Description of oxygen permeability in various high polymers using a graph theoretical approach

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Abstract
Graph theory methods are shown to complement group additivity methods of predicting oxygen permeability in certain types of polymers. Graph theory is a topological approach that assigns a set of indices to a molecule to describe its structure. Since many physical properties of molecules depend upon their structure, graph theory indices can be used to describe important properties of molecules. In this work a set of graph theory indices are used to describe the property of a polymer based on a modified representation of the monomer unit. More specifically, Randic indices are used to describe the log of the oxygen permeability with 3.2% average relative error. Polymers comprising the basis set contain backbones of sp2, sp3, or aromatic carbons, oxygen, or silicon and have substituents that contain chloride, fluoride, alkyl groups, hydrogen, oxygen, aromatic carbons, or chloro and/or fluoro substituted alkyl groups. The correlation coefficient (R2) (0 ≤ R2 ≤ 1) of a nonlinear model is 0.91. The graph theory method for describing the oxygen permeability of these selected groups of polymers is in good agreement with that predicted by the permachor model. The permachor method makes oxygen permeability predictions based upon group additivity and distinguishes the degree of crystallinity of a polymer by empirically assigning different permachor (π) values to identical groups based upon the polymer crystallinity. The inability of graph theory to explain the remaining 9% of the scatter in the data is probably due to failure to incorporate into the graph theory model terms which quantify crystallinity.

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