Safety Investigations with Model Free Kinetics

Hexel Composites is a company that manufactures epoxy resin formulations at its production site in Duxford, Cambridge, UK. In order to assure safety in the chemical plant, a thorough understanding of the potential thermal hazards of these materials is essential.

Recently, we started a program to assess the contribution that DSC kinetic data can make.

In particular, we wanted to compare the results based on conventional nth order kinetics and the new model free kinetics (MFK) with the data obtained by direct measurement of the adiabatic behavior in hot storage tests (SPS6).

Introduction

Safety investigations frequently assume adiabatic conditions (worst case), in which an initial low level of exothermic energy slowly warms the reaction mass thereby causing the reaction rate to increase until the reaction finally "runs away".

The temperature increases by an amount corresponding to the heat of reaction divided by the average specific heat of the reaction mass. At this temperature, organic substances can decompose and give rise to gases and vapors. The time taken to reach the maximum reaction rate (TMR, or as a symbol tmr) is of great importance.

This is also sometimes called the intervention time because up until this time an intervention (e.g. cooling) can still successfully prevent an uncontrolled reaction. The TMR can be read off from the curve of the adiabatic temperature increase (point of inflection).

The higher the adiabatic starting temperature chosen for the measurement, the shorter the TMR. Adiabatic hot storage testing is more difficult and expensive to conduct than DSC measurements because it requires both large amounts of sample (up to 1 kg) and specially equipped laboratories to cope ecologically with the fumes that are given off. An alternative to hot storage testing could save much time and expense.

Formulations

Six epoxy resins formulations with amine hardeners were chosen for our investigations. In order to cover a larger temperature range, three formulations with accelerator systems were used (marked with an *), which lower the temperature of cure from 175 °C to 120 °C.

Nth order kinetics

DSC measurements were performed at two different temperatures, namely at the starting temperature of interest T0 for the calculation of tmr and at a temperature that was 20 °C higher (T1). (DSC measurements at temperatures below those of the hot storage tests are hardly possible because experimental times are too long and the DSC signals too weak). The activation energy Ea was calculated from these curves using Equation 1. 

R is the gas constant 8.314 J mol-1 K-1 and φ is the peak height (in W/g) of the DSC curve at the temperature T, the isothermal temperature in degrees Kelvin. The activation energy could also be calculated directly using the nth order kinetics software option.

The time required to reach the maximum reaction rate under adiabatic conditions, tmr, is then given by Equation 2

c_p is the specific heat of the reaction mixture, T₀ the adiabatic starting temperature in degrees K and φ₀ the maximum heat output in W/g at T₀.

As can be seen in Table 2, the results obtained from the nth order kinetics do not agree with those from SPS6 measurements. This was in fact expected because the isothermal DSC curves do not take the usual course described by nth order kinetics (the formulations exhibit a delayed increase (formal autocatalysis)) instead of immediately reaching a maximum rate and then steadily decreasing.

Model Free Kinetics

For these experiments, we performed dynamic DSC measurements at three different heating rates. The model free kinetics software calculates the activation energy as a function of reaction conversion. Model free kinetics allows predictions to be made of the reaction course at almost any temperature (conversion plot).

The maximum reaction rate can be read off from each of these conversion curves (most easily from the first derivative). This is multiplied by the heat of reaction (in J/g), in order to obtain φ₀ for Equation 2.

The value for t_mr from model free kinetics correlates well that from SPS6. This has to do with the fact that model free kinetics can also describe complex reactions with a good degree of accuracy

_{Safety Investigations with Model Free Kinetics | Thermal Analysis Application No. UC 105 | Application published in METTLER TOLEDO Thermal Analysis UserCom 10}