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'''Dynamic mechanical analysis''' (abbreviated '''DMA''') is a technique used to study and characterize materials. It is most useful for studying the [[
==Theory==
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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.<ref name="Meyers1999">{{cite book|last=Meyers|first=M.A.|author2=Chawla K.K.|title=Mechanical Behavior of Materials|publisher=Prentice-Hall|year=1999}}</ref> Viscoelastic polymers have the characteristics in between where some [[phase lag]] will occur during DMA tests.<ref name=Meyers1999/> When the strain is applied and the stress lags behind, the following equations hold:<ref name="Meyers1999"/>
*Stress: <math> \sigma = \sigma_0 \sin(t\omega + \delta) \,</math>
*Strain: <math> \varepsilon = \varepsilon_0 \sin(t\omega)</math>
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====Derivation of dynamic moduli====
Shear stress <math>\sigma(t)=\int_{-\infty}^t G(t-t') \dot{\gamma}(t')dt'</math> of a finite element in one direction can be expressed with relaxation modulus <math>G(t-t')</math> and strain rate, integrated over all past times <math>t'</math> up to the current time <math>t</math>. With strain rate <math> \dot{\gamma(t)}=\omega \cdot \gamma_0 \cdot \cos(\omega t)</math>and
:<math>
\frac{\sigma(t)}{\gamma(t)}=\underbrace{[\omega\int_o^{\infty}G(s)\sin(\omega s) ds]}_{\text{shear storage modulus }G'} \sin(\omega t)+\underbrace{[\omega\int_o^{\infty}G(s)\cos(\omega s) ds]}_{\text{shear loss modulus }G''} \cos(\omega t).
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===Measuring glass transition temperature===
One important application of DMA is measurement of the [[Glass transition#Transition temperature Tg|glass transition temperature]] of polymers. Amorphous polymers have different glass transition temperatures, above which the material will have [[rubber]]y properties instead of glassy behavior and the stiffness of the material will drop dramatically along with a reduction in its viscosity. At the glass transition, the storage modulus decreases dramatically and the loss modulus reaches a maximum. Temperature-sweeping DMA is often used to characterize the glass transition temperature of a material.[[File:2019-10-17 20 23 45-DMA Reference Measurements Linear Drive - Anton Paar RheoCompass™.png|alt=|thumb|325x325px|Figure 2. Typical DMA thermogram of an amorphous thermoplastic (polycarbonate). Storage Modulus (E’) and Loss Modulus (E’’) and Loss Factor
===Polymer composition===
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[[Image:Schematic of DMA.png|thumb|Figure 3. General schematic of a DMA instrument.]]
The instrumentation of a DMA consists of a displacement sensor such as a [[linear variable differential transformer]], which measures a change in voltage as a result of the instrument probe moving through a magnetic core, a temperature control system or furnace, a drive motor (a linear motor for probe loading which provides load for the applied force), a drive shaft support and guidance system to act as a guide for the
===Types of analyzers===
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