Envlron. Sci. Technol. 1093, 27, 539-547
Fractal Geometry of Carbonaceous Aggregates from an Urban Aerosol Karen A. Katrinak,*nt-’ Peter Re&§ Paul R. Perkes,§ and Peter R. Buseckt-”
Departments of Geology and Chemistry and Center for Solid State Science, Arizona State University, Tempe, Arizona 85287
rn Carbonaceous aerosol aggregates collected in Phoenix, AZ, have an irregular branched morphology. Fractal analysis of transmission electron microscope (TEM) images provides a means of quantifying morphologic variations among aggregates and relating them to mechanisms of formation. The 38 aggregates analyzed, ranging in length from 0.21 to 2.61 pm, were divided into three groups: fractal (D < 2), possibly nonfractal (D 1 2), and mixed geometry. For the 23 fractal aggregates,fractal dimensions (D)range from 1.35 to 1.89 and are interpretable using cluster-cluster and particle-cluster models, which are variations of diffusion-limited aggregation. The 13 aggregates with D 1 2 were divided into two categories: uncoated and coated. The uncoated aggregates have branching shapes and may have formed through particle-cluster aggregation. The coated aggregates have an underlying morphology which may be fractal; the coatings were probably deposited from the ambient atmosphere. The two mixed aggregates have interiors with D 1 2 surrounded by outer regions with D < 2.
Introduction Fractal analysis has been applied to a variety of natural objects, from coastlines and star clusters to marine particles and combustion products (1-4). It provides a geometric parameter, the fractal dimension, useful in comparing many different materials on the basis of their morphology. Fractal analysis is a means of characterizing irregularly shaped objects on the basis of how their volumes vary relative to their sizes. For a nonfractal object such as a solid sphere, an increase in radius results in an increase in volume equal to the radius raised to the third power, 3 being the spatial dimension of the object. In contrast, the growth of a fractal object involves an increase in volume equal to its radius raised to a power equivalent to its fractal dimension, which is less than its spatial dimension. Fractal objects thus characteristically have large surface areas relative to their volumes. A fractal object is self-similar; i.e., its morphology is, in a statistical sense, unvaried regardless of whether the entire object or only a small part of it is considered. The scale-invariant morphology of a fractal object is described by the relationship N a ID, where N is the number of areal units occupied by the object inside a square of length 1 and D is the fractal dimension ( I ) . A series of squares of varied sizes, centered on the object of interest, are used to measure the fractal dimension. Pixels commonly serve as the areal units. In order for an object to be identified as fractal, D must be less than the spatial dimension, e.g., less than 3 for a three-dimensional object, or less than 2 for a two-dimensional image. Carbon blacks and soots,as well as inorganic combustion products, have low-density, branched shapes characteristic of fractal objects. This morphology results from the interconnection of hundreds of spherules, each formed in+ Department
of Geology. Current address: Energy and Environmental Research Center, Box 8213, University of North Dakota, Grand Fofks, ND 58202-8213. f Center for Solid State Science. Department of Chemistry. 0013-936X/93/0927-0539$04.00/0
dividually. Variations in fractal dimensions apparently reflect differences in the processes causing the spherules to aggregate. Fractal analysis is thus useful in comparing aggregation processes for combustion products or other materials. Fractal dimensions of combustion products are commonly measured using two-dimensional projections such as electron microscope images. The fractal geometry of combustion products was first described for aggregates of Fe, Zn, and SiOz, all with D = 1.7-1.9 (5). Soot produced from an acetylene flame was found to have D = 1.5-1.6 for aggregates with length of
