Modeling and evaluation for encapsulation efficiency of zircon-based heteromorphic encapsulation pigments

•The tridimensional function αmax = [1 − (k + 1)(D/L)]3 for encapsulation efficiency evaluation has been proposed.•The modeling presents a very effective approach for higher encapsulation efficiency by reducing the size of pigmental cores.•A modified sol–gel route endowed the pigment with better chromaticity and efficiency elevated by 24.65%.•There exists a critical point for efficiency elevation approximately at L/[(k + 1)D] = 2.0.•From a new prospective, the modeling has accounted for the under stability of ZBHM pigments.

Zircon-based heteromorphic encapsulation pigments have been widely investigated and applied since 1970s and the issue concerning their low encapsulation efficiency has however not been intensively explored by researchers. In the current investigations, we established a heteromorphic encapsulation modeling upon series of hypotheses and preconditions and correspondingly proposed a theoretical function αmax = [1 − (k + 1)(D/L)]3 for encapsulation efficiency evaluation. The function has presented different encapsulation efficiencies for the pigments with varying k-D-L constitutions and meanwhile indicated a most effective approach for efficiency elevation by size reduction of pigmental cores. Demonstrations for higher efficiency were comparatively conducted by two representative CdS@ZrSiO4 pigments, in which finer pigmental cores had endowed the semi-products and final pigments with remarkable encapsulation elevation by 64.39% and 24.65% respectively. The modeling has also exhibited that it is approachable for higher efficiency in excess of 12% if superfine pigmental cores can be guaranteed during the encapsulation process.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slide