Measurement of dynamic modulus

There are plenty of measurements of dynamic modulus of nearly monodisperse polymers starting with pioneering works of Onogi et al. (1970) and Vinogradov et al. (1972a). The more recent examples of the similar dependencies can be found in papers by Baumgaertel et al. (1990, 1992) for polybutadiene and for polystyrene and in paper by Pakula et al. (1996) for polyisoprene. 

Very useful properties of GPO include outstanding room temperature hysteresis and good dynamic properties over a wide temperature range. For example in measurements of dynamic modulus the flatness of the curve is observed between —40° C and 140° C and this property is maintained even after aging the polymer 7 days at 150° C, which is not the case with natural rubber. 

Plexiglas GP Poly(methyl methacrylate) 111 107.8 725 138 134.6 132 Measurements of Dynamic Modulus by DMA Multiplex 2 C step heating... 

Measurement of dynamic modulus of elasticity (Young s modulus, E) and modulus of rigidity (G) can be determined by measurement of the fundamental longitudinal and fundamental torsional resonant fi-equencies of regular shaped test specimens. Resonant frequencies are detected by means of either a mechanical or electrostatic drive or detection technique by means of a commercially available apparatus. 

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. 

An apparatus for measuring the dynamic modulus and hysteresis of elastomers. The stress-strain oscillogram is shown on a ground-glass screen by means of an optical system. Now superseded by modem computer controlled servo hydraulic and dynamic mechanical thermal analysis machines. Roll Bending... 

Dynamic Modulus. Measurement of dynamic viscoelasticity was made by the use of a direct-reading dynamic viscoelastometer from the Toyo Measuring Instrument Co., at a frequency of 110 Hz. 

Dynamic mechanical measurements, 407 Dynamic modulus, 451,508 Dynamic network of blobs, 279 Dynamic or absolute system of units, 53 Dynamic shear viscosity, 410 Dynamictensile viscosity, 410 Dynamic transitions, 418... 

The design of effective sound and vibration damping materials assumes an understanding of the mechanisms controlling the dissipation process and knowledge of candidate material properties. The use of viscoelastic materials as sound and vibration absorbers is wide-spread and well-known. Accurate measurement of the complex dynamic moduli of these materials is therefore vital to the control of acoustic and vibrational energy. This chapter discusses and compares three apparatus used to measure the dynamic modulus of viscoelastic materials. 

Rheovibron (dynamic) viscometer is widely used for measurements of dynamic mechanical properties such as loss modulus, storage modulus, and dissipation factor, each as a function of temperature. In this instrument, the test specimen is clamped between strain gauges and subjected to low order of sinusoidal strain at a specified frequency. The value of tan d is directly read and the storage and loss moduli are calculated using sample dimensions and instrument readings. 

In attempting to predict the direction that future research in carbon black technology will follow, a review of the literature suggests that carbon black-elastomer interactions will provide the most potential to enhance compound performance. Le Bras demonstrated that carboxyl, phenolic, quinone, and other functional groups on the carbon black surface react with the polymer and provided evidence that chemical crosslinks exist between these materials in vul-canizates (LeBras and Papirer, 1979). Ayala et al. (1990, 1990) determined a rubber-filler interaction parameter directly from vulcanizatemeasurements. The authors identified the ratio a jn, where a = slope of the stress-strain curve that relates to the black-polymer interaction, and n = the ratio of dynamic modulus E at 1 and 25% strain amplitude and is a measure of filler-filler interaction. This interaction parameter emphasizes the contribution of carbon black-polymer interactions and reduces the influence of physical phenomena associated with networking. Use of this defined parameter enabled a number of conclusions to be made ... 

In 1956 Thompson and Woods reported that dynamic experiments in extension indicated that orientation increased the temperature of the p transition, about 80°C, for oriented crystalline fibres, and reduced the drop in modulus occurring at higher temperatures. Subsequently nuclear magnetic resonance was used to demonstrate that orientation reduced molecular mobility above the glass transition temperature. Measurements of dynamic extensional and torsional moduli of hot stretched filaments and films were reported in 1963 by Pinnock and Ward, who found that the relations between measured compliances below the glass transition temperature were consistent with the deformation of an incompressible elastic solid. 

By combining static-creep and dynamic tests, a range of stiffness modulus can be obtained. When measurements of stiffness modulus as a function at time, at various temperatures, are carried out and the results are plotted in logarithmic scales, a graph of the type shown in Figure 4.16 is obtained. 

Another characteristics feature of the glass transition is the associated change in the modulus. The stress, elongation, is related to the strain, the force applied to a material by the modulus. Conventionally there are two approaches to the measurement of the modulus static and dynamic. The static method involves measurement of the stress strain profile and from the slope of the curve the elastic modulus can be determined. The dynamic method subjects the sample to a periodic oscillation and explores the variation of the amplitude and phase of the response of the sample as a function of temperature. A small sample of the test material is subjected to displacement as shown in Figure 7.3. 

Carbon black or silica filled NR generally demonstrates viscoelastic behaviour that is usually evaluated by dynamic viscoelastic measurements. One of the most widely discussed in the literature is the strain dependency of dynamic modulus known as the Payne effect. In such cases a high dynamic modulus at low strains (< 1%) is measured, which decreases at higher strains (> 10%), as shown in Figure 24.1. The reason for this phenomenon is the formation of a network created by filler-filler interactions. For carbon black the interactions are Van der Waals forces and for silica, much stronger hydrogen... 

Figure 36 presents a case of polyamide 6 where we measured the dynamic modulus, during irradiation of the sample by UV light with a wavelength... 

Some details of the equipment are illustrated by Fig. 16. The upper die can be raised to separate it from the lower die. A sample of uncured rubber compound can be then introduced and the upper die lowered into place as in the illustration. In this work, the dies were first heated and controlled at an elevated temperature (e.g., 90°C), then the temperature of the dies and sample can then be quite rapidly changed to a desired temperature for testing or for vulcanizing the sample. The sample can be introduced at one temperature, measurements of dynamic mechanical properties (e.g., storage shear modulus G and loss shear modulus G ) can then be made at the same temperature or at another temperature. Then, if desired the sample can be heated to a vulcanization temperature and vulcanized (with the recording of a cure curve, i.e., modulus versus time) and then the temperature can be changed and dynamic mechanical properties can then be measured again. 

FIG. 7-4. Apparatus of Ballou and Smith for measurement of dynamic Young s modulus of fibers by free vibrations. 

FIG. 7-5. Apparatus of Fujino, Kawai, and Horino for measurement of dynamic Young s modulus of fibers by free vibrations. (A. A ) Chucks (B) sample fibers (C) clamps (D) inertial disc (E) idler pulleys (F) piano wire (C) mirror to reflect light beam (H) weight to adjust static tension. 

FIG. 7-7. Measurement of dynamic shear modulus of a fiber by forcedtorsional vibrations. (Wakelin... 

As was the case with the measurement of coating modulus (Section 2.1), viscoelastic behaviour and the influence of the substrate can affect hardness measurements. With organic coatings, it is common to distinguish between conventional quasi-static hardness and dynamic hardness, p, defined as the resistance to plastic indentation at very high strain rates, where it is assumed that both viscoelastic and elastic effects are negligible. 

Figure 6 shows dynamic viscoelasticity of DL and KL. In order to measure the dynamic viscoelasticity, films or sheets are required. Since lignin samples were in powder form, THF solution of DL or KL was prepared and strips of filter paper were immersed in the above solution, and then dried completely. Filter paper without lignin shows no transition in a temperature range of 100-200°C. Decrease of dynamic modulus ( ) was observed at around 160°C, tan 5 peak is clearly observed for DL. A broad shoulder in tan 5 curve is also observed for KL at around 120°C [38]. 

Dynamic measurements of elastic modulus will yield a complex quantity defined as... 

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