Modulus glassy

Substituting this information into the last equation gives an equation for the glassy modulus as a function of the fraction of covalent bonding... 

In general, as the ion content is raised, the modulus or stiffness of the ionomer is increased, as shown by the data in Fig. 2. While the increase is much greater in the elevated temperature range, where the polymer is acting more like a crosslinked rubber, there is still a significant increase in the glassy modulus below Tg. For example, for the PMMA-based ionomer of Fig. 2, the modulus at 30°C is almost 20% above that of the homopolymer for an ionomer having an ion content of 12.4 mol%. For the... 

Plasticization, whose main manifestation is the decrease of the glass transition temperature (a transition in dynamic mechanical spectra), is generally accompanied by an increase of the glassy modulus in the temperature interval between Tp and T. , an effect is known as antiplasticization. 

At temperatures well below Tg, when entropic motions are frozen and only elastic bond deformations are possible, polymers exhibit a relatively high modulus, called the glassy modulus (Eg) which is on the order of 3 Gpa. As the temperature is increased through Tg the stiffness drops dramatically, by perhaps two orders of magnitude, to a value called rubbery modulus Er. In elastomers that have been permanently crosslinked by sulphur vulcanization or other means, the values of Er, is determined primarily by the crosslink density the kinetics theory of rubber elasticity gives the relation as... 

At still higher frequencies than the highest frequency in Fig. 8.14, polymer liquids exhibit a solid response, with storage modulus G independent of frequency and equal to the glassy modulus Cg. A typical value of the glassy modulus is of order lO Pa (see Table 8.2). The glassy modulus... 

This same glassy modulus describes the linear elastic response of the polymer at temperatures below its glass transition temperature Tg, [see Hooke s law, Eq. (7.98)]. The physical reason that the liquid s response becomes similar to that of the glass is that at such high frequencies (or short time scales) monomers (and even small parts of monomers) do not have time to move and relax stress. 

Among the three variables Aq, (3, and s, Aq is basically dictated by the glassy modulus, the reciprocal of the glassy compliance Jq, and (3 is determined by the Jp t) line shape over the small-compliance region, < 10 cm /dyne. The determination of s (Eq. (14.5)), which sensitively correlates with the if-normalized time scales of the Jp t) curve in the 10 5 X 10 cm /dyne region and is effectively decoupled from how... 

There are other reasons why a readily identifiable frequency shirt may not be seen at the T for the FPOL curves. As noted earlier, a SAW device coated with a glassy material having a modulus value of 10 ° dyne/cm would exhibit a frequency shift of the order of 3.3 kHz. If the glassy modulus is only lo dyne/cm, however, the expected shift decreases to 0.33 kHz or less. If the transition occurs over, a 5 degree temperature range, this is equivalent to a shift of only 0.42 ppm/°C, and is small compared to the frequency shifts observed for the... 

In this equation represents the glassy modulus (3 x lO dyn/cm ), T in is a characteristic relaxation time, E2 represents the rubbery plateau modulus, and E it) is the relaxation modulus as a function of time. 

Figure 11.14. Effect of plasticizer type and content used for plasticization of PMMA ionomer on glassy modulus. [Adapted, by permission, from Ma X Sauer J A Kara M, Polymer, 38, No, 17, 1997, p.4425-31.]...

This model describes both creep and stress relaxation and the transition from the glassy modulus E (for E E ) at short times, where the viscous dashpot has an infinite viscosity, to the rubbery modulus E at long times. 

A more modern explanation of the glassy modulus of polymers starts with a consideration of the carbon-carbon bonding force fields adopted for the explanation of vibrational frequencies (10). For perfectly oriented polyethylene, a value of E = 3.4 x 10" Pa was calculated, with a slightly lower value,... 

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