Organic semiconductors are an attractive class of materials with large application in various fields, from optoelectronics to biomedicine. Usually, organic semiconductors have low electrical conductivity, and different routes towards improving said conductivity are being investigated. One such method is to increase their ordering degree, which not only improves electrical conduction but promotes cell growth, adhesion, and proliferation at the polymer-tissue interface. The current paper proposes a mathematical model for understanding the influence of the ordering state on the electrical properties of the organic semiconductors. To this end, a series of aromatic poly(azomethine)s were prepared as thin films in both amorphous and ordered states, and their supramolecular and electrical properties were analyzed by polarized light microscopy and surface type cells, respectively. Furthermore, the film surface characteristics were investigated by atomic force microscopy. It was established that the manufacture of thin films from mesophase state induced an electrical conductivity improvement of one order of magnitude. A mathematical model was developed in the framework of a multifractal theory of motion in its Schrodinger representation. The model used the order degree of the thin films as a fractality measure of the physical system's representation in the multifractal space. It proposed two types of conductivity, which manifest at different ranges of fractalization degrees. The mathematical predictions were found to be in line with the empirical data.
Keywords: biomedicine; mesophase; multifractal model; poly(azomethine); semiconducting.