Single-Molecule Fluorescence Trajectories for Investigating Molecular Transport in Thin Silica Sol−Gel Films

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Abstract
Single-molecule fluorescence tracking has been used to examine diffusion of small molecules in sol−gel films in order to identify spatial heterogeneity in the structure and molecular diffusivities for different regions of the film. Fluorescence intensity profiles from single molecules are fit to a two-dimensional Gaussian function to determine their x,y positions with subpixel resolution. Scatter plots and histograms of molecular step sizes indicate that the trajectories conform to the predictions of a two-dimensional random walk. The mean-square step size is shown to be an unbiased estimate of the variance of the step-size probability distribution and a valid statistic for determining the diffusion coefficient from a molecular trajectory. The diffusion coefficients measured for different molecules are subjected to an F test, which showed that the sol−gel film exhibits spatial variation in the diffusion coefficient on a micrometer-length scale. The spatial variation in diffusivities is a measure of structural heterogeneity of these films.