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We present a modeling approach to determine the permeability-selectivity tradeoff for microfiltration and ultrafiltration membranes with a distribution of pore sizes and pore shapes. Using the formulated permeability-selectivity model, the effect of pore aspect ratio and pore size distribution on the permeability-selectivity tradeoff of the membrane is analyzed. A finite element model is developed to study the effect of membrane stretching on the distribution of pore sizes and shapes in the stretched membrane. The effect of membrane stretching on the permeability-selectivity tradeoff of membranes is also analyzed. The results show that increasing pore aspect ratio improves membrane performance while increasing the width of pore size distribution deteriorates the performance. It was also found that the effect of membrane stretching on the permeability-selectivity tradeoff is greatly affected by the uniformity of pore distribution in the membrane. Stretching showed a positive shift in the permeability-selectivity tradeoff curve of membranes with well-dispersed pores while in the case of pore clustering, a negative shift in the permeability-selectivity tradeoff curve was observed.

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Metal and ceramic matrix composites have been developed to enhance the stiffness and strength of metals and alloys, and improve the toughness of monolithic ceramics, respectively. It is possible to further improve their properties by using nanoreinforcement, which led to the development of metal and ceramic matrix nanocomposites, in which case, the dimension of the reinforcement is on the order of nanometer, typically less than 100 nm. However, in many cases, the properties measured experimentally remain far from those estimated theoretically. This is mainly due to the fact that the properties of nanocomposites depend not only on the properties of the individual constituents, i.e., the matrix and reinforcement as well as the interface between them, but also on the extent of nanoreinforcement dispersion. Therefore, obtaining a uniform dispersion of the nanoreinforcement in the matrix remains a key issue in the development of nanocomposites with the desired properties. The issue of nanoreinforcement dispersion was not fully addressed in review papers dedicated to processing, characterization, and properties of inorganic nanocomposites. In addition, characterization of nanoparticles dispersion, reported in literature, remains largely qualitative. The objective of this review is to provide a comprehensive description of characterization techniques used to evaluate the extent of nanoreinforcement dispersion in inorganic nanocomposites and critically review published work. Moreover, methodologies and techniques used to characterize reinforcement dispersion in conventional composites, which may be used for quantitative characterization of nanoreinforcement dispersion in nanocomposites, is also presented.