Dynamic mechanical analysis: Difference between revisions

Revision as of 16:41, 27 November 2014

Revision as of 05:21, 11 December 2014

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==Theory==

===Viscoelastic properties of materials===

[[Image:Dynamic+Tests+Setup+Chem+538.jpg|thumb|325px|Figure 1. A typical DMA tester with grips to hold sample and 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.]]

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===Dynamic moduli of polymers===

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">{{cite book|last=Meyers|first=M.A.|author2=Chawla K.K.|title=Mechanical Behavior of Materials|publisher=Prentice-Hall|year=1999}}</ref>:

*Stress: <math> \sigma = \sigma_0 \sin(t\omega + \delta) \,</math> <ref name=Meyers1999/>

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*Storage Modulus: <math> E' = \frac {\sigma_0} {\varepsilon_0} \cos \delta </math>

*Loss Modulus: <math> E'' = \frac {\sigma_0} {\varepsilon_0} \sin \delta </math>

*Phase Angle: <math> \delta = \arctan\frac {E''}{E'} </math>

Similarly we also define [[Shear modulus|shear storage]] and loss moduli, <math>G'</math> and <math>G''</math>.

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==Applications==

===Measuring glass transition temperature===

[[Image:Temp Sweep Chem538.jpg|thumb|325px|Figure 2. A temperature sweep test on Polycarbonate. Storage Modulus (E’) and Loss Modulus (E’’) against temperature were plotted. Different initial static load and strain were used. The glass transition temperature of Polycarbonate was detected to be around 150 degree C.The Polycarbonate samples were made from the material purchased from Mcmaster-Carr, #8574k26]] One important application of DMA is measurement of the [[Glass_transitionGlass transition#Transition_temperature_TgTransition 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 with an increase in 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.

===Polymer composition===

Varying the composition of monomers and [[cross-link|cross-linking]]ing can add or change the functionality of a polymer that can alter the results obtained from DMA. An example of such changes can be seen by blending ethylene-propylene-diene monomer (EPDM) with [[styrene-butadiene rubber]] (SBR) and different cross-linking or curing systems. Nair ''et al.'' abbreviate blends as E₀S, E₂₀S, etc., where E₀S equals the weight percent of EPDM in the blend and S denotes sulfur as the curing agent.<ref name="Nair">{{cite journal|last=Nair|first=T.M.|author2=Kumaran, M.G. |author3=Unnikrishnan, G. |author4= Pillai, V.B. |year=2009|title=Dynamic Mechanical Analysis of Ethylene-Propylene-Diene Monomer Rubber and Styrene-Butadiene Rubber Blends|journal=Journal of Applied Polymer Science|volume=112|pages=72–81|doi = 10.1002/app.29367}}</ref>

Increasing the amount of SBR in the blend decreased the storage modulus due to [[intermolecular]] and [[intramolecular]] interactions that can alter the physical state of the polymer. Within the glassy region, EPDM shows the highest storage modulus due to stronger intermolecular interactions (SBR has more [[steric]] hindrance that makes it less crystalline). In the rubbery region, SBR shows the highest storage modulus resulting from its ability to resist intermolecular slippage.<ref name="Nair" />

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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 &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==