Storage modulus illustrations

At low frequencies the loss modulus is linear in frequency and the storage modulus is quadratic for both models. As the frequency exceeds the reciprocal of the relaxation time ii the Rouse model approaches a square root dependence on frequency. The Zimm model varies as the 2/3rd power in frequency. At high frequencies there is some experimental evidence that suggests the storage modulus reaches a plateau value. The loss modulus has a linear dependence on frequency with a slope controlled by the solvent viscosity. Hearst and Tschoegl32 have both illustrated how a parameter h can be introduced into a bead spring... 

A schematic of the system is illustrated in Figure 1. For dynamic frequency sweeps (refer to Figure 2), the polymer is strained sinusoidally and the stress is measured as a function of the frequency. The strain amplitude is kept small enough to evoke only a linear response. The advantage of this test is that it separates the moduli into an elastic one, the dynamic storage modulus (G ) and into a viscous one, the dynamic loss modulus (G"). From these measurements one can determine fundamental properties such as ... 

Medalia [8,9] and Voet and Cook [10,11]. The effect is illustrated schematically in Fig. 1 for the compression mode. For a specific frequency and specific temperature the storage modulus decreases from a zero-amplitude plateau value, E0 (or G o in shearing) to a high-amplitude plateau value, E (or G j, with increasing amplitude, whereas the loss modulus shows a pronounced peak. 

The effect of entanglements on the relaxation of polymer chains is illustrated in Fig. 3-22, which shows the storage modulus G for a series of polystyrene melts of differing... 

Figure 5.22 Master curves of the storage modulus at a reduced temperature of 0 C for polybutadiene (Af = 26,000) which has been modified by attachment of 4-phenyl-1,2,4-triazoline-3,5-dione groups, as illustrated in Fig. 5-11. The degree of modification is jc = 0 ( ), 0.5 (+), 2( ), 5(x), and 7.5(0) where x = 7.5 corresponds to 36 functional groups per chain. (Reprinted with permis-sion from de Lucca Freitas and Stadler, Macromolecules 20 2478. Copyright 1987 American Chemical Society.)...

Since many of the DSC scans did not show Tg s of the ccnpositions, Tg s were determined by dynamic mechanical thermal analysis (EMTA) with injection-molded bars. The tan 6 and storage modulus (log E1) curves obtained for the BDA/HD honcpolyester are illustrated in Figure 4. Figure 5 is a plot of the Tg s (tan S peaks) obtained with BDVHD/EG oopolyesters. 

While this paper reports only preliminary findings. It does Illustrate the usefulness of photocalorimetry to define optimum cure conditions for UV curable adhesives. In addition, once the mechanical spectrum of fully cured adhesive has been mapped, mechanical spectroscopy can be used to monitor cure efficiency. In this paper we have not explored the molecular weight Implications of Incomplete polymerization. Preliminary evaluation of loss and storage modulus data would suggest that time-temperature superposition may be necessary to evaluate molecular welght/degree of cure relationships and terminal, plateau, and transition zones (4). 

Figure 12.13 The rubber storage modulus of two cyanate ester resins as a function of moisture absorption with thermal spiking temperature illustrating the hydrolytical instability of the thermally cured AroCy LIO ( ) compared to the stability of an epoxy-cured AroCy LIO (o) [7,19].

Spike temperature is more important than the presence of water. This is illustrated in Fig. 3.8, where the heat distortion point of the laminates (defined as the onset of the relaxation region from the temperature dependence of the storage modulus) is plotted against thermal spike temperature. The reduced stability of the resins at higher thermal spike temperatures appears to reflect the chemistry by which the modifiers interact with the base epoxy resin. 

Figure 12.41. Schematic showing storage modulus G and dissipation factor tan 5 as a function of temperature for two cases of filler-matrix systems I, case of simple volume replacement and stiffening by filler, with no effect on relaxation behavior of filled polymer F II, case of volume replacement and stiffening with an effect of filler on relaxation behavior. (No attempt has been made to illustrate specific effects such as transition broadening, enhanced stiffening in the rubbery region, or additional peaks due to bound resin.)...

Fig. 6.12 Illustration of (a) the storage modulus, the loss modulus and the loss factor as a function of frequency across the glass transition temperature of amorphous polymers (b) the loss factor as a function of temperature according to the time-temperature superposition principle. Below the a peak for glass transition, there are secondary relaxation peaks...

It is important to note that an unusual property possessed by these CHDI-based PUs is the apparently constant dynamic storage modulus (F) possessed over the large temperature ranges of +20 to + 160°C for the 1 2 1 PU and +20 to +180°C for the 1 3 2 PU. Figures 3.17 and 3.18 illustrate these constant modulus temperature values. 

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