Dynamic mechanical analysis: Difference between revisions

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{{Short description|Technique used to study & characterize materials}}

{{Infobox chemical analysis

| name = Dynamic mechanical analysis

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| hyphenated =

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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 [[viscoelastic]] behavior of [[polymer|polymers]]. A sinusoidal stress is applied and the strain in the material is measured, allowing one to determine the [[Dynamic modulus|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<ref>{{cite web |url=https://coventivecomposites.com/explainers/dynamic-mechanical-analysis-dma/|accessdate=2018-10-01|title=What is Dynamic Mechanical Analysis (DMA)?|date=22 April 2018 }}</ref> of the material, as well as to identify transitions corresponding to other molecular motions.

==Theory==

===Viscoelastic properties of materials===

[[Image:Dynamic+Tests+Setup+Chem+538.jpg|thumb|325px|Figure 1. A typical DMA tester with grips to hold the sample and an environmental chamber to provide different temperature conditions. A sample is mounted on the grips and the environmental chamber can slide over to enclose the sample.]]

Polymers composed of long molecular chains have unique viscoelastic properties, which combine the characteristics of [[Elasticity (physics)|elastic solid]]s and [[Newtonian fluid]]s. The classical theory of elasticity describes the mechanical properties of elastic solidsolids where stress is proportional to strain in small deformations. Such response ofto stress is independent of [[strain rate]]. The classical theory of hydrodynamics describes the properties of viscous fluid, for which thestress response of stress is dependentdepends on strain rate.<ref name="Ferry1980">{{cite book|last=Ferry|first=J.D.|title=Viscoelastic properties of polymers|publisher=Wiley|year=1980|edition=3}}</ref> This solidlike and liquidlike behaviorbehaviour of polymers can be modeledmodelled mechanically with combinations of springs and dashpots, making for both elastic and viscous behaviour of viscoelastic materials such as bitumen.<ref name="Ferry1991">{{cite journal|last=Ferry|first=J.D|year=1991|title=Some reflections on the early development of polymer dynamics: Viscoelasticity, dielectric dispersion and self-diffusion|doi=10.1021/ma00019a001|journal=Macromolecules|volume=24|issue=19|pages=5237–5245|bibcode = 1991MaMol..24.5237F }}</ref>

===Dynamic moduli of polymers===

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where

:<math> \omega </math> is the frequency of strain oscillation,

:<math>t</math> is time,

:<math> \delta </math> is phase lag between stress and strain.

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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 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:AnalyzersTwo 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>

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[[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. Note that thisThis 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.