Directory UMM :Data Elmu:jurnal:S:Soil & Tillage Research:Vol55.Issue1-2.May2000:
Soil & Tillage Research 55 (2000) 63±70
Soil pore surface properties in managed grasslands
Meczislaw Hajnosa, Ludmila Korsunskaiab, Yakov Pachepskyc,*
a
Institute of Agrophysics, Lublin 20536, Poland
Institute of Physical, Chemical, and Biological Problems in Soil Science, Pushchino 142292, Russia
c
USDA:ARS:BA:NRI:RSML, Hydrology Laboratory, Bldg. 007, Rm. 104, BARC-WEST, Beltsville, MD 20705, USA
b
Received 3 August 1999; received in revised form 7 January 2000; accepted 28 January 2000
Abstract
Properties of pore surfaces control adsorption and transport of water and chemicals in soils. Parameters are needed to
recognize and monitor changes in pore surfaces caused by differences in soil management. Data on gas adsorption in soils can
be compressed into parameters characterizing (a) area available to a particular adsorbate, and (b) surface roughness or
irregularity. Our objectives were to see (a) whether models of adsorption on fractal surfaces are applicable to water vapor
adsorption in soils in the capillary condensation range, and (b) whether differences in long-term management of grasslands are
re¯ected by soil pore surface properties. Water vapor adsorption was measured in Gray Forest soil (Udic Argiboroll, Orthic
Greyezem, clay loam) samples taken at four plots, where a long-term experiment on grassing arable land had been carried out
for 12 years. The experiment had 22 design. Factors were `harvest±no-harvest' and `fertilizer±no-fertilizer'. The hay was cut
after over-seeding in harvested treatments every year. Ammonium nitrate, superphosphate, and potassium chloride were
applied annually after the snowmelt to get the total amount of nutrients of 60 kg haÿ1. The monolayer adsorption capacity was
estimated from the Brunauer±Emmett±Teller model. A fractal Frenkel±Halsey±Hill model of adsorption on a fractal surface,
and a thermodynamic adsorption model were applied in the range of relative pressures from 0.7 to 0.98 and provided good ®t
of data. Values of the surface fractal dimension Ds were in the range from 2.75 to 2.85. Removal of carbohydrates resulted in
increase of Ds. Differences in management practices did not affect values of Ds in the scale range studied, whereas the
monolayer capacity was affected. Both fertilization and harvesting resulted in an increase of the monolayer capacity, with the
largest increase observed in soil that was fertilized but not harvested. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Water vapor; Adsorption; Fractal surface; Grassland; Gray Forest soil
1. Introduction
Properties of pore surfaces control adsorption and
transport of water and chemicals in soils. Parameters
are needed to recognize and monitor changes in pore
*
Corresponding author. Tel.: 1-301-504-7468;
fax: 1-301-504-5823.
E-mail address: ypachepsky@asrr.arsusda.gov (Y. Pachepsky)
surfaces caused by differences in soil management.
Once established, such diagnostic parameters can be
used to quantify effects of management on soil functioning by means of land quality or soil quality indices
(Singer and Ewing, 2000).
Data on gas adsorption in soils can be compressed
into parameters characterizing (a) area available to a
particular adsorbate, and (b) surface roughness or
irregularity. Speci®c surface area is known to char-
0167-1987/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 1 9 8 7 ( 0 0 ) 0 0 0 9 9 - 4
64
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
acterize the ability of soil to retain and transport
nutrients and water. Speci®c surface area of soils
correlates with the sorptive capacity and ion exchange
capacity (Jurinak and Volman, 1957; Ben-Dor and
Banin, 1995), retention and release of chemicals
(Rhue et al., 1988; Valverde-Garcia et al., 1988;
Ong and Lion, 1991), swelling (Sapozhnikov,
1985), water retention (Kapilevich et al., 1987),
dry-aggregate stability (Skidmore and Layton,
1992). Tester (1990) observed an increase in speci®c
surface area parallel to the increase in organic matter
content after compost application.
Pore surfaces in soils are irregular. Fractal models
were found useful in the description of natural and
man-made irregular surfaces. Fractal surfaces exhibit
dependencies of their area S on the resolution, or scale,
R at which the area is measured (Russ, 1994). These
dependencies have a power law form
S / R2ÿDs
(1)
where Ds is the surface fractal dimension. The surface
fractal dimension characterizes the degree of roughness or disorder of the surface. Numerical values of
surface fractal dimensions vary from 2.0 (perfectly
smooth) to a maximum value of 3.0. The larger the
value of Ds, the greater is the irregularity of the
surface.
Theoretical studies of adsorption on fractal surfaces
predicted the effect of the surface fractal dimension on
diffusion-limited adsorption kinetics (Seri-Levy and
Avnir, 1993; Giona and Giustiniani, 1996). Douglas
(1989) showed that adsorption of polymers on rough
surfaces should be affected by the surface fractal
dimension. The increase in fractal dimensions should
cause tighter binding of polymer with a surface. Surface fractal dimensions were studied with relation to
technological parameters in production of ionexchange ®bers (Kutarov and Kats, 1992), carbon
blacks (Darmstadt et al., 1995), cements (Niklasson,
1993), food products (Aguerre et al., 1996), and wood
(Hatzikiriakos and Avramidis, 1994).
Fractal scaling was demonstrated for soil pore
surfaces. Sokoøowska (1989) used a fractal model to
analyze the soil particle surface heterogeneity with
data on water vapor adsorption experiments. Toledo
et al. (1990) showed that fractal dimensions of soil
particle surfaces could be estimated from water retention data at low moisture contents. Bartoli et al. (1991)
introduced the use of mercury porosimetry to estimate
surface fractal dimensions in soils. Soil constituents,
such as humus materials and clay minerals, were
found to be surface fractals (Rice et al., 1999; Sokoøowska and Sokoøowski, 1999).
The management-related change in soil quality is a
current topic of interest. Efforts were made to de®ne
soil quality and suggest a minimum set of analyses to
aid in evaluating soil quality as affected by long-term
management practices (Doran and Parkin, 1994).
Long-term and short-term management effects on soil
pore surface fractal dimensions were observed using
soil thin sections (Pachepsky et al., 1996b; GimeÂnez
et al., 1997; Oleschko et al., 1998). Fractal dimension
analysis provided additional information by describing the changes in pore shapes.
Adsorption isotherms of gases present an attractive
source of data on surface roughness. Several theories
of adsorption on a fractal surface were developed
during last 15 years. Two types of adsorption data
analysis have been used most often. One of them uses
several different adsorbates and employs the mean
radius of each adsorbate's molecules as the resolution,
or scale, R in Eq. (1). The logarithmic transform of this
equation and the subsequent regression `radius vs.
speci®c surface' in log±log scale provides the value
of Ds as the slope subtracted from 2 (Farin and Avnir,
1989). With this approach, data on adsorption at low
relative pressures are used at which the monolayer
coverage is known to occur. Another type of the
adsorption data analysis employs the data at high
relative pressures, where capillary condensation
occurs so that micropores become ®lled with adsorbate. Then the micropore radius becomes a measure of
scale R in Eq. (1). Avnir and Jaroniec (1989) obtained
a relationship between the adsorbed amount and vapor
pressure by assuming the applicability of the Dubinin±
Radushkievich equation to describe the adsorption in
micropores, and assuming fractal pore volume distribution on the surface. The same equation was obtained
by Neimark (1990) and Yin (1991) from the assumption that the capillary condensation was present. A
different model was proposed by Neimark (1990). He
did not assume validity of any adsorption isotherm
equation, but used directly the scaling relationship (1)
with the surface curvature radius as a scale measure.
Although both models mentioned above were applied
in experimental studies, no unambiguous way was
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
found to see which one is superior (Jaroniec et al.,
1997).
Our objectives were to see (a) whether models of
adsorption on fractal surfaces are applicable to water
vapor adsorption in soils in the capillary condensation
range, and (b) whether differences in long-term management of grasslands are re¯ected by soil pore surface properties.
2. Materials and methods
2.1. Soil sampling and analyses
Gray Forest soil (Udic Argiboroll) was sampled in
April 1994 near Pushchino, Moscow Region, Russia.
Samples were taken at a site, where an experiment on
grassing arable land had been carried out since 1982
(Yermolayev and Shirshova, 1994). Grass mixture
consisted of Festuca Pratensis, Huds., Phleum Pratense L., and Trifolium Pratense L. The experiment
had 22 design. Factors were `harvest±no-harvest'
and `fertilizer±no-fertilizer'. The hay was cut after
over-seeding in harvested treatments every year.
Ammonium nitrate, superphosphate, and potassium
chloride were applied annually after the snowmelt to
get the total amount of nutrients of 60 kg haÿ1. Area of
each plot was 0.5 ha. The soil was in no-till, since
1982. The soil had the pH 6.3, a loamy texture with
45% particles less than 0.01 mm and 20% particles
less than 0.001 mm, and contained illite, kaolinite, and
smectites in its clay fraction. Sampling depth was 10±
30 cm. Five samples were taken from each plot, and
the mixed sample was used in adsorption measurements for each of the four combinations of factors.
Soil was air-dried and sieved, and aggregates less
than 2 mm were used. Each sample was split, and
carbohydrates were removed in one of the two subsamples. The oxidation of carbohydrates has been
performed with 0.02 M NaIO4 solution (Cheshire
et al., 1984).
Water vapor adsorption isotherms were measured
with a vacuum microbalance technique. The temperature was kept within the range of 2940.1 K. The
adsorption isotherms were measured in duplicate at 14
relative pressure levels of 0.0217, 0.0902, 0.1246,
0.2142, 0.3008, 0.3404, 0.4112, 0.5324, 0.6075,
0.6533, 0.7320, 0.7727, 0.8680, 0.9826.
65
For comparison purposes, we also used published
data on water vapor adsorption on clay minerals
(Mooney et al., 1952; Orchiston, 1954; Jurinak, 1963).
The BET equation (Adamson, 1967)
N N0
c p=p0
1 ÿ p=p0 1 ÿ c ÿ 1p=p0
(2)
was ®tted to the experimental isotherms in the range of
relative pressures p/p0 between 0.02 and 0.34. Here
and below N is the adsorbate amount, p/p0 is the
relative pressure de®ned as a ratio of the actual
pressure p to the saturation vapor pressure p0. The
monolayer capacity N0 and thermodynamic constant c
were adjusted to achieve the best ®t.
3. Estimating fractal dimensions
Avnir and Jaroniec (1989) developed the fractal
analogue of the Frenkel±Halsey±Hill (FHH) equation
in the following form:
p
(3)
ln N C ÿ Ds ÿ 3 ln
p0
Here C is the intercept. The same equation was derived
by Yin (1991) and Neimark (1990) by assuming the
sequential ®lling of pores from small size to large, that
is capillary condensation-type local adsorption isotherm. A similar equation was derived by Pfeifer and
Cole (1990) by generalization of the classical FHH
adsorption theory for the capillary condensation
regime. Neimark pointed out that Eq. (1) should be
used with data obtained for p/p0>0.7. Results of
Pfeifer and Cole (1990) also indicate that Eq. (1) is
valid at high p/p0 values when the capillary condensation is the dominant mechanism. We estimated the
surface fractal dimension Ds from the slope of the
regression given by Eq. (1) at relative pressures p/p0 in
the range from 0.7320 to 0.9826.
Neimark (1990) and Neimark and Unger (1993)
proposed a different model for calculating the fractal
dimension Ds from the adsorption isotherm data. It
was called the thermodynamic model. The model
re¯ects the idea that during the adsorption on a fractal
surface, the surface is smoothed by the adsorbate,
and the surface of the adsorbent covered with an
adsorbate is smaller than the surface of the uncovered
adsorbent. The area of the `condensed adsorbate±
66
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
vapor' equilibrium interface is obtained from the
Kiselev equation
Z
RT Nmax
p
ÿln
dN
(4)
S
g N
p0
Here Nmax is the maximum adsorption, R the gas
constant, T the Kelvin temperature, and g is the surface
tension of the liquid adsorbate. This area is related by
the fractal scaling law (1) to the mean scaling radius of
this interface R which is calculated from Kelvin's
equation
R
2gVm
RT ÿln p=p0
(5)
where Vm is the molar volume of the liquid adsorbate.
The logarithmic transform of (1) with S from (4)
and R from (5) results in the equation of the thermodynamic model:
p
(6)
ln S a Ds ÿ 2 ÿln
p0
Here a is the intercept. We estimated the surface
fractal dimension Ds from the slope of the regression
given by Eq. (6) at relative pressure p/p0 in the range
from 0.7320 to 0.9826. The integral in the left-hand
side of Eq. (4) was evaluated numerically with the
trapezoid method. The maximum adsorbed amount
was approximately equated to the adsorbed amount at
p/p00.9826.
Parameters of regression equations and their standard error estimates were found using the SigmaPlot
Fig. 1. Water vapor adsorption isotherms on Gray Forest soil (Udic
Argiboroll) in grasslands; N is the adsorbed amount, p the actual
vapor pressure, and p0 is the vapor pressure at saturation; (*, *)
no harvesting, no fertilization, (&, & ) no harvesting, 60 kg NPK
annually, (~, ~) harvested, no fertilization, (!, 5) harvested,
60 kg NPK annually; hollow symbols show data for the samples in
which carbohydrates have been removed.
Version 2 software package. The statistical signi®cance of differences was tested with the t-test at the
0.05 signi®cance level.
4. Results and discussion
Adsorption data are shown in Fig. 1. Shapes of the
curves are similar. At the same relative pressure
values, the adsorbed amount is the highest in soil
from the non-harvested, fertilized plot, and is the
lowest in soil from the non-harvested, non-fertilized
plot. Intermediate values of adsorbed water amounts
Table 1
Parameters of soil pore surfaces from water vapor adsorption data
Sample
Organic carbon Treatment
content (%)
No harvest, no fertilizer 1.92
Ndb
No harvest, 60 kg NPK 1.76
Nd
Harvested, no fertilizer 1.68
Nd
Harvested, 60 kg NPK
1.64
Nd
a
b
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Standard errors are shown after the `' sign.
Not determined.
Surface fractal dimensions
Parameters of the BET equation
Fractal FHH
model
Thermodynamic
model
Monolayer
BET
capacity (g kgÿ1) c-value
2.770.01a
2.790.01
2.780.00
2.790.01
2.780.00
2.780.01
2.780.00
2.780.01
2.750.08
2.790.08
2.760.04
2.830.04
2.780.03
2.850.03
2.740.05
2.850.05
9.510.11
8.780.10
15.650.16
16.640.17
13.610.16
13.040.15
14.190.18
12.670.15
11118
14527
8611
15026
8512
7410
7410
719
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
Fig. 2. Fractal scaling of pore surface from data on water vapor
adsorption on clay minerals; N is the adsorbed amount, p the actual
vapor pressure, and p0 is the vapor pressure at saturation; (*) Namontmorillonite (Mooney et al., 1952), (*) Li-kaolinite (Jurinak,
1963), (~) illite (Orchiston, 1954).
are found in soils from harvested plots. These effects
of treatments are re¯ected in values of the monolayer
capacity N0 found from the BET equation (Table 1).
The monolayer capacity did not correlate with the
organic carbon content in this study. This could be
related to the differences in composition of organic
matter formed in soil under different management in
this experiment (Yermolayev and Shirshova, 1988;
Shirshova and Yermolayev, 1990).
67
Removal of carbohydrates caused a small decrease
of the monolayer capacity of water adsorption in soil
from all but non-harvested, fertilized plots. Feller et al.
(1992) observed that partial removal of carbon by
treatments with H2O2 increased the surface area of
clay-sized organo-mineral complexes while surface
areas of silt and sand were less affected. Oades (1984)
suggested that clays were embedded in a matrix of soil
organic matter. Therefore, in our study, differences in
composition of soil organic matter could be related to
the type of particles to which it was bounded.
Application of the fractal FHH model to data on soil
minerals is shown in Fig. 2. The FHH model provides
a reasonably good ®t to the adsorption data. Surface
fractal dimensions increase in the sequence `illite±Likaolinite±Na-montmorillonite'. The values of Ds are
2.49, 2.62, and 2.74, respectively.
Application of both the fractal FHH model and
the thermodynamic model to soil data is shown in
Fig. 3. The dependencies between transformed data
are very close to linear ones as predicted by both
models. Estimated values of surface fractal dimensions are given in Table 1. The standard errors of
the fractal dimension estimates are larger for the
thermodynamic model than for the fractal FHH model.
Estimated values of Ds range from 2.73 to 2.78 for
untreated samples and from 2.78 to 2.85 in samples,
where carbohydrates were removed. Our data do not
indicate that either of the two compared models is
superior.
Fig. 3. Fractal scaling of the pore surface demonstrated with two models of vapor adsorption on fractal surfaces: (a) fractal Frenkel±Halsey±
Hill model, (b) thermodynamic model; N is the adsorbed amount, Nmax the maximum adsorbed amount, p the actual vapor pressure, and p0 is
the vapor pressure at saturation; (*) no harvesting, no fertilization, (&) no harvesting, 60 kg NPK annually, (~) harvested, no fertilization,
(!) harvested, 60 kg NPK annually.
68
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
The values of fractal dimensions are close for both
models applied to the same sample, and no statistically
signi®cant differences are encountered. This might be
expected since we used data in the range of relative
pressures, where the capillary condensation was a
dominating adsorption process. Jaroniec (1995) had
shown that the Eq. (6) can be derived from the FHH
equation under the assumption of the condensation
approximation validity. Sahouli et al. (1996) observed
the equivalence in results of application both the
fractal FHH equation and the thermodynamic model
(6) when the adsorption process was dominated by the
capillary condensation in carbon black. Darmstadt
et al. (1995) applied both the fractal FHH model
(3) and the thermodynamic model (6) to data on N2
adsorption on carbon blacks. They found the fractal
dimensions from both models to be very close in three
of four samples. Their fourth sample had much lower
fractal dimensions than the other three. It was suggested that this sample had mesopores where the
capillary condensation occurred which led to overcompensating the reduced adsorption due to the fractal
surface.
Fractal dimension values did not differ between the
experimental treatments. The soil surface irregularity
remained the same. The intercepts in graphs of Fig. 2
show differences among the treatments. Soil in harvested plots displayed similarities in parameters of
both fractal models. For non-harvested plots, the
intercepts are different from each other and from
the harvested plots. The differences in intercepts
re¯ect the difference in ®lm surface area at the same
capillary radius value. The larger the intercept, the
larger is the ®lm surface area. Therefore, within the
studied radii range from 3 to 60 nm, the number
of pores of any given radius is the largest in the soil
of the non-harvested fertilized plot. As the radius
changes, this number scales in a similar manner in
all plots.
Several fractal models of pore surfaces were successfully used to distinguish effects of tillage and
compaction on soil structure (Perfect and Kay,
1995). Scales in these studies corresponded to the
aggregate sizes in dry sieving, i.e. 0.3±30 mm (GimeÂnez et al., 1997), or to the recognizable features in soil
thick and thin sections, i.e. 0.008±3 mm (Pachepsky
et al., 1996b; Oleszko et al., 1998). In the above
studies, the authors measured soil structure directly
using variants of the box-counting method. Scales
were much smaller in this study, and the resolution
was de®ned indirectly by converting pressures to the
radii. Different sensitivity of fractal parameters to
long-term soil management and laboratory treatments
was found in different ranges of scales (Pachepsky
et al., 1996a; GimeÂnez et al., 1997). The absence of
differences in fractal dimensions in the capillary
condensation region does not imply that the grassland
management does not affect surface roughness at all.
The differences are absent in the speci®c range of pore
radii from 3 to 60 nm, but it is possible that differences
in surface roughness exist in other ranges of radii.
Carbohydrate removal had an effect on the values of
fractal dimensions estimated with the thermodynamic
model but not with the fractal FHH (Table 1). No
statistically signi®cant differences were found
between the fractal dimension estimates in original
samples and samples with removed carbohydrates.
The increase in surface fractal dimension values
was expected since the irregularity of the surface
should increase after the removal of structure-forming
organic compounds. Removal of organic matter
caused an increase in surface fractal dimensions measured with the mercury porosimetry in three soils
studied by Pachepsky et al. (1996a).
Compared with pure minerals in Fig. 2, the soil in
this study had larger values of surface fractal dimensions. Mixed mineral composition and the presence of
organic matter are probable reasons for that. Application of other fractal models to quantify irregularity of
soil composition and structure also resulted in obtaining high, close to three, values of mass and fragmentation fractal dimensions for ®ne textured soils
(Perfect and Kay, 1995).
A caution has to be exercised in interpreting values
of fractal dimensions obtained with water adsorption
because of speci®c interactions of water molecules
with surfaces. Niklasson (1993) has found that data on
nitrogen adsorption tend to give larger values of surface fractal dimensions than data on water adsorption.
This author observed a close correspondence between
fractal dimensions obtained from water adsorption and
from small-angle neutron scattering. Pachepsky et al.
(1996b) used mercury porosimetry to measure the
surface fractal dimension under developing barley
crop for the same soil as in this study but in agricultural use. In samples taken during spring, they found
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
values of Ds2.870.10 which did not differ signi®cantly from the values in Table 1.
Fractal scaling presents additional parameters to
characterize soil pore surfaces. Speci®c surface area
was shown to be related to various physical and
chemical properties of soil (Petersen et al., 1996).
The region of relative pressures between 0.05 and 0.3
is used to ®nd the speci®c surface area (Adamson,
1967; Kutilek and Nielsen, 1994). Fractal scaling
parameters as de®ned in this paper give information
about different range of relative pressures, and therefore, different range of pore radii. There is a growing
interest in competitive adsorption of volatile organic
compounds and water in soils as related to soil bioremediation and fate of fumigants (e.g. Pennell et al.,
1992; Poulsen et al., 1998). Fractal parameters of pore
surfaces may ®nd applications in this ®eld.
In conclusion, the models of adsorption on fractal
surfaces appear to be applicable to water adsorption in
soil in this study. Differences in long-term management of the grassland did not affect surface fractal
dimensions, although the surface area was affected.
References
Adamson, A.W., 1967. Physical Chemical of Surfaces. Interscience, New York.
Aguerre, R.J., Viollaz, R.E., Suarez, C., 1996. A fractal isotherm
for multilayered adsorption in foods. J. Food Eng. 30, 227±238.
Avnir, D., Jaroniec, M., 1989. An isotherm equation for adsorption
on fractal surfaces of heterogeneous porous material. Langmuir
5, 1431±1433.
Bartoli, F., Phylippy, R., Doirisse, M., Niquet, S., Dubuit, M., 1991.
Structure and self-similarity in silty and sandy soils: the fractal
approach. J. Soil Sci. 42, 167±185.
Ben-Dor, E., Banin, A., 1995. Near-infrared analysis as a rapid
method to simultaneously evaluate several soil properties. Soil
Sci. Soc. Am. J. 59, 364±372.
Cheshire, M.W., Sparling, J.P., Mundle, C.M., 1984. In¯uence of
soil type, crop, and air drying on residual carbohydrate content.
Plant and Soil 76, 339±347.
Darmstadt, H., Roy, C., Kallaguine, S., Sahouli, B., Blasher, S.,
Pirard, R., Brouers, F., 1995. Fractal analysis of commercial
and pyrolytic carbon blacks using nitrogen adsorption data.
Rubber Chem. Technol. 68, 330±341.
Doran, J.W., Parkin, T.B., 1994. De®ning and assessing soil quality.
In: Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A.
(Eds.), De®ning Soil Quality for a Sustainable Environment.
SSSA Special Publ. No. 35, Madison, WI, pp. 3±21.
Douglas, J.F., 1989. How does surface roughness affect polymer±
surface interactions? Macromolecules 22, 3707±3716.
69
Farin, D., Avnir, D., 1989. The fractal nature of molecule±surface
interactions and reactions. In: Avnir, D. (Ed.), The Fractal
Approach to Heterogeneous Chemistry. Wiley, New York,
pp. 271±293.
Feller, C., Shouller, E., Thomas, F., Rouiller, J., Herbillon, A.J.,
1992. N2-BET speci®c surface areas of some low activity clay
soils and their relationships with secondary constituents and
organic matter contents. Soil Sci. 153, 293±299.
GimeÂnez, D., Allmaras, R.R., Nater, E.A., Huggins, D.R., 1997.
Fractal dimensions for volume and surface of interaggregate
pores: scale effects. Geoderma 77, 19±38.
Giona, M., Giustiniani, M., 1996. Adsorption kinetics on fractal
surfaces. J. Phys. Chem. 100, 16690±16699.
Hatzikiriakos, S.G., Avramidis, S., 1994. Fractal dimension of
wood surfaces from sorption isotherms. Wood Sci. Technol. 28,
275±284.
Jaroniec, M., 1995. Evaluation of the fractal dimension from a
single adsorption isotherm. Langmuir 11, 2316±2317.
Jaroniec, M., Kruk, M., Olivier, J., 1997. Fractal analysis of
composite adsorption isotherms obtained by using density
functional theory data for argon in slitlike pores. Langmuir 13,
1031±1035.
Jurinak, J.J., 1963. Multilayer adsorption of water by kaolinite. Soil
Sci. Soc. Am. Proc. 27, 269±272.
Jurinak, J.J., Volman, D.H., 1957. Application of Brunauer,
Emmett and Teller equation to ethylene dibromide adsorption
by soils. Soil Sci. 83, 487±496.
Kapilevich, Zh.A., Pisentsky, G.A., Vysochenko, A.V., 1987.
Speci®c surface as a basic parameter for evaluating hydromelioration characteristics of mineral soils. Sov. Soil Sci. 19,
68±76.
Kutarov, V.V., Kats, B.M., 1992. Determination of the fractal
dimension of ion-exchange ®bers from adsorption data. Russ. J.
Phys. Chem. 67, 1854±1856.
Kutilek, M., Nielsen, D., 1994. Soil Hydrology. Catena Verlag,
Cremlingen-Destedt, Germany.
Mooney, R.W., Keenan, A.G., Wood, L.A., 1952. Adsorption of
water vapor by montmorillonite. Part I. Heat of desorption
and application of BET theory. J. Am. Chem. Soc. 74, 1367±
1371.
Neimark, A.V., 1990. Determination of surface fractal dimension
from the results of an adsorption experiment. Russ. J. Phys.
Chem. 64, 1398±1403.
Neimark, A.V., Unger, K.K., 1993. Method of discrimination of
surface fractality. J. Colloid Interf. Sci. 158, 412±419.
Niklasson, G.A., 1993. Adsorption on fractal structures: applications to cement materials. Cem. Conc. Res. 23, 1153±1158.
Oades, J.M., 1984. Soil organic matter and structural stability:
mechanisms and implications for management. Plant and Soil
76, 319±337.
Oleschko, K., Brambila, F., Acess, F., Mora, L.P., 1998. From
fractal analysis along a line to fractals on the plane. Soil and
Tillage Research 45, 389±406.
Ong, S.K., Lion, L.W., 1991. Trichloroethylene vapor sorption onto
soil minerals. Soil Sci. Soc. Am. J. 55, 1559±1568.
Orchiston, H.D., 1954. Adsorption of water vapor: clays at 258C.
Soil Sci. 78, 463±480.
70
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
Pachepsky, Ya.A., Korsunskaia, L.P., Hajnos, M., 1996a. Fractal
parameters of soil pore surface area under a developing crop.
Fractals 4, 97±110.
Pachepsky, Ya.A., Yakovchenko, V., Rabenhorst, M.C., Pooley, C.,
Sikora, L.J., 1996b. Fractal parameters of pore surfaces as
derived from micromorphological data: effect of long-term
management practices. Geoderma 74, 305±325.
Pennell, K.D., Rhue, R.D., Rao, P.S.C., 1992. Vapor-phase sorption
of p-xylene and water on soils and clay minerals. Environ. Sci.
Technol. 26, 756±765.
Perfect, E., Kay, B.D., 1995. Applications of fractals in soil and
tillage research: a review. Soil Till. Res. 36, 1±20.
Petersen, L.W., Moldrup, P., Jacobsen, O.H., Rolston, D.E., 1996.
Relation between soil speci®c area and soil physical and
chemical properties. Soil Sci. 161, 9±21.
Pfeifer, P., Cole, M.W., 1990. Fractals in surface science: scattering
and thermodynamics of adsorbed ®lms. II. New J. Chem. 14,
221±232.
Poulsen, T.G., Moldrup, P., Hansen, J.A., 1998. VOC vapor
sorption in soil: soil type dependent model and implications for
vapor extraction. J. Environ. Eng. 124, 145±157.
Rhue, R.D., Rao, P.S.C., Smith, R.E., 1988. Vapor phase adsorption
of alkylbenzenes and water on soils and clays. Chemosphere
17, 727±741.
Rice, J.A., Tombacz, E., Malekani, K., 1999. Applications of light
and X-ray scattering to characterize the fractal properties of soil
organic matter. Geoderma 88, 251±267.
Russ, J.C., 1994. Fractal Surfaces. Plenum Press, New York.
Sahouli, B., Blacher, S., Brouers, F., 1996. Fractal surface analysis
by using nitrogen adsorption data: the case of the capillary
condensation regime. Langmuir 12, 2872±2874.
Sapozhnikov, P.M., 1985. Relationship between the swelling of
some soils and speci®c surface categories and the energetics of
soil moisture. Sov. Soil Sci. 17, 87±93.
Seri-Levy, A., Avnir, D., 1993. Kinetics of diffusion-limited
adsorption on fractal surfaces. J. Phys. Chem. 97, 10380±
10385.
Shirshova, L.T., Yermolayev, A.M., 1990. Pecularities of humus
accumulation in arable Gray Forest Soil during grassing. J.
Gen. Biol. 51, 642±650.
Singer, M.J., Ewing, S., 2000. Soil quality. In: M.E. Sumner (Ed.),
Handbook of Soil Science. CRC Press, Boca Raton, FL,
pp. G271±G297.
Skidmore, E.L., Layton, J.B., 1992. Dry-soil aggregate stability as
in¯uenced by selected soil properties. Soil Sci. Soc. Am. J. 56,
557±561.
Sokoøowska, Z., 1989. On the role of energetic and geometric
heterogeneity in sorption of water vapor by soils: application of
a fractal approach. Geoderma 45, 251±265.
Sokoøowska, Z., Sokoøowski, S., 1999. In¯uence of humic acid on
surface fractal dimension of kaolin: analysis of mercury porosimetry and water vapor adsorption data. Geoderma 88, 233±245.
Tester, C.F., 1990. Organic amendment effects on physical and
chemical properties of a sandy soil. Soil Sci. Soc. Am. J. 54,
827±831.
Toledo, P.G., Nony, R.A., Davis, H.T., Scriven, L.E., 1990.
Hydraulic conductivity of porous media at low water content.
Soil Sci. Soc. Am. J. 54, 673±679.
Valverde-Garcia, A., Gonzales-Pradas, E., Villafranca-Sanchez,
M., del Rey-Beno, F., Garcia-Rodrigues, A., 1988. Adsorption
of thiram and dimethoate on Almeria soils. Soil Sci. Soc. Am.
J. 52, 1571±1574.
Yermolayev, A.M., Shirshova, L.T., 1988. Dynamics of plant
organic matter and certain humus fractions in Gray Forest soil
under arti®cial grassland. Sov. J. Ecol. 19, 10±16.
Yermolayev, A.M., Shirshova, L.T., 1994. Productivity and
functioning of a perennial sown meadow of various management type. Pochvovedenie 12, 97±105 (in Russian).
Yin, Y., 1991. Adsorption isotherm of fractally porous material.
Langmuir 7, 216±217.
Soil pore surface properties in managed grasslands
Meczislaw Hajnosa, Ludmila Korsunskaiab, Yakov Pachepskyc,*
a
Institute of Agrophysics, Lublin 20536, Poland
Institute of Physical, Chemical, and Biological Problems in Soil Science, Pushchino 142292, Russia
c
USDA:ARS:BA:NRI:RSML, Hydrology Laboratory, Bldg. 007, Rm. 104, BARC-WEST, Beltsville, MD 20705, USA
b
Received 3 August 1999; received in revised form 7 January 2000; accepted 28 January 2000
Abstract
Properties of pore surfaces control adsorption and transport of water and chemicals in soils. Parameters are needed to
recognize and monitor changes in pore surfaces caused by differences in soil management. Data on gas adsorption in soils can
be compressed into parameters characterizing (a) area available to a particular adsorbate, and (b) surface roughness or
irregularity. Our objectives were to see (a) whether models of adsorption on fractal surfaces are applicable to water vapor
adsorption in soils in the capillary condensation range, and (b) whether differences in long-term management of grasslands are
re¯ected by soil pore surface properties. Water vapor adsorption was measured in Gray Forest soil (Udic Argiboroll, Orthic
Greyezem, clay loam) samples taken at four plots, where a long-term experiment on grassing arable land had been carried out
for 12 years. The experiment had 22 design. Factors were `harvest±no-harvest' and `fertilizer±no-fertilizer'. The hay was cut
after over-seeding in harvested treatments every year. Ammonium nitrate, superphosphate, and potassium chloride were
applied annually after the snowmelt to get the total amount of nutrients of 60 kg haÿ1. The monolayer adsorption capacity was
estimated from the Brunauer±Emmett±Teller model. A fractal Frenkel±Halsey±Hill model of adsorption on a fractal surface,
and a thermodynamic adsorption model were applied in the range of relative pressures from 0.7 to 0.98 and provided good ®t
of data. Values of the surface fractal dimension Ds were in the range from 2.75 to 2.85. Removal of carbohydrates resulted in
increase of Ds. Differences in management practices did not affect values of Ds in the scale range studied, whereas the
monolayer capacity was affected. Both fertilization and harvesting resulted in an increase of the monolayer capacity, with the
largest increase observed in soil that was fertilized but not harvested. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Water vapor; Adsorption; Fractal surface; Grassland; Gray Forest soil
1. Introduction
Properties of pore surfaces control adsorption and
transport of water and chemicals in soils. Parameters
are needed to recognize and monitor changes in pore
*
Corresponding author. Tel.: 1-301-504-7468;
fax: 1-301-504-5823.
E-mail address: ypachepsky@asrr.arsusda.gov (Y. Pachepsky)
surfaces caused by differences in soil management.
Once established, such diagnostic parameters can be
used to quantify effects of management on soil functioning by means of land quality or soil quality indices
(Singer and Ewing, 2000).
Data on gas adsorption in soils can be compressed
into parameters characterizing (a) area available to a
particular adsorbate, and (b) surface roughness or
irregularity. Speci®c surface area is known to char-
0167-1987/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 1 9 8 7 ( 0 0 ) 0 0 0 9 9 - 4
64
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
acterize the ability of soil to retain and transport
nutrients and water. Speci®c surface area of soils
correlates with the sorptive capacity and ion exchange
capacity (Jurinak and Volman, 1957; Ben-Dor and
Banin, 1995), retention and release of chemicals
(Rhue et al., 1988; Valverde-Garcia et al., 1988;
Ong and Lion, 1991), swelling (Sapozhnikov,
1985), water retention (Kapilevich et al., 1987),
dry-aggregate stability (Skidmore and Layton,
1992). Tester (1990) observed an increase in speci®c
surface area parallel to the increase in organic matter
content after compost application.
Pore surfaces in soils are irregular. Fractal models
were found useful in the description of natural and
man-made irregular surfaces. Fractal surfaces exhibit
dependencies of their area S on the resolution, or scale,
R at which the area is measured (Russ, 1994). These
dependencies have a power law form
S / R2ÿDs
(1)
where Ds is the surface fractal dimension. The surface
fractal dimension characterizes the degree of roughness or disorder of the surface. Numerical values of
surface fractal dimensions vary from 2.0 (perfectly
smooth) to a maximum value of 3.0. The larger the
value of Ds, the greater is the irregularity of the
surface.
Theoretical studies of adsorption on fractal surfaces
predicted the effect of the surface fractal dimension on
diffusion-limited adsorption kinetics (Seri-Levy and
Avnir, 1993; Giona and Giustiniani, 1996). Douglas
(1989) showed that adsorption of polymers on rough
surfaces should be affected by the surface fractal
dimension. The increase in fractal dimensions should
cause tighter binding of polymer with a surface. Surface fractal dimensions were studied with relation to
technological parameters in production of ionexchange ®bers (Kutarov and Kats, 1992), carbon
blacks (Darmstadt et al., 1995), cements (Niklasson,
1993), food products (Aguerre et al., 1996), and wood
(Hatzikiriakos and Avramidis, 1994).
Fractal scaling was demonstrated for soil pore
surfaces. Sokoøowska (1989) used a fractal model to
analyze the soil particle surface heterogeneity with
data on water vapor adsorption experiments. Toledo
et al. (1990) showed that fractal dimensions of soil
particle surfaces could be estimated from water retention data at low moisture contents. Bartoli et al. (1991)
introduced the use of mercury porosimetry to estimate
surface fractal dimensions in soils. Soil constituents,
such as humus materials and clay minerals, were
found to be surface fractals (Rice et al., 1999; Sokoøowska and Sokoøowski, 1999).
The management-related change in soil quality is a
current topic of interest. Efforts were made to de®ne
soil quality and suggest a minimum set of analyses to
aid in evaluating soil quality as affected by long-term
management practices (Doran and Parkin, 1994).
Long-term and short-term management effects on soil
pore surface fractal dimensions were observed using
soil thin sections (Pachepsky et al., 1996b; GimeÂnez
et al., 1997; Oleschko et al., 1998). Fractal dimension
analysis provided additional information by describing the changes in pore shapes.
Adsorption isotherms of gases present an attractive
source of data on surface roughness. Several theories
of adsorption on a fractal surface were developed
during last 15 years. Two types of adsorption data
analysis have been used most often. One of them uses
several different adsorbates and employs the mean
radius of each adsorbate's molecules as the resolution,
or scale, R in Eq. (1). The logarithmic transform of this
equation and the subsequent regression `radius vs.
speci®c surface' in log±log scale provides the value
of Ds as the slope subtracted from 2 (Farin and Avnir,
1989). With this approach, data on adsorption at low
relative pressures are used at which the monolayer
coverage is known to occur. Another type of the
adsorption data analysis employs the data at high
relative pressures, where capillary condensation
occurs so that micropores become ®lled with adsorbate. Then the micropore radius becomes a measure of
scale R in Eq. (1). Avnir and Jaroniec (1989) obtained
a relationship between the adsorbed amount and vapor
pressure by assuming the applicability of the Dubinin±
Radushkievich equation to describe the adsorption in
micropores, and assuming fractal pore volume distribution on the surface. The same equation was obtained
by Neimark (1990) and Yin (1991) from the assumption that the capillary condensation was present. A
different model was proposed by Neimark (1990). He
did not assume validity of any adsorption isotherm
equation, but used directly the scaling relationship (1)
with the surface curvature radius as a scale measure.
Although both models mentioned above were applied
in experimental studies, no unambiguous way was
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
found to see which one is superior (Jaroniec et al.,
1997).
Our objectives were to see (a) whether models of
adsorption on fractal surfaces are applicable to water
vapor adsorption in soils in the capillary condensation
range, and (b) whether differences in long-term management of grasslands are re¯ected by soil pore surface properties.
2. Materials and methods
2.1. Soil sampling and analyses
Gray Forest soil (Udic Argiboroll) was sampled in
April 1994 near Pushchino, Moscow Region, Russia.
Samples were taken at a site, where an experiment on
grassing arable land had been carried out since 1982
(Yermolayev and Shirshova, 1994). Grass mixture
consisted of Festuca Pratensis, Huds., Phleum Pratense L., and Trifolium Pratense L. The experiment
had 22 design. Factors were `harvest±no-harvest'
and `fertilizer±no-fertilizer'. The hay was cut after
over-seeding in harvested treatments every year.
Ammonium nitrate, superphosphate, and potassium
chloride were applied annually after the snowmelt to
get the total amount of nutrients of 60 kg haÿ1. Area of
each plot was 0.5 ha. The soil was in no-till, since
1982. The soil had the pH 6.3, a loamy texture with
45% particles less than 0.01 mm and 20% particles
less than 0.001 mm, and contained illite, kaolinite, and
smectites in its clay fraction. Sampling depth was 10±
30 cm. Five samples were taken from each plot, and
the mixed sample was used in adsorption measurements for each of the four combinations of factors.
Soil was air-dried and sieved, and aggregates less
than 2 mm were used. Each sample was split, and
carbohydrates were removed in one of the two subsamples. The oxidation of carbohydrates has been
performed with 0.02 M NaIO4 solution (Cheshire
et al., 1984).
Water vapor adsorption isotherms were measured
with a vacuum microbalance technique. The temperature was kept within the range of 2940.1 K. The
adsorption isotherms were measured in duplicate at 14
relative pressure levels of 0.0217, 0.0902, 0.1246,
0.2142, 0.3008, 0.3404, 0.4112, 0.5324, 0.6075,
0.6533, 0.7320, 0.7727, 0.8680, 0.9826.
65
For comparison purposes, we also used published
data on water vapor adsorption on clay minerals
(Mooney et al., 1952; Orchiston, 1954; Jurinak, 1963).
The BET equation (Adamson, 1967)
N N0
c p=p0
1 ÿ p=p0 1 ÿ c ÿ 1p=p0
(2)
was ®tted to the experimental isotherms in the range of
relative pressures p/p0 between 0.02 and 0.34. Here
and below N is the adsorbate amount, p/p0 is the
relative pressure de®ned as a ratio of the actual
pressure p to the saturation vapor pressure p0. The
monolayer capacity N0 and thermodynamic constant c
were adjusted to achieve the best ®t.
3. Estimating fractal dimensions
Avnir and Jaroniec (1989) developed the fractal
analogue of the Frenkel±Halsey±Hill (FHH) equation
in the following form:
p
(3)
ln N C ÿ Ds ÿ 3 ln
p0
Here C is the intercept. The same equation was derived
by Yin (1991) and Neimark (1990) by assuming the
sequential ®lling of pores from small size to large, that
is capillary condensation-type local adsorption isotherm. A similar equation was derived by Pfeifer and
Cole (1990) by generalization of the classical FHH
adsorption theory for the capillary condensation
regime. Neimark pointed out that Eq. (1) should be
used with data obtained for p/p0>0.7. Results of
Pfeifer and Cole (1990) also indicate that Eq. (1) is
valid at high p/p0 values when the capillary condensation is the dominant mechanism. We estimated the
surface fractal dimension Ds from the slope of the
regression given by Eq. (1) at relative pressures p/p0 in
the range from 0.7320 to 0.9826.
Neimark (1990) and Neimark and Unger (1993)
proposed a different model for calculating the fractal
dimension Ds from the adsorption isotherm data. It
was called the thermodynamic model. The model
re¯ects the idea that during the adsorption on a fractal
surface, the surface is smoothed by the adsorbate,
and the surface of the adsorbent covered with an
adsorbate is smaller than the surface of the uncovered
adsorbent. The area of the `condensed adsorbate±
66
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
vapor' equilibrium interface is obtained from the
Kiselev equation
Z
RT Nmax
p
ÿln
dN
(4)
S
g N
p0
Here Nmax is the maximum adsorption, R the gas
constant, T the Kelvin temperature, and g is the surface
tension of the liquid adsorbate. This area is related by
the fractal scaling law (1) to the mean scaling radius of
this interface R which is calculated from Kelvin's
equation
R
2gVm
RT ÿln p=p0
(5)
where Vm is the molar volume of the liquid adsorbate.
The logarithmic transform of (1) with S from (4)
and R from (5) results in the equation of the thermodynamic model:
p
(6)
ln S a Ds ÿ 2 ÿln
p0
Here a is the intercept. We estimated the surface
fractal dimension Ds from the slope of the regression
given by Eq. (6) at relative pressure p/p0 in the range
from 0.7320 to 0.9826. The integral in the left-hand
side of Eq. (4) was evaluated numerically with the
trapezoid method. The maximum adsorbed amount
was approximately equated to the adsorbed amount at
p/p00.9826.
Parameters of regression equations and their standard error estimates were found using the SigmaPlot
Fig. 1. Water vapor adsorption isotherms on Gray Forest soil (Udic
Argiboroll) in grasslands; N is the adsorbed amount, p the actual
vapor pressure, and p0 is the vapor pressure at saturation; (*, *)
no harvesting, no fertilization, (&, & ) no harvesting, 60 kg NPK
annually, (~, ~) harvested, no fertilization, (!, 5) harvested,
60 kg NPK annually; hollow symbols show data for the samples in
which carbohydrates have been removed.
Version 2 software package. The statistical signi®cance of differences was tested with the t-test at the
0.05 signi®cance level.
4. Results and discussion
Adsorption data are shown in Fig. 1. Shapes of the
curves are similar. At the same relative pressure
values, the adsorbed amount is the highest in soil
from the non-harvested, fertilized plot, and is the
lowest in soil from the non-harvested, non-fertilized
plot. Intermediate values of adsorbed water amounts
Table 1
Parameters of soil pore surfaces from water vapor adsorption data
Sample
Organic carbon Treatment
content (%)
No harvest, no fertilizer 1.92
Ndb
No harvest, 60 kg NPK 1.76
Nd
Harvested, no fertilizer 1.68
Nd
Harvested, 60 kg NPK
1.64
Nd
a
b
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Original sample
Carbohydrates removed
Standard errors are shown after the `' sign.
Not determined.
Surface fractal dimensions
Parameters of the BET equation
Fractal FHH
model
Thermodynamic
model
Monolayer
BET
capacity (g kgÿ1) c-value
2.770.01a
2.790.01
2.780.00
2.790.01
2.780.00
2.780.01
2.780.00
2.780.01
2.750.08
2.790.08
2.760.04
2.830.04
2.780.03
2.850.03
2.740.05
2.850.05
9.510.11
8.780.10
15.650.16
16.640.17
13.610.16
13.040.15
14.190.18
12.670.15
11118
14527
8611
15026
8512
7410
7410
719
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
Fig. 2. Fractal scaling of pore surface from data on water vapor
adsorption on clay minerals; N is the adsorbed amount, p the actual
vapor pressure, and p0 is the vapor pressure at saturation; (*) Namontmorillonite (Mooney et al., 1952), (*) Li-kaolinite (Jurinak,
1963), (~) illite (Orchiston, 1954).
are found in soils from harvested plots. These effects
of treatments are re¯ected in values of the monolayer
capacity N0 found from the BET equation (Table 1).
The monolayer capacity did not correlate with the
organic carbon content in this study. This could be
related to the differences in composition of organic
matter formed in soil under different management in
this experiment (Yermolayev and Shirshova, 1988;
Shirshova and Yermolayev, 1990).
67
Removal of carbohydrates caused a small decrease
of the monolayer capacity of water adsorption in soil
from all but non-harvested, fertilized plots. Feller et al.
(1992) observed that partial removal of carbon by
treatments with H2O2 increased the surface area of
clay-sized organo-mineral complexes while surface
areas of silt and sand were less affected. Oades (1984)
suggested that clays were embedded in a matrix of soil
organic matter. Therefore, in our study, differences in
composition of soil organic matter could be related to
the type of particles to which it was bounded.
Application of the fractal FHH model to data on soil
minerals is shown in Fig. 2. The FHH model provides
a reasonably good ®t to the adsorption data. Surface
fractal dimensions increase in the sequence `illite±Likaolinite±Na-montmorillonite'. The values of Ds are
2.49, 2.62, and 2.74, respectively.
Application of both the fractal FHH model and
the thermodynamic model to soil data is shown in
Fig. 3. The dependencies between transformed data
are very close to linear ones as predicted by both
models. Estimated values of surface fractal dimensions are given in Table 1. The standard errors of
the fractal dimension estimates are larger for the
thermodynamic model than for the fractal FHH model.
Estimated values of Ds range from 2.73 to 2.78 for
untreated samples and from 2.78 to 2.85 in samples,
where carbohydrates were removed. Our data do not
indicate that either of the two compared models is
superior.
Fig. 3. Fractal scaling of the pore surface demonstrated with two models of vapor adsorption on fractal surfaces: (a) fractal Frenkel±Halsey±
Hill model, (b) thermodynamic model; N is the adsorbed amount, Nmax the maximum adsorbed amount, p the actual vapor pressure, and p0 is
the vapor pressure at saturation; (*) no harvesting, no fertilization, (&) no harvesting, 60 kg NPK annually, (~) harvested, no fertilization,
(!) harvested, 60 kg NPK annually.
68
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
The values of fractal dimensions are close for both
models applied to the same sample, and no statistically
signi®cant differences are encountered. This might be
expected since we used data in the range of relative
pressures, where the capillary condensation was a
dominating adsorption process. Jaroniec (1995) had
shown that the Eq. (6) can be derived from the FHH
equation under the assumption of the condensation
approximation validity. Sahouli et al. (1996) observed
the equivalence in results of application both the
fractal FHH equation and the thermodynamic model
(6) when the adsorption process was dominated by the
capillary condensation in carbon black. Darmstadt
et al. (1995) applied both the fractal FHH model
(3) and the thermodynamic model (6) to data on N2
adsorption on carbon blacks. They found the fractal
dimensions from both models to be very close in three
of four samples. Their fourth sample had much lower
fractal dimensions than the other three. It was suggested that this sample had mesopores where the
capillary condensation occurred which led to overcompensating the reduced adsorption due to the fractal
surface.
Fractal dimension values did not differ between the
experimental treatments. The soil surface irregularity
remained the same. The intercepts in graphs of Fig. 2
show differences among the treatments. Soil in harvested plots displayed similarities in parameters of
both fractal models. For non-harvested plots, the
intercepts are different from each other and from
the harvested plots. The differences in intercepts
re¯ect the difference in ®lm surface area at the same
capillary radius value. The larger the intercept, the
larger is the ®lm surface area. Therefore, within the
studied radii range from 3 to 60 nm, the number
of pores of any given radius is the largest in the soil
of the non-harvested fertilized plot. As the radius
changes, this number scales in a similar manner in
all plots.
Several fractal models of pore surfaces were successfully used to distinguish effects of tillage and
compaction on soil structure (Perfect and Kay,
1995). Scales in these studies corresponded to the
aggregate sizes in dry sieving, i.e. 0.3±30 mm (GimeÂnez et al., 1997), or to the recognizable features in soil
thick and thin sections, i.e. 0.008±3 mm (Pachepsky
et al., 1996b; Oleszko et al., 1998). In the above
studies, the authors measured soil structure directly
using variants of the box-counting method. Scales
were much smaller in this study, and the resolution
was de®ned indirectly by converting pressures to the
radii. Different sensitivity of fractal parameters to
long-term soil management and laboratory treatments
was found in different ranges of scales (Pachepsky
et al., 1996a; GimeÂnez et al., 1997). The absence of
differences in fractal dimensions in the capillary
condensation region does not imply that the grassland
management does not affect surface roughness at all.
The differences are absent in the speci®c range of pore
radii from 3 to 60 nm, but it is possible that differences
in surface roughness exist in other ranges of radii.
Carbohydrate removal had an effect on the values of
fractal dimensions estimated with the thermodynamic
model but not with the fractal FHH (Table 1). No
statistically signi®cant differences were found
between the fractal dimension estimates in original
samples and samples with removed carbohydrates.
The increase in surface fractal dimension values
was expected since the irregularity of the surface
should increase after the removal of structure-forming
organic compounds. Removal of organic matter
caused an increase in surface fractal dimensions measured with the mercury porosimetry in three soils
studied by Pachepsky et al. (1996a).
Compared with pure minerals in Fig. 2, the soil in
this study had larger values of surface fractal dimensions. Mixed mineral composition and the presence of
organic matter are probable reasons for that. Application of other fractal models to quantify irregularity of
soil composition and structure also resulted in obtaining high, close to three, values of mass and fragmentation fractal dimensions for ®ne textured soils
(Perfect and Kay, 1995).
A caution has to be exercised in interpreting values
of fractal dimensions obtained with water adsorption
because of speci®c interactions of water molecules
with surfaces. Niklasson (1993) has found that data on
nitrogen adsorption tend to give larger values of surface fractal dimensions than data on water adsorption.
This author observed a close correspondence between
fractal dimensions obtained from water adsorption and
from small-angle neutron scattering. Pachepsky et al.
(1996b) used mercury porosimetry to measure the
surface fractal dimension under developing barley
crop for the same soil as in this study but in agricultural use. In samples taken during spring, they found
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
values of Ds2.870.10 which did not differ signi®cantly from the values in Table 1.
Fractal scaling presents additional parameters to
characterize soil pore surfaces. Speci®c surface area
was shown to be related to various physical and
chemical properties of soil (Petersen et al., 1996).
The region of relative pressures between 0.05 and 0.3
is used to ®nd the speci®c surface area (Adamson,
1967; Kutilek and Nielsen, 1994). Fractal scaling
parameters as de®ned in this paper give information
about different range of relative pressures, and therefore, different range of pore radii. There is a growing
interest in competitive adsorption of volatile organic
compounds and water in soils as related to soil bioremediation and fate of fumigants (e.g. Pennell et al.,
1992; Poulsen et al., 1998). Fractal parameters of pore
surfaces may ®nd applications in this ®eld.
In conclusion, the models of adsorption on fractal
surfaces appear to be applicable to water adsorption in
soil in this study. Differences in long-term management of the grassland did not affect surface fractal
dimensions, although the surface area was affected.
References
Adamson, A.W., 1967. Physical Chemical of Surfaces. Interscience, New York.
Aguerre, R.J., Viollaz, R.E., Suarez, C., 1996. A fractal isotherm
for multilayered adsorption in foods. J. Food Eng. 30, 227±238.
Avnir, D., Jaroniec, M., 1989. An isotherm equation for adsorption
on fractal surfaces of heterogeneous porous material. Langmuir
5, 1431±1433.
Bartoli, F., Phylippy, R., Doirisse, M., Niquet, S., Dubuit, M., 1991.
Structure and self-similarity in silty and sandy soils: the fractal
approach. J. Soil Sci. 42, 167±185.
Ben-Dor, E., Banin, A., 1995. Near-infrared analysis as a rapid
method to simultaneously evaluate several soil properties. Soil
Sci. Soc. Am. J. 59, 364±372.
Cheshire, M.W., Sparling, J.P., Mundle, C.M., 1984. In¯uence of
soil type, crop, and air drying on residual carbohydrate content.
Plant and Soil 76, 339±347.
Darmstadt, H., Roy, C., Kallaguine, S., Sahouli, B., Blasher, S.,
Pirard, R., Brouers, F., 1995. Fractal analysis of commercial
and pyrolytic carbon blacks using nitrogen adsorption data.
Rubber Chem. Technol. 68, 330±341.
Doran, J.W., Parkin, T.B., 1994. De®ning and assessing soil quality.
In: Doran, J.W., Coleman, D.C., Bezdicek, D.F., Stewart, B.A.
(Eds.), De®ning Soil Quality for a Sustainable Environment.
SSSA Special Publ. No. 35, Madison, WI, pp. 3±21.
Douglas, J.F., 1989. How does surface roughness affect polymer±
surface interactions? Macromolecules 22, 3707±3716.
69
Farin, D., Avnir, D., 1989. The fractal nature of molecule±surface
interactions and reactions. In: Avnir, D. (Ed.), The Fractal
Approach to Heterogeneous Chemistry. Wiley, New York,
pp. 271±293.
Feller, C., Shouller, E., Thomas, F., Rouiller, J., Herbillon, A.J.,
1992. N2-BET speci®c surface areas of some low activity clay
soils and their relationships with secondary constituents and
organic matter contents. Soil Sci. 153, 293±299.
GimeÂnez, D., Allmaras, R.R., Nater, E.A., Huggins, D.R., 1997.
Fractal dimensions for volume and surface of interaggregate
pores: scale effects. Geoderma 77, 19±38.
Giona, M., Giustiniani, M., 1996. Adsorption kinetics on fractal
surfaces. J. Phys. Chem. 100, 16690±16699.
Hatzikiriakos, S.G., Avramidis, S., 1994. Fractal dimension of
wood surfaces from sorption isotherms. Wood Sci. Technol. 28,
275±284.
Jaroniec, M., 1995. Evaluation of the fractal dimension from a
single adsorption isotherm. Langmuir 11, 2316±2317.
Jaroniec, M., Kruk, M., Olivier, J., 1997. Fractal analysis of
composite adsorption isotherms obtained by using density
functional theory data for argon in slitlike pores. Langmuir 13,
1031±1035.
Jurinak, J.J., 1963. Multilayer adsorption of water by kaolinite. Soil
Sci. Soc. Am. Proc. 27, 269±272.
Jurinak, J.J., Volman, D.H., 1957. Application of Brunauer,
Emmett and Teller equation to ethylene dibromide adsorption
by soils. Soil Sci. 83, 487±496.
Kapilevich, Zh.A., Pisentsky, G.A., Vysochenko, A.V., 1987.
Speci®c surface as a basic parameter for evaluating hydromelioration characteristics of mineral soils. Sov. Soil Sci. 19,
68±76.
Kutarov, V.V., Kats, B.M., 1992. Determination of the fractal
dimension of ion-exchange ®bers from adsorption data. Russ. J.
Phys. Chem. 67, 1854±1856.
Kutilek, M., Nielsen, D., 1994. Soil Hydrology. Catena Verlag,
Cremlingen-Destedt, Germany.
Mooney, R.W., Keenan, A.G., Wood, L.A., 1952. Adsorption of
water vapor by montmorillonite. Part I. Heat of desorption
and application of BET theory. J. Am. Chem. Soc. 74, 1367±
1371.
Neimark, A.V., 1990. Determination of surface fractal dimension
from the results of an adsorption experiment. Russ. J. Phys.
Chem. 64, 1398±1403.
Neimark, A.V., Unger, K.K., 1993. Method of discrimination of
surface fractality. J. Colloid Interf. Sci. 158, 412±419.
Niklasson, G.A., 1993. Adsorption on fractal structures: applications to cement materials. Cem. Conc. Res. 23, 1153±1158.
Oades, J.M., 1984. Soil organic matter and structural stability:
mechanisms and implications for management. Plant and Soil
76, 319±337.
Oleschko, K., Brambila, F., Acess, F., Mora, L.P., 1998. From
fractal analysis along a line to fractals on the plane. Soil and
Tillage Research 45, 389±406.
Ong, S.K., Lion, L.W., 1991. Trichloroethylene vapor sorption onto
soil minerals. Soil Sci. Soc. Am. J. 55, 1559±1568.
Orchiston, H.D., 1954. Adsorption of water vapor: clays at 258C.
Soil Sci. 78, 463±480.
70
M. Hajnos et al. / Soil & Tillage Research 55 (2000) 63±70
Pachepsky, Ya.A., Korsunskaia, L.P., Hajnos, M., 1996a. Fractal
parameters of soil pore surface area under a developing crop.
Fractals 4, 97±110.
Pachepsky, Ya.A., Yakovchenko, V., Rabenhorst, M.C., Pooley, C.,
Sikora, L.J., 1996b. Fractal parameters of pore surfaces as
derived from micromorphological data: effect of long-term
management practices. Geoderma 74, 305±325.
Pennell, K.D., Rhue, R.D., Rao, P.S.C., 1992. Vapor-phase sorption
of p-xylene and water on soils and clay minerals. Environ. Sci.
Technol. 26, 756±765.
Perfect, E., Kay, B.D., 1995. Applications of fractals in soil and
tillage research: a review. Soil Till. Res. 36, 1±20.
Petersen, L.W., Moldrup, P., Jacobsen, O.H., Rolston, D.E., 1996.
Relation between soil speci®c area and soil physical and
chemical properties. Soil Sci. 161, 9±21.
Pfeifer, P., Cole, M.W., 1990. Fractals in surface science: scattering
and thermodynamics of adsorbed ®lms. II. New J. Chem. 14,
221±232.
Poulsen, T.G., Moldrup, P., Hansen, J.A., 1998. VOC vapor
sorption in soil: soil type dependent model and implications for
vapor extraction. J. Environ. Eng. 124, 145±157.
Rhue, R.D., Rao, P.S.C., Smith, R.E., 1988. Vapor phase adsorption
of alkylbenzenes and water on soils and clays. Chemosphere
17, 727±741.
Rice, J.A., Tombacz, E., Malekani, K., 1999. Applications of light
and X-ray scattering to characterize the fractal properties of soil
organic matter. Geoderma 88, 251±267.
Russ, J.C., 1994. Fractal Surfaces. Plenum Press, New York.
Sahouli, B., Blacher, S., Brouers, F., 1996. Fractal surface analysis
by using nitrogen adsorption data: the case of the capillary
condensation regime. Langmuir 12, 2872±2874.
Sapozhnikov, P.M., 1985. Relationship between the swelling of
some soils and speci®c surface categories and the energetics of
soil moisture. Sov. Soil Sci. 17, 87±93.
Seri-Levy, A., Avnir, D., 1993. Kinetics of diffusion-limited
adsorption on fractal surfaces. J. Phys. Chem. 97, 10380±
10385.
Shirshova, L.T., Yermolayev, A.M., 1990. Pecularities of humus
accumulation in arable Gray Forest Soil during grassing. J.
Gen. Biol. 51, 642±650.
Singer, M.J., Ewing, S., 2000. Soil quality. In: M.E. Sumner (Ed.),
Handbook of Soil Science. CRC Press, Boca Raton, FL,
pp. G271±G297.
Skidmore, E.L., Layton, J.B., 1992. Dry-soil aggregate stability as
in¯uenced by selected soil properties. Soil Sci. Soc. Am. J. 56,
557±561.
Sokoøowska, Z., 1989. On the role of energetic and geometric
heterogeneity in sorption of water vapor by soils: application of
a fractal approach. Geoderma 45, 251±265.
Sokoøowska, Z., Sokoøowski, S., 1999. In¯uence of humic acid on
surface fractal dimension of kaolin: analysis of mercury porosimetry and water vapor adsorption data. Geoderma 88, 233±245.
Tester, C.F., 1990. Organic amendment effects on physical and
chemical properties of a sandy soil. Soil Sci. Soc. Am. J. 54,
827±831.
Toledo, P.G., Nony, R.A., Davis, H.T., Scriven, L.E., 1990.
Hydraulic conductivity of porous media at low water content.
Soil Sci. Soc. Am. J. 54, 673±679.
Valverde-Garcia, A., Gonzales-Pradas, E., Villafranca-Sanchez,
M., del Rey-Beno, F., Garcia-Rodrigues, A., 1988. Adsorption
of thiram and dimethoate on Almeria soils. Soil Sci. Soc. Am.
J. 52, 1571±1574.
Yermolayev, A.M., Shirshova, L.T., 1988. Dynamics of plant
organic matter and certain humus fractions in Gray Forest soil
under arti®cial grassland. Sov. J. Ecol. 19, 10±16.
Yermolayev, A.M., Shirshova, L.T., 1994. Productivity and
functioning of a perennial sown meadow of various management type. Pochvovedenie 12, 97±105 (in Russian).
Yin, Y., 1991. Adsorption isotherm of fractally porous material.
Langmuir 7, 216±217.