Editing Dynamic mechanical analysis (section)

===Test modes===
Two major kinds of test modes can be used to probe the viscoelastic properties of polymers: temperature sweep and frequency sweep tests. A third, less commonly studied test mode is dynamic stress–strain testing.

====Temperature sweep====
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'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====
[[Image:Freq Sweep Chem538.jpg|thumb|325px|Figure 5. A frequency sweep test on Polycarbonate under room temperature (25 °C). Storage Modulus (E’) and Loss Modulus (E’’) were plotted against frequency. The increase of frequency “freezes” the chain movements and a stiffer behavior was observed.]]

A sample can be held to a fixed temperature and can be tested at varying frequency. Peaks in <math>\tan(\delta)</math> and in E’’ with respect to frequency can be associated with the glass transition, which corresponds to the ability of chains to move past each other. This implies that the glass transition is dependent on strain rate in addition to temperature. Secondary transitions may be observed as well.

The [[Maxwell material|Maxwell model]] provides a convenient, if not strictly accurate, description of viscoelastic materials. Applying a sinusoidal stress to a Maxwell model gives: <math> E'' = \frac{E \tau_0 \omega}{\tau_0^2 \omega^2 + 1} ,</math> where <math>\tau_0 = \eta/E</math> is the Maxwell relaxation time. Thus, a peak in E’’ is observed at the frequency <math>1/\tau_0</math>.<ref name="Young" /> A real polymer may have several different relaxation times associated with different molecular motions.

====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'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<sub>g</sub> ≈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" />