Empirical Formulation
Reaction rate expressions for crosslinking polymers combine basic nth-order kinetics with an autocatalytic acceleration term to simulate thermoset conversion curves over time. In board assembly processing, the kamal sourour model characterizes how underfills, glob tops, and structural adhesive formulations cure under fluctuating thermal reflow profiles. The dual-pathway equation captures both the initial uncatalyzed crosslinking reaction and the secondary self-accelerating chain propagation catalyzed by developing chemical end-groups.
Differential scanning calorimetry data supply the Arrhenius coefficients, reaction orders, and activation energies required to populate its variable matrix.
Dispensing Assurance
Numerical models of electronic resins guide process planning during capillary underfill delivery beneath area array devices. Viscosity drops initially during substrate heating, but the onset of rapid chemical crosslinking curtails fluid advancement before the underfill envelops interior solder bumps. The kamal sourour model predicts the precise moment when internal chemical reaction shifts liquid underfill into a rigid, non-flowing gel network.
Process engineers leverage these calculations to tune nozzle dispensing temperatures, substrate platen heating, and carrier conveyer speeds. Accurate kinetic curves prevent the development of underfill voids, acoustic microscopy acoustic shadows, and trapped moisture reservoirs beneath die corners.
Model Constraints
Mathematical simulation accurately matches conversion rates up to the onset of diffusion control, but standard equations diverge as resin vitrification arrests molecular mobility. The unmodified kamal sourour model fails to predict the dramatic deceleration of crosslinking once the polymer glass transition temperature climbs above the curing oven temperature. Modern implementations append empirical diffusion functions to throttle predicted cure speed in the high-conversion glassy regime.
Thermal analysis software applies the kamal sourour model to establish realistic baking windows for demanding automotive power assemblies.
