Time optimal cyclic crystallization

Abstract A time optimal cyclic control scheme for shape manipulation of multivariate crystal populations involving sequences of subsequent growth and dissolution phases is proposed in this note. Such strategies employ the unequal growth and dissolution rates for attaining morphologies that do not result directly from a pure growth or dissolution phase only. We prove that minimum time trajectories can be constructed by means of convex programs resulting in globally optimal bimodal control policies with piecewise constant supersaturation.

[1]  Michael F. Doherty,et al.  Manipulation of crystal shape by cycles of growth and dissolution , 2007 .

[2]  K. Sundmacher,et al.  Morphology Evolution of Crystal Populations: Modeling and Observation Analysis , 2012 .

[3]  R. Popovitz‐Biro,et al.  Understanding and control of nucleation, growth, habit, dissolution and structure of two‐ and three‐dimensional crystals using `tailor‐made' auxiliaries , 1995 .

[4]  J. Raisch,et al.  Optimal control solutions for crystal shape manipulation , 2010 .

[5]  James B. Rawlings,et al.  Particle-shape monitoring and control in crystallization processes , 2001 .

[6]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[7]  Michael F. Doherty,et al.  Crystal shape modification through cycles of dissolution and growth: Attainable regions and experimental validation , 2012 .

[8]  Marco Mazzotti,et al.  Measurement of size and shape distributions of particles through image analysis , 2008 .

[9]  Marjatta Louhi-Kultanen,et al.  Crystal Shape Control by Manipulating Supersaturation in Batch Cooling Crystallization , 2006 .

[10]  A. Myerson.  Handbook of Industrial Crystallization , 2002 .

[11]  Jin Zou,et al.  Anatase TiO2 single crystals with a large percentage of reactive facets , 2008, Nature.

[12]  N. Bajçinca.  Analytic solutions to optimal control problems in crystal growth processes , 2013 .

[13]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[14]  Convex optimization for shape manipulation of multidimensional crystal particles , 2011 .

[15]  J. Mullin,et al.  Growth kinetics of ammonium‐ and potassium‐dihydrogen phosphate crystals , 2007 .