Dynamic mechanical analysis frequency dependence

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

The measured viscosities depended on the frequency used during the DMA (dynamic mechanical analysis) measurements. At high frequencies... 

Dynamic mechanical analysis is routinely used to investigate the morphology of polymers, composites and other materials. The technique can be particularly sensitive to low energy transitions which are not readily observed by differential scanning calorimetry. Many of these processes are time-dependent, and by using a range of mechanical deformation frequencies the kinetic nature of these processes can be investigated. 

Figure 3.2 Temperature-dependent conversion degree of glass transition and volume fraction of glassy state (derived from glass transition of an E-glass fiber polyester composite during a dynamic mechanical analysis (DMA) test at a heating rate of5°Cmin and a dynamic oscillation frequency of 1 Hz) [3]. (With permission from SAGE.)...

Dynamic mechanical analyzer n. An instrument that can test in an oscillating-flexural mode over a range of temperature and frequency to provide estimates of the real , i.e., in-phase, and imaginary , i.e., out-of-phase parts of the complex modulus. The real part is the elastic component, the imaginary part is the loss component. The square root of the sum of their squares is the complex modulus. With polymers, the components and the modulus are usually dependent on both temperature and frequency. ASTM D 4065 spells out the standard practice for reporting dynamic mechanical properties of plastics. An example of a DMA thermogram of different Perkin-Elmer Inc., manufactures the Diamond DMA instrument. Polymer films is shown. Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York. 

Dynamic mechanical analysis (DMA) has been used to study the flow behavior of hot-melt adhesives.Drummer and co-workers used DMA to study the viscoelastic behavior of adhesives. They found that dynamic mechanical measurements in adhesives provided insight in the macromolecular mobility of the polymer or rubber system studied. The viscoelastic behavior at various temperatures can be correlated with standard measurements such as adhesive force, shear strength, and tack. The authors concluded that three-dimensional DMA plots from frequency-temperature sweeps provide a complete overview of the frequency and temperature dependence ofthe adhesive. Foster, etal., characterized the hot-tack differences in hot-melt adhesives using DMTA. 

Dynamic mechanical analysis (DMA) consists in applying a periodical stress field to a material. We can anticipate from Section 6.4.2 that the behaviour of a viscoelastic material will depend strongly on the frequency of the applied stress. 

Note that when viscoelastic materials are considered, it is important to control carefully the loading-unloading procedure (Fischer-Cripps, 2004a Mammeri et al 2004, 2005). In fact, for such kinds of materials indentation response is time dependent with a characteristic relaxation time T = t]IG, where // and G are the viscosity and shear modulus of the material (Chapter 6 see also Section H.5.1). Interestingly, some instrumented machines allow for adding a force modulation to the applied force at a given frequency and hence dynamic mechanical analysis can be performed (Chapter 6 Fischer-Cripps, 2004a). 

Transitions temperatures vary with the method and the rate of measurements. This is a potentially confusing situation. The transitions associated with the relaxation processes are highly frequency-dependent. Glass transition temperature obtained in measurement by dynamic methods [acoustic, dynamic mechanical analysis (DMA), ultrasonic, or dielectric methods] should reasonably be denoted as T to differ it from Tg measured, for instance, by DSC. At low fi equen-cies, that is, at 1 Hz or least, Ta is close to Tg. As the measurement fi equency is increased, increases while Tg remains the same, giving rise to two separate transition temperatures. In the literature, the distinction between the static and dynamic glass transitions is not always made clear. 

The principles of time-temperature superposition can be used with equal success for dielectric measurements as well as dynamic mechanical tests. Analysis of the frequency dependence of the glass transition of the adhesive in the system described above shows that it follows a WLF type dependence whereas the transition of PET obeys Arrhenius behaviour. This type of study can be used to distinguish between different types of relaxation phenomena in materials. 

Description of the mechanics of elastin requires the understanding of two interlinked but distinct physical processes the development of entropic elastic force and the occurrence of hydrophobic association. Elementary statistical-mechanical analysis of AFM single-chain force-extension data of elastin model molecules identifies damping of internal chain dynamics on extension as a fundamental source of entropic elastic force and eliminates the requirement of random chain networks. For elastin and its models, this simple analysis is substantiated experimentally by the observation of mechanical resonances in the dielectric relaxation and acoustic absorption spectra, and theoretically by the dependence of entropy on frequency of torsion-angle oscillations, and by classical molecular-mechanics and dynamics calculations of relaxed and extended states of the P-spiral description of the elastin repeat, (GVGVP) . The role of hydrophobic hydration in the mechanics of elastin becomes apparent under conditions of isometric contraction. 

Other thermal analysis techniques such as dilatometry in Sect. 4.1 or thermo-mechanical analysis in Sect. 4.5 can also be used to study the time dependence of T. Especially suited for measurement of the frequency response are dynamic mechanic analyses in Sects. 4.5.4 and 4.5.5, and dielectric thermal analyses in Sect. 4.5.6. Although the different techniques respond to different external excitations, the obtained relaxation times are similar, as shown in Fig. 6.117. Over wider temperature... 

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