Controls on the Fractal Dimension

In 1999, Homer [32] noted that 'sparse' data existed to correlate the chemical characteristics of a humic material with its fractal dimension or aggregation mechanism. For example, a preliminary study is described that may be the only attempt to correlate the carbon types present in a humic sample to its fractal properties. Humic acids with a greater proportion of aromatic carbon than carbohydrate carbon (determined from a 13C NMR spectrum) had larger fractal dimensions than those with smaller proportions of aromatic carbon. In the same report, Homer [32] suggested that functional group concentrations might also play a role. Though they represent a very limited data set, the fractal dimensions presented in Rice and Lin [12] seem to suggest that humic particle morphologies may vary with source environment. While the correlations from these comparisons may only weakly infer a cause-and-effect relationship, a systematic study of the chemical properties of a suite of carefully-characterized humic and fulvic acids could, at the very least, point the way towards more specific studies of the chemical interactions resulting in the fractal aggregate structures observed for humic materials.

7.4.2 Effect of Environmental Variables on Aggregate Structure

While the solution parameters discussed certainly fall within the realm of environmental variables, their limits in most natural environments are relatively constrained; for example, pH usually varies only between ~ 5 and 8 [56]. Humic materials are strong ligands for multivalent cations and these same cations readily flocculate humic materials, for some cations at very low concentrations. The resulting aggregates and the aggregation process(es) that form them could be studied with a fractal approach. For example, Ca2+ [35] and Fe3+ [32] have been cursorily examined. Calcium ions produced a particle with surface fractal properties (as opposed to mass fractal behavior) at all pH values. Contrary to the expected increase in fractal dimension, Fe3+ did not change the observed value of Dm for the humic acid studied, but it did increase the intensity of scattered neutrons as a result of what was believed to be an increase in aggregate size. Homer [32] proposes that this could be the result of either an increase in humic aggregate cluster size or the formation of new clusters from previously unaggregated components in a humic sample.

7.4.3 Environmental Applications of the Fractal Nature for Humic Materials

Studies carried out on humic materials that have utilized fractals have focused on characterizing their structural organization and/or their aggregation behavior. The real power of a fractal approach lies not in simply characterizing humic materials, but in applying it to modeling and predicting the chemical and geochemical behavior of these materials in the environment.

For example, Dachs and coworkers [57, 58] have developed a fractal approach that takes the 'geometric heterogeneity' of humic materials into account when modeling their interaction with organic contaminants. This approach [57] utilizes the different interaction probabilities of the active contaminant binding sites on fractal surfaces to accommodate linear and nonlinear sorption isotherms (i.e. 'dual-mode' sorption) using coverage extent, physical and chemical properties of the adsorbate and the existence of equilibrium conditions. An extension of this approach [58] treats partitioning as sorption to the inner sites of a fractal sorbent, in much the same manner that a hydrophobic organic chemical is viewed as partitioning into a humic material. In this approach, molecules are adsorbed at the outer sites on a fractal aggregate in a relatively fast process. With time, molecules slowly diffuse into the fractal aggregate and bind to the inner sites. In this process, partitioning is a significant contribution to the overall sorption process at long equilibration times. Interestingly, this sequence of events is what Kohl et al. [59] have observed when solid-state 19F NMR is used to follow the interaction of hexafluorobenzene with natural organic matter sorbents.

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