On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)

In a previous paper, we showed how one can obtain from the action of a locally compact quantum group on a type I-factor a possibly new locally compact quantum group. In another paper, we applied this construction method to the action of quantum SU(2) on the standard Podles sphere to obtain Woronowicz' quantum E(2). In this paper, we will apply this technique to the action of quantum SU(2) on the quantum projective plane (whose associated von Neumann algebra is indeed a type I-factor). The locally compact quantum group which then comes out at the other side turns out to be the extended SU(1,1) quantum group, as constructed by Koelink and Kustermans. We also show that there exists a (non-trivial) quantum groupoid which has at its corners (the duals of) the three quantum groups mentioned above.Comment: 35 page

Enhancing proton mobility in polymer electrolyte membranes : lessons from molecular dynamic simulation

Typical proton-conducting polymer electrolyte membranes (PEM) for fuel cell applications consist of a perfluorinated polymeric backbone and side chains with SO3H groups. The latter dissociate upon sufficient water uptake into SO3- groups on the chains and protons in the aqueous subphase, which percolates through the membrane. We report here systematic molecular dynamics simulations of proton transport through the aqueous subphase of wet PEMs. The simulations utilize a recently developed simplified version (Walbran, A.; Kornyshev, A. A. J. Chem. Phys. 2001, 114, 10039) of an empirical valence bond (EVB) model, which is designed to describe the structural diffusion during proton transfer in a multiproton environment. The polymer subphase is described as an excluded volume for water, in which pores of a fixed slab-shaped geometry are considered. We study the effects on proton mobility of the charge delocalization inside the SO3- groups, of the headgroup density (PPM "equivalent weight"), and of the motion of headgroups and side chains. We analyze the correlation between the proton mobility and the degree of proton confinement in proton-carrying clusters near SO3- parent groups. We have found and rationalized the following factors that facilitate the proton transfer: (i) charge delocalization within the SO3- groups, (ii) fluctuational motions of the headgroups and side chains, and (iii) water content

Computersimulationen und theoretische Modellierung der Protonendynamik von Modellporen einer Polymer-Elektrolyt-Membran

The proton transport in pore models of a polymer electrolyte membrane (PEM) is investigated by molecular dynamics (MD) computer simulations and continuum theory in order to understand the effects of molecular properties of the membrane on proton mobility. These investigations aim at making structural proposals for membrane design with the goal to achieve better performance of the membrane, specifically better proton conductivity and less permeation of other molecules, such as methanol and water. The proton diffusion is studied in a single pore, using a slab-like or cylindrical model. The models focus on the perfluorinated sulfonic acid ionomers, which are at present the material of choice in polymer electrolyte fuel cells (PEFC). The ionomers consist of a perfluorinated polymeric backbone with SO3H-terminated side chains.SIGLEAvailable from: http://diss.ub.uni-duesseldorf.de/ebib/file?dissid=696 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Modeling of proton transfer in polymer electrolyte membranes on different time and length scales

Polymer electrolyte membranes (PEMs) are key component materials in fuel cell technology. Understanding the relationship between the elementary acts of proton transport and the operation of the entire cell on different time and length scales is therefore particularly rewarding. We discuss the results of recent atomistic computer simulations of proton transport in porous PEMs. Different models cover the range from individual local proton hops to diffusion processes with polymer mobility included