Characterization of polymer structures based on Burnside’s lemma

Abstract

Polymer structure modeling is a trend of recent material sciences. Developments of computational science and nanotechnology make it possible to predict properties of complicated molecular structures. Many theoretical and computational methods have succeeded in elucidating the nature of polymer structures. It is not always best to model whole complicated structures depending on computer capabilities. Significant properties of materials may be manifested in simple structural aspects. In the present study, characteristics of a polymer structure are investigated by applying Burnside's lemma to the modeling procedure. This method is expected to be available to model polymers or molecular crystals in which functional groups play an important role in expressing their functions. Every structure under the symmetry and periodicity is counted completely and the energy distribution caused by the conformations of functional groups can be clarified. The detailed procedure is introduced and the present method is applied to a problem for investigating molecular structures of sulfonated poly(ether ether ketone) (SPEEK). SPEEK is focused on a candidate for proton exchange membranes in polymer electrolyte fuel cells. Sulfonic groups have a significant role in proton exchange membranes to make proton conduction channels. From our analysis, it is found that sulfonic groups tend to be dispersed in SPEEK membranes at their stable conditions. These are unfavorable characteristics for proton exchange membranes due to their difficulty to form desirable water channels inevitable for the high proton conductivity. This is one reason why SPEEK membranes are inferior to Nafion® membranes that express the highest performance as proton exchange membranes. Using the present method, experimental and theoretical results previously reported are confirmed and detailed characteristics are discussed in terms of structural simplicities.