The Electrical Potential due to the “Fixed” Anionic Groups in Nanopores of Proton Exchange Membranes
A. R. Gillespie, R. Paul, and S. J. Paddison
Keywords: PEM Fuel Cells
The study of the transport of ionic species through nanopores is a subject of wide interest covering several diverse fields such as biophysics, electrochemistry and polymer science. While, during recent decades, considerable advances have been made, several fundamental questions remain unanswered. In the present investigation we focus our attention upon the transport of protons through the hydrated nanopores of polymer electrolyte membranes, the separator in a PEM fuel cell. The nanopores in these membranes are often characterized by the presence of pendant groups carrying negative charges; in sulfonic acid based ionomers due to the presence of ions. Since these groups are attached to the pore walls they produce strong inhomogeneous electrical fields in the enclosed volume space through which the ions are transported. It follows, therefore that these fields will profoundly affect the membrane conductivity and thus the functioning of the fuel cell. An understanding of the nature and influence of these fields will aid in the design and eventual synthesis of membranes with improved properties.
One of the problems is, clearly, the development of a model that would adequately portray the anionic potential within the pore volume. Such a result is required for the construction of a Hamiltonian that would enable the application of the full machinery of statistical mechanics in the calculation of such macroscopic properties like the proton self-diffusion coefficient. In the present work we model the nanopore as a cylinder to the walls of which are attached a sequence of rings that are located at equal distances from each other along the pore axis. Each ring contains pendant groups arranged in such a manner that all the angles between the radii drawn from the center of the ring (on the pore axis) to the pendant groups are equal. Clearly, the product of the number of rings with the number of pendant groups contained in each ring must be equal to the number of pendant groups in the pore. Since the pore, in general, contains several cations the negative charges on the pendant groups will be shielded and therefore we calculate the potential at any point by summing a sequence of Yukawa potentials.
NSTI Nanotech 2003 Conference Technical Program Abstract