Obtaining and Interpreting Information from the Sample

The TEM image in Figure 9.16a illustrates some of the challenges associated with measuring size by microscopy. In general, if the fibers are arrayed side-on without overlap in the field of view and show contrast that is uniformly darker or brighter than their surroundings (including any contaminants), then available image-processing software can easily determine their lengths and diameters. These conditions are rarely met. For example, the fibers in the image are not uniformly darker than the carbon lace that supports them, and they are neither free from overlap nor lying side-on in the viewing field.

Most image-processing programs will have trouble determining fiber sizes from the source image in Figure 9.16 [83,84]. Nonetheless, there is ample information with which to work. Individual nanofibers have their own distinctive internal structure [85], so a close look at the source image allows one to easily distinguish fibers from the support and to follow fibers from beginning to end. Moreover, the majority of the fibers have internal partitions, which can be counted for a length estimate even as tube segments move in the third dimension (into and out of the plane of the image). This is labor intensive, however, and the job of putting statistical limits on the accuracy of microscopy assertions about the distribution of fiber sizes will continue to be a challenge, just as it was for asbestos testing in past decades [80]. Quantifying the extra microscopic details themselves (e.g., fiber curvature, cross-sectional circularity, fibrillation, inside-diameter, and chirality) is a developing challenge as well [75-79, 86].

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Figure 9.16. Carbon nanofiber dimensions from a TEM image: (a) brightfield image 8.3-|im wide; (b) fiber length versus diameter superposed on a bivariate log-normal distribution inferred from a subset of the fibers.

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Figure 9.16. Carbon nanofiber dimensions from a TEM image: (a) brightfield image 8.3-|im wide; (b) fiber length versus diameter superposed on a bivariate log-normal distribution inferred from a subset of the fibers.

The incentive for doing statistically significant work of this type of analysis is high for two reasons. First, it allows one to quantify correlations between diameter and length as illustrated in Figure 9.16b above. This is important in terms of online analysis as discussed in previous sections. If a quantitative relationship between the length and diameter of a collection of fibers can be determined, even if both vary over wide ranges, a classification process that depends on knowledge of one to infer the other can put the relationship to use and constrain both unambiguously. For example, in its simplest form, the relationship between length L and diameter D in nanometers for the fitted subset of fibers in Figure 9.16 might look like L = 8.1 D15.

Secondly, the connection between these variables and other physical features of each fiber is often important. The microscopy techniques described here give broad access to other properties of fiber structure. For example, the source image for Figure 9.16 suggests that only some of the smaller carbon fibers in the field of view are hollow. Additional properties include crystallinity along with internal defect structure and surface reconstructions along with surface facet/edge/kink geometry. Other properties accessible to microscopy include the relationship of fibers to, and the structure of, additional nonfiber components (e.g., nanocatalyst particles), as well as the relationship between fibers and their matrix and/or support (e.g., the silicon substrate upon which fibers in a nanoelectronic display are fastened).

Finally, as the thrust of this chapter is online methods for accurately characterizing particles by size, microscopy of individual particles is a natural tool for calibration and monitoring their effectiveness. Structures of known geometry (such as nanotubes and nanospheres) can allow one to infer mass or volume indirectly and thus relate local measurements to bulk constraints on quantities such as number concentration. In addition to elemental ratios by X-ray spectroscopy [87], the number of atoms per unit area in a field of view can sometimes be determined directly by electron energy loss spectroscopy [88,89]. Inasmuch as microscopes also quantify the area in a field of view, the number of a given image feature per gram may thus be measured as well.

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