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Clay Minerals; March 2004; v. 39; no. 1; p. 75-84; DOI: 10.1180/0009855043910121
© 2004 Mineralogical Society of Great Britain and Ireland
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Research Paper

Kaolin fractal dimension. Comparison with other properties

P. APARICIO1,*, J. L. PÉREZ-BERNAL2, E. GALÁN1 and M. A. BELLO2

1 Departamento de Cristalografía, Mineralogía y Química Agrícola, Universidad de Sevilla, Apdo. 553, 41071 Sevilla, 2 Departamento de Química Analítica, Universidad de Sevilla, Apdo. 553, 41071 Sevilla, Spain

* E-mail: paparicio{at}us.es

(Received 21 July 2003; revised 27 October 2003)


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGMENTS
 REFERENCES
 
The fractal dimension values of several kaolins with different structural order and properties have been calculated from N2-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.

KEYWORDS: kaolin fractal dimension, kaolin technological properties, multivariate analysis

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
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGMENTS
 REFERENCES
 
Materials
Eight kaolins of variable structural order and genesis were studied (Table 1Go). Most were industrial (washed) kaolin samples used in ceramics, as filler or coating in paper, or in plastics and paints.


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  		TABLE 1. Description of kaolins.
 
Methods
Mineralogical analyses were performed using a Philips PW1130/90 X-ray diffractometer using Ni-filtered Cu-K{alpha} 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 02l and 11l reflections of X-ray diffraction (XRD) patterns (Fig. 1Go). 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).



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  		FIG. 1. Methods for determining (a) Hinckley Index (HI), (b) Stoch Index (IK), and (c) Aparicio-Galán-Ferrell Index (AGFI) by XRD.

 
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 N2-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/Po) is the area for a given value of relative pressure (P/Po), Po the saturation pressure, ac the mean curvature radius at P/Po, and Ds the fractal dimension.

S(P/Po) can be calculated using the Kiselev equation (Neimark et al., 1993):


(2)

where N is the amount of adsorbate, Nmax the adsorbate as P/Po tends towards 1, {sigma} 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 Vm is the molecular volume of the adsorbate.

The graph of log S(P/Po) vs. log ac(P/Po) 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
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 ACKNOWLEDGMENTS
 REFERENCES
 
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 2Go).


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  		TABLE 2. Mineralogical composition (wt.%) of kaolins.
 
The kaolinite structural order ranges from poorly ordered (La Guardia) to well ordered (Montecastelo, Poveda, Mevaiela). The BET surface areas vary markedly: 25.78 m2/g for St. Austell and 3.71 m2/g for Bustelo kaolins. Brightness (ISO) also ranges widely between 96 for Mevaiela and 61 for La Guardia kaolins (Table 3Go).


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  		TABLE 3. Kaolinite structural order, specific surface area (m2/g) (BET) and particle-size distribution (wt.%) for all the kaolins studied.
 
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 3Go).

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



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  		FIG. 2. N2-adsorption isotherms.

 


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  		FIG. 3. Logarithmic area at P/Po (S(P/Po)) vs. logarithmic curvature radius plot for the studied samples (y axis arbitrarily scaled to avoid superpositions).

 

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  		TABLE 4. Fractal dimension results.
 
Fractal dimension is directly correlated with the kaolin morphology (Fig. 4Go). 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.



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  		FIG. 4. SEM images of the kaolins studied.

 
Statistical analysis
Correlation coefficients are given in Table 5Go. 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).


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  		TABLE 5. Correlation matrix between fractal dimension kaolinite structural order, specific surface area and particle-size distribution for all the kaolins studied.
 
The factor analysis of all the variables provides two factors that account for 82% of the overall variance of the system (Table 6Go). 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. 5Go).


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  		TABLE 6. Factor loadings and varimax normalized for kaolins. Extraction: principal factors (comm = multiple R-square).
 


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  		FIG. 5. Plot of factor loadings F2 vs. F1.

 
The principal components analysis (Fig. 6Go) 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. 4Go).



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  		FIG. 6. Principal components analysis. Projection of the cases on the factor-plane (1x2). Cases with sum of cosine square ≥0.00.

 

   CONCLUSIONS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
ACKNOWLEDGMENTS
 REFERENCES
 
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
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGMENTS
REFERENCES
 
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.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGMENTS
 REFERENCES
 

Aparicio P. & Galán E. (1999) Mineralogical interference on kaolinite crystallinity index measurements. Clays and Clay Minerals, 47, 12–27.[Abstract][CrossRef][ISI][GeoRef]

Aparicio P., Ferrell E. & Galán E. (1999) A new kaolinite crystallinity index from mathematical modelling of XRD data. Abstracts volume of the 9th EUROCLAY conference, p. 57.

Aparicio P., Ferrell E. & Galán E. (2001) Aplicación de la modelización matemática a los diagramas de DRX de la caolinita para mejorar el cálculo de ‘indices de cristalinidad’. Pp. 21–29 in: Integración de Cienca-Tecnología de las arcillas en el Contexto Tecnológico-Social del Nuevo Milenio. (J. Pascual Cosp, J. Zapatero Arenzana, A.J. Ramírez del Valle and M.V. Moya García, editors). Sociedad Española de Arcillas, Málaga, Spain.

Bristow C.M. (1993) The genesis of the China Clays of South-west England. A Multistage story. Pp. 171–203 in: Kaolin, Genesis and Utilization (H.H. Murray, W. Bundy & C. Harvey, editors). Special Publication, 1. The Clay Minerals Society, Bloomington, Indiana, USA.

Bundy W.M. (1993) The diverse industrial applications of kaolins. Pp. 43–73 in: Kaolin, Genesis and Utilizations. (H.H. Murray, W. Bundy & C. Harvey, editors). Special Publication, 1. The Clay Minerals Society, Bloomington, Indiana.

Celis R., Cornejo J. & Hermosín M.C. (1996) Surface fractal dimensions of synthetic clay-hydrous iron oxide associations from nitrogen adsorption isotherms and mercury porosimetry. Clay Minerals, 31, 355–363.[Abstract][CrossRef][ISI][GeoRef]

De Souza Santos P. (1993) The use of clay particle morphology studies to characterize industrial clay deposits: examples from Brazil. Clay Minerals, 28, 539–553.[Abstract][ISI][GeoRef]

Galán E. & Martín Pozas J.M. (1971) Mineralogía de los caolines de La Guardia y El Rosal (Pontevedra, España). Estudios Geológicos, XXVII, 75–80.

Galán E. & Martín Vivaldi J.L. (1973) Caolines españoles: Geología, Mineralogía y Génesis. Parte I. Boletín Sociedad Española de Cerámica y Vidrio, 12, 79–98.

Galán E., Mattias P.P. & Galvan J. (1977) Correlation between crystallinity size, genesis and age of some Spanish kaolinites. K-8, 8 pp. in: Proceedings of the 8th International Kaolin Symposium and Meeting on Alunite, Madrid-Rome (E. Galán, editor). Ministerio de Industria y Energía, Madrid, Spain.

Galán E., Aparicio P., González I. & Miras A. (1998) Contribution of multivariate analysis to the correlations of some properties of kaolin with its mineralogical and chemical composition. Clay Minerals, 33, 65–75.[Abstract][GeoRef]

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Gomes C., Velho J.A. & Guimaraes F. (1994) Kaolin deposits of Mevaiela (Angola) alteration product of anorthosite: assessment of kaolin potentialities for application paper. Applied Clay Science, 9, 97–106.[GeoRef]

Hinckley D. (1963) Variability in ‘crystallinity’ values among the kaolin deposits of the Coastal Plain of Georgia and South Carolina. Pp. 229–235 in: 11th National Conference on Clays and Clay Minerals. Pergamon Press, New York.

Keller W.D. (1976a,b,c) Scan electron micrographs of kaolin collected from diverse environments of origin –I, II, III. Clays and Clay Minerals, 24, 107–113, 113–117, 262–264.[Abstract][CrossRef][ISI][GeoRef]

Keller W.D. (1977) Scan electron micrograph of kaolins collected from diverse environments of origin – IV. Georgia kaolins and kaolinizing source rocks. Clays and Clay Minerals, 25, 311–346.[Abstract][CrossRef][ISI][GeoRef]

Keller W.D. (1978) Classification of kaolins exemplified by their textures in scan electron micrographs Clays and Clay Minerals, 26, 1–20.[Abstract][CrossRef][ISI][GeoRef]

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Vam Damme H. (1992) Stacking, deformation and rupture in smectite clays. Pp. 45–88 in: Conferencias de la XI Reunión Científica de la Sociedad Española de Arcillas (E. Galán & M. Ortega, editors), Madrid.

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