Non-Markovian Diffusion Imaging

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With support from the Chemical Measurement & Imaging program and co-funding from the Atomic, Molecular, and Optical Physics - Experiment and Theory programs, Professor Bouchard at the University of California, Los Angeles is developing new methods to study gaseous diffusion - the random motions of molecules in gases. In traditional models of these processes, a snapshot (state) at any given moment is assumed to be independent of past collisions between molecules swimming in the gas. However, if the picture can be taken quickly enough, it is possible to detect molecules’ "memory" of collisions from the recent past, and thus to investigate the nature of surfaces encountered by the molecules. Dr. Bouchard's group is developing both experimental methods and the underlying theory to advance understanding in systems (e.g., catalysts and lungs) where the memory of these collisions are important. They use nuclear magnetic resonance (NMR) spectroscopy, the tool at the heart of Magnetic Resonance Imaging (MRI, an important medical diagnostic tool) which avoids the use of harmful ionizing radiation like x-rays. Graduate and undergraduate students engaged in this research receive broad interdisciplinary training, and contribute to the development of relevant introductory chemistry materials that will be made freely available to the public. Self-diffusion in a dense gas of neutral molecules is non-Markovian and must be modeled by a Langevin equation with memory kernel. The Bouchard group has obtained experimental NMR spectroscopy results that are consistent with a generalized Langevin description, as confirmed by an unexpected temperature dependence of the NMR linewidth as well as dependence on inter-pulse spacing during Carr-Purcell-Meiboom-Gill (CPMG) experiments. While the new theory describes the results of free self-diffusion well, the diffusion behavior in the presence of boundaries has not yet been explored. Dr. Bouchard is now probing restricted diffusion in porous media possessing various types of boundaries, and developing new extensions of the underlying theory based on the stochastic calculus of bounded diffusions (sticky, reflecting, killing, and absorbing boundaries). The new NMR-based methods may shed new light into the kinetic theory of gases, benefitting chemical physics and medical imaging by offering new tools to extract information about pore structure and function in media such as porous rocks, soils, or lungs. The tools also show promise for both characterization of catalytically reactive surfaces and mass transport during reactions and provision of a better understanding of hyperpolarized gas MRI. Educational impacts will derive from the training and active participation of multiple students in the research as well as the creation of free online educational course materials disseminated via the institution's web site.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.