Fractals in Soil Science Editors: Ya.A. Pachepsky, J.W. Crawford and W.J. Rawls �9 2000 Elsevier Science B.V. All rights reserved. 161

Applications of light and X-ray scattering to characterize the fractal properties of soil organic

matter

James A. Rice a,,, E. Tombficz b Kalumbu Malekani a,1

a South Dakota State University, Department of Chemistry and Biochemistry, Brookings, SD 57007-0896, USA

b Attila Jdzsef University, Department of Colloid Chemistry, Aradi V rtanuk tere 1, Szeged, Hungary

Received 16 October 1997; accepted 28 September 1998

Abstract

Soil organic matter (SOM) is a heterogeneous assemblage of organic molecules that interact in a variety of ways with each other, with soil mineral surfaces, and with soil mineral colloids. Because of SOM's heterogeneity it is very difficult to define its surface, or the surfaces of the composite materials produced by its interaction with soil minerals. Yet it is at these interfaces where chemical reactions that involve SOM take place. Results are presented which describe the fractal characterization of humic materials using static X-ray and light scattering, and dynamic light scattering (DLS) experiments. The applicability of static X-ray scattering to the direct determination of the fractal dimension of humic materials is established using DLS. Over the length scales studied, humic materials are surface fractals in the solid state, and mass fractals in solution. The longer characterization length scales possible in the static light scattering experi- ments suggest that at longer characterization length scales humic acid is not fractal, at least not under the solution conditions employed in these experiments. Application of fractal analysis to the characterization of the surface morphology of soil and peat humin samples, the calculation of the hydrodynamic radius of humic acid particles, and the study of humic acid aggregation are discussed. �9 1999 Elsevier Science B.V. All rights reserved.

Keywords: fractal; humic acid; humin; fulvic acid; soil organic matter; dynamic light scattering; static light scattering; small-angle X-ray scattering

* Corresponding author. Tel.: + 1-605-688-4252; Fax: + 1-605-688-6364; E-mail: ricej @ur.sdstate.edu

Present address: The Connecticut Agricultural Experiment Station, PO Box 1106, New Haven, CT 06504, USA.

Reprinted from Geoderma 88 (1999) �9 1999 Elsevier Science B.V. All rights reserved

162

1. Introduction

Soil organic matter is divided into humic and nonhumic substances (Steven- son, 1982). Nonhumic substances are organic materials that belong to recogniz- able compound classes such as carbohydrates and other polysaccharides, pro- teins or peptides, lipids, and lignin. Humic substances are organic materials that are formed by the profound alteration of organic matter in natural environments. They are operationally divided into three fractions based on their solubility as a function of the pH of the aqueous solution used to extract them: humic acid is defined as the fraction soluble at alkaline pH values, fulvic acid is defined as the fraction soluble at all pH values, and humin is defined as the fraction insoluble at any pH value (Hayes et al., 1989). It is possible to fractionate humin into a bound-humic acid fraction, a solvent extractable lipid fraction (bitumen), a bound-lipid fraction, and a mineral component (Rice and MacCarthy, 1990). This paper will focus on the humic materials.

Each humic fraction has been shown to be an extremely complex mixture of organic substances that apparently cannot be described by a single chemical structure (Dubach and Mehta, 1963; Felbeck, 1965; Hurst and Burges, 1967). Essentially all analytical methods that can be used to characterize the structure of a substance, such as NMR or mass spectrometry, operate under the assump- tion that the material being characterized is a pure substance. But because humic materials are mixtures, the most that can be realistically hoped for from such a chemical characterization is an 'average' or 'bulk' chemical description of the substances that comprise it. While such an approach has some utility describing the chemical and geochemical behavior of humic materials, it provides limited information that can be used to study their structural morphology. Humic materials have proven so intractable to repeated attempts to impose structural order onto them because they may represent the ultimate in molecular disorder (MacCarthy and Rice, 1991). Even lignin, which has been shown to some indication of structure on a long-range scale (Srzic et al., 1995), does not appear to approach the molecular complexity embodied by humic materials. Based on the characteristics that humic materials must possess in order to perform their functions in a natural system, it has been proposed that the fundamental characteristic of humic materials is not a discrete chemical structure (MacCarthy and Rice, 1991). Conversely, it is entirely probable that humic materials are best described by a profound absence of discrete structure (MacCarthy and Rice, 1991).

It is only recently that the application of fractal geometry to the study of the nature and chemistry of humic materials in natural systems has been described. In the interval since a fractal nature for humic materials was first reported, there have been few papers to actually exploit the fractal concept to better understand these enigmatic substances. Rice and Lin (1992, 1993, 1994) and Malekani and Rice (1997) have used small-angle X-ray scattering (SAXS) to demonstrate that

163

all three humic substances are fractal materials in solution or in the solid state. Osterberg and Mortensen (1992a,b), Osterberg et al. (1994) and Senesi et al. (1994, 1996a,b) using small-angle neutron scattering and turbidimetry, respec- tively, have also shown that humic materials can be characterized by fractal geometry. These references describe investigations into the effects of concentra- tion, pH, temperature, and ionic strength on the aggregation behavior of humic acids.

The purpose of this paper is to provide an overview of the combination of light and X-ray scattering methods with fractal geometry to probe the chemistry and geochemistry of humic materials.

2. Materials and methods

2.1. Materials

A peat and a soil classified as a Cryohemist (Moore, 1986) and a fine-silty, mixed Udic Haploboroll (Malo, 1994), respectively, were the primary source for the humic materials used in this study. Humic acid and fulvic acid were isolated from the peat and the soil using a traditional alkaline extraction procedure. Humin was isolated as the residue remaining after alkaline extraction of the humic and fulvic acids from the soil, and two others as well. Detailed descrip- tions of these other two soils are given elsewhere (Rice, 1987; Malekani, 1997). Solution samples were prepared by dissolving the humic acid or fulvic acid in 0.1 M NaOH or deionized, distilled water, respectively. When necessary, the pH was adjusted with NaOH or HC1, and the ionic strength was adjusted using NaC1. Prior to scattering measurements, solution samples were filtered through 0.22 txm membrane filters.

The organic components of the humin samples were removed in the following manner. The samples were first extracted with chloroform in a Soxhlet apparatus for 48 h (humin minus lipids), followed by disaggregation of the humin using the MIBK method (Rice and MacCarthy, 1990) and then oxidation of the remaining organic matter with bromine (humin minus organic matter). Malekani and Rice (1997) discuss these procedures in detail.

2.2. Scattering methods

Small-angle X-ray scattering measurements were performed on the 10-m SAXS camera at the Center for Small Angle Scattering at Oak Ridge National Laboratory, Oak Ridge, TN. The instrument has been described by Wignall et al. (1990). A X-ray wavelength of A = 1.54 /k was employed for all experi- ments. Additional methodological details can be found elsewhere (Rice and Lin, 1992, 1993, 1994).

164

Static light-scattering (SLS) and dynamic light scattering (DLS) measure- ments were performed on an ALV-5000/E light scattering apparatus fitted with an argon-ion laser operated at A = 514.5 nm. Further instrumental details have been described elsewhere (Ren et al., 1996). The correlation functions were evaluated using cumulant and Contin analysis, and the z-average particle radius was calculated as described by Martin and Leyvraz (1986) and Martin (1987).

Solid samples were placed into 1 mm thick holders fitted with Kapton windows for SAXS characterization. Solution samples were run in 1 mm flattened Lindeman glass capillaries using the airpath SAXS insert. Quartz cuvettes (8 mm i.d.) were used for SLS characterization of solution samples, DLS measurements were performed in 8 mm (i.d.) glass cuvettes.

2.3. Fractal analysis of scattering data

The scattering vector, q, is related to the angle of the scattered radiation, O, by Eq. (1):

4nTr ( 0 ) ~ s i n (1)

q = A -2

where n is the refractive index of the scattering medium. The size of the scatterer is described by a characteristic length, l (i.e., the particle diameter), and scattering depends on the product 'ql'. Most of the information from a scattering measurement can be obtained at scattering angles such that 0.1 ~< ql. The size of the scatterer is inversely related to q; larger particles will scatter at smaller angles and smaller values of q. Scattering which results from fractal substances conforms to a power law where the intensity of the scattered radiation as a function of q is proportional to q raised to some exponent (i.e., I(q) ct q-exp) (Schmidt, 1989). The magnitude of this exponent is directly related to the fractal dimension, D, of the scatterer. To determine if scattering by humic materials conforms to a power law, log-log plots of I(q) vs. q were constructed. If scattering from a sample obeys a power law, the plot will be a straight line. The slope of this plot is the power law exponent, and can be used to calculate D.

Two types of fractals~mass fractals and surface fractals~are relevant to these studies. Mass fractals are objects whose surface and mass distribution are characterized by fractal properties. The power-law behavior of a mass fractal is described by Eq. (2):

I ( q ) ~ q -Dm. (2)

For a mass fractal, the power-law exponent is the fractal dimension. A scatterer is a mass fractal when the exponent (and hence the mass fractal dimension, D m) is less than or equal to 3 (Schmidt, 1989). A surface fractal is

165

one in which only the surface of the scatterer exhibits fractal properties. The power-law scattering behavior of a surface fractal is given by Eq. (3)"

I(q) -- q-(6-D~). (3)

The power law exponent for a surface fractal falls within the range" 3 < 6 - D~ < 4. Once the exponent is known, the surface fractal dimension, D s, can be readily calculated.

3. Results and discussion

3.1. Small-angle X-ray scattering

Figs. 1-3 are log-log plots of the intensity of the scattered X-rays as a function of the scattering vector (q) vs. q for the solid- and solution-state peat humic acid and fulvic acid, and the solid-state humin samples used in this study. All plots are straight lines, indicating that SAXS scattering by humic materials

10000

1000

100

10 m

0.1

0.01 , , l , , , , | . | i ,

0." 1 .... ' . . . . . . . 0.01 1 10

q (nm-1)

[] Solution-state

�9 Solid-state

Fig. 1. Log-log plots of l(q) vs. q for the peat humic acid SAXS data. Solution data represent a smaller q-range because a shorter sample-to-detector distance was used during data acquisition. The intensity scale [l(q)] is in arbitrary units, and each plot has been vertically offset to clarify presentation.

166

1000000

C3" v

100000-

10000

I

1000-=

100-

10

4

I

\

. 1 "

o . . . . . . o . . . . . . . . . . . . . . 10

[] Solution-state

�9 Solid-state

q(nm -1)

Fig. 2. Log-log plots of l(q) vs. q for the peat fulvic acid SAXS data. Solution data represent a smaller q-range because a shorter sample-to-detector distance was used during data acquisition. The intensity scale [l(q)] is in arbitrary units, and each plot has been vertically offset to clarify presentation.

in either form can be described by a power law. The humin scattering curve (Fig. 3) shows a change in slope. This is attributed to the presence of mass and surface fracta! scatterers in this sample. This is discussed in more detail in Section 3.3.

Power-law scattering is observed over more than one order of magnitude of q. Avnir et al. (1998) have pointed that power-law behavior coveting a limited range of characterization lengthscales (in this case, q) does not truly conform to Mandelbrot's original definition (Mandelbrot, 1983) of the concept of a fractal. The combination of SAXS and SLS data described in Section 3.2 is a first attempt to try to determine if power-law behavior is actually observed over a wide scaling range. Even if humic materials are not truly fractal, the fractal

167

10000 -~

1000

100

"~ 10

0.1

0.01

Ds

_

0.01 o.1 1 10

q (nm -1)

Fig. 3. Log-log plots of I(q) vs. q for the peat humin SAXS data. Because of humin's insolubility, data are for the solid-state.

approach to the analysis of the scattering behavior of humic materials greatly simplifies what is, by almost all accounts, an extraordinarily complex structural geometry and it provides a means to correlate humic material structure to a variety of processes and properties such its aggregation. These are advantages to a fractal approach to data analysis acknowledged by Avnir et al. (1998).

The power-law exponent and the fractal dimension of each humic material are shown in Table 1. In the solid-state, humic materials can be classified as surface fractals. In contrast humic materials in solution are found to be mass fractals. The fractal dimension of each humic material in the solid- and solution-state indicates a convoluted, space-filling morphology for each material. Using dynamic light scattering and dynamic scaling theory, Ren et al. (1996) and Tombficz et al. (1997) have shown that the fractal dimension can, in fact, be calculated directly from the SAXS data without the necessity of correcting for polydispersity, validating these results. For systems with a greater degree of polydispersity, corrections to the measured value of D would have to be made as described by Schmidt (1989) and Martin and Leyvraz (1986). It is apparent from these results that the morphologies of humic materials are amenable to description by fractal geometry.

Scattering by any material can be placed into categories based on the behavior of the scattering intensity as a function of q (Fig. 4). Each of the q-regions of a scattering curve provides different types of information about a substance. For example, power-law behavior (and hence, fractal nature) is observed in the Porod region, X-ray diffraction is performed in the Bragg

168

Table 1

Power-law exponents and fractal dimensions (D) for the humic acids, fulvic acids and humins characterized in this study. In the solution-state, humic and fulvic acids are mass fractals, in the

solid-state they are surface fractals. Humin is, by definition, insoluble, so there are no solution values. The uncertainty associated with each D value is < 0.1

Sample Power-law exponent Fractal dimension

Solution Solid Solution Solid

Peat

Fulvic acid 2.2 3.3 2.2 2.7 Humic acid 2.5 3.8 2.5 2.2 Humin - 3.1 - 2.9

Soil

Fulvic acid 2.3 3.5 2.3 2.5 Humic acid 2.6 3.7 2.6 2.3

Humin - 3.5, 3.9 a - 2.5, 2.1 a

aSee Section 3.3.2 for a brief discussion of the two fractal dimensions.

region, and the size of a material can be calculated from data in the Guinier region. In order to extend the q-range, and the size of scatterer that can be characterized by fractal geometry, the solution samples were characterized by SLS.

, , . . . . . , ,

v

0 0

Limiting

~Gu in ie r

Bragg

q (nm-1)

Limiting: uniformity at large length scales

Guinier: information on particle size (correlation length scale)

Porod: scattering by fractal particles

Bragg: atomic level correlations (x-ray diffraction)

Fig. 4. A generalized scattering curve. Modified after Fleischmann (1989).

169

3.2. Static light scattering

Fig. 5 shows SLS log-log plot of I(q) vs. q for the peat and soil humic acids. Fulvic acid was found to be too weak a scatterer to characterize at this time. It is evident that the exponent (i.e., the slope) in this q-range is very different than that displayed by the same samples in the q-range accessible by SAXS (Fig. 1). This indicates that the scattering behavior of humic acid is no longer Porod-type (i.e., fractal) scattering, but has now entered the Guinier or limiting regions of the scattering curve (Fig. 4).

The combination of SAXS and SLS scattering data help to clearly delineate the large-particle limit to the characterization of humic materials in solution by scattering techniques and fractal geometry. Based on these measurements, it appears that humic acid in an alkaline aqueous solution exhibits a fractal nature over a q-range of ~ 0.03 nm-~ to ~ 3 nm-~. This corresponds to a characteri- zation length-scale of ~ 3 A to ~ 33 nm. It is not possible to identify the absolute lower limit of the characterization length scale where humic and fulvic acid are fractal (i.e., the beginning of the Bragg re~ion in Fig. 4). It should be noted that the lower limit in these experiments (3 A) is approaching molecular

I O Peat

I A Soil

le+2 _-

o 0 O le+1 _

~ o

le+0 ~

1 le-1 - ...i

- - - i ~ le-2 -

? le-3 -

1e-4. ! - i -1

le-5 ~

le-6 1

A

' ' 1 ' ' '

0.01 o.1

q (rim "1)

Fig. 5. Log- log plots of l (q ) vs. q for the soil and peat humic acid SLS data.

170

bond lengths, and probably represents a value very near the transition to Bragg scattering.

3.3. Applications in studies of soil organic matter

3.3.1. Particle-size measurement An interest in fractal morphology of humic materials leads to an interest in

the study of its dynamics in solution. In principle, information on the size of the fractal particle, its growth during aggregation and conformational changes in response to changing solution conditions can be obtained from the autocorrela- tion function of the temporal variation in light scattered from the particles (Lin et al., 1989). Such determinations are imprecise measurements that depend on many characteristics of the system under investigation, the particle-size distribu- tion. The molecular-weight distribution of humic materials, regardless of the method used for its measurement, typically shows a polydisperse size distribu- tion that displays an asymptotic, high-mass tail (Becket et al., 1989; Hernandez et al., 1989; Novotny et al., 1995). The shape of this distribution suggests power-law polydispersity that is consistent with a fractal nature for humic materials.

Power-law polydispersity makes the interpretation of DLS data on the basis of simple particle dynamics difficult. Martin (1987) has shown that in solutions of power-law polydisperse particles, relaxation rates scale with q in the DLS measurement by noninteger exponents, an observation that is inconsistent with monodisperse or Gaussian-polydisperse particle-size distributions. Martin and Ackerson (1985) and Martin and Leyvraz (1986) have shown that the dynamics of power-law polydisperse fractal aggregates can be scaled with q using a power law whose exponents may have noninteger values that are related to D and the polydispersity of the particle-size distribution. We have recently de- scribed the application of this 'dynamic scaling' theory to humic materials (Ren et al., 1996). From the application of this theory to scattering data it is possible to calculate the z-averaged particle radius, R:, and in fact the unusual angle dependence often displayed by DLS data from humic acid often make direct calculation of the particle radius essentially impossible without its application (Tomb~cz et al., 1997).

The D and the polydispersity exponent found by Ren et al. (1996) and Tombacz et al. (1997) are typical of values observed for fractal colloids produced by reaction-limited cluster-cluster aggregation. Reaction-limited clus- ter-cluster aggregation is a slow process in which clusters must overcome the repulsive forces (in this case, probably the negative charges associated with the humic colloids) before aggregation, and the formation of larger aggregates, can occur. In light of the polyelectrolyte nature demonstrated below, and elsewhere (Swift, 1989; Tombacz and Meleg, 1990), this is an interesting observation on which to base further studies of the aggregation behavior of this environmentally

171

Table 2 Effect of added electrolyte (NaC1) on the z-averaged particle radius (R=) of the peat humic acid

Electrolyte concentration (mM) R z (nm)

5 96 10 85 50 66

100 48

important colloidal material. Senesi et al. (1996b) also report that a reaction- limited particle-cluster aggregation model can be used to describe the aggrega- tion of fractal humic acid colloids. They also conclude that the applicability of this model may vary as function of pH.

Table 2 shows the effect of increasing added electrolyte concentration on R~. As charge screening effects increase (i.e., the added electrolyte concentration increases), electrostatic repulsion between the individual components of humic acid forming the aggregates decreases. This results in the aggregates shrinking and R z decreasing which is typical polyelectrolyte behavior.

3.3.2. Humic organic coatings on mineral surfaces The humin samples, and the components of humin, exhibit both mass and

surface fractal behavior (Fig. 3 and Table 3). There is precedent for such an observation in mineral-based soils. Avnir et al. (1985) found that fractal dimensions in soils can be different at different observation length scales. In this instance, mass fractal behavior is displayed over a smaller observation range, i.e., 0.4 to ~ 4 nm whereas surface fractal behavior is observed over a larger length scale of ~ 1 to 10 nm. The two different D values obtained for each of these materials could be attributed to the presence of two different classes of

Table 3 Fractal dimensions of humin, humin after lipid removal (Humin-L) , and humin after complete removal of organic matter (Humin-OM, i.e., the mineral surface). Values in brackets represent characterization lengthscale in nanometers. The uncertainty associated with each D value is < 0.1

Soil fraction Fractal dimensions

Om Soil Humin 2.9(1-10) 2.9(0.4-4) Soil Humin - L 2.7(1-10) 2.9(0.4-4) Soil Humin - OM 2.3(2-8) 3.0(0.4-3)

2.9(1-9) 3.0(0.3-4)

Peat Humin 2.2(2-8) 2.2(0.5-1) Peat Humin- L 2.0(2-8) 2.6(0.4-2) Peat Humin - OM 2.0(2-8) 2.6(0.4-1)

172

grain size and /o r mineral composition (Avnir et al., 1985) in the humin samples characterized here. Further fractionation of these materials into different s ize /or mineral groups constituting the two fractality regions would be appropriate in attempt to try to resolve these fractal subsets.

The fractal dimensions in Table 3 show that humin and its fractions produced by organic matter removal display surface fractal behavior over length scales ranging from ~ 1 to ~ 10 A, with the humin samples having the largest fractal dimension. The removal of organic matter resulted in a decrease in surface fractal dimensions. Malekani et al. (1996) have shown that clay minerals typically have fractal dimensions of D ~ 2 which are considerably less than the values for the intact humin samples, indicating that it is the organic matter coatings on mineral surfaces which are responsible for their surface roughness. Thus it seems reasonable to attribute the surface roughness of humin particles to organic matter coatings. Malekani and Rice (1997) have explored the effects of organic matter removal on the surface roughness of soils and humin using surface area measurements and fractal analysis of the soil and humin samples.

4. Summary

Humic materials can be characterized by fractal geometry. In addition, fractal geometry has been shown to be applicable to incorporating the polydispersity of humic materials into the characterization of its molecular size in the form of the z-averaged particle radius. The information from these experiments has indicated that a reaction-limited aggregation may be appropriate model to study aggrega- tion phenomena that these colloids undergo. Fractal geometry has also been shown to be a valuable tool in elucidating the surface morphology of the organic-coated mineral grains that comprise the humin fraction of soil organic matter, and how the nature of the surface changes as the organic matter is removed.

Acknowledgements

This work was supported by the National Science Foundation under grants OSR-9452894 and OSR-9108773, and the South Dakota Future Fund.

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