Thermally activated processes are one of the four main types of aging described in Chapter 1. We now ask: how does the free energy change as degradation work occurs? Sometimes, the system path to the free energy minimum is smooth and downhill all the way to the bottom. For other systems, the path may descend to a relative minimum, but not an absolute minimum, something resembling a roller coaster. The path goes downhill to what looks like the bottom and faces a small uphill region. If that small hill could be scaled, then the final drop to the true minimum would be just over the top of the small hill. The small climb before the final descent to the true minimum is called a free energy barrier. The system may stay for a long period of time in the relative minimum before the final decay to true equilibrium.
Often the time spent in the neighborhood of the relative minimum is the lifetime of a fabricated product, and the final descent to the true free energy minimum represents the catastrophic failure of the product.
The estimated lifetime τ over which the system stays at the relative minimum obeys the Arrhenius law in Equation 5.21 as where Δφ is the height of the free energy barrier (φc).
The activation energy can be thought of as the amount of energy needed for the degradation process. This defines a ...