University of Notre Dame

About: University of Notre Dame is a education organization based out in Notre Dame, Indiana, United States. It is known for research contribution in the topics: Population & Context (language use). The organization has 22238 authors who have published 55201 publications receiving 2032925 citations. The organization is also known as: University of Notre Dame du Lac & University of Notre Dame, South Bend.

Catalysis in a Cage: Condition-Dependent Speciation and Dynamics of Exchanged Cu Cations in SSZ-13 Zeolites

Abstract: The relationships among the macroscopic compositional parameters of a Cu-exchanged SSZ-13 zeolite catalyst, the types and numbers of Cu active sites, and activity for the selective catalytic reduction (SCR) of NOx with NH3 are established through experimental interrogation and computational analysis of materials across the catalyst composition space. Density functional theory, stochastic models, and experimental characterizations demonstrate that within the synthesis protocols applied here and across Si:Al ratios, the volumetric density of six-membered-rings (6MR) containing two Al (2Al sites) is consistent with a random Al siting in the SSZ-13 lattice subject to Lowenstein’s rule. Further, exchanged CuII ions first populate these 2Al sites before populating remaining unpaired, or 1Al, sites as CuIIOH. These sites are distinguished and enumerated ex situ through vibrational and X-ray absorption spectroscopies (XAS) and chemical titrations. In situ and operando XAS follow Cu oxidation state and coordinatio...

Recovery of Organic Products from Ionic Liquids Using Supercritical Carbon Dioxide

Abstract: Ionic liquids (ILs) hold great potential as replacements for traditional volatile organic solvents and have been shown to be a viable medium for numerous types of reactions. This work investigates the feasibility of using supercritical carbon dioxide, another environmentally benign solvent, for the separation of organic solutes from an ionic liquid. Recovery rates of aromatic and aliphatic solutes from 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) are given. Supercritical fluid extraction is shown to be a viable separation technique with the additional benefits of environmental sustainability and pure product recovery.

Lie Groups, Lie Algebras, and Representations

Abstract: An important concept in physics is that of symmetry, whether it be rotational symmetry for many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group of symmetries of a system is a continuous group, that is, a group that is parameterized by one or more real parameters. More precisely, the symmetry group is often a Lie group, that is, a smooth manifold endowed with a group structure in such a way that operations of inversion and group multiplication are smooth. The tangent space at the identity in a Lie group has a natural “bracket” operation that makes the tangent space into a Lie algebra. The Lie algebra of a Lie group encodes many of the properties of the Lie group, and yet the Lie algebra is easier to work with because it is a linear space.