Mechanical loss moduli, dynamic

Fig. 53 Temperature dependence of the dynamic mechanical loss modulus, El, at 1 Hz, for PMMA and various MGIMx copolymers (From [52])...

Before considering the various mechanical properties, it is important to notice that the transition of these copolyamides, as shown by the dynamic mechanical loss modulus, E", in Figs. 84 and 85 for the xTyl -y and MTyIi y series, respectively, occurs at quite low temperatures. Indeed, for the first series the ft peak maximum occurs at - 60 °C at 1 Hz, and at - 110 °C for the second series. From this point of view, these copolyamides look more like BPA-PC (Sect. 4) than PMMA (Sect. 3). 

Figure 4. Dielectric loss factor e at lOHz and dynamic mechanical loss modulus E at 1 Hz as functions of temperature for polycarbonate. (Adapted from ref. 34 and 35.)...

Figure 17 PEEK dynamic mechanical loss modulus (linear scale) vs. temperature for samples crystallized for different times at 156 °C. The experimental data (+) have been separated into the sum of two loss peaks (ai and aa). The result of the decomposition is displayed with dashed lines. With permission from Ivanov, D. A. Legras, R. Jonas, A. M. Macmmolecules 9SS, 32,1582. ...

Finally, it is worth comparing the dynamic mechanical and dielectric results. For this purpose, Fig. 130 shows the temperature dependence of the mechanical loss modulus, E", and the dielectric loss modulus, m", at 1 Hz, obtained by superposing the low-temperature part of the P transition. 

Figure 9.14. Dynamic mechanical loss at 110 Hz for three PPO-PS mixtures as a function of temperature. ( ) 25 PPO/75 PS ( ) 50 PPO/50 PS ( ) 75 PPO/25 PS. Note broadening of the loss modulus, especially for the 50/50 blend. (MacKnight et al, 1971.)...

The study of the dynamic-mechanical properties comprises the determination of the following values dynamic storage modulus (real part of the complex modulus) E loss modulus (imaginary part of the complex modulus) E" and their ratio E"/E, called the factor of dynamic-mechanical loss, tan S. 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

Relaxations of a-PVDF have been investigated by various methods including dielectric, dynamic mechanical, nmr, dilatometric, and piezoelectric and reviewed (3). Significant relaxation ranges are seen in the loss-modulus curve of the dynamic mechanical spectmm for a-PVDF at about 100°C (a ), 50°C (a ), —38° C (P), and —70° C (y). PVDF relaxation temperatures are rather complex because the behavior of PVDF varies with thermal or mechanical history and with the testing methodology (131). 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

The dynamic mechanical properties of VDC—VC copolymers have been studied in detail. The incorporation of VC units in the polymer results in a drop in dynamic modulus because of the reduction in crystallinity. However, the glass-transition temperature is raised therefore, the softening effect observed at room temperature is accompanied by increased brittleness at lower temperatures. These copolymers are normally plasticized in order to avoid this. Small amounts of plasticizer (2—10 wt %) depress T significantly without loss of strength at room temperature. At higher levels of VC, the T of the copolymer is above room temperature and the modulus rises again. A minimum in modulus or maximum in softness is usually observed in copolymers in which T is above room temperature. A thermomechanical analysis of VDC—AN (acrylonitrile) and VDC—MMA (methyl methacrylate) copolymer systems shows a minimum in softening point at 79.4 and 68.1 mol % VDC, respectively (86). 

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). 

Experimentally DMTA is carried out on a small specimen of polymer held in a temperature-controlled chamber. The specimen is subjected to a sinusoidal mechanical loading (stress), which induces a corresponding extension (strain) in the material. The technique of DMTA essentially uses these measurements to evaluate a property known as the complex dynamic modulus, , which is resolved into two component parts, the storage modulus, E and the loss modulus, E . Mathematically these moduli are out of phase by an angle 5, the ratio of these moduli being defined as tan 5, Le. 

The B-series of silica samples were also blended with rubber and the compound formulation is shown in Table 17.6. The uncured gums were then tested according to ISO 5794-2 1998. The uncured samples were tested using a Mooney viscometer and an RPA, which measures the dynamic mechanical properties as the samples cure. Figure 17.7 shows the results of these two tests for the Mooney viscosity at 100°C, storage modulus, loss modulus, and tan 8. 

In the case of dynamic mechanical relaxation the Zimm model leads to a specific frequency ( ) dependence of the storage [G ( )] and loss [G"(cd)] part of the intrinsic shear modulus [G ( )] [1]. The smallest relaxation rate l/xz [see Eq. (80)], which determines the position of the log G (oi) and log G"(o>) curves on the logarithmic -scale relates to 2Z(Q), if R3/xz is compared with Q(Q)/Q3. The experimental results from dilute PDMS and PS solutions under -conditions [113,114] fit perfectly to the theoretically predicted line shape of the components of the modulus. In addition l/xz is in complete agreement with the theoretical prediction based on the pre-averaged Oseen tensor. 

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