Optimal Control of Polymer Morphologies

This paper is devoted to the optimal design of polymeric materials through control of the cooling during the crystallization process. The optimality is defined in terms of optimal mechanical properties, which are directly related to the morphology of the solidified polymeric material. As a characterizing mathematical entity to be controlled the contact interface density is introduced and its relations to other structure variables such as temperature and crystallinity is discussed. Not only a general optimal control approach is presented, but also some relevant special cases are discussed, for which a more detailed analysis can be carried out. It is shown that under reasonable conditions on the parameters and the process, these optimal-control problems have solutions in appropriate function spaces and the optimality conditions derived from the Lagrangian formulation are discussed. Finally, the numerical approximation is discussed and results for some test examples are presented.