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Concept
Dynamic mechanical analysis
Summary
Dynamic mechanical analysis (abbreviated DMA) is a technique used to study and characterize materials. It is most useful for studying the viscoelastic behavior of polymers. A sinusoidal stress is applied and the strain in the material is measured, allowing one to determine the complex modulus. The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach can be used to locate the glass transition temperature of the material, as well as to identify transitions corresponding to other molecular motions.
Polymers composed of long molecular chains have unique viscoelastic properties, which combine the characteristics of elastic solids and Newtonian fluids. The classical theory of elasticity describes the mechanical properties of elastic solid where stress is proportional to strain in small deformations. Such response of stress is independent of strain rate. The classical theory of hydrodynamics describes the properties of viscous fluid, for which the response of stress is dependent on strain rate. This solidlike and liquidlike behavior of polymers can be modeled mechanically with combinations of springs and dashpots.
The viscoelastic property of a polymer is studied by dynamic mechanical analysis where a sinusoidal force (stress σ) is applied to a material and the resulting displacement (strain) is measured. For a perfectly elastic solid, the resulting strain and the stress will be perfectly in phase. For a purely viscous fluid, there will be a 90 degree phase lag of strain with respect to stress. Viscoelastic polymers have the characteristics in between where some phase lag will occur during DMA tests. When the strain is applied and the stress lags behind, the following equations hold:
Stress:
Strain:
where
is frequency of strain oscillation,
is time,
is phase lag between stress and strain.
Consider the purely elastic case, where stress is proportional to strain given by Young's modulus . We have
Now for the purely viscous case, where stress is proportional to strain rate.
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