Plateau modulus table

Figure 11.11 shows the stress-strain curves of PET, PTT and PBT fibers [4], Both PTT and PBT have a knee or a plateau region at about 5 and 7 % strains respectively, whereas PET stress increases smoothly with strain and does not have the plateau region. Table 11.6 compares the moduli of the three polyesters before and after annealing. The modulus of PET is nearly four times higher than those of PTT and PBT. After annealing, the PET modulus decreased by nearly half due to relaxation and loss of orientation. However, the PTT modulus increased by... 

Table 9.1 shows and calculated from the measured plateau modulus. All flexible polymers have Pg —20 overlapping entanglement strands defining the entanglement volume a, which is the overlap criterion for entanglement in polymer melts. 

Creep, Swelling, and Extraction Studies. Additional indications of component interaction were found in the results of creep experiments with the xl series shown in Tables VI and VII. Creep in the xl series is fully recoverable, i. e. there is no permanent set, consistent with a PUx continuous phase. The increase in recoverable compliance, however, indicates a reduction in apparent crosslink density with increasing delay time before irradiation. This result is reinforced by the data in Table VII Ci and Cg are the material constants in the Mooney-Rivlin equation. The rubbery plateau modulus and the crosslink density of PUx prepared in BHA, which mimics xl formation, is less than that of PU prepared neat. 

To Study the effects of concentration on tan 5 peak temperature and plateau modulus, a number of compositions known to give pressure sensitive adhesive performance at some concentration were examined at varying rubber-resin ratios. The resins examined are described in Table 5. 

This number appears to be constant for flexible polymers, with the average value = 20.6( 8%). Table 25.1 shows data for polyolefin melts listing density p, plateau modulus Ge, melt chain dimensions from SANS o/M, entanglement molar mass Me calculated from Eq. (25.6), Kuhn length b, packing length p, tube diameter a, and the overlap parameter for entanglement P, all at temperature T. 

Values of and Me for several polymer species in the melt state are listed in Table 3.1 (for melts, c is the mass density p). Values of for many other species are available in recent reviews [12,13,46]. On the basis of aproposal first made by Lin [47], Fetters et al. [12] have shown that the plateau modulus in the melt state is related in a simple manner to the chain dimensions and mass density of the species though the packing length ... 

Polysulfone and polycarbonate, for example, are high plateau modulus materials, often referred to as engineering plastics. These are listed in Table 11, which, in the main, is based on a collection of data given by Roovers, Toporowski and Ethier [254]. As can be seen in Fig. 7, generally good agreement is found with the predicted behavior, which is based on the data given in Table 11. This demonstrates that the behavior reported is independent of polymer type. 

In Table 1, we have reproduced a compilation of experimental values of and Ng for a variety of polymers along with respective values of p and f. The values of Ng are derived from the experimental values of the plateau modulus, G, which is related to Ng according to... 

The length of a macromolecule between adjacent entanglements Me is used as an individual characteristic of a polymer system. Table 1 contains values of Me for certain polymer systems. The more complete list of estimates of the quantity Me can be found in work by Aharoni (1983, 1986). One can compare expressions (6.52) and (6.54) for the value of the modulus on the plateau to see that the length of a macromolecule between adjacent entanglements Me is closely connected with one of the parameters of the theory... 

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

Table 1 Comparison of the glass transition temperature and the rubbery plateau storage modulus of aerylate co- and homopolymers...

Heat Deflection Temperature. This is increased slightly in amorphous polymers, because the fillers or fibers reduce the mobility of the polymer molecules. It may be increased tremendously in crystalline polymers, because fillers and especially fibers raise the plateau of the modulus versus temperature curve just enough to extend the pass/fail limit of the standard test by hundreds of degrees (Fig. 5.7, Table 5.18). The practical significance of this obviously depends on the judgment of the product designer. 

A clearly visible application for the grafted from materials is also in ballistic protection. With a relatively low modulus (e.g., 148 MPa for polystyrene-crosslinked samples -Table 13.2) and bulk density (0.46 gcm ), it is calculated that the speed of sound (equal to [modulus/bulk density] ) is 635 m s This value is very low for a solid material and highly desirable because it will extend the duration of an impact reducing the effective force on the material. The relatively low yield stress (7.2 MPa) will allow early activation of the energy absorption mechanism, while the long stress plateau will allow for large energy absorption. 

From the value taken by the elastic modulus at the mbbery plateau, the molar mass between entanglements (Me) can be indeed deduced using the relation E=4p RT/5Me, where p is the density. Plotting the variation of the Newtonian viscosity (rio) as a function of the molar mass also gives a critical value (Me) above which entanglements occur (see Figure 13.7), where Me is roughly equal to 10/4 of Mg (see Table 13.1). 

Table 13.1. Critical molar masses between entanglements (Me) determined from viscosity measurements and molar mass between entanglements (Me) drawn from the value of the elastic modulus at the rubbery plateau...

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