ABSTRACT
Recently we complemented the raster image correlation spectroscopy (RICS) method of analysing raster images via estimation of the image correlation function with the method single particle raster image analysis (SPRIA). In SPRIA, individual particles are identified and the diffusion coefficient of each particle is estimated by a maximum likelihood method. In this paper, we extend the SPRIA method to analyse mixtures of particles with a finite set of diffusion coefficients in a homogeneous medium. In examples with simulated and experimental data with two and three different diffusion coefficients, we show that SPRIA gives accurate estimates of the diffusion coefficients and their proportions. A simple technique for finding the number of different diffusion coefficients is also suggested. Further, we study the use of RICS for mixtures with two different diffusion coefficents and investigate, by plotting level curves of the correlation function, how large the quotient between diffusion coefficients needs to be in order to allow discrimination between models with one and two diffusion coefficients. We also describe a minor correction (compared to published papers) of the RICS autocorrelation function.
ABSTRACT
We have used Electron Tomography (ET) to reveal the detailed three-dimensional structure of particulate hydrogels, a material category common in e.g. controlled release, food science, battery and biomedical applications. A full understanding of the transport properties of these gels requires knowledge about the pore structure and in particular the interconnectivity in three dimensions, since the transport takes the path of lowest resistance. The image series for ET were recorded using High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HAADF-STEM). We have studied three different particulate silica hydrogels based on primary particles with sizes ranging from 3.6nm to 22nm and with pore-size averages from 18nm to 310nm. Here, we highlight the nanostructure of the particle network and the interpenetrating pore network in two and three dimensions. The interconnectivity and distribution of width of the porous channels were obtained from the three-dimensional tomography studies while they cannot unambiguously be obtained from the two-dimensional data. Using ET, we compared the interconnectivity and accessible pore volume fraction as a function of pore size, based on direct images on the nanoscale of three different hydrogels. From this comparison, it was clear that the finest of the gels differentiated from the other two. Despite the almost identical flow properties of the two finer gels, they showed large differences concerning the accessible pore volume fraction for probes corresponding to their (two-dimensional) mean pore size. Using 2D pore size data, the finest gel provided an accessible pore volume fraction of over 90%, but for the other two gels the equivalent was only 10-20%. However, all the gels provided an accessible pore volume fraction of 30-40% when taking the third dimension into account.
