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.

Sub-ambient Tg of Thermoset Prepreg

Scientists and engineers use the term “sub-ambient glass transition temperature” (aka “sub-Tg”) to denote the Tg of an uncured thermoset material such as resin or prepreg. This terminology comes about because a cured, engineered thermoset system has a Tg that is high (i.e., significantly above room temperature) whereas in its uncured state the Tg is below ambient temperature. The terminology is used intending to void confusion. When sub-Tg is used it is only referring to Tg of uncured thermoset materials. When the material is being cured, the glass transition increases with respect to its degree-of-cure and it is called the typical Tg instead.

Many thermoset materials are processed to thin sheets such as in resin film or prepreg. At temperature below the sub-Tg it remains a solid and the uncured resin film is brittle and easily flaked off if bent. At temperature above sub-Tg, the uncured resin film or prepreg becomes resinous and pliable. It is possible to relate sub-Tg to drapeability of prepreg or resin film for material handle ability purpose. Also the study of sub-Tg can be linked with the goal of determining the material usage time and allowable out time. In addition to drape, people have also been relating sub-Tg to prepreg tack, although tack is a material quality that has been elusive to quantify as it is found to also depend on environmental factors such as ambient humidity and processing factors such as peeling speed.

The sub-Tg can be measured by thermal analysis techniques such as DSC and DMA. Sample should be at ambient temperature during sample preparation and handling. Be sure to eliminate moisture condensation on the sample while it is equilibrating to ambient temperature. Use the same kind of care to perform sub-Tg measurement as you would with measuring Tg of a polymer.

Obtaining Modulus Values from Thermal Mechanical Analyzer (TMA)

We mentioned using DMA to measure modulus in the previous blog. In this blog, we will discuss the usefulness of using TMA to measure modulus.

The TMA film set up is especially useful for tensile modulus measurement of plastic films. This set up is similar to typical tensile testing set up such as an Instron machine. A film sample is clamped at top and bottom at a constant temperature and the film sample is subjected to a controlled elongation strain or tensile force. The main difference being that in the TMA set up sample is not pulled till rupture. A stress-strain curve of the film sample is plotted and the tensile modulus is calculated from the initial slope of the graph where linear viscoelastic response is observed.

The Young’s modulus of a polymer sample can also be measured by TMA using the penetration probe set up. See equation below:

E = 3 F / (4 D d)

E = modulus, MPa,
F = force, N,
D = diameter of a circular, flat tipped probe, mm, and
d = penetration depth, mm.

ASTM E2347 utilizes this equation to calculate the indentation softening temperature (similar to Vicat softening temperature) when the sample reaches a certain modulus value. For this TMA penetration set up sample is placed under a constant force while temperature increases at a constant heat rate.

Obtaining Modulus Values from Dynamic Mechanical Analyzer (DMA)

Dynamic mechanical measurement of plastics is a very useful technique in viscoelastic behavior characterizations. Historically, scientists have been studying DMA thermographs to detect thermal transitions resulting from molecular motions and evaluate process-structure-property relationships. In recent years, however, there has been an increased application in DMA testing to mainly measure elastic modulus values of plastics. I wonder if this recent interest might be correlated with the increase usage of finite element analysis simulations, where people require mechanical data to be inputted into the simulation software, such as AutoCAD.

One advantage of using DMA testing is the sample size. DMA testing uses a much smaller sample size than the dog bone coupons for tensile testing or the large rectangular size for flexure testing. The smaller sample size is preferable as it is easier to fabricate a smaller piece without flaws that may affect the test results. However, the dimensional accuracy of the sample becomes more demanding in order to achieve accurate modulus values. Another advantage of using DMA testing is the ease to obtain modulus values at different temperatures. Only one sample is required in this case during a temperature ramp test.

Calculating modulus from DMA testing can be done easily as the test uses a small strain on the sample. However, strength data is not always possible to obtain. This is because DMA is designed as a tool to study polymer molecular behavior where resolution and sensitivity are important. So most commercial available DMA models have a very limited z-direction travelling distance and a small force range.

DMA thermograph is typically presented in storage modulus (E’), loss modulus (E’’), and tan delta, with respect to time or temperature. The dynamic modulus values are converted to elastic modulus value by the approximation

Elastic Modulus ~ |E*| = [E’2 + E’’2] 1/2

In an ideal elastic material, elastic modulus becomes E’ as tan delta approaches zero and E’’ becomes negligible.

TGA Analysis for Quality Assurance

Thermal gravimetric analysis (TGA) is a technique that measures the sample mass as a function of temperature. Imagine that you put a sample on a balance and track its weight as it is heated in an oven. By tracking the sample mass you can observe if there is any weight loss or weight gain during heating. And the weight loss or weight gain you observe from a TGA test can usually be correlated to some aspect of the sample.

TGA analysis is useful in measuring residual solvent content and percent solids. In some instances, TGA analysis is adapted for quality assurance, which replaces other analytical methods such as drying samples in an oven and quantitative GC analysis of solvents.

There are many products made in solutions. While in solution, the solids content is controlled so that the manufacturing process can be executed as desired. TGA analysis has been used here to measure the percent solids content of the solution. At the end of manufacturing process, solvents are removed from the finishing products. The residual solvent content in a product can also be verified by TGA analysis.

TGA analysis is also useful in applications where very low volatile content is expected of a material. For example, in semiconductor industry and in solar panel industry where outgassing may interfere with product performance, material selection is chosen so that minimal weight loss occurs during product life. In this case, TGA analysis has been used to screen samples for material selection during product development and it is adapted for quality control during material manufacturing.

Handling Powder Samples for DSC Runs

There are powdery materials such as finely ground polymers, polymer microspheres and active pharmaceutical ingredients (APIs) that may require DSC analysis and characterization.  Powder samples can be difficult to pack into DSC pans especially if they are static or low bulk density.  It could be a messy business with jumpy powders where they cling to your spatula and both inside and outside of the DSC pan.  Low bulk density prohibits the sample to have good contact with the bottom of the DSC pan.  And if small transitions are of importance where a large sample amount is needed, low bulk density also makes it difficult to pack more powders in a pan.

One way to overcome these difficulties from a powdery material is to make it into a pellet.  A pallet with its diameter slightly smaller than your DSC pan will enable you to pack a larger amount of sample into the pan with much improved surface contact and with no static issues.  All you need is a pellet maker with the correct diameter, about 3/16” to fit into most DSC pans.  If you work in an analytical lab and happen to have a KBr pellet maker (traditionally used for FTIR), I find it to be an excellent pellet maker for this purpose.

Happy New Year 2015!

A new year is here.  We hope you had a wonderful holiday season.  We are looking forward to this new year with anticipation as we will be adding a Dynamic Mechanical Analyzer (DMA) to our equipment line up.  We are very excited about our pending new addition as it will expand our testing capabilities.