Loss modulus spectrum

Below Tg, there often exist several more dispersion peaks of the loss modulus spectrum, where some additional dissipation of the applied mechanical energy takes place. The positions of these peaks are called sub-Tg or secondary transition regions. They are called the P-transition temperature, y-transition temperature, and so on, in the descending order, as the a-transition of an amorphous material is the glass-to-rubber transition. The storage modulus spectrum is usually quite insensitive to the secondary transitions virtually no changes are observed at transition temperatures corresponding to the peaks of a loss modulus spectrum. 

Certain macroscopic properties of materials sometimes show major changes near the secondary transitions detected by the loss modulus spectrum. It is well known that the toughness of certain resins, such as polycarbonate, suddenly disappears and the material becomes brittle below the... 

In the limit of high frequencies the integral for the loss modulus tends to zero as the denominator in Equation 4.50 tends to infinity. The storage modulus tends to G(oo) which is just the integral under the relaxation spectrum ... 

Figure 5. Dynamic mechanical spectrum (torsion pendulum) of a cured film of Epon 828/PACM-20. Both the shear modulus G ( Z ) and its approximation O (0) are plotted on the upper curve the lower three curves are loss modulus G" (CT), logarithmic decrement A ( ), and damping coefficient a (+j-...

Figure L The low-temperature dynamic mechanical spectrum of Halthane 73-14 is typical of the 73-series polyurethane adhesives. Two secondary relaxations, Tp and Ty, are shown as peaks in the loss modulus at —100° and —150°C. The soft segment glass transition, Tg(SS), occurs at about —50°C. The frequency of oscillation was held constant during the measurement at 0.1 Hz.

Figure 8. The high-temperature dynamic mechanical spectrum of Halthane 88-2 shows that some further curing is occurring above 100°C because both storage and loss modulus increase over a...

Since the Gross frequency relaxation spectrum can be computed from r , i.e., from the loss modulus, G = T co, the agreement between the computed and measured G values provides good means of verifying both the computational and experimental procedures. It has been found that Eqs 7.83 and 7.84 are useful to evaluate the rheological performance of systems that obey the linear viscoelastic principles. 

The reduced storage modulus, reduced loss modulus, and relaxation time spectrum are given by... 

The measured G and G" (or equivalently rj and 77") values, as a function of the frequency w, can be displayed as a spectrum — the viscoelastic spectrum. Figures 4.9 and 4.10 show the storage modulus spectra G lo) and the loss modulus spectra G" oj), respectively, of a series of nearly monodisperse polystyrene samples. 

The relaxation spectrum H t), where t is the relaxation time, characterizes the contribution to the shear modulus G(t), the dynamic storage modulus G ((o), and the dynamic loss modulus G"(co) according to the following relations (for a viscoelastic solid for a viscoelastic liquid Ge = 0 in the following equations). 

Abstract In the present study a nonlinear regression with regularization and inverse Fourier transformation methods were developed to determine the relaxation spectrum from the frequency-dependent storage and loss modulus data. The spectra obtained were used for the determination of the molecular mass distribution in a calculation process... 

Figure 6.19. Comparison of DRS and TSC data of PMMA selected isochronal dielectric loss spectra and the typical (global) TSC spectrum (Kalogeras and Vassilikou-Dova, unpublished results). Arrows indicate the location of the main signals in the case of the isochronal plot at 10 Hz. The inset shows a comparative plot of the temperature dependence of the dielectric loss (e") and the mechanical loss modulus E") for PMMA [DMA data taken from de Deus et al. (2004)].

In zero approximation, the loss modulus at co has sometimes been directly taken as the relaxation spectrum at t = 1 /co, but there is no need to use such a crude approximation when very simple methods are available to improve it. 

In 1997, Winter and Mours (1997) were the first ones to discover a behavior according to the power law at the gel point for the storage modulus G and the loss modulus G" over a wide frequency spectrum. This behavior can be calculated with the following equation ... 

Fig. 13 Storage modulus G and loss modulus G" of unfilled LDPE and highly filled LDPE/LDH nanocomposite (20 wt%) in the frequency sweep experiment. Also shown are the fits of G and G" obtained from conversion of the LDPE relaxation spectrum (see Table 2)...

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