Relaxation time mechanical

A qualitative relationship exists between the electric and mechanical relaxation times. Both are increased by the addition of fillers and reduced by the addition of plasticizers. 

An impact modifier is a rubber phase dispersed in particulate form throughout the matrix of a polymer solid. Unlike plasticizers, the rubber particles retain their intrinsic properties as a separate phase. The glass transition temperature of the parent matrix is not lowered by the addition of an impact modifier. The rubber particles do two things to the parent matrix phase (2,3,4) they act as stress concentrators (i.e., a large strain will start in the matrix near the interface) and they enhance the multi-axiality in stress. As multiaxial tensile strength near the interface further enhances dilatation, which shortens the mechanical relaxation time, the otherwise brittle polymer solid of the matrix will undergo plastic deformation in the vicinities of the rubber particles. 

Fig. 7.1.4 Mechanical relaxation strength H as a function of the mechanical relaxation time r for SBR. Filled circles unaged material. Open circles material aged in air at 180 °C for 24 h. The timescale is shifted towards shorter times, because the curves are referenced to 25 °C and not to the glass transition temperature. Adapted from [Fiill] with permission from Hiithig Gmbh.

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... 

There are no infinite mechanical relaxation times for reversible gels. If the macroscopic coherent network present at any instant is deformed rapidly by some applied strain, the stress stored in this deformation can relax through the chemical reaction, even if the mechanical relaxation time of the network (had the cross-links been permanent) would have been infinite. 

A simple formula gives the effective relaxation time, t/, of a mechanism, i, of inherent mechanical relaxation, time Tj, when the rate at which mechanisms i are transformed chemically into other structures is fcj (JO, 11). 

If ki is zero, the gel is permanent and the measured relaxation time and the observed relaxation behavior correspond to t,. In that case, if t, is infinite, so is t/. On the other hand, if ki is finite, then t/ will be finite, even if is infinite. In other words, even if, over any period of time, the reversible and permanent gel have indistinguishable structures and, inherently, possess the same spectrum of mechanical relaxation times, t, the reversible gel will be characterized by a truncated spectrum. Relaxation times longer than l/ki will be bypassed by relaxation through the chemical reaction. A reversible gel is thus liquidlike and cannot support itself against mechanical stresses over times in excess of l/ki. Moreover, if the volume of solvent... 

Table 1. Chain relaxation and diffusion mechanisms relaxation time (t) and molecular weight...

Fig. 4 The characteristic time Zs of the slow mode above Cn and the mechanical relaxation time zm are plotted against PVA concentration C...

Effective relaxation time Spin separation in radical pair Correlation time of radical rotation Mechanical relaxation time... 

This relationship is analogous to the empirical one established by Williams, Landel, and Ferry (WLF equation) which serves to relate the dielectric and mechanical relaxation times measured at a temperature T with those measured at the reference temperature (here Tg). 

Chain relaxation and diffusion mechanisms relaxation time (r) and molecular weight (M) relationships. Me is molecular weight between chain entanglements Te is the Rouse relaxation time between chain entanglements tro is the Rouse relaxation time of the whole chain Tr is the Reptation relaxation time... 

If the deformation time A< is much less than the mechanical relaxation time XiaiT), no rate dependence is expected for elastic moduli and the Poisson s ratio. 

It was found that the relaxation behaviour was dependent on the degree of imdercooling from 2 and that the mechanical relaxation times and calorimetetric behaviour were correlated. 

PEO, which are typical matrices for polymer electrolytes, has been reported to be 10 to 10 s at room temperature, and its temperature dependence obeys the WLF equation [24]. These features are shown in Fig. 5 [11]. The temperature dependence of the inverse of the dielectric relaxation time t(T), owing to the backbone motion of the PPO network polymer, obeys the WLF equation shown in this figure. How small ions migrate in these rubbery media is an interesting question. The percentage change in the conductivity with temperature is comparable with that in the dielectric [11,25] or mechanical relaxation time [16,26,27] of the backbone motion for the PPO-and PEO-based polymer electrolytes, when is used as reference temperature. A typical result is shown in Fig. 6 [26], in which the ratio of ionic conductivity at T, to that at T, o (Tg), and the ratio of mechanical... 

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