Kaolin fractal dimension. Comparison with other properties

Clay Minerals (2004) 39, 75–84
Kaolin fractal dimension. Comparison with
other properties
P . A P A R I C I O 1 , * , J . L . P É R E Z - B E R N A L 2 , E . G A L Á N 1
1
AND
M. A. BELLO2
Departamento de Cristalografı́a, Mineralogı́a y Quı́mica Agrı́cola, Universidad de Sevilla, Apdo. 553, 41071 Sevilla,
2
Departamento de Quı́mica Analı́tica, Universidad de Sevilla, Apdo. 553, 41071 Sevilla, Spain
(Received 21 July 2003; revised 27 October 2003)
AB ST R ACT : 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,
1977, 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).
* E-mail: [email protected]
DOI: 10.1180/0009855043910121
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
# 2004 The Mineralogical Society
76
P. Aparicio et al.
(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 Nifiltered Cu-Ka 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 550ºC
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 Martı́n
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. 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-GalánFerrell 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
TABLE 1. Description of kaolins.
Location
Montecastelo (Spain)
Alvaraes (Portugal)
Bustelo (Portugal)
St. Austell (UK)
Genesis
Warren (Georgia, USA)
Granite weathering
Granite weathering
Gneiss weathering
Hydrothermal alteration
of granite
Hydrothermal alteration
of anorthosite
Sedimentary (Tertiary)
Poveda de la Sierra (Spain)
La Guardia (Spain)
Sedimentary (Cretaceous)
Sedimentary (Tertiary)
Mevaiela (Angola)
Structural order
References
High
Medium
Medium
High
Galán (pers. comm.)
Gomes et al. (1990)
Gomes et al. (1990)
Bristow (1993)
High
Gomes et al. (1994)
Medium–low
Patterson & Murray (1975)
Van Olphen & Fripiat (1979)
Galán et al. (1977)
Galán & Martı́n Pozas (1971)
Medium–high
Low
77
Kaolin fractal dimension
a
8 9
8 92Ds
P
P
: >
; / ac >
: >
;
S>
Po
Po
A+B
At
A+B
HI =
4190
3690
ð1Þ
110
3190
111
020
2690
A
2190
1690
B
At
1190
690
1 9 .1 4 5
2 0 .1 4 5
2 1 .1 4 5
2 2 .1 4 5
2 3 .1 4 5
2 4 .1 4 5
2 5 .1 4 5
2 6 .1 4 5
°2θ
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):
Z
8 9
8 9
P
RT N8max 9 > P >
: >
;¼
ln: ;dN
ð2Þ
S>
Po
s V :PP ;
Po
o
b
C
IK =
D
4190
3690
where N is the amount of adsorbate, Nmax the
adsorbate as P/Po tends towards 1, s 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:
8 9
P
2sVm
8 9
: >
;¼
ac >
ð3Þ
Po
RT ln:Po ;
110
3190
111
020
2690
2190
1690
C
1190
D
690
P
1 9 .1 4 5
2 0 .1 4 5
2 1 .1 4 5
2 2 .1 4 5
2 3 .1 4 5
2 4 .1 4 5
2 5 .1 4 5
2 6 .1 4 5
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).
°2θ
c
4190
3690
110
3190
2690
AGFI =
111
IA+I B
2IC
020
2190
1690
C A
1190
B
RESULTS AND DISCUSSION
690
191
. 45
201
. 45
2 1 .1 4 5
221
. 45
231
. 45
2 4 .1 4 5
251
. 45
261
. 45
Kaolin characterization
°2θ
FIG. 1. Methods for determining (a) Hinckley Index
(HI), (b) Stoch Index (IK), and (c) Aparicio-GalánFerrell Index (AGFI) by XRD.
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:
Kaolinite accounts for 8097 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 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 3).
The <2 mm fraction accounts for >80% of the
mass in half of the samples studied and exceeds
50 wt.% for all the kaolins. The <0.5 mm fraction
78
P. Aparicio et al.
TABLE 2. Mineralogical composition (wt.%) of kaolins.
Kaolinite
Halloysite
Quartz
Feldspar
Illite
Amorphous
silica
Amorphous
Fe oxide
97
85
80
92
85
97
90
83
–
tr
tr
tr
12
–
tr
tr
<5
8
15
<5
<5
tr
8
5
tr
<5
–
–
–
–
–
tr
tr
<5
5
tr
tr
–
<5
10
tr
–
–
<5
tr
–
–
tr
–
tr
–
–
–
<5
–
–
Montecastelo
Alvaraes
Bustelo
St. Austell
Mevaiela
Warren
Poveda
La Guardia
tr: present in quantities of <2 wt.%
TABLE 3. Kaolinite structural order, specific surface area (m2/g) (BET) and particle-size distribution (wt.%) for all
the kaolins studied.
Montecastelo
Alvaraes
Bustelo
St. Austell
Mevaiela
Warren
Poveda
La Guardia
HI
IK
AGFI
BET
1.10
0.71
0.67
0.88
0.99
0.59
0.94
0.30
0.67
0.84
0.90
0.70
0.59
0.97
0.82
1.18
1.36
0.90
0.68
0.87
1.34
0.77
1.18
0.52
11.26
10.63
3.71
25.78
17.34
13.68
12.83
8.53
Brightness (ISO)
86
80
84
87
96
88
89
61
<10 mm <4 mm
100
93
100
90
96
100
100
82
91
75
65
96
91
95
76
67
<2 mm <1 mm <0.5 mm
80
65
58
93
82
83
57
63
68
53
57
81
72
68
41
52
52
46
57
64
63
51
26
36
HI: Hinckley index, IK: Stoch index; AGFI: Aparicio-Galán-Ferrell index
accounts for a widely variable proportion, from
26 wt.% in La Guardia to 6364 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 ac 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
(52.55) 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
TABLE 4. Fractal dimension results.
Ds
Montecastelo
Alvaraes
Bustelo
St. Austell
Mevaiela
Warren
Poveda
La Guardia
2.57
2.47
2.48
2.43
2.55
2.45
2.47
2.38
79
Kaolin fractal dimension
RelVol
RelVol
Montecastelo
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
Mevaiela
0
0
0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
RelVol
0.6
0.8
1
0.6
0.8
1
0.8
1
P/P 0
P/P 0
RelVol
Bustelo
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
Alvaraes
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
P/P 0
RelVol
P/P 0
RelVol
Poveda
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
Warren
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
P/P 0
RelVol
0.6
P/P 0
LaGuardia
RelVol
St. Austell
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
P/P 0
0.4
0.6
P/P 0
FIG. 2. N2-adsorption isotherms.
0.8
1
80
P. Aparicio et al.
La Guardia
log (S(P/P0))
St. Austell
Warren
Poveda
Alvaraes
Bustelo
Mevaiela
Montecastelo
-1
-0.5
0
0.5
1
1.5
2
log (ac)
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).
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 AparicioGalán-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 mm fraction. The second factor relates to the
specific surface area (BET) and <4 mm 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
TABLE 5. Correlation matrix between fractal dimension kaolinite structural order, specific surface area and
particle-size distribution for all the kaolins studied.
HI
HI
IK
AGFI
Ds
BET
Brightness
<10 mm
<4 mm
<2 mm
<1 mm
<0.5 mm
1.00
0.94
0.92
0.82
0.41
0.80
0.59
0.54
0.36
0.31
0.29
IK
AGFI
1.00
0.85
0.79
0.53
0.82
0.46
0.60
0.50
0.51
0.54
1.00
0.86
0.31
0.71
0.52
0.50
0.28
0.18
0.12
Ds
1.00
0.01
0.69
0.67
0.36
0.20
0.25
0.36
BET
1.00
0.43
0.17
0.78
0.80
0.67
0.41
Brightness <10 mm <4 mm <2 mm <1 mm <0.5 mm
1.00
0.76
0.62
0.41
0.40
0.45
1.00
0.25
0.02
0.01
0.11
1.00
0.93
0.79
0.52
1.00
0.94
0.70
1.00
0.89
1.00
81
Kaolin fractal dimension
Montecastelo
Mevaiela
5 µm
5 µm
Bustelo
Alvaraes
5 µm
Poveda
5 µm
Warren
200 nm
2 µm
St. Austell
La Guardia
200 nm
FIG. 4. SEM images of the kaolins studied.
5 µm
82
P. Aparicio et al.
TABLE 6. Factor loadings and varimax normalized for
kaolins. Extraction: principal factors (comm = multiple
R-square).
HI
IK
AGFI
Ds
BET
Brightness
<10 mm
<4 mm
<2 mm
<1 mm
<0.5 mm
% Total variance
Cumul. %
Factor 1
Factor 2
0.908247
0.817622
0.901146
0.915075
0.080619
0.829064
0.812816
0.357828
0.105679
0.090414
0.174143
57.12635
6.283898
0.284007
0.481706
0.165673
0.089320
0.847621
0.367562
0.147732
0.843161
0.972778
0.951753
0.758492
25.02769
9.036945
fractal dimension values (Ds 52.55). 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 Andalucı́a
through Research Group RNM 135.
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1.2
1.0
2 µm
<1 µm
0.8
4 µm
BET
<0.5 µm
0.6
Brightness
HI
AGFI
Ds
Factor 2
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0.6
0.8
1.0
83
Kaolin fractal dimension
4
3
Poveda
2
Bustelo
Montecastelo
Factor 2: 25.03%
1
Alvaraes
Mevaiela
0
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-1
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