Meaning
Kinetic models for thermoset resins require a mathematical correction to account for the slowing of reactions as the material turns into a solid glass. The rabinowitch decay factor is a multiplier applied to the chemical rate constant that reduces its value as the system approaches its glass transition. This adjustment allows the same model to describe both the fast liquid-phase reaction and the slow diffusion-controlled stage.
Diffusion Limitation
Molecular motion becomes the primary constraint on the reaction rate as cross-linking progresses. The rabinowitch decay factor is calculated based on the difference between the current temperature and the increasing glass transition temperature of the resin. When the material is in the liquid state, the factor is close to one and has no effect on the speed.
As the resin vitrifies, the factor drops toward zero, effectively pausing the reaction in the glassy state.
Free Volume
Physical space between the polymer chains determines the ease with which reactive groups can find each other. The rabinowitch decay factor is often derived from free volume theory, which relates the mobility of the system to the available unoccupied space. As the temperature drops or the cross-link density increases, the free volume shrinks and the factor decreases.
This mechanism explains why reactions in solids are much slower than those in liquids.
Model Accuracy
Incorporating this term is essential for predicting the final degree of cure in industrial processes. Without the rabinowitch decay factor, a kinetic simulation would predict that a reaction reaches full conversion faster than it actually does. This discrepancy can lead to the premature removal of parts from a mold, resulting in warping or structural failure.
Including the factor ensures that the simulation captures the long tail of the reaction that occurs during the later stages of the cure cycle.
