Monthly Archives: December 2015

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.

cure_temp1

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

cure_tg

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.