Geometrical and topological model of formation, selection, and evolution of precursor nanoclusters in the convergent matrix self-assembly mechanism of crystal formation

Abstract

Combinatorial-topological analysis algorithms have been developed to reconstruct the code of convergent matrix self-assembly in the form of a sequence of significant elementary events ei proceeding from structure data in a crystal-forming system that contains diverse structural units (atoms, molecules, and polyheral clusters). Mechanisms of selection of suprastructural units with maximal values of their connectivity indices to form chains from precursor clusters are considered. Two special cluster formation mechanisms are recognized. One is a linear mechanism where the number of particles is constantly increasing. The other is a discrete mechanism with an obligatory transiton of the evolving system to the matrix (complementary) selfassembly mode. Structure self-assembly follows the principle of the maximal filling of the crystal space and, accordingly, obeys the requirement for the maximal degree of complementary connectivity of precursor nanoclusters at all evolution steps. The model developed in this way has been used to interpret the formation and structural-topology specifics of carbon allotropes (fullerenes C60 and C70) and polymorphs of metals, H2O (ice), silica, hydrido- and chlorosiloxanes, MEP clathrate family, some aluminosilicates (feldspar and zeolites), and C204H756Cl36Mn84O462 (V = 20992 A).