Envlron. Sci. Technol. 1993, 27, 413-414
Fractal Nature of Humic Materials James A. Rlce”
Department of Chemistry, South Dakota State University, Brookings, South Dakota 57007-0896 Jar-Shyong Lin
Center for Small-Angle Scattering Research, Solid-state Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Introduction Fractals are geometric representations of strongly disordered systems whose structures are described by nonintegral dimensions (1,2).The nonintegral nature of these “fractal dimensions” is the result of the realization that a fractal object must possess more structural detail to accommodate its disorder than an ordered object with classical dimensions of 1,2, or 3. A fundamental tenet of fractal geometry is that disorder exists at any characterization scale used to examine the substance. Regardless of the “magnification”used, the disorder of a fractal object cannot be resolved. From this perspective, disorder is seen as an inherent characteristic of a fractal material rather than as a perturbative phenomenon forced upon it (2). Humic substances are organic materials that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into three fractions: humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fractions has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder (3). In fact, on the basis of the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a profound lack of order on a molecular level (3). If the fundamental chemical characteristic of a humic material is a strongly disordered nature, then humic materials should be amenable to characterization by fractal geometry. The purpose of this communication is to report a test of this hypothesis. Experimental Section Humic acid (HA) and/or fulvic acid (FA) from a stream sediment, soil, and lignite and an aquatic humus sample were isolated using traditional techniques, converted to the acid form, and lyophilized (4-6). These solid-state materials were pressed into l-mm-thick sample holders. The aquatic humus sample and the stream sediment humic acid were also examined while in solution. Enough of the aquatic humus sample was added to deionized distilled water to give a dissolved organic carbon concentration of 45 mg/L. Enough stream sediment humic acid was dissolved in 0.1 M NaOH to give a humic acid concentration of 6.7 g/L. The samples were then transferred to glass capillaries. The disorder of each humic material was examined by small-angleX-ray scattering (SAXS)using the 10-m SAXS camera at the Center for Small-Angle Scattering Research at Oak Ridge National Laboratory. The X-ray source in this instrument produces monochromatized Cu K a radiation. The source was operated at 40 kV and 100 mA. In separate experiments, scattering was recorded at sample to detector distances of 5.1 and 1.7 m. This allowed the scattering behavior of each humic material to be measured 0013-936X/93/0927-0413$04.00/0
over the entire working range of the SAXS instrument. The scattering data from each analysis were then combined. Scattering which results from fractal substances conforms to a power law where the intensity of the scattered X-rays, [I(q)], as a function of the scattering vector, q, is proportional to q raised to some exponent. The magnitude of this exponent is a function of the fractal dimension (0) of the substance (7). To determine if scattering from humic materials follows a power law, log-log plots of I(q) vs q were constructed for each humic acid, fulvic acid, or aquatic humus sample from the combined scattering data sets. If scattering from humic materials obeys a power law, this plot will be a straight line. The slope of this plot is the power law exponent and it can be used to determine D. Results and Discussion Can Humic Materials Be Described by Fractal Geometry? Figure 1is a log-log plot of the small-angle X-ray scattering behavior typical of the humic materials characterized in this study. This plot is a straight line, which indicates that small-angleX-ray scattering by humic materials can be described by a power law. Power-law scattering by humic materials is observed over a range of scattering vectors covering approximately 2 orders of magnitude of the scattering vector. This satisfies the criterion that disorder in the sample must exist regardless of the scale length used to examine the material. Consequently, humic materials can be described by fractal geometry. What Type of Fractals Are Humic Materials? A mass fractal is an object whose surface and mass are characterized by fractal properties. Its power-law behavior is described by eq 1. For a mass fractal the power-law I(q) a 4-D” (1) exponent, D,, is less than or equal to 3 (7). An example of mass fractal is a substance with a dendritic morphology (1). A surface fractal is one in which only the surface of the material exhibits fractal properties. The power-law behavior of a surface fractal is described by eq 2. A surface (2) fractal has a power-law exponent whose magnitude is within the following range: 3 < 6 - D, I 4 (7). An example of a surface fractal is a solid object with a highly irregular surface; the coastline of an island has been used as an example (1). Examination of the power-law exponents in Table I readily identifies humic materials in the solid state as surface fractals. Examination of the power-law exponents in Table I1 identifies the dissolved aquatic humus sample and the dissolved stream sediment humic acid as mass fractals. Thus, there appears to be a fundamental difference in the nature of the disorder of humic materials
0 1993 American Chemical Society
I(q)
a
q6-D~
Environ. Sci. Technol., Vol. 27, No. 2, 1993
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Table 11. Power-Law Exponents and Fractal Dimensions of Various Humic Materials in Solution"
l
o
o
o
sample
power-law exponent
fractal dimension
stream sediment HA aquatic humus
2.5 1.6
2.5 1.6
r
*Absolute uncertainty associated with each power-law exponent is f0.1.
of the sample in solution suggests that the dissolved aquatic humus sample has a less compact, more open form than it does when it is dried. The fractal dimension of the dissolved stream sediment humic acid is slightly larger than that of the same material in the solid state. This again indicates a difference between the nature of the stream sediment humic acid in solution and in the solid state.
Flgure 1. Smaikngle X-ray scattering intensity for a dissolved stream sediment humlc acid.
Table I. Power-Law Exponents and Fractal Dimensions of Various Humic Materials in the Solid Statea
sample
power-law exponent
fractal dimension
stream sediment FA soil FA lignite FA stream sediment HA lignite HA aquatic humus
3.7 3.5 3.2 3.8 3.7 3.5
2.3 2.5 2.8 2.2
2.3 2.5
a Absolute uncertainty associated with each power-law exponent is fO.l.
in solution and in the solid state. What Are the Fractal Dimensions of Humic Materials? In eq l, D, is the fractal dimension of a mass fractal. In eq 2, D,is the fractal dimension of a surface fractal. Thus, the fractal dimension can be readily calculated from the power-law exponent. Table I gives the fractal dimension of the solid-state humic and fulvic acids characterized in this study. While there are a limited number of humic and fulvic acids, it appears that humic acid may be characterized by a smaller D,than fulvic acid. Table I1 gives the fractal dimension of the dissolved aquatic humus and dissolved stream sediment humic acid. The dissolved aquatic humus sample displays a fractal dimension of 1.6. This is considerably lower than the fractal dimension of 2.5 observed for this same material in the solid state (Table I). The lower fractal dimension
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Summary These results demonstrate that it is possible to describe the nature of humic materials using the concepts of fractal geometry. Fractal analysis has revealed fundamental differences between the nature of humic materials in the solid state and in solution. The recognition of the fractal properties of humic materials provides a tool to create a detailed picture of a variety of geochemical processes in natural environmental systems such as the aggregation of organic colloids, the structural evolution of organic matter during its diagenesis, the interaction of humic materials with anthropogenic organic chemicals, or perhaps even the fundamental nature of humic materials themselves. Literature Cited (1) Mandelbrot, B. B. T h e Fractal Geometry of Nature;
Freeman: San Francisco, 1983. (2) Pfeiffer, P.; Obert, M. In T h e Fractal Approach t o Heterogeneous Chemistry; Avnir, D., Ed.; Wiley: Chichester, England, 1989. (3) MacCarthy, P.; Rice, J. A. In Proceedings of the Chapman Conference on the Gaia Hypothesis; MIT Press: Cambridge, MA, 1992. (4) Rice, J. A.; MacCarthy, P. In Organic Substances and Sediments i n Water. Volume 1. Humics and Soils; Baker, R. A., Ed.; Lewis Publishers: Chelsea, MI, 1991. (5) Rice, J. A. Studies on Humus: I. Statistical Studies on the Elemental Composition of Humus 11. The Humin Fraction of Humus. Dissertation, Colorado School of Mines, Golden, CO, 1987, NO. T-3204. (6) Thurman, E. M.; Malcolm, R. L. Environ. Sci. Technol. 1981, 15, 463. (7) Schmidt, P. W. In The Fractal Approach to Heterogeneous Chemistry; Avnir, D., Ed.; Wiley: Chichester, England, 1989. Received for review July 24, 1992. Revised manuscript received October 6, 1992. Accepted October 29, 1992. This work was supported by the U.S. Geological Survey (USGS),Department of the Interior, through USGS Award 14-08-0001-G1911. The views and conclusions contained i n this paper are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. government.
