Finite-Time Thermodynamics and the Optimal Control of Chemical Syntheses

The optimization of chemical processes that take place in a finite time constitutes an important application of finite-time thermodynamics. In this study we investigate two generic optimal control problems for nucleation-and-growth based syntheses: the maximization of the amount of a crystalline solid phase generated via cooling from the melt within a finite time tau, and the maximization of the difference between two metastable crystalline modifications again synthesized by crystallization from a supercooled melt. In both cases the optimal temperature program consists in a bang-bang solution with constant values of the temperature, where a switch from a temperature T-1, where nucleation rates are high, to a temperature T-0 > T-1, where the growth rates of the crystallites are maximal, occurs. The location of the switching time t(s)* (0 <= t(s)* <= tau) is analyzed as function of the parameters of the models describing the chemical systems, and an application to the synthesis of glycerol crystals is given.