Membrane durability in proton-exchange membrane fuel cells (PEMFCs) is one of the major obstacles limiting its applications, especially in heavy-duty vehicles. Membrane degradation reactions are thought to be attacks by radicals such as hydroxyl (HO•) or hydrogen atom (H•) generated during fuel cell operation. For the H• case, computational modeling results have suggested that the reaction between H• and the sulfonic group should be the dominant degradation pathway. However, experimental work implies that the tertiary fluorine (t-F) attack is the dominant H• reaction pathway, apparently contradicting the theoretical prediction. Based on previous experimental evidence on isotopic substitution, we postulate that the hydronium radical (H3O•) might be present in PEMFCs. Our ab initio modeling indicates that this radical can be stabilized by the sulfonic anion on the polymer side chain. With the assistance of explicit water, the polymer side chain can undergo a conformational change, leading to a greatly reduced barrier for the t-F degradation reaction. Thus, our H3O• hypothesis is able to explain not only the previous isotopic substitution experiment but also why the t-F degradation reaction is a highly plausible H• degradation mechanism for proton-exchange membranes. To our knowledge, this is the first suggestion that H3O• radicals could be present in electrochemical devices with both experimental and theoretical support.

The formula d = rt when applied to living conditions teems with romance and adventure. This formula can be related to the pupils' experience. It can open the door to a wealth of information, and can bring into the classroom some of that feeling of the magic of travel today. The pupils are already familiar with the idea if not with the actual formula. A few days spent on transportation at the beginning of the study of equations and formulas can motivate the entire unit.

With the change in the philosophy of education and with mathematics on the defensive, I found it necessary to change my method of teaching geometry and to stimulate interest in the subject. I found it necessary to connect geometry with daily life and to have activities suited to the needs, in terests, and abilities of the pupils.