Poly shear elastic modulus

Now, it has been shown for materials such as poly(propylene diol) (wherein both the absorption maximum for loss shear modulus and loss permittivity overlap near the frequency of IHz) that their normalized curves perfectly superimpose over their frequency band width. - As shown in Figure 9.15, the lower frequency loss shear modulus curves uniquely overlap with the loss permittivity data at higher frequency. As such the former is melded to calibrate the loss permittivity data to obtain a coarse estimate of the elastic modulus values. This provides an independent demonstration of the mechanic il resonance near 3 kHz and also allows reference to the 5 MHz dielectric relaxation as a mechanical resonance. Thus, as the folding and assembly of the elastic protein-based polymers proceed through the phase (inverse temperature) transition, the pentamers wrap up into a structurally repeating helical arrangement like that represented in Figure 9.17. 

Using trouser tear tests, Gent and Tobias [21] showed that the Lake-Thomas model held reasonably well for a number of elastomers. In their analysis, they took the molecular mass of a strand as that extracted from the elastic modulus and thereby incorporated the effect of entanglements (Section 9.8.2). More recent results on poly(dimethyl siloxane) (PDMS) elastomers using simple shear tests [22,23] over a wide range of structure (extent of cross-links and trapped entanglements) indicate that the role of entanglements in elastomer fracture needs to be elucidated further. 

Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly (propylene oxide) (1,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, vc, is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are trifunctional, their concentration always... 

Figure 5.11 Dependence of the reduced equilibrium shear modulus, Ge/wg// 7" on the molar ratio of [OH]/[NCO] groups, ah, for poly(oxypropylene)triol (Niax LG 56)-4,4 -diisocyanatodiphenylmethane system (—-) limits of the Flory-Erman junction fluctuation rubber elasticity theory. The dependence has been reconstructed from data of ref. [78]...

Figure 17. Variations of bulk properties derived from variations of the individual elastic constants of stishovite. (a) Bulk modulus (K) and shear modulus (G). Solid lines are the average of Reuss and Voigt limits the latter are shown as dotted lines (Voigt limit > Reuss limit), (b) Velocities of P (top) and S (lower) waves through a poly crystalline aggregate of stishovite. Circles indicate experimental values obtained by Li et al. (1996) at room pressure and 3GPa. After Carpenter et al. (2000a).

Ultrasonic interferometry, in which the travel time of high-frequency elastic waves through a sample is measured, also yields elastic moduli. Because it is a physical property measurement, rather than an optical spectroscopy, it can be used equally well on poly-crystalline samples as single-crystals, although polycrystalline measurements only yield the bulk elastic properties, bulk modulus and shear modulus, G. High-pressure ultrasonic interferometry techniques were initially developed in the piston cylinder... 

The product studied was produced in THF with a diphenylphos-phine-lithium catalyst it had a molecular weight of 8300. After shear modulus plotting over temperature, a glass stage of 81 °C, a modulus of elasticity of 32,000 kg/cm2 (poly styrene 30,000), and a flexural strength of 661 kg/cm2 (polystyrene 1000) were found. The glass temperature was 20 °C lower than that of polystyrene, but the polymer is more resistant to swelling by aromatics. 

Analogous experiments have been carried out on single electrospun fibers made by poly(trimethyl hexamethylene terephthalamide), which also show an increase of the Young s modulus and of the yield stress upon decreasing the diameter below about 500 nm (Figure 4.2b,c)/ Other polymer systems showing an abrupt increase of the elastic or of the shear modulus for diameters below or approaching the scale of 100 nm include fibers made of... 

Figure 2 illustrates the length-temperature data for one of the elastomers, poly-cis-1, U-butadiene cured with 0.5 p.h.r. dicumyl peroxide, at a series of loads. From the slopes of the straight lines in this plot, the linear thermal expansion coefficients of the strained rubber can be readily obtained. In order to compute the relative energy contribution to rubber elasticity by eq. 6, we need the linear thermal expansion coefficients of the unstrained rubber and the temperature coefficient of the shear modulus. These can be determined by plotting a as a function of the quantity (X -l)/(X +2). If eq. 7 is indeed valid, then one would expect a linear relation. From the intercept and slope of such a plot, values of and dilnG/dT can be easily obtained. 

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