# Clay Minerals

- © The Mineralogical Society

## Abstract

The fractal dimension values of several kaolins with different structural order and properties have been calculated from N_{2}-adsorption isotherm data according to the Neimark method. All kaolins show a fractal regime in the same nitrogen relative pressure range, with fractal dimension values ranging between 2.38 and 2.57.

The correlation between fractal dimension and other kaolin characteristics (structural order of kaolinite, BET surface area, brightness and particle-size distribution) was determined. The correlation matrix shows that the fractal dimension (Ds) is highly correlated with the degree of structural order-disorder and is also moderately correlated with the particle-size distribution and brightness. No correlation was observed between BET and Ds, probably because the first is a measurement of the accessible surface while Ds represents the scaling properties of the area.

As Ds is a parameter easily calculated and related to the degree of surface heterogeneity, and well correlated with other kaolinite parameters, it can be used to estimate a set of kaolin technical properties for suitability of the kaolin in the paper industry.

Kaolin physical and physicochemical properties are dependent on features such as particle-size distribution, structural order and shape, kaolin delamination and fabric. These properties determine the potential applications as an industrial material (Lyons, 1966; Murray, 1976; Bundy, 1993). A correlation between some properties of kaolins (structural order, specific surface area, brightness and particle-size distribution) with their mineralogical and chemical compositions was found by Galán *et al.* (1998). On the other hand, a detailed study of kaolin morphology was conducted by Keller (1976a,b,c, 1977a,b,c, 1978), who related the kaolin texture to its genesis. In general, morphological studies of kaolinites can be used to determine the origin, and possible industrial uses (De Souza Santos, 1993).

Kaolins can have a complex surface with roughness and a high degree of heterogeneity, which make description of a kaolin surface difficult when based only on the surface area measurement. Fractal geometry considerations make it possible to characterize this heterogeneity or irregularity through the so called ‘fractal dimension’ (Ds), i.e. by a single value.

The main characteristic of fractal objects is that they are invariant with respect to the scale used to examine them, what is known as self similarity. In brief, a particular value of Ds means that any typical part of the system unfolds into m·Ds similar pieces upon an m-fold magnification. Fractal dimension can be seen as the extension of the Euclidean dimension (Ds = 0: point, Ds = 1: curve; Ds = 2: surface, Ds = 3: volume) with possible fractional values. A rock such as kaolin should have a fractal dimension between 2 (the Euclidean dimension of a flat or smooth surface) and 3 (corresponding to the embedding space). A higher Ds value corresponds to a rougher surface.

An ideal fractal should have details or irregularities upon an infinitely small measuring scale. On the surface of a rock, such kaolins could have irregularities of a limited scale range. The accessible measuring scale depends on the measuring technique, so the fractal behaviour would be determined for a definite scale range.

Van Damme (1992), using the concept of scaling and fractal geometry considerations, has described different smectite clay properties (structure, deformation and rupture). The evolution of those properties as the observation scale is changed can reveal features more general than when detected at a single scale. On the other hand, Celis *et al.* (1996) studied the structure of soil colloidal aggregates using fractal geometry, deducing that a morphological change occurs in clays when associated with Fe species.

The aims of this work are to determine the fractal dimensions of different kaolins, to relate them to several properties of industrial interest (using multivariate analysis), and to evaluate their possible use, and to make a first estimate of a set of technical kaolin properties important to the paper industry.

## MATERIALS AND METHODS

### Materials

Eight kaolins of variable structural order and genesis were studied (Table 1⇓). Most were industrial (washed) kaolin samples used in ceramics, as filler or coating in paper, or in plastics and paints.

### Methods

Mineralogical analyses were performed using a Philips PW1130/90 X-ray diffractometer using Ni-filtered Cu-*K*α radiation and automatic divergence slit. Bulk quantitative analyses were carried out using the Schultz (1964) method corrected for an automatic slit. Clay minerals were studied in orientated aggregates, using standard methods involving drying at room temperature, solvation with ethylene glycol and heating at 350 and 550°C for 2 h. Phases were quantified using the method of Martin Pozas (1975), also corrected for automatic slit, and from data reported by Galán and Martín Vivaldi (1973).

Kaolinite structural order was evaluated using the Hinckley (1963), Stoch (1974), and Aparicio *et al.* (1999, 2001) indices, determined from the 02*l* and 11*l* reflections of X-ray diffraction (XRD) patterns (Fig. 1⇓). A side-loading sample holder was utilized to avoid mineral orientation. According to Aparicio & Galán (1999) the Hinckley index is influenced by quartz, feldspar, Fe hydroxide gels, illite, smectite and halloysite. On the other hand, the Stoch index can be used in the presence of quartz, feldspar and amorphous silica and Fe but not in the presence of other phyllosilicates. Finally the Aparicio-Galán-Ferrell index is less influenced by associated minerals and amorphous phases than the Hinckley and Stoch indices (Aparicio *et al.*, 1999, 2001).

Kaolin morphology was determined by scanning electron microscopy, using a Jeol, mod. JSM-5400, electron microscope.

The following technical properties were also determined: particle-size distribution by an X-ray absorption instrument (Sedigraph 5100), brightness with Photovolt equipment, and nitrogen-BET surface area, using a Micromeritics Gemini 2360 porosimeter.

Fractal analysis from N_{2}-adsorption data was carried out using the so called ‘thermodynamic method’, proposed by Neimark *et al.* (1993). The main equation of the method is:

(1)

where *S*(*P/P*_{o}) is the area for a given value of relative pressure (*P/P*_{o}), *P*_{o} the saturation pressure, *a*_{c} the mean curvature radius at *P/P*_{o}, and Ds the fractal dimension.

*S*(*P/P*_{o}) can be calculated using the Kiselev equation (Neimark *et al.*, 1993):

(2)

where *N* is the amount of adsorbate, *N*_{max} the adsorbate as *P/P*_{o} tends towards 1, σ the surface tension of liquid adsorbate, R the gas constant and *T* the temperature (in Kelvin).

The mean values of curvature radius are calculated using the Kelvin equation:

(3)

where *V*_{m} is the molecular volume of the adsorbate.

The graph of log *S*(*P/P*_{o}) *vs.* log *a*_{c}(*P/P*_{o}) is a straight line in the fractal region with a 2-Ds slope value.

The results obtained were then exploited using the multivariate analysis method (principal components analysis and principal factor analysis).

## RESULTS AND DISCUSSION

### Kaolin characterization

Kaolinite accounts for 80–97 wt.% of the samples. It is associated with halloysite, in trace amounts (<2 wt.%) in many samples except for the Mevaiela kaolin which contains 12 wt.%. Quartz and illite are minor components. Feldspars, silica and Fe hydroxide gels are rare (Table 2⇓).

The kaolinite structural order ranges from poorly ordered (La Guardia) to well ordered (Montecastelo, Poveda, Mevaiela). The BET surface areas vary markedly: 25.78 m^{2}/g for St. Austell and 3.71 m^{2}/g for Bustelo kaolins. Brightness (ISO) also ranges widely between 96 for Mevaiela and 61 for La Guardia kaolins (Table 3⇓).

The <2 μm fraction accounts for >80% of the mass in half of the samples studied and exceeds 50 wt.% for all the kaolins. The <0.5 μm fraction accounts for a widely variable proportion, from 26 wt.% in La Guardia to 63–64 wt.% in Mevaiela and St. Austell kaolins (Table 3⇑).

### Fractal analysis

The adsorption branch of all the kaolins studied corresponds to a Gibbs II adsorption isotherm (Fig. 2⇓). A curvature radius interval in which fractal regime behaviour is observed, ranges between 0.3 and 220 Å (Fig. 3⇓). All the samples show approximately the same range of *a*_{c} where fractal behaviour is observed. Table 4⇓ summarizes the results of the Ds calculation.

Fractal dimension is directly correlated with the kaolin morphology (Fig. 4⇓). The highest Ds values (≥2.55) are those of Montecastelo and Mevaiela kaolins, which show books, straight or curved (vermicular), built of crystal plates or flakes. A second group including the Bustelo, Alvaraes and Poveda kaolins (Ds = 2.47), displays more broken books and crystal associations (face to face, or edge to face). In the third group, the Georgia and St. Austell kaolins show a decrease in the crystal size and an increase of face-to-face association, resulting in a reduction of the fractal dimension. This reduction is greater in La Guardia kaolin, with isolated books and irregular crystals of different sizes.

### Statistical analysis

Correlation coefficients are given in Table 5⇓. Kaolinite structural order indices of Aparicio-Galán-Ferrell, Hinckley and Stoch are correlated between them, brightness is moderately correlated with these indices and fractal dimension is well correlated with the structural order, especially with the Aparicio-Galán-Ferrell index, which is less influenced by the presence of other mineralogical components (Aparicio *et al.*, 1999, 2000).

The factor analysis of all the variables provides two factors that account for 82% of the overall variance of the system (Table 6⇓). The first factor includes fractal dimension, kaolinite structural order measurements, brightness and percentage of <10 μm fraction. The second factor relates to the specific surface area (BET) and <4 μm fractions (Fig. 5⇓).

The principal components analysis (Fig. 6⇓) shows two groups of kaolins. The first group includes the Montecastelo and Mevaiela kaolins, both with high fractal dimension values (Ds ≥2.55). The second group comprises the Bustelo, Alvaraes and Poveda kaolins with Ds values ranging between 2.48 and 2.47. Finally Georgia kaolin (Ds = 2.45), St. Austell kaolin (Ds = 2.43) and La Guardia kaolin (Ds = 2.38) are independent of these groups. These results are in agreement with the morphology classification (Fig. 4⇑).

## CONCLUSIONS

Fractal dimension is well correlated with brightness, morphology and the measurement of structural order in kaolinite. It constitutes a surface descriptor which is easily calculated, and which can be used to estimate a set of technical properties for kaolins used in paper industry.

Fractal dimension values can suggest the degree of delamination required in the kaolin processing, high values of Ds being related to the abundance of kaolinite books.

## Acknowledgments

The authors are grateful to A. Plançon and H.H. Murray for carefully reviewing this paper. This work was partially supported by the Junta de Andalucía through Research Group RNM 135.

- Received July 21, 2003.
- Revision received October 27, 2003.