Deviation from Beer's law and relationship of aggregation with the effective TPA coefficient: UV-vis studies on a series of low symmetry monophthalocyanines bearing a cyclotriphosphazene substituent

In this work, we have carried out a comprehensive study of the aggregation properties of low-symmetry monophthalocyanines containing one fragment of penta(chloro)cyclotriphosphazene in the structure. A new Extinction model has been developed to calculate the concentration, after which the extinction drops sharply, or aggregation becomes noticeable visually. Also, a special descriptor was introduced to estimate the total spectral nonlinearity based on four spectral parameters related to the attenuation of light with increasing concentration: linear (epsilon) and non-linear (xi) extinction coefficients, and threshold concentrations for the beginning (C- backward difference ) and completion (C- null ) of the development of aggregation processes. A special numerical method was developed to find correlations between the cumulative spectral nonlinearity of a medium and the effective two-photon absorption coefficient (TPA) for a series of dyes presented in this paper. The proposed methodology has allowed not only to prove the influence of the complexing metal nature on the non-linear properties of the medium but also to demonstrate how to realize a scheme for choosing the most effective dyes for a given research goal.