Temperature dynamic modulus

For a single lot of material, just the cost of generating single-point data alone is reported to exceed 2600 (Table 11.24), while the cost of generating a multipoint data package comprising tensile stress-strain curves at five temperatures (23°C and four additional temperatures), dynamic modulus versus temperature at 1-Hz frequency, and tensile creep curves at four stress levels at each of the three temperatures (23° C and two elevated temperatures) amount to nearly 9000, as shown in Table 11.25. 

Nylon-6. Nylon-6—clay nanometer composites using montmorillonite clay intercalated with 12-aminolauric acid have been produced (37,38). When mixed with S-caprolactam and polymerized at 100°C for 30 min, a nylon clay—hybrid (NCH) was produced. Transmission electron microscopy (tern) and x-ray diffraction of the NCH confirm both the intercalation and molecular level of mixing between the two phases. The benefits of such materials over ordinary nylon-6 or nonmolecularly mixed, clay-reinforced nylon-6 include increased heat distortion temperature, elastic modulus, tensile strength, and dynamic elastic modulus throughout the —150 to 250°C temperature range. 

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). 

Butyl-type polymers exhibit high damping, and the viscous part of the dynamic modulus is uniquely broad as a function of frequency or temperature. Molded mbber parts for damping and shock absorption find wide appHcation in automotive suspension bumpers, auto exhaust hangers, and body mounts. 

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. 

FIGURE 1.7 Construction of a master curve of dynamic modulus /a versus log (frequency) by lateral shifting of experimental results made over a small frequency range but at several different temperatures. 

Dynamic Mechanical and Thermomechanical Analysis. A DuPont Model 981 DMA was used to determine the dynamic modulus and damping characteristics of baseline and irradiated specimens. Transverse composite samples 1.27 cm x 2.5 cm were used so that the modulus and damping data were primarily sensitive to matrix effects. Data were generally determined from -120°C through the glass transition temperature (Tg) of each material using a heating rate of 5°C/min. 

Figure 1. Temperature dependence of dynamic modulus and loss tangent (11 Hz) of monomer I cured for 7 days at 280°C.

Fig. 1.2 Richness of dynamic modulus in a bulk polymer and its molecular origin. The associated length scales vary from the typical bond length ( A) at low temperatures to interchain distances ( 10 A) around the glass transition. In the plateau regime of the modulus typical scales involve distances between entanglements of the order of 50-100 A. In the flow regime the relevant length scale is determined by the proper chain dimensions...

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

The measurements of Young s modulus in dependence of the temperature (dynamic-mechanical measurements, see Sect. 2.3.5.2) and the differential thermal analysis (DTA or DSC) are the most frequently used methods for determination of the glass transition temperature. In Table 2.10 are listed and values for several amorphous and crystalline polymers. 

T = 140 °C. Here, during solidification, the H increase from 140 °C down to about 100 °C is the result of a double contribution of (a) the crystallization of the fraction of molten crystals and (b) the thermal contraction of the nonpolar phase crystals. The hysteresis behavior is also found in other mechanical properties (dynamic modulus) derived from micromechanical spectroscopy [66, 67], where it is shown that the hysteresis cycle shifts to lower temperatures if the samples are irradiated with electrons. It has also been pointed out that the samples remain in the paraelectric phase, when cooling, if the irradiation dose is larger than 100 Mrad. 

Figure 4.15. Time evolution of the shear dynamic modulus during curing at two temperatures 23°C (curves 1 - 3) and 61°C (curves 4 to 6) and different frequencies 3 s 1 (curves 1 and 4) 12 s 1 (curves 2 and 5) and 25 s 1 (curves 3 and

Thus, one may conclude that, in the region of comparatively low frequencies, the schematic representation of the macromolecule by a subchain, taking into account intramolecular friction, the volume effects, and the hydrodynamic interaction, make it possible to explain the dependence of the viscoelastic behaviour of dilute polymer solutions on the molecular weight, temperature, and frequency. At low frequencies, the description becomes universal. In order to describe the frequency dependence of the dynamic modulus at higher frequencies, internal relaxation process has to be considered as was shown in Section 6.2.4. 

The intermediate length (tube diameter) 2 can be estimated from the modulus with the aid of the above equations. Comparison of values of the intermediate length found from dynamic modulus and from neutron-scattering experiments was presented by Ewen and Richter (1995). They found the values to be close to each other, though there is a difference in the temperature dependence of the values of intermediate length found by different methods. 

To determine the procedure for the reduction, we shall write down the dynamic modulus at two different temperatures, one of which is a reference temperature Tref and the other is an arbitrary temperature T,... 

The above expressions confirm the known (Ferry 1980) method of reducing the dynamic modulus measured at different temperatures to an arbitrarily chosen standard temperature Tref, while offering a relatively insignificant improvement on the usual shift coefficient... 

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