Dynamic mechanical analysis: Difference between revisions

Revision as of 22:22, 28 May 2019

Revision as of 21:12, 30 May 2019

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:<math> \frac{\sigma(t)}{\gamma(t)}=\underbrace{\frac{\sigma_0}{\gamma_0} \cdot \cos(\Delta \varphi)}_{G'}\cdot \sin (\omega \cdot t)+ \underbrace{\frac{\sigma_0}{\gamma_0} \cdot \sin(\Delta \varphi)}_{G''} \cdot \cos (\omega \cdot t)

\,</math>.

Comparison of the two <math>\frac{\sigma(t)}{\gamma(t)}</math> equations lead to the definition of <math>G'</math> and <math>G''</math> .<ref name="Ferry">{{cite journal|last=Ferry|first=J.D.|author2 = Myers, Henry S |year=1961|title=Viscoelastic properties of polymers|journal=The Electrochemical Society |volume=108 }}</ref>.

==Applications==

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A common test method involves measuring the complex modulus at low constant frequency while varying the sample temperature. A prominent peak in <math>\tan(\delta)</math> appears at the glass transition temperature of the polymer. Secondary transitions can also be observed, which can be attributed to the temperature-dependent activation of a wide variety of chain motions.<ref name = "Young">{{cite book|last=Young|first=R.J.|author2=P.A. Lovell|title=Introduction to Polymers|publisher=Nelson Thornes|year=1991|edition=2}}</ref> In [[semi-crystalline polymer]]s, separate transitions can be observed for the crystalline and amorphous sections. Similarly, multiple transitions are often found in polymer blends.

For instance, blends of [[polycarbonate]] and poly([[acrylonitrile-butadiene-styrene]]) were studied with the intention of developing a polycarbonate-based material without polycarbonate’spolycarbonate's tendency towards [[brittle failure]]. Temperature-sweeping DMA of the blends showed two strong transitions coincident with the glass transition temperatures of PC and PABS, consistent with the finding that the two polymers were immiscible.<ref name=Mas>{{cite journal|last=J. Màs |year=2002|title=Dynamic mechanical properties of polycarbonate and acrylonitrile-butadiene-styrene copolymer blends|doi=10.1002/app.10043|journal=Journal of Applied Polymer Science|volume=83|issue=7|pages=1507–1516|display-authors=etal}}</ref>

====Frequency sweep====

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====Dynamic stress–strain studies====

By gradually increasing the amplitude of oscillations, one can perform a dynamic stress–strain measurement. The variation of storage and loss moduli with increasing stress can be used for materials characterization, and to determine the upper bound of the material’smaterial's linear stress–strain regime.<ref name="book" />

====Combined sweep====

Because glass transitions and secondary transitions are seen in both frequency studies and temperature studies, there is interest in multidimensional studies, where temperature sweeps are conducted at a variety of frequencies or frequency sweeps are conducted at a variety of temperatures. This sort of study provides a rich characterization of the material, and can lend information about the nature of the molecular motion responsible for the transition.

For instance, studies of [[polystyrene]] (T_g ~ 110≈110&nbsp;°C) have noted a secondary transition near room temperature. Temperature-frequency studies showed that the transition temperature is largely frequency-independent, suggesting that this transition results from a motion of a small number of atoms; it has been suggested that this is the result of the rotation of the [[phenyl]] group around the main chain.<ref name = "Young" />

==See also==