Loss modulus tangent

The loss tangent rather than the loss modulus is plotted, also at 1 Hz. 

G is called the loss modulus. It arises from the out-of-phase components of y and T and is associated with viscous energy dissipation, ie, damping. The ratio of G and G gives another measure of damping, the dissipation factor or loss tangent (often just called tan 5), which is the ratio of energy dissipated to energy stored (eq. 16). 

Figure 15 Storage modulus, (E ), loss tangent (tanS), and loss modulus, (E ), as a function of temperature for P7MB and P8MB at 3 Hz.

There are also some far-fetched proposals for the LST a maximum in tan S [151] or a maximum in G" [152] at LST. However, these expectations are not consistent with the observed behavior. The G" maximum seems to occur much beyond the gel point. It also has been proposed that the gel point may be reached when the storage modulus equals the loss modulus, G = G" [153,154], but this is contradicted by the observation that the G — G" crossover depends on the specific choice of frequency [154], Obviously, the gel point cannot depend on the probing frequency. Chambon and Winter [5, 6], however, showed that there is one exception for the special group of materials with a relaxation exponent value n = 0.5, the loss tangent becomes unity, tan Sc = 1, and the G — G" crossover coincides with the gel point. This shows that the crossover G = G" does not in general coincide with the LST. 

TANDEL is the loss tangent, GSP and GDP is the loss modulus. is the storage modulus... 

Note that VTD-variance of Loss Tangent, and that SDTD is the standard deviation of Loss Tangent with similar definitions for GSP (G or real modulus) and GDP (G or loss modulus). 

Fibrin is a viscoelastic polymer, which means that it has both elastic and viscous properties (Ferry, 1988). Thus, the properties of fibrin may be characterized by stiffness or storage modulus (representing its elastic properties) and creep compliance or loss modulus/loss tangent (representing its inelastic properties). These parameters will determine how the clot responds to the forces applied to it in flowing blood. For example, a stiff clot will not deform as much as a less stiff one with applied stress. 

The dynamic mechanical response of a material can be characterised through the loss modulus, the loss tangent, tan S, or the loss compliance, However, as already mentioned for Ar-Al-PA (Sect. 6), the loss compliance can be considered the most relevant parameter for quantitatively comparing different materials, at least for additive purposes. For this reason, the semi-quantitative analysis and the comparison of viscoelastic data determined for different systems have been performed [63] in terms of /", whereas the determination of activation energies and entropies are based on loss modulus data. 

Fig. 2.67 Storage, loss modulus and loss tangent for ( ) PIPI, and (o) PIBI as a function of the temperature at 1 Hz. (From ref. [238])...

Figure 10.12 Chain scission in polyethylene oxide) matrix, (a) Carbonyl region of photoaged PEO samples irradiated at lOOmWcnr2 and 75°C for various times (0, 1,2 and 4 minutes). The main band at 1725cm-1 is attributed to formate functions, whereas the shoulder at 1 750cm"1 is assigned to esters, (b) Evolution of the storage modulus (G ), the loss modulus (G"), and the tangent of the phase angle tan(8) versus time (temperature 90°C). The increase in tan(8) is evidence of chain scission, (c) Endotherms of the fusion of PEOs samples recorded at...

An additional relaxation can be detected in plots of the loss tangent as a function of temperature for 2,6-T-2P-43, not shown. The relaxation occurred at 60°C (11 Hz) in the first examination of this sample. A weak ah relaxation can be detected in the loss modulus vs. temperature plots in Figure 13, but the process is more readily apparent in the tan(8) data. Upon retesting of this sample, the h dispersion was shifted to 71 °C. The activation energy for the ah relaxation did not change significantly with thermal history and was extremely weak or undetectable in 2,6-T-2P samples which contained less than 43 wt% hard segments. 

When using small deformation rheology there are several useful parameters that may be obtained to describe a material the complex modulus (G ), storage modulus (G ), loss modulus (G") and the tangent of the phase shift or phase angle (tan 5). These values must be taken from within the LVR, and are obtained using a dynamic oscillatory rheometer (Rao 1999). Outside the LVR, important information may be obtained such as the yield stress and yield strain. 

Viscoelastic data are commonly represented in the form of a master curve which allows the extrapolation of the data over broad temperature and frequency ranges. Master curves have, historically been presented as either storage modulus and loss modulus (or loss tangent) vs. reduced frequency. This representation requires a table of conversions to obtain meaningful frequency or temperature data. 

Dynamic mechanical relaxation tests were carried out by use of a Piezotron apparatus. Thin reedlike samples were subject to alternating tension at low applied stress and at a fixed frequency of 3 Hz. From the recorded observations, made as a function of temperature at a controlled rate of 2 °C/min, the storage modulus, E, the loss modulus, E", and the loss tangent, tan 6 = E"/E were determined. 

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