While the first step of chemical investigations is often the synthesis of a new product, a careful analysis quickly forces us to deal with issues concerning the purity of the product, the amount of product, or, especially in chemical engineering contexts, the cost of the product obtained. Addressing these issues, directly leads us to the formulation of one or more objective functions that need to be optimized during the synthesis process. A common approach to solve such problems consists in performing many experiments with carefully chosen sets of synthesis parameters and then using statistical analyses to find optimal sets of these parameters. However, in many cases, it is possible to write down (phenomenological) rate equations that describe the processes involved in the development of the chemical system. This allows us to formulate analytical objective functions as function of state and control variables, casting the optimization of the chemical synthesis into the language of optimal control.[1-4]

In this talk, I am going to present a number of examples of the application of optimal control methods to the optimization of chemical processes, such as the optimization of a liquid-gas phase transition,[3] the optimal control of homogeneous nucleation and growth of crystals,[4] and the optimal control of the transfer of a chemical system between different crystalline modifications.[5]

[1] J. C. Schön: On the way to a theory of solid state synthesis: Issues and open questions, Advances in Chemical Physics, (2015), 175, 125-133

[2] J. C. Schön, B. Andresen: Finite-Time Optimization of Chemical Reactions: n_A⇄ n_B , Journal of Physical Chemistry, (1996), 100, 8843-8853

[3] M. Santoro, J. C. Schön, M. Jansen: Finite-time thermodynamics and the Gas-Liquid phase transition, Physical Review E, (2007), 76, 061120-1-14

[4] J. C. Schön: Finite-Time Thermodynamics and the Optimal Control of Chemical Syntheses, Zeitschrift für Anorganische und Allgemeine Chemie, (2009), 635, 1794-1806

[5] K. H. Hoffmann, J. C. Schön: Controlled dynamics on energy landscapes, European Physics Journal, (2013), 86, 220_1-10; Combining pressure and temperature control in dynamics on energy landscapes, European Physics Journal B, (2017), 90, 84_1-12

This seminar will take place on** Monday 19 ^{th} February, at 4 p.m, in Room A2-002**.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726, iain.moyles@ul.ie).

A full list of upcoming seminars can be found at http://www.ulsites.ul.ie/macsi/node/48011

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.