Dynamic-mechanical relaxation times

Of particular importance for detection of chemical or physical change in polymer materials are mobility filters, which are sensitive to differences in the numbers of molecules within a given window of correlation times. Within reasonable approximation such filters are relaxation filters. Here, Tj filters are sensitive to differences in the fast motion regime while T2 and Tip filters are sensitive to the slow motion regime. Which time window is of importance can be seen from Fig. 5.7 [101]. It shows a double-logarithmic plot of the mechanical relaxation strengths Hi(t) for two carbon-black filled styrene-butadiene rubber (SBR) samples as a function of the mechanical relaxation time T. They have been measured by dynamic mechanical relaxation spectroscopy. In terms of NMR, the curves correspond to spectral densities of motion. But the spectral densities relevant to NMR are mainly those referring... 

Fig. 19. Temperature dependence of the shift factors of the viscosity (T), terminal dispersion ( ), and softening dispersion (0) of app from Ref. 73. The temperature dependence of the local segmental relaxation time determined by dynamic light scattering ( ) (30) and by dynamic mechanical relaxation (o) (74). The two solid lines are separate fits to the terminal shift factor and local segmental relaxation by the Vogel-Fulcher-Tammann-Hesse equation. The uppermost dashed line is the global relaxation time tr, deduced from nmr relaxation data (75). The dashed curve in the middle is tr after a vertical shift indicated by the arrow to line up with the shift factor of viscosity (73). The lowest dashed curve is the local segmental relaxation time tgeg deduced from nmr relaxation data (75).

Attempts to improve the mechanical properties have focused on biocompatible plasticizers. Blending with PEG, the conventional name for low molecular weight (<20 000) PEG, improves elongation at break and softness of PLA. At ambient temperature, the desired mechanical properties are achieved by blending PLA with 30 wt% PEG Table 4.2 shows the effect of PEG content on the thermal and mechanical properties of quenched PLA/PEG blends. However, there is evidence that the blend is not stable and the attractive mechanical properties are lost over time. The dynamic mechanical relaxation behavior and tensile stress-strain behavior of PLA and PLA/PEG blends are shown in Figs. 4.19 and Fig. 4.20 respectively. 

Both the time dependent stress/strain measurements and the frequency dependent observations are collectively known as dynamic mechanical relaxation. 

Unfortunately, the behaviour observed in dynamic mechanical relaxation rarely conforms to the simple ideal. Usually the data have to be fitted to equations that allow for the breadth to be increased, so accommodating a distribution of relaxation times and the possibility of more than one distinct process being involved. 

Such a duality of representations is well-known in dynamic mechanical relaxation [3] for compliance and modulus. The apparent correlation times Incompliance nd are related through the ratios = where... 

These are termed the single relaxation time (SRT) functions and are shown in Figure 1. In practice solid polymers exhibit several processes each of which are broader in the frequency domain than that for a single relaxation time process. It has been customary both for dielectric and dynamic mechanical relaxation data for polymers to simply use empirical modifications of the single... 

Before discussing tire complex mechanical behaviour of polymers, consider a simple system whose mechanical response is characterized by a single relaxation time x, due to tire transition between two states. For such a system, tire dynamical shear compliance is [42]... 

Figure C2.1.14. (a) Real part and (b) imaginary part of tire dynamic shear compliance of a system whose mechanical response results from tire transition between two different states characterized by a single relaxation time X.

The simulations also revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin. The fluctuation time for this loop as well as the relaxation time for many of the processes in proteins can be on the order of microseconds and longer (Eaton et al., 1997). The loop has enough time to fluctuate into an open state on experimental time scales (1 ms), but the fluctuation time is too long for this event to take place on the nanosecond time scale of simulations. To facilitate the exit of biotin from its binding pocket, the conformation of this loop was altered (Izrailev et al., 1997) using the interactive molecular dynamics features of MDScope (Nelson et al., 1995 Nelson et al., 1996 Humphrey et al., 1996). 

The dynamic mechanical properties of PTFE have been measured at frequencies from 0.033 to 90 Uz. Abmpt changes in the distribution of relaxation times are associated with the crystalline transitions at 19 and 30°C (75). The activation energies are 102.5 kj/mol (24.5 kcal/mol) below 19°C, 510.4 kJ/mol (122 kcal/mol) between the transitions, and 31.4 kJ/mol (7.5 kcal/mol) above 30°C. 

In conclusion, the different thermal histories imposed to PTEB have a minor effect on the /3 and y relaxations, while the a. transition is greatly dependent on the annealing of the samples, being considerably more intense and narrower for the specimen freshly quenched from the melt, which exhibits only a liquid crystalline order. The increase of the storage modulus produced by the aging process confirms the dynamic mechanical results obtained for PDEB [24], a polyester of the same series, as well as the micro-hardness increase [22] (a direct consequence of the modulus rise) with the aging time. 

The glass transition temperature can be chosen as the reference temperature, though this was not recommended by Williams, Landel, and Ferry, who preferred to use a temperature slightly above T. In order to determine relaxation times, and hence a, use can be made of dynamic mechanical, stress relaxation, or viscosity measurements. 

Contrary to the phase separation curve, the sol/gel transition is very sensitive to the temperature more cations are required to get a gel phase when the temperature increases and thus the extension of the gel phase decreases [8]. The sol/gel transition as determined above is well reproducible but overestimates the real amount of cation at the transition. Gelation is a transition from liquid to solid during which the polymeric systems suffers dramatic modifications on their macroscopic viscoelastic behavior. The whole phenomenon can be thus followed by the evolution of the mechanical properties through dynamic experiments. The behaviour of the complex shear modulus G (o)) reflects the distribution of the relaxation time of the growing clusters. At the gel point the broad distribution of... 

The dynamic mechanical experiment has another advantage which was recognized a long time ago [10] each of the moduli G and G" independently contains all the information about the relaxation time distribution. However, the information is weighted differently in the two moduli. This helps in detecting systematic errors in dynamic mechanical data (by means of the Kramers-Kronig relation [54]) and allows an easy conversion from the frequency to the time domain [8,116]. 

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

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