The previous sections of this article described the synthesis, morphologies, and properties of a variety of low-density microcellular materials. This section discusses several of the analytical methods used and developed at the DOE laboratories to characterize these state-of-the-art materials.In some LDMM applications, quantitative measurements of the material's average cell size and cell size distribution are desired. Indeed, the term “microcellular” has little meaning without such information. As seen throughout this article, however, most LDMMs do not have a readily defined cellular character. The more general problem is to quantify the spatial scale(s) of the foam. For this purpose it is necessary to define one or more “measures” of the spatial scale. The possibilities are many and include not only single numbers (e.g., cell size and cell size standard deviation, where “cell size” is meaningful) but also functional descriptions (e.g., correlation functions).SEM provides direct images and, therefore, is the most popular technique for examining LDMM morphology. SEM, however, suffers from at least three limitations: (1) SEM examines only a very small volume of material, and thus is impractical for obtaining average morphological properties; (2) SEM requires that nonconductive LDMMs be coated, a process step that can alter the structure and introduce artifacts (particularly with delicate structures); and (3) SEM images are only two-dimensional projections of real three-dimensional structures.
The Sampling Distribution of Disease-Associated Alleles
