Editing Dynamic mechanical analysis (section)

==Instrumentation==
[[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 force from the motor to the sample, and sample clamps in order to hold the sample being tested.  Depending on what is being measured, samples will be prepared and handled differently.  A general schematic of the primary components of a DMA instrument is shown in figure 3.<ref>{{cite web|url=http://www.mse.iastate.edu/research/research-groups/gom/laboratory-facilities/charaterization-lab/dma.html|title=DMA|accessdate=2010-02-02|url-status=dead|archiveurl=https://web.archive.org/web/20100610052549/http://www.mse.iastate.edu/research/research-groups/gom/laboratory-facilities/charaterization-lab/dma.html|archivedate=2010-06-10}}</ref>

===Types of analyzers===
There are two main types of DMA analyzers used currently: forced resonance analyzers and free resonance analyzers.  Free resonance analyzers measure the free oscillations of damping of the sample being tested by suspending and swinging the sample.  A restriction to free resonance analyzers is that it is limited to rod or rectangular shaped samples, but samples that can be woven/braided are also applicable.  Forced resonance analyzers are the more common type of analyzers available in instrumentation today.  These types of analyzers force the sample to oscillate at a certain frequency and are reliable for performing a temperature sweep.

[[Image:Two types of DMA analyzers.png|thumb|left|Figure 4. Torsional versus Axial Motions.]]

Analyzers are made for both stress (force) and strain (displacement) control.  In strain control, the probe is displaced and the resulting stress of the sample is measured by implementing a force balance transducer, which utilizes different shafts.  The advantages of strain control include a better short time response for materials of low viscosity and experiments of stress relaxation are done with relative ease.  In stress control, a set force is applied to the sample and several other experimental conditions (temperature, frequency, or time) can be varied.  Stress control is typically less expensive than strain control because only one shaft is needed, but this also makes it harder to use.  Some advantages of stress control include the fact that the structure of the sample is less likely to be destroyed and longer relaxation times/ longer creep studies can be done with much more ease.  Characterizing low viscous materials come at a disadvantage of short time responses that are limited by [[inertia]].  Stress and strain control analyzers give about the same results as long as characterization is within the linear region of the polymer in question.  However, stress control lends a more realistic response because polymers have a tendency to resist a load.<ref name="book">{{cite book|last=Menard|first=Kevin P.|title=Dynamic Mechanical Analysis: A Practical Introduction|publisher=CRC Press|year=1999|chapter= 4 |isbn=0-8493-8688-8}}</ref>

Stress and strain can be applied via torsional or axial analyzers.  Torsional analyzers are mainly used for liquids or melts but can also be implemented for some solid samples since the force is applied in a twisting motion. The instrument can do creep-recovery, stress–relaxation, and stress–strain experiments.  Axial analyzers are used for solid or semisolid materials.  It can do flexure, tensile, and compression testing (even shear and liquid specimens if desired).  These analyzers can test higher modulus materials than torsional analyzers.  The instrument can do [[thermomechanical analysis]] (TMA) studies in addition to the experiments that torsional analyzers can do. Figure 4 shows the general difference between the two applications of stress and strain.<ref name="book" />

Changing sample geometry and fixtures can make stress and strain analyzers virtually indifferent of one another except at the extreme ends of sample phases, i.e. really fluid or rigid materials.  Common geometries and fixtures for axial analyzers include three-point and four-point bending, dual and single cantilever, parallel plate and variants, bulk, extension/tensile, and shear plates and sandwiches.  Geometries and fixtures for torsional analyzers consist of parallel plates, cone-and-plate, couette, and torsional beam and braid.  In order to utilize DMA to characterize materials, the fact that small dimensional changes can also lead to large inaccuracies in certain tests needs to be addressed.  Inertia and shear heating can affect the results of either forced or free resonance analyzers, especially in fluid samples.<ref name="book" />

===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" />