Faculty Bibliography

Living tissues and other heterogeneous media generally consist of structural units with different diffusion coefficients and NMR properties. These blocks, such as cells or clusters of cells, can be much smaller than the imaging voxel, and are often comparable with the diffusion length. We have developed a general approach to quantify the medium heterogeneity when it is much finer than the sample size or the imaging resolution. The approach is based on the treatment of the medium statistically in terms of the correlation functions of the local parameters. The diffusion-weighted signal is explicity found for the case in which the local diffusivity varies in space, in the lowest order in the diffusivity variance. We demonstrate how the correlation length and the variance of the local diffusivity contribute to the time-dependent diffusion coefficient and the time-dependent kurtosis. Our results are corroborated by Monte Carlo simulations of diffusion in a two-dimensional heterogeneous medium

The Mott insulating state is a manifestation of strong electron interactions in nominally metallic systems. Using transport spectroscopy, we showed that an energy gap exists in nominally metallic carbon nanotubes and occurs in addition to the band gap in small-band-gap nanotubes, indicating that carbon nanotubes are never metallic. This gap has a magnitude of approximately 10 to 100 milli-electron volts and a nanotube radius (r) dependence of approximately 1/r, which is in good agreement with predictions for a nanotube Mott insulating state. We also observed neutral excitations within the gap, as predicted for this state. Our results underscore nanotubes' exceptional capabilities for use in studying correlated electron phenomena in one dimension

We report fluorescence of single semiconductor nanorods (NRs) and few-NR clusters, correlated with transmission electron microscopy for direct determination of the number of NRs present in a single fluorescent source. For samples drop-cast from dilute solutions, we show that the majority of the blinking sources (approximately 75%) are individual NRs while the remaining sources are small clusters consisting of up to 15 NRs. Clusters containing two or three NRs exhibit intermittent fluorescence intensity trajectories, I(t), similar to those of individual NRs. The associated statistical parameters of on- and off-time probability densities for two- and three-NR clusters are indistinguishable from those of individual NRs. In contrast, statistically distinguishable blinking parameters are observed for clusters of five or more particles. In particular, the 'truncation time' of the on-time probability density, i.e., the time characterizing the transition from a power law to an exponential decay, was found to increase superlinearly with the number of particles. Our long (2.4 x 10(4) s) blinking measurements also directly reveal the previously unobserved truncation of the power law distribution of the off-times for single nanoparticles

We consider the NMR signal from a permeable medium with a heterogeneous Larmor frequency component that varies on a scale comparable to the spin-carrier diffusion length. We focus on the mesoscopic part of the transverse relaxation, that occurs due to dispersion of precession phases of spins accumulated during diffusive motion. By relating the spectral lineshape to correlation functions of the spatially varying Larmor frequency, we demonstrate how the correlation length and the variance of the Larmor frequency distribution can be determined from the NMR spectrum. We corroborate our results by numerical simulations, and apply them to quantify human blood spectra.