Information Entropy of Regular Dendrimer Aggregates and Irregular Intermediate Structures

Abstract

Dendrimer molecules and aggregates are chemical structures with regular branching that underlies their physicochemical properties. Regular dendrimers have been studied both theoretically and experimentally, but the irregular intermediate structures between the dendrimers of neighboring generations have not. In the present work, dendrimer aggregates, both regular and intermediate, are investigated in terms of the information entropy approach. As found, the information entropy of the regular dendrimer asymptotically increases with the generation number; herewith, its maximal value equals 2. The intermediate structures have been studied for the growing dendrimer G1 → G2 → G3 → G4 with the tricoordinated building block. The plot of the information entropy of the growing dendrimer on the size has the frontier consisting of the lowest values that correspond to the regular and irregular structures described with the symmetrical graphs. Other intermediate structures have information entropies higher than the regular dendrimers. Thus, to move the system from one informationally stable state to another, its information capacity must be temporarily increased.

Information Entropy in Chemistry: An Overview

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“…Additional advances are expected from the information estimates of imperfect structures. In dendrimer series, we have found that the stable compounds with closed shells have lower information entropies than the intermediate structures with incompletely filled external shells [102]. Therefore, we assume that the information capacity must be temporarily increased to move the system from one informationally stable state to another.…”

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“…The Shannon's entropy conceptinspired graph entropies with topological indices to act as the units of information for calculating the structural information of chemical graphs and complicated networks. Discrete mathematics, biology, and chemistry are just a few of the fields where the graph entropy measures are crucial (1)(2)(3) . https://www.indjst.org/ Dendrimer is a member of a group of macromolecules that combine the benefits of oligomers and polymers.…”