Modulus dynamic loss

Dynamic mechanical testers apply a small sinusoidal stress or strain to a small sample of the polymer to be examined and measure resonant frequency and damping versus temperature and forced frequency. Instrument software computes dynamic storage modulus (G ), dynamic loss modulus (G") and tan delta or damping factor. Measurements over a wide range of frequency and temperature provide a fingerprint of the polymer with sensitivity highly superior to DSC. 

Figure 5. The variation of the dynamic loss modulus (G") with oscillation frequency at 25 C for UHMWPE pseudo-gel (4% w/w) first run 0 second run A, third run , fourth run.

Figure 9. The variation of the dynamic loss modulus (G") of UHMWPE...

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 ... 

Tensile work recovery can be considered a dynamic-loss modulus obtained at very low cycling rates. A fiber Is stressed to 3 g/den. and Immediately allowed to recover. The work recovered exhibits a marked reduction at the glass transition temperature (Figure 7). 

Dynamic loss modulus maximum. b Calculated from data in Refs., 58, 77, 01. 

Figure 9.6 shows the (shifted along the E" axis) dynamic loss modulus (E")/temperature curves of the cold compressed powder sample and that of the compression moulded sheet sample. The crystallinity of the cold compressed sample is about 57%, while the crystallinity of the sample after compression moulding at 240°C i.e. after recrystallisation from the melt, is decreased to about 42%. Both samples are measured at a frequency of 1 Hertz and a heating rate of 2°C/minute. The relaxation behaviour proved to be clearly changed due to this difference in crystallinity of about 15 %. 

Viscoelastic properties of polypeptides in the solid state have been popular subjects of study however, they appear not to have been studied in the light of liquid crystals so far, except in a few cases (90, 91). The dynamic loss modulus (measured... 

FIGURE 5.11 Logarithmic comparison plot of the reduced dynamic loss modulus, G p (in dyne/cm = 0.1 Pa), against the logarithm of the reduced frequency, coaj-is ). The reduced reference temperatures give correspondence in the softening dispersion and match the positions of the loss tangent primary maxima. 

Figure 3.12. Temperature dependence of dynamic modulus E and dynamic loss modulus E" for PVC/ PBD blends (an incompatible system) (—) 100/0 (---) 100/5 (-----) 100/15. Note the two dis-...

The Autovibron system is designed to measure the temperature dependence of the complex modulus (E ), dynamic storage modulus (E ), dynamic loss modulus (E") and dynamic loss tangent (tan 6) of viscoelastic materials at specific selected frequencies (0.01 to 1 Hz, 3.5, 11, 35, 110 Hz) of strain input. During measurement, a sinusoidal tensile strain is imposed on one end of the sample, and a sinusoidal tensile stress is measured at the other end. The phase angle 6 between strain and stress in the sample is measured. The instrument uses two transducers for detection of the complex dynamic modulus (ratio of maximum stress amplitude to maximum strain amplitude) and the phase angle 6 between stress and strain. From these two quantities, the real part (E ) and the imaginary part (E ) of the complex dynamic modulus (E ) can be calculated. 

The quantitative relation between the stress amplitude and the strain at the frequency is shown in equation 59. Here, E ( ) is the dynamie modulus, which consists of the dynamic storage modulus (E ( )) and the dynamic loss modulus (E"( )) (equation 60). The dynamic storage modulus (E ( )) describes the elastic behavior of the sample that results in eneigy storage. The dynamic loss modulus E"( ) characterizes the viscous behavior of the sample that leads to a dissipation of energy. 

E (o) and E" (o) are the dynamic storage modulus and the dynamic loss modulus, respectively. For a viscoelastic polymer E characterizes the ability of the polymer to store energy (elastic behaviour), while E" reveals the tendency of the material to dissipate energy (viscous behaviour). The phase angle is calculated from... 

Dynamic mechanical analysis curve Graphical representation of the data collected by a dynamic mechanical analyser, where the dynamic loss modulus, dynamic storage modulus and tan 5 are plotted as a function of temperature (scanning mode) or time (isothermal mode). 

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). 

Viscoelastic properties may be expressed in terms of a dynamic storage modulus (E ), dynamic loss modulus (E ) and mechanical damping factor (tan8). Mathematically, they are defined as follows ... 

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