Thermal Analysis References

Occasionally I send references to my clients when questions were asked on complicated concepts or on general material behaviors under thermal analysis.  It is imperative to have scholarly references to explain these concepts in these occasions.  It is unfortunate, however, that the subject is not taught as a regular discipline at schools and that most of the research were done in the 70’s and 80’s and since then has been scattered due to its wide use but not in one concentrated area.

Given the readily available web search it has made literature research much easier now than ever.  You can search for a technical term you are interested in and many scholarly articles will appear from your web search.  Here I give a list of literature on thermal analysis, both books and websites that I refer to frequently as I find them very useful.

Useful books that summarize various techniques of thermal analysis:
Thermal characterization of polymeric materials / 2nd ed., edited by Edith A. Turi, 1981
Thermal analysis of polymers: fundamentals and applications / edited by Joseph D. Menczel and R. Bruce Prime, 2009

Useful application notes you can find from instrumentation companies:
TA Instruments website
Perkin Elmer website
Mettler Toledo website

And here are some more books that are useful for in-depth and theoretical concepts concerning thermal analysis:
Thermal Analysis / by Bernhard Wunderlich, 1990
Dynamic Mechanical Analysis of Polymeric Material / by T. Murayama, 1978
Thermal Methods / by James W. Dodd and Kenneth H. Tonge, 1987

Do you have a reference you use a lot with thermal analysis besides the ones I listed?  You can share your favorite books or sites here.

DMA Clamp Selections and Sample Geometries

A modern DMA instrument nowadays comes with several clamping fixtures to accommodate a wide variety of samples.  Modern DMA instrument also comes with sophisticated computer programming where you have a wider range of test parameter choices such as fixed frequency, frequency sweep, fixed force, fixed strain, stress relaxation, etc.  This is an evolution from early commercially available DMA instruments such as the Rheovibron, DuPont DMA 983, or Polymer Laboratories DMTA Mk II.  In my mind, it is analogous to how kitchen appliance hand-held blenders evolved: a modern hand-held blender allows for multiple rotating speed, and blade styles can be changed out for different culinary tasks.

The main advantage that comes with this evolution is versatility.  Now you have one instrument in the lab that you may use for various sample types and test modes instead of buying several machines.  The main disadvantage that comes with this evolution is, alas, also versatility.  Now you have a more complicated machine to learn, to use and to maintain. You may eventually find that some clamps or modes are never useful on this more expensive equipment you bought.

I describe DMA testing in simple terms: You hold a sample firmly, put the sample in an oven so you can heat it up, and observe how it moves when you push it this way and that way.  The said sample is usually a polymer, usually a solid, and usually cut to a rectangular shape so that the math can be applied.  The said force is usually small so that the math can be applied to calculate modulus values.

(1)  This said force is called “flexure” when you push the sample in the middle or at the end of it.  Sample is positioned either in a cantilever clamp (dual cantilever mode or single cantilever mode) or in a three-point bend clamp.

DMA flexure set up: three-point bend and cantilever

DMA flexure set up: three-point bend and cantilever

(2)  This said force is called “tension” when you pull on the sample along its length, with the sample positioned in a film clamp.

DMA tensile set up

DMA tensile set up

These two, flexure and tension, are the most commonly used set up in a DMA instrument.  The tension set up is also commonly used in a TMA instrument for film testing.

Two other clamp set up that are also included in a modern DMA instrument but are less used are compression clamp and shear clamp, which are designed for soft materials such as foam, gel, rubber, etc. and which would overlap with applications with a rheometer instrument.

DMA compression set up

DMA compression set up

DMA shear set up

DMA shear set up

In addition to flexure and tension set up as mentioned above, there is one more mode for a solid, stiff sample.  This said force is called “torsion” when you twist on the sample, with the sample held on both ends.  This set up requires a rheometer (note: not using a “DMA” instrument!) with a solid sample accessory fixture.  Historically this set up uses the Rheometric Scientific RDA instrument.

Solid torsion DMA

Solid torsion DMA

Measuring in-plane direction thermal expansion and shrinkage of a film or a sheet on a TMA

Thermal mechanical analyzer (TMA) is frequently used for coefficient of thermal expansion (CTE) measurement.  In a previous blog  CTE by TMA I mentioned that the expansion probe is used to measure linear CTE of a solid block of sample and the through-thickness expansion of a film sample.  To measure in-plane behaviors such as thermal expansion and shrinkage of a film sample, the tension probe with film sample assembly is used, see the photograph below.

TMA - film probe set up

TMA – film probe set up

Depending on how a film or a sheet is made it is likely to have directional differences in its machine direction (MD) and transverse direction (TD).  One common example that everyone can relate to is the shrinkage of a T-shirt after wash and dry.  I’ve had T-shirts that did not change size or shape after wash and dry, and I’ve had T-shirts that became smaller all around afterwards.  There was one T-shirt I had that became shorter but not narrower after wash and dry.  All these differences point to the various materials and processes that can be used to weave a fabric and to make a T-shirt which cause a difference in how the shirt behaves after wash and dry cycles.

This means the film or sheet sample should be tested in both directions and care should be taken to align directions during sample preparation.  One problem that can happen when sample is not aligned or when a sample is particularly heterogeneous is that the thermal stress differences in directions might cause the sample to twist during thermal testing.

Using DMA Analysis for Heat Forming Applications

Many plastics come in flat sheet and one way to bend the sheet to desired shapes is to perform what is called heat forming or thermoforming process.  In thermoforming, the plastic sheet is heated until it is softened to allow bending without breaking.  Once the shape is formed the plastic is cooled and it will retain its shape without springing back to flat sheet.

So how do you know what temperature to heat up the plastic in order to thermoforming?  One way to find out is to ask the plastic manufacturer.  The plastic manufacturer typically would provide a recommended working temperature for the said plastic for thermal forming processes.  Another way to find out the process temperature is to do a little bit of scientific investigation yourself.  The rule of thumb for working temperature range is above its glass transition temperature where it softens significantly but below its melting temperature (if it has one) where it may flow too freely.  Once you find out what kind of polymer your plastic sheet is, you can look up its Tg and Tm values and come up with a working temperature for the thermoforming process.

If you are dealing with specialty polymers and you do need hard data, you can perform a simple DMA analysis to help you determine the temperature range and to verify thermoforming process ability.  A DMA thermograph will display the material’s storage modulus values with respect to temperature, as illustrated in the graph below.

DMA thermograph showing storage modulus E’ of the polymer dropped during Tg transition into the rubbery plateau region

DMA thermograph showing storage modulus E’ of the polymer dropped during Tg transition into the rubbery plateau region

The DMA thermograph shows that the polymer material softens during the Tg transition.  Typically, the modulus drop is between one to three orders of magnitude.  For example, a polymer that has a modulus drop of 2-order of magnitude during its Tg transition means its modulus value is reduced from ~ 100 MPa in the glassy state to ~ 1 MPa in the rubbery state.

The rule of thumb for working temperature range I mentioned several paragraphs before means that you should process your polymer while it is in the rubbery state, and at its rubbery plateau.

There are polymers such as high crystallinity thermoplastic polymers or highly crosslinked thermoset polymers, however, where this rule of thumb does not work well.  The reason is because the modulus drop from glassy state to the rubbery plateau region is simply not significant enough to bend the plastic.  The modulus changes in thermographs with respect to polymer structures are well documented in scientific literature and textbooks.  The classic DMA thermograph (shown below as a cartoon drawing) you find in textbooks shows how Mc (molecular weight between crosslinks) of a thermoset polymer or crystallinity of a thermoplastic polymer affect the material modulus.  In a thermoset polymer, the higher the crosslinking density (i.e., low Mc) the less modulus drop after Tg transition.  In parallel, in a thermoplastic polymer, the higher the crystallinity the less modulus drop after Tg transition.

DMA thermograph to illustrate how storage modulus of a polymer changes with increasing crosslinking density or increasing crystallinity, around Tg transition

DMA thermograph to illustrate how storage modulus of a polymer changes with increasing crosslinking density or increasing crystallinity, around Tg transition

With little changes in modulus values even by taking up the temperature to rubbery plateau region, we can explain why those high crystallinity polymers or those high thermoset polymers are difficult to form shapes using thermoforming process.

In summary, thermoforming process works well for polymers at temperature range between its Tg and Tm except for polymers that are either highly crosslinked or crystallinity.  When data is needed to assess thermoforming ability, a simple DMA analysis can be performed to obtain the needed answer.

Measuring Glass Transition Temperature (Tg)

Glass transition (Tg) describes a material moving from rubbery to glassy state.  Unlike phase transitions, which are first-order phenomena, glass transition is a second-order phenomenon.  Glass transition is a kinetic phenomenon where it occurs over a range of temperature and its activation energy can be evaluated and it has relevancy to time-temperature-superposition.

Thermal analysis is particularly useful for glass transition temperature (Tg) evaluations of polymers.  For example, Tg can be studied using DSC, DMA and TMA analyses.  We show cartoon drawings below to illustrate typical thermographs depicting glass transition using thermal analysis techniques.  Depending on material type and sample geometry limitation, certain techniques are better suited than others.

Because glass transition is a kinetic phenomenon, Tg varies with heat rate in the thermal analysis testing.  This is one reason that heat rate should always be specified when reporting Tg values.  In general, Tg measured with a slower heat rate (such as at 1C/min) is lower than Tg measured with a higher heat rate (such as at 20 C/min).  The difference in measured Tg values due to heat rate differences may be as little as a few degrees to as much as 10 deg-C.

And because different material properties are being measured depending on the techniques, the measured glass transition temperature from one technique to another should not be expected to be “identical” or “equivalent” even with the same heat rate.  This is the reason that the type of thermal analysis should always be specified when reporting Tg values.  Although the measured Tg values should not be expected to be identical, the variation in Tg values obtained from various techniques are typically to be less than 10 or 20 deg-C.


Typical Tg transition in DSC

Typical Tg transition in DSC

Typical Tg transition in TMA

Typical Tg transition in TMA

Typical glass transitions in DMTA

Typical glass transitions in DMTA

Measuring Linear Thermal Expansion of Solid Materials by TMA

The thermal mechanical analyzer (TMA) with an expansion probe can be used to determine linear thermal expansion (aka CTE) of solid materials. The standard test method ASTM E 831 describes the instrumentation and how the testing is performed and analyzed.  A sample is cut to a small cube or cylinder to fit on the sample stage with the two faces flat and parallel in the direction of interest for CTE measurement, see picture below.  The sample length should be long enough to provide adequate resolution but not too long to cause thermal gradient within the sample.  A small load or force is placed on the sample from the contacting probe to ensure good contact but not inhibit sample expansion during heating.

To measure the through-thickness CTE of a film sample it is sometimes necessary to stack multiple sheets to increase overall sample length/thickness in order to improve resolution of the measurement.

TMA expansion probe with sample

TMA expansion probe with sample

Glass Transition, Degree-of-Cure, and Cure Kinetics Relationship of a Thermoset

There are many reasons to study a thermoset system from its uncured state to the fully cured state.  The ultimate material properties and attributes in a product is intimately tied with a well cured polymer.  For example, people want to know the rate of advancement at elevated temperature for curing an epoxy formulation.  We may want to know:  Is the resin fully cured?  What is the glass transition temperature when the resin is fully cured?  Can we speed up cure?  Can we optimize cure in terms of time, temperature and pressure?  Would the resin be cured properly without safety hazard?

Resin advancement is expressed mathematically by the degree-of-cure, α.  The degree-of-cure may be evaluated experimentally by DSC or various chemical analyses such as HPLC, NMR, or FTIR, depending on the thermoset chemistry. Frequently people are interested in the relationship between degree-of-cure and glass transition temperature, which helps us relate material properties to process conditions.  As the materials cure, the Tg values increase with respect to its degree-of-cure.  Therefore, we can track the curing process by measuring the Tg values of a thermoset material.  For example, we may be interested in knowing the ultimate Tg when the thermoset is completely cured.

For many thermoset systems it is found that there is a unique relationship between Tg and α.  In other word, a material cured at different temperatures with the same a has the same Tg.  See graphs below.  This unique relationship implies that the molecular structure of materials cured at different temperature is the same or is not significantly affecting Tg.


Time and degree-of-cure relationship from isothermal experimental data


Glass transition temperature and degree-of-cure relationship

The one-to-one relationship between Tg and α is convenient because Tg in most cases is easier to measure than α.  As I mentioned above, α may be evaluated experimentally by DSC or various chemical analyses such as HPLC, NMR, or FTIR.  Tg can be analyzed by thermal analysis techniques such as DSC, TMA or DMA.  Therefore, Tg measurement can be easily applied to characterize thermoset materials and to quality control testing.

This one-to-one relationship between Tg and α also suggests that a kinetic model (i.e., nth order, autocatalytic, or model-free) can be applied to describe the polymerization reaction of the resin in the temperature region.  We can use the kinetic model to predict material behaviors under all kinds of temperature conditions.  For example, we can use the kinetic model to predict thermal safety such as the time-to-maximum reaction rate under adiabatic condition, “TMRad”, or to develop a cure cycle for a large and bulky part.

Determine Purity of an Organic Compound by DSC

DSC is a convenient technique to determine the purity of an organic compound, such as monomers and low-molecular weight crystalline substances. The calculation utilizes the van’t Hoff equation, which describes the melting point depression from impurities. The DSC technique is relatively easy to perform and the purity value is quick to obtain since modern DSC equipment are equipped with sophisticated software where the software will calculate purity value once the DSC thermograph is obtained. It provides you with the information of total purity level in a few hours. However, keep in mind that this technique will not give any specifics to the nature of the impurities.

You can fine more information in the book “Thermal Analysis of Polymers – Fundamentals and Applications”. The ASTM E928 standard method is also a good reference where it describes the principle of the method and goes into details on how to perform the test method.