Modeling of crystal morphology distributions. Towards crystals with preferred asymmetry

Morphological population balance modelling of the effect of crystallisation environment on the evolution of crystal size and shape of para-aminobenzoic acid

“…The aspect was first addressed by , followed by other researchers (e.g., (Borchert et al, 2009, Borchert and Sundmacher, 2012, Chakraborty et al, 2010, Kwon et al, 2013, Kwon et al, 2014, Liu et al, 2013, Liu et al, 2010b, Liu et al, 2010a, Ma et al, 2016, Ma and Wang, 2012, Wan et al, 2009, Majumder and Nagy, 2013). A crystal has its face forms identified as {hkl}.…”

Combining Morphological Population Balances with Face-Specific Growth Kinetics Data to Model and Predict the Crystallization Processes for Ibuprofen

“…Researches were also carried out to extend and generalise the MPB concepts for different cases including the simulation of a population of asymmetric crystals, inclusion of face appearance and disappearance, the influence of crystal growth modifiers, modelling investigation of protein crystallisation processes etc. 12,[55][56][57][59][60][61][62][63] . Two-dimensional PB was applied to simulate the crystallisation of potash dihydrogen phosphate (KDP) with high resolution algorithms 15 .…”

“…The MPB models identify the individual crystal faces with the help of crystal morphology predications, then define the corresponding normal distances from these faces to the center of the crystal as individual dimensions for forming multidimensional, morphological based PB equations. ,,,− ,− The solution of these equations simulates the dynamic evolution of these normal distances for a population of crystals during a crystallization process, and with the known crystal morphology, the dynamic crystal shape and size distributions can be established from these normal distances. Research was also carried out to extend and generalize the MPB concepts for different cases including the simulation of a population of asymmetric crystals, inclusion of face appearance and disappearance, influence of crystal growth modifiers, modeling investigation of protein crystallization processes, etc. ,− ,− Two-dimensional PB was applied to simulate the crystallization of potash dihydrogen phosphate (KDP) with high resolution algorithms . The KDP crystals were treated as a rectangular prism, i.e., one dimension for length and another dimension for width with the width equaling the depth.…”

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

“…Optimal scenarios with subsequent growth and dissolution phases were investigated and it was found that minimum-time scenarios were composed of constant supersaturation trajectory sections. Chakraborty et al [101] presented a PB model for morphology distribution considering the diversity of symmetry. The symmetry of a population of crystals was analyzed using group theory and the population was divided into various symmetry classes, which, in turn, is subdivided into various morphological forms.…”

“…[104] also carried out multi-objective optimization of protein crystal shape and size, in which the aspect ratio of the mean normal distances from two independent faces (101) and (110) representing 12 faces of the crystal of hen egg white lysozyme was identified as the objective function with the lower and upper boundaries of the cooling rate to constrain the optimisation. The genetic algorithm was used to perform the optimization.…”