Finite-Time Thermodynamics and the Optimal Control of Chemical Syntheses

Christian Schoen (1)

1 Max-Planck-Institut für Festkörperforschung

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 τ, 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 T₁, where nucleation rates are high, to a temperature T₀>T₁, where the growth rates of the crystallites are maximal, occurs. The location of the switching time t_s*, 0≤t_s*≤τ , 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.

Mots clés: Physical Sciences

Christian Schoen. Finite-Time Thermodynamics and the Optimal Control of Chemical Syntheses. Journal of Inorganic and General Chemistry / Zeitschrift für anorganische und allgemeine Chemie, 2009, 635 (12), pp.1794. ⟨10.1002/zaac.200900207⟩. ⟨hal-00507771⟩