondary transitions. On the other hand, however, attempts to calculate and interpret the extent of energy losses, i.e. the relaxation strength, in terms of the barrier model have so far been less successful. Theories employing a model with the same depth of potential energy minima1,76,77 do not seem suitable... 

This equation implies that the relaxation strength of a molecular motion passes through a maximum at AH° = 2.4 RT and that for AH° = 0 no relaxation process can exist. An equation for the loss factor tan 6 derived from this theory was attempted81 for the... 

The y Relaxation. In common with many other polymers (8) both PPO and PS display significant loss maxima below room temperature at the frequencies under consideration. Whereas the process responsible for the a loss is at least qualitatively understood in terms of a main chain relaxation associated with the glass transition, y losses can often only tentatively be attributed to specific mechanisms. In PPO, for example, it does not seem unreasonable to propose that the y loss is associated with librations in the two pendant methyl groups this view is somewhat reinforced by the observation that in the dielectric measurements the relaxational strengths of the y and a loss processes are comparable. As the latter can be well interpreted (6) in terms of a dipolar relaxation of the main chain in which the entire dipolar contributions arise from the methyl groupings, it seems plausible to assume that the same dipoles are responsible for the y loss mechanism. In polystyrene there is a similar... 

Because the y loss maxima of the constituent polymers are so close in temperature, we would not expect to find any change in this parameter in the mixtures, and indeed none was observed. The maxima in pure PPO are somewhat stronger than in PS at 1 kHz, the c"max are 2.5 X 10 3 and 9 X 10"4, respectively. Consequently, it is not unexpected also to find a uniform change in the c"max values for the mixtures roughly proportional to the respective compositions. More information, however, can be obtained by considering the relaxational strengths themselves—i.e., of the areas under the loss peaks. The values of eR — were obtained from the following equation (10) ... 

As usual, the relaxation strength of the subglass processes increases as the frequency decreases. The relaxation strength of the y relaxation in P4THPMA is close to the corresponding to PCHMA [30] and significantly lower than that of the corresponding to PDMA [38,104],... 

With the static cross-correlations contained in the Kirkwood-Frohlich correlation factor (e.g., Ref. 44) gk 1 I (Pi(0) i P (0))/p2, which is finally absorbed in the relaxation strength, C (f) reduces to... 

The inflection point/of the two-step correlation functions observed in Fig. 13 may be taken as a measure of what is called the nonergodicity parameter within MCT. It quantifies the relaxation strength of the slow degrees of freedom, that is, the a-process. Correspondingly, the quantity 1 / specifies the strength of the... 

Fig. 6. Schematic correlation function close to Tg defining the relaxation strengths / and S (cf. Eqs. (3) and (4)).

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